YouSaid · the spoken record

Edward Frenkel

lines on the record: 257
first: 2023-04-10
most recent: 2023-04-10
sittings or episodes: 1
sources: podcast

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“Solve a problem. You can't solve a problem, and scrupless teacher says you're an idiot. Sit down and you feel ashamed and lowly. And that stays with you. And so I think that unfortunately, that's where we are. One could dream. And so my dream is that one day we'll be able to overcome this and actually all of these treasures of mathematics.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So I'm just kind of riffing on this. Imagine a world in which this will not be shocking or like, in this case, it's not even shocking because I haven't really explained the details because I can't do it in two minutes. I indicated what this is all about and so on. But imagine a world in which this is not foreign to most people, that most people have seen it before. They're not afraid to approach this type of questions because we talked a little bit about math education, but I really believe that a lot of people in our society not only in the United States, but throughout the world, a lot of people have been traumatized. It's really PTSD. That's why people, when they see mathematical formula or even calculate, you need to calculate tip on a bill. They're terrified because it brings up those memories when they were kids and being called to blackboard.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So boson stars, for example, photons or carriers of other forces, or the Higgs boson. It is called a boson for a reason, because it is a boson in honor of Indian mathematician Bose, B-O-S-E, and Einstein. So these particles obey what's called Bose-Einstein statistics. But then there are other particles called fermions. honor of Enrique Fermi, Italian born mathematician who worked in the US. And they follow what's called Iraq Fermi statistics. And those are electrons and constituents of matter, electrons, protons, neutrons, and so on. And they have a certain duplicity, if you will. And that duplicity is rooted mathematically in this experiment, this little experiment that I have just done. So I imagine, speaking of vegetation, okay?”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“It is magical, okay? Because I'm tricking you. So you start with a bottle like this or a cup. You start twisting it, and at the same time, you twist your arm. Then you come, so this is actually going to rotate at 360 degrees full turn. Then you say, okay, I won't be able to do another turn because then my arm would really get twisted. I'll have to go see a doctor. Yet if I do it second time, it untwists. Is the by one of SO3 is talking about? So, there is something where The first motion is not trivial, but if you double down on it, you come back to the initial position. Very closely connected to the fact that we have elementary particles of two types bosons and fermions.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Diverges goes to infinity because you get a bigger and bigger number, and yet there is a way to make sense of it in which it comes up to minus 1 over 12. How fascinating. First of all, the answer is not even a positive number and it's not an integer, it's not a whole number. It's minus one over 12. So sometimes people ask me, what is your favorite number? And it's a kind of a joke. I say minus 1 over 12. It's actually 42.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“No, let me give my mind. I cannot see, by the way, what you have, so but I can guess some of them. I'm going to try to do something different from him. So, I already mentioned one, which is that you have one-dimensional numerical system, which is real numbers. You have two-dimensional, which is complex numbers. You have four-dimensional. It's probably connected to what he wrote because it has to do with some homotopy groups of spheres and stuff like that. Then, of course, one I love, okay, one plus two plus three plus four Plus five, plus six, and so on. It makes any sense, the sum you probably heard about this one, it became very popular at some point. One plus two plus three, I did a video for number file, the YouTube channel about it maybe 10 years ago. So one plus two plus three plus four plus five ostensibly”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Mathematical formulas cannot be patented, like Einstein could not patent E equals MC squared. It doesn't belong to him because if the formula is correct, then it belongs to everyone.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“A play, so you come out, it's like, Hey, you want to play? You don't talk about what happened. You don't rehash this, you know, just keep going. And sometimes I think we are on the verge, maybe, of learning that Because I think that if we continue to push. Each of us, our set of ideas and ideologies and like. What matters to us and so on, like, yeah, no, no, what matters to you, but there are other ways to approach other people. There are other ways you can find point of contact. Speaking of which, mathematics. Mathematical form Universal, represent universal knowledge. Two plus two is four. Whether you vote for this guy or that guy in the election, you know, how about that as a point of contact of commonality? And nobody can patent those formals. Do you know that? There is a Supreme Court decision.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“And also, it's like. With realizing how much I have screwed up, you know Comes this humility also. So, like, I find it extremely hard now to really lush out at somebody and to say you're horrible, whatever. Because immediately the question is, who am I to criticize? So is there another way to have a dialogue? Is there a way to, speaking, since we talked about the innocence of a child and how much it drives a discovery in science and so on, you know, I remember, I think I heard it was Adyashanti who gave this nice example. He's like, when you're a kid, you know, you go and you play with your friends and then you fight with another kid. And he's like, I hate you. I don't want to see you again. And you just go home after half an hour. Okay, what are you going to do?”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Was it him who was creating sterling the trouble, or was it my mind, you see? And so as I become, as I became self-aware, suddenly other possibilities opened and suddenly that conflict, which by the way, if I kept giving this Nasty talks about him one day, I suppose we'll have a debate, and so you have this one person says this. And what I learned is that it's a never ending. This conflict just does not end But there is an alternative, there is a better way, which is to realize that it is you arguing with yourself. Now, if you want to continue arguing with yourself, Continue as long as you need, just be careful not to destroy too many things in the process. But there is an option of actually dropping it, of actually dropping it. This is so, I was so surprised by this.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“I stopped seeing him in the news. Like before that, I would always see him in the news saying, We're going to put nanobots in your brain by the year 2030 or whatever, you know, and then we upload you to 24. And I would be like, no, you know, the story terrible. Suddenly I didn't see him anymore. So now makes me question who was creating the trouble.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“That's Takes courage and it takes a certain self awareness, I would say, and which brings me, you know, I think the crucial is that which was inscribed, you know, on the temple of Apollo in Delphi. There was a statement, know thyself, know yourself, you know, like, who am I? Ultimately, it boils down to this. And all these debates. And the point is that it's like I used to be, like I said, you know, pessimistic at some point and I was scared even of where development of AI was going. This is about 2014, 2015. And now I'm much more so for instance after I saw Recours as a human being, after I could relate to him and sympathize with him, suddenly.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Then we have a series, then we understand the opposite of it would be not risk closing. Just. Pretending that this is how it's supposed to be in scientific terms, I was replacing your real emotion but come from the heart by some kind of a theory which comes from the mind. And this is where we can go astray because then we become captives of... Frameworks and conceptual systems, which may not be beneficial to our society.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Still, I can't deny that it's a certain leap of faith from his perspective to try to say that this is the way we can all connect to our loved ones. And because it is sincere, and I see it now, it's sincere, and in fact, in your interview, you teased it out of human. I was really moved by it, I have to say. He has mellowed a little bit too, I said. It was really, really sweet when he talked about his father. And I can relate, you know, my father died four years ago. I can relate what a heartbreak I was much older than Ray was when his father died. But I can relate to this longing and that grief, you know. And when somebody is sincere and he puts his... Opens these cards and Says, this is why, that's what I want to do it because I want to recreate my father and want to be able to talk to him this way.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“But I think it's also, it can also be called imagination from his perspective. And look, motivated by that, how much he has brought, how many interesting inventions, like his musical invention, for instance, naturally because his father was a composer, music composer and a conductor. So in other words, in a bigger scheme of things, even if I think he's misguided.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Receive things differently. And so for him, that's his imagination. So, you know, who is this Voltaire, I think, is ascribed to Voltaire. I disagree with you, but I will fight to death for you to have the right to say it. So now that I feel like my position is more like I disagree with him, that this is the way to approach death and to approach the death of loved arm. How we miss them and how Know that sense of loneliness and inability to interact directly. That's not something that resonates with”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“That exemplified all my fears, but as a human being, who a child longing for his father, grieving for his father. So suddenly it became a story, a love story. And, you know, so that is, so in other words, I've seen it in myself. Capacity to project my own fears and then fight with other people over something that actually was my own. And as soon as I got to this point of seeing him and then my next lecture actually I talked about it about him in this way and I said look you know it's a love story and he is actually Um, Not how I would want to reunite with my father. But like you said, if I am consistent, I have to allow the possibility that different people”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Came up to that, and there was a big screen and there was a picture of him there. And I came up to the screen and I kind of touched it with my hand. And I said, but... Don't want to pick on Mr. Kosova because he's me. I had this revelation that I'm actually fighting with myself, with my own fears. And then I learned about his father, that his father died when he was young. And that, in fact, he's very to his credit, he's very sincere and upfront about it. Self-disclosure, I think it's very essential, by the way, in all this discussion. Like, what really motivates you? He said it. He said it publicly many times, even as early as 2015, I could find this information. That he wanted to reunite with his father in the cloud. And suddenly I saw him not as a grey caricature.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“And that's not balance yet. So, balance is when you recognize that it's you actually. And I had this moment actually, and it was so amazing. Like I would give this mean, I would talk about AI and the dangers. And he would always be my foil. You know, I would put a sinister photograph of him on the slide. And it's like, look at this guy, he wants to put nanobolts into your brain, and he's also a top executive at Google and so on. So, I would create this whole narrative. And then something happened where I was giving a lecture. This is 2015 in Aspen Ideas Festival, which is a wonderful festival. So keynote speech, actually. And I was doing my usual stick. And then suddenly I said,”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Kind of awakening moment in a sense, kind of a moment where I suddenly started to see the other side. But I wasn't sure yet.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“I trust that he will not do something. That's not human. That's not right. I just feel that, you know, like there's some people you just kind of feel that they won't cross that line. And that's a huge thing today. Because I have to say, looking back, definitely, I have not heard people personally, but I could be mean, for instance. I could be harsh. And now I see it as a sign of weakness, as a sign of insecurity Know, I saw your interview with Richard Sweil the other day. Beautiful. I was really moved by it. But at some point I was like, I looked at him at this sort of like Dr. Evil. I'm kind of ashamed of it now, but coming clean. And I would, you know, because, well, why? Because I needed an adversary in my mind. Because I projected onto him kind of the fears that I had, that AI will conquer us and so on. And this was rooted in my...”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“They just basically bought into this idea and checked out their humanity at the door. So I would say that antidote to this type of thing is not necessarily even imagination in a kind of elevated sense that we have been discussing today that is exemplified by our greatest scientists. Philosoph But just basic humanity, you know, basic common sense of just like knowing that that's just not right and I don't care what my ideology tells me, but I'm just not going to do it. That I think is kind of missing a little bit into the society. People get a lot too caught up in the ideology, in certain conceptual frameworks.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Humanity also would say, you know, like we talk about imagination as a kind of a counterpoint to knowledge or logic. But just basic humanity, you know, just basic compassion, just being able to. Every destructive, I would say, like every destructive Society, you know, like be it Germany and the Hitler or Soviet Union and there's Stalin and so on was based on some kind of what was considered unassailable truth so kind of a conceptual system you know if you think about it right there is a beautiful episode of this series by Jacob Ranovsky you know Where he talks about, he filmed it in Auschwitz, talking about the certainty that what led the Nazis to killing people wholesale was a certain, it was almost a mathematical idea.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“The way he sort of straddles so many different disciplines. It's like a Very few people like that at any given moment, let alone the 21st century, where information has become so Know huge that it's almost physically impossible to be able to keep track of things. And yet he does and he has his own unique vision and unique point of view and he has integrity, which is like almost impossible. I can't think of so many people who possess that, those qualities. Almost no one.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“I'm here to shock So, first of all, Eric Einstein is a very dear friend, I have to say, and I really, really, really appreciate and love him. He's just like my brother. So, you know, it's interesting to have a question posed by him.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Intersection, yes. But I would say that after the initial shock, you look at the proof of this equation and it actually does make sense. And actually it's nothing but the statement that the circumference of the circle is. And in fact, in this case, it's the circumference of a semicircle is equal to pi. That's where it comes from.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Is an element of surprise in it? How is it possible? We always think of pie. The ratio between the circumference of a circle and its diameter. Here we are taking some number to the power pi not even pi, mind you, but pi multiplied by square root of negative 1. Surely this is something completely incomprehensible, and yet the result is negative one, you see. And if you take e to the power 2 pi i, you get 1 actually one. So, I would guess that in other words, the initial reaction is just that of a surprise, I guess. I guess for anyone. Who first comes across?”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Richard Feynman chose one, which I think one of the best is that if you take E, the base of natural logarithm to the power pi i, so you have e in it, the base of natural logarithm, you have pi i, which is square root of negative 1. The result is negative one. That's up there for sure in the Pantheon of Beautiful Formulas, you know, that I think pretty much every mathematician would agree. I don't know what my favorite one is.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, you see in mathematics, we have this idea that we have an idea of a set, right? So a collection of things. For instance, the set of tables, the set of chairs, and so on outside of microphones, but could be set of numbers. Be set of ideas, could be a set of formulas, mathematical equations, and then we have the notion of an ordered set, ordered, like the set in which there is order, which means that for every two members of the set, we'll say which one is better than the other or greater than the other. For instance, all numbers are ordered. Five is greater than 3, 5 is less than 7, and so on. But not all sets are ordered. So the set of beautiful theorems is not what beautiful equations is not ordered. So, in other words, there are many best equations. And so”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Know in the past hundred years strongly suggesting, if not proving, the existence of what Carl Jung called the personal unconscious and also collective unconscious, the kind of circle of ideas which are under the radar screen, which lead us to some strong emotions and inspire us to act in certain ways, even if we cannot really understand. So if we accept that, then the proposition that somehow everything can still be covered by our actions, which are totally kind of neutral and totally like righteous and totally conscious, that it becomes really tenuous.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“There's some things that they like, there's some things they don't like, which can kind of appear under the radar screen. They may not be aware that they are exercising those biases. That's the point. What you brought up is a very important issue here, not so much issue, but it's not a bug. It's a feature, in my opinion, that implicit in the discussion of the question is thinking computational and so on, is the idea that our conscious awareness covers everything within our psyche. And we just know that that's not the case. All of us have observed other people who have had sort of destructive tendencies. So obviously they did things destructive for themselves. And many of us have observed ourselves to doing that as part of human nature, right? There is great research in analytic psychology and”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So the best explanation I find is from Niels Bohr's complementarity principle. So it is like particle and wave. There are different ways to look at it. And when you look at it in a particular way, another side will be obscured. Think about it like the other side of the moon, you know? So like we are observing the moon from one side and then we don't see the other side. There is a complementary perspective where we see the other side, but not the side we normally see. But the moon is the same. It's still there. It's our limitations of being able to grasp the whole. That's complementarity. And we know that from quantum mechanics that our physical reality is like that rather than being certain rather than being one way or another.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“My mind immediately interprets it in a particular way. But because I know that other people could see it differently, I would then strain my mind and strain my eyes and stare at it and try to see it in a different way. And sometimes I could see it right away and then I could go back and forth between the two. And sometimes it took me a while for some pictures. So in that sense, even if these probabilities exist, they are subjective. Some people immediately see it this way, some people immediately see it that way. And I think that nobody knows, not psychologists, not neuroscientists, not philosophers what to make of it. Best answer, of course, as a scientific mind. Even though I say, no, don't look for interpretation. Leave some place for mysticism or mystery, right? I say that. But of course, I want a theory, I want an explanation.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“A good approach, but also I would say there is no given percentages. For instance, actually at some point I was really curious about it and I looked. And for each picture of this nature, and there are a bunch of them you can easily find online.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Neural network which would be able to decide which one is it the dog or a cat or whatever but sometimes it doesn't have a definite answer So, what do you do then? So, do actually it's a question I actually don't know has modern AI even come to appreciate this question that actually sometimes you can have a picture on which you cannot say what it is in it from one perspective it's a rabbit from another perspective is a duck how are you supposed to train if you have a neural network which is supposed to discriminate between distinguish between ducks and rabbits how is it going to process this you see”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So there are many examples like that where you can perceive things differently and there is no way of saying which is correct and which is not. For instance, You got this, the baz, the Rubens vase, you know, where you have, from one perspective, it's a vase. From another perspective, it's two faces. There is this duck rabbit picture where you can Google it if somebody doesn't know, you can Google it and find it very easy. Actually, Ludwig Wiggenstein devoted several pages duck rabbit in his book. And so on. There are many others that are like squares where you can square you can see from different perspective this way, that way, and so on. So when we talk about neural networks, talking about training. And stuff, and so that you have some pictures, for example, that you feed to your program and you try to find the most optimal”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“99%, maybe we'll be able to describe it with 99 certainty or 99% accuracy. And then maybe, you know. In 100 years or next year, somebody will come up with a different point of view, which suddenly will change our perspective. To this point, I want to say also one thing that I find fascinating speaking of paradoxes and so on. Do you remember how everybody was freaking out about this blue dress? And was it blue or was it black? Was the yell, I think yellow or white, or black and blue. It almost broke Twitter, you know. I remember that.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Deciding once and for all how it is or how it should be, but kind of like accepting it as an open-ended process. I think that's much more valuable in some sense than deciding things one way or another.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“To discover something new, which maybe a computer will not be able to again with a caveat, according to our current understanding, maybe some new technology, some new ideas will be brought into the subject. And the meaning of the word computation, like now we think of computation in a particular framework, turning machines or church thesis and stuff like that. But what if in the future another genius like Alan Turing will come and propose something else, the theory will evolve the way we went from Newton's gravity to Einstein's gravity. Maybe in the framework of that concept some other things will become possible. Know so it's not To me, it's kind of like not so much about”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“So you're right, it's depressing if we are sold on a certain idea from the outset, and then suddenly this doesn't pan out. But okay, to which I retort What if he proved that actually everything can be proved? So then what? What is left to do if you're a mathematician? So that would be depressing to me. Here, there is an opportunity to”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Turing was Alan Turing, who is considered as the father of modern computing, right? So he actually did something very similar. So he had this halting problem that he proved that halting problem cannot be solved algorithmically, that you cannot out of all computer programs, roughly speaking, you cannot have an algorithm of choosing out of all possible computer programs, which ones are meaningful, which ones will halt.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Really incredible. So, this was a revolution 1931, a revolution in logic, revolution in mathematics. We're still feeling the tremors of this discovery.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Depending on its capacity, would produce every true statement. So Geodel's first incompleteness theorem says that that's not the case. And it not just says it, but it proves it at the highest level of rigor that is available in mathematics. That is to say, within another formal system that he was operating in. So, more precisely He proved was that if you have a sufficiently sophisticated formal system, that is to say that you can talk about numbers. Whole numbers in it that you have whole numbers one, two, three, four, you have formalized the operation of addition and multiplication within the system. If it is consistent, that is to say, if it's not completely useless. There will be a true statement in it, which cannot be derived by this linear syntactic process of proving theorems from axioms.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Now think about it. What is special about this process? In this process, you are just manipulating. Symbols You're going from one statement to another without really understanding the meaning of it. So it's an ideal playground for computer program. It's a purely syntactic process where there are some rules, some rigid rules, Of passing from one statement to the next Most mathematicians believed that this way you can produce all true statements. And if this were true, it would give a lot of credibility to the thesis that everything in life is computational. Life is competition because then at least mathematics is computational because then it can be programmed and a computer after sufficient time.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Because if you prove everything, it would mean that it's self contradictory that you prove a statement A and it's negation So that's kind of useless. It has to be discriminating enough. So that it doesn't prove contradictory statements. So there is already a question of that mathematician called consistency. It has to be consistent in the sense that Not self contradictory. And then the idea that was basically prevalent in the world of mathematics by the beginning of the 20th century was that in principle all of mathematics could be derived this way. We just have to find the correct system of axioms and then everything you ever need would be could be produced by this procedure, which is really algorithmic procedure, which actually could be run on a computer.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Those statements you take for granted. And this is where you have a choice. And by making different choices, you actually create different mathematics. After that, there are rules of inference Logical rules such as if A is true and A applies B, then B is true. Most of them were actually introduced already by Aristotle even before Euclid. And then it runs as follows. You have the axioms which are accepted as true statements. Then you have a way to produce new statements. By using the rules of logical inference from the axioms. Every statement you obtain, you call a theorem. You kind of add it to the collection of true statements And then the question is, how far can you go? How many statements can you prove this way? Of course, you want it to be the system to be non-trivial in the sense that you don't prove everything.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“And it was only almost 2000 years later that mathematicians realized that you can't. Not only you cannot derive, but you can actually replace it with its opposite. You'll still get a bona fide consistent, not self contradictory. Which is called non nucleide enjoyment. Which of course sounds very complicated, but it's not. Think of a sphere, just the surface of basketball or the surface of the earth, idealized. The analogs, so you have points, you have analogs of lines which are meridians. Every two meridians intersect. Unlike parallel lines on the flat space. Is also so called hyperbolic plane where the infinitely many lines which do not intersect. So every possibility can be realized. There are different flavors. This is a good illustration of what a formal system is. Start with a set of axioms.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“Is based on axioms and the fact that That there is no unique choice, that there are many choices. And so Euclidean geometry is actually a good illustration of this. Euclid had five axioms. Four of them were kind of obvious, like the one I just mentioned. And the fifth Which came to be known famously as the fifth postulate was that if you have a line and you have a point outside of this line, there is a unique line passing through that point which is parallel to the first line, meaning that doesn't intersect it. And Euclid himself was uncomfortable about this because he felt that it was kind of, he takes for granted something that is not obvious. And for many centuries after that, mathematicians were trying to derive this axiom from other axioms, which were more obvious in some sense. And they failed.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“That it's all sitting on top of is Alan what you know like to say who is watching the watchers. And so, in mathematics, what you see in mathematicians are so clever. It's really kind of like a little game of mirrors. We often like to say, and I used to say that. That mathematics is objective. It's really the only objective science. That's because we hide this fact.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source
“In mathematics, you have to have a seed, so to speak. You have to start with something. And you have to choose certain postulates or statements which you simply take for granted, which do not require proof. Usually they are ones which kind of intuitively clear to you, but in any case, you cannot have any mathematics without choosing those axioms.”
2023-04-10 · Lex Fridman Podcast · #370 – Edward Frenkel: Reality is a Paradox – Mathematics, Physics, Truth & Love · IDENTIFIED FROM THE TRANSCRIPT · source