14: London Tsai - The Reclusive Dean of The New Escherians: Difference between revisions

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What happened to the Mathematical and Scientific art movement after [[M. C. Escher|MC Escher]]? It went underground.  

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'''Eric Weinstein:''' Hello everyone. The episode you're about to see has held up our YouTube channel for a while. It was recorded remotely in New York City along with two other episodes, and apparently it is a bit blurry. We couldn't control for it. We tried correcting it digitally, but that met with only limited success. There was a question about whether to release a still image over this audio, but we decided instead to release the blurred product because, in fact, it is a visual episode with artist London Tsai. We hope we've made the right decision. We apologize for the blurriness and the fact that it has held up the sequence of releases. But given that we've now decided to bite the bullet, we hope to return to releasing episodes on a regular basis on this channel. We hope you like it. We think very highly of London Tsai and we hope to have him back on the program, hopefully with a little bit better focus.

'''London Tsai:''' No author, yeah. And it's just, 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. And, you know, all the mathematical writing that was on the blackboards, like 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 for example, behind you right now, there's an amazing painting that I've seen for years—and I think I've actually used it in a talk at Columbia as the cover art for the first slide—of what I assume is Heinz Hopf's famous fibration from the early 1930s. And so it's the series of interlocking partial torii, each of which is filled up by circles, and it's a very impressionistic, 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?  

J'accuse—well, no, I mean, this is an important link. I guess this 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, which—what do we call this Hopf fibration behind you?

'''London Tsai:''' Yeah, call it The Hopf Fibration.  

'''London Tsai:''' Call it Purple Vector Bundle.

'''Eric Weinstein:''' Purple Vector Bundle. All right, so we've got a principal bundle, which is The Hopf Fibration, [and] a Purple Vector Bundle. Talk to me about what you were thinking when you created them.  

'''London Tsai:''' 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 Teixidor, and she's actually quite known in algebraic geometry. And she had this kind of deep, 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 "Let f be a fiber bundle."  

'''Eric Weinstein:''' Have you ever read C.N. Yang, of Yang–Mills theory fame, talking about his discovery of the importance of fiber bundles?

And in that story, the x-axis gets replaced by spacetime, 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 spinors that are attached to something that you can visualize as the Philippine wineglass dance. Sometimes you call this the principal bundle that governs all of particle theory the SU(3) x SU(2) x U(1) bundle over spacetime. And where each of those weird—SU(3), for example—is what we'd call a collection of symmetries that form what mathematicians term a group. Same thing with SU(2). And U(1) is just a fancy name for the circle.  

'''Eric Weinstein:''' 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 Bar-Natan, who came up with a picture of this, which he termed Planet Hopf, which I used—

'''Eric Weinstein:''' I'm going to try to figure out what name to give it later. But, tell me if any of the following have impacted you. John Archibald Wheeler, who was Feynman's teacher. Very famous physicist. 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?  

'''Eric Weinstein:''' 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 Hopf fibration that I had ever seen. It is strikingly like your own. Have you seen that?

'''London Tsai:''' I have. I have that book, The Road to Reality. And I have some some of his more recent books as well. But I think the first picture of a Hopf fibration I ever saw was Bill Thurston's, in his Three-dimensional Geometry and Topology.

'''Eric Weinstein:''' So Bill Thurston, of course, was famous within mathematics as being a Fields medalist, who contributed to Grisha Perelman's program for solving the Poincare conjecture in dimension 3, proving that any sphere that was sufficiently simple from its algebraic properties had to actually be the 3-dimensional version of the sphere.

'''Eric Weinstein:''' 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 skillset. 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 Meyer, in—I guess—Temecula, is doing Hopf fibration sculpture right now.

'''Eric Weinstein:''' Well in part because, you know, 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. So I think that what there needs to be is a movement. I mentioned an artist named Luke Jerram, who did these beautiful glass sculptures of pathogens and viruses, and he does malaria and HIV and it's just absolutely, stunningly beautiful. Who are—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?

'''Eric Weinstein:''' 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.  

'''Eric Weinstein:''' Like Bathsheba Grossman, or Cliff Stoll.

'''London Tsai:''' Oh no, I'm not. I'm not. No, I know who they are, yeah, yeah, yeah. I think you and Andrew had the Klein bottles during that interview.

'''Eric Weinstein:''' We don't call—just to steelman your point—we don't call Salvador Dali a mathematical artist, and yet, if he puts Jesus on a 4-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 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 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 realize 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, as Shakespeare said, "Signifying nothing."  

'''London Tsai:''' No, that's a good, that's a great—well, I did a series of talks when I lived in Seattle. So I went to University of Washington, where I knew a couple mathematicians. And it was a series of works I called Demonstrations. It was kind of inspired by da Vinci's scientific drawings, dimostrazione. And so I invited UW mathematicians to supply me with theorems of theirs, and I would attempt to come up with my own interpretation. That was that was a fun project, I got to know a few mathematicians at the UW. And yeah, that sort of collaboration was something I was very interested in, about 10 years ago.

'''Eric Weinstein:''' Kervaire invariant 1 problem.

'''Eric Weinstein:''' 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, propagate inside of the special theory of relativity, and then you sort of showed this algebraic—how do you say it, algebraic degeneration? So it looks like I'm looking at some mass shells, and this diagram that should be familiar from Einstein's famous Annus Mirabilis of 1905, when he figured out special relativity, has been sort of augmented with this extra structure of of mass shells and hyperboloids. And what can you say about what motivated you here?

'''London Tsai:''' Well, so I painted a painting of some of my favorite things from Calculus III, quadric surfaces. And I showed it to Loring Tu, and he said, "Well, that's very interesting, but can you tell me how they're related?" And so that was a direct challenge from Loring. So I thought about, 'Well, if I vary a certain parameter, this was what happened.' But as I went from one of these types of surfaces to the other type, from the hyperbola of two sheets to the hyperbola of one sheet, I had to go through the cone. And so I showed that relation—that was basically the idea behind that piece.

'''Eric Weinstein:''' 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 Frenkel's short film Love and Math. And then he wrote a book.

'''Eric Weinstein:''' 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 counterexample to this would be—have you ever been to the Exploratorium in San Francisco?

'''Eric Weinstein:''' I've been to the Math Museum, is Google sponsoring it now?

'''London Tsai:''' Yeah. So my site is just londontsai.com.  

'''Eric Weinstein:''' Yeah. And other than that, we're going to continue plugging your work, pointing people to your Instagram page, and trying to drum up some interest so that you'll make more of this gorgeous stuff for all of us.  

'''Eric Weinstein:''' London, it's been pleasure having you. You've been through The Portal with London Tsai. Look for him on Instagram, on Twitter, and 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.