Lex Fridman Podcast
#370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love
10 Apr 2023
Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality. Please support this podcast by checking out our sponsors: - House of Macadamias: https://houseofmacadamias.com/lex and use code LEX to get 20% off your first order - Shopify: https://shopify.com/lex to get free trial - ExpressVPN: https://expressvpn.com/lexpod to get 3 months free EPISODE LINKS: Edward's Website: https://edwardfrenkel.com Edward's Book - Love and Math: https://amzn.to/40Bgxh0 Edward's Twitter: https://twitter.com/edfrenkel Edward's YouTube: https://youtube.com/edfrenkel Edward's Instagram: https://instagram.com/edfrenkel PODCAST INFO: Podcast website: https://lexfridman.com/podcast Apple Podcasts: https://apple.co/2lwqZIr Spotify: https://spoti.fi/2nEwCF8 RSS: https://lexfridman.com/feed/podcast/ YouTube Full Episodes: https://youtube.com/lexfridman YouTube Clips: https://youtube.com/lexclips SUPPORT & CONNECT: - Check out the sponsors above, it's the best way to support this podcast - Support on Patreon: https://www.patreon.com/lexfridman - Twitter: https://twitter.com/lexfridman - Instagram: https://www.instagram.com/lexfridman - LinkedIn: https://www.linkedin.com/in/lexfridman - Facebook: https://www.facebook.com/lexfridman - Medium: https://medium.com/@lexfridman OUTLINE: Here's the timestamps for the episode. On some podcast players you should be able to click the timestamp to jump to that time. (00:00) - Introduction (05:54) - Mathematics in the Soviet Union (16:05) - Nature of reality (27:23) - Scientific discoveries (40:45) - Observing reality (56:57) - Complex numbers (1:05:42) - Imagination (1:13:33) - Pythagoreanism (1:21:28) - AI and love (1:34:07) - Gödel's Incompleteness Theorems (1:54:32) - Beauty in mathematics (1:59:02) - Eric Weinstein (2:20:57) - Langlands Program (2:27:36) - Edward Witten (2:30:41) - String theory (2:36:10) - Theory of everything (2:45:03) - Mathematics in academia (2:50:30) - How to think (2:56:16) - Fermat's Last Theorem (3:11:07) - Eric Weinstein and Harvard (3:18:32) - Antisemitism (3:38:45) - Mortality (3:46:42) - Love
Chapter 1: What is discussed at the start of this section?
The following is a conversation with Edward Frankel, one of the greatest living mathematicians, doing research on the interface of mathematics and quantum physics, with an emphasis on the Langlands program, which he describes as a grand unified theory of mathematics. He also is the author of Love and Math, the Heart of Hidden Reality. And now, a quick few second mention of each sponsor.
Check them out in the description. It's the best way to support this podcast. We've got House of Macadamias for healthy snacks, Shopify for e-commerce, and ExpressVPN for security and privacy on the internet. Choose wisely, my friends. Also, if you want to work with our amazing team, we're always hiring. Go to lexfriedman.com slash hiring. And now onto the full ad reads.
As always, no ads in the middle. I try to make these interesting, but if you must skip them, please still check out our sponsors. I enjoy their stuff. Maybe you will too. This show is brought to you by House of Macadamias, a company that ships delicious, high-quality and healthy macadamia nuts and macadamia nut-based snacks directly to your door.
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will be generated by language models, large language models that form deep representations, compressions of human knowledge, and are able to access, search, query, integrate, and generate wisdom far, far better than I ever can, which is why... I will not be generating wisdom.
I will be sitting on a couch with a Zen-like look on my face, appreciating every single moment that passes by as I slowly put some macadamia nuts in my mouth and say, damn, it's good to be alive. Go to HouseOfMacadamias.com slash Lex to get 20% off your order for every order.
The listeners, that's you, will also get 4-ounce bag of macadamias when you order 3 or more boxes of any macadamia product. That's HouseOfMacadamias.com slash Lex. This show is also brought to you by Shopify, a platform designed for anyone to sell anywhere with a great-looking online store that brings your ideas to life and gives you tools to manage day-to-day operations.
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Chapter 2: How did Edward Frenkel's early experiences shape his view of mathematics?
And artists are probably one of the most fun, one of the most inspiring sets of humans to get a chance to meet and interact with. So hopefully... I'm not too lazy and one day, many years from now, we will launch a Shopify store where you can get a couple of shirts if that's the kind of thing you are at all interested in. Sign up for a $1 per month trial period at Shopify.com slash Lex.
That's all lowercase. Go to Shopify.com slash Lex to take your business to the next level today. This show is also brought to you by ExpressVPN, a piece of software that I've used for many, many years to bring me joy and happiness. Well, that's not necessarily the feature itself, but it did do that for me because it's a simple piece of software that does one thing. It does it extremely well.
It's fast, works on any operating system, and it gives you a basic first layer of protection of your privacy on the internet. Everybody should be using a VPN. at least part-time when you're doing all the kinds of shady stuff you do on the internet, which I'm talking to you, I know you're doing.
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I've used them for a long, long, long, long time before they were ever a sponsor. So we flirted for a while, we dated for a while, and now we're fully committed together and married and not looking for any extramarital affairs, in case you're wondering. I'm happy.
I'm happy on Linux, I'm happy on Windows, on Android, on every single iPhone, everything I got, every device got ExpressVPN on it, and I'm happy. And if you want to be happy like me, go to expressvpn.com slash lexpod for an extra three months. free. This is the Lex Friedman Podcast. To support it, please check out our sponsors in the description. And now, dear friends, here's Edward Frankel.
You open your book, Love and Math, with a question, how does one become a mathematician? There are many ways that this can happen. Let me tell you how it happened to me. So how did it happen to you?
So first of all, I grew up in the Soviet Union in a small town near Moscow called Kolomna. And I was a smart kid, you know, in school, but mathematics was probably my least favorite subject. Not because I couldn't do it. I was a straight-A student and I could do all the problems easily, but I thought it was incredibly boring.
And since the only math I knew was what was presented at school, I thought that was it. And I was like, what kind of boring subject is this? So what I really liked was physics. And especially quantum physics. So I would go to a bookstore and buy popular books about elementary particles and atoms and things like that and read them, devour them.
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Chapter 3: What role do paradoxes play in understanding mathematics and reality?
I said, for example, do you know about quarks? And I said, yes, of course I know about quarks. Quarks are the constituents of particles like protons and neutrons. And it was one of the greatest discoveries in theoretical physics in the 60s that those particles were not elementary, but in fact had the smaller parts. And he said, oh, so then you probably know representation theory of the group SU3.
I said, like, SU what? So in fact... I wanted to know what were the underpinnings of those theories. I knew the story. I knew the narrative. I knew kind of this basic story of what these particles look like. But how did physicists come up with these ideas? How were they able to theorize them? And so I remembered, you know, like it was yesterday. So he pulls out a book.
And it's kind of like a Bible, like a substantial book. And he opens it somewhere in the middle. And there I see the diagrams that I saw in popular books, but in popular books, there was no explanation. And now I see all this weird symbols and equations. It's clear that it is explained in there. Oh my God. He said, you think what they teach you at school is mathematics?
It's like, no, this is real mathematics. So I was instantly converted.
That you understand the underpinnings of physical reality, you have to understand what SU3 is.
You have to learn what are groups, what is group SU3, what are representations of SU3. There was a coherent and beautiful, I could appreciate the beauty even though I could not understand heads and tails of it.
But you were drawn to the methodology, the machinery of how such understanding could be attained.
Well, in retrospect, I think what I was really craving was a deeper understanding. And up to that point, the deepest that I could see was for those diagrams, but for that story that a proton consists of three quarks and the neutron consists of three quarks and they're called up and down and so on. But I didn't know that there was actually beneath the surface, there was this mathematical theory.
If you can just linger on it, what drew you to quantum mechanics? Is there some romantic notion of understanding the universe? What is interesting to you? Is it the puzzle of it or is it like the philosophical thing?
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Chapter 4: How does imagination influence the pursuit of knowledge?
I don't think there are so few, to be honest, because I find a lot of people are actually interested. If you talk to people you wouldn't expect to be interested in this, from all walks of life, from people of... all kinds of professions. I tell them I'm a mathematician, and they, a mathematician, okay, so that's a separate story.
A lot of people, I think, have been traumatized by their experience in their math classes. We can talk about it later. But then they ask me what kind of research I do, and I mentioned that I work on the interface of math and quantum physics. And their eyes light up and say, oh, quantum physics or Einstein's relativity. I'm really curious about it.
I watched this podcast or I watched that podcast, you know, and I've learned this. It's like, what do you think about that? So I actually find that actually physicists are doing a great job educating the public, so to speak, in terms of... popular books and videos and so on. Mathematicians are behind.
We're starting to catch up a little bit, have been starting the last 10 years, but we're still behind. But I think people are curious. Science is still very much something that people want to learn because that's the best way we know to establish some sort of objective reality, whatever that might be.
Yeah, to figure out this whole puzzle, to figure out the secrets that the universe holds.
Things that we can agree on. Even though for me, at this point, I always make an argument that our physical theories always change. They get updated. So you had Newton's theory of gravity. Then Einstein's theory superseded it. But in mathematics... it seems that theories don't change. Pythagoras' theorem has been the same for the last 2,500 years. X squared plus Y squared equals Z squared.
We don't expect that next year suddenly it will be Z cubed. And so that to me is actually even more, hints even more at how much we are connected to each other. Because Pythagoras' theory, if you think about it, or any other mathematical theorem, means the same thing to anyone in the world today, regardless of their cultural upbringing, religion, ideas, ideology, gender, whatever.
nationality, race, whatever, right? And it has meant the same to everyone everywhere, and most likely will mean the same. So that's to me kind of an antidote to the kind of divisiveness that we sometimes observe these days, where it seems that we can't agree on anything.
To the political complexity of two plus two equals five in George Orwell's 1984.
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Chapter 5: What is the significance of Eric Weinstein in Edward Frenkel's life?
And that's where it comes from.
In the end, the truth is simple.
In the end, the truth is simple. Not necessarily easy, but simple.
So I mentioned to you offline that I desperately, in trying to figure out the optimal in an order set questions to ask you, I texted Eric Weinstein asking for what questions he can ask you. And he said that you are definitively one of the greatest living mathematicians, so don't screw this up. But he did give me a few questions.
So he asked to ask you, what are the most shockingly passionate, this is in Eric's language, what are the most shockingly passionate mathematical structures? And he gave a list of four for him, but he said he really wanted your list. Okay, let me say that. Shockingly passionate mathematical structures.
Shocking.
Is there something you can, is there something that jumps to mind? Sure.
I'm here to shock. So first of all, Eric Weinstein is a very dear friend, I have to say. And I really, really, really appreciate and love him. He's just like my brother. So it's interesting to have a question posed by him.
And maybe if we can linger for a moment, what do you think is special about Eric Weinstein for what you know of his work and his mind?
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Chapter 6: How does personal experience shape Edward's view on humanity and compassion?
So it's kind of a conceptual system, if you think about it. There is a beautiful episode of this series by Jacob Bronowski, where he talks about, he filmed it in Auschwitz, talking about the certainty that what led the Nazis to killing people wholesale was almost a mathematical idea. And they just basically bought into this idea and checked out their humanity at the door.
So I would say that antidote to this type of thing is not necessarily even imagination in a kind of elevated sense that we have been discussing today, that is exemplified by our greatest scientists and philosophers. But just basic humanity, basic common sense of just knowing that it's just not right. And I don't care what my ideology tells me, but I'm just not going to do it.
So that, I think, is kind of missing a little bit in today's society. People get a lot too caught up in the ideology, in certain conceptual frameworks.
So societies that lose that basic human compassion, that basic humanity run into trouble.
Oh, very much so. But not only society, like a human being. And Eric is one of the people, I agree with you, keeps that flame of... Like I trust that he will not do something that's not human, that's not right. You know, there's some people you just kind of feel that they won't cross that line. And that's a huge thing, you know, today.
Because I have to say, looking back, definitely, I have not hurt people personally, but I could be mean, for instance. I could be harsh. And now I see it as a sign of weakness, as a sign of insecurity. Yeah. I saw your interview with Ray Kurzweil the other day. Beautiful. I was really moved by it. But at some point I was like, I looked at him at this sort of like Dr. Evil.
I'm kind of ashamed of it now, but like, you know, I'm kind of coming clean. And I would, you know, because, well, why? Because I needed an adversary in my mind because I projected onto him kind of the fears that I had, that AI will conquer us and so on. And this was rooted in my, kind of awakening moment in a sense, a kind of a moment where I suddenly started to see the other side.
So, but I wasn't sure yet. You see?
You had to feel it.
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Chapter 7: What lessons does Edward share about the impact of trauma on creativity?
And I had this moment, actually. It was so amazing. Like, I would give this meme. I would talk about AI and the dangers. And he would always be my, like, foil. You know? I would put, like, a sinister photograph of him on the slide. And I was like, look at this guy. He wants to put nanobots into your brain. And he's also, like, a top executive at Google and so on.
So I would create this whole narrative. And then something happened where I was giving a lecture, this is 2015, in Aspen, Aspen Ideas Festival, which is a wonderful festival. So keynote speech, actually. And I was doing my usual shtick. And then suddenly I said, I came up to that, there was a big screen and there was a picture of him there.
And I came up to the screen and I kind of touched it with my hand. And I said, but I don't want to pick on Mr. Kusval because he's me. I had this revelation that I'm actually fighting with myself, with my own fears. And then I learned about his father, that his father died when he was young. And that he's, in fact, he's very, to his credit, he's very sincere and upfront about it.
Self-disclosure, I think it's very essential, by the way, in all this discussion. Like what really motivates you? He said it publicly many times, even as early as 2015, I could find this information, that he wanted to reunite with his father in the cloud. And suddenly I saw him not as a caricature,
that exemplified all my fears, but as a human being, a child longing for his father, grieving for his father. So suddenly it became a love story. So in other words, I've seen it in myself, this capacity to project my own fears and then fight with other people over something that actually was my own.
And as soon as I got to this point of seeing him and then my next lecture, actually, I talked about it, about him in this way. And I, and I said, look, you know, it's a, it's a love story. And he is actually, um, it's not how I would want to reunite with my father, uh, But like you said, if I am consistent, I have to allow the possibility that different people perceive things differently.
And so for him, that's his imagination. So you know how, who is this? Voltaire, I think. It's ascribed to Voltaire. It's like, I disagree with you, but I will fight to death for you to have the right to say it. So now that I feel like my position is more like, I disagree with him, that this is the way to approach death and to approach the death of our loved ones and how we miss them and how we...
You know, that sense of loneliness and inability to interact directly. That's not something that resonates with me, but I think it can also be called imagination from his perspective. And look, motivated by that, how much he has brought, how many interesting inventions. Like his musical invention, for instance, naturally because his father was a composer, a music composer and a conductor.
So in other words, in the bigger scheme of things, even if I think he's misguided, Still, I can't deny that it's a certain leap of faith from his perspective to try to say that this is the way we can all connect to our loved ones. And because it is sincere, and I see it now, it's sincere. And in fact, in your interview, you really teased it out to him. I was really moved by it, I have to say.
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Chapter 8: How does love influence the pursuit of mathematics and life?
And this is where we can go astray, because then we become captives of frameworks and conceptual systems which may not be beneficial to our society.
In tough times, we need the people that have not lost their way in the ideologies. We need the people who are still in touch with their heart. And you mentioned this with Eric, it's certainly true. I disagree with him on a lot of stuff, but I feel like when the world is burning down, Eric is one of the people that you can still count on to have a heart.
I've talked a lot over the past year about the war in Ukraine and the possibility of nuclear war, and it feels like he's one of the people I would call first if, God forbid, something like a nuclear war began, because you look for people with a heart, no matter their ideas.
That's right. It takes courage, and it takes a certain self-awareness, I would say. And which brings me to, you know, I think the crucial is that which was inscribed, you know, on the temple of Apollo in Delphi. There was a statement, know thyself, know yourself, you know, like, who am I? Ultimately, it boils down to this and all these debates.
And the point is that I used to be, like I said, you know, pessimistic at some point, and I was scared even of where development of AI was going. This is about 2014, 2015. And now I'm much more. So for instance, after I saw Ray Kurzweil as a human being, after I could relate to him and sympathize with him, suddenly I stopped seeing him in the news.
Like before that, I would always see him in the news saying, we're going to put nanobots in your brain by the year 2030, whatever, you know? And then we upload you to the 21st. And I would be like, no, you know, that's sort of terrible. Suddenly I didn't see him anymore. So now it makes me question, who was creating the trouble? Was it him who was creating the trouble or was it my mind?
And so as I became self-aware, suddenly other possibilities opened. And suddenly that conflict, which by the way, if I kept giving this nasty, you know, talks about him, one day I suppose we'd have a debate. And so you have this, one person stays this. And what I learned is that it's a never ending conflict. This conflict just does not end. But there is an alternative.
There is a better way, which is to realize that it is you arguing with yourself Now, if you want to continue arguing with yourself, continue as long as you need. Just be careful not to destroy too many things, you know, in the process. But there is an option of actually dropping it, of actually dropping it. This is so, I was so surprised by this.
Yeah, it's discovering in yourself. the capacity, the human capacity for compassion. And you understand that he has a perspective, he is operating in the space of imagination, a human being like you, and we're all in this kind of together trying to figure this out.
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