YouSaid · the spoken record

Jordan Ellenberg

lines on the record: 193
first: 2021-06-13
most recent: 2021-06-13
sittings or episodes: 1
sources: podcast

Every line below is reproduced as it was said and linked to the record it came from. Nothing here is summarised or generated. Directory · Search · Corrections

“Yes, this is what I was trying to keep in my head all at once while I was writing. And I probably should have drawn this picture earlier in the process. Maybe it would have made my organization easier. I actually drew it only at the end.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Opposite if you ask Blaise Pascal, like, why do you believe in God? He'd be like, Oh, because I met God. You know, he had this kind of psychedelic experience, this kind of mystical experience where as he tells it, he just like directly encountered God. He's like, okay, I guess there's a God. I met him last night. So that's it. That's why he believed. It didn't have to do with any kind of, you know, the mathematical argument was like about certain reasons for behaviing in a certain way. But he basically said, like, look, math doesn't tell you that God's there or not. If God's there, he'll tell you. You know, you don't even love this. So you had.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Questions. But what's interesting when I really read Pascal about what he wrote about this, you know, I started to see that people often think, oh, this is him saying I'm going to use mathematics. Sort of show you why you should believe in God. You know, to really, mathematics has the answer to this question. But he really doesn't say that. He almost kind of says”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I mean, look, the way I feel is that mathematics, as we've discussed, it underlies the way we think about constructing learning machines. It underlies physics. It can be used. I mean, it does all this stuff. Also, you want the meaning of life? I mean, it's like we already did a lot for you. Like, ask a rabbi. No, I mean, you know, I wrote a lot in the last book, How Not to Be Wrong. I wrote a lot about Pascal, a fascinating guy who is a sort of very serious religious mystic as well as being an amazing mathematician. And he's well known for Pascal's wager. I mean, he's probably, among all mathematicians, he's the one who's best known for this, can you actually apply mathematics to kind of these transcendent...”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, but it doesn't mean I would never say to somebody you should just go have high self-esteem You shouldn't have doubts. No, you probably should have doubts. It's okay to have them, but sometimes it's good to act in the way that the person who didn't have them would act.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“You didn't have those, you can probably figure out what the version of youth feels completely confident would do. Do that and see what happens. And I think that's often pretty good.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And you know, I have kids, so this is actually a live issue for me, right? I actually, it's not a thought experiment. I actually do have to give advice to two young people all the time. They don't listen, but I still give it. You know, one thing I often say to students, I don't think I've actually said this to my kids yet, but I say it to students a lot is. You come to these decision points Everybody is beset by self doubt, right? It's like not sure like what they're capable of, like not sure What they really want to do. I sort of tell people often when you have a decision to make One of the choices is the high self esteem choice. And I always thought make the high self esteem choice, make the choice sort of take yourself out of it and like.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“In the long arc of fistry. That man is onto something. Up this question What advice would you give to young people today thinking about About their Whether it's in mathematics,”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“You say that, but like, what about the guy who wins the Nathan's hot dog eating contest every year? Like, when he eats his 35th hot dog, he correctly says, like, okay, most people would stop here. Are you like lauding that he's like, no, I'm gonna eat the 36 hot dogs? I am.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“With learning math from a textbook or from a video, there's a nice. I think you have to enjoy the dead ends, but I think you have to accept the dead ends. Let's put it that way. Well, yeah Enjoy the suffering of it. So The way I think about it, I do I don't enjoy the suffering. It pisses me off, except that it's part of the process. Interesting, there's a lot of ways to kind of deal with that dead end. There's a guy who's the ultra marathon runner on Navy. David Gog There's a certain philosophy of like. Most people would quit here. And so, if most people would quit here I don't. I'll have an opportunity to discover something beautiful that others haven't yet. Any feeling that really sucks Most people would just like go do something small. If I stick with this, I will New gard Fruit trees that I”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And like keep pushing forward through the frustration of really obviously not understanding certain like parts of the picture. Like you have giant missing parts of the picture and still not giving up. It's the same way I feel about running. And there's something about falling in love with the feeling of after you went through the journey of Not having a complete picture. At the end, having a complete picture, and then you get to appreciate. Beauty and just remembering that it sucked for a long time and how great it felt when you figured it out, at least at the basic. That's not sort of research thinking because with research you probably also have to enjoy the dead end.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Again, maybe this is my own learning. Friends Think it's of value to fall in love with the process of doing something. Hard, overcoming it. Becoming a better person because of it. Like, I hate running. I hate exercise to bring it down to the simplest heart. And I enjoy the part once it's done. Person I feel like for the in the rest of the day, once I've accomplished it, the actual process, especially the process of getting started. The initial, like it really I don't feel like doing it. And I really have the way I feel about running is the way I feel about really anything difficult in the intellectual space, especially mathematics, but also Just something that requires holding a bunch of concepts in your mind with some uncertainty, like where the terminology or the notation is not very clear. And so you have to Of hold all those”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Math is really hard Fact, anything that you do right is hard. Because it's hard, you might sort of have some idea that somebody else gives you, oh, I should learn X, Y, and Z. Well, if you don't actually care, you're not going to do it. You might feel like you should. Maybe somebody told you you should. I think you have to hook it to something that you actually care about. So, for a lot of people, that's the way in you have an engineering problem you're trying to handle. You have a physics problem you're trying to handle. You have a machine learning problem you're trying to handle. Let that, not a kind of abstract idea of what the curriculum is, drive your mathematical learning.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And he was like, and Professor Harris was like, that's a really stupid idea. And I was like, why is that a stupid idea? Then I would know more algebraic geometry. He's like, because you're not actually going to do it. You learn. I mean, he knew me well enough to say, like, you're going to learn because you're going to be working on a problem. And then there's going to be a fact from EGA you need in order to solve your problem that you want to solve. And that's how you're going to learn it. You're not going to learn it without a problem to bring you into it. And so for a lot of people, I think if you're like, I'm trying to understand machine learning and I'm like, I can see that there's sort of some mathematical technology that I don't have. I think you let that problem that you actually care about drive your learning. I mean, one thing I've learned from advising students, you know,”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Joe Harris, who was an algebraic geometer, a professor in my department, I was like, I really feel like I don't know enough and I should just like take a year of leave and just like read EGA, the holy textbook and Le Monde de Geometri algebrique, the elements of algebraic geometry. I feel like I don't know enough, so I'm just going to sit and like read this 1500-page many volume book.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Reading a formal textbook, which for some people would be the right thing to do. And working contest style problems too, those are bound to books, like especially Russian and Bulgarian problems, right? There's book after book problems from those contexts. That's going to motivate some people. For some people, it's going to be like watching well-produced videos, like a totally different format. Like, I feel like I'm not answering your question. I'm sort of saying there's no one answer. And it's a journey where you figure out what resonates with you. For some people, the self-discovery is trying to figure out why is it that I want to know. Okay, I'll tell you a story. Once when I was in grad school, I was very frustrated with my lack of knowledge of a lot of things, as we all are, because no matter how much we know, we don't know what more and going to grad school means just coming face to face with like the incredible overflowing vault of your ignorance, right? So I told.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I mean, the thing is, it's in part a journey of self-knowledge. You have to know what's going to work for you and that's going to be different for different people. So there are totally people who at any stage of life just start reading math textbooks. That is a thing that you can do and it works for some people and not for others. For others, a gateway is, you know, I always recommend like the books of Martin Gardner, another sort of person we haven't talked about, but who also, like Conway embodies that spirit of play, he wrote a column in Scientific American for decades called Mathematical Recreations. And there's such joy in it and such fun. And these books, the columns are collected into books and the books are old now, but for each generation of people who discover them, they're completely fresh. And they give a totally different way into the subject than”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“In this very specialized skill. And by the way, it was a very Cold War activity. You know, in 1987, the first year I went, it was in Havana. Americans couldn't go to Havana back then. It was a very complicated process to get there. And they took the whole American team on a field trip to the Museum of American Imperialism in Havana so we could see what America was all about.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, there's something I have to explain to people because it says, I think it says on Wikipedia that I won a gold medal. And the real Olympics, they only give one gold medal in each event. I just have to emphasize that the International Math Olympiad is not like that. The gold medals are awarded to the top 12th of all participants. So sorry to bust the legend or anything like that. Well, you wouldn't accept.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“You know, it's a good opportunity. Let's posit that that's his reasoning because I truly don't know. It's an interesting opportunity to go back to almost the very first thing we talked about, the idea of the mathematical Olympiad. Because, of course, that is, so the International Mathematical Olympiad is like a competition for high school students solving math problems. In some sense, it's absolutely false to the reality of mathematics because just as you say, it is a contest where you win prizes. The aim is to sort of be faster than other people. You're working on sort of canned problems that someone already knows the answer to, like not problems that are unknown. In my own life, I think when I was in high school, I was like very motivated by those competitions. And like I went to the Math Limbiad and.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Most people accept, you know, most people have given a prize. Most people take it. I mean, people like to be appreciated, but like I said, we're people.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, it's interesting because on the one hand, I think it's absolutely true that right in some kind of. Vast spiritual sense, like awards are not important, like not important the way that sort of like understanding the universe is important. On the other hand, most people who are offered that prize accept it. So there's something unusual about his. His choice there. I wouldn't say I see it as tragic. I mean, maybe if I don't really feel like I have a clear picture of why he chose not to take it. I mean, it's not, he's not alone in doing things like this. People sometimes turn down prizes for ideological reasons, but probably more often in mathematics. I mean, I think I'm right in saying that Peter Scholze turned down sort of some big monetary prize because he just, you know, I mean, I think he At some point you have plenty of money.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Seeing the whole thing globally at once, that you can really make progress on understanding the one thing you thought you were looking at.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, but yeah, so what I like about it is that it's just one of many examples of where it's not about the geometry you think it's about. It's about the geometry of all geometries, so to speak. And it's only by kind of like being jerked out of flatland, right? Same idea. It's only by sort of.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“But of course, in this context, singularity just means acquiring a sharp kink. It just means becoming non smooth at some point.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And now you let it flow. You sort of let it move and it's natural path according to some almost physical process and ask where it winds up. And what you find is that it always winds up. You've continuously deformed it. There's that word deformation again. And what you can prove is that the process doesn't stop until you get to the usual three dimensional space. And since you can get from the mystery thing to the standard space by this process of continually changing and never kind of having any sharp transitions, then the original shape must have been the same as the standard shape. That's the nature of the proof. Now, of course, it's incredibly technical. I think as I understand it, I think the hard part is proving that the favorite word of AI people, you don't get any singularities along the way.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes So, what is this idea? The idea is that, well, of course, the geometry of the three dimensional object itself is relevant, but the real geometry you have to understand is the geometry of the space of all three dimensional geometries. Whoa. You're going up a higher level. Because when you do that, you can say now, let's trace out a path. In that space. There's a mechanism called Richy Flow. And again, we're outside my research area. So for all the geometric analysts and differential geometers out there listening to this, please, I'm doing my best and I'm roughly saying it. So the Ricci flow allows you to say like, okay, let's start from some mystery three-dimensional space, which Poincar ⁇ would conjecture is essentially the same thing as our familiar three-dimensional space, but we don't know that.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Understands. And by the way, in a tradition that involves Richard Hamilton and many other people, like most really important mathematical advances, this doesn't happen alone. It doesn't happen in a vacuum. It happens as the culmination of a program that involves many people. Same with Wiles, by the way. I mean, we talked about Wiles, and I want to emphasize that starting all the way back with Kumer, who I mentioned in the 19th century, but Gerhard Fry and Mazer and Ken Ribbit and many other people are involved in building the other pieces of the arch before you put the keystone in.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I mean, one thing I really like about the proof, and partly that's because it's sort of a thing that happens again and again in this book. I mean, I'm writing about geometry and the way it sort of appears in all these kind of real-world problems. But it happens so often that the geometry you think you're studying is somehow not enough. You have to go one level higher in abstraction and study a higher level of geometry. And the way that plays out is that Point Aray asks a question about a certain kind of three-dimensional object. Is it the usual three-dimensional space that we know or is it some kind of exotic thing? And so, of course, this sounds like it's a question about the geometry of the three-dimensional space. But no.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Let me make a crazy metaphor. Maybe it's a little bit like the relationship between prose and poetry, right? I mean, if you might say, why do we need anything more than prose? You're trying to convey some information. So you just say it. Well, poetry does something, right? It's sort of, you might think of it as a kind of compression, of course not all poetry is compressed, like some of it is quite baggy, but like... You are kind of often it's compressed, right? A lyric poem is often sort of like a compression of what would take a long time and be complicated to explain in prose into sort of. Different mode that is going to hit in a different way.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I'm just saying, nobody goes back to what we were saying about teaching that people are different and what they'll respond to. So I think there's no, I mean, I'm very opposed to the idea that there's one right way to explain things. I think there's a huge variation in like, you know, our brains have all these weird hooks and loops and it's like very hard to know what's going to latch on. And it's not going to be the same thing for everybody. I think monoculture is bad, right? I think that's, and I think we're agreeing on that point that it's good that there's a lot of different ways in and a lot of different ways to describe these ideas because different people are going to find different things illuminating.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I mean, you could say that, but I would say for me, a picture of the hop vibration does nothing for me. Whereas, like, when you're like, oh, it's about the quaternions, it's like a subgroup of the quaternions. And I'm like, oh, so now I see what's going on. Like, why didn't you just say that? Why were you like showing me this stupid picture instead of telling me what you were talking about?”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Programmatically. That's great. I mean, this is what we try to train our students to do, right? I mean, in class, this is exactly what this is like best pedagogical practice.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Nearly the speed of light. Well, under the new framework, it's much better to go, oh no, it wasn't changing in street. You were just wrong about what counted as the symmetry. Now that we have this new group, the so-called Lorenz group, now that we understand what the symmetries really are, we see it was just an illusion that the thing was changing shape.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“There becomes a question what are the symmetries of the actual world with its physical laws? And one way of thinking is an oversimplification, but like one way of thinking of this big Shift from Before Einstein to after is that we just changed our idea about what the fundamental group of symmetries were so that things like the Lorentz contraction, things like these bizarre relativistic phenomena, where Lorenz would have said, oh, to make this work, we need a thing to... Change its shape. It's moving”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I'm not a mathematical physicist, but I can say this it is certainly true that it has been a very useful notion in physics to try to say what are the symmetry groups like of the world? Like what are the symmetries under which things don't change, right? So we just, I think we talked a little bit earlier about it should be a basic principle that a theorem that's true here is also true over there. Same for a physical law, right? I mean, if gravity is like this over here, it should also be like this over there. Okay, what that's saying is we think translation in space should be asymmetry. All the laws of physics should be unchanged if the symmetry we have in mind is a very simple one like translation. And so then.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Oh, yeah Well, okay, ready? Think about the symmetries of the line. You're like, okay, I can reflect it. To right, you know, around the origin. Okay, but I could also reflect it left to right grabbing somewhere else, like at one or two or pi or anywhere. Or I could just slide at some distance. That's a symmetry. Slide it five units over. So there's clearly infinitely many symmetries of the line. That's an example of an infinite group of symmetries.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“It's just some collection of transformations you can do to a thing where you can combine any two of them to get a third. So, you know, a place where this comes up in computer science is in sorting because the ways of permuting a set, the ways of taking sort of some set of things you have on the table and putting them in a different order, shuffling a deck of cards, for instance. Those are the symmetries of the deck. And there's a lot of them. There's not two. There's not four. There's not eight. Think about how many different orders the deck of card can be in. Each one of those is the result of applying asymmetry to the original deck. So a shuffle is a symmetry, right? You're reordering the cards. If I shuffle and then you shuffle, the result is some other kind of thing you might call the double shuffle, which is a more complicated symmetry. So group theory is kind of the study of the general abstract world that encompasses all these kinds of things. But then, of course, like...”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“So there's actually four symmetries. There's do nothing, flip it left to right, and flip it top to bottom, or do both of those things. Square There's even more because now you can rotate it. You can rotate it by 90 degrees. So you can't do that. That's not a symmetry at the rectangle. If you try to rotate it 90 degrees, you get a rectangle oriented in a different way. So a person has two symmetries, a rectangle for a square eight, different kinds of shapes have different numbers of symmetries. And the real observation is that that's just not a set of things. They can be combined. You do one symmetry, then you do another. The result of that is some third symmetry. So a group really abstracts away this notion of saying”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, so I would say group theory sort of starts as the general theory of symmetry is that people looked at different kinds of things and said, as we said, like, oh, it could have maybe all there is is symmetry from left to right, like a human being, right? Or that's roughly bilaterally symmetric, as we say. So there's two symmetries. And then you think, well, wait, didn't I say there's just one? There's just left to right. Well, we always count the symmetry of doing nothing. We always count the symmetry that's like, there's flip and don't flip. Those are the two configurations that you can be in. So there's two. You know, something like a rectangle is bilaterally symmetric. You can flip it left to right, but you can also flip it top to bottom.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Not sure I think Conway thought that. It's something that, I mean, Conway always had a rather ambivalent relationship with Game of Life because I think he saw it as It was certainly the thing he was most famous for in the outside world. And I think that his view, which is correct, is that he had done things that were much deeper mathematically than that. And I think it always grieved him a bit that he was like the game of life guy when he proved all these wonderful theorems and created all these wonderful games, created the surreal numbers. He just did an incredibly variegated array of stuff. So he was exactly the kind of person who you would never want to like reduce to like one achievement. You know what I mean?”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“It's a wonderful laboratory, and it's kind of a rebuke to someone who doesn't think that very, very rich complex structure can come from very simple underlying laws. Like it definitely can. Now, here's what's interesting. If you just picked like some random rule. Wouldn't get interesting complexity. I think that's one of the most interesting things of these, one of the most interesting features of this whole subject. The rules have to be tuned just right, like a sort of typical rule set doesn't generate any kind of interesting behavior. Some do, and I don't think we have a clear way of understanding which do and which don't. I don't know. Maybe Stephen thinks he does. I don't know.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“The rule is very simple. You can write it on one line. And then the great miracle is that you can start from some very innocent looking little small set of boxes and get these results of incredible richness. And of course, nowadays you don't do it on paper. Nowadays you do it on a computer. There's actually a great iPad app called Golly, which I really like that has like Conway's original rule and like, gosh, like hundreds of other variants and it's lightning fast. So you can just be like, Of this rule play out faster than your eye can even follow. And it's amazing. So I highly recommend it if this is at all intriguing to you getting golly on your iOS device.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Experiment of life is this, it's a very simple algorithm. It's not really a game per se in the sense of the kinds of games that he liked, whereas people played against each other. Essentially, it's a game that you play with marking little squares on the graph paper. And in the 70s, I think he was literally doing it with like a pen on graph paper. You have some configuration of squares. Some of the squares in the graph paper are filled in. Some are not. And then there's a rule, a single rule that tells you at the next stage which squares are filled in and which squares are not. Sometimes an empty square gets filled in. That's called birth. Sometimes a square that's filled in gets erased. That's called death. And there's rules for which squares are born and which squares die.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Anytime you turned him on, you know what I mean? You sort of ask the question, it was just like turning a knob and winding him up and he would just go and you would get a response that was like, So rich and went so many places and taught you so much, and usually had nothing to do with your question. Usually, your question was just a prompt. To him, you couldn't count on actually getting the question”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And he too kind of has his own crazy number system, in which, by the way, there are these infinitesimals, the ghosts of departed quantities. They're in there, not as ghosts, but as certain kind of two-player games. He was a guy. So I knew him when I was a postdoc, and I knew him at Princeton. And our research overlapped in some ways. Now, it was on stuff that he had worked on many years before, the stuff I was working on kind of connected with stuff in group theory, which somehow seems to keep coming up. And so I often would like to sort of ask him a question. I would sort of come upon him in the common room, and I would ask him a question about something.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“What you may think I'm going to say, and it's true, is that he sort of was very playful in his way of doing mathematics, but it's also true, it went both ways. He also sort of made mathematics out of games. He looked at, he was a constant inventor of games with crazy names. And then he would sort of analyze those games mathematically to the point that he and then later collaborating with Knuth, like created this number system, the serial numbers, in which actually each number is a game. There's a wonderful book about this called. I mean, there are his own books and then there's like a book that he wrote with Burla Kamp and Guy called Winning Ways, which is... Such a rich source of ideas”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, and Conway is such a perfect example of somebody whose humanity was and his personality was like wound up with his mathematics, right? So it's not sometimes I think people who are outside the field think of mathematics as this kind of like cold thing that you do separate from your existence as a human being. No way your personality is in there just as it would be in like a novel you wrote or a painting you painted or just like the way you walk down the street. It's in there. It's you doing it. And Conway was certainly a singular personality. I think anybody would say That he was playful, like everything was a game to him. Now,”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I was about to say, I feel like you have a very elevated idea of how famous. This is what happens when you grow up in the Soviet Union, or you think the mathematicians are very, very famous.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I don't know if you saw the one I'm talking about where they were like learning the texture is like let's try to like Reverse engineer and like learn a cellular automaton that can reduce texture that looks like this from the images. Very cool. And as you say, The thing you said is, I feel the same way when I read machine learning paper, is that what's especially interesting is the cases where it doesn't work. Like, what does it do when it doesn't do the thing that you tried to train in? Do. That's extremely interesting. Yeah, yeah. That was a cool paper. So, yeah, so let's start with the game of life. Let's start with, or let's start with John Conway. So Conway.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source