The following is a conversation with Peter White, a theoretical physicist at Columbia, outspoken critic of string theory, and the author of the popular physics and mathematics blog called Not Even Wrong. This is the Lex Friedman podcast. To support it, please check out our sponsors in the description. And now, here's my conversation with Peter White. You're both a physicist and a mathematician. So let me ask, what is the difference between physics and mathematics? Well, there's kind of a conventional understanding of the subject that they're two quite different things. So that mathematics is about making rigorous statements about these abstract things, things of mathematics, and proving them rigorously. And physics is about doing experiments and testing various models and that. But I think the more interesting thing is that there's a wide variety of what people do as mathematics, what they do as physics, and there's a significant overlap. And that, I think, is actually a very interesting area. And if you go back kind of far enough in history and look at figures like Newton or something, at that point, you can't really tell, was Newton a physicist or a mathematician? Mathematicians will tell you he was a mathematician. The physicists will tell you he was a physicist. But he would say he's a philosopher. Yeah, that's interesting. But yeah, anyway, there was kind of no such distinction then that's more of a modern thing. But anyway, I think these days, there's a very interesting space in between the two. So in the story of the 20th century and the early 21st century, what is the overlap between mathematics and physics, would you say? Well, I think it's actually become very, very complicated. I think it's really interesting to see a lot of what my colleagues in the math department are doing, most of what they're doing, they're doing all sorts of different things, but most of them have some kind of overlap with physics or other. So, I mean, I'm personally interested in one particular aspect of this overlap, which I think has a lot to do with the most fundamental ideas about physics and about mathematics. But you kind of see this really everywhere at this point. Which particular overlap are you looking at, group theory? Yeah, so at least the way it seems to me that if you look at physics and look at our most successful laws of fundamental physics, they have a certain kind of mathematical structure, it's based upon certain kind of mathematical objects and geometry, connections and curvature, the spinners, the Dirac equation. And this very deep mathematics provides kind of a unifying set of ways of thinking that allow you to make a unified theory of physics. But the interesting thing is that if you go to mathematics and look at what's been going on in mathematics the last 50, 100 years, and even especially recently, there's a similarly some kind of unifying ideas which bring together different areas of mathematics and which have been established in the last 50, 100 years. Especially powerful in number theory recently. And there's a book, for instance, by Edward Frankel about love and math. Yeah, that book's great, I recommend it highly. It's partially accessible. But there's a nice audio book that I listened to while running an exceptionally long distance, like across the San Francisco bridge. And there's something magic about the way he writes about it. But some of the group theory in there is a little bit difficult. Yeah, that's the problem with any of these things, to kind of really say what's going on and make it accessible is very hard. He, in this book and elsewhere, I think takes the attitude that kinds of mathematics he's interested in and that he's talking about provide kind of a grand unified theory of mathematics. They bring together geometry and number theory and representation theory, a lot of different ideas in a really unexpected way. But I think, to me, the most fascinating thing is if you look at the kind of grand unified theory of mathematics he's talking about and you look at the physicist kind of ideas about unification, it's more or less the same mathematical objects are appearing in both. So it's this, I think there's a really, we're seeing a really strong indication that the deepest ideas that we're discovering about physics and some of the deepest ideas that mathematicians are learning about are really, are intimately connected. Is there something, like if I was five years old and you were trying to explain this to me, is there ways to try to sneak up to what this unified world of mathematics looks like? You said number theory, you said geometry, words like topology. What does this universe begin to look like? Are these, what should we imagine in our mind? Is it a three dimensional surface? And we're trying to say something about it. Is it triangles and squares and cubes? Like what are we supposed to imagine in our minds? Is this natural number? What's a good thing to try to, for people that don't know any of these tools except maybe some basic calculus and geometry from high school that they should keep in their minds as to the unified world of mathematics that also allows us to explore the unified world of physics. I mean, what I find kind of remarkable about this is the way in which these, we've discovered these ideas, but they're actually quite alien to our everyday understanding. We grow up in this three spatial dimensional world and we have intimate understanding of certain kinds of geometry and certain kinds of things. But these things that we've discovered in both math and physics are, that they're not at all close, have any obvious connection to kind of human everyday experience. They're really quite different. And I can say some of my initial fascination with this when I was young and starting to learn about it was actually exactly this kind of arcane nature of these things. It was a little bit like being told, well, there are these kind of semi mystical experience that you can acquire by a long study and whatever, except that it was actually true. There's actually evidence that this actually works. So I'm a little bit wary of trying to give people that kind of thing, because I think it's mostly misleading. But one thing to say is that geometry is a large part of it. And maybe one interesting thing to say very, that's about more recent, some of the most recent ideas is that when we think about the geometry of our space and time, it's kind of three spatial and one time dimension. It's a physics is in some sense about something that's kind of four dimensional in a way. And a really interesting thing about some of the recent developments and number theory have been to realize that these ideas that we were looking at naturally fit into a context where your theory is kind of four dimensional. So, geometry is a big part of this and we know a lot and feel a lot about two, one, two, three dimensional geometry. So wait a minute, so we can at least rely on the four dimensions of space and time and say that we can get pretty far by working in those four dimensions. I thought you were gonna scare me that we're gonna have to go to many, many, many, many more dimensions than that. My point of view, which goes against a lot of these ideas about unification is that no, this is really, everything we know about really is about four dimensions and that you can actually understand a lot of these structures that we've been seeing in fundamental physics and in number theory, just in terms of four dimensions, that it's kind of, it's in some sense I would claim has been a really, has been kind of a mistake that physicists have made for decades and decades to try to go to higher dimensions, to try to formulate a theory in higher dimensions and then you're stuck with the problem of how do you get rid of all these extra dimensions that you've created because we only ever see anything in four dimensions. That kind of thing leaves us astray, you think? So creating all these extra dimensions just to give yourself extra degrees of freedom. Isn't that the process of mathematics is to create all of these trajectories for yourself but eventually you have to end up at the final place but it's okay to sort of create abstract objects on your path to proving something. Yeah, certainly and from a mathematician's point of view, I mean, the kinds of, mathematicians also are very different than physicists in that we like to develop very general theories. We like to, if we have an idea, we want to see what's the greatest generality in which you can talk about it. So from the point of view of most of the ways geometry is formulated by mathematicians, it really doesn't matter, it works in any dimension. We can do one, two, three, four, any number. There's no particular, for most of geometry, there's no particular special thing about four. But anyway, but what physicists have been trying to do over the years is try to understand these fundamental theories in a geometrical way and it's very tempting to kind of just start bringing in extra dimensions and using them to explain the structure. But typically this attempt kind of founders because you just don't know, you end up not being able to explain why we only see four. It is nice in the space of physics that like if you look at Fermat's last theorem, it's much easier to prove that there's no solution for n equals three than it is for the general case. And so I guess that's the nice benefit of being a physicist is you don't have to worry about the general case because we live in a universe with n equals four in this case. Yeah, physicists are very interested in saying something about specific examples and I find that interesting when I'm trying to do things in mathematics and I'm even teaching courses into mathematics students, I find that I'm teaching them in a different way than most mathematicians because I'm very often very focused on examples on what's kind of the crucial example that shows how this powerful new mathematical technique, how it works and why you would want to do it. And I'm less interested in kind of proving a precise theorem about exactly when it's gonna work and when it's not gonna work. Do you usually think about really simple examples, like both for teaching and when you try to solve a difficult problem, do you construct the simplest possible examples that captures the fundamentals of the problem and try to solve it? Yeah, exactly, that's often a really fruitful way to if you've got some idea to just kind of try to boil it down to what's the simplest situation in which this kind of thing is gonna happen and then try to really understand that and understand that and that is almost always a really good way to get insight into it. Do you work with paper and pen or like, for example, for me coming from the programming side, if I look at a model, if I look at some kind of mathematical object, I like to mess around with it sort of numerically. I just visualize different parts of it, visualize however I can so most of the work is like when you're on networks, for example, is you try to play with the simplest possible example and just to build up intuition by any kind of object has a bunch of variables in it and you start to mess around with them in different ways and visualize in different ways to start to build intuition or do you go the Einstein route and just imagine everything inside your mind and sort of build thought experiments and then work purely on paper and pen? Well, the problem with this kind of stuff I'm interested in is you rarely can kind of, it's rarely something that is really kind of, or even the simplest example, you can kind of see what's going on by looking at something happening in three dimensions. There's generally the structures involved are either they're more abstract or if you try to kind of embed them in some kind of space and where you could manipulate them in some kind of geometrical way, it's gonna be a much higher dimensional space. So even simple examples, the embedding them into three dimensional space, you're losing a lot. Yeah, but to capture what you're trying to understand about them, you have to go to four or more dimensions. So it starts to get to be hard to, I mean, you can train yourself to try it as much as to kind of think about things in your mind and I often use pad and paper and often if I'm in my office, I have to use the blackboard and you are kind of drawing things but they're really kind of more abstract representations of how things are supposed to fit together and they're not really, unfortunately, not just kind of really living in three dimensions where you can. Are we supposed to be sad or excited by the fact that our human minds can't fully comprehend the kind of mathematics you're talking about? I mean, what do we make of that? I mean, to me, that makes you quite sad. It makes it seem like there's a giant mystery out there that we'll never truly get to experience directly. It is kind of sad how difficult this is. I mean, or I would put it a different way that most questions that people have about this kind of thing, you can give them a really true answer and really understand it but the problem is one more of time. It's like, yes, I could explain to you how this works but you'd have to be willing to sit down with me and work at this repeatedly for hours and days and weeks and it's just gonna take that long for your mind to really wrap itself around what's going on and so that does make things inaccessible which is sad but it's just kind of part of life that we all have a limited amount of time and we have to decide what we're gonna spend our time doing. Speaking of a limited amount of time, we only have a few hours, maybe a few days together here on this podcast. Let me ask you the question of amongst many of the ideas that you work on in mathematics and physics, which is the most beautiful idea or one of the most beautiful ideas, maybe a surprising idea and once again, unfortunately, the way life works, we only have a limited time together to try to convey such an idea. Okay, well, actually, let me just tell you something which I'm tempted to kind of start trying to explain what I think is this most powerful idea that brings together math and physics, ideas about groups and representations and how it fits in quantum mechanics but in some sense, I wrote a whole textbook about that and I don't think we really have time to get very far into it so. Well, can I actually, on a small tangent, you did write a paper towards a grant unified theory mathematics and physics, maybe you could step there first, what is the key idea in that paper? Well, I think we've kind of gone over that. I think that the key idea is what we were talking about earlier that just kind of a claim that if you look and see what have been successful ideas in unification in physics and over the last 50 years or so and what's been happening in mathematics and the kind of thing that Frankel's book is about that these are very much the same kind of mathematics and so it's kind of an argument that there really is, you shouldn't be looking to unify just math or just fundamental physics but taking inspiration for looking for new ideas in fundamental physics that they are gonna be in the same direction of getting deeper into mathematics and looking for more inspiration in mathematics from these successful ideas about fundamental physics. Could you put words to sort of the disciplines we're trying to unify? So you said number theory, are we literally talking about all the major fields of mathematics? So it's like the number theory, geometry, so the differential geometry, topology. Yeah, so the, I mean, one name for this that this is acquired in mathematics is the so called Langlands program and so this started out in mathematics. It's that Robert Langlands kind of realized that a lot of what people were doing and that was starting to be really successful in number theory in the 60s and so that this actually was, anyway, that this could be thought of in terms of these ideas about symmetry and groups and representations and in a way that was also close to some ideas about geometry and then more later on in the 80s, 90s, there was something called geometric Langlands that people realize that you could take what people have been doing in number theory in Langlands and get rid, just forget about the number theory and ask what is this telling you about geometry and you get a whole, some new insights into certain kinds of geometry that way. So it's, anyway, that's kind of the name for this area is Langlands and geometric Langlands and just recently in the last few months, there's been, there's kind of really major paper that appeared by Peter Schultze and Laurent Farg where they made some serious advance to try to understand very much kind of a local problem of what happens in number theory near a certain prime number and they turned this into a problem of exactly the kind that geometric Langlands people had been doing, this kind of pure geometry problem and they found by generalizing mathematics, they could actually reformulate it in that way and it worked perfectly well. One of the things that makes me sad is I'm a pretty knowledgeable person and then, what is it? At least I'm in the neighborhood like theoretical computer science, right? And it's still way out of my reach and so many people talk about like Langlands, for example, is one of the most brilliant people in mathematics and just really admire his work and I can't, it's like almost I can't hear the music that he composed and it makes me sad. Yeah, well, I mean, I think unfortunately, it's not just you, it's I think even most mathematicians have no, really don't actually understand what this is about. I mean, the group of people who really understand all these ideas and so for instance, this paper of Schultz and Farg that I was talking about, the number of people who really actually understand how that works is anyway, very, very small and so I think even you find if you talk to mathematicians and physicists, even they will often feel that, there's this really interesting sounding stuff going on and which I should be able to understand, it's kind of in my own field, I have a PhD in but it still seems pretty clearly far beyond me right now. Well, if we can step into the back to the question of beauty, is there an idea that maybe is a little bit smaller that you find beautiful in the space of mathematics or physics? in the space of machine learning, there was a time when they were extremely popular. They became much, much less popular to a point where if you mentioned neural networks, you're getting no funding and you're not going to be respected at conferences. And then once again, neural networks became all the rage about 10, 15 years ago. And as it goes up and down and a lot of people would argue that using terminology like machine learning and deep learning is often misused over general, everything that works is deep learning, everything that doesn't, isn't something like that. That's just the way, again, we're back to sociological things, but I guess what I'm trying to get at is if we leave the sociological mess aside, do we throw out the baby with the bathwater? Is there some, besides the side effects of nice ideas from the Ed Wittons of the world, is there some core truths there that we should stick by in the full beautiful mess of a space that we call string theory, that people call string theory? You're right, it is kind of a common problem that how what you call some field changes and evolves and in interesting ways as the field changes. But I mean, I guess what I would argue is the initial understanding of string theory that was quite specific, we're talking about a specific idea, 10 dimensional super strings compactified to six dimensions. That to my mind, the really bad thing has happened to the subject is that it's hard to get people to admit, at least publicly, that that was a failure, that this really didn't work. And so de facto, what people do is people stop doing that and they start doing more interesting things, but they keep talking to the public about string theory and referring back to that idea and using that as kind of the starting point and as kind of the place where the whole tribe starts and everything else comes from. So the problem with this is that having as your initial name and what everything points back to, something which really didn't work out, it kind of makes everybody, it makes everything, you've created this potentially very, very interesting field with interesting things happening, but people in graduate school take courses on string theory and everything kind of, and this is what you tell the public in which you're continually pointing back. So you're continually pointing back to this idea which never worked out as your guiding inspiration. And it really kind of deforms your whole way of your hopes of making progress. And that's, to me, I think the kind of worst thing that's happened in this field. Okay, sure, so there's a lack of transparency, sort of authenticity about communicating the things that failed in the past. And so you don't have a clear picture of like firm ground that you're standing on. But again, those are sociological things. And there's a bunch of questions I want to ask you. So one, what's your intuition about why the original idea failed? So what can you say about why you're pretty sure it has failed? I mean, the initial idea was, as I try to explain it, it was quite seductive in that you could see why Whitten and others got excited by it. It was, you know, at the time it looked like there were only a few of these possible clobby owls that would work. And it looked like, okay, we just have to understand this very specific model and these very specific six dimensional spaces, and we're going to get everything. And so it was a very seductive idea, but it just, you know, as people learned, worked more and more about it, it just didn't, they just kind of realized that there are just more and more things you can do with these six dimensions and you can't, and this is just not going to work. Meaning like, it's, I mean, what was the failure mode here? Is it, you could just have an infinite number of possibilities that you could do so you can come up with any theory you want, you can fit quantum mechanics, you can explain gravity, you can explain anything you want with it. Is that the basic failure mode? Yeah, so it's a failure mode of kind of that this idea ended up being kind of being essentially empty, that it just doesn't, ends up not telling you anything because it's consistent with just about anything. And so, I mean, there's a complex, if you try and talk with string theorists about this now, I mean, there's an argument, there's a long argument over this about whether, oh no, no, no, maybe there still are constraints coming out of this idea or not. Or maybe we live in a multiverse and everything is true anyway, so you can, there are various ways you can kind of, that string theorists have kind of react to this kind of argument that I'm making, but I try to hold onto it. What about experimental validation? Is that a fair standard to hold before a theory of everything that's trying to unify quantum mechanics and gravity? Yeah, I mean, ultimately, to be really convinced that some new idea about unification really works, you need some kind of, you need to look at the real world and see that this is telling you something true about it. I mean, either telling you that if you do some experiment and go out and do it, you'll get some unexpected result and that's the kind of gold standard, or it may be just that like all those numbers that are, we don't know how to explain, it will show you how to calculate them. I mean, it can be various kinds of experimental validation, but that's certainly ideally what you're looking for. How tough is this, do you think, for a theory of everything, not just string theory, for something that unifies gravity and quantum mechanics, so the very big and the very small? Is this, let me ask you one way, is it a physics problem, a math problem, or an engineering problem? My guess is it's a combination of a physics and a math problem that you really need. It's not really engineering, it's not like there's some kind of well defined thing you can write down and we just don't have enough computer power to do the calculation. That's not the kind of problem it is at all. But the question is, what mathematical tools you need to properly formulate the problem is unclear. So one reasonable conjecture is the way, the reason that we haven't had any success yet is just that we're missing, either we're missing certain physical ideas or we're missing certain mathematical tools, which there are some combination of them, which we need to kind of properly formulate the problem and see that it has a solution that looks like the real world. But those you need, I guess you don't, but there's a sense that you need both gravity, like all the laws of physics to be operating on the same level. So it feels like you need an object like a black hole or something like that in order to make predictions about. Otherwise, you're always making predictions about this joint phenomena or can you do that as long as the theory is consistent and doesn't have special cases for each of the phenomena? Well, your theory should, I mean, if your theory is gonna include gravity, our current understanding of gravity is that you should have, there should be black hole states in it. You should be able to describe black holes in this theory. And just one aspect that people have concentrated a lot on is just this kind of questions about if your theory includes black holes like it's supposed to and it includes quantum mechanics, then there's certain kinds of paradoxes which come up. And so that's been a huge focus of kind of quantum gravity work has been just those paradoxes. So stepping outside of string theory, can you just say first at a high level, what is the theory of everything? What is the theory of everything seek to accomplish? Well, I mean, this is very much a kind of reductionist point of view in the sense that, so it's not a theory. This is not gonna explain to you anything. It doesn't really, this kind of theory, this kind of theory of everything we're talking about doesn't say anything interesting, particularly about like macroscopic objects, about what the weather is gonna be tomorrow, or things are happening at this scale. But just what we've discovered is that as you look at the universe that kind of, if you kind of start, you can start breaking it apart into, and you end up with some fairly simple pieces, quanta, if you like, and which are doing, which are interacting in some fairly simple way. And it's, so what we mean by theory of everything is a theory that describes all the object, all the correct objects you need to describe what's happening in the world and describes how they're interacting with each other at our most fundamental level. How you get from that theory to describing some macroscopic, incredibly complicated thing is, there that becomes, again, more of an engineering problem and you may need machine learning, or you may, you know, a lot of very different things to do it, but. Well, I don't even think it's just engineering. It's also science. One thing that I find kind of interesting talking to physicists is a little bit, there's a, a little bit of hubris. Some of the most brilliant people I know are physicists, both philosophy and just in terms of mathematics, in terms of understanding the world. But there's a kind of either hubris or what would I call it? Like a confidence that if we have a theory of everything, we will understand everything. Like this is the deepest thing to understand. And I would say, and like the rest is details, right? That's the old Rutherford thing. But to me, there's like, this is like a cake or something. There's layers to this thing and each one has a theory of everything. Like at every level from biology, like how life originates, that itself, like complex systems. Like that in itself is like this gigantic thing that requires a theory of everything. And then there's the, in the space of humans, psychology, like intelligence, collective intelligence, the way it emerges among species, that feels like a complex system that requires its own theory of everything. On top of that is things like in the computing space, artificial intelligence systems, like that feels like it needs a theory of everything. And it's almost like once we solve, once we come up with a theory of everything that explains the basic laws of physics that gave us the universe, even stuff that's super complex, like how the universe might be able to originate, even explaining something that you're not a big fan of, like multiverses or stuff that we don't have any evidence of yet. Still, we won't be able to have a strong explanation of why food tastes delicious. Yeah, I know. No, anyway, yeah, I agree completely. I mean, there is something kind of completely wrong with this terminology of theory of everything. It's not, it's really in some sense a very bad term, very hubristic and bad terminology, because it's not, this is explaining, this is a purely kind of reductionist point of view that you're trying to understand a certain very specific kind of things, which in principle, other things emerge from, but to actually understand how anything emerges from this is, it can't be understood in terms of this underlying fundamental theory is gonna be hopeless in terms of kind of telling you what about this, this various emergent behavior. And as you go to different levels of explanation, you're gonna need to develop new, different, completely different ideas, completely different ways of thinking. And I guess there's a famous kind of Phil Anderson's slogan is that, you know, more is different. And so it's just, even once you understand how, what a couple of things, if you have a collection of stuff and you understand perfectly well how each thing is interacting with the others, what the whole thing is gonna do is just a completely different problem. It's just not, and you need completely different ways of thinking about it. What do you think about this? I got to ask you at a few different attempts that a theory of everything, especially recently. So I've been for many years, a big fan of cellular automata of complex systems. And obviously because of that, a fan of Stephen Wolfram's work in that space, but he's recently been talking about a theory of everything through his physics project, essentially. What do you think about this kind of discreet theory of everything like from simple rules and simple objects on the hypergraphs emerges all of our reality where time and space are emergent. Basically everything we see around us is emergent. Yeah, I have to say, unfortunately, I've kind of pretty much zero sympathy for that. I mean, I don't, I spent a little time looking at it and I just don't see, it doesn't seem to me to get anywhere. And it really is just really, really doesn't agree at all with what I'm seeing, this kind of unification of math and physics that I'm kind of talking about around certain kinds of very deep ideas about geometry and stuff. This, if you want to believe that your things are really coming out of cellular automata at the most fundamental level, you have to believe that everything that I've seen my whole career and as beautiful, powerful ideas, that that's all just kind of a mirage, which just kind of randomly is emerging from these more basic, very, very simple minded things. And you have to give me some serious evidence for that and I'm seeing nothing. So Mirage, you don't think there could be a consistency where things like quantum mechanics could emerge from much, much, much smaller, discreet, like computational type systems. I think from the point of view of certain mathematical point of view, quantum mechanics is already mathematically as simple as it gets. It really is a story about really the fundamental objects that you work within when you write down a quantum theory are in some form point of view, precisely the fundamental objects at these deepest levels of mathematics that you're working with, they're exactly the same. So, and cellular automata are something completely different which don't fit into these structures. And so I just don't see why, anyway, I don't see it as a promising thing to do. And then just looking at it and saying, does this go anywhere? Does this solve any problem that I've ever, that I didn't, does this solve any problem of any kind? I just don't see it. Yeah, to me, cellular automata and these hypergraphs, I'm not sure solving a problem is even the standard to apply here at this moment. To me, the fascinating thing is that the question it asks have no good answers. So there's not good math explaining, forget the physics of it, math explaining the behavior of complex systems. And that to me is both exciting and paralyzing. Like we're at the very early days of understanding how complicated and fascinating things emerge from simple rules. Yeah, and I agree. I think that is a truly great problem. And depending where it goes, it may be, it may start to develop some kind of connections to the things that I've kind of found more fruitful and hard to know. It just, I think a lot of that area, I kind of strongly feel I best not say too much about it because I just, I don't know too much about it. And again, we're back to this original problem that your time in life is limited. You have to figure out what you're gonna spend your time thinking about. And that's something I've just never seen enough to convince me to spend more time thinking about. Well, also timing, it's not just that our time is limited, but the timing of the kind of things you think about. There's some aspect to cellular automata, these kinds of objects that it feels like we're very many years away from having big breakthroughs on. And so it's like, you have to pick the problems that are solvable today. In fact, my intuition, again, perhaps biased, is it feels like the kind of systems that, complex systems that cellular automata are, would not be solved by human brains. It feels like something post human that will solve that problem. Or like significantly enhanced humans, meaning like using computational tools, very powerful computational tools to crack these problems open. That's if our approach to science, our ability to understand science, our ability to understand physics will become more and more computational, or there'll be a whole field that's computational in nature, which currently is not the case. Currently, computation is the thing that sort of assists us in understanding science the way we've been doing it all along, but if there's a whole new, I mean, we're from a new kind of science, right? It's a little bit dramatic, but you know, if computers could do science on their own, computational systems, perhaps that's the way they would do the science. They would try to understand the cellular automata, and that feels like we're decades away. So perhaps it'll crack open some interesting facets of this physics problem, but it's very far away. So timing is everything. That's perfectly possible, yeah. Well, let me ask you then, in the space of geometry, I don't know how well you know Eric Weinstein. Oh, quite well, yeah. What are your thoughts about his geometric community and the space of ideas that he's playing with in his proposal for theory of everything? Well, I think that he has, he fundamentally has, I think, the same problems that everybody has had trying to do this, and there are really versions of the same problem that you try to get unity by putting everything into some bigger structure. So he has some other ones that are not so conventional that he's trying to work with, but he has the same problem that even if he can, if he can get a lot farther in terms of having a really well defined, well understood, clear picture of these things he's working with, they're really kind of large geometrical structures of many dimensions of many kinds, and I just don't see any way, he's gonna have the same problem the string theorists have, how do you get back down to the structures of the standard model, and how do you, yeah. So I just, anyway, it's the same, and there's another interesting example of a similar kind of thing is Garrett Leasy's theory of everything. Again, there, it's a little bit more specific than Eric's, he's working with this E8, but it, again, I think all these things found are at the same point, that you don't, you know, you create this unity, but then you have no, you don't actually have a good idea how you're gonna get back to the actual, to the objects we've seen, how are you gonna, you create these big symmetries, how are you gonna break them? And, because we don't see those symmetries in the real world, and so ultimately, there would need to be a simple process for collapsing it to four dimensions. You'd have to explain, well, yeah, I forget in his case, but it's not just four dimensions, it's also these structures you see in the standard model, there's, you know, there's certain very small dimensional groups of symmetries, so called U1, SU2, and SU3, and the problem with, and this has been a problem since the beginning, almost immediately after 1973, about a year later, two years later, people started talking about grand unified theories, so you take the U1, the SU2, and the SU3, and you put them together into this bigger structure called SU5 or SO10, but then you're stuck with this problem that, wait a minute, now how, why does the world not look, why do I not see these SU5 symmetries in the world, I only see these, and so, and I think, you know, the kind of thing that Eric, and all of a sudden Garrett, and lots of people who try to do it, they all kind of found her in that same way, that they don't have a good answer to that. Are there lessons, ideas to be learned from theories like that, from Garrett Leacy's, from Eric's? I don't know, it depends, I have to confess, I haven't looked that closely at Eric's, I mean, he explained this to me personally a few times, and I've looked a bit at his paper, but it's, again, we're back to the problem of a limited amount of time in life. Yeah, I mean, it's an interesting effect, right? Why don't more physicists look at it? I mean, I'm in this position that somehow, you know, I've, people write me emails, for whatever reason, and I've worked in the space of AI, and so there's a lot of people, perhaps AI is even way more accessible than physics, in a certain sense, and so a lot of people write to me with different theories about what they have for how to create general intelligence, and it's, again, a little bit of an excuse, I say to myself, like, well, I only have a limited amount of time, so that's why I'm not investigating it, but I wonder if there's ideas out there that are still powerful, that are still fascinating, and that I'm missing because I'm dismissing them because they're outside of the sort of the usual process of academic research. Yeah, well, I mean, the same thing, and pretty much every day in my email, there's somebody who's got a theory or everything about why all of what physicists are doing, and perhaps the most disturbing thing I should say about being a critic of string theory is that when you realize who your fans are, every day I hear from somebody who says, oh, well, since you don't like string theory, you must, of course, agree with me that this is the right way to think about everything. Oh, no, oh, no, and most of these are, you quickly can see this person doesn't know very much and doesn't know what they're doing, but there's a whole continuum to, people who are quite serious physicists and mathematicians who are making a fairly serious attempt to try to do something, like Eric and Eric, and then your problem is you do try to spend more time looking at it and trying to figure out what they're really doing, but then at some point you just realize, wait a minute, for me to really, really understand exactly what's going on here would just take time I just don't have. Yeah, it takes a long time, which is the nice thing about AI is unlike the kind of physics we're talking about, if your idea is good, that should quite naturally lead to you being able to build a system that's intelligent. So you don't need to get approval from somebody that's saying you have a good idea here. You can just utilize that idea in an engineer system, like naturally leads to engineering. With physics here, if you have a perfect theory that explains everything, that still doesn't obviously lead one, to scientific experiments that can validate that theory, and two, to like trinkets you can build and sell at a store for $5. You can't make money off of it. So that makes it much more challenging. Well, let me also ask you about something that you found, especially recently appealing, which is Roger Penrose's Twister theory. What is it? What kind of questions might it allow us to answer? What will the answers look like? It's only in the last couple of years that I really, really kind of come to really, I think, to appreciate it and to see how to really, I believe to see how to really do something with it. And I've gotten very excited about that the last year or two. I mean, one way of saying one idea of Twister theory is that it's a different way of thinking about what space and time are and about what points in space and time are, which is very interesting that it only really works in four dimensions. So four dimensions behaves very, very specially unlike other dimensions. And in four dimensions, there is a way of thinking about space and time geometry, as well as just thinking about points in space and time. You can also think about different objects, these so called twisters. And then when you do that, you end up with a kind of a really interesting insight that you can formulate a theory, and you can formulate a very, take a standard theory that we formulate in terms of points of space and time, and you can reformulate in this Twister language. And in this Twister language, it's the fundamental objects actually are more kind of the, are actually spheres in some sense, kind of the light cone. So maybe one way to say it, which actually I think is really, is quite amazing. If you ask yourself, what do we know about the world? We have this idea that the world out there is all these different points and these points of time. Well, that's kind of a derived quantity. What we really know about the world is when we open our eyes, what do you see? You see a sphere. And that what you're looking at is you're looking at, a sphere is worth of light rays coming into your eyes. And what Penrose says is that, well, what a point in space time is, is that sphere, that sphere of all the light rays coming in. And he says, and you should formulate your, instead of thinking about points, you should think about the space of those spheres, if you like, and formulate the degrees of freedom as physics as living on those spheres, living on, so you're kind of living on, your degrees of freedom are living on light rays, not on points. And it's a very different way of thinking about physics. And he and others working with him developed a beautiful mathematical formulas and a way to go back from forth between some aspects of our standard way we write these things down and work in the so called twister space. And certain things worked out very well, but they ended up, I think kind of stuck by the 80s or 90s that they weren't a little bit like string theory that they, by using these ideas about twisters, they could develop them in different directions and find all sorts of other interesting things, but they were getting, they weren't finding any way of doing that that brought them back to kind of new insights into physics. And my own, I mean, what's kind of gotten me excited really is what I think I have an idea about that I think does actually work, that goes more in that direction. And I can go on about that endlessly or talk a little bit about it, but that's the, I think that's the one kind of easy to explain insight about twister theory. There are some more technical ones. I should mean, I think it's also very convincing what it tells you about spinners, for instance, but that's a more technical. Well, first let's like linger on the spheres and the light cones. You're saying twisted theory allows you to make that the fundamental object with which you're operating. Yeah. How that, I mean, first of all, like philosophically that's weird and beautiful, maybe because it maps, it feels like it moves us so much closer to the way human brains perceive reality. Yeah. So it's almost like our perception is like the content of our perception is the fundamental object of reality. That's very appealing. Yeah. Is it mathematically powerful? Is there something you can say, can you say a little bit more about what the heck that even means for, because it's much easier to think about mathematically like a point in space time. What does it mean to be operating on the light cone? It uses a kind of mathematics that's relative, that kind of goes back to the 19th century among mathematicians. It's not, anyway, it's a bit of a long story, but one problem is that you have to start, it's crucial that you think in terms of complex numbers and not just real numbers. And this, for most people, that makes it harder to, for mathematicians, that's fine. We love doing that. But for most people, that makes it harder to think about. I think perhaps the most, the way that there is something you can say very specifically about it in terms of spinners, which I don't know if you want to, I think at some point you want to talk, so maybe you can. What are spinners? Let's start with spinners, because I think that if we can introduce that, then I can say it. By the way, twister is spelled with an O and spinner is spelled with an O as well. Yes, okay. In case you want to Google it and look it up, there's very nice Wikipedia pages as a starting point. I don't know what is a good starting point for twister theory. Well, one thing you say about Penrose, I mean, Penrose is actually a very good writer and also a very good draftsman. He's a draftsman, to the extent this is visualizable, he actually has done some very nice drawings. So, I mean, almost any kind of expository thing you can find him writing is a very good place to start. He's a remarkable person. But the, so spinners are something that independently came out of mathematics and out of physics. And to say where they came out of physics, I mean, what people realized when they started looking at elementary particles like electrons or whatever, that there seem to be some kind of doubling of the degrees of freedom going on. If you counted what was there in some sense in the way you would expect it and when you started doing quantum mechanics and started looking at elementary particles, there were seen to be two degrees of freedom, they're not one. And one way of seeing it was that if you put your electron in a strong magnetic field and asked what was the energy of it, instead of it having one energy, it would have two energies, there'd be two energy levels. And as you increase magnetic field, the splitting would increase. So physicists kind of realized that, wait a minute. So we thought when we were doing, first started doing quantum mechanics, that the way to describe particles was in terms of wave functions and these wave functions were complex to complex values. Well, if we actually look at particles, that that's not right. They're pairs of complex numbers. They're pairs of complex numbers. So one of the kind of fundamental, from the physics point of view, the fundamental question is why are all our kind of fundamental particles described by pairs of complex numbers? Just weird. And then you can ask, well, what happens if you like take an electron and rotate it? So how do things move in this pair of complex numbers? Well, now, if you go back to mathematics, what had been understood in mathematics, some years earlier, not that many years earlier, was that if you ask very, very generally, think about geometry of three dimensions and ask, and if you think about things that are happening in three dimensions in the standard way, everything, the standard way of doing geometry, everything is about vectors, right? So if you've taken any mathematics classes, you probably see vectors at some point. They're just triplets of numbers tell you what a direction is or how far you're going in three dimensional space. And most of everything we teach in most standard courses in mathematics is about vectors and things you build out of vectors. So you express everything about geometry in terms of vectors or how they're changing or how you put two of them together and get planes and whatever. But what had been realized that, Rianna, is that if you ask very, very generally, what are the, if you have, what are the things that you can kind of consistently think about rotating? And so you ask a technical question, what are the representations of the rotation group? Well, you find that one answer is they're vectors and everything you build out of vectors, but then people found, but wait a minute, there's also these other things, which you can build out of vectors, but which you can consistently rotate. And they're described by pairs of complex numbers, by two complex numbers. And they're the spinners also. And to make a lot, and to make, and you can think of spinners in some sense as more fundamental than vectors because you can build vectors out of spinners. You can take two spinners and make a vector, but you can't, if you only have vectors, you can't get spinners. So they're in some sense, there's some kind of level of lower level of geometry beyond what we thought it was, which was kind of spinner geometry. And this is something which even to this day, when we teach graduate courses in geometry, we mostly don't talk about this because it's a bit hard to do correctly. If you start with your whole setup is in terms of vectors, describing things in terms of spinners is a whole different ball game. But anyway, it was just this amazing fact that this kind of more fundamental piece of geometry, spinners, and what we were actually seeing, if you look at electron, are one and the same. So it's, I think it's kind of a mind blowing thing, but it's very counterintuitive. What are some weird properties of spinners that are counterintuitive? That there are some things that they do, for instance, if you rotate a spinner around 360 degrees, it doesn't come back towards, it becomes minus what it was. Or, so it's, anyway, so the way rotations work, there's a kind of a funny sign you have to keep track of in some sense. So they're kind of too valued in another weird way. But the fundamental problem is that it's just not, if you're used to visualizing vectors, you just, there's nothing you can do visualizing in terms of vectors that will ever give you a spinner. It just is not gonna ever work. As you were saying that I was visualizing a vector walking along a Mobius strip, and it ends up being upside down. But you're saying that doesn't really capture. So, I mean, what really captures it? The problem is that it's really, the simplest way to describe it is in terms of two complex numbers. And your problem with two complex numbers is that's four real numbers. So your spinner kind of lies in a four dimensional space. So you, that makes it hard to visualize. And it's crucial that it's not just any four dimensions. It's just, it's actually complex numbers. You're really gonna use the fact that these are two complex numbers. So it's very hard to visualize. But to get back to what I think is mind blowing about twisters is that the, another way of saying this idea about talking about spheres, another way of saying the fundamental idea of twister theory is in some sense, the fundamental idea of twister theory is that a point is a two complex dimensional space. So that every, and that it lives inside, the space that it lies inside is twister space. So in the simplest case, it's four, twister space is four dimensional and a point in space time is a two complex dimensional subspace of all the four complex dimensions. And as you move around in space time, you're just moving, your planes are just moving around. Okay. And that, but then the. So it's a plane in a four dimensional space. It's a plane. Complex. Complex plane. So it's two complex dimensions in four complex. Got it. But then to me, the mind blowing thing about this is this then kind of tautologically answers the question is what is a spinner? Well, a spinner is a point. I mean, the space of spinners at a point is the point. In twister theory, the points are the complex two planes. And you want me to, and you're asking what a spinner is. Well, a spinner, the space of spinners is that two plane. So it's, you know, just your whole definition of what a point in space time was just told you what a spinner was. It's, they're just, it's the same thing. Yeah, but we're trying to project that into a three dimensional space and trying to intuit, but you can't. Yeah, so the intuition becomes very difficult, but from, if you don't, not using twister theory, you have to kind of go through a certain fairly complicated rigmarole to even describe spinners to describe electrons. Whereas using twister theory, it's just completely tautological. They're just what you want to describe. The electron is fundamentally the way that you're describing the point in space time already. It's just there, so. Do you have a hope? You mentioned that you found it appealing recently. Is it just because of certain aspects of its mathematical beauty, or do you actually have a hope that this might lead to a theory of everything? Yeah, I mean, I certainly do have such a hope because what I've found, I think the thing which I've done, which I don't think, as far as I can tell, no one had really looked at from this point of view before is, has to do with this question of how do you treat time in your quantum theory? And so there's another long story about how we do quantum theories and about how we treat time in quantum theories, which is a long story. But the short version of it is that what people have found when you try and write down a quantum theory, that it's often a good idea to take your time coordinate, whatever you're using to your time coordinate, and multiply it by the square root of minus one and to make it purely imaginary. And so all these formulas, which you have in your standard theory, if you do that to those, I mean, those formulas have some very strange behavior and they're kind of singular. If you ask even some simple questions, you have to take very delicate singular limits in order to get the correct answer, and you have to take them from the right direction, otherwise it doesn't work. Whereas if you just take time, and if you just put a factor of square root of minus one, wherever you see the time coordinate, you end up with much simpler formulas, which are much better behaved mathematically. And what I hadn't really appreciated until fairly recently is also how dramatically that changes the whole structure of the theory. You end up with a consistent way of talking about these quantum theories, but it has some very different flavor and very different aspects that I hadn't really appreciated. And in particular, the way symmetries act on it is not at all what I originally had expected. And so that's the new thing that I have, or I think gives you something, is to do this move, which people often think of as just kind of a mathematical trick that you're doing to make some formulas work out nicely, but to take that mathematical trick as really fundamental. And it turns out in Twister theory allows you to simultaneously talk about your usual time and the time times the square root of minus one, they both fit very nicely into Twister theory. And you end up with some structures which look a lot like the standard models. Well, let me ask you about some Nobel prizes. Okay. Do you think there will be, there was a bet between Michio Kaku and somebody else about. John Horgan. John Horgan about, by the way, maybe discover a cool website, longbets.com or.org. Better, yeah, yeah. Yeah, it's cool. It's cool that you can make a bet with people and then check in 20 years later. I really love it. There's a lot of interesting bets on there. I would love to participate, but it's interesting to see, time flies and you make a bet about what's going to happen in 20 years. You don't realize 20 years just goes like this. And then you get to face out and you get to wonder what was that person? What was I thinking? That person 20 years ago was almost like a different person. What was I thinking back then to think that? It's interesting. So let me ask you this on record, 20 years from now or some number of years from now, do you think there will be a Nobel Prize given for something directly connected to a first broadly theory of everything? And second, of course, one of the possibilities, one of them, string theory? String theory, definitely not. Things have gone, yeah. So if you were giving financial advice, you would say not to bet on that? No, do not. And even, I actually suspect if you ask string theorists that question, you're gonna get a few of them saying, I mean, if you'd asked them that question 20 years ago, again, when Kaku was making this bet or whatever, I think some of them would have taken you up on it. And certainly back in 1984, a bunch of them would have said, oh, sure, yeah. But now I get the impression that even they realize that things are not looking good for that particular idea. Again, it depends what you mean by string theory, whether maybe the term will evolve to mean something else, which will work out. But I don't think that's not gonna like it to work out, whether something else. I mean, I still think it's relatively unlikely that you'll have any really successful theory of everything. And the main problem is just the, it's become so difficult to do experiments at higher energy that we've really lost this ability to kind of get unexpected input from experiment. And you can, while it's maybe hard to figure out what people's thinking is gonna be 20 years from now, looking at high energy particle, high energy colliders and their technology, it's actually pretty easy to make a pretty accurate guess what you're gonna be doing 20 years from now. And I think actually, I would actually claim that it's pretty clear where you're gonna be 20 years from now. And what it's gonna be is you're gonna have the LHC, you're gonna have a lot more data, an order of magnitude or more data from the LHC, but at the same energy. You're not gonna see a higher energy accelerator operating successfully in the next 20 years. And like maybe machine learning or great sort of data science methodologies that process that data will not reveal any major shifts in our understanding of the underlying physics, you think? I don't think so. I mean, I think that field, my understanding is they're starting to make a great use of those techniques, but it seems to look like it will help them solve certain technical problems and be able to do things somewhat better, but not completely change the way they're looking at things. What do you think about the potential quantum computers simulating quantum mechanical systems and through that sneak up to sort of through simulation, sneak up to a deep understanding of the fundamental physics? The problem there is that that's promising more for this, for Phil Anderson's problem, that if you wanna, there's lots and lots of, you start putting together lots and lots of things and we think we know they're pair by pair interactions, but what this thing is gonna do, we don't have any good calculational techniques. Quantum computers may very well give you those. And so they may, what we think of is kind of a strong coupling behavior. We have no good way to calculate. Even though we can write down the theory, we don't know how to calculate anything with any accuracy and the quantum computer may solve that problem. But the problem is that I don't think that they're gonna solve the problem that they help you with the problem of not having the, of knowing what the right underlying theory is. As somebody who likes experimental validation, let me ask you the perhaps ridiculous sounding, but I don't think it's actually a ridiculous question of do you think we live in a simulation? Do you find that thought experiment at all useful or interesting? Not really, I don't, it just doesn't. Yeah, anyway, to me, it doesn't actually lead to any kind of interesting, lead anywhere interesting. Yeah, to me, so maybe I'll throw a wrench into your thing. To me, it's super interesting from an engineering perspective. So if you look at virtual reality systems, the actual question is how much computation and how difficult is it to construct a world that like there are several levels here. One is you won't know the difference, our human perception systems and maybe even the tools of physics won't know the difference between the simulated world and the real world. That's sort of more of a physics question. The most interesting question to me has more to do with why food tastes delicious, which is create how difficult and how much computation is required to construct a simulation where you kind of know it's a simulation at first, but you want to stay there anyway. And over time, you don't even remember. Yeah, well, anyway, I agree, these are kind of fascinating questions and they may be very, very relevant to our future as a species, but yeah, they're just very far from anything I think. Well, so from a physics perspective, it's not useful to you to think, taking a computational perspective to our universe, thinking of it as an information processing system and then they give it as doing computation and then you think about the resources required to do that kind of computation and all that kind of stuff. You could just look at the basic physics and who cares what the computer it's running on is. Yeah, it just, I mean, the kinds of, I mean, I'm willing to agree that you can get into interesting kinds of questions going down that road, but they're just so different from anything from what I've found interesting and I just, again, I just have to kind of go back to life is too short and I'm very glad other people are thinking about this, but I just don't see anything I can do with it. What about space itself? So I have to ask you about aliens. Again, something, since you emphasize evidence, do you think there is, how many, do you think there are and how many intelligent alien civilizations are out there? Yeah, I have no idea, but I have certainly, as far as I know, unless the government's covering it up or something, we haven't heard from, we don't have any evidence for such things yet, but there seems to be no, there's no particular obstruction why there shouldn't be, so. I mean, do you, you work on some fundamental questions about the physics of reality. When you look up to the stars, do you think about whether somebody's looking back at us? Yes, yeah, well, actually, I originally got interested in physics. I actually started out as a kid interested in astronomy, exactly that, and a telescope and whatever that, and certainly read a lot of science fiction and thought about that. I find over the years, I find myself kind of less, anyway, less and less interested in that one, just because I don't really know what to do with them. I also kind of, at some point, kind of stopped reading science fiction that much, kind of feeling that there was just too, that the actual science I was kind of learning about was perfectly kind of weird and fascinating, and unusual enough, and better than any of the stuff that Isaac Asimov, so why should I? Yeah, and you can mess with the science much more than the distant science fiction, the one that exists in our imagination or the one that exists out there among the stars. Well, you mentioned science fiction. You've written quite a few book reviews. I gotta ask you about some books, perhaps, if you don't mind. Is there one or two books that you would recommend to others and maybe if you can, what ideas you drew from them? Either negative recommendations or positive recommendations. Do not read this book for sure. Well, I must say, I mean, unfortunately, yeah, you can go to my website and you can click on book reviews and you can see I've written, read a lot of, a lot of, I mean, as you can tell from my views about string theory, I'm not a fan of a lot of the kind of popular books about, oh, isn't string theory great? And yes, I'm not a fan of a lot of things of that kind. Can I ask you a quick question on this, a small tangent? Are you a fan, can you explore the pros and cons of, if I get string theory, sort of science communication, sort of Cosmos style communication of concepts to people that are outside of physics, outside of mathematics, outside of even the sciences and helping people to sort of dream and fill them with awe about the full range of mysteries in our universe? That's a complicated issue. You know, I think, you know, I certainly go back and go back to like what inspired me and maybe to connect it a little bit to this question about books. I mean, certainly when the books, some books that I remember reading when I was a kid were about the early history of quantum mechanics, like Heisenberg's books that he wrote about, you know, kind of looking back at telling the history of what happened when he developed quantum mechanics. It's just kind of a totally fascinating, romantic, great story, and those were very inspirational to me. And I would think maybe other people might also find them that, but the... And that's almost like the human story of the development of the ideas. Yeah, the human story, but yeah, just also how, you know, there are these very, very weird ideas that didn't seem to make sense, and how they were struggling with them and how, you know, they actually... Anyway, it's, I think it's the period of physics kind of beginning, you know, 1905 with Planck and Einstein and ending up with the war when these things get used to, you know, make massively destructive weapons. It's just the truly amazing... And so many, so many new ideas. Let me, on another, a tangent on top of a tangent on top of a tangent, ask, if we didn't have Einstein, so how does science progress? Is it the lone geniuses? Or is it some kind of weird network of ideas swimming in the air and just kind of the geniuses pop up to catch them and others would anyway? Without Einstein, would we have special relativity, general relativity? I mean, it's an interesting case to case basis. I mean, special relativity, I think we would have had, I mean, there are other people. Anyway, you could even argue that it was already there in some form in some ways, but I think special relativity you would have had without Einstein fairly quickly. General relativity, that was a much, much harder thing to do and required a much more effort, much more sophisticated. That I think you would have had sooner or later, but it would have taken quite a bit longer. That took a bunch of years to validate scientifically, the general relativity. But even for Einstein, from the point where he had kind of a general idea of what he was trying to do to the point where he actually had a well defined theory that you could actually compare to the real world, that was, I forget the number of the order of magnitude, 10 years of very serious work. And if he hadn't been around to do that, it would have taken a while before anyone else got around to it. On the other hand, there are things like, with quantum mechanics, you have Heisenberg and Schrodinger came up with two, which ultimately equivalent, but two different approaches to it within months of each other. And so if Heisenberg hadn't been there, you already would have had Schrodinger or whatever. And if neither of them had been there, it would have been somebody else a few months later. So there are times when the, just the, a lot often is the combination of the right ideas are in place and the right experimental data is in place to point in the right direction. And it's just waiting for somebody who's gonna find it. Maybe to go back to your aliens, I guess the one thing that I often wonder about aliens is, would they have the same fundamental physics ideas as we have in mathematics? Would their math, you know, would they, you know, how much is this really intrinsic to our minds? If you start out with a different kind of mind when you end up with a different ideas of what fundamental physics is or what the structure of mathematics is. So this is why, like if I was, you know, I like video games, the way I would do it as a curious being, so first experiment I'd like to do is run Earth over many thousands of times and see if our particular, no, you know what? I wouldn't do the full evolution. I would start at Homo sapiens first and then see the evolution of Homo sapiens millions of times and see how the ideas of science would evolve. Like, would you get, like how would physics evolve? How would math evolves? I would particularly just be curious about the notation they come up with. Every once in a while I would like throw miracles at them to like, to mess with them and stuff. And then I would also like to run Earth from the very beginning to see if evolution will produce different kinds of brains that would then produce different kinds of mathematics and physics. And then finally, I would probably millions of times run the universe over to see what kind of, what kind of environments and what kind of life would be created to then lead to intelligent life, to then lead to theories of mathematics and physics and to see the full range. And like, sort of like Darwin kind of mark, okay. It took them, what is it, several hundred million years to come up with calculus. I would just like keep noting how long it took and get an average and see which ideas are difficult, which are not and then conclusively sort of figure out if it's more collective intelligence or singular intelligence that's responsible for shifts and for big phase shifts and breakthroughs in science. If I was playing a video game and ran, I got a chance to run this whole thing. Yeah, but we're talking about books before I distracted us horribly. About books, okay, so books, yeah, go back, books. Yeah, so and then, yeah, so that's one thing I'd recommend is the books about the, from the original people, especially Heisenberg about the, how that happened. And there's also a very, very good kind of history of the kind of what happened during this 20th century in physics and up to the time of the Standard Model in 1973. It's called The Second Creation by Bob Kreis and Mann. That's one of the best ones. I know that's, but the one thing that I can say is that, so that book, I think, I forget when it was, late 80s, 90s. The problem is that there just hasn't been much that's actually worked out since then. So most of the books that are kind of trying to tell you about all the glorious things that have happened since 1973 are, they're mostly telling you about how glorious things are, which actually don't really work. And it's really, the argument people sometimes make in favor of these books as well, oh, they're really great because you want to do something that will get kids excited. And then, so they're getting excited about things, something that's not really quite working. It doesn't really matter, the main thing is get them excited. The other argument is, wait a minute, if you're getting people excited about ideas that are wrong, you're really kind of, you're actually kind of discrediting the whole scientific enterprise in a not really good way. So there's this problem. So my general feeling about expository stuff is, yeah, it's to the extent you can do it kind of honestly and, well, that's great. There are a lot of people doing that now, but to the extent that you're just trying to get people excited and enthusiastic by kind of telling them stuff, which isn't really true, you really shouldn't be doing that. You obviously have a much better intuition about physics. I tend to, in the space of AI, for example, you could use certain kinds of language, like calling things intelligent that could rub people the wrong way. But I never had a problem with that kind of thing, saying that a program can learn its way without any human supervision as AlphaZero does to play chess. To me, that may not be intelligence, but it sure as heck seems like a few steps There's an idea that I kind of went, got a physics PhD and spent a lot of time learning about mathematics and I guess it was embarrassing that I hadn't really actually understand this very simple idea until I kind of learned it when I actually started teaching math classes, which is maybe that there's a simple way to explain kind of the fundamental way in which algebra and geometry are connected. So you normally think of geometry as about these spaces and these points and you think of algebra as this very abstract thing about these abstract objects that satisfy certain kinds of relations, you can multiply them and add them and do stuff but it's completely abstract, there's nothing geometric about it but the kind of really fundamental idea is that unifies algebra and geometry is to think whenever anybody gives you what you call an algebra, some abstract thing of things that you can multiply and add that you should ask yourself, is that algebra the space of functions on some geometry? So one of the most surprising examples of this, for instance, is a standard kind of thing that seems to have nothing to do with geometry is the integers. So you can multiply them and add them, it's an algebra but it seems to have nothing to do with geometry but what you can, it turns out, but if you ask yourself this question and ask, you know, are integers, can you think, if somebody gives you an integer, can you think of it as a function on some space, on some geometry? And it turns out that yes, you can and the space is the space of prime numbers and so what you do is you just, if somebody gives you an integer, you can make a function on the prime numbers by just, you know, at each prime number taking that, that integer modulo that prime. So if you say, I don't know, if you're given 10, you know, 10 and you ask, what is its value at two? Well, it's five times two, so mod two, it's zero, so it's zero one. What is its value at three? Well, it's nine plus one, so it's one mod three. So it's zero at two, it's one at three and you can kind of keep going. And so this is really kind of a truly fundamental idea. It's at the basis of what's called algebraic geometry and it just links these two parts of mathematics that look completely different and it's just an incredibly powerful idea and so much of mathematics emerges from this kind of simple relation. So you're talking about mapping from one discrete space to another. So for a second, I thought perhaps mapping like a continuous space to a discrete space, like functions over a continuous space, because yeah. Well, I mean, you can take, if somebody gives you a space, you can ask, you can say, well, let's, and this is also, this is part of the same idea. The part of the same idea is that if you try and do geometry and somebody tells you, here's a space, that what you should do is you should wait, so say, wait a minute, maybe I should be trying to solve this using algebra. And so if I do that, the way to start is, you give me the space, I start to think about the functions of the space, okay? So for each point in the space, I associate a number. I can take different kinds of functions and different kinds of values, but basically functions on a space. So what this insight is telling you is that if you're a geometer, often the way to work is to change your problem into algebra by changing your space, stop thinking about your space and the points in it and think about the functions on it. And if you're an algebraist and you've got these abstract algebraic gadgets that you're multiplying and adding, say, wait a minute, are those gadgets, can I think of them in some way as a function on a space? What would that space be and what kind of functions would they be? And that going back and forth really brings these two completely different looking areas of mathematics together. Do you have particular examples where it allowed to prove some difficult things by jumping from one to the other? Is that something that's a part of modern mathematics where such jumps are made? Oh yeah, this is kind of all the time. Much of modern number theory is kind of based on this idea. But, and when you start doing this, you start to realize that you need, what simple things on one side of the algebra start to require you to think about the other side, about geometry in a new way. You have to kind of get a more sophisticated idea about geometry, or if you start thinking about the functions on a space, you may need a more sophisticated kind of algebra. But in some sense, I mean, much or most of modern number theory is based upon this move to geometry. And there's also a lot of geometry and topology is also based upon, yeah, change. If you want to understand the topology of something, you look at the functions, you do drum comology and you get the topology. Anyway. Well, let me ask you then the ridiculous question. You said that this idea is beautiful. Can you formalize the definition of the word beautiful? And why is this beautiful? First, why is this beautiful? And second, what is beautiful? Yeah, well, and I think there are many different things you can find beautiful for different reasons. I mean, I think in this context, the notion of beauty, I think really is just kind of an idea is beautiful if it's packages a huge amount of kind of power and information into something very simple. So in some sense, you can almost kind of try and measure it in the sense of what are the implications of this idea? What non trivial things does it tell you versus how simply can you express the idea? And so. So the level of compression, what is it correlates with beauty? Yeah, that's one aspect of it. And so you can start to tell that an idea is becoming uglier and uglier as you start kind of having to, it doesn't quite do what you want. So you throw in something else to the idea and you keep doing that until you get what you want. But that's how you know you're doing something uglier and uglier when you have to kind of keep adding and more into what was originally a fairly simple idea and making it more and more complicated to get what you want. Okay, so let's put some philosophical words on the table and try to make some sense of them. One word is beauty, another one is simplicity as you mentioned, another one is truth. So do you have a sense if I give you two theories, one is simpler, one is more complicated. Do you have a sense of which one is more likely to be true to capture deeply the fabric of reality, the simple one or the more complicated one? Yeah, I think all of our evidence, what we see in the history of the subject is the simpler one though. Often it's a surprise, it's simpler in a surprising way. But yeah, that we just don't, we just, anyway, the kind of best theories we've been coming up with are ultimately when properly understood, relatively simple and much, much simpler than you would expect them to be. Do you have a good explanation why that is? Is it just because humans want it to be that way? Are we just like ultra biased and we just kind of convince ourselves that simple is better because we find simplicity beautiful? Or is there something about our actual universe that at the core is simple? My own belief is that there is something about a universe that's simple and as I was trying to say that, there is some kind of fundamental thing about math, physics and all this picture, which is in some sense simple. It's true that, it's of course true that our minds have certain, are very limited and can certainly do certain things and not others. So it's in principle possible that there's some great insight in, there are a lot of insights into the way the world works, which just aren't accessible to us because that's not the way our minds work, we don't. And that what we're seeing, this kind of simplicity is just because that's all we ever have any hope of seeing. So there's a brilliant physicist by the name of Sabine Hassenfelder who both agrees and disagrees with you. I suppose agrees that the final answer will be simple. Yeah. But simplicity and beauty leads us astray in the local pockets of scientific progress. Do you agree with her disagreement and do you disagree with her agreement? And agree with the agreement and so on. Anyway, yes, I found it was really fascinating reading her book and anyway, I was finding disagreeing with a lot, but then at the end when she says yes, when we find, when we actually figure this out, it will be simple and okay, so we agree in the end. But does beauty lead us astray, which is the core thesis of her work in that book. I actually, I guess I do disagree with her on that so much. I don't think, and especially, and I actually fairly strongly disagree with her about sometimes the way she'll refer to math. And so the problem is, physicists and people in general just refer to it as math and they're often meaning not what I would call math, which is the interesting ideas of math, but just some complicated calculation. down the path towards intelligence. And so I think that's a very peculiar property of systems that can be engineered. So even if the idea is fuzzy, even if you're not really sure what intelligence is, or if you don't have a deep fundamental understanding or even a model what intelligence is, if you build a system that sure as heck is impressive and showing some of the signs of what previously thought impossible for a nonintelligent system, then that's impressive and that's inspiring and that's okay to celebrate. In physics, because you're not engineering anything, you're just now swimming in the space, directly when you do theoretical physics, that it could be more dangerous. You could be out too far away from shore. Yeah, well, the problem, I think physics is, I think it's actually hard for people even to believe or really understand how that this particular kind of physics has gotten itself into a really unusual and strange and historically unusual state, which is not really. I mean, I spent half my life among mathematicians and half of the physicists, and mathematics is kind of doing fine. People are making progress and it has all the usual problems, but also, so you could have a, but I just, I don't know, I've never seen anything at all happening in mathematics like what's happened in this specific area in physics. It's just the kind of sociology of this, the way this field works banging up against this harder problem without anything from experiment to help it. It's really, it's led to some really kind of problematic things. And those, so it's one thing to kind of oversimplify or to slightly misrepresent, to try to explain things in a way that's not quite right, but it's another thing to start promoting to people as a success as ideas, which really completely failed. And so, I mean, I've kind of a very, very specific, if you used to have people, I won't name any names, for instance, coming on certain podcasts like yours, telling the world, this is a huge success and this is really wonderful. And it's just not true. And this is really problematic and it carries a serious danger of once, when people realize that this is what's going on, that the loss of credibility of science is a real, real problem for our society. And you don't want people to have an all too good reason to think that what they're being told by kind of some of the best institutions or a country or authorities is not true. You know, it's not true, it's a problem. That's obviously characteristic of not just physics, it's sociology. And it's, I mean, obviously in the space of politics, it's the history of politics is you sell ideas to people, even when you don't have any proof that those ideas actually work in the US because if they've worked in that, that seems to be the case throughout history. And just like you said, it's human beings running up against a really hard problem. I'm not sure if this is like a particular like trajectory through the progress of physics that we're dealing with now or it's just a natural progress of science. You run up against a really difficult stage of a field and different people behave differently in the face of that. Some sell books and sort of tell narratives that are beautiful and so on. They're not necessarily grounded in solutions that have proven themselves. Others kind of put their head down quietly, keep doing the work. Others sort of pivot to different fields and that's kind of like, yeah, ants scattering. And then you have fields like machine learning, which there was a few folks mostly scattered away from machine learning in the 90s, in the winter of AI, AI winter, as they call it. But a few people kept their head down and now they're called the fathers of deep learning. And they didn't think of it that way. And in fact, if there's another AI winter, they'll just probably keep working on it anyway, sort of like loyal ants sticking to a particular thing. So it's interesting, but you're sort of saying that we should be careful over hyping things that have not proven themselves because people will lose trust in the scientific process. But unfortunately, there's been other ways in which people have lost trust in the scientific process. That ultimately has to do actually with all the same kind of behavior as you're highlighting, which is not being honest and transparent about the flaws of mistakes of the past. Yeah, I mean, that's always a problem. But this particular field is kind of fun. It's always a strange one. I mean, I think in the sense that there's a lot of public fascination with it that it seems to speak to kind of our deepest questions about what is this physical reality? Where do we come from? And these kind of deep issues. So there's this unusual fascination with it. Mathematics is very different. Nobody's that interested in mathematics. Nobody really kind of expects to learn really great, deep things about the world from mathematics that much. They don't ask mathematicians that. So it's a very unusual, it draws this kind of unusual amount of attention. And it really is historically in a really unusual state. It's gotten itself way kind of down a blind alley in a way which it's hard to find other historical parallels to. But sort of to push back a little bit, there's power to inspiring people. And if I just empirically look, physicists are really good at combining science and philosophy and communicating it. Like there's something about physics often that forces you to build a strong intuition about the way reality works, right? And that allows you to think through sort of and communicate about all kinds of questions. Like if you see physicists, it's always fascinating to take on problems that have nothing to do with their particular discipline. They think in interesting ways and they're able to communicate their thinking in interesting ways. And so in some sense, they have a responsibility not just to do science, but to inspire. And not responsibility, but the opportunity. And thereby, I would say a little bit of a responsibility. Yeah, yeah. But I don't know, anyway, it's hard to say because there's many, many people doing this kind of thing with different degrees of success and whatever. I guess one thing, but I mean, what's kind of front and center for me is kind of a more parochial interest is just kind of what damage do you do to the subject itself, ignoring, okay, misrepresenting what high school students think about string theory and that doesn't matter much, but what the smartest undergraduates or the smartest graduate students in the world think about it and what paths you're leading them down and what story you're telling them and what textbooks you're making them read and what they're hearing. And so a lot of what's motivated me is more to try to speak to this kind of a specific population of people to make sure that, look, people, it doesn't matter so much what the average person on the street thinks about string theory, but what the best students at Columbia or Harvard or Princeton or whatever who really wanna change, work in this field and wanna work that way, what they know about it, what they think about it and that they not be going to the field being misled and believing that a certain story, this is where this is all going, this is what I gotta do, that's important to me. Well, in general, for graduate students, for people who seek to be experts in the field, diversity of ideas is really powerful and is getting into this local pocket of ideas that people hold on to for several decades is not good, no matter what the idea. I would say no matter if the idea is right or wrong, because there's no such thing as right in the long term, like it's right for now until somebody builds on something much bigger on top of it. It might end up being right, but being a tiny subset of a much bigger thing. So you always should question sort of the ways of the past. Yeah, so how to kind of achieve that kind of diversity of thought and within kind of the sociology of how we organize scientific researches. I know this is one thing that I think it's very interesting that Sabina Hassenfelder has very interesting things to say about it. And I think also Lee Smolin in his book, which is also about that very much in agreement with them that there's a really kind of important questions about how research in this field is organized and what can you do to kind of get more diversity of thought and get people thinking about a wider range of ideas. At the bottom, I think humility always helps. Well, the problem is that it's also, it's a combination of humility to know when you're wrong and also, but also you have to have a certain very serious lack of humility to believe that you're gonna make progress on some of these problems. I think you have to have like both modes and switch between them when needed. Let me ask you a question you're probably not gonna wanna answer because you're focused on the mathematics of things and mathematics can't answer the why questions, but let me ask you anyway. Do you think there's meaning to this whole thing? What do you think is the meaning of life? Why are we here? I don't know. Yeah, I was thinking about this. So the, and it did occur to me, one interesting thing about that question is that you don't, yeah, so I have this life in mathematics and this life in physics and I see some of my physicist colleagues, kind of seem to be, people are often asking them, what's the meaning of life? And they're writing books about the meaning of life and teaching courses about the meaning of life. But then I realized that no one ever asked my mathematician colleagues. Nobody ever asked mathematicians. Yeah, that's funny. So yeah, everybody just kind of assumes, okay, well, you people are studying mathematics, whatever you're doing, it's maybe very interesting, but it's clearly not gonna tell me anything useful about the meaning of my life. And I'm afraid a lot of my point of view is that if people realized how little difference there was between what the mathematicians are doing and what a lot of these theoretical physicists are doing, they might understand that it's a bit misguided to look for deep insight into the meaning of life from many theoretical physicists. It's not, they're people, they may have interesting things to say about this. You're right, they know a lot about physical reality and about, in some sense about metaphysics, about what is real of this kind. But you're also, to my mind, I think you're also making a bit of a mistake that you're looking to, I mean, I'm very, very aware that I've led a very pleasant and fairly privileged existence and fairly without many challenges of different kinds and of a certain kind. And I'm really not in no way the kind of person that a lot of people who are looking for to try to understand in some sense the meaning of life in the sense of the challenges that they're facing in life. I can't really, I'm really the wrong person for you to be asking about this. Well, if struggle is somehow a thing that's core to meaning, perhaps mathematicians are just quietly the ones who are most equipped to answer that question if, in fact, the creation or at least experiencing beauty is at the core of the meaning of life. Because it seems like mathematics is the methodology by which you can most purely explore beautiful things, right? Yeah, yeah. So in some sense, maybe we should talk to mathematicians more. Yeah, yeah, maybe, but unfortunately, people do have a somewhat correct perception that what these people are doing every day or whatever is pretty far removed from anything. Yeah, from what's kind of close to what I do every day and what my typical concerns are. So you may learn something very interesting by talking to mathematicians, but it's probably not gonna be, you're probably not gonna get what you were hoping. So when you put the pen and paper down, you're not thinking about physics and you're not thinking about mathematics and you just get to breathe in the air and look around you and realize that you're going to die one day. Yeah. Do you think about that? Your ideas will live on, but you, the human. Not especially much. Certainly, I've been getting older. I'm now 64 years old. You start to realize, well, there's probably less ahead than there was behind. And so you start to, that starts to become, what do I think about that? Maybe I should actually get serious about getting some things done, which I may not have, which I may otherwise not have time to do, which I didn't see. And this didn't seem to be a problem when I was younger, but that's the main, I think the main way in which that thought occurred. But it doesn't, you know, the stoics are big on this. Meditating on mortality helps you more intensely appreciate the beauty when you do experience it. I suppose that's true, but it's not, yeah, it's not something I've spent a lot of time trying, but yeah. Day to day, you just enjoy the positives, the mathematics. Just enjoy, yeah, our life in general. Life is, I have a perfectly pleasant life and enjoy it. And I often think, wow, this is, things are, I'm really enjoying this. Things are going well. Yeah, life is pretty amazing. I think you and I are pretty lucky. We get to live on this nice little earth with a nice little comfortable climate, and we get to have this nice little podcast conversation. Thank you so much for spending your valuable time with me today and having this conversation. Thank you. Glad to, thank you, thank you. Thanks for listening to this conversation with Peter White. To support this podcast, please check out our sponsors in the description. And now, let me leave you with some words from Richard Feynman. The first principle is that you must not fool yourself, and you are the easiest person to fool. Thank you for listening and hope to see you next time. And so I guess my feeling about it is more that it's very, the problem with talking about simplicity and using simplicity as a guide is that it's very, it's very easy to fool yourself and it's very easy to decide to fall in love with an idea. You have an idea, you think, oh, this is great and you fall in love with it. And it's like any kind of love affair, it's very easy to believe that the object of your affections is much more beautiful than the others might think and that they really are. And that's very, very easy to do. So if you say, I'm just gonna pursue ideas about beauty and this and mathematics and this, it's extremely easy to just fool yourself, I think. And I think that's a lot of what the story she was thinking of about where people have gone astray, that I think it's, I would argue that it's more people, it's not that there was some simple, powerful, wonderful idea which they'd found and it turned out not to be useful, but it was more that they kind of fooled themselves that this was actually a better idea than it really was and that it was simpler and more beautiful than it really was, is a lot of the story. I see, so it's not that the simplicity of beauty leads us astray, it's just people are people and they fall in love with whatever idea they have and then they weave narratives around that idea or they present it in such a way that emphasizes the simplicity and the beauty. Yeah, that's part of it. But I mean, the thing about physics that you have is that what really can tell, if you can do an experiment and check and see if nature is really doing what your idea expects, you do in principle have a way of really testing it and it's certainly true that if you thought you had a simple idea and that doesn't work and you go out and do an experiment and what actually does work is some more, maybe some more complicated version of it, that can certainly happen and that can be true. I think her emphasis is more, that I don't really disagree with, is that people should be concentrating on when they're trying to develop better theories on more on self consistency, not so much on beauty, but not is this idea beautiful, but is there something about the theory which is not quite consistent and use that as a guide that there's something wrong there which needs fixing. And so I think that part of her argument, I think we're on the same page about. What is consistency and inconsistencies? What exactly, do you have examples in mind? Well, it can be just simple inconsistency between theory and an experiment that if you, so we have this great fundamental theory, but there are some things that we see out there which don't seem to fit in it, like dark energy and dark matter, for instance. But if there's something which you can't test experimentally, I think she would argue and I would agree that, for instance, if you're trying to think about gravity and how are you gonna have a quantum theory of gravity, you should kind of test any of your ideas with kind of a thought experiment. Does this actually give a consistent picture of what's gonna happen, of what happens in this particular situation or not? So this is a good example. You've written about this. Since quantum gravitational effects are really small, super small, arguably unobservably small, should we have hope to arrive at a theory of quantum gravity somehow? What are the different ways we can get there? You've mentioned that you're not as interested in that effort because basically, yes, you cannot have ways to scientifically validate it given the tools of today. Yeah, I've actually, you know, I've over the years certainly spent a lot of time learning about gravity and about attempts to quantize it, but it hasn't been that much in the past the focus of what I've been thinking about. But I mean, my feeling was always, you know, as I think Sabina would agree that the, you know, one way you can pursue this if you can't do experiments is just this kind of search for consistency. You know, it can be remarkably hard to come up with a completely consistent model of this in a way that brings together quantum mechanics and general relativity. And that's, I think, kind of been the traditional way that people who have pursued quantum gravity have often pursued, you know, we have the best route to finding a consistent theory of quantum gravity and string theorists will tell you this, other people will tell you it, it's kind of what people argue about. But the problem with all of that is that you end up, you know, the danger is that you end up with, that everybody could be successful. Everybody's program for how to find a theory of quantum gravity, you know, ends up with something that is consistent. And so, and in some sense you could argue this is what happened to the string theorists. They solved their problem of finding a consistent theory of quantum gravity and they ended up, but they found 10 to the 500 solutions. So you, you know, if you believe that everything that they would like to be true is true, well, okay, you've got a theory, but it ends up being kind of useless because it's just one of an infinite, essentially infinite number of things which you have no way to experimentally distinguish. And so this is just a depressing situation. But I do think that there is a, so again, I think pursuing ideas about what, more about beauty and how can you integrate and unify these issues about gravity with other things we know about physics. And can you find a theory where these fit together in a way that makes sense and hopefully predict something. That's much more promising. Well, it makes sense and hopefully, I mean, we'll sneak up onto this question a bunch of times because you kind of said a few slightly contradictory things which is like, it's nice to have a theory that's consistent, but then if the theory is consistent, it doesn't necessarily mean anything. So like. It's not enough, it's not enough. It's not enough and that's the problem. So it's like, it keeps coming back to, okay, there should be some experimental validation. So, okay, let's talk a little bit about strength theory. You've been a bit of an outspoken critic of strength theory. Maybe one question first to ask is what is strength theory? And beyond that, why is it wrong? Or rather as the title of your blog says, not even wrong. Okay. Well, one interesting thing about the current state of strength theory is that, I think it, I'd argue it's actually very, very difficult to at this point to say what strength theory means. If people say they're a strength theorist, what they mean and what they're doing is kind of hard to pin down the meaning of the term. But the initial meaning I think goes back to, there was kind of a series of developments starting in 1984 in which people felt that they had found a unified theory of our so called standard model of all the standard, well known kind of particle interactions and gravity and it all fit together in a quantum theory. And that you could do this in a very specific way by instead of thinking about having a quantum theory of particles moving around in space time, think about a quantum theory of kind of one dimensional loops moving around in space time, so called strings. And so instead of one degree of freedom, these have an infinite number of degrees of freedom. It's a much more complicated theory, but you can imagine, okay, we're gonna quantize this theory of loops moving around in space time. And what they found is that you could do this and you could fairly, relatively straightforwardly make sense of such a quantum theory, but only if space and time together were 10 dimensional. And so then you had this problem, again, the problem I referred to at the beginning of, okay, now once you make that move, you gotta get rid of six dimensions. And so the hope was that you could get rid of the six dimensions by making them very small and that consistency of the theory would require that these six dimensions satisfy a very specific condition called being a Calabi out manifold. And that we knew very, very few examples of this. So what got a lot of people very excited back in 84, 85 was the hope that you could just take this 10 dimensional string theory and find one of a limited number of possible ways of getting rid of six dimensions by making them small and then you would end up with an effective four dimensional theory, which looked like the real world. This was the hope. So then there's then a very long story about what happened to that hope over the years. I would argue and part of the point of the book and its title was that this ultimately was a failure that you ended up, that this idea just didn't, there ended up being just too many ways of doing this and you didn't know how to do this consistently, that it was kind of not even wrong in the sense that you couldn't even, you never could pin it down well enough to actually get a real falsifiable prediction out of it that would tell you it was wrong. But it was kind of in the realm of ideas which initially looked good, but the more you look at them, they just, they don't work out the way you want and they don't actually end up carrying the power or that you originally had this vision of. And yes, the book title is not even wrong. Your blog, your excellent blog title is not even wrong. Okay, but there's nevertheless been a lot of excitement about string theory through the decades, as you mentioned. What are the different flavors of ideas that came, like that branched out? You mentioned 10 dimensions. You mentioned loops with infinite degrees of freedom. What other interesting ideas to you that kind of emerged from this world? Well, yeah, I mean, the problem with talking about the whole subject and part of the reason I wrote the book is that it gets very, very complicated. I mean, there's a huge amount, a lot of people got very interested in this, a lot of people worked on it. And in some sense, I think what happened is exactly because the idea didn't really work that this caused people to, instead of focusing on this one idea and digging in and working on that, they just kind of kept trying new things. And so people, I think, ended up wandering around in a very, very rich space of ideas about mathematics and physics and discovering all sorts of really interesting things. It's just the problem is there tended to be an inverse relationship between how interesting and beautiful and fruitful this new idea that they were trying to pursue was and how much it looked like the real world. So there's a lot of beautiful mathematics came out of it. I think one of the most spectacular is what the physicists call two dimensional conformal field theory. And so these are basically quantum field theories and kind of think of it as one space and one time dimension, which have just this huge amount of symmetry and a huge amount of structure, which there's some totally fantastic mathematics behind it. And again, and some of that mathematics is exactly also what appears in the Langlands program. So a lot of the first interaction between math and physics around the Langlands program has been around these two dimensional conformal field theories. Is there something you could say about what are the major problems are with string theory? So like, besides that there's no experimental validation, you've written that a big hole in string theory has been its perturbative definition. Perhaps that's one, can you explain what that means? Well, maybe to begin with, I think the simplest thing to say is, the initial idea really was that, okay, we have this, instead of what's great is we have this thing that only works, it's very structured and has to work in a certain way for it to make sense. But then you ended up in 10 space time dimensions. And so to get back to physics, you had to get rid of five of the dimensions, six of the dimensions. And the bottom line I would say in some sense is very simple that what people just discovered is just, there's kind of no particularly nice way of doing this, there's an infinite number of ways of doing it and you can get whatever you want depending on how you do it. So you end up the whole program of starting at 10 dimensions and getting to four just kind of collapses out of a lack of any way to kind of get to where you want because you can get anything. The hope around that problem has always been that the standard formulation that we have of string theory, which is, you can go by the name perturbative, but it's kind of, there's a standard way we know of given a classical theory of constructing a quantum theory and working with it, which is the so called perturbation theory that we know how to do. And that by itself just doesn't give you any hint as to what to do about the six dimensions. So actual perturbed string theory by itself really only works in 10 dimensions. So you have to start making some kinds of assumptions about how I'm gonna go beyond this formulation that we really understand of string theory and get rid of these six dimensions. So kind of the simplest one was the Klabiau postulate, but when that didn't really work out, people have tried more and more different things. And the hope has always been that the solution, this problem would be that you would find a deeper and better understanding of what string theory is that would actually go beyond this perturbative expansion and which would generalize this. And that once you had that, it would solve this problem of, it would pick out what to do with the six dimensions. How difficult is this problem? So if I could restate the problem, it seems like there's a very consistent physical world operating in four dimensions. And how do you map a consistent physical world in 10 dimensions to a consistent physical world in four dimensions? And how difficult is this problem? Is that something you can even answer? Just in terms of physics intuition, in terms of mathematics, mapping from 10 dimensions to four dimensions. Well, basically, I mean, you have to get rid of the six of the dimensions. So there's kind of two ways of doing it. One is what we called compactification. You say that there really are 10 dimensions, but for whatever reason, six of them are so, so small, we can't see them. So you basically start out with 10 dimensions and what we call, make six of them not go out to infinity, but just kind of a finite extent and then make that size go down so small, it's unobservable. But that's like, that's a math trick. So can you also help me build an intuition about how rich and interesting the world in those six dimensions is? So compactification seems to imply... Well, it's not very interesting. Well, no, but the problem is that what you learn if you start doing mathematics and looking at geometry and topology and more and more dimensions is that, I mean, asking the question like, what are all possible six dimensional spaces? It's just, it's kind of an unnatural question. It's just, I mean, it's even kind of technically undecidable in some way. There are too many things you can do with all these, if you start trying to make, if you start trying to make one dimensional spaces, it's like, well, you got a line, you can make a circle, you can make graphs, you can kind of see what you can do. But as you go to higher and higher dimensions, there are just so many ways you can put things together of and get something of that dimensionality. And so unless you have some very, very strong principle, we're just gonna pick out some very specific ones of these six dimensional spaces. And there are just too many of them and you can get anything you want. So if you have 10 dimensions, the kind of things that happen, say that's actually the way, that's actually the fabric of our reality is 10 dimensions. There's a limited set of behaviors of objects. I don't know even know what the right terminology to use that can occur within those dimensions, like in reality. And so like what I'm getting at is like, is there some consistent constraints? So if you have some constraints that map to reality, then you can start saying like, dimension number seven is kind of boring. All the excitement happens in the spatial dimensions, one, two, three. And time is also kind of boring. And like some are more exciting than others, or we can use our metric of beauty. Some dimensions are more beautiful than others. Once you have an actual understanding of what actually happens in those dimensions in our physical world, as opposed to sort of all the possible things that could happen. In some sense, I mean, just the basic fact is you need to get rid of them. We don't see them. So you need to somehow explain them. The main thing you're trying to do is to explain why we're not seeing them. And so you have to come up with some theory of these extra dimensions and how they're gonna behave. And string theory gives you some ideas about how to do that. But the bottom line is where you're trying to go with this whole theory you're creating is to just make all of its effects essentially unobservable. So it's not a really, it's an inherently kind of dubious and worrisome thing that you're trying to do there. Why are you just adding in all this stuff and then trying to explain why we don't see it? Exactly. This may be a dumb question, but is this an obvious thing to state that those six dimensions are unobservable or anything beyond four dimensions is unobservable? Or do you leave a little door open to saying the current tools of physics, and obviously our brains aren't unable to observe them, but we may need to come up with methodologies for observing them. So as opposed to collapsing your mathematical theory into four dimensions, leaving the door open a little bit too, maybe we need to come up with tools that actually allow us to directly measure those dimensions. Yes, I mean, you can certainly ask, assume that we've got model, look at models with more dimensions and ask, what would the observable effects, how would we know this? And you go out and do experiments. So for instance, you have a, like gravitationally you have an inverse square law of forces. If you had more dimensions, that inverse square law would change to something else. So you can go and start measuring the inverse square law and say, okay, inverse square law is working, but maybe if I get, and it turns out to be actually kind of very, very hard to measure gravitational effects and even kind of somewhat macroscopic distances because they're so small. So you can start looking at the inverse square law and say, start trying to measure it at shorter and shorter distances and see if there were extra dimensions at those distance scales, you would start to see the inverse square law fail. And so people look for that and again, you don't see it, but you can, I mean, there's all sorts of experiments of this kind you can imagine which test for effects of extra dimensions at different distance scales, but none of them, I mean, they all just don't work. Nothing yet. Nothing yet, but you could say, ah, but it's just much, much smaller, you can say that. Which by the way makes LIGO and the detection of gravitational waves quite an incredible project. Ed Witten is often brought up as one of the most brilliant mathematicians and physicists ever. What do you make of him and his work on string theory? Well, I think he's a truly remarkable figure. I've had the pleasure of meeting him first when he was a postdoc. And I mean, he's just completely amazing mathematician and physicist. And he's quite a bit smarter than just about any of the rest of us and also more hardworking. It's a kind of frightening combination to see how much he's been able to do. But I would actually argue that his greatest work, the things that he's done that have been of just this mind blowing significance of giving us, I mean, he's completely revolutionized some areas of mathematics. He's totally revolutionized the way we understand the relations between mathematics and physics. And most of those, his greatest work is stuff that has little or nothing to do with string theory. I mean, for instance, so he was actually one of Fields. The very strange thing about him in some sense is that he doesn't have a Nobel Prize. So there's a very large number of people who are nowhere near as smart as he is and don't work anywhere near as hard who have Nobel Prizes. I think he just had the misfortune of coming into the field at a time when things had gotten much, much, much tougher and nobody really had, no matter how smart you were, it was very hard to come up with a new idea that was gonna work physically and get you a Nobel Prize. But he got a Fields Medal for a certain work he did in mathematics, and that's just completely unheard of. For mathematicians to give a Fields Medal to someone outside their field in physics is really, you wouldn't have, before he came around, I don't think anybody would have thought that was even conceivable. So you're saying he came into the field of theoretical physics at a time when, and still to today, is you can't get a Nobel Prize for purely theoretical work. The specific problem of trying to do better than the standard, the standard model is just this insanely successful thing, and it kind of came together in 1973, pretty much. And all of the people who kind of were involved in that coming together, many of them ended up with Nobel Prizes for that. But if you look post 1973, pretty much, it's a little bit more, there's some edge cases, if you like, but if you look post 1973 at what people have done to try to do better than the standard model and to get a better idea, it really hasn't, it's been too hard a problem. It hasn't worked. The theory's too good. And so it's not that other people went out there and did it, and not him, and that they got Nobel Prizes for doing it, it's just that no one really, the kind of thing he's been trying to do with string theory is not, no one has been able to do since 1973. Is there something you can say about the standard model, so the four laws of physics that seems to work very well, and yet people are striving to do more? Talking about unification, so on, why? What's wrong, what's broken about the standard model? Why does it need to be improved? I mean, the thing that's gets most attention is gravity, that we have trouble. So you want to, in some sense, integrate what we know about the gravitational force with it and have a unified quantum field theory that has gravitational interactions also. So that's the big problem everybody talks about. I mean, but it's also true that if you look at the standard model, it has these very, very deep, beautiful ideas, but there's certain aspects of it that are very, let's just say that they're not beautiful. They're not, you have to, to make the thing work, you have to throw in lots and lots of extra parameters at various points, and a lot of this has to do with the so called Higgs mechanism and the Higgs field, that if you look at the theory, it's everything is, if you forget about the Higgs field and what it needs to do, the rest of the theory is very, very constrained and has very, very few free parameters, really a very small number. There's very small number of parameters and a few integers which tell you what the theory is. To make this work as a theory of the real world, you need a Higgs field and you need to, it needs to do something. And once you introduce that Higgs field, all sorts of parameters make an appearance. So now we've got 20 or 30 or whatever parameters that are gonna tell you what all the masses of things are and what's gonna happen. So you've gone from a very tightly constrained thing with a couple of parameters to this thing, which the minute you put it in, you had to add all this extra, all these extra parameters to make things work. And so that, it may be one argument as well, that's just the way the world is, and the fact that you don't find that aesthetically pleasing is just your problem, or maybe we live in a multiverse and those numbers are just different in every universe. But another reasonable conjecture is just that, well, this is just telling us that there's something we don't understand about what's going on in a deeper way, which would explain those numbers. And there's some kind of deeper idea about where the Higgs field comes from and what's going on, which we haven't figured out yet. And that's what we should look for. But to stick on string theory a little bit longer, could you play devil's advocate and try to argue for string theory, why it is something that deserved the effort that it got, and still, like if you think of it as a flame, still should be a little flame that keeps burning? Well, I think the, I mean, the most positive argument for it is all sorts of new ideas about mathematics and about parts of physics really emerge from it. That was very a fruitful source of ideas. And I think this is actually one argument you'll definitely, which I kind of agree with, I'll hear from Whitten and from other string theorists, say that this is just such a fruitful and inspiring idea and it's led to so many other different things coming out of it that there must be something right about this. And that's, okay, anyway, I think that's probably the strongest thing that they've got. But you don't think there's aspects to it that could be neighboring to a theory that does unify everything, to a theory of everything. Like it could, it may not be exactly, exactly the theory, but sticking on it longer might get us closer to the theory of everything. Well, the problem with it now really is that you really don't know what it is now. You've never, nobody has ever kind of come up with this nonperturbative theory. So it's become more and more frustrating and an odd activity to try to argue with a string theorist about string theory because it's become less and less well defined what it is. And it's become actually more and more kind of a, whether you have this weird phenomenon of people calling themselves string theorists when they've never actually worked on any theory where there are any strings anywhere. So what has actually happened kind of sociologically is that you started out with this fairly well defined proposal. And then I would argue because that didn't work, people branched out in all sorts of directions doing all sorts of things. It became farther and farther removed from that. And for sociological reasons, the ones who kind of started out or now or were trained by the people who worked on that have now become this string theorists. And, but it's becoming almost more kind of a tribal denominator than a, I think so it's very hard to know what you're arguing about when you're arguing about string theory these days. Well, to push back on that a little bit, I mean, string theory is just a term, right? It doesn't, like you could, like this is the way language evolves is it could start to represent something more than just the theory that involves strings. It could represent the effort to unify the laws of physics. Right? At high dimensions with these super tiny objects, right? Or something like that. I mean, we can sort of put string theory aside. So for example, neural networks