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[Assistant] Maybe there was direct competition for the same food, and maybe megalodon lost. Unfortunately, the number of teeth the team had for these two species was pretty limited, so the results could just be a statistical fluke. And since it's still largely unknown how much the amounts of different zinc isotopes change from one marine species to the next,


[User] Please transcribe this text

[Assistant] We can't really tell much beyond the general trophic level. For all we know, they could have had different enough diets that they didn't get too much in each other's way. Now, in slightly more recent news, we're getting to know some of our ancient relatives a little bit better. The Roman port city of Pompeii was buried under meters of ash in 79 CE, following the eruption of Mount Vesuvius. And it was buried so well that it wasn't properly rediscovered until the 18th century.


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[Assistant] Telling us a little more about the people who live there. On one hand, volcanic eruption can be pretty bad for preserving remains.


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[Assistant] The intense temperatures can break down the molecular structure of not just DNA, but bone. But on the other hand, DNA can also be protected from decay when it gets buried under a bunch of ash for well over a millennium. So over the years, scientists have been working to analyze ancient DNA from various bodies they've uncovered at


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[Assistant] This new study looked at two sets of remains. Previous research into the DNA of these ancient Romans had been limited to short segments of DNA. Specifically, mitochondrial DNA.


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[Assistant] It's short, so it's easier to retrieve in sequence, and it's often used for studying ancestry. But that wasn't enough for this team. They wanted to look at the full sequence. Back in 2015, scientists proposed that one of the best places to find preserved ancient human DNA is in part of the human skull. It's called the petrous bone.


[User] Please transcribe this text

[Assistant] It protects your inner ear structures, and it's great at preserving DNA because it's super dense. So that's where the team pulled their DNA samples from. But only one set of remains designated individual A


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[Assistant] Still, the fact that scientists have successfully sequenced the DNA of an ancient Roman opens the door to further and more in-depth investigations of this ancient culture and others around the world. So we may never know about the daily lives of your average megalodon or person from Pompeii, but research like this helps scientists piece together as clear a picture of the past as we can get… until, like, someone invents a time machine.


[User] Please transcribe this text

[Assistant] If your curiosity about zinc has been piqued and you want to learn more, you can turn to Brilliant. Brilliant is an online learning platform that offers guided, problem-solving-based courses in science, computer science, and math.


[User] Please transcribe this text

[Assistant] Their course, The Chemical Reaction, provides you with the basics and tools to dive deeper into the topics I talked about in this SciShow News video. For example, zinc is the 30th chemical on the periodic table of elements, and this brilliant course shows you how to build the periodic table block by block.


[User] Please transcribe this text

[Assistant] By working through puzzles and patterns. So by the end of the course, you'll be able to predict how a chemical reaction will shake out, based on charge, energy, and probability. To get started, click the link in the description below or visit Brilliant.org slash SciShow, and you'll get 20% off the annual premium subscription. Thanks to Brilliant for supporting this video, and thank you for watching!


[User] Please transcribe this text

[Assistant] I love my high school because I have great teachers and my classmates are really nice.


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[Assistant] We often go on school outings to the mountains or to the seaside, which I enjoy a lot.


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[Assistant] I'm hoping to go to university and study business.


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[Assistant] I am responsible and hard working, so I study hard to obtain good grades.


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[Assistant] There are six people in my family. I have two brothers and a sister.


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[Assistant] There is no such thing as a perfect family, but when we are together, we have a lot of perfect moments.


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[Assistant] Brighton is on the seaside, surrounded by nature. So I love to go swimming at the beach.


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[Assistant] Stroll along the shore or take a cycle ride through the parks.


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[Assistant] Gardening is my passion. It inspires me to do something new.


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[Assistant] Whenever I cast a glance over my small, beautiful lawn my heart blossoms.


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[Assistant] With every new flower there is new happiness.


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[Assistant] I hate it when somebody shouts at me. I just can't bear it. Scold me or whatever, but don't shout.


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[Assistant] I also don't like when people borrow money, but they never give it back to you.


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[Assistant] The result is that I have a difficult time speaking up in groups.


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[Assistant] Even if I have good ideas, I have trouble assigning them.


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[Assistant] Okay, so uhm, actually I have a, I know where people are working on projects.


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[Assistant] And you're not responsible for any material, new material in the lectures. Thank you for coming.


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[Assistant] But, I do have something, an important topic, which is a revised version about the construction of neural nets, the basic structure that we're


[User] Please transcribe this text

[Assistant] We're working with. So that's, uh, on the open web at section 7.1. That's, uh, so construction of


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[Assistant] Really, it's a construction of the learning function.


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[Assistant] So that's the function that you optimize by gradient descent or stochastic gradient descent and you apply to the training data.


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[Assistant] To, uh, minimize the loss, you, so,


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[Assistant] Just thinking about it in a more organized way because I wrote that section before I knew anything more than how to spell neural nets. Uh, but now I'm thought about it more. So the key point maybe compared to what I had in the past


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[Assistant] Is that I now think of this as a function of 2.


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[Assistant] And v are the feature vectors, the sample.


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[Assistant] Either one at a time if we're doing stochastic gradient descent with mini-batch size 1, or B at a time if we're doing mini-batch of size B, or the whole thing, a whole epoch at once if we're doing full-scale gradient descent.


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[Assistant] So those are the feature vectors. And these are the numbers in the linear steps where the weights, so they're the matrices.


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[Assistant] Ak that you multiply by, multiply v by, and also the bias vectors.


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[Assistant] Bk that you add on to shift the origin. Okay. And these are the, and these are, it's these that you optimize. Those are to optimize.


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[Assistant] And what's the structure of the whole, uh,


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[Assistant] The whole of the learning function and how do you use it? What does the neural net look like? So you take f.


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[Assistant] Of a first set of weights, so f of the first set of weights would be A1 and B1. So that's the x part. And the, and the, uh,


[User] Please transcribe this text

[Assistant] Actual sample vector, the sample vectors are v0 in the iteration, and this produces, and then you do the nonlinear step to each component, and that produces v1. So there is a typical, uh,


[User] Please transcribe this text

[Assistant] I could write out what this is here. A1 v0 plus v1.


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[Assistant] So that's, the two steps are the linear step. The input is v0.


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[Assistant] You take the linear step using the first weights, a1 and b1. Then you take the nonlinear step, and that gives you v1. So that's really better than my line above. So I'll erase that line above. Yeah.


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[Assistant] So that produces V1 from V0 and the first weights. And then the next level.


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[Assistant] Inputs v1, so I'll just call this vk.


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[Assistant] Or vk minus 1, and I'll call this one vk. Okay, so, so k equal to 1 up to however many layers you are, L layers.


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[Assistant] So the input was v0, so this v is really v0, you could say. And you, this is the neural net, and this is the,


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[Assistant] Input and output from each layer. And then VL is the final output from the final layer. So, so let's just do a picture here. Here, here is V0.


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[Assistant] A sample vector, or if we're doing image processing, it's all the pixels in the, in the


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[Assistant] In the, in the, in the data, in the training from one sample. This is one training sample.


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[Assistant] And then you multiply by a1, and you add b1, and you take relu of that vector.


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[Assistant] And that gives you v2, v1, sorry, that gives you v1. And then you iterate.


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[Assistant] To finally VL, the last layer. You don't do ReLU at the last layer, so it's just AL VL minus 1 plus VL. And you may not do a bias vector also at that layer, but you might.


[User] Please transcribe this text

[Assistant] Uh, and that's, this is the, finally the output.


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[Assistant] So is that picture, so that picture is clearer for me than it was previously to distinguish between the weights. So in the, in the gradient descent algorithm, it's these x's that you're choosing. The v's are not


[User] Please transcribe this text

[Assistant] These are given by the training data. That's not part of the optimization part. That's not part of, it's x in chapter 6.


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[Assistant] Where you're finding the optimal weights. So this x really stands for, x stands for the, all the weights that you compute.


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[Assistant] So that's, that's, that's a collection of all the weights. And the important part for


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[Assistant] applications for practice is to realize that there are often more weights than


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[Assistant] More components in the weights than there are components in the feature vectors, in the samples, in the V's.


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[Assistant] So often the size of x is greater than the size of v.


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[Assistant] Which is an interesting and sort of unexpected, uh, situation. So often I'll just write that.


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[Assistant] Exceeds and often far exceeds the number of V's, the number of


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[Assistant] The cardinality, the number of weights in, this is in the A's and B's.


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[Assistant] And these are in the samples in the training set.


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[Assistant] Features of all the samples in the training set. So, uh, I'll get that new section, 7.1, up.


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[Assistant] Uhm, hopefully this week on the, uh,


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[Assistant] On the open, that's the open set and I'll email to you on Stellar.


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[Assistant] Uhm, is there more I should say about this? You see here the, I can draw the picture, but of course a hand drawn picture is far inferior to, uh, to a, uh,


[User] Please transcribe this text

[Assistant] Uh, machine drawn picture, but online picture, but let me just do it. So there's V.


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[Assistant] The training sample has some components, and then they're multiplied. Now here's going to be V1, uh, the first hidden layer.


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[Assistant] And that can have a different number of, of, uh, of components in,


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[Assistant] In the first layer, different number of neurons, and then each one comes from the, from the V's by a, so I won't keep going here, but.


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[Assistant] You see the picture. So there's a matrix, that describes a matrix A1 that tells you what the weights are on those. And then there's a B1 that's added.


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[Assistant] The bias vector is added to all those to get the v1. So v1 is a1 v0 plus b1. And then onwards.


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[Assistant] So this, this is the, the spot where drawing it by hand is clearly inferior to any other possible way to do it. Okay, uhm, so uhm, now I haven't yet put into the picture


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[Assistant] The loss function, so that's the function that you want to minimize. So what is the loss function?


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[Assistant] Function L. Okay. So it's this part that Professor Schwarz lecture was about. Uh, so he, he said L is often a finite sum, uh, over all the


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[Assistant] From the, with weights, with weights in x from sample number i. And if we're doing batch processing, that is, we're doing a whole batch at once, then we compute that for all i. And that's the computation that's ridiculously expensive. And you go instead to stochastic gradient, and you just choose one of those.


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[Assistant] Or B of those, a small number B like 32 or 128 of these F's, but, but full scale gradient descent.


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[Assistant] Chooses the weights x to minimize the loss. Now so, I haven't got the loss here yet. It's this function. The loss would be minus the true.


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[Assistant] I don't write, I haven't got a good notation for that. I'm open to suggestions. So how do I want to write the error? Suppose, suppose I'm, uh, so that would be


[User] Please transcribe this text

[Assistant] If it was least squares, I would maybe be squaring that.


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[Assistant] So that would be a sum of squares of errors squared over all the samples.


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[Assistant] Or if I'm doing stochastic gradient descent, I would minimize, I guess I'm minimizing this.


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[Assistant] But the question is do I use the whole function L in at each iteration or do I just


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[Assistant] Just to keep the notation straight, uhm, I have this function of x and v's, I find its


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[Assistant] What, what v, what, this is what the, the, uh, neural net produces. It's supposed to be close to the true.


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[Assistant] We don't want it to be exactly, we don't expect this to be exactly zero, but it could be because we have lots of weights to achieve that.


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[Assistant] Uhm, so, uh, that's what, anyway, that would be the loss we minimize and it'd be squared for square loss. I guess I haven't really spoken about the, about loss functions. Let me just put those here.


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[Assistant] And number two, I've never seen it used quite this directly, would be the L1 loss.


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[Assistant] These are squared in the L2 norm. The L1 loss could be the sum over i of the L1 losses.


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[Assistant] Well, this comes into specific other problems like Lasso and other important problems you're minimizing in L1 norm, but not in deep learning.


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[Assistant] Now, and three would be hinge loss.


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[Assistant] The formula and the background behind hinge loss, this is for, this is for


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[Assistant] Uh, minus 1, 1 classification problems.


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[Assistant] And then finally, the most important for neural nets is cross entropy loss.


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[Assistant] So this is really our, the most used, uh, lost function in the,


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[Assistant] In the setup that we are mostly thinking of. And I'll try to say more about that before the course ends. So is that, I don't know.


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[Assistant] For me, I hadn't got this straight, uh, until rewriting that section. And, uh, it's now in better form. But comments are welcome. Okay. And so that...


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[Assistant] Just complete what I wanted to say and you'll see the new section.


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[Assistant] Any comment on that before I go to a different topic entirely?


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[Assistant] Uh, okay. Oh, and any questions? Let me, before I go to this topic, which I'll tell you what it is, it's...


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[Assistant] It's, it's a short section in the book called distance, about distance matrices.


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[Assistant] And what we know is we know


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[Assistant] The distances between the points.


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[Assistant] And it's convenient to talk about distances squared here.


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[Assistant] And how would we know these distances? Maybe by radar or, or any measurement. They might be, uhm, sensors which we've placed around and we can measure the distances between them. And the question is, what's their position? So that's the, the,


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[Assistant] That's the question. So let me talk a little bit about this question and then pause. Find, uh, positions.


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[Assistant] Well, in space, but I don't know, we don't know ahead of time maybe whether the space is ordinary 3D space, or whether these are sensors in a plane, or whether we have to go to higher dimensions, I'll just put D. And we also, I'll just say then, we're also finding D.


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[Assistant] And what are these positions? These are positions x, xi. So the distance between xi minus xj squared is the given.


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[Assistant] Dij. So we're given distances between them, and we want to find their positions. Find their, so we know distances and we want to find positions.


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[Assistant] That's the question. It's just a neat math question.


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[Assistant] That is solved and you'll see a complete solution and, uh, and it has lots of applications.


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[Assistant] And it's, yeaah, it's just a nice, it's a nice question. So it occupies a section of the book, but that section is only two pages long because it's just a straightforward solution to that question.


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[Assistant] Given the distances, find the positions. Given the distances, find the x's.


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[Assistant] So I'm going to speak about that. Let me, um, uh, I had a suggestion, a good suggestion, by email. Well, I questioned about the, uh,


[User] Please transcribe this text

[Assistant] Projects are beginning to come in, and at least at the beginning I'm, I,


[User] Please transcribe this text

[Assistant] Well, in all cases, beginning and end, I'll read them carefully.


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[Assistant] And as long as I can, I'll send back suggestions for a final rewrite. And as I said,


[User] Please transcribe this text

[Assistant] So I like to get a, a printout is great. You could leave it in the envelope outside my office. But of course, uh, uh, online is, uh, is what everybody's doing.


[User] Please transcribe this text

[Assistant] So those are just beginning to come in and they're not, uh, if we can get them in by a week from today I'm really, really happy. Yeah.


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[Assistant] And just feel free to email me. I would email me about projects rather than not Jonathan and not anonymous Stellar. I think it's probably better just to ask me the question. That's fine.


[User] Please transcribe this text

[Assistant] And I'll try to answer you in a useful way. Yeaah. So that's...


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[Assistant] And I'm always open to questions, so you could email me, like, how long should this project be?


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[Assistant] My tutor in Oxford said something like when you were writing essays, that's the Oxford system, is to write an essay. And he said just start where it starts and end when it finishes. So that's the idea, certainly not


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[Assistant] And then a question was raised and I can ask you if you, uh, are interested in that.


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[Assistant] The question was, what course is after this one?


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[Assistant] Are natural, are sort of natural to take, to go forward.


[User] Please transcribe this text

[Assistant] Uh, and I don't know how many of you are thinking to take, have time to take.


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[Assistant] Another MIT, other MIT courses in this area of deep learning, machine learning, optimization, all the topics we've had here.


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[Assistant] Anybody expecting to take more courses? Just stick up a hand. Yeah.


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[Assistant] And do you already know, like, what MIT offers, or, uh,


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[Assistant] So that was the question that came to me. What does MIT offer, eh, in this direction?


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[Assistant] Uh, and I haven't looked up to see the number of Professor Sra's course, SRA, but after, in course 6, it's 6 point high number.


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[Assistant] And, uh, and after his good lecture, I think that's gotta be worthwhile.


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[Assistant] So I looked in course six, I didn't find a really very, an institute-wide list. Maybe course six feels that they are the institute, but there are other courses around, and, uh, uhm,


[User] Please transcribe this text

[Assistant] But I found in the operations research site, ORC, the Operations Research Center, uhm, let me just put there.


[User] Please transcribe this text

[Assistant] This is just in case you would like to think about any of these things.


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[Assistant] As I write that. So I heard the lecture by Tim Berners-Lee, did others hear that this week or so ago? He created the


[User] Please transcribe this text

[Assistant] The web, so that's a pretty amazing, uh, it wasn't Al Gore after all, uh, and uh,


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[Assistant] You know, do you know his name? Well, he's now Sir Tim Berners-Lee.


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[Assistant] So that double name makes you suspect it's, he's from England and he is. Uh, but he, so anyway, I was going to say he's, I hold him responsible for these


[User] Please transcribe this text

[Assistant] Excessive letters in the, in the, uh, address in the URL.


[User] Please transcribe this text

[Assistant] I mean, he's made us all say w, w, w for a year or find some other way to say it, but it's not easy to say, I think. Okay, whatever. This is the operate, the OR center at MIT.


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[Assistant] And then it's, uh, academics or something.


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[Assistant] And then it's something like core software. That's approximately right.


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[Assistant] That's, you know, there's a heading of data analytics, there's statistics, there's optimization, there's OOR, operations research, other lists, but a good list of courses from


[User] Please transcribe this text

[Assistant] Uh, many departments, especially, especially, so especially, uh, course six.


[User] Please transcribe this text

[Assistant] Uh, Course 15, which is where the Operations Research Center are, is Course 18. And there are others in Course 2 and elsewhere. Yeaah.


[User] Please transcribe this text

[Assistant] Would somebody like to say what course you have in mind to take next after this one?


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[Assistant] If you looked at the, looked ahead to next year, any, any suggestions of what looks like a good course? I, I, you know, I only know, I sat in once on 6.036, the really basic course, and you, you would want to go higher.


[User] Please transcribe this text

[Assistant] Okay, I won't any, maybe this is just to say I'd be interested to know what you do next, what your experience is, or I'd be happy to give advice, but maybe my general advice is that that's a useful list of courses.


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[Assistant] Back to distance matrices. Okay, so here is the problem.


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[Assistant] Okay, I'll probably have to erase that, but I'll leave it for a minute. Okay, so we know these distances.


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[Assistant] And we want to find the x's. So let's call this Dij maybe.


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[Assistant] So we have a D matrix, and we want to find a position matrix. Let me just see what notation. So this is section 3.9. No, 4.9.


[User] Please transcribe this text

[Assistant] Previously 3.9, but chapters 3 and 4 got switched.


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[Assistant] So, and maybe, maybe actually, yeah, I think it's, it's eight or nine or ten. It's, other topics are, are trying to find their way in. Okay, so that's the.


[User] Please transcribe this text

[Assistant] That's the reference on the, on the web, and I'll get these sections onto Stellar. Okay. So the question is,


[User] Please transcribe this text

[Assistant] Can we recover the positions from the distances?


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[Assistant] In fact, there's also a question, are there always positions from the given distances?


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[Assistant] So let me, and, and I mentioned several applications. I've already spoken about wireless sensor networks.


[User] Please transcribe this text

[Assistant] Where you, you can measure travel times between them, between the sensors, and then you, that gives you the distances, and then you use this neat little bit of math to find the positions. Well, of course, you can't find the positions uniquely, clearly.


[User] Please transcribe this text

[Assistant] You could, any rigid motion of all the positions.


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[Assistant] If I have a set of positions, uh, what am I going to call that, x? So, so, I'll write here and then, so I'm given the D matrix.


[User] Please transcribe this text

[Assistant] That's distances, and the job is to find the X matrix.


[User] Please transcribe this text

[Assistant] And what I'm just going to say, and you already saw that, saw it in your mind, that if I have a set of positions, I could do a translation.


[User] Please transcribe this text

[Assistant] The distances wouldn't change, or I could do a rigid motion, a rigid rotation. So positions, uh, are not unique, but I can make, I can come closer by saying put the center of,


[User] Please transcribe this text

[Assistant] Centroid at the origin or something like that. That will take out the translations at least. Okay, so find the X matrix. That's the job.


[User] Please transcribe this text

[Assistant] Okay, and I was going to, before I start on that, the shapes of molecules is another application. Nuclear magnetic resonance gives distances.


[User] Please transcribe this text

[Assistant] Gives d, and then we find the positions m, x. And of course, there's noise in there, and sometimes missing entries. And machine learning could be described also as a


[User] Please transcribe this text

[Assistant] You're given a whole lot of points in space, feature vectors in a high dimensional space. Actually, this is a big deal. You're given a whole lot of points with, where the, in high dimensional space.


[User] Please transcribe this text

[Assistant] And those are related, they're, they're, they're, they sort of come together naturally. So they tend to fit on a surface.


[User] Please transcribe this text

[Assistant] In high dimensional space. A low dimensional surface in high dimensional space. And really, a lot of mathematics is devoted to finding that


[User] Please transcribe this text

[Assistant] Low dimensional, that subspace, but it w- it could be curved, so subspace is not the...


[User] Please transcribe this text

[Assistant] Correct word, really, manifold, this curved manifold is what a math, a geometer would say.


[User] Please transcribe this text

[Assistant] That is close to all the points, smooth and close to all the points. And you can linearize it. You could flatten it out.


[User] Please transcribe this text

[Assistant] And, uh, then you have a much reduced problem. The dimension is reduced from the original dimension of the, of the, where the points lie with a lot of data to the true dimension of the problem.


[User] Please transcribe this text

[Assistant] Which, uh, of course if the points were all on a straight line, the true dimension of the problem would be 1. Well we, so we have to discover this, uh,


[User] Please transcribe this text

[Assistant] That, uh, we also have to find that dimension, D. Okay. Okay, so how do we do it?


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[Assistant] So it's a classical problem, it just has a neat answer. Okay. Okay.


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[Assistant] All right. So let's recognize the connection between distances and positions. So Dij.


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[Assistant] Is the length of, it's the square distance between them. So that is xi dot xi minus xi


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[Assistant] So those are the DIJs in a matrix. And these are entries.


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[Assistant] So this is going to be, this will, this part will produce a rank 1 matrix.


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[Assistant] Because things depend only on the row, but not on j, the column number. So, uh, uh, columns repeated.


[User] Please transcribe this text

[Assistant] Produces, similarly, something that depends only on j, only on the column number. So the rows are all the same. So this is also a rank one matrix.


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[Assistant] If I change i, nothing changes in that inner product. So really, these are the terms that, uh, uh,


[User] Please transcribe this text

[Assistant] Produce the, uh, most of the matrix. The significant part of the matrix. Okay. So uhm, what do we do with those? So, what, what, uh,


[User] Please transcribe this text

[Assistant] So let's see, did I give a name for the matrix that I'm looking for? I think in the notes I call it X.


[User] Please transcribe this text

[Assistant] So, so I'm given D, given D, find x.


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[Assistant] And what I'll actually find, you can see it coming here, is actually find


[User] Please transcribe this text

[Assistant] Because what I'm given is dot products of x's.


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[Assistant] So, uh, so I, I would like to find, to discover out of, out of all this what x i dotted with x j is. That'll be the correct dot product. Let's call this matrix.


[User] Please transcribe this text

[Assistant] G for the dot product matrix, and then


[User] Please transcribe this text

[Assistant] This is a nice argument. So what this tells me is a bunch of some information about dot product.


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[Assistant] And of course that's, this is the point at which x is not unique. If there's, if I put in a rotation into x, then that rotation q will, I'll see a q transpose q and it'll disappear. So the, so the, I'm free to rotate the x's because that doesn't change the dot product. But, so it's g that I want to know.


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[Assistant] And this tells me something about G, and this tells me something about G.


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[Assistant] And so does that, but that's what I have to, uh, see. So what do those tell me?


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[Assistant] Let's see, let me write down what I have here.


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[Assistant] So, so the, the, the, so let's say a diagonal matrix.


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[Assistant] With dii as the inner product xi with xi that we, uh, that we're getting partial information from here. So, so is that okay? I'm introducing that notation.


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[Assistant] Because this is now going to tell me that my D matrix is, so what is that?


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[Assistant] So this is the diagonal matrix. Maybe it's just a vector, I should say.


[User] Please transcribe this text

[Assistant] Yep. So can I write down the equation that, that, that's, that is fundamental here? And then I'll, then we'll figure out what it means.


[User] Please transcribe this text

[Assistant] So it's a equation for G.


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[Assistant] Or the dot product matrix. Okay, let me make space for that equation. So here's the


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[Assistant] I believe that we can get the dot product matrix, which I'm calling G as, as,


[User] Please transcribe this text

[Assistant] According to this, it's minus a half of the D matrix.


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[Assistant] That's a matrix with constant rows. That matrix is


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[Assistant] This here is, this is coming from there. This is a matrix with always the same columns.


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[Assistant] So, uh, let me see. No, I haven't got those right yet. I mean, I want these to be ranked one matrices, so I've, it's this one that's, let me fix that.


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[Assistant] 1, 1, 1, 1 times D transpose. So it's column times row. And this one is also column times row.


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[Assistant] Okay, now let me look at that properly. So every row in this guy is a multiple of 1, 1, 1, 1.


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[Assistant] So what is that telling me? That all columns are the same? All columns are? This part is reflecting these ones where the columns are repeated.


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[Assistant] This one is reflecting this where the rows are repeated. The D is just the set of D numbers. Let's call that DI.


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[Assistant] So part of the, so part of the D matrix is, is these, is this pit and this bit each giving a rank 1.


[User] Please transcribe this text

[Assistant] Now, it's this part that I have to understand, so let me, while you're checking on that, let me,


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[Assistant] Let's just see where we are if this is true. If this is true, I'm given the D matrix and then these dot products


[User] Please transcribe this text

[Assistant] I can find. So I can find these. So in other words, this is the key equation that tells me D. That's


[User] Please transcribe this text

[Assistant] That's the key equation, and it's going to come just from that simple identity. Just from checking each term. This term we identified, that last term we identified, and now this term is d. Well, of course it's d.


[User] Please transcribe this text

[Assistant] And I'm gonna take half of, half of that to get d, I think. Let's, I'm not, uhm.


[User] Please transcribe this text

[Assistant] Yep, yep, and we'll, we'll look. So, so, uh,


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[Assistant] So I guess I'm not seeing right away why this half is in here.


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[Assistant] But that's, but I think I had it right and there's a reason. But you see that this matrix, this X transpose X matrix is coming from these rank one places and these pieces which are the cross products. Oh! Oh, I see. I see.


[User] Please transcribe this text

[Assistant] What really, what that equation is really saying is that the D matrix is this


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[Assistant] If I just read that along and translate it and put it in matrix language, is this, uh, 1, 1, 1, 1,


[User] Please transcribe this text

[Assistant] Uh, d1 to d4, let's say, transpose, is this rank 1 matrix. And the other one is the d's.


[User] Please transcribe this text

[Assistant] Times the 1, 1, which is the transpose of that. And then the other one was a minus 2 of the cross product matrices. Ah, I see. Yeah, yeah. So when I write that equation in matrix language, I just get that.


[User] Please transcribe this text

[Assistant] One set of cross products and then this is the same as this so I have minus two of them. So now I'm just


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[Assistant] Rewriting that, when I rewrite that equation, I have that. Do you see that?


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[Assistant] I put that onto this side, I put the d over here as a minus d, I divide by 2, and then that's the formula. So ultimately, this simple identity just looked at because


[User] Please transcribe this text

[Assistant] These pieces were so simple, just rank one pieces.


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[Assistant] And this, these pieces are exactly what we want, the x transpose x pieces, the g. Uh, that equation told us the d. We, we know all, all this is known.


[User] Please transcribe this text

[Assistant] So what's really, yeaah, what's known as D and this and this, so now we have the equation for x transpose x.


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[Assistant] I remember that Raj Rao talking about it last spring also, the algebra, uh, got flustered, but, so we get it. So we know x transpose x, that matrix.


[User] Please transcribe this text

[Assistant] Now, can you just, can we just do four minutes of linear algebra at the end, uh, today?


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[Assistant] How would you do that? Could you do it? Would there be just one x? No.


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[Assistant] What, so, so any, if, if you had, if you had one x, multiply that by a rotation by an orthogonal matrix, you'd have another one.


[User] Please transcribe this text

[Assistant] So, so this is finding x up to an orthogonal transformation. But how would you actually do that? What do we know about this matrix? x transpose x?


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[Assistant] Symmetric, clearly. And what we especially know is that it's also positive or semi-definite. So this is semi-definite.


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[Assistant] So I'm given a semi-definite matrix, and I want to find a square root, you could say.


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[Assistant] That matrix is the X transpose X and I want to find X. I think there are two leading candidates.


[User] Please transcribe this text

[Assistant] There are many candidates because if you find one, then, then any.


[User] Please transcribe this text

[Assistant] Yeah, because if I put a Q transpose Q in there, it's the identity. Okay. So one way is to use eigenvalues.


[User] Please transcribe this text

[Assistant] Of x transpose x. And the other way would be to use elimination on x transpose x.


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[Assistant] So if I use eigenvalues of x, if I find the eigenvalues of x transpose x, then I'm writing this as, it's a symmetric positive definite, I'm writing it as q lambda q transpose. Right? That's the fundamental.


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[Assistant] Most important theorem in, in linear algebra you could say.


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[Assistant] That a symmetric positive semi-definite matrix has


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[Assistant] Greater eigenvalues, greater equals 0, and eigenvectors that are orthogonal. So now if I know that, what's a good x? Then take


[User] Please transcribe this text

[Assistant] So I've got the eigenvalues and eigenvectors of x transpose x, and I'm looking for an x that will work. And one idea is just to take the same eigenvalues, eigenvectors, and take the square roots of the eigenvalues.


[User] Please transcribe this text

[Assistant] Because if I multiply, if I trans, that's symmetric now, this is equal to x transpose.


[User] Please transcribe this text

[Assistant] And if I, so that was a, that's a square root symbol or a lambda to the one half. I could, I could say, so when I multiply that, I'm really, x transpose x is just x squared here. When I square it, the,


[User] Please transcribe this text

[Assistant] Q transpose Q multiplies itself to give the identity the square root of lambda times the square root of lambda. Those are diagonal matrices that give lambda, and I get the right answer. So one way is, in a few words,


[User] Please transcribe this text

[Assistant] Take the square roots of the eigenvalues and keep the eigenvector. So that's the eigenvalue construction. So that's producing an x that is symmetric, positive, semi-definite. That might be what you want.


[User] Please transcribe this text

[Assistant] It's a little work because you're computing eigenvalues and eigenvectors to do it. But that's one choice.


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[Assistant] Now I believe that elimination would give us another choice.


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[Assistant] So elimination produces what factorization of this? This is still our symmetric positive definite matrix.


[User] Please transcribe this text

[Assistant] If you do elimination on that, you usually expect


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[Assistant] The pivots times u, the upper triangular, that's the usual result of elimination, L, D, U. I'm factoring out the pivots, so they're ones on the diagonals of L and U.


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[Assistant] But now if it's a symmetric matrix, what's up?


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[Assistant] We zipped by elimination regarding that as a 1806, uh, trivial bit of linear algebra, but of course it's highly important. So what's the situation here when the matrix is actually symmetric?


[User] Please transcribe this text

[Assistant] So I want something to look symmetric. How do I make that look symmetric?


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[Assistant] The u gets replaced by L transpose. If I, if I, uh,


[User] Please transcribe this text

[Assistant] If I'm working on a positive definite, say positive definite matrix, then I get positive pivots and L and the lower triangular and upper triangular are transposes of each other.


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[Assistant] So now what is, then, then what's the x?


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[Assistant] I'll use L square root of D L transpose. Is that right?


[User] Please transcribe this text

[Assistant] Ooh, wait a minute. What's up? No, that's not going to work. Because I don't have L transpose L. Where I had Q transpose Q was good. No, sorry. Let's get that totally erased.


[User] Please transcribe this text

[Assistant] The x part should just be the square root of D L transpose. That's, that's...


[User] Please transcribe this text

[Assistant] The x is now a triangular matrix. The square root of the pivots and the L transpose part. And now when I do x transpose x, then you see x transpose x coming correctly. X transpose will be L transpose.


[User] Please transcribe this text

[Assistant] Will be L transpose transpose will give me the L square root of D times square root of D will give the D and then the L transpose is right. So this is called the, the, uh, do I try to write it here? This is my last word for today, the Cholesky.


[User] Please transcribe this text

[Assistant] Those are the, this is the Cholesky factorization, named after a French guy who, a French soldier actually.


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[Assistant] Uh, so LDL transpose is Cholesky and that's, that's, uh, easy to compute, much faster to compute than the eigenvalue square root. But this square root is triangular, this square root is symmetric. Those are the two sort of pieces of linear algebra to find things, to reduce things to triangular form or to reduce them to


[User] Please transcribe this text

[Assistant] Okay, thank you for attention today. So today we did, uhm,


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[Assistant] The distance matrices, and this was the final step to get the x, and also, uh,


[User] Please transcribe this text

[Assistant] The getting the more, most important was to get the structure of a, of a neural net straight, separating the V's, the sample vectors, from the X's, the weights.


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[Assistant] Okay, so Friday, I've got one volunteer to talk about a project and I'm desperately looking for more. Please just send me an email.


[User] Please transcribe this text

[Assistant] You're, you're, uh, you're, uh, it'll be appreciated. Or I'll send you an email if, if necessary. Okay, thanks.


[User] Please transcribe this text

[Assistant] I think both candidates are very good, and their academic background is excellent.


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[Assistant] But I was more impressed by Evelyn because she was very confident and talkative. Victoria was too shy, I guess. What do you think?


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[Assistant] She is quieter, yes, but she's obviously less confident too. Did you notice her weak handshake?


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[Assistant] She also had poor eye contact She was extremely nervous.


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[Assistant] Great CV, great qualifications, but total lack of confidence. And she never smiled.


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[Assistant] I think she is a person who doesn't work well in stressful situations.


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[Assistant] Evelyn had an expressive face, was smiling, and had very good eye contact.


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[Assistant] How do we choose then, given the fact that their qualifications are almost identical?


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[Assistant] Great! Thank you so much for your help. I'll make sure to keep the filter clean from now on.


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[Assistant] Good afternoon, Community Clinic, Sophia speaking. How can I help you?


[User] Please transcribe this text

[Assistant] Let me see. Thursday's pretty full. How does 5.30 on Friday suit you?


[User] Please transcribe this text

[Assistant] Okay then, Paul, we'll see you on Friday at 5.30.


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[Assistant] It's dangerous to tilt your head back if you have a nosebleed, honey. Blood can get into your throat if you sit in that position. You may swallow it and that can irritate your stomach. But what should I do then, Mom?


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[Assistant] You should lean your head forward and block your nostrils with your thumb and index finger.


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[Assistant] How long should I hold it? Keep holding it for about 10 minutes and let it go. I see. I didn't know that.


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[Assistant] Thanks for watching, and be sure to subscribe to our YouTube channel for more videos like this.


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[Assistant] I want to start by asking everyone in the audience here a question. How many of you are completely comfortable with calling yourselves a leader?


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[Assistant] See, I've asked that question all the way across the country and everywhere I ask it, no matter where, there's always a huge portion of the audience that won't put up their hand.


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[Assistant] And I've come to realize that we have made leadership into something bigger than us. We made it into something beyond us. We made it about changing the world. And we've taken this title of leader and we treat it as if it's something that one day we're going to deserve. But to give it to ourselves right now means a level of arrogance or cockiness that we're not comfortable with.


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[Assistant] And I worry sometimes that we spend so much time celebrating amazing things that hardly anybody can do, that we've convinced ourselves that those are the only things we're celebrating. And we start to devalue the things that we can do everyday. And we start to take moments where we truly are a leader, and we don't let ourselves take credit for it, and we don't let ourselves feel good about it.


[User] Please transcribe this text

[Assistant] And I've been lucky enough over the last 10 years to work with some amazing people who have helped me redefine leadership in a way that I think has made me happier. And with my short time today, I just want to share with you the one story that is probably most responsible for that redefinition.


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[Assistant] I went to a school in a little school called Mount Allison University in Sackville, New Brunswick. And on my last day there, a girl came up to me and she said, I remember the first time that I met you.


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[Assistant] And then she told me a story that happened four years earlier. She said,


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[Assistant] On my day before I started university, I was in the hotel room with my mom and my dad. And I was so scared and so convinced that I couldn't do this, that I wasn't ready for university, that I just burst into tears. And my mom and my dad were amazing. They were like, look, we know you're scared.


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[Assistant] But let's just go tomorrow. Let's go to the first day. And if at any point you feel as if you can't do this, that's fine. Just tell us and we will take you home. We love you no matter what.


[User] Please transcribe this text

[Assistant] And she says, so I went the next day and I was standing in line getting ready for registration and I looked around and I just knew I couldn't do it. I knew I wasn't ready, I knew I had to quit. And she says, I made that decision and as soon as I made it there was this incredible feeling of peace that came over me.


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[Assistant] And you had a big sign, uh, promoting Shinerama, which is students fighting cystic fibrosis, a charity I've worked with for years. And you had a bucket full of lollipops. And you were walking along and you were handing the lollipops out to people in line and talking about Shinerama. And all of a sudden, you got to me, and you just stopped. And you stared. It was creepy. This girl right here knows exactly what I'm talking about.


[User] Please transcribe this text

[Assistant] And then you looked at the guy next to me, and you smiled, and you reached in your bucket, you pulled out a lollipop, and you held it out to him, and you said, you need to give a lollipop to the beautiful woman standing next to you. And she said, I have never seen anyone get more embarrassed faster in my life. He turned beet red, and he wouldn't even look at me, he just kinda held the lollipop out like this.


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[Assistant] And I felt so bad for this dude that I took the lollipop and as soon as I did, you got this incredibly severe look on your face and you looked at my mom and my dad and you said, look at that. Look at that. First day away from home and already she's taking candy from a stranger.


[User] Please transcribe this text

[Assistant] And she said everybody lost it. Twenty feet in every direction, everyone started to howl. And I know this is cheesy, and I don't know why I'm telling you this. But in that moment when everyone was laughing, I knew that I shouldn't quit. I knew that I was where I was supposed to be, and I knew that I was home.


[User] Please transcribe this text

[Assistant] And I haven't spoken to you once in the four years since that day. But I heard that you were leaving. And I had to come up and tell you that you've been an incredibly important person in my life. And I'm gonna miss you. Good luck. And she walks away, and I'm flattened.


[User] Please transcribe this text

[Assistant] And she gets about six feet away, she turns around and smiles and goes, you should probably know this too. I'm still dating that guy four years later.


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[Assistant] How many of you guys have a lollipop moment? A moment where someone said something or did something that you feel fundamentally made your life better? Alright. How many of you have told that person they did it?


[User] Please transcribe this text

[Assistant] Marianne Williamson said, Our greatest fear is not that we are inadequate. Our greatest fear is that we are powerful beyond measure. It is our light and not our darkness that frightens us. And my call to action today is that we need to get over that. We need to get over our fear of how extraordinarily powerful we can be in each other's lives. We need to get over it so we can move beyond it. And our little brothers and our little sisters and one day our kids,


[User] Please transcribe this text

[Assistant] Or our kids right now can watch us start to value the impact we can have on each other's lives more than money and power and titles and influence. We need to redefine leadership as being about lollipop moments. How many of them we create, how many of them we acknowledge, how many of them we pay forward, and how many of them we say thank you for.


[User] Please transcribe this text

[Assistant] Because we've made leadership about changing the world, and there is no world. There's only 6 billion understandings of it. And if you change one person's understanding of it, one person's understanding of what they're capable of, one person's understanding of how much people care about them, one person's understanding of how powerful and agent for change they can be in this world, you change the whole thing.


[User] Please transcribe this text

[Assistant] And if we can change, understand leadership like that, I think if we can redefine leadership like that, I think we can change everything.


[User] Please transcribe this text

[Assistant] And it's a simple idea, but I don't think it's a small one. And I want to thank you all so much for letting me share it with you today.


[User] Please transcribe this text

[Assistant] Hey, look at the weather outside. It is too cloudy. No, don't go near that bonfire. It is going to be warm tonight. You don't want to listen to me, right? Alright, go ahead.


[User] Please transcribe this text

[Assistant] Now, during a clear night, that is, when there are no clouds. This heat easily escapes through the atmosphere into space, resulting in cooling of the earth.


[User] Please transcribe this text

[Assistant] Vision is the most important and prioritized sense that we have. We are constantly looking at the world around us, and quickly we identify and make sense of what it is that we see.


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[Assistant] Let's just start with an example of that very fact. I'm going to show you a photograph of a person just for a second or two.


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[Assistant] And I'd like for you to identify what emotion is on his face. Ready? Here you go. Go with your gut reaction. Okay, what'd you see?


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[Assistant] Well, we actually surveyed over 120 individuals and the results were mixed. People did not agree on what emotion they saw on his face.


[User] Please transcribe this text

[Assistant] Is actually filtered through our own mind's eye.


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[Assistant] So dieters, for instance, see apples as larger than people who are not counting calories. Softball players see the ball as smaller if they've just come out of a slump compared to people who had a hot night at the plate.


[User] Please transcribe this text

[Assistant] So my research team and I decided to test this question. Uh, in 2008, Barack Obama was running for president for the very first time, and we surveyed hundreds of Americans one month before the election.


[User] Please transcribe this text

[Assistant] Of these people, 75 percent voted for Obama in the actual election. Other people, though, thought photographs like these best reflect how Obama really looks. 89 percent of these people voted for McCain.


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[Assistant] So, vision scientists know that the amount of information that we can see with


[User] Please transcribe this text

[Assistant] What we can see with great sharpness and clarity and accuracy


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[Assistant] Is the equivalent of the surface area of our thumb on our outstretched arm. Everything else around that is blurry.


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[Assistant] Rendering much of what is presented to our eyes as ambiguous.


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[Assistant] But we have to clarify and make sense of what it is that we see. And it's our mind that helps us fill in that gap.


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[Assistant] As a result, perception is a subjective experience, and that's how we end up seeing through our own mind's eye.


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[Assistant] Why is it that somebody might literally see the glass as half full and somebody literally sees it as half empty?


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[Assistant] What is it about what one person is thinking and feeling that leads them to see the world in an entirely different way? And does that even matter?


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[Assistant] So to begin to tackle these questions, my research team and I decided to delve deeply into an issue that has received international attention, our health and fitness.


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[Assistant] Across the world, people are struggling to manage their weight. And there's a variety of strategies that we have to help us keep the pounds off.


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[Assistant] But actually, the majority of Americans find that their New Year's resolutions are broken by Valentine's Day.


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[Assistant] Of course, there is no simple answer, but one reason I argue is that our mind's eye might work against us.


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[Assistant] So as a first step to testing these questions, we gathered objective measurements of individuals' physical fitness.


[User] Please transcribe this text

[Assistant] We measured the circumference of their waist compared to that to the circumference of their hips.


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[Assistant] After gathering these measurements, we told our participants that they would walk to a finish line while carrying extra weight in a sort of race. But before they did that, we asked them to estimate the distance to the finish line. We thought that the physical states of their body might change how they perceived the distance. So, what did we find?


[User] Please transcribe this text

[Assistant] Well, waist to hip ratio predicted perceptions of distance. People who were out of shape and unfit actually saw the distance to the finish line as significantly greater than people who were in better shape.


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[Assistant] But so too can our mind. In fact, our bodies and our mind work in tandem to change how we see the world around us.


[User] Please transcribe this text

[Assistant] Again, we gathered objective measurements of people's physical fitness, measuring their circumference of their waist and the circumference of their hips, and we had them do a few other tests of fitness. Based on feedback that we gave them,


[User] Please transcribe this text

[Assistant] Some of our participants told us they're not motivated to exercise anymore. They felt like they already met their fitness goals and they weren't going to do anything else. These people were not motivated.


[User] Please transcribe this text

[Assistant] So our bodies can change how far away that finish line looks.


[User] Please transcribe this text

[Assistant] But people who had committed to a manageable goal that they could accomplish in the near future and who believed that they were capable of meeting that goal actually saw the exercise as easier.


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[Assistant] That led us to wonder, is there a strategy that we could use and teach people that would help make


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[Assistant] Change their perceptions of the distance. Make, help them make exercise look easier.


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[Assistant] So we turned to the vision science literature to figure out what should we do. And based on what we read, we came up with a strategy that we called Keep Your Eyes on the Prize.


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[Assistant] So, this is not the slogan from an inspirational poster.


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[Assistant] It's an actual directive for how to look around your environment.


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[Assistant] People that we trained in this strategy, we, we told them to focus their attention on the finish line, to avoid looking around.


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[Assistant] To imagine a spotlight was shining on that goal and that everything else around it was blurry and perhaps difficult to see.


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[Assistant] We thought that this strategy would help make the exercise look easier. We compared this group to a baseline group.


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[Assistant] This group we said just look around the environment as you naturally would. You will notice the finish line, but you might also notice the garbage can off to the right, or the people in the lampposts off to the left.


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[Assistant] We thought that people who use this strategy would see the distance as farther. So.


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[Assistant] What did we find? When we had them estimate the distance, was this strategy successful for changing their perceptual experience?


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[Assistant] We thought this was great. We were really excited because it meant that this strategy helped make the exercise look easier.


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[Assistant] So next, we told our participants you are going to walk to the finish line while wearing extra weight.


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[Assistant] We added weights to their ankles that amounted to 15% of their body weight. We told them to lift their knees up high and walk to the finish line quickly.


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[Assistant] Like most exercises that actually improve our fitness.


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[Assistant] So, a big question then. Did keeping your eyes on the prize and narrowly focusing on the finish line change their experience of the exercise? It did.


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[Assistant] People who kept their eyes on the prize told us afterwards that it required 17% less exertion for them to do this exercise than people who looked around naturally.


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[Assistant] It changed their subjective experience of the exercise.


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[Assistant] We were so excited by this, because this meant that a strategy that costs nothing, that is easy for people to use, regardless of whether they're in shape or struggling to get there, had a big effect.


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[Assistant] Keeping your eyes on the prize made the exercise look and feel easier even when people were working harder because they were moving faster.


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[Assistant] Now, I know there's more to good health than walking a little bit faster.


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[Assistant] But keeping your eyes on the prize might be one additional strategy that you can use to help promote a healthy lifestyle.


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[Assistant] If you're not convinced yet that we all see the world through our own mind's eye, let me leave you with one final example. Here's a photograph of a beautiful street in Stockholm.


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[Assistant] But two cars. The car in the back looks much larger than the car in the front.


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[Assistant] So does this mean that our eyes have gone haywire and that our brains are a mess? No, it doesn't mean that at all. It's just how our eyes work. We might see the world in a different way, and sometimes that might not line up with reality.


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[Assistant] We all see the world through our mind's eye, but we can teach ourselves to see it differently.


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[Assistant] My colleague at work looks annoyed when I ask for an extension on a deadline.


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[Assistant] And on days like these when everybody looks upset and angry to me, I try to remind myself that there are other ways of seeing them. Perhaps my colleague was confused. Perhaps my friend was concerned. And perhaps my husband was feeling empathy instead. So we all see the world through our own mind's eye.


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[Assistant] And on some days it might look like the world is a dangerous and challenging and insurmountable place.


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[Assistant] And when we find a way to make the world look nicer and easier, it might actually become so. Thank you.


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[Assistant] Bop-de-bop-de-dub-de-bop. Bop-bop-bop-bop-bop-bop.


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[Assistant] I have a nosebleed. I have to wait until the bleeding stops.


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[Assistant] I got hit in the nose by a ball just before coming in.


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[Assistant] It was an accident. Some kids were playing soccer. I think it already stopped.


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[Assistant] Oh wow, look over there. Look at all the herbs.


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[Assistant] Are you guys Italian? No, we're Greek. She loves Italian food. Greeks and Italians, we're the same. You start rolling, rolling, keep rolling.


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[Assistant] I've cooked you, I'm going to try and say it the Italian way, so it's called Pinci, or I've been calling it Piki, pasta with an ala norma sauce, and I have done a panna grottata. I said it's some poor man's parmesan on top.


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[Assistant] I didn't get my oil on top guys, I'm sorry. My time ran out. And I did not taste my food.


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[Assistant] I've cooked you a pinchy pasta with a ala norma sauce and a panna grottata. But I did not taste my food, I'm sorry.


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[Assistant] It's simple. I really hope that my dish is enough. Got it in the bag.


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[Assistant] I just love how food brings people together. Give me the spatula please. Thank you. Scalpel. Too soon.


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[Assistant] Knowing that it was potentially life threatening. It was really scary. Definitely made me take stock of everything. My mum was my biggest support. She got me through it.


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[Assistant] Caramelised scallops. A caramelised shallot puree. We've got some freshly potted garden peas, asparagus, pea shoot tendrils and prosciutto. This is a tarragon herb oil.


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[Assistant] Hi guys! Can you guess the title of my next video?


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[Assistant] Why are giraffes so tall? Because they pull each other's necks and legs. Nah.


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[Assistant] Some scientists believe that being tall helps giraffes feed on leaves which are present at greater heights. As shorter herbivores are not able to reach those heights, it decreases the competition for food.


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[Assistant] Another study suggests that a giraffe's long neck is evolved to compete or fight for females.


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[Assistant] Male giraffes whip their neck and swing their heads violently into each other's ribs and neck. This is called necking. The giraffe having longer neck tends to win and hence is preferred by the female giraffe.


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[Assistant] The study also suggests that as the legs of giraffes got longer, their necks also gradually got longer, so that they could easily drink water by bending their necks.


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[Assistant] However, if we suddenly move from a bright room to a dark room, our eyes take some time to adapt to the darkness.


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[Assistant] Hence, a pirate worn eye patch over a single eye so that, that eye can get adapted to darkness. Now, while fighting in case the pirate had to go under the deck where it is quite dark, he just removed the patch from the covered eye which was already adapted to darkness. Helping the pirate to immediately see in the dark.


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[Assistant] Cuz it contains gold. No. Some scientists suggest that when sperm whales eat animals like squids. They digest most of their body parts. However, their sharp beaks are indigestible which can cause irritation in the digestive tract.


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[Assistant] Now, some people thought that whales vomited this ambergris. However, a research suggests that it is expelled from the other end. Then, over time, this ambergris reacts with air, salty water, etc. And hardens to form a waxy rock. This waxy rock or ambergris is used by some perfume companies. Eww. But why?


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[Assistant] Why is a diver able to cut through water in a swimming pool? Simple, because I taught him.


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[Assistant] No, this is because of intermolecular force. Huh?


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[Assistant] Intermolecular force is the force of attraction present in between the molecules of solids, liquids or gases.


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[Assistant] Boo! This means I'm the strongest of all. Oh, please listen.


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[Assistant] Since the intermolecular forces are not strong. The molecules of a liquid are loosely packed and they have empty spaces in between them. As a result, the molecules can be displaced from their original position.


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[Assistant] Hence, when a diver jumps into water, its molecules get displaced from their original position. And the diver is able to cut through the water.


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[Assistant] The exact opposite process happens in nuclear fission. Here, a heavier nucleus splits into two lighter nuclei.


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[Assistant] Robbie, it's alright. We forgive you. You have always been dear to us. Yes.


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[Assistant] First listen and then answer the following question. What was the main objective of early mountain climbers? Modern alpinists try to climb mountains by a route which will give them good sport. And the more difficult it is, the more highly it is regarded


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[Assistant] In the pioneering days, however, this was not the case at all


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[Assistant] The early climbers were looking for the easiest way to the top, because the summit was the prize they sought, especially if it had never been attained before.


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[Assistant] It is hard for us to realize nowadays how difficult it was for the pioneers


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[Assistant] Except for one or two places such as Zermatt and Chamonix, which had rapidly become popular, alpine villages tended to be impoverished settlements cut off from civilization by the high mountains.


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[Assistant] Such inns as there were generally dirty and flea-ridden


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[Assistant] The food simply local cheese accompanied by bread often 12 months old, all washed down with coarse wine


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[Assistant] Often a valley boasted no inn at all, and climbers found shelter wherever they could—sometimes with the local priest who was usually as poor as his parishioners, sometimes with shepherds or cheesemakers.


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[Assistant] Invariably the background was the same. Dirt and poverty, and very uncomfortable.


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[Assistant] For men accustomed to eating seven-course dinners and sleeping between fine linen sheets at home, the change to the Alps must have been very hard indeed


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[Assistant] Last week I went to Paris. In just a few minutes, I was able to book the flight in a hotel online.


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[Assistant] Do you remember how things used to be when we were kids and there was no internet?


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[Assistant] And mobile phones were very expensive, and you could not afford one. When I was out with my friends and missed the last bus home, I had to look for a phone box so I could call for a taxi.


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[Assistant] Now we can pick up our phones and we can phone anyone, anywhere in the world, anytime we feel like it.


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[Assistant] We can access internet on our mobile phones. We can shop whenever we want, wherever we are.


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[Assistant] I can't finish this crossword puzzle. I have one more word left. I might be able to help you. Do you know a country with a five letter name? There must be hundreds. It could be China.


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[Assistant] No, it can't be Italy because it ends with the letter A.


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[Assistant] Did you see the boss looked in a really bad mood as he came in today? I wonder what that's all about.


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[Assistant] Well, he might have had an argument with his wife this morning. They don't seem to get along lately.


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[Assistant] No, he couldn't have. He doesn't have any injuries. He could have found out about you Skyping instead of working. Ha ha.


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[Assistant] No, she can't have done anything wrong. She is very hardworking and honest. Hmm, I wonder what that is.


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[Assistant] Well, we better get back to work anyway, before he sees us gossiping.


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[Assistant] Don't go to bed too late. We have to get up early tomorrow. Why?


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[Assistant] Have you forgotten? Pam has to move to a new apartment tomorrow. And we promised we would help her. Does she have to move out by a particular time?


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[Assistant] No, there's no rush. She doesn't have to leave her old apartment before the afternoon. But there are lots of things that she has to pack, so we must get there fairly early.


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[Assistant] She said that I mustn't tell you because she wants to tell you herself. When she sees you tomorrow. That's strange. Anyway.


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[Assistant] I must write an email to my friend Gabriel first. I can't go to sleep yet. You can write it tomorrow! No, it's something important.


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[Assistant] Okay, suit yourself, but we must leave before nine in the morning.


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[Assistant] Is this really necessary? I didn't need to do that at my previous club.


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[Assistant] Hello? I'd like to get some prints made. Here's my camera.


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[Assistant] Oh, I see. I didn't know that. And I want to take some more photos. Do I need to buy more film?


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[Assistant] Hi Anne, nice to meet you. I'm Joshua.


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[Assistant] In the office? Usually we don't use phones in the office.


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[Assistant] If it's an emergency, yes, of course, you may use it. No problem.


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[Assistant] I'm afraid you may not do that. We usually try not to put things up in the office. Not personal things anyway.


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[Assistant] You really can't park there. You need to move your car.


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[Assistant] Hey, come in, nice to see you. Have a seat, just make yourself at home. Thanks, what a wonderful house you have here. Thanks, is there anything I can get you? No thanks, by the way, can I use your bathroom? Sure, it's just down the hall. Okay.


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[Assistant] Can I turn on the television? I'm dying to watch the football game. Go ahead, the remote's on the chair. Thanks.


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[Assistant] How's the game? Great! The volume is too low. Would it be alright to turn the volume up a bit? Sure, go ahead.


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[Assistant] Can we also turn on the air conditioner? It's really getting hot here. Yeah, I'll get it. Thanks.


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[Assistant] Right. How about looking at some of these ones? Hmm.


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[Assistant] We also wanna take it with us when we travel and those ones look pretty heavy. Would you get one down so we can try carrying it?


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[Assistant] Hello, I'd like to check in please. I'm here for the conference on technology in schools.


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[Assistant] Oh, right. Well, I've got quite a lot of bags.


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[Assistant] I've parked my car in the street outside the back entrance of the hotel. Is that okay?


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[Assistant] Top four, massive advantage, getting to cook for immunity. So I'm thinking, what would I love to eat every day?


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[Assistant] Lamb is just so delicious. See, I'm coming in. Ah, cool. There's no way I would get tired of chomping on a lamb cutlet for the rest of my life.


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[Assistant] My desert island dish is going to be marinated lamb cutlets with a roast pumpkin puree, a goat's cheese mousse and some candied walnuts.


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[Assistant] The first thing I need to crack on with is the marinating of the lamb cutlets. I'm doing it with rosemary, honey, garlic and chilli. That's, um, that's, yeah, my favourite thing to eat.


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[Assistant] Look at that, you picked yourself some lamb cutlets. I was going to French him, but I thought food you want to eat every day, nibbling on that bone, that's my favourite bit, chewing the bone, I mean, come on. Gonna pair it up with typical flavours of rosemary, garlic, some chilli, pumpkin puree, goat's cheese mousse, and some candied walnuts.


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[Assistant] You pick yourself some lamb cutlets. Yeah. Gonna pair it up with a pumpkin puree.


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[Assistant] I haven't left myself with any time for any stuff ups. I need to move like I've never moved before. I've got a lot of elements on the go.


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[Assistant] I'm scared and excited, there's hardly any time left on the clock and I need to plate this dish. I start with a nice circle of pumpkin puree on the plate.


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[Assistant] On top of the pumpkin puree, I lay my lamb cutlets and just pray that the inside's beautiful and pink.


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[Assistant] Those 75 minutes just go so fast. You don't understand until you're actually in here doing it. I'm feeling good. I mean, I'm relaxed because no one's getting eliminated from this challenge, but I still want to impress the judges and to get in the top four would be awesome. I just hope what I've put up on the plate is enough.


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[Assistant] Today I've made marinated lamb cutlets with roast pumpkin puree, goat's cheese mousse, candied walnuts, and there's a parsley oil to drizzle onto.


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[Assistant] Uhm, I don't believe so. There was some honey on the marinade as well, so that's probably why it's uhm. Alrighty, let's find out.


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[Assistant] When I was president of the American Psychological Association, they tried to media train me. And they, uh, an encounter I had with CNN, uh, summarizes


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[Assistant] What I'm gonna be talking about today, which is the eleventh reason to be optimistic. The, uh, editor of Discover told us, uh, ten of them. I'm gonna give you the eleventh.


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[Assistant] Cameras rolled and she said, uh, Professor Seligman, what is the state of psychology today? Good.


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[Assistant] Dr. Seligman, what is the state of psychology today? Not good.


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[Assistant] Look, Dr. Seligman, we can see you're really not comfortable in this medium. We'd better give you a real sound bite. This time you can have three words. Professor Seligman, what is the state of psychology today? Not good enough.


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[Assistant] And that's what I'm going to be talking about. I want to say why psychology was good, why it was not good, and how it may become in the next ten years good enough. And by parallel summary, I want to say the same thing about technology, about entertainment and design, because I think the issues are very similar.


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[Assistant] And because quite rightly they were saying psychology is about finding what's wrong with you. Uh, spot the loony. And now when I tell people what I do, uh, they move toward me. And what was good,


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[Assistant] Take fuzzy concepts like depression, alcoholism and measure them with rigor. That we could create a classification of the mental illnesses. That we could


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[Assistant] Uh, understand the causality of the mental illness as we could, uh, look across time at the same people. People, for example, who are genetically vulnerable to schizophrenia.


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[Assistant] And, uh, best of all, we were able in the last 50 years to invent, uh, drug treatments and psychological treatments, uh, and then we were able to test them rigorously in random assignment, placebo-controlled designs, throw out the things that didn't work.


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[Assistant] Keep the things that actively did. And the conclusion of that is that psychology and psychiatry of the last 60 years can actually claim that we can make miserable people less miserable.


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[Assistant] The second cost was that we forgot about you people. We forgot about improving normal lives. We forgot about a mission to make, uh,


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[Assistant] Relatively untroubled people, happier, more fulfilled, more productive. And genius, high talent, became a dirty word. No one works on that.


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[Assistant] We never occurred to us to develop interventions to make people happier.


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[Assistant] Positive interventions. So that was not good. And so that's what led, uh, uh, people like Nancy Etkoff, Dan Gilbert, Mike Chick sent my, Mihaly and myself to work in something I call positive psychology, which has three aims. The first,


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[Assistant] Is that psychology should be just as concerned with human strength as it is with weakness?


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[Assistant] It should be, uh, just as concerned with building strength as with repairing damage. It should be interested in the best things in life. And it should be just as concerned with making the lives of normal people fulfilling and


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[Assistant] It turns out that we can measure different forms of happiness and any of you for free can go to that website and take


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[Assistant] Uh, we found that we could discover the causation of the positive states. The relationship between left hemispheric activity and right hemispheric activity as a, uh, uh, cause of happiness.


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[Assistant] I've spent my life working on extremely miserable people. And I've asked the question, how do extremely miserable people differ from the rest of you? And starting about...


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[Assistant] Six years ago, we asked about extremely happy people, and how do they differ from the rest of us. And it turns out there's one way, they're not more religious, they're not in better shape, they don't have more money, they're not better looking, they, uh,


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[Assistant] They don't have more good events and fewer bad events. The one way in which they differ, they're extremely social.


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[Assistant] Uhm, we found we could begin to look at interventions over the centuries from the Buddha to Tony Robbins. About 120 interventions have been proposed that allegedly make people happy.


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[Assistant] And we find that we've been able to manualize many of them and we actually carry out random assignment.


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[Assistant] I want psychology to have, in addition to its mission of curing the mentally ill, in addition to its mission of making miserable people less miserable, is, can psychology actually make people happier?


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[Assistant] And I call them different because different interventions build them. It's possible to have one rather than the other. Three different happy lives. The first happy life is the pleasant life. This is a life in which you have as much positive emotion as you possibly can.


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[Assistant] And the skills to amplify it. The second is a life of engagement. A life in your work, your parenting, your love, your leisure. Time stops for you.


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[Assistant] Uh, that's what Aristotle was talking about. And third, the meaningful life. So I want to say a little bit about each of those lives and what we know about them. The first life is the pleasant life, and it's simply as best we can find it. It's having as many of the pleasures as you can, as much positive emotion as you can, and


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[Assistant] The first drawback is that it turns out the pleasant life, your experience of positive emotion is


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[Assistant] Tricks, getting more of it. Second is that positive emotion, uh, habituates. It habituates, uh, rapidly, indeed. It's all like French vanilla ice cream. The first taste is a hundred percent, by the time you're down to the sixth taste, it's gone. And, uh,


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[Assistant] As I said, it's not particularly malleable.


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[Assistant] Uhm, and this leads to the second life, and I have to tell you about my friend Len to talk about why positive psychology is more than positive emotion, more than building pleasure. In two of the three great arenas of life, by the time Len was 30, Len was enormously successful. The first arena,


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[Assistant] But in the third great arena of life, love, Len is an abysmal failure. And the reason he was, was that Len is a cold fish.


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[Assistant] American women said to Len, when he dated them, you're no fun. You don't have positive emotion. Get lost.


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[Assistant] And, uh, uh, Len was wealthy enough to be able to afford a Park Avenue psychoanalyst who for five years tried to find the sexual trauma that had somehow locked positive emotion inside of him.


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[Assistant] But it turned out there wasn't any sexual trauma. It turned out that, uh, uh, Ling grew up in Long Island and he played football and, uh, watched football and, uh, uh, played bridge.


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[Assistant] And I want to say not. Contrary to what psychology told us about the bottom 50% of the human race and positive affectivity, I think Len is one of the happiest people I know. He's not consigned to the hell of unhappiness. And that's because Len, like most of you,


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[Assistant] Time stops for him. And it stops till the closing bell. When the first card is played, till ten days later the tournament is over, time stops for when.


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[Assistant] And this is indeed what Mike Cheek sent me high has been talking about, about flow. And it's distinct from pleasure in a very important way. Pleasure has raw feels. You know it's happening.


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[Assistant] Thought and feeling, but what Mike told you yesterday during flow.


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[Assistant] Five highest strengths are, and then recrafting your life to use them as much as you possibly can. Recrafting your work, your love, your play, your friendship, your parenting. Just one example, uhm, one person I worked with was a beggar at Gnardi's. Hated the job, she's working her way through college.


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[Assistant] Her highest strength was social intelligence. So she recrafted bagging to make the encounter with her the social highlight of every customer's day. Now obviously she failed, but what she did was to take her highest strengths and recraft work to use them as much as possible.


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[Assistant] What you get out of that is not smiliness. You don't look like Debbie Reynolds. You don't giggle a lot. What you get is more absorption.


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[Assistant] That's the second path. The first path, positive emotion. The second path is eudaimonia and flow. And the third path is meaning. This is the most venerable level of happiness is


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[Assistant] Uh, traditionally, and meaning in this view consists of, uh, very parallel to eudaimonia. It consists of knowing what your highest strengths are and using them


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[Assistant] To belong to and in the service of something larger than you are.


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[Assistant] Pleasant life, the good life, the meaningful life. People are now hard at work on the question, are there things that lastingly change those lives?


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[Assistant] And, uh, the answer seems to be yes, and I'll just give you some samples of it. Uh, it's being done in a rigorous manner. It's being done in the same way that we test drugs to see what really works. Uh, so we do...


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[Assistant] When we teach people about the pleasant life, how to have more pleasure in your life, one of your assignments is to take the mindfulness skills, the savoring skills, and you're assigned to design a beautiful day.


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[Assistant] Next Saturday, set a day aside, design yourself a beautiful day, and use savoring and mindfulness to enhance those pleasures. And we can show in that way that the pleasant life is enhanced. Gratitude visit.


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[Assistant] Remember, someone who did something enormously important that changed your life in a good direction who you never properly thanked. Person has to be alive. Okay? Now,


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[Assistant] Okay, you can open your eyes. I hope all of you have such a person. Your assignment, when you're learning the gratitude visit, is to write a 300-word testimonial to that person.


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[Assistant] Call them on the phone in Phoenix. Ask if you can visit. Don't tell them why. Show up at their door. Uh, you read the testimonial. Everyone weeps when this happens. And what happens is when we test people


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[Assistant] One week later, a month later, three months later, they're both happier and less depressed.


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[Assistant] And fun versus philanthropy, but it's so heartening to be in a group like this in which, uh, so many of you have turned your lives to philanthropy. Well, my undergraduates and the people I work with haven't discovered this, so we actually have people do something altruistic, uh, and do something fun.


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[Assistant] And to contrast it. And what you find is when you do something fun, it has a square wave walk set. When you do something philanthropic to help another person, it lasts. And it lasts.


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[Assistant] So those are examples of positive interventions. So the next to last thing I want to say is uhm,


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[Assistant] So we ask, and we've done this in fifteen replications involving thousands of people, to what extent does the pursuit of pleasure, the pursuit of positive emotion, the pleasant life, the pursuit of engagement,


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[Assistant] And our results surprised us. They were backward of what we thought. It turns out the pursuit of pleasure has almost no contribution to life satisfaction. The pursuit of meaning is the strongest. And this is, the pursuit of engagement is also very strong.


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[Assistant] Where pleasure matters is if you have both engagement and you have meaning, then pleasure is the whipped cream and the cherry, which is to say the


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[Assistant] Full life, the sum is greater than the parts, if you've got all three. Conversely, if you have none of the three, the empty life, the sum is less than the part.


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[Assistant] And what we're asking now is does the very same relationship, physical health, morbidity, how long you live.


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[Assistant] Productivity follow the same relationship that is in a corporation is


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[Assistant] Productivity, a function of positive emotion, engagement, and meaning, is health, a function of positive engagement, of pleasure, and of meaning in life. And there is reason to think the answer to both of those may well be yes.


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[Assistant] So, Chris said that the last speaker had a chance to try to integrate what he heard, and so this was amazing for me. I've never been in a gathering like this. I've never seen speakers stretch beyond themselves so much, which is one of the remarkable things.


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[Assistant] But I found that the problems of psychology seem to be parallel to the problems of technology, entertainment, and design.


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[Assistant] In the following way, we all know that technology, entertainment and design have been and can be used for destructive purposes. Uh, we also know that technology, entertainment and design can be used to relieve misery.


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[Assistant] And I never found that. I found the best you could ever do was to get to zero.


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[Assistant] That they were empty. And it turns out the skills of happiness, the skills of the pleasant life, the skills of engagement, the skills of meaning are different from the skills of relieving misery.


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[Assistant] And so the parallel thing holds with technology.


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[Assistant] Entertainment and design, I believe. That is, it is possible for these three drivers of our world to increase happiness, to increase positive emotion, and that's typically how they've been used. But once you fractionate happiness the way I do, not just positive emotion, that's not nearly enough,


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[Assistant] There's flow in life and there's meaning in life. As Laura Lee told us, design, and I believe entertainment and technology, can be used to increase meaning engagement in life as well. So in conclusion, the eleventh reason for optimism, in addition to


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[Assistant] With technology, entertainment and design, we can actually increase the amount of tonnage of human happiness on the planet.


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[Assistant] And if technology can in the next decade or two increase the pleasant life, the good life, and the meaningful life, it will be good enough. If entertainment can be diverted to also increase positive emotion, meaning


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[Assistant] What we're all doing together will become good enough. Thank you.


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[Assistant] You've been called to serve for the army, to fight against the civil war. Please get ready.