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

“Things get, I mean, things get more complicated. And now, because you were praising simplicity before, you were like, it's so beautiful, unique factorization. It's so great. So when I tell you that in more general number systems, there is no unique factorization. Maybe you're like, that's bad. I'm like, no, that's good because there's like a whole new world of phenomena to study that you just can't see through the lens of the numbers that we're used to. So I'm for complication. I'm highly in favor of complication because every complication is like an opportunity for new things to study.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I love it. I mean, what I teach undergraduate number theory, it's like. It's the first really deep theorem that you prove. What's amazing is the fact that you can factor a number into primes is much easier. Essentially, Euclid knew it although he didn't quite put it in that way. The fact that you can do it at all. What's deep is the fact that there's only one way to do it, or however you sort of chop the number up, you end up with the same set of prime factors. And indeed, what people finally understood at the end of the 19th century is that if you work in number systems slightly more general than the ones we're used to, which it turns out are relevant to Ferma, all of a sudden this stops being true.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“You can factor them and you can factor them uniquely. There's only one way to break a number up into primes. Like if we think of a number like 12, 12 is two times three times two. I had to think about it. Or it's two times two times three. Of course, you can reorder them. But there's no other way to do it. There's no universe in which 12 is something comes five or in which there's like four threes in it. Nope, 12 is like two twos and a three. Like that is what it is. And that's such a fundamental feature of arithmetic that we almost think of it like God's law. You know what I mean? It has to be that way.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“On the other hand, work on the Fermat problem, that's what we like to call it because it's not really his theorem because we don't think he proved that. So, I mean, work on the Fermat problem developed this incredible richness of number theory that we now live in today. And not, by the way, just Wiles, Andrew Wiles being the person who together with Richard Taylor finally proved this theorem. You know how you have this whole moment that people try to prove this theorem and they fail, and there's a famous false proof by LeMay from the 19th century where Kumer, in understanding what mistake LeMay had made in his incorrect proof, basically understand something incredible, which is that, you know, a thing we know about numbers is that”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Maybe, but I think, but you're right that that is a noble. But I think what we can know is that later he certainly did not think that he had a proof that he was concealing from people. Yes. He thought he didn't know how to prove it, and I also think he didn't know how to prove it now. Understand the appeal of saying, wouldn't it be cool if this very simple equation there were a very simple, clever, wonderful proof that you could do in a page or two? And that would be great, but you know what? There's lots of equations like that that are solved by very clever methods like that, including the special cases that Fairmont wrote about, the method of descent, which is like very wonderful and important. In the end, Those are nice things that you teach in an undergraduate class, and it is what it is, but they're not big.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“In his copy of the Disquistiones Arithmetic Eye. He wrote, here's an equation. It has no solutions. I can prove it, but the proof's a little too long to fit in the margin of this book. He was just writing a note to himself. Now, let me just say historically, we know that Vermont did not have a proof of this theorem. For a long time, people were like this mysterious proof that was lost, a very romantic story, right? But Fairmau later, he did prove special cases of this theorem and wrote about it to talk to people about the problem. And it's very clear from the way that he wrote where he can solve certain examples of this type of equation that he did not know how to do the whole thing.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so right. So to give, let me just say the background because I don't know if everybody listening knows the story. So Fermat was an early number theorist. At least sort of an early mathematician, those special adjacents didn't really exist back then. He comes up in the book actually in the context of a different theorem of his that has to do with testing whether a number is prime or not. So I write about, he was one of the ones who was salty and he would exchange these letters where he and his correspondents would try to top each other and vex each other with questions and stuff like this. But this particular thing. Called for Mazla's theorem because it's a note he wrote.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“If I remember correctly. The reverse. There's a lot of really interesting richness to this story. One thing about it is her paper was rather was very short. It was very short and simple, nine pages of which two were pictures. Very short for a paper solving a major conjecture. And it really makes you think about what we mean by difficulty in mathematics. Like, do you say, oh, actually, the problem wasn't difficult because you could solve it so simply? Or do you say, well, no, evidently it was difficult because the world's top topologist worked on it for 20 years and nobody could solve it. So therefore it is difficult. Or is it that we need sort of some new category of things that about which it's difficult to figure out that they're not difficult?”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so there was a question. And again, it doesn't matter the technicalities of the question, but it's a question of whether the knot is sliced. It has to do with. Something about what kinds of three dimensional surfaces in four dimensions can be bounded by this knot. But never mind what it means. It's some question. And it's actually very hard to compute whether or not is slice or not. And in particular, the question of the Conway Knot whether it was slice or not, was particularly vexed. Until it was solved just a few years ago by Lisa Picarillo, who actually, now that I think of it, was here in Austin, I believe she was a grad student at UT Austin at the time. I didn't even realize there was an Austin connection to this story until I started.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I am sorry that you didn't get a chance because having had the chance to talk to him a lot when I was a postdoc. You missed out. There's no way to sugarcoat it. I'm sorry that you didn't get that chance.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“So, like somebody wrote this down. Maybe this is so. Looking at what the AI came up with, you're like, you know, I bet if like five grad students had thought about that problem, they would have come up with that. I mean, when you see it, you're like, okay, that is one of the things you might try if you sort of like. Put some work into it. Still. Pretty awesome. But the story I tell. In the book, which I'm fascinated by, is, okay, we're going to go back to knots. A knot called the Conway knot. After John Conway, who maybe we'll talk about a very interesting character also.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“They are now, for most mathematicians, I would say part of the process of mathematics. And so, you know, there's a story I tell in the book, which I'm fascinated by, which is, you know, so far, Attempts to get AIs to prove interesting theorems have not Done so well doesn't mean they can. It's actually a paper I just saw, which has a very nice use of a neural net defined counter examples to conjecture. Somebody said like, well, maybe this is always that. And you can be like, well, let me sort of train an AI to sort of try to find. Things where that's not true. And it actually succeeded. Now, in this case, if you look at the things that it found, You say I mean, these are not famous conjectures.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Here, too, I think it's important to be kind of historical because it's certainly true that there's lots of things that we used to call research in mathematics that we would now call computation. Tasks that we've now offloaded to machines like, you know, in 1890, somebody could be like, here's my PhD thesis. computed all the invariants of this polynomial ring under the action of some finite group. Doesn't matter what those words mean, just it's like some thing that in 1890 would take a person a year to do and would be a valuable thing that you might want to know. And it's still a valuable thing that you might want to know, but now you type a few lines of code in Macaulay or SAGE or Magma and you just have it. So we don't think of that as math anymore, even though it's the same thing.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I mean, I am tremendously interested in what AI can do in pure mathematics. I mean, of course, it's a parochial interest, right? You're like, why am I not interested in how it can help feed the world or help solve the real such problems? I'm like, can it do more math? What can I do? We all have our interests, right? But I think it is a really interesting conceptual question.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“For example, the Institute for Computational Experimental Mathematics at Brown, which is like an NSF funded math institute very much part of sort of traditional math academia, they did an entire theme semester about visualizing mathematics, like the same kind of thing that they would do for an up-and-coming research topic. Like that's pretty cool. So I think there really is buy-in from. The mathematics community to recognize that this kind of stuff is important and counts as part of mathematics, like part of what we're actually here to do”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“To be honest, it's something that I think we haven't quite figured out how to value inside academic mathematics in the same way, and this is a bit older, that I think we haven't quite figured out how to value the development of computational infrastructure. You know, we all have computers as our partners now and people Build computers that sort of assist and participate in our mathematics. They build those systems and that's a kind of mathematics too, but not in the traditional form of proving theorems and writing papers. But I think it's coming. Look, I mean, I think”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Probably somewhere out there, there's probably sort of some heavy metal band that's like teaching math through heavy metal and using their skills to do that. I hope there is at any rate.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And then those are, you know, some of them are longer, 20 minutes long, some of them are five minutes long, but they're shorter. And even some of you look like Eugenia Chang is a wonderful category theorist in Chicago. I mean, she was on, I think, the Daily Show. I mean, she was on, you know, she has 30 seconds, but then there's like 30 seconds to sort of say something about mathematics to like untold millions of people. So everywhere along this curve is important. One thing I feel like is great right now is that people are just broadcasting on all the channels because we each have our skills, right? Somehow along the way, like I learned how to write books, I had this kind of weird life as a writer where I sort of spent a lot of time thinking about how to put English words together into sentences and sentences together into paragraphs at length, which is this kind of like weird specialized scale. And that's one thing. But like sort of being able to make, you know, winning good looking eye catching videos is like a totally different skill.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“This can get to a lot more people that are ever going to sit in my classroom and you spend however many hours it takes to read a book. Somebody like Three Blue One Brown or Number File or people like Vie Hart. I mean, YouTube, let's face it, has bigger reach than a book. Like there's YouTube videos that have many, many, many more views than any hardback book, like not written by a Kardashian or an Obama is going to sell, right? So that's, I mean.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“That many, right? And you can, and there's kind of an inverse relationship where the more the fewer people you're talking to, the more engagement you can ask for. The ultimate, of course, is like the mentorship relation of like a PhD advisor and a graduate student where you spend a lot of one-on-one time together for three to five years And the ultimate high level of engagement to one person. You know, books.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“It's fantastic. I mean, the flowering of math YouTube is like such a wonderful thing because Math teaching, there's so many different venues through which we can teach people math. There's the traditional one, right? Where I'm in a classroom with, you know, depending on the class, it could be 30 people, it could be 100 people, it could, God help me be 500 people if it's like the big calculus lecture or whatever it may be. And there's sort of some, but there's some set of people of that order of magnitude. And I'm with them. We have a long time. I'm with them for a whole semester. And I can ask them to do homework and we talk together. We have office hours if they have one-on-one questions. That's like a very high level of engagement. But how many people am I actually hitting at a time? Like”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I mean, there's, you know, there's a lot of books that are like, I don't quite know how to express this well. I'm still laboring to do it. There's a lot of books that are about stuff. But I want my books to not only be about stuff, but to actually have some stuff there on the page in the book for people to interact with directly and not just sort of hear me talk about distant features about distant features of it.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Topics that are you can't really compress and really truly say exactly what they are in this amount of space. I try to say something interesting about them, something meaningful about them so that readers can get the flavor. And then another places. I really try to get up close and personal and really do the math and have it take place on the page.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Exactly. So, this idea that I mean, I think Poincar ⁇ really have this idea, this sort of modern idea. I mean, building on stuff other people did, Betty is an important one of this kind of modern notion of relations between wholes. But the idea that holes really had an arithmetic, the really modern view was really Emmy Nurtur's idea. So she kind of comes in and sort of truly puts the subject on its modern footing that we have now. So, you know, it's always a challenge in the book. I'm not going to say I give. There are some things. You can really do on the page, and the math is there. And there's other things which it's too much in a book like this to do them all the page. You can only say something about them, if that makes sense. So, you know, in the book, I try to do some of both. I try to...”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Is that your weekly routine or just in preparation for talking about geometry for three hours? You need to decline for this.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“The amount of milkshake that's coming in the left leg of the pants plus the amount of milkshake that's coming in the right leg of the pants is the same that's coming out The waste of the pants.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“The first version would be to say, well, there are two holes, but they're really both the same hole. Well, that's not quite right. A better way to say it is there's two holes, but one is the negative of the other. What can that mean? One way of thinking about what it means is that if you sip something like a milkshake through the straw, no matter what, the amount of milkshake that's flowing in one end, that same amount is flowing out the other end. So they're not independent from each other. There's some relationship between them. In the same way that if you somehow could suck a milkshake through a pair of pants. The amount of milkshake, just go with me on this thought experiment.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“She's a one holder for the straw, too. That really does capture something. It captures this fact, which is central to the theory of what's called homology, which is like a central part of modern topology, that holes, whatever we may mean by them, they're somehow things which have an arithmetic to them. There are things which can be added, like the waste equals leg plus leg is kind of an equation, but it's not an equation about numbers. It's an equation about some kind of geometric, some kind of topological thing, which is very strange. And so, you know, when I come down. Like a rabbi, I like to kind of come up with these answers to somehow dodge the original question and say, you're both right, my children. Okay, so So for the straw, I think what a modern mathematician would say is like,”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“She said, Well, yeah, I feel a pair of pants just has two holes because, yes, there's the waist, but that's just the two leg holes stuck together”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“There you go. So many people would say there's three holes in a pair of pants. But for instance, my daughter, when I asked this, by the way, talking to kids about this is super fun. I highly recommend it.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“How many holes are there in a pair of pants? So I think most people who say there's two holes in a straw would say there's three holes in a pair of pants. I guess we're filming only from here. I could take up. No, I'm not going to do it. You'll just have to imagine the pants. Sorry. If you want to. No, okay, no.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“And yet, if you're a two hole or the one hole where we'll say, like, okay, where does one hole begin and the other hole end? And in the book, I sort of, you know, in math, there's two things we do when we're faced with a problem that's confusing us. We can make the problem simpler. That's what we were doing a minute ago when we were talking about high-dimensional space. And I was like, let's talk about circles and line segments. Let's go down a dimension to make it easier. The other big move we have is to make the problem harder and try to sort of really face up to what are the complications. So what I do in the book is say, let's stop talking about straws for a minute and talk about pants.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“You know, once they look, there's like a hole and it goes all the way through the straw, right? It's one reason of space that's the hole. And there's one. And two whole people would say, well, look, there's a hole in the top and the hole. The bottom. I think a common thing you see when people Argue about this, they would take something like this bottle of water I'm holding. Maybe I'll open it. Say, well, how many holes are there in this? And you say, Well, there's one, there's one hole at the top. Okay, what if I poke a hole here so that all the water spills out? Well, now it's a straw. So, if you're a one hole, or I say to you, how many holes are in it now? There was one hole in it before and I poked a new hole in it. And then you think there's still one hole, even though there was one hole, and I made one more?”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I think that would be somebody whose account, I mean What I would say is you could say the same thing. About a bagel. You could say, I can make a bagel by taking a long cylinder of dough, which doesn't have a hole, and then smushing the ends together. Now it's a bagel. So if you're really committed, you can be like, okay, a bagel doesn't have a hole either, but like, who are you if you say a bagel doesn't have a hole? I mean, 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
“Sure. So I think, you know, most people, the zero holers are rare. They would say like, well, look, you can make a straw by taking a rectangular piece of plastic and closing it up. The rectangular piece of plastic doesn't have a hole in it. I didn't poke a hole in it when I... So, how can I have a hole? They'd be like, it's just one thing. Okay, most people don't see it that way. That's like, um,”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“It's one of these questions where people on first hearing it think it's a triviality and they're like, well, the answer is obvious. And then what happens if you ever ask a group of people this, something wonderfully comic happens, which is that everyone's like, well, it's completely obvious. And then each person realizes that half the person, the other people in the room have a different obvious answer for the way they have. And then people get really heated. People are like, I can't believe that you think it has two holes or like, I can't believe that you think it has one. And then, you know, you really like people really learn something about each other. And people get heated.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“It's in fact not beyond our capability. It may be beyond our cognitive capabilities to visualize a four-dimensional cube, a tesseract, as some like to call it, or a five-dimensional cube or a six-dimensional cube. But it is not beyond our cognitive capabilities to figure out how many corners a six-dimensional cube would have. That's what's so cool about us, whether we can visualize it or not, we can still talk about it. We can still reason about it. We can still figure things out about it. That's amazing.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Conceptualize that there could actually be yet another dimension. So, yeah, that takes the religious allegory to like a very weird place that I don't really understand theologically, but...”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“But what happens in this book, in this part now, looking at it through a Christian lens, it becomes a bit subversive, is the square is so excited about what he's learned from the sphere and the sphere explains to him what a cube would be. Oh, it's like U, but three-dimensional and the square is very excited. And the square is like, okay, I get it now. So now that you explain to me how just by reason I can figure out what a cube would be like, like a three-dimensional version of me, like let's figure out what a four-dimensional version of me would be like. And then the sphere is like, What the hell are you talking about? There's no fourth dimension, that's ridiculous. Like, there's only there's three dimensions. Like, that's how many there are. I can see. So it's this sort of comic moment where the sphere is completely unable to.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“So, the whole Christian subtext of this book, I had completely not grasped reading this as a kid, that it means a very different thing, right? If sort of a theologian is saying, like, oh, what if a higher being could pull you out of this earthly world you live in so that you can sort of see the truth and really see it from above, as it were? So that's one of the things that's going on for him. And it's a testament to his skill as a writer that his story just works the framework you're coming to it from or not.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, but what happens in the book? I didn't even tell you the whole plot. What happens is the square is so excited and so filled with intellectual joy. By the way, maybe to give the story some context, you ask like, is it possible for us humans to have this experience of being transcendentally jerked out of our world so we can sort of truly see it from above? Well, Edwin Abbott, who wrote the book, certainly thought so because Edwin Abbott was a minister.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Oh, I certainly think that's possible. Now how would you figure out whether it was true or not is another question? I don't know. And I suppose what you would do, as with anything else that you can't directly perceive, You would try to understand what effect the presence of those extra dimensions. Out there would have on the things we can perceive. Like, what else can you do, right? And in some sense, if the answer is they would have no effect, then maybe it becomes like a little bit of a sterile question because what question are you even asking, right? You can kind of pause it however many entities that are. You”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Sterile argument where the square is not able to kind of like follow the mathematical reasoning of the sphere until the sphere just kind of grabs him and jerks him out of the plane and pulls him up and it's like now like now do you see like now do you see your World that you didn't understand before.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Adult comic novel from the 19th century about an entire two-dimensional world, it's narrated by a square. That's the main character. And the kind of strangeness that befalls him when one day he's in his house and suddenly there's like a little circle there and there with him. But then the circle starts getting bigger and bigger and bigger. And he's like, what the hell is going on? It's like a horror movie for two-dimensional people. And of course, what's happening is that a sphere is entering his world. And as the sphere kind of like moves farther and farther into the plane, it's cross-section, the part of it that he can see. To him, it looks like there's like this kind of bizarre being that's like getting larger and larger and larger until it's exactly sort of halfway through. And then they have this kind of like philosophical argument where the sphere is like, I'm a sphere, I'm from the third dimension. The square is like, what are you talking about? There's no such thing. And they have this kind of like.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“People have thought about this a lot. I mean, this metaphor of what if we're little creatures in some sort of smaller world, like how could we apprehend what's outside? That metaphor just comes back and back. And actually, I didn't even realize how frequent it is. It comes up in the book a lot. I know it from a book called Flatland. I don't know if you ever read this when you were a kid.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I think somehow this depends on something of how the physics of light works in this scenario, which I'm sort of finding it hard to bend my.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Think that on what's called the real projective plane, which is kind of even more sort of like messed up version of the Mabia strip, but with very similar features, this feature of kind of like only having one side, that has the feature that there's a loop of string which can't be pulled close. But if you loop it around twice along the same path, that you can pull closed. That's extremely weird. But that would be a way you could know without leaving your world”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“Which one? Because what you do is you tell your friend, hey, stay right here. I'm just going to go for a walk. And then you walk for a long time in one direction. And then you come back and you see your friend again. And if your friend is reversed, then you know you live on a Mobia strip.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“I'm going to be honest with you. I don't know if I fear you won't like this answer, but it does not bother me at all. I don't lose one minute of sleep over it.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source
“If you can't tell whether you live in a circle or a Imagine a non floating in three dimensional space. The person who lives on that knot, to them, it's a circle. They walk a long way, they come back to where they started. Now, we with our three dimensional eyes can be like, oh, this one's just a plain circle and this one's knotted up. But that has to do with how they sit in three-dimensional space. It doesn't have to do with intrinsic features of those people's world.”
2021-06-13 · Lex Fridman Podcast · #190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries · IDENTIFIED FROM THE TRANSCRIPT · source