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.
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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 there are 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.
And 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 much, much very, very interesting area.
And if you go back kind of far enough to in history and look at figures like Newton or
something, I mean, at that point, you can't really tell, you know, was Newton a physicist
or a mathematician.
Yeah, mathematicians will tell you as a mathematician, the physicists will tell you as a physicist,
but he will say he's a philosopher.
Yeah, that's interesting, but 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'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, really everywhere at this point.
Which particular overlap are you looking at, Goop theory?
Yeah, so at least the way it seems to me that if you look at physics and look at the, our
most successful laws of fundamental physics, they're really, 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 that these, this very deep mathematics provides
kind of a unifying set of math, 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 1500 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 Edward Frankel about love and math.
Oh 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 are, 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 physicists' 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, 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?
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?
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?
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, they're not at all close, have any obvious connection
to kind of human everyday experience that they're really quite different.
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 and 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.
Let's say 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 that in those four dimensions.
I thought you were going to scare me that we're going to 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,
you know, 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 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 it's sort of creating all these extra
dimensions just to give yourself extra degrees of freedom, isn't that the process of mathematics
is to create all 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.
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 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.
But when I'm trying to do things in mathematics, and I'm trying 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
going to work and when it's not going to 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 example 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, just to kind of try
to boil it down to what's the simplest situation in which this kind of thing is going to 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 with neural networks, for example, is you try to play with a simple
simple example and just to build up intuition by any kind of object has a bunch of variables
in it.
Yeah.
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 everything inside your mind and sort
of build like 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 going to be a much higher dimensional space.
So even simple examples, embedding them into three dimensional space, you're losing a lot.
Yeah.
Or 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.
You can train yourself to try it as much as to kind of think about things in your mind.
You know, I often use pad and paper and often if my office office, I'll 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 me quite sad.
It makes me, it makes it seem like there's a giant mystery out there that will 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, you know, I could explain to you how this works, but you'd have to be
willing to sit down with me and, you know, work at this repeatedly for, you know, hours
and days and weeks and you'd, I mean, it's just going to take that long for your mind
to really wrap itself around what's going on and that, so that does make things inaccessible,
which is sad, but again, I mean, 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 going to 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, what's used 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 attempted 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 quantum mechanics.
And 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.
Well, can I actually, on a small tangent, you did write a paper towards the Grant Unified
Theory of 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
in 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 going to 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.
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 in them that was starting to be really successful in number
theory in the 60s.
So that this actually was, anyway, that this could be thought of in terms of these ideas
about symmetry in groups and representations and in a way that was also close to some ideas
about geometry.
And then more later on in the 80s and 90s, there was something called geometric Langlands
that people realized that you could take what people have been doing in number theory in
Langlands and 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 Schultz and Laurel Farg, where they made some serious advance
and try to understand a very much kind of a local problem of what happens in number theory
near a certain prime number, and they turn this into a problem of exactly the kind of
geometric Langlands people had been doing these kind of pure geometry problem.
And they found by generalizing mathematics, they could actually reformulate it in that
way.
And it worked perfectly well.
So one of the things that makes me sad is, you know, I'm a pretty knowledgeable person
and then what is it, at least I'm in the neighborhood of 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 them in the group of people
who really understand all these ideas.
And so for instance, this paper of Shultz 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 it's a, so I think even you find if you talk to mathematicians and physicists,
even they will often feel that, 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 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 this pace of mathematics or physics?
There's an idea that, you know, 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
understood this very simple idea until I kind of learned it when I actually started teaching
math classes, which is maybe that there, maybe there's a simple way to explain kind of fundamental
way in which algebra and geometry are connected.
So you normally think of geometry is about these spaces and these points and you think
of algebra is this very abstract thing about, with 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 is nothing geometric about it, but the kind of really fundamental
idea is that unifies algebra and geometry is to, is to realize, 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, you know, a standard
kind of thing that seems to have nothing to do with geometry is the, is the, the integer.
So then there, you can, you can multiply them and add them, it's an algebra, but the, 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 our 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
modular, that prime.
So if, as you say, I don't know, if you give, give in 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 zero, one, what is, what is this value at three?
Well, it's nine plus one.
So it's, it's one mod three.
So 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 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 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, you, I mean, you can take, if somebody gives you a space, you can
ask, you can say, well, let's, 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 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 on 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, 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 work is to trans change your problem into algebra by changing your space, stop thinking
about your space and the points in it and thinking about the functions on it.
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.
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.
So this is kind of all the time.
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, you know, 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, you may need a more sophisticated kind of algebra.
But, but in some sense, I mean, much or most of modern number theory is based upon this
move to, to geometry.
And there's 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 dirham, homology, and you get the topology.
Yeah.
Anyway.
Well, let me, 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?
Like first, why is this beautiful?
And second, what is beautiful?
Well, and I think there are many different things you can find beautiful for different
reasons.
And 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, I mean, you can almost kind of try and measure it in the sense of,
you know, what's the, what are the implications of this idea?
But non-trivial things as it tell you versus, you know, how, how, how, how simply can you,
can you express the idea and so, so the level of compression, what does it correlates with
beauty?
Yeah.
That's, that's one, 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, 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, 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, the, 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, I mean, the kind of best theories we've been coming, coming
up with are ultimately when properly understood, relatively simple and much, much simpler than
they, 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 or we just like ultra biased and we, we,
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 at the core is simple?
My own belief is that there is something about a universe that is that simple and I was trying
to say that, you know, there is some, some kind of fundamental thing about math, physics
and physics and all this, all this picture, which is, which is in some sense simple.
It's true that, you know, 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 in there.
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.
So there's a brilliant physicist by the name of Sabine Hassanfelder who both agrees and
disagrees with you.
I suppose agrees that the final answer will be simple, but simplicity and beauty leads
us astray in the, in the local pockets of scientific progress.
Do you, do you agree with her disagreement and do you disagree with her agreement and
agree with the agreement?
Well, I, anyway, I, I, I, I, yes, I thought it was really fascinating reading her book
and, you know, and anyway, I was finding disagreeing with, with a lot, but then at the end when
she says, yes, when we find there, when we actually figure this out, it will, it will
be simple.
And yeah.
Okay.
So we agree in the end.
But does beauty lead us astray, which is the, the core thesis of her work in that book?
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, they're often meaning
not what I would call math, which is the interesting ideas of math, but just some complicated calculation.
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, 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 it's like any kind of love affair.
It's very easy to believe that, you know, you're 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 going to 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 is 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, 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 think so it's not that the simplicity would be Lisa's astrays that 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 in a situation that emphasizes the simplicity and the beauty.
Yeah, that's part of it.
But the thing about physics that you have is that you, you know, what really can tell
it, if you can do an experiment and check and see if nature is really doing what your
idea expects that you do in principle have a way of really testing it.
And it's certainly true that if you, you know, if you thought you had a simple idea and that
doesn't work and you got into 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, 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 that there's something wrong there which needs fixing.
And so I think that part of her argument, I think I was, we're on the same page about.
What is consistency and inconsistency?
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, you know, she
would argue and I would agree that, for instance, if you're trying to think about gravity and
how are you going to have a quantum theory of gravity, you should kind of be, you know,
just any of your ideas with kind of a thought experiment, you know, is, does this actually
give a consistent picture of what's going to happen, of what happens in this particular
situation or not?
So this is a good example you've written about this, 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 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 speed 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 a 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, where 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, 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, 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 of the 500 solutions.
So, 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 such an infinite number of things which you have no way to experimentally distinguish.
So this is just a depressing situation.
But I do think 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, 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 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, it's 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 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 going to quantize this theory of loops moving around
in space-time.
And what they found is that you could do this and you could 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 got to 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 Klabi-Au 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 mean, 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 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 don't work out the way you want and they don't actually end up carrying the
power 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 they're branched out.
You mentioned 10 dimensions.
You mentioned loops with infinite degrees of freedom.
What are the interesting ideas to you that kind of emerged from this world?
Well, yeah.
I mean, the problem in talking about the whole subject and partly one of the reasons I wrote
the book is that it gets very, very complicated.
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 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.
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 is some totally fantastic mathematics behind it.
And again, and some of that mathematics is exactly also what appears in the Langlis program.
So a lot of the first interaction between math and physics around the Langlis program
has been around these two-dimensional conformal field theories.
Is there something you could say about what are the major problems are with strength theory?
So besides that there's no experimental validation, you've written that a big hole in strength
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, 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 or 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 in by the name perturbative, but there's a standard
way we know of giving 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 with string theory by itself really only works in 10 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
dimensions.
So kind of the simplest one was the claviao postulate.
But when that didn't really work out, people have tried more and more different things.
And the hope has always been that this 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 perturbed expansion, 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, you have to get rid of the six dimensions.
So there's kind of two ways of doing it.
One is what we call 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 that 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 in more and more dimensions is that, I mean, asking the question
like what are all possible six-dimensional spaces, it's just a, it's kind of an unanswerable
question.
It's just, I mean, it's even kind of technically undecidable in some way.
There are just 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've 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's just so many ways you can put things
together of and get something of that dimensionality.
So unless you have some very, very strong principle, which is going to pick out some
very specific ones of these six-dimensional spaces, and there's 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's 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 that 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
going to 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 the stuff and then trying to explain why we don't see
it?
I mean, it just-
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 or 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, you know, assume that we've got model, look at models
with more dimensions and ask, you know, what would the observable effects, how would we
know this?
And then you go out and do experiments.
So for instance, you have like gravitationally, you have an inverse square law of forces.
Okay, if you had more dimensions, that inverse square law would change or 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
at even kind of, you know, 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.
But you can 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 Whitten 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.
And, but I would actually argue that, you know, 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 doesn't have, has little or nothing to
do with string theory.
I mean, for instance, he, you know, he, so he was actually one of fields, the very strange
thing about him in some sense is that he, 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 he was, it was very
hard to come up with a new idea that was going to work physically and get you a Nobel Prize.
And he, you know, he got a Fields Medal for a certain work he did in mathematics and that's
just completely unheard of, you know, for mathematicians to give a Fields Medal to someone
outside their field and physics is really, you know, you wouldn't have before he came
around and I don't think anybody would have thought that was even conceivable.
So you see things, 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 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.
And 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, you know, idea, 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 it and not him and that they
got Nobel Prizes for doing it and 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 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, you know, the so-called Higgs mechanism in
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, a 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, to do something.
And once you introduce that Higgs field, all sorts of parameters make it apparent.
So now when we've got 20 or 30 or whatever parameters that are going to tell you what
all the masses of things are and what's going to happen.
So you've gone from a very tightly constrained thing with a couple 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 couldn't, like if you
think of it as a flame, still should be a little flame that keeps burning?
Well, I think the most positive argument for it is all sorts of new ideas about mathematics
and about parts of physics really emerge from it.
So it was very fruitful source of ideas.
And I think this is actually one argument you'll definitely, which I kind of agree with all
here from Witton and from other string theorists, 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 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?
It may not be 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.
Nobody has ever kind of come up with this non-perturbative theory.
So it's become more and more frustrating and an odd activity to try to argue with string
theorists 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, were there 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 that became farther and farther removed from that.
And for sociological reasons, the ones who kind of started out or were trained by the
people who worked on that have now become this string theorists, but it's become almost
more kind of a tribal denominator than a, 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, it's 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?
Yeah.
And 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 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 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 admittance 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 what you call some field changes and evolves in interesting
ways as the field changes.
But 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
as six dimensions, that, to my mind, the really bad thing that's 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, and this
is what you tell the public in which you 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 and 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?
And the initial idea was, as I try to explain it, it was quite seductive in that you could
see why Whitton and others got excited by it.
At the time, it looked like there were only a few of these possible clobby hours that
would work.
And it looked like, okay, we just have to understand this very specific model in these
very specific six dimensional spaces, and we're going to get everything.
And so it was a very seductive idea.
But it just, as people learn more and more about it, they just kind of realize that they're
just more and more things you can do with these six dimensions, and this is just not
going to work.
Meaning like, I mean, what was the failure mode here?
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 essentially empty.
It just doesn't end up not telling you anything because it's consistent with just about anything.
And so, I mean, there's a conflict.
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, you know, 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 there are various ways that string theorists have kind of react to this kind of argument
that I'm making, but try to hold on to 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, you know, that on some new idea about
invocation really works, you need some kind of, you need to look at the real world and
see that this is telling you something, something true about it.
You know, 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 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 be various kinds of experimental validation, but that's certainly ideally
what you're looking for.
How tough is this, do you think?
For 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 it 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 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 are some combination of them, which we need to 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,
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 going to 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 kind of paradoxes which come up.
And so that's been a huge focus of quantum gravity where it has been just those paradoxes.
So stepping outside of string theory, can you just say first at a high level, what is
a theory of everything?
What does a 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 going to 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 going to be tomorrow or things are happening at this scale.
But just what we've discovered is that as you look at the universe, you can start breaking
it apart and you end up with some fairly simple pieces, quanta, if you like, and which are
interacting in some fairly simple way.
And so what we mean by the theory of everything is a theory that describes 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, again, more of an engineering problem and you may need machine learning
or you made a lot of very different things to do it.
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 little
bit of hubris.
So 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 a hubris or what would I call it, like a confidence that if
we have a theory of everything, we will understand everything.
This is the deepest thing to understand and I would say, and like the rest is details.
That's the old Rutherford thing.
But to me, this is like a cake or something.
There's layers to this thing and each one has a theory of everything.
At every level from biology, like how life originates, that itself like complex systems.
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.
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.
Oh yeah.
I know.
No, anyway, 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 very bad term, very heuristic and bad to terminology
because it's not.
This is explaining, this is a purely kind of reductionist point of view that you're trying
to understand certain very specific kind of things which in principle, other things emerge
from.
But to actually understand how anything emerges from this, it can't be understood in terms
of this underlying fund wealth area is going to be hopeless in terms of kind of telling
you what about this various emergent behavior and as you go to different levels of explanation,
you're going to need to develop completely different ideas, completely different ways
of thinking.
I guess there's a famous kind of Phil Anderson's slogan is that more is different.
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 it, with the others,
what the whole thing is going to do is just a completely different problem 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 at a theory of everything, especially recently.
So I've been for many years a big fan of cellular automata of complex systems and obviously
if 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 discrete theory of everything 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 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.
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.
You have to give me some serious evidence for that and I'm saying nothing.
So mirage, you don't think there could be a consistency where things like quantum mechanics
could emerge from much, much, much smaller, discrete, like computational type systems?
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 about really the fundamental objects that you work with when you write
down a quantum theory are, in some point of view, precisely the fundamental objects at
the deepest levels of mathematics that you're working with are exactly the same.
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 a great problem and depending where it goes, it may start to develop
some kind of connections to the things that I've kind of found more fruitful and hard
to know.
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 I mean, again, we're back to this original problem that your time in life is limited.
You have to figure out what you're going to 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
or 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, 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.
It feels like, well, like 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 us 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 as computational
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 new kind of science, right?
It's a little bit dramatic, but 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.
Well, let me ask you then, in the space of geometry, I don't know how well you know
Eric Weinstein, quite well.
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 they're various, they're 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 get a lot farther in terms of having a
really well-defined, well-understood, clear picture of these things he is working with,
they're really kind of large geometrical structures, many dimensions, many kinds.
And I just don't see any way he's going to have the same problem the string there has
had.
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 Luzi's theory of everything.
And it's a little bit more specific than Eric's, he's working with this E8.
But again, I think all these things founder at the same point that you don't, you create
this unity, but then you have no, you don't actually have a good idea how you're going
to get back to the actual, to the objects we've seen, how are you going to, you create
these big symmetries, how are you going to break them, 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 it.
Well, yeah, and 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 a, 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 the 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 in together into this bigger
structure called the 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, those ideas, the kind of thing that Eric and also Garrett
and lots of people who try to do, they all kind of found her in that same, in that same
way that they don't have, they don't have a good answer to that.
Are there lessons, ideas to be learned from theories like that, from Garrett Leases 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 to 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, they're, I mean, I'm in this position that somehow,
you know, I've, people write me emails for whatever reason, and I'd 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 or 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, they're still fascinating,
and that I'm missing because I'm, 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 a, somebody's
got a theory or everything about why all of what physicists are doing, perhaps the most
disturbing thing I should say about my critique, being a critic of string theory is that when
you realize who your fans are, that they, every day I hear from somebody that, 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 you know, most of these are, you know, 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, you know,
people who are quite serious physicists and mathematicians who are making a fairly serious
attempt to try to do something and like, like Garrett and Eric, and then your problem is,
you know, you spent you, you do want to try to spend more time looking at it and try to
figure out what they're really doing, but then at some point you just realize, wait
a minute, you know, for me to really, really understand exactly what's going on here would
you 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 and engineer a system, like naturally leads to engineering.
And 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, 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, but 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 where
as well as just thinking about points in space and time, you can also think about different
objects, it's all 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 be the fundamental objects are actually 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 is if
you ask yourself, you know, what do we know about the world?
We have this idea that the world out there is this, 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 what you're looking at is you're looking at, you know, 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, you're kind of living
on your degrees of freedom or living on light rays, not on points.
And it's a very different way of thinking about, about, about physics.
And you know, he and others working with him developed a, you know, a beautiful mathematical,
this beautiful mathematical formalism and a way to go back from forth between our kind
of, some aspects of our standard way we write these things down and work in the so-called
twister space.
And you know, they, certain things worked out very well, but they ended up, you know,
I think kind of stuck by the 80s or 90s, that they weren't a little bit like string theory,
that they, 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, 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, is what I think I have
an, an idea about that I think does actually, does actually work, that goes more in that
direction.
And I can, can go on about that endlessly or talk a little bit about it.
But that's the, I think that that's the, the one kind of easy to explain insight about
twister theory.
There are some more technical ones, I should, I 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.
So it's almost like our perception is like the, 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.
Like what does it mean to be operating on the light cone?
It uses a kind of mathematics that's relative, that, you know, what was 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.
But I think perhaps the most, the way that there is something you can say very specifically
about it, you know, 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.
Well, what are spinners?
Let's start with spinners.
Because I think that if we can introduce that, then I can.
By the way.
So, twister is spelled with an O, and spinner is spelled with an O as well.
Yes.
Okay.
So, 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 3.
Well, one thing you say about Penrose, I mean, Penrose is actually a very good writer and
also very good draftsman.
He's on drafts.
To the extent this is visualizable, he actually has done some very nice drawings.
So, almost any kind of expository thing you can find in 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
ask 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 of all, 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's not right.
They're pairs of complex numbers, 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?
It's just weird.
And then you can ask, well, what happens if you 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 if you think about things that are happening
in three dimensions in the standard way, the standard way of doing geometry, everything
is about vectors.
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 I'd been realized that, Leon, is that if you ask very, very generally, 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, wait a minute, there's also these other things which you can't 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 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 there 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 ballgame.
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 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?
There are some things that they do.
If you rotate a spinner around 360 degrees, it becomes minus what it was.
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,
there's nothing you can do visualizing in terms of vectors that will ever give you a
spinner.
It just is not going to 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 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 that makes it hard to visualize.
And it's crucial that it's not just any four dimensions, it's actually complex numbers.
You're really going to 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 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, twister space is four-dimensional and a point in spacetime is
a two complex dimensional subspace of all the four complex dimensions.
And as you move around in spacetime, your planes are just moving around.
And then the-
So it's a plane in four-dimensional space.
It's a plane-
Complex plane.
So it's two complex dimensions in four complex dimensions.
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 in the space of spinners is that two plane.
So it's just your whole definition of what a pointed spacetime was just told you what
a spinner was.
They're just-
It's the same thing.
They're just trying to project that into a three-dimensional space and trying to intuit
when you can't.
Yeah.
So the intuition becomes very difficult.
But 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 spacetime already.
It's just there.
So-
Do you have a hope?
You mentioned that you've been, you found an 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 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 had originally
had expected.
And so that's the new thing that 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 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, yeah.
John Horgan about, by the way, maybe discover a cool website, longbets.com or.org.
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 are a lot of interesting bets on there.
Yeah.
I would love to participate.
But it's interesting to see, you know, 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 and you get to wonder like, what was that person, what was I thinking?
That person 20 years ago is almost like a different person.
What was I thinking back then to think that is interesting?
So let me ask you this, on record, you know, 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 is definitely not that things have gone.
Yeah.
So if you were giving financial advice, you would say not to bet on it.
No, I do not.
And even I actually suspect if you ask string theory, is that question, you're going to
get 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 yeah, I don't think that's not going to 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 that hire energy
that we've really lost this ability to get unexpected input from experiment.
And while it's maybe hard to figure out what people's thinking is going to be 20 years
from now, looking at energy particle, energy colliders, and their technology, it's actually
pretty easy to make a pretty accurate guess what you're going to be doing 20 years from
now.
And I think actually, I would actually claim that it's pretty clear where you're going
to be 20 years from now.
And what it's going to be is you're going to have the LHC, you're going to have a lot
more data, an order of magnitude or more data from the LHC, but at the same energy, you're
not going to see a higher energy accelerator operating successfully in the next 20 years.
Even like maybe machine learning or great data science methodologies that process that
data will not reveal any major like shifts in our understanding of the underlying physics,
do you think?
I don't think so.
I mean, I think that feel that my understanding is that 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 computer 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 want to, there's lots and lots of, you start pointing together lots and lots
of things and we think we know they're pair by pair interactions, but what this thing
is going to 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 as
kind of 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 in
it.
The quantum computer may solve that problem, but the problem is that I don't think that
they're going to solve the problem, that they help you with a problem of not 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 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, 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 different, 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.
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 can just look at the basic physics and who
cares what the computer that'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 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?
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.
There used to be no, there's no particular obstruction, why there shouldn't be, so.
I mean, do you work on some fundamental questions about the physics of reality when you look
up to the stars?
Yeah.
Do you think about whether somebody's looking back at us?
Actually, I originally got interested in physics, I actually started out as a kid interested
in astronomy, exactly that, and a telescope, and I read 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, 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 two, 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
this stuff that, you know, Isaac Asimov, so why shouldn't 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.
Yeah.
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.
Well, do not read this book for sure.
Well, I must say that, I mean, unfortunately, yeah, you can go to my website and there's
a, 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 about, yeah, so I'm not a
fan of a lot of things of that kind.
Can I ask you a good question on this, a small tangent?
Are you a fan, okay, can you explore the pros and cons of, I forget 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 a little bit to this question about books, I mean, certainly one,
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, also find them that, but the, and that's
that's almost like the human story of the development of the ideas.
Yeah, the human story, but yeah, just also how, you know, they, these very, very weird
ideas that didn't seem to make sense that how they were struggling with them and how,
you know, they actually, anyway, it's, it's, it's, I think it's the period of physics kind
of beginning in 1905, Plank and Einstein, and ending up with the war when these things
are, get used to, you know, make passively destructive weapons are just, it's just the
totally amazing.
So many, so many new ideas.
Let me, on another 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 a special relativity, general relativity?
I mean, it's an interesting case to case base.
I mean, I mean, special, special relativity, I think we would have had, I mean, there are
other people, you could even argue that it was already there in some form and some is,
but I think special relativity would have had, without Einstein fairly, 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 he 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, you know, 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, you know, I don't forget
the number of the order of magnitude, ten 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, you know, Heisenberg
and Schrodinger came up with two, which ultimately equivalent, but two different approaches to
it, you know, within months of each other.
And you know, so if Heisenberg hadn't been there, he 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, you know, 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 going to find it.
Maybe to go back to your, to your aliens, I guess the one thing I often wonder about
aliens is would they have the same fundamental physics ideas as we, if 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, wouldn't you end up with a different ideas
of what fundamental physics is or what, 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 evolve?
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 or 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.
But we're talking about books before I distract this horribly.
Yeah, go back to books and yeah, so that's one thing I'd recommend is the books about
the, from the original people, especially Heisenberg about 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 Creuson and Man.
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, 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, you know, 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, you know, 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, enthusiastic by kind
of telling them stuff, which isn't really true, this is, 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, you know, 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's sure that as heck seems like a few steps down
the path towards intelligence.
And so like, 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 like,
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 non-intelligent system, then that's impressive and that's inspiring
and that's okay to celebrate.
And 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.
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 having a physicist and you know, 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 you just, I just, I don't know, I've never seen anything at all happening in mathematics
like what's happened in the 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, you know, 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 the 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 won't
name any names, for instance, coming on certain podcasts like yours telling the world, you
know, 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, you know, once when people
realize that this is what's going on, you know, 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 US because if they have worked and 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 that 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's 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 a loyal ants to a particular area.
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, you know, what is this physical reality?
Where do we come from?
And what on these kind of deep issues?
So there's this unusual fascination with it.
Mathematics versus very different.
Nobody is 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 kind of, 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 are 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
misrepresenting, you know, what a high school students think about string theory and not
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, you know, people, it doesn't matter so much
what the average person on the street thinks about string theory, but you know, what the
best students at Columbia or Harvard or Princeton or whatever who really want to change work
in this field and want to 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 got to do is 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.
Yeah.
So how to kind of achieve that kind of diversity of thought and within kind of the sociology
of how we organize scientific research is, I know this is one thing that I think it's
very interesting that Sabina Hossenfelder is very interesting things to say about it.
And I think also at least Moen and his book, which is also about that very, very much in
agreement with them that there's, anyway, there's a really kind of important questions
about how research in this field is organized and how people, what can you do to kind of
get more diversity of thought and get more, and get people thinking about a wider range
of ideas?
At the bottom, I think humility always helps.
Well, but 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 serious, very serious lack of humility
to believe that you're going to make progress on some of these problems.
I think you have to have like both modes, which between them when needed.
Let me ask you a question you're probably not going to want to 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.
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 physicists 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 colleague.
Nobody ever asked mathematicians.
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 going to 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 realize 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, you know, they're people and 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, you know, I've led a very pleasant and
fairly privileged existence of a 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 and 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.
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 is pretty far removed from anything, 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 going to be, you're probably not going to 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 something is done, which I may not
have, which I may otherwise not have time to do, which I didn't see.
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, 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 something I spend a lot of time trying, but yeah.
Day to day, you just enjoy the positives of mathematics.
Just enjoy, yeah, or life in general, life is, have a perfectly pleasant life and enjoy
it and often think, wow, this is, things are, I'm really enjoying this, things are going
well.
Yeah.
Life is pretty amazing.
Yeah.
If 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.
Good.
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 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.