Peter Woit: Theories of Everything & Why String Theory is Not Even Wrong | Lex Fridman Podcast #246

Lex Fridman 0:00 The following is a conversation with Peter Woit, 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 Fridman Podcast. To support it, please check out our sponsors in the description. And now, here's my conversation with Peter Woit.

Lex Fridman 0:23 You're both a physicist and a mathematician. So let me ask, what is the difference between physics and mathematics?

Peter Woit 0:31 Well, there's kind of a conventional understanding of the subject that they're two, you know, quite different things, so that mathematics is about, you know, making rigorous statements about these abstract, you know, abstract things, things of mathematics, and- and prov- proving them rigorously. And physics is about, you know, doing experiments and testing various models and that. But I think, uh, the more interesting thing is that the- there's a- (laughs) 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- I think is actually the much, much- very, very interesting area. And if you go back kind of far enough to- in- in- in history, and look at figures like Newton or something, I mean, they're- at that point, you can't really tell, you know, was Newton a physicist or a mathematician? The, uh, mathematicians will tell you he was a mathematician, the physicists will tell you he was a physicist. But-

Lex Fridman 1:24 He would say he's a philosopher. (laughs)

Peter Woit 1:27 Yeah. (laughs) That's- that's interesting. But, uh, yeah, anyway, there- there- there was kind of no such distinction then, that's more of a modern thing. And but anyway, I think these days, there's a very interesting space in between the two.

Lex Fridman 1:38 So, in the story of the 20th century and the early 21st century, what is the overlap between mathematics and physics, would you say?

Peter Woit 1:46 Well, I think (clears throat) it's actually become very, very complicated. I think it- it's really interesting to see a lot of what my colleagues in the math department are doing. They- most of what they're doing, they're doing all sorts of different things, but, um, most of them have some kind of overlap with physics or other. Um, so I mean, I'm personally interested in- in one spec- 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, um, there's just- it- it- you- you kind of see this- this, uh, re- really everywhere at this point.

Lex Fridman 2:18 Which particular overlap are you looking at? Group theory?

Peter Woit 2:22 Yeah. So the, um, at least what- the way it seems to me that if you look at physics and look at the- our most successful, um, laws of fundamental physics, they're really, you know, they have a certain kind of mathematical structure. It's based upon certain kind of mathematical objects and geometry, connections, and curvature of the spinors, the Dirac equation. And, uh, that- these- this very deep mathematics provides kind of a unifying set of math- of ways of thinking that allow you to- to make a unified theory of physics. But the interesting thing is that if you go to mathematics and- 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 especially powerful in number theory recently. And there's a book, for instance, by, um, Edward Frenkel about love and math, and-

Lex Fridman 3:19 Oh, yeah, that book's great. I recommend it highly. It's, uh, partially accessible. But it is a nice audiobook, s- uh, that I listened to while running an exceptionally long distance, uh, like across the, uh, San Francisco, uh, Bridge. And, uh, there's something magic about the way he writes about it. But s- some of the group theory in there is a little bit difficult.

Peter Woit 3:42 Uh, yeah. That's the problem with- with any of these things, to kind of really say what's going on and- is- and make it accessible is very hard. He, in this book and elsewhere, I think, you know, takes the attitude that kinds of mathematics he's interested in and that he's talking about are- provide kind of a grand unified theory of mathematics. They, um, they bring together geometry and number theory and representation theory, a lot of different ideas in- in a really unexpected way. But I think to- 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's kind of ideas about unification, it's more or less the same mathematical objects are appearing in both. So it's this, um, I think there's a really- we're seeing a really strong indication that, you know, the deepest ideas that we're discovering about physics and some of the deepest ideas that mathematicians are learning about are really- are, you know, intimately connected.

Lex Fridman 4:36 Is there something, like if I was five years old and you were trying to explain this to me-

Peter Woit 4:40 (laughs) .

Lex Fridman 4:40 ... is there ways to try to sneak up to this- to- 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- a three-dimensional surface? And we're s- trying to say something about it. Is it, uh, triangles and squares and cubes?

Peter Woit 5:07 (laughs) .

Lex Fridman 5:07 Like what- what are we supposed to imagine in our minds? Is this natural number? What- 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?

Peter Woit 5:30 The (laughs) I mean, what- what I (laughs) find kind of remarkable about this is the way in which these- we've discovered these ideas but they're- they're actually quite alien to our everyday understanding. You know, 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, um, these things that we've discovered in both math and physics are- that they're not at all close in- have any obvious connection to kind of human everyday experience. They're- they're really quite different. And I can say some of my initial fascination with this when I was, uh-... young and starting to learn about it was actually exactly this, um, th- this kind of arcane nature of these things. It was a little bit like being- being told, "Well, there are these kind of s- sem- semi-mystical experience that you can acquire by a long study," and whatever, except that it w- that it was actually true. I mean, there's actually evidence that this actually works. So, you know, I'm a l- a little bit wary of- of trying to give people that kind of thing, 'cause I think it's mostly misleading. But one thing to say is that, you know, that geometry is- is a large part of it, and, um, maybe one interesting thing to say very- that's about more recent- some of the most recent ideas is that it, um... When we think about the geometry of our space and time, it's kind of three spatial and one time dimension. It- it's a, um... Physics is, in some sense, about something that's kind of four-dimensional in a way.

Lex Fridman 7:00 Mm-hmm.

Peter Woit 7:00 And the... A- a really interesting thing about, um, some of the recent developments in number theory have been to realize that the, um, these ideas that we were looking at, you know, naturally fit into a context where your- your theory is four- is kind of four-dimensional, so... So- so- so geom- I mean, geometry is a big part of this, and- and- and we know a lot and feel a lot about, you know, two, one, two, three-dimensional geometry.

Lex Fridman 7:24 So wa- wait a minute. So we can at least rely on, uh, the four dimensions of space and time and say that we can get pretty far by working in that- 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.

Peter Woit 7:40 My- my- my point of view which is- w- which goes against a lot of these ideas about unification is that, no, this is really... Everything we s- we know about really is about four dimensions that, um... And- and that you can actually understand a lot of these structures that we've been seeing in fundamental physics and in- 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, um... Has been kind of a mistake that- that physicists have made in- for decades and decades to try to- to tr- try to go to higher dimensions, to try to- to formulate a theory in higher dimensions, and then- then you're stuck with the problem of how do you get rid of all these extra dimensions that you've created, and... 'C- 'cause we only ever see anything in four dimensions.

Lex Fridman 8:27 That kind of thing leads us astray, you think? So- so creating all these extra dimensions just to get, uh, give yourself extra degrees of freedom.

Peter Woit 8:35 Yeah.

Lex Fridman 8:36 I- isn't that... I mean, isn't that the process of mathematics is to create all these trajectories for yourself but eventually you have to end up at the, uh, at the- at a, like a final place, but it's okay to... It's- it's okay to sort of, um, create abstract objects on your path to, uh, proving something?

Peter Woit 8:56 Yeah. S- yeah, certainly, but... And from- from mathematicians' 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, um, see what's the greatest generality in which you can talk about it.

Lex Fridman 9:10 Mm-hmm.

Peter Woit 9:11 So from the point of view of most of the ways geometry is formulated, um, by mathematicians, it- it really doesn't ma- it works in any dimension. We can do one, two, three, four, any- any number. There's no particular... For most of geometry there's no particular special thing about four. But, um... And s- anyway, but- but what physicists have- have found- 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 to- and- and using them to explain the structure, but it, um... Typ- typically this- this attempt kind of founders because you just don't know... You- you end up not being able to explain why we only see four. (laughs) and anyway...

Lex Fridman 9:59 It i- it is nice in the space of physics that, uh, 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.

Peter Woit 10:11 Right.

Lex Fridman 10:11 And- and so I guess that's the nice benefit of being a physicist is you don't have to worry about the general case 'cause we live in a universe with N equals four in this case.

Peter Woit 10:23 Yeah, yeah. Physi- physicists are very interested in saying something about specific examples, and I find that interesting e- even when- when I'm trying to do things, uh, in mathematics and I'm trying... Even teaching courses to mathematics students, I find that I'm teaching them in a different way than, um, most mathematicians because I'm very often f- very focused on examples, on- on what's-

Lex Fridman 10:45 Mm-hmm.

Peter Woit 10:46 ...what's kind of the crucial example that shows how this, um, this powerful new mathematical technique, how it works and why you would wanna- to do it, um, and I'm less interested in kind of, you know, proving a precise theorem about exactly when it's gonna work and when it's not gonna work.

Lex Fridman 11:02 Do you usually think about really simple examples like, uh, both for teaching and when you try to solve a difficult problem? Are you... Do you construct like the simplest possible examples that captures the fundamentals of the problem and try to solve it?

Peter Woit 11:15 Yeah, yeah. E- e- exactly. That's often a really fruitful way to... If you've got some idea to... Y- just to kind of try to boil it down to what's the simplest s- situation in which this kind of thing is gonna happen and- and then try to really understand that- uh, understand that. And that- that is almost always a really good way to get insight into...

Lex Fridman 11:34 Do you work with, uh, paper and pen or like for example for me, um, c- coming from the programming side if you- if I look at a model, if I look at s- some kind of mathematical object, I like to mess around with it sort of numerically. Uh, I just visualize different parts of it, visualize however I can so most of the work is like with neural networks for example.

Peter Woit 11:56 Yeah.

Lex Fridman 11:56 Is you try to play with the simplest possible example and just to build up intuition by, um, you know... Any kind of object has a bunch of variables in it. (laughs)

Peter Woit 12:06 Yeah.

Lex Fridman 12:06 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, like, (laughs) everything inside your mind and sort of build, like, thought experiments and then m- work purely on paper and pen?

Peter Woit 12:24 Well, the, the problem with this kind of stuff that I'm interested is, it, you, you rarely can kind of... it's rarely something that is really kind of... or even the simplest example, it... you know, it can... is you could kind of see what's going on by, uh, looking at something happening in three dimensions.

Lex Fridman 12:42 Right.

Peter Woit 12:42 'cause there's... generally, the s- the structures involved are, um, either they're more abstract or if you try to kind of embed them in some kind of space and where you could, um, manipulate them in some kind of geometrical way, it- it's gonna be a much higher dimensional space.

Lex Fridman 12:57 So even simple examples, the embedding them into three-dimensional space, you're losing a lot.

Peter Woit 13:03 Yeah. Or, but, but to capture what you're, 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, to try to as much as to kind of think about things in, in your mind. And, you know, I often use, use pad and paper, and I'm often... if I'm in my office, I often use the blackboard. Um, 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 s- really living in three dimensions where you can under-

Lex Fridman 13:39 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, I mean, (laughs) what do we make of that? I mean, to me, that makes me quite sad. It makes me, it makes it seem like there's a giant mystery out there that we'll never truly get to experience directly.

Peter Woit 13:58 It is kind of sad, you know, how difficult this is. I mean, or I would put it a, a different way, that, um, you know, most questions that people have about this kind of thing, you know, you couldn't... you can give them a really a- a true answer and really understand it, but the problem is, is one more of, um, of time. It's like, yes, you know, I could explain to you how this works, but you'd have to be willing to sit down with me and, and, you know, work at this repeatedly for, you know, for hours and days and weeks, and you'd, you'd... I mean, it's just gonna take that long for your mind to really wrap itself around what's going on, and, um, and that... so that does make things ina- in- inaccessible, which is, uh, which is sad, but it... again, I mean, it's just kind of part of life that we all have-

Lex Fridman 14:43 (laughs)

Peter Woit 14:43 ... a limited amount of time and we have to decide what we're gonna, what we're gonna spend our time doing.

Lex Fridman 14:49 Well, speaking of a limited amount of time,

Lex Fridman 14:52 we only have, uh, a few hours, maybe a few days together here on this podcast.

Peter Woit 14:56 Yeah. (laughs)

Lex Fridman 14:57 Uh, let me ask you the question of, um, amongst many of the ideas that you work on in mathematics and physics, what to you 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-

Peter Woit 15:15 (laughs)

Lex Fridman 15:15 ... to try to convey such an idea.

Peter Woit 15:18 Okay. Well, actually, le- let me just te- tell you something, which I, I, I'm tempted to kind of ex- 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 quantum mechanics, and... but i- 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.

Lex Fridman 15:39 Well, can I actually... on a small tangent, you, you did write a paper Towards A Grand Unified Theory Of Mathematics And Physics. Um, maybe you could step there first. What is the key idea in that paper?

Peter Woit 15:49 Well, I think we, we've kind of gone, gone over that. I think the, the key idea is what we were talking about earlier, that, um, that just kind of a claim that if you look and see what's the... have been successful ideas unification in physics in the... over the last, um, 50 years or so and what, um, has been happening in mathematics and the kind of thing that Frankl'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, um, uh, getting deeper into mathematics and looking for more inspiration in mathematics from these successful ideas about fundamental physics.

Lex Fridman 16:37 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, uh, the number theory geometry, uh, so the... like, differential geometry, topology, like...

Peter Woit 16:51 Yeah. So the... I mean, one, one name for this, uh, that this is acquired in, in mathematics is the so-called Langlands program.

Lex Fridman 16:59 Mm-hmm.

Peter Woit 16:59 And, uh, so this started out in mathematics. It's the... you know, Robert Langlands kind of realized that a lot of what people were doing and, um... that was starting to be really successful in, in number theory in the '60s, and so th- that this actually was... anyway, that, that this could be, could be thought of in terms of, um, these ideas about symmetry in groups and representations and, and in a way that was also close to some ideas about, about geometry. And, um, then, uh, more later on in the '80s and '90s, there was something called, um, geometric Langlands, that people realized that you could take what people have been doing in number theory in Langlands and, and, and get re-... just forget about the number theory and ask, "What is this telling you about geometry?"

Lex Fridman 17:47 Mm-hmm.

Peter Woit 17:48 And you get a whole... some new insights into certain kinds of geometry that way. So it's... anyway, that, that's kind of the name for this area, is Langlands and geometric Langlands. And, and just recently in the last few months, there's been, um... there's kind of a really major paper that, uh, appeared by, uh, Peter Schulze and Laurent Fargue, where they, you know, made, you know, some, some... a serious advance in trying to understand a very much, uh-... kind of a local problem of what happens i- in number theory near a certain prime number, and they turned this into a problem of exactly the- the kind that geometric Langlands people had been doing, these kind of pure, uh, pure geometry problem. And they found by generalizing the mathematics, they could actually reformulate it in that way, and it- it worked perfectly well, so.

Lex Fridman 18:36 W- one of the things that makes me sad is, you know, I'm a pretty knowledgeable person in, uh, what is it? At least I'm in the neighborhood-

Peter Woit 18:48 (laughs)

Lex Fridman 18:48 ... of, like, theoretical computer science, right? And it's still way out of my reach. And s- so many people talk about like Langlands, for example, is one of the most brilliant people in mathematics-

Peter Woit 18:57 Yeah.

Lex Fridman 18:57 ... 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.

Peter Woit 19:05 Yeah.

Lex Fridman 19:06 You know?

Peter Woit 19:06 Well, I mean, I- I think that (laughs) unfortunately, it's not just you, it's I- I- 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 Lo- of Scholze and Fargue that I was talking about, the number of people who really actually understand how that works is, anyway,

Narrator 19:28 (laughs)

Peter Woit 19:29 ... very, very small. And so it's, uh, so, uh, I think even you find if you talk to mathematicians and physicists, even they will often feel that, uh, you know, 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-

Lex Fridman 19:46 (laughs)

Peter Woit 19:46 ... pretty clearly far beyond me right now.

Lex Fridman 19:49 Well, if we can step into the, back to the question of beauty. Uh, is- is there an idea that maybe is a little bit smaller-

Peter Woit 19:58 Yeah.

Lex Fridman 19:58 ... that you find beautiful in the space of mathematics or physics?

Peter Woit 20:01 There's- there's an idea that, uh, you know, I kind of went and got a physics PhD and spent a lot of time learning about mathematics, and I guess it- it was embarrassing that I- I hadn't really actually understood this very simple idea, um, until... And kind of lear- learned it when I actually started teaching math classes, which is that maybe that- that there- there maybe... 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- 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- it's completely abstract, it has nothing geometric about it. But the, um, the kind of really fundamental idea is, uh, that unifies algebra and geometry is to th- is to reali- is to think whenev- 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, uh, I mean, a standard kind of thing that seems to have nothing to do with geometry is the, um, is the- the- the integers. Uh, then there you can- you can multiply them and add them, it's a- it's- it's an algebra. But the, um, it has- 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, is... 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, uh, as you say, I don't know, if you're gi- given 10, you know, 10 and you ask what is its value at two, well, it's- it's five times two, so mod two, it's zero, so it has (01:00:55) . What i- what is- what is its value at three? Well, it's nine plus one, so it's- it's one mod three. So it- it's v- it's- 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- 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- it's just an incredibly powerful idea, and- and so much of mathematics emerges from this kind of simple relation.

Lex Fridman 22:39 So, uh, you're talking about mapping from one discrete space to ano- to another. So s- uh, um, for a second I thought perhaps mapping like a continuous space to a discrete space, like functions over a continuous space, uh, 'cause yeah...

Peter Woit 22:56 Well, you can- I mean, you can take... If somebody gives you a space, you can ask... You can say, "Well, let's- let's..." And- 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- 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- to each point in the space, I associate a number. I can take different kinds of functions and different kinds of values, but- but basically functions on a space. So what this insight is telling you is that if you're a geometer, often the way to- to- to- to work is to trans- change your problem into algebra by changing your spa- stop thinking about your space and the points in it, and think about the functions on it.

Lex Fridman 23:47 Got it.

Peter Woit 23:48 And if you're- and if you're an algebraist and you've- 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.

Lex Fridman 24:09 Do you have, um, 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?

Peter Woit 24:21 ... oh, yes. This is, kind of all the time, uh, a lot... Much, much of modern number theory is kind of based on this idea. But... And, and, when you start doing this, you start to realize that you need, you know, what simple things, 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 at a space, you may ha- you may need a more sophisticated kind of algebra. But, um, but in some sense, I mean, much or most of modern number theory is based upon this move to, to geometry, and, um, is also a lot of geometry and topology is also based upon. Yeah, change, change. If you want to understand the topology of something, you look at the functions, you do De Rham cohomology and you get the topology. (laughs) Anyway.

Lex Fridman 25:13 Well, let me, let me then ask you then the ridiculous question. You said that this idea is beautiful. Uh, can you formalize the definition of bea- the word beautiful and why is this beautiful? Like, well, first, why is this beautiful? And second, um, what is beautiful?

Peter Woit 25:29 Well, uh, 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, yeah, I mean, (laughs) the re- you can almost try and measure it in the sense of, you know, what's the... What are the implications of this idea? What non-trivial things does it tell you? Versus, you know, how, h- h- how, how simply can you, can you express the idea? And so-

Lex Fridman 26:06 So the level of compression?

Peter Woit 26:08 Yeah.

Lex Fridman 26:08 Cor- uh, what is it? Correlates with, uh, beauty?

Peter Woit 26:12 Yeah. That's that's one, one aspect of it.

Lex Fridman 26:14 Mm-hmm.

Peter Woit 26:15 And so you can start to tell that an idea is becoming uglier and uglier as you start kind of having to... You know, 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 in more, more (laughs) more into what was originally a fairly simple idea and making it more and more complicated to get what you want.

Lex Fridman 26:41 Okay, so let's put some, uh, 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.

Peter Woit 26:52 Mm-hmm.

Lex Fridman 26:53 So do you have a sense... If I give you two theories, one is simpler, one is more complicated, do you have a sense which one is more likely to be true to, um, capture deeply the fabric of reality? The simple one or the more complicated one?

Peter Woit 27:15 I, yeah, I think all of our evidence, what we see in the history of the subject is the, the simpler one. Though often it's a surprise. It's simpler in a surprising way, but, um, yeah. That, that we just don't... We just... Anyway, when... The kind of best theories we've been coming, coming up with are ultimately when not properly understood relatively simple and, uh, much, much simpler than they, you would expect them to be.

Lex Fridman 27:41 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-

Peter Woit 27:47 (laughs) .

Lex Fridman 27:48 ... we just kind of convince ourselves that simple is better because we find simplicity beautiful? Or is there something about at the, our actual universe that, uh, at the core is simple?

Peter Woit 28:00 My own belief is that there is something about a universe that's simple and that, as I was trying to say that, you know, there is some, some kind of fundamental thing about math, physics, physics in all, all this picture which is, um, which, which is in some sense simple. It's true that, you know, it, it... It's of course true that, you know, our minds have certain... Have... Are very limited and can certainly do certain things and not others, so it, it's, it's in principle possible that there's some great insight... There are a lot of insights into the way the world works which is 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 but...

Lex Fridman 28:42 So there's a, uh, brilliant physicist by the name of Sabine Hossenfelder who both agrees and disagrees with you. Or I suppose agrees that, uh, the final answer will be simple.

Peter Woit 28:57 Yeah. (laughs)

Lex Fridman 28:58 But, uh, simplicity and beauty leads us astray in the lo- in the local pockets of scientific progress. Uh, do you... Uh, do you agree with her disagreement? Do you disagree with her agreement?

Peter Woit 29:10 (laughs)

Lex Fridman 29:11 And agree with the agreement, uh, and so on.

Peter Woit 29:13 Well, I, I, anyway, I, I... Yes, I thought it was really fascinating reading her book and, and I... Anyway, I was finding disagreeing with a lot but then at the end when she says yes, when we find-

Lex Fridman 29:24 Yeah. (laughs)

Peter Woit 29:25 ... when we actually figure this out, it will, it will be simple and, okay, so we agree in the end.

Lex Fridman 29:31 But does beauty lead us astray which is the core thesis of her work in that book?

Peter Woit 29:37 I actually... I guess I do disagree with her on, on that so much. I don't think... And especially... And I actually fairly strongly disagree with her about sometimes, sometimes the way she'll refer to math and... So the problem is, you know, physicists and people in general just refer to it as math and, and they're often, um... They're often meaning not what I would call math which is the interesting ideas of math but just some complicated calculation and, and so, um... I, I guess my feeling about it is more that it's very... The problem with talking about simplicity and, and using simplicity as a guide is that it's very, um... It's very easy to fool yourself and, you know, it's very easy to decide to, you know, to fall in love with an idea. You have an idea, you think, "Oh, this is, this is great," and you fall in love with it and like any kind of love affair, it's very easy to believe that, you know, your... 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, um, if you say, "I'm just gonna pursue ideas about beauty and this, and mathematics and this," it's extremely easy to, to just fool yourself, I think. Um, and I think that's a lot of what sh- the th- the story she was thinking of about where people have gone astray that I think it's... I would argue that as more people... It's not that there was some simple, powerful, wonderful idea which they'd found, and it turned out not to be, um, not to be useful, but it was more that they kind of fooled themselves that this was actually a better idea than, than it, it really was, and that it was simpler and more beautiful than it really was, is, is, is a lot of the story. Um-

Lex Fridman 31:18 I see. So it's not that the simplicity would be that just people are people, and they, uh, fall in love with, with whatever idea they have, and then they s- they weave narratives around that idea, or they present it in such a way that, uh, emphasizes, uh, the simplicity and the beauty.

Peter Woit 31:36 Uh, yeah, that's part of it. But, I mean, the thing about physics that you have... is that you, you know, what, what really can tell... If you can do an experiment and check and see if nature is really doing what your, your idea expects, that you, you do in principle have a way of, of really, of testing it. And, and it's certainly true that if you, um, you know, uh, 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, that, that, that, that can be true. I think her emphasis is more, that I don't really disagree with, is that, um, people should be concentrating on, um, when they're trying to get, develop better theories on, more on s- on self-consistency, not so much on beauty, but, you know, not, "Is this idea beautiful?" But, you know, "Is there something about the theory which is not quite consistent?" And that, and use that as a guide to... that there's something wrong there which needs fixing. And, and so I, I think that part of her argument, I think I was... we're, we're on the same page about.

Lex Fridman 32:44 Uh, what's, what is consistency and inconsistencies? Wh- what, what exactly, um... Do you have examples in mind?

Peter Woit 32:53 Well, it, it, it can be just simple inconsistency between theory and, and, and experiment, that if you... So we have this great fundamental theory, but there are some things we see out there which don't seem to fit in it, like, like, like dark energy and dark matter, for instance. But if there's something which you can't test experimentally, I think, you know, 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 be, you know... test any of your ideas with kind of, kind of a tho- a thought experiment. You know, is... does this actually give a consistent picture of what's gonna happen, of what happens in this particular situation or not?

Lex Fridman 33:32 So, this is a good example. You've written about this. Um, you know, 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, uh, have, uh, ways to scientifically validate it given the tools of today.

Peter Woit 34:04 Yeah. I've actually, you know, I've, I've over the years certainly spent a lot of time learning about gravity and about attempts to quantize it, but it, it, it hasn't been that much in the past the focus of what I've been thinking about. But me- my feeling was always, you know, as I think Svetlana would agree, that the, uh... You know, one way you can pursue this if you, if you can't do experiments is just this kind of search for consistency. You know, it, it can be remarkably hard to come up with a completely consistent model of, model of this in, 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... W- w- where we have the best route to finding a consistent theory of quantum gravity. And string theorists will tell you this. Other pe- other people will tell you it. It's, it's kind of what people argue about. But, but the problem w- with all of that is that you end up, um... The danger is that you end up with... That, that everybody could be successful. Everybody, 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, um, they solved their problem of finding a consistent theory of quantum gravity, and they ended... But they found 10 of 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's, it's... it ends up being kind of useless, because it's just one of an infinite, essentially infinite number of things which you have no i- way to experimentally distinguish. And so this is a... just a depressing situation. Um, but, but I, but I do think that there is a, um... So, 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 which... where they, where these fit together in a, in a way that makes sense and, and, and hopefully predicts something that's much more promising.

Lex Fridman 36:14 Well, makes sense and hopefully pre- I mean, we'll sneak up-

Peter Woit 36:17 Yeah.

Lex Fridman 36:17 ... onto this question a bunch of times, 'cause you kinda said, uh, 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. (laughs) So, like-

Peter Woit 36:33 It- it's, it- it's not enough. It's not enough.

Lex Fridman 36:35 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.

Peter Woit 36:42 Yeah.

Lex Fridman 36:42 So,

Lex Fridman 36:43 okay. Let's talk a little bit about string theory. You've been a- a bit of an outspoken critic-

Peter Woit 36:50 (laughs)

Lex Fridman 36:50 ... of string theory. Maybe one question first to ask is what is string theory, and, uh, beyond that, why is it wrong, or rather as the title of your blog says, Not Even Wrong?

Peter Woit 37:06 Okay. (laughs) Well, one interesting thing about the current state of string theory is that (laughs) I- I think it, I'd argue it's actually very, very difficult to, at this point, to say what string theory means. If people say they're a string theorists, what they mean and what they're doing is a- it's kind of hard t- it's hard to pin down the meaning of the term. But the- but the initial meaning I think goes back to, um ... there was kind of a- a series of developments starting in 1984 in which people felt that they had found a unified theory of- of a so-called standard model of- of- of all the standard, uh, well- 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 spacetime, think about, uh, a quantum theory of kind of one-dimensional loops moving around in spacetime, so-called strings. And so, um, instead of one degree of freedom, these have an infinite number of degree 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 spacetime, and what they found is that they, is that you could make ... you could do this and you could fairly relatively straightforwardly make sense of- of- of such a quantum theory, but only if s- 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 these, that these six dimensions, um, satisfy a very specific condition called being a Calabi-Yau 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, um, 10-dimensional string theory and find one of a limited number of possible ways of- of getting rid of six dimensions by making them small, and then you would end up with a- an effective four-dimensional theory which looked like the real world. This was the hope. So then there's the- (laughs) a very long story about what happened to that hope over the years. I mean, I- I would argue and pro- part of the te- point of the book and its title was that, um, you know, that this- this ultimately wa- wa- was a failure, that you ended up ... that this idea just didn't, um ... there ended up being just too many ways of doing this, and you didn't know how to do this consistently, um, that it was kind of n- not even wrong in the sense that you couldn't even pin ... you- 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, um ... it was kind of in the i- in- in the realm of ideas which initially look good but the more you look at them, they just, um, they don't work out the way- the way you want and they- they don't actually end up carrying the power or the ... that you originally had this vision of.

Lex Fridman 40:11 And yes, the- the book title is Not Even Wrong, your blog, your excellent blog title, Is Not Even Wrong. Okay. But there has nevertheless been a lot of excitement about string theory through the decades as you've mentioned. Uh, what are the different flavors of ideas that came, uh, like that branched out? You mentioned 10 dimensions, you mentioned loops with i- infinite degrees of freedom. What- what other interesting ideas to you that kind of emerged from this world?

Peter Woit 40:41 Well, yeah, I mean, th- the problem with talking about the whole subject and, well, partly one of the reasons I wrote the book is that it ... it gets very, very complicated. I mean, there's a- a huge amount ... you know, hu- a lot of people got very interested in this, a lot of people worked on it, and in- and in some sense I think what happened is exactly because the idea didn't really work, that this caused people to, you know, 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, you know, 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 (laughs) . So there's a lot of beautiful mathematics came out of it. I think one of the most spectacular is what the, um, 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, you know, have just this huge amount of symmetry and- and, um, a huge amount of structure which ... yeah, and just some totally fantastic mathematics behind it, and, um ... and again, and- and some of that mathematics is exactly also what appears in the Langlands program.

Lex Fridman 42:03 Mm-hmm.

Peter Woit 42:03 So a lot of the, um ... first interaction between math and physics around the Langlands program has been around these two-dimensional conformal field theories.

Lex Fridman 42:12 Is there, um, something you could say about what the major problems are with string theory? So th- well, like, um ... besides th- that there's no experimental validation, you've, uh, written that a big hole in string theory has been its perturbative definition.

Peter Woit 42:33 Yeah.

Lex Fridman 42:34 Perhaps that's one. Can you explain what that means?

Peter Woit 42:36 Well, th- maybe to begin with, I mean, I- I think the, I mean, the simplest thing to- to say is, you know, the- the initial idea really was that ...... "Okay, we're- we have this..." Instead of... What's great is we have this thing that only works, that's very structured and has to work in a certain way for it to make sense. And, um, but- but then you ended up, you ended up in 10 space time dimensions. And so to get back to physics, you had to get rid of five of the dimens- six of the dimensions. And the bottom line, I would say, in some sense, it's very simple. That what people just discovered is just there- 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 the- you- you end up the whole program of starting at 10 dimensions and getting to four just kind of collapses out of a- a lack of any way to kind of get to where you want because you can get anything. The be- 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- it's kind of... Um, there's a standard way we know of giving a classical theory of constructing a quantum theory and- and working with it, which is this- the so-called perturbation theory. That, um, that we know how to do, and that- that by itself just- just doesn't- doesn't give you any hint as to what to do about the six dimensions. So actual perturbed with string theory by itself really only works in ten dimensions. So you have to start making some kinds of assumptions about how I'm going to go beyond this formulation that we really understand of string theory and get rid of these six- six dimensions. So kind of the simplest one was the, um, Cladial postulate. But, um, when that didn't really work out, people tried more and more different things. And- and the hope has always been that the solution to 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- which would generalize this. And- and that once you had that, it would, um- it would solve this problem of... It would pick out what to do with the six dimensions.

Lex Fridman 44:59 How difficult is- is this problem so... (sighs) If I could restate the problem, it seems like there's a very consistent physical world operating in four dimensions. And, uh, how do you map a consistent physical world in ten dimensions to a consistent physical world in four dimensions?

Peter Woit 45:20 Right.

Lex Fridman 45:21 And how- how difficult is this problem? Is it- is that something you can even answer, um, just in terms of physics intuition, in terms of mathematics mapping from ten dimensions to four dimensions?

Peter Woit 45:35 Well, basically, I mean, you have to get rid of the six of the dimensions. So- so there's... There- there's kind of two ways of doing it. One is what we call compactification. You say that there really are ten dimensions, but for whatever reason, six of them are really, are so, so small we can't see them. So you basically start out with ten dimensions and what we call... You know, make- make- 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.

Lex Fridman 46:05 That's like, that's a math trick. So c- c- 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 (laughs) it's not very interesting.

Peter Woit 46:22 Well, no, but- but the problem is that what you learn if you start doing math- mathematics and looking at geometry and topology in- in more and more dimensions is that, I mean, asking the question like, "What are all possible six dimensional spaces?" is just, it's kind of an unanswerable question. It's just, uh, I mean, there- it's even kind of technically undecidable in some way. There's just, there's just too, too... 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 it- it- it... Um, unless you have some very, very strong principle which is going to pick out some very specific ones of these six dimensional spaces, and they're just too many of them and you can get anything you want, but, um...

Lex Fridman 47:19 So if you have ten dimensions, the kind of things that happen, or say that's actually the way, that's actually the fabric of our reality is ten 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.

Peter Woit 47:40 Yeah.

Lex Fridman 47:41 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."

Peter Woit 48:00 Yeah.

Lex Fridman 48:00 And time is also kind of boring.

Peter Woit 48:02 Yeah.

Lex Fridman 48:03 And like, some are more exciting than others. Or we can use our metric of beauty. Uh, 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.

Peter Woit 48:19 In some sense, I mean, just the basic fact is you need to get rid of them. We don't see them, so you- you need to somehow explain them. What you have to... The main thing you're trying to do is to explain why we're not seeing them. And so you- you can... You have to come up with some theory of these extra dimensions and- and how they're going to behave, and string theory gives you some ideas about how to do that, but- 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 a- it's not a really... (laughs) It- 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? I mean, it just...

Lex Fridman 49:03 This may be a dumb question, but it's, 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-

Peter Woit 49:26 Yeah.

Lex Fridman 49:27 ... 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 to maybe we need to come up with tools that actually allow us to directly measure those dimensions.

Peter Woit 49:42 Yeah, so I mean, but you, I mean, you can certainly ask, you know, assume that we've got model... Look, look at models with more dimensions and ask, you know, what would the observable effects, how would we-

Lex Fridman 49:53 Right.

Peter Woit 49:53 ... 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, okay? If you had more dimensions, that inverse square law would change into 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, get... And it turns out to be actually kind of very, very hard to measure gravitational effects at even kind of, you know, somewhat macroscopic distances, because they're so small.

Lex Fridman 50:22 Mm-hmm.

Peter Woit 50:23 So you can, 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, um, 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, you can imagine which test for effects of extra dimensions at different, at different distance scales, but, you know, none of them... You, I mean, they all just don't work.

Lex Fridman 50:57 Nothing yet.

Peter Woit 50:58 Nothing yet. But you could say, "Ah, but it, it's if..." It's just, it's just much, much smaller. You can say that.

Lex Fridman 51:04 (laughs) Which, by the way, makes LIGO and, uh, the detection of gravitational waves quite an incredible project.

Peter Woit 51:11 Yeah.

Lex Fridman 51:13 Ed Witten is often brought up as one of the most brilliant mathematicians and physicists ever. Uh, what do you make of him and his work on string theory?

Peter Woit 51:24 Well, I think, you know, he's a truly remarkable figure. I've, you know, had the pleasure of meeting him first when he was a post-doc. And, um, I mean, he's a just completely amazing mathematician and physicist. And, uh, you know, he's quite a bit smarter than just about, about any of the rest of us, and also more hardworking. And it's a, it's a kind of frightening combination to see how much he's been able to do. And, um, but I would actually argue that, you know, his, 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, his greatest work is stuff that doesn't have, has little or nothing to do with string theory. I mean, for instance, he, um, you know, so he was actually one of Fields... The very strange thing about him in some sense is that he, um, he doesn't have a Nobel Prize. So there, 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, is it would have been very hard to come up with a new idea that was gonna work physically and get you a Nobel Prize. But he, but he, um, you know, he had got a Fields Medal for certain work he did in, um, in mathematics. And that's just completely unheard of, you know, for mathematicians to give a Fields Medal to someone outside their field.

Lex Fridman 52:59 Mm-hmm.

Peter Woit 53:00 And physics is really, um, you know, you wouldn't have before he came around, I don't think anybody would have thought that was even conceivable.

Lex Fridman 53:08 So you're saying he came into the field of theoretical physics at a time when, uh, and still today, is you can't get a Nobel Prize for purely theoretical work.

Peter Woit 53:20 A specific problem of trying to do better than the standard- the standard model is just this insanely successful thing, and- and it kind of came together in 1973 pretty much. And post... And so- and all of the people who kind of were involved in that coming together, you know, many of them ended up with Nobel Prizes for that. But- but if you look post-1973 pretty much, it's a little bit more, there's some edge cases, if you like. But the, if you look post-1973 at what people have done to try to do better than the standard model and to get a better unified theory, it really hasn't... It's been too hard a problem. It hasn't worked. The theory is too good. And so it's not that other people went out there and did, and did it and, uh, 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, um, no one has been able to do since 1973.

Lex Fridman 54:15 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 and so on. Why? What's wrong? What's broken about the standard model? Why- why does it need to be improved?

Peter Woit 54:33 I mean, the thing which gets most attention is, um, is gravity that we have trouble. Um, so you want to, you want to, in some sense, integrate, 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- 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... (laughs) That- that- that are, let- let's just say that they're not beautiful. They're not, um, you have to th- to make the thing work, you have to throw in lot- lots and lots of extra parameters at various points. Um, and a lot of this has to do with the so-called, uh, you know, 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, um, is- 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- a Higgs field and you need to, it needs to do, to do something. And once you introduce that Higgs field, all sorts of parameters, um, make an appearance. So now we've got 20 or 30 or whate- 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 parameters to a... This- 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 i- 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 it- but, you know, 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 that's... That's what we should look for, but-

Lex Fridman 56:53 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 can... Like, if you think of it as a flame, still should be a little flame that keeps- keeps burning?

Peter Woit 57:14 Well, I- I think the, I mean, the- the most positive argument for it is, is all the, um, you know, all sorts of new ideas about mathematics and about parts of physics really emerge from it. So, it was very, a fruitful, um, source of ideas. And I think, you know, this is actually one argument you'll definitely, which I kind of agree with, you'll hear from- from Witten and from other string theorists, is that, you know, this is a, this is just such a fruitful and inspiring idea and it's led to so many other different things coming out of it that, you know, there must be something right about this.

Lex Fridman 57:44 (laughs)

Peter Woit 57:45 And, um-

Lex Fridman 57:45 Yeah.

Peter Woit 57:46 ... that's, you know, okay, that, anyway, I think that- that's probably the stro- the strongest thing that they, that- that they've got, um-

Lex Fridman 57:52 But you- you don't think there's aspects to it that could be, uh, neighboring to- to- to th- uh, to a theory that does unify everything, to a theory of everything? Like, it could, it may not be exactly, um, uh, exactly the theory, but, uh, sticking on it longer might get us closer to the theory of everything?

Peter Woit 58:14 Well, the problem with it now really is that you really don't know what it is now. You- you've never... Nobody has ever kind of come up with this non-perturbative theory. So there- there, it's- it's become more and more frustrating and- and an odd activity to try to argue with a string theorist about string theory because- because it's become less and less well defined what- what- what it is. And it's become actually more and more kind of a... Whether... (laughs) You- 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 then branched out in all sorts of directions doing all sorts of things that became farther and farther removed from that. And for sociological reasons the ones who kind of started out or- or now or- or were trained by the people who worked on that have now become this string- string theorists, and, um, and but- but- but it's becoming almost more kind of a tribal denominator than a, um-

Lex Fridman 59:26 Well-

Peter Woit 59:26 ... I think, so it's very hard to know what you're arguing about when you're arguing about string theory these days.

Lex Fridman 59:30 Well, to push back on that a little bit, I mean, string theory, that's just a term, right? It doesn't... Like, you could, uh, like, this is the way language evolves, is it could start to represent something more than just a theory that involves strings. It could represent the, uh, the effort to unify the laws of physics, right?

Peter Woit 59:49 Yeah.

Lex Fridman 59:50 At- at a, at high dimensions with these super tiny objects, right? Or something like that. I mean, we- we can sort of, uh, put string theory aside. So for example, neural networks in the space of machine learning, there was a- a time when they were extremely popular. They became much, much less popular to the point where if you mention neural networks, you're getting no funding and, uh, you're not going to be respected at conferences, and then once again, uh, neural networks became all the- all the rage about 10, 15 years ago. And as it goes up and down and a lot of people would argue that, uh, using terminology like machine learning and deep learning is, um, is th- uh, you know, often misused, over general, you know, everything that works is deep learning, everything that doesn't isn't-

Peter Woit 1:00:37 Yeah.

Lex Fridman 1:00:37 ... something like that. You know, that's just the way, uh, hum- again, we're back to sociological things.

Peter Woit 1:00:42 Yeah.

Lex Fridman 1:00:43 But I guess what I'm trying to get at is if- if we leave the sociological mess aside, uh, do we throw out the- the baby with the bath water? Is there some...... besides the side effects of nice ideas from the Ed Witten's of the world, is there some core truths there that we should s- stick by in, in, in the full beautiful mess of a space that we call string theory, that people call string theory?

Peter Woit 1:01:11 You're right. It is kind of a common problem that, you know, how, what you, what you call some field changes and evolves and in interesting ways as, as the field changes. But it, I mean, I guess what, what I would argue is the, you know, the initial understanding of string theory that was quite specific, we're talking about a specific idea, 10 dimensional super strings compactified in six dimensions. That, to my mind, the, the really bad thing that's happened to the subject is that you c- 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 tell- talking to the public about, about str- string theory and referring back to that idea and using that as kind of the starting point and as kind of the, the place where the, the whole, where, where the whole tribe starts and everything has, comes from. And so the, the problem with this is that having as your, as your initial name and, and what e- what everything points back to something which, um, whi- whi- which really didn't work out, it kind of makes everybody, makes everything... You created this potentially very, very interesting field with interesting things happening, but you know, people in h- in graduate school take courses on string theory and, 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, it really kind of deforms the whole, your whole way of, um, your, your hopes of making progress. And I, that's, to me, I think, you know, the kind of worst thing has, that's happened in this, in this field.

Lex Fridman 1:02:59 Okay, sure. So there's a lack of transparency and sort of authenticity about communicating the things that failed, uh, in, in the past.

Peter Woit 1:03:07 Yeah.

Lex Fridman 1:03:07 And so you don't have a clear picture of, like, firm ground that you're standing on. Again, those are sociological things, and-

Peter Woit 1:03:14 Yeah.

Lex Fridman 1:03:15 ... I, I... There's a bunch of questions I want to ask you. So one, what's your intuition about, um, why the original idea failed? So what can you say about why you're pretty sure has, it has failed?

Peter Woit 1:03:32 You know, and the initial idea was, as I tried to explain it, it was quite seductive in that, that you could see why Witten and others got excited by it. It was, um... You know, at the time, it looked like there were only a few of these possible cAlbi-Yau's 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, it just didn't, um... They, 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, this is just not going to work.

Lex Fridman 1:04:12 Meaning like, it's... (laughs) I mean, wh- what, in, what was the failure, um, mode here? Is it, is... You could just have an infinite number of possibilities that you could do so it's, you can come up with any theory you want, you can fit quantum mechanics, you can f- you can explain gravity, you can explain anything you want with it?

Peter Woit 1:04:32 R- right.

Lex Fridman 1:04:32 Is that the basic failure mode?

Peter Woit 1:04:34 Yeah, so it's a failure mode of kind of that this idea ended up being, kind of being essentially empty, that it, it just didn't, doesn't... ends up not telling you anything because it's consistent with just about an- just about anything. And so, I mean, there's a c- comple... If you try and talk with string theorists about this now, I mean, there's a, there's an argument, there's a long argument over this about whether, um, you know, "Oh, no, no, no, maybe there still are constraints coming fr- coming out of this idea or not," and... Or maybe we live in a multiverse and, you know, every- everything is true anyway, so you can... There're, there're various ways you can kind of... that string theorists have kind of rea- reacted to this k- kind of argument that I'm making. They try to hold onto it.

Lex Fridman 1:05:15 (laughs)

Lex Fridman 1:05:16 Um, what about experimental validation? Is that, uh, is that a fair standard to hold before a theory of everything that's trying to unify quantum mechanics and gravity?

Peter Woit 1:05:29 Yeah, I mean, u- ultimately to be really convinced that, you know, that, that un-... some new y- idea about unification really works, you need some kind of a... You need to look at the real world and see that this is telling you something, something true about it. I mean, you know, either, 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, it will show you how to calculate them. I mean, it can, it can be various kinds of experimental validation, but that, that's certainly ideally what you're looking for.

Lex Fridman 1:06:08 How tough is this, do you think, for a theory of everything, not just string theory? So for something that unifies gravity and quantum mechanics, so the, the very big and the very small, is this, um... Let me ask it one way, is, uh, is it a physics problem, a math problem or an engineering problem?

Peter Woit 1:06:28 My, my guess is it, it's a combination of a physics and a, and a math problem that you really need... It's, it's not really engineering. It, it's not like there's some kind of well-defined thing you can write down and, and we just don't have enough computer power to do the calculation. It... That's not the kind of problem it is at all. Um, but the question is, you know, what mathematical tools you need to properly formulate the problem i- i- is unclear, so one reasonable conjecture is the way... the reason that we haven't had any success yet is just that, um, we're missing... either we're missing certain-... physical ideas, or we're missing certain mathematical tools which, or some combination of them, which would, uh, whi- which we need to kind of properly formulate the problem and see w- and, and, and see that it, it has a solution that looks like the real world.

Lex Fridman 1:07:17 But does she need, uh, I g- I guess you don't but, there's a sense that, uh, you need both gravity, like, all the laws of physics to be operating on the same level, so this isn't, it feels like you need an object like a black hole or something like that, um, in order to make predictions about. Otherwise, you're always making predictions about this joint phenomena. Uh, or, or can you do that as long as the theory is consistent and doesn't have special cases for each of the phenomena?

Peter Woit 1:07:48 Well, your, your theory should mean, s- if your theory is gonna include gravity, our current understanding of gravity is that you should have, um ... there should be black hole states and then you should be able to describe black holes in this theory, and, um, 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 are certain kind of paradoxes which come up. And so that's, that's been a huge focus of kind of quantum gravity work, work has been not just those paradoxes, but ...

Lex Fridman 1:08:20 So stepping outside of string theory, uh, can you just say first at a high level, what is a theory of everything? What is a theory of everything seek to accomplish?

Peter Woit 1:08:32 Well, I mean, this is very much a kind of reductionist point of view in, in the sense that so it's not a theory. This is not gonna explain to you, you know, anything. It doesn't really, this kind of theory, theory, this kind of theory of everything we're talking about doesn't ex- say anything interesting, particularly about like macroscopic objects, about what the weather is gonna be tomorrow, or, you know, things that are happening at this scale. But just what we've discovered is that as you look at, um, the universe that kind of, you know, if you kinda start break, you can start breaking it apart into ... and yet you end up with some fairly simple pieces, quanta, if you like, and w- and which are doing, which are interacting in some fair- in some fairly simple way. And it's, um, it's got th- so what we mean by a theory of everything is a theory that describes all, a- 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 a most fundamental level. How you get from that theory to describing some macroscopic incredibly complicated thing is, there that becomes m- again more of an engineering problem than ... you may need machine learning or you may, you know, a lot of very different things to do it, but ...

Lex Fridman 1:09:45 Well, I don't even n- think it's, uh, just engineering. It's also science. It-

Peter Woit 1:09:50 Yeah.

Lex Fridman 1:09:50 One thing that I find, um, kind of interesting talking to physicists is, is a little bit ... there's, um, a little bit of hubris. Some of the most brilliant people I know are physicists, both philosophy and just in, in terms of mathematics, in terms of understanding the world. But there is a kind of a, either a hubris or w- what would I call it? Uh, 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, the old Rutherford thing. Uh, 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.

Peter Woit 1:10:41 Yeah.

Lex Fridman 1:10:42 Like at, at every le- level from biology, like how life originates, that itself, like complex systems.

Peter Woit 1:10:52 Yeah.

Lex Fridman 1:10:52 Like, that in itself is like this gigantic thing that requires a theory of everything. And then there is the, wha- 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.

Peter Woit 1:11:16 Yeah.

Lex Fridman 1:11:16 Like that feels like it needs a theory of everything. And it's almost like, um, once we solve, uh, o- 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, uh, how, like how the, uh, 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-

Peter Woit 1:11:42 Yeah.

Lex Fridman 1:11:43 ... still we won't be able to have a strong explanation of, uh, why food tastes delicious. (laughs)

Peter Woit 1:11:52 Oh, yeah, yeah. No, no anyway, I, I, yeah, I agree completely. I mean this, there is something kind of completely wrong with this terminology of theory of everything. It, it, it's not, um, it's really in some sense very bad ter- very hubristic and bad ter- terminology because it's not, um ... this is explaining, this is a purely kind of reductionist point of view that you're, you're trying to understand cer- certain, uh, certain very specific kind of things which, you know, in principle other things, you know, emerge from. But to actually understand how anything emerges from this is i- it's ho- it can't be understood in terms of this, this underlying fundamental theory is gonna be ho- hopeless in terms of kind of telling you what a- about this, um, this various emergent behavior. And as you go to different levels of explanation you're gonna need to develop new, you know, different, completely different ideas, completely different ways of thinking and I guess there's a famous kind of, um, Phil Anderson's slogan is that, you know, more is different.

Lex Fridman 1:12:54 (laughs)

Peter Woit 1:12:54 And then, yeah, so, and, i- i- it's just, it's, it's ju- yeah, e- even once you understand how what a couple thing ... well, if you have a collection of stuff and you understand perfectly well how each thing is interacting with it-... with, with the others. What the whole thing is gonna do is just a completely different problem, and it's just not ... And you need completely different ways of thinking about it.

Lex Fridman 1:13:13 What do you think about this ... Uh, I gotta ask you. At a few different attempts at a theory of everything, especially recently, uh, so I've been, for many years, a big fan of cellular automata, complex systems, and obviously if, uh, because of that, a fan of Steven Wolfram's work on, in that space. But he's recently been talking about a theory of everything through his physics project-

Peter Woit 1:13:36 Yeah.

Lex Fridman 1:13:36 ... essentially. Uh, what do you think about this kind of discrete theory of everything for like from simple rules and simple objects and hypergraphs emerges all of our reality, where time and space are emergent. Basically everything we see around us is emergent.

Peter Woit 1:13:53 Yeah, I, yeah, I- I have to say, unfortunately, I've kind of pretty much zero sympathy for that. I mean, I don't, um, I s- I spent a little time looking at it, and I just don't see ... It doesn't seem to me to get anywhere. And, and it, it really is, just really, really doesn't agree at all with, with what, what, with what I'm seeing. This, the 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 wanna believe that, that your things are really coming out of cellular automata at the most, um, fundamental level, you have to believe that everything that I've seen my whole career and, and as, as beautiful, powerful ideas, that that's all just kind of a mirage which is kind of randomly is emerging from these more basic, very, very simple-minded things. And I'm ... You have to give me some serious evidence for that, and I'm seeing nothing.

Lex Fridman 1:14:46 So, mirage. You, you don't think there could be a consistency where, um, things like quantum mechanics could, could emerge from much, much, much smaller, discrete like computational-type systems?

Peter Woit 1:15:00 Well, 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 a- a- about really f- ... The fundamental objects that you work with and when you write down a quantum theory are in some s- in some f- one 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. Any- anyway, I don't see it as, as a promising, uh, you know, promising thing to do, and then just looking at it and seeing 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? It ju- I just don't see it.

Lex Fridman 1:15:46 Yeah. To me, cellular automata and these hypergraphs, I'm not sure if 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.

Peter Woit 1:16:02 Yeah.

Lex Fridman 1:16:02 So there's not good math explaining, forget the physics of it, math explaining the behavior of complex systems.

Peter Woit 1:16:08 Yeah.

Lex Fridman 1:16:09 And that to me is both exciting and paralyzing, like we're at the very early days of understanding, you know, how complicated and fascinating things emerge from simple rules.

Peter Woit 1:16:21 Yeah. You know, and I- I agree. I think that is a truly great problem, and depending where it goes, it may be, um ... You know, it- it may start to develop some kind of connections to the, the things that I've kind of found more fruitful and hard to know. It just, uh ... I think a lot of that area, I, I kind of strongly feel I best not say too much about it 'cause I, I just ... I don't know too much about it, and, uh, I mean, again, we're back to this original problem that, you know, your time and life is, uh, is limited. You have to figure out what you're gonna spend your time thinking about, and that, that's something I've just never seen enough to convince me to spend more time thinking about it.

Lex Fridman 1:17:01 Well, also timing. It's not just that our time is limited, but-

Peter Woit 1:17:04 Yeah.

Lex Fridman 1:17:04 ... uh, the timing of the kind of things you think about. There, 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.

Peter Woit 1:17:18 Yeah.

Lex Fridman 1:17:18 And so it's like you have to pick the problems that are solvable today. In fact, my intuition, again, not ... Perhaps biased, is it feels like the kind of systems that, complex systems that cellular automata are would not be solved by human brains.

Peter Woit 1:17:35 Yeah.

Lex Fridman 1:17:36 It feels like we'll ... Like it feels like something post-human that will solve that problem. (laughs) Or like-

Peter Woit 1:17:42 (laughs) That's right, yeah.

Lex Fridman 1:17:42 ... significantly enhanced humans, meaning like using computational tools, very powerful computational tools, to us ... to, to, to crack these problems open. Um, that's, 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. Uh, currently, computation is the thing that sort of assists us in, um, understanding science the way we've been doing it all along. But if there's a whole new ... I mean, that, well, from new kind of science, right? It's a little bit dramatic.

Peter Woit 1:18:22 (laughs)

Lex Fridman 1:18:22 But, you know, this ... I- if computers could do science on their own, computational systems, perhaps, um, 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-

Peter Woit 1:18:41 Yeah.

Lex Fridman 1:18:41 ... uh, perhaps it'll crack open some interesting facets of this physics problem, but it's, it's very far away. So timing is everything.

Peter Woit 1:18:47 Th- that, that, that's perfectly possible, yeah.

Lex Fridman 1:18:50 Uh, well, let me ask you then, in the space of geometry ... I don't know how well you know Eric Weinstein.

Peter Woit 1:18:57 Oh, quite well, yeah.

Lex Fridman 1:19:00 What are your thoughts about his geometric community and the space of ideas that he's playing with on, um ... in his proposal for a theory of everything?

Peter Woit 1:19:09 Well, I, I think he, that he has ... He, he fundamentally has, I think, the same problems that everybody has had trying to do this, and, you know, they're various v- they're, they're really versions of the same problem that you try to, um ...... you try to get unity by put- putting everything into some bigger structure. So, he's- has- has- has some other ones that- that he- that are not so conventional that he's trying to work with. But, um, he has the- he has the same problem, that even if he can- (laughs) i- if he can get a lot farther in terms of having a- a really well-defined, well-understood, clear picture of this- these lar- these things he's working with, they're really kind of large geometrical structures with 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, um... Yeah. So- so I- I just... Anyway, it- it- it's the same, and the- and there's- and another interesting example of a simi- similar kind of thing is, um, Garrett Lisi's th- theory of everything. Again, you know, he's- there, it's a little bit more specific than Eric's. He was working with this E8. But it, um... Again, it- it, I think all these things founder at