cover of episode 14: London Tsai - The Reclusive Dean of The New Escherians

14: London Tsai - The Reclusive Dean of The New Escherians

Publish Date: 2019/12/1
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Hello, you found the portal. I'm your host, Eric Weinstein, and I'm here in Manhattan with artist London Tsai, a person I've been looking to meet for quite some time. And I just met him yesterday for the first time in London. Welcome. Thank you. So I have been eyeing your artwork for years on the internet. I've used it in talks and

And you are one of the most important people that we've had come on the portal, even though very few people will know who you are or what you've been up to. Can you say a little bit about your background as a mathematical artist? Oh, my background. So my background as an artist, well, I studied mathematics in undergrad, and maybe I should start over.

So actually I went to college and... So you admit you went to college. Yeah, I did. And I wanted to actually study French literature and international relations. Okay. And my freshman year, I took the standard courses and I really delved into 20th century French literature and...

This was at Duke? This was at Tufts. Oh, at Tufts. Okay. So at Tufts, I took all these kind of liberal arts classes, humanities classes, and I was actually disappointed. I had all these ideas about what I wanted to accomplish in literature and what I would learn, and I would ultimately find some sort of meaning, some understanding of the world we live in.

And instead, I was frustrated, and I didn't seem to be able to get answers to the questions I had. And to my surprise, I was enjoying calculus much more than any of the classes I took. Dear sweet child. So what happened was that in my sophomore year, I declared my math major. Okay, so you came out of the closet. Came out of the closet, yeah. Declared yourself as a...

Proto-mathematician. Yes. And then? And then I, well, of course, I grew up in an artistic household. And I always thought I would do some sort of artwork. But once I discovered mathematics, I found that it was more artistic than anything that I'd ever seen before. It's more creative. Yeah.

is more ingenious, is more abstract. With no author. No author, yeah. And it's just there. And you could study it, and it was infinitely deep. You could pick up any part, and you could just keep going. And everything just fit together so nicely. And I just wanted to see more and understand more about

And all the mathematical writing that was on the blackboards from the graduate classes and things like that, I wanted to understand what they were about. And they must be representatives of some sort of world that I didn't have access to at the time.

So I'm looking into your eyes and I'm seeing something that looks like a religious convert or maybe like Ray Charles the first time he tried heroin or something. You got the bug. Absolutely. Okay. Yeah, absolutely. I mean, it's the only thing I thought about for about six years. I just... You're obsessed. I just dived into it. In fact, I don't think I had like kind of this really strong mathematical ability. I was just fascinated by it and...

And for me, it didn't come as naturally as it did for my brother. And I really had to struggle. I really had to. I felt it was a real challenge to my self-worth. I felt like if I couldn't do this, if I couldn't understand mathematics, that life was just not worth living. Whoa. It was pretty, it was like that. I just decided I would prove to myself that I could do it. And I

To the exclusion of almost everything else. This is, I mean, I'm joking around a little bit about heroin, but it does behave like that. Once you find out that there is a hidden world and that this hidden world is strangely meaningful and that it's clearly too beautiful to be constructed by any human mind. Like the most beautiful human minds can barely understand this world, but it's more like they're dusting off

I guess in my understanding, I think about like the ruins of Petra and imagine that Petra were buried in sand and you were just whisking away sand and uncovering ruins. You'd be pretty convinced that you weren't authoring the ruins of Petra. You would know that you didn't build this thing, but you, you know, it's just such a privilege to be able to touch something this beautiful that's apparently unauthored by anything known to be human. Yeah.

I mean, that's kind of my feeling. So like of reverence and transcendence. Yeah, like there's this kind of eternal stillness in this world. And recently I've just picked up my old math texts. The ideas there are just as fresh as they were 30 years ago when I was studying them. And they still have that pure beauty about them. Let me...

Let you in a little bit on why I'm having you on this program. It's not just because I'm so devoted to your work. It's also because my belief is that we have the most beautiful symphonies in the world locked inside of our journals and our math libraries, let's say, as text. And you can ask, well, if you have a symphony of Brahms,

Is it a symphony if it only resides in the sheet music and is never performed? That's a very disturbing question because the instructions for its performance are present. And it may be that a tiny number of people can actually read a sheet of sheet music and say, oh my God, that's gorgeous because they can hear it in their head. But the rest of us actually need the thing to be performed. And yet there is no orchestra available.

or analog of an orchestra that performs works of great mathematical or physical beauty. - Yeah, that's true. I mean, part of my interest in mathematics initially was that I could take mathematics and the beautiful images that I saw

Yeah. During math class and bring them out as artistic things. Well, so this is where I start to also get a little bit pissed off with you, which is, no, I'm not kidding. Yeah. I'm angry about the fact that we have these papers and books that form the sheet music that's never performed. And then I find out that you exist.

And that you have been performing and recording effectively these masterworks. And then what do you do with like the vinyl? You put it under bubble wrap in some loft in Soho in Manhattan, and it doesn't come out for years or decades at a time. So effectively you're sitting on some of the only known recordings, if you will, of some of the great masterworks of the mathematical universe. Yeah.

WTF, London? What are you doing, man? Well, I think what's happened is that I'm always kind of interested in the next idea or the next theorem or the next project. And all these things that are made by me, just sort of, you know, after I'm done with it, it's not...

Doesn't seem that important anymore. Well, I think that's great for the artist, but whoever's doing your PR and marketing, I'm firing them and taking over. As somebody who studied mathematics, I had the same feeling. I wasn't necessarily made to do mathematics. That wasn't how my brain, I didn't find the symbolic layer very easy, but I was exposed to things of such beauty and depth that

that I couldn't find any other analog on planet Earth. Once you understand how rich the mathematical universe actually is, you can't believe that it was somehow just created out of logical necessity. And there's a tiny portion of it that is actually visualizable by our visual cortex. And

What's odd is that when we talk about things as being visual in mathematics, we're often talking about things that we can't actually see. We have an intuition that comes from one, two, and three dimensions. And then we have to take that intuition where we can actually visualize something. We can construct a model of it. And we have a series of tricks by which we use our minds to visualize things that we can't actually see.

I mean, I don't even know what to call this process. I'm not sure if it has a description. Yeah, I know what you mean. It's definitely an intuition that you have. And it's some kind of vague mental image. And what I have to do is I have to somehow, in my artwork, I have to take this vague mental image and...

And try to make it concrete. And it's, it's not always. Well, this is the thing I keep in mind. There are going to be people who are listening to this as audio, and then we will later release it as video. And I don't know how much of it will be seeable on the channel, but one of the things that's very interesting to me is that what happens in our minds when we really start to open the portal to the deepest secrets that the universe has to offer is

is that we use this mixture, and the mixture is some amount of the world that we can construct as models so that we can actually directly visualize it, as if we could use our eyes to make a clay model of, let's say, an algebraic variety or what have you.

And then there's this extra intuition that we have to build in from texts and from symbology to remind ourselves that usually we're not able to see the full totality of whatever it is we're discussing. And your art very often has a geometric picture together with prose that is kind of fading in and out of perceptibility together with a bunch of mathematical symbols that are describing what has been constructed.

And I thought that what's very interesting is that that actually mirrors what a mathematician's model is of one of these higher structures that can't be seen directly, but it's basically intuition from a low dimensional thing that can be visualized together with prose and mathematical symbols that actually rigorously describe the object. And so that in some sense, it is a faithful recreation of,

by combining, you know, gorgeous form together with text and prose and symbology in order to recreate the mathematical state that we mean by saying, well, that's very, that mathematics is very visual. So for example, behind you right now, there's an amazing painting that I've

seen for years. I think I've actually used in a talk at Columbia as the cover art for the first slide of what I assume is Heinz Hoff's famous vibration from the early 1930s. And so it's the series of interlocking partial tori, each of which is filled up by circles. And it's a very impressionistic series.

but also somewhat rigorous description of this object that on the Joe Rogan program, I said may be the most important object in the universe because when we talk about physics being ultimately a theory of waves, we want to know, well, what are those waves waves in? What is the analog of the ocean?

for an ocean wave inside of physics. So those waves are waves in bundles and the bundles come in two basic types for most purposes. One is called a principal bundle, which is what you have behind you.

And you've been so good as to put a depiction of another kind of bundle, which is sort of even closer to the wave concept, a vector bundle, which is what is behind me. Now, I think it's very strange that we have all of these programs, let's say on public television or, you know, Brian Green talking about the elegant universe and all of these things. And yet when I ask people, well, do you know, you're interested in wave particle duality? Do you know what the waves are waves in? Nobody seems to know about bundles.

It's surprising. Well, it's disturbing. And the idea is that there are very few people depicting bundles artistically. And essentially the only person doing it is hiding their artwork away so that nobody even knows it's there. Je cues. Well, no, I mean, like this is an important link, I guess is what I'm trying to say, is that you are somehow breaking the secrecy. It's like, you know, Prometheus...

gave fire to man. Okay, well, you are now bringing bundles to the masses. And I think it's fantastic because it allows people to skip the symbolic step, which is usually what leaves them out of participating, at least as observers of the amazing museum of mathematical finds.

Can you talk a little bit about what caused you to do these two works, the principal bundle behind you? What do we call this hop vibration behind you? - Yeah, I call it hop vibration. - And behind me? - I called it purple vector bundle. - Purple vector bundle. All right, so we've got a principal bundle, which is the hop vibration, a purple vector bundle. Talk to me about what you were thinking when you created them. - Well, like, so I had the fortune in undergrad

to be the first advisee of an algebraic geometer. She was an assistant professor at the time. Her name is Montserrat Tejidor, and she's actually quite known in algebraic geometry. And she had this kind of deep, kind of quiet confidence about her. And I would go to her office hours religiously, and I would sit there and annoy her with my questions from undergrad math.

But she was always working with a little pencil sharpened all the way to the eraser almost. And she would be always writing the word that led F being a fiber bundle. And so I was a freshman and I was thinking to myself, what the heck is a fiber bundle? No one's ever told me about that. And so kind of one of the goals was,

in studying math was to figure out just what it was that she was thinking about. What were these fiber bundles that she was constantly writing about? And so in my mind, I always had this idea that I needed to understand that. And so that was kind of probably the germ of my interest in bundles. And then later on in grad school, I encountered them. And then later on when I started painting,

I just, I don't know, we were talking about intuition earlier and I just feel like there's some sort of sieve in us when we see lots of mathematical things or anything in the world for that matter. There's something that tells us, well, this, there's some content here and that it

this is worthy of our attention. And somehow these bundles, vector bundles, fiber bundles, principle fiber bundles, were just objects that to me were worthy of thinking a lot of time and thought and making artwork of. So I don't really know what it was that drew me to them, except that I was drawn to them.

Have you ever read C.N. Yang of Yang-Mills theory fame talking about his discovery of the importance of fiber bundles? I think I have, yeah. It's a short essay, right? He's written a few, I think. But he talks about, and I wish I had the exact quote here, Einstein was questing for a structure to unify physics. And in Yang's estimation, the fiber bundle was the answer to

to Einstein's quest. Now, of course, this cropped up in something called Kaluza-Klein theory. Einstein used what we would now call the tangent bundle and cotangent bundle of space-time. So he would

let's just throw some jargon out there. So a fiber bundle is sort of like the X, Y plane growing up and going off to graduate school. And the analog of the X axis would be called the base space and the Y axis and all its translates, those vertical lines would be called the fibers and the X, Y plane would be called the total space. And in that story,

The X axis gets replaced by space time and the Y axis gets replaced by various things like a 16 dimensional vector bundle to give the particles their 16 dimensions worth of personalities. There are these things called spinners that are attached to something that you can visualize as the Philippine wine glance, wine glass dance. The, um,

Sometimes you call this the principal bundle that governs all of particle theory, the SU3 cross SU2 cross U1 bundle over spacetime, and where each of those weird SU3, for example, is what we would call a collection of symmetries,

that form what mathematicians term a group. Same thing with SU2. And U1 is just a fancy name for the circle. So behind you, what you see is a simplified version of the

a principle bundle that we might use for, for doing physics research. But this one lives on top of a two dimensional sphere, like the surface of the earth. And it adds an extra circle for every point in space and time. And those are the lines, as I understand it, that are in these partial Tori that are nested behind you. So you're, it's, it's pretty tough going, but you're almost able to visualize the structure of the,

on which electromagnetism, which is how you and I are looking at each other through photon exchange, and the way in which the magnetic, like if these microphones have magnetic membranes that are turning our pressure waves into electrical impulses, all of that is described in some sense by patterns attached to the circles

on that painting upgraded to make it a story of space and time rather than just a story of circles over a two-dimensional surface of the globe. Yeah.

So it'd be pretty crazy if it wasn't like one of the coolest looking objects in the universe. It is pretty cool. Right. I mean, the interesting thing about painting it or making it visual is that you actually have to cut away parts to reveal what's the actual structure. Because it's too densely packed. It's too densely packed. So I'm only picking, you know, a select few of these torii and I'm only showing like

of them so I can actually reveal what's underneath because they're all nested. Now, the odd thing is that before I knew about your work, I think, and before I knew about, I don't know if you've encountered Dror Barnatan, who came up with a picture of this, which he termed Planet Hopf, which I used. Yeah, yeah, yeah. I think you pointed me to it. Yeah. Now, I did a version of this in a

a Python release by a group called N thought. And I got them to help me out. I had to use the transparency of some of the visual structures to allow me to see through. So I didn't have the occlusion phenomena. You don't have that luxury with paint, right? It is very tough to see, but the fact that it can be seen, and I think this is the really interesting thing.

means that a giant chunk of physics and mathematics is almost within reach of the person who can't trust her or his ability to negotiate the world of mathematical symbols. And, you know, this is a huge problem. A lot of people think that they're bad at music in the West because our music is so dependent on notation. Right.

However, in lots of cultures, notation isn't what carries music. It's just personal instruction. And a lot of those people who are bad at symbols would be good at music if it were in any other culture that wasn't symbolically so dependent. And I view this as being, well, what if I was in a culture in which mathematics wasn't transmitted as much symbolically? Fair? Unfair? It's an interesting approach. I'm not totally sure, but yeah. Yeah.

Maybe I can buy that. Because one of the things that drew me to math was the symbols, actually. Well, I want to talk about this mathematical art movement that has never been named. Okay. Right? And I'm going to try to figure out what name to give it later. But tell me if any of the following have impacted. John Archibald Wheeler, who was Feynman's teacher, very famous physicist, said,

He seemed to have an incredible passion for doing the kinds of things you're doing on blackboards to give these masterful lectures. Have you ever encountered his blackboard? No, I haven't. Okay. Let me try another one. Roger Penrose, who wrote The Road to Reality, is of course a relatively famous person, drew the first copy of The Hop Vibration that I'd ever seen in

It's strikingly like your own. Have you seen that? I have. I have that book, Back to Reality. And I have some of his more recent books as well. But I think the first picture of a hot version I ever saw was Bill Thurston's in his...

Three-dimensional geometry and topology. Oh, were these the Princeton lecture notes that were never released as a book? Or did they eventually become a book? They eventually became a book. Okay. Yeah. This is the thing is that mathematicians would trade these mimeograph notes that weren't quite books, but we would all look at them and we felt like we were looking into secret tomes that only some people could have. That's right. I think later it became a book and that's when I first saw it.

So Bill Thurston, of course, was famous within mathematics as being a Fields medalist who contributed to Grisha Perlman's program for solving the Poincaré conjecture in dimension three, proving that any sphere that was sufficiently simple from its algebraic properties had to actually be the three-dimensional version of the sphere. Right.

Did you know Bill Thurston at all? I didn't. I knew people who knew him. I knew him a little bit. He came through Harvard when I was a graduate student there. And one of the odd comments he made, he said, you want to know what keeps this field great? And I said, tell me. He said,

Mike Tirico here with some of the 2024 Team USA athletes. What's your message for the team of tomorrow? To young athletes, never forget why you started doing it in the first place.

You have to pursue something that you're passionate about. Win, lose, or draw, I'm always going to be the one having a smile on my face. Finding joy in why you do it keeps you doing it. Be authentic, be you, and have fun. Joy is powering Team USA during the Olympic and Paralympic Games. Comcast is proud to be bringing that inspiration home for the team of tomorrow. My talk, because we're just not that pretentious. And I thought, that's interesting, because he recognized that he would be a big shot, and he really valued the fact that

that nothing was being made over his presence beyond the mathematics. That's so great, yeah. In fact, I was reading his book on my honeymoon. I brought it along. Oh, you really have a book, sir. We were in Honolulu, and we had this nice place with a beautiful lanai, and here I was.

reading Thurston. And that's when I saw. Well, you had to be surrounded by beauty, of course. Yes, I was. What is it that you think you're supposed to be doing? I mean, you have this ability to understand mathematics and you have the ability to look into your own mind and see, well, how is it registering? And then you have the ability to externalize it. That's a relatively...

unusual skill set. I mean, there's, I should continue mentioning the remaining names like Fomenko is this crazy mathematical artist. I like the fact that Bathsheba Grossman is doing some beautiful mathematical sculpture, a guy named Nico Myers in, I guess, Temecula.

is doing hop vibration sculpture right now. Wow. Okay. Well, in part because we're now talking about this on these large programs and rather than people just turning off and saying, well, I don't know what that was, because it's visual, people are getting super intrigued and just going out and trying to learn the math for themselves, including artists. Right. So I think that what there needs to be is a movement. I mentioned an artist named Luc Gerome who did these beautiful glass sculptures

sculpture of pathogens and viruses. He does malaria and HIV, and it's just absolutely stunningly beautiful. Obviously, M.C. Escher is probably the biggest mathematical artist of them all. Why aren't there more people working in this movement? Why isn't the movement named? Why aren't you guys collected? Why aren't there exhibitions of this stuff? Why, why, why, why, why? I don't really know. It could be that...

It could be that the people who feel that they can actually do this stuff don't really have... Maybe it's just the mathematics is too attractive to them. It's like you'd rather do math than make paintings about math or make representations of it. It's so much more beautiful to spend your time... The analogy I have is of a mountaineer. You'd rather be out climbing your mountains...

Yeah, but all right. I'm going to get you with you here. Okay. Tell me you don't feel cut off from people who you can't show this to. Like you've gone someplace on a trek as a mountaineer, which is so spectacularly gorgeous, you can't even believe that it exists. Yeah. And you have somebody you love who's not knowledgeable. Yeah.

And you're trying to figure out, well, can I charter a helicopter? Can I get this person to get into really good physical shape and make the long trek? Is there any way I can bring back a picture that can communicate? I guess I feel cut off from everyone on the planet who hasn't seen that this stuff exists and is real. Don't you? I do. I mean, as an artist, as a contemporary artist, I'm often told not to.

Not to mention the math behind my work. Who told you that? I mean, in general, people just say they're not interested in the math. They're not. All right, maybe you're not supposed to mention it, but I'm certainly supposed to. I think people, when they see that there is mathematics behind it, I think it scares them off. Yeah. And most people have bad memories of their mathematical upbringing or education that they...

They have this reflex to just turn away from it. Well, it's like the bad ex-boyfriend problem is that if you meet somebody who's had a bad relationship, they're always going to live through some of that trauma in every subsequent relationship. And I think that we have to recognize, you know, we talk about iatrogenic harm as the harm done by physicians to patients. And we have to talk about mathogenic harm where there is this

like destruction of the love and appreciation for the beauty of math that is mediated by math teachers and mathematicians and math professors. Like somehow we're keeping the beauty for ourselves. And a large number of people have no idea. They've just been like, I don't know, they've had their knuckles wrapped with a ruler and they're now in some damaged state. And, and,

I guess when you look at this stuff, some percentage of people say, I don't get it. It's not that interesting. It leaves me cold. Some other percentage of people are going to look at it and say, I've got to figure out what that was about. I didn't know that that was there. Yeah. Are you connected with any of these people I mentioned? You mean the people that are not? Like Bathsheba Grossman. Oh, no, I'm not. Or Cliff Stoll. No, I know who they are. Yeah, yeah, yeah. I think you and Andrew had...

Klein bottles during that interview. Oh, Andrew Yang. Yeah. Yeah. You guys are tricky. Sorry. Are you a Yang supporter? Yeah. Okay. Well, so he's got these math hats. I would love to be a math czar in a coming Yang industry. I think I should get my, my hands on one. Yeah. Well, what do you, so to some extent, this is actually interesting.

not the first generation of mathematical or physical art in your family. Am I right that your father somehow was mining this vein as well? - Yeah, so my father trained as an engineer and worked as a mechanical engineer for 10 years, quite successfully in New York City. And the whole time he wanted to be an artist and he was painting at the Art Students League

And he made all these paintings, figurative and then abstract and so on. Then he won a prize for painting. And then the stipulation for the prize was that he had to quit his engineering career and devote himself to art. And upon quitting, he found he couldn't paint anymore. And he kind of did some soul searching, traveled around the world. And that's when he realized that there was something

that he could do with his engineering background. Somehow he could bring engineering and science into his artwork. And that's when he started developing his cybernetic sculptures. And he never turned back. He always made these kind of scientific engineering

I just saw them for the first time at your studio. Yeah. They're gorgeous. I mean, I love your stuff and I love, I didn't know that I was going to love his. He had these gorgeous standing waves. Yeah. And then by the use of clever use of stroboscopic light, he's able to freeze them and show this like very subtle motion and,

that would otherwise be lost. And I think that the wave equation, which is a particular class of equations well known in mathematics, is one of the most beautiful things I've ever seen. And to be able to visualize waves is precious to me. Astounding that I wasn't aware of his work. - Yeah. I think the lesson from my father, he never thought of himself as

as a scientist or as a technological artist. He thought of himself just as an artist. I think what he was trying to say with that was that technology and science, they're not really like tools or that you could just say, oh, that's a technological artist.

that these are just things that as artists that are part of our culture and part of our society, that we have a right to use them just as much as professional scientists do. And I think in that way, I think of myself as an artist, not as a mathematical artist, but as an artist. And it turns out that

having seen mathematics and having been exposed to mathematics, it just, it's just like part of humanity that I've incorporated in myself. And the artwork that I make has those features because it's kind of my life experience. So I'm not sure that

We can term this movement as mathematical art, but I think we're just artists who are kind of expanding our understanding to those realms that are difficult for most people to reach. And I think, but that's part of what it means to be human, you know? It means to expand ourselves. We don't call, I mean, just to steal me on your point, we don't call Salvador Dali human.

a mathematical artist. And yet, you know, if he puts Jesus on a four-dimensional polytope

in the case of a tesseract or hypercube, we just accept that he's mining some amount of mathematics as an inspiration for his art. You know, the development of the use of linear perspective wasn't viewed as mathematical art. A lot of like op art. I mean, if you think about Vasarely, I think that a lot of those patterned structures that he depicted that appear to be showing curvature are

by using various optical tricks. We don't call that mathematical art necessarily. However, you are going beyond that. And so I don't know whether it's exactly fair to avoid the label. I mean, I'll try to come up with a better one. But, you know, I often look at my own soul, for lack of a better word. And I realized that

I may not be able to believe in angels or religious origin stories, but I still have a place in my consciousness or my heart or whatever you want to call it that wants to be connected with something larger than the human experience. I don't want to just die on a random rock and having it all, you know, as Shakespeare said, signifying nothing. And one of the things that I actually take spiritual solace from is

is that at a minimum, there is this world of structures that would have passed by completely unknown, like the hop vibration, which was only found in the 1930s. So we have people who are alive who are older than the knowledge that the hop vibration exists. And these things are like angels. We know that they're there. It's not speculative.

And we know that we didn't create them. And we know that they seem to be transcendent. And I would just assume fill my life with transcendent structures that are beyond any kind of human authorship. And not call, you know, I mean, the art here to me is your decision to depict this in the way in which you chose to depict it. But the source that you're mining has nothing to do with our humanity. I see you.

- Yeah, I agree. - I mean, in essence, the thing that you have behind you right now is to me a modern picture of an angel, where I can't believe in angels, but I can believe in principle fiber bundles generating the world of electromagnetic activity, which then grew up and not only became Maxwell's equations, became every kind of force other than gravity. - I mean, yeah, maybe math is not a product of humanity.

But I feel that the struggle to understand math, to create these mathematical texts, I mean, that in itself has a very human aspect to it. And that's one of the properties I'm trying to express in my art, is just trying to express that maybe even though math is not a human thing, it's somehow much deeper, it's a universal thing,

But that its practice is human and that I want to show the humanness by... That's what you're doing for me. You just humanized an angel. Right. Yeah. I want to bring that out. It's very important that the hand of the artist be present. Kind of like expressing the difficulty that as a human being I have to try to understand these things. I mean, I see struggle, the...

You know, I look at all of the text that's going in and around the color or in the charcoal drawings, and I struggle to read it. It's hard to read it because it's not presented to be read in a typical fashion. And I love the fact that it is slightly irregular. And it shows, in some sense, a perfect structure that cannot be depicted perfectly. Right. Yeah.

Do you ever feel like freaked out being in direct touch with these otherworldly structures? I feel inadequate. Yeah. That no matter how much time I spend with them, I can really never quite grasp it in its totality. It's somehow beyond me.

My reach. And of course, you know, then sometimes I blame, oh, well, maybe that's my ability. I'm just not, I just don't have. No, I think that we have to back away from how creepy it is that these things are even there to be found. You know, I typically give the example of exceptional league groups or exotic seven spheres, which are structures people can look up if they, if they dare as things that,

both make me feel not alone and make me feel vaguely terrified. You know, it's like, what if a cigar-shaped object just started hovering over the earth and it didn't do anything malignant, but we knew it wasn't from us and we didn't know what it was. It didn't show any signs of life other than the fact that it was there. When I was a child, I used to have dreams like that, nightmares like that.

And this was long before I knew anything about math. I would dream about these huge surfaces. And I was so tiny, like the size of an ant. And they would be so smooth. Yeah. Like infinitely smooth. Even though I had no idea what infinitely smooth meant. But they were so smooth and they were terrifying. And maybe that's kind of like my very first kind of mathematical experience. Just these things that appeared in my dreams.

Now, one of the weird things that we're doing on this podcast is we're picking on people who don't necessarily know that we're coming and promoting what they do. And we call this reverse sponsorship. And the hope is, is that if we have a successful business and we can pick on it, that as we generate interest in that business from our audience, that maybe some of those businesses will come and sponsor the portal business.

and keep us on the air when we go into very difficult topics. I'm not going to ever ask that of you, but I do want to say that in some sense, this episode is part of something akin to reverse sponsorship. I think that the biggest problem, and tell me if this rings true or not, is that a lot of us do work that never gets curated by a second person. That in general, I used to think curation was a parasitic behavior.

If you couldn't create, you could point at things that were great. And I later realized with my own stuff that until somebody else said, hey, this person is saying something, that you don't actually get heard or processed because you can't actually curate yourself. Somebody else has to be the pointer and saying, hey, people pay attention. And I think it's way past time that this be done for you. And most mathematicians are

don't have large audiences. This is not a field. Physics has a few, a tiny number of physicists who have large audiences. But I really believe that it's essential for a curation process to happen with this kind of work so that people can see more of what is out there. Are you open for business? Will you sell your work? I found you on the internet. Yeah, sure. Yeah? Yeah.

Okay. So hopefully supporters of the program can look for London and his storefront on the internet somewhere. What about exhibiting with other artists and showing this kind of new wave of whatever we want to call it other than mathematical art? Right. Oh, I'm open to that. Oh yeah? Yeah, absolutely. So you would do it, you'd do like a group show? Yeah, yeah, of course.

Are you up for like suggestions? I've been horrible to you. I've told you a bunch of things that I've never seen depicted and asked you to look in on it. Is that a, is that an overbearing question? No, that's a, that's a great, well, I did, I did a series of talks when I lived in Seattle and the, so yeah, so I went to the university of Washington where I knew a couple of mathematicians and it was a series of works I called demonstrations and,

And it was kind of inspired by da Vinci's kind of scientific drawings, demonstrationi. And so I invited UW mathematicians to supply me with theorems of theirs. And I would attempt to come up with my own interpretation. And so that was a fun project. And I got to know a few mathematicians at the UW.

But yeah, that sort of collaboration was something I was very interested in about 10 years ago. What are you thinking about now? What am I thinking about now? I'm always open to new ideas. And your list of topics is a printout I carry with me every day. So I'm always looking at it on the subway. Yeah. So a Tia Singer index theorem. Yes. I'm trying to wrap my head around that.

I think you had something like Kervera. Kerverian variant 1 problem? Yes. Yeah, that's gorgeous stuff. Yeah. And so I look at it, and I have my mathematician friends, and I have a whole library of math textbooks that I try to consult. So maybe if I'm correct, the vector bundle painting that is behind me is masking –

another work that's underneath it. Maybe we could take the top painting off and take a look at what you have there. Okay, sure. Let's do it. Don't sell this to anyone until you've let me bid for it. If you look at these little fibers, they sort of look like my dad's. I saw that. Yeah, it's gorgeous. He's always kind of in the back of my mind, of course. It's part of my inheritance. Yeah. You ready to start? Okay.

All right. So London, you've just unveiled this other structure and I'm looking at it and it's on its side from what I normally expect so that we can get into the shot. That's right. Yeah. But what it looks to me like is that you've taken the light cone on which particles with no rest mass or waves with no rest mass collide.

propagate inside of the special theory of relativity. And then you sort of showed this algebraic, how do you say it? Algebraic generation. So it looks like I'm looking at some mass shells and this diagram that should be familiar from Einstein's, uh,

famous Anis Moravoulos of 1905 when he figured out special relativity, um, has been sort of augmented with this extra structure of, of, of mass shells and hyperboloids. And what can you say about what motivated you here? Well, so I painted a painting of, um, some of my favorite things from calculus three, um, quadric surfaces. And, uh, I showed it to Lauren too. And, um,

He said, well, that's very interesting, but can you tell me how they're related? And so that was the direct challenge from Loring. And so I thought about, well, if I vary a certain parameter, this is what would happen. But as I went from one of these types of surfaces to the other type, from the hyperboloid of two sheets, hyperboloid of one sheet, I had to go through the cone. And so I showed that relation. That was interesting.

the idea behind that piece. It's gorgeous. Do you find sort of any comparable source of rich imagery from any other area other than, let's say, mathematics and physics? I would say nature. Are you as fascinated by it?

I'm not, maybe I'm not as fascinated by it, but you know, if I'm walking on the beach and I pick up some shells. No, no, no. It's unbelievably gorgeous. But I have to admit that nature weirdly, though it completely inspires me. And I think no less than it inspires other people. I'm weirdly slightly less inspired by physical nature than I am by what we might call mathematical. I have to say I'm the same. Although I am, I'm,

I'm a scuba diver. I'm a downhill skier. Yeah. But downhill skiing is pretty close to differential geometry. Yes, it is. Yeah. I'm constantly thinking about the curvature. Right. Of the terrain I'm on. Yeah. And what are you fascinated by in scuba diving? Scuba diving, when I go down, I just see the strange sea creatures everywhere.

residing on the ocean floor or on the coral reefs and the shapes of them. - Any particular ones you're obsessed with? - I can't say I'm obsessed about them. I just find them interesting. Yeah. - I thought maybe cuttlefish. - Cuttlefish? - I mean, the skin of the cuttlefish is a nearly mathematical phenomenon. If you've ever watched them propagate these waves through the chromatophores on the skin when they're mesmerizing their prey before they strike,

The patterns, it's sort of like Times Square with some giant neon sign that's moving through these pulses of light. I guess I've never seen that diving. Okay. But, yeah. And in music, what do you find yourself most inspired by? I like, well, when I work in my studio, I'm often listening to jazz, usually Miles Davis or Dave Brubeck or...

Dave Brubeck, obviously famous for experimenting with funny time signatures, which is somewhat mathematical. Yeah, yeah, yeah. I also listen to a lot of classical music. Yeah. Favorite composer? Oh, gosh. Mozart, Rachmaninoff. Really? I never trust a mathematician who doesn't say Bach first. Oh, Bach, that's true. Okay. Well, no, maybe the idea is that that's not your jam when it comes to the opera. No, I do love Brendan Birkenau. Yeah, yeah. Yeah.

I rock to that. And are you at all familiar with any of these attempts to push math and reverence for math out to the general public that are somewhat off of the direct depiction? I don't know if you've ever seen my friend Edward Frankel's short film, Love and Math. And then he wrote a book. No, I don't think I've seen that. A slightly erotic art film. Really? Okay. No, I haven't.

And I guess, you know, one of the things that I'm very frustrated by is that it's just so difficult to communicate it. A counter example to this would be, have you ever been to the Exploratorium in San Francisco? Yeah, I have. Long time ago, though, a couple decades ago. So Frank Oppenheimer, who was Robert Oppenheimer's brother, created this totally anomalous science museum that was much more effective, so far as I could tell, in conveying the wonder of science

in a way that people actually got some kind of a take home. Like it was viscerally engaging. And yet I didn't see that kind of science museum duplicated anywhere else. Does that, might that be a paradigm where someone somewhere could do something truly unique with the visual depiction of geometry and topology, let's say, and completely crack this open? I mean, like,

To take the Promethean analogy, all it really takes is one of us to steal fire effectively. Yeah, that might work. Have you been to the Google Math Museum in Madison Square Park?

I've been to the math museum. Yeah. Is Google sponsoring it? I thought it was sponsored by Google. Maybe I'm wrong. I didn't think it was. Okay. I didn't know. I just assumed it was. Yeah. I thought it was somewhat inspiring. Yeah. But, but yeah. Like a lot of this stuff is, is sort of strangely slightly off. There's this beautiful limestone wall that,

in Stony Brook, Stony Brook, Long Island, that has some of the most beautiful formulas in all of mathematics and some pictures. But it, to me, even that has like errors and flaws and it doesn't fully evoke what it is that it was trying to depict. I feel like we've failed. What do you think? Yeah, I feel that too. I mean, that's partially why I, I,

I don't think of my art as mathematical art because I don't want it to be associated with this kind of like, oh, bring math to the people, that kind of thing. It has to be somehow something. I mean, like the wonder of math that we experienced. Yeah. That is not...

I don't feel that when I go and look at these kind of displays of mathematical art. Oh, how interesting how these things fit together. Right. And you're just like, okay, let me just play with this a little bit and then move on to this other exhibit. What did you feel when you look at Escher? I didn't... Well, my initial reaction when people were, oh, you're a math major, you should love Escher. I was like, oh, that's great.

I viewed the art and the math as somehow strangely separate. And it was a great way of getting a certain amount of math out into the world. And I found him quite artistic. I just didn't feel that the art and the math were always kind of hand in glove. Yeah. Well, first of all, symmetry groups of the plane, I mean, that's cool. But still, it's...

it doesn't capture the real depth of math. There's so much more to math than just kind of pretty patterns or symmetrical patterns. - Are you obsessed with physics? - Not as much as I wish to be, yeah. - I think one of the great mysteries for me

has been why is it the physical universe is such an amazing client of the best mathematics? Right? Like you could have done this with substandard mathematics, maybe just a little bit of calculus and some linear algebra, but it just goes way above and beyond and actually uses our best stuff and our most beautiful stuff.

And I've always thought that was quite odd, that it didn't have to be the way. The biological world does not seem to use mathematics at a truly profound level. There's some cute stuff with like Fibonacci sequences. But I would say that the biological world mostly turned up its nose at the mathematical offerings that were possible. Right, right, right.

I guess I see physics and math as so like... Intertwined. Intertwined, yeah. Well, you know, there's this expression, the map is not the territory. And I think that the weird thing about physics is that physics may be the one place in the real world in which the map, that is the math that describes it, may actually be the territory. That is, it would not astound me if life really was about vector bundles, principal bundles, and wave equations that take place upon. Yeah. So...

We're going to try to figure out how to get you as part of an exhibition so people can come and see your work. And they can find you on the internet. You have a site? Yeah. So my site is just londonshi.com. That's T-S-A-I? Yeah. Okay. And first name improbably is London. Yes. L-O-N-D-O-N. Yeah. And other than that, we're going to continue plugging your work, pointing people to your Instagram page.

page and trying to drum up some interest so that you'll make more of this gorgeous stuff for all of us. Well, thank you very much, Eric. London. It's been a pleasure having you. You've been through the portal with London. I look for him on Instagram, on Twitter, and most, most importantly at his website and consider making a bid to keep me from buying this art. I think you'll find that it's just gorgeous stuff.

Look for us at the portal on Apple, on Spotify, on Stitcher, wherever you listen to podcasts. Please subscribe and go over to YouTube and see if you can't subscribe to us there and click the bell icon to make sure that you're notified when our next episode drops. Hopefully, if you've listened to this on audio, you will go over there and watch it on video. So you've had a little bit of a taste of the great stuff that London has been doing. London, thanks very much. Thank you, Eric. All right, everybody. Be well.

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Thank you.