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Edward Frenkel: Infinity, String Theory, Death, The Self
September 20, 2023
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But I think that you actually get it, you know, it's half-tongued cheek, the way you call it. And you don't call it theory of everything, right? You call it theories of everything. So which kind of suggests that it's not as simple as one might think.
Edward Frankel is a prominent figure in the mathematical community. In fact, he was a professor at Harvard at 21, which is unparalleled. He's known for his work on the Langlands program, which is a blueprint aiming to bridge seemingly unrelated areas of math. A key aspect of Frankel's contributions lie in his investigations of Hitchin moduli spaces and Cac-Moody algebras. But what are they? Hitchin moduli spaces generalize certain types of differential equations.
Specifically, ones related to something called connections on vector bundles over Riemann surfaces. These are akin to trying to categorize different shapes based on how many corners they have. Technically, these are called invariants. On the other hand, Kakmudi algebras are infinite dimensional algebras, which are usually introduced as extensions of other familiar structures in math. In fact, there's even a question posed by Richard Borchards, a field medalist, who took the Kakmudi concept and put it on steroids with something called vertex operator algebras, posing a question to Edward.
Also, to be clear, certain representations of those Kakmudi algebras are realized as vector operator algebras. VOAs aren't an extension of Kakmudi. As usual, timestamps to everything mentioned are in the description, as well as links to everything mentioned are in the description. You can even skip this intro if you like. More important than the math, this podcast delves into Edward's personal reflections. Edward touches on what it means to reconnect with yourself, and he does so while confronting vast topics like infinity, death, and
My name is Kurt J. Mungle, and on this channel, I use my background in mathematical physics to analyze various theories of everything from Wolfram's to string theory. We even explore consciousness and AI. As an aside, though this is an important theme in this conversation, is a theme that I resonate with from The Lord of the Rings, which is the story where Frodo gets stabbed by a special blade early on in the book.
And then toward the end of the book, while everyone else is happy and the problems are resolved, including with Frodo, he succeeded in what he was attempting to do, the scar never heals. The wound still hurts him years and years later. And the lesson or the symbolism is that there are some things that can happen to you that don't go away. There are some wounds that while on the surface they heal, they shape you. That's always touched me. That touches me more than any other aspect of Lord of the Rings. And it's something that comes up in this conversation.
Enjoy this revelatory podcast, this intimate podcast with Professor of Mathematics at Berkeley, Edward Frankel, one of my favorite podcasts. Welcome, Professor Frankel. Thank you. I've been very much looking forward to this conversation for weeks and weeks. So it's an honor. I'm happy. I'm privileged. Thank you for coming on. It's my pleasure. It's great to be here on being interviewed by you, Kurt. You know, I have
Watch some of the videos on your channel and found them inspiring and fascinating. So I'm glad to join the family. Even that's an honor that you've watched that you've heard of the channel, let alone watch some of them. What are you up to these days? And what excites you about it? Okay. Well, well, I'm a mathematician and, and the Berkeley professor. And so my
I feel like my day job, in other words, something that has been the constant throughout my life, is my research. Teaching too, but research is something that I have really devoted, I suppose, most of my energy in, you know, in my adult life. So my research is on a subject which is called the Langlands program. It's named after mathematician Robert Langlands.
who is a professor emeritus now at the Institute for Advanced Study in Princeton, where, you know, I always like to mention that he used to occupy the office that was formerly Albert Einstein's office at the Institute. So in the late 1960s, Langlands came up with a bunch of conjectures and ideas, which became known as Langlands program.
And what this is, what it was originally, was trying to connect, uh, seemingly unrelated questions in different parts of mathematics, specifically number theory on one side and harmonic analysis on the other side. And we can talk more about this if you like later, I can explain more detail, but just, just to set the stage. So this is something that excited mathematicians for several generations, more than 50 years, obviously. And.
In the 1980s a new sort of a new domain in the language program emerged which has to do with things that are connected not so much to number theory but to geometry and eventually quantum physics and it has to do with what's called Riemann surfaces such as a sphere or the surface of a donut and so on, so called Riemann surfaces. And so my research has been on this subject for many years but
There was something interesting about it that distinguished it from the original formulation of the language program. And the language program, it's about functions and operators acting on functions. It's actually, you know, we can think about it in terms of quantum mechanics. There's Hilbert space and there is some computing operators acting in the Hilbert space. And we want to diagonalize them. We want to find their eigenvectors and eigenvalues. That's the original formulation. But in the geometric formulation,
People couldn't find it initially, a framework like that. So instead, what was proposed was that it should be about this weird esoteric object called sheaves. And so it became known as a geometrical English correspondence. But in the last five years or so with my two colleagues, Pavel Ettingov and David Kasdan, we were able to find this new formulation in the geometric setting, in the setting of Riemann surfaces.
where in fact we do have a Hilbert space and we do have computing operators and we can pose the question of their finding the eigenvectors and eigenvalues. And so it's kind of a new flavor of the language program. So something that really excited me for the last five years, you know, it's so interesting because for me, it's been like my research has been, it's not been like a linear path in some sense. So like for a long time, it was, you know, like when you're young and ambitious,
You want to be the best that you can be. And it's all about achieving and kind of like finding your place in the community and so on. So, and so then that was kind of a period of rapid growth. And then, then at some point I kind of realized, I started asking myself, why am I doing this? You know, so what's, am I doing it because I want to achieve something, recognition or awards, or am I doing it really because I love it? You see,
and it's not so easy in a later point in life to to regain that you know and so there was kind of a period where I suppose I was a little jaded you know maybe about 10 years ago well conveniently around that time I wrote my book Love and Math and so I was in high demand for public speaking and so on so it's kind of like it worked out actually in a way that gave me a little more time to reflect and so interestingly enough
I did remember that excitement that I had as a student, as a teenager, as in my early twenties, where I literally went to sleep, I went to fall asleep faster so I could wake up in the morning and resume my inquiry, my asking those questions and working on this. And so I kind of regained, I kind of remembered this. It was so exciting. So I'm just kind of trying to give you a sense where I am.
This project especially, which like I said, I've been working on for about five years now and it still excites me and it's still something that I feel that there are so many interesting questions there that draw my attention.
This appetite that you have to be number one or that you used to have when you were in your younger years, the striving, you said that you started to question it and think, okay, well, what am I truly motivated by? That's right. Versus what do I want other people to recognize me for? When did you start to question that? You mentioned 10 years ago. Yeah, yeah, maybe about 10 years ago.
I read this book cover to cover. And when I say cover to cover, I mean, including the index and the glossary. So I love this book. Oh, thank you.
Thank you, thank you, appreciate it. The book is called Love and Math, and it'll be in the description. It's on screen right now if you're watching this on video. The first half is like an ode to mathematics in general. This is my perspective, so you have your own. And then the last half is some, I'm surprised if anyone who isn't a mathematician can keep up with the last half. But it's something that for me, who is extremely interested in math was extremely interested in, especially love the dictionaries.
Which by the way are like translation dictionaries. Mathematicians call them dictionaries, but they're more like translation dictionaries or thesauruses because you can substitute the words. Whereas a dictionary is like a word and then you have a longer word that defines it. Whereas a translation dictionary is the Rosetta Stone. Rosetta Stone, yes. And I do frame it as Rosetta Stone, right? And it is about the language program. It's exactly the subject that I gave a brief outline of just now.
I would love to talk to you about the process of writing this book later on this interview as well, if you don't mind. Yeah, sure, sure. Of course. But anyway, we're getting to you questioning your own motivations, how that came about, how that unfolded and where that led you now. Yes. So, you know, it's so interesting. Well, you're an artist, so you know how it works. It's the results when you actually dedicate yourself to an artistic project. You cannot know what will come out. And of course, a true dedication means that you
you it's sincere it's a sincere effort you want to connect your audience right so i wanted to connect my audience i wanted them to be excited about the subject so what the primary motivation for writing love and math for me was that.
I thought that nobody knows what mathematics is really about, apart from a very small elite, a very small group of people, professional mathematicians like myself. And I opened the book with this analogy of saying, imagine you had an art class in which they only taught you how to paint fences and walls and never taught you the paintings of the great masters, never showed them to you, never even told you that they existed, never told you there were museums where you could go and look at them. What would you think of art?
The art, the way art is presented to you is just painting fences and walls and then watching paint dry. So, of course, years later you'll say, art is not for me, okay, so it's not something I financially, you know, maybe there are these weird people who like painting fences and walls, but if I ever need that, I will just hire someone to do it. And that's it. So then they completely miss what this is all about. In both cases, of course, paint is involved, but in very different ways. And so I felt my job was to try to convey that.
what is it about what are these things what are the picassos of mathematics you know and cutting through the you know obviously if you have to if you are math major you take courses and it takes a long time but i was i wanted to address the general audience people who don't have time to go and and take classes and and and learn the basics and i wanted to cut through those
I sort of the technical stuff and just get to the sense of your sense of what is like what are the objects we talking about we're not talking about numbers. Necessarily right we're not talking about quadratic equations we're not talking to you clearly in geometry all the subjects that we are it's a very limited part of mathematics that will get exposed.
What is this like what is it also what is it like to do it what is it like why did i get excited about it so i wanted to couple it was a human story.
Okay, so that's the initial motivation. In other words, I set out to write this book to teach something, to teach the world something, to connect to my readers, to let them experience something which perhaps they haven't had a chance to experience yet. But in a weird way, what art does is if you're successful in connecting to your audience, guess what? You will receive feedback too from the book. It's a two-way street. This is what's amazing thing about art. With mathematics, by the way, not quite so because we operate and such.
Within such you know a rigid framework very rigorous rules and so on so it's not as It is a passionate pursuit, but I discovered that you know Writing a book or earlier I had a chance to be involved in filmmaking and now recently I started you know recording my DJ sets electronic music I discovered that I discovered that this is a totally different game
And because not only you have a chance to give something to your audience, but also you receive something if you are sincere, if you really put your heart to it. And so in that sense, the book was a revelation for me. I learned so many things about it. It catalyzed a process of self-inquiry, you could say, where I start questioning things about myself, about my life, about my outlook.
In a very strange way, like it wasn't programmed in some sense. It was just like happening, you know, and it brought me to in contact with people who helped me to accelerate that process. And one of the questions like, you know, as I mentioned, one of the questions was indeed what is this all about? Why am I doing this? You know, is it real? By that time I understood that it's not real if it is just driven by ambition.
uh and and the desire to be recognized and rewarded it's not real it may still be have a real undercurrent but it's not fully real and the sooner one realizes that the better um you know so that was that that's how i came to that question but then there were other things too i
I realized to what extent we are driven by our emotions, you know, that scientists would like to pretend that we are these sterile beings and we're just analyzing the so-called objective reality, but nothing to do with me. There is this, electrons are weird, but not me. It has nothing to do with my life, you know. So I suddenly realized how much I'm driven by this undercurrent of emotions and unconsciously
I'm aware of all those weird processes that are happening in my psyche. And that's when it brought me to reading a lot of interesting stuff like Carl Jung is one of my teachers. I've read a lot of Carl Jung and Marie-Louise von Franz, one of his students, because, you know, I love both Jung and von Franz. And to me, it's like a source, endless source of inspiration and insight.
I'd like to add to that. So you mentioned that art is a bit different than math, because there's more, at least if it's true art, there's an aspect of receiving.
But immediate, immediate, immediate. It's like a wave, you know, like it's a frequent, different frequency. So yes, of course, with Matthew also received eventually, and Alison Grothendieck, my hero, my hero. And he, he obviously was one of the, was a revolutionary mathematician of the second half of the 20th century. And then he had, he had an awakening, one could, one could say in a kind of traditional Eastern Eastern Eastern philosophy sense.
um awakening where he realized he
was brought, that some questions of human existence and suffering were really hit him hard and brought, you know, were brought into his attention. And you could say that that's because he went very deep into mathematics. So it's another portal too. But I feel it's like, it takes longer in some sense. It's like a wave, which is much longer wave, whereas the art is fluctuates much faster. And so response time is much faster also.
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Carl Jung said that great art is one where you don't know what you're creating when you go into it. And then by the end of it, you learn something. Well, you mentioned learn something about yourself, but it could be learned something about almost anything. So you shouldn't if you were to know what you're doing when you start, then he called it propaganda.
Cause you're trying to convince people of something. It's not love. It's not, you're not conveying love, you're conveying power. And so, right. And so Jung is famous for saying also that where love ends, the power begins and conversely, it's which I find, I find a very good way to look at things. Uh, in other words, the impact is real when it comes from the place of love. It can also be, it can also be
A historical prelude to the Langlands program is the vile conjectures, which he infamously came up with while he was in jail. So can you please talk about that?
Well, Langlands would disagree with that, because Langlands was not particular. So first of all, we pronounce his way, we say it way, Andre Way, because there is also Hal Herman Wilde, to make things even more confusing, right? So there are two great mathematicians.
who have very similar names. And then there was also Andrew Weil. Yes, yes. And so for people like myself who read it, I was confused for the longest time between Andre Weil or Andre Weil and Andrew Weil. Who comes up? Who comes up with this? And also, I still don't know how to pronounce Hecke operators or Hecke operators or Majorana particles. I don't know because I just read them. I think for one year I called it Lie Algebras, instead of Lie Algebras. That's right. That's right. Yes.
Who writes a script, right? I don't know, but it's true that there are three mathematicians with like exceedingly similar names.
There is Hermann Weill who was a great German mathematician who worked at the Institute for Advanced Study, was one of the founding professors or first professors there. He is the one who was famous and made famous contributions to study of groups and big groups, specifically in quantum mechanics and so on, and also a very brilliant philosopher. Then there is André Wey, who is a French mathematician, also ended up working at the Institute for Advanced Study a little bit later.
and he came up with this way conjectures so his name is spelled w e i l and in french tradition we pronounce it way oh okay so that's my mistake whereas helenweil last name is spelled w e y l and in the german tradition we say while
I just assume everything is German. Right. So there is also the Andrew Wiles who proved Fermat's last theorem with Richard Taylor. So that's more contemporary mathematician. So Andre Wey was a very brilliant mathematician who came up with this Wey conjectures, one of the most important, most fascinating and original contributions. He also was the one who
created this framework, came up with this framework of Rosetta Stone of mathematics, where number theory and geometry were connected in a particular way, which actually gives a good context for understanding the Langlands program. But it would not necessarily be correct to say that Langlands was motivated by the very conjectures. They're kind of a little bit apart from each other. So Langlands was motivated by other issues.
Well, the way that I understand it is that even if Langlands didn't see it when he was coming up with his program as an extension of the whale, sorry, how do I pronounce it?
like way like way no way the way the way okay this is the way all right yeah that's right this is the way so the way conjectures that it's seen now and i think even in your book you had on the x-axis like in this matrix this translation dictionary the way conjectures but then if you go downward on one of them you have the langlands program so in a sense the way conjectures are more general more encompassing well but it's not exactly so there is way conjectures which is a very specific technical term for some specific statements
But Wei conjectures were an outcome of a certain overarching framework that Andrei Wei came up with. And you're right, he wrote that letter in 1940 to his sister, Simone Wei, who was a famous philosopher and humanist, trying to explain his ideas. And that's where he outlined this picture of Rosetta Stone, so to speak.
The Bay conjectures were an outcome for him from that conceptual understanding of how things fit in mathematics, that he was able to argue by analogy. So you have Riemann hypothesis in number theory, and because he had this framework where he could move things from number theory to other domains, then he said, what would the Riemann hypothesis look like in this domain? And it came up with Bay conjectures, more or less.
Right. So what, what matters here, if we talk about the language program is not very conjectures themselves, which is a very particular application of that general overarching framework, but the framework itself, the framework itself helps you see how the language program can play out in different domains. That's what, that's the point I was trying to make in my book. And Wei, Andre Wei, right. He gave an analogy of
Curves, points, and surfaces as being different avatars of Vishnu. So can you please tell the audience about that as well? Oh, yes. So this is very interesting. So Andrei Wei was very attuned to the Eastern tradition and he actually visited India and I think lectured at the Tata Institute Fundamental Science in Bombay, Mumbai. And so in his letter to his sister, which was written in 1940,
He talks about this, how mathematicians perceive this analogies. And so it's kind of a very interesting, I don't know if I should actually, I have my book here, so I don't know if I could, if I should actually quote, this quote is here somewhere. And he mentions about Gita.
Abhagavad Gita, which is a kind of a sacred text of Hinduism. And he says, when you get an insight, it's just kind of an inkling of an idea, as opposed to when it's already understood. He talks about this dialectics of the experience of passing from that moment of recognition, but you're not sure yet. You just start seeing the outline. And then when it's actually
already done and it's something very interesting because like you fall in love kind of you know kind of like so you wouldn't you would most people probably would least expect a mathematician to be so poetic about it about the about the nature of discovery in mathematics but he says so what happened it is a translation into english so when what happens when this
inkling of an analogy between two theories turned into concrete knowledge he says gone are the two theories gone they are troubles and delicious delicious reflections in one another they're furtive caresses they're inexplicable quarrels alas we have but one theory now whose majestic beauty can no longer excite us so the excitement comes from that moment recognition he's basically saying
Nothing is more fertile than this illicit liaisons. Nothing gives more pleasure to the connoisseur. This initial moment of discovery, this initial moment of insight. And he says, the pleasure comes from the illusion and the kindling of the senses. Once the illusion disappears and knowledge is acquired, we attain indifference. In the Bhagavad Gita, there are some lucid verses to this effect. And then he goes, but let's go back to the algebraic function.
so in other words there is this depth of understanding so mathematics does give one this vantage point i suppose which is very poetic and one could say romantic and i can i can i can feel that viscerally what he's talking about because you know
Coming up with a discovery in mathematics does feel like that, but so does everything else. Falling in love is kind of like this. Although one could say it's not necessarily that you kind of attain indifference once it settles. The idea is that that's the difference between human relationship, which is living, which can live and evolve and transform itself and reinvent itself forever or for a long time. In mathematics, once
Yes, yes. Something that's popular nowadays is to say that there is no theory of everything and in part
They'll quote Feynman and say, well, it's supposed to be like an onion, even though onions are finite, they have like 10 to 20 layers. So that's actually, it's a poor analogy because we've revolutionized physics, maybe 10 to 20 times in different ways. So we should be at the core, but also that there's something romantic about it, about there not being a theory of everything, because if there was, then we think the ultimate questions are done.
The theory of everything in physics has a certain meaning of like reconciling dynamic space time with quantum theory. And so that's not exactly like the answers to everything, quote unquote. But even if there was, it could be that the answer to everything, quote unquote, is something that's animated. So it could be something like at the bottom of I know this is extremely poetic to say, but it could be like the theory of everything is to live lovingly, in which case it's not like an apprehensible, timeless, dead fact.
certain theorems are, but rather something to rather a process rather than a state. I agree. That's a process. It's a process. It's a process. It's a connotation. I think most people have a studio. Everything is that it's something static that is done. And, and then we have this note that this knowledge, which somehow will cover everything.
and that is very counterproductive in my view and even I would say dangerous and has unfortunately impeded progress and cause a lot of suffering to scientists but not only because it's a mindset if we because today people trust scientists to be the forward-looking and kind of like
up to theologians or priests or poets or artists. Now, for better or for worse, it's the scientists who are the priests, so to speak, in this era. And so if we are confused about this, if we entertain these ideas, that they propagate to a general culture,
And this is what happened in some sense. This idea of insatiable, in my view, this insatiable appetite for trying to explain everything with the knowledge I have right now. If you think about it, this is absurd. And all the history of humanity shows that it's absurd. And yet the impulse is so strong. And I'm not going to say it's those other people have to. It's me. I have been like this all my life, up until maybe very recently.
So I know exactly how tempting this is. I also know how, how counterproductive it is and how much suffering comes from it. So like, you know, it's entertaining. It's kind of fun to engage in this activity, but I think it's a, it's a very important, and I'm glad you are, I'm speaking about this on the podcast, which is called theories of everything, which is a bit paradoxical.
but i think that you actually get it kind of you know it's kind of half tongue and cheek the way you call it and you don't call it theory of everything yes right you call it theories of everything so it's not as simple as one might one might think that's the observant mathematician in you
I think that the drive to come up with a theory of everything isn't even though people would say, well, I care about humanity and I want to solve global problems.
I don't think it's that. I think it's the desire to be crowned the title of the next Einstein. Yeah, so it's ego driven. So we can agree on that. Yeah, of course. To me, that means that you're not the next Einstein because Einstein never cared about being the next Einstein because there was not. And also something I think about when people say so and so is the next Einstein, we generally think of it in terms of, okay, are they creating something that's a paradigm shift in physics or math? But it's unclear to me if Einstein was to be born today.
Would he be doing physics and math? So he was a creative, tuneful, poetic, romantic person. Maybe he would, maybe the next Einstein is Christopher Nolan. Also, he played violin. He played violin. Yes. Yeah. So literally maybe he would be violinist. Yeah. Yo-Yo Ma, maybe Yo-Yo Ma is the next Einstein. That's a good point. The term theory of everything. Let's unpack this. Cause I think you've tongue in cheek called the Langley's program a grand unified
theory, which some people then take to say it's a theory of everything of math. Of mathematics, yes, because, you know, I was like, how come physicists always talk about grand unified theories? This, I literally, I gave a colloquium in Princeton, and that's when I first came up with this. It was kind of like, on the spur of the moment, I was like, how come physicists always talk about grand unified theories, but we mathematicians don't? And actually, I was sitting in the audience.
and i said well guess what i would like to call the language program the grand unified theory of mathematics and they're laughing because of course it doesn't make sense because mathematics is just so diverse it cannot have a nobody wants to have a theory of everything and then i said well maybe it doesn't describe everything but at least it describes something so it's kind of a little you know like so that's how it came about
Well, in a sense, math already has a theory of everything. What I mean by that is, it's the axioms. So it's just, it's not interesting to anyone. Why I say that is that in physics, but axioms, but axioms now you're trading on a very treacherous theory. I'll explain. In other words, the toll in physics is what are all those principles from which all observations slash theories are emergent slash effective.
That is what we measure in the lab are just corollaries of these axioms. If we knew the axioms, like the drive for a theory of everything in physics is what is the axioms of nature? And so in math, I know that there's some controversies. But in math, we don't know what the axioms are either. That's the whole point. That's the whole point, which is lost. Usually people don't realize because most people think mathematics is written in stone. So of course it's so predetermined. No, it's not.
It is a very important issue. The way I like to talk about it is that there is an observer problem in mathematics, just like quote unquote, or measurement problem in mathematics, just like in quantum physics, where the observer is involved in quantum physics. We know that from experiments. In mathematics, it is much easier to miss. And where it comes is, there are several places where it comes, but one of the most essential ones is who chooses the axioms.
There isn't one axiomatic system which is God-given. And even great mathematicians like Kurt Gödel, for example, apparently he did believe that there is a kind of ultimate correct system. And then he thought that his job as a mathematician was to find it. In other words, it is somewhere there in some platonic world and you have to go and find it. But it's not obvious at all which one it is.
So it's just the way you frame the search for it. In other words, you may think that there is one special one, but you don't know what it is and you can devote, dedicate your life to finding it. Another alternative position is plurality, kind of multiverse of axioms. So there are various axiomatic systems, they lead you to different mathematics. And it's very interesting to analyze what are the differences, which is more fruitful, which is less fruitful.
so that you can say okay well there must be some objective criteria as to which a system of axioms is better and the weird thing is that there isn't even consistency cannot serve as a criterion because the second incompleteness theorem of Kurt Gödel shows that a formal system formal system that's kind of a assemblage of all the statements that you can get out of a particular system of axioms
Formal system cannot prove its own consistency. You have to step out of it. You have to step out of it. You have to adjoin some other axioms to be able to speak about consistency. Consistency means that it's useful. You can't prove everything.
And consistency means that every statement can be derived. So it derives contradictions. It can derive statement A, and then it's negation. And if that's the case, then it's true for every other statement. So it means that it proves everything, so then it's useless. Yeah, you actually don't want to be able to prove everything, because then it's trivial. That's right. You have to prove only some select statements. And that is a property of a formal system called consistency.
And the point is that the system cannot prove its own consistency. So then how you cannot be sure even that it's consistent. You have to take it on faith. And that's where the observer comes. So then how does Kurt Gödel, for instance, how would he decide which system is the God given one? Because he did believe apparently that there was a correct one that you have to find. And obviously you do it on other principles like aesthetic principles.
this principle of beauty principles of being concise and stuff like that. But that's where you as a subject, as a first person, your first person perspective becomes imprinted on this because there isn't an objective criterion. Ultimately, there isn't. So the other possibility, which is as nice with me is this idea. Um,
i'm which is there is a lot of money who has written about this and i really like the way she framed it it's mathematical practice the system is. The better system is the one which is more fruitful which allows you to prove more things.
And this is some, but it's beautiful because it means, but who decides? It's us, the living mathematicians today. We decide because we're practicing mathematicians, we're applying those axioms in our practical work. And then it becomes a marketplace of axioms, system of axioms, if you will. They compete with each other as different stories, so to speak. And we choose the ones which are more fruitful, which give us more diverse, more beautiful mathematics.
you know so in in other words we're deciding it right now not referring to authority of Pythagoras or Kurt Gödel or Bertrand Russell or some such you know great individual but it's up to us it's a little that's where mathematics becomes a living process so in that sense one has to be careful to say that
whether mathematics is based on some unassailable foundation. It's not. If you look more closely, it's actually very similar to
other subjects of human endeavor or other parts of science like physics and so on. And I agree with you that in a way you almost you could say that the job of a physicist is to try to find the axioms of the physical world of this universe. We don't see the laws themselves, we observe the ramifications. Or at least some of them, right? So then
What is my place actually is the same but it's much more difficult to notice it unless you actually are pressing my efficient because the way my face is perceived by the general public is that it is something where where nothing ever changes.
And the foundation is also perceived by many mathematicians and actually managed. I personally have not really thought about it deeply until recently, you know, because you, you do, you, you, you do. And I think it's very common, you know, in general that you, you find something that interests you. Like for me, language program, you can work on language program without
questioning the foundations. The reason I question the foundation is because of my interest in philosophy. Perhaps it's because of public speaking, kind of doing interviews, like conversations like this, where these kind of questions would come up and I would really be curious. So I'm really interested in those philosophical underpinnings of mathematics. But a lot of people, as you know, they actually claim that philosophy is completely useless for scientists.
We shall not name any names, right? Yes, yes, yes. I will put an image on screen. I disagree. I disagree violently with this position. I think it's very limiting. And I think there are probably some parts of science where, you know, you can get by, but I think we all benefit from opening our horizon and from being interested in the foundations of what we're doing. This is called self-awareness. Right? What are you doing?
So in other words, the public has the perception that there's the practical aspect of science. So STEM, science, technology, engineering, mathematics, and the practical side of the first three years, the science, the technology, the engineering and physics is seen as a pure form of engineering. And then the most purest form of physics or the purest form of science is math. And that's something that's extremely objective.
But you're saying, well, in order for us to establish something mathematically, we have to agree on the axioms. When we do so, we generally do so with practical concerns like empiricism. And so there's something that's about... Or you're driven by your Platon, if you are a Platonist, which means that you believe that mathematical ideas exist in this ideal domain, this platonic world, which is outside of space and time and so on, which I respect this position. And I actually, to some extent, adhere to this position when I was writing Love and Math.
Then also you have your own methodology. You're kind of, you're searching for the correct one in that platonic realm, which is also, you know, it's a methodology. But there has to be some kind of methodology for you too, because there is no objective methodology. You cannot even use consistency as a tool, because it cannot prove its own consistency. So you have to take it on faith. It's a very practical thing. For instance, you have the Z of C.
The standard axiomatics of set theory. Set is the most fundamental notion in modern mathematics, introduced by German mathematician Georg Cantor. And actually, it's never been defined. This is already a place where a whole of mirrors, you know. We pretend that it is something that is concrete and definite. But in fact, there is no definition of it. There are only circular definitions.
Cantor himself gave a very poetic definition. He said, a set is a collection of many that thinks of itself as one. You see, so it's a poetic definition. Now, in other words, here's a notion which we accept on faith. Then you have this axiomatics which was developed in the first half of the 20th century and has become sort of a staple. So you kind of learn, most mathematicians follow it even if they're not aware. It's called ZFC.
Z for Zermelo and one mathematician, F for Franco, almost the same spelling as my name, no connection as far as I know. And C is the axiom of choice, so ZFC. Now, we do not know that it is consistent. We can prove its consistency from another system, which is a bigger system where you introduce additional axioms, but you don't know whether that system is consistent. And like this ad infinitum. So how can we then do mathematics?
You ask, well, we have to accept it on faith. People don't talk about it. And most people probably never actually thought about it deeply. But if you think about it, it's and it's all information is available. I'm not saying something that does not know everybody knows it. Certainly logicians know it. And, uh, and the point is that we take it on faith that it is consistent because if you don't, then how can you do mathematics?
without assuming that it is consistent you see yes if it's not consistent means that you can prove anything by from these axioms including contradictory statements right so there is this element of faith even in mathematics there is an element of fiction there is an element of story and i think it's a very important observation because it points us again to the importance of the first person perspective
A science of the 19th century tried to expunge the first-person perspective, even earlier science. And the whole point of science was to come up with this narrative that somehow there is a subjective reality and we are just detached observers, we are not participants in it. Science of the 20th century, physics of the 20th century put an end to this through quantum mechanics, through Einstein's relativity theory, where the observer is involved and cannot be separated from what
the observer is observing but then you could say well at least mathematics is objective and so my point is
It's not. It's more camouflage. It's better camouflage. Your current deliberation is that it's all subjective or it's an intermingling of subjective and objective? It's always intermingling, of course. But the point is that there is no objective core. There isn't something. There's a strong foundation. Somebody who is not a mathematician may think
Obviously there are some axioms in mathematics which have existed forever and nobody questions them. That's not true. The simplest example of this is non-Euclidean geometry. Euclid actually was the first one to come up with a functional system of axioms, what we call formal system of Euclidean geometry. So about 2300 years ago, of course, building on earlier works by Pythagoras and Pythagoreans,
where he came up with a list of five axioms and tried to derive hundreds of different statements in his book, Elements, a series of books, derived from those axioms. Now, the first four axioms were kind of natural, and the fifth axiom was about parallel lines, that if you have a line on the... So, creating geometry, as I'm sure everybody knows, since this is actually one subject that is studied in school,
It's about the plane. Plane means a tabletop extended to infinity in all directions and on that plane we have points, we have lines, we have circles, we have triangles and then they intersect and there are all kinds of statements that you want to make. For instance, Pythagoras theorem that you have a right triangle and the square of the hypotenuse is equal to the sum of squares of two other sides. This is the type of statements that we're talking about which you would like to
Did you drive from a small number of actions? But then how do you choose these actions? First of all, you want them to be non-contradictory. That's consistency that I talked about. And yet you want them to be broad enough so that you can derive many interesting things. So he came up with these five axioms. And the fifth axiom was the one which kind of looked weird. And it stated that if you have a line on the plane and you have a point outside of this line, then there is a unique line passing through it, which is parallel to the original.
Parallel means that they never intersect. So there is one, and it's unique. And after that, for centuries, people tried to derive this fifth axiom, they used to call it fifth postulate, from the first four. And they've all failed for about 2000 years.
when several mathematicians around the same time said what if we replace it with another axiom where either you say there are no such lines and there was every line that passes through this point intersects the original line or you say that there are infinitely many lines not one which do not which do not intersect and this way you get what's called non-Euclidean geometry the first example now when you say axioms
When you talk about Euclidean geometry, you have to make it very detached from reality. So we have a model of this Euclidean geometry where we really think of lines and dots and circles and triangles. But when you formulate things in mathematics in the formal system, it has to be completely detached from reality. It's all syntactic. It's just symbolic manipulation. So you don't necessarily have to refer to a particular model for it.
So then you say, well, in my experience on the line on the plane, I can't imagine that there's no parallel line passing to another point, but you don't have to look on the plane. You can look on the sphere and on the sphere, the role of lines is played by meridians and every two meridians intersect. You see, so in other words, the formal system doesn't care about how you want to model it.
Formal system only cares about things like consistency, whether these axioms contradict each other or not. And it turns out that if you replace the fifth axiom of Euclid with another statement, it turns out that in this case, we can actually prove its consistency because it's kind of from without doing much. So it is actually independent from the other axioms and you can actually replace it by its negation and you'll still get a consistent system. And that system can be realized either on the sphere
that's the kind of spherical geometry where every two instead of but it's not a line it's a meridian which plays the role of the light so you take all the statements but lines in euclid but they replace lines by meridians meaning big circles on the on the sphere it doesn't mean this has to go through north and south pole you could have any any big circle is a lot is what plays the role of a line in spherical geometry
And if you replace the axiom in the opposite direction, you say that there are infinitely many lines which do not intersect. You get what's called hyperbolic geometry. So it's a geometry on a hyperboloid where the role of the lines is played by hyperbolas. And then you can see that there are infinitely many hyperbolas which do not intersect. Okay, so this is a good illustration of the fallacy of the idea that
There is one axiomatic system which services all of mathematics, which has been given to us somehow, the way the tablets, you know, the Ten Commandments were given to Moses. That's just not the case at all. However, it doesn't mean that it's not a postmodernist position either, that anything goes. This is what I also try to explain to my students always, because then the next temptation is to say, okay, it's all fiction. Yes, that's what it sounds like. Then what are we talking about?
but the point is that there is practice this axioms they don't nobody needs this axioms if you're not going to apply them to actually prove statements and make progress in mathematics and different and it's not true that all axiomatic systems are created equal no in some of them you get a lot of interesting stuff done and in some of them it's some of my limiting and a good example of this is whether you accept
The existence of infinity existence of infinite sets like the set of natural numbers one two three four five and so on as a totality not just infinity like that for every number there is a number greater by one this is called potential infinity but you accept absolute infinity that there is such a thing as a collection of all natural number.
This is a very, it seems like a small thing, but actually leads to a lot of paradoxical statements like the famous Hilbert Hotel, you know, where you have infinitely many rooms and then you can always accommodate more people because you could shift them all by one to the next room and then freeing up, freeing up. There was very paradoxical behavior. So now what is the status of this statement of existence of absolute infinity?
It is one of the axioms in ZFC, in this axiomatic system that I talked about, Zermelo-Franco axiom of choice. And there are mathematicians which are called finitists who refuse to accept this axiom. So they consider ZFC without the axiom of infinity. And then the race is on. Okay, so here 99% of mathematicians who accept infinity and they work with this axiom whether they're aware of it or not. Okay. And here is a small group of mathematicians
I've spoken to some people who dislike the axiom of infinity and the axiom of choice. Norman Wildberger and George Barnett. Do you know George Barnett?
This is very interesting. How do you decide which is correct and which is not? So my point is, this is a market of ideas. This is a market of formal systems.
You show me what you can do with your formal system and I'll show you what I can do with my formal system. People will look at this and they will decide which way they want to go for now. Maybe somebody else will come up with a third system of actions which will be superior to both and so on. I don't want to do it on ideological grounds. You see and this is where a lot of people go astray today into the science.
They pretend that they are not ideological. They pretend that they are not driven by their metaphysical preferences, ontological preferences. For instance, that I like local determinism or I dislike local determinism. And then I am willing to sacrifice this and this and this for that particular thing, aspect of a theory. But it's not because it's my preference. It's just a better theory. No, it doesn't work this way.
You have to detach yourself from your ideology. If you want to do good science, it's my opinion, which in this particular scenario that I'm talking about, and it's not a scenario, it's reality of modern mathematics. You have a small number of people who refuse to take Axiom of Infinity. Now my feeling is that there is something deep in their psychology, which rebels against the idea of infinity. They believe it's not real and they would like to do mathematics according to this ideology. Okay.
I accept also that on the contrary, I like the idea of infinity. To me, infinity in mathematics symbolizes transcendence, symbolizes something that is beyond logic and reason in some sense. But we formalize it in mathematics as an infinite set. You see? Interesting. I admit
Okay. I admit that I am drawn to it because of my psychological composition. That's what it is. It's my preference, my psychological preference, my aesthetic preference, my ontological philosophical preference. Like you don't mind the paradoxes that come about. In fact, they're welcome, but it cannot be, but the whole point of science that we do not resolve our disputes on ideological ground. This is
This is not a fruitful approach. There's a much better way to do it. I will work with the system of axioms, which is closer to me, to my psychological, philosophical, you know, metaphysical ideas. But I should not be judged on that. Me and my colleagues who accept that we will work and we will produce results.
and my colleagues who do not accept infinity will work and produce results and will compare and then we will see in the next generation young mathematicians who are not yet burdened by all this ideology they will look and they will vote with your legs with your feet they will go in the direction which is more fruitful that is real science in my opinion that's how you resolve it you resolve it now the problem is that you can have people
who are blocking that process. For instance, let's suppose somebody is attracting a lot of resources to their theory, you know, because they say it's correct. Then it puts others at disadvantage. So I think that's unfair. So everybody has to have a chance to develop things unless it's clearly like wrong inconsistency. Do you have an example in mind when you're saying this? Oh, yes. Many examples are just one in particular.
One very special example. I'll get to it. So, for instance, what affinities do, it does not resonate with me. It does not resonate with me because I think, because, you know, I'll tell you why. So they basically accept only finite sets because they exclude this axiom. So, okay, but then you can prove, for example, that within their formal system, you cannot prove some statements even about finite sets.
In other words, some statements about finite sets, you can only prove if you accept the axiom of infinity. That's the weird paradoxical aspect of it. You can actually prove that you cannot, you can prove that you cannot prove some statement about finite sets. So to me, it means a straight jacket. You put a straight jacket on yourself. You limit yourself. Why? Simply because you don't like the idea of infinity. Well, okay.
Why limit yourself? Why limit yourself when you can... So that's my view. But I respect them. And I would like, for instance, there is a project to try to re-prove various statements. For instance, Fermat's last theorem, proof of Fermat's last theorem. Try to write a proof which never uses infinite sets. There's a project on which several very distinguished logicians, you know, mathematicians have worked on. And last time I looked, it's inconclusive.
they don't claim that they can do it but there are some other famous problems in mathematics that they were able to prove without appealing to infinity and i applaud that because at the end of the day it's also helpful to know what is a minimal set of requirements for you to prove something okay but ultimately i think the correct argument why the theory with the action of infinity is superior today to the ax to the uh system actions without infinity is that we can produce a lot more
and it is there are many statements which are not known to be derivable by without axiom infinity there are many states which we know cannot be derived without axiom of infinity and so on so therefore it becomes limiting limiting to our progress and you know i also the other thing i want to say is that today there are algorithms based on um elliptic curve encryption stuff like that which is actually used in in in the bitcoin blockchain for instance and it's not clear to me whether
The mathematical theorems which underpin this algorithms can be proved without the actual infinity. So in fact, if that is the case, effectively, it means that it becomes part of our life. The infinity finds a back door into our life through various theoretical statements on which our technology is based. Now, I'm not claiming that that's the case, but that's how, for instance, that's how it can actually affect us because somebody could say, okay, this is some really esoteric argument because in this weird mathematicians like who cares?
You care because technology is woven into the fabric of our lives to such an extent that yes, a lot of very hard, difficult mathematics is now being used. In fact, for instance, in transactions on the Bitcoin blockchain. And this is one example. Okay, we're going to get to examples. These examples I have given were to illustrate the point that number one is mathematics is also based on there is a choice involved.
But number two, so in other words, there is a subjective element. And this is only one, so just a brief addition to this. This is one way in which the observer is involved, the first-person perspective is involved. The other one is, of course, when we write proofs, who decides whether it is correct or not. We are not yet at the stage of full automation of
Verification of proofs and eventually probably some of it can be done by computers. It's not there yet. So it's human mathematicians who are reading those papers and ascertaining whether the proof is correct or not. A famous example is Andrew Wiles. We talked about earlier his original proof of Fermat's last theorem had a gap. How was it found? It was found by the gap was found by by a mathematician, Nicholas Katz, who was Andrew Wiles colleague at Princeton University.
who looked very carefully and he asked questions probing questions that you finally asked the question how does this follow from this and then the west could not answer it so it was determined that there is a gap and luckily a year later andrew wiles with the help of his former student richard taylor was able to close this gap and after that so what gives us the the confidence that the proof is correct what if there is another gap we cannot be 100 sure this is the point it is the accepted as a
is a true is a true proof by other practicing mathematicians that's the market of ideas that i'm talking about even in mathematics you have this market of ideas
There isn't something that is objective and completely detached from our personalities, from our real living breathing mathematician. That is something that is very important and it's an indication that even mathematics is like this, then for sure it's like this in many other subjects which do not even have the appearance of the subjective reality. Of objective reality, right? Mathematics does have the appearance of objective reality more so than any other subject in science, in my opinion. But what I'm trying to argue is that this is an illusion. At the bottom of it,
There is a choice that choices made by living mathematicians. Okay. That's the first point. The second point. However, it doesn't mean that anything goes. It doesn't mean that anyone come up with some fancy like like objects in it. Somehow there is a notion of a group. It's one of the cornerstones of mathematics notion of a group. A group is like a symmetry is a collection of symmetries operating on a particular object, like a glass glass around glass or rotations of the glass. So it can be, it is encapsulated by some axioms.
Where you have some binary operation to satisfy such and such purpose, associativity being the most important one. What if somebody comes up and replace associativity with something else? Some other kind of, you know, different property. And actually people try to do that.
How, guess what? Groups are fundamental. Those other things are not. Why? Because groups have led to very important advances. They have applications in many areas. And those other fancy objects don't. And that's how, that's why mathematics work on groups and not on those other things, which to detached observer who is not involved in the subject will look like, okay, so in this axiom you have three terms and this I have four terms. What's the difference? They look very similar.
But we choose one and not the other for a reason. And that is an objective element, you see, because it comes now from the community of mathematicians working on it, applying it to different areas. And there's a criterion of fruitfulness. That's what replaces objectivity in some sense. But it's a notion which is accepted today by the community. Maybe one of those fancy objects that we don't pay attention to today because we think that they are useless. Maybe somebody will find applications for them.
How do we overcome this then need or this fallacy of confusing something's effectiveness, its ubiquitous application with its ontological status?
So this is something that computationalists do, where they see the effectiveness of computers and they say, well, then at the basis of reality is computers. Yeah, that's right. Or some people. Well, I have several examples in mind. This absolutely. And that's why I am. That's why I devote time to talk about this, because this is one of the policies that you said that I have in mind. And I think that this discussion of what mathematics is about is very much relevant to understanding why it is a policy.
We have to overcome this temptation to believe that the knowledge we have acquired is sufficient to explain everything or at least like a large portion of reality. This has never worked. It has never worked and never will work in my opinion and case in point computation. A lot of people today say that everything is computation. And what do they mean by this? So they learned computation. They think they've learned.
computer science or computer mathematics. And it's a child who learned trigonometry, 11 year old who learned trigonometry. And now he sees trigonometry in everything. Look, there is a wheel, it's trigonometry. Look at the triangle, it's trigonometry. Everything is trigonometry. It's a very natural and almost endearing quality of human beings, but unfortunately leads us astray. And I think that maybe
Time has come for us to finally let go of this, of this approach. And for instance, in the case of competition, since you mentioned, it's something that, which is very much relevant today because all the computer, so-called AI, all this computer programs that charge GPT and so on. I have spent some time reading the founders, like Alan Turing. Okay. So Alan Turing is,
What was the most important result that he immediately proved after he came up with his idea of encapsulating computation as a Turing machine? It was a statement that there are things which are not computable by Turing machines. In other words, computation, the paradigm of computation contains within itself its own demise, the realization that it's not everything.
And the great ones, in this case, the founder Alan Turing, one of the smartest people who have ever lived, he saw it right away and he did not see it as a bug. He saw it as a feature. And if you read his work, it's an incredibly deep and honest, sincere analysis of what it means or what its implications are. Because of course he was fascinated with the idea of thinking machines, of intelligent machines.
But if you read his paper on intelligent machines, I actually have it somewhere. So first of all, he writes in 1945, the class of problems capable of solutions by the machine can be defined fairly specifically. They are a subset of those problems which can be solved by human clerical labor working to fixed rules and without understanding, without understanding. Now, intelligence, by the way, comes from the word intelligere.
Which means to understand how can we talk about intelligence of computers when the father of computing can see that the point that they're not understanding what they're doing. How many countries scientists are aware computer scientists who speak out on this and say we are already entered the age of AI.
It's going to take over human beings. If we are lucky, they will use it as, as plans, you know, as decorations in their homes and so on. How many of them are even aware of this quote? That's my first question. Yes. Okay. My second question. So my second question. So there's another paper in which, which is, uh, which is called, which is called intelligent machinery.
i think it's called intelligent machinery and he talks about objections to the possibility of intelligent machines he says the original question can machines think is too meaningless to deserve discussion nevertheless i believe that at the end of the century the use of words and general educate opinion
will have altered so much that that one will be able to speak to much of machine thinking without expecting to be contradicted. You see, we'll have what so much. I believe that at the end of the century, and that means 20th century, the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted. In other words, he's basically saying that's not a good way to phrase it, but he's resigned to the fact that that's how people will talk about it. Uh huh.
I believe further that no useful purpose is served by concealing these beliefs. The popular view that scientists proceed inexorably from well-established fact to well-established fact, never being influenced by any unproved conjecture, is quite mistaken. Conjectures are of great importance since they suggest useful lines of research. So for him, from the beginning, the possibility of intelligent machines was a conjecture.
And now he says, and now he says, I now proceed to consider opinions opposed to my own. And he comes up, he comes up, listen to this, he comes up, not with one, not with two, he comes up with nine objections, nine objections. And he carefully considers each and every one of them. And the one which he finds most powerful is what he calls mathematical objection. The fact that he himself,
Show that there are problems which are not decided which are not computer which are not sold by a machine by computer. This is a very important point this is called how to problem. How do you promise he realized that you can not be sold by the question which machines will help which machines will not go into the loop.
because you can enumerate all the Turing machines and you're going to ask whether there is an algorithm or a Turing machine, which will, which will. Does the halting problem implicitly have an idea of the concept of infinity? Yes. Yes. So the objection would be, well, Hey, we just get rid of the infinity. You can't get rid of it. That's the point. You even, you have to accept at least potential infinity because otherwise the position is untenable. Otherwise your position is that there is a biggest number and an N plus one does not exist.
This even finitists today, they would not agree with. Finitists do not say that there isn't a number greater by one than any given number, meaning there is a billion, there's a billion and one, there's a gazillion, there's a gazillion and one, okay? They don't argue with that. That's called potential infinity. What they argue about is whether there is such a thing as a totality of all positive natural numbers, whether it exists as a thing in and of itself.
For them, what exists is always a finite set of numbers from 1 to n, or from 1 to n plus 1, from 1 to n plus 2, and so on, but not from 1 to infinity. That is, it seems like a subtle difference, but that is what separates finitists from the rest of mathematicians. It's that. I don't know of any mathematician who actually seriously entertains the idea that there is a biggest number. Yeah.
Because you know that there is this number and there is also number one and there is not the operational additional number. So how can it not give you n plus one? You see, so therefore you cannot avoid potential infinity. You can avoid absolute infinity, which is what finite is do by saying that the set of natural all natural numbers does not exist. Only it's finite subsets at any moment. That is a reasonable position. But
They still cannot avoid the fact that for every number there is one more. And that is what gives the halting problem. You don't need to assume absolute infinity for it at all. Just the thing that the machine runs, if it stops, you're in luck. But what if it doesn't stop? It means that in finite time you cannot decide whether it stops, you see. That is the cornerstone of the impossibility of solving the halting problem. Infinity is
Underneath it, but it's it's a lot infinity light. It's a potential infinity I was speaking with drawer drawer barnetton. He's an ultra-finitist So I asked him explicitly Do you believe the number five to the power 100 to the power 100 to the power 200? Doesn't exist and he paused and thought about it. He said no doesn't exist Okay, yeah, and yeah, you you just described it. So that's very interesting Yet you just named it. So what did you name?
Yes. Well, you named a unicorn. You named something, right? Yeah. But anyway, I could be misquoting him or misremembering, so who knows. But there are ultra-finitists. Maybe. I don't know. I think it's a bit of a... If I may say so, a little bit of posturing. It's a bit of posturing. So, Professor, this seems... I see the same passion that you have for math, that you have for this subject, this new philosophical subject.
No, for sure. When did this start? This also started 10 years ago? Yes. So this started with the questioning of what am I doing this for? Is it correlated? It very much correlated, very much correlated. Yeah. So I was going to say, yes. So I wanted to say what I quoted. I want to say which source is called computing, machinery and intelligence. It's an article during growth in 1950. Okay. And so where he gives nine, he gives nine objections.
to his own ideas and he analyzes them carefully. How many computer scientists do you know today who number one aware of the fact that Turing was trying to grapple with these issues from the outset and he was very uneasy about them, right? Yes.
How many computer scientists and proponents of AI, so to speak, or like acolytes of AI, how many of them actually aware what the father of their subject was thinking about it? And it's number two, how many of them put in their papers objections to their own ideas and seriously engage with those objections instead of dismissing them outright? I'm not sure how many will answer yes to both questions.
I'm not sure. And that is, we say troubling, so we say disconcerting. Why is it that the father of the subject felt it imperative upon himself to engage critics in a very serious way and sincere way? And by the way, it was in dialogue with Gödel because it's very connected to Gödel's incompleteness. And he was aware right away of this and Gödel too.
And even years later, so Turing died in 1954. In 1973, Gödel decided to add a remark to his earlier paper in which he argues with Turing. So it's kind of weird because you could say kind of unfair because Turing cannot respond. But I think it's on the contrary, it shows the great respect of Gödel to Turing.
So he writes a philosophical error in Turing's work, Turing and Gödel writes, and this is, I think, I believe in 1973, 74. And he says, Gödel, Kurt Gödel says, Turing in his 1937 paper gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However, this argument is inconclusive.
Okay. During this regards completely is the fact that mind in its use is not static, but constantly developing. For example, we understand abstract terms more and more precisely as we go on using them and that more and more abstract terms enter the sphere of our understanding and so on. So he has a technical argument and I'm not trying to say he's right or he's wrong. They engaged with each other in a dialogue from the beginning because they understood the importance of this question.
When this to the implications for our society and doing was right he said by the end of the century this will become common place a lot of people will be saying this even if i think the question do can machines think is not a productive one this is this is reality this is going to happen so we might as well i might as well now i will lay the foundations of this and have a framework for discussing this what does it mean and he goes to nine arguments nine arguments against it.
And then the third argument is the mathematical objection, which is Gödel's incompleteness theorem. He writes, there are a number of results of mathematical logic which can be used to show that there are limitations to the powers of discrete state machines. The best known of these results is known as Gödel's theorem and shows that in any sufficiently powerful logical system, statements can be formulated which can neither be proved nor disproved within the system, unless possibly the system itself is inconsistent.
And so on. And then he writes, I do not think this view can be dismissed quite so lightly. You see, he's himself, not sure. And in fact, the year he died in 1954, he talked about in his last article published in 1954, you know, kind of a popular, in a popular magazine, science news at the very end, this is 1954, just about the time he died.
He says the results, it's called solvable and unsolvable problems. And he's arguing that what theory of computer science shows is that there are unsolvable problems. There are things which cannot be solved by an algorithm.
and this is important i think a lot of people have not really had the chance to think about it to a large extent because of atrocious state of our education and i feel it's imperative for somebody like me who actually got exposed to it and i'm not saying i'm not saying i'm presenting some truth which has not been known it's all very well known to specialists whether they would like to turn a blind eye to it or not
It is well known, but to most people it is not well known. So I think that this is not present in the conversation about AI. At least I don't see it that much present, you see. And this idea that as soon as you, that the competition includes within itself, the idea that things are uncomputable, they are undecidable, unsolvable. Here's a book that, for instance, there's a whole collection of articles here. What are the words which are used in the title? Undecidable.
Can you show that book once more? Okay, the Undecidable by Martin Davis, and that'll be in the description, as well as the link to the two articles that you mentioned of Turing. The limitations, the inherent limitations of computation. Okay. He grappled with this from the beginning because he's understood the power of it, the potentiality of it. He also liked the idea of intelligent machine.
But he also understood that it's not so simple. There are serious arguments why it's not possible. So in 1954, I have read through several papers of his to see the evolution of his views also. He's not dogmatic. He's not like,
It's like that. And then I'm going to prove it, you know, all the power that I have while ignoring all opposite arguments, which unfortunately we see that today. That's not his approach at all. And his last paper, his last paper, in fact, he finishes with saying the results which have been described in this article are mainly of a negative character, setting certain bounds to what we can hope to achieve purely by reasoning. See, he's already expanding from computation to reasoning.
He says this and some other results of mathematical logic may be regarded as going some way towards a demonstration within mathematics itself of the inadequacy of reason, quote unquote, unsupported by common sense, inadequacy of reason unsupported by common sense. Are you aware of Penrose's and Lucas's argument that says that? Oh, yes. Penrose is fantastic book. I have it here. You know, uh, the book,
This and actually there are two books, but this I love this one. You see how many bookmarks. Yeah. Yeah. So here's something that you made me think about. There's something called. In ancient Greece, there's something called the unity of virtues. Have you heard of that? To some extent, I suppose, yes. Yeah. OK, so basically it says that you can't have one of the virtues without incorporating the rest as you increase in the virtues. You can't be brave without being honest. True bravery requires honesty.
And then true honesty requires courage. I wish it were so simple, but okay. Yeah. Well, anyway, they were saying that as you have more and more of them, they unify at something like the most good, which they would equate with God. Then you had me thinking, well, okay, look at this. We're taught more to think algebraically and algorithmically than we are to think in the way that the Greeks did with lines and circles. So less geometric.
At least in this is my case for my education. And then I was thinking, well, the people who are the most playful with their ideas and creative and poetic and romantic, they tend to be the more geometric side of the mathematician. So for instance, Einstein, Penrose, Michael Attia. And then I was wondering, this is a huge speculative jump. Is this in some way related to prioritizing
this algorithmic, symbolic, syntactic manipulation over something that's more physical and geometric. I'll give another quick example. I never cared about why can't you put a circle in a square, something like squaring the circle or a circle outside of the square, because I'm like, who cares? You can just draw that. But then there's a specific set of rules with compasses and so on that never, I'm just trained algebraically, like trains in terms of that's how I studied in school.
I wonder, and most of my generation is, maybe even your generation, and I wonder how much of this dismissal of these grand ideas comes from a dismissal of geometry, like picture proofs are of, hey, look, if you rearrange this... You can have... There is something to what you're saying, and there is a famous quote, which I don't remember who said it, maybe it's here, that God is like, influenced mathematicians through geometry and devil through algebra, you know.
Okay, so there is some truth to it. In other words, there is more imagination in some sense in geometry. Lineman's program, in a way, is what tries to unify discrete and continuous and symbolic algebraic with geometric imaginative in a way. That's what I find beautiful. Ultimately, all of these distinctions that we make, these are all distinctions in our mind. They're all the distinctions. There's a story we tell ourselves. If I believe that there is a
Boundary there is a line between the two. This is how it is for me then but it's like people say truth and beauty, you know So it's already implicit in that is that the truth they will find they don't expect to be beautiful and the beauty they find They don't expect to be true, but you yourself made the distinction you yourself drew the line between the two It doesn't have to be this way. You can say truth slash beauty one thing or truth dash beauty You know one thing and then in your life you are more likely to encounter two things which are beautiful
and beautiful things which are true. Same with geometry, algebra, and so on. These are all frameworks that we create. In modern mathematics, you cannot do one without the other. The progress is made when they hit upon each other, when they touch each other. Algebraic methods, geometric methods, and so on. That's why we have algebraic geometry, which was created in the modern version, was created by the genius Alexander Gross, whom we mentioned earlier.
his genius was precisely to be able to connect them, put them together, you see. But there are people who are dogmatic on both sides, who are predominantly algebraic or predominantly geometric. I think what is essential to understand is how much we are informed by our own psychology, how much we are informed by our own aesthetic preferences, our philosophical preferences, our metaphysical preferences. In other words, the quantity of subjective objectives
Some, you know, a friend of mine who listened to my recent interview with Lex Friedman, conversation with Lex Friedman, where I talked about subjective, kind of like similar to what we discussed on the subjective. He's like, well, but it's kind of troubled. I feel it's uncomfortable with it because you're proposing to replace some objective things by subjective. That is totally missing the point. What the point is to realize that you have always been doing this. You have always had mixed your subjective to what you believe is objective. And then you try to come up with an argument.
presenting your ideas as if they're detached from you. I would content that that's not the case, that is always present. So it is not about replacing something with something, it's about acknowledging that's what you have been doing all along or what I have been doing all along. To what extent my theories, which I like to think of as objective, are driven
I'm motivated by my subjective preferences. For instance, we talked about, I like infinity. I just like it. So it's my aesthetic preference. But if on the basis of this, I will start saying that everybody should like it. And those people who don't accept infinity are stupid or misguided. That's where I go astray. And that's where I introduce unnecessary, unnecessary strain on my mathematics.
And you know it always, when somebody is really emotional about it, they give themselves away. You know, because as a friend of mine once said, a very smart fellow, he said, you know, you're not going to argue with someone who will say gravity doesn't exist. He said, oh yeah, good luck. Good luck. Gravity doesn't exist. You're not going to argue with the frozen, you know, the corners of your mouth. That's not the case.
And likewise, when somebody is arguing too passionately about something, it means that it's something there, in here, unresolved.
We are not paying attention to this. We are pretending that in science, we are really driven by some objective reality. Yes, we are to a large extent. Like I said, as a community, we decide which actions are more fruitful and so on. But as a human being, as an individual, I'm also very much driven by things which come from my psychology, my philosophical preferences, from my, you know,
And my job is to be aware of it. That's called self-awareness. Otherwise, I'm asleep. I'm half asleep. I am not here. I'm not. And so therefore I am not doing my job correctly, in my opinion. So Alan Turing was aware. So here is a good example. Alan Turing, as someone who was aware of this raises very interesting question. He was not, it was not, it was not
uh, frustrated by it. I think it made it even more interesting for him in many ways. It's a shame that the way he was treated by the British government, as I'm sure you know, that is subjected to hormonal therapy, you know, because he was gay and he died at the age of 32, as most people believe, by suicide. What a travesty, you know? And that's the machine, the machine, that's the real machine that we should be aware of.
Careful about you know, what do you mean? That's the machine the machine the government the government power Which is unleashed to destroy an individual a brilliant individual and you say was because he's gay No, he wasn't because he was different. Uh-huh. So more broadly speaking societal norms or the government in particular
What I mean to say is the machine in general for us, is it in your mind, is it the government or is it societal norms or is it? I don't know. I purposely drop this word because the machine could mean computer or artificial intelligence, which people are arguing about now, whether it has the power to subjugate humans and so on.
So here is a man who actually theorized that possibility in the most advanced way possible during and he's actually destroyed by a machine of a different kind. Interesting. I see how interesting. I'm not, I don't, I'm not going to spoil it by revealing the punch line. You know, let's think about this. Let's think about what does this tell us? What does it tell us?
In other words, he was so inconvenient somehow, and this is a man who was instrumental in deciphering the enigma machine, you know, who has contributed so much to the defense of the United Kingdom. And how many years passed before they finally apologized for what they did, or at least acknowledged the government of UK? What does it tell us? Is this like an isolated incident? Or is this something that has been kind of a norm?
that somebody who is different, somebody who is different, no matter how much they contributed to a given society is ostracized and ultimately destroyed. So how do you not get destroyed from thinking about, well, okay, you mentioned self-awareness, self-awareness. So he is a man who was self-aware, you see, and that's why I would like to, I would like to,
Emphasize this point and I would like more people to pay attention and say Alan Turing could do that. Can I also look in a kind of, what's the word, a neutral kind of way on the things without emotional investment in it? But look at the facts, way different ideas, different opinions without being engaging in ad homino attacks or, you know, like getting overly
emotional about it. Can I? And if not, and if I can't, let's find out why. Let's find out what is really what within me is creating trouble, so to speak. And it's not a bad thing. It's not a bad thing. Is there something that's bad about being emotional about it? Because you're clearly passionate about what you're saying. But I wouldn't say that what you said is wrong because it means you're emotional. So yes, but it's important for me to know where it comes from.
You did ask me this, and I can explain briefly. But yes, I'm not arguing that there shouldn't be passion. Of course, this is the engine of progress. But the question is, your passion comes from something you're aware of, or something in your unconscious. And that is essential. Because if I'm not aware of what is actually driving me,
chances are i'm not actually going to be effective even if i am proposing good ideas and so on because there's too much spurious stuff i'd mix which are on me which i can resolve within me i don't need albert einstein to resolve it for me or alan turing i can resolve it myself if i'm interested you see
Yeah, specifically speaking, how did you come to this? How do you realize quote unquote realize I have to be careful about how did I get interested in this subject? More like let's say you have predilections or flaws or pros and cons, but they're unconscious. And then to go back to this onion metaphor. That's right. There's a finite layer, but you can start to peel away the layers. What is this process of peeling for you? Is it I go to therapy?
Is it I read a certain amount of books and I ask myself this is it I meditate the process is different for everyone. Yes, there isn't one I believe there's no one formula.
Actually, all the methods. Yeah, it's useful to hear the stories from people who have gone through. Absolutely. I think that we absolutely the way the best way that we can address this is by actually sharing our stories and not trying to say it should be done this way or that way. Yeah, but this is was the first step. You see, this is what led me to the process of self inquiry. So I already mentioned how
It led me to question for instance why am i doing mathematics am i doing it because i love it or am i doing it because i want to achieve recognition and awards and so on that's what was one of the things came out of it but the much bigger thing that came out of is the whole idea of self-inquiry the whole idea that there are some things which are not aware of the question who am i i thought i heard this question before i knew that it was inscribed on the apollo the apollo temple in delphi but i didn't understand what it meant
Who am I? I'm Edward Frankel. I'm a Berkeley professor. It's a dangerous question. It's a very dangerous question when you actually engage with it, for real. Yeah, it's a terrifying question. And we can't do it on our own, I think, because ultimately it has to be somebody in your life. So it could be a therapist, for instance. In my case, I was lucky. There was some human being who just came into my world, who was a wise woman, let's just say, a wise woman, and somebody I respected.
who, and this is about a year after the book came out, so this is summer of 2014. The book was published in October 2013. So I was ready to go beyond from Edward 1.0 to Edward 2.0. You have to be ready for it in some sense, and then the universe, quote unquote, will conspire. At least that's what happened to me, and I have since heard stories, similar stories from other people.
So what happened was that she basically, so we start talking about life and so on. And I was very curious about reality. What is reality? Because I was obsessed with the idea that where mathematics comes from. It was very clear to me, it doesn't come from human minds, specific human minds. Like Pythagoras did not create Pythagoras theorem, you know? Or Evariste Galois did not create Galois groups. They were there for him to discover. But then what does it mean? What is reality then? What is at the base of reality?
And in fact, if you look and the title of my book is love and math and the subtitle is the heart of hidden reality. So it's kind of like my search for hidden reality was happening, even if I was not fully aware of what I'm doing, even when I was writing it. And then the crucial thing that she told me, she said, yes, Edward, there is hidden reality, quote unquote, but it's not outside. You think you find it somewhere. In fact, it's within you. You have to learn more about yourself. And so.
What does it mean? She told me some stories of what it means, what it meant in her case that she was able to connect to some childhood experiences that she had when she was an adult already. And that completely changed her view, her outlook. And suddenly things start happening. I started remembering things that happened to me as a child. In particular, the experience that I described in the book.
chapter three about my exam when i was 16 years old and i was not accepted was not was failed ruthlessly at the exam at moscow university i thought i knew i remembered it i remembered it factually i remembered it as a third person from a third person perspective but i did not remember it from the first person and so then suddenly this happened in september of 2014
where i was asked to speak about it and the night before at my hotel i was able to connect with a boy and it was like a tsunami i realize what happened what did you break down crying of course but it was it was worse because in some sense it was worse because the thought that i had in my mind was no amount of tears justify this world justify this life why what is the point
oh jeez it's really really kind of sad moment because you realize a part of you died i realized part of me died when i was 16 years old and i was not even aware of it for 30 years okay so i am moving is the battlefield of life crippled basically like i'm missing a limb and i'm not even aware of it and my mind my course my concept don't look there don't look there don't look there that's why i was coming up with all of these ideas about the universe and reality the objective reality and so on because how convenient
It's all deterministic and it's all a bag of particles. So particles don't feel pain or a human is an algorithm. So it's a coping mechanism. Coping mechanism for me, for me, it definitely was. And I will never say that it's true for everybody. Maybe it is for some people. Maybe it's not. All I'm doing, I'm sharing my story. This is my story. I am convinced that some of the naive and quite frankly ideas that I entertained about the world.
were to a large extent motivated by me not willing to find out what happened to me when I was 16 years old, because it was too painful. Because it was too painful. I wrote a piece about this, by the way, I was asked to, I spoken about this number of times, including my last conversation with Lex Reedman. But I also wrote a short piece for volume by
my my my friend who is an expert Kim Polsky who is a friend who is an expert on AI safety so he published a volume I'll link it in the description yeah academic volume on AI safety and security and he asked me to contribute about first person perspective so I wrote about this and to what extent this defined me you know not knowing not knowing because then
your life becomes driven to a large extent by creating barriers of finding out and that's what it means who you are who am i right so i understood what it means if i if there is this part of me which i chopped off why because it was too painful so it is a defense mechanism nothing wrong with it we all happens to all of us i believe to some extent and there is a lot of literature about this by the way and neuroscience confirmations and so on so
But it's me, it's part of me, and yet I'm no longer connected to it. So do I know who I am? No, because there is this part of me which I'm not connected to. So that's one way in which you can, it becomes a very practical question. Who am I? Am I aware of all my secret little adverts?
And not necessarily, it could happen in adolescence and in adult life, but most traumatic experience, most difficult experiences usually happen when the children were not yet equipped to deal with this pain. And for me, it definitely defined my life. It gave me a lot of fuel, it propelled me to become a mathematician and so to achieve and so on, to prove those guys who failed me that how good I am, you see.
Five years after I failed at 16, I get a letter from the president of Harvard University inviting me to come to Harvard as a visiting professor. I'm barely 21 because I wrote some papers which became famous or well known. You know why? Because the drive, you know, but then the cost of it, the downside of it is that I'm not, I lose that spontaneity, spontaneity of a child.
that ability to look at the world with fresh eyes. I'm afraid of things. I'm scared. I want control. I want safety. Do you feel like that was a cause that if you were able to rewind time, you wouldn't pay? Because another perspective is, you know what, Edward? Everything that happened to you made you. I did it myself. Of course. Of course. I would not change a thing.
but i can say it only now because i have connected to that child i connect to some other painful experiences that i can say it if somebody came to me before it happened and told me that edward you should be grateful to your examiners who failed you because that's what gave made you who you are i would just hit them in the face like what are you talking about how dare you but now of course i know yes of course i would not change a thing it was all me all along
And I am not, uh, no qualms about it. I would not have been who I am without any of those experiences unless I still refuse to connect to them. If I'm still refusing, then I'm not myself fully. You see what I mean? And so you ask, how did I get interested in the subject? So then this is 2014. Then I started getting invited to various forums to speak about this thing. And that's when that was the first wave when AI
became controversial. This is, mind you, nine years ago. But already you had people like Stephen Hawking and Elon Musk and Bill Gates already voiced concerns. And so this becomes my playground, this conversation, because I think up until that point, I haven't sort of this half asleep state.
where i'm still i'm still thinking partially about myself as a kind of a machine i would like to be a machine because the machine doesn't feel pain so you know kind of feel safe also i feel that i know how things work again feel makes me feel in control you know suddenly i all of that is swept away my child my inner child you know such becomes such a trope um i don't want to use this expression but um
But it's true. It's like you again, this dimension, this dimension over, uh, you know, you talked about this, this archetype of divine child. That's the part of you which always wants to grow, which wants to look at the world in a fresh, with a fresh eyes, which is spontaneous, which is spontaneous, which is playful. I lost it to a large extent because my real, my connection to a very specific child, 16 year old Edward was severe.
I am going opposite extreme and i'm saying
So then for me, AI becomes this idea of AI, the idea of uploading the singularity and uploading your mind and so on. It becomes totally opposite to what I'm experiencing, right? It almost becomes the idea of me being captured by this, again, by my cerebral side.
because ultimately for me, this discussion with AI, it's just a safe way to talk about ourselves. AI represents our, our, um, cerebral logical side, like in the movie, uh, the 2001 space odyssey by, by the great Stanley Kubrick, how 9,000, what is how 9,000 is that the cerebral part of Dave Bowman, the astronaut, which has run amok. I know if you're familiar with this movie. Yes, yes, yes, yes.
so that becomes the motivation for this for this for this interest you see and so ultimately i understand also that we need to find balance because of course this is amazing technological innovations and there's nothing wrong with them as long as we put the phrase the phrase our inquiry our questions properly not as a question of
It's not a good way, are they thinking, are they conscious, are they intelligent? The question is to what extent they help, they are here to facilitate, to help me to be as good an Edward as I can be. It's like artists in the end of 19th century, beginning of 20th century after photography was discovered. So suddenly you don't need to be, being an artist is not about rendering things realistically.
Because a camera can do it better than you. So what do you do if artists say? It's over for us. We become the captives, the slaves of the photo camera. No, they discover other ways to express themselves. That's how you get impressionism, abstract art.
Cubism, surrealism, and so on, where the focus is more on the experience of the viewer and the artist. You see, they accepted the challenge and it propelled them to the next level. And likewise for us, I think, it's very clear that Ciao GPT is showing us
But some of the things that perhaps we thought were creative, they're not that creative. The computer program, which is basically trained on just correlations of things in various texts throughout the internet, can actually reproduce it and maybe do a better job than you do. So I take it as a challenge. What am I bringing to the table if this computer program can replace these things? So what can I do that it cannot do? Yes. You see? Yeah. So there's something called
The moving of the goalpost fallacy, which I don't see as always a fallacy. So for instance, you just mentioned we thought that creativity was the ability to draw accurately. Let's say in the early days. That's right. Then we realized, okay, something else can do that. So we changed what creative means. But it's not because in the one sense, you can say we've moved the goalpost, but it's not a fallacy because our original definition reflects our ignorance.
we realize because we can grow. That's the whole point. Everybody, especially I love it when it comes from people who actually completely sold on evolution. They say it's only, it's only force in development of say human beings or other species. You may agree or disagree with it. And some people say that maybe there are some other things that have to be taken account. I'm not going to make a judgment, but I'm just curious. What do you think evolution is?
Human beings if it's not this is a very good example How we can evolve is because we are challenged by the technology that we ourselves create Now this is a very different framework a very different mindset that the mindset of the sort of end of the world And how these things are going to capture us and kill us and so on it's not productive obviously But this challenge take it as a challenge take how you respond to it You know, I think it's very productive
I'm not saying something original. I've heard a lot of people say that. It's just that it's not necessarily represented in the debate that you could see in the media, because usually it's computer scientists who are being questioned. And let me tell you, if somebody asked me 10 years ago, before I started to ask the question, who am I? I would have given you an answer. Very confidently.
You know, maybe that's another sign that you shouldn't trust someone is how assertive and how little self doubt do they show. I want to be personal, if you don't mind, and reveal something to you. Maybe this will go and maybe it won't. When you mentioned, look, you had some childhood issues. I've always heard this like childhood issues, childhood issues, and I've explored my childhood. I can't find issues. But then I realized, okay, well, you said 16. So I think I had well,
When I was 17, I had my heart so broken. I don't think it's been broken as much since ever. And man, with this podcast, Edward, almost with everything I do, I struggle so hard. I struggle, struggle, struggle, struggle, struggle. I push, and there's this ambition, competitiveness, and
There's a desire in me. It has to be the best. It has to be undeniably the best. Like when I interview someone, it has to be that someone could watch all the interviews of that person say this whole series of everything was the deepest with this person. And luckily, luckily, often I'll get the interviewees saying something like, like this, these were insightful questions. I've never been asked this or whatever. Okay. So I get some validation or from the commenters, but, but
So I'd often think, you know what, I don't have childhood issues, I have adult issues. Meaning that like, I have this distinct feeling that 10 years from now, I'll look at myself now and want to hug him. Like just say, Hey, man, like you, I'm sorry, like I'm broken now. But I also think that much of that comes from crippling feelings of self doubt and inadequacy from when I was 17.
Sure, exactly right. Exactly right. And then the thing is, in what you say, it resonates completely. But one thing one has to be very careful of saying, there was no issue with it. It's our thinking mind who says that. Our thinking mind is very limited. So Jung, one of the main ideas that he brought sort of out and became part of our collective discourse is the idea of unconscious.
Freud talked about subconscious, I prefer unconscious. So this idea that there are some realms of the psyche which are not accessible to the thinking mind yet. And it's very important to accept that, I think, because then it's not anymore that the thinking mind is the final arbiter of what did or did not happen. In my case, if you ask me in 2014, before I had my sort of experience of reconnection,
Are you connected to that boy that was suffered in 1984 in this exam? I would say yes, of course, because I remember every fact of it. And in fact, I wrote it. I wrote the story in my book, which was published a year before. Interestingly enough, a lot of people were inspired by it.
and a lot of people wrote to me or talked to me about it, that they were touched by it. And I was surprised because I was not yet touched by it. But because that's the power of art. Because I wanted to write a book and to connect to my readers, I allowed the boy to speak. I was not yet ready to speak to the boy, me, adult Edward, in 2013 or 2012. But because I wanted the book to be real,
I delegated this chapter to him and was the first time that he was unfiltered. He spoke not to me yet. He spoke to the readers of the book, but the ice was broken. So we are barely a year later. I finally found the courage and the strength to speak to him directly and to understand, to remember what happened. So my thinking mind was not aware of it. It's very important to understand and it's, it cannot force it.
it's very important not to force because if you're not ready for it i could commit suicide easily easily i could see that easily because you're so disenchanted you're so disappointed in this in this cruel cruel world you feel like there is no reason to live and you have to be very strong to to withstand that and in fact the point is that it passes it passed and i have this amazing experience of like
He comes alive. He's within me. Like I hold him. He's here. And I, and I, and I spoke to him to the little Edward and I said, look, you know, I'm sorry. I have neglected you for 30 years. I did not know, but look what we have done. Look what we have done. It was not in vain. It was not in vain. And now you're back and I will never let anybody hurt you. What did the little boy say in response? It was just beaming, you know, and
The next day I was invited to speak at this spoken word kind of event in New York in 2014. There is actually audio of it on my website. It's called a test. And I spoke and the boy spoke and it was like, I never experienced that kind of connection with the audience. It was the first time he actually spoke through a microphone into the audience because he was with me. I let him speak. So the point I was trying to make is that when we are ready,
If we're sincere, if we are not actively trying to prevent this type of experience, it will happen. Don't try to force it, but always ask when something is off, like when you feel get agitated. For me, it's like this, you get agitated unnecessarily triggered. What is the source? When was the first time I experienced that? Under what circumstances? So that kind of gives a path to finding out the source, because usually some kind of event
It could be a series of things. It may not be just a single event, I suppose. But most powerful are events, like you said, when we get broken. And it doesn't have to be a child. It could be adolescent, teenager. It could even be a young adult. But an experience as a young adult, once you process it, it may lead you to an experience as a teenager and which can lead you to an experience when you were six years old or something.
There is nothing wrong, ultimately it becomes this beautiful journey.
self discovery is beautiful because it's you you learn more about yourself people go you know like columbus you have to get on the ship and try to find india then he doesn't find india he finds america and so on here it's you you're here you cannot run away from yourself anyway and it becomes a beautiful process of self discovery and each time a new layer is left you see you start for me it's like this it's been like this i start saying things which i couldn't see before
and i'm pretty sure it influenced my mathematics also did you feel like a weight was lifted and you're actually even physically more flexible oh of course oh it's on the level of body it's an incredible uh restructuring which by the way is another way so there is yoga there's meditation all kinds of things which are also
meant to reconnect us to this other dimension. The problem is for somebody like me is in the mind, I'm in the mind, I'm in the mind, in the mind, meaning like the cerebral logical stuff, and I become a prisoner of it, that I try to apply that becomes my only tool. So if I'm confused, if I'm, if I'm not sure, it means used to be in for me, think about it harder, think about it more. That's the only way
Through logic, through reason, and so on. William James said that that's like trying to see more of the darkness by turning up the gas. Yeah, or it's like trying to find darkness with a lamp at night. You know, just where is it? Where is it? Or, you know, trying to find the white snow when you have orange-skinned glasses on you. Where is the white? Where is the white? Let me put on more glasses, more glasses. More, more yellow, more yellow.
I mean, it's very clear. So the thing is, and then going back to your earlier question, if you asked me 10 years ago about AI and all this stuff, or, you know, before all this experience. So of course I'll give you a particular answer because I actually chose mathematics as a way to escape from reality because the reality was too cruel for me. I didn't want to deal with this stuff. So I found this what I consider to be a pure world of platonic forms where there was no bigotry.
There was nobody to hurt me where I could just rebel in the beauty of it, you know, and don't bother me with your so-called wicked world, you know. So then how can you trust me? So some people, then people would come if they came to me and they, because they look up to me as a scientist, as a mathematician, so I have some expertise that they don't have. They would trust me to give them a kind of a wise answer, but I was not capable of giving a wise answer.
What's up what's up.
a good answer, but people don't realize because they think of us as their gurus, you know, and because they don't have, because our education system is broken. And also the popular book sometimes suggests things which are like, I go like, Whoa, this is 19th century science, which has been thoroughly repudiated by 20th century math and physics. So that's where we are. But I think luckily because of you have your, your podcasts and others,
And I think that it starts moving, it starts moving finally in the right direction. And the right direction is understanding that our personality, our first person perspective is intricately connected, is intertwined with our series. They do not exist on their own and we are not independent spectators and observers. We are in the thick of it. With you forgiving your examiners,
Did you have to, well, okay, firstly, do you still feel like you're able to forgive them? Or is there a part of you that? Absolutely. They suffered. I know one of them actually, um, it came to my attention that one of them around the same time when I was, um, reconnecting 2014, he died in a, he w he was a kind of a, he liked to go on hiking trips, like in the north of Russia alone.
And they found his body and he died in one of those trips in 2014. And the other one, I don't know, the other guy, I don't know. But I absolutely believe that they suffered. They must have suffered. I mean, how do you feel by
If you do this to a young kid who's done nothing wrong, right? So it's just because of my Jewish name, last name, my dad is Jewish. So Franko is a Jewish name. My mom's Russian, by the way, you know, by, by blood, you know, and not religious at all and so on. And then yet you single out somebody like that. And then they give this, you give this hard questions. It's a setup, right? So this is well documented. I'm trying to say, I see that they must have suffered.
I see that they were misguided. And so that's number one. And number two, also, you know, thank you for giving me all this fuel. Without which, I mean, if I was accepted to Moscow University, oh boy, I would be living in a dorm. Okay. And probably party like there is no tomorrow. Would I become a good mathematician? I'm not sure. Which okay, would still be an interesting life.
But this definitely shaped my life in a particular way and brought me to places which I may not have been able to reach otherwise. So in some sense, yes, thank you. It sounds weird, but it's only because my boy is here and he's not going to let me lie. You know, it's not going to say he's laughing with me. It's like, yeah.
That's the paradox. That's the transformation of life. That is evolution and growth from somebody who is not willing to look that pain in the eye, so to speak, you know, face that reality and therefore is bound to run away from certain experiences in life or from certain insights or from certain ways of understanding life to someone who becomes friends with that.
through suffering of course through suffering you cannot avoid it in my opinion and by the way you know it's not i am i listen to there's a great conversation uh you know but in lex pridman and uh you are karate you know that you wrote sapiens and a great historian and writer and he's something he said a bunch of things which i really resonate with me he's suffering he's a human this is what
distinguishes that from robots ultimately. So in other words, Turing had this imitation game where you have a conversation with an interrogator and the robot is trying to convince the interrogator that it is human. But in fact, the real criterion is can it suffer? Because that is, I would say unavoidable, an essential part of human life. You know, and so
Running away from it limits us. Being able to process it liberates us. That's my view. Okay. Again, I preface it by saying that's been true for me. It may not be the case for everyone else. I don't know. I have no way of knowing. I do have anecdotal evidence that it works for other people in this way too, but I cannot be sure. Is your forgiveness of your examiners predicated on them suffering?
So that is to say, if you thought that they didn't suffer, would you still forgive them? This Marshawn beast mode Lynch prize pick is making sports season even more fun on projects. Whether you're a football fan, a basketball fan, you always feel good to be ranked right now. New users get $50 instantly in line up when you play your first five hours. The app is simple to use. Pick two or more players. Pick more or less on their stat projections.
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Good question. Good question.
I mean, like I said, there are two aspects of it. First of all, me recognizing that they may have suffered themselves. And second, my gratitude for participating in this experience, which gave me so much fuel that it launched me into the stratosphere. So they were participants in this, maybe motivated by something
You're making me realize something, which is that I, so again, I don't know how much of this I'll keep in, but for myself with when I was 17, I would say that, oh no, no, no, I forgive this person because I'm the wretched, sordid, despicable person who
who looks at other people who are successful and I'm like, I have no mentor. I, when I went to university, like I had depression for seven years. So I skipped classes. I didn't have a peer group and I would look at people who are successful and be like, yeah, well that's because you had advantages and I didn't. So in a sense it's like a prisoner with a door locked from the inside. And I say all of this with some, well with a large amount of saltiness and, and just,
Because I'm trying to be blunt, but also because I'm overcompensating for my urge to sugarcoat it. And I just lost years of my life. And so I would point the finger at myself. And I think part of the problem is
is that some of what was done to me, let's just put that in quotations, was not okay. But I'm not able to say that because I have to point the finger to myself. But then subconsciously, I'm still pointing the finger at someone else. And that's okay. Don't force it. That's my advice. In other words, don't forgive prematurely because then it means you're trying to short circuit something. That's my view. There may well be something
for you to discover in this memory, in this memory. Don't try to do it fast. What's the point of, you know, it's like Alan Watts said, you know, when you play music, the purpose is not to get to the end of the piece. Because if that were the case, then the fastest musicians would be the best. No, it's the point is to play. And so just be open, maybe be open to the idea that there is more to discover.
Hey, who knows? Yeah.
that that the struggle, sorry, not suffering. I don't I don't I don't suffer. Sure, whatever, whatever. Yeah, more and more. I've been biking recently, Edward. So and there's this new feeling, a new feeling. I don't know how to describe it other than when I look out at the world, it's like a it's like the feeling when you're extremely thirsty and then you take a gulp, but it's of satisfaction and beauty. Something like being transfixed by
the splendor of the world or amazement. Something I look out, I'm like, whoa, and I haven't seen that for my entire life, except for the past few months, like more and more and more. And I don't know where I was going with that. But what I'm saying is that despite all of this talk, like of working super, super hard, working hard, like understanding different physical theories and dealing with consciousness theories, like that's rattling.
And at the same time, juggling editing, family obligations, so on so. Okay, this is what an honor that I get to speak with you. Like, holy moly, you're like for years, I actually, I didn't I remember recognizing your face. And you've influenced me years ago, and I'd forgotten. And now I get to speak with you. Now I get to read your book and speak with the author.
I get to study the Langlands program. I get to make contributions that stay in math
Man, what lives. Yeah, well, it's it's beautiful. It is beautiful. Edward. OK, one last thing. Now I feel guilty because this is something that comes up is that whenever I have this feeling of, wow, look how great life is. Then I think, yeah, but most other people or at least in my mind, most other people and many other people are suffering. Who am I to feel so good? And then that impinges. And it prevents me from fully appreciating a moment because I'm like, yeah, but there are people who are starving. Yeah, but there are people who can't make ends meet.
And yeah, but there are people who so and so and so. So how do you ever struggle with that? And how do you deal with that? No, of course. But I don't know. I feel that we cannot do it. But we have a life, a human being that has limited resources, we have limited life, you know, like in terms of time, longevity, you know, how many years we got, we have limited spatial dimensions, and so on. And resources, energy. So the question is not to spread themselves thin. And
That's why i'm not so happy when people go on twitter and they start venting their anger because it actually means run away from your true responsibilities. It's cheap to go and accuse and blame on people. It's an emotional discharge. So if you really care about this, just go to that war zone and go to that poor country and so on and do it. Do it. Action is not the same as words which are not supported by action.
so so then what's the what's the how to resolve what's the resolution of this resolution is to find what you truly love and dedicate yourself to it hundred percent and this way you will contribute in a positive way to the society and then your own you know self-recriminations and thoughts about you deserve don't deserve and so on is is you're blocking yourself from being fully dedicating and really impacting it takes energy away
that's how i see it that's like self-doubt it's natural i'm not i'm not saying it's not it's where i'm i'm given to sometimes two bouts of self-doubt and self criticism and so on it's normal i think but ideally ideally i would like i consider it as something that is a waste and the way to
to overcome it is to truly do what you love and and just keep going with it and look you know how successful your podcast is for instance you know it's only been around a couple of years you have so many some people such a dedicated audience and really great interviews you know i've watched a bunch of them so that's how that's what we can do when we really dedicate ourselves to something that we truly love and i think that's the that's the only way we can do is human beings what else can we do
we be aware of yourself be aware of the world be aware of the suffering in the world but also be aware that you cannot go you cannot pretend that you are the almighty god who is going to solve everything for everybody no that's not how we set up you have your mission it's not also it's not like a mission which is written which is given by somebody i feel like it's it happens as we go you choose it as you are live it's part of life
But if you're open, you don't believe it's co-created, like there's a part that's innate and there's a part that you choose. It's a narrative. So maybe, who knows? I feel like all of this, what you described, any such theory is a theory, is a story that we tell ourselves and
We are human. A very important essential part of being human is the ability to tell stories to each other and to ourselves. By the way, this is where I love Yuval Harari also. He explains very clearly the history of ours.
Civilization is a history of ideas and and stories that mostly still I not even ideas stories We tell each other stories and it creates this sort of market of stories and they evolve and they merge and they separate and Who knows how it happens, but we also tell ourselves stories now in this story Stories are different. So if it's if it's helping me to Be the best I can be and this is something which we can feel right?
Am I on the right path? Am I not on the right path? Kind of. It kind of like a general sense. Then okay, go along with the story, be open to changing the story at some point when it becomes more of a hindrance than something that propels you, you know. So what you described is a very reasonable way to think about things. But I've tried many other ways to approach and conceptualize and
My feeling today is that sometimes I need it, sometimes I don't, sometimes I just feel, you know, sometimes I'm guided by something like you described, that there is this higher self and lower self and this collaboration between the two or something.
Sometimes I feel that I don't need it. It changes. But what's important is not to say it's like that. And that's it. That's would be theory. Right, right. Death is love exposed. That's a quotation from a wise man. Oh, yeah. Yeah. Do you know who said this? You said this.
Death is love at its barest or at its most exposed, its most wrong. Yes, when you are faced with death, this is when you face unfiltered love. Yeah, explain that, please. Well, I feel like, you know, death is something that does not accept any spurious stuff. For instance, you can
I specifically talked about my experience when my father died four and a half years ago. And we were very close and I was devastated by it. And I tried, I was kind of mature enough, so to speak, to ask myself to say, just live through it and observe and observe what is happening, what is happening here. So I was able to see these things, which maybe if I was just completely
Overwhelmed by grief, we wouldn't be able to see. And what I saw was that there was a natural tendency to come up with some explanation of what's going on. It's like we just discussed, you know, that story, some story, but they, they could not hold those stories. Like they melted in the face of that. Like this is staring at you and any stories you throw at it, took a story to protect yourself.
So then what is it then? And then why do I feel so much pain? And then I realized that the intensity is simply my realization that my father, you know, my father, well, you could say my father's gone, I will not be able to spend time with him and to, to laugh together and to enjoy things together. But also why does it bother me so much? Because I love him. So the root of it is love. And then I thought the reason why it is so painful is because
Normally, we put filters because we pretend that it's two different beings communicating with each other. But ultimately, when you're in love, and I strongly believe in this, you cannot love another. You always love. When it is true love in this moment of experiencing it, you become one. It could be your father, your parent, it could be your friend, it could be your lover, your partner, you know.
But this is a kind of cornerstone of the Eastern tradition for me, this idea of oneness. And it sounds, it has been perverted, obviously, by new agey stuff and all this kind of when it becomes, it makes it a bit facile, you know, a bit too facetious, you know. But the corner, the core of idea, the core idea is precisely that, in my interpretation, is that the moment of love is the moment when a separate being
It ceases to exist when the boundary melts. Whether we conceptualize it this way or not, it doesn't matter. We feel it. We feel this very strong emotion. It's a particular way of conceptualizing it, of course, but I think it's a helpful one because ultimately it points out to another way of cognition, which is not tainted by the sense of a separate being, which is to me the root of a lot of suffering is the idea that there is a separate being actually.
I can always argue to what extent it's real and to what extent is a construct. Obviously, it's a very useful concept since I'm using it, you know, but it's important to know that there are other ways of experiencing life and love to me is what points to it, what points to the ability to experience life without the burden of an idea of there being a separate individual who is experiencing it.
But something bigger, something bigger than that. And so death is one experience where one is force. If indeed who died is somebody you deeply love. I think that in this experience that that comes to the fore that it's a sense of love so intense that it feels like pain.
Well, Professor, I have so many questions on algebraic varieties and L functions and automorphic sheaves, but this was an unexpected turn and I hope to speak with you again. I appreciate you spending so much time with me. That's my pleasure. Well, we talk, I just want to comment on this. We talk about what interests us.
Yeah, well, speaking of not architecting prior to engaging, like the union conception of what true art is versus constructing the CN Tower beforehand. The other option is you just like watch the diffusion of an ink drop and Bohm would call that the unfoldment and you just go where it flows.
Yeah, that's what it felt. And it's good that we can do it because I think that most interesting things in some sense are the surprise, things which are not pre-set or kind of like premeditated, but the things which arise spontaneously kind of, you know? And so that's why I really enjoyed it too. I had a question from Richard Borchards, to you.
Okay. Yeah, his question was, what role do function fields play in higher dimensional algebraic varieties in the Langlands program? So we may as well just touch on a couple math questions. Oh, yeah, yeah, yeah, for sure. So, well, Richard Burch person was my colleague at UC Berkeley. It's a very brilliant mathematician.
He won the Fields Medal, but also, you know, apart from that, he did some groundbreaking, really, really amazing work. He was the first one to formalize the concept of a vertex algebra, which has actually been a staple in my research. And he proved the moonshine conjecture. And he's a very, very nice human being as well. So I'm kind of pleased to have a question from him.
What he's asking about is the following. So we just talked a little bit about the language program. So language program, a regional formulation is for number fields, for numbers, numerical systems, like. Reels, complex and so on. That's right. But on the other side of it is the human surfaces. Which are like sphere or surface of a donut and so on. And so Andre Vey in his Rosetta Stone that we discussed,
he found a bridge between the two which is very similar on one side you have this vertical systems on the other side you have this geometry of surfaces and the the bridge that he found is the following you should look at instead of looking at the surface itself you look at functions on it and these functions are they're going to be what's called meromorphic functions or rational functions so they have they have zeros and poles that sometimes at some points are not defined they go to infinity
and this gives you what's called the function field of the Riemann surface from which you can basically recover it and that field is very much like the number field like rational numbers but what stands in between is when you take a so Riemann surface as a curve from the point of view of algebraic geometry it's a curve over complex numbers but you can also so it's defined by some equations with complex coefficients renormal equations with complex coefficients
coefficients in the field of complex numbers. But you can also write such equations with coefficients in other numerical systems, for example, in finite fields. So modular prime, modular prime, like clock arithmetic, modular prime numbers. And then it really becomes that the function field of that is really very much like, like rational numbers or a field of rational number. And so this way you found a bridge between the two. So that's what is referred to as a function field case.
But in the Langlands program, it's about curves. So it's one-dimensional, geometrical objects. And what Richard is asking, what about two-dimensional? Now, Riemann surface ostensibly is two-dimensional from the point of view as a real manifold, right? And so a sphere has a longitude and altitude, no, longitude and latitude, right?
two coordinates, so its real dimension is two, but its complex dimension, because remember complex numbers are two dimensional over the real numbers, because there is square root of negative one, there is an independent element. So complex numbers are two dimensional from the perspective of real numbers, therefore a two dimensional real thing is one dimensional from the perspective of complex numbers. So as a complex geometric shape it's one dimensional,
So the question is, can you extend the ideas of the language program to two dimensional objects or three dimensional and so on? And unfortunately today with the very few, there is very little information about this, very scant. So there's a few examples where some analog exists, but by and large we don't have a picture. So the answer is in the negative right now. But the hope is that eventually we will be, it was just much more complex, I guess.
You know, you had a chapter in your book called A Delicate Dance. I think it's chapter 16. Doesn't matter. The point is that in it, you had a film script. You spoke about you and Drinfield. Yes, right. Yeah. Why did you choose to frame it like that? Because I have been a cinema aficionado, you know, a film lover for many years. I also co-directed a star in a short film.
I was given a lot of trouble. Yeah, you co-directed and started. I co-directed, co-wrote and started in it. It's called Rights and Love and Math. Rights like R-I-T-E-S. And also I wrote a script. I actually wrote a script for a feature film with my friend and mentor, Thomas Farber, who's a writer and teaches literature, creative writing at UC Berkeley.
So we wrote a script called The Two-Body Problem about a writer and a mathematician who meet in the south of France and they talk about their love affairs, hearts broken and so on and how to become, how to be better humans. So I, for instance, I had a software, I had a script writing software already and I thought that
It's always good to put it in a kind of artistic framework. Since my job was to shake people's understanding of what mathematics is like. So for instance, there are these boring people talking to each other about some boring stuff. So I want to make it come more alive. So I was suggesting, imagine it as a movie, as a Netflix series, which by the way, you know,
This thought came to me because I watched on your channel, on your podcast, you had a conversation, a debate between two very brilliant people, Sabine Hassenfelder and Bernardo Castro. I've never met Sabine in person, but I've followed her a little bit. And Bernardo I have actually met. And they argued about super determinism.
And to me, I watched it like a great Netflix series, episode of a Netflix series. It was like the impact in terms of like, there's so many subtleties there. There's so many layers. And there's such, we could do a whole conversation of me like trying to unpack that. But I'm just trying to say,
I am lucky to have the expertise to follow the discussion and actually have my own opinions and so on, but also to observe the psychology. So to me, it was a case study in what we discussed earlier, how much our
preferences, like psychological, metaphysical, philosophical, how much they are, how intricate, how intertwined they are with our theory, supposedly abstract theories of supposed objective reality, how much we are driven and passionate about certain ideas. You know, it was a case study for both of them, actually, and they were because they were so sincere about it.
Interesting. You felt both were staunch in their opinion. Sorry, for the people who are watching, the link to that will be in the description. And it's the debate between Bernardo Castro and Sabine Haassenfelder called the new theory or new super determinism, something like that. It'll be in the description. It's fascinating because, you know, I don't know, I just want to say it's such an it's actually brought me to read some stuff about it. And I find it very
So in this case, the way I see it is that Sabin is very adamant about the particular idea that is local determinism. She wants to preserve it. And where does it come from? So of course, she probably would deny that this is really her preference, but that's what comes across. I have no horse in this race, okay? I'm just looking as an observer. And it's very clear that
she is sometimes a little too emotional about it like for instance she basically says this people who don't understand it are idiots but not quite paraphrasing she by and large she was incredibly you know gracious she was very calm and so on but i also read some other stuff she wrote about it and saw a video and sometimes she goes a little overboard but also like i see how
So the way she wants to sacrifice this was called Statistical Independence and Bernard was arguing that then science is over. I think that he's exaggerating too a little bit. So for him, obviously, the Statistical Independence is dear and local determinism is not. You see, but then neither of them would actually come out and say, look, this is what I hold dear to me. And that's why I build a theory around it. They wouldn't say that. They would say,
But of course you can't do that because then science would be finished or something, both of them kind of, because this is where I feel this is where we can make one more step as a community. Where we really would advance as as scientists and human beings is when we will admit to ourselves to what extent we are motivated by dearly held principles.
Like, why does Sabin care about local determinism so much? I'm asking for a friend, you know, like maybe if she finds out, if she finds out, maybe she'll learn something about herself. I can tell you why I don't care about it, for instance, because I think the world is inherently indeterministic. In my experience, it's not. But also for me, actually, this is not so essential with this Bell's experiment, the
Entanglement is not a big deal. What is a big deal in quantum mechanics is non-commutativity. The observables, familiar observables like coordinate, momentum, and so on, which in classical physics, they commute with each other. They're like numbers or functions. They become non-commutative. That's why they have to be realized as accurate. And this non-commutativity is an absolutely essential phenomenon.
Now, mind you, the commutator between, say, momentum operator and coordinate operator is very small. It's proportional to the Planck constant. So classical physics, therefore, can be thought of as a limit of quantum when the Planck constant goes to zero. Likewise, Newtonian mechanics can be thought of as a limit of Einstein's special relativity when the speed of light goes to infinity. And likewise,
In general relativity, we have curved spacetime and it's our traditional view was that we live in the Euclidean space, which has no curvature. So there are three parameters, non-zero parameters that were introduced in the 20th century. The Planck constant, which makes the world non-commutative. And to me, I feel that it is a very essential thing and it is fundamental. And if you accept that, I don't think super-determinism can save you. I have not really studied this.
even if you drop um that is going depends and so on there will be phenomena which will not in principle you cannot describe by classical physics because it is commutative so you're trying to feed non-commutative world into commutative world i don't think it's possible but i'm not 100 sure to me it's a feature not a bug likewise the fact that
The speed of light is finite, and it's the same to all observers, which is the feature of special activity. It's a special thing. It's not something you fight. My question would be, how much do we want to sacrifice of the things we have discovered in the 20th century to accommodate our belief systems? For instance, let's suppose I am interested in preservation of local determinism. So then I'm willing to postulate that my experimental apparatus somehow magically
he is
It's undoubtedly crazy. The question is whether it's crazy enough. So the fact that it's weird to me doesn't mean it's wrong. So I keep open mind. It may well be that super determinism will become prevalent scientific theory in the next few years. Who knows? I would not be surprised to argue that it's impossible because it's weird is disingenuous.
You know, for me, the point is not that. The point is that, let's admit why this is put as the forefront of a theory. It's because of a preference. You know, there is this Samuelson, the great economist had this theory called revealed preference in economics, that sometimes observing agents behavior, you can actually find out what their preferences are. That's called the revealed preference. To me, it's a revealed preference. So
Then my question is, okay, so suppose you have a preference for preservation of local determinism and you're willing to sacrifice this, this and this. Okay. Suppose you have a preference for classical Newtonian mechanics, how much you willing to sacrifice to pretend that Einstein's relativity can be accommodated by experimental apparatus. So for instance, we know that what happens, one of the predictions of special relativity is
that as you move faster, time slows down and distances shrink, right? How much you're willing to ascribe it to some kind of conspiracy between detectors that you use in your experimental apparatus. Like, I don't think anybody asked super determinists this question, like, would you be willing also to do that? And if not, why not? Also, Einstein's generativity says there is curvature.
The curvature of space-time is the signature of gravity. Suppose you are an adherent of Euclidean geometry and you don't believe it's true, because when I look outside of my window, I don't see any curvature. Well, except curvature of the Earth, but I talk about the curvature of space-time. How far are you willing to go to preserve zero curvature in your theory by ascribing different observed phenomena? For instance, Eddington discovered that
You know, famously in 1919, Arthur Eddington's expedition discovered that the ray of light bends around the massive star. Let's suppose you, and this is considered as experimental verification of Einstein's relativity, the fact that space-time is curved around massive bodies emitting gravitational force.
Let's suppose that you like Euclidean geometry, and you are adamant that the world is Euclidean. No courage. Are you willing to then say that your experiment is playing away all this experimental data by saying that we should look deeper into how these measuring devices are set up? Maybe there is some weird communication between them, which we are not aware of, which creates this illusion.
Now i have to be consistent so if you say yes in principle you could do that you could do that and it's kind of one we are kind of like in the same game here because for us super determinists is very essential to believe that there is local determinism we are willing to sacrifice other aspects of our theory to accommodate this then it's a it's a different story but
Ask this questions to also see maybe to what extent you are investing yourself and your preferences into your city something you may actually use others for example she has been extremely sad been. How's it feel extremely helpful in unraveling sort of this.
policy of the strength theory and the fact that practitioners of strength theory still not willing to admit the failure of their enterprise. Sabin has been extremely positive in my opinion in this. She wrote a whole book called Lost in Math saying that we are led astray by our preferences for what we consider beauty and so on. But can we also be led astray by our preferences for certain philosophy or metaphysics?
And it's always nice, easy to see it in other people. Can we see it in ourselves that we're actually doing something very similar? Now, then the next question is, do I see it in me too? Because I'm now saying, I'm not criticizing actually, I'm trying to explain why to me it was like an amazing Netflix movie. Unfortunately, you need to have some background to understand.
But if you do, it is an incredible case study in how we are being human, and it's normal. But it shows to me also, it helps me, it's almost, I want to say thank you so much for showing this to me so clearly. It's informative about yourself. Yes, because I'm also, and by the way, it extends beyond science. How often, you know, do I find myself
in my life, in my personal life, adhering to certain ideas, knowing full well that there is no proof for them, but it's just like how I want it to be. And then suffering is a result. And to see in a microcosm, this process, how we fool ourselves, how easy it is for us to fool ourselves. You know? Also, for instance, she goes like,
I really want to work on this because I am alarmed by the fact that the collapse of the wave function happens faster than the speed of light. But excuse me, quantum mechanics contradict special relativity. Everybody knows this. That's the whole point. That's why we have the next level theory, which is called quantum field theory. I have not yet seen any super determinism addressing local determinism.
In the framework of quantum field theory, they tried to do it in quantum mechanics, and then they- Okay, so this has been a bit too harsh on Sabin. So to be fair now, what would you say about Bernardo? No, he was a bit harsh on her, that's what I would say. But I'm just saying, Schrodinger equation is non-relativistic. It has a first-order time derivative, second-order coordinate, space derivative.
So it is not relativistic. So therefore to say that the collapse of the wave function is somehow alarming to us, but how about Schrodinger equation? It's also not relativistic. You see what I'm saying? But it's such a subtle point that it is lost because like most people don't really pay attention to this. I'm trying to say, I, I feel it. I am like this too. I'm not trying to criticize. You know, Richard Hamming? Yeah. Yeah. He said something which jives completely with what you're saying.
It's something I wrote down, but I'm going to paraphrase. It's that we tend to think that we arrive at our interpretations of quantum mechanics. But he said, you start with God, even as a secular person, and then you see which interpretation is most consistent with that. I think, look, the beautiful thing to me is like, my approach is,
It's all beautiful. It's all beautiful. I love seeing both of them. And I wouldn't change a thing. And I don't want them to change except one little thing. Ask yourself, each of us ask ourselves, what is driving us really here? And is it really just scientific principles or there is some preference in it? And it's a very small thing. It's not no shame in having a preference. There's no shame in it.
of course i do i do just be aware of it because that's what leads us astray i think is not being aware that's all but i think the idea is very interesting it is worth exploring
It is not fair to say that you shouldn't explore because it sounds crazy or whatever. You know, like it's weird. Quantum mechanics is weird. So also Bernardo said something I disagree. He's like, so basically you're saying that the moon depends what you see in the moon. It depends on how you set up your apparatus detector. But we know that in quantum mechanics, the result depends on how you set up your apparatus. If you do a double-seed experiment without detectors, you will see the interference pattern. If you do it with a detector,
You will see barricades behavior. So it's not, it's not an argument either. You see what I mean? We are all in, we are in the jungle. You know, we are in the jungle. We're trying to find our way. Let's cooperate. Let's cooperate. And let's understand that we all want the same thing. We want to the best theory, the most beautiful theory, the most interesting theory, the one which fits with experiment on this path, on this journey. We are informed by many things.
Which are personal and nothing wrong with it. Just accept it and this will give us maybe new insights. Over email you mentioned you want to speak about String Theory or the Hans Bethe Ansatz. So String Theory is a good example of where people have gone astray and Sabina has been one of the people that called them on this correctly in my opinion. Was this the example you were thinking of earlier when you had said you can recapitulate and not me? Yeah, so the theory
A theory of everything, you know, it's like this idea that I was recently invited to a conference, Sting Theory Conference, and it was a very interesting experience for me to not just look at it abstractly, but to actually interact with people who consider themselves Sting Theorists. And
I saw that. A KFC tale in the pursuit of flavor. The holidays were tricky for the Colonel. He loved people, but he also loved peace and quiet. So he cooked up KFC's 499 Chicken Pot Pie. Warm, flaky, with savory sauce and vegetables. It's a tender chicken-filled excuse to get some time to yourself and step away from decking the halls. Whatever that means. The Colonel lived so we could chicken. KFC's Chicken Pot Pie. The best 499 you'll spend this season.
It's not a very healthy kind of situation where it's still not been acknowledged by... A bit too much hubris? Not hubris. I think it's more like unwillingness to accept responsibility. Which is, again, totally human, you know?
It's hard. When was the last time I accepted this responsibility? So maybe I will start with myself. I'm not a string theorist. I've never been a string theorist. But I have collaborated with Edward Witten, who my great respect. And yes, I found it over the years very useful to drop the names and say, I collaborate with Witten, you know, I know something about string theory, because when I talk to my non-science friends, so
Also in Love and Math I talk about string theory, but I'm kind of trying to be diplomatic about it. That it's great for mathematics and physically it hasn't quite worked, but maybe. The fact of the matter is that the original promise of string theory, which was to describe this universe by using a theory which starts out in 10 dimensions of space-time,
has not worked out and nobody knows how in principle it could work and it's already been a situation for at least 10 years yet this is not acknowledged and how can you move forward and achieve greatness if you're still pretending that your original program is somehow
If you're not acknowledging that your original program failed, it's just a kind of like a simple question at the human level, not even scientific level. I did not see that. And I saw young people very brilliant, but confused because their elders are not giving them proper guidance. That's my impression. I may be wrong. I may be completely off base here, but I sensed that
They're already not doing string theory properly. So very few talks were about string theory actually proper. And the kind of stuff people work on that I discussed. It's quantum field theory more generally, or maybe study of black holes and stuff like that. But the original promise was
We will find the collaboration of many photos in which six dimensional, which will do away with the six dimensions. And then we will get the physics of this four dimensional universe. It has not worked out and nobody knows how to do it apart from some ideas of what's called landscape, this multiverse and so on, which I think a lot of people find problematic. Right. So, so this to me is an example of
How again our personal interferes with the project which is of science. Unwillingness to accept reality of it.
You know, it doesn't mean that the people should be, it's not, I'm not saying nobody needs to be punished. No needs to be punished. I understand. So what is a string theorist to do? When you say acknowledge, what is the goal? Is it Ed Whitten writes an article? Is it, he goes on a podium? Is it, he sends an email out and then what happens afterward? What does a string theorist do after one spends four decades, five decades studying it and then says this wasn't fruitful?
But then are they going to continue studying it for the next decade? I'll tell you what not to do. Okay, how about this? Let me start with that simple thing. So this I'm actually supposed that not even wrong. Blog by Peter White, Peter White was one of the one of the early critics. He's coming on the podcast in a couple of weeks. Yeah, yeah, it's great. Yeah, he's great. And he was very brave.
Because I do remember what happened. He was one of the lone voice. He and Lee Smallin at the time were basically the only voices. Also, they were ostracized. They were ostracized. They were criticized like they were stupid. They didn't understand, you know. And for instance, how about in Nepal? How about an apology or at least acknowledgement? OK, so maybe he was not so stupid. After all, Peter Voigt or Lee Smallin, maybe actually they were
saying something which was meaningful how about that but also like i'm looking here so in um august of 19 there was so there is a video discussion about super gravity and so on and there's a quote here so i haven't actually watched the video but i i trust that peter void transcribed it correctly andy strominger who is a harvard professor uh and one of the leaders of string theory i mean i greatly respect of course he's a great scientist
Here's what he said. I think that the idea that people were excited about back in 1995 was really a small thing. That's the idea of describing the physics of this universe from string theory. So he says, it was really a small thing, you know, to kind of complete that table that you put down at the beginning of the spectrum of particles.
Who cares about that, right? So except how much resources were taken to fulfill, to fulfill this promise, right? That was a big promise. And that was the idea on the, because of which I think there is used to say it's only game in town. If you want to do statistical physics, you better come to us because nobody else is doing anything interesting. Right? So now in 2019, we hear from one of the leaders,
I think that this idea was actually a really small thing. Okay. We didn't do that. We didn't predict new things that were going to be measured at the Large Hadron Collider. But what has happened is so much more exciting than our original vision. We are getting little hints of a radical new view of the nature of space and time in which it really just is an approximate concept emerging from something deeper.
That is really, really more exciting. So, in other words, so first of all, correct, the beautiful ideas came out of string theory. But that was not the original promise of string theory. The original promise was to describe the physics of this universe, to unify all forces of nature, the three forces, electromagnetic, strong and weak, described by the standard model and the quantum theory of gravity. This has not happened.
And now we hear that actually was not such a big deal, such a big thing. We've learned so much more. It's like, you know, I tried to think of a good analogy. It's like, remember Moses, you took Israelites out of Egypt and he told them that he will lead them to the promised land. Yes. So imagine Moses after 40 years of wandering in the desert.
You would say, you know, guys, this idea of a promised land is not such a big thing. Look how much we've learned. We've learned about the desert. We've learned so much about the sand. That's a great analogy. Who cares about the promised land? What do you think would people say to him? And yet here we are. It's, you know, this is what this is called, by the way, people call you mentioned this expression, moving the goalposts.
This is not moving goalposts. This is going to a different stadium. It's starting to play a different game. Like you used to play soccer at one stadium. Then you go to another stadium. You start playing baseball and you say, no, we are playing soccer. We're still playing soccer. Yes, yes, yes. Stating that your original goal is not meaningful. It did not work out. It did not work out. How about just starting with that? It did not work out unequivocally. Not by saying the next 10 years. You know, I saw a great video.
I don't know if you know this channel. She's called Angela Collier. You know, she has a very nice YouTube channel and she did a video about string theory and I really enjoyed it. She kind of, and one of the things that she kept saying, like she traced the evolution 90s to 2000s and so on. And each time she's like, just wait another 10 years, just wait another 10 years.
That's the attitude even today. I am sorry to say, you know, what, how does, if a young person who is in the subject, it's still called string theory. Okay. You have to go to conferences, string theory, and maybe 20% of the talks are about string theory. The rest is about other things. People are already doing other things. It's like, you know, in the Soviet Union, when I was growing up, before Gorbachev, like eighties, early eighties, everybody already did not believe in the ideology.
They did their own thing, but people were still trapped. Because the official ideology, official party line is this. So you have to somehow accommodate it. You know, so for instance, if you work in the history of social science, you always start preface every article you write with the great comrade Lenin said this, you know, things like that. What a liberation it is when you don't have to do it anymore. What a
Wait, so in this analogy, what would be the equivalent of praising Lenin or Marx? Because when you go to a string conference, not like you're saying, hey, string theory is great. Now here's my talk. The string theory somehow is still true. It's still trying to search, still trying to describe this universe. It's not because, well, there are some people trying, but there's so many at least say that
It did not work out the way we expected. People thought, and I also understand, to be carried away as a human being, it's natural. The theory is beautiful. And I have to say also very strongly that it has impacted mathematics in incredibly powerful ways. For instance, what Stromilus talks about is real, the idea of emergence of space-time.
And the different space times can appear at different limits of the same theory, like mirror symmetry, stuff like that, incredibly powerful. Okay. But yes, this came up. But what about your original promise? What about your original promise? The idea was that you find what this thing, there is only defined super string theory in 10 dimensions of space time. You have to find six dimensions, which extra.
because what we observe is four dimensions of space-time. So, the idea was we will find the right manifold, the right shape on which to compactify. Reasonable, reasonable. What turned out is that there are too many choices. But there is more. Actually, there's one question I said, you cannot pin it down.
It's worse because actually dynamically it doesn't stay static. It changes also the Calabi-Yau because our modular space of Calabi-Yau is not rigid. Many of them are not. So it's moving and it becomes singular and nobody knows what to do with this. So in other words, the magnitude of the problem. Yes, it's possible that somebody can solve it. And I'm not saying this should not work on it. Of course work on it.
But they shouldn't deride other attempts. But they were extremely heavy handed. There is no question, like in the same blog of Peter Voigt, I suggest people to read a testimony from David E. Kaplan. He gave an interview, it says post from October 22. It's a devastating, devastating testimony of someone who was not a string theorist in the heyday of string theory and what he felt about it. How many others felt the same way?
Not to acknowledge it, not to admit that this would happen. And the original promise did not pan out. It's something that holds people back. In my opinion, they have to be free. You have to liberate it from this weight. And the only people who can do it are the leaders of the theory. And it doesn't take much. It just opened the door a little bit for the possibility that our original project did not work out.
Let's see what we can make out of what we have. How do you think Ed Whitten would respond if he heard what you said? You've collaborated with him. You know, you're part of that community or adjacent to that community. I'm adjacent and I've been paying lip service to this community. I have to admit. So in the interest of following my own admonition of like, what's, what is Edwards and meaning Edward Frankel, not Edward Whitten. What is Edward Frankel's involvement?
I was never a Sting Theorist, but I paid the lip service because it was convenient to me. It was nice for me to feel that I am collaborating with such great physicists.
that I would write in love and math that yeah, who knows, maybe they will find this collabio when I knew full well that it seems way more. I didn't know that. I didn't say it in this input in this world, but I was kind of giving the validity given in principle, kind of paying lip service to it. Okay, so maybe not yet, but as this woman who has Angela, you know, said, and then you wait in the next 10 years. So I was kind of giving lip service to it. You see,
That's my contribution and which I see now was unhelpful. And I am grateful that there were people like Peter Voigt and Lee Small and Sabin Hassenfelder as well who were principled about it. Eric Weinstein as well. Eric Weinstein. Yes. Yes, absolutely. Eric Weinstein.
Who said this for many years? They were had a principled approach to it. And you know, it's always like this, because you don't want to say because you don't want to offend anybody. I understand. But at some point, you ask, what is the interest of the community as opposed to the interest of a single human being or a few single few individuals? Yeah, how do you think the leaders would react to what you just said? Let's let's let's find out.
forward this to Ed. Look, I look, I respect, I want to say I respect all the people. I just want to say I respect and I think they're brilliant. There's no question, brilliant, absolutely brilliant. And I am honored that I'm honored to have collaborate with with him. No, no doubt about it. We're talking here about not so much about science involved, but the way human element
Somehow it became the theme of our conversation. So I kind of felt that this would be appropriate. Appropriate because also is one theory which purported to which sold itself as a theory of everything. You know, and so now 40 years later, after 40 years wandering in the desert, we hear that actually this promised land is not a big deal. That's not how you deal with this. That's not we've seen that happen in history. It is detrimental. It puts a burden on young people who are
This is a recent opinion of yours now because you've given this talk at the strings conference. I have not spoken about this publicly other than I tweeted a little bit about it.
I was at the conference, I was invited to give a challenge talk about mathematical developments. And I put a lot of effort into it. I put a lot of effort into it. I was very sincere. And I went there with an open mind. What I saw and experienced during this week, five days in this conference was what led me to reconsider my position.
and led me to speak about it now, say what I have just said. Because on the one hand, I saw brilliant young minds. Yes. On the other hand, I saw the leaders and no hint from the leaders that somehow maybe we need to rebrand or pivot or evolve, you know.
Does this strike a nerve with you because you also see a parallel with what happened to you when you were 16, which is this older generation leading astray the younger one? No, or no, that's too loose of an analogy.
I don't know how you make this connection. No, of course it is, of course, but because I put myself in position of this young people. So, you know what I mean? So yes, of course, but this only proves that. I'm not saying that makes it irrelevant or that impacts the power of it. But see, I am aware, I am aware, I am aware that my sensitivity of this.
And so you're also able to observe it much like
People who advocate for breast cancer research, maybe someone who was close to them was affected. It doesn't mean breast cancer, you shouldn't invest in it just because you have a personal motivation. No, no, I'm able to see it. I'm able to feel it. And now before we go, something else that you mentioned on the Lex program, and you didn't say that it was a large problem in math, but the problem of sometimes not giving credit where credit is due. You've seen this happen a couple times.
You mentioned that in other fields there's some unsaid ethical rules, but in math there isn't, maybe in physics. Do you mind expounding on that? Well, it's again integrity and like, you know, but it's a human community. So this is the thing, which I think is the root of it is we like to think that we are this impartial arbiters of pure science and that we're driven by purely by the interest of science. And I have, I,
I have no doubt that we would like to aspire to be like that. To what extent we actually can is not clear to me by observing myself, first of all. And so my suggestion is that it's like, you know, Aldous Huxley talked about the idea about power that we have to have
Restrictions on power and we gave an interview to CBS. It's a beautiful video. And the interviewer, Mike Wallace, great journalist. It's really fantastic. Like he's smoking a cigarette, you know, it's like in the 50s and he says, why, why do we have to put this is because the whole point is that power is dangerous. It's because people can succumb to the temptation of power. That's why you have to restrict it. That's the whole point.
Because the idea that somehow unrestricted power can be good for anyone has been repudiated and disproved by centuries and millennia of human history. And it's the same, it's the same, I think, with the idea of, you know, that somehow my personal preferences are not involved.
in what I do in science. Today we have discussed several examples of
We seem to suggest that this is not so, or it's not so simple. It's, it's much more subtle somehow than that. You see? And so I think that we will not get to the next level of our evolution because also people say, okay, who cares? How many people involved hundreds, maybe a few thousand, but it's like Henry. It's a canary in a coal mine. In my opinion, we are the Vanguard. We scientists, we are the Vanguard. First of all, because you think it bleeds out into the public. Yes.
Because people unconsciously, they feel it. And actually, Angela Collier, she makes this point. She actually says people got felt that they were lied to with string theory. And now they are fed up with physics. They don't want, they said, you lied to us. And I think, okay, I think so maybe a little hard, too harsh, but she definitely has a point. So for instance, then people will not be so interested in the developments of theoretical physics, maybe for next decade or something, because they got burned. They feel that they were like,
And a lot of the things people feel it, even if they don't know how to verbalize it, they feel it. You see, so if we don't get our house in order, and when I say our house, I don't mean strength, I mean science in general, we also have the other side of flip side of it is this people, so called AI practitioners who are feeding lies to people, telling them that AI is already here and you should pray to our AI overlords, that they will not destroy you, stuff like that, you know.
In each of these instances, what I think will help us to go to the next level and to do the job that we're supposed to do. Which is? Is to realize how much our personal psychology, our personal aesthetic, metaphysical, philosophical preferences
how much they are intertwined with what you do as scientists. Just acknowledge that and then use it as a starting point for self-inquiry and to raise your self-awareness. The same goes with the attributions and papers and so on. And sometimes much lesser issue in my opinion. If you have a subject where the leaders of the subject still cannot acknowledge that mistakes were made, you know, mistakes were made, lessons were learned.
Before we close, for me to take responsibility for a lack of attribution on my part unintentional, but it was still
a lack of attribution. I did this video on quantum gravity, the controversial history of quantum gravity's connection to antigravity. I didn't credit Eric Weinstein in the video itself, because I didn't use him as a source directly. I used other people like David Kaiser and a few others as sources. And I didn't know that some of the people that I had used as sources used Erica sources and didn't credit him. And so I just feel bad about that. And so Eric, if you're watching like, unfortunately, YouTube doesn't allow you to
extend a video, but I can change it. You can put a comment. You can put a comment. Yeah, I did put a comment and I know I'm leaving this and I apologize. And so see, that's what I'm talking about. This is what I'm talking about. This is, I admire, you know, I admire, admire you for this for accepting responsibility. It's much easier to, you know, the authority of is to find excuses. Yeah, but yes, if he was involved, but that somehow did this other people did not quote him. So it's not my fault. You see, this, this is a difference.
And you're not going down that road. And thank you for that. Because, you know, that's how we change it, because we change our own. Well, thank you, because you inspired me, honestly, in many ways, not only through this conversation, but others that I've seen of you, like on Lexus and also in this book. Well, thank you, Kurt. Thank you. Me overcoming my embarrassment of, like, I find myself being begrudging, if I'm being honest.
because there are some other podcasters who have large names who have helped them and they're tweeting about them and I don't have any of that. We can all exhale because something is weighing on us when there is something which is not true. It's weighing on us and when that simple thing of just acknowledging is such a breath of fresh air that we can all take a breath, exhale and move on. That's all.
Well, again, man, oh man, what a conversation. Thank you. Thank you. Okay. I think this is the second time, one hour apart that I said, all right, let's end it. That just shows you what an engrossing, well, how grossing the topics are and how fun this was. Thank you. A lot of interesting stuff. So thank you for the grid. I really enjoyed it.
All right. Well, I hope you enjoyed that podcast. It's almost three hours over three hour podcast. Thank you for sticking all the way to the end. Hope you enjoyed it. I think you have because you're still here. I want to recommend a couple videos, a couple podcasts from theories of everything. If you liked this podcast, you'll like the ones that I'm about to recommend. But I'd also like to acknowledge a comment every episode from now on, or at least every other episode. I'm going to highlight one of your comments.
The reason is that I don't know if you're like me, but I love talking about these subjects. I love dealing with these subjects. But it's not like we have, at least for me, many people in my personal life to speak to about it. So in a sense, it's just relegated to speaking to the screen or conversing with people over text. And many people take the time to write detailed comments, which I love because I read almost every single comment. And I would like to encourage.
This comment comes from user Bijou with the pseudonym Acronon Master and it's on the Carlo Rovelli clip called There's No Wave Function of the Universe that will be linked in the description. Bijou says one way of viewing quantum mechanics is as a measurement theory. To measure the universe, you really have to be outside the universe. So yes, in that sense, you could have a wave function of the universe, but it would do you no good. By definition, if you're external and conducting measurements, you'd be interacting with the system.
So you'd not be truly separate from the system. You'd be at least coupled to it by whatever means you have from making the measurement. So in that sense, there could not literally be a the universe, quote unquote. I do like aspects of relational quantum mechanics. The trouble is RQM is like the mother of all bootstraps, something in brackets, Rovelli's God. And I know he considers himself atheistic.
Which is not a scientific stance, so whatever has to be absolute for everything else to gauge off of, so to speak. Okay, you can read the rest of the comment by going to that video. You'll see and I didn't plan this that there's even a reference.
to the interpretations of quantum mechanics having to do with our conception of God or even the lack of God and reasoning backward from these prejudicial axioms rather than what we think of which is hey I'm this rational being I'm going to reason forward to my interpretation or to my conclusions. Now if you liked this episode then you'll enjoy the Bernardo Castro solo episode that's
Somewhere on screen here and it'll also be in the description as well as the Sabina Haassenfelder interview with Bernardo Castro where they talk about super determinism clip that was just mentioned with Carl Orveli will also be in the description and the clip with Neil deGrasse Tyson that was alluded to about philosophy is quote unquote useless or that philosophy is little to contribute to modern day physics and mathematics.
Also, because Richard Borchards asked a question, you may not know this, but Richard Borchards was interviewed twice on theories of everything. Part one and part two are linked in the description as well. Thank you so much for your viewership. And I'm glad or at least I hope that you enjoy this episode.
The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked that like button, now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. You should also know that there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, disagree respectfully about theories, and build as a community our own toes.
Links to both are in the description. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc., it shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well.
Last but not least, you should know that this podcast is on iTunes, it's on Spotify, it's on every one of the audio platforms. Just type in theories of everything and you'll find it. Often I gain from rewatching lectures and podcasts and I read that in the comments, hey, toll listeners also gain from replaying. So how about instead re-listening on those platforms?
iTunes, Spotify, Google Podcasts, whichever podcast catcher you use. If you'd like to support more conversations like this, then do consider visiting patreon.com slash Kurt Jaimungal and donating with whatever you like. Again, it's support from the sponsors and you that allow me to work on toe full time. You get early access to ad free audio episodes there as well. For instance, this episode was released a few days earlier. Every dollar helps far more than you think. Either way, your viewership is generosity enough.
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"index": 6,
"start_time": 136.954,
"text": " Also, to be clear, certain representations of those Kakmudi algebras are realized as vector operator algebras. VOAs aren't an extension of Kakmudi. As usual, timestamps to everything mentioned are in the description, as well as links to everything mentioned are in the description. You can even skip this intro if you like. More important than the math, this podcast delves into Edward's personal reflections. Edward touches on what it means to reconnect with yourself, and he does so while confronting vast topics like infinity, death, and"
},
{
"end_time": 193.148,
"index": 7,
"start_time": 166.766,
"text": " My name is Kurt J. Mungle, and on this channel, I use my background in mathematical physics to analyze various theories of everything from Wolfram's to string theory. We even explore consciousness and AI. As an aside, though this is an important theme in this conversation, is a theme that I resonate with from The Lord of the Rings, which is the story where Frodo gets stabbed by a special blade early on in the book."
},
{
"end_time": 222.739,
"index": 8,
"start_time": 193.575,
"text": " And then toward the end of the book, while everyone else is happy and the problems are resolved, including with Frodo, he succeeded in what he was attempting to do, the scar never heals. The wound still hurts him years and years later. And the lesson or the symbolism is that there are some things that can happen to you that don't go away. There are some wounds that while on the surface they heal, they shape you. That's always touched me. That touches me more than any other aspect of Lord of the Rings. And it's something that comes up in this conversation."
},
{
"end_time": 251.015,
"index": 9,
"start_time": 222.739,
"text": " Enjoy this revelatory podcast, this intimate podcast with Professor of Mathematics at Berkeley, Edward Frankel, one of my favorite podcasts. Welcome, Professor Frankel. Thank you. I've been very much looking forward to this conversation for weeks and weeks. So it's an honor. I'm happy. I'm privileged. Thank you for coming on. It's my pleasure. It's great to be here on being interviewed by you, Kurt. You know, I have"
},
{
"end_time": 278.097,
"index": 10,
"start_time": 251.732,
"text": " Watch some of the videos on your channel and found them inspiring and fascinating. So I'm glad to join the family. Even that's an honor that you've watched that you've heard of the channel, let alone watch some of them. What are you up to these days? And what excites you about it? Okay. Well, well, I'm a mathematician and, and the Berkeley professor. And so my"
},
{
"end_time": 305.828,
"index": 11,
"start_time": 278.916,
"text": " I feel like my day job, in other words, something that has been the constant throughout my life, is my research. Teaching too, but research is something that I have really devoted, I suppose, most of my energy in, you know, in my adult life. So my research is on a subject which is called the Langlands program. It's named after mathematician Robert Langlands."
},
{
"end_time": 332.722,
"index": 12,
"start_time": 306.596,
"text": " who is a professor emeritus now at the Institute for Advanced Study in Princeton, where, you know, I always like to mention that he used to occupy the office that was formerly Albert Einstein's office at the Institute. So in the late 1960s, Langlands came up with a bunch of conjectures and ideas, which became known as Langlands program."
},
{
"end_time": 362.142,
"index": 13,
"start_time": 333.097,
"text": " And what this is, what it was originally, was trying to connect, uh, seemingly unrelated questions in different parts of mathematics, specifically number theory on one side and harmonic analysis on the other side. And we can talk more about this if you like later, I can explain more detail, but just, just to set the stage. So this is something that excited mathematicians for several generations, more than 50 years, obviously. And."
},
{
"end_time": 392.432,
"index": 14,
"start_time": 362.756,
"text": " In the 1980s a new sort of a new domain in the language program emerged which has to do with things that are connected not so much to number theory but to geometry and eventually quantum physics and it has to do with what's called Riemann surfaces such as a sphere or the surface of a donut and so on, so called Riemann surfaces. And so my research has been on this subject for many years but"
},
{
"end_time": 421.152,
"index": 15,
"start_time": 392.773,
"text": " There was something interesting about it that distinguished it from the original formulation of the language program. And the language program, it's about functions and operators acting on functions. It's actually, you know, we can think about it in terms of quantum mechanics. There's Hilbert space and there is some computing operators acting in the Hilbert space. And we want to diagonalize them. We want to find their eigenvectors and eigenvalues. That's the original formulation. But in the geometric formulation,"
},
{
"end_time": 449.821,
"index": 16,
"start_time": 421.834,
"text": " People couldn't find it initially, a framework like that. So instead, what was proposed was that it should be about this weird esoteric object called sheaves. And so it became known as a geometrical English correspondence. But in the last five years or so with my two colleagues, Pavel Ettingov and David Kasdan, we were able to find this new formulation in the geometric setting, in the setting of Riemann surfaces."
},
{
"end_time": 474.053,
"index": 17,
"start_time": 450.128,
"text": " where in fact we do have a Hilbert space and we do have computing operators and we can pose the question of their finding the eigenvectors and eigenvalues. And so it's kind of a new flavor of the language program. So something that really excited me for the last five years, you know, it's so interesting because for me, it's been like my research has been, it's not been like a linear path in some sense. So like for a long time, it was, you know, like when you're young and ambitious,"
},
{
"end_time": 503.933,
"index": 18,
"start_time": 475.009,
"text": " You want to be the best that you can be. And it's all about achieving and kind of like finding your place in the community and so on. So, and so then that was kind of a period of rapid growth. And then, then at some point I kind of realized, I started asking myself, why am I doing this? You know, so what's, am I doing it because I want to achieve something, recognition or awards, or am I doing it really because I love it? You see,"
},
{
"end_time": 533.814,
"index": 19,
"start_time": 504.224,
"text": " and it's not so easy in a later point in life to to regain that you know and so there was kind of a period where I suppose I was a little jaded you know maybe about 10 years ago well conveniently around that time I wrote my book Love and Math and so I was in high demand for public speaking and so on so it's kind of like it worked out actually in a way that gave me a little more time to reflect and so interestingly enough"
},
{
"end_time": 563.712,
"index": 20,
"start_time": 535.009,
"text": " I did remember that excitement that I had as a student, as a teenager, as in my early twenties, where I literally went to sleep, I went to fall asleep faster so I could wake up in the morning and resume my inquiry, my asking those questions and working on this. And so I kind of regained, I kind of remembered this. It was so exciting. So I'm just kind of trying to give you a sense where I am."
},
{
"end_time": 581.971,
"index": 21,
"start_time": 564.036,
"text": " This project especially, which like I said, I've been working on for about five years now and it still excites me and it's still something that I feel that there are so many interesting questions there that draw my attention."
},
{
"end_time": 606.288,
"index": 22,
"start_time": 582.722,
"text": " This appetite that you have to be number one or that you used to have when you were in your younger years, the striving, you said that you started to question it and think, okay, well, what am I truly motivated by? That's right. Versus what do I want other people to recognize me for? When did you start to question that? You mentioned 10 years ago. Yeah, yeah, maybe about 10 years ago."
},
{
"end_time": 625.742,
"index": 23,
"start_time": 606.749,
"text": " I read this book cover to cover. And when I say cover to cover, I mean, including the index and the glossary. So I love this book. Oh, thank you."
},
{
"end_time": 652.875,
"index": 24,
"start_time": 626.408,
"text": " Thank you, thank you, appreciate it. The book is called Love and Math, and it'll be in the description. It's on screen right now if you're watching this on video. The first half is like an ode to mathematics in general. This is my perspective, so you have your own. And then the last half is some, I'm surprised if anyone who isn't a mathematician can keep up with the last half. But it's something that for me, who is extremely interested in math was extremely interested in, especially love the dictionaries."
},
{
"end_time": 681.169,
"index": 25,
"start_time": 653.729,
"text": " Which by the way are like translation dictionaries. Mathematicians call them dictionaries, but they're more like translation dictionaries or thesauruses because you can substitute the words. Whereas a dictionary is like a word and then you have a longer word that defines it. Whereas a translation dictionary is the Rosetta Stone. Rosetta Stone, yes. And I do frame it as Rosetta Stone, right? And it is about the language program. It's exactly the subject that I gave a brief outline of just now."
},
{
"end_time": 711.049,
"index": 26,
"start_time": 681.51,
"text": " I would love to talk to you about the process of writing this book later on this interview as well, if you don't mind. Yeah, sure, sure. Of course. But anyway, we're getting to you questioning your own motivations, how that came about, how that unfolded and where that led you now. Yes. So, you know, it's so interesting. Well, you're an artist, so you know how it works. It's the results when you actually dedicate yourself to an artistic project. You cannot know what will come out. And of course, a true dedication means that you"
},
{
"end_time": 726.527,
"index": 27,
"start_time": 712.056,
"text": " you it's sincere it's a sincere effort you want to connect your audience right so i wanted to connect my audience i wanted them to be excited about the subject so what the primary motivation for writing love and math for me was that."
},
{
"end_time": 757.005,
"index": 28,
"start_time": 727.432,
"text": " I thought that nobody knows what mathematics is really about, apart from a very small elite, a very small group of people, professional mathematicians like myself. And I opened the book with this analogy of saying, imagine you had an art class in which they only taught you how to paint fences and walls and never taught you the paintings of the great masters, never showed them to you, never even told you that they existed, never told you there were museums where you could go and look at them. What would you think of art?"
},
{
"end_time": 786.493,
"index": 29,
"start_time": 757.449,
"text": " The art, the way art is presented to you is just painting fences and walls and then watching paint dry. So, of course, years later you'll say, art is not for me, okay, so it's not something I financially, you know, maybe there are these weird people who like painting fences and walls, but if I ever need that, I will just hire someone to do it. And that's it. So then they completely miss what this is all about. In both cases, of course, paint is involved, but in very different ways. And so I felt my job was to try to convey that."
},
{
"end_time": 807.79,
"index": 30,
"start_time": 786.869,
"text": " what is it about what are these things what are the picassos of mathematics you know and cutting through the you know obviously if you have to if you are math major you take courses and it takes a long time but i was i wanted to address the general audience people who don't have time to go and and take classes and and and learn the basics and i wanted to cut through those"
},
{
"end_time": 826.937,
"index": 31,
"start_time": 807.79,
"text": " I sort of the technical stuff and just get to the sense of your sense of what is like what are the objects we talking about we're not talking about numbers. Necessarily right we're not talking about quadratic equations we're not talking to you clearly in geometry all the subjects that we are it's a very limited part of mathematics that will get exposed."
},
{
"end_time": 846.357,
"index": 32,
"start_time": 826.937,
"text": " What is this like what is it also what is it like to do it what is it like why did i get excited about it so i wanted to couple it was a human story."
},
{
"end_time": 875.759,
"index": 33,
"start_time": 847.039,
"text": " Okay, so that's the initial motivation. In other words, I set out to write this book to teach something, to teach the world something, to connect to my readers, to let them experience something which perhaps they haven't had a chance to experience yet. But in a weird way, what art does is if you're successful in connecting to your audience, guess what? You will receive feedback too from the book. It's a two-way street. This is what's amazing thing about art. With mathematics, by the way, not quite so because we operate and such."
},
{
"end_time": 906.049,
"index": 34,
"start_time": 876.049,
"text": " Within such you know a rigid framework very rigorous rules and so on so it's not as It is a passionate pursuit, but I discovered that you know Writing a book or earlier I had a chance to be involved in filmmaking and now recently I started you know recording my DJ sets electronic music I discovered that I discovered that this is a totally different game"
},
{
"end_time": 934.667,
"index": 35,
"start_time": 906.715,
"text": " And because not only you have a chance to give something to your audience, but also you receive something if you are sincere, if you really put your heart to it. And so in that sense, the book was a revelation for me. I learned so many things about it. It catalyzed a process of self-inquiry, you could say, where I start questioning things about myself, about my life, about my outlook."
},
{
"end_time": 962.193,
"index": 36,
"start_time": 935.811,
"text": " In a very strange way, like it wasn't programmed in some sense. It was just like happening, you know, and it brought me to in contact with people who helped me to accelerate that process. And one of the questions like, you know, as I mentioned, one of the questions was indeed what is this all about? Why am I doing this? You know, is it real? By that time I understood that it's not real if it is just driven by ambition."
},
{
"end_time": 980.981,
"index": 37,
"start_time": 963.046,
"text": " uh and and the desire to be recognized and rewarded it's not real it may still be have a real undercurrent but it's not fully real and the sooner one realizes that the better um you know so that was that that's how i came to that question but then there were other things too i"
},
{
"end_time": 1005.776,
"index": 38,
"start_time": 981.374,
"text": " I realized to what extent we are driven by our emotions, you know, that scientists would like to pretend that we are these sterile beings and we're just analyzing the so-called objective reality, but nothing to do with me. There is this, electrons are weird, but not me. It has nothing to do with my life, you know. So I suddenly realized how much I'm driven by this undercurrent of emotions and unconsciously"
},
{
"end_time": 1029.07,
"index": 39,
"start_time": 1006.152,
"text": " I'm aware of all those weird processes that are happening in my psyche. And that's when it brought me to reading a lot of interesting stuff like Carl Jung is one of my teachers. I've read a lot of Carl Jung and Marie-Louise von Franz, one of his students, because, you know, I love both Jung and von Franz. And to me, it's like a source, endless source of inspiration and insight."
},
{
"end_time": 1058.524,
"index": 40,
"start_time": 1029.497,
"text": " I'd like to add to that. So you mentioned that art is a bit different than math, because there's more, at least if it's true art, there's an aspect of receiving."
},
{
"end_time": 1088.899,
"index": 41,
"start_time": 1059.906,
"text": " But immediate, immediate, immediate. It's like a wave, you know, like it's a frequent, different frequency. So yes, of course, with Matthew also received eventually, and Alison Grothendieck, my hero, my hero. And he, he obviously was one of the, was a revolutionary mathematician of the second half of the 20th century. And then he had, he had an awakening, one could, one could say in a kind of traditional Eastern Eastern Eastern philosophy sense."
},
{
"end_time": 1094.65,
"index": 42,
"start_time": 1089.189,
"text": " um awakening where he realized he"
},
{
"end_time": 1121.698,
"index": 43,
"start_time": 1095.64,
"text": " was brought, that some questions of human existence and suffering were really hit him hard and brought, you know, were brought into his attention. And you could say that that's because he went very deep into mathematics. So it's another portal too. But I feel it's like, it takes longer in some sense. It's like a wave, which is much longer wave, whereas the art is fluctuates much faster. And so response time is much faster also."
},
{
"end_time": 1149.309,
"index": 44,
"start_time": 1122.073,
"text": " With TD Early Pay, you get your paycheck up to two business days early, which means you can go to tonight's game on a whim, check out a pop-up art show, or even try those limited edition donuts. Because why not? TD Early Pay. Get your paycheck automatically deposited up to two business days early for free. That's how TD makes Payday unexpectedly human."
},
{
"end_time": 1170.879,
"index": 45,
"start_time": 1152.705,
"text": " Carl Jung said that great art is one where you don't know what you're creating when you go into it. And then by the end of it, you learn something. Well, you mentioned learn something about yourself, but it could be learned something about almost anything. So you shouldn't if you were to know what you're doing when you start, then he called it propaganda."
},
{
"end_time": 1197.875,
"index": 46,
"start_time": 1171.101,
"text": " Cause you're trying to convince people of something. It's not love. It's not, you're not conveying love, you're conveying power. And so, right. And so Jung is famous for saying also that where love ends, the power begins and conversely, it's which I find, I find a very good way to look at things. Uh, in other words, the impact is real when it comes from the place of love. It can also be, it can also be"
},
{
"end_time": 1215.316,
"index": 47,
"start_time": 1198.37,
"text": " A historical prelude to the Langlands program is the vile conjectures, which he infamously came up with while he was in jail. So can you please talk about that?"
},
{
"end_time": 1229.957,
"index": 48,
"start_time": 1215.589,
"text": " Well, Langlands would disagree with that, because Langlands was not particular. So first of all, we pronounce his way, we say it way, Andre Way, because there is also Hal Herman Wilde, to make things even more confusing, right? So there are two great mathematicians."
},
{
"end_time": 1258.524,
"index": 49,
"start_time": 1230.367,
"text": " who have very similar names. And then there was also Andrew Weil. Yes, yes. And so for people like myself who read it, I was confused for the longest time between Andre Weil or Andre Weil and Andrew Weil. Who comes up? Who comes up with this? And also, I still don't know how to pronounce Hecke operators or Hecke operators or Majorana particles. I don't know because I just read them. I think for one year I called it Lie Algebras, instead of Lie Algebras. That's right. That's right. Yes."
},
{
"end_time": 1269.292,
"index": 50,
"start_time": 1259.462,
"text": " Who writes a script, right? I don't know, but it's true that there are three mathematicians with like exceedingly similar names."
},
{
"end_time": 1296.34,
"index": 51,
"start_time": 1269.616,
"text": " There is Hermann Weill who was a great German mathematician who worked at the Institute for Advanced Study, was one of the founding professors or first professors there. He is the one who was famous and made famous contributions to study of groups and big groups, specifically in quantum mechanics and so on, and also a very brilliant philosopher. Then there is André Wey, who is a French mathematician, also ended up working at the Institute for Advanced Study a little bit later."
},
{
"end_time": 1312.875,
"index": 52,
"start_time": 1296.937,
"text": " and he came up with this way conjectures so his name is spelled w e i l and in french tradition we pronounce it way oh okay so that's my mistake whereas helenweil last name is spelled w e y l and in the german tradition we say while"
},
{
"end_time": 1339.172,
"index": 53,
"start_time": 1313.677,
"text": " I just assume everything is German. Right. So there is also the Andrew Wiles who proved Fermat's last theorem with Richard Taylor. So that's more contemporary mathematician. So Andre Wey was a very brilliant mathematician who came up with this Wey conjectures, one of the most important, most fascinating and original contributions. He also was the one who"
},
{
"end_time": 1370.196,
"index": 54,
"start_time": 1340.964,
"text": " created this framework, came up with this framework of Rosetta Stone of mathematics, where number theory and geometry were connected in a particular way, which actually gives a good context for understanding the Langlands program. But it would not necessarily be correct to say that Langlands was motivated by the very conjectures. They're kind of a little bit apart from each other. So Langlands was motivated by other issues."
},
{
"end_time": 1392.056,
"index": 55,
"start_time": 1371.374,
"text": " Well, the way that I understand it is that even if Langlands didn't see it when he was coming up with his program as an extension of the whale, sorry, how do I pronounce it?"
},
{
"end_time": 1422.21,
"index": 56,
"start_time": 1392.363,
"text": " like way like way no way the way the way okay this is the way all right yeah that's right this is the way so the way conjectures that it's seen now and i think even in your book you had on the x-axis like in this matrix this translation dictionary the way conjectures but then if you go downward on one of them you have the langlands program so in a sense the way conjectures are more general more encompassing well but it's not exactly so there is way conjectures which is a very specific technical term for some specific statements"
},
{
"end_time": 1447.79,
"index": 57,
"start_time": 1422.619,
"text": " But Wei conjectures were an outcome of a certain overarching framework that Andrei Wei came up with. And you're right, he wrote that letter in 1940 to his sister, Simone Wei, who was a famous philosopher and humanist, trying to explain his ideas. And that's where he outlined this picture of Rosetta Stone, so to speak."
},
{
"end_time": 1471.732,
"index": 58,
"start_time": 1448.251,
"text": " The Bay conjectures were an outcome for him from that conceptual understanding of how things fit in mathematics, that he was able to argue by analogy. So you have Riemann hypothesis in number theory, and because he had this framework where he could move things from number theory to other domains, then he said, what would the Riemann hypothesis look like in this domain? And it came up with Bay conjectures, more or less."
},
{
"end_time": 1499.053,
"index": 59,
"start_time": 1472.193,
"text": " Right. So what, what matters here, if we talk about the language program is not very conjectures themselves, which is a very particular application of that general overarching framework, but the framework itself, the framework itself helps you see how the language program can play out in different domains. That's what, that's the point I was trying to make in my book. And Wei, Andre Wei, right. He gave an analogy of"
},
{
"end_time": 1528.66,
"index": 60,
"start_time": 1499.514,
"text": " Curves, points, and surfaces as being different avatars of Vishnu. So can you please tell the audience about that as well? Oh, yes. So this is very interesting. So Andrei Wei was very attuned to the Eastern tradition and he actually visited India and I think lectured at the Tata Institute Fundamental Science in Bombay, Mumbai. And so in his letter to his sister, which was written in 1940,"
},
{
"end_time": 1555.196,
"index": 61,
"start_time": 1529.019,
"text": " He talks about this, how mathematicians perceive this analogies. And so it's kind of a very interesting, I don't know if I should actually, I have my book here, so I don't know if I could, if I should actually quote, this quote is here somewhere. And he mentions about Gita."
},
{
"end_time": 1585.879,
"index": 62,
"start_time": 1556.015,
"text": " Abhagavad Gita, which is a kind of a sacred text of Hinduism. And he says, when you get an insight, it's just kind of an inkling of an idea, as opposed to when it's already understood. He talks about this dialectics of the experience of passing from that moment of recognition, but you're not sure yet. You just start seeing the outline. And then when it's actually"
},
{
"end_time": 1611.937,
"index": 63,
"start_time": 1586.442,
"text": " already done and it's something very interesting because like you fall in love kind of you know kind of like so you wouldn't you would most people probably would least expect a mathematician to be so poetic about it about the about the nature of discovery in mathematics but he says so what happened it is a translation into english so when what happens when this"
},
{
"end_time": 1638.968,
"index": 64,
"start_time": 1612.415,
"text": " inkling of an analogy between two theories turned into concrete knowledge he says gone are the two theories gone they are troubles and delicious delicious reflections in one another they're furtive caresses they're inexplicable quarrels alas we have but one theory now whose majestic beauty can no longer excite us so the excitement comes from that moment recognition he's basically saying"
},
{
"end_time": 1668.046,
"index": 65,
"start_time": 1639.48,
"text": " Nothing is more fertile than this illicit liaisons. Nothing gives more pleasure to the connoisseur. This initial moment of discovery, this initial moment of insight. And he says, the pleasure comes from the illusion and the kindling of the senses. Once the illusion disappears and knowledge is acquired, we attain indifference. In the Bhagavad Gita, there are some lucid verses to this effect. And then he goes, but let's go back to the algebraic function."
},
{
"end_time": 1689.189,
"index": 66,
"start_time": 1668.541,
"text": " so in other words there is this depth of understanding so mathematics does give one this vantage point i suppose which is very poetic and one could say romantic and i can i can i can feel that viscerally what he's talking about because you know"
},
{
"end_time": 1721.8,
"index": 67,
"start_time": 1692.142,
"text": " Coming up with a discovery in mathematics does feel like that, but so does everything else. Falling in love is kind of like this. Although one could say it's not necessarily that you kind of attain indifference once it settles. The idea is that that's the difference between human relationship, which is living, which can live and evolve and transform itself and reinvent itself forever or for a long time. In mathematics, once"
},
{
"end_time": 1751.664,
"index": 68,
"start_time": 1722.602,
"text": " Yes, yes. Something that's popular nowadays is to say that there is no theory of everything and in part"
},
{
"end_time": 1779.019,
"index": 69,
"start_time": 1752.517,
"text": " They'll quote Feynman and say, well, it's supposed to be like an onion, even though onions are finite, they have like 10 to 20 layers. So that's actually, it's a poor analogy because we've revolutionized physics, maybe 10 to 20 times in different ways. So we should be at the core, but also that there's something romantic about it, about there not being a theory of everything, because if there was, then we think the ultimate questions are done."
},
{
"end_time": 1809.224,
"index": 70,
"start_time": 1779.991,
"text": " The theory of everything in physics has a certain meaning of like reconciling dynamic space time with quantum theory. And so that's not exactly like the answers to everything, quote unquote. But even if there was, it could be that the answer to everything, quote unquote, is something that's animated. So it could be something like at the bottom of I know this is extremely poetic to say, but it could be like the theory of everything is to live lovingly, in which case it's not like an apprehensible, timeless, dead fact."
},
{
"end_time": 1836.903,
"index": 71,
"start_time": 1810.179,
"text": " certain theorems are, but rather something to rather a process rather than a state. I agree. That's a process. It's a process. It's a process. It's a connotation. I think most people have a studio. Everything is that it's something static that is done. And, and then we have this note that this knowledge, which somehow will cover everything."
},
{
"end_time": 1859.599,
"index": 72,
"start_time": 1838.541,
"text": " and that is very counterproductive in my view and even I would say dangerous and has unfortunately impeded progress and cause a lot of suffering to scientists but not only because it's a mindset if we because today people trust scientists to be the forward-looking and kind of like"
},
{
"end_time": 1883.285,
"index": 73,
"start_time": 1862.295,
"text": " up to theologians or priests or poets or artists. Now, for better or for worse, it's the scientists who are the priests, so to speak, in this era. And so if we are confused about this, if we entertain these ideas, that they propagate to a general culture,"
},
{
"end_time": 1910.418,
"index": 74,
"start_time": 1884.172,
"text": " And this is what happened in some sense. This idea of insatiable, in my view, this insatiable appetite for trying to explain everything with the knowledge I have right now. If you think about it, this is absurd. And all the history of humanity shows that it's absurd. And yet the impulse is so strong. And I'm not going to say it's those other people have to. It's me. I have been like this all my life, up until maybe very recently."
},
{
"end_time": 1937.278,
"index": 75,
"start_time": 1910.93,
"text": " So I know exactly how tempting this is. I also know how, how counterproductive it is and how much suffering comes from it. So like, you know, it's entertaining. It's kind of fun to engage in this activity, but I think it's a, it's a very important, and I'm glad you are, I'm speaking about this on the podcast, which is called theories of everything, which is a bit paradoxical."
},
{
"end_time": 1956.186,
"index": 76,
"start_time": 1938.763,
"text": " but i think that you actually get it kind of you know it's kind of half tongue and cheek the way you call it and you don't call it theory of everything yes right you call it theories of everything so it's not as simple as one might one might think that's the observant mathematician in you"
},
{
"end_time": 1973.183,
"index": 77,
"start_time": 1958.148,
"text": " I think that the drive to come up with a theory of everything isn't even though people would say, well, I care about humanity and I want to solve global problems."
},
{
"end_time": 2002.773,
"index": 78,
"start_time": 1973.422,
"text": " I don't think it's that. I think it's the desire to be crowned the title of the next Einstein. Yeah, so it's ego driven. So we can agree on that. Yeah, of course. To me, that means that you're not the next Einstein because Einstein never cared about being the next Einstein because there was not. And also something I think about when people say so and so is the next Einstein, we generally think of it in terms of, okay, are they creating something that's a paradigm shift in physics or math? But it's unclear to me if Einstein was to be born today."
},
{
"end_time": 2030.145,
"index": 79,
"start_time": 2003.558,
"text": " Would he be doing physics and math? So he was a creative, tuneful, poetic, romantic person. Maybe he would, maybe the next Einstein is Christopher Nolan. Also, he played violin. He played violin. Yes. Yeah. So literally maybe he would be violinist. Yeah. Yo-Yo Ma, maybe Yo-Yo Ma is the next Einstein. That's a good point. The term theory of everything. Let's unpack this. Cause I think you've tongue in cheek called the Langley's program a grand unified"
},
{
"end_time": 2051.8,
"index": 80,
"start_time": 2030.435,
"text": " theory, which some people then take to say it's a theory of everything of math. Of mathematics, yes, because, you know, I was like, how come physicists always talk about grand unified theories? This, I literally, I gave a colloquium in Princeton, and that's when I first came up with this. It was kind of like, on the spur of the moment, I was like, how come physicists always talk about grand unified theories, but we mathematicians don't? And actually, I was sitting in the audience."
},
{
"end_time": 2078.729,
"index": 81,
"start_time": 2052.21,
"text": " and i said well guess what i would like to call the language program the grand unified theory of mathematics and they're laughing because of course it doesn't make sense because mathematics is just so diverse it cannot have a nobody wants to have a theory of everything and then i said well maybe it doesn't describe everything but at least it describes something so it's kind of a little you know like so that's how it came about"
},
{
"end_time": 2103.968,
"index": 82,
"start_time": 2079.701,
"text": " Well, in a sense, math already has a theory of everything. What I mean by that is, it's the axioms. So it's just, it's not interesting to anyone. Why I say that is that in physics, but axioms, but axioms now you're trading on a very treacherous theory. I'll explain. In other words, the toll in physics is what are all those principles from which all observations slash theories are emergent slash effective."
},
{
"end_time": 2127.756,
"index": 83,
"start_time": 2104.548,
"text": " That is what we measure in the lab are just corollaries of these axioms. If we knew the axioms, like the drive for a theory of everything in physics is what is the axioms of nature? And so in math, I know that there's some controversies. But in math, we don't know what the axioms are either. That's the whole point. That's the whole point, which is lost. Usually people don't realize because most people think mathematics is written in stone. So of course it's so predetermined. No, it's not."
},
{
"end_time": 2157.176,
"index": 84,
"start_time": 2128.507,
"text": " It is a very important issue. The way I like to talk about it is that there is an observer problem in mathematics, just like quote unquote, or measurement problem in mathematics, just like in quantum physics, where the observer is involved in quantum physics. We know that from experiments. In mathematics, it is much easier to miss. And where it comes is, there are several places where it comes, but one of the most essential ones is who chooses the axioms."
},
{
"end_time": 2185.896,
"index": 85,
"start_time": 2157.739,
"text": " There isn't one axiomatic system which is God-given. And even great mathematicians like Kurt Gödel, for example, apparently he did believe that there is a kind of ultimate correct system. And then he thought that his job as a mathematician was to find it. In other words, it is somewhere there in some platonic world and you have to go and find it. But it's not obvious at all which one it is."
},
{
"end_time": 2210.674,
"index": 86,
"start_time": 2186.527,
"text": " So it's just the way you frame the search for it. In other words, you may think that there is one special one, but you don't know what it is and you can devote, dedicate your life to finding it. Another alternative position is plurality, kind of multiverse of axioms. So there are various axiomatic systems, they lead you to different mathematics. And it's very interesting to analyze what are the differences, which is more fruitful, which is less fruitful."
},
{
"end_time": 2239.087,
"index": 87,
"start_time": 2211.937,
"text": " so that you can say okay well there must be some objective criteria as to which a system of axioms is better and the weird thing is that there isn't even consistency cannot serve as a criterion because the second incompleteness theorem of Kurt Gödel shows that a formal system formal system that's kind of a assemblage of all the statements that you can get out of a particular system of axioms"
},
{
"end_time": 2256.63,
"index": 88,
"start_time": 2239.974,
"text": " Formal system cannot prove its own consistency. You have to step out of it. You have to step out of it. You have to adjoin some other axioms to be able to speak about consistency. Consistency means that it's useful. You can't prove everything."
},
{
"end_time": 2281.408,
"index": 89,
"start_time": 2257.005,
"text": " And consistency means that every statement can be derived. So it derives contradictions. It can derive statement A, and then it's negation. And if that's the case, then it's true for every other statement. So it means that it proves everything, so then it's useless. Yeah, you actually don't want to be able to prove everything, because then it's trivial. That's right. You have to prove only some select statements. And that is a property of a formal system called consistency."
},
{
"end_time": 2308.985,
"index": 90,
"start_time": 2281.971,
"text": " And the point is that the system cannot prove its own consistency. So then how you cannot be sure even that it's consistent. You have to take it on faith. And that's where the observer comes. So then how does Kurt Gödel, for instance, how would he decide which system is the God given one? Because he did believe apparently that there was a correct one that you have to find. And obviously you do it on other principles like aesthetic principles."
},
{
"end_time": 2332.739,
"index": 91,
"start_time": 2309.241,
"text": " this principle of beauty principles of being concise and stuff like that. But that's where you as a subject, as a first person, your first person perspective becomes imprinted on this because there isn't an objective criterion. Ultimately, there isn't. So the other possibility, which is as nice with me is this idea. Um,"
},
{
"end_time": 2349.104,
"index": 92,
"start_time": 2333.677,
"text": " i'm which is there is a lot of money who has written about this and i really like the way she framed it it's mathematical practice the system is. The better system is the one which is more fruitful which allows you to prove more things."
},
{
"end_time": 2376.135,
"index": 93,
"start_time": 2349.497,
"text": " And this is some, but it's beautiful because it means, but who decides? It's us, the living mathematicians today. We decide because we're practicing mathematicians, we're applying those axioms in our practical work. And then it becomes a marketplace of axioms, system of axioms, if you will. They compete with each other as different stories, so to speak. And we choose the ones which are more fruitful, which give us more diverse, more beautiful mathematics."
},
{
"end_time": 2396.374,
"index": 94,
"start_time": 2376.374,
"text": " you know so in in other words we're deciding it right now not referring to authority of Pythagoras or Kurt Gödel or Bertrand Russell or some such you know great individual but it's up to us it's a little that's where mathematics becomes a living process so in that sense one has to be careful to say that"
},
{
"end_time": 2406.561,
"index": 95,
"start_time": 2396.834,
"text": " whether mathematics is based on some unassailable foundation. It's not. If you look more closely, it's actually very similar to"
},
{
"end_time": 2427.363,
"index": 96,
"start_time": 2406.971,
"text": " other subjects of human endeavor or other parts of science like physics and so on. And I agree with you that in a way you almost you could say that the job of a physicist is to try to find the axioms of the physical world of this universe. We don't see the laws themselves, we observe the ramifications. Or at least some of them, right? So then"
},
{
"end_time": 2445.179,
"index": 97,
"start_time": 2428.131,
"text": " What is my place actually is the same but it's much more difficult to notice it unless you actually are pressing my efficient because the way my face is perceived by the general public is that it is something where where nothing ever changes."
},
{
"end_time": 2467.449,
"index": 98,
"start_time": 2445.725,
"text": " And the foundation is also perceived by many mathematicians and actually managed. I personally have not really thought about it deeply until recently, you know, because you, you do, you, you, you do. And I think it's very common, you know, in general that you, you find something that interests you. Like for me, language program, you can work on language program without"
},
{
"end_time": 2491.988,
"index": 99,
"start_time": 2467.995,
"text": " questioning the foundations. The reason I question the foundation is because of my interest in philosophy. Perhaps it's because of public speaking, kind of doing interviews, like conversations like this, where these kind of questions would come up and I would really be curious. So I'm really interested in those philosophical underpinnings of mathematics. But a lot of people, as you know, they actually claim that philosophy is completely useless for scientists."
},
{
"end_time": 2520.418,
"index": 100,
"start_time": 2493.063,
"text": " We shall not name any names, right? Yes, yes, yes. I will put an image on screen. I disagree. I disagree violently with this position. I think it's very limiting. And I think there are probably some parts of science where, you know, you can get by, but I think we all benefit from opening our horizon and from being interested in the foundations of what we're doing. This is called self-awareness. Right? What are you doing?"
},
{
"end_time": 2542.773,
"index": 101,
"start_time": 2520.998,
"text": " So in other words, the public has the perception that there's the practical aspect of science. So STEM, science, technology, engineering, mathematics, and the practical side of the first three years, the science, the technology, the engineering and physics is seen as a pure form of engineering. And then the most purest form of physics or the purest form of science is math. And that's something that's extremely objective."
},
{
"end_time": 2571.527,
"index": 102,
"start_time": 2543.422,
"text": " But you're saying, well, in order for us to establish something mathematically, we have to agree on the axioms. When we do so, we generally do so with practical concerns like empiricism. And so there's something that's about... Or you're driven by your Platon, if you are a Platonist, which means that you believe that mathematical ideas exist in this ideal domain, this platonic world, which is outside of space and time and so on, which I respect this position. And I actually, to some extent, adhere to this position when I was writing Love and Math."
},
{
"end_time": 2601.732,
"index": 103,
"start_time": 2572.125,
"text": " Then also you have your own methodology. You're kind of, you're searching for the correct one in that platonic realm, which is also, you know, it's a methodology. But there has to be some kind of methodology for you too, because there is no objective methodology. You cannot even use consistency as a tool, because it cannot prove its own consistency. So you have to take it on faith. It's a very practical thing. For instance, you have the Z of C."
},
{
"end_time": 2631.988,
"index": 104,
"start_time": 2602.21,
"text": " The standard axiomatics of set theory. Set is the most fundamental notion in modern mathematics, introduced by German mathematician Georg Cantor. And actually, it's never been defined. This is already a place where a whole of mirrors, you know. We pretend that it is something that is concrete and definite. But in fact, there is no definition of it. There are only circular definitions."
},
{
"end_time": 2658.558,
"index": 105,
"start_time": 2632.5,
"text": " Cantor himself gave a very poetic definition. He said, a set is a collection of many that thinks of itself as one. You see, so it's a poetic definition. Now, in other words, here's a notion which we accept on faith. Then you have this axiomatics which was developed in the first half of the 20th century and has become sort of a staple. So you kind of learn, most mathematicians follow it even if they're not aware. It's called ZFC."
},
{
"end_time": 2688.353,
"index": 106,
"start_time": 2659.053,
"text": " Z for Zermelo and one mathematician, F for Franco, almost the same spelling as my name, no connection as far as I know. And C is the axiom of choice, so ZFC. Now, we do not know that it is consistent. We can prove its consistency from another system, which is a bigger system where you introduce additional axioms, but you don't know whether that system is consistent. And like this ad infinitum. So how can we then do mathematics?"
},
{
"end_time": 2716.749,
"index": 107,
"start_time": 2688.729,
"text": " You ask, well, we have to accept it on faith. People don't talk about it. And most people probably never actually thought about it deeply. But if you think about it, it's and it's all information is available. I'm not saying something that does not know everybody knows it. Certainly logicians know it. And, uh, and the point is that we take it on faith that it is consistent because if you don't, then how can you do mathematics?"
},
{
"end_time": 2743.814,
"index": 108,
"start_time": 2717.244,
"text": " without assuming that it is consistent you see yes if it's not consistent means that you can prove anything by from these axioms including contradictory statements right so there is this element of faith even in mathematics there is an element of fiction there is an element of story and i think it's a very important observation because it points us again to the importance of the first person perspective"
},
{
"end_time": 2772.892,
"index": 109,
"start_time": 2744.428,
"text": " A science of the 19th century tried to expunge the first-person perspective, even earlier science. And the whole point of science was to come up with this narrative that somehow there is a subjective reality and we are just detached observers, we are not participants in it. Science of the 20th century, physics of the 20th century put an end to this through quantum mechanics, through Einstein's relativity theory, where the observer is involved and cannot be separated from what"
},
{
"end_time": 2781.049,
"index": 110,
"start_time": 2773.234,
"text": " the observer is observing but then you could say well at least mathematics is objective and so my point is"
},
{
"end_time": 2803.558,
"index": 111,
"start_time": 2781.817,
"text": " It's not. It's more camouflage. It's better camouflage. Your current deliberation is that it's all subjective or it's an intermingling of subjective and objective? It's always intermingling, of course. But the point is that there is no objective core. There isn't something. There's a strong foundation. Somebody who is not a mathematician may think"
},
{
"end_time": 2827.108,
"index": 112,
"start_time": 2804.07,
"text": " Obviously there are some axioms in mathematics which have existed forever and nobody questions them. That's not true. The simplest example of this is non-Euclidean geometry. Euclid actually was the first one to come up with a functional system of axioms, what we call formal system of Euclidean geometry. So about 2300 years ago, of course, building on earlier works by Pythagoras and Pythagoreans,"
},
{
"end_time": 2856.152,
"index": 113,
"start_time": 2827.858,
"text": " where he came up with a list of five axioms and tried to derive hundreds of different statements in his book, Elements, a series of books, derived from those axioms. Now, the first four axioms were kind of natural, and the fifth axiom was about parallel lines, that if you have a line on the... So, creating geometry, as I'm sure everybody knows, since this is actually one subject that is studied in school,"
},
{
"end_time": 2882.619,
"index": 114,
"start_time": 2856.459,
"text": " It's about the plane. Plane means a tabletop extended to infinity in all directions and on that plane we have points, we have lines, we have circles, we have triangles and then they intersect and there are all kinds of statements that you want to make. For instance, Pythagoras theorem that you have a right triangle and the square of the hypotenuse is equal to the sum of squares of two other sides. This is the type of statements that we're talking about which you would like to"
},
{
"end_time": 2912.619,
"index": 115,
"start_time": 2883.268,
"text": " Did you drive from a small number of actions? But then how do you choose these actions? First of all, you want them to be non-contradictory. That's consistency that I talked about. And yet you want them to be broad enough so that you can derive many interesting things. So he came up with these five axioms. And the fifth axiom was the one which kind of looked weird. And it stated that if you have a line on the plane and you have a point outside of this line, then there is a unique line passing through it, which is parallel to the original."
},
{
"end_time": 2933.831,
"index": 116,
"start_time": 2913.114,
"text": " Parallel means that they never intersect. So there is one, and it's unique. And after that, for centuries, people tried to derive this fifth axiom, they used to call it fifth postulate, from the first four. And they've all failed for about 2000 years."
},
{
"end_time": 2964.138,
"index": 117,
"start_time": 2934.616,
"text": " when several mathematicians around the same time said what if we replace it with another axiom where either you say there are no such lines and there was every line that passes through this point intersects the original line or you say that there are infinitely many lines not one which do not which do not intersect and this way you get what's called non-Euclidean geometry the first example now when you say axioms"
},
{
"end_time": 2989.684,
"index": 118,
"start_time": 2964.855,
"text": " When you talk about Euclidean geometry, you have to make it very detached from reality. So we have a model of this Euclidean geometry where we really think of lines and dots and circles and triangles. But when you formulate things in mathematics in the formal system, it has to be completely detached from reality. It's all syntactic. It's just symbolic manipulation. So you don't necessarily have to refer to a particular model for it."
},
{
"end_time": 3015.606,
"index": 119,
"start_time": 2990.145,
"text": " So then you say, well, in my experience on the line on the plane, I can't imagine that there's no parallel line passing to another point, but you don't have to look on the plane. You can look on the sphere and on the sphere, the role of lines is played by meridians and every two meridians intersect. You see, so in other words, the formal system doesn't care about how you want to model it."
},
{
"end_time": 3045.299,
"index": 120,
"start_time": 3016.118,
"text": " Formal system only cares about things like consistency, whether these axioms contradict each other or not. And it turns out that if you replace the fifth axiom of Euclid with another statement, it turns out that in this case, we can actually prove its consistency because it's kind of from without doing much. So it is actually independent from the other axioms and you can actually replace it by its negation and you'll still get a consistent system. And that system can be realized either on the sphere"
},
{
"end_time": 3070.009,
"index": 121,
"start_time": 3045.794,
"text": " that's the kind of spherical geometry where every two instead of but it's not a line it's a meridian which plays the role of the light so you take all the statements but lines in euclid but they replace lines by meridians meaning big circles on the on the sphere it doesn't mean this has to go through north and south pole you could have any any big circle is a lot is what plays the role of a line in spherical geometry"
},
{
"end_time": 3096.8,
"index": 122,
"start_time": 3070.862,
"text": " And if you replace the axiom in the opposite direction, you say that there are infinitely many lines which do not intersect. You get what's called hyperbolic geometry. So it's a geometry on a hyperboloid where the role of the lines is played by hyperbolas. And then you can see that there are infinitely many hyperbolas which do not intersect. Okay, so this is a good illustration of the fallacy of the idea that"
},
{
"end_time": 3125.981,
"index": 123,
"start_time": 3097.056,
"text": " There is one axiomatic system which services all of mathematics, which has been given to us somehow, the way the tablets, you know, the Ten Commandments were given to Moses. That's just not the case at all. However, it doesn't mean that it's not a postmodernist position either, that anything goes. This is what I also try to explain to my students always, because then the next temptation is to say, okay, it's all fiction. Yes, that's what it sounds like. Then what are we talking about?"
},
{
"end_time": 3150.572,
"index": 124,
"start_time": 3126.852,
"text": " but the point is that there is practice this axioms they don't nobody needs this axioms if you're not going to apply them to actually prove statements and make progress in mathematics and different and it's not true that all axiomatic systems are created equal no in some of them you get a lot of interesting stuff done and in some of them it's some of my limiting and a good example of this is whether you accept"
},
{
"end_time": 3171.425,
"index": 125,
"start_time": 3151.049,
"text": " The existence of infinity existence of infinite sets like the set of natural numbers one two three four five and so on as a totality not just infinity like that for every number there is a number greater by one this is called potential infinity but you accept absolute infinity that there is such a thing as a collection of all natural number."
},
{
"end_time": 3195.657,
"index": 126,
"start_time": 3171.852,
"text": " This is a very, it seems like a small thing, but actually leads to a lot of paradoxical statements like the famous Hilbert Hotel, you know, where you have infinitely many rooms and then you can always accommodate more people because you could shift them all by one to the next room and then freeing up, freeing up. There was very paradoxical behavior. So now what is the status of this statement of existence of absolute infinity?"
},
{
"end_time": 3230.265,
"index": 127,
"start_time": 3200.418,
"text": " It is one of the axioms in ZFC, in this axiomatic system that I talked about, Zermelo-Franco axiom of choice. And there are mathematicians which are called finitists who refuse to accept this axiom. So they consider ZFC without the axiom of infinity. And then the race is on. Okay, so here 99% of mathematicians who accept infinity and they work with this axiom whether they're aware of it or not. Okay. And here is a small group of mathematicians"
},
{
"end_time": 3251.305,
"index": 128,
"start_time": 3230.794,
"text": " I've spoken to some people who dislike the axiom of infinity and the axiom of choice. Norman Wildberger and George Barnett. Do you know George Barnett?"
},
{
"end_time": 3269.974,
"index": 129,
"start_time": 3251.596,
"text": " This is very interesting. How do you decide which is correct and which is not? So my point is, this is a market of ideas. This is a market of formal systems."
},
{
"end_time": 3294.462,
"index": 130,
"start_time": 3270.725,
"text": " You show me what you can do with your formal system and I'll show you what I can do with my formal system. People will look at this and they will decide which way they want to go for now. Maybe somebody else will come up with a third system of actions which will be superior to both and so on. I don't want to do it on ideological grounds. You see and this is where a lot of people go astray today into the science."
},
{
"end_time": 3319.155,
"index": 131,
"start_time": 3295.094,
"text": " They pretend that they are not ideological. They pretend that they are not driven by their metaphysical preferences, ontological preferences. For instance, that I like local determinism or I dislike local determinism. And then I am willing to sacrifice this and this and this for that particular thing, aspect of a theory. But it's not because it's my preference. It's just a better theory. No, it doesn't work this way."
},
{
"end_time": 3348.626,
"index": 132,
"start_time": 3319.77,
"text": " You have to detach yourself from your ideology. If you want to do good science, it's my opinion, which in this particular scenario that I'm talking about, and it's not a scenario, it's reality of modern mathematics. You have a small number of people who refuse to take Axiom of Infinity. Now my feeling is that there is something deep in their psychology, which rebels against the idea of infinity. They believe it's not real and they would like to do mathematics according to this ideology. Okay."
},
{
"end_time": 3369.889,
"index": 133,
"start_time": 3349.48,
"text": " I accept also that on the contrary, I like the idea of infinity. To me, infinity in mathematics symbolizes transcendence, symbolizes something that is beyond logic and reason in some sense. But we formalize it in mathematics as an infinite set. You see? Interesting. I admit"
},
{
"end_time": 3397.961,
"index": 134,
"start_time": 3370.811,
"text": " Okay. I admit that I am drawn to it because of my psychological composition. That's what it is. It's my preference, my psychological preference, my aesthetic preference, my ontological philosophical preference. Like you don't mind the paradoxes that come about. In fact, they're welcome, but it cannot be, but the whole point of science that we do not resolve our disputes on ideological ground. This is"
},
{
"end_time": 3423.166,
"index": 135,
"start_time": 3398.985,
"text": " This is not a fruitful approach. There's a much better way to do it. I will work with the system of axioms, which is closer to me, to my psychological, philosophical, you know, metaphysical ideas. But I should not be judged on that. Me and my colleagues who accept that we will work and we will produce results."
},
{
"end_time": 3451.135,
"index": 136,
"start_time": 3423.643,
"text": " and my colleagues who do not accept infinity will work and produce results and will compare and then we will see in the next generation young mathematicians who are not yet burdened by all this ideology they will look and they will vote with your legs with your feet they will go in the direction which is more fruitful that is real science in my opinion that's how you resolve it you resolve it now the problem is that you can have people"
},
{
"end_time": 3476.766,
"index": 137,
"start_time": 3451.442,
"text": " who are blocking that process. For instance, let's suppose somebody is attracting a lot of resources to their theory, you know, because they say it's correct. Then it puts others at disadvantage. So I think that's unfair. So everybody has to have a chance to develop things unless it's clearly like wrong inconsistency. Do you have an example in mind when you're saying this? Oh, yes. Many examples are just one in particular."
},
{
"end_time": 3502.534,
"index": 138,
"start_time": 3477.09,
"text": " One very special example. I'll get to it. So, for instance, what affinities do, it does not resonate with me. It does not resonate with me because I think, because, you know, I'll tell you why. So they basically accept only finite sets because they exclude this axiom. So, okay, but then you can prove, for example, that within their formal system, you cannot prove some statements even about finite sets."
},
{
"end_time": 3524.224,
"index": 139,
"start_time": 3502.705,
"text": " In other words, some statements about finite sets, you can only prove if you accept the axiom of infinity. That's the weird paradoxical aspect of it. You can actually prove that you cannot, you can prove that you cannot prove some statement about finite sets. So to me, it means a straight jacket. You put a straight jacket on yourself. You limit yourself. Why? Simply because you don't like the idea of infinity. Well, okay."
},
{
"end_time": 3551.544,
"index": 140,
"start_time": 3524.974,
"text": " Why limit yourself? Why limit yourself when you can... So that's my view. But I respect them. And I would like, for instance, there is a project to try to re-prove various statements. For instance, Fermat's last theorem, proof of Fermat's last theorem. Try to write a proof which never uses infinite sets. There's a project on which several very distinguished logicians, you know, mathematicians have worked on. And last time I looked, it's inconclusive."
},
{
"end_time": 3579.633,
"index": 141,
"start_time": 3551.886,
"text": " they don't claim that they can do it but there are some other famous problems in mathematics that they were able to prove without appealing to infinity and i applaud that because at the end of the day it's also helpful to know what is a minimal set of requirements for you to prove something okay but ultimately i think the correct argument why the theory with the action of infinity is superior today to the ax to the uh system actions without infinity is that we can produce a lot more"
},
{
"end_time": 3608.319,
"index": 142,
"start_time": 3579.991,
"text": " and it is there are many statements which are not known to be derivable by without axiom infinity there are many states which we know cannot be derived without axiom of infinity and so on so therefore it becomes limiting limiting to our progress and you know i also the other thing i want to say is that today there are algorithms based on um elliptic curve encryption stuff like that which is actually used in in in the bitcoin blockchain for instance and it's not clear to me whether"
},
{
"end_time": 3637.807,
"index": 143,
"start_time": 3608.729,
"text": " The mathematical theorems which underpin this algorithms can be proved without the actual infinity. So in fact, if that is the case, effectively, it means that it becomes part of our life. The infinity finds a back door into our life through various theoretical statements on which our technology is based. Now, I'm not claiming that that's the case, but that's how, for instance, that's how it can actually affect us because somebody could say, okay, this is some really esoteric argument because in this weird mathematicians like who cares?"
},
{
"end_time": 3666.493,
"index": 144,
"start_time": 3638.865,
"text": " You care because technology is woven into the fabric of our lives to such an extent that yes, a lot of very hard, difficult mathematics is now being used. In fact, for instance, in transactions on the Bitcoin blockchain. And this is one example. Okay, we're going to get to examples. These examples I have given were to illustrate the point that number one is mathematics is also based on there is a choice involved."
},
{
"end_time": 3694.701,
"index": 145,
"start_time": 3667.875,
"text": " But number two, so in other words, there is a subjective element. And this is only one, so just a brief addition to this. This is one way in which the observer is involved, the first-person perspective is involved. The other one is, of course, when we write proofs, who decides whether it is correct or not. We are not yet at the stage of full automation of"
},
{
"end_time": 3724.65,
"index": 146,
"start_time": 3695.23,
"text": " Verification of proofs and eventually probably some of it can be done by computers. It's not there yet. So it's human mathematicians who are reading those papers and ascertaining whether the proof is correct or not. A famous example is Andrew Wiles. We talked about earlier his original proof of Fermat's last theorem had a gap. How was it found? It was found by the gap was found by by a mathematician, Nicholas Katz, who was Andrew Wiles colleague at Princeton University."
},
{
"end_time": 3754.445,
"index": 147,
"start_time": 3724.974,
"text": " who looked very carefully and he asked questions probing questions that you finally asked the question how does this follow from this and then the west could not answer it so it was determined that there is a gap and luckily a year later andrew wiles with the help of his former student richard taylor was able to close this gap and after that so what gives us the the confidence that the proof is correct what if there is another gap we cannot be 100 sure this is the point it is the accepted as a"
},
{
"end_time": 3763.336,
"index": 148,
"start_time": 3754.735,
"text": " is a true is a true proof by other practicing mathematicians that's the market of ideas that i'm talking about even in mathematics you have this market of ideas"
},
{
"end_time": 3793.285,
"index": 149,
"start_time": 3763.729,
"text": " There isn't something that is objective and completely detached from our personalities, from our real living breathing mathematician. That is something that is very important and it's an indication that even mathematics is like this, then for sure it's like this in many other subjects which do not even have the appearance of the subjective reality. Of objective reality, right? Mathematics does have the appearance of objective reality more so than any other subject in science, in my opinion. But what I'm trying to argue is that this is an illusion. At the bottom of it,"
},
{
"end_time": 3823.951,
"index": 150,
"start_time": 3794.138,
"text": " There is a choice that choices made by living mathematicians. Okay. That's the first point. The second point. However, it doesn't mean that anything goes. It doesn't mean that anyone come up with some fancy like like objects in it. Somehow there is a notion of a group. It's one of the cornerstones of mathematics notion of a group. A group is like a symmetry is a collection of symmetries operating on a particular object, like a glass glass around glass or rotations of the glass. So it can be, it is encapsulated by some axioms."
},
{
"end_time": 3838.336,
"index": 151,
"start_time": 3824.445,
"text": " Where you have some binary operation to satisfy such and such purpose, associativity being the most important one. What if somebody comes up and replace associativity with something else? Some other kind of, you know, different property. And actually people try to do that."
},
{
"end_time": 3867.551,
"index": 152,
"start_time": 3839.377,
"text": " How, guess what? Groups are fundamental. Those other things are not. Why? Because groups have led to very important advances. They have applications in many areas. And those other fancy objects don't. And that's how, that's why mathematics work on groups and not on those other things, which to detached observer who is not involved in the subject will look like, okay, so in this axiom you have three terms and this I have four terms. What's the difference? They look very similar."
},
{
"end_time": 3896.732,
"index": 153,
"start_time": 3867.91,
"text": " But we choose one and not the other for a reason. And that is an objective element, you see, because it comes now from the community of mathematicians working on it, applying it to different areas. And there's a criterion of fruitfulness. That's what replaces objectivity in some sense. But it's a notion which is accepted today by the community. Maybe one of those fancy objects that we don't pay attention to today because we think that they are useless. Maybe somebody will find applications for them."
},
{
"end_time": 3922.961,
"index": 154,
"start_time": 3897.927,
"text": " How do we overcome this then need or this fallacy of confusing something's effectiveness, its ubiquitous application with its ontological status?"
},
{
"end_time": 3951.032,
"index": 155,
"start_time": 3923.37,
"text": " So this is something that computationalists do, where they see the effectiveness of computers and they say, well, then at the basis of reality is computers. Yeah, that's right. Or some people. Well, I have several examples in mind. This absolutely. And that's why I am. That's why I devote time to talk about this, because this is one of the policies that you said that I have in mind. And I think that this discussion of what mathematics is about is very much relevant to understanding why it is a policy."
},
{
"end_time": 3980.759,
"index": 156,
"start_time": 3952.005,
"text": " We have to overcome this temptation to believe that the knowledge we have acquired is sufficient to explain everything or at least like a large portion of reality. This has never worked. It has never worked and never will work in my opinion and case in point computation. A lot of people today say that everything is computation. And what do they mean by this? So they learned computation. They think they've learned."
},
{
"end_time": 4006.527,
"index": 157,
"start_time": 3981.118,
"text": " computer science or computer mathematics. And it's a child who learned trigonometry, 11 year old who learned trigonometry. And now he sees trigonometry in everything. Look, there is a wheel, it's trigonometry. Look at the triangle, it's trigonometry. Everything is trigonometry. It's a very natural and almost endearing quality of human beings, but unfortunately leads us astray. And I think that maybe"
},
{
"end_time": 4033.114,
"index": 158,
"start_time": 4007.022,
"text": " Time has come for us to finally let go of this, of this approach. And for instance, in the case of competition, since you mentioned, it's something that, which is very much relevant today because all the computer, so-called AI, all this computer programs that charge GPT and so on. I have spent some time reading the founders, like Alan Turing. Okay. So Alan Turing is,"
},
{
"end_time": 4063.046,
"index": 159,
"start_time": 4033.78,
"text": " What was the most important result that he immediately proved after he came up with his idea of encapsulating computation as a Turing machine? It was a statement that there are things which are not computable by Turing machines. In other words, computation, the paradigm of computation contains within itself its own demise, the realization that it's not everything."
},
{
"end_time": 4091.817,
"index": 160,
"start_time": 4063.78,
"text": " And the great ones, in this case, the founder Alan Turing, one of the smartest people who have ever lived, he saw it right away and he did not see it as a bug. He saw it as a feature. And if you read his work, it's an incredibly deep and honest, sincere analysis of what it means or what its implications are. Because of course he was fascinated with the idea of thinking machines, of intelligent machines."
},
{
"end_time": 4120.538,
"index": 161,
"start_time": 4092.466,
"text": " But if you read his paper on intelligent machines, I actually have it somewhere. So first of all, he writes in 1945, the class of problems capable of solutions by the machine can be defined fairly specifically. They are a subset of those problems which can be solved by human clerical labor working to fixed rules and without understanding, without understanding. Now, intelligence, by the way, comes from the word intelligere."
},
{
"end_time": 4142.398,
"index": 162,
"start_time": 4121.152,
"text": " Which means to understand how can we talk about intelligence of computers when the father of computing can see that the point that they're not understanding what they're doing. How many countries scientists are aware computer scientists who speak out on this and say we are already entered the age of AI."
},
{
"end_time": 4171.135,
"index": 163,
"start_time": 4142.705,
"text": " It's going to take over human beings. If we are lucky, they will use it as, as plans, you know, as decorations in their homes and so on. How many of them are even aware of this quote? That's my first question. Yes. Okay. My second question. So my second question. So there's another paper in which, which is, uh, which is called, which is called intelligent machinery."
},
{
"end_time": 4193.029,
"index": 164,
"start_time": 4172.193,
"text": " i think it's called intelligent machinery and he talks about objections to the possibility of intelligent machines he says the original question can machines think is too meaningless to deserve discussion nevertheless i believe that at the end of the century the use of words and general educate opinion"
},
{
"end_time": 4222.022,
"index": 165,
"start_time": 4193.541,
"text": " will have altered so much that that one will be able to speak to much of machine thinking without expecting to be contradicted. You see, we'll have what so much. I believe that at the end of the century, and that means 20th century, the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted. In other words, he's basically saying that's not a good way to phrase it, but he's resigned to the fact that that's how people will talk about it. Uh huh."
},
{
"end_time": 4250.606,
"index": 166,
"start_time": 4222.824,
"text": " I believe further that no useful purpose is served by concealing these beliefs. The popular view that scientists proceed inexorably from well-established fact to well-established fact, never being influenced by any unproved conjecture, is quite mistaken. Conjectures are of great importance since they suggest useful lines of research. So for him, from the beginning, the possibility of intelligent machines was a conjecture."
},
{
"end_time": 4279.104,
"index": 167,
"start_time": 4251.476,
"text": " And now he says, and now he says, I now proceed to consider opinions opposed to my own. And he comes up, he comes up, listen to this, he comes up, not with one, not with two, he comes up with nine objections, nine objections. And he carefully considers each and every one of them. And the one which he finds most powerful is what he calls mathematical objection. The fact that he himself,"
},
{
"end_time": 4300.538,
"index": 168,
"start_time": 4279.753,
"text": " Show that there are problems which are not decided which are not computer which are not sold by a machine by computer. This is a very important point this is called how to problem. How do you promise he realized that you can not be sold by the question which machines will help which machines will not go into the loop."
},
{
"end_time": 4330.282,
"index": 169,
"start_time": 4302.09,
"text": " because you can enumerate all the Turing machines and you're going to ask whether there is an algorithm or a Turing machine, which will, which will. Does the halting problem implicitly have an idea of the concept of infinity? Yes. Yes. So the objection would be, well, Hey, we just get rid of the infinity. You can't get rid of it. That's the point. You even, you have to accept at least potential infinity because otherwise the position is untenable. Otherwise your position is that there is a biggest number and an N plus one does not exist."
},
{
"end_time": 4356.903,
"index": 170,
"start_time": 4330.691,
"text": " This even finitists today, they would not agree with. Finitists do not say that there isn't a number greater by one than any given number, meaning there is a billion, there's a billion and one, there's a gazillion, there's a gazillion and one, okay? They don't argue with that. That's called potential infinity. What they argue about is whether there is such a thing as a totality of all positive natural numbers, whether it exists as a thing in and of itself."
},
{
"end_time": 4381.732,
"index": 171,
"start_time": 4357.722,
"text": " For them, what exists is always a finite set of numbers from 1 to n, or from 1 to n plus 1, from 1 to n plus 2, and so on, but not from 1 to infinity. That is, it seems like a subtle difference, but that is what separates finitists from the rest of mathematicians. It's that. I don't know of any mathematician who actually seriously entertains the idea that there is a biggest number. Yeah."
},
{
"end_time": 4409.309,
"index": 172,
"start_time": 4382.449,
"text": " Because you know that there is this number and there is also number one and there is not the operational additional number. So how can it not give you n plus one? You see, so therefore you cannot avoid potential infinity. You can avoid absolute infinity, which is what finite is do by saying that the set of natural all natural numbers does not exist. Only it's finite subsets at any moment. That is a reasonable position. But"
},
{
"end_time": 4437.739,
"index": 173,
"start_time": 4409.667,
"text": " They still cannot avoid the fact that for every number there is one more. And that is what gives the halting problem. You don't need to assume absolute infinity for it at all. Just the thing that the machine runs, if it stops, you're in luck. But what if it doesn't stop? It means that in finite time you cannot decide whether it stops, you see. That is the cornerstone of the impossibility of solving the halting problem. Infinity is"
},
{
"end_time": 4466.783,
"index": 174,
"start_time": 4438.336,
"text": " Underneath it, but it's it's a lot infinity light. It's a potential infinity I was speaking with drawer drawer barnetton. He's an ultra-finitist So I asked him explicitly Do you believe the number five to the power 100 to the power 100 to the power 200? Doesn't exist and he paused and thought about it. He said no doesn't exist Okay, yeah, and yeah, you you just described it. So that's very interesting Yet you just named it. So what did you name?"
},
{
"end_time": 4496.971,
"index": 175,
"start_time": 4467.039,
"text": " Yes. Well, you named a unicorn. You named something, right? Yeah. But anyway, I could be misquoting him or misremembering, so who knows. But there are ultra-finitists. Maybe. I don't know. I think it's a bit of a... If I may say so, a little bit of posturing. It's a bit of posturing. So, Professor, this seems... I see the same passion that you have for math, that you have for this subject, this new philosophical subject."
},
{
"end_time": 4526.305,
"index": 176,
"start_time": 4497.381,
"text": " No, for sure. When did this start? This also started 10 years ago? Yes. So this started with the questioning of what am I doing this for? Is it correlated? It very much correlated, very much correlated. Yeah. So I was going to say, yes. So I wanted to say what I quoted. I want to say which source is called computing, machinery and intelligence. It's an article during growth in 1950. Okay. And so where he gives nine, he gives nine objections."
},
{
"end_time": 4548.166,
"index": 177,
"start_time": 4526.8,
"text": " to his own ideas and he analyzes them carefully. How many computer scientists do you know today who number one aware of the fact that Turing was trying to grapple with these issues from the outset and he was very uneasy about them, right? Yes."
},
{
"end_time": 4577.449,
"index": 178,
"start_time": 4548.387,
"text": " How many computer scientists and proponents of AI, so to speak, or like acolytes of AI, how many of them actually aware what the father of their subject was thinking about it? And it's number two, how many of them put in their papers objections to their own ideas and seriously engage with those objections instead of dismissing them outright? I'm not sure how many will answer yes to both questions."
},
{
"end_time": 4605.145,
"index": 179,
"start_time": 4578.268,
"text": " I'm not sure. And that is, we say troubling, so we say disconcerting. Why is it that the father of the subject felt it imperative upon himself to engage critics in a very serious way and sincere way? And by the way, it was in dialogue with Gödel because it's very connected to Gödel's incompleteness. And he was aware right away of this and Gödel too."
},
{
"end_time": 4627.551,
"index": 180,
"start_time": 4605.52,
"text": " And even years later, so Turing died in 1954. In 1973, Gödel decided to add a remark to his earlier paper in which he argues with Turing. So it's kind of weird because you could say kind of unfair because Turing cannot respond. But I think it's on the contrary, it shows the great respect of Gödel to Turing."
},
{
"end_time": 4651.101,
"index": 181,
"start_time": 4628.404,
"text": " So he writes a philosophical error in Turing's work, Turing and Gödel writes, and this is, I think, I believe in 1973, 74. And he says, Gödel, Kurt Gödel says, Turing in his 1937 paper gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However, this argument is inconclusive."
},
{
"end_time": 4680.179,
"index": 182,
"start_time": 4651.937,
"text": " Okay. During this regards completely is the fact that mind in its use is not static, but constantly developing. For example, we understand abstract terms more and more precisely as we go on using them and that more and more abstract terms enter the sphere of our understanding and so on. So he has a technical argument and I'm not trying to say he's right or he's wrong. They engaged with each other in a dialogue from the beginning because they understood the importance of this question."
},
{
"end_time": 4708.695,
"index": 183,
"start_time": 4680.35,
"text": " When this to the implications for our society and doing was right he said by the end of the century this will become common place a lot of people will be saying this even if i think the question do can machines think is not a productive one this is this is reality this is going to happen so we might as well i might as well now i will lay the foundations of this and have a framework for discussing this what does it mean and he goes to nine arguments nine arguments against it."
},
{
"end_time": 4738.951,
"index": 184,
"start_time": 4709.036,
"text": " And then the third argument is the mathematical objection, which is Gödel's incompleteness theorem. He writes, there are a number of results of mathematical logic which can be used to show that there are limitations to the powers of discrete state machines. The best known of these results is known as Gödel's theorem and shows that in any sufficiently powerful logical system, statements can be formulated which can neither be proved nor disproved within the system, unless possibly the system itself is inconsistent."
},
{
"end_time": 4766.834,
"index": 185,
"start_time": 4739.616,
"text": " And so on. And then he writes, I do not think this view can be dismissed quite so lightly. You see, he's himself, not sure. And in fact, the year he died in 1954, he talked about in his last article published in 1954, you know, kind of a popular, in a popular magazine, science news at the very end, this is 1954, just about the time he died."
},
{
"end_time": 4779.548,
"index": 186,
"start_time": 4767.312,
"text": " He says the results, it's called solvable and unsolvable problems. And he's arguing that what theory of computer science shows is that there are unsolvable problems. There are things which cannot be solved by an algorithm."
},
{
"end_time": 4802.739,
"index": 187,
"start_time": 4780.418,
"text": " and this is important i think a lot of people have not really had the chance to think about it to a large extent because of atrocious state of our education and i feel it's imperative for somebody like me who actually got exposed to it and i'm not saying i'm not saying i'm presenting some truth which has not been known it's all very well known to specialists whether they would like to turn a blind eye to it or not"
},
{
"end_time": 4833.336,
"index": 188,
"start_time": 4803.609,
"text": " It is well known, but to most people it is not well known. So I think that this is not present in the conversation about AI. At least I don't see it that much present, you see. And this idea that as soon as you, that the competition includes within itself, the idea that things are uncomputable, they are undecidable, unsolvable. Here's a book that, for instance, there's a whole collection of articles here. What are the words which are used in the title? Undecidable."
},
{
"end_time": 4863.558,
"index": 189,
"start_time": 4833.78,
"text": " Can you show that book once more? Okay, the Undecidable by Martin Davis, and that'll be in the description, as well as the link to the two articles that you mentioned of Turing. The limitations, the inherent limitations of computation. Okay. He grappled with this from the beginning because he's understood the power of it, the potentiality of it. He also liked the idea of intelligent machine."
},
{
"end_time": 4882.722,
"index": 190,
"start_time": 4864.002,
"text": " But he also understood that it's not so simple. There are serious arguments why it's not possible. So in 1954, I have read through several papers of his to see the evolution of his views also. He's not dogmatic. He's not like,"
},
{
"end_time": 4913.148,
"index": 191,
"start_time": 4883.166,
"text": " It's like that. And then I'm going to prove it, you know, all the power that I have while ignoring all opposite arguments, which unfortunately we see that today. That's not his approach at all. And his last paper, his last paper, in fact, he finishes with saying the results which have been described in this article are mainly of a negative character, setting certain bounds to what we can hope to achieve purely by reasoning. See, he's already expanding from computation to reasoning."
},
{
"end_time": 4942.875,
"index": 192,
"start_time": 4914.019,
"text": " He says this and some other results of mathematical logic may be regarded as going some way towards a demonstration within mathematics itself of the inadequacy of reason, quote unquote, unsupported by common sense, inadequacy of reason unsupported by common sense. Are you aware of Penrose's and Lucas's argument that says that? Oh, yes. Penrose is fantastic book. I have it here. You know, uh, the book,"
},
{
"end_time": 4972.381,
"index": 193,
"start_time": 4943.609,
"text": " This and actually there are two books, but this I love this one. You see how many bookmarks. Yeah. Yeah. So here's something that you made me think about. There's something called. In ancient Greece, there's something called the unity of virtues. Have you heard of that? To some extent, I suppose, yes. Yeah. OK, so basically it says that you can't have one of the virtues without incorporating the rest as you increase in the virtues. You can't be brave without being honest. True bravery requires honesty."
},
{
"end_time": 5002.159,
"index": 194,
"start_time": 4972.79,
"text": " And then true honesty requires courage. I wish it were so simple, but okay. Yeah. Well, anyway, they were saying that as you have more and more of them, they unify at something like the most good, which they would equate with God. Then you had me thinking, well, okay, look at this. We're taught more to think algebraically and algorithmically than we are to think in the way that the Greeks did with lines and circles. So less geometric."
},
{
"end_time": 5030.282,
"index": 195,
"start_time": 5002.875,
"text": " At least in this is my case for my education. And then I was thinking, well, the people who are the most playful with their ideas and creative and poetic and romantic, they tend to be the more geometric side of the mathematician. So for instance, Einstein, Penrose, Michael Attia. And then I was wondering, this is a huge speculative jump. Is this in some way related to prioritizing"
},
{
"end_time": 5059.753,
"index": 196,
"start_time": 5030.674,
"text": " this algorithmic, symbolic, syntactic manipulation over something that's more physical and geometric. I'll give another quick example. I never cared about why can't you put a circle in a square, something like squaring the circle or a circle outside of the square, because I'm like, who cares? You can just draw that. But then there's a specific set of rules with compasses and so on that never, I'm just trained algebraically, like trains in terms of that's how I studied in school."
},
{
"end_time": 5087.944,
"index": 197,
"start_time": 5059.804,
"text": " I wonder, and most of my generation is, maybe even your generation, and I wonder how much of this dismissal of these grand ideas comes from a dismissal of geometry, like picture proofs are of, hey, look, if you rearrange this... You can have... There is something to what you're saying, and there is a famous quote, which I don't remember who said it, maybe it's here, that God is like, influenced mathematicians through geometry and devil through algebra, you know."
},
{
"end_time": 5113.217,
"index": 198,
"start_time": 5088.234,
"text": " Okay, so there is some truth to it. In other words, there is more imagination in some sense in geometry. Lineman's program, in a way, is what tries to unify discrete and continuous and symbolic algebraic with geometric imaginative in a way. That's what I find beautiful. Ultimately, all of these distinctions that we make, these are all distinctions in our mind. They're all the distinctions. There's a story we tell ourselves. If I believe that there is a"
},
{
"end_time": 5143.49,
"index": 199,
"start_time": 5113.592,
"text": " Boundary there is a line between the two. This is how it is for me then but it's like people say truth and beauty, you know So it's already implicit in that is that the truth they will find they don't expect to be beautiful and the beauty they find They don't expect to be true, but you yourself made the distinction you yourself drew the line between the two It doesn't have to be this way. You can say truth slash beauty one thing or truth dash beauty You know one thing and then in your life you are more likely to encounter two things which are beautiful"
},
{
"end_time": 5170.913,
"index": 200,
"start_time": 5143.49,
"text": " and beautiful things which are true. Same with geometry, algebra, and so on. These are all frameworks that we create. In modern mathematics, you cannot do one without the other. The progress is made when they hit upon each other, when they touch each other. Algebraic methods, geometric methods, and so on. That's why we have algebraic geometry, which was created in the modern version, was created by the genius Alexander Gross, whom we mentioned earlier."
},
{
"end_time": 5198.882,
"index": 201,
"start_time": 5170.913,
"text": " his genius was precisely to be able to connect them, put them together, you see. But there are people who are dogmatic on both sides, who are predominantly algebraic or predominantly geometric. I think what is essential to understand is how much we are informed by our own psychology, how much we are informed by our own aesthetic preferences, our philosophical preferences, our metaphysical preferences. In other words, the quantity of subjective objectives"
},
{
"end_time": 5229.701,
"index": 202,
"start_time": 5199.77,
"text": " Some, you know, a friend of mine who listened to my recent interview with Lex Friedman, conversation with Lex Friedman, where I talked about subjective, kind of like similar to what we discussed on the subjective. He's like, well, but it's kind of troubled. I feel it's uncomfortable with it because you're proposing to replace some objective things by subjective. That is totally missing the point. What the point is to realize that you have always been doing this. You have always had mixed your subjective to what you believe is objective. And then you try to come up with an argument."
},
{
"end_time": 5255.503,
"index": 203,
"start_time": 5230.213,
"text": " presenting your ideas as if they're detached from you. I would content that that's not the case, that is always present. So it is not about replacing something with something, it's about acknowledging that's what you have been doing all along or what I have been doing all along. To what extent my theories, which I like to think of as objective, are driven"
},
{
"end_time": 5284.121,
"index": 204,
"start_time": 5255.998,
"text": " I'm motivated by my subjective preferences. For instance, we talked about, I like infinity. I just like it. So it's my aesthetic preference. But if on the basis of this, I will start saying that everybody should like it. And those people who don't accept infinity are stupid or misguided. That's where I go astray. And that's where I introduce unnecessary, unnecessary strain on my mathematics."
},
{
"end_time": 5313.131,
"index": 205,
"start_time": 5285.964,
"text": " And you know it always, when somebody is really emotional about it, they give themselves away. You know, because as a friend of mine once said, a very smart fellow, he said, you know, you're not going to argue with someone who will say gravity doesn't exist. He said, oh yeah, good luck. Good luck. Gravity doesn't exist. You're not going to argue with the frozen, you know, the corners of your mouth. That's not the case."
},
{
"end_time": 5322.278,
"index": 206,
"start_time": 5314.241,
"text": " And likewise, when somebody is arguing too passionately about something, it means that it's something there, in here, unresolved."
},
{
"end_time": 5347.329,
"index": 207,
"start_time": 5323.712,
"text": " We are not paying attention to this. We are pretending that in science, we are really driven by some objective reality. Yes, we are to a large extent. Like I said, as a community, we decide which actions are more fruitful and so on. But as a human being, as an individual, I'm also very much driven by things which come from my psychology, my philosophical preferences, from my, you know,"
},
{
"end_time": 5375.93,
"index": 208,
"start_time": 5347.773,
"text": " And my job is to be aware of it. That's called self-awareness. Otherwise, I'm asleep. I'm half asleep. I am not here. I'm not. And so therefore I am not doing my job correctly, in my opinion. So Alan Turing was aware. So here is a good example. Alan Turing, as someone who was aware of this raises very interesting question. He was not, it was not, it was not"
},
{
"end_time": 5405.623,
"index": 209,
"start_time": 5376.34,
"text": " uh, frustrated by it. I think it made it even more interesting for him in many ways. It's a shame that the way he was treated by the British government, as I'm sure you know, that is subjected to hormonal therapy, you know, because he was gay and he died at the age of 32, as most people believe, by suicide. What a travesty, you know? And that's the machine, the machine, that's the real machine that we should be aware of."
},
{
"end_time": 5426.391,
"index": 210,
"start_time": 5406.288,
"text": " Careful about you know, what do you mean? That's the machine the machine the government the government power Which is unleashed to destroy an individual a brilliant individual and you say was because he's gay No, he wasn't because he was different. Uh-huh. So more broadly speaking societal norms or the government in particular"
},
{
"end_time": 5456.647,
"index": 211,
"start_time": 5427.551,
"text": " What I mean to say is the machine in general for us, is it in your mind, is it the government or is it societal norms or is it? I don't know. I purposely drop this word because the machine could mean computer or artificial intelligence, which people are arguing about now, whether it has the power to subjugate humans and so on."
},
{
"end_time": 5481.34,
"index": 212,
"start_time": 5457.329,
"text": " So here is a man who actually theorized that possibility in the most advanced way possible during and he's actually destroyed by a machine of a different kind. Interesting. I see how interesting. I'm not, I don't, I'm not going to spoil it by revealing the punch line. You know, let's think about this. Let's think about what does this tell us? What does it tell us?"
},
{
"end_time": 5509.906,
"index": 213,
"start_time": 5481.954,
"text": " In other words, he was so inconvenient somehow, and this is a man who was instrumental in deciphering the enigma machine, you know, who has contributed so much to the defense of the United Kingdom. And how many years passed before they finally apologized for what they did, or at least acknowledged the government of UK? What does it tell us? Is this like an isolated incident? Or is this something that has been kind of a norm?"
},
{
"end_time": 5536.8,
"index": 214,
"start_time": 5510.503,
"text": " that somebody who is different, somebody who is different, no matter how much they contributed to a given society is ostracized and ultimately destroyed. So how do you not get destroyed from thinking about, well, okay, you mentioned self-awareness, self-awareness. So he is a man who was self-aware, you see, and that's why I would like to, I would like to,"
},
{
"end_time": 5565.145,
"index": 215,
"start_time": 5537.705,
"text": " Emphasize this point and I would like more people to pay attention and say Alan Turing could do that. Can I also look in a kind of, what's the word, a neutral kind of way on the things without emotional investment in it? But look at the facts, way different ideas, different opinions without being engaging in ad homino attacks or, you know, like getting overly"
},
{
"end_time": 5593.78,
"index": 216,
"start_time": 5565.589,
"text": " emotional about it. Can I? And if not, and if I can't, let's find out why. Let's find out what is really what within me is creating trouble, so to speak. And it's not a bad thing. It's not a bad thing. Is there something that's bad about being emotional about it? Because you're clearly passionate about what you're saying. But I wouldn't say that what you said is wrong because it means you're emotional. So yes, but it's important for me to know where it comes from."
},
{
"end_time": 5621.954,
"index": 217,
"start_time": 5595.776,
"text": " You did ask me this, and I can explain briefly. But yes, I'm not arguing that there shouldn't be passion. Of course, this is the engine of progress. But the question is, your passion comes from something you're aware of, or something in your unconscious. And that is essential. Because if I'm not aware of what is actually driving me,"
},
{
"end_time": 5642.381,
"index": 218,
"start_time": 5623.814,
"text": " chances are i'm not actually going to be effective even if i am proposing good ideas and so on because there's too much spurious stuff i'd mix which are on me which i can resolve within me i don't need albert einstein to resolve it for me or alan turing i can resolve it myself if i'm interested you see"
},
{
"end_time": 5669.138,
"index": 219,
"start_time": 5642.824,
"text": " Yeah, specifically speaking, how did you come to this? How do you realize quote unquote realize I have to be careful about how did I get interested in this subject? More like let's say you have predilections or flaws or pros and cons, but they're unconscious. And then to go back to this onion metaphor. That's right. There's a finite layer, but you can start to peel away the layers. What is this process of peeling for you? Is it I go to therapy?"
},
{
"end_time": 5679.326,
"index": 220,
"start_time": 5669.462,
"text": " Is it I read a certain amount of books and I ask myself this is it I meditate the process is different for everyone. Yes, there isn't one I believe there's no one formula."
},
{
"end_time": 5702.619,
"index": 221,
"start_time": 5679.497,
"text": " Actually, all the methods. Yeah, it's useful to hear the stories from people who have gone through. Absolutely. I think that we absolutely the way the best way that we can address this is by actually sharing our stories and not trying to say it should be done this way or that way. Yeah, but this is was the first step. You see, this is what led me to the process of self inquiry. So I already mentioned how"
},
{
"end_time": 5730.486,
"index": 222,
"start_time": 5703.131,
"text": " It led me to question for instance why am i doing mathematics am i doing it because i love it or am i doing it because i want to achieve recognition and awards and so on that's what was one of the things came out of it but the much bigger thing that came out of is the whole idea of self-inquiry the whole idea that there are some things which are not aware of the question who am i i thought i heard this question before i knew that it was inscribed on the apollo the apollo temple in delphi but i didn't understand what it meant"
},
{
"end_time": 5758.882,
"index": 223,
"start_time": 5731.271,
"text": " Who am I? I'm Edward Frankel. I'm a Berkeley professor. It's a dangerous question. It's a very dangerous question when you actually engage with it, for real. Yeah, it's a terrifying question. And we can't do it on our own, I think, because ultimately it has to be somebody in your life. So it could be a therapist, for instance. In my case, I was lucky. There was some human being who just came into my world, who was a wise woman, let's just say, a wise woman, and somebody I respected."
},
{
"end_time": 5786.032,
"index": 224,
"start_time": 5759.514,
"text": " who, and this is about a year after the book came out, so this is summer of 2014. The book was published in October 2013. So I was ready to go beyond from Edward 1.0 to Edward 2.0. You have to be ready for it in some sense, and then the universe, quote unquote, will conspire. At least that's what happened to me, and I have since heard stories, similar stories from other people."
},
{
"end_time": 5815.879,
"index": 225,
"start_time": 5787.176,
"text": " So what happened was that she basically, so we start talking about life and so on. And I was very curious about reality. What is reality? Because I was obsessed with the idea that where mathematics comes from. It was very clear to me, it doesn't come from human minds, specific human minds. Like Pythagoras did not create Pythagoras theorem, you know? Or Evariste Galois did not create Galois groups. They were there for him to discover. But then what does it mean? What is reality then? What is at the base of reality?"
},
{
"end_time": 5846.834,
"index": 226,
"start_time": 5817.449,
"text": " And in fact, if you look and the title of my book is love and math and the subtitle is the heart of hidden reality. So it's kind of like my search for hidden reality was happening, even if I was not fully aware of what I'm doing, even when I was writing it. And then the crucial thing that she told me, she said, yes, Edward, there is hidden reality, quote unquote, but it's not outside. You think you find it somewhere. In fact, it's within you. You have to learn more about yourself. And so."
},
{
"end_time": 5870.845,
"index": 227,
"start_time": 5847.875,
"text": " What does it mean? She told me some stories of what it means, what it meant in her case that she was able to connect to some childhood experiences that she had when she was an adult already. And that completely changed her view, her outlook. And suddenly things start happening. I started remembering things that happened to me as a child. In particular, the experience that I described in the book."
},
{
"end_time": 5894.565,
"index": 228,
"start_time": 5871.288,
"text": " chapter three about my exam when i was 16 years old and i was not accepted was not was failed ruthlessly at the exam at moscow university i thought i knew i remembered it i remembered it factually i remembered it as a third person from a third person perspective but i did not remember it from the first person and so then suddenly this happened in september of 2014"
},
{
"end_time": 5921.749,
"index": 229,
"start_time": 5895.06,
"text": " where i was asked to speak about it and the night before at my hotel i was able to connect with a boy and it was like a tsunami i realize what happened what did you break down crying of course but it was it was worse because in some sense it was worse because the thought that i had in my mind was no amount of tears justify this world justify this life why what is the point"
},
{
"end_time": 5951.118,
"index": 230,
"start_time": 5922.056,
"text": " oh jeez it's really really kind of sad moment because you realize a part of you died i realized part of me died when i was 16 years old and i was not even aware of it for 30 years okay so i am moving is the battlefield of life crippled basically like i'm missing a limb and i'm not even aware of it and my mind my course my concept don't look there don't look there don't look there that's why i was coming up with all of these ideas about the universe and reality the objective reality and so on because how convenient"
},
{
"end_time": 5982.056,
"index": 231,
"start_time": 5952.108,
"text": " It's all deterministic and it's all a bag of particles. So particles don't feel pain or a human is an algorithm. So it's a coping mechanism. Coping mechanism for me, for me, it definitely was. And I will never say that it's true for everybody. Maybe it is for some people. Maybe it's not. All I'm doing, I'm sharing my story. This is my story. I am convinced that some of the naive and quite frankly ideas that I entertained about the world."
},
{
"end_time": 6010.247,
"index": 232,
"start_time": 5982.534,
"text": " were to a large extent motivated by me not willing to find out what happened to me when I was 16 years old, because it was too painful. Because it was too painful. I wrote a piece about this, by the way, I was asked to, I spoken about this number of times, including my last conversation with Lex Reedman. But I also wrote a short piece for volume by"
},
{
"end_time": 6040.52,
"index": 233,
"start_time": 6010.674,
"text": " my my my friend who is an expert Kim Polsky who is a friend who is an expert on AI safety so he published a volume I'll link it in the description yeah academic volume on AI safety and security and he asked me to contribute about first person perspective so I wrote about this and to what extent this defined me you know not knowing not knowing because then"
},
{
"end_time": 6071.323,
"index": 234,
"start_time": 6041.408,
"text": " your life becomes driven to a large extent by creating barriers of finding out and that's what it means who you are who am i right so i understood what it means if i if there is this part of me which i chopped off why because it was too painful so it is a defense mechanism nothing wrong with it we all happens to all of us i believe to some extent and there is a lot of literature about this by the way and neuroscience confirmations and so on so"
},
{
"end_time": 6095.316,
"index": 235,
"start_time": 6072.466,
"text": " But it's me, it's part of me, and yet I'm no longer connected to it. So do I know who I am? No, because there is this part of me which I'm not connected to. So that's one way in which you can, it becomes a very practical question. Who am I? Am I aware of all my secret little adverts?"
},
{
"end_time": 6125.06,
"index": 236,
"start_time": 6096.049,
"text": " And not necessarily, it could happen in adolescence and in adult life, but most traumatic experience, most difficult experiences usually happen when the children were not yet equipped to deal with this pain. And for me, it definitely defined my life. It gave me a lot of fuel, it propelled me to become a mathematician and so to achieve and so on, to prove those guys who failed me that how good I am, you see."
},
{
"end_time": 6152.637,
"index": 237,
"start_time": 6125.316,
"text": " Five years after I failed at 16, I get a letter from the president of Harvard University inviting me to come to Harvard as a visiting professor. I'm barely 21 because I wrote some papers which became famous or well known. You know why? Because the drive, you know, but then the cost of it, the downside of it is that I'm not, I lose that spontaneity, spontaneity of a child."
},
{
"end_time": 6181.561,
"index": 238,
"start_time": 6153.422,
"text": " that ability to look at the world with fresh eyes. I'm afraid of things. I'm scared. I want control. I want safety. Do you feel like that was a cause that if you were able to rewind time, you wouldn't pay? Because another perspective is, you know what, Edward? Everything that happened to you made you. I did it myself. Of course. Of course. I would not change a thing."
},
{
"end_time": 6210.418,
"index": 239,
"start_time": 6181.988,
"text": " but i can say it only now because i have connected to that child i connect to some other painful experiences that i can say it if somebody came to me before it happened and told me that edward you should be grateful to your examiners who failed you because that's what gave made you who you are i would just hit them in the face like what are you talking about how dare you but now of course i know yes of course i would not change a thing it was all me all along"
},
{
"end_time": 6241.732,
"index": 240,
"start_time": 6212.312,
"text": " And I am not, uh, no qualms about it. I would not have been who I am without any of those experiences unless I still refuse to connect to them. If I'm still refusing, then I'm not myself fully. You see what I mean? And so you ask, how did I get interested in the subject? So then this is 2014. Then I started getting invited to various forums to speak about this thing. And that's when that was the first wave when AI"
},
{
"end_time": 6262.722,
"index": 241,
"start_time": 6242.108,
"text": " became controversial. This is, mind you, nine years ago. But already you had people like Stephen Hawking and Elon Musk and Bill Gates already voiced concerns. And so this becomes my playground, this conversation, because I think up until that point, I haven't sort of this half asleep state."
},
{
"end_time": 6290.606,
"index": 242,
"start_time": 6263.046,
"text": " where i'm still i'm still thinking partially about myself as a kind of a machine i would like to be a machine because the machine doesn't feel pain so you know kind of feel safe also i feel that i know how things work again feel makes me feel in control you know suddenly i all of that is swept away my child my inner child you know such becomes such a trope um i don't want to use this expression but um"
},
{
"end_time": 6317.602,
"index": 243,
"start_time": 6291.049,
"text": " But it's true. It's like you again, this dimension, this dimension over, uh, you know, you talked about this, this archetype of divine child. That's the part of you which always wants to grow, which wants to look at the world in a fresh, with a fresh eyes, which is spontaneous, which is spontaneous, which is playful. I lost it to a large extent because my real, my connection to a very specific child, 16 year old Edward was severe."
},
{
"end_time": 6330.879,
"index": 244,
"start_time": 6318.524,
"text": " I am going opposite extreme and i'm saying"
},
{
"end_time": 6352.363,
"index": 245,
"start_time": 6332.927,
"text": " So then for me, AI becomes this idea of AI, the idea of uploading the singularity and uploading your mind and so on. It becomes totally opposite to what I'm experiencing, right? It almost becomes the idea of me being captured by this, again, by my cerebral side."
},
{
"end_time": 6381.698,
"index": 246,
"start_time": 6353.285,
"text": " because ultimately for me, this discussion with AI, it's just a safe way to talk about ourselves. AI represents our, our, um, cerebral logical side, like in the movie, uh, the 2001 space odyssey by, by the great Stanley Kubrick, how 9,000, what is how 9,000 is that the cerebral part of Dave Bowman, the astronaut, which has run amok. I know if you're familiar with this movie. Yes, yes, yes, yes."
},
{
"end_time": 6407.688,
"index": 247,
"start_time": 6382.193,
"text": " so that becomes the motivation for this for this for this interest you see and so ultimately i understand also that we need to find balance because of course this is amazing technological innovations and there's nothing wrong with them as long as we put the phrase the phrase our inquiry our questions properly not as a question of"
},
{
"end_time": 6436.561,
"index": 248,
"start_time": 6408.814,
"text": " It's not a good way, are they thinking, are they conscious, are they intelligent? The question is to what extent they help, they are here to facilitate, to help me to be as good an Edward as I can be. It's like artists in the end of 19th century, beginning of 20th century after photography was discovered. So suddenly you don't need to be, being an artist is not about rendering things realistically."
},
{
"end_time": 6458.148,
"index": 249,
"start_time": 6437.415,
"text": " Because a camera can do it better than you. So what do you do if artists say? It's over for us. We become the captives, the slaves of the photo camera. No, they discover other ways to express themselves. That's how you get impressionism, abstract art."
},
{
"end_time": 6476.015,
"index": 250,
"start_time": 6458.49,
"text": " Cubism, surrealism, and so on, where the focus is more on the experience of the viewer and the artist. You see, they accepted the challenge and it propelled them to the next level. And likewise for us, I think, it's very clear that Ciao GPT is showing us"
},
{
"end_time": 6505.981,
"index": 251,
"start_time": 6476.408,
"text": " But some of the things that perhaps we thought were creative, they're not that creative. The computer program, which is basically trained on just correlations of things in various texts throughout the internet, can actually reproduce it and maybe do a better job than you do. So I take it as a challenge. What am I bringing to the table if this computer program can replace these things? So what can I do that it cannot do? Yes. You see? Yeah. So there's something called"
},
{
"end_time": 6531.527,
"index": 252,
"start_time": 6506.527,
"text": " The moving of the goalpost fallacy, which I don't see as always a fallacy. So for instance, you just mentioned we thought that creativity was the ability to draw accurately. Let's say in the early days. That's right. Then we realized, okay, something else can do that. So we changed what creative means. But it's not because in the one sense, you can say we've moved the goalpost, but it's not a fallacy because our original definition reflects our ignorance."
},
{
"end_time": 6557.978,
"index": 253,
"start_time": 6532.09,
"text": " we realize because we can grow. That's the whole point. Everybody, especially I love it when it comes from people who actually completely sold on evolution. They say it's only, it's only force in development of say human beings or other species. You may agree or disagree with it. And some people say that maybe there are some other things that have to be taken account. I'm not going to make a judgment, but I'm just curious. What do you think evolution is?"
},
{
"end_time": 6587.824,
"index": 254,
"start_time": 6558.37,
"text": " Human beings if it's not this is a very good example How we can evolve is because we are challenged by the technology that we ourselves create Now this is a very different framework a very different mindset that the mindset of the sort of end of the world And how these things are going to capture us and kill us and so on it's not productive obviously But this challenge take it as a challenge take how you respond to it You know, I think it's very productive"
},
{
"end_time": 6617.892,
"index": 255,
"start_time": 6588.148,
"text": " I'm not saying something original. I've heard a lot of people say that. It's just that it's not necessarily represented in the debate that you could see in the media, because usually it's computer scientists who are being questioned. And let me tell you, if somebody asked me 10 years ago, before I started to ask the question, who am I? I would have given you an answer. Very confidently."
},
{
"end_time": 6647.995,
"index": 256,
"start_time": 6618.473,
"text": " You know, maybe that's another sign that you shouldn't trust someone is how assertive and how little self doubt do they show. I want to be personal, if you don't mind, and reveal something to you. Maybe this will go and maybe it won't. When you mentioned, look, you had some childhood issues. I've always heard this like childhood issues, childhood issues, and I've explored my childhood. I can't find issues. But then I realized, okay, well, you said 16. So I think I had well,"
},
{
"end_time": 6675.486,
"index": 257,
"start_time": 6648.933,
"text": " When I was 17, I had my heart so broken. I don't think it's been broken as much since ever. And man, with this podcast, Edward, almost with everything I do, I struggle so hard. I struggle, struggle, struggle, struggle, struggle. I push, and there's this ambition, competitiveness, and"
},
{
"end_time": 6706.015,
"index": 258,
"start_time": 6677.585,
"text": " There's a desire in me. It has to be the best. It has to be undeniably the best. Like when I interview someone, it has to be that someone could watch all the interviews of that person say this whole series of everything was the deepest with this person. And luckily, luckily, often I'll get the interviewees saying something like, like this, these were insightful questions. I've never been asked this or whatever. Okay. So I get some validation or from the commenters, but, but"
},
{
"end_time": 6730.401,
"index": 259,
"start_time": 6706.323,
"text": " So I'd often think, you know what, I don't have childhood issues, I have adult issues. Meaning that like, I have this distinct feeling that 10 years from now, I'll look at myself now and want to hug him. Like just say, Hey, man, like you, I'm sorry, like I'm broken now. But I also think that much of that comes from crippling feelings of self doubt and inadequacy from when I was 17."
},
{
"end_time": 6759.394,
"index": 260,
"start_time": 6731.032,
"text": " Sure, exactly right. Exactly right. And then the thing is, in what you say, it resonates completely. But one thing one has to be very careful of saying, there was no issue with it. It's our thinking mind who says that. Our thinking mind is very limited. So Jung, one of the main ideas that he brought sort of out and became part of our collective discourse is the idea of unconscious."
},
{
"end_time": 6783.814,
"index": 261,
"start_time": 6760.23,
"text": " Freud talked about subconscious, I prefer unconscious. So this idea that there are some realms of the psyche which are not accessible to the thinking mind yet. And it's very important to accept that, I think, because then it's not anymore that the thinking mind is the final arbiter of what did or did not happen. In my case, if you ask me in 2014, before I had my sort of experience of reconnection,"
},
{
"end_time": 6805.026,
"index": 262,
"start_time": 6784.804,
"text": " Are you connected to that boy that was suffered in 1984 in this exam? I would say yes, of course, because I remember every fact of it. And in fact, I wrote it. I wrote the story in my book, which was published a year before. Interestingly enough, a lot of people were inspired by it."
},
{
"end_time": 6831.51,
"index": 263,
"start_time": 6805.572,
"text": " and a lot of people wrote to me or talked to me about it, that they were touched by it. And I was surprised because I was not yet touched by it. But because that's the power of art. Because I wanted to write a book and to connect to my readers, I allowed the boy to speak. I was not yet ready to speak to the boy, me, adult Edward, in 2013 or 2012. But because I wanted the book to be real,"
},
{
"end_time": 6857.5,
"index": 264,
"start_time": 6832.244,
"text": " I delegated this chapter to him and was the first time that he was unfiltered. He spoke not to me yet. He spoke to the readers of the book, but the ice was broken. So we are barely a year later. I finally found the courage and the strength to speak to him directly and to understand, to remember what happened. So my thinking mind was not aware of it. It's very important to understand and it's, it cannot force it."
},
{
"end_time": 6885.52,
"index": 265,
"start_time": 6858.183,
"text": " it's very important not to force because if you're not ready for it i could commit suicide easily easily i could see that easily because you're so disenchanted you're so disappointed in this in this cruel cruel world you feel like there is no reason to live and you have to be very strong to to withstand that and in fact the point is that it passes it passed and i have this amazing experience of like"
},
{
"end_time": 6915.503,
"index": 266,
"start_time": 6886.51,
"text": " He comes alive. He's within me. Like I hold him. He's here. And I, and I, and I spoke to him to the little Edward and I said, look, you know, I'm sorry. I have neglected you for 30 years. I did not know, but look what we have done. Look what we have done. It was not in vain. It was not in vain. And now you're back and I will never let anybody hurt you. What did the little boy say in response? It was just beaming, you know, and"
},
{
"end_time": 6944.872,
"index": 267,
"start_time": 6915.913,
"text": " The next day I was invited to speak at this spoken word kind of event in New York in 2014. There is actually audio of it on my website. It's called a test. And I spoke and the boy spoke and it was like, I never experienced that kind of connection with the audience. It was the first time he actually spoke through a microphone into the audience because he was with me. I let him speak. So the point I was trying to make is that when we are ready,"
},
{
"end_time": 6973.695,
"index": 268,
"start_time": 6945.606,
"text": " If we're sincere, if we are not actively trying to prevent this type of experience, it will happen. Don't try to force it, but always ask when something is off, like when you feel get agitated. For me, it's like this, you get agitated unnecessarily triggered. What is the source? When was the first time I experienced that? Under what circumstances? So that kind of gives a path to finding out the source, because usually some kind of event"
},
{
"end_time": 7004.394,
"index": 269,
"start_time": 6975.196,
"text": " It could be a series of things. It may not be just a single event, I suppose. But most powerful are events, like you said, when we get broken. And it doesn't have to be a child. It could be adolescent, teenager. It could even be a young adult. But an experience as a young adult, once you process it, it may lead you to an experience as a teenager and which can lead you to an experience when you were six years old or something."
},
{
"end_time": 7009.65,
"index": 270,
"start_time": 7005.299,
"text": " There is nothing wrong, ultimately it becomes this beautiful journey."
},
{
"end_time": 7035.947,
"index": 271,
"start_time": 7010.111,
"text": " self discovery is beautiful because it's you you learn more about yourself people go you know like columbus you have to get on the ship and try to find india then he doesn't find india he finds america and so on here it's you you're here you cannot run away from yourself anyway and it becomes a beautiful process of self discovery and each time a new layer is left you see you start for me it's like this it's been like this i start saying things which i couldn't see before"
},
{
"end_time": 7056.237,
"index": 272,
"start_time": 7036.323,
"text": " and i'm pretty sure it influenced my mathematics also did you feel like a weight was lifted and you're actually even physically more flexible oh of course oh it's on the level of body it's an incredible uh restructuring which by the way is another way so there is yoga there's meditation all kinds of things which are also"
},
{
"end_time": 7083.217,
"index": 273,
"start_time": 7057.108,
"text": " meant to reconnect us to this other dimension. The problem is for somebody like me is in the mind, I'm in the mind, I'm in the mind, in the mind, meaning like the cerebral logical stuff, and I become a prisoner of it, that I try to apply that becomes my only tool. So if I'm confused, if I'm, if I'm not sure, it means used to be in for me, think about it harder, think about it more. That's the only way"
},
{
"end_time": 7113.097,
"index": 274,
"start_time": 7083.592,
"text": " Through logic, through reason, and so on. William James said that that's like trying to see more of the darkness by turning up the gas. Yeah, or it's like trying to find darkness with a lamp at night. You know, just where is it? Where is it? Or, you know, trying to find the white snow when you have orange-skinned glasses on you. Where is the white? Where is the white? Let me put on more glasses, more glasses. More, more yellow, more yellow."
},
{
"end_time": 7142.227,
"index": 275,
"start_time": 7113.575,
"text": " I mean, it's very clear. So the thing is, and then going back to your earlier question, if you asked me 10 years ago about AI and all this stuff, or, you know, before all this experience. So of course I'll give you a particular answer because I actually chose mathematics as a way to escape from reality because the reality was too cruel for me. I didn't want to deal with this stuff. So I found this what I consider to be a pure world of platonic forms where there was no bigotry."
},
{
"end_time": 7172.159,
"index": 276,
"start_time": 7142.756,
"text": " There was nobody to hurt me where I could just rebel in the beauty of it, you know, and don't bother me with your so-called wicked world, you know. So then how can you trust me? So some people, then people would come if they came to me and they, because they look up to me as a scientist, as a mathematician, so I have some expertise that they don't have. They would trust me to give them a kind of a wise answer, but I was not capable of giving a wise answer."
},
{
"end_time": 7187.432,
"index": 277,
"start_time": 7172.807,
"text": " What's up what's up."
},
{
"end_time": 7216.323,
"index": 278,
"start_time": 7187.927,
"text": " a good answer, but people don't realize because they think of us as their gurus, you know, and because they don't have, because our education system is broken. And also the popular book sometimes suggests things which are like, I go like, Whoa, this is 19th century science, which has been thoroughly repudiated by 20th century math and physics. So that's where we are. But I think luckily because of you have your, your podcasts and others,"
},
{
"end_time": 7246.63,
"index": 279,
"start_time": 7216.732,
"text": " And I think that it starts moving, it starts moving finally in the right direction. And the right direction is understanding that our personality, our first person perspective is intricately connected, is intertwined with our series. They do not exist on their own and we are not independent spectators and observers. We are in the thick of it. With you forgiving your examiners,"
},
{
"end_time": 7274.497,
"index": 280,
"start_time": 7247.79,
"text": " Did you have to, well, okay, firstly, do you still feel like you're able to forgive them? Or is there a part of you that? Absolutely. They suffered. I know one of them actually, um, it came to my attention that one of them around the same time when I was, um, reconnecting 2014, he died in a, he w he was a kind of a, he liked to go on hiking trips, like in the north of Russia alone."
},
{
"end_time": 7287.995,
"index": 281,
"start_time": 7274.821,
"text": " And they found his body and he died in one of those trips in 2014. And the other one, I don't know, the other guy, I don't know. But I absolutely believe that they suffered. They must have suffered. I mean, how do you feel by"
},
{
"end_time": 7316.8,
"index": 282,
"start_time": 7288.353,
"text": " If you do this to a young kid who's done nothing wrong, right? So it's just because of my Jewish name, last name, my dad is Jewish. So Franko is a Jewish name. My mom's Russian, by the way, you know, by, by blood, you know, and not religious at all and so on. And then yet you single out somebody like that. And then they give this, you give this hard questions. It's a setup, right? So this is well documented. I'm trying to say, I see that they must have suffered."
},
{
"end_time": 7346.237,
"index": 283,
"start_time": 7317.756,
"text": " I see that they were misguided. And so that's number one. And number two, also, you know, thank you for giving me all this fuel. Without which, I mean, if I was accepted to Moscow University, oh boy, I would be living in a dorm. Okay. And probably party like there is no tomorrow. Would I become a good mathematician? I'm not sure. Which okay, would still be an interesting life."
},
{
"end_time": 7369.206,
"index": 284,
"start_time": 7346.766,
"text": " But this definitely shaped my life in a particular way and brought me to places which I may not have been able to reach otherwise. So in some sense, yes, thank you. It sounds weird, but it's only because my boy is here and he's not going to let me lie. You know, it's not going to say he's laughing with me. It's like, yeah."
},
{
"end_time": 7395.998,
"index": 285,
"start_time": 7370.776,
"text": " That's the paradox. That's the transformation of life. That is evolution and growth from somebody who is not willing to look that pain in the eye, so to speak, you know, face that reality and therefore is bound to run away from certain experiences in life or from certain insights or from certain ways of understanding life to someone who becomes friends with that."
},
{
"end_time": 7422.927,
"index": 286,
"start_time": 7397.159,
"text": " through suffering of course through suffering you cannot avoid it in my opinion and by the way you know it's not i am i listen to there's a great conversation uh you know but in lex pridman and uh you are karate you know that you wrote sapiens and a great historian and writer and he's something he said a bunch of things which i really resonate with me he's suffering he's a human this is what"
},
{
"end_time": 7452.483,
"index": 287,
"start_time": 7423.814,
"text": " distinguishes that from robots ultimately. So in other words, Turing had this imitation game where you have a conversation with an interrogator and the robot is trying to convince the interrogator that it is human. But in fact, the real criterion is can it suffer? Because that is, I would say unavoidable, an essential part of human life. You know, and so"
},
{
"end_time": 7480.179,
"index": 288,
"start_time": 7452.807,
"text": " Running away from it limits us. Being able to process it liberates us. That's my view. Okay. Again, I preface it by saying that's been true for me. It may not be the case for everyone else. I don't know. I have no way of knowing. I do have anecdotal evidence that it works for other people in this way too, but I cannot be sure. Is your forgiveness of your examiners predicated on them suffering?"
},
{
"end_time": 7508.046,
"index": 289,
"start_time": 7480.845,
"text": " So that is to say, if you thought that they didn't suffer, would you still forgive them? This Marshawn beast mode Lynch prize pick is making sports season even more fun on projects. Whether you're a football fan, a basketball fan, you always feel good to be ranked right now. New users get $50 instantly in line up when you play your first five hours. The app is simple to use. Pick two or more players. Pick more or less on their stat projections."
},
{
"end_time": 7523.404,
"index": 290,
"start_time": 7508.046,
"text": " Anything from touchdown to threes and if you're right you can win big. Mix and match players from any sport on PrizePix, America's number one daily fantasy sports app. PrizePix is available in 40 plus states including California, Texas,"
},
{
"end_time": 7551.442,
"index": 291,
"start_time": 7523.626,
"text": " Good question. Good question."
},
{
"end_time": 7578.37,
"index": 292,
"start_time": 7552.142,
"text": " I mean, like I said, there are two aspects of it. First of all, me recognizing that they may have suffered themselves. And second, my gratitude for participating in this experience, which gave me so much fuel that it launched me into the stratosphere. So they were participants in this, maybe motivated by something"
},
{
"end_time": 7605.179,
"index": 293,
"start_time": 7579.172,
"text": " You're making me realize something, which is that I, so again, I don't know how much of this I'll keep in, but for myself with when I was 17, I would say that, oh no, no, no, I forgive this person because I'm the wretched, sordid, despicable person who"
},
{
"end_time": 7633.063,
"index": 294,
"start_time": 7605.759,
"text": " who looks at other people who are successful and I'm like, I have no mentor. I, when I went to university, like I had depression for seven years. So I skipped classes. I didn't have a peer group and I would look at people who are successful and be like, yeah, well that's because you had advantages and I didn't. So in a sense it's like a prisoner with a door locked from the inside. And I say all of this with some, well with a large amount of saltiness and, and just,"
},
{
"end_time": 7649.77,
"index": 295,
"start_time": 7634.087,
"text": " Because I'm trying to be blunt, but also because I'm overcompensating for my urge to sugarcoat it. And I just lost years of my life. And so I would point the finger at myself. And I think part of the problem is"
},
{
"end_time": 7677.432,
"index": 296,
"start_time": 7650.35,
"text": " is that some of what was done to me, let's just put that in quotations, was not okay. But I'm not able to say that because I have to point the finger to myself. But then subconsciously, I'm still pointing the finger at someone else. And that's okay. Don't force it. That's my advice. In other words, don't forgive prematurely because then it means you're trying to short circuit something. That's my view. There may well be something"
},
{
"end_time": 7704.258,
"index": 297,
"start_time": 7677.892,
"text": " for you to discover in this memory, in this memory. Don't try to do it fast. What's the point of, you know, it's like Alan Watts said, you know, when you play music, the purpose is not to get to the end of the piece. Because if that were the case, then the fastest musicians would be the best. No, it's the point is to play. And so just be open, maybe be open to the idea that there is more to discover."
},
{
"end_time": 7734.991,
"index": 298,
"start_time": 7706.169,
"text": " Hey, who knows? Yeah."
},
{
"end_time": 7764.462,
"index": 299,
"start_time": 7735.418,
"text": " that that the struggle, sorry, not suffering. I don't I don't I don't suffer. Sure, whatever, whatever. Yeah, more and more. I've been biking recently, Edward. So and there's this new feeling, a new feeling. I don't know how to describe it other than when I look out at the world, it's like a it's like the feeling when you're extremely thirsty and then you take a gulp, but it's of satisfaction and beauty. Something like being transfixed by"
},
{
"end_time": 7794.497,
"index": 300,
"start_time": 7765.094,
"text": " the splendor of the world or amazement. Something I look out, I'm like, whoa, and I haven't seen that for my entire life, except for the past few months, like more and more and more. And I don't know where I was going with that. But what I'm saying is that despite all of this talk, like of working super, super hard, working hard, like understanding different physical theories and dealing with consciousness theories, like that's rattling."
},
{
"end_time": 7817.995,
"index": 301,
"start_time": 7795.111,
"text": " And at the same time, juggling editing, family obligations, so on so. Okay, this is what an honor that I get to speak with you. Like, holy moly, you're like for years, I actually, I didn't I remember recognizing your face. And you've influenced me years ago, and I'd forgotten. And now I get to speak with you. Now I get to read your book and speak with the author."
},
{
"end_time": 7835.845,
"index": 302,
"start_time": 7818.66,
"text": " I get to study the Langlands program. I get to make contributions that stay in math"
},
{
"end_time": 7865.316,
"index": 303,
"start_time": 7836.237,
"text": " Man, what lives. Yeah, well, it's it's beautiful. It is beautiful. Edward. OK, one last thing. Now I feel guilty because this is something that comes up is that whenever I have this feeling of, wow, look how great life is. Then I think, yeah, but most other people or at least in my mind, most other people and many other people are suffering. Who am I to feel so good? And then that impinges. And it prevents me from fully appreciating a moment because I'm like, yeah, but there are people who are starving. Yeah, but there are people who can't make ends meet."
},
{
"end_time": 7893.968,
"index": 304,
"start_time": 7865.316,
"text": " And yeah, but there are people who so and so and so. So how do you ever struggle with that? And how do you deal with that? No, of course. But I don't know. I feel that we cannot do it. But we have a life, a human being that has limited resources, we have limited life, you know, like in terms of time, longevity, you know, how many years we got, we have limited spatial dimensions, and so on. And resources, energy. So the question is not to spread themselves thin. And"
},
{
"end_time": 7922.756,
"index": 305,
"start_time": 7895.162,
"text": " That's why i'm not so happy when people go on twitter and they start venting their anger because it actually means run away from your true responsibilities. It's cheap to go and accuse and blame on people. It's an emotional discharge. So if you really care about this, just go to that war zone and go to that poor country and so on and do it. Do it. Action is not the same as words which are not supported by action."
},
{
"end_time": 7952.381,
"index": 306,
"start_time": 7923.251,
"text": " so so then what's the what's the how to resolve what's the resolution of this resolution is to find what you truly love and dedicate yourself to it hundred percent and this way you will contribute in a positive way to the society and then your own you know self-recriminations and thoughts about you deserve don't deserve and so on is is you're blocking yourself from being fully dedicating and really impacting it takes energy away"
},
{
"end_time": 7973.899,
"index": 307,
"start_time": 7952.773,
"text": " that's how i see it that's like self-doubt it's natural i'm not i'm not saying it's not it's where i'm i'm given to sometimes two bouts of self-doubt and self criticism and so on it's normal i think but ideally ideally i would like i consider it as something that is a waste and the way to"
},
{
"end_time": 8003.575,
"index": 308,
"start_time": 7974.258,
"text": " to overcome it is to truly do what you love and and just keep going with it and look you know how successful your podcast is for instance you know it's only been around a couple of years you have so many some people such a dedicated audience and really great interviews you know i've watched a bunch of them so that's how that's what we can do when we really dedicate ourselves to something that we truly love and i think that's the that's the only way we can do is human beings what else can we do"
},
{
"end_time": 8031.459,
"index": 309,
"start_time": 8003.916,
"text": " we be aware of yourself be aware of the world be aware of the suffering in the world but also be aware that you cannot go you cannot pretend that you are the almighty god who is going to solve everything for everybody no that's not how we set up you have your mission it's not also it's not like a mission which is written which is given by somebody i feel like it's it happens as we go you choose it as you are live it's part of life"
},
{
"end_time": 8049.582,
"index": 310,
"start_time": 8031.852,
"text": " But if you're open, you don't believe it's co-created, like there's a part that's innate and there's a part that you choose. It's a narrative. So maybe, who knows? I feel like all of this, what you described, any such theory is a theory, is a story that we tell ourselves and"
},
{
"end_time": 8063.831,
"index": 311,
"start_time": 8050.879,
"text": " We are human. A very important essential part of being human is the ability to tell stories to each other and to ourselves. By the way, this is where I love Yuval Harari also. He explains very clearly the history of ours."
},
{
"end_time": 8092.858,
"index": 312,
"start_time": 8064.821,
"text": " Civilization is a history of ideas and and stories that mostly still I not even ideas stories We tell each other stories and it creates this sort of market of stories and they evolve and they merge and they separate and Who knows how it happens, but we also tell ourselves stories now in this story Stories are different. So if it's if it's helping me to Be the best I can be and this is something which we can feel right?"
},
{
"end_time": 8122.91,
"index": 313,
"start_time": 8093.439,
"text": " Am I on the right path? Am I not on the right path? Kind of. It kind of like a general sense. Then okay, go along with the story, be open to changing the story at some point when it becomes more of a hindrance than something that propels you, you know. So what you described is a very reasonable way to think about things. But I've tried many other ways to approach and conceptualize and"
},
{
"end_time": 8145.503,
"index": 314,
"start_time": 8123.268,
"text": " My feeling today is that sometimes I need it, sometimes I don't, sometimes I just feel, you know, sometimes I'm guided by something like you described, that there is this higher self and lower self and this collaboration between the two or something."
},
{
"end_time": 8166.613,
"index": 315,
"start_time": 8146.015,
"text": " Sometimes I feel that I don't need it. It changes. But what's important is not to say it's like that. And that's it. That's would be theory. Right, right. Death is love exposed. That's a quotation from a wise man. Oh, yeah. Yeah. Do you know who said this? You said this."
},
{
"end_time": 8196.186,
"index": 316,
"start_time": 8167.022,
"text": " Death is love at its barest or at its most exposed, its most wrong. Yes, when you are faced with death, this is when you face unfiltered love. Yeah, explain that, please. Well, I feel like, you know, death is something that does not accept any spurious stuff. For instance, you can"
},
{
"end_time": 8225.623,
"index": 317,
"start_time": 8196.459,
"text": " I specifically talked about my experience when my father died four and a half years ago. And we were very close and I was devastated by it. And I tried, I was kind of mature enough, so to speak, to ask myself to say, just live through it and observe and observe what is happening, what is happening here. So I was able to see these things, which maybe if I was just completely"
},
{
"end_time": 8254.599,
"index": 318,
"start_time": 8226.254,
"text": " Overwhelmed by grief, we wouldn't be able to see. And what I saw was that there was a natural tendency to come up with some explanation of what's going on. It's like we just discussed, you know, that story, some story, but they, they could not hold those stories. Like they melted in the face of that. Like this is staring at you and any stories you throw at it, took a story to protect yourself."
},
{
"end_time": 8283.695,
"index": 319,
"start_time": 8255.657,
"text": " So then what is it then? And then why do I feel so much pain? And then I realized that the intensity is simply my realization that my father, you know, my father, well, you could say my father's gone, I will not be able to spend time with him and to, to laugh together and to enjoy things together. But also why does it bother me so much? Because I love him. So the root of it is love. And then I thought the reason why it is so painful is because"
},
{
"end_time": 8313.319,
"index": 320,
"start_time": 8284.48,
"text": " Normally, we put filters because we pretend that it's two different beings communicating with each other. But ultimately, when you're in love, and I strongly believe in this, you cannot love another. You always love. When it is true love in this moment of experiencing it, you become one. It could be your father, your parent, it could be your friend, it could be your lover, your partner, you know."
},
{
"end_time": 8343.899,
"index": 321,
"start_time": 8314.275,
"text": " But this is a kind of cornerstone of the Eastern tradition for me, this idea of oneness. And it sounds, it has been perverted, obviously, by new agey stuff and all this kind of when it becomes, it makes it a bit facile, you know, a bit too facetious, you know. But the corner, the core of idea, the core idea is precisely that, in my interpretation, is that the moment of love is the moment when a separate being"
},
{
"end_time": 8371.869,
"index": 322,
"start_time": 8344.258,
"text": " It ceases to exist when the boundary melts. Whether we conceptualize it this way or not, it doesn't matter. We feel it. We feel this very strong emotion. It's a particular way of conceptualizing it, of course, but I think it's a helpful one because ultimately it points out to another way of cognition, which is not tainted by the sense of a separate being, which is to me the root of a lot of suffering is the idea that there is a separate being actually."
},
{
"end_time": 8401.834,
"index": 323,
"start_time": 8373.626,
"text": " I can always argue to what extent it's real and to what extent is a construct. Obviously, it's a very useful concept since I'm using it, you know, but it's important to know that there are other ways of experiencing life and love to me is what points to it, what points to the ability to experience life without the burden of an idea of there being a separate individual who is experiencing it."
},
{
"end_time": 8431.118,
"index": 324,
"start_time": 8402.466,
"text": " But something bigger, something bigger than that. And so death is one experience where one is force. If indeed who died is somebody you deeply love. I think that in this experience that that comes to the fore that it's a sense of love so intense that it feels like pain."
},
{
"end_time": 8456.596,
"index": 325,
"start_time": 8432.21,
"text": " Well, Professor, I have so many questions on algebraic varieties and L functions and automorphic sheaves, but this was an unexpected turn and I hope to speak with you again. I appreciate you spending so much time with me. That's my pleasure. Well, we talk, I just want to comment on this. We talk about what interests us."
},
{
"end_time": 8476.749,
"index": 326,
"start_time": 8458.063,
"text": " Yeah, well, speaking of not architecting prior to engaging, like the union conception of what true art is versus constructing the CN Tower beforehand. The other option is you just like watch the diffusion of an ink drop and Bohm would call that the unfoldment and you just go where it flows."
},
{
"end_time": 8505.572,
"index": 327,
"start_time": 8477.176,
"text": " Yeah, that's what it felt. And it's good that we can do it because I think that most interesting things in some sense are the surprise, things which are not pre-set or kind of like premeditated, but the things which arise spontaneously kind of, you know? And so that's why I really enjoyed it too. I had a question from Richard Borchards, to you."
},
{
"end_time": 8527.756,
"index": 328,
"start_time": 8506.203,
"text": " Okay. Yeah, his question was, what role do function fields play in higher dimensional algebraic varieties in the Langlands program? So we may as well just touch on a couple math questions. Oh, yeah, yeah, yeah, for sure. So, well, Richard Burch person was my colleague at UC Berkeley. It's a very brilliant mathematician."
},
{
"end_time": 8556.288,
"index": 329,
"start_time": 8528.114,
"text": " He won the Fields Medal, but also, you know, apart from that, he did some groundbreaking, really, really amazing work. He was the first one to formalize the concept of a vertex algebra, which has actually been a staple in my research. And he proved the moonshine conjecture. And he's a very, very nice human being as well. So I'm kind of pleased to have a question from him."
},
{
"end_time": 8586.049,
"index": 330,
"start_time": 8556.647,
"text": " What he's asking about is the following. So we just talked a little bit about the language program. So language program, a regional formulation is for number fields, for numbers, numerical systems, like. Reels, complex and so on. That's right. But on the other side of it is the human surfaces. Which are like sphere or surface of a donut and so on. And so Andre Vey in his Rosetta Stone that we discussed,"
},
{
"end_time": 8615.247,
"index": 331,
"start_time": 8586.374,
"text": " he found a bridge between the two which is very similar on one side you have this vertical systems on the other side you have this geometry of surfaces and the the bridge that he found is the following you should look at instead of looking at the surface itself you look at functions on it and these functions are they're going to be what's called meromorphic functions or rational functions so they have they have zeros and poles that sometimes at some points are not defined they go to infinity"
},
{
"end_time": 8644.718,
"index": 332,
"start_time": 8616.271,
"text": " and this gives you what's called the function field of the Riemann surface from which you can basically recover it and that field is very much like the number field like rational numbers but what stands in between is when you take a so Riemann surface as a curve from the point of view of algebraic geometry it's a curve over complex numbers but you can also so it's defined by some equations with complex coefficients renormal equations with complex coefficients"
},
{
"end_time": 8674.718,
"index": 333,
"start_time": 8646.254,
"text": " coefficients in the field of complex numbers. But you can also write such equations with coefficients in other numerical systems, for example, in finite fields. So modular prime, modular prime, like clock arithmetic, modular prime numbers. And then it really becomes that the function field of that is really very much like, like rational numbers or a field of rational number. And so this way you found a bridge between the two. So that's what is referred to as a function field case."
},
{
"end_time": 8698.234,
"index": 334,
"start_time": 8675.35,
"text": " But in the Langlands program, it's about curves. So it's one-dimensional, geometrical objects. And what Richard is asking, what about two-dimensional? Now, Riemann surface ostensibly is two-dimensional from the point of view as a real manifold, right? And so a sphere has a longitude and altitude, no, longitude and latitude, right?"
},
{
"end_time": 8727.5,
"index": 335,
"start_time": 8698.882,
"text": " two coordinates, so its real dimension is two, but its complex dimension, because remember complex numbers are two dimensional over the real numbers, because there is square root of negative one, there is an independent element. So complex numbers are two dimensional from the perspective of real numbers, therefore a two dimensional real thing is one dimensional from the perspective of complex numbers. So as a complex geometric shape it's one dimensional,"
},
{
"end_time": 8757.193,
"index": 336,
"start_time": 8728.387,
"text": " So the question is, can you extend the ideas of the language program to two dimensional objects or three dimensional and so on? And unfortunately today with the very few, there is very little information about this, very scant. So there's a few examples where some analog exists, but by and large we don't have a picture. So the answer is in the negative right now. But the hope is that eventually we will be, it was just much more complex, I guess."
},
{
"end_time": 8786.015,
"index": 337,
"start_time": 8757.705,
"text": " You know, you had a chapter in your book called A Delicate Dance. I think it's chapter 16. Doesn't matter. The point is that in it, you had a film script. You spoke about you and Drinfield. Yes, right. Yeah. Why did you choose to frame it like that? Because I have been a cinema aficionado, you know, a film lover for many years. I also co-directed a star in a short film."
},
{
"end_time": 8812.756,
"index": 338,
"start_time": 8786.237,
"text": " I was given a lot of trouble. Yeah, you co-directed and started. I co-directed, co-wrote and started in it. It's called Rights and Love and Math. Rights like R-I-T-E-S. And also I wrote a script. I actually wrote a script for a feature film with my friend and mentor, Thomas Farber, who's a writer and teaches literature, creative writing at UC Berkeley."
},
{
"end_time": 8840.452,
"index": 339,
"start_time": 8813.49,
"text": " So we wrote a script called The Two-Body Problem about a writer and a mathematician who meet in the south of France and they talk about their love affairs, hearts broken and so on and how to become, how to be better humans. So I, for instance, I had a software, I had a script writing software already and I thought that"
},
{
"end_time": 8868.046,
"index": 340,
"start_time": 8841.203,
"text": " It's always good to put it in a kind of artistic framework. Since my job was to shake people's understanding of what mathematics is like. So for instance, there are these boring people talking to each other about some boring stuff. So I want to make it come more alive. So I was suggesting, imagine it as a movie, as a Netflix series, which by the way, you know,"
},
{
"end_time": 8897.415,
"index": 341,
"start_time": 8868.558,
"text": " This thought came to me because I watched on your channel, on your podcast, you had a conversation, a debate between two very brilliant people, Sabine Hassenfelder and Bernardo Castro. I've never met Sabine in person, but I've followed her a little bit. And Bernardo I have actually met. And they argued about super determinism."
},
{
"end_time": 8922.79,
"index": 342,
"start_time": 8897.739,
"text": " And to me, I watched it like a great Netflix series, episode of a Netflix series. It was like the impact in terms of like, there's so many subtleties there. There's so many layers. And there's such, we could do a whole conversation of me like trying to unpack that. But I'm just trying to say,"
},
{
"end_time": 8937.363,
"index": 343,
"start_time": 8923.814,
"text": " I am lucky to have the expertise to follow the discussion and actually have my own opinions and so on, but also to observe the psychology. So to me, it was a case study in what we discussed earlier, how much our"
},
{
"end_time": 8966.186,
"index": 344,
"start_time": 8939.48,
"text": " preferences, like psychological, metaphysical, philosophical, how much they are, how intricate, how intertwined they are with our theory, supposedly abstract theories of supposed objective reality, how much we are driven and passionate about certain ideas. You know, it was a case study for both of them, actually, and they were because they were so sincere about it."
},
{
"end_time": 8995.35,
"index": 345,
"start_time": 8966.391,
"text": " Interesting. You felt both were staunch in their opinion. Sorry, for the people who are watching, the link to that will be in the description. And it's the debate between Bernardo Castro and Sabine Haassenfelder called the new theory or new super determinism, something like that. It'll be in the description. It's fascinating because, you know, I don't know, I just want to say it's such an it's actually brought me to read some stuff about it. And I find it very"
},
{
"end_time": 9021.357,
"index": 346,
"start_time": 8995.845,
"text": " So in this case, the way I see it is that Sabin is very adamant about the particular idea that is local determinism. She wants to preserve it. And where does it come from? So of course, she probably would deny that this is really her preference, but that's what comes across. I have no horse in this race, okay? I'm just looking as an observer. And it's very clear that"
},
{
"end_time": 9045.111,
"index": 347,
"start_time": 9021.834,
"text": " she is sometimes a little too emotional about it like for instance she basically says this people who don't understand it are idiots but not quite paraphrasing she by and large she was incredibly you know gracious she was very calm and so on but i also read some other stuff she wrote about it and saw a video and sometimes she goes a little overboard but also like i see how"
},
{
"end_time": 9076.22,
"index": 348,
"start_time": 9046.613,
"text": " So the way she wants to sacrifice this was called Statistical Independence and Bernard was arguing that then science is over. I think that he's exaggerating too a little bit. So for him, obviously, the Statistical Independence is dear and local determinism is not. You see, but then neither of them would actually come out and say, look, this is what I hold dear to me. And that's why I build a theory around it. They wouldn't say that. They would say,"
},
{
"end_time": 9103.046,
"index": 349,
"start_time": 9076.869,
"text": " But of course you can't do that because then science would be finished or something, both of them kind of, because this is where I feel this is where we can make one more step as a community. Where we really would advance as as scientists and human beings is when we will admit to ourselves to what extent we are motivated by dearly held principles."
},
{
"end_time": 9131.305,
"index": 350,
"start_time": 9104.002,
"text": " Like, why does Sabin care about local determinism so much? I'm asking for a friend, you know, like maybe if she finds out, if she finds out, maybe she'll learn something about herself. I can tell you why I don't care about it, for instance, because I think the world is inherently indeterministic. In my experience, it's not. But also for me, actually, this is not so essential with this Bell's experiment, the"
},
{
"end_time": 9155.367,
"index": 351,
"start_time": 9131.664,
"text": " Entanglement is not a big deal. What is a big deal in quantum mechanics is non-commutativity. The observables, familiar observables like coordinate, momentum, and so on, which in classical physics, they commute with each other. They're like numbers or functions. They become non-commutative. That's why they have to be realized as accurate. And this non-commutativity is an absolutely essential phenomenon."
},
{
"end_time": 9185.794,
"index": 352,
"start_time": 9156.288,
"text": " Now, mind you, the commutator between, say, momentum operator and coordinate operator is very small. It's proportional to the Planck constant. So classical physics, therefore, can be thought of as a limit of quantum when the Planck constant goes to zero. Likewise, Newtonian mechanics can be thought of as a limit of Einstein's special relativity when the speed of light goes to infinity. And likewise,"
},
{
"end_time": 9213.916,
"index": 353,
"start_time": 9186.203,
"text": " In general relativity, we have curved spacetime and it's our traditional view was that we live in the Euclidean space, which has no curvature. So there are three parameters, non-zero parameters that were introduced in the 20th century. The Planck constant, which makes the world non-commutative. And to me, I feel that it is a very essential thing and it is fundamental. And if you accept that, I don't think super-determinism can save you. I have not really studied this."
},
{
"end_time": 9237.858,
"index": 354,
"start_time": 9214.48,
"text": " even if you drop um that is going depends and so on there will be phenomena which will not in principle you cannot describe by classical physics because it is commutative so you're trying to feed non-commutative world into commutative world i don't think it's possible but i'm not 100 sure to me it's a feature not a bug likewise the fact that"
},
{
"end_time": 9268.063,
"index": 355,
"start_time": 9238.916,
"text": " The speed of light is finite, and it's the same to all observers, which is the feature of special activity. It's a special thing. It's not something you fight. My question would be, how much do we want to sacrifice of the things we have discovered in the 20th century to accommodate our belief systems? For instance, let's suppose I am interested in preservation of local determinism. So then I'm willing to postulate that my experimental apparatus somehow magically"
},
{
"end_time": 9282.568,
"index": 356,
"start_time": 9270.316,
"text": " he is"
},
{
"end_time": 9302.585,
"index": 357,
"start_time": 9283.234,
"text": " It's undoubtedly crazy. The question is whether it's crazy enough. So the fact that it's weird to me doesn't mean it's wrong. So I keep open mind. It may well be that super determinism will become prevalent scientific theory in the next few years. Who knows? I would not be surprised to argue that it's impossible because it's weird is disingenuous."
},
{
"end_time": 9329.94,
"index": 358,
"start_time": 9303.37,
"text": " You know, for me, the point is not that. The point is that, let's admit why this is put as the forefront of a theory. It's because of a preference. You know, there is this Samuelson, the great economist had this theory called revealed preference in economics, that sometimes observing agents behavior, you can actually find out what their preferences are. That's called the revealed preference. To me, it's a revealed preference. So"
},
{
"end_time": 9359.445,
"index": 359,
"start_time": 9330.538,
"text": " Then my question is, okay, so suppose you have a preference for preservation of local determinism and you're willing to sacrifice this, this and this. Okay. Suppose you have a preference for classical Newtonian mechanics, how much you willing to sacrifice to pretend that Einstein's relativity can be accommodated by experimental apparatus. So for instance, we know that what happens, one of the predictions of special relativity is"
},
{
"end_time": 9390.077,
"index": 360,
"start_time": 9360.128,
"text": " that as you move faster, time slows down and distances shrink, right? How much you're willing to ascribe it to some kind of conspiracy between detectors that you use in your experimental apparatus. Like, I don't think anybody asked super determinists this question, like, would you be willing also to do that? And if not, why not? Also, Einstein's generativity says there is curvature."
},
{
"end_time": 9417.671,
"index": 361,
"start_time": 9390.452,
"text": " The curvature of space-time is the signature of gravity. Suppose you are an adherent of Euclidean geometry and you don't believe it's true, because when I look outside of my window, I don't see any curvature. Well, except curvature of the Earth, but I talk about the curvature of space-time. How far are you willing to go to preserve zero curvature in your theory by ascribing different observed phenomena? For instance, Eddington discovered that"
},
{
"end_time": 9442.585,
"index": 362,
"start_time": 9418.729,
"text": " You know, famously in 1919, Arthur Eddington's expedition discovered that the ray of light bends around the massive star. Let's suppose you, and this is considered as experimental verification of Einstein's relativity, the fact that space-time is curved around massive bodies emitting gravitational force."
},
{
"end_time": 9471.852,
"index": 363,
"start_time": 9443.626,
"text": " Let's suppose that you like Euclidean geometry, and you are adamant that the world is Euclidean. No courage. Are you willing to then say that your experiment is playing away all this experimental data by saying that we should look deeper into how these measuring devices are set up? Maybe there is some weird communication between them, which we are not aware of, which creates this illusion."
},
{
"end_time": 9498.063,
"index": 364,
"start_time": 9473.012,
"text": " Now i have to be consistent so if you say yes in principle you could do that you could do that and it's kind of one we are kind of like in the same game here because for us super determinists is very essential to believe that there is local determinism we are willing to sacrifice other aspects of our theory to accommodate this then it's a it's a different story but"
},
{
"end_time": 9516.903,
"index": 365,
"start_time": 9498.729,
"text": " Ask this questions to also see maybe to what extent you are investing yourself and your preferences into your city something you may actually use others for example she has been extremely sad been. How's it feel extremely helpful in unraveling sort of this."
},
{
"end_time": 9544.991,
"index": 366,
"start_time": 9519.07,
"text": " policy of the strength theory and the fact that practitioners of strength theory still not willing to admit the failure of their enterprise. Sabin has been extremely positive in my opinion in this. She wrote a whole book called Lost in Math saying that we are led astray by our preferences for what we consider beauty and so on. But can we also be led astray by our preferences for certain philosophy or metaphysics?"
},
{
"end_time": 9574.701,
"index": 367,
"start_time": 9545.435,
"text": " And it's always nice, easy to see it in other people. Can we see it in ourselves that we're actually doing something very similar? Now, then the next question is, do I see it in me too? Because I'm now saying, I'm not criticizing actually, I'm trying to explain why to me it was like an amazing Netflix movie. Unfortunately, you need to have some background to understand."
},
{
"end_time": 9601.937,
"index": 368,
"start_time": 9575.674,
"text": " But if you do, it is an incredible case study in how we are being human, and it's normal. But it shows to me also, it helps me, it's almost, I want to say thank you so much for showing this to me so clearly. It's informative about yourself. Yes, because I'm also, and by the way, it extends beyond science. How often, you know, do I find myself"
},
{
"end_time": 9628.592,
"index": 369,
"start_time": 9602.415,
"text": " in my life, in my personal life, adhering to certain ideas, knowing full well that there is no proof for them, but it's just like how I want it to be. And then suffering is a result. And to see in a microcosm, this process, how we fool ourselves, how easy it is for us to fool ourselves. You know? Also, for instance, she goes like,"
},
{
"end_time": 9653.012,
"index": 370,
"start_time": 9629.275,
"text": " I really want to work on this because I am alarmed by the fact that the collapse of the wave function happens faster than the speed of light. But excuse me, quantum mechanics contradict special relativity. Everybody knows this. That's the whole point. That's why we have the next level theory, which is called quantum field theory. I have not yet seen any super determinism addressing local determinism."
},
{
"end_time": 9680.879,
"index": 371,
"start_time": 9654.77,
"text": " In the framework of quantum field theory, they tried to do it in quantum mechanics, and then they- Okay, so this has been a bit too harsh on Sabin. So to be fair now, what would you say about Bernardo? No, he was a bit harsh on her, that's what I would say. But I'm just saying, Schrodinger equation is non-relativistic. It has a first-order time derivative, second-order coordinate, space derivative."
},
{
"end_time": 9709.445,
"index": 372,
"start_time": 9681.664,
"text": " So it is not relativistic. So therefore to say that the collapse of the wave function is somehow alarming to us, but how about Schrodinger equation? It's also not relativistic. You see what I'm saying? But it's such a subtle point that it is lost because like most people don't really pay attention to this. I'm trying to say, I, I feel it. I am like this too. I'm not trying to criticize. You know, Richard Hamming? Yeah. Yeah. He said something which jives completely with what you're saying."
},
{
"end_time": 9735.247,
"index": 373,
"start_time": 9709.77,
"text": " It's something I wrote down, but I'm going to paraphrase. It's that we tend to think that we arrive at our interpretations of quantum mechanics. But he said, you start with God, even as a secular person, and then you see which interpretation is most consistent with that. I think, look, the beautiful thing to me is like, my approach is,"
},
{
"end_time": 9763.422,
"index": 374,
"start_time": 9736.015,
"text": " It's all beautiful. It's all beautiful. I love seeing both of them. And I wouldn't change a thing. And I don't want them to change except one little thing. Ask yourself, each of us ask ourselves, what is driving us really here? And is it really just scientific principles or there is some preference in it? And it's a very small thing. It's not no shame in having a preference. There's no shame in it."
},
{
"end_time": 9776.51,
"index": 375,
"start_time": 9764.241,
"text": " of course i do i do just be aware of it because that's what leads us astray i think is not being aware that's all but i think the idea is very interesting it is worth exploring"
},
{
"end_time": 9806.032,
"index": 376,
"start_time": 9776.852,
"text": " It is not fair to say that you shouldn't explore because it sounds crazy or whatever. You know, like it's weird. Quantum mechanics is weird. So also Bernardo said something I disagree. He's like, so basically you're saying that the moon depends what you see in the moon. It depends on how you set up your apparatus detector. But we know that in quantum mechanics, the result depends on how you set up your apparatus. If you do a double-seed experiment without detectors, you will see the interference pattern. If you do it with a detector,"
},
{
"end_time": 9835.026,
"index": 377,
"start_time": 9806.357,
"text": " You will see barricades behavior. So it's not, it's not an argument either. You see what I mean? We are all in, we are in the jungle. You know, we are in the jungle. We're trying to find our way. Let's cooperate. Let's cooperate. And let's understand that we all want the same thing. We want to the best theory, the most beautiful theory, the most interesting theory, the one which fits with experiment on this path, on this journey. We are informed by many things."
},
{
"end_time": 9865.486,
"index": 378,
"start_time": 9836.015,
"text": " Which are personal and nothing wrong with it. Just accept it and this will give us maybe new insights. Over email you mentioned you want to speak about String Theory or the Hans Bethe Ansatz. So String Theory is a good example of where people have gone astray and Sabina has been one of the people that called them on this correctly in my opinion. Was this the example you were thinking of earlier when you had said you can recapitulate and not me? Yeah, so the theory"
},
{
"end_time": 9892.022,
"index": 379,
"start_time": 9865.742,
"text": " A theory of everything, you know, it's like this idea that I was recently invited to a conference, Sting Theory Conference, and it was a very interesting experience for me to not just look at it abstractly, but to actually interact with people who consider themselves Sting Theorists. And"
},
{
"end_time": 9921.51,
"index": 380,
"start_time": 9893.166,
"text": " I saw that. A KFC tale in the pursuit of flavor. The holidays were tricky for the Colonel. He loved people, but he also loved peace and quiet. So he cooked up KFC's 499 Chicken Pot Pie. Warm, flaky, with savory sauce and vegetables. It's a tender chicken-filled excuse to get some time to yourself and step away from decking the halls. Whatever that means. The Colonel lived so we could chicken. KFC's Chicken Pot Pie. The best 499 you'll spend this season."
},
{
"end_time": 9951.135,
"index": 381,
"start_time": 9921.51,
"text": " It's not a very healthy kind of situation where it's still not been acknowledged by... A bit too much hubris? Not hubris. I think it's more like unwillingness to accept responsibility. Which is, again, totally human, you know?"
},
{
"end_time": 9978.66,
"index": 382,
"start_time": 9952.022,
"text": " It's hard. When was the last time I accepted this responsibility? So maybe I will start with myself. I'm not a string theorist. I've never been a string theorist. But I have collaborated with Edward Witten, who my great respect. And yes, I found it over the years very useful to drop the names and say, I collaborate with Witten, you know, I know something about string theory, because when I talk to my non-science friends, so"
},
{
"end_time": 10007.142,
"index": 383,
"start_time": 9979.206,
"text": " Also in Love and Math I talk about string theory, but I'm kind of trying to be diplomatic about it. That it's great for mathematics and physically it hasn't quite worked, but maybe. The fact of the matter is that the original promise of string theory, which was to describe this universe by using a theory which starts out in 10 dimensions of space-time,"
},
{
"end_time": 10033.285,
"index": 384,
"start_time": 10008.268,
"text": " has not worked out and nobody knows how in principle it could work and it's already been a situation for at least 10 years yet this is not acknowledged and how can you move forward and achieve greatness if you're still pretending that your original program is somehow"
},
{
"end_time": 10060.913,
"index": 385,
"start_time": 10035.555,
"text": " If you're not acknowledging that your original program failed, it's just a kind of like a simple question at the human level, not even scientific level. I did not see that. And I saw young people very brilliant, but confused because their elders are not giving them proper guidance. That's my impression. I may be wrong. I may be completely off base here, but I sensed that"
},
{
"end_time": 10086.271,
"index": 386,
"start_time": 10061.442,
"text": " They're already not doing string theory properly. So very few talks were about string theory actually proper. And the kind of stuff people work on that I discussed. It's quantum field theory more generally, or maybe study of black holes and stuff like that. But the original promise was"
},
{
"end_time": 10113.746,
"index": 387,
"start_time": 10086.647,
"text": " We will find the collaboration of many photos in which six dimensional, which will do away with the six dimensions. And then we will get the physics of this four dimensional universe. It has not worked out and nobody knows how to do it apart from some ideas of what's called landscape, this multiverse and so on, which I think a lot of people find problematic. Right. So, so this to me is an example of"
},
{
"end_time": 10129.445,
"index": 388,
"start_time": 10114.548,
"text": " How again our personal interferes with the project which is of science. Unwillingness to accept reality of it."
},
{
"end_time": 10155.026,
"index": 389,
"start_time": 10130.213,
"text": " You know, it doesn't mean that the people should be, it's not, I'm not saying nobody needs to be punished. No needs to be punished. I understand. So what is a string theorist to do? When you say acknowledge, what is the goal? Is it Ed Whitten writes an article? Is it, he goes on a podium? Is it, he sends an email out and then what happens afterward? What does a string theorist do after one spends four decades, five decades studying it and then says this wasn't fruitful?"
},
{
"end_time": 10181.374,
"index": 390,
"start_time": 10155.23,
"text": " But then are they going to continue studying it for the next decade? I'll tell you what not to do. Okay, how about this? Let me start with that simple thing. So this I'm actually supposed that not even wrong. Blog by Peter White, Peter White was one of the one of the early critics. He's coming on the podcast in a couple of weeks. Yeah, yeah, it's great. Yeah, he's great. And he was very brave."
},
{
"end_time": 10211.323,
"index": 391,
"start_time": 10181.766,
"text": " Because I do remember what happened. He was one of the lone voice. He and Lee Smallin at the time were basically the only voices. Also, they were ostracized. They were ostracized. They were criticized like they were stupid. They didn't understand, you know. And for instance, how about in Nepal? How about an apology or at least acknowledgement? OK, so maybe he was not so stupid. After all, Peter Voigt or Lee Smallin, maybe actually they were"
},
{
"end_time": 10242.125,
"index": 392,
"start_time": 10212.619,
"text": " saying something which was meaningful how about that but also like i'm looking here so in um august of 19 there was so there is a video discussion about super gravity and so on and there's a quote here so i haven't actually watched the video but i i trust that peter void transcribed it correctly andy strominger who is a harvard professor uh and one of the leaders of string theory i mean i greatly respect of course he's a great scientist"
},
{
"end_time": 10268.217,
"index": 393,
"start_time": 10243.473,
"text": " Here's what he said. I think that the idea that people were excited about back in 1995 was really a small thing. That's the idea of describing the physics of this universe from string theory. So he says, it was really a small thing, you know, to kind of complete that table that you put down at the beginning of the spectrum of particles."
},
{
"end_time": 10297.739,
"index": 394,
"start_time": 10268.729,
"text": " Who cares about that, right? So except how much resources were taken to fulfill, to fulfill this promise, right? That was a big promise. And that was the idea on the, because of which I think there is used to say it's only game in town. If you want to do statistical physics, you better come to us because nobody else is doing anything interesting. Right? So now in 2019, we hear from one of the leaders,"
},
{
"end_time": 10327.09,
"index": 395,
"start_time": 10299.07,
"text": " I think that this idea was actually a really small thing. Okay. We didn't do that. We didn't predict new things that were going to be measured at the Large Hadron Collider. But what has happened is so much more exciting than our original vision. We are getting little hints of a radical new view of the nature of space and time in which it really just is an approximate concept emerging from something deeper."
},
{
"end_time": 10356.118,
"index": 396,
"start_time": 10327.346,
"text": " That is really, really more exciting. So, in other words, so first of all, correct, the beautiful ideas came out of string theory. But that was not the original promise of string theory. The original promise was to describe the physics of this universe, to unify all forces of nature, the three forces, electromagnetic, strong and weak, described by the standard model and the quantum theory of gravity. This has not happened."
},
{
"end_time": 10383.063,
"index": 397,
"start_time": 10357.039,
"text": " And now we hear that actually was not such a big deal, such a big thing. We've learned so much more. It's like, you know, I tried to think of a good analogy. It's like, remember Moses, you took Israelites out of Egypt and he told them that he will lead them to the promised land. Yes. So imagine Moses after 40 years of wandering in the desert."
},
{
"end_time": 10412.227,
"index": 398,
"start_time": 10383.985,
"text": " You would say, you know, guys, this idea of a promised land is not such a big thing. Look how much we've learned. We've learned about the desert. We've learned so much about the sand. That's a great analogy. Who cares about the promised land? What do you think would people say to him? And yet here we are. It's, you know, this is what this is called, by the way, people call you mentioned this expression, moving the goalposts."
},
{
"end_time": 10440.657,
"index": 399,
"start_time": 10412.688,
"text": " This is not moving goalposts. This is going to a different stadium. It's starting to play a different game. Like you used to play soccer at one stadium. Then you go to another stadium. You start playing baseball and you say, no, we are playing soccer. We're still playing soccer. Yes, yes, yes. Stating that your original goal is not meaningful. It did not work out. It did not work out. How about just starting with that? It did not work out unequivocally. Not by saying the next 10 years. You know, I saw a great video."
},
{
"end_time": 10470.145,
"index": 400,
"start_time": 10440.981,
"text": " I don't know if you know this channel. She's called Angela Collier. You know, she has a very nice YouTube channel and she did a video about string theory and I really enjoyed it. She kind of, and one of the things that she kept saying, like she traced the evolution 90s to 2000s and so on. And each time she's like, just wait another 10 years, just wait another 10 years."
},
{
"end_time": 10499.275,
"index": 401,
"start_time": 10470.708,
"text": " That's the attitude even today. I am sorry to say, you know, what, how does, if a young person who is in the subject, it's still called string theory. Okay. You have to go to conferences, string theory, and maybe 20% of the talks are about string theory. The rest is about other things. People are already doing other things. It's like, you know, in the Soviet Union, when I was growing up, before Gorbachev, like eighties, early eighties, everybody already did not believe in the ideology."
},
{
"end_time": 10527.875,
"index": 402,
"start_time": 10499.906,
"text": " They did their own thing, but people were still trapped. Because the official ideology, official party line is this. So you have to somehow accommodate it. You know, so for instance, if you work in the history of social science, you always start preface every article you write with the great comrade Lenin said this, you know, things like that. What a liberation it is when you don't have to do it anymore. What a"
},
{
"end_time": 10557.022,
"index": 403,
"start_time": 10529.514,
"text": " Wait, so in this analogy, what would be the equivalent of praising Lenin or Marx? Because when you go to a string conference, not like you're saying, hey, string theory is great. Now here's my talk. The string theory somehow is still true. It's still trying to search, still trying to describe this universe. It's not because, well, there are some people trying, but there's so many at least say that"
},
{
"end_time": 10582.056,
"index": 404,
"start_time": 10558.166,
"text": " It did not work out the way we expected. People thought, and I also understand, to be carried away as a human being, it's natural. The theory is beautiful. And I have to say also very strongly that it has impacted mathematics in incredibly powerful ways. For instance, what Stromilus talks about is real, the idea of emergence of space-time."
},
{
"end_time": 10610.589,
"index": 405,
"start_time": 10582.432,
"text": " And the different space times can appear at different limits of the same theory, like mirror symmetry, stuff like that, incredibly powerful. Okay. But yes, this came up. But what about your original promise? What about your original promise? The idea was that you find what this thing, there is only defined super string theory in 10 dimensions of space time. You have to find six dimensions, which extra."
},
{
"end_time": 10636.067,
"index": 406,
"start_time": 10611.169,
"text": " because what we observe is four dimensions of space-time. So, the idea was we will find the right manifold, the right shape on which to compactify. Reasonable, reasonable. What turned out is that there are too many choices. But there is more. Actually, there's one question I said, you cannot pin it down."
},
{
"end_time": 10664.138,
"index": 407,
"start_time": 10636.561,
"text": " It's worse because actually dynamically it doesn't stay static. It changes also the Calabi-Yau because our modular space of Calabi-Yau is not rigid. Many of them are not. So it's moving and it becomes singular and nobody knows what to do with this. So in other words, the magnitude of the problem. Yes, it's possible that somebody can solve it. And I'm not saying this should not work on it. Of course work on it."
},
{
"end_time": 10694.684,
"index": 408,
"start_time": 10665.401,
"text": " But they shouldn't deride other attempts. But they were extremely heavy handed. There is no question, like in the same blog of Peter Voigt, I suggest people to read a testimony from David E. Kaplan. He gave an interview, it says post from October 22. It's a devastating, devastating testimony of someone who was not a string theorist in the heyday of string theory and what he felt about it. How many others felt the same way?"
},
{
"end_time": 10722.21,
"index": 409,
"start_time": 10695.265,
"text": " Not to acknowledge it, not to admit that this would happen. And the original promise did not pan out. It's something that holds people back. In my opinion, they have to be free. You have to liberate it from this weight. And the only people who can do it are the leaders of the theory. And it doesn't take much. It just opened the door a little bit for the possibility that our original project did not work out."
},
{
"end_time": 10752.363,
"index": 410,
"start_time": 10722.91,
"text": " Let's see what we can make out of what we have. How do you think Ed Whitten would respond if he heard what you said? You've collaborated with him. You know, you're part of that community or adjacent to that community. I'm adjacent and I've been paying lip service to this community. I have to admit. So in the interest of following my own admonition of like, what's, what is Edwards and meaning Edward Frankel, not Edward Whitten. What is Edward Frankel's involvement?"
},
{
"end_time": 10762.927,
"index": 411,
"start_time": 10753.626,
"text": " I was never a Sting Theorist, but I paid the lip service because it was convenient to me. It was nice for me to feel that I am collaborating with such great physicists."
},
{
"end_time": 10793.046,
"index": 412,
"start_time": 10763.404,
"text": " that I would write in love and math that yeah, who knows, maybe they will find this collabio when I knew full well that it seems way more. I didn't know that. I didn't say it in this input in this world, but I was kind of giving the validity given in principle, kind of paying lip service to it. Okay, so maybe not yet, but as this woman who has Angela, you know, said, and then you wait in the next 10 years. So I was kind of giving lip service to it. You see,"
},
{
"end_time": 10813.524,
"index": 413,
"start_time": 10793.507,
"text": " That's my contribution and which I see now was unhelpful. And I am grateful that there were people like Peter Voigt and Lee Small and Sabin Hassenfelder as well who were principled about it. Eric Weinstein as well. Eric Weinstein. Yes. Yes, absolutely. Eric Weinstein."
},
{
"end_time": 10842.312,
"index": 414,
"start_time": 10814.65,
"text": " Who said this for many years? They were had a principled approach to it. And you know, it's always like this, because you don't want to say because you don't want to offend anybody. I understand. But at some point, you ask, what is the interest of the community as opposed to the interest of a single human being or a few single few individuals? Yeah, how do you think the leaders would react to what you just said? Let's let's let's find out."
},
{
"end_time": 10870.93,
"index": 415,
"start_time": 10844.241,
"text": " forward this to Ed. Look, I look, I respect, I want to say I respect all the people. I just want to say I respect and I think they're brilliant. There's no question, brilliant, absolutely brilliant. And I am honored that I'm honored to have collaborate with with him. No, no doubt about it. We're talking here about not so much about science involved, but the way human element"
},
{
"end_time": 10901.596,
"index": 416,
"start_time": 10871.766,
"text": " Somehow it became the theme of our conversation. So I kind of felt that this would be appropriate. Appropriate because also is one theory which purported to which sold itself as a theory of everything. You know, and so now 40 years later, after 40 years wandering in the desert, we hear that actually this promised land is not a big deal. That's not how you deal with this. That's not we've seen that happen in history. It is detrimental. It puts a burden on young people who are"
},
{
"end_time": 10929.411,
"index": 417,
"start_time": 10902.415,
"text": " This is a recent opinion of yours now because you've given this talk at the strings conference. I have not spoken about this publicly other than I tweeted a little bit about it."
},
{
"end_time": 10957.5,
"index": 418,
"start_time": 10930.06,
"text": " I was at the conference, I was invited to give a challenge talk about mathematical developments. And I put a lot of effort into it. I put a lot of effort into it. I was very sincere. And I went there with an open mind. What I saw and experienced during this week, five days in this conference was what led me to reconsider my position."
},
{
"end_time": 10981.118,
"index": 419,
"start_time": 10957.807,
"text": " and led me to speak about it now, say what I have just said. Because on the one hand, I saw brilliant young minds. Yes. On the other hand, I saw the leaders and no hint from the leaders that somehow maybe we need to rebrand or pivot or evolve, you know."
},
{
"end_time": 11009.497,
"index": 420,
"start_time": 10982.312,
"text": " Does this strike a nerve with you because you also see a parallel with what happened to you when you were 16, which is this older generation leading astray the younger one? No, or no, that's too loose of an analogy."
},
{
"end_time": 11030.555,
"index": 421,
"start_time": 11011.118,
"text": " I don't know how you make this connection. No, of course it is, of course, but because I put myself in position of this young people. So, you know what I mean? So yes, of course, but this only proves that. I'm not saying that makes it irrelevant or that impacts the power of it. But see, I am aware, I am aware, I am aware that my sensitivity of this."
},
{
"end_time": 11056.596,
"index": 422,
"start_time": 11031.715,
"text": " And so you're also able to observe it much like"
},
{
"end_time": 11084.258,
"index": 423,
"start_time": 11057.005,
"text": " People who advocate for breast cancer research, maybe someone who was close to them was affected. It doesn't mean breast cancer, you shouldn't invest in it just because you have a personal motivation. No, no, I'm able to see it. I'm able to feel it. And now before we go, something else that you mentioned on the Lex program, and you didn't say that it was a large problem in math, but the problem of sometimes not giving credit where credit is due. You've seen this happen a couple times."
},
{
"end_time": 11113.951,
"index": 424,
"start_time": 11084.548,
"text": " You mentioned that in other fields there's some unsaid ethical rules, but in math there isn't, maybe in physics. Do you mind expounding on that? Well, it's again integrity and like, you know, but it's a human community. So this is the thing, which I think is the root of it is we like to think that we are this impartial arbiters of pure science and that we're driven by purely by the interest of science. And I have, I,"
},
{
"end_time": 11144.36,
"index": 425,
"start_time": 11114.855,
"text": " I have no doubt that we would like to aspire to be like that. To what extent we actually can is not clear to me by observing myself, first of all. And so my suggestion is that it's like, you know, Aldous Huxley talked about the idea about power that we have to have"
},
{
"end_time": 11174.667,
"index": 426,
"start_time": 11145.213,
"text": " Restrictions on power and we gave an interview to CBS. It's a beautiful video. And the interviewer, Mike Wallace, great journalist. It's really fantastic. Like he's smoking a cigarette, you know, it's like in the 50s and he says, why, why do we have to put this is because the whole point is that power is dangerous. It's because people can succumb to the temptation of power. That's why you have to restrict it. That's the whole point."
},
{
"end_time": 11204.343,
"index": 427,
"start_time": 11175.794,
"text": " Because the idea that somehow unrestricted power can be good for anyone has been repudiated and disproved by centuries and millennia of human history. And it's the same, it's the same, I think, with the idea of, you know, that somehow my personal preferences are not involved."
},
{
"end_time": 11212.022,
"index": 428,
"start_time": 11205.367,
"text": " in what I do in science. Today we have discussed several examples of"
},
{
"end_time": 11242.619,
"index": 429,
"start_time": 11213.183,
"text": " We seem to suggest that this is not so, or it's not so simple. It's, it's much more subtle somehow than that. You see? And so I think that we will not get to the next level of our evolution because also people say, okay, who cares? How many people involved hundreds, maybe a few thousand, but it's like Henry. It's a canary in a coal mine. In my opinion, we are the Vanguard. We scientists, we are the Vanguard. First of all, because you think it bleeds out into the public. Yes."
},
{
"end_time": 11270.913,
"index": 430,
"start_time": 11243.097,
"text": " Because people unconsciously, they feel it. And actually, Angela Collier, she makes this point. She actually says people got felt that they were lied to with string theory. And now they are fed up with physics. They don't want, they said, you lied to us. And I think, okay, I think so maybe a little hard, too harsh, but she definitely has a point. So for instance, then people will not be so interested in the developments of theoretical physics, maybe for next decade or something, because they got burned. They feel that they were like,"
},
{
"end_time": 11300.538,
"index": 431,
"start_time": 11271.408,
"text": " And a lot of the things people feel it, even if they don't know how to verbalize it, they feel it. You see, so if we don't get our house in order, and when I say our house, I don't mean strength, I mean science in general, we also have the other side of flip side of it is this people, so called AI practitioners who are feeding lies to people, telling them that AI is already here and you should pray to our AI overlords, that they will not destroy you, stuff like that, you know."
},
{
"end_time": 11322.585,
"index": 432,
"start_time": 11302.261,
"text": " In each of these instances, what I think will help us to go to the next level and to do the job that we're supposed to do. Which is? Is to realize how much our personal psychology, our personal aesthetic, metaphysical, philosophical preferences"
},
{
"end_time": 11351.869,
"index": 433,
"start_time": 11324.753,
"text": " how much they are intertwined with what you do as scientists. Just acknowledge that and then use it as a starting point for self-inquiry and to raise your self-awareness. The same goes with the attributions and papers and so on. And sometimes much lesser issue in my opinion. If you have a subject where the leaders of the subject still cannot acknowledge that mistakes were made, you know, mistakes were made, lessons were learned."
},
{
"end_time": 11375.879,
"index": 434,
"start_time": 11353.285,
"text": " Before we close, for me to take responsibility for a lack of attribution on my part unintentional, but it was still"
},
{
"end_time": 11405.913,
"index": 435,
"start_time": 11376.203,
"text": " a lack of attribution. I did this video on quantum gravity, the controversial history of quantum gravity's connection to antigravity. I didn't credit Eric Weinstein in the video itself, because I didn't use him as a source directly. I used other people like David Kaiser and a few others as sources. And I didn't know that some of the people that I had used as sources used Erica sources and didn't credit him. And so I just feel bad about that. And so Eric, if you're watching like, unfortunately, YouTube doesn't allow you to"
},
{
"end_time": 11436.408,
"index": 436,
"start_time": 11406.732,
"text": " extend a video, but I can change it. You can put a comment. You can put a comment. Yeah, I did put a comment and I know I'm leaving this and I apologize. And so see, that's what I'm talking about. This is what I'm talking about. This is, I admire, you know, I admire, admire you for this for accepting responsibility. It's much easier to, you know, the authority of is to find excuses. Yeah, but yes, if he was involved, but that somehow did this other people did not quote him. So it's not my fault. You see, this, this is a difference."
},
{
"end_time": 11460.776,
"index": 437,
"start_time": 11436.869,
"text": " And you're not going down that road. And thank you for that. Because, you know, that's how we change it, because we change our own. Well, thank you, because you inspired me, honestly, in many ways, not only through this conversation, but others that I've seen of you, like on Lexus and also in this book. Well, thank you, Kurt. Thank you. Me overcoming my embarrassment of, like, I find myself being begrudging, if I'm being honest."
},
{
"end_time": 11490.503,
"index": 438,
"start_time": 11461.032,
"text": " because there are some other podcasters who have large names who have helped them and they're tweeting about them and I don't have any of that. We can all exhale because something is weighing on us when there is something which is not true. It's weighing on us and when that simple thing of just acknowledging is such a breath of fresh air that we can all take a breath, exhale and move on. That's all."
},
{
"end_time": 11513.865,
"index": 439,
"start_time": 11491.834,
"text": " Well, again, man, oh man, what a conversation. Thank you. Thank you. Okay. I think this is the second time, one hour apart that I said, all right, let's end it. That just shows you what an engrossing, well, how grossing the topics are and how fun this was. Thank you. A lot of interesting stuff. So thank you for the grid. I really enjoyed it."
},
{
"end_time": 11540.06,
"index": 440,
"start_time": 11514.087,
"text": " All right. Well, I hope you enjoyed that podcast. It's almost three hours over three hour podcast. Thank you for sticking all the way to the end. Hope you enjoyed it. I think you have because you're still here. I want to recommend a couple videos, a couple podcasts from theories of everything. If you liked this podcast, you'll like the ones that I'm about to recommend. But I'd also like to acknowledge a comment every episode from now on, or at least every other episode. I'm going to highlight one of your comments."
},
{
"end_time": 11564.224,
"index": 441,
"start_time": 11540.247,
"text": " The reason is that I don't know if you're like me, but I love talking about these subjects. I love dealing with these subjects. But it's not like we have, at least for me, many people in my personal life to speak to about it. So in a sense, it's just relegated to speaking to the screen or conversing with people over text. And many people take the time to write detailed comments, which I love because I read almost every single comment. And I would like to encourage."
},
{
"end_time": 11588.933,
"index": 442,
"start_time": 11564.65,
"text": " This comment comes from user Bijou with the pseudonym Acronon Master and it's on the Carlo Rovelli clip called There's No Wave Function of the Universe that will be linked in the description. Bijou says one way of viewing quantum mechanics is as a measurement theory. To measure the universe, you really have to be outside the universe. So yes, in that sense, you could have a wave function of the universe, but it would do you no good. By definition, if you're external and conducting measurements, you'd be interacting with the system."
},
{
"end_time": 11609.684,
"index": 443,
"start_time": 11588.933,
"text": " So you'd not be truly separate from the system. You'd be at least coupled to it by whatever means you have from making the measurement. So in that sense, there could not literally be a the universe, quote unquote. I do like aspects of relational quantum mechanics. The trouble is RQM is like the mother of all bootstraps, something in brackets, Rovelli's God. And I know he considers himself atheistic."
},
{
"end_time": 11622.312,
"index": 444,
"start_time": 11610.043,
"text": " Which is not a scientific stance, so whatever has to be absolute for everything else to gauge off of, so to speak. Okay, you can read the rest of the comment by going to that video. You'll see and I didn't plan this that there's even a reference."
},
{
"end_time": 11642.278,
"index": 445,
"start_time": 11622.534,
"text": " to the interpretations of quantum mechanics having to do with our conception of God or even the lack of God and reasoning backward from these prejudicial axioms rather than what we think of which is hey I'm this rational being I'm going to reason forward to my interpretation or to my conclusions. Now if you liked this episode then you'll enjoy the Bernardo Castro solo episode that's"
},
{
"end_time": 11662.176,
"index": 446,
"start_time": 11642.278,
"text": " Somewhere on screen here and it'll also be in the description as well as the Sabina Haassenfelder interview with Bernardo Castro where they talk about super determinism clip that was just mentioned with Carl Orveli will also be in the description and the clip with Neil deGrasse Tyson that was alluded to about philosophy is quote unquote useless or that philosophy is little to contribute to modern day physics and mathematics."
},
{
"end_time": 11675.691,
"index": 447,
"start_time": 11662.176,
"text": " Also, because Richard Borchards asked a question, you may not know this, but Richard Borchards was interviewed twice on theories of everything. Part one and part two are linked in the description as well. Thank you so much for your viewership. And I'm glad or at least I hope that you enjoy this episode."
},
{
"end_time": 11701.288,
"index": 448,
"start_time": 11676.937,
"text": " The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked that like button, now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. You should also know that there's a remarkably active Discord and subreddit for theories of everything where people explicate toes, disagree respectfully about theories, and build as a community our own toes."
},
{
"end_time": 11719.36,
"index": 449,
"start_time": 11701.288,
"text": " Links to both are in the description. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc., it shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well."
},
{
"end_time": 11740.077,
"index": 450,
"start_time": 11719.36,
"text": " Last but not least, you should know that this podcast is on iTunes, it's on Spotify, it's on every one of the audio platforms. Just type in theories of everything and you'll find it. Often I gain from rewatching lectures and podcasts and I read that in the comments, hey, toll listeners also gain from replaying. So how about instead re-listening on those platforms?"
},
{
"end_time": 11769.326,
"index": 451,
"start_time": 11740.077,
"text": " iTunes, Spotify, Google Podcasts, whichever podcast catcher you use. If you'd like to support more conversations like this, then do consider visiting patreon.com slash Kurt Jaimungal and donating with whatever you like. Again, it's support from the sponsors and you that allow me to work on toe full time. You get early access to ad free audio episodes there as well. For instance, this episode was released a few days earlier. Every dollar helps far more than you think. Either way, your viewership is generosity enough."
},
{
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"text": " Think Verizon, the best 5G network is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
},
{
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"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal."
}
]
}No transcript available.