Edward Frenkel: Reality is a Paradox - Mathematics, Physics, Truth & Love

00:00:00.000 | There is a famous story about Einstein

00:00:02.160 | that he used to go think, think, think,

00:00:04.840 | and then go for a walk,

00:00:06.280 | and he would whistle sometimes.

00:00:08.040 | So I remember the first time I heard this story,

00:00:10.880 | I thought, "Hmm, how interesting.

00:00:12.120 | "So what a coincidence that this came to him

00:00:13.960 | "when he was whistling."

00:00:15.440 | But in fact, it's not.

00:00:16.360 | This is how it works, in some sense,

00:00:19.040 | that you have to prepare for it,

00:00:21.820 | but then it happens when you stop thinking, actually.

00:00:24.440 | So the moment of discovery is the moment when thinking stops

00:00:28.840 | and you kind of almost become that truth

00:00:33.840 | that you're seeking.

00:00:35.800 | - The following is a conversation with Edward Frenkel,

00:00:41.120 | one of the greatest living mathematicians,

00:00:43.600 | doing research on the interface of mathematics

00:00:46.400 | and quantum physics,

00:00:47.620 | with an emphasis on the Langlands program,

00:00:50.320 | which he describes as a grand unified theory of mathematics.

00:00:54.520 | He also is the author of "Love and Math,

00:00:57.640 | "the Heart of Hidden Reality."

00:01:00.280 | This is the Lex Friedman Podcast.

00:01:02.240 | To support it,

00:01:03.080 | please check out our sponsors in the description.

00:01:05.440 | And now, dear friends, here's Edward Frenkel.

00:01:09.060 | You open your book, "Love and Math," with a question,

00:01:14.040 | how does one become a mathematician?

00:01:16.280 | There are many ways that this can happen.

00:01:18.240 | Let me tell you how it happened to me.

00:01:20.300 | So how did it happen to you?

00:01:22.440 | - So first of all, I grew up in the Soviet Union,

00:01:26.700 | in a small town near Moscow called Kolomna.

00:01:30.300 | And I was a smart kid, you know, in school,

00:01:35.280 | but mathematics was probably my least favorite subject.

00:01:38.760 | Not because I couldn't do it.

00:01:41.000 | I was a straight A student

00:01:42.960 | and I could do all the problems easily,

00:01:46.800 | but I thought it was incredibly boring.

00:01:48.840 | And since the only math I knew

00:01:53.480 | was what was presented at school,

00:01:56.740 | I thought that was it.

00:01:58.420 | And I was like, what kind of boring subject is this?

00:02:01.540 | So what I really liked was physics,

00:02:04.300 | and especially quantum physics.

00:02:05.820 | So I was buying,

00:02:07.840 | I would go to a bookstore and buy popular books

00:02:12.620 | about elementary particles and atoms and things like that,

00:02:17.620 | and read them, you know, devour them.

00:02:21.920 | And so I thought,

00:02:23.640 | my dream was to become a theoretical physicist

00:02:25.940 | and to delve into this finer structure of the universe.

00:02:31.560 | So then something happened when I was 15 years old.

00:02:35.180 | It turns out that a friend of my parents

00:02:39.160 | was a mathematician who was a professor at the local college.

00:02:42.760 | It was a small college preparing educators and teachers.

00:02:46.520 | It's a provincial town.

00:02:47.560 | Imagine it's like 117 kilometers from Moscow,

00:02:51.000 | which would be something like 70 miles, I guess.

00:02:53.500 | You do the math. (laughs)

00:02:55.340 | - I like how you remember the number exactly.

00:02:57.140 | - Yeah, isn't it funny how we remember numbers?

00:03:00.080 | So his name was Yevgeny Yevgenyevich Petrov.

00:03:04.120 | And if this doesn't remind you

00:03:06.740 | of the great works of Russian literature,

00:03:09.700 | then you haven't read them. (laughs)

00:03:12.060 | Like "War and Peace," you know,

00:03:13.660 | with the patronymic names.

00:03:15.060 | But this was all real, this was all happening.

00:03:17.860 | So my mom one day by chance met Yevgeny Yevgenyevich

00:03:22.040 | and told him about me, that I was a bright kid

00:03:25.760 | and interested in physics.

00:03:28.240 | And he said, "Oh, I wanna meet him.

00:03:31.260 | "I'm going to convert him into math."

00:03:33.280 | And my mom's like, "Nah, math, he doesn't like mathematics."

00:03:37.320 | So I was like, "Okay, let's see what I can do."

00:03:39.760 | So I went to see him, so I'm about 15.

00:03:43.940 | And a bit arrogant, I would say.

00:03:46.640 | You know, like average teenager.

00:03:48.740 | So he says to me, "So I hear that you are

00:03:54.640 | "interested in physics and elementary particles."

00:03:59.040 | I was like, "Yeah, sure."

00:04:01.000 | And he said, "For example, do you know about quarks?"

00:04:03.600 | And I said, "Yes, of course I know about quarks.

00:04:06.740 | "Quarks are the constituents of particles

00:04:11.740 | "like protons and neutrons."

00:04:13.640 | And it was one of the greatest discoveries

00:04:15.600 | in theoretical physics in the '60s

00:04:18.240 | that those particles were not elementary,

00:04:20.720 | but in fact had the smaller parts.

00:04:23.680 | And he said, "Oh, so then you probably know

00:04:25.280 | "representation theory of the group SU(3)."

00:04:27.800 | (laughing)

00:04:29.120 | I'm like, "SU what?"

00:04:31.440 | So in fact, I wanted to know what were the underpinnings

00:04:36.440 | of those theories.

00:04:38.880 | I knew the story, I knew the narrative,

00:04:40.680 | I knew kind of the basic story

00:04:42.920 | of what these particles looked like.

00:04:44.580 | But how did physicists come up with these ideas?

00:04:48.320 | How were they able to theorize them?

00:04:50.920 | And so I remembered, like it was yesterday,

00:04:53.160 | so he pulls out a book, and it's kind of like a Bible,

00:04:58.160 | like a substantial book, and he opens it

00:05:01.760 | somewhere in the middle.

00:05:02.680 | And there I see the diagrams that I saw in popular books,

00:05:06.480 | but in popular books, there was no explanation.

00:05:09.520 | And now I see all these weird symbols and equations.

00:05:12.800 | It's clear that it is explained in there.

00:05:15.460 | Oh my God.

00:05:16.300 | He said, "You think what they teach you at school

00:05:20.260 | "is mathematics?"

00:05:22.180 | It's like, "No, this is real mathematics."

00:05:25.620 | So I was instantly converted.

00:05:28.220 | - That to understand the underpinnings of physical reality,

00:05:32.940 | you have to understand what SU(3) is.

00:05:34.860 | - You have to learn what are groups, what is group SU(3),

00:05:39.860 | what are representations of SU(3).

00:05:42.660 | There was a coherent and beautiful,

00:05:45.560 | I could appreciate the beauty,

00:05:46.840 | even though I could not understand heads and tails of it.

00:05:50.760 | - But you were drawn to the methodology,

00:05:52.920 | the machinery of how such understanding could be attained.

00:05:57.600 | - Well, in retrospect, I think what I was really craving

00:06:02.000 | was a deeper understanding.

00:06:04.260 | And up to that point, the deepest that I could see

00:06:07.200 | were those diagrams, but for that story

00:06:09.920 | that a proton consists of three quarks

00:06:12.780 | and a neutron consists of three quarks

00:06:14.500 | and they're called up and down and so on.

00:06:17.100 | But I didn't know that there was actually underneath,

00:06:21.460 | beneath the surface, there was this mathematical theory.

00:06:24.900 | - If you can just link around it,

00:06:26.340 | what drew you to quantum mechanics?

00:06:28.560 | Is there some romantic notion of understanding the universe?

00:06:34.020 | What is interesting to you?

00:06:35.300 | Is it the puzzle of it

00:06:36.420 | or is it the philosophical thing?

00:06:38.220 | - Now I am looking back.

00:06:40.600 | So whatever I say about Edward at 15,

00:06:45.600 | he's colored by all my experiences that happen

00:06:51.960 | in the meantime, my current views and so on.

00:06:55.580 | - For the people who may not know you,

00:06:57.400 | I think your book and your presentations

00:07:00.000 | kind of revealed that that 15-year-old

00:07:01.720 | is still in there somewhere.

00:07:02.880 | - Well, I take it as a compliment.

00:07:05.120 | - Some of the joy.

00:07:06.160 | - He's probably still here now, yes.

00:07:08.520 | In some way.

00:07:09.360 | - Yeah, I think it was a joy of discovery

00:07:11.980 | and the joy of going deeper into the kind of the,

00:07:15.640 | to the root, to the deepest structures of the universe,

00:07:21.340 | the secrets, the secrets.

00:07:24.480 | And we may not discover all of them,

00:07:27.140 | we may not be able to understand,

00:07:28.620 | but we're going to try and go as far and as deep as we can.

00:07:32.980 | I think that's what was the motivating factor in this.

00:07:37.540 | - Yeah, there's this mystery, there's this dark room,

00:07:40.480 | and there's a few of these mathematical physicists

00:07:42.680 | that are able to shine a flashlight briefly into there.

00:07:47.680 | We'll talk about it, but it also kind of makes me sad

00:07:51.480 | that there's so few of your kind

00:07:55.000 | that have the flashlight to look into the room.

00:08:00.000 | It's interesting.

00:08:01.900 | - I don't think there are so few, to be honest,

00:08:04.740 | because I think, I find a lot of people

00:08:07.660 | are actually interested.

00:08:09.560 | If you talk to people, you know,

00:08:11.220 | like some people you wouldn't expect

00:08:14.100 | to be interested in this,

00:08:17.460 | from all walks of life,

00:08:18.620 | from people of all kinds of professions.

00:08:22.620 | I tell them I'm a mathematician,

00:08:23.880 | and they, "Mathematician, okay, so that's a separate story."

00:08:26.920 | A lot of people, I think, have been traumatized

00:08:29.060 | by their experience in the math classes.

00:08:31.260 | We can talk about it later.

00:08:33.100 | But then they ask me what kind of research I do,

00:08:35.100 | and I mentioned that I work on the interface

00:08:39.380 | of math and quantum physics,

00:08:41.580 | and their eyes light up.

00:08:42.660 | It's like, "Oh, quantum physics,"

00:08:43.860 | or like Einstein's relativity,

00:08:45.300 | or I'm really curious about it.

00:08:46.540 | I watch this podcast, or I watch that podcast,

00:08:48.820 | you know, and I've learned this.

00:08:50.140 | It's like, "What do you think about that?"

00:08:51.940 | So I actually find that actually physicists

00:08:54.660 | are doing a great job educating the public, so to speak,

00:08:58.660 | in terms of popular books and videos and so on.

00:09:03.660 | Mathematicians are behind.

00:09:08.620 | We're starting to catch up a little bit,

00:09:10.620 | have been starting last 10 years,

00:09:12.380 | but we are still behind.

00:09:13.780 | But I think people are curious.

00:09:16.660 | Science is still very much something

00:09:19.980 | that people want to learn,

00:09:21.340 | because that's our kind of, the best way we know

00:09:24.140 | to establish some sort of objective reality,

00:09:27.800 | whatever that might be.

00:09:29.340 | - Yeah, to figure out this whole puzzle,

00:09:31.300 | to figure out the secrets that the universe holds.

00:09:33.140 | - Things that we can agree on, kind of, you know?

00:09:35.300 | Even though, for me, at this point,

00:09:37.220 | I always make an argument

00:09:38.980 | that our physical theories always change.

00:09:41.100 | They get updated.

00:09:42.140 | So you had Newton's theory of gravity.

00:09:44.820 | Then Einstein's theory superseded it.

00:09:49.740 | But in mathematics, it seems that theories don't change.

00:09:53.780 | Pythagoras' theorem has been the same

00:09:56.860 | for the last 2,500 years.

00:09:59.000 | X squared plus y squared equals z squared.

00:10:01.680 | We don't expect that next year, suddenly,

00:10:03.360 | it will be z cubed, you know?

00:10:06.080 | So that, to me, is actually even more,

00:10:10.480 | hints even more at how much we are connected to each other,

00:10:14.200 | because Pythagoras' theory, if you think about it,

00:10:16.720 | or any other mathematical theorem,

00:10:18.700 | means the same thing to anyone in the world today,

00:10:22.960 | regardless of their cultural, you know,

00:10:25.600 | bringing religion, you know, ideas, ideology,

00:10:30.600 | gender, whatever, nationality, race, whatever, right?

00:10:35.140 | And it has meant the same to everyone, everywhere,

00:10:39.500 | and most likely will mean the same.

00:10:41.900 | So that's, to me, kind of an antidote

00:10:44.680 | to the kind of divisiveness

00:10:48.900 | that we sometimes observe these days,

00:10:51.180 | where it seems that we can't agree on anything.

00:10:55.060 | - To the political complexity of two plus two equals five

00:10:58.720 | in George Orwell's "1984."

00:11:01.140 | - I was in the Soviet Union in 1984,

00:11:02.860 | and so in many ways, I see that it was prescient,

00:11:07.580 | the novel was prescient,

00:11:09.140 | but we still have not found a dictator

00:11:11.620 | who would actually say two plus two equals five,

00:11:14.060 | and would demand their citizens to repeat that.

00:11:17.060 | - The knight is still young.

00:11:18.060 | - Has not happened yet, okay?

00:11:19.820 | - Yeah, it does feel like math and physics

00:11:22.980 | are both sneaking up to a deep truth

00:11:25.860 | from slightly different angles,

00:11:27.540 | and you stand at the crossroads

00:11:29.820 | or at the intersection of the two.

00:11:31.900 | It's interesting to ask,

00:11:32.820 | what do you think is the difference

00:11:33.820 | between physics and mathematics,

00:11:35.700 | and the way physics and mathematics look at the world?

00:11:39.060 | - There is actually an essential difference,

00:11:41.840 | which is that physicists are interested

00:11:44.420 | in describing this universe, okay?

00:11:48.060 | And mathematicians are interested in describing

00:11:50.380 | all possible mathematical universes,

00:11:52.380 | of which, in some of our work,

00:11:55.940 | I still consider myself more of a mathematician

00:11:57.700 | than a physicist, my first love for physics notwithstanding.

00:12:02.220 | Mathematicians are, in a way,

00:12:06.000 | we have more diversity, if you might say.

00:12:09.940 | So we are accepting, for instance,

00:12:12.380 | our universe has three spatial dimensions,

00:12:18.380 | and one time dimension, right?

00:12:19.780 | So what I mean is that--

00:12:22.100 | - Allegedly.

00:12:22.980 | - Allegedly, observed, but that we can observe today, right?

00:12:26.420 | So of course there are theories

00:12:27.740 | where there are some hidden dimensions as well.

00:12:30.260 | Well, let's just say observed dimensions.

00:12:32.500 | So this tabletop has two dimensions

00:12:36.660 | because you can have two coordinate axes,

00:12:39.940 | X and Y, but then there is also a third one

00:12:43.740 | to describe the space of this room.

00:12:46.860 | And then there's a time dimension.

00:12:48.900 | So realistic theories of physics have to be

00:12:51.700 | about spaces of three dimensions,

00:12:57.220 | or space-time, so four dimensions.

00:12:59.580 | But mathematically, we are just as interested

00:13:02.700 | in theories in 10 space-time dimensions,

00:13:06.220 | or 11, or 25, or whatever,

00:13:08.500 | or infinite dimensional spaces, you know?

00:13:12.680 | So that's the difference.

00:13:14.900 | On the other hand, I have to give it to the physicists,

00:13:17.740 | we don't have the same satisfaction that they have

00:13:20.460 | of having their theories confirmed by an experiment.

00:13:25.460 | We don't get to play with big machines like LHC in Geneva,

00:13:31.020 | large Hadron Collider that recently discovered,

00:13:34.180 | you know, the Higgs boson and some other things.

00:13:37.140 | For us, it's all like a mental exercise in some sense.

00:13:40.220 | We prove things by using rules of logic,

00:13:44.620 | and that's our way of confirming,

00:13:47.420 | experimental confirmation, if you will.

00:13:49.660 | But I think I kind of envy a little bit

00:13:51.940 | my friends physicists that they get to experience

00:13:55.220 | this sort of, these big toys, you know, and play with them.

00:13:59.180 | - But it does seem that sometimes,

00:14:00.620 | as you've spoken about, abstract mathematical concepts

00:14:03.340 | map to reality, and it seems to happen quite a bit.

00:14:06.620 | - That's right, so mathematics underpins physics, obviously.

00:14:09.860 | It's a language.

00:14:10.980 | The book of nature, as Galileo famously said,

00:14:16.020 | is written in the language of mathematics.

00:14:18.540 | And the letters in it are the circles, triangles, and squares

00:14:25.100 | and those who don't know the language, I'm paraphrasing,

00:14:30.260 | are left to wander in a dark labyrinth.

00:14:33.700 | That's a famous quote from Galileo, which is very true

00:14:36.940 | and has become even more true more recently

00:14:39.660 | in theoretical physics in the most sort of far out,

00:14:45.020 | far out parts of the theoretical physics

00:14:48.300 | that have to do with elementary particles

00:14:50.060 | and as well as the structure of the cosmos

00:14:53.980 | at the large scale.

00:14:55.220 | - What do you think of Max Tegmarker

00:14:57.540 | who wrote the book Mathematical Universe?

00:14:59.660 | So do you think, just lingering on that point,

00:15:04.460 | you think at the end of the day,

00:15:06.320 | the future generations will all be mathematicians?

00:15:09.940 | Meaning the ones that deeply understand

00:15:14.340 | the way the universe works.

00:15:15.420 | At the core, is it just mathematics?

00:15:19.980 | - At the core of, you know,

00:15:21.980 | I would say mathematics is one half of the core.

00:15:28.140 | So the book is called Love and Math.

00:15:30.140 | - Yeah. - Okay, so these are

00:15:30.980 | the two pillars. (laughs)

00:15:33.460 | - Yeah. - In my view.

00:15:35.860 | In other words, you can't cover everything by math.

00:15:39.220 | So mathematics gives you tools,

00:15:40.780 | it gives you a kind of a clear vision.

00:15:45.780 | But mathematics by itself is not enough

00:15:50.060 | for one to have a harmonious and balanced life.

00:15:55.060 | So I am suspicious of any theory

00:15:59.580 | that declares that everything is mathematics.

00:16:03.520 | - So math can generate things that are beautiful,

00:16:07.620 | but it can't explain why it's beautiful.

00:16:10.300 | Math, you could say, is a way to discern patterns,

00:16:13.180 | to find regularities in the universe,

00:16:15.620 | and both physical and mental universe.

00:16:18.780 | Mathematics explores the mind

00:16:20.780 | as much as it explores the physical world around us.

00:16:25.780 | And it helps us to find those patterns,

00:16:28.180 | which makes our perception more sophisticated,

00:16:33.180 | our ability to perceive things such as beauty.

00:16:39.820 | It sharpens our ability to see beauty,

00:16:42.340 | to understand beauty.

00:16:43.300 | So our world becomes more complex

00:16:46.180 | from thinking that Earth is flat,

00:16:51.660 | we go to realizing that it is round,

00:16:54.180 | that it's the shape of the sphere,

00:16:56.340 | so that we can actually travel around the Earth,

00:16:59.420 | so there isn't a place where we hit the end, so to speak.

00:17:02.440 | And then proceeding in the same vein,

00:17:08.220 | then Einstein's general relativity theory tells us

00:17:11.420 | that our space-time is not flat either.

00:17:15.400 | This is much harder to imagine,

00:17:19.060 | the bent three-dimensional or four-dimensional space,

00:17:22.940 | or four-dimensional space-time,

00:17:24.380 | because this idea that the space around us is flat

00:17:27.260 | is so deeply entrenched.

00:17:28.860 | And yet we know from this theory

00:17:32.260 | and from the experiments that have confirmed it,

00:17:35.780 | that a ray of light bends around a star

00:17:40.660 | as if being attracted by the force of gravity.

00:17:43.340 | But in fact, the force of gravity is the bending.

00:17:46.040 | It's just that it's not only the bending of the space,

00:17:48.440 | it's also the bending of space-time.

00:17:50.460 | There is a curvature,

00:17:52.020 | not only between spatial dimensions,

00:17:55.500 | the way parallels and meridians come together.

00:17:59.020 | In a small scale, they look like perpendicular lines,

00:18:03.020 | but if you zoom out, you see that the space,

00:18:05.860 | are they curving the space?

00:18:07.100 | They are sort of the tracks

00:18:09.620 | along which the space gets curved.

00:18:11.820 | That would be the curvature of spatial dimensions.

00:18:15.140 | But in fact, now throwing time,

00:18:17.060 | and one time, imagine a sphere which has,

00:18:21.140 | one of the meridians correspond to time,

00:18:23.700 | and the parallels correspond to space.

00:18:25.260 | I can't imagine it, but I can write a mathematical formula

00:18:28.580 | expressing that curvature.

00:18:30.420 | And that's, in fact, that curvature is responsible

00:18:32.940 | for the force of gravity, attraction between,

00:18:35.820 | the sort of simplest instantiation of it,

00:18:37.940 | attraction between two planets,

00:18:40.100 | or between two human beings.

00:18:41.740 | (laughs)

00:18:42.580 | What does matter?

00:18:43.780 | - Yeah, the time, bending time,

00:18:47.300 | it's not very nice what that theory did to time,

00:18:50.740 | because it feels like the marching of time forward

00:18:55.100 | is fundamental to our human experience.

00:18:57.780 | The arrow of time marching forward nicely

00:19:02.260 | seems to be the only way we can understand the universe.

00:19:05.220 | And the fact that you can start--

00:19:06.060 | - Up to now, up to now.

00:19:07.620 | There are people who claim that they can,

00:19:09.260 | that they possess other ways of experiencing it.

00:19:12.500 | - So truly can visualize messing with time.

00:19:16.100 | - Well, messing with time,

00:19:17.540 | but not necessarily messing with time,

00:19:18.860 | because one point of view is that,

00:19:21.540 | I think, who was it?

00:19:24.420 | I think William Blake,

00:19:25.660 | who wrote that eternity loves time production.

00:19:30.820 | So one point of view is that it is eternity

00:19:35.220 | which is fundamental, where time stands still,

00:19:38.300 | which our mind conceptualizes as the time.

00:19:41.720 | But in fact, it's not something mystical.

00:19:45.660 | If you think about it,

00:19:48.380 | when you're really absorbed in something,

00:19:51.220 | time does stand still.

00:19:53.740 | And then you look at the clock, and it's like,

00:19:54.820 | "Oh my God, two hours have passed."

00:19:56.940 | And it felt like a couple of seconds.

00:19:59.360 | When you are absorbed, when you're in love,

00:20:01.940 | when you are passionate about something,

00:20:04.500 | when you're creating something,

00:20:06.060 | we lose ourselves, and we lose the sense of time,

00:20:10.580 | and space, for that matter, you see?

00:20:12.260 | So there is only that which is happening,

00:20:14.380 | that creative process.

00:20:16.600 | So I think that this is familiar to all of us.

00:20:20.820 | - And we may be actually the closest

00:20:22.340 | to the truth at that moment,

00:20:23.900 | to the true natural reality.

00:20:25.140 | - So yes, so then there is a point of view

00:20:27.540 | that this is where we are, we are who we are,

00:20:30.720 | at our sort of fundamental, at our fundamental level.

00:20:34.280 | And after that, the mind comes in,

00:20:37.080 | and tries to conceptualize it.

00:20:38.840 | It's like, "Oh, because I was writing something.

00:20:41.240 | "I was writing a book, I was painting this painting,

00:20:45.760 | "or maybe I was watching this painting,

00:20:47.480 | "and got totally absorbed in it.

00:20:49.240 | "Or I fell in love with this person, that's what happened."

00:20:52.240 | But in the moment when it's happening,

00:20:53.560 | you're not thinking about it.

00:20:55.520 | You're just there.

00:20:57.000 | - Yeah, we construct narratives around

00:20:58.620 | the set of memories that seem to have happened in sequence,

00:21:02.040 | or at least that's the way we tell ourselves that.

00:21:04.920 | And we also have a bunch of weird human things,

00:21:07.820 | like consciousness, and the experience of free will,

00:21:11.340 | that we chose a set of actions as the time unrolled forward.

00:21:16.340 | And we are intelligent, conscious agents,

00:21:21.540 | taking those actions.

00:21:25.020 | But what if all of that is just--

00:21:26.860 | - An illusion.

00:21:27.700 | - An illusion, and a nice narrative we tell ourselves?

00:21:30.320 | - Sure.

00:21:31.160 | - That's a really difficult thing to internalize.

00:21:32.000 | - It's possible.

00:21:32.840 | And imagine that to make it really Catch-22.

00:21:36.480 | Imagine that our minds are set up in such a way

00:21:39.340 | that they can't approach the world,

00:21:42.560 | or experience otherwise.

00:21:44.920 | So in other words, to understand,

00:21:47.240 | to see that from a more

00:21:49.320 | kind of all-encompassing point of view,

00:21:53.080 | we have to step out of the mind.

00:21:55.680 | - Well, I wonder what's the more honest way

00:21:57.180 | to look at things.

00:21:59.000 | - But I think we like to play with time.

00:22:01.560 | I think we like to play with these experiences,

00:22:03.600 | with all the drama of it, with all the memories,

00:22:05.560 | with all the tribulations.

00:22:07.820 | - I think that's--

00:22:08.660 | - We love it, we love it.

00:22:09.720 | Otherwise, we wouldn't be doing it.

00:22:11.720 | - I think that's, or Earth loves it.

00:22:13.920 | The evolutionary process somehow loves it.

00:22:16.000 | Whatever this thing that's being created here on Earth,

00:22:19.760 | it seems to like to create,

00:22:23.000 | like to allow its children to play with certain

00:22:25.640 | truths that they hold, the subjective truths

00:22:30.480 | that are useful for the competition,

00:22:32.140 | or whatever this dance that we call life

00:22:34.400 | broadly is defined, not just humans.

00:22:36.480 | - And you know, I'm glad you mentioned that,

00:22:38.400 | because what I find fascinating

00:22:40.680 | is that the greatest scientists are on record

00:22:44.040 | saying that when they were making their discoveries,

00:22:47.320 | they felt like children.

00:22:49.000 | So Isaac Newton said to myself,

00:22:50.720 | "I only appeared as a child playing on the seashore,

00:22:53.480 | "and every once in a while finding a prettier pebble

00:22:55.960 | "or a prettier shell," whilst I think he said something like

00:22:59.820 | "The infinite ocean of knowledge was lying before me."

00:23:04.820 | Alexander Grothendieck, who probably was

00:23:08.640 | the greatest mathematician of the second half

00:23:10.680 | of the 20th century, the French mathematician,

00:23:13.760 | Alexander Grothendieck, wrote that

00:23:17.240 | discovery is a privilege of a child.

00:23:20.380 | A child who is not afraid to be wrong once again,

00:23:22.480 | to look like an idiot, to try this and that,

00:23:26.800 | I'm paraphrasing, and go through trial and error.

00:23:29.560 | That is for them, in other words, for them,

00:23:32.500 | that innocence of a child who is not afraid,

00:23:39.220 | who has not yet been told that it cannot be done,

00:23:41.720 | that was essential to scientific pursuit,

00:23:46.360 | to scientific discovery.

00:23:48.320 | And now, also, compare it to Pablo Picasso,

00:23:53.320 | a great artist, right, who said,

00:23:55.680 | "Every child is an artist."

00:23:57.920 | The question is how to preserve that as we grow up.

00:24:02.220 | - Do you struggle with that?

00:24:03.320 | You're one of the most respected

00:24:05.920 | mathematicians in the world.

00:24:07.380 | You're Berkeley, you're like, there's a statue,

00:24:12.040 | you're supposed to be very like, you know--

00:24:14.560 | - Ivory Tower.

00:24:15.400 | - Yeah. - Sometimes I joke, I say,

00:24:17.960 | I take an elevator to the top of the Ivory Tower every day.

00:24:20.960 | - And you're supposed to speak like royalty.

00:24:24.640 | Do you struggle to strip all of that away

00:24:29.080 | to rediscover the child when you're thinking about problems,

00:24:32.640 | when you're teaching, when you're thinking about the world?

00:24:35.280 | - Absolutely.

00:24:36.400 | I mean, that's part of being human,

00:24:37.720 | because when we grow up, I mean,

00:24:40.200 | all of these great scientists,

00:24:42.960 | I think they were so great in part,

00:24:44.720 | because they were able, they maintained that connection,

00:24:47.840 | okay, and that fascination, that vulnerability,

00:24:50.940 | that spontaneity, you know,

00:24:53.680 | and kind of looking at the world

00:24:58.000 | through the eyes of a child.

00:24:59.680 | But it's difficult, because you go through education system,

00:25:03.120 | and for many of us, it's not especially helpful

00:25:08.120 | for maintaining that connection,

00:25:10.760 | that we kind of like, we're being told certain things

00:25:14.000 | that we accept, take for granted, and so on,

00:25:17.080 | and little by little, and also, we get hit

00:25:19.560 | every time we act different, okay?

00:25:22.640 | Every time we act in a way

00:25:25.480 | that doesn't fit sort of the pattern.

00:25:27.400 | We get punished by the teachers,

00:25:28.960 | get punished by parents, and so on.

00:25:32.560 | - And don't get respect when you act childlike

00:25:35.240 | in your thinking, when you are fearless

00:25:38.360 | and looking like an idiot.

00:25:40.840 | - That's right.

00:25:41.680 | - Because there's a hierarchy in society.

00:25:42.840 | - Nobody wants to look like an idiot, you know?

00:25:44.600 | Once you start growing up, or you think you're growing up.

00:25:47.720 | In the beginning, you don't even think in these terms.

00:25:52.640 | You just play, you're just playing,

00:25:54.980 | and you are open to possibilities,

00:25:57.240 | to these infinite possibilities

00:25:58.600 | that this world presents to us.

00:26:00.600 | So how do we, I'm not saying that education system

00:26:05.480 | should not be also kind of taming that a little bit.

00:26:11.360 | Obviously, the goal is balance,

00:26:15.120 | that acquiring knowledge so that we can be more mature

00:26:20.120 | and more discerning, more discriminating

00:26:25.080 | in terms of our approach to the world,

00:26:26.880 | in terms of our connections to the world

00:26:28.800 | and people and so on.

00:26:30.440 | But how do we do that while also preserving

00:26:34.040 | that innocence of a child?

00:26:36.760 | And my guess is that there is no formula for this.

00:26:40.640 | It is, a life is an answer.

00:26:43.760 | Every life, every human being is one particular answer

00:26:47.640 | to how do we find balance.

00:26:49.800 | - That's one imperfect approximation,

00:26:55.120 | approximate solution to the problem.

00:26:58.000 | - But we can look up to the great ones

00:27:01.360 | who have credentials in the sense that they have shown

00:27:06.360 | and they have proved that they have done something

00:27:09.280 | that other humans appreciate, our civilization appreciates,

00:27:13.400 | say, Isaac Newton or Alexander Grotendieck

00:27:15.960 | or Pablo Picasso.

00:27:17.280 | So they have established their right

00:27:19.760 | to speak about these matters.

00:27:21.640 | And we cannot dismiss them as mere madmen.

00:27:25.720 | They say, okay, well, if the same thing was said

00:27:28.280 | by somebody who never achieved anything

00:27:31.200 | in their field of endeavor,

00:27:34.200 | it would be easy for us to dismiss it.

00:27:37.600 | But when it comes from someone like Isaac Newton,

00:27:41.280 | we take notice.

00:27:43.880 | So I think there's something important that they teach us.

00:27:46.720 | And especially today, in this age of AI,

00:27:49.880 | of course, there's a big elephant in the room always,

00:27:53.440 | which is called AI, right?

00:27:55.320 | And so I know that you are an expert in the subject

00:27:58.520 | and we are living now in this very interesting times

00:28:02.000 | of new AI systems coming online,

00:28:04.960 | pretty much every couple of weeks.

00:28:07.440 | So I kind of, to me, that whole debate about

00:28:12.440 | what is it, what is artificial intelligence,

00:28:15.960 | where is it going, what should we do about it,

00:28:18.240 | needs an influx of this type of considerations

00:28:23.520 | that we've just been talking about.

00:28:25.600 | That, for instance, the idea that inspiration,

00:28:30.240 | creativity doesn't come from accumulation of knowledge,

00:28:33.240 | because obviously a child has not yet accumulated knowledge.

00:28:37.420 | And yet the great ones are on record

00:28:40.540 | saying that a child has a capacity to create.

00:28:45.540 | And an adult credits the inner child--

00:28:50.220 | - The inner child, yeah.

00:28:51.900 | - For this capacity to create as an adult, you see.

00:28:56.180 | That's kind of weird if we take the point of view

00:28:58.980 | that everything is computation,

00:29:01.660 | everything is accumulation of knowledge,

00:29:03.340 | that just bigger and bigger data sets,

00:29:06.060 | finer and finer neural networks,

00:29:08.340 | and then we will be able to replicate human consciousness.

00:29:11.480 | If we take that point of view,

00:29:13.060 | then what I just said kind of doesn't fit,

00:29:15.820 | because obviously a child has not been fed

00:29:17.780 | any training data as far as we know,

00:29:20.540 | yet they're perfectly capable of distinguishing

00:29:24.140 | between cats and dogs, for instance, and stuff like that.

00:29:26.660 | But much more than that, they're also capable of that

00:29:29.620 | wide-eyed sort of perspective.

00:29:35.000 | So can it really be captured, that perspective,

00:29:38.940 | that sense of awe, can it really be captured

00:29:42.820 | by computation alone?

00:29:45.060 | I actually, I don't know the answer,

00:29:46.500 | so I'm not sort of trying to present

00:29:50.980 | a particular point of view.

00:29:52.100 | I'm just trying to question any theory

00:29:56.060 | that starts out by saying life is this,

00:30:00.620 | or consciousness is this.

00:30:03.700 | Because when you look more closely,

00:30:05.800 | you recognize that there are some other things at play,

00:30:09.660 | which do not quite fit the narrative.

00:30:11.660 | - And it's hard to know where they come from.

00:30:14.260 | It's also possible that the evolutionary process

00:30:17.740 | that's created is the very, it is computation,

00:30:22.500 | and the child is actually not a blank slate,

00:30:25.560 | but the result of one of the most incredible,

00:30:30.060 | several billion year old computations

00:30:33.340 | that had explored all kinds of aspects of life on Earth,

00:30:39.740 | of war and love and terror and ambition

00:30:48.020 | and violence and invention, all of that,

00:30:52.020 | from the bacteria to today.

00:30:54.500 | So that young child is not a blank slate.

00:30:58.300 | They're coming, they're actually,

00:31:00.500 | hold within them the knowledge

00:31:03.660 | of several billions of years.

00:31:06.140 | - Right, the question is whether, as a child,

00:31:08.660 | you carry that in the form of the kind

00:31:11.300 | of computational algorithms that we are aware today.

00:31:14.180 | You see, what strikes me as unlikely is that,

00:31:18.980 | how should I put it?

00:31:21.420 | How interesting that, you know,

00:31:24.180 | you are a computer scientist,

00:31:25.760 | and there are other people,

00:31:27.020 | I have studied computer science, so I know a little bit.

00:31:30.220 | And so it's tempting to say,

00:31:33.100 | oh, the whole world is computer science,

00:31:37.060 | or is based, can be explained by computer science.

00:31:39.460 | Why?

00:31:40.300 | Because it makes me feel good.

00:31:41.500 | Because I have mastered it, I have learned it.

00:31:43.620 | My ego is very happy, and people come to me,

00:31:47.120 | and they look up to me, and they revere me.

00:31:50.100 | Kind of like priests in old days,

00:31:52.260 | when religion was paramount,

00:31:53.700 | when you would tend to explain things

00:31:56.540 | in theological, religious terms.

00:31:58.940 | Today, science has progressed.

00:32:00.460 | There are fewer people who kind of buy into official religion.

00:32:04.460 | You know?

00:32:05.280 | So we have this urge, I suppose, to explain,

00:32:09.980 | and to know, and to dissect, and to analyze,

00:32:13.180 | and to conceptualize, which is a wonderful quality

00:32:16.140 | that we have, and we should definitely pursue that.

00:32:19.980 | But I find it a little bit unlikely

00:32:24.700 | that the universe is just exactly what I have learned,

00:32:28.380 | and not something that I don't know, you see?

00:32:30.860 | - Well, there's a lot of interesting aspects

00:32:34.220 | to the current large language models

00:32:36.900 | that one perspective of it, I think,

00:32:40.020 | speaks to the love in math that you talk to,

00:32:43.300 | which is they're trained on human data from the internet.

00:32:48.300 | So at its best, a large language model,

00:32:53.980 | like GPT-4, captures the magic of the human condition

00:32:58.980 | on its full display, its full complexity.

00:33:03.780 | And so it's mimicking, it's trying to compress

00:33:06.540 | all the weirdness of humans,

00:33:08.900 | of all the debates and discussions, the perspectives,

00:33:13.100 | all the different ways that people approach

00:33:15.300 | solving different problems, all of that compressed.

00:33:17.740 | So we live, we're each individual ants.

00:33:20.300 | We only have, like, we have a family,

00:33:22.160 | we interact with a few little ants.

00:33:24.300 | And here comes AI that's able to summarize,

00:33:27.980 | like a TLDR, Report of Humanity.

00:33:31.740 | - And that's the beauty of it.

00:33:33.260 | So I embrace it.

00:33:34.780 | - But I wonder if-- - I'm very impressed by it.

00:33:37.020 | - I wonder if it can be very impressive,

00:33:41.580 | meaning way more impressive in being able to fake

00:33:46.580 | or simulate or emulate a human.

00:33:49.500 | - Fake, I'm glad you mentioned that,

00:33:51.580 | because that seems to be the mantra.

00:33:53.880 | - It's just a word, though.

00:33:54.720 | - Fake it 'til you make it.

00:33:56.060 | - Yeah. - Isn't it?

00:33:56.900 | - Isn't that what we all do, though?

00:33:58.800 | - No, well, yes, we do that, but we also do other things.

00:34:02.680 | We can be truly in love, we can be truly inspired

00:34:05.520 | when it is not fake.

00:34:06.500 | I do believe, call me romantic, okay, but I do believe,

00:34:10.320 | and this is a very good, I'm glad you're putting it

00:34:12.240 | in these terms, because I've had conversations like that.

00:34:14.960 | That, yeah, fake it 'til you make it,

00:34:16.760 | but that's like, that's what humans do.

00:34:18.760 | Yes, we do that, but not all the time.

00:34:20.840 | So, and that is debatable,

00:34:23.020 | because also I speak from my own experience,

00:34:25.460 | and that's where the first-person perspective comes in,

00:34:28.220 | the subjective view.

00:34:30.100 | I cannot prove to you, for instance, or anyone else,

00:34:33.480 | that there are certain moments in my life

00:34:36.000 | where I am genuine, I am pure, so to speak,

00:34:39.820 | when it's not faking it,

00:34:42.200 | but I do have a tremendous certainty of it,

00:34:46.920 | and that's a subjective certainty.

00:34:48.960 | Now, I am, as a scientist, I'm also trained

00:34:52.040 | to give more credibility to objective arguments

00:34:55.760 | that are things that can be reproduced,

00:34:58.280 | things that I can demonstrate, that I can show.

00:35:01.420 | But as I get older, (laughs)

00:35:03.200 | show me, Steve. - There we go.

00:35:04.720 | - As I get more mature, hopefully, you know,

00:35:07.420 | I'm starting to question why I am not giving

00:35:11.400 | as much credibility to my subjective understanding

00:35:15.840 | of the world, the kind of the first-person perspective.

00:35:18.520 | When actually, modern science has already sold on that.

00:35:23.300 | You know, quantum mechanics has shown unambiguously

00:35:27.520 | that the observer is always involved in the observation.

00:35:32.240 | Likewise, Gödel's incompleteness theorems, to me,

00:35:35.500 | show how essential is the observer

00:35:41.600 | of a mathematical theory.

00:35:44.640 | For one thing, that's the one who chooses the axioms.

00:35:48.160 | And we can talk about this in more detail.

00:35:49.880 | Likewise, Einstein's relativity,

00:35:51.400 | where time is relative to the observer, for instance.

00:35:54.880 | - That's brilliant.

00:35:55.720 | You're just describing all of these different scales,

00:35:58.200 | the observer, what the observer means.

00:35:59.760 | - So, science of 19th century had the,

00:36:03.000 | from modern perspective, and I don't want to offend anybody,

00:36:06.640 | had the delusion that somehow you could analyze the world

00:36:10.280 | being completely detached from it.

00:36:12.200 | We now know, after the landmark achievements

00:36:15.200 | of the first half of the 20th century,

00:36:17.180 | that this is nonsense, that it's simply not true.

00:36:20.120 | And this has been experimentally proved time and time again.

00:36:23.760 | So, to me, I'm thinking maybe it's a hint

00:36:27.600 | that I should take my first-person perspective

00:36:30.500 | seriously as well, and not just rely

00:36:33.740 | on kind of objective phenomena,

00:36:35.960 | things that can be proved in a traditional,

00:36:40.960 | sort of objective way, by setting up an experiment

00:36:43.440 | that can be repeated many times.

00:36:45.340 | Maybe I fall in love, the deepest love of my life,

00:36:49.160 | perhaps, perhaps hasn't happened yet,

00:36:51.440 | perhaps I will fall in love, but it's unique.

00:36:53.360 | It's a unique event.

00:36:54.320 | You can't reproduce it, necessarily, you see?

00:36:56.800 | So, in that sense, you see how these things

00:37:00.080 | are closely connected.

00:37:01.600 | I think that if we are declaring from the outset

00:37:05.640 | that all there is to life is computation

00:37:10.240 | in the form of neural networks or something like this,

00:37:13.280 | however sophisticated they might be,

00:37:15.300 | I think we are, from the outset, denying to ourselves

00:37:19.380 | the possibility that, yes, there is a side of me

00:37:22.660 | which is not faking it.

00:37:24.060 | Yes, there is a side of me which cannot be captured

00:37:27.220 | by logic and reason.

00:37:28.580 | And you know what another great scientist said,

00:37:30.700 | bless Pascal, he said, "The heart has its reasons,

00:37:35.700 | "of which the reason knows nothing."

00:37:39.500 | And then he also said, "The last step of reason

00:37:42.400 | "is to grasp that there are infinitely many things

00:37:45.620 | "beyond reason."

00:37:46.700 | How interesting, this was not a theologian,

00:37:49.860 | this was not a priest, this was not a spiritual guru.

00:37:53.400 | It was a hardcore scientist who actually developed,

00:37:58.900 | I think, one of the very first calculators.

00:38:01.100 | How interesting that this guy also was able

00:38:04.140 | to impart on us that wisdom.

00:38:08.520 | Now, you can always say that's not the case.

00:38:11.860 | But why should we, from the outset,

00:38:16.860 | exclude this possibility that there is something

00:38:20.000 | to what he was saying?

00:38:22.200 | That is my question.

00:38:23.360 | I'm not taking sides.

00:38:25.460 | What I'm trying to do is to shake a little bit the debate

00:38:30.140 | because most mathematicians that I know,

00:38:33.140 | and computer scientists even more so,

00:38:35.040 | they're kind of already sold on this.

00:38:38.740 | We are just, you know, it reminds me of this famous

00:38:41.380 | Lord Kelvin's quote from the end of 19th century.

00:38:44.420 | There's some debate whether he actually said that,

00:38:47.460 | but never let a good story stand in the way of truth.

00:38:52.460 | He said, "Physics is basically finished.

00:38:57.380 | "All that remains is more precise measurement."

00:39:00.740 | So I find a lot of my colleagues are happy to say,

00:39:04.460 | "Everything's finished, we got it, we got it."

00:39:07.940 | Maybe a little tweaks in our large language models.

00:39:12.940 | So now, here's my question.

00:39:14.780 | I'm kind of playing devil's advocate a little bit

00:39:17.820 | because I don't see the other side

00:39:19.700 | of the so-called code represented that much.

00:39:22.680 | And I'm saying, okay, could it be also that

00:39:25.080 | if you believe in that, that that becomes your reality?

00:39:28.060 | That you can kind of put yourself in a box

00:39:31.020 | where everything is computation,

00:39:34.520 | and then you start seeing things as being such.

00:39:37.340 | It's confirmation bias, if you will.

00:39:39.300 | This also reminds me, I think a good analogy

00:39:42.540 | is a friend of mine, Philippe Cauchon,

00:39:44.460 | told me that in France, there is this literary movement,

00:39:47.700 | which is called Oulipo, O-U-L-I-P-O.

00:39:52.700 | And it's a bunch of writers and mathematicians

00:39:57.980 | who create works of literature

00:40:00.540 | in which they basically impose certain constraints.

00:40:05.300 | A good example of this.

00:40:07.480 | Is a novel, which is called "The Void or Disappearance"

00:40:10.240 | by a writer named Georges Pirek,

00:40:13.560 | which is a 300-page novel in French,

00:40:16.360 | which never uses the letter E,

00:40:22.060 | which is the most widely used letter of the French language.

00:40:26.900 | So in other words, he set these parameters for himself.

00:40:30.820 | I'm going to write a book where I don't use this letter,

00:40:34.060 | which is a great experiment.

00:40:36.480 | And I applaud it.

00:40:38.360 | But it's one thing to do that

00:40:40.720 | and to kind of show his gamesmanship, if you will,

00:40:45.320 | and his ability as a writer.

00:40:48.840 | But it's another thing if at the end of writing this book,

00:40:52.240 | when you finish the book,

00:40:53.080 | he would say letter E actually doesn't exist.

00:40:55.200 | And try to convince us that in fact,

00:40:59.640 | French language does not have that letter,

00:41:01.640 | simply because he was able to go so far

00:41:03.800 | without using it, you see.

00:41:05.700 | So self-imposed limitation, that's how I see it.

00:41:09.160 | And I wonder why we should do that.

00:41:13.080 | Do we really feel the urge to say the world is like that?

00:41:17.880 | The world can be explained this way or that way.

00:41:20.520 | And I'm saying it, it's a personal question for me,

00:41:22.760 | because I am addicted to knowledge myself.

00:41:26.140 | Hi, my name is Edward.

00:41:28.720 | (both laughing)

00:41:29.560 | - I'm addicted to knowledge.

00:41:30.400 | - And I'm a knowledge addict, okay?

00:41:31.880 | I'm being serious, I'm not being facetious.

00:41:34.240 | Up until very recently, maybe a couple of years ago,

00:41:37.900 | I simply did not feel comfortable

00:41:40.100 | if I could not say, give an answer, explanation.

00:41:44.220 | It's like, oh, there has to be some explanation.

00:41:45.740 | And I try to frantically search for it.

00:41:48.220 | Just for somebody like me, a nerd, a left brainiac,

00:41:53.220 | and that's kind of typical for a scientist,

00:41:59.380 | for a mathematician, it is incredibly hard.

00:42:03.160 | Just to allow the possibility that it's a mystery

00:42:08.160 | and not to feel the urge to get the answer,

00:42:14.000 | it is incredibly hard, but it's possible.

00:42:16.200 | And it is liberating.

00:42:17.720 | It's recovering, it's recovering, I think.

00:42:19.840 | (both laughing)

00:42:21.080 | To knowledge.

00:42:22.600 | Let me say what you gain from it.

00:42:25.960 | For instance, I understand the value of paradoxes.

00:42:29.200 | I appreciate paradoxes more.

00:42:31.840 | And to use another philosopher, Soren Kierkegaard,

00:42:36.840 | the Danish philosopher, said,

00:42:38.480 | "A thinker without paradox is like a lover without passion."

00:42:43.920 | (both laughing)

00:42:46.000 | A paltry mediocrity.

00:42:47.200 | - Ooh, that's a good line.

00:42:48.440 | - All right?

00:42:49.560 | So, and Niels Bohr said, in the same vein,

00:42:54.560 | the great Danish also.

00:42:57.920 | It's something about Danes.

00:43:00.120 | I think it all started with Hamlet.

00:43:01.920 | (both laughing)

00:43:03.680 | He said, "The opposite of a simple truth is a falsity,

00:43:08.680 | "but the opposite of a great truth is another great truth."

00:43:13.720 | In other words, things are not black and white.

00:43:17.120 | You know, they're not...

00:43:18.520 | And I would even venture to say,

00:43:20.720 | the most interesting things in life are like that.

00:43:25.720 | The ones which are ambiguous.

00:43:28.920 | Is an electron a particle or a wave?

00:43:31.560 | It depends how you set up an experiment.

00:43:33.220 | It will reveal itself as this or that,

00:43:36.200 | depending on how you set up an experiment.

00:43:38.460 | This bottle, if you project it down onto the table,

00:43:44.000 | you will see more or less a square.

00:43:46.040 | If you project it onto a wall, you will see a different shape.

00:43:49.240 | A naive question would be, is it this or that?

00:43:52.280 | Because we understand that it's neither.

00:43:56.360 | But both projections reveal something.

00:43:58.720 | They reveal different sides of it.

00:44:00.840 | A paradox is like that.

00:44:02.560 | It's only paradoxical if we are confined

00:44:07.040 | in a particular vision,

00:44:10.640 | if we are wedded to a particular point of view.

00:44:13.800 | It's a harbinger, if you will,

00:44:16.080 | of a possibility of seeing things as they are,

00:44:20.080 | as more sophisticated than we thought before.

00:44:25.760 | You see?

00:44:26.600 | - This is such a difficult idea for science to grapple with.

00:44:31.360 | That, you know, I don't know how,

00:44:33.640 | there's so many ways to describe this,

00:44:34.920 | but you could say maybe that the subjective experience

00:44:38.720 | of the world from an observer is actually fundamental.

00:44:43.720 | - But we know that.

00:44:45.440 | Our best physical theories tell us that unambiguously.

00:44:49.320 | In quantum mechanics, actually, you know,

00:44:51.520 | Heisenberg, I think, captured it the best

00:44:54.080 | when he said, "What we observe is not reality itself,

00:44:57.560 | "but reality subjected to our method of questioning."

00:45:01.680 | When I talk about electrons, for instance,

00:45:06.320 | so that there is a very specific way

00:45:07.840 | in which this is realized.

00:45:09.760 | There is a so-called double-slit experiment, right?

00:45:11.760 | So for those who don't know,

00:45:14.520 | it's you have a screen and you have an emitter

00:45:18.920 | from which you send, you kind of shoot electrons.

00:45:21.800 | And in between, you put another screen

00:45:23.440 | which has two vertical slits parallel to each other.

00:45:26.680 | If we were shooting, you know, tennis balls,

00:45:29.800 | each ball would go through one slit or another

00:45:32.120 | and then hit the screen behind this or that slit.

00:45:35.640 | So you would have, let's say they're colored,

00:45:37.920 | they're painted.

00:45:39.120 | So there'll be sort of bumps or spots of paint

00:45:43.080 | behind this or that.

00:45:44.920 | But that's not what happens when we shoot electrons.

00:45:48.920 | We see an interference pattern

00:45:50.400 | as if we were actually sending a wave

00:45:52.600 | so that each electron,

00:45:54.520 | it seems like each electron goes through both slits at once

00:45:57.080 | and then has the audacity to interfere with itself.

00:46:00.960 | Where at some points, you know, two crests would amplify

00:46:04.080 | and at some points, a crest and a trough

00:46:05.440 | would cancel each other.

00:46:07.520 | Yet, so that suggests, okay, so an electron is a wave?

00:46:10.920 | Not so fast, because if you put a detector

00:46:13.400 | behind one of the slits and you say,

00:46:14.840 | I'm going to capture you. (laughs)

00:46:18.480 | I'm going to find out which slit you went through,

00:46:21.520 | the pattern will change

00:46:22.720 | and it will look like they're particles.

00:46:24.960 | So that's a very concrete realization of the idea

00:46:28.000 | that depending on how we set up an experiment,

00:46:30.520 | we will see different results.

00:46:32.040 | And the problem is that our psyche, I feel,

00:46:37.880 | kind of is lagging behind,

00:46:39.360 | in part because maybe our scientists

00:46:41.240 | are not doing such a great job.

00:46:43.360 | So I take responsibility for this,

00:46:45.000 | that why haven't I explained this properly?

00:46:47.680 | I tried, you know, in a bunch of talks and so on.

00:46:51.160 | So now I'm talking about this again.

00:46:53.520 | Our psyche kind of is lagging behind.

00:46:54.880 | We're still, even though our science has progressed so much

00:46:57.560 | from the certainty and the determinism

00:47:00.720 | and all of that of the 19th century,

00:47:04.400 | our psyche is somehow still attached to those ideas.

00:47:07.920 | The ideas of causality, of this naive determinism,

00:47:10.120 | that the world is a bunch of billiard balls

00:47:13.520 | hitting each other, driven by some blind forces.

00:47:16.880 | You know, that's not at all like it is.

00:47:18.560 | And we've known this for over,

00:47:20.680 | well, for about 100 years at least, you know?

00:47:23.880 | - And you call this self-imposed limitation.

00:47:26.680 | - It is a self-imposed limitation when we pretend that,

00:47:30.040 | for instance, that these naive ideas of 19th century physics

00:47:36.640 | are still valid and then start applying them to our lives

00:47:40.680 | and then also derive conclusions from it.

00:47:42.640 | And for instance, people say, "There is no free will."

00:47:45.600 | Why?

00:47:46.760 | "Oh, because the world is just a bunch of billiard balls.

00:47:49.840 | "So where is the free will?"

00:47:50.760 | But excuse me, didn't you get the memo

00:47:53.040 | that this has been debunked thoroughly

00:47:55.160 | by the so-called quantum mechanics,

00:47:56.840 | which is our best scientific theory?

00:47:58.800 | This is not some kind of bullshit

00:48:01.160 | or some kind of concoction of a madman.

00:48:06.160 | This is our scientific theory,

00:48:08.000 | which has been confirmed by experiment.

00:48:09.600 | So we should pay attention to that.

00:48:11.280 | So, but of course, it's not just self-imposed limitation.

00:48:14.720 | Unfortunately, in this case,

00:48:16.040 | there is a big issue of education.

00:48:18.520 | So a lot of people are not aware of it

00:48:20.600 | through no fault of their own,

00:48:22.060 | because they were never properly taught that,

00:48:24.520 | because our system is broken, education system is broken,

00:48:27.280 | especially in math.

00:48:28.920 | And then our, so where do we get information?

00:48:31.720 | You get information from our scientists

00:48:34.440 | who actually write popular books and so on,

00:48:37.320 | which is a great, you know, great thing that they do.

00:48:42.040 | But a lot of scientists somehow,

00:48:43.900 | when it comes to explaining the laws of physics,

00:48:49.240 | they're doing a fantastic job

00:48:50.760 | talking about this phenomenon,

00:48:54.920 | for instance, double-slit experiment and things like that.

00:48:57.520 | But then, you know, interviewed by Science Magazine

00:49:00.560 | about free will and so on,

00:49:01.720 | they revert back to 19th century physics

00:49:05.160 | as if those developments actually never happened.

00:49:07.360 | So to me, this is single most

00:49:09.640 | important sort of issue in our popular science.

00:49:16.640 | The idea that somehow there is this world out there,

00:49:21.120 | but it has nothing to do with me.

00:49:23.140 | So I can revel in the intricacies

00:49:28.440 | of these particles and their interactions,

00:49:31.040 | but completely ignore what implications this has

00:49:37.020 | for my own relationship to physical reality,

00:49:40.800 | to my own life, you know?

00:49:42.600 | Because it's kind of scary, I guess, you know?

00:49:44.400 | - But also, what are the tools

00:49:47.080 | with which we can talk about the observer,

00:49:51.800 | the subjective view on reality?

00:49:55.700 | What are the tools with which we could talk about,

00:49:58.760 | rigorously talk about free will and consciousness?

00:50:01.880 | What are the tools of mathematics that allow that?

00:50:04.240 | I don't think we have those tools.

00:50:05.680 | - Because we haven't been taught properly.

00:50:07.860 | So actually, tools are there.

00:50:10.060 | For instance, I think, well,

00:50:14.760 | here we have to, I have to say,

00:50:17.600 | my conviction is that everybody knows.

00:50:20.320 | In the heart of hearts, everybody knows that there is that.

00:50:25.700 | There is something ineffable.

00:50:28.620 | There is something mysterious.

00:50:32.420 | And in fact, you know, somehow,

00:50:34.680 | immediately I feel the impulse to quote somebody on this,

00:50:39.680 | because as if my own opinion doesn't count.

00:50:42.020 | (laughing)

00:50:43.320 | - There's a long-dead expert that has said it.

00:50:45.600 | - Even Einstein said that, you know?

00:50:46.980 | So like, how, see, look at me.

00:50:49.940 | I am supposedly like this smart, intelligent person.

00:50:53.860 | I am afraid to say it and own it myself.

00:50:56.260 | I have to find confirmation.

00:50:58.620 | I have to find an authority who agrees with me.

00:51:01.780 | And in fact, it's not so difficult to find,

00:51:03.340 | because Albert Einstein literally said

00:51:05.200 | the most important thing in life is the mysterious.

00:51:07.940 | Okay, he actually said that.

00:51:09.840 | There are some quotes which are attributed to him,

00:51:12.300 | which he never said, but this he did.

00:51:14.480 | I investigated, okay?

00:51:15.780 | (laughing)

00:51:17.540 | But more importantly, you know, how do you feel about it?

00:51:21.280 | I think that everybody knows.

00:51:25.160 | But in other words, he also said, Einstein,

00:51:30.500 | imagination is more important than knowledge, okay?

00:51:33.620 | And he explained, for knowledge is always limited.

00:51:36.180 | Whereas imagination embraces the entire world,

00:51:40.180 | giving birth to evolution.

00:51:41.780 | It is, strictly speaking, a real factor

00:51:44.620 | in scientific research, he says.

00:51:46.100 | And he says, I am enough of an artist

00:51:47.940 | to follow my intuition and imagination.

00:51:50.460 | That's Albert Einstein, again.

00:51:52.220 | So, and I feel the same way, to be honest.

00:51:54.860 | If I think about my own mathematical research,

00:51:58.160 | it's never linear.

00:52:00.060 | It's never like, give me more data, give me more data,

00:52:02.340 | give me more data, boom, the glass is full,

00:52:05.020 | and then I come up with a discovery.

00:52:06.460 | No, it's always felt as a jump, as a leap.

00:52:11.060 | And I have actually been studying various examples

00:52:16.980 | in history of mathematics, of some fundamental discoveries,

00:52:20.060 | like discovery of complex numbers,

00:52:21.380 | like square root of negative one.

00:52:23.020 | I wonder if a large language model

00:52:27.180 | could actually ever come up with the idea

00:52:29.060 | that square root of negative one

00:52:31.260 | is something that is essential or meaningful.

00:52:36.580 | Because if all the information that you get,

00:52:40.180 | that all the knowledge that had been accumulated

00:52:42.460 | up to that point, tells you that you cannot

00:52:46.340 | have a square root of a negative number, why?

00:52:48.540 | Because if you had such a square root,

00:52:51.760 | we know that if you square it, you get a negative number.

00:52:56.220 | But we know that if you square any real number,

00:52:59.020 | positive or negative, you will always get a positive number.

00:53:02.540 | So, checkmate, it's over.

00:53:05.940 | Square root of negative one doesn't exist.

00:53:07.700 | Yet, we know that these numbers make sense,

00:53:10.940 | they're called complex numbers,

00:53:12.300 | and in fact, quantum mechanics is based on complex numbers.

00:53:15.940 | They are essential and indispensable for quantum mechanics.

00:53:20.100 | Could one discover that?

00:53:22.300 | So, to me, that sounds like a discontinuity

00:53:26.340 | in the process of discovery.

00:53:27.900 | It's a jump, it's a departure.

00:53:29.900 | It is like a child who is experimenting.

00:53:32.220 | It's like a child who says, "I'm not afraid to be an idiot."

00:53:34.580 | Everybody says, the adults are saying,

00:53:37.780 | square root of negative number doesn't exist,

00:53:40.380 | but guess what?

00:53:41.540 | I'm going to accept it, and I'm going to play with it,

00:53:44.940 | and I'm going to see what happens.

00:53:46.700 | This is literally how they were discovered.

00:53:48.620 | There was an Italian mathematician, astronomer, astrologer.

00:53:53.620 | He made money, apparently, by compiling astrological

00:53:58.580 | sort of readings for the elite of his era.

00:54:02.740 | - As one does.

00:54:03.580 | - This is 16th century, as one does.

00:54:05.260 | A gambler. (laughs)

00:54:07.300 | All around interesting guy.

00:54:08.500 | I'm sure we would have an interesting conversation with him.

00:54:10.620 | Gerolamo Cardano.

00:54:12.380 | He also invented what's called cardan shaft,

00:54:15.780 | which is an essential component of a car.

00:54:19.540 | Cardano Vival, we say in Russian.

00:54:22.980 | So he wrote a book which is called Ars Magna,

00:54:28.940 | which is like the great art of algebra.

00:54:31.260 | And he was writing solutions

00:54:32.540 | for the cubic and quartic equations.

00:54:36.020 | This is something that is familiar,

00:54:37.420 | because at school we study solutions of quadratic equations,

00:54:42.180 | equations of degree two.

00:54:43.660 | So you have AX squared plus BX plus C equals zero.

00:54:47.140 | And there is a formula which solves it using radicals,

00:54:50.060 | using square roots.

00:54:51.620 | And Cardano was trying to find a similar formula

00:54:53.900 | for the cubic and quartic equations,

00:54:56.620 | for which would start with X cubed or X to the power four,

00:55:00.300 | as opposed to X squared.

00:55:02.340 | And in the process of solving these equations,

00:55:05.020 | he came up with square root of a negative number,

00:55:07.660 | specifically square root of minus 17.

00:55:10.820 | And he wrote that I have to forego some mental tortures

00:55:14.460 | to deal with it, but I am going to accept it

00:55:19.540 | and see what happens.

00:55:20.700 | And in fact, at the end of the calculation,

00:55:23.740 | these weird numbers got canceled.

00:55:27.540 | They kind of canceled out.

00:55:28.540 | And the formula appeared, square root of negative 17,

00:55:31.740 | and it's negation.

00:55:32.580 | So they kind of conveniently gave the right answer,

00:55:35.340 | which did not involve those numbers.

00:55:37.020 | So he was like, "Okay, what does it mean?

00:55:40.780 | "Mental tortures."

00:55:42.300 | So you see, from the point of view of the thinking mind,

00:55:47.100 | it is something almost unbearable.

00:55:50.140 | It's almost, I feel, that a large language model,

00:55:53.100 | a computer running a large language model

00:55:55.220 | trying to do that would just explode.

00:55:57.580 | And yet a human mathematician was able to find the courage

00:56:01.500 | and inspiration to say, "You know what?

00:56:04.420 | "What is wrong?

00:56:05.460 | "Why are we so adamant that these things don't exist?

00:56:08.740 | "That's just our past."

00:56:10.700 | Knowledge is based on what our past knowledge is,

00:56:13.220 | and knowledge is limited.

00:56:14.180 | What if we make the next step?

00:56:15.940 | Today, for us mathematicians,

00:56:18.740 | complex numbers, that we call them,

00:56:21.140 | are not at all mysterious.

00:56:23.020 | The idea is simply that you plot real numbers,

00:56:26.740 | that is to say, all the whole numbers,

00:56:28.420 | like zero, one, and so on, two, and so on, right?

00:56:30.860 | All fractions, like one half or three halves,

00:56:33.620 | or four over three.

00:56:34.860 | But then also numbers like square root of two, or pi.

00:56:39.220 | We plot them as points on the real line.

00:56:41.500 | So we draw, this is one of the perennial concepts,

00:56:45.540 | even in our very poor math curriculum at school.

00:56:50.540 | But now imagine that instead of one line,

00:56:52.660 | you have a second axis.

00:56:56.820 | And so numbers now have two coordinates, x and y,

00:57:01.620 | and you associate to this point with coordinates x and y,

00:57:05.700 | the number x, which is a real number,

00:57:07.860 | plus y times square root of negative one.

00:57:10.260 | This is a graphical, geometrical representation

00:57:13.380 | of complex numbers, which is not mysterious at all.

00:57:16.220 | Now it took another 200 or 300 years

00:57:18.180 | for mathematicians to figure that out,

00:57:20.260 | but initially it looked like a completely crazy idea.

00:57:23.980 | - So all it is, all a complex number is,

00:57:27.940 | is just an expansion. - Two real numbers.

00:57:29.340 | Two real numbers. - Yeah, it's just two--

00:57:30.180 | - The real part and the imaginary part.

00:57:31.940 | - It's just an expansion of your view

00:57:34.300 | of the mathematical world. - That's right.

00:57:36.080 | The fact that you can actually add them up

00:57:39.000 | by adding together the real parts and imaginary parts,

00:57:41.980 | that's easy.

00:57:42.920 | But there is also a formula for the product,

00:57:45.240 | for the multiplication, which uses the fact

00:57:47.440 | that square root of minus one squared is minus one.

00:57:50.840 | And the amazing thing is that that product,

00:57:54.120 | that multiplication, satisfies the same rules,

00:57:57.000 | the same properties that are usual operation

00:58:00.360 | of multiplication for real numbers.

00:58:02.160 | For instance, there is an inverse

00:58:03.220 | for every non-zero number that you can find.

00:58:05.560 | Like number five has an inverse, one over five.

00:58:09.000 | But one plus I also has an inverse, for instance.

00:58:12.920 | - That was always there in the mathematical universe,

00:58:16.160 | but we humans didn't know it.

00:58:18.240 | And here comes along this guy

00:58:20.240 | who engages in the mental torture,

00:58:22.080 | who takes a leap off the cliff of comfort,

00:58:25.440 | of like mathematical comfort--

00:58:26.840 | - Established knowledge. - Of established knowledge.

00:58:28.680 | - Right, and now, obviously,

00:58:30.680 | for each sort of fruitful leap like that,

00:58:35.400 | there probably were thousands of things

00:58:37.440 | which went nowhere.

00:58:38.600 | I'm not saying that every leap,

00:58:40.240 | it's an open shooting game.

00:58:43.440 | Because, for example, you can try to do the same

00:58:45.720 | with three-dimensional space.

00:58:46.880 | So you have coordinates X, Y, and Z.

00:58:48.960 | And you can say, oh, if it's one-dimensional,

00:58:53.400 | we have a bona fide numerical system called real numbers.

00:58:56.740 | If it's two-dimensional, which is like,

00:58:59.280 | geometrically, it's just like this tabletop

00:59:01.240 | extended to infinity in all directions,

00:59:03.740 | these are complex numbers.

00:59:04.880 | And we can define addition and multiplication,

00:59:08.040 | and they will satisfy the same properties

00:59:09.560 | as real numbers that we're used to.

00:59:11.200 | What about three-dimensional space?

00:59:12.840 | Is it possible to also define some operation

00:59:15.920 | of addition and multiplication on it

00:59:18.160 | so that these operations would satisfy

00:59:21.040 | the properties that we're used to?

00:59:23.640 | And the answer is no.

00:59:24.760 | You can define addition,

00:59:25.980 | but you can't define multiplication

00:59:27.680 | for which there would be an inverse, for instance.

00:59:30.120 | So there is something special about the plane,

00:59:32.440 | the two-dimensional case.

00:59:33.920 | And by the way, next question would be,

00:59:36.600 | what about four-dimensional?

00:59:38.040 | In four-dimensional space, again, you can,

00:59:41.040 | and you get what's called quaternions,

00:59:43.720 | discovered by an Irish mathematician, Hamilton,

00:59:46.760 | in the 19th century.

00:59:48.500 | And then in the eight-dimensional,

00:59:51.100 | there is something similar called octonions,

00:59:53.440 | and that's about it.

00:59:54.640 | So how interesting.

00:59:56.240 | These structures exist in dimension one, two, four, and eight,

01:00:01.240 | which are all powers of two.

01:00:03.940 | Two squared is four, two to the third power is eight.

01:00:06.740 | That's one of the bigger mysteries in mathematics,

01:00:08.820 | why it is so.

01:00:09.820 | So that's a hint.

01:00:12.060 | That's a hint of what's missing

01:00:15.260 | in our high school curriculum.

01:00:17.580 | (laughs)

01:00:18.740 | The kind of fascinating--

01:00:21.160 | - The mystery. - Mysteries, yes.

01:00:23.300 | - The appreciation of the mysteries.

01:00:24.660 | - So in other words, yes, we resolved this one mystery,

01:00:27.340 | that we understood that square root of negative one

01:00:30.700 | is real, is meaningful.

01:00:33.060 | We build a theory to service those,

01:00:36.460 | to describe those numbers.

01:00:38.540 | Did we find the theory of everything?

01:00:40.100 | No, because we then invited other mysteries,

01:00:43.380 | because we pulled the veil, so to speak,

01:00:47.660 | or we pushed the frontier,

01:00:49.060 | and then new things come, get illuminated,

01:00:52.400 | which we couldn't see before.

01:00:53.620 | That's how I see the process of discovery in mathematics.

01:00:56.100 | It's an endless, limitless pursuit.

01:00:58.340 | - Can you comment on what you think

01:01:01.260 | this human capability of imagination

01:01:03.360 | that Einstein spoke about,

01:01:04.980 | of the artists following their intuition

01:01:07.780 | in this big Alice in Wonderland world of imagination,

01:01:12.780 | what is it?

01:01:14.780 | You visit there sometimes.

01:01:15.740 | - What does it feel like?

01:01:17.740 | - Yeah, what does it feel like?

01:01:18.980 | What is it?

01:01:19.820 | What is that place? - It feels like playing,

01:01:20.860 | but I think all of us are engaged in that kind of play.

01:01:24.500 | No matter, when we do what we love,

01:01:26.820 | I think it always feels the same.

01:01:28.900 | - But it's not real, right?

01:01:30.860 | So, you're describing a feeling,

01:01:33.640 | but that place you go to in the imagination,

01:01:36.220 | it's bigger than the real world.

01:01:38.840 | - So, there is a big conundrum

01:01:41.180 | as to whether mathematics is invented or discovered.

01:01:44.020 | And mathematicians are divided on this.

01:01:49.540 | Nobody knows.

01:01:50.380 | - Where do you bet your money on, financially?

01:01:53.300 | (Lex laughing)

01:01:55.180 | Investment advice.

01:01:56.060 | - So, let me tell you something.

01:01:57.700 | My views have evolved, okay?

01:02:00.300 | When I wrote "Love and Math," when I wrote my book,

01:02:03.020 | I was squarely on the side of mathematics is discovered.

01:02:07.420 | What does it mean?

01:02:10.020 | Usually, mathematicians or others who have this idea,

01:02:14.300 | or belief, are called Platonists,

01:02:18.060 | in honor of the great philosopher Plato,

01:02:20.740 | who talked about these absolute perfect forms.

01:02:23.540 | So, for me, about 10 years ago,

01:02:27.120 | the world of mathematics was this world of pure forms,

01:02:31.620 | this beautiful, pure forms,

01:02:33.760 | which existed outside of space and time,

01:02:36.240 | but I was able to connect to it through my mind,

01:02:39.220 | and as it were, kind of dive into it,

01:02:41.860 | and bring treasures back into this world,

01:02:44.540 | into this space and time.

01:02:46.540 | That's how I viewed the process of mathematical discovery.

01:02:49.580 | How nice, how neat, very neat.

01:02:51.380 | (Lex laughing)

01:02:52.220 | That's the picture.

01:02:53.180 | Also makes you feel connected to something divine.

01:02:56.780 | Allows you this sense of escape

01:02:59.060 | from the cruelty and injustice of this world,

01:03:02.620 | which I now recognize.

01:03:04.140 | - And the divine world of forms is stable, reliable.

01:03:07.860 | - It's something stable.

01:03:09.220 | And in that world, everything is clear-cut.

01:03:12.180 | It's either true or false.

01:03:13.860 | (Lex laughing)

01:03:14.700 | - Yeah.

01:03:15.520 | - How nice, huh?

01:03:16.360 | - It's very nice.

01:03:17.200 | - Oh my God.

01:03:18.020 | (Lex laughing)

01:03:18.860 | The biggest illusion of all.

01:03:19.700 | (Lex laughing)

01:03:20.820 | - Allegedly.

01:03:22.060 | - Now, I think now I understand why I liked it,

01:03:26.260 | because I think that I was very dissatisfied

01:03:28.660 | with what we call the real world, the world around me.

01:03:33.180 | The cruelty, the injustice of it.

01:03:35.660 | And I went through certain experiences as a kid,

01:03:38.380 | which made me love mathematics even more,

01:03:40.540 | as this place where I could be safe and in control.

01:03:44.020 | - Made you see the human world

01:03:45.300 | as lesser than the mathematical world.

01:03:47.060 | - Yes.

01:03:47.900 | - As more limited than the mathematical world.

01:03:49.220 | - Yes, yes.

01:03:51.180 | And I think that,

01:03:52.080 | I think that it's still missing the mark in some sense,

01:03:58.300 | because in fact, what I now think,

01:04:02.460 | the question whether mathematics is invented or discovered,

01:04:09.460 | whether there is this world of pure forms and so on,

01:04:12.060 | is another paradoxical question,

01:04:15.820 | which doesn't have a simple answer.

01:04:18.880 | Like whether electron is a particle or a wave.

01:04:21.400 | From one point of view, yes, it's true.

01:04:25.860 | And just the fact that so many mathematicians today

01:04:29.500 | actually subscribe to this idea,

01:04:31.700 | gives it a certain credibility, because that's what we feel.

01:04:33.900 | We do feel that we dive into that mindscape, so to speak,

01:04:38.900 | but a very structured mindscape,

01:04:41.420 | where I wrote in "Love and Math"

01:04:44.180 | that the enchanted gardens of Platonic reality,

01:04:49.180 | where all this fruit grows,

01:04:52.000 | and then we might be,

01:04:53.480 | it gives you this sort of romantic sense of an explorer.

01:04:56.920 | And someone may be stuck in some provincial town

01:05:01.920 | in Russia, for instance,

01:05:04.480 | but have the sense of a Magellan,

01:05:07.760 | of traveling around the world.

01:05:09.240 | It's just not in the world that we usually think of.

01:05:12.840 | So it's one point of view,

01:05:14.940 | but the other point of view is that,

01:05:16.380 | yes, it is a human process.

01:05:17.940 | Of course it is.

01:05:18.780 | I mean, you cannot deny that.

01:05:20.380 | It's human beings who have so far

01:05:22.460 | discovered new mathematics.

01:05:24.180 | And I do not deny the possibility

01:05:25.820 | that computer programs will be able

01:05:27.860 | to discover new mathematics,

01:05:29.740 | but so far it's been humans.

01:05:32.700 | So whatever it is, whether it's discovered or invented,

01:05:37.700 | it is a human activity.

01:05:41.140 | The possibility that paradoxes are actually fundamental

01:05:44.920 | to reality and really, really internalizing that,

01:05:48.400 | that we exist in a world of not forms, but of paradoxes.

01:05:53.080 | - Bingo.

01:05:53.920 | And so it's like what I said.

01:05:55.800 | - Weird world.

01:05:56.640 | (laughs)

01:05:57.460 | - But if you think it's weird,

01:05:59.120 | and I agree with you as a recovering addict to knowledge,

01:06:02.720 | but I am liking it more and more

01:06:05.680 | because there's so much freedom in it.

01:06:08.680 | And like Niels Bohr said, I quoted that earlier,

01:06:12.480 | the opposite of a great truth is another great truth.

01:06:17.580 | He's pointing out to this fact that,

01:06:21.060 | and he also said that some things in quantum physics

01:06:25.340 | are so complicated, the only way you can speak of them

01:06:27.500 | is in poetry.

01:06:28.600 | So in other words, what is it about poetry?

01:06:32.580 | What is it about art?

01:06:34.160 | Why are we so drawn to that?

01:06:36.100 | Why are we so captivated by those forms?

01:06:39.940 | They are not intellectual necessarily.

01:06:42.860 | They are not, when you look at a painting that you like,

01:06:45.960 | when you listen to music that you love,

01:06:48.220 | you get lost in it, you get absorbed in it.

01:06:50.300 | It can make you cry, it can make you laugh,

01:06:52.340 | it can make you remember something,

01:06:55.380 | it can make you feel more confident,

01:06:57.660 | it can make you feel sad or happy and so on.

01:07:00.460 | What is this all about?

01:07:02.180 | Is it really just some play between,

01:07:05.220 | some kind of like cellophane play or some neurons

01:07:07.940 | hitting on each other?

01:07:09.180 | Is it really that only?

01:07:11.100 | - Maybe.

01:07:11.940 | - It could be both.

01:07:14.980 | I'm just worried about kids these days

01:07:17.060 | that might live in a world of paradoxes.

01:07:20.620 | If there's no God, everything is possible.

01:07:22.500 | And yet just, they'll have a little too much fun.

01:07:25.220 | And we have to put a constraint to the fun.

01:07:27.220 | - Have you looked at the world lately?

01:07:29.460 | - I haven't checked in in a while.

01:07:31.340 | - You think it's perfect the way it is now?

01:07:33.980 | The world without paradoxes?

01:07:36.100 | The world in which we believe that every question

01:07:38.740 | can be answered as yes or no, that it is this or that,

01:07:43.100 | and if you disagree with me, you're my enemy?

01:07:45.940 | - Wouldn't that be interesting if this 21st century

01:07:49.180 | is a transition into seeing the world

01:07:51.540 | as a world of paradoxes?

01:07:52.900 | - I'm telling you, people predicted that.

01:07:55.220 | The age of Aquarius, the axis of the Earth is rotating

01:08:00.060 | relative to the plane in which the Earth

01:08:01.780 | goes around the Sun, and the period of this revolution

01:08:05.620 | is around 2,000 years.

01:08:07.500 | So there is a traditional way of measuring that

01:08:10.900 | by this eras, the ages.

01:08:14.420 | So the previous one is called the Age of Pisces

01:08:17.180 | because of the constellation of Pisces

01:08:19.100 | that it points to, so to speak.

01:08:20.980 | And now, as in famous musical hair,

01:08:26.100 | they said the age of Aquarius is upon us.

01:08:28.820 | So the different people, they did differently,

01:08:31.100 | but somewhere around the time where we are finding ourselves.

01:08:36.100 | How interesting, right, is all the strife

01:08:38.500 | and all the difficulties the world is experiencing.

01:08:43.500 | This might actually be the transition to something

01:08:47.180 | more harmonious, wouldn't it be nice?

01:08:49.140 | - It's also interesting that people from long ago

01:08:52.500 | are able to predict certain things.

01:08:54.340 | And it's almost like from long ago,

01:08:59.340 | and you've talked about this with Pythagoras,

01:09:01.860 | that it seems that they had a deep sense of truth.

01:09:10.980 | - That's right. - That's what permeates

01:09:13.060 | all of this, even now.

01:09:14.940 | So it's not just a linear trajectory

01:09:17.660 | of an expanding knowledge.

01:09:19.740 | There's a deep truth that permeates the whole thing.

01:09:22.620 | - Yes, so that's how I see it.

01:09:24.100 | Actually, I gave a talk about Pythagoras and Pythagoreans

01:09:27.540 | just a few weeks ago at the Commonwealth Club

01:09:30.380 | of California in San Francisco.

01:09:32.860 | And because of that, I did a kind of a deep dive

01:09:35.660 | into the subject.

01:09:36.980 | And I learned that I actually totally misunderstood

01:09:40.620 | Pythagoras and Pythagoreans,

01:09:42.020 | that they were much deeper than I thought.

01:09:44.780 | Because most of us remember Pythagoras

01:09:47.660 | from the Pythagoras theorem about the right triangles.

01:09:52.100 | We also know that Pythagoreans were instrumental

01:09:56.380 | in introducing the tuning system for the musical scale,

01:10:00.660 | the famous perfect fifth,

01:10:06.060 | three halves for the G, for the sol,

01:10:10.100 | compared to the frequency of do or si.

01:10:13.540 | But actually, they were much more interesting.

01:10:19.580 | So for them, numbers were not just clerical devices,

01:10:24.660 | not the kind of thing that you would use in accounting only.

01:10:28.260 | They were imbued with the divine.

01:10:30.780 | And I cannot say that I think we lost it.

01:10:35.220 | At least I have lost it.

01:10:36.620 | I look at numbers, and I don't really see that--

01:10:40.580 | - The divine. - The divine.

01:10:42.060 | That they clearly did.

01:10:43.220 | And so why else, how else would you explain?

01:10:46.980 | So in other words, divine is, of course,

01:10:49.100 | is a term which is, it's a bit loaded,

01:10:51.740 | so it's hard to escape that.

01:10:54.340 | Let's just say something that more from the world

01:10:58.500 | of imagination and intuition

01:11:00.100 | than from the world of knowledge.

01:11:01.380 | Let's just put it this way.

01:11:03.380 | They were able to divine, okay, strike that,

01:11:06.660 | to intuit that the planets were not revolving,

01:11:11.660 | the sun and the planets were not revolving around the Earth.

01:11:16.300 | They were the first ones,

01:11:18.220 | at least in the Western culture, as far as I know.

01:11:20.700 | And in fact, Copernicus gave credit to Pythagoreans

01:11:24.220 | as being his predecessors.

01:11:26.180 | They did not quite have the Copernicus model

01:11:31.580 | with the sun in the middle.

01:11:33.260 | They had what they called the central fire in the middle.

01:11:36.380 | And all the planets and the sun were revolving around,

01:11:39.460 | around the central fire, or hearth, they called it hearth.

01:11:43.580 | So, but still, what a departure from the dogma,

01:11:47.780 | from the knowledge of the era

01:11:51.340 | that the Earth was at the center.

01:11:54.020 | So how could they come up with this idea?

01:11:57.380 | The reason was, in my opinion, that for them,

01:12:00.940 | the movement of celestial bodies was like music.

01:12:04.700 | In fact, we call it music universalis,

01:12:07.380 | or music of the spheres.

01:12:09.060 | For them, the universe was this infinite symphony

01:12:14.020 | in which every being, you know, humans, animals,

01:12:18.140 | as well as the Earth and other celestial bodies

01:12:21.940 | were moving in harmony,

01:12:24.660 | like different notes of different instruments

01:12:26.540 | in a symphony.

01:12:27.620 | And so they applied the same reasoning

01:12:29.900 | to the, you know, the cosmological model,

01:12:34.860 | as they applied to their model of music.

01:12:38.460 | And from that perspective,

01:12:41.340 | they could see things deeper than their contemporaries.

01:12:46.340 | You see, so in other words,

01:12:48.300 | they saw mathematics as a tool,

01:12:50.980 | but that tool was not limited to itself.

01:12:54.460 | And they always knew that there is more.

01:12:57.580 | And they knew also that every pattern that you detect

01:13:01.580 | is finite, but the world is infinite.

01:13:04.620 | They actually accepted infinity.

01:13:06.020 | They believed that infinity is real.

01:13:08.620 | And if you discern a pattern, great,

01:13:13.060 | you can play with it, and you can use that.

01:13:15.940 | It gives you a certain lens through which to see

01:13:20.220 | the world in a particular way,

01:13:21.860 | which could be beneficial for you to learn more and so on.

01:13:25.780 | But they never had the illusion

01:13:27.380 | that that was the final word,

01:13:28.940 | that they always knew that it's not the whole thing.

01:13:31.660 | So there is more.

01:13:32.500 | There are more sophisticated patterns

01:13:33.900 | that could be discovered using mathematics or otherwise.

01:13:36.700 | And I think that what happened was

01:13:39.420 | we kind of lost this other side of their teachings.

01:13:42.780 | We took their numbers and their idea

01:13:46.020 | that you could use mathematics to discern patterns

01:13:48.700 | and to find regularities

01:13:50.220 | and to explain things about the world.

01:13:52.700 | We took that and we ran with it.

01:13:54.820 | And we kind of dropped the other idea

01:13:56.980 | that in fact there is another side to it,

01:14:01.420 | which is kind of, to us now,

01:14:04.180 | we say, oh, that's mystical.

01:14:08.940 | But what does it mean mystical

01:14:11.700 | if it is something that helps you to make great discoveries?

01:14:14.900 | - And the interesting thing is

01:14:16.380 | that the people who are in touch with the mystical among us

01:14:19.700 | are often seen as mad.

01:14:22.260 | And many of them are, most of them are.

01:14:25.780 | (Lex laughing)

01:14:27.060 | - Well-- - But not all of them.

01:14:27.900 | - But not all of them.

01:14:28.940 | We mentioned Niels Bohr and Newton and Albert Einstein.

01:14:33.060 | So that's where the conundrum is.

01:14:35.900 | How do you find the balance between the two?

01:14:38.740 | So the point I'm trying to make,

01:14:42.900 | and this is what I feel,

01:14:45.780 | if you ask me what I find most important today,

01:14:48.420 | what makes me excited and enthusiastic and passionate,

01:14:53.020 | is this idea of balance.

01:14:57.820 | So Nietzsche wrote this book in the 19th century

01:15:03.900 | called "The Birth of Tragedy."

01:15:07.140 | And he presented this theory,

01:15:10.780 | which I think is kind of very useful,

01:15:13.900 | of these two sides of a human.

01:15:17.020 | One that comes from God Apollo,

01:15:19.500 | and that's our left brain, so to speak,

01:15:22.260 | proverbial left brain.

01:15:23.300 | So it's everything that has to do with logic and reason

01:15:27.740 | and analyzing, dissecting, conceptualizing.

01:15:30.860 | And the other side, which comes from God Dionysus, Dionysus,

01:15:40.980 | and that's responsible for intuition, imagination, love.

01:15:45.500 | Dionysus was also God of wine.

01:15:48.300 | So it's also that side of a human that makes us sing

01:15:53.300 | and engage in revelry and drink wine

01:16:00.620 | and spend time with friends and love and enjoy it.

01:16:06.580 | So Nietzsche advocated this point of view

01:16:08.780 | that those were two complementary sides of every human,

01:16:12.500 | as well as society.

01:16:13.780 | And the purpose of human life

01:16:18.220 | is to find balance between them.

01:16:21.420 | - So math is both discovered and invented.

01:16:26.540 | We should be okay with having both ideas in our head

01:16:31.540 | and living in the balance.

01:16:33.580 | - But more importantly, for me,

01:16:35.500 | Apollo is like math and Dionysus is like love.

01:16:38.820 | So Dionysus and Apollo, in modern version, is love and math.

01:16:43.820 | - I return to that question we had

01:16:46.580 | about GPT and the language models,

01:16:49.140 | and I think about this quite a lot,

01:16:52.680 | which is when the model, and we know what it's trained on,

01:16:57.180 | we know the parameters, we know all the different hacks

01:17:00.660 | that are involved in the training process

01:17:02.340 | and the fine-tuning process,

01:17:04.740 | and the final result, whether it's GPT-5, six, or seven,

01:17:09.740 | will result in hundreds of millions of people

01:17:13.380 | falling deeply in love with that language model

01:17:17.300 | and to be able to have conversations

01:17:19.660 | that are very much like the conversations we have

01:17:23.500 | with somebody we're deeply in love with.

01:17:25.580 | And not only that, the model will say

01:17:29.500 | that it's deeply in love with us.

01:17:32.300 | And who are we to say it is not?

01:17:34.400 | I think there's, it's the same imperative

01:17:40.740 | that you described in the scientific mind

01:17:43.460 | that wants to throw away the subjective.

01:17:46.140 | That same imperative wants to throw away

01:17:48.260 | the feelings that AI might have.

01:17:50.660 | And I'm very careful to not ignore

01:17:55.300 | when an AI system says it's lonely, it's afraid,

01:18:00.420 | it doesn't want to die, it misses you, it loves you.

01:18:03.860 | - I am with you.

01:18:05.260 | I would also say that you could try to,

01:18:08.220 | you could, for instance, say that the origin of that

01:18:12.780 | is the romantic novels that were fed to it, for instance.

01:18:18.700 | - Yes.

01:18:19.980 | - However, you could also, then you can retort,

01:18:22.980 | but what if my, what I consider my subjective,

01:18:25.660 | unique feelings are also--

01:18:27.980 | - Novels you were fed.

01:18:29.060 | - The reverberations of the novels I have read,

01:18:31.780 | because I have learned, or movies I have seen.

01:18:34.140 | Because that's the purpose of movies,

01:18:35.460 | kind of to teach us how to express ourselves,

01:18:37.940 | how to feel, maybe, even.

01:18:39.260 | One could argue that, some people have argued that.

01:18:42.380 | I agree that this is,

01:18:43.940 | there is no obvious answer to this.

01:18:48.900 | But see, that's exactly my point.

01:18:51.500 | That is an example of something which is paradoxical,

01:18:54.900 | for which there is no answer.

01:18:56.740 | And that's where the subjective has an important role.

01:19:01.740 | For someone, that type of interaction

01:19:05.820 | would be helpful, would be consoling,

01:19:11.500 | would feel, would make them happy, or sad, or whatever,

01:19:16.140 | you know, would kind of strike the nerve.

01:19:19.100 | For some, it won't.

01:19:20.860 | And I agree with you that, in principle,

01:19:24.180 | there is no one to judge this.

01:19:26.340 | This is where subjective is paramount.

01:19:28.700 | But remember, a lot of this has been anticipated

01:19:32.540 | by artists.

01:19:34.140 | The great movie "Her", there you have this guy

01:19:37.660 | who is this lonely, he kind of writes letters.

01:19:41.820 | - The romantic letters, yeah.

01:19:42.660 | - Kind of romantic letters for other people.

01:19:44.420 | But he doesn't have a partner, he's lonely.

01:19:47.940 | And then he gets this sort of enhanced version of Siri,

01:19:51.820 | with the voice of Scarlett Johansson,

01:19:56.700 | which is a very sexy voice, you know?

01:19:58.860 | Obviously, she's a great actress.

01:20:00.540 | So, and then, at first, it looks like

01:20:04.820 | a fantastic arrangement.

01:20:06.940 | He confides in her, she tells him things,

01:20:11.940 | she makes him happy, and so on,

01:20:14.340 | until he finds out that she has a relationship,

01:20:16.780 | quote unquote, if you can call it that,

01:20:18.820 | with 10,000 other people.

01:20:20.140 | - Not two others, not three others, but thousands.

01:20:23.260 | - Because it has the computing capability.

01:20:25.820 | So yes, definitely.

01:20:27.020 | - Oh, it certainly makes sense, it's a good explanation.

01:20:28.700 | - And the guy is heartbroken.

01:20:30.860 | But see, so here's my analysis of this, okay?

01:20:33.860 | It's like a couch therapist, okay?

01:20:36.840 | The guy did not have the courage to go out

01:20:41.620 | in the real world and to meet a woman

01:20:44.460 | and to get a girlfriend, and so on.

01:20:47.900 | It's true, no fault of his own, perhaps,

01:20:49.500 | because he may have had some experiences

01:20:51.500 | which made him withdrawn and closed, and so on.

01:20:54.340 | And a lot of us are like this.

01:20:55.820 | I had periods like that myself.

01:20:57.620 | Definitely can sympathize and relate.

01:21:00.860 | However, part of the joy of having

01:21:05.860 | this Siri-like relationship for him, one could say,

01:21:10.900 | was the absence of that fear that she would abandon him,

01:21:16.940 | which prevented him from initiating a relationship

01:21:21.940 | with a human being.

01:21:23.180 | And yet, it turns out that he could be "betrayed,"

01:21:28.100 | that she could be unfaithful to him, anyway.

01:21:31.860 | So then, that means that it did not resolve

01:21:34.900 | the underlying fear, having that relationship.

01:21:38.260 | So in other words, that human element of the relationship

01:21:42.720 | still found its way into the seemingly sterilized,

01:21:47.000 | protected partnership.

01:21:51.640 | So the human being rears its head anyway.

01:21:56.440 | - And I think the lesson there is that the system

01:22:00.580 | in the movie "Her" actually gave him a lesson

01:22:05.380 | that even AI could betray you, even AI can leave you,

01:22:09.240 | even AI can be unfaithful to you.

01:22:12.800 | And I would argue that the next AI he meets

01:22:16.720 | will be one he actually falls in deep love with,

01:22:19.960 | because he knows the possibility of betrayal is there,

01:22:22.600 | the possibility of death is there,

01:22:24.400 | the possibility of infidelity is there,

01:22:26.820 | because we need that possibility to truly feel--

01:22:30.160 | - Or, or he would turn off his Siri program

01:22:33.760 | and get out of his house, go to a local bar,

01:22:36.800 | and strike a conversation with a human being.

01:22:39.120 | Although you might say, by then,

01:22:42.400 | some of those might be androids.

01:22:44.000 | (laughing)

01:22:45.840 | So who knows? - And we don't even have

01:22:47.320 | a good test to know the difference between one or the other.

01:22:50.000 | - And that was predicted by another great movie.

01:22:52.560 | - Yeah. - Right?

01:22:54.840 | The "Blade Runner." - "Blade Runner."

01:22:56.840 | - How interesting that artists could see that so long ago.

01:23:01.840 | Of course, "Blade Runner" was based on a novel

01:23:04.800 | by Philip K. Dick, "The Androids Dream of Electric Sheep."

01:23:08.160 | That guy was a genius, you know?

01:23:11.240 | - It's somehow that artists have their eyes open

01:23:14.480 | to a bigger reality. - How is it that they

01:23:15.480 | anticipate, is it also a large language model

01:23:17.680 | that they're using for that? (laughing)

01:23:20.480 | - An even larger one. - An even larger.

01:23:23.080 | - I hesitate to dismiss the magic in large language models.

01:23:28.080 | A lot of the work I've done is in robotics,

01:23:31.680 | and the robotics community generally doesn't notice

01:23:33.920 | the magic of feeling.

01:23:36.760 | I've been working a lot with quadrupeds recently,

01:23:40.640 | legged robots with four legs,

01:23:42.920 | and the feelings I feel when I see,

01:23:47.680 | I'm programming the thing, but when the thing

01:23:51.600 | is excited to see me, or shows with its physical movement

01:23:54.680 | that it's excited to see me,

01:23:56.100 | I cannot dismiss the feeling I feel

01:23:59.800 | as not somehow fundamental to what it means

01:24:02.760 | to program robots, and I don't want to dismiss that.

01:24:07.760 | - Please don't, please don't.

01:24:08.840 | - The robotics community often doesn't gender robots.

01:24:11.720 | They really try to work hard to not anthropomorphize

01:24:14.360 | the robots, which is good for technical development

01:24:17.800 | of how to do control, how to do perception,

01:24:21.160 | but when the final thing is alive and moving,

01:24:25.120 | and it does whatever, like I've been doing

01:24:27.960 | a lot of butt wiggling, it can wiggle its butt,

01:24:29.920 | it can turn around and look up excited.

01:24:33.320 | That's not just, I know how it's programmed,

01:24:36.240 | but the feeling I feel, that's something.

01:24:39.160 | I don't know what that is.

01:24:40.000 | - I agree, I agree with you.

01:24:40.920 | I hear you when you speak about it,

01:24:44.240 | you speak with passion, and that's,

01:24:46.800 | to me, that is proof that it is magical, you see.

01:24:50.800 | So don't, I would say, don't dismiss that,

01:24:54.240 | don't discard that.

01:24:55.920 | On the contrary, I think magic is everywhere.

01:24:59.160 | So I used to be, okay, kind of confession, okay?

01:25:02.720 | (laughing)

01:25:04.800 | - Yeah, you already confessed to quite a few addictions.

01:25:07.480 | - Yeah, I'm kind of, yes, I'm kind of worried.

01:25:09.520 | - Recovering from many.

01:25:11.880 | - But you know, I, in old days, I was more on the side

01:25:16.880 | of everything is computational, or everything

01:25:20.840 | can be explained by science and whatever, you know?

01:25:23.440 | I would dismiss and disregard the intuitive

01:25:27.360 | or imaginative things.

01:25:29.120 | So then I had a flip, that suddenly I started feeling it,

01:25:32.720 | and started seeing it, and so on.

01:25:34.840 | But so then the pendulum had swung in the opposite direction.

01:25:39.200 | Then I was arguing that, you know, somehow that was real,

01:25:44.200 | that imagination was intuitive, imaginative was real,

01:25:51.040 | and discounting what you just described.

01:25:55.680 | And I would argue with people, saying,

01:25:57.320 | "No, no, this is not real, this is all imitation game,"

01:26:01.320 | and so on.

01:26:02.160 | But you see that what's new now, the new Edward, okay,

01:26:07.980 | is the 2.0, 3.0, is the one who is seeking balance,

01:26:12.780 | who is not, who is, because suddenly become aware

01:26:17.120 | that no matter which one-sided, lopsided point of view

01:26:20.480 | you take, you're limiting yourself.

01:26:23.240 | So whereas even a couple of years ago, you know,

01:26:26.080 | if you just told me what you just described,

01:26:28.680 | I would be like, you know, being polite, I would just,

01:26:30.880 | I wouldn't contradict you, since you're the host anyway,

01:26:33.680 | right? (laughs)

01:26:35.080 | - Not a law.

01:26:35.920 | - But I would be like, "Uh-huh, uh-huh,"

01:26:37.320 | but I wouldn't say anything.

01:26:39.020 | But suddenly I find this moving, I find it,

01:26:43.400 | I honestly, I'm not being facetious, I find it moving,

01:26:46.120 | and I almost feel like I can see it through your eyes,

01:26:49.240 | because the way you describe so vividly,

01:26:51.280 | and you're passionate about it.

01:26:52.520 | And this is what's real, so ultimately,

01:26:54.600 | love is not, is neither in lush language models,

01:26:59.360 | nor in something mystical.

01:27:00.960 | It's exactly in this moment of passion.

01:27:04.240 | And I would, I would, I would even go as far as saying

01:27:08.120 | that in this moment when you're describing it,

01:27:11.100 | there was a connection of sorts,

01:27:14.280 | so that I could feel your passion for it.

01:27:17.200 | And in this moment, something else comes up,

01:27:19.520 | which is far beyond any theories that we can come up with.

01:27:24.400 | And that's what we, for now, exactly.

01:27:26.600 | So on the one side, there is this impulse

01:27:29.760 | of finding a theory, and then there is another impulse

01:27:33.720 | to escape from what has already been known.

01:27:36.600 | So one, in other words, like in my basic example,

01:27:39.920 | is one impulse to say everything is a real number,

01:27:42.040 | square root of negative one doesn't exist,

01:27:43.380 | but another impulse is I'm going to be this naughty child

01:27:47.480 | who is not afraid to be an idiot,

01:27:48.920 | and I will say square root of negative 15 is real.

01:27:52.120 | And both are essential when it's done with conviction,

01:27:55.840 | when it's done with passion,

01:27:57.400 | when it's not like, you know, meh, you know, gratuitous.

01:28:02.400 | Or when it's not, it doesn't come from self-limiting,

01:28:07.960 | but comes from this sense of this is how I am,

01:28:12.720 | this is how I feel, it is real.

01:28:14.820 | That's where the progress is, that's where creativity is,

01:28:18.320 | and that's where, I would even say, a real connection is.

01:28:21.720 | Because the strife, to me, that I observe today

01:28:25.280 | in our society, and the society level,

01:28:27.560 | and the level of humans, and so on,

01:28:29.720 | it comes from not seeing the other person, actually,

01:28:32.520 | and being caught up in a very specific conceptual bubble,

01:28:36.800 | you see, and the way out of it is not to refine the bubble,

01:28:41.420 | but just break out of it.

01:28:43.080 | - A good guide out of the bubble is a childlike passion.

01:28:47.600 | Discovering that and following it.

01:28:49.480 | - Goosebumps.

01:28:50.320 | - Yeah, following the goosebumps.

01:28:52.200 | Not the rigor of science, but the magic of goosebumps.

01:28:59.400 | - And then, if you're interested,

01:29:01.840 | try to find a confirmation of those goosebumps

01:29:04.760 | in science, or whatever you find interesting.

01:29:09.760 | - And most of the time, you'll fail.

01:29:11.840 | - And most of the time you fail, which we also love,

01:29:13.920 | because then it sets us up for that moment of bliss

01:29:16.820 | when we succeed, right?

01:29:18.720 | - Exactly.

01:29:20.280 | Quick pause, bathroom break.

01:29:21.680 | You mentioned Gato's Completeness Theorem.

01:29:25.440 | Can you talk a little bit about it?

01:29:28.080 | What is it, as you understand it?

01:29:29.740 | Did it break mathematics?

01:29:31.400 | Maybe another question is,

01:29:33.000 | what are the limits of mathematics?

01:29:35.600 | What is mathematics from the perspective

01:29:37.920 | of Gato's Completeness Theorem?

01:29:40.040 | - Well, yes.

01:29:41.240 | How much time do you have?

01:29:42.480 | (both laughing)

01:29:44.240 | - So we talked about time previously, so it's--

01:29:46.600 | - Time is an illusion, right?

01:29:47.560 | So we agreed.

01:29:48.400 | (both laughing)

01:29:49.960 | So Kurt Gödel was a great Austrian mathematician

01:29:53.520 | and logician.

01:29:55.000 | He moved to the United States before Second World War,

01:29:58.760 | and worked at the Institute for Advanced Study in Princeton,

01:30:02.780 | where he was a colleague of Einstein

01:30:05.160 | and other great scientists,

01:30:06.980 | von Neumann, Herman Weyl, and so on.

01:30:10.840 | But one interesting quote that I like in this regard

01:30:16.600 | is that Einstein said that, at some point he said

01:30:20.240 | that the only reason he came to the Institute

01:30:23.720 | was that he would have the privilege

01:30:25.640 | of walking back home with Gödel in the evening.

01:30:28.960 | So in other words, Einstein thought

01:30:30.400 | that Gödel was the smart one, okay?

01:30:32.560 | So his most important contribution

01:30:38.240 | was his two incompleteness theorems,

01:30:41.960 | the first incompleteness theorem

01:30:43.240 | and the second incompleteness theorem.

01:30:45.480 | And what is this about?

01:30:49.000 | It's really about inherent limitations

01:30:51.760 | of mathematical reasoning,

01:30:54.200 | way of producing mathematical theorems, the way we do it.

01:30:59.800 | So to set the stage, how do we actually do mathematics?

01:31:04.800 | So we know that we discussed that,

01:31:08.360 | say physics is based on mathematics,

01:31:11.280 | and you could say chemistry is based on physics,

01:31:12.880 | biology based on chemistry.

01:31:13.960 | Okay, so it comes to mathematics.

01:31:15.000 | What is mathematics based on?

01:31:16.440 | Well, mathematics is based on axioms.

01:31:21.280 | So any field of mathematics

01:31:25.400 | can be presented as what is called the formal system.

01:31:31.680 | And at the core of the formal system

01:31:34.200 | is a system of axioms or postulates.

01:31:37.360 | These are the statements which are taken for granted.

01:31:42.000 | - Given without proof.

01:31:43.240 | - Without proof.

01:31:44.500 | An example would be,

01:31:45.560 | so one of the very first formal systems

01:31:47.760 | was the system, was Euclidean geometry,

01:31:50.160 | developed by Euclid in his famous book "Elements"

01:31:52.960 | about 2,200 years ago.

01:31:54.680 | And it's about, well, it's a subject familiar from school

01:31:59.640 | 'cause we studied, but what it's really about

01:32:02.480 | is about the geometry of the plane.

01:32:05.480 | And the plane, by plane I mean just this table top

01:32:08.000 | extended to infinity in all directions,

01:32:09.560 | kind of a perfect plane, a perfectly even table.

01:32:14.640 | And so Euclidean geometry is about

01:32:19.360 | various geometric figures on the plane,

01:32:21.240 | specifically lines, triangles, circles, things like that.

01:32:25.820 | So what's an example of an axiom?

01:32:28.640 | An example of an axiom is that if you have two points

01:32:32.000 | which are distinct, two points on the plane,

01:32:35.440 | then there is a unique line which passes through them.

01:32:39.000 | Now, it kind of sounds reasonable,

01:32:41.120 | but this is an example of an axiom.

01:32:43.300 | In mathematics, you have to have a seed, so to speak.

01:32:48.140 | You have to start with something.

01:32:50.060 | And you have to choose certain postulates or statements

01:32:54.940 | which you simply take for granted,

01:32:56.220 | which do not require proof.

01:32:58.200 | Usually, they are ones which kind of intuitively clear

01:33:01.100 | to you, but in any case, you cannot have any mathematics

01:33:06.100 | without choosing those axioms.

01:33:08.100 | - And you refer to those as the observer

01:33:10.500 | because they're kind of subjective.

01:33:12.820 | - The observer comes in the process of choosing the axioms.

01:33:16.620 | Who chooses the axioms?

01:33:18.980 | - The turtles that it's all sitting on top of.

01:33:21.220 | - As Alan Watts like to say, "Who is watching the water?"

01:33:25.620 | And so in mathematics,

01:33:27.860 | but you see, mathematicians are so clever.

01:33:30.460 | It's really kind of like a little kind of a game of mirrors.

01:33:34.260 | We often like to say, and I used to say that,

01:33:36.940 | that mathematics is objective.

01:33:39.980 | It's really the only objective science.

01:33:42.480 | But that's because we hide this fact.

01:33:48.780 | Actually, it's based on axioms.

01:33:51.220 | And the fact that there is no unique choice,

01:33:56.220 | that there are many choices.

01:33:59.380 | And so Euclidean geometry is actually a good illustration

01:34:01.700 | of this because Euclid had five axioms.

01:34:06.560 | Four of them were kind of obvious,

01:34:08.180 | like the one I just mentioned.

01:34:09.620 | And the fifth, which came to be known famously

01:34:13.060 | as the fifth postulate, was that if you have a line

01:34:17.060 | and you have a point outside of this line,

01:34:19.460 | there is a unique line passing through that point,

01:34:22.060 | which is parallel to the first line,

01:34:24.500 | meaning that it doesn't intersect it.

01:34:27.220 | And Euclid himself was uncomfortable about this

01:34:29.540 | because he felt that it was kind of,

01:34:31.580 | he takes for granted something that is not obvious.

01:34:37.160 | And for many centuries after that,

01:34:40.400 | mathematicians were trying to derive this axiom

01:34:43.040 | from other axioms, which were more obvious in some sense,

01:34:46.040 | and they failed.

01:34:46.880 | It was only almost 2,000 years later

01:34:50.600 | that mathematicians realized that you can't,

01:34:52.260 | not only you cannot derive,

01:34:53.760 | but you can actually replace it with its opposite.

01:34:56.860 | And you will still get a bona fide,

01:34:58.920 | consistent, not self-contradictory,

01:35:02.480 | which is called non-Euclidean geometry.

01:35:06.000 | Which of course sounds very complicated, but it's not.

01:35:09.720 | Think of a sphere, just the surface of a basketball,

01:35:12.480 | or the surface of the Earth idealized.

01:35:14.820 | The analogs, so you have points,

01:35:19.060 | you have analogs of lines which are meridians,

01:35:21.360 | and every two meridians intersect,

01:35:24.340 | unlike parallel lines on a flat space.

01:35:28.460 | There is also a so-called hyperbolic plane

01:35:30.920 | where there are infinitely many lines

01:35:34.520 | which do not intersect.

01:35:36.160 | So every possibility can be realized,

01:35:38.600 | there are different flavors.

01:35:39.880 | This is a good illustration of what a formal system is.

01:35:42.920 | You start with a set of axioms,

01:35:46.800 | those statements you take for granted,

01:35:48.740 | and this is where you have a choice.

01:35:50.560 | And by making different choices,

01:35:51.800 | you actually create different mathematics.

01:35:54.080 | After that, there are rules of inference,

01:35:56.120 | logical rules such as if A is true and A applies B,

01:36:01.240 | then B is true.

01:36:03.160 | Most of them were actually introduced already

01:36:07.640 | by Aristotle, even before Euclid.

01:36:11.120 | And then it runs as follows.

01:36:13.160 | You have the axioms which are accepted as true statements,

01:36:17.360 | then you have a way to produce new statements

01:36:20.320 | by using the rules of logical inference from the axioms.

01:36:25.400 | Every statement you obtain, you call a theorem,

01:36:27.760 | and you kind of add it to the collection of true statements.

01:36:32.480 | And then the question is, how far can you go?

01:36:35.840 | How many statements can you prove this way?

01:36:38.240 | Of course, you want the system to be non-trivial

01:36:43.080 | in the sense that you don't prove everything.

01:36:45.760 | Because if you prove everything,

01:36:46.880 | it would mean that it's self-contradictory,

01:36:48.600 | that you prove a statement A and it's negation.

01:36:51.680 | So that's kind of useless.

01:36:54.160 | It has to be discriminating enough

01:36:55.840 | so that it doesn't prove contradictory statements.

01:37:01.100 | So there is already a question

01:37:02.400 | of that mathematicians call consistency.

01:37:04.200 | It has to be consistent in the sense

01:37:05.660 | that it is not self-contradictory.

01:37:08.200 | And then the idea that was basically prevalent

01:37:14.080 | in the world of mathematics

01:37:15.400 | by the beginning of the 20th century

01:37:17.640 | was that in principle,

01:37:18.600 | all of mathematics could be derived this way.

01:37:20.360 | We just have to find the correct system of axioms,

01:37:23.640 | and then everything you ever need

01:37:28.280 | could be produced by this procedure,

01:37:32.100 | which is really algorithmic procedure,

01:37:33.700 | which actually could be run on a computer.

01:37:37.480 | Now, think about it.

01:37:40.260 | What is special about this process?

01:37:42.860 | In this process, you are just manipulating symbols,

01:37:46.660 | basically.

01:37:47.500 | You're going from one statement to another

01:37:49.620 | without really understanding the meaning of it.

01:37:52.860 | So it's an ideal playground for a computer program.

01:37:56.160 | It's a purely syntactic process

01:37:58.360 | where there are some rules, some rigid rules

01:38:01.260 | of passing from one statement to the next.

01:38:04.320 | Most mathematicians believed that this way

01:38:08.020 | you can produce all true statements.

01:38:10.220 | And if this were true,

01:38:11.840 | it would give a lot of credibility to the thesis

01:38:14.100 | that everything in life is computational,

01:38:16.500 | or life is computation,

01:38:19.220 | because then at least mathematics is computational

01:38:21.100 | because then it can be programmed,

01:38:23.300 | and a computer, after sufficient time,

01:38:26.820 | depending on its capacity,

01:38:29.620 | would produce every true statement.

01:38:31.780 | So Gödel's first incompleteness theorem

01:38:33.500 | says that that's not the case.

01:38:35.280 | And it not just says it, but it proves it

01:38:37.420 | at the highest level of rigor

01:38:39.660 | that is available in mathematics,

01:38:40.900 | that is to say within another formal system

01:38:43.120 | that he was operating in.

01:38:44.420 | So more precisely, what he proved was that

01:38:49.260 | if you have a sufficiently sophisticated formal system,

01:38:51.900 | that is to say that you can talk about numbers,

01:38:56.020 | whole numbers in it,

01:38:57.060 | that you have whole numbers, one, two, three, four,

01:38:58.860 | you have formalized the operation of addition

01:39:02.660 | and multiplication within the system.

01:39:05.340 | If it is consistent, that is to say,

01:39:08.940 | if it's not completely useless,

01:39:11.100 | then there will be a true statement in it

01:39:14.060 | which cannot be derived by this linear syntactic process

01:39:18.260 | of proving theorems from axioms.

01:39:21.580 | It's really incredible.

01:39:23.620 | So this was a revolution.

01:39:25.060 | 1931, a revolution in logic, a revolution in mathematics,

01:39:28.340 | and we're still feeling the tremors of this discovery.

01:39:33.340 | - And at a similar time, the computer is being born.

01:39:38.180 | The actual engineering of the computational system

01:39:41.020 | is being born, which is ironic.

01:39:43.540 | - Turing was, Alan Turing, who is considered

01:39:47.420 | as the father of modern computing, right?

01:39:49.220 | So he actually did something very similar.

01:39:51.900 | So he had this halting problem.

01:39:53.460 | He proved that halting problem

01:39:56.340 | cannot be solved algorithmically,

01:39:57.940 | that you cannot, out of all computer programs,

01:40:00.420 | roughly speaking, you cannot have an algorithm

01:40:03.380 | of choosing out of all possible computer programs

01:40:05.940 | which ones are meaningful, which ones will halt.

01:40:10.500 | - Very depressing results all across the table.

01:40:13.060 | - Or, on the contrary, life-affirming.

01:40:16.700 | Depends on your point of view.

01:40:19.060 | - Because everything is full of paradoxes.

01:40:21.180 | - So that means, you're right, it's depressing

01:40:23.700 | if we are sold on a certain idea from the outset,

01:40:26.860 | and then suddenly this doesn't pan out.

01:40:28.860 | But, okay, to which I retort,

01:40:32.620 | what if he proved that actually everything can be proved?

01:40:37.620 | So then what?

01:40:38.580 | What is left to do if you're a mathematician?

01:40:41.140 | So that would be depressing to me.

01:40:43.700 | And here, there is an opportunity to do something new,

01:40:46.900 | to discover something new,

01:40:47.940 | which maybe a computer will not be able to.

01:40:50.580 | Again, with a caveat,

01:40:52.620 | according to our current understanding,

01:40:54.260 | maybe some new technology, some new ideas

01:40:56.420 | will be brought into the subject.

01:40:58.980 | And the meaning of the word computation,

01:41:01.940 | like now we think of computation in a particular framework,

01:41:04.220 | Turing machines or Church thesis and stuff like that.

01:41:07.140 | But what if, in the future, another genius

01:41:10.100 | like Alan Turing will come and propose something else?

01:41:13.060 | The theory will evolve the way we went

01:41:15.900 | from Newton's gravity to Einstein's gravity.

01:41:18.380 | Maybe in the framework of that concept,

01:41:20.860 | some other things will become possible.

01:41:22.820 | So it's not,

01:41:26.820 | to me, it's kind of like not so much about

01:41:32.740 | deciding once and for all how it is or how it should be,

01:41:38.100 | but kind of like accepting it as an open-ended process.

01:41:42.460 | I think that's much more valuable in some sense

01:41:44.820 | than deciding things one way or another.

01:41:47.620 | - I wonder, I don't know if you think

01:41:52.340 | or know much about cellular automata

01:41:54.420 | and the idea of emergence.

01:41:57.660 | I often return to Game of Life and just look at the thing.

01:42:03.220 | - Amazing, right?

01:42:04.220 | - And wonder--

01:42:05.060 | - The kind of things we can do with such a small tools.

01:42:09.140 | - That from simple rules, a distributed system

01:42:12.340 | can create complex behavior.

01:42:14.940 | And it makes you wonder that maybe

01:42:16.660 | the thing we'll call computation is simple

01:42:20.700 | at the base layer, but when you start looking

01:42:23.580 | at greater and greater layers of abstraction,

01:42:25.740 | you zoom out with blurry vision,

01:42:27.540 | maybe after a few drinks, you start to see

01:42:29.740 | something that's much, much, much more complicated

01:42:33.940 | and interesting and beautiful than the original rules

01:42:37.900 | that our scientific intuition says

01:42:40.340 | cannot possibly produce complexity and beauty.

01:42:43.060 | I don't know if anyone has a good answer,

01:42:45.980 | a good model of why stuff emerges,

01:42:49.720 | why complexity emerges from a lot of simple things.

01:42:54.620 | It's a why question, I suppose, not a,

01:42:57.900 | but every why question will eventually

01:43:00.380 | have a rigorous answer.

01:43:03.460 | - Not necessarily, we could have an approximate answer

01:43:06.700 | which still eludes something.

01:43:09.540 | Like quantum mechanics.

01:43:10.380 | - 99%, maybe.

01:43:11.700 | We will be able to describe it with 99% certainty

01:43:15.460 | or 99% accuracy.

01:43:17.260 | And then maybe in 100 years or next year,

01:43:23.220 | somebody will come up with a different point of view

01:43:28.100 | which suddenly will change our perspective.

01:43:30.260 | To this point, I want to say also one thing

01:43:33.940 | that I find fascinating, speaking of paradoxes and so on.

01:43:38.100 | Do you remember how everybody was freaking out

01:43:40.180 | about this blue dress?

01:43:41.900 | And the blue, was it blue or was it black?

01:43:44.460 | - Yeah.

01:43:45.300 | - It was the yellow, I think, yellow and white

01:43:47.060 | or black and blue.

01:43:48.380 | It almost broke Twitter, you know, I remember that.

01:43:51.420 | - Yeah. - That night.

01:43:53.140 | So there are many examples like that

01:43:55.100 | where you can perceive things differently

01:43:57.340 | and there is no way of saying which is correct

01:44:00.380 | and which is not.

01:44:01.220 | For instance, you got this, the vase, the Rubin's vase,

01:44:05.380 | you know, where you have, from one perspective it's a vase,

01:44:08.460 | from another perspective it's two faces.

01:44:10.620 | Then there is this duck-rabbit picture

01:44:14.420 | where you can Google it.

01:44:15.940 | If somebody doesn't know, they can Google it

01:44:17.620 | and find it, it's very easy.

01:44:19.140 | Actually, Ludwig Wittgenstein devoted several pages,

01:44:22.380 | duck-rabbit, in his book.

01:44:24.860 | And so on, there are many others.

01:44:26.440 | There are like squares where you can see,

01:44:28.060 | a square you can see from different perspective,

01:44:30.140 | this way, that way and so on.

01:44:32.140 | So, when we talk about neural networks,

01:44:35.900 | we're talking about training data and stuff

01:44:40.020 | so that you have some pictures, for example,

01:44:42.980 | that you feed to your program

01:44:46.100 | and you try to find the most optimal neural network

01:44:50.180 | which would be able to decide which one is it,

01:44:52.580 | is it a dog or a cat or whatever.

01:44:54.340 | But sometimes it doesn't have a definite answer.

01:44:57.180 | So what do you do then?

01:44:59.940 | So, actually, it's a question, I actually don't know.

01:45:03.900 | Has modern AI even come to appreciate this question?

01:45:08.900 | That actually sometimes you can have a picture

01:45:12.020 | on which you cannot say what it is in it.

01:45:14.540 | From one perspective, it's a rabbit,

01:45:16.460 | from another perspective, it's a duck.

01:45:18.260 | How are you supposed to train,

01:45:20.180 | if you have a neural network which is supposed

01:45:21.820 | to distinguish between ducks and rabbits,

01:45:25.020 | how is it going to process this, you see?

01:45:27.260 | - Well, so the trivial trick it does is to say

01:45:31.060 | there's this X probability that it's a duck

01:45:34.140 | and this probability that it's a rabbit.

01:45:36.460 | - Well, that's a good approach,

01:45:37.300 | but also I would say there's no given percentages.

01:45:40.780 | For instance, actually, at some point

01:45:42.940 | I was really curious about it and I looked.

01:45:46.140 | And for each picture of this nature,

01:45:50.340 | and there are a bunch of them you can easily find online,

01:45:53.300 | my mind immediately interprets it in a particular way.

01:45:57.220 | But because I know that other people

01:46:00.020 | could see it differently, I would then strain my mind,

01:46:03.020 | and strain my eyes, and stare at it,

01:46:05.580 | and try to see it in a different way.

01:46:07.540 | And sometimes I could see it right away,

01:46:09.500 | and then I could go back and forth between the two.

01:46:11.980 | And sometimes it took me a while for some pictures.

01:46:16.380 | So in that sense, even if these probabilities exist,

01:46:19.380 | they are subjective.

01:46:20.420 | Some people immediately see it this way,

01:46:22.340 | some people immediately see it that way,

01:46:23.620 | and I think that nobody knows.

01:46:25.860 | Not psychologists, not neuroscientists, not philosophers

01:46:28.380 | what to make of it.

01:46:29.380 | The best answer, of course, as a scientific mind,

01:46:34.940 | even though I say, no, don't look for interpretation,

01:46:38.100 | leave some place for mysticism or mystery, right?

01:46:40.740 | I say that.

01:46:41.580 | But of course I want a theory, I want an explanation.

01:46:44.180 | So the best explanation I find

01:46:46.580 | is from Niels Bohr's complementarity principle.

01:46:49.660 | So it is like particle and wave,

01:46:51.500 | that there are different ways to look at it.

01:46:54.660 | And when you look at it in a particular way,

01:46:56.940 | another side will be obscured.

01:46:58.580 | Think about it like the other side of the moon.

01:47:00.420 | So we are observing the moon from one side,

01:47:03.380 | and then we don't see the other side.

01:47:05.360 | There is a complementary perspective

01:47:07.020 | where we see the other side,

01:47:08.500 | but not the side we normally see.

01:47:10.300 | But the moon is the same, it's still there.

01:47:13.120 | It's our limitations of being able to grasp the whole.

01:47:17.860 | That's complementarity.

01:47:18.980 | And we know that from quantum mechanics

01:47:21.780 | that our physical reality is like that.

01:47:24.740 | Rather than being certain,

01:47:26.380 | rather than being one way or another.

01:47:28.220 | - And we should just, as a small aside,

01:47:32.080 | in terms of neural networks, mention that

01:47:34.980 | at the end of the day, there's humans,

01:47:37.580 | it's built on top of humans.

01:47:39.100 | Or with Chad GPT that is using reinforcement learning

01:47:43.140 | by human feedback, we're actually using a set of humans

01:47:48.140 | to teach the networks.

01:47:50.460 | And that's the thing that people don't often talk about,

01:47:52.400 | because, or I sometimes think about that

01:47:56.580 | those humans all have a life story.

01:47:59.700 | Each human, the annotated data,

01:48:02.520 | that fed data to the network, or did the RLHF,

01:48:05.980 | they have a life story.

01:48:08.180 | They grew up, they have biases.

01:48:10.220 | - They have biases, there's some things that they like,

01:48:11.780 | there's some things they don't like,

01:48:13.380 | which can kind of appear under their radar screen.

01:48:18.220 | They may not be aware that they are exercising those biases.

01:48:21.100 | - That's the point, what you brought up

01:48:22.960 | is a very important issue here.

01:48:25.400 | Not so much issue, but it's not a bug,

01:48:27.320 | it's a feature in my opinion.

01:48:29.680 | That implicit in the discussion of the question

01:48:34.440 | is thinking computational and so on,

01:48:37.720 | is the idea that our conscious awareness

01:48:40.800 | covers everything within our psyche.

01:48:43.680 | And we just know that that's not the case.

01:48:46.640 | We have, all of us have observed other people

01:48:49.720 | who have had sort of destructive tendencies.

01:48:52.280 | So obviously, they did things destructive for themselves.

01:48:55.440 | And many of us have observed ourselves doing that

01:48:59.120 | as part of human nature.

01:49:00.500 | And there is great research in analytic psychology

01:49:04.680 | and in the past 100 years, strongly suggesting,

01:49:09.680 | if not proving, the existence of what Carl Jung called

01:49:13.040 | the personal unconscious and also collective unconscious.

01:49:16.320 | This kind of a circle of ideas,

01:49:18.360 | which are under the radar screen,

01:49:21.000 | which lead us to some strong emotions

01:49:24.000 | and inspire us to act in certain ways,

01:49:26.760 | even if we cannot really understand.

01:49:29.160 | So if we accept that, then the proposition

01:49:32.640 | that somehow everything can still be covered by our actions,

01:49:37.640 | which are totally kind of neutral

01:49:40.320 | and totally righteous and totally conscious,

01:49:44.760 | that it becomes really tenuous.

01:49:46.480 | - Let me ask you some tricky questions.

01:49:50.800 | - Uh-oh.

01:49:51.800 | - In terms of how big they are.

01:49:53.480 | In terms of how, you know, they become difficult

01:49:56.960 | because of how much of a romantic you are.

01:49:59.060 | What to you is the most beautiful idea in mathematics?

01:50:05.720 | Another one we can ask is,

01:50:09.440 | what is the most beautiful equation in mathematics?

01:50:12.820 | - Hmm.

01:50:13.660 | Well, I mean.

01:50:17.500 | (Lex laughing)

01:50:19.140 | - I may have just broken your brain.

01:50:20.940 | Because what your brain is doing

01:50:24.620 | is walking down a long memory lane of beautiful experiences.

01:50:29.620 | - Well, you see, in mathematics,

01:50:31.780 | we have this idea that, we have an idea of a set, right?

01:50:35.620 | So we have a collection of things.

01:50:37.340 | For instance, you know, the set of tables,

01:50:39.700 | the set of chairs, and so on, or set of microphones.

01:50:43.420 | But it could be a set of numbers.

01:50:45.780 | Could be a set of ideas.

01:50:47.260 | Could be a set of formulas, mathematical equations.

01:50:50.420 | And then we have the notion of an ordered set,

01:50:53.020 | ordered, like the set in which there is order.

01:50:55.740 | Which means that for every two members of the set,

01:50:58.740 | we'll say which one is better than the other

01:51:00.460 | or greater than the other.

01:51:01.860 | For instance, all numbers are ordered.

01:51:04.700 | Five is greater than three,

01:51:06.020 | five is less than seven, and so on.

01:51:08.740 | But not all sets are ordered.

01:51:10.780 | So the set of beautiful theorems is not,

01:51:13.060 | beautiful equations is not ordered.

01:51:15.020 | (both laughing)

01:51:17.660 | So in other words, there are many best equations.

01:51:20.540 | And so, Richard Feynman chose one,

01:51:25.540 | which I think one of the best,

01:51:27.420 | is that if you take E, the base of natural logarithm,

01:51:31.580 | to the power pi i, so you have pi,

01:51:33.740 | you have E in it, the base of natural logarithm,

01:51:36.380 | you have pi, i, which is square root of negative one,

01:51:39.900 | then the result is negative one.

01:51:44.100 | So that's up there, for sure,

01:51:46.780 | in the pantheon of beautiful formulas, you know?

01:51:49.860 | That I think pretty much every mathematician would agree.

01:51:53.260 | I don't know what my favorite one is.

01:51:56.260 | - I'm just lingering on that one, Euler's Identity.

01:51:59.780 | What makes it beautiful?

01:52:01.460 | Just a few symbols together.

01:52:03.660 | - Right.

01:52:06.020 | - I mean, part of it is actually just trying to define

01:52:08.140 | what is beautiful about mathematics.

01:52:10.320 | That is,

01:52:12.380 | laid in there, in this particular equation,

01:52:15.900 | that is somehow revealed when the human eye looks at it.

01:52:18.700 | Why is it beautiful, do you think?

01:52:21.560 | Pi, i--

01:52:23.660 | - There is an element of surprise in it.

01:52:27.220 | How is it possible?

01:52:28.420 | We always think of pi as the ratio

01:52:31.420 | between the circumference of a circle and its diameter.

01:52:35.900 | Here, we are taking some number to the power pi.

01:52:39.780 | Not even pi, mind you.

01:52:41.900 | But pi multiplied by square root of negative one.

01:52:44.340 | Surely, this is something completely incomprehensible.

01:52:51.420 | And yet, the result is negative one, you see?

01:52:54.740 | And if you take e to the power two pi i,

01:52:57.020 | you get one, actually one.

01:52:58.380 | So I would guess that that's, but in other words,

01:53:03.880 | the initial reaction is just that it was surprise, I guess.

01:53:08.880 | I guess for anyone who first comes across.

01:53:13.260 | - That these three folks, four folks got together.

01:53:17.220 | It reminds me of the idea that Hitler, Stalin,

01:53:22.220 | Trotsky, and Freud were all in Vienna

01:53:24.940 | in some early, at the beginning of the '20s.

01:53:27.700 | - And Wittgenstein was a classmate of Hitler, you know this.

01:53:31.580 | - I did not know this, no.

01:53:33.180 | - So there, it makes you, you know,

01:53:35.360 | you can imagine a situation where they're all

01:53:37.180 | sitting at a bar together at some point, not knowing it.

01:53:40.980 | But they somehow, it all made sense in space, time,

01:53:43.940 | to be located there.

01:53:45.660 | And that's what this feels like, some kind of intersection.

01:53:48.140 | - Intersection, yes.

01:53:49.460 | But I would say that after the initial shock,

01:53:53.220 | you look at the proof of this equation.

01:53:56.340 | And it actually does make sense.

01:53:58.140 | And actually, it is nothing but the statement

01:54:02.020 | that the circumference of the circle is.

01:54:04.940 | And in fact, in this case, it's the circumference

01:54:07.020 | of a semicircle is equal to pi.

01:54:10.140 | And that's where it comes from.

01:54:11.740 | - In the end, the truth is simple.

01:54:14.220 | - In the end, the truth is simple.

01:54:15.220 | Not necessarily easy, but simple.

01:54:17.480 | - So I mentioned to you offline that I desperately,

01:54:21.420 | in trying to figure out the optimal,

01:54:24.700 | in an ordered set, questions to ask you,

01:54:27.520 | texted Eric Weinstein asking for what questions

01:54:30.380 | he can ask you.

01:54:31.660 | And he said that you are definitively

01:54:36.100 | one of the greatest living mathematicians,

01:54:38.220 | so don't screw this up.

01:54:39.820 | But he did give me a few questions.

01:54:42.580 | So he asked to ask you,

01:54:46.340 | what are the most shockingly passionate,

01:54:48.380 | this is in Eric's language,

01:54:50.140 | what are the most shockingly passionate

01:54:52.100 | mathematical structures?

01:54:53.580 | And he gave a list of four for him.

01:54:56.460 | But he said he really wanted your list.

01:55:00.500 | Okay, let me say that.

01:55:01.420 | Shockingly passionate mathematical structures.

01:55:05.740 | - Shocking.

01:55:06.580 | (Lex laughing)

01:55:09.100 | - Is there something you can,

01:55:10.740 | is there something that jumps to mind?

01:55:12.420 | - Sure.

01:55:13.260 | I'm here to shock.

01:55:16.860 | - Yes, yeah.

01:55:18.300 | - So first of all, Eric Weinstein is a very dear friend,

01:55:21.700 | I have to say.

01:55:22.580 | And I really, really, really appreciate and love him.

01:55:25.700 | He's just like my brother.

01:55:26.980 | So it's interesting to have a question posed by him.

01:55:31.980 | - And maybe if we can linger for a moment,

01:55:34.740 | what do you think is special about Eric Weinstein

01:55:38.260 | for you know of his work and his mind?

01:55:40.540 | - The way he sort of straddles so many different disciplines.

01:55:44.900 | It's like a Renaissance man.

01:55:46.340 | There are very few people like that at any given moment,

01:55:48.620 | let alone the 21st century,

01:55:50.740 | where information has become so huge

01:55:55.020 | that it's almost physically impossible

01:55:56.740 | to be able to keep track of things.

01:55:58.140 | And yet, he does, and he has his own unique vision

01:56:02.860 | and unique point of view, and he has integrity,

01:56:05.580 | which is like almost impossible.

01:56:07.620 | Like I can't think of so many people

01:56:10.420 | who possess those qualities, almost no one.

01:56:13.540 | - And also the ability, in some sense,

01:56:19.060 | to embody the balance that you talked about,

01:56:23.300 | of both the rigor of mathematics and the imagination.

01:56:28.300 | - Humanity also, I would say.

01:56:30.260 | You know, like we talk about imagination

01:56:32.340 | as a kind of a counterpoint to knowledge or logic.

01:56:38.060 | But just basic humanity, you know,

01:56:39.620 | just basic compassion, just being able to,

01:56:43.580 | because every destructive, I would say,

01:56:48.180 | like every destructive society,

01:56:51.940 | you know, like be it Germany under Hitler

01:56:54.660 | or Soviet Union under Stalin and so on,

01:56:57.700 | was based on some kind of what was considered

01:57:00.340 | unassailable truths.

01:57:02.260 | So a kind of conceptual system, you know,

01:57:04.100 | if you think about it, right?

01:57:05.780 | There is a beautiful episode of this series

01:57:10.020 | by Jacob Bronowski, you know,

01:57:13.320 | where he talks about, he filmed it in Auschwitz,

01:57:18.980 | talking about the certainty that what led the Nazis

01:57:22.780 | to killing people wholesale was a certain,

01:57:27.780 | it was almost a mathematical idea.

01:57:30.260 | And they just basically bought into this idea

01:57:32.620 | and checked out their humanity at the door.

01:57:35.140 | So I would say that antidote to this type of thing

01:57:38.700 | is not necessarily even imagination

01:57:41.020 | in a kind of elevated sense

01:57:42.380 | that we have been discussing today,

01:57:44.620 | that is exemplified by our greatest scientists

01:57:49.260 | and philosophers, but just basic humanity,

01:57:55.340 | you know, basic common sense of just like knowing

01:57:58.980 | that it's just not right.

01:58:00.780 | And I don't care what my ideology tells me,

01:58:03.980 | but I'm just not going to do it.

01:58:05.920 | So that I think is kind of missing a little bit

01:58:10.260 | in today's society, 'cause people get a lot too caught up

01:58:12.900 | in the ideology, in certain conceptual frameworks.

01:58:16.620 | - So societies that lose that basic human compassion,

01:58:19.980 | that basic humanity, run into trouble.

01:58:22.540 | - Oh, very much so.

01:58:23.380 | But not only society, like a human being.

01:58:25.220 | - And Eric is one of the people, I agree with you,

01:58:29.480 | keeps that flame of--

01:58:30.580 | - Like I trust that he will not do something

01:58:33.340 | that's not human, that's not right.

01:58:37.260 | I just feel, you know, like there's some people

01:58:39.300 | you just kind of feel that they won't cross that line.

01:58:42.540 | And that's a huge thing, you know, today.

01:58:45.460 | Because I have to say, looking back,

01:58:47.340 | definitely I have not hurt people personally,

01:58:51.140 | but I could be mean, for instance, I could be harsh.

01:58:55.940 | And now I see it as a sign of weakness,

01:58:58.900 | as a sign of insecurity.

01:59:00.540 | You know, I saw your interview with Ray Kurzweil

01:59:05.620 | the other day.

01:59:07.020 | Beautiful, I was really moved by it.

01:59:09.060 | But you know, at some point I was like,

01:59:11.820 | I looked at him at this sort of like Dr. Evil.

01:59:14.580 | (both laughing)

01:59:16.660 | I'm kind of ashamed of it now,

01:59:17.820 | but like, you know, I'm kind of coming clean.

01:59:20.700 | And I would, you know, because, well, why?

01:59:25.060 | Because I needed an adversary in my mind.

01:59:28.380 | Because I projected onto him kind of the fears that I had,

01:59:32.140 | that AI will conquer us and so on.

01:59:35.240 | And this was rooted in my kind of awakening moment,

01:59:40.380 | in a sense, a kind of a moment where I suddenly started

01:59:42.620 | to see the other side.

01:59:44.340 | So, but I wasn't sure yet, you see?

01:59:47.460 | - You had to feel it.

01:59:48.300 | - So I had to have a fight about it.

01:59:50.020 | - Yeah, you had to actually have the projection.

01:59:52.380 | - I had to, so it was not in,

01:59:53.980 | I believe that it was not in me already,

01:59:55.860 | so I had to throw it onto somebody.

01:59:57.780 | - Yeah.

01:59:58.900 | - And that's not balance yet.

02:00:00.180 | So balance is when you recognize that it's you, actually.

02:00:03.500 | And I had this moment, actually, it was so amazing.

02:00:06.380 | Like, I would give this mean,

02:00:07.820 | I would talk about AI and the dangers,

02:00:09.820 | and he would always be my foil.

02:00:12.780 | You know, I would put a sinister photograph

02:00:15.380 | of him on the slide.

02:00:17.620 | And I was like, "Look at this guy.

02:00:19.420 | "He wants to put nanobots into your brain.

02:00:22.260 | "And he's also a top executive at Google," and so on.

02:00:27.060 | So I would create this whole narrative.

02:00:29.020 | And then something happened,

02:00:31.460 | where I was giving a lecture, this is 2015,

02:00:36.140 | in Aspen, Aspen Ideas Festival,

02:00:38.660 | which is a wonderful festival.

02:00:41.220 | So keynote speech, actually.

02:00:43.180 | And I was doing my usual shtick.

02:00:46.100 | And then suddenly I said,

02:00:47.580 | I came up to that,

02:00:49.740 | oh, there was a big screen,

02:00:52.220 | and there was a picture of him there.

02:00:53.820 | And I came up to the screen,

02:00:54.820 | and I kind of touched it with my hand,

02:00:56.300 | and I said, "But I don't want to pick on Mr. Kusla,

02:00:59.860 | "because he's me."

02:01:01.540 | I had this revelation

02:01:03.620 | that I'm actually fighting with myself,

02:01:05.180 | with my own fears.

02:01:06.260 | And then I learned about

02:01:10.020 | his father, that his father died when he was young.

02:01:16.220 | And that he's, in fact,

02:01:19.900 | he's very, to his credit,

02:01:22.300 | he's very sincere and upfront about it.

02:01:25.420 | Self-disclosure, I think, is very essential,

02:01:27.340 | by the way, in all this discussion.

02:01:28.460 | Like, what really motivates you?

02:01:30.620 | He said it publicly many times,

02:01:33.660 | even as early as 2015,

02:01:36.140 | I could find this information,

02:01:37.660 | that he wanted to reunite with his father in the cloud.

02:01:43.860 | And suddenly I saw him not as a caricature

02:01:46.780 | that exemplified all my fears,

02:01:50.820 | but as a human being,

02:01:52.060 | a child longing for his father,

02:01:54.980 | grieving for his father.

02:01:56.780 | So suddenly it became a story, a love story.

02:02:01.580 | And, you know,

02:02:03.820 | so that is,

02:02:05.420 | so in other words, I've seen it in myself,

02:02:08.180 | this

02:02:09.020 | capacity to project my own fears

02:02:15.300 | and then fight with other people over something

02:02:18.140 | that actually was my own.

02:02:20.460 | And as soon as I got to this point of seeing him,

02:02:23.180 | and then my next lecture,

02:02:24.300 | actually I talked about it,

02:02:25.980 | about him in this way.

02:02:28.300 | And I said, "Look, it's a love story.

02:02:31.180 | And he is actually,

02:02:32.460 | it's not how I would want to reunite with my father.

02:02:37.500 | But like you said,

02:02:42.260 | if I am consistent,

02:02:45.420 | I have to allow the possibility that different people

02:02:48.060 | perceive things differently.

02:02:51.580 | And so for him,

02:02:53.940 | that's his imagination.

02:02:55.860 | So, you know how,

02:02:57.260 | who is this, Voltaire, I think,

02:02:58.780 | he's ascribed to Voltaire.

02:02:59.900 | So it's like, I disagree with you,

02:03:01.180 | but I will fight to death

02:03:02.860 | for you to have the right to say it.

02:03:04.740 | So now that I feel like my position is more like,

02:03:08.540 | I disagree with him,

02:03:09.540 | that this is the way to approach death

02:03:13.380 | and to approach the death of loved ones

02:03:15.940 | and how we miss them and how we,

02:03:18.700 | you know, that sense of loneliness

02:03:21.420 | and inability to interact directly.

02:03:23.700 | That's not something that resonates with me,

02:03:28.940 | but I think it's also,

02:03:31.300 | it can also be called imagination from his perspective.

02:03:33.940 | And look, motivated by that,

02:03:36.860 | how much he has brought,

02:03:39.300 | how many interesting inventions,

02:03:41.300 | like his musical inventions, for instance,

02:03:43.820 | naturally, because his father was a composer,

02:03:46.900 | music composer and a conductor.

02:03:49.780 | So in other words, in the bigger scheme of things,

02:03:53.580 | even if I think he's misguided,

02:03:58.300 | still, I can't deny that it's a certain leap of faith

02:04:03.300 | from his perspective to try to say

02:04:05.460 | that this is the way we can all connect to our loved ones.

02:04:08.660 | And because it is sincere,

02:04:10.260 | and I see it now, it's sincere.

02:04:11.700 | And in fact, in your interview,

02:04:13.020 | you really teased it out of him.

02:04:15.660 | I was really moved by it, I have to say.

02:04:17.420 | It's like, he has mellowed a little bit too, I say.

02:04:20.020 | It was really, really sweet

02:04:23.060 | when he talked about his father.

02:04:24.460 | And I can relate, you know, my father died four years ago,

02:04:27.140 | and I can relate what a heartbreak,

02:04:30.580 | I was much older than Ray was when his father died.

02:04:33.860 | But I can relate to this longing and that grief, you know.

02:04:38.860 | And when somebody is sincere,

02:04:41.300 | and he puts his, opens his cards,

02:04:45.100 | and says, "This is why, this is why I want to do it,

02:04:48.500 | "because I want to recreate my father,

02:04:50.660 | "and I want to be able to talk to him this way."

02:04:53.740 | Then we have a serious, then we understand,

02:04:56.620 | you know, the opposite of it would be not disclosing,

02:05:01.620 | and just pretending that this is how

02:05:07.700 | it's supposed to be in scientific terms.

02:05:10.140 | So, it was replacing your real emotion

02:05:13.460 | that comes from the heart,

02:05:14.820 | by some kind of a theory which comes from the mind.

02:05:17.180 | And this is where we can go astray,

02:05:19.020 | because then we become captives of frameworks

02:05:23.660 | and conceptual systems,

02:05:25.420 | which may not be beneficial to our society.

02:05:28.420 | - In tough times, we need the people

02:05:30.180 | that have not lost their way in the ideologies.

02:05:33.580 | We need the people who are still in touch with their heart.

02:05:35.620 | And you mentioned this with Eric, it's certainly true.

02:05:38.580 | I disagree with him on a lot of stuff,

02:05:40.860 | but I feel like when the world is burning down,

02:05:44.020 | Eric is one of the people that you can still count on

02:05:46.900 | to have a heart.

02:05:48.260 | We've talked a lot over the past year

02:05:49.700 | about the war in Ukraine,

02:05:52.060 | the possibility of nuclear war,

02:05:54.820 | and it feels like he's one of the people I would call first,

02:05:58.220 | if, God forbid, something like a nuclear war would begin.

02:06:05.460 | Because you look for people with a heart,

02:06:07.820 | no matter their ideas.

02:06:09.100 | - That's right.

02:06:10.220 | It takes courage, and it takes a certain self-awareness,

02:06:12.700 | I would say.

02:06:13.540 | I think the crucial is that which was inscribed

02:06:19.180 | on the temple of Apollo in Delphi.

02:06:21.380 | There was a statement, "Know thyself, know yourself."

02:06:23.820 | You know, like, who am I?

02:06:25.420 | Ultimately, it boils down to this, and all these debates.

02:06:28.900 | And the point is that I used to be, like I said,

02:06:32.540 | pessimistic at some point,

02:06:33.660 | and I was scared, even, of where development of AI was going.

02:06:38.180 | This is about 2014, 2015.

02:06:40.460 | And now I'm much more...

02:06:43.260 | So, for instance, after I saw Ray Kurzweil as a human being,

02:06:47.940 | after I could relate to him, and sympathize with him,

02:06:52.380 | suddenly, I stopped seeing him in the news.

02:06:55.620 | Like, before that, I would always see him in the news,

02:06:57.660 | saying, "We're going to put nanobots in your brain,

02:07:00.020 | "da-da-da, by the year 2030," or whatever, you know?

02:07:02.140 | "And then we upload you by 21st,"

02:07:04.300 | and I would be like, "No, you know, that's sort of terrible."

02:07:07.660 | Suddenly, I didn't see him anymore.

02:07:09.940 | I had to, you know?

02:07:11.420 | So now, it makes me question,

02:07:13.500 | who was creating the trouble? (laughs)

02:07:15.940 | - What was all with it?

02:07:16.780 | - Was it him who was creating the trouble,

02:07:18.740 | or was it my mind, you see?

02:07:21.100 | And so, as I became self-aware,

02:07:25.180 | suddenly, other possibilities opened.

02:07:27.980 | And suddenly, that conflict, which, by the way,

02:07:29.820 | if I kept giving these nasty talks about him,

02:07:34.820 | one day, I suppose, we'd have a debate,

02:07:37.260 | and so you have this, one person says this,

02:07:40.380 | and then that, and what I learned

02:07:42.220 | is that it's a never-ending conflict.

02:07:44.780 | This conflict just does not end.

02:07:46.700 | But there is an alternative, there is a better way,

02:07:50.700 | which is to realize that it is you, arguing with yourself.

02:07:55.180 | Now, if you want to continue arguing with yourself,

02:07:57.860 | continue, as long as you need.

02:08:01.860 | Just be careful not to destroy too many things,

02:08:04.100 | you know, in the process.

02:08:05.280 | But there is an option of actually dropping it,

02:08:08.180 | of actually dropping it.

02:08:09.500 | This is so, I was so surprised by this.

02:08:12.300 | - Yeah, it's discovering in yourself

02:08:14.300 | the human capacity for compassion,

02:08:17.540 | and you understand that he has a perspective,

02:08:20.580 | he is operating in the space of imagination,

02:08:22.820 | a human being like you,

02:08:24.300 | and we're all in this kind of together,

02:08:25.740 | trying to figure this out. - But we're on the same boat,

02:08:27.500 | ultimately, and also, it's like,

02:08:29.360 | with realizing how much I have screwed up,

02:08:32.580 | you know, comes this humility also.

02:08:34.860 | So, I find it extremely hard now

02:08:37.180 | to really lash out at somebody,

02:08:39.340 | and to say, like, you're horrible, whatever,

02:08:41.500 | because immediately, the question is,

02:08:43.900 | who am I to criticize, you know?

02:08:46.300 | So, is there another way to have a dialogue?

02:08:48.520 | Is there a way to, you know, speaking,

02:08:50.900 | you know, since we talked about the innocence of a child,

02:08:54.940 | and how much it drives a discovery in science, and so on,

02:08:58.220 | you know, I remember, I think I heard,

02:09:00.500 | Adyashanti, who gave this nice example,

02:09:02.460 | he's like, when you're a kid, you know,

02:09:04.380 | you go and you play with your friends,

02:09:06.220 | and then you fight with another kid,

02:09:07.660 | and he was like, I hate you, I don't wanna see you again,

02:09:10.500 | and you just go home, like, after half an hour,

02:09:12.540 | okay, what are you gonna do?

02:09:13.600 | You wanna play?

02:09:14.780 | So, you come out, it's like, hey, you wanna play?

02:09:17.940 | You don't talk about what happened,

02:09:19.700 | you don't rehash this, you know, just keep going.

02:09:23.340 | And sometimes, I think we are on the verge,

02:09:26.180 | maybe, of learning that,

02:09:28.340 | because I think that if we continue to push each of us,

02:09:34.180 | our set of ideas, and ideologies,

02:09:38.300 | and, you know, what matters to us, and so on,

02:09:42.340 | like, yeah, no, no, what matters to you,

02:09:44.240 | but like, there are other ways to approach other people,

02:09:47.520 | there are other ways, you can find point of contact.

02:09:50.120 | Speaking of which, mathematics, mathematical formulas,

02:09:54.980 | are universal, represent universal knowledge.

02:09:58.460 | Two plus two is four, whether you vote for this guy

02:10:01.520 | or that guy in the election, you know,

02:10:03.520 | how about that as a point of contact, of commonality,

02:10:08.140 | you know, and nobody can patent those formulas,

02:10:10.360 | did you know that?

02:10:11.520 | And there is a Supreme Court decision

02:10:13.600 | that mathematical formulas cannot be patented,

02:10:15.600 | like Einstein could not patent E equals MC squared,

02:10:19.200 | it doesn't belong to him,

02:10:20.160 | because if the formula is correct,

02:10:22.840 | then it belongs to everyone.

02:10:24.240 | - So what do you think of that all too tricky question?

02:10:29.800 | If you want, I can deeply bias your answer

02:10:32.560 | by giving the list of four that Eric provided.

02:10:35.120 | - Oh, no, let me give mine,

02:10:36.360 | I cannot see, by the way, what you have, so,

02:10:38.760 | but I can guess some of them.

02:10:40.560 | So I'm going to try to do something different from him.

02:10:43.160 | So I already mentioned one,

02:10:44.920 | which is that you have one-dimensional numerical system,

02:10:49.880 | which is real numbers, you have two-dimensional,

02:10:51.840 | which is complex numbers, you have four-dimensional,

02:10:54.240 | and it's probably connected to what he wrote,

02:10:56.440 | because it has to do with some homotopic groups of spheres

02:10:59.200 | and stuff like that.

02:11:00.200 | Then, of course, one I love, okay,

02:11:04.640 | one plus two plus three plus four,

02:11:06.720 | plus five plus six, and so on.

02:11:10.660 | Does it make any sense, the sum?

02:11:14.020 | You probably heard about this one,

02:11:15.580 | it became very popular at some point.

02:11:18.020 | One plus two plus three, I did a video for Numberphile,

02:11:21.180 | the YouTube channel about it, maybe 10 years ago.

02:11:23.660 | So one plus two plus three plus four plus five

02:11:25.900 | ostensibly diverges, goes to infinity,

02:11:30.700 | because you get a bigger and bigger number.

02:11:32.500 | And yet, there is a way to make sense of it,

02:11:35.700 | in which it comes up to minus one over 12.

02:11:39.500 | How fascinating.

02:11:41.420 | First of all, the answer is not even a positive number,

02:11:43.820 | and it's not an integer, it's not a whole number,

02:11:45.740 | it's minus one over 12.

02:11:47.180 | So sometimes people ask me, what is your favorite number?

02:11:49.940 | And it's kind of a joke, I say minus one over 12.

02:11:52.500 | (laughing)

02:11:53.660 | It's actually 42.

02:11:54.780 | (laughing)

02:11:56.980 | - So your favorite number is not an ordered set.

02:11:59.380 | - Right. - So what else?

02:12:01.940 | - What else?

02:12:02.780 | - So-- - Langlands program,

02:12:04.040 | of course, I have to mention that.

02:12:05.680 | - And we'll explore that in depth.

02:12:07.260 | Do you know what Eric said?

02:12:09.420 | - Sure.

02:12:10.420 | - Sphere aversion, Boy's surface, hop vibration--

02:12:15.420 | - Co-vibration, okay.

02:12:16.940 | - And pi one of SO three.

02:12:21.100 | - Okay, oh yes, so that's the famous cup trick, you know?

02:12:25.180 | Okay, look, so this is how it works.

02:12:26.900 | (laughing)

02:12:28.460 | - No tricks. - No tricks.

02:12:29.660 | - No magic. - So honest.

02:12:31.060 | It is magical, okay?

02:12:32.260 | But not because I'm tricking you.

02:12:35.420 | So you start with a bottle like this, or a cup,

02:12:39.020 | and you start twisting it,

02:12:41.060 | and at the same time you twist your arm.

02:12:44.140 | Then you come, so this is actually going to

02:12:46.780 | rotate it 360 degrees, the full turn.

02:12:50.500 | Then you say, okay, I won't be able to do another turn

02:12:53.780 | because then my arm would really get twisted,

02:12:55.660 | I'll have to go see a doctor.

02:12:57.140 | Yet, if I do it a second time, it untwists.

02:13:00.260 | This is the pi one of SO three.

02:13:04.740 | Eric is talking about it.

02:13:06.260 | So there is something where the first motion is not trivial,

02:13:10.180 | but if you double down on it,

02:13:12.380 | you come back to the initial position.

02:13:15.020 | It's very closely connected to the fact that

02:13:16.900 | we have elementary particles of two types,

02:13:18.860 | bosons and fermions.

02:13:20.020 | So bosons are, for example, photons,

02:13:23.900 | or carriers of other forces, or the Higgs boson.

02:13:26.660 | It is called a boson for a reason, because it is a boson.

02:13:30.780 | In honor of Indian mathematician Bose, B-O-S-E, and Einstein.

02:13:35.780 | So these particles obey what's called

02:13:38.180 | Bose-Einstein statistics.

02:13:40.280 | But then there are other particles called fermions,

02:13:42.820 | in honor of Enrico Fermi, Italian-born mathematician

02:13:47.900 | who worked in the US.

02:13:49.440 | And they follow what's called Dirac-Fermi statistics.

02:13:54.540 | And those are electrons and constituents of matter,

02:13:57.780 | electrons, protons, neutrons, and so on.

02:14:00.380 | And they have a certain duplicity, if you will.

02:14:04.380 | And that duplicity is rooted mathematically

02:14:06.620 | in this experiment, this little experiment

02:14:08.980 | that I have just done.

02:14:10.080 | So I can, I imagine, speaking of imagination, okay?

02:14:14.260 | So I'm just kind of riffing on this.

02:14:16.180 | Imagine a world in which this will not be shocking,

02:14:19.920 | or like, in this case it's not even shocking

02:14:21.940 | because I haven't really explained the details,

02:14:24.340 | because I can't do it in two minutes.

02:14:26.400 | I indicated what this is all about, and so on.

02:14:31.280 | But imagine a world in which this is not foreign

02:14:34.440 | to most people, that most people have seen it before.

02:14:36.840 | They're not afraid to approach this type of questions,

02:14:40.160 | because, you know, we talked a little bit

02:14:43.160 | about math education, but I really believe

02:14:45.000 | that a lot of people in our society,

02:14:47.000 | and it is not only in the United States,

02:14:49.720 | but throughout the world, a lot of people

02:14:51.920 | have been traumatized.

02:14:53.780 | It's really PTSD.

02:14:55.620 | That's why people, when they see a mathematical formula,

02:14:57.800 | or even like, how do you need to calculate tip on a bill?

02:15:01.880 | They're just, they're terrified,

02:15:03.440 | because it brings up those memories

02:15:05.560 | when they were kids and being called to blackboard

02:15:09.680 | and solve a problem, you can't solve a problem,

02:15:14.360 | and unscrupulous teacher says, "You're an idiot.

02:15:16.400 | "Sit down," and you feel ashamed and lowly,

02:15:20.960 | and that stays with you.

02:15:22.620 | And so I think that, unfortunately, that's where we are.

02:15:25.380 | But I, one can dream, and so my dream is that one day

02:15:29.360 | we'll be able to overcome this,

02:15:31.440 | and actually, all of these treasures of mathematics

02:15:34.560 | will become widely available,

02:15:37.960 | or at least people will know where to find them,

02:15:40.320 | and they will not be afraid of going there and looking.

02:15:43.080 | And I think this will help, because like I said,

02:15:44.800 | for one thing, it gives you a sense of belonging.

02:15:48.000 | It gives you, it kind of is an antidote

02:15:51.120 | to the kind of alienation and separation

02:15:53.560 | that we feel today, oftentimes,

02:15:55.360 | because of ideological divide, sectarian strife,

02:15:58.800 | and all kinds of things like that.

02:16:00.020 | Because then you will, once you see,

02:16:01.920 | there's like a critical mass of this beauty

02:16:04.440 | that kind of dawns on you, it's like,

02:16:07.080 | my God, this is what we all have in common.

02:16:09.340 | - You mentioned Langlands program.

02:16:14.960 | We have to talk about it.

02:16:16.080 | - Sure.

02:16:16.920 | - At the core of your book and your work

02:16:18.480 | is the Langlands program.

02:16:19.800 | Can you describe what it is?

02:16:23.080 | - Sure, so Langlands is a mathematician.

02:16:28.080 | It's a name of a mathematician, Robert Langlands.

02:16:30.960 | Canadian born, still alive.

02:16:35.080 | He was a professor at the Institute for Advanced Study

02:16:37.840 | that we talked about, where Einstein and Gödel

02:16:40.840 | and other great scientists have worked.

02:16:43.240 | In fact, he used to occupy the office of Albert Einstein

02:16:47.400 | at the Institute for Advanced Study.

02:16:50.040 | So he, in the late '60s,

02:16:55.040 | he came up with a set of ideas

02:16:58.440 | which captivated a lot of mathematicians,

02:17:01.240 | several generations of mathematicians by now,

02:17:04.200 | which came to be known as the Langlands program.

02:17:06.600 | And what it is about is connecting

02:17:09.800 | different fields of mathematics,

02:17:11.560 | which seem to be far away from each other.

02:17:13.760 | For example, number theory,

02:17:16.000 | which as the name suggests, deals with numbers,

02:17:19.640 | and various equations with, you know,

02:17:23.600 | like x squared plus y squared equals one.

02:17:25.640 | And on the other side, harmonic analysis,

02:17:31.680 | something that any music lover can appreciate

02:17:37.000 | because the sound of a symphony can be kind of decomposed

02:17:40.860 | into sounds of different instruments,

02:17:42.440 | and each of those sounds can be represented

02:17:44.120 | by a wave like this, like a sine function.

02:17:47.640 | Those are the harmonics.

02:17:49.040 | They oscillate, the period of a harmonic,

02:17:51.520 | periods of different notes are different,

02:17:54.240 | they correspond to different notes,

02:17:55.520 | and different instruments, different semitones, if you will.

02:17:58.800 | But they all combine together into something,

02:18:01.280 | something special, which is not,

02:18:04.340 | cannot be reduced to any one of those.

02:18:07.200 | So it's that, mathematically, it's the idea

02:18:08.980 | that you can decompose a signal into,

02:18:13.120 | as a collection, as a simultaneous oscillation

02:18:16.240 | of several elementary signals.

02:18:18.400 | That's called harmonic analysis.

02:18:21.040 | So what Langlands found is that some really difficult

02:18:24.380 | questions in number theory can be translated

02:18:27.780 | into much more easily tractable questions

02:18:31.740 | in harmonic analysis.

02:18:32.720 | That was his initial idea.

02:18:35.020 | But what happened next surprised everybody,

02:18:38.680 | that the kind of patterns that he was able to observe,

02:18:41.000 | the kind of regularities that he was able to observe,

02:18:42.960 | which were quite surprising,

02:18:44.760 | were subsequently found in other areas of mathematics.

02:18:47.740 | For example, in geometry.

02:18:50.480 | And eventually in quantum physics.

02:18:53.000 | So in fact, Ed Witten, who is kind of a dean

02:18:57.560 | of modern theoretical physicists,

02:18:59.600 | professor at the Institute for Advanced Study as well,

02:19:02.480 | got interested in this subject.

02:19:03.880 | I describe in my book how it happened.

02:19:06.000 | And he was instrumental in bridging the gap

02:19:11.880 | between these patterns found in physics and in geometry,

02:19:16.120 | finding kind of a superstratum, if you will,

02:19:21.120 | or a way to connect these two things,

02:19:24.600 | kind of a bridge between these two fields.

02:19:26.600 | So subsequently I collaborate with Witten on this,

02:19:30.240 | and this has been one of the major themes of my research.

02:19:33.160 | I always found it interesting to connect things,

02:19:40.000 | to unite things.

02:19:42.120 | When I was younger, I couldn't understand why,

02:19:47.000 | but I was always interested in,

02:19:48.660 | not in working in specific field,

02:19:53.540 | but kind of cutting across fields.

02:19:55.800 | And then I would discover that, for instance,

02:20:01.920 | I talked to some people who know what happens in this field,

02:20:04.440 | but don't know what happens in that field, or conversely.

02:20:09.000 | And then I would find it imperative

02:20:13.360 | to go out and explain to them,

02:20:16.480 | to the different sides what this is all about,

02:20:19.540 | so that more people are aware of these hidden structures,

02:20:22.640 | of these hidden parallels, if you will.

02:20:25.860 | So that has been sort of a theme in my research.

02:20:28.800 | And so I guess now I kind of understand more why

02:20:32.680 | it's kind of a balance, like what we talked about earlier.

02:20:37.120 | - So can you elucidate a little bit how,

02:20:40.840 | what are the mathematical tools that allow you

02:20:43.080 | to connect these different continents of mathematics?

02:20:47.840 | Is there something you can convert into words

02:20:51.640 | that Langlands was able to find,

02:20:53.800 | and you were able to explore further?

02:20:55.640 | - I would say what it suggests is that there is some

02:20:59.240 | hidden principles, which we still don't understand.

02:21:02.800 | My view is that we still don't know why.

02:21:06.200 | That we can prove some instances of this,

02:21:09.440 | correspondences and connections,

02:21:12.900 | but we still don't know the real underlying reasons,

02:21:16.880 | which means that there is a certain layer

02:21:19.320 | beneath the surface that we see now.

02:21:22.800 | It is like, so the way I see it now is like this,

02:21:27.140 | that there is something three-dimensional, like this bottle,

02:21:30.580 | but what we are seeing is this projection onto the table,

02:21:33.240 | and the projection onto a wall.

02:21:34.640 | And then we can map things from one projection to another,

02:21:37.400 | and you say, oh my God, that's incredible.

02:21:39.880 | But the real explanation is that both of them

02:21:42.120 | are projections of the same thing,

02:21:43.840 | and that we haven't found yet.

02:21:45.520 | But that's what I want to find,

02:21:46.560 | so that's what motivates me, I would say.

02:21:48.900 | - From number theory to geometry to quantum physics.

02:21:53.440 | - So there is this one thing,

02:21:55.000 | which has different projections,

02:21:56.640 | except it's not just the table and the wall,

02:21:58.960 | but there are like many different walls, if you will.

02:22:02.720 | - So what is the philosophical implication

02:22:05.480 | that there is commonalities like that

02:22:08.280 | across these very disparate fields?

02:22:11.080 | - It means that what we believe

02:22:13.020 | are the fundamental elements of mathematics

02:22:17.160 | are not fundamental, there is something beyond.

02:22:19.560 | It's like we previously thought that atoms were indivisible.

02:22:24.480 | Then we found out that there is a nucleus and electrons,

02:22:27.360 | and the nucleus consists of protons and neutrons.

02:22:29.680 | Then we thought, okay,

02:22:30.640 | protons and neutrons must be elementary.

02:22:33.200 | Now we know they consist of quarks.

02:22:35.840 | So it's about kind of finding the quarks of mathematics.

02:22:39.060 | (Lex laughing)

02:22:40.440 | - Of course, beyond that, there's maybe even more.

02:22:42.680 | - Which was my initial motivation

02:22:44.180 | to study mathematics, by the way, right?

02:22:46.280 | - Quarks was the first time you fell in love

02:22:49.180 | with understanding the nature of reality.

02:22:50.800 | - Yeah.

02:22:52.120 | - What was it like working with Ed Witten,

02:22:54.080 | who many people say is one of the smartest humans in history?

02:22:59.920 | Or at least mathematical physicist in history?

02:23:04.920 | - Yes, fascinating.

02:23:07.320 | I enjoyed it very much.

02:23:08.600 | I also felt that I have to keep up, you know?

02:23:11.640 | And so we wrote this long paper in 2007,

02:23:16.280 | and we collaborated for about a year.

02:23:19.180 | I have known him before, and we talked before,

02:23:22.160 | and I've seen him since, and we talked.

02:23:24.640 | But it's very different to just meet somebody

02:23:27.200 | at conferences and have a conversation,

02:23:29.200 | as opposed to actually working on a project together.

02:23:33.520 | So he's very, very serious, very focused.

02:23:38.280 | This is one thing which I have to say,

02:23:40.480 | I was really struck by this.

02:23:42.640 | - Why is he considered to be such a powerful intellect

02:23:47.120 | by many other powerful intellects?

02:23:49.820 | - He has had this unique vision of the subject.

02:23:56.240 | He was able to connect different things,

02:23:59.280 | especially find connections

02:24:03.400 | between quantum physics and mathematics.

02:24:05.780 | Almost unparalleled.

02:24:08.160 | I don't think anyone comes close, in some sense,

02:24:11.000 | in the last 50 years to him,

02:24:14.800 | in terms of finding just consistently, time after time,

02:24:18.880 | breaking ground, new ground, new ground.

02:24:20.360 | So he would basically, one way one could describe it is,

02:24:26.200 | he would take some idea in physics,

02:24:28.760 | and then find an interpretation of it in mathematics,

02:24:35.120 | and then say, distill it, present it in mathematical terms,

02:24:40.280 | and tell mathematicians, this should be like that.

02:24:43.560 | Kind of like, one plus two plus three plus four

02:24:45.820 | is minus one over 12.

02:24:47.680 | And mathematicians would be like, no way.

02:24:50.040 | And then it would pan out,

02:24:54.320 | and mathematicians would then,

02:24:56.200 | like a whole industry would be created

02:24:58.480 | of groups of mathematicians trying to prove

02:25:01.400 | his conjectures and his ideas,

02:25:03.760 | and he would always be proven right.

02:25:06.640 | So in other words, being able to glean

02:25:09.440 | some mathematical truths from physical theories.

02:25:13.440 | That's one side.

02:25:14.640 | On the other hand, conversely,

02:25:16.800 | applying sophisticated mathematics.

02:25:18.920 | He's probably the physicist who could learn

02:25:24.120 | mathematics the fastest, I don't think.

02:25:26.580 | Some younger physicists maybe could come close,

02:25:30.760 | but it's still quite, for them a long way to go

02:25:33.640 | to get, to be comparable to Witten.

02:25:37.840 | To take some of the most sophisticated mathematics,

02:25:40.840 | and not learn it to the point where

02:25:44.640 | he becomes a practitioner of the subject practically.

02:25:47.240 | And then use it to gain some new insights

02:25:52.000 | on the physics side.

02:25:53.720 | Now, of course the thing is that,

02:25:56.120 | the theories that physics, one could say,

02:25:58.760 | is in a sort of a crisis in some sense,

02:26:00.580 | because of a current gap between the sophisticated theories

02:26:05.580 | which came from applying sophisticated mathematics,

02:26:11.020 | and the actual universe.

02:26:13.300 | So we have theories, for instance,

02:26:14.800 | which describe 10 dimensional worlds,

02:26:17.360 | 10 dimensional space time,

02:26:19.360 | coming from string theory, and things like that.

02:26:22.600 | But we don't know yet how to apply it

02:26:25.640 | to understanding our universe.

02:26:27.920 | A lot of progress has been made,

02:26:30.440 | but it's kind of at a kind of an impasse right now.

02:26:34.600 | And at the same time, our most realistic theories,

02:26:38.680 | most advanced theories of the four dimensional universe

02:26:41.480 | are in contradiction with each other.

02:26:44.840 | The standard model describing the three known forces

02:26:48.640 | of nature, electromagnetic, strong and weak,

02:26:52.480 | with great accuracy.

02:26:54.120 | And Einstein's relativity,

02:26:55.240 | which describes the force called gravity.

02:26:58.200 | (laughing)

02:27:00.000 | Everybody above a certain age knows that one.

02:27:03.400 | (laughing)

02:27:05.640 | So these two theories are in contradiction at the moment.

02:27:09.480 | And string theory was one of the,

02:27:11.520 | the promise of string theory was that

02:27:13.000 | it would unify those two.

02:27:14.840 | And so far it has not happened.

02:27:17.660 | So we are kind of at a very interesting place right now.

02:27:20.600 | And I think that new ideas perhaps are needed.

02:27:24.720 | And I wouldn't be surprised if Witten

02:27:27.120 | is one of those people who come up with those ideas.

02:27:29.840 | - Well he has been one of the people

02:27:33.400 | that added a lot of ideas under the flag of string theory.

02:27:36.520 | What do you think about this theory?

02:27:40.040 | What do you think is beautiful about it, string theory?

02:27:42.840 | - Well first of all, kind of,

02:27:46.060 | you remember we talked about Pythagoreans.

02:27:49.400 | And how for Pythagoreans,

02:27:52.480 | the whole world was this symphony

02:27:54.560 | where you have these different vibrations of all the humans.

02:27:57.880 | Every human is a vibration, every animal,

02:28:00.840 | you know, every being, every tree,

02:28:02.880 | and every celestial body and so on.

02:28:05.400 | So string theory is kind of like that

02:28:06.920 | because in string theory there is this fundamental object

02:28:09.400 | which is a vibrating string.

02:28:10.800 | And all particles are in a sense supposed to be

02:28:15.400 | different modulations or vibrations of that string.

02:28:18.800 | So that by itself is already interesting.

02:28:20.800 | That you kind of describe this diversity

02:28:25.320 | of various particles and interactions between them

02:28:27.880 | using one guiding principle in some sense.

02:28:30.640 | But also just the mathematical things that come out of it.

02:28:34.380 | It looks impossible to satisfy various constraints

02:28:39.280 | and then there is sort of like a unique way to do it.

02:28:42.320 | So that's sort of the,

02:28:44.760 | every time that happens when you have some system

02:28:47.840 | over, like over determined system.

02:28:50.040 | Let's suppose you have to do like five interviews

02:28:53.960 | in one day and you wake up in the morning

02:28:57.040 | and you're like, that's impossible.

02:29:00.000 | Because then so many things have to align.

02:29:02.240 | For instance, let's suppose you have to go

02:29:03.520 | from one place to another, so then you have a commute

02:29:05.940 | and then who knows, maybe there is a traffic jam

02:29:08.160 | and stuff like that.

02:29:09.400 | And now suppose that it all works seamlessly

02:29:12.680 | and there were like a bunch of places

02:29:14.320 | where it could have gone hopelessly wrong and it didn't.

02:29:18.560 | And then in the evening you're like, wow, it worked.

02:29:22.120 | That's beautiful, right?

02:29:23.680 | That's kind of like great luck, you know, we would say.

02:29:27.600 | But in science this happens sometimes.

02:29:30.880 | That you have this theory which is not supposed to work

02:29:33.400 | because there's so many seemingly contradictory demands

02:29:36.640 | on it and yet there is a sweet spot

02:29:39.520 | where they balance each other.

02:29:41.200 | So string theory is kind of like this.

02:29:43.720 | The unfortunate aspect of it is that it balances itself

02:29:47.160 | in 10 dimensions and not in four.

02:29:49.000 | So maybe there is another universe somewhere.

02:29:52.240 | But see, as a mathematician, for me,

02:29:58.080 | all spaces are created equal.

02:29:59.760 | 10 dimensional, four dimensional.

02:30:02.340 | So mathematicians love string theory

02:30:04.120 | because it has given us so much food for thought.

02:30:07.440 | - But do you think it's a correct or a wrong way

02:30:13.560 | or a incorrect theory for understanding this reality?

02:30:17.960 | So it might be a theory that explains

02:30:20.440 | some 10th dimensional reality in some other universe,

02:30:23.120 | but is it potentially, what do you think are the odds?

02:30:26.200 | Again, financial advice, you are to bet.

02:30:29.000 | What do you think are the odds that it gets us closer

02:30:33.480 | to understanding this reality?

02:30:35.800 | - Well, in the form that it is now, that seems unlikely.

02:30:39.760 | But it could well be that based on these ideas

02:30:42.200 | with some modifications, with some essential new elements,

02:30:46.000 | it could work out.

02:30:47.720 | So I would say right now it doesn't look so good

02:30:50.520 | from the point of view of what we know.

02:30:53.940 | But maybe somebody will come and introduce

02:30:57.280 | square root of negative number.

02:30:59.480 | I mean, they already introduced,

02:31:00.560 | but I mean kind of like as a metaphor.

02:31:02.780 | Maybe somebody will come and say, what if we do this?

02:31:06.600 | It looks crazy.

02:31:07.520 | Speaking of Niels Bohr, he had this famous quote

02:31:11.600 | that he said to somebody,

02:31:12.940 | "There is no doubt that your theory is crazy.

02:31:16.680 | "The question is whether it's crazy enough

02:31:19.960 | "to describe reality."

02:31:21.640 | So that's where we are kind of.

02:31:23.560 | - Speaking of crazy and crazy enough,

02:31:26.360 | let me ask for therapy, for advice, for wisdom

02:31:31.360 | in returning to Eric Weinstein

02:31:36.880 | and maybe give some guidance to understanding

02:31:41.140 | his view on his attempt at a theory of everything

02:31:45.360 | that he calls geometric unity,

02:31:47.160 | that he told me that you may have

02:31:49.160 | some inkling of an understanding of.

02:31:52.200 | If you were to describe this theory

02:31:54.700 | to aliens that visited Earth,

02:31:56.380 | how would you do it?

02:32:00.460 | Or you could try if it was just me visiting Earth,

02:32:04.280 | how would you describe it, your best understanding of it?

02:32:08.320 | - He shared with me some of it

02:32:10.880 | when I was in New York at Columbia, like 11 years ago.

02:32:13.860 | We actually spent a lot of time where he explained to me,

02:32:16.320 | and I found it beautiful.

02:32:17.580 | He has a very original idea at the core of it,

02:32:23.480 | where you have this, instead of four-dimensional,

02:32:25.380 | instead of 10-dimensional, he has 14-dimensional space.

02:32:29.080 | And I thought it was really original.

02:32:32.200 | And this exactly goes to the point I made earlier

02:32:35.680 | that we need new ideas.

02:32:37.980 | I feel that without some fundamentally new idea,

02:32:40.880 | we won't be able to get closer

02:32:43.460 | to understanding our universe.

02:32:45.960 | Now, I have a problem with the whole idea

02:32:47.940 | of theory of everything.

02:32:49.140 | I don't believe that one exists,

02:32:51.980 | nor that we should aim to construct one.

02:32:56.980 | And I think it's really, not to offend anybody,

02:33:02.240 | but it's ultimately a fault

02:33:04.980 | of education system of physicists.

02:33:07.480 | Like in mathematics, we're not brought up,

02:33:10.800 | we're not educated as mathematicians

02:33:12.420 | with the idea that one day we will come up

02:33:15.580 | with the theory of everything.

02:33:16.940 | Even though, as a joke, I said that Langlands program

02:33:20.140 | is mathematical theory of everything.

02:33:22.200 | But I meant it as kind of a tongue-in-cheek.

02:33:25.460 | - But isn't it a little bit kind of that?

02:33:28.260 | - It's not really, because first of all,

02:33:29.820 | it doesn't cover all fields of mathematics,

02:33:32.060 | and it covers specific phenomena.

02:33:33.980 | - But isn't it spiritually striving

02:33:37.180 | towards the same platonic form of the theory of everything?

02:33:41.340 | Like connecting, connecting fields.

02:33:43.100 | - But connecting doesn't mean that it covers everything.

02:33:45.540 | So you could connect two things,

02:33:47.340 | and then you have infinitely many other things

02:33:49.700 | which are outside of the purview of this connection.

02:33:53.180 | That's how it is in mathematics, I feel.

02:33:56.520 | And I would venture to say that

02:33:59.980 | most mathematicians look at it this way.

02:34:01.780 | There's no idea that somehow,

02:34:03.100 | I think it's actually impossible,

02:34:04.380 | because we're not talking about such a thing

02:34:06.380 | as like one universe.

02:34:07.700 | We're talking about all possible universes

02:34:09.300 | of all possible dimensions and so on.

02:34:10.620 | It is just not feasible to have a unified,

02:34:13.780 | unify everything in one equation.

02:34:15.880 | Now, physicists, on the other hand,

02:34:19.380 | have been brought up, educated for decades with this idea.

02:34:23.060 | And to me, and I am not sure I should say that,

02:34:26.180 | but I feel like it's kind of an ultimate ego trip.

02:34:29.540 | So that I have come up with the unified,

02:34:32.260 | I have found the theory of everything, it's me,

02:34:34.620 | and my name will be on it.

02:34:36.540 | I think a lot of physicists get educated this way,

02:34:40.580 | especially men take it seriously.

02:34:43.020 | And I've seen that happen,

02:34:44.260 | and I think it is counterproductive.

02:34:46.160 | I think that a lot of people agree

02:34:48.100 | that this debate is kind of,

02:34:49.900 | I feel like it's kind of settled.

02:34:51.260 | I think I hear it less and less.

02:34:53.780 | But I disagree with the whole premise.

02:34:57.260 | - So you, it's interesting,

02:35:00.100 | 'cause both are interesting points you made,

02:35:02.500 | which is you don't think a theory of everything

02:35:04.540 | exists, and you don't think the pursuit

02:35:08.380 | of a theory of everything is good.

02:35:09.580 | So I think you spoke to the second thing,

02:35:12.060 | which is basically that the pursuit

02:35:15.620 | of a theory of everything becomes

02:35:17.500 | like a drug to the human ego.

02:35:19.300 | - That's right, so it's a huge motivating factor.

02:35:21.740 | I don't deny that.

02:35:23.260 | But I feel that there are better ways

02:35:26.340 | to motivate people than like that, than this way, okay?

02:35:30.980 | So I would say, for instance,

02:35:33.980 | if one, because then it's not a game

02:35:36.700 | of winner takes all in some sense.

02:35:39.420 | And in fairness, when physicists say

02:35:41.860 | theory of everything, the grand unified theory,

02:35:44.620 | they mean something very specific,

02:35:46.060 | which is unifying the standard model

02:35:47.580 | and Einstein's relativity theory,

02:35:49.620 | which is a theory of gravity.

02:35:51.420 | So they don't necessarily, a lot of physicists

02:35:54.060 | may say these words, but they don't really mean them.

02:35:56.700 | I think it's important to realize that,

02:35:59.420 | that in my opinion, that's not productive,

02:36:01.820 | and it's not feasible anyway.

02:36:03.580 | So having said that, there are some theories

02:36:05.780 | are better than others, obviously.

02:36:06.940 | So for instance, Eric's theory has,

02:36:09.140 | as far as I understand, does have a certain way

02:36:12.260 | of producing some of the elementary particles

02:36:15.300 | that we see, and as well as the force of gravity.

02:36:18.420 | So it does have that promise.

02:36:20.700 | I feel that, at least from the place

02:36:23.460 | where I had seen it about 10 years ago,

02:36:26.900 | it still required a lot of work

02:36:28.220 | to get to the point of actually saying

02:36:30.340 | that it does work, because, you know,

02:36:34.220 | there are a lot of elements.

02:36:35.780 | It's a huge enterprise to have a theory,

02:36:37.860 | because you have, just to describe the fields,

02:36:41.340 | sort of the building blocks of the theory,

02:36:43.980 | it's already a tremendous undertaking,

02:36:45.660 | and he's trying to do it for curved spaces

02:36:48.020 | in greater generality, which is what makes it

02:36:50.340 | so unique and so beautiful.

02:36:52.300 | But then, on top of that, there are all these issues

02:36:54.540 | of quantization, of actually describing them

02:36:56.820 | as quantum field theory.

02:36:58.740 | And the quantum field theory, even as a language,

02:37:02.060 | as a framework, is currently incomplete, in my opinion.

02:37:06.100 | And not only my opinion, it's like everybody's,

02:37:08.500 | it's, everybody agrees on that,

02:37:10.220 | that it's a, it's a, it's a collection of tricks,

02:37:15.220 | so to speak, it's a collection of tools.

02:37:16.940 | It's a toolbox, but it is not a consistent,

02:37:21.940 | rigorous theory, like number theory in mathematics.

02:37:26.420 | Physicists have still been able to derive predictions

02:37:30.540 | from it, and confirm them to great accuracy,

02:37:37.020 | but the underpinnings, it doesn't have

02:37:41.100 | the real rigorous foundation from mathematical perspective.

02:37:44.420 | So in that sense, even if, in that framework,

02:37:48.860 | a new theory could lead to an explanation of some,

02:37:55.380 | some new explanation of some phenomena,

02:37:57.300 | it would still be incomplete, in a sense,

02:37:58.980 | because it wouldn't be mathematically rigorous,

02:38:00.540 | you see what I mean?

02:38:01.900 | Because the whole framework is not yet

02:38:04.220 | on a firm foundation.

02:38:06.540 | - So it's not consistent.

02:38:07.980 | Why is it that the universe should have,

02:38:11.580 | so that's to your first point,

02:38:13.220 | do you think the universe has a beautiful, clean,

02:38:16.380 | when you show up and meet God,

02:38:19.180 | and there's one equation on the board,

02:38:21.900 | and the two of you just chuckle,

02:38:23.900 | do you think such equation exists?

02:38:25.700 | - Yeah, there are such equations, for instance,

02:38:29.980 | let's say I am interested in a particular question, right?

02:38:34.100 | So in the Langlands program,

02:38:36.660 | so moving away from physics, so let's talk about math.

02:38:39.780 | So in the context of Langlands program,

02:38:43.140 | I have recently developed with my co-authors,

02:38:46.980 | Ettingoff and Kasdan, a kind of a new strength,

02:38:49.420 | a new flavor of the Langlands program, if you will.

02:38:53.140 | But so far, it's a vision, it's a set of conjectures,

02:38:57.660 | which we have proved in some cases,

02:38:59.180 | but not in full generality.

02:39:01.340 | So yes, I would like to use your framework,

02:39:05.700 | meet the creator, and ask her,

02:39:08.940 | (laughs)

02:39:11.020 | what is the explanation of this?

02:39:13.180 | And it may well be that she will answer

02:39:14.900 | in a way that I will just burst out laughing,

02:39:16.940 | it's like, how could we not see it, you see?

02:39:19.380 | So that I totally see.

02:39:21.300 | But I don't see one equation governing,

02:39:24.800 | one equation governing them all.

02:39:26.980 | - Not one equation to govern them all,

02:39:29.780 | but it does seem that such equations exist,

02:39:32.920 | where she will tell you something,

02:39:34.400 | and you look back and say, how could I not see it?

02:39:37.140 | It seems like the truth at the end of the day is simple,

02:39:40.580 | that we're seeking, especially through mathematics.

02:39:45.320 | It seems somehow simple.

02:39:47.220 | The nature of reality, the thing that governs it

02:39:50.020 | seems to be simple.

02:39:51.340 | I wonder why that is.

02:39:52.460 | And I also wonder if it's not totally incorrect,

02:39:56.300 | and we're just craving the simplicity.

02:39:58.860 | And then, mixing into the whole conversation

02:40:03.660 | about how much the observer that craves simplicity

02:40:07.500 | is part of the answer.

02:40:09.620 | It's a whole big, giant mess.

02:40:13.020 | - Or a whole big, beautiful painting, or symphony.

02:40:19.000 | You said of Eric Weinstein that,

02:40:21.400 | "I find it remarkable that Eric was able to come up

02:40:24.320 | "with such beautiful and original ideas,

02:40:26.580 | "even though he has been out of academia for so long,

02:40:29.460 | "doing wonderful things in other areas,

02:40:31.120 | "such as economics and finance."

02:40:33.540 | I'd like to use that kind of quote

02:40:35.580 | as just a question to you about different places

02:40:38.020 | where people of your level can operate,

02:40:42.220 | so inside academia and outside.

02:40:45.460 | What is the difference of doing mathematics

02:40:49.600 | inside academia and outside?

02:40:51.240 | Not even mathematics,

02:40:54.320 | but developing beautiful, original ideas.

02:40:56.400 | Where's the place that your imagination can flourish most?

02:41:03.000 | So the limitations of academia is,

02:41:06.720 | there's a community of people that take a set of axioms

02:41:11.120 | as gospel, so it's harder to take that leap

02:41:14.360 | into the unknown, but it's also,

02:41:16.980 | the nice thing about academia

02:41:18.420 | is some of the most brilliant people in the world are there.

02:41:21.860 | It's that community, both the competition

02:41:24.380 | and the collaboration is there.

02:41:25.940 | I wonder if there's something you could say

02:41:29.380 | sort of to further about this world

02:41:33.060 | that people might not be familiar with.

02:41:35.700 | - But I think you gave a very good description.

02:41:38.020 | I'm not sure I can improve on it,

02:41:40.020 | because I don't have an overarching theory of--

02:41:42.500 | - Academia. - Academia.

02:41:44.100 | I definitely have been part of it,

02:41:46.240 | and I'm grateful, because it gives you

02:41:49.480 | a great sense of security,

02:41:51.020 | which comes with its own downside, too,

02:41:55.440 | because you kind of get a little disconnected

02:41:57.400 | from the real world, because you get tenure,

02:41:59.900 | so you feel financially secure.

02:42:01.960 | You know, they don't pay you that much, so to speak,

02:42:03.960 | you know, relatively speaking,

02:42:05.080 | and it's comfortable, but it's not that much,

02:42:08.680 | but you can't be fired, so there is something about this

02:42:13.200 | which I definitely have benefit from it, you know,

02:42:16.800 | and it does, people are not even aware

02:42:20.480 | what it's like to live outside of,

02:42:23.080 | where you don't have this type of security.

02:42:26.320 | On the other hand, that also means

02:42:29.400 | that we're lacking certain skills

02:42:31.240 | that sort of real people in the real world

02:42:33.520 | have developed out of necessity

02:42:37.080 | to deal with that sort of insecurity.

02:42:39.800 | So it kind of always cuts both ways.

02:42:41.720 | You know, on the one hand, it gives,

02:42:43.120 | and on the other hand, it takes away,

02:42:45.160 | and it's a very interesting setup,

02:42:47.120 | and also, on the one hand,

02:42:48.720 | we are all supposed to be the truth seekers,

02:42:51.840 | but in reality, of course, it is a human activity,

02:42:55.440 | and it is a human community,

02:42:57.400 | and it was all kinds of good, bad, and ugly things

02:43:00.360 | that happen, a lot of them under the radar screen,

02:43:02.760 | so to speak, and so, but maybe there is something to it.

02:43:07.760 | There is definitely, there are definitely people

02:43:10.120 | who are upholding kind of that old tradition, definitely,

02:43:14.800 | and that is inspiring, and I aspire to be one of those,

02:43:18.720 | do my best, so whether this is a system

02:43:23.640 | that will stay or should stay, I don't know.

02:43:26.520 | I really don't know.

02:43:27.360 | - That's really fascinating.

02:43:28.200 | Yeah, it's fascinating what, especially with,

02:43:31.360 | just to introduce the bit of AI poison into the mix,

02:43:35.280 | as that changes the nature of education, perhaps, as well,

02:43:38.920 | what the role of the university is

02:43:40.600 | in the next 10, 20, 50, 100 years, I wonder.

02:43:43.960 | I wonder, and I wonder that, you know,

02:43:49.000 | how do you make sense that Einstein was working,

02:43:51.840 | after attempting, I believe, to be a university professor,

02:43:55.360 | was, did most of-- - He was in the patent office.

02:43:57.840 | - Yeah, as a patent clerk.

02:43:59.960 | - But I have to say, to these days,

02:44:01.720 | the science has become so much faster.

02:44:06.800 | It is really hard to do it being outside.

02:44:09.720 | Now, Eric is unique in this way,

02:44:12.520 | even though he did go to great undergraduate

02:44:17.120 | and graduate schools,

02:44:20.440 | but, and then worked for a while in academia.

02:44:24.140 | There are very few examples like this.

02:44:27.800 | There's Yutong Zhang, who proved

02:44:29.320 | the important conjecture number theory about 10 years ago,

02:44:32.800 | and is now, as I understand,

02:44:34.560 | is a professor at UC Santa Barbara.

02:44:36.960 | He worked outside of academia

02:44:38.600 | and was able to make a tremendous advance on his own.

02:44:42.620 | This case is exceedingly rare,

02:44:45.500 | in part because academia is trying to protect its turf,

02:44:49.400 | and it's kind of, it's creating

02:44:51.800 | this sort of prohibitive cost of an outsider.

02:44:55.200 | That is true, but there is also something about

02:44:58.680 | how much concentration.

02:45:00.560 | In mathematics, I don't think people

02:45:03.280 | who are not in the field understand

02:45:06.120 | what kind of focus and concentration

02:45:10.040 | actually doing, like, mathematics

02:45:12.560 | at the top level these days requires,

02:45:16.920 | because we're not talking about something

02:45:18.600 | that is more or less good.

02:45:20.800 | It is something which is unassailable.

02:45:22.440 | You know, it's finding this treasure

02:45:25.020 | at the bottom of the ocean, you know,

02:45:26.840 | without, you know, the aqualung, you know,

02:45:30.600 | without oxygen.

02:45:32.560 | And that's why, you know,

02:45:34.720 | it's not, people go crazy sometimes, you know?

02:45:38.120 | But there is a reason for that.

02:45:39.200 | - Well, let me ask about that,

02:45:40.880 | sort of just to linger on that,

02:45:42.560 | the amount of concentration required.

02:45:44.640 | Cal Newport wrote a book called Deep Work,

02:45:49.400 | and he's a theoretical computer scientist.

02:45:51.500 | He took quite seriously the task

02:45:57.920 | of allocating the hours in the day

02:45:59.600 | for that kind of deep thinking,

02:46:01.220 | and then the mathematician is theoretical

02:46:03.800 | computer scientist on steroids.

02:46:07.080 | So for your own life and what you've observed,

02:46:09.880 | let me ask the big question, how to think,

02:46:15.240 | how to think deeply,

02:46:17.120 | how to find the mental, psychological,

02:46:19.580 | pragmatic space to really sit there and think deeply.

02:46:24.260 | How do you do it?

02:46:26.800 | In the moments you remember

02:46:28.120 | where you really deeply thought,

02:46:30.720 | what, was it an accident, was it deliberate?

02:46:34.840 | - No, it's deliberate because, you know,

02:46:37.720 | first of all, my first years as a mathematician, you know,

02:46:43.760 | I worked every day, weekends, holidays, doesn't matter.

02:46:50.760 | I didn't even question that,

02:46:54.300 | so I would feel something's missing if I took a day off.

02:46:58.640 | - Mm-hmm.

02:47:00.040 | - And, you know, so it was just a kind of a sustained effort.

02:47:05.040 | The point is that still the process is nonlinear,

02:47:08.880 | to go back to what we discussed earlier,

02:47:11.480 | that, in other words, the way I see it

02:47:13.920 | is you are making an effort to bring all the information

02:47:18.920 | into focus, what you believe is correct,

02:47:22.900 | and you're playing with different ways of connecting things.

02:47:28.900 | But it is a total miracle

02:47:31.500 | when suddenly there is inside strikes.

02:47:35.700 | It is not something that, in my experience,

02:47:38.020 | could be predicted or even anticipated,

02:47:41.820 | you know, or like brought closer.

02:47:44.060 | There is a famous story about Einstein

02:47:48.020 | that he used to, you know, go think, think, think,

02:47:50.700 | and then go for a walk,

02:47:52.100 | and like he would whistle sometimes.

02:47:53.860 | So I remember the first time I heard this story,

02:47:56.740 | I thought, "Mm, how interesting.

02:47:57.940 | "So what a coincidence that this came to him

02:47:59.780 | "when he was whistling."

02:48:01.260 | But in fact, it's not.

02:48:02.180 | This is how it works in some sense,

02:48:04.860 | that you have to prepare for it,

02:48:07.620 | but then it happens when you stop thinking, actually.

02:48:10.260 | So the moment of discovery is the moment when thinking stops,

02:48:14.660 | and you kind of almost become that truth that you're seeking.

02:48:19.660 | But you cannot do it by will in some sense.

02:48:25.220 | It's kind of like, you know how in the Eastern tradition

02:48:27.780 | they have this concept of satori,

02:48:29.340 | like in Zen Buddhism you have this satori,

02:48:31.820 | which is enlightenment.

02:48:33.820 | And so there are various reports of Buddhist monks

02:48:38.500 | or Buddhist masters who have had experience satori.

02:48:41.380 | But they say you can't do it by will.

02:48:47.780 | You cannot make it happen.

02:48:49.940 | If anything, you have to relax to let it come to you.

02:48:52.860 | It's kind of like that.

02:48:54.100 | It's kind of like that.

02:48:54.940 | So I think that what matters,

02:48:59.940 | but you say how to think.

02:49:01.580 | The point is that we're talking about such an esoteric area.

02:49:05.220 | Mathematics is really an esoteric area.

02:49:07.060 | It's a really strange subject

02:49:08.900 | where you try to fit everything

02:49:12.500 | in this very, very stringent set of rules,

02:49:16.380 | to obey those rules.

02:49:18.180 | - Isn't it basically the pure,

02:49:20.740 | the hardest manifestation of a puzzle

02:49:23.180 | that we're all solving in different other disciplines,

02:49:25.100 | but this is the hardest puzzle?

02:49:27.380 | - Yes and no, because there is just a different,

02:49:30.020 | for instance, there is a different criterion

02:49:33.100 | for what constitutes progress.

02:49:35.360 | For instance, physics, a lot of arguments they make,

02:49:38.540 | they are not rigorous from mathematical perspective.

02:49:40.820 | It is kind of an intuitive argument.

02:49:42.540 | We think it is like this.

02:49:43.820 | And this is acceptable in the subject, for a good reason.

02:49:47.460 | And so there is some play.

02:49:49.660 | It's more like human activity, day-to-day activity.

02:49:53.140 | For instance, if you and I discuss something,

02:49:55.460 | you have an idea and I have an idea,

02:49:57.020 | and we argue about it,

02:49:58.420 | and something seems more plausible,

02:50:00.780 | something seems less plausible.

02:50:02.500 | And so we may decide to take this point of view

02:50:05.060 | or that point of view as a provisional

02:50:07.220 | sort of like point of view and go with it.

02:50:10.800 | In mathematics, it doesn't work this way.

02:50:13.780 | You either prove it or you don't.

02:50:15.620 | And oftentimes, you get to the point

02:50:19.380 | where there is this much you need to prove,

02:50:21.540 | and it just wouldn't come to you.

02:50:25.060 | And you just don't see it.

02:50:26.660 | And it can go on for months.

02:50:29.000 | Super frustrating.

02:50:31.940 | But without it, it is nothing, kind of.

02:50:35.740 | - I would love to hear your opinion,

02:50:37.820 | to the degree that you know it,

02:50:39.980 | of the proof of Fermat's Last Theorem by Andrew Wiles,

02:50:43.540 | which seems to have this element, perhaps for years.

02:50:48.540 | To the degree that you know,

02:50:49.740 | perhaps can you explain Fermat's Last Theorem

02:50:52.620 | and what your thoughts are in the process

02:50:54.740 | that Andrew Wiles took that seemed to,

02:50:57.140 | at least from my sort of romantic perspective,

02:50:59.220 | seemed to be very lonely.

02:51:01.220 | - Yes, it's a lonely profession.

02:51:03.480 | - And hopeless.

02:51:05.380 | You put it really nicely because it feels like

02:51:13.960 | there's a lot of moments where you feel like you're close.

02:51:16.020 | - You feel like 99% is done.

02:51:17.340 | - Yeah.

02:51:18.180 | - But there's one stubborn thing

02:51:20.020 | which just does not compute, you know, doesn't happen.

02:51:23.660 | And you're trying to find that push for this last link.

02:51:28.300 | And it could take,

02:51:30.340 | and nobody knows how long it's going to take.

02:51:32.100 | - Would it be useful to maybe try to explain

02:51:34.700 | Fermat's Last Theorem?

02:51:35.780 | - Sure, it's easy to do.

02:51:37.380 | (laughing)

02:51:39.140 | I am an optimist, I am an optimist.

02:51:41.380 | I think, I always think that everything can be explained.

02:51:44.940 | Even though I say that not everything can be explained.

02:51:47.760 | But in mathematics, you know,

02:51:50.580 | within this particular framework,

02:51:52.060 | I think that I always feel optimistic

02:51:54.620 | when people ask me to explain something.

02:51:57.180 | I always start with the assumption

02:51:58.460 | that they will understand, you know?

02:52:01.340 | So, let's try.

02:52:03.140 | Fermat's Last Theorem,

02:52:06.540 | one of the jewels sort of of mathematics of all time.

02:52:10.500 | A beautiful story also behind it.

02:52:13.820 | Pierre Fermat, a great French mathematician

02:52:16.760 | who lived in the beginning of,

02:52:18.580 | mostly worked at the beginning of, what, 17th century.

02:52:22.820 | And he actually has to his credit

02:52:26.020 | a number of important contributions.

02:52:28.620 | But the most famous is called Fermat's Last Theorem,

02:52:31.260 | or Fermat's Great Theorem.

02:52:33.380 | And the reason why it became so famous

02:52:35.900 | is in part because he actually claimed

02:52:38.580 | to have proved it himself.

02:52:40.860 | And he did it on the margin of a book that he was reading,

02:52:44.420 | which was actually an important book by Diophantus,

02:52:46.700 | about equations with coefficients in whole numbers.

02:52:51.340 | And he wrote on the margin, literally,

02:52:53.460 | this equation, this problem,

02:52:57.040 | which I will explain in a moment,

02:52:58.680 | I have solved it, I have found a proof,

02:53:02.940 | but this margin is too small to contain it.

02:53:05.340 | At some point, I was giving a public talk about this,

02:53:09.700 | and I made, as a joke, I made a tweet

02:53:12.480 | in which I wrote that I have proved this theorem,

02:53:14.920 | but 280 characters are not enough,

02:53:16.860 | and it kind of cuts me in mid-sentence.

02:53:18.660 | So this was 17th century Twitter-style proof, okay?

02:53:22.980 | But a lot of mathematicians took it seriously

02:53:24.700 | because he had great credibility,

02:53:27.020 | he did make some major contributions.

02:53:32.020 | And the search was on.

02:53:33.380 | So for 350 years, about 350 years,

02:53:37.300 | it remained unproved,

02:53:41.140 | with many people trying and failing

02:53:44.700 | until in 1994, no, in 1993,

02:53:49.500 | Andrew Wiles announced,

02:53:51.660 | a mathematician from Princeton University,

02:53:53.980 | announced the proof, and it was very exciting

02:53:56.420 | because he was one of the top number theorists in the world.

02:54:00.540 | And unfortunately, about a year later, a gap was found.

02:54:04.260 | So this is exactly what we were talking about earlier.

02:54:06.540 | You have 99% of the proof,

02:54:07.980 | this one little thing does not quite connect,

02:54:11.040 | and this nullifies the whole thing.

02:54:12.760 | Even though, well, you could say

02:54:13.800 | there are some interesting ideas,

02:54:15.040 | but it's not the same as actually having a proof.

02:54:18.540 | So he apparently was really frustrated,

02:54:20.320 | and he was really, a lot of people thought

02:54:22.840 | that it's going to be another 100 years or whatever.

02:54:26.060 | And then luckily, he was able to enlist,

02:54:28.760 | with the help, assistance of his former student,

02:54:33.400 | also great number theorist, Richard Taylor,

02:54:35.840 | they were able to do that 1%, so to speak.

02:54:38.920 | Well, some people might say it may be not 1%,

02:54:40.760 | but 5% or whatever,

02:54:41.780 | but it definitely was an important ingredient,

02:54:44.240 | but it was not, he had a sort of like a big new set of ideas,

02:54:48.560 | and this one thing didn't pan out.

02:54:50.480 | They were able to close it with Taylor,

02:54:52.600 | and it finally was published,

02:54:54.160 | and I think was accepted and refereed in '95,

02:54:57.360 | and is believed to be correct.

02:54:59.900 | Now, what he proved actually was not Fermat's theorem itself,

02:55:06.840 | but a certain statement,

02:55:09.360 | which is called Shimura-Taniyama-Wei conjecture,

02:55:12.340 | named after three mathematicians,

02:55:13.740 | two Japanese mathematicians and one French-born mathematician

02:55:17.380 | who worked also at the Institute for Advanced Study

02:55:19.820 | in Princeton.

02:55:21.800 | And it was my colleague at UC Berkeley, Ken Ribbit,

02:55:25.740 | who in the '80s connected the two problems.

02:55:28.520 | So this is how it often works in mathematics.

02:55:30.660 | You want to prove statement A.

02:55:32.740 | Instead, you prove that A is equivalent to B.

02:55:36.020 | So after that, if you can prove B,

02:55:37.620 | this would automatically imply that A is correct.

02:55:40.160 | So this is what happened here.

02:55:41.640 | A was Fermat's last theorem,

02:55:42.880 | B was Shimura-Taniyama-Wei conjecture,

02:55:44.960 | and that's what Andrew Wiles and Richard Taylor

02:55:48.000 | really proved.

02:55:49.240 | So it requires, to get to Fermat's last theorem,

02:55:51.440 | it requires that bridge,

02:55:52.400 | which was established by my colleague,

02:55:53.960 | Ken Ribbit, at UC Berkeley.

02:55:56.400 | So now, what is the statement of Fermat's last theorem?

02:55:59.100 | Let me start with Pythagoras,

02:56:03.000 | since we already talked about it.

02:56:04.200 | Let me start with Pythagoras' theorem,

02:56:06.920 | which describes the right triangles.

02:56:10.020 | So what is the right triangle?

02:56:11.260 | It's a triangle in which one of the angles is 90 degrees,

02:56:14.420 | like this.

02:56:15.900 | So it has three sides.

02:56:17.420 | The longer side is called hypotenuse,

02:56:20.220 | and then there's two other sides.

02:56:21.680 | So if we denote the lengths of hypotenuse by z,

02:56:25.860 | and the two other sides, x and y,

02:56:28.540 | then z squared is equal to x squared plus y squared.

02:56:31.240 | So that's the equation,

02:56:34.080 | or x squared plus y squared equals z squared.

02:56:36.520 | And it turns out that this equation

02:56:41.160 | has solutions in natural numbers.

02:56:44.080 | Many, actually infinitely many solutions in natural numbers.

02:56:47.840 | For example, if x is, you take x equals three,

02:56:50.980 | y equals four, and z equals five,

02:56:54.360 | then they solve this equation,

02:56:58.160 | because three squared is nine,

02:57:00.540 | four squared is 16.

02:57:04.040 | Nine plus 16, 25.

02:57:06.340 | And that's five squared.

02:57:07.600 | So x squared plus y squared equals z squared

02:57:11.880 | is solved by x equals three, y equals four, z equals five.

02:57:15.880 | And there are many other solutions of that nature.

02:57:18.440 | - And we should say that natural numbers

02:57:19.960 | are whole numbers that are non-negative.

02:57:23.320 | - That's right.

02:57:24.160 | One, two, three, four, five, six, and so on.

02:57:26.040 | Now, what's Fermat's last theorem?

02:57:27.640 | Fermat asked, what about,

02:57:29.840 | what will happen if we replace squares by cubes, for example?

02:57:33.560 | So x cubed plus y cubed equals z cubed.

02:57:36.920 | Are there any solutions in,

02:57:41.160 | what do you call, natural numbers?

02:57:43.160 | It turns out there are none.

02:57:46.720 | What about fourth powers?

02:57:48.000 | Again, none.

02:57:50.000 | - Well, it seems like none, right?

02:57:51.800 | - So that was the statement.

02:57:53.960 | So this theorem says that the equation

02:57:57.200 | x cubed plus y cubed equals z cubed

02:57:59.860 | has no solutions in natural numbers.

02:58:02.500 | Remember, natural means positive whole numbers.

02:58:06.900 | So of course there is a trivial solution, zero, zero, zero,

02:58:09.100 | so that this works, but you need all of them to be positive.

02:58:12.100 | X to the fourth plus y to the fourth equals z to the fourth

02:58:17.100 | also has no solutions.

02:58:18.600 | X to the fifth plus y to the fifth equals z to the fifth,

02:58:23.940 | no solutions, so you kind of see the trend.

02:58:26.140 | X to the n plus y to the n equals z to the n.

02:58:30.740 | If n is greater than two,

02:58:32.220 | has no solutions in natural numbers.

02:58:35.180 | That is a statement of Fermat's last theorem.

02:58:38.300 | Deceptively simple as far as famous theorems are concerned.

02:58:42.180 | You don't need to know anything beyond standard arithmetic,

02:58:45.340 | addition and multiplication of natural numbers.

02:58:48.240 | That's why a lot of people,

02:58:49.580 | both specialists and amateurs,

02:58:54.440 | try to prove it.

02:58:56.260 | - It's so tempting.

02:58:57.100 | - It's so tempting, it's so easy to formulate.

02:59:00.300 | So in fact I think Fermat proved the case of cubes.

02:59:03.620 | I think he did actually prove some elsewhere,

02:59:05.900 | the case of cubes, but so it remained like fourth.

02:59:08.740 | There are infinitely many cases, right?

02:59:10.020 | You have to, even if you prove it for cubes

02:59:11.700 | and for fourth power and fifth,

02:59:12.900 | then still there's sixth, seventh and so on.

02:59:15.140 | There are infinitely many cases in which it has to be proved.

02:59:18.140 | And so you see, the deceptively simple result

02:59:24.460 | took 350 years to prove.

02:59:27.700 | And, but in a sense it's like mathematicians,

02:59:30.500 | you would think mathematics is such a sterile profession.

02:59:33.100 | Everybody's so serious,

02:59:35.140 | almost like we're all wearing lab coats

02:59:37.500 | and take an elevator to the ivory tower.

02:59:42.500 | However, look at all this drama.

02:59:45.560 | Look at all this drama.

02:59:46.400 | It's like we also like drama.

02:59:47.900 | We also have narratives.

02:59:49.420 | We also have our myths.

02:59:51.040 | Here is a guy, he's a 16th century mathematician

02:59:54.880 | or 17th century mathematician

02:59:56.380 | who leaves a note on the margin

02:59:58.820 | and motivates others to find the proof.

03:00:01.460 | Then how many hearts were broken

03:00:03.900 | that they believe that they found the proof

03:00:05.700 | and then later it was realized that the proof was incorrect

03:00:09.540 | and so on and brings us to modern day.

03:00:12.460 | And one last attempt, Andrew Wiles,

03:00:14.900 | who is very serious and respected

03:00:16.940 | and esteemed mathematician announces the proof

03:00:19.120 | only to be faced with the same reality

03:00:21.380 | of his hopes dashed, seemingly dashed.

03:00:24.140 | And like there is a mistake, it doesn't work.

03:00:27.140 | And then to be able to recover a year later,

03:00:29.300 | how much drama in this one story, huh?

03:00:31.780 | - It's amazing.

03:00:32.620 | But from what you understand, from what you know,

03:00:36.040 | what was the process for him

03:00:37.940 | that is similar perhaps to your own life

03:00:40.860 | of walking along with the problem for months, not years?

03:00:47.220 | - Yes, so he worked,

03:00:49.820 | he has given interviews about it afterwards.

03:00:52.780 | So we know that he described his process,

03:00:55.900 | that number one, he did not want to tell anybody

03:00:58.940 | because he was afraid that people find out

03:01:02.180 | that he's working on it.

03:01:03.380 | Because he was such a top level mathematician,

03:01:08.140 | people would guess that he has some idea,

03:01:10.540 | that there is some idea.

03:01:11.380 | So, you know, if you just know that somebody has an idea,

03:01:16.380 | this already gives you a great boost of confidence, right?

03:01:19.900 | So he didn't want people to have that information.

03:01:23.340 | So he didn't tell anybody that he was working on it,

03:01:25.500 | number one. - Must be lonely.

03:01:27.140 | - Number two, he worked on it for seven years,

03:01:29.500 | if I remember correctly, by himself.

03:01:32.660 | And then he thought he had it and he was elated.

03:01:37.660 | Obviously, he was, you know, very happy.

03:01:40.700 | And he announced it at a conference,

03:01:42.940 | I think it was in Cambridge University

03:01:44.460 | or Oxford University in the UK in 1993, I believe.

03:01:48.700 | So, you know, this is really interesting

03:01:53.700 | because all of us, all mathematicians can relate to this

03:01:59.060 | because I remember very well my first problem,

03:02:02.100 | how I solved my first problem.

03:02:03.600 | I describe it in "Love and Math" in my book.

03:02:07.860 | So it was, how old was I?

03:02:12.340 | I was 18 years old, I was a student in Moscow,

03:02:16.620 | and I just lucked out that I was introduced

03:02:19.540 | to this great mathematician.

03:02:21.180 | Since I was not studying at Moscow University

03:02:24.540 | because of antisemitism in the Soviet Union,

03:02:26.500 | so I was in this technical school,

03:02:28.380 | but I was lucky that I had a mathematician

03:02:30.660 | who took me under his wing,

03:02:32.020 | and Dmitry Fuchs, who actually later came to the US,

03:02:38.900 | and he's still a professor at UC Davis, actually.

03:02:42.220 | Not so far from me.

03:02:45.860 | So he gave me this problem, and it was rather technical,

03:02:50.140 | so I will not try to describe it,

03:02:51.780 | but I do remember how much effort, that excitement,

03:02:56.780 | but also kind of a fear.

03:02:58.580 | What if I don't have what it takes?

03:03:00.540 | You know?

03:03:01.380 | I lost sleep, so this was one consequence of this.

03:03:04.500 | For the first time in my life, I had trouble falling asleep,

03:03:07.860 | and this actually stayed for a couple years afterwards.

03:03:11.140 | So then it was kind of like a wake-up call

03:03:12.860 | that I should be, take care of myself,

03:03:14.700 | not work too late, and so on.

03:03:16.180 | So that was sort of like that experience.

03:03:18.720 | And I was lucky that I was able to find a solution,

03:03:21.340 | number one, within two months, maybe.

03:03:24.040 | And it was surprising, and it was beautiful.

03:03:27.700 | The answer was in terms of something

03:03:29.900 | which seemed to be from a different world,

03:03:31.820 | from a different area of mathematics.

03:03:34.180 | So I was very happy.

03:03:35.860 | But I do remember this moment when suddenly you see that.

03:03:39.940 | In this case, it was literally,

03:03:43.380 | I had to compile these diagrams

03:03:45.660 | with what mathematicians call cohomology groups

03:03:48.380 | and spectral sequences,

03:03:49.900 | and manually calculate some numbers,

03:03:53.580 | and trying to discern some system in it.

03:03:55.860 | And suddenly I saw that,

03:03:57.380 | how they all were governed by this one force,

03:04:01.260 | so to speak, one pattern.

03:04:03.180 | And that was absolutely wow.

03:04:05.580 | So it's like. (laughs)

03:04:07.580 | - I mean, what was it?

03:04:08.400 | So you were sitting there at a desk.

03:04:10.460 | - Actually, you know, I lived in a town outside of Moscow,

03:04:13.060 | so I used to take, I would take a train to Moscow.

03:04:15.780 | So it's what we call in Russia, elektrichka,

03:04:17.580 | you know, like this electric train, which was super slow.

03:04:20.420 | It took more than two hours to cover that distance.

03:04:23.060 | And I think that the crucial insight came

03:04:24.700 | when I was in this.

03:04:26.640 | And I just, I had to contain myself

03:04:29.220 | so I don't start screaming, you know,

03:04:30.540 | because there were other passengers in the car.

03:04:34.780 | So I was sitting there and staring at this paper.

03:04:39.060 | So you know what I remember that what came to me?

03:04:43.060 | I have something now which nobody else in the world has.

03:04:47.180 | I have a proof of, first of all, I did not,

03:04:49.060 | it was not just a proof.

03:04:50.180 | Like in the case of Fermat, the statement is already made.

03:04:53.300 | That's why it's called conjecture, you know.

03:04:54.820 | You make a statement, you don't have a proof yet.

03:04:57.220 | Then you try to prove it.

03:04:58.180 | In my case, I did not know what the answer would be.

03:05:00.420 | There was a type of question where the answer was unknown.

03:05:03.860 | So I had to find the answer and prove it.

03:05:06.420 | And the answer was very nice.

03:05:08.060 | So nobody knew, as far as I could tell,

03:05:09.980 | nobody knew because my teacher told me

03:05:12.740 | that he explored all the literature.

03:05:14.820 | This was not known.

03:05:15.820 | Suddenly I felt that I was in possession of this.

03:05:22.100 | Now, it was a little thing.

03:05:24.980 | It was not cure for cancer.

03:05:27.060 | It was not a large language model.

03:05:30.100 | But it was something undeniably real, meaningful,

03:05:36.200 | and it was mine, kind of.

03:05:37.540 | You know, like I had it, nobody else.

03:05:38.980 | I had not published it yet.

03:05:39.860 | I hadn't even told anybody.

03:05:42.180 | And it is a very strange feeling to have that.

03:05:45.340 | - Were you worried that this treasure could be stolen?

03:05:48.780 | - Not at the time, not at the time.

03:05:50.660 | So later on, there were situations

03:05:52.500 | where I was exposed to those type of experiences.

03:05:55.300 | By that time, I didn't think of that.

03:05:56.620 | I was still this starry-eyed kid

03:05:59.940 | who was just obsessed with mathematics,

03:06:02.820 | with this beauty and discovering those beautiful facts,

03:06:06.740 | beautiful results.

03:06:08.260 | So I didn't think about,

03:06:09.760 | I didn't even think that it could be possible

03:06:11.580 | that somebody could steal it or whatever.

03:06:13.580 | I just wanted to share it with my teacher

03:06:15.860 | as soon as possible, you know?

03:06:17.620 | And he understood quickly,

03:06:19.940 | and he's like, "Yeah, good job," you know?

03:06:22.940 | - Is there something you can give color to the drama?

03:06:26.260 | Eric Weinstein has spoken about some of the challenges,

03:06:30.860 | some of the triumphs and challenges of his time at Harvard.

03:06:34.740 | So is there something to that drama

03:06:39.740 | of people stealing each other's ideas

03:06:42.900 | or not allocating credit enough?

03:06:45.500 | - Oh, sure, yes.

03:06:46.980 | - All of that and creating psychological stresses

03:06:50.020 | because of that.

03:06:50.980 | - Happens all the time, yes, unfortunately.

03:06:53.100 | - On young minds and so on.

03:06:54.900 | - Could have a very bad effect.

03:06:57.020 | - Is that just the way of life, or is this?

03:06:59.300 | - I think we can definitely do better.

03:07:02.980 | And I think the first step is to kind of admit

03:07:06.260 | that we are not 100% seekers of truth,

03:07:10.740 | that we are human beings,

03:07:12.020 | and all the good and bad and the ugly qualities

03:07:17.020 | can be present,

03:07:20.300 | and to have some kind of dialogue in my subject,

03:07:24.660 | in mathematics.

03:07:26.220 | This has not happened yet.

03:07:27.620 | There have been some famous cases

03:07:28.980 | where people have been accused,

03:07:30.420 | which had been resolved or partially resolved or unresolved.

03:07:34.820 | And everybody knows it,

03:07:36.900 | but there isn't a systematic effort,

03:07:38.900 | as far as I can tell,

03:07:40.500 | of really trying to create some rules, some ethics rules.

03:07:44.340 | This is fair game, this is not fair game.

03:07:47.260 | So that as a community, we strive to get better.

03:07:50.780 | I think that for most people,

03:07:52.580 | it's more like keeping your head in the sand

03:07:55.180 | and kind of pretending that it doesn't happen.

03:07:57.500 | Or it happens, some isolated incidents.

03:07:59.660 | Well, my experience is not like that at all.

03:08:02.500 | I think it does happen much more often than it should.

03:08:05.860 | That's my opinion.

03:08:07.460 | - So there's the pool of academia is fascinating.

03:08:10.780 | One of the reasons I really love it

03:08:12.300 | is you have young minds with fresh ideas.

03:08:16.580 | And that same innocence you had

03:08:18.220 | with when you first on the train

03:08:19.500 | have that brilliant breakthrough.

03:08:21.420 | And then you throw that in together

03:08:23.260 | with senior exceptional world-class scientists

03:08:27.580 | who have, first of all, are getting older.

03:08:30.220 | Second of all, maybe they have partaken

03:08:35.700 | in the drug of fame and money and status and recognition.

03:08:40.380 | So that starts to a little bit corrupt

03:08:43.100 | all of our human minds.

03:08:45.340 | And you throw that mix in together.

03:08:47.420 | - Yeah.

03:08:48.620 | - Mostly without rules.

03:08:50.200 | And it's beautiful because that's where the ideas of old

03:08:56.980 | contend with the new wild-eyed crazy ideas.

03:09:00.380 | And they clash and there's a tension

03:09:02.740 | and there's a dance to it.

03:09:04.840 | But then there's the old human corruption

03:09:06.780 | that can take advantage of the young minds.

03:09:09.360 | It's unclear what to do with that.

03:09:12.620 | I mean, part of that is just the way of life

03:09:14.180 | and there's tragedies.

03:09:15.320 | And oftentimes when you look at who wins the Nobel Prize,

03:09:19.260 | it's also tragic because sometimes so many minds are,

03:09:25.500 | the trajectory to the breakthrough idea

03:09:28.140 | involves so many different minds, young and old.

03:09:30.900 | - Yeah, I mean, you're right.

03:09:35.900 | I think it's like with everything else.

03:09:38.520 | The path is to more self-awareness.

03:09:42.900 | And it's like owning up your own stuff

03:09:46.440 | and not blaming other people,

03:09:48.380 | not projecting onto other people,

03:09:50.020 | but taking responsibility.

03:09:52.100 | And that's true for everything.

03:09:53.820 | And the problem here, unique problem for mathematics,

03:09:58.220 | I would say physicists and chemists are better.

03:10:00.660 | They actually have better sort of ethical rules and so on,

03:10:03.820 | especially biologists.

03:10:05.060 | Because I think in part it's because

03:10:06.780 | there is much more money involved,

03:10:08.460 | because they have to get grants and so on.

03:10:09.900 | So for them, the question of priority,

03:10:11.460 | who discovered what first, is much more serious

03:10:13.820 | because there's really some serious money.

03:10:15.780 | Mathematics, who cares?

03:10:16.820 | You know, the Fermat's last theorem was proved.

03:10:18.860 | Did Andrew Wiles become a millionaire?

03:10:20.460 | No.

03:10:21.300 | - But I think he got a prize.

03:10:22.580 | - He won a prize, but those prizes are not--

03:10:25.900 | (laughing)

03:10:26.740 | - I think that one was a big prize,

03:10:27.900 | but in general, there's not going to be--

03:10:30.300 | - I think he won the Nobel Prize,

03:10:31.700 | eventually, which is about a million dollars.

03:10:34.220 | So, but, you know, sometimes I joke about this,

03:10:38.220 | that this is the hardest way to win a million dollars.

03:10:40.860 | (laughing)

03:10:42.620 | So, you know, but amongst mathematicians,

03:10:47.260 | I think the trouble is that we are so insulated

03:10:52.300 | from society, because it's such a pure subject.

03:10:56.700 | It draws in very specific psychological types.

03:11:01.620 | And I can speak about myself.

03:11:03.220 | I did not realize it at the time,

03:11:04.740 | but later on, I definitely saw,

03:11:07.140 | I mentioned some of it earlier,

03:11:08.860 | that for me, mathematics was a refuge

03:11:11.300 | from the cruelty of the life I experienced,

03:11:13.140 | from discrimination that I experienced

03:11:15.420 | when I applied to Moscow University at 16,

03:11:17.380 | being failed at the exam and stuff like that,

03:11:19.540 | which I describe in my book as well.

03:11:21.100 | But that was my way.

03:11:24.420 | I was like, I don't trust this world.

03:11:27.140 | I don't want to deal with it.

03:11:29.060 | I want to hide in this platonic reality of pure forms.

03:11:33.860 | This is where I know how to operate.

03:11:36.840 | I love this, and I couldn't be bothered, in some sense,

03:11:40.460 | for a while, up to a point.

03:11:42.420 | As I was getting older and more mature,

03:11:45.060 | I was becoming more and more interested in other things.

03:11:47.820 | But I think that's one of the reasons.

03:11:50.600 | And one of the reasons why I wrote "Love and Math"

03:11:55.600 | was precisely to break that cycle,

03:11:58.560 | that it's the quiet guy in the corner that goes into math,

03:12:02.940 | and not the flamboyant jock or DJ.

03:12:07.940 | I wanted to show how beautiful the subject is,

03:12:14.140 | to attract this new blood,

03:12:16.160 | so that different psychological types,

03:12:17.660 | and more women would join.

03:12:22.660 | Because then they would have students

03:12:26.240 | who would look at them, whom they will inspire.

03:12:29.560 | And then it would be, instead of a vicious circle,

03:12:32.620 | it would be a virtuous circle.

03:12:34.600 | And I have to say, I think it's happening,

03:12:36.440 | not because of my efforts alone.

03:12:38.520 | Obviously, there are many other mathematicians

03:12:40.000 | who are, around the same time,

03:12:41.760 | started to put more effort.

03:12:42.960 | Because see, if the old stereotype of mathematician,

03:12:46.800 | you're so enclosed, you're not interested

03:12:48.700 | in even exposing the beauty of your subject to other people.

03:12:52.860 | And then it becomes this vicious circle.

03:12:55.300 | But you know, this one day,

03:12:57.080 | not one day, all the time I meet the students who say,

03:13:00.520 | your book is the reason why I chose math as my major.

03:13:04.940 | And I am proud, especially when it's women

03:13:07.140 | who tell me this.

03:13:08.180 | And they are cool, they are DJs at the same time,

03:13:11.840 | and they are social, and they have friends,

03:13:14.860 | and they go out, and so on.

03:13:16.340 | You see, so then they carry the torch.

03:13:18.980 | Because then they will be more likely

03:13:20.940 | to share this beauty with others,

03:13:26.720 | to attract more students, and so on.

03:13:28.300 | So I think this kind of, this dam was broken.

03:13:30.500 | So now you have more influx.

03:13:32.320 | And once we have people who are more able to connect

03:13:35.460 | at the personal level, that's when we also become

03:13:38.260 | more self-aware as a community, I think.

03:13:40.700 | And that's when we should be able to have a chance

03:13:44.180 | to improve in terms of our ethical rules

03:13:46.660 | and stuff like that.

03:13:48.140 | - So let me return to our friend, Eric Weinstein,

03:13:51.600 | for a question that I would ask anyway.

03:13:53.860 | But let's have a non-Russian ask the Russian question.

03:13:57.900 | Ask him about the Russian concepts of friendship,

03:14:03.220 | science, gender, and love versus the American.

03:14:06.060 | (laughing)

03:14:09.660 | You can, so there is a deep romanticism that you have

03:14:14.660 | that runs through your book, Love and Math.

03:14:19.460 | Is part of that something you've picked up

03:14:24.540 | from the Russian culture?

03:14:26.060 | What can you speak to that fueled both your fascination

03:14:31.640 | with math and your fascination, no,

03:14:33.740 | your prioritization of the human experience of love?

03:14:39.660 | - Hmm, good question.

03:14:41.780 | Definitely there is some influence of the Russian culture,

03:14:46.220 | Russian literature, perhaps.

03:14:48.080 | But also, there's so many things.

03:14:52.220 | How do we develop certain sensibilities?

03:14:54.740 | Like, why do we care about this and not that?

03:14:57.300 | Like, why do I care, for instance, about, like you said,

03:15:00.460 | about this romantic ideal, so to speak, of mathematics?

03:15:04.460 | That's certainly not something that is automatic.

03:15:07.460 | Some people care about it, some people don't.

03:15:09.140 | And I'm not saying it is superior or inferior.

03:15:11.420 | It's just how my composition,

03:15:13.220 | my psychological composition is like that.

03:15:16.420 | And it's an interesting question, like,

03:15:20.140 | what is the cause of it?

03:15:21.780 | So I think that we cannot really know,

03:15:25.220 | but there are some aspects of it, of course.

03:15:27.260 | The experiences, life experiences are bringing family.

03:15:34.260 | Like, I was surrounded by love, by my parents,

03:15:38.380 | on the one hand, but on the other side,

03:15:41.780 | perhaps they were a little overprotective of me.

03:15:44.420 | So I was kind of like, you know,

03:15:47.020 | too much kind of like taken care of.

03:15:51.100 | So then when I, on one hand,

03:15:53.740 | it developed certain sensitivity,

03:15:55.220 | but I was kind of not ready for the challenges.

03:15:58.620 | - Of the real world. - Of the real world.

03:16:00.300 | So then that struggle, and then being lost,

03:16:04.740 | and then being able to overcome and to learn.

03:16:07.420 | And then if you do, in other words,

03:16:10.540 | if you don't lose, you don't appreciate maybe.

03:16:13.900 | But sometimes when we lose something and then regain it,

03:16:18.100 | then we cherish it, we appreciate it,

03:16:19.620 | and then it becomes something important.

03:16:21.180 | Also, various difficulties, you know,

03:16:25.940 | the upsetting experiences,

03:16:28.420 | or one could say traumatic experiences.

03:16:31.260 | Growing up in the Soviet Union,

03:16:33.020 | that was not a walk in the park.

03:16:36.260 | There were a lot of issues there

03:16:38.140 | that I had to go through.

03:16:40.860 | And then it doesn't break you, makes you stronger.

03:16:45.860 | But in my case, what happened was that,

03:16:51.460 | for some of it, it took me 30 years

03:16:55.060 | to really come to terms with it

03:16:56.500 | and to really understand what happened.

03:16:58.500 | It gave me this motivation

03:17:01.420 | to strive to become a mathematician,

03:17:06.660 | which maybe I wouldn't have otherwise.

03:17:08.100 | It charged me, supercharged me.

03:17:10.300 | I'm talking about, for instance,

03:17:11.460 | the experience with exam at Moscow University.

03:17:14.700 | - Can you take me through that experience?

03:17:16.460 | - So this is 1984, we spoke about Orwell earlier.

03:17:21.460 | And I was applying to Moscow University.

03:17:26.540 | Mathematics department, it's called Mehmat.

03:17:30.380 | - Which is like, for people who don't know,

03:17:32.860 | like the place--

03:17:33.980 | - Was the only place to study pure mathematics

03:17:35.780 | in Moscow, period.

03:17:36.740 | - But also--

03:17:37.780 | - But also--

03:17:38.620 | - Considered to be one of the great places on Earth.

03:17:40.860 | - And it's like a huge building,

03:17:42.540 | this monolith of a building of Moscow University.

03:17:47.420 | So, because, as I said, a year earlier,

03:17:53.380 | Yevgeny Yevgenyevich converted me into math,

03:17:56.100 | capitalizing on my love for quantum physics.

03:17:59.060 | And so I spent a whole year studying with him

03:18:01.620 | and I was already kind of at the level of,

03:18:03.700 | in some subjects, a level of early graduate studies.

03:18:10.420 | So it seemed like it would be a breeze

03:18:12.740 | to get into Moscow University.

03:18:14.940 | But in fact, little did I know that there was

03:18:22.100 | a policy of antisemitism where students like me

03:18:25.860 | would be failed by special examiners,

03:18:29.180 | mostly during the oral exam with mathematics,

03:18:32.060 | but occasionally there would be written tests and stuff.

03:18:36.460 | Now, my father is Jewish by blood.

03:18:41.540 | It was not religious, his family was not religious.

03:18:43.740 | My mom is Russian.

03:18:44.780 | But since my last name was my father's name,

03:18:49.020 | so it was very easy to read what my nationality was.

03:18:54.020 | And so, can you imagine, there were special people

03:18:57.340 | who would screen up applicants,

03:18:58.940 | who would put aside the files of the undesirables.

03:19:03.500 | There would be special examiners

03:19:04.860 | who were actually professors at this university,

03:19:07.740 | who would be designated as those who would take the exam

03:19:12.740 | from those undesirables.

03:19:15.020 | It's almost comical when you look back now.

03:19:17.660 | And also, questions of why.

03:19:19.820 | There was no reason other than just hatred of the other.

03:19:22.780 | That's how I see it.

03:19:23.620 | - And just to give a little bit more color,

03:19:25.740 | because you mentioned nationality,

03:19:29.420 | it's a little quirk that perhaps gives an insight

03:19:32.580 | to the bigger system, that the nationality

03:19:35.100 | listed on your birth certificate when you're Jewish

03:19:37.220 | is Jewish, and when you're non-Jewish, it lists as Russian.

03:19:40.860 | - For me, it was Russian.

03:19:42.140 | So first of all, in the inner part,

03:19:43.980 | everybody has an internal passport.

03:19:47.100 | And there, you have first name, patronymic name,

03:19:50.900 | last name, date of birth, so there's four.

03:19:54.140 | And the fifth colon is nationality,

03:19:57.460 | which comes from the nationality of the parents and so on.

03:20:01.820 | In my case, it was written Russian

03:20:02.860 | because my mom was Russian, but it didn't save me.

03:20:05.340 | (both laughing)

03:20:07.980 | 'Cause that was my dad's last name.

03:20:10.380 | And so anyway, this was the toughest experience

03:20:15.060 | that I had up until that point.

03:20:17.660 | And there was these two people who came into the room

03:20:22.060 | where I was the only undesirable.

03:20:24.340 | All other kids were being questioned by other examiners,

03:20:27.300 | but they told me that we cannot question you.

03:20:30.540 | We are waiting for special examiners.

03:20:32.900 | So I was like, uh-oh, something is afoot.

03:20:36.420 | And so these two guys came, and it was for four hours,

03:20:39.420 | basically, and were asking me questions

03:20:41.060 | which were not in the program and so on.

03:20:42.580 | But I was a kid, I was 16 years old.

03:20:44.220 | I tried to answer the best I can, but it was a setup.

03:20:46.860 | It's been documented since then.

03:20:50.060 | There are even lists of problems

03:20:52.820 | that were given to undesirables in those days.

03:20:55.980 | In my year, no Jewish applicants, as far as I know.

03:21:00.380 | Jewish, by this metric, were accepted.

03:21:04.140 | So then I had to go to this,

03:21:05.580 | there was one school, technical school in Moscow,

03:21:10.580 | which was the Institute for Oil and Gas Exploration,

03:21:13.380 | which had an applied mathematics program.

03:21:16.780 | And that's where many of the kids

03:21:21.500 | who were not accepted to Moscow University ended up.

03:21:24.420 | And so, but the point is, so,

03:21:28.820 | and then I was so motivated by this,

03:21:31.860 | because I wanted to show those guys, you know,

03:21:36.780 | that within five years, less than five years,

03:21:39.860 | I got a letter from the president of Harvard University

03:21:43.180 | inviting me as a visiting professor to Harvard.

03:21:45.580 | I was 21, I was barely 21,

03:21:47.860 | because I already did some research in the meantime.

03:21:51.180 | That's how motivated I was, you know.

03:21:54.340 | So, but the interesting aspect of it is that

03:21:57.420 | for the longest time afterwards,

03:22:01.820 | I was telling myself a story that nothing really happened.

03:22:05.020 | It wasn't so bad.

03:22:07.340 | Okay, so I was failed,

03:22:08.340 | but I knew that I was going to succeed.

03:22:13.260 | It was 30 years later that I finally got to meet that boy,

03:22:18.260 | that 16-year-old, that I neglected at this time.

03:22:24.180 | And I realized that he died,

03:22:25.900 | that it was a crushing blow.

03:22:28.580 | - The innocence?

03:22:29.940 | - Not just the innocence, because there was no way,

03:22:32.820 | it looked like there was no way

03:22:33.980 | I could become a mathematician.

03:22:35.300 | Because if they don't accept me there, it's over.

03:22:40.220 | I didn't know that I could actually find this striving

03:22:44.620 | applied math program,

03:22:46.300 | and then eventually somebody would take me under his wing

03:22:48.620 | and so on, and then could move to the United States.

03:22:51.300 | This was not in the realm of possibilities.

03:22:54.300 | So in other words, there was nothing to look forward to.

03:22:57.380 | It was clear that it's over.

03:22:59.140 | I cannot, I cannot do what I love.

03:23:03.300 | And so when I finally,

03:23:09.060 | when I finally connected to that boy, oh my God,

03:23:12.900 | that was a totally different experience.

03:23:14.260 | All the pain and all the trauma came to the surface,

03:23:19.020 | and it was a kind of a tsunami.

03:23:22.740 | I wasn't sure I would survive this.

03:23:24.940 | It was so hard.

03:23:26.980 | And what happened was I was invited

03:23:28.820 | to give a talk about this in New York.

03:23:32.060 | It was kind of a spoken word event about science,

03:23:37.380 | but like personal experiences related to science.

03:23:39.780 | This was almost a year after my book came out.

03:23:43.820 | In my book, one of the first chapters

03:23:46.460 | is a chapter about this experience.

03:23:48.820 | But what I realize now is that I wrote it

03:23:51.980 | from the third-person perspective.

03:23:54.140 | I knew the facts,

03:23:55.180 | but I was not emotionally connected to that experience.

03:23:58.140 | However, since I wanted to write the book

03:24:00.700 | and to connect to my readers, I allowed the boy to write it.

03:24:05.740 | So a lot of people were touched by it,

03:24:07.780 | and they would, people would say,

03:24:09.180 | "Wow, that chapter, it really got a lot of resonance.

03:24:12.300 | "It was translated into other language

03:24:13.740 | "even before the book was published."

03:24:16.380 | I was surprised by this because I didn't know yet.

03:24:19.380 | So the adult Edward was not yet in touch,

03:24:22.540 | but the book gave the outlet to the child.

03:24:26.780 | And that kind of started the process.

03:24:32.380 | So finally, almost a year later,

03:24:36.620 | I'm in New York in this event,

03:24:40.340 | and the night before, I'm in my hotel room,

03:24:43.980 | and I was like, "Okay, what am I going to talk about tomorrow?"

03:24:46.500 | And I take a piece of paper just to,

03:24:48.180 | you know, my usual preparation for things.

03:24:50.980 | And then suddenly I have this vision

03:24:53.420 | that I will walk up to the microphone tomorrow,

03:24:55.900 | and I will just start crying.

03:25:00.820 | And I was like, by that time, I already had an insight

03:25:05.820 | that it's possible to have that kind of a splitting,

03:25:09.980 | kind of dissociation.

03:25:11.100 | But things were happening quickly.

03:25:14.900 | There was someone in my life who explained to me this idea

03:25:16.980 | that some things are under the radar of awareness,

03:25:20.980 | but they may still influence you,

03:25:23.260 | and a lot of that could be connected

03:25:25.900 | to some experiences in your childhood.

03:25:29.420 | So I was kind of ready for it from different angles,

03:25:32.860 | but I was so surprised because I was like,

03:25:35.420 | "What is there to remember?

03:25:36.420 | "I know, I know everything."

03:25:38.500 | So then my inner voice says,

03:25:39.980 | "All right, then, you have nothing to worry about.

03:25:42.460 | "We'll go tomorrow, and you will speak about this.

03:25:46.220 | "And if you start crying, it's not a problem."

03:25:48.700 | And I was like, "No, I don't want to cry in front of people.

03:25:51.980 | "I want to find out what it is, what happened."

03:25:54.900 | And I sat on my bed, closed my eyes, and it came.

03:25:59.700 | So it's hard to describe.

03:26:03.140 | So this is what, and the sheer energy of it,

03:26:07.940 | and how much effort it took to suppress it, actually,

03:26:10.700 | for all these years, how much effort it took

03:26:13.300 | to build that panzer, I want to say in Russian,

03:26:17.020 | you know, that hardcore around myself.

03:26:20.380 | So that, and the thing, later I realized

03:26:23.500 | there were moments when it could come out.

03:26:26.420 | And for instance, I developed this fear of public speaking.

03:26:31.020 | All kinds of little things that I now feel were connected.

03:26:35.140 | So anyway, I saw what happened now

03:26:37.940 | through the eyes of that child.

03:26:39.860 | I saw how difficult it was, how crushed he was.

03:26:43.020 | And it looked completely hopeless.

03:26:46.020 | And I felt like, what's the point of living now for me,

03:26:48.660 | now that I know how cruel this world is,

03:26:52.300 | which I didn't realize before,

03:26:53.460 | because I prefer to wear this pink,

03:26:55.980 | you know, the rose-colored glasses.

03:26:59.180 | But then something happened, it's so strange.

03:27:03.300 | It's like you feel that inside of you

03:27:05.900 | there is this dead child.

03:27:07.660 | And it is incredibly sad.

03:27:09.500 | I mean, it's like, I can't even describe it.

03:27:13.780 | But suddenly he comes alive.

03:27:15.620 | And suddenly it's like, oh, he's here.

03:27:19.140 | And I had a little talk with him,

03:27:20.820 | and I said, "Look, I know, and now I thank you.

03:27:23.380 | "I'm so sorry that I neglected you for so long.

03:27:27.300 | "I didn't know.

03:27:29.100 | "I thank you for doing this."

03:27:32.060 | And it's almost like, I felt like the image came to mind

03:27:35.380 | is like a fallen soldier,

03:27:36.620 | like you leave a fallen soldier on the battlefield,

03:27:39.300 | a wounded soldier,

03:27:40.580 | and then you come back to take him with you.

03:27:44.500 | And I said, "But look, look what we have done.

03:27:47.940 | "Look at us now."

03:27:49.500 | It was not in vain.

03:27:51.020 | We are doing okay.

03:27:52.260 | And it's kind of almost just like holding,

03:27:56.420 | holding, holding that child

03:28:00.420 | and that sense of who I am, you know,

03:28:05.140 | and feeling it.

03:28:06.700 | So the next day I went to the microphone

03:28:11.100 | and I let him speak for the first time

03:28:12.940 | about his experience in his own voice.

03:28:17.060 | It was incredible.

03:28:17.980 | People were crying and afterwards came up to me

03:28:21.180 | and started sharing stories and so on.

03:28:22.980 | Because it is a story, it's a universal story.

03:28:25.300 | It's archetypal story.

03:28:27.260 | It's the story of rejection and being treated unfairly.

03:28:32.260 | We all know it.

03:28:35.140 | And I think it's so important to realize

03:28:38.060 | that it's possible to revisit those moments.

03:28:41.980 | It's possible to reconnect to our little ones.

03:28:44.780 | It's possible to bring them back.

03:28:47.340 | And we are better for it

03:28:49.580 | because this changed my life, this experience.

03:28:53.060 | Then suddenly it's like a floodgates.

03:28:55.340 | There were many other things that came.

03:28:58.100 | That's when I became interested

03:29:00.940 | in the dimensions of imagination and intuition and so on.

03:29:04.300 | Because suddenly I realized that I was deprived

03:29:07.140 | of that possibility of looking at the world

03:29:09.500 | through the eyes of a child

03:29:10.340 | because that child was frozen in time.

03:29:13.220 | I was not connected to him.

03:29:15.180 | But suddenly he's with me

03:29:17.140 | and he's like, almost like opens his doors

03:29:20.740 | and he says, "Look at this, look at this."

03:29:24.380 | So.

03:29:29.980 | - If I could ask you about, there's a difficult idea here.

03:29:36.140 | There's a tension.

03:29:37.460 | I've interacted with a few folks in my personal life

03:29:41.060 | and in general that have lived through this experience

03:29:45.020 | of unfairness and cruelty in the world as young people.

03:29:50.020 | And what wisdom do you draw from the action you took

03:29:56.980 | of not acknowledging that you're a victim to cruelty

03:30:04.140 | but instead just working your ass off, working harder?

03:30:07.040 | And then the flip side of that

03:30:12.180 | is you eventually reconnecting

03:30:14.500 | with the cruelty that you experienced.

03:30:16.500 | Because if you did that early on--

03:30:18.580 | - I was not ready for it.

03:30:19.420 | It is a defense mechanism.

03:30:21.020 | You know, there were kids who commit suicide

03:30:24.420 | after this experience.

03:30:25.580 | I could have committed suicide because it's too much.

03:30:28.180 | And it is well known afterwards, of course,

03:30:31.020 | I became aware of all the literature

03:30:32.820 | about childhood trauma and so on.

03:30:36.340 | And I've been speaking publicly about it since then too.

03:30:40.940 | And so, it is a well-known issue

03:30:44.500 | and a well-known kind of a universal phenomenon.

03:30:49.500 | I think that, interestingly enough,

03:30:53.220 | even though now I see a lot of discussion of it,

03:30:56.780 | now that my eyes are open,

03:30:58.380 | but somehow before I didn't see it.

03:31:01.220 | Which also shows you how our confirmation bias,

03:31:04.020 | kind of like how we screen ourselves,

03:31:06.140 | how we turn a blind eye to things

03:31:07.760 | which do not confirm our views

03:31:09.060 | or for which we are not yet ready.

03:31:10.540 | And by the way, nobody should push to do it too soon.

03:31:13.620 | I'm glad I developed certain strength.

03:31:18.620 | I was confident.

03:31:20.820 | I was strong to withstand this.

03:31:25.140 | And if I weren't, who knows how it could turn out.

03:31:28.420 | So it is a very subtle kind of alchemical process,

03:31:31.900 | which I don't think there is a recipe, there's a formula.

03:31:35.380 | The reason I'm talking about this

03:31:38.180 | is just to share this experience

03:31:40.340 | because I think that the only thing we can do in this,

03:31:43.180 | in some sense, is to share with each other.

03:31:45.440 | Because then we can find, for instance,

03:31:49.300 | if somebody shared with me,

03:31:52.740 | it would naturally lead me maybe to get closer to that,

03:31:55.580 | to kind of understanding.

03:31:57.180 | It's really just personal stories.

03:31:59.220 | It's not, obviously there is a component

03:32:04.220 | where professionals could be involved,

03:32:06.740 | professional therapists and so on.

03:32:08.540 | In my case, it somehow happened miraculously.

03:32:11.540 | Well, I did have support,

03:32:12.940 | but not from professional therapists,

03:32:15.380 | but from dear friends.

03:32:17.340 | So I did have, you do need,

03:32:19.340 | I had somebody at the time who basically held my hand

03:32:22.500 | and through this experience, yes, it was invaluable

03:32:25.220 | and it could not be done otherwise.

03:32:26.980 | So I think it's very common.

03:32:30.580 | And here's the thing.

03:32:35.620 | I would not do it any other way.

03:32:39.700 | When I reconnected and I saw all the horrors and so on,

03:32:44.700 | but I also was able to see that my examiners

03:32:49.060 | were victims of their own situation,

03:32:54.060 | that they fell for this bogus theories,

03:32:58.420 | or maybe it was more of an issue

03:33:00.340 | of career advancement or something.

03:33:02.540 | And I also realized they must have suffered,

03:33:05.520 | as well, because they must have had

03:33:07.500 | some kind of consciousness about it,

03:33:10.420 | that acting this way towards sort of basically kids.

03:33:14.600 | So it wasn't pretty from their point of view.

03:33:17.900 | So I could forgive them.

03:33:19.340 | And I could also appreciate

03:33:23.020 | what a boost of energy it gave me.

03:33:27.140 | If I was accepted and I was just where,

03:33:29.820 | I was a first year student,

03:33:31.500 | I would live in a dorm because I was in,

03:33:33.980 | you know, I'd be probably partying and drinking,

03:33:36.440 | and who knows what,

03:33:37.580 | maybe I wouldn't even become a mathematician.

03:33:40.020 | But this focused me like a laser

03:33:43.800 | without me even thinking about it.

03:33:45.460 | It just happened.

03:33:46.500 | I didn't care about anything but doing mathematics.

03:33:50.100 | And it paid off.

03:33:51.180 | You know, it changed my life.

03:33:52.540 | So was it good or bad?

03:33:54.180 | Paradox.

03:33:56.500 | (laughing)

03:33:57.860 | - Seems like life is full of those.

03:33:59.560 | You said you lost your father four years ago.

03:34:03.620 | - Yeah.

03:34:04.980 | - What have you learned about life from your dad?

03:34:08.380 | - That's another big one.

03:34:10.140 | Yeah, because I was very close to him.

03:34:12.100 | And it was tough, it was tough.

03:34:15.860 | And I was not,

03:34:17.660 | I was sort of not ready for it

03:34:21.980 | because up until that point,

03:34:23.500 | I lived pretending that death does not exist.

03:34:26.100 | When my grandparents died,

03:34:29.060 | I was already in the US.

03:34:31.260 | So it was very convenient.

03:34:32.660 | And I couldn't go back, so I grieved.

03:34:35.460 | But it kind of was a bit abstract for me.

03:34:38.300 | I didn't see their dead bodies, you know?

03:34:39.940 | I didn't bury them and so on.

03:34:43.580 | So I waited till the,

03:34:46.380 | so the first death in my life was my father,

03:34:49.500 | like of really close loved ones.

03:34:52.220 | And I was absolutely devastated.

03:34:53.860 | You know, he was such an amazing creature,

03:34:58.020 | such an amazing human being.

03:34:59.220 | He was the kindest, the smartest,

03:35:01.820 | the most funny, just really funny.

03:35:05.140 | And just really fun to be with, you know?

03:35:07.780 | This is what I miss, obviously.

03:35:09.220 | I mean, I would just love to hang out with him.

03:35:12.380 | So, and then suddenly he's not there.

03:35:15.580 | So it was tough, but it kind of changed my perspective.

03:35:19.260 | - You miss him?

03:35:20.540 | - I miss him tremendously.

03:35:21.860 | I miss him tremendously.

03:35:25.060 | But in a way, I learned that he never left me.

03:35:28.660 | I mean, it sounds so,

03:35:30.580 | the words are so, you know, like,

03:35:32.420 | they are,

03:35:33.260 | you cannot express in words this,

03:35:37.020 | what I'm trying to say.

03:35:38.860 | But--

03:35:40.380 | - Do you carry him with you?

03:35:42.860 | - Yeah.

03:35:43.980 | And in some sense, I always did.

03:35:45.740 | I saw that, that it's always been,

03:35:51.380 | it was really, we were one in some sense, you know?

03:35:56.740 | But there was this experience of,

03:35:59.140 | two people being together,

03:36:04.540 | and that I miss tremendously.

03:36:06.540 | But he gave me so much.

03:36:09.740 | And, you know, let me tell you one aspect of it,

03:36:12.820 | for instance.

03:36:13.660 | When he was a kid, his father was sent to Gulag

03:36:17.780 | on bogus pretenses, right?

03:36:19.300 | So he, when he was 16, he applied to a university.

03:36:22.860 | He wanted to become a theoretical physicist.

03:36:25.180 | By the way, my love for theoretical physics

03:36:26.780 | was to a large extent because of that.

03:36:30.420 | And he was not accepted, even though he was brilliant,

03:36:33.180 | because he was the son of the enemy of the people.

03:36:35.700 | And he,

03:36:37.940 | it kind of broke him, this experience,

03:36:41.380 | that he didn't care when he was,

03:36:44.940 | he went to a technical school,

03:36:46.100 | and he didn't really care.

03:36:47.180 | That's my take on it.

03:36:48.540 | And then he ended up in this little provincial town,

03:36:53.460 | and he thought he would escape from it as soon as possible.

03:36:55.580 | And then he met my mother, and they fell in love.

03:36:57.980 | (laughs)

03:37:00.060 | And so I am sort of the product of that, you know?

03:37:04.380 | - Of physics.

03:37:05.220 | - But then what I learned is that

03:37:07.620 | because he was not able to overcome

03:37:11.140 | that specific experience,

03:37:13.620 | it fell to me to do it.

03:37:15.260 | And if I didn't, my son or my daughter would have.

03:37:18.580 | I think that that was one of the things I learned,

03:37:21.300 | that it was not by chance,

03:37:22.580 | that about the same age, for slightly different reasons,

03:37:27.020 | I was subjected to the same kind of unfairness and cruelty.

03:37:30.380 | And in some ways, I feel like I did it for him also.

03:37:35.060 | Because he was also always so proud of me,

03:37:38.420 | and was so happy.

03:37:39.740 | And I had this tremendous gift.

03:37:42.700 | Twice, I was invited by American Mathematical Society

03:37:46.260 | to give these big lectures, twice.

03:37:48.380 | It was in 2012 and in 2018.

03:37:52.420 | And both times, they were in Boston.

03:37:54.620 | It could be anywhere in the US.

03:37:56.340 | Both times, it was in Boston,

03:37:58.260 | walking distance from my parents' place.

03:38:00.860 | So he could be there, and my mom as well.

03:38:02.900 | And that was such a gift, that he was beaming,

03:38:06.660 | you know, like seeing me on the stage.

03:38:08.900 | Like, "Ah!"

03:38:10.420 | So, you know.

03:38:12.860 | - Now that he's no longer here, and it's just you.

03:38:17.980 | - Well, I still have my mom, I still have my sister.

03:38:19.980 | - Yeah, but as a man,

03:38:21.820 | there's some aspect that it's,

03:38:23.700 | that it does hit you hard.

03:38:29.060 | Are you afraid of your own death?

03:38:30.780 | Do you think about your death?

03:38:32.940 | Are you afraid of it?

03:38:34.740 | - I have a certain conceptual view of life and death today,

03:38:38.820 | which is informed by my experiences.

03:38:40.380 | In particular, going through my father's death.

03:38:43.100 | And that is something which cannot be conceptualized.

03:38:48.260 | That experience, like you cannot give it to somebody.

03:38:51.580 | One thing I will say is that I felt that what it was,

03:38:56.620 | it was actually love totally exposed, like naked.

03:39:00.620 | And you try to throw, it is so acute.

03:39:04.620 | So being, facing that love is incredibly painful,

03:39:07.980 | because it's so intense.

03:39:09.940 | When a person is alive, we have conversation,

03:39:14.340 | we have words, we have some actions,

03:39:16.100 | we have some stuff is going on.

03:39:17.700 | And it puts a filter.

03:39:19.020 | So we rarely actually feel love

03:39:22.460 | in this totally, completely pure, unadulterated state.

03:39:26.820 | But when a person dies, it's there.

03:39:28.940 | And it's staring at you,

03:39:30.260 | and no matter what you do, you cannot turn away.

03:39:32.220 | Like, I tried to, it's like,

03:39:33.780 | almost I felt like I wanna throw a blanket over it.

03:39:36.380 | - Yeah.

03:39:37.220 | - It burns, like, immediately.

03:39:39.540 | Like, boom, gone.

03:39:41.140 | It's there.

03:39:41.980 | Live through it.

03:39:44.460 | And I kept saying to myself,

03:39:46.220 | live through it, live through it.

03:39:47.980 | That's how you, and that's how you know,

03:39:49.580 | also learn what is love, for example.

03:39:52.020 | What is it really?

03:39:53.660 | What is love?

03:39:54.500 | What is life, also?

03:39:55.660 | Because I was completely, I had no idea.

03:39:59.300 | And then you kind of learn that, okay,

03:40:02.500 | so maybe it's not quite,

03:40:05.900 | there's more to it.

03:40:08.940 | There is more to it.

03:40:09.940 | There's more to this experience

03:40:11.740 | than what can be put in a concept

03:40:14.380 | or in a sentence, in a,

03:40:18.380 | maybe poetry or music can do some justice to it.

03:40:22.620 | But if so, then my own life has that component,

03:40:26.060 | has that dimension,

03:40:27.740 | which is beyond anything I can say about it, you know?

03:40:31.060 | And even though I love this, being this, playing this role,

03:40:35.300 | I love it.

03:40:36.140 | And I kind of, it kind of makes me feel different

03:40:40.820 | about all kinds of difficulties that arise,

03:40:43.140 | because it's almost like I want to enjoy it,

03:40:46.060 | because that's what being human is.

03:40:48.220 | It's being terrified.

03:40:51.020 | It's being frustrated.

03:40:52.980 | It's being self-loathing sometimes.

03:40:55.900 | It's not knowing, but also being joyful

03:40:59.700 | and just like, ah, let's just enjoy it, kind of all of it.

03:41:04.700 | That's why you came here for, in some sense, you know?

03:41:08.940 | It's like not trying to run away from things,

03:41:12.140 | but kind of trying to just live through them and appreciate.

03:41:15.740 | So the biggest thing is gratitude, in some sense.

03:41:17.940 | It's just gratitude.

03:41:18.780 | So thank you for letting me play.

03:41:20.740 | - It's gratitude for every single moment,

03:41:22.380 | even if it's dark, even if it's lost.

03:41:23.740 | - Yes, and that's why I am so,

03:41:25.900 | people around me, they all say that it's total doom

03:41:28.420 | and gloom and the world is ending.

03:41:30.820 | And I'm like, first of all,

03:41:33.300 | that's how you see it, okay?

03:41:36.060 | That's not the only point of view.

03:41:37.860 | But also, even if it is, that's your challenge.

03:41:40.660 | What are you going to do about it?

03:41:41.860 | Stop complaining about other people.

03:41:43.940 | Do something yourself.

03:41:45.020 | How can you make it a better world, you know?

03:41:48.220 | - And I think all of that starts with just a gratitude

03:41:51.340 | for the moment, to be able to play this game.

03:41:54.140 | - Yeah, how beautiful it is.

03:41:56.380 | - We've talked about love, but let me ask,

03:42:00.740 | what role does love play in this whole game,

03:42:03.580 | in the human condition?

03:42:04.820 | - It's like the glue, you know?

03:42:06.500 | It's like, for me, it's like that.

03:42:07.900 | (both laughing)

03:42:10.180 | And it's not because people say love is like,

03:42:12.940 | for a human being, like a romantic love,

03:42:14.980 | which is a huge component of it, obviously,

03:42:17.220 | because it's so, so beautiful to be able

03:42:19.540 | to express it in this way.

03:42:21.900 | But it could be love for what you do,

03:42:24.700 | for your passion for something, you know?

03:42:27.500 | And, or love for your friends, for instance,

03:42:32.500 | or love, it doesn't have to be.

03:42:36.260 | And so, in some sense, that's what it's all about,

03:42:41.060 | in the ultimate, because living without love,

03:42:44.700 | it's kind of bland, boring, and so--

03:42:49.420 | - And I don't think it's possible for science

03:42:51.140 | to explain exactly what it is.

03:42:53.820 | You can do a evolutionary biology perspective,

03:42:56.860 | you can talk about some kind of sociology perspective,

03:42:59.980 | psychology perspective, but the experience,

03:43:02.420 | the intensity-- - The experience itself.

03:43:03.580 | - Where you forget, where time,

03:43:05.740 | where reminded becomes an illusion,

03:43:07.780 | and everything just freezes. - Oh my God.

03:43:10.700 | - And then, it's kind of beautiful and painful

03:43:13.660 | to hear you say that, when you've experienced love,

03:43:16.660 | the deepest is when you lost it.

03:43:19.080 | - Yes, but in a sense, you can say that

03:43:21.220 | you could not have one without the other.

03:43:23.980 | I could not have that deep connection with my father,

03:43:27.060 | like, really, on so, so many levels,

03:43:30.020 | if there weren't a moment, that's how I see it,

03:43:32.780 | and I'm not trying to say that's how everybody should see.

03:43:34.940 | For instance, I respect Ray Kurzweil,

03:43:37.060 | I respect, and I feel, and I almost like,

03:43:39.180 | I feel good bumps right now.

03:43:41.100 | I feel that desire to reconnect,

03:43:45.860 | even if it is in the form of a computer program,

03:43:51.220 | let's be honest about it.

03:43:52.940 | I find it to be very moving, I find it very moving,

03:43:56.460 | and I understand, because he actually didn't have a chance

03:43:58.460 | to spend much time, I think he was 16 or 17,

03:44:01.620 | he was a teenager when his dad died.

03:44:03.100 | I was lucky, because my father died, I was much older.

03:44:05.660 | I've had so many moments with him, but that's not my thing.

03:44:08.660 | I think it is a feature, it's not a bug,

03:44:12.140 | and it sounds crazy, like, I would love,

03:44:13.940 | I would give anything to have him here right now.

03:44:16.540 | Right now, everything I have, I give it away, right now.

03:44:19.700 | Where do I sign?

03:44:20.740 | Just see him for one hour, I promise you, I will.

03:44:24.500 | But I also know that then I'll still lose him,

03:44:30.060 | or I will die, or whatever, you know, so that thing.

03:44:32.700 | So why is it so worth to just hold on to it?

03:44:36.740 | Why, why are we holding on to this?

03:44:39.060 | And I am the first sucker, I'm the first one to hold on,

03:44:41.560 | but I'm questioning it now.

03:44:43.020 | I'm like, is there another way to approach life

03:44:46.020 | where you just, you know how Buddha is like,

03:44:48.220 | (exhaling)

03:44:50.140 | just let it go, enjoy, and let it go,

03:44:53.460 | enjoy, and let it go, is it possible?

03:44:56.400 | - Accept the paradox of it.

03:44:59.260 | - Well, ask me in a couple of years, you know,

03:45:01.420 | I will report.

03:45:02.660 | But I think that, but to my mathematical mind,

03:45:06.100 | it sounds like a very interesting idea, to be honest.

03:45:09.680 | Because to me, the idea of holding sounds like an impasse.

03:45:14.180 | Because no matter, in all my experience,

03:45:16.180 | and if you look in history, every time somebody's holding,

03:45:19.940 | you know, it's how they said in the Matrix,

03:45:21.420 | whatever has a beginning has an end.

03:45:22.980 | It's like, you cannot go around it.

03:45:24.900 | If you have a beginning, you will have an end.

03:45:27.180 | So then, might as well just enjoy it

03:45:29.820 | and not worry too much about extending it longer.

03:45:32.940 | That's how I see it now,

03:45:34.940 | but maybe tomorrow will be something else, you know?

03:45:36.820 | (laughing)

03:45:38.500 | - Yeah, the rollercoaster of life, the paradox of life.

03:45:41.060 | - Right.

03:45:41.900 | - Edward, you're an incredible human being.

03:45:43.060 | I've been a fan for a long time.

03:45:44.220 | Thank you for writing Love and Math.

03:45:45.620 | Thank you, thank you for being who you are,

03:45:48.480 | being both one of the greatest living mathematicians

03:45:52.060 | and still childlike wanderer of the exploring world.

03:45:57.060 | Exploring how this whole world works,

03:45:59.820 | the nature of the universe.

03:46:01.260 | And thank you so much for speaking with me today.

03:46:03.660 | This is amazing.

03:46:04.540 | - It's been a pleasure, thank you.

03:46:08.040 | - Thanks for listening to this conversation

03:46:09.460 | with Edward Frenkel.

03:46:10.620 | To support this podcast,

03:46:11.780 | please check out our sponsors in the description.

03:46:14.020 | And now, let me leave you with some words

03:46:16.460 | from Sofia Kovalevskaya, a Russian mathematician.

03:46:20.940 | "It is impossible to be a mathematician

03:46:23.520 | "without being a poet in the soul.

03:46:27.040 | "Thank you for listening and hope to see you next time."

03:46:30.140 | (upbeat music)

03:46:32.720 | (upbeat music)

03:46:35.300 | [BLANK_AUDIO]

Edward Frenkel: Reality is a Paradox - Mathematics, Physics, Truth & Love | Lex Fridman Podcast #370

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