[User] Please transcribe this text

[Assistant] And for a circulant, that's all I need to know because these diagonals are constant. This diagonal is constant C1 and then gets completed here. C2 diagonal come to C2 and then gets completed cyclically here.


[User] Please transcribe this text

[Assistant] N numbers, and not N squared. And that, the reason I mention that, or a reason, is that's their


[User] Please transcribe this text

[Assistant] That's a big selling point when you go to applications, say machine learning, in, uh, for images.


[User] Please transcribe this text

[Assistant] So you remember the big picture of machine learning.


[User] Please transcribe this text

[Assistant] Deep learning. Was that you had samples.


[User] Please transcribe this text

[Assistant] A lot of samples, let's say n samples maybe, and then each sample in this image part will be an image. So the thing is that an image is described by its pixels. And if I have a thousand by thousand pixel, so that's a million, a million pixels.


[User] Please transcribe this text

[Assistant] The feature vector, the vector that's associated with one sample is enormous, is enormous.


[User] Please transcribe this text

[Assistant] So, so, so I've n samples, but maybe, maybe, uh, well, if they're in color,


[User] Please transcribe this text

[Assistant] That million suddenly becomes three million, so say three million features.


[User] Please transcribe this text

[Assistant] So our vectors, our vector of the whole


[User] Please transcribe this text

[Assistant] Computation of deep learning works with our vectors with three million components.


[User] Please transcribe this text

[Assistant] And that means that in the ordinary way, if we didn't do anything special, we would be multiplying those by matrices of size like 3 million times 3 million. We would be computing that many weights. That's like impossible. That's like...


[User] Please transcribe this text

[Assistant] Uh, and we would be computing that for, for each layer in the deep network. So it would go up, uh, a norm, go up, uh, so 3 million by 3 million is just, we can't compute.


[User] Please transcribe this text

[Assistant] We can't use gradient descent to optimize that many weights. So the point is that the matrices in deep learning are special.


[User] Please transcribe this text

[Assistant] And they don't depend, they are like circulant matrices. They might not loop around.


[User] Please transcribe this text

[Assistant] So the circulant matrices have this cyclic feature.


[User] Please transcribe this text

[Assistant] That, that makes the theory perf, extremely nice. But, of course, in general we have matrices


[User] Please transcribe this text

[Assistant] And maybe a bunch of diagonals down here.


[User] Please transcribe this text

[Assistant] Not necessarily symmetric, or they might be symmetric, but they're not cyclic. So what are these matrices called? Uhm, well they have a bunch of names because they're so important. They're, they're, uh, linear shift invariant, or linear time invariant, whatever is the right word in your context. So, so they're,


[User] Please transcribe this text

[Assistant] They're convolutions, you could call it a convolution matrix.


[User] Please transcribe this text

[Assistant] When they multiply by one of these matrices, I guess I'm going to call it T.


[User] Please transcribe this text

[Assistant] Uh, and I'll better write down the formula for our convolution.


[User] Please transcribe this text

[Assistant] Uh, you're not doing a cyclic convolution unless the matrix cycles round. This would, when you multiply by c, this would give you a cyclic convolution.


[User] Please transcribe this text

[Assistant] Say if I multiply c by some vector v, the result is the cyclic convolution.


[User] Please transcribe this text

[Assistant] With the V vector. So big C is a matrix, but it's completely defined by its first row or first column. So it's really, I just have a vector operation there. And it's a cyclic one. And over here, T times a vector V will be the convolution of a T vector with V, but not cyclic.


[User] Please transcribe this text

[Assistant] And probably these are the ones that would actually come into machine learning.


[User] Please transcribe this text

[Assistant] Uh, linear shift invariant, linear time invariant, uh, I would call it, so math people would call it a Tuplitz matrix, so that's


[User] Please transcribe this text

[Assistant] That's why I used the letter T. Uh, in engineering it would be a filter.


[User] Please transcribe this text

[Assistant] Or a convolution, or a constant diagonal matrix.


[User] Please transcribe this text

[Assistant] These come up at all sorts of places, and they come up in, in, uh, machine learning and with image processing, uh, basically because


[User] Please transcribe this text

[Assistant] What you're doing at one point in an image is pretty much what you're going to do at the other point. You're not going to figure out special weights for each little pixel in the image. You're going to take, if you have an image, say you have an image with zillions of pixels, well you might want to


[User] Please transcribe this text

[Assistant] Uh, cut down, I mean, you'd be very sensible to do some max pooling, uh, some pooling operation to make it smaller.


[User] Please transcribe this text

[Assistant] So that's really like, okay, we can't, we don't want this larger system. Let's just reduce it. So max pooling, that operation would be, say, take them three at a time, so nine pixels, and replace that nine pixels by one pixel. The, the max of those nine numbers. That would be a,


[User] Please transcribe this text

[Assistant] Very simple operation that just reduces the dimension. That's, make it smaller, reduce the dimension.


[User] Please transcribe this text

[Assistant] Okay, so that's a cheap way to make an image.


[User] Please transcribe this text

[Assistant] Four, four times or nine times or sixty-four times smaller. But,


[User] Please transcribe this text

[Assistant] The convolution part now, so that's not involving convolution. That's a different operation here. Not even linear if I take the max in each.


[User] Please transcribe this text

[Assistant] Uh, box, that's not a linear operation, so, uh, but it's a fast one. Okay, so now where do


[User] Please transcribe this text

[Assistant] Circulants, or convolution, or tuplets, matrices, or filters come into it.


[User] Please transcribe this text

[Assistant] Uh, so I'll forget about the max pooling, suppose that's happened and I still have a very big system with n squared, uh, pixels, n squared features in the, for each sample. So that's, so I want to operate on that by,


[User] Please transcribe this text

[Assistant] Matrices, as usual, I want to choose the weights, uh, to bring out the important points. So the whole idea is, on an image like that, I'll use a convolution. I'll use...


[User] Please transcribe this text

[Assistant] Uh, the same operation is happening at each point. So, so forget the max part, let me erase.


[User] Please transcribe this text

[Assistant] If I can find an eraser here. Okay, so I'm, I'm not gonna, we've done this, so that's done. Now I want to,


[User] Please transcribe this text

[Assistant] Kill or nearly kill the high frequencies. The noise. So if I wanted to, uh,


[User] Please transcribe this text

[Assistant] Get, uh, a simpler image there. I would use a low pass filter, which might just, it might be this, uh,


[User] Please transcribe this text

[Assistant] This, uh, filter here with, uh, let me just put in some numbers that would, that would, uh, say a half and a half.


[User] Please transcribe this text

[Assistant] So I'm averaging each pixel with its neighbor just to take out some of the high frequencies. The low frequencies are constant.


[User] Please transcribe this text

[Assistant] All black image would come out, not changed. But, uh, a


[User] Please transcribe this text

[Assistant] A speck, very highly speckled image would get largely removed by that averaging.


[User] Please transcribe this text

[Assistant] It's the same idea that comes up in all of, uhm, signal processing filtering. So, just to complete this thought.


[User] Please transcribe this text

[Assistant] Uh, why do neural nets, so I'm answering.


[User] Please transcribe this text

[Assistant] This question, how do they come in machine learning? So they come when the samples are images.


[User] Please transcribe this text

[Assistant] And then it's natural to use a


[User] Please transcribe this text

[Assistant] A constant diagonal matrix, a shift invariant matrix, and not an arbitrary matrix. So we're, we only have to compute, uh, n weights and not n squared.


[User] Please transcribe this text

[Assistant] Yeah, so that's the point. So that's one reason for talking about


[User] Please transcribe this text

[Assistant] Uh, convolution and circulant matrices in this course. I guess I feel another reason is that everything to do with


[User] Please transcribe this text

[Assistant] The DFT with Fourier, with Fourier and Fourier transforms and Fourier matrices, that's just like stuff you gotta know. I mean that's every time you have a, uh, uh, you're dealing with vectors that are sort of


[User] Please transcribe this text

[Assistant] Shift, where shifting the vectors comes into it, that's Fourier is going to come in.


[User] Please transcribe this text

[Assistant] So it's just, we should see for you. Okay. So now can I, I'll go back to this, uh,


[User] Please transcribe this text

[Assistant] Specially nice case where the matrix loops around where I have this cyclic convolution. So this would be cyclic because of the looping around.


[User] Please transcribe this text

[Assistant] Stuff and let's find the, oh, so what was the point of last time? I, I started with this permutation matrix.


[User] Please transcribe this text

[Assistant] And the permutation matrix has C0 equals 0, C1 equals 1, and the rest of the C's are 0. So it's just the effect of multiplying by this.


[User] Please transcribe this text

[Assistant] Get a box around it here. The effect of multiplying by this permutation matrix is to shift everything and then bring the last one up to the top.


[User] Please transcribe this text

[Assistant] So it's a cyclic shift. So cyclic shift.


[User] Please transcribe this text

[Assistant] And I guess at the very end of last time I was asking about its eigenvalues and eigenvectors. So can we come to that question? So that's a starting question for everything here. I guess we've understood that to get deeper into a matrix,


[User] Please transcribe this text

[Assistant] It's eigenvalues, eigenvectors, or singular values, singular vectors are the way to go.


[User] Please transcribe this text

[Assistant] Actually, what would be the singular values of that matrix? So that's a...


[User] Please transcribe this text

[Assistant] Yeah, just let's, let's just think about singular values and then we'll see why, why it's eigenvalues we want.


[User] Please transcribe this text

[Assistant] Singular, what are the singular values of a permutation matrix? They're all one. All one.


[User] Please transcribe this text

[Assistant] That matrix is a orthogonal matrix, so the


[User] Please transcribe this text

[Assistant] The, uh, SVD of the matrix just has like the permutation and then the identity is there for the sigma. So sigma is I for this matrix.


[User] Please transcribe this text

[Assistant] Not. So the singular values don't.


[User] Please transcribe this text

[Assistant] And now I guess if we, that's because P transpose P is the identity matrix.


[User] Please transcribe this text

[Assistant] Anytime I have a, that's an orthogonal matrix then. Anytime P transpose P is the identity.


[User] Please transcribe this text

[Assistant] The singular values will be the eigenvalues of the identity and that's, they're all just 1.


[User] Please transcribe this text

[Assistant] The eigenvalues of P, that's what we want to find. So let's do that. Okay, eigenvalues of P.


[User] Please transcribe this text

[Assistant] So one way is to take p minus lambda i.


[User] Please transcribe this text

[Assistant] That's just the way we teach in 1806 and never use again. Uh, so.


[User] Please transcribe this text

[Assistant] Puts minus lambda on the diagonal and of course P is sitting up here and then the rest is zero. Okay, so now,


[User] Please transcribe this text

[Assistant] Following the 1806 rule, I should take that determinant, right? And set it to 0.


[User] Please transcribe this text

[Assistant] This is one of the very few occasions we can actually do it, so allow me to do it. So what is the determinant of this? Well, there's that lambda to the fourth.


[User] Please transcribe this text

[Assistant] And I guess I think it's lambda to the fourth minus one. Uh, I think that's the right determinant.


[User] Please transcribe this text

[Assistant] That certainly has, has, uh, property, so I would set that to zero, then I would find that the


[User] Please transcribe this text

[Assistant] The eigenvalues for that will be 1 and minus 1, and i and minus i, and they're the


[User] Please transcribe this text

[Assistant] Four, four, they're the fourth roots of one. Lambda to the fourth equals one. That's our, that's our


[User] Please transcribe this text

[Assistant] Equation, that's our eigenvalue equation. Lambda to the fourth equal one. Or lambda to the nth equal one. So what would be the eigenvalues for, for the free P eight by eight?


[User] Please transcribe this text

[Assistant] This is the complex plane, of course, real and imaginary. So that's got eight eigenvalues. We want a p to the eighth power would be the identity.


[User] Please transcribe this text

[Assistant] And that means that lambda to the eighth power is one for the eigenvalues. And what are the eight solutions? Every polynomial equation of degree eight has got to have eight solutions. That's Gauss's fundamental theorem of algebra. Eight solutions, so what are they?


[User] Please transcribe this text

[Assistant] What are the eight numbers whose eighth power gives one?


[User] Please transcribe this text

[Assistant] The eighth power of minus one, the eighth power of minus i, and the other guys are just here.


[User] Please transcribe this text

[Assistant] The roots of one are equally spaced around the circle. So Fourier has come in. You know, Fourier wakes up when he sees that picture. Fourier is going to be here.


[User] Please transcribe this text

[Assistant] And, uh, it'll be in the eigenvectors. So, you okay with the eigenvalues? The eigenvalues of P will be


[User] Please transcribe this text

[Assistant] This number, so we better give a name to this number. Uh, let's see, I'm going to call that number w.


[User] Please transcribe this text

[Assistant] And it'll be e to the 2 pi i over 8. Right? Because the angle is 2 pi, the whole angle is 2 pi.


[User] Please transcribe this text

[Assistant] Divided it by, in 8 pieces, so the, that's 2 pi i over 8, 2 pi i over n, for a matrix of, for the n by n permutation. Yeah.


[User] Please transcribe this text

[Assistant] So that's number w, and of course this guy is, is w squared. This one is w cubed, w fourth, w fifth, sixth, seventh, and w eighth is the same as one.


[User] Please transcribe this text

[Assistant] Right. Well, those, the reason I put those numbers up there is that they come into the eigenvectors as well as the eigenvalues. They are the eigenvalues.


[User] Please transcribe this text

[Assistant] Are the eight eigenvalues of the matrix? It's, uh, here's the four, four by four case. The matrix is an orthogonal matrix. Oh! What does that tell us about the eigenvectors?


[User] Please transcribe this text

[Assistant] The eigenvectors of an orthogonal matrix are orthogonal, just like symmetric matrices.


[User] Please transcribe this text

[Assistant] So do you know that little list of matrices?


[User] Please transcribe this text

[Assistant] Dotted with QJ, the inner product is


[User] Please transcribe this text

[Assistant] Orthogonal eigenvectors. Now what matrices have orthogonal eigenvectors? We're going back to


[User] Please transcribe this text

[Assistant] Linear algebra, because this is, this is like a fundamental fact, to know this family of wonderful matrices, matrices with


[User] Please transcribe this text

[Assistant] Orthogonal eigenvectors. So tell me one bunch of matrices that you know has orthogonal eigenvectors. Symmetric.


[User] Please transcribe this text

[Assistant] And what is special about the eigenvalues? They're real. But there are other matrices that have orthogonal eigenvectors.


[User] Please transcribe this text

[Assistant] And we really should know the whole story about those guys. They're too important not to know.


[User] Please transcribe this text

[Assistant] So what's another fam, another bunch of matrices? So these symmetric matrices have orthogonal eigenvectors and real symmetric, then the eigenvalues will be real.


[User] Please transcribe this text

[Assistant] What other family, what other kind of matrices have orthogonal eigenvectors? But they might be complex, and the eigenvalues might be complex.


[User] Please transcribe this text

[Assistant] So, and you just have to, you can't know Fourier without


[User] Please transcribe this text

[Assistant] Saying okay, I can deal with this complex number.


[User] Please transcribe this text

[Assistant] Okay, so what's another family of matrices that has orthogonal eigenvectors? Yes. Diagonal for sure, right? And then we know


[User] Please transcribe this text

[Assistant] That we, uh, we, we have, uh, the eigenvectors are, are, go into the identity matrix, right? Yeah, so we know everything about diagonal ones.


[User] Please transcribe this text

[Assistant] You could say those are included in symmetric. Now let's get some new ones. What else? Orthogonal matrices count. Orthogonal matrices, like permutations or like rotations or like reflections, orthogonal matrices.


[User] Please transcribe this text

[Assistant] And what's special about their eigenvalues? The eigenvalues of an orthogonal matrix.


[User] Please transcribe this text

[Assistant] There has to be one because an orthogonal matrix doesn't change the length of the vector. Q times X has the same length as X for all vectors.


[User] Please transcribe this text

[Assistant] And in particular for eigenvectors. So if this was an eigenvector, qx would equal the lambda x. And now if that equals that, then lambda has to be 1. The magnitude of lambda has to be 1. Of course, complex numbers are expected here.


[User] Please transcribe this text

[Assistant] And that's exactly what we're seeing here, all the eigenvalues of


[User] Please transcribe this text

[Assistant] Permutations are very special orthogonal matrices. I won't add permutations separately to the list, but they count. Now, what


[User] Please transcribe this text

[Assistant] So this has, the fact that this is on the list.


[User] Please transcribe this text

[Assistant] Tells us that the eigenvectors that we're going to find are orthogonal. We don't have to do a separate check to see that they are, once we compute them. They have to be.


[User] Please transcribe this text

[Assistant] There are the eigenvectors of an orthogonal matrix.


[User] Please transcribe this text

[Assistant] Uh, I could ask you, let's keep going with this, get the whole list here. Uhm, along with symmetric, there's another


[User] Please transcribe this text

[Assistant] Bunch of guys anti-symmetric, big deal, but those are important. So symmetric means A transpose equals A. Diagonal, you know, A transpose equals A inverse for orthogonal matrices.


[User] Please transcribe this text

[Assistant] Now I'm going to put in anti-symmetric matrices where A transpose is minus A.


[User] Please transcribe this text

[Assistant] What do you think you know about the eigenvalues for anti-symmetric matrices?


[User] Please transcribe this text

[Assistant] Shall we take a example? Uh, anti-symmetric matrix.


[User] Please transcribe this text

[Assistant] What are the eigenvalues of that? Well, if I subtract lambda from the, from the diagonal and take the determinant, I get


[User] Please transcribe this text

[Assistant] Lambda squared plus 1, right, equals 0. So lambda is i or minus i.


[User] Please transcribe this text

[Assistant] That's a rotation matrix. It's also, yeah, yeah, it's a, it's a rotation.


[User] Please transcribe this text

[Assistant] Or a real eigenvector. If I rotate every vector,


[User] Please transcribe this text

[Assistant] How could a vector come out a multiple of itself? How could I have, uh, A transpose times a vector equal lambda times a vector? I rotated it and yet it's in the same direction. Well, somehow that's possible in, uh, imaginary.


[User] Please transcribe this text

[Assistant] In, in, in imaginary space and not, not possible in real space. Okay, so, so here's uh, the lambdas are imaginary.


[User] Please transcribe this text

[Assistant] Tell me if you know the name of


[User] Please transcribe this text

[Assistant] The whole family of matrices and includes all of those and more.


[User] Please transcribe this text

[Assistant] Times the diagonal times q transpose.


[User] Please transcribe this text

[Assistant] That's, well, I've really written down somehow, I haven't written a name down for them, but that's the way they, way to get them. I'm allowing


[User] Please transcribe this text

[Assistant] Sorry, this is diagonalized. Diagonalize the matrix.


[User] Please transcribe this text

[Assistant] And here are the eigen, any eigenvalues. So I want to, the final guy on this list allows any eigenvalue, any complex number. But the eigenvectors, I want to be orthogonal. So that's why I have the q.


[User] Please transcribe this text

[Assistant] So how would you recognize such a matrix and what is the name for them?


[User] Please transcribe this text

[Assistant] So that, so this, we're going beyond 1806 because probably I don't mention that name.


[User] Please transcribe this text

[Assistant] The name for these matrices in 1806, but I could. And anybody know it?


[User] Please transcribe this text

[Assistant] A matrix of that form is a normal matrix, normal. So that's the total list is a normal matrix.


[User] Please transcribe this text

[Assistant] I have to apologize for whoever sawed up that name normal. I mean, like, that's like, okay. A little more thought, you could have come up with something more meaningful than just say normal.


[User] Please transcribe this text

[Assistant] That's a matrix, that's the absolute opposite of normal. Almost all matrices are not normal.


[User] Please transcribe this text

[Assistant] So anyway, but that's what they're called, normal matrices. And finally, how do you recognize a normal matrix?


[User] Please transcribe this text

[Assistant] Everybody knows how to recognize a symmetric matrix or a diagonal matrix.


[User] Please transcribe this text

[Assistant] And we even know how to recognize an orthogonal matrix, or skew, or anti-symmetric, but how do you, what's the quick test for a normal matrix?


[User] Please transcribe this text

[Assistant] Well, I'll just tell you that a normal matrix has


[User] Please transcribe this text

[Assistant] I'm talking here about real matrices, and I really should move to complex, but let me, uh, just think of them as real. So if, uh, well, the trouble is, the matrices might be real, but the eigenvectors are not going to be real.


[User] Please transcribe this text

[Assistant] And the eigenvalues are not going to be real, so really I, I'm sorry to say really again, uh, I should get out of the, out of the limitation to real, uh, yeaah.


[User] Please transcribe this text

[Assistant] And how do I get out of the limitation to real? What do I change here if M is a complex matrix instead of a real matrix? Then whenever you transpose it, you should take its complex conjugate. So now that, that's the real thing. That's the normal thing.


[User] Please transcribe this text

[Assistant] So that's the normal matrix. And you can check that if you took that M and you figured out M transpose and did that, it would work.


[User] Please transcribe this text

[Assistant] Because in the end the q's cancel and you're just, uh, uh, have two diagonal matrices there and that's, uhm,


[User] Please transcribe this text

[Assistant] Sort of automatic that diagonal matrices commute. So a normal matrix is one that commutes with its transpose, commutes with its transpose or its conjugate transpose in the complex case. Okay. Why did I say all that? Simply because, oh, I guess that, so the permutation P is, uhm,


[User] Please transcribe this text

[Assistant] So its eigenvectors, which we're going to write down in a minute, are orthogonal. But actually, this matrix C will be a normal matrix.


[User] Please transcribe this text

[Assistant] I didn't see that coming as I started talking about these guys.


[User] Please transcribe this text

[Assistant] Yeah, so that's a normal matrix if I, because, because circulant matrices commute. Any two circulant matrices commute.


[User] Please transcribe this text

[Assistant] And now if C2 is the transpose of, so here's a matrix, uh, yeaah. So these are matrices here.


[User] Please transcribe this text

[Assistant] Of matrices, when you multiply them together, you get more of them. You're just staying in that little circulant world with n parameters.


[User] Please transcribe this text

[Assistant] And once you know the first row, you know all the other rows. And, uh, so in fact,


[User] Please transcribe this text

[Assistant] They all have the same eigenvector, so now let me.


[User] Please transcribe this text

[Assistant] Let me, uh, be sure we get the eigenvectors straight. Okay.


[User] Please transcribe this text

[Assistant] of c is, because it's a combination of powers of p.


[User] Please transcribe this text

[Assistant] So, once I find the eigenvectors of P, I've found the eigenvectors of any circulant matrix.


[User] Please transcribe this text

[Assistant] And these eigenvectors are very special. And that's the connection to Fourier. That's why we expect a connection to Fourier because


[User] Please transcribe this text

[Assistant] We have something periodic, and that's what Fourier is entirely about. Okay, so what are these eigenvectors? Let's take P to be 4 by 4.


[User] Please transcribe this text

[Assistant] Okay, so the eigenvectors are, so we remember the eigenvalues are lambda equal 1, lambda equal minus 1, lambda equal i, and lambda equal minus i. We've got four eigenvectors to find, and when we find those you'll


[User] Please transcribe this text

[Assistant] Have the picture. Okay, what's the eigenvalue, eigenvector for lambda equal 1?


[User] Please transcribe this text

[Assistant] So let me make it into a vector. And the eigenvector for lambda equal minus 1 is?


[User] Please transcribe this text

[Assistant] So I want this shift to change every sign. So if I, I better alternate those signs.


[User] Please transcribe this text

[Assistant] So that if I shift it, the 1 goes to the minus 1, minus 1 goes to the 1, so the eigenvalue is minus 1. Now, what about the eigenvalues of i? Sorry, the eigenvector that goes with eigenvalue i.


[User] Please transcribe this text

[Assistant] So I'm looking, I want, if I start it with 1,


[User] Please transcribe this text

[Assistant] And I do the permutation. I think I just want i, i squared, i cubed there.


[User] Please transcribe this text

[Assistant] And I think with this guy, with minus i, I think I want the vector 1 minus i, minus i squared, minus i cubed.


[User] Please transcribe this text

[Assistant] Without stopping to check, let's just see the nice point here.


[User] Please transcribe this text

[Assistant] All the components of eigenvectors are on the, in this picture.


[User] Please transcribe this text

[Assistant] All the, here we've got eight eigenvectors. Eight eigenvalues, eight eigenvectors. The eigenvectors have eight components. And every component is a power, is one of these eight numbers.


[User] Please transcribe this text

[Assistant] The whole thing is constructed from the same eight numbers, the eigenvalues and the eigenvectors. And really the key point is what is the matrix of eigenvectors. So let's just write that down.


[User] Please transcribe this text

[Assistant] They all have the same eigenvectors, including, including p.


[User] Please transcribe this text

[Assistant] All circulants C of size N, including P of size N, which were, that's what we...


[User] Please transcribe this text

[Assistant] So what's the eigenvector matrix? What are the eigenvectors?


[User] Please transcribe this text

[Assistant] So that's an eigenvector of P, right? Because if I multiply by P, I do a shift, a cyclic shift, and I've got all 1.


[User] Please transcribe this text

[Assistant] The next eigenvector is powers of w.


[User] Please transcribe this text

[Assistant] And let me remind you, everything is going to be powers of w. e to the 2 pi i over n. It's that complex number.


[User] Please transcribe this text

[Assistant] That's 1 nth of the way around. So that's the, so what happens if I multiply that by p, it shifts it, and it multiplies by w.


[User] Please transcribe this text

[Assistant] Or 1 over W, which is W trans, which is another eigenvector.


[User] Please transcribe this text

[Assistant] Okay, and then the next one in this list will be


[User] Please transcribe this text

[Assistant] We'll be going with w squared, so it'll be w fourth, w to the sixth, w to the eighth. Ooh, wait a minute. Did I get these lined up right? W goes with w squared up, whoops.


[User] Please transcribe this text

[Assistant] W squared now is w to the fourth, w to the sixth, w to the eighth, w to the tenth, w to the twelfth, and w to the fourteenth.


[User] Please transcribe this text

[Assistant] So that's the eigenvector with eigenvalue 1. This will have the eigenvalue. It's either w or the conjugate might be the conjugate, w bar. And you see this matrix. So what would be the last eigenvector? It would be w. So this is 8 by 8.


[User] Please transcribe this text

[Assistant] This is, I'm going to call that the Fourier matrix of size 8.


[User] Please transcribe this text

[Assistant] And it's the eigenvector matrix, so Fourier matrix.


[User] Please transcribe this text

[Assistant] So I'm just, what I'm saying is that the linear algebra for these circulants is fantastic.


[User] Please transcribe this text

[Assistant] They all have the same eigenvector matrix that happens to be the most important complex matrix in the world.


[User] Please transcribe this text

[Assistant] And, uh, its properties are golden. And it allows the fast Fourier transform, uhm, which we could write in matrix language next time. And all the entries are powers of w, all the entries are in the


[User] Please transcribe this text

[Assistant] On the unit circle at, at one of those eight points. And the last guy would be w to the 7th, w to the 14th, w to the 21st, 28th.


[User] Please transcribe this text

[Assistant] So w to the 49th would be the last w to the 7 squared. It starts out with w to the 0 times 0.


[User] Please transcribe this text

[Assistant] All these are, the entry is, yeaah, yeaah, you see the picture.


[User] Please transcribe this text

[Assistant] W to the 49th. What is actually w to the 49th? If w is the eighth root of 1, so we have w to the eighth.


[User] Please transcribe this text

[Assistant] It's 1, because I'm doing 8 by 8. What is w to the 49th power?


[User] Please transcribe this text

[Assistant] W? It's the same as W. Okay. Because W to the 48th is 1.


[User] Please transcribe this text

[Assistant] I take the sixth power of this, and I get that w to the 48th is 1, so w to the 49th is the same as w.


[User] Please transcribe this text

[Assistant] Every, every, uh, every column, every entry in the matrix is a power of W.


[User] Please transcribe this text

[Assistant] And in fact, that power is just the column number times the row number. Yeah, so those are, those are the good matrices.


[User] Please transcribe this text

[Assistant] So uh, that, so that is an orthogonal matrix. Well, almost. It's not, it has orthogonal columns, but it doesn't have orthonormal columns. What's the, what's the length of that column, of that column vector?


[User] Please transcribe this text

[Assistant] I add up 1 squared 8 times and I take the square root, I get the square root of 8. So, so this is really


[User] Please transcribe this text

[Assistant] Of course the square root of 8 is just a number to divide out to make the matrix.


[User] Please transcribe this text

[Assistant] To make the columns orthonormal instead of just orthogonal.


[User] Please transcribe this text

[Assistant] But how do I know that those are orthogonal? How do I?


[User] Please transcribe this text

[Assistant] Well, I know they have to be, but I'd like to see it clearly. Why is that vector orthogonal to that vector?


[User] Please transcribe this text

[Assistant] First of all, they have to be because the matrix is a normal matrix. Normal matrices have orthogonal. Oh yeah.


[User] Please transcribe this text

[Assistant] How do I know it's a normal matrix? Oh, I guess I can do the test, uh, if I have


[User] Please transcribe this text

[Assistant] If I have the permutation P, I know that P transpose P equals P P transpose. The permutations commute. So, so it's a normal matrix.


[User] Please transcribe this text

[Assistant] But I'd like to see directly, why is that?


[User] Please transcribe this text

[Assistant] Why is the dot product of the first or the zeroth eigenvector and the next eigenvector


[User] Please transcribe this text

[Assistant] Let me take that dot product. 1 times 1 is 1. 1 times w is w.


[User] Please transcribe this text

[Assistant] One times w squared is w squared, up to w to the seventh, I guess I'm going to finish at, equals zero.


[User] Please transcribe this text

[Assistant] Well that's, what's that saying? Those numbers are the...


[User] Please transcribe this text

[Assistant] Are these points in my picture? Those eight points.


[User] Please transcribe this text

[Assistant] So those are the eight numbers that go into the


[User] Please transcribe this text

[Assistant] That column of that eigenvector, why do they add to zero?


[User] Please transcribe this text

[Assistant] How do you see that the sum of those eight numbers is zero?


[User] Please transcribe this text

[Assistant] Yeaah, the symmetry would do it when I add that guy to that guy.


[User] Please transcribe this text

[Assistant] W to the zero, or w to the eighth, or w to the zero.


[User] Please transcribe this text

[Assistant] Yeah, when I add 1 and minus 1, I get 0. When I add these guys, I get 0. When I add these, these, by pairs. But, but, uh, what about a 3 by 3?


[User] Please transcribe this text

[Assistant] So 3 by 3, I'll go 2w to the, this would be e to the 2 pi i over 3, and then this would be


[User] Please transcribe this text

[Assistant] W to the 4 pi, this would be w squared, e to the 4 pi i over 3.


[User] Please transcribe this text

[Assistant] And I believe that those add, those three vectors add to zero.


[User] Please transcribe this text

[Assistant] And therefore they're orthogonal to the 1, 1, 1 eigenvector.


[User] Please transcribe this text

[Assistant] Because the dot product will just, I'll just want to add those three numbers. So why is that true?


[User] Please transcribe this text

[Assistant] 1 plus e to the 2 pi i over 3 plus e to the 4 pi over 3 equals 0.


[User] Please transcribe this text

[Assistant] Last minute of class today we can figure out how to do that. Well, I could get a formula for that.


[User] Please transcribe this text

[Assistant] That sum is one I could get a closed form and check that I get the answer 0. The quick way to see it is maybe suppose I multiply by


[User] Please transcribe this text

[Assistant] So I multiply every term, so that's e to the 2 pi i over 3, e to the 4 pi i over 3, and e to the 6 pi i over 3. Okay, what do I learn from this?


[User] Please transcribe this text

[Assistant] It's the same because e to the 6 pi over 3 is, is 1.


[User] Please transcribe this text

[Assistant] That's 2 pi i, so that's 1. So I got the same sum, 1 plus this plus this, this plus this plus 1.


[User] Please transcribe this text

[Assistant] So I got the same sum when I multiplied by that number, and that sum has to be zero. I can't get the same sum.


[User] Please transcribe this text

[Assistant] I can't multiply by this and get the same answer unless I'm multiplying 0. So that shows me that also in the odd, when n is odd, I also have those n numbers adding to 0. Okay, that's, those are the basic, the beautiful picture of the eigenvalues.


[User] Please transcribe this text

[Assistant] The eigenvectors being orthogonal, and then the actual details here.


[User] Please transcribe this text

[Assistant] Of what those eigenvectors are. Okay, good. Hope you have a good weekend. And, uh, so we've just got a week and a half left of class. I may probably have one more thing to do about Fourier, and then we'll come back to other topics.


[User] Please transcribe this text

[Assistant] Ask any questions on the topics that you'd like to see included here. We're closing out 18.065 while you guys do the projects. Okay, thank you.


[User] Please transcribe this text

[Assistant] I must walk beside the donkey keeping an eye on them. I don't want any of them to fall on the way.


[User] Please transcribe this text

[Assistant] Why didn't I put some of it on the horse? I am sorry.


[User] Please transcribe this text

[Assistant] Sorry, but I am sure you understand that we must give good ol' Donkey a rest today.


[User] Please transcribe this text

[Assistant] Aha! Thank you for the tip, my friend. I must start selling salt soon.


[User] Please transcribe this text

[Assistant] Oh, poor animal. It must be getting too heavy for him. There, I will take a sack off. This should do.


[User] Please transcribe this text

[Assistant] Oh come on now, don't be so lazy. You have rested enough. We need to go to the market.


[User] Please transcribe this text

[Assistant] Oh, all my effort is gone. What do I sell now? Thank god that my donkey isn't hurt.


[User] Please transcribe this text

[Assistant] There is no point in going to the market now. I should just go home. What?


[User] Please transcribe this text

[Assistant] Did this donkey sit down in the river on purpose? Oh, what a lazy animal.


[User] Please transcribe this text

[Assistant] He he he he he he he! You thought you could fool me?


[User] Please transcribe this text

[Assistant] Long, long ago, the town of Florence faced a crisis.


[User] Please transcribe this text

[Assistant] They didn't earn much, but they were happy to follow their passion.


[User] Please transcribe this text

[Assistant] The benches by the road, the steps in his building, even the trees. He was among the rare painters who tried to keep the spirit of Artsville alive. Being a painter himself, Mr. Behrman often helped Sue with her work.


[User] Please transcribe this text

[Assistant] Johncy fell very ill, and no matter what the doctor did, Johncy would not recover. She will be fine, right?


[User] Please transcribe this text

[Assistant] Sue would always ask the doctor for some alternate treatment and all he would say is, she has to make her mind stronger.


[User] Please transcribe this text

[Assistant] You painted them all in one day? That is too much work. And how did you get all wet? They all are under the roof.


[User] Please transcribe this text

[Assistant] Oh, right now I see no way and I am losing my will. I will go.


[User] Please transcribe this text

[Assistant] John C.'s health could get worse if they opened the window and let the rough wind inside. John C. agreed.


[User] Please transcribe this text

[Assistant] Little did she know that Sue was also worried about the last leaf. The next morning, sun shone brightly. The hail storm had passed. Sue knew she had to open the windows now. For how long could she keep them shut? She shut her eyes, opened the curtains. She was surprised. Oh, Chouncy, the last


[User] Please transcribe this text

[Assistant] I told him the last leaf of the ivy plant had given you strength. He passed away, John C. No! Oh no!


[User] Please transcribe this text

[Assistant] Soon, the word about the last leaf and Mr. Bearman spread through the whole town. Painters, poets, dancers, singers, all the artists were inspired. They all gathered under the ivy plant and swore to bring art back to the Artsville street.


[User] Please transcribe this text

[Assistant] And that's what happened. The streets came alive again. There were paintings on every wall. And on some people too.


[User] Please transcribe this text

[Assistant] Because that leaf would teach a very important lesson to all. Where there is a will, there is always a way.


[User] Please transcribe this text

[Assistant] The tree cherished the little moments it had with the boy.


[User] Please transcribe this text

[Assistant] And slowly the boy stopped visiting the tree. The tree was mostly alone, waiting to see the boy. Then one day the boy came to visit the tree. The tree was happy to see him.


[User] Please transcribe this text

[Assistant] So the boy climbed up the trunk, gathered all the apples from the tree and carried them away to sell them in the market. The tree was happy to help the boy. But the boy stayed away for a long time and the tree was sad. Years passed.


[User] Please transcribe this text

[Assistant] And the tree waited, standing tall with its long branches at the edge of the cliff, waiting for the boy to come back. And then one day, the boy came back. The tree shook with joy.


[User] Please transcribe this text

[Assistant] The tree was happy to help the boy, but the boy stayed away for a long time, and the tree was sad.


[User] Please transcribe this text

[Assistant] Years passed, but the boy didn't come to visit the tree. The tree could no longer talk to the birds, as they would now just circle and fly away.


[User] Please transcribe this text

[Assistant] While on the ground, the tree always asked the birds about the boy, but no one had seen him. The tree grew lonely.


[User] Please transcribe this text

[Assistant] The tree was so happy to see the boy that he could hardly speak, but the boy looked very sad. The boy sat down leaning against the tree and started crying. It broke the tree's heart to see him crying. The tree had no branches to pat the boy. It had no apples to cheer him up. It could give him a support to lean on.


[User] Please transcribe this text

[Assistant] Years passed, and the tree grew lonelier.


[User] Please transcribe this text

[Assistant] He could no longer see the far away buildings or hills.


[User] Please transcribe this text

[Assistant] He missed the birds. He missed looking at faraway pastures. He missed the comfort of his house. But more than anything, he missed the boy. The boy finally came back to the tree. The city was not the same anymore.


[User] Please transcribe this text

[Assistant] The tree didn't respond. It had nothing to say.


[User] Please transcribe this text

[Assistant] Trees needs man, as man needs trees. Preserve forests, preserve nature.


[User] Please transcribe this text

[Assistant] Hello, Dr. Harris will be with you in a few moments. Please have a seat in the waiting room to wait for him.


[User] Please transcribe this text

[Assistant] I'm looking for a new phone, but I'm not sure which one to buy. Can you help me choose one?


[User] Please transcribe this text

[Assistant] I wanted to have a good camera which can take high quality pictures. What budget do you have in mind?


[User] Please transcribe this text

[Assistant] Good evening. I would like to make a reservation for the last weekend in June. Do you have any rooms available then?


[User] Please transcribe this text

[Assistant] That sounds wonderful. Do you have a laundry service too?


[User] Please transcribe this text

[Assistant] There's a nice swimming pool near my house, and I go there pretty often with my friends. It's great fun!


[User] Please transcribe this text

[Assistant] Well, we love shopping, so we usually meet often to go in the shopping centre. How often do you go there?


[User] Please transcribe this text

[Assistant] We usually go to the shopping centre once a week in the holidays.


[User] Please transcribe this text

[Assistant] Well, we often go for an ice cream when it's hot.


[User] Please transcribe this text

[Assistant] There's a new ice cream parlor near my house, and they have Italian ice creams. They're delicious! There's also a big park near our house.


[User] Please transcribe this text

[Assistant] At weekends, I generally go there with my parents and my sister, and we have a picnic and play games there. Those are my favorite days out.


[User] Please transcribe this text

[Assistant] I'm starving. Let's get something to eat.


[User] Please transcribe this text

[Assistant] I've read the book and I love it. It is so realistic and very well written, but I enjoyed the movie too. Both are good, just in different ways. The actor's performances are superb. Hemsworth is really great, isn't he?


[User] Please transcribe this text

[Assistant] And he plays all of them marvellously, doesn't he?


[User] Please transcribe this text

[Assistant] Sorry, I'm getting too enthusiastic, aren't I?


[User] Please transcribe this text

[Assistant] Oh, that was Jerry. He's the one that came to the party which our teachers organized.


[User] Please transcribe this text

[Assistant] Yeah, that's him. He's in love with my classmate, Grace, whom he met last year.


[User] Please transcribe this text

[Assistant] I'm taking the same math class that he took last semester.


[User] Please transcribe this text

[Assistant] Yes, and she is the professor whose homework assignments are very difficult.


[User] Please transcribe this text

[Assistant] I was failing the class, so I had to get help from somebody who understood it.


[User] Please transcribe this text

[Assistant] You aced that class in the end. That's so funny.


[User] Please transcribe this text

[Assistant] Jessica is very skilled at drawing. She is so talented.


[User] Please transcribe this text

[Assistant] Yes, I know. You're already a tennis star. You are very talented at this sport.


[User] Please transcribe this text

[Assistant] Well, I think I have a natural talent, but I also have to work very hard. How many hours a day do you practice? I have to train two hours a day. When did you start playing tennis?


[User] Please transcribe this text

[Assistant] I can't believe your mother bought us tickets to the theater. That's so nice of her.


[User] Please transcribe this text

[Assistant] Anyway, if I see her tomorrow at your house, I'll thank her in person. She is such an amazing person.


[User] Please transcribe this text

[Assistant] If I had more time, I would take drama classes. I just love acting!


[User] Please transcribe this text

[Assistant] I think you could find the time to take drama classes while continuing with your formal education.


[User] Please transcribe this text

[Assistant] If I see the director of the theater group tomorrow, I'll ask him what it takes to be part of his group. Do you like to perform in front of many people? Yes, I do.


[User] Please transcribe this text

[Assistant] If I saw you on stage, I would be extremely proud of you.


[User] Please transcribe this text

[Assistant] The merchant bought the pearls for his eldest daughter and diamonds for his second daughter. He searched everywhere for a singing nightingale.


[User] Please transcribe this text

[Assistant] His youngest daughter Amelia ran towards him and hugged him tightly. After seeing that he brought the Nightingale,


[User] Please transcribe this text

[Assistant] She was filled with joy. The merchant could not rejoice and began to cry.


[User] Please transcribe this text

[Assistant] Emilia left for the forest while her father and sisters cried as they waved her goodbye.


[User] Please transcribe this text

[Assistant] And were delighted to learn about the Lion Prince. They welcomed the Lion Prince with love.


[User] Please transcribe this text

[Assistant] This was where the lion was to retire when the torches and candles were kindled. But since the wood was fresh, it split, causing a crack so small.


[User] Please transcribe this text

[Assistant] A small ray of light about the size of a hair fell upon the lion prince.


[User] Please transcribe this text

[Assistant] Within a second, the lion prince turned into a dove.


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[Assistant] Amelia followed the trail of white feathers all the way without any rest. Oh, I am so glad that these seven years are almost over. We shall soon be free of our troubles.


[User] Please transcribe this text

[Assistant] Oh sun, so bright you shine from valleys to mountain peaks, from land to mine.


[User] Please transcribe this text

[Assistant] Princess Amelia thanked the moon, went on looking for the prince. As the night wind blew, she asked, You, blow among all the trees and leaves. Have you seen a white dove flying by?


[User] Please transcribe this text

[Assistant] The magic from the wand hit the dragon and it dropped into the ground. The lion prince put his paw on the dragon's head and immediately returned to his human form. The dragon too returned to her human form.


[User] Please transcribe this text

[Assistant] Amelia understood that this is where her prince was.


[User] Please transcribe this text

[Assistant] Just then, Amelia opened the casket, given by the sun, and out came a beautiful dress, as brilliant as the sun itself. She also cracked open the egg that the moon had given her, and out came a golden hen.


[User] Please transcribe this text

[Assistant] Princess hysteria was so amazed by Amelia's dress and the golden hen that she went up to her immediately.


[User] Please transcribe this text

[Assistant] But she wanted the dress and the hen so bad that she finally consented.


[User] Please transcribe this text

[Assistant] The prince who was nearby heard some murmurs and later asked the chamberlain what it was all about.


[User] Please transcribe this text

[Assistant] The Chamberlain confessed to the Prince that he was ordered to slip in a sleeping draught in his drink, as a poor girl was to be in the room with him that night.


[User] Please transcribe this text

[Assistant] Princess Amelia was taken to the chambers to speak with the prince. The lion prince, meanwhile, pretended to be asleep.


[User] Please transcribe this text

[Assistant] I helped you master the dragon. Will you forget me now?


[User] Please transcribe this text

[Assistant] For it was her determination and will that had finally restored happiness in their lives.


[User] Please transcribe this text

[Assistant] Also, as the face is not pressed against the pillow, it avoids overwrinkling.


[User] Please transcribe this text

[Assistant] However, this position is prone to more snoring.


[User] Please transcribe this text

[Assistant] Sleeping on our stomach prevents snoring but makes it difficult to maintain a neutral spine position. It puts pressure on our joints and muscles, leading to numbness, neck and back pain, etc.


[User] Please transcribe this text

[Assistant] Sleeping especially on the left side decreases acid reflux, improves blood circulation, digestion, etc. However, side sleeping presses our face against the pillow and increases the chances of wrinkling. Some people even curl up tightly while sleeping on one side. This restricts breathing.


[User] Please transcribe this text

[Assistant] However, some people can bend their body parts more than normal.


[User] Please transcribe this text

[Assistant] It is said that hypermobility is because the individual has more or double joints which give him extended range of motion. However, this is incorrect. Hypermobility in some people is the result of flexible ligaments which enable their body parts to bend more than normal.


[User] Please transcribe this text

[Assistant] Dude, that really looks creepy. Besides this, hypermobility can also be seen around ball and socket joints, which involve the ball-shaped end of one bone fitting into an indentation on the other bone. The shallower the indentation is, the greater the range of motion, thus giving that individual hypermobility. Hmm.


[User] Please transcribe this text

[Assistant] How is coffee decaffeinated? Using a vacuum clean!


[User] Please transcribe this text

[Assistant] Oh. Nah. Coffee contains caffeine. Caffeine boosts our energy and keeps us focused for a short duration.


[User] Please transcribe this text

[Assistant] However, caffeine can also cause headaches, nervousness, etc. Hence, decaffeinated coffee is a very good alternative. Now, there are various methods to decaffeinate coffee. One of them is solvent based method. In this, green coffee beans are first soaked in hot water for several hours.


[User] Please transcribe this text

[Assistant] Then this water, which still has the flavor of coffee in it, is added back to the coffee beans so that they reabsorb the flavor. In this way, coffee is decaffeinated without compromising its flavor. Topic, thermoregulation.


[User] Please transcribe this text

[Assistant] No, they panned for thermoregulation. Thermoregulation is the process by which organisms maintain their internal body temperature.


[User] Please transcribe this text

[Assistant] Oh, you're unbelievable. When we humans feel hot, the sweat glands which are present all over our body produce sweat. Sweat is about 99% water. This water takes our body heat and evaporates, helping us to lose heat.


[User] Please transcribe this text

[Assistant] Dogs also have sweat glands. However, they are present under their paws.


[User] Please transcribe this text

[Assistant] Shall I call the fire brigade? Oh, just listen. Capsaicin present in spicy food is not necessarily bad for everybody. Only those people who have a low tolerance level or don't have a habit of eating spicy food. Can experience some problems like burning mouth, irritation of the stomach lining, heartburn, etc.


[User] Please transcribe this text

[Assistant] This SciShow video is supported by Shopify, an e-commerce platform that helps you start, grow, and manage your business. Head to Shopify.com slash SciShow to learn more and for a 14-day free trial.


[User] Please transcribe this text

[Assistant] Why is the sea salty? Seems like one of those questions a preschooler asks pretty early on, right after why is the sky blue. But here, the answer is relatively straightforward.


[User] Please transcribe this text

[Assistant] Rain erodes salts out of rocks, and rivers transport this salt to the oceans, where it accumulates. Globally, rivers put four billion tons of salt into the sea every year. But then, when it evaporates back out of the ocean into rain, it doesn't take the salt with it. Most of this is sodium and chlorine, together as sodium chloride, what we know as table salt. But there are also smaller amounts of magnesium, sulfate, calcium, and potassium ions, among others,


[User] Please transcribe this text

[Assistant] All of which chemists file under the umbrella of salts. If you took a kilogram of seawater from the ocean today and evaporated it, you would be left with about 35 grams of all of these salts. But this is one of those cases where a simple question and a fairly simple answer leads


[User] Please transcribe this text

[Assistant] To a way more interesting question, with rivers adding all this salt every year,


[User] Please transcribe this text

[Assistant] It's a smart idea. If the rivers add a little bit of salt to the oceans every year, you could backtrack and figure out when a fresh ocean first formed. This calculation says that the Earth, or at least its oceans, are somewhere between 25 and 150 million years old. Take that with a very big grain of salt.


[User] Please transcribe this text

[Assistant] The issue is that this calculation did not consider the ways that salt


[User] Please transcribe this text

[Assistant] See, salinity is balanced. Sources like rivers that add more salt are counterbalanced by sinks, which remove it. Sinks, like evaporite deposits. These form when an area of water is cut off from the rest of the ocean, and the water evaporates, leaving behind salt flats. Around five and a half million years ago, the Mediterranean Sea was cut off from the rest of the world and almost completely dried up.


[User] Please transcribe this text

[Assistant] Took about 10% of the salt out of the world's oceans. The Mediterranean got better. But today, the Dead Sea fills a similar role. Hydrothermal vents also have an impact. They heat up seawater as it flows through rocks near magma and cause chemical reactions that remove magnesium and sulfate — again, salts — from seawater. But because the total amount of salt in the ocean is large compared to what gets added or removed each year, the balance is remarkably consistent overall. So the ocean stays saltier than rivers.


[User] Please transcribe this text

[Assistant] However, salinity can still change from place to place over time. That is because salinity is the amount of salt


[User] Please transcribe this text

[Assistant] In water, so if you change the amount of water, you can change the salinity. Rain and rivers add fresh water. Intense rains like monsoons can have a big effect on the nearby ocean. Evaporation can also take water away and increase the salinity of a particular area. Ice can also be a big factor. When seawater freezes into ice, that salt stays behind in a process called brine rejection. So, sea ice forming can increase the salinity of an area, and any ice melting can add fresh water.


[User] Please transcribe this text

[Assistant] And all these processes happen at the ocean's surface.


[User] Please transcribe this text

[Assistant] So they affect the saltiness of about the top 200 meters of water. Add all of these up and you see some global patterns. The surface ocean is saltier as you get closer to the equator, since it's warmer and evaporation rates are higher than near the poles. The exception is right at the equator, where there's a lot of rain and lower salinity. For example, the Baltic Sea has many rivers flowing into it, so its salinity is lower than average. The Mediterranean and Red Seas have lots of evaporation, so their salinity is higher. So even though the ocean's overall salinity is relatively constant,


[User] Please transcribe this text

[Assistant] This means that, overall, both evaporation and precipitation rates are going up, and this could mean both more intense droughts and floods on land. Salinity itself can also have a direct effect on climate. Salinity and temperature are the primary factors that determine the density of seawater.


[User] Please transcribe this text

[Assistant] Denser water will, of course, sink to the bottom of the ocean, and this movement drives global ocean circulation, which has a significant effect on how heat flows around our planet. All this means that understanding these salinity patterns throughout the oceans and how they are changing is crucial. So in 2011, NASA launched the Aquarius satellite, which can measure the ocean's surface salinity from space. This probe can survey the salinity of the entire globe in a week. And that means that we should be able to track how the water cycle is changing.


[User] Please transcribe this text

[Assistant] We get new ways to understand and monitor the effects of the climate crisis. Preschoolers!


[User] Please transcribe this text

[Assistant] Ask some pretty great questions sometimes. Thanks for watching this SciShow video, and thanks to Shopify for supporting it. Shopify helps you sell stuff online, no matter how big or small your business is. Even if you're a one-person operation, Shopify is committed to breaking down barriers and making it easy for anyone to start their own business. If you've seen me advertise for, like, the Awesome Socks Club on other SciShow videos, or talking about the SciShow Pin Club, or anything that SciShow sells, you're already familiar


[User] Please transcribe this text

[Assistant] With some of the work that Shopify has helped across the finish line. Right now, we're selling the Crash Course coin, which is a way to get a beautiful coin and also help to fund Crash Course. That is also built on Shopify. They provide affordable fulfillment and free guides on their websites for all levels of technical ability and experience. They also give you access to resources like a business encyclopedia,


[User] Please transcribe this text

[Assistant] And listings of community events. To check out Shopify, head to Shopify.com slash SciShow. And if you use our link, you'll also get a 14-day free trial.


[User] Please transcribe this text

[Assistant] As ethic falls, she remembers. She remembers the world before they unearthed the crystal. She remembers the glee she felt when she built her first robot. But mostly, she remembers the friends she's made these last few days— courageous Adila and her resistance movement.


[User] Please transcribe this text

[Assistant] Adila has been in radio contact with Octavia, whom the robots captured and imprisoned in the same jail that held Ethic. Ethic explains that Hedge has manipulated them all.


[User] Please transcribe this text

[Assistant] And will now try to break down the Brad barrier and cover the entire world in a giant maze, unless they can stop him. But she has a plan. Ethic herself will go to the crystal at the center of the maze and use its powers to stop Hedge.


[User] Please transcribe this text

[Assistant] Meanwhile, Adila and Lemma will do whatever they can to slow Hedge down.


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[Assistant] She remembers a few things from when she flew over the maze days earlier. It centers on the crystal. There are many dead ends, but no paths that loop back on themselves.


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[Assistant] Ethic has one opportunity to radio the members of the resistance a simple set of instructions before they plunge into the labyrinth in search of the exit. What directions can she give them so they can quickly navigate the maze, open the door, and guide Ethic straight back to the crystal?


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[Assistant] One of the challenges here is to find a way to indicate where dead ends are so that the resistance members don't keep going down them.


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[Assistant] Try simplifying the maze to something like this. Let's say you've just hit this dead end, then came back to this intersection. What could you do to show the next person who gets here that they don't need to explore that path?


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[Assistant] Most programming puzzles involve giving instructions to a single actor so that they can accomplish a goal.


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[Assistant] Instead, here we have a swarm of individuals, each of whom can follow basic instructions. That's unusual in programming, but not unheard of. Researchers are currently experimenting with swarms of small robots to do things like conduct search and rescue missions.


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[Assistant] The prisoners aren't robots, but for ethics purposes, they'll act like them.


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[Assistant] And by working together, they can achieve their goal much more efficiently.


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[Assistant] Because you have a lot of prisoners, you'll want them to cover a lot of ground. This matches up well to a maze mapping technique called a depth-first search. It's called that because it involves going as deeply down a path as possible before going back.


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[Assistant] In other words, if you had a maze like this, you'd want to explore all the way down one of these branches before returning to this intersection and trying another.


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[Assistant] Everyone needs a clear set of instructions for what they should do, like, first, tie down the loose end of your wire by the crystal so it leads back there.


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[Assistant] If you find the door, open it and hand your spool to Ethic. If you're in a passageway, keep going until you hit a dead end or an intersection. But what happens at either of those places?


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[Assistant] If someone encounters a dead end, they should backtrack to the last intersection. But they also need to mark it, so no one wastes time and goes back there.


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[Assistant] The best tool for that is the wire. One option is to break both sections that lead down the dead-end path and tie the spool to the wire that leads back to the crystal. The broken wires tell everyone else who gets to this intersection, don't go this way.


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[Assistant] They'll also guarantee the final path will lead straight to the crystal, rather than visiting dead ends.


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[Assistant] Okay, so let's say someone's at an intersection. Now which way should they go? The first priority is to have everyone cover fresh ground to minimize doubling up. So if there's no wire down a direction, go that way. If there are multiple choices, choose one at random.


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[Assistant] What if they're in a subsection like this, with three marked dead ends? The only thing to do is to go back where they came from. We now know that this whole section is one big dead end, so they should break and re-tie the wire when they get to the next intersection.


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[Assistant] But let's say they get there and find two options where someone's exploring, but no one's hit a dead end yet. They may as well choose at random and go help explore that path further, in case it's the right direction for the exit.


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[Assistant] This isn't the only way to solve this challenge, but in any correct method, someone will eventually find the way out. The moment of truth will be when ethic takes their wire and follows it back inward towards her goal.


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[Assistant] The great thing about this method is that Ethic's path is straight and true. The maze doesn't have loops, so there's only one path from door to crystal.


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[Assistant] And because everyone has been breaking and re-tying their wires, ethic won't go down any dead-end paths.


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[Assistant] Face to face with her creation, Ethic has a choice. She can destroy Hedge or set things right. All of this destruction was her fault, not Hedge's. It was her oversight that instructed him to build an infinitely large maze.


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[Assistant] This saga may be over, but with your new skills, new adventures await.


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[Assistant] Think Like a Coder was Ted Ed's first episodic series, bringing together artists and educators from across the globe. If you enjoyed it, please support us on Patreon, and be a part of our mission to bring free, high-quality educational resources to the world.


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[Assistant] Oh, to the market again. Master should take a day off someday. I love holidays.


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[Assistant] Oh, eight sacks. Why can't I feel the burden?


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[Assistant] Why does it matter? Let Master put as many sacks on my back as he wants. I am not going to the market anyway, didn't you?


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[Assistant] Excuse me sir, I would like to report a stolen purse.


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[Assistant] Hi, my name's Gary and I live in Auckland, New Zealand.


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[Assistant] I'm 35 years old and I'm a lecturer in psychology at Auckland International College. I'm married and I have two children.


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[Assistant] I'm an eVid reader. I read probably a hundred pages a day.


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[Assistant] I can read a good book in three hours if it's a really good book.


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[Assistant] But reading just helps me to unwind. I prefer a good book over the TV any day.


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[Assistant] I also really enjoy being in the outdoors. I enjoy sunshine and hiking with my family. I love public transportation.


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[Assistant] I love walking to the bus, getting on, reading a book, and after I finish a chapter or two, I'm at work. I love how relaxing that is.


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[Assistant] I usually exercise pretty often. I go jogging and swimming once a week. I also exercise in the apartment.


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[Assistant] I love to eat. I like food. I would eat just about anything that came across my path.


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[Assistant] Even worse, my wife is a wonderful cook.


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[Assistant] And that means I have a lot of good food to eat.


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[Assistant] And if I didn't exercise, I would have to stop eating as much.


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[Assistant] As for my personality, I think I'm pretty responsible, trustworthy, reliable, and punctual.


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[Assistant] I'm organised and always stick to my schedule.


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[Assistant] I don't like waiting. Sometimes I'm not very patient and I like to hurry things along.


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[Assistant] People queuing to buy the latest phone? I think that's a complete waste of time.


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[Assistant] Life is too short to wait in a queue for anything. Unless you really have to.


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[Assistant] What keeps us healthy and happy as we go through life?


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[Assistant] If you were going to invest now in your future best self, where would you put your time and your energy?


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[Assistant] There was a recent survey of millennials asking them what their most important life goals were.


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[Assistant] And over 80% said that a major life goal for them was to get rich.


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[Assistant] And another 50 percent of those same young adults said that another major life goal was to become famous.


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[Assistant] We're given the impression that these are the things that we need to go after in order to have a good life. Pictures of entire lives, of the choices that people make and how those choices work out for them, those pictures are almost impossible to get.


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[Assistant] Most of what we know about human life, we know from asking people to remember the past.


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[Assistant] We forget vast amounts of what happens to us in life, and sometimes memory is downright creative. But ...


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[Assistant] What if we could watch entire lives as they unfold through time? What if we could study people from the time that they were teenagers all the way into old age to see what really keeps people happy and healthy? We did that.


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[Assistant] The Harvard study of adult development may be the longest study of adult life that's ever been done.


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[Assistant] Almost all projects of this kind fall apart within a decade because too many people drop out of the study or funding for the research dries up.


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[Assistant] Or the researchers get distracted, or they die, and nobody moves the ball further down the field.


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[Assistant] But through a combination of luck and the persistence of several generations of researchers, this study has survived.


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[Assistant] About 60 of our original 724 men are still alive, still participating in the study, most of them in their 90s.


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[Assistant] Since 1938, we've tracked the lives of two groups of men.


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[Assistant] The first group started in the study when they were sophomores at Harvard College. They all finished college during World War II, and then most went off to serve in the war.


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[Assistant] And the second group that we followed was a group of boys from Boston's poorest neighborhoods.


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[Assistant] Boys who were chosen for the study specifically because they were from some of the most troubled and disadvantaged families in the Boston of the 1930s. Most lived in tenements, many without hot and cold running water.


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[Assistant] All of these teenagers were interviewed, they were given medical exams. We went to their homes and we interviewed their parents.


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[Assistant] And then these teenagers grew up into adults who entered all walks of life.


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[Assistant] Climb the social ladder from the bottom all the way to the very top. And some made that journey in the opposite direction. The founders of this study.


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[Assistant] Every two years, our patient and dedicated research staff calls up our men and asks them if we can send them yet one more set of questions about their lives.


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[Assistant] Many of the inner-city Boston men ask us,


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[Assistant] To get the clearest picture of these lives, we don't just send them questionnaires.


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[Assistant] We interview them in their living rooms. We get their medical records from their doctors. We draw their blood. We scan their brains. We talk to their children. We videotape them talking with their wives about their deepest concerns.


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[Assistant] What are the lessons that come from the tens of thousands of pages of information that we've generated on these lives?


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[Assistant] Well, the lessons aren't about wealth or fame or working harder and harder.


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[Assistant] The clearest message that we get from this 75 year study is this.


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[Assistant] Good relationships keep us happier and healthier. Period.


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[Assistant] The first is that social connections are really good for us and that loneliness kills.


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[Assistant] It turns out that people who are more socially connected to family, to friends, to community are happier.


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[Assistant] They're physically healthier and they live longer than people who are less well connected.


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[Assistant] Their health declines earlier in midlife, their brain functioning declines sooner, and they live shorter lives than people who are not lonely.


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[Assistant] So the second big lesson that we learned is that it's not just the number of friends you have and it's not whether or not you're in a committed relationship, but it's the quality of your close relationships that matters.


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[Assistant] It turns out that living in the midst of conflict is really bad for our health.


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[Assistant] High conflict marriages, for example, without much affection turn out to be very bad for our health, perhaps worse than getting divorced. And living in the midst of good, warm relationships is protective.


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[Assistant] Once we had followed our men all the way into their 80s, we wanted to look back at them at midlife.


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[Assistant] And to see if we could predict who was going to grow into a happy, healthy octogenarian and who wasn't. And when we gathered together everything we knew about them at age 50,


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[Assistant] It was how satisfied they were in their relationships. The people who were the most satisfied in their relationships at age 50 were the healthiest at age 80.


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[Assistant] And good, close relationships seem to buffer us from some of the slings and arrows of getting old.


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[Assistant] ...reported in their 80s that on the days when they had more physical pain, their mood stayed just as happy.


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[Assistant] But the people who were in unhappy relationships, on the days when they reported more physical pain, it was magnified by more emotional pain. And the third big lesson that we learned


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[Assistant] About relationships and our health is that good relationships don't just protect our bodies, they protect our brains.


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[Assistant] It turns out that being in a securely attached relationship to another person in your eighties


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[Assistant] Is protective that the people who are in relationships where they really feel they can count on the other person in times of need, those people's memories stay sharper longer.


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[Assistant] And the people in relationships where they feel they really can't count on the other one.


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[Assistant] Those are the people who experience earlier memory decline.


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[Assistant] And those good relationships, they don't have to be smooth all the time. Some of our octogenarian couples could bicker with each other day in and day out. But as long as they felt that they could really count on the other when the going got tough, those arguments didn't take a toll on their memories. So, this message that


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[Assistant] Good, close relationships are good for our health and wellbeing. This is wisdom that's as old as the hills.


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[Assistant] Well, we're human. What we'd really like is a quick fix. Something we can get that'll make our lives good and keep them that way.


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[Assistant] Relationships are messy, and they're complicated, and the hard work of tending to family and friends, that's not sexy or glamorous. It's also lifelong. It never ends.


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[Assistant] The people in our 75 year study who were the happiest in retirement were the people who had actively worked to replace workmates with new playmates.


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[Assistant] Let's say you're 25 or you're 40 or you're 60. What might leaning into relationships even look like?


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[Assistant] Well the possibilities are practically endless.


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[Assistant] It might be something as simple as replacing screen time with people time.


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[Assistant] Or livening up a stale relationship by doing something new together. Long walks or date nights.


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[Assistant] We're reaching out to that family member who you haven't spoken to in years because those all too common family feuds take a terrible toll on the people who hold the grudges.


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[Assistant] Knowing that we've got Matt, Poe and Billy as our mentors gives me goosebumps. They've been in our shoes and they've reached such a high level is absolutely amazing and inspirational to me.


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[Assistant] This SciShow video is sponsored by Helix Sleep, which makes premium mattresses that are customized to fit your needs. And if you click on the link below or go to helixsleep.com slash SciShow, you can get up to $200 off your Helix Sleep mattress, plus two free pillows.


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[Assistant] Spider silk is one of the world's toughest materials. It is stretchy and incredibly strong, a combination that can outperform virtually any material that humans have made. And that is just the start of silk's many remarkable properties. To take advantage of them, scientists and engineers will need to figure out how to mass-produce something that can normally only come out of the body of a tiny organism. But if we can figure out how to reproduce it efficiently and sustainably, spider silk


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[Assistant] Might just become one of the most important materials around.


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[Assistant] From replacing plastics to fending off plant pests, here are six amazing ways spider silk may one day be used to improve on existing


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[Assistant] Spiders have been using silk for around 380 million years, and have evolved at least eight kinds of silk for various uses. Such as dragline silk strands. They're the ones that spiders use to repel themselves from your ceiling while you lie in bed. They're not actually very sticky, unlike the strands used to ensnare prey. Dragline silk is made by the majority of spider species, beginning from when they are tiny spiderlings.


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[Assistant] They make and release this silk constantly, and it trails behind them as they go about their days.


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[Assistant] One of the reasons it's so strong is thanks to its semi-crystalline properties. As the silk is produced, some components of its proteins are crystallized,


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[Assistant] Science can use these super strong strands as inspiration to improve on and replace the synthetic materials we currently use, such as those in bulletproof vests


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[Assistant] That is, as long as we can figure out a way to practically reproduce it. And scientists are getting close. They've created genetically engineered bacteria to produce proteins like those found in spider silk. Unfortunately, the bacteria have a tendency to chop up the silk DNA sequence into smaller pieces. Those shorter strands of DNA result in smaller proteins.


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[Assistant] Bigger proteins mean stronger silk, so recreating large enough silk proteins is key. But more recently, a biosynthetic silk was created by adding a new sequence into the silk DNA.


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[Assistant] Causing a chemical reaction that fuses the smaller proteins


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[Assistant] into larger ones. And in 2021, this was improved even further, adding new properties into the already impressive silk-like material. The result was even stronger and tougher than natural silk, while still maintaining its amazing stretching abilities. This is getting us one step closer to replacing a lot of our strongest materials from steel to kevlar.


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[Assistant] Now, if you don't associate spider silk with strength, you might think of it first and foremost as sticky. Making it into a glue could really up the ante on current adhesives. For instance, spider silk could help better secure things to damp surfaces. After all, spiders don't have the luxury of waiting around for a nice sunny day to catch a meal. Roughly 3,000 species of spiders make orb webs, like the one you're seeing right now. Within the web, different kinds of silk perform different roles. Much like dragline silk, stiff and tough silk strands absorb energy when something hits the web.


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[Assistant] These special strands are sticky thanks to a layer of glue along the silk that looked like beaded droplets under a microscope. Each droplet has a liquid coating with a glycoprotein core.


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[Assistant] A unique combination of proteins that anchors the glue to the thread. And a key feature is that each strand has a lot of stretch in it.


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[Assistant] This gluey stickiness, combined with the stiffness and strength of the silk strand, gives spiders an unparalleled adhesion that we could greatly benefit from. And while we have some pretty great glues out there already, spider silk is special because it stays sticky


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[Assistant] Under humid or wet conditions, water permeates most materials, forming a non-adhesive layer between the sticky substance and the surface it's supposed to be sticking to. But it seems that certain proteins in spider silk have hygroscopic


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[Assistant] Which means that we could depend on it to function in extreme environments. Engineers are already working on powerful adhesives inspired by spiders, using water-soluble plastic polymers to create a hygroscopic sheath to mimic the absorbing properties of their silk.


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[Assistant] This lab-made silk-mimicking glue keeps its stick at negative 196 degrees Celsius. Plus, it holds up even after violent shaking, splashing, and additional pressure from weight loading. So soon enough, you may finally be able to stick a label to a wet surface with success.


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[Assistant] Many people have a fear of spiders, but humanity's true animal enemies are the pests that eat our crops. This has led to the widespread use of insecticides to help keep crops healthy. But while insecticides are effective, they come with significant risks, including the accidental death of beneficial invertebrates like


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[Assistant] So we might be better finding new ways to protect our crops, rather than blithely killing pests. What if farmers could simply


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[Assistant] That's a tactic taken by some plants which use thread-like hairs.


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[Assistant] And in a study focused on two common agricultural pests in North America, Japanese beetles and Mexican bean beetles,


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[Assistant] That alone acted as an insect deterrent. Seeing as spiders are one of Earth's most ubiquitous predators, it makes sense that other arthropods have evolved some ways


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[Assistant] Now, there's plenty of work to do to make this practical. After all, it probably is not economical to individually place strands of silk.


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[Assistant] Plastic is an increasingly diverse and handy material, but we need to keep looking for more sustainable options. Combining spider silk with plant pulp


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[Assistant] might just be the answer the world needs. Cellulose is the basic structure of the cell walls of plants. Grind up a plant, and you end up with nanofibrils.


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[Assistant] Cellulose chains that are only a few nanometers in diameter. This nanocellulose is super versatile and fairly easy to obtain, but on its own, it has limitations as a building material.


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[Assistant] For instance, it can be quite brittle, so a big no-no for plastic replacement. To solve the brittleness problem, researchers in 2019 engineered protein sequences originally derived from dragline silk to make even better cellulose-based materials. Much like other studies, this was done by copying the structure of spider silk DNA and using bacteria to reproduce it. Then, these structurally modified spider silk protein blocks were combined.


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[Assistant] of our current petrol-based products. It's not just silk's strength and ability to biodegrade that makes it a desirable substance. Silk might actually improve how we see the world.


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[Assistant] Literally. In truth, you are unlikely to directly experience spider silk-inspired superlenses, since we're not talking about binoculars or eyeglasses here. But improvements in nanoscale lenses would help advance fields where scientists need to make observations at a minute scale.


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[Assistant] We have come a long way since the invention of the microscope, and we already have incredible nanoscopes that achieve extremely high resolution. But how clear an image they produce is limited by how well they focus light.


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[Assistant] might be able to solve that problem. The non-sticky web silk strands from both the Australian golden orb weaving spider and the long-bodied cellar spider have been shown to function like optical superlenses. The silk's cylindrical shape helps it act as a tiny transparent lens


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[Assistant] Place a small section directly on top of a substrate, and voila!


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[Assistant] Since silk has powerful liquid-collecting abilities, this can be harnessed to produce not only a cylindrical lens, but also a hemispherical magnifier called a dome microlens.


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[Assistant] Which makes for an even clearer image. Resin dropped onto a strand of silk forms a teeny dome-shaped droplet, which is then coated in a gold nano layer to further amplify the light. This could really change the future of lenses.


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[Assistant] And in this case, it doesn't appear that a synthetic equivalent would necessarily need to be created. Engineers just need to perfect the setup for using strands of extracted silk


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[Assistant] Or this purpose. Maybe nanotech labs will just purposefully house helpful spiders in the future to act as the ultimate lab assistants. While nanoscopes require extreme imaging precision, robots need to be designed with precise control over their motion.


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[Assistant] robotic muscles need to produce enough force to carry out the required movement, like


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[Assistant] Opening a valve, but also do it very precisely, and a strange property of spider silk


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[Assistant] Might help do just that. It turns out that spider silk supercontracts, meaning that it can rapidly shrink when moisture levels change. A study published in the journal Science Advances in 2019 described this accidental discovery. Researchers learned that not only do silk threads contract, but they also simultaneously


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[Assistant] It appears that under high humidity, water molecules disrupt molecular interactions between protein fibers in the silk strand, creating an asymmetry that triggers the twisting motion in one specific direction.


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[Assistant] Don't do this? So it's a really special discovery. While the team wasn't totally sure why the spider silk evolved this twisting, shrinking ability, they suspect it might have something to do with morning dew. This early morning moisture could trigger the web to be


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[Assistant] While it is no easy task to create materials from spider silk,


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[Assistant] Research on its incredible properties is so promising that it's definitely worth the effort to figure out how to make these innovative ideas a reality. The potential applications are so


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[Assistant] Broad, spider silk might just become one of the most useful materials in our engineering toolkit. It highlights the importance of biomimicry, in which complex problems are solved by looking to nature.


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[Assistant] They'll pick it up for you, and you'll get a full refund. So you will have done your due diligence to get the perfect mattress for you. And if anything happens to it to make it less perfect,


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[Assistant] Helix offers a 10-year warranty. If you're looking for a new bed, check out Helix. When you're ready to buy, they make it easy to pay using a bunch of different financing options and flexible payment plans. And if you click on the link below or go to helixsleep.com slash SciShow, you can get up to $200 off your Helix Sleep mattress, plus


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[Assistant] Two free pillows. Thanks to Helix for supporting this SciShow video, and thank you for watching.


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[Assistant] Be strong, sister! Be strong! Be strong, sister! Be strong!


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[Assistant] Little while, I've been a model uhm, actually for 10 years.


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[Assistant] Uhm, and I feel like there's an uncomfortable tension in the room right now because I should not have worn this dress.


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[Assistant] So, luckily I brought an outfit change. Uhm, this is the first outfit change on the TED stage. So you guys are pretty lucky to witness it, I think.


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[Assistant] I'd also note that I'm quite privileged to be able to transform what you think of me, uhm, in a very brief 10 seconds. Not everybody gets to do that.


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[Assistant] These heels are very uncomfortable, so good thing I wasn't going to wear them.


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[Assistant] The worst part is putting this sweater over my head because that's when you'll laugh at me. So, don't do anything while it's over my head.


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[Assistant] I just totally transformed what you thought of me in six seconds.


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[Assistant] Uhm, I was totally uncomfortable and the photographer was telling me to arch my back and put my hand in that guy's hair. Uhm, and of course barring surgery,


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[Assistant] Uhm, or the fake tan that I got two days ago for work. Uhm, there's very little that we can do to transform how we look.


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[Assistant] And how we look, though it is superficial and immutable, has a huge impact on our lives.


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[Assistant] So today, for me, being fearless means being honest. And I am on this stage because I am a model. I am on this stage because I am a pretty white woman. In my industry, we call that a sexy girl.


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[Assistant] Uhm, and I'm gonna answer the questions that people always ask me, but with an honest twist. So the first question is how do you become a model? Uhm, and I always just say I was scouted, but that means nothing. Uhm, the real way that I became a model,


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[Assistant] Is, I won a genetic lottery, and I am the recipient of a legacy. And maybe you're wondering what is a legacy. Well,


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[Assistant] For the past few centuries, we have defined beauty not just as uhm,


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[Assistant] Uhm, and I know there are people in the audience who are skeptical at this point, and maybe there are some fashionistas who are like, Wait, Naomi, Tyra, Joan Smalls, Lu Wen, and first, I commend you on your model knowledge, very impressive.


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[Assistant] The next question people always ask me is, can I be a model when I grow up?


[User] Please transcribe this text

[Assistant] But the second answer and what I really want to say to these little girls is, why? You know, you can be anything. You could be the president of the United States or the inventor of the next internet or...


[User] Please transcribe this text

[Assistant] If after this amazing list, they still are like, no, no, Cameron, I want to be a model. Well, then I say, be my boss because I'm not in charge of anything and you could be the editor in chief of American Vogue or the CEO of H&M or the next Stephen Maizel.


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[Assistant] It's, you know, out of your control and it's awesome and it's not a career path. I will demonstrate for you now 10 years of accumulated model knowledge.


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[Assistant] Because unlike cardiothoracic surgeons, it can just be distilled right into right now.


[User] Please transcribe this text

[Assistant] If you say you want to be the president of the United States, but your resume reads underwear model 10 years, people give you a funny look.


[User] Please transcribe this text

[Assistant] The next question people always ask me is, do they retouch all the photos? And yeaah, they pretty much retouch all the photos, but that is only a small component of what's happening. This picture is the very first picture that I ever took, and it's also the very first time that I had worn a bikini.


[User] Please transcribe this text

[Assistant] And I didn't even have my period yet. I know we're getting personal, but uh,


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[Assistant] You know, I was a young girl. This is what I looked like with my grandma just, uhm, a few months earlier.


[User] Please transcribe this text

[Assistant] Here's me on the same day as this shoot my friend got to come with me. Here's me at a slumber party a few days before I shot French Vogue. Uhm, here's me on the soccer team and in V Magazine. And here's me today.


[User] Please transcribe this text

[Assistant] And I hope what you're seeing is that these pictures are not pictures of me. They are constructions and.


[User] Please transcribe this text

[Assistant] They are constructions by professionals, by hairstylists, and makeup artists, and photographers, and stylists, and all of their assistants, and pre-production, and post-production. And they build this. That's not me. Uhm, okay, so the next question people always ask me is, do you get free stuff?