Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas - 18 | Clifford Johnson on What's So Great About Superstring Theory

Episode Date: October 15, 2018

String theory is a speculative and highly technical proposal for uniting the known forces of nature, including gravity, under a single quantum-mechanical framework. This doesn't seem like a recipe for creating a lightning rod of controversy, but somehow string theory has become just that. To get to the bottom of why anyone (indeed, a substantial majority of experts in the field) would think that replacing particles with little loops of string was a promising way forward for theoretical physics, I spoke with expert string theorist Clifford Johnson. We talk about the road string theory has taken from a tentative proposal dealing with the strong interactions, through a number of revolutions, to the point it's at today. Also, where all those extra dimensions might have gone. At the end we touch on Clifford's latest project, a graphic novel that he wrote and illustrated about how science is done. Clifford Johnson is a Professor of Physics at the University of Southern California. He received his Ph.D. in mathematics and physics from the University of Southampton. His research area is theoretical physics, focusing on string theory and quantum field theory. He was awarded the Maxwell Medal from the Institute of Physics. Johnson is the author of the technical monograph D-Branes, as well as the graphic novel The Dialogues. Home page Wikipedia page Publications A talk on The Dialogues Asymptotia blog Twitter

On this episode of Plant Killers, we'll explore one nation's most notorious fruit and vegetable killer, bad dirt. What makes Bad Dirt so bad? The answer? The ingredients. But fear not, true crime enthusiasts. This story has a happy ending. Miracle Grow organic raised bed and garden soil. It's made with quality organic ingredients from upcycled green waste like compost and aged bark. Unlike the other guys who can't say the same, looks like Bad Dirt's murdering days are over. Thanks to Miracle Grow. Join us next time on Plant Killers. During Memorial Day at Lowe's, shop household must-haves for less. Save $80 on the Charbroil Performance Series 4-burner grill to chef up something special. Plus, get up to 45% off select major appliances to keep things fresh. Our best lineup is here at Lowe's. Lowe's, We Help, You Save. Valid through 527, while supplies last. Selection varies by location.

See Lowe's.com for details. Visit your nearby Lowe's on West Pico Boulevard in Los Angeles. Hello, everybody, and welcome to the Mindscape Podcast. I'm your host, Sean Carroll. And I remember a time, it must have been like 20 years ago by now. Oh, my goodness. I was a postdoctoral fellow doing research at the Institute for Theoretical Physics at UC Santa Barbara. And in fact, I was not doing research at the moment.

I was just wandering through one of the local bookstores. And I saw this kid. He couldn't have been more than nine or ten years old. And he found a book and his eyes lit up. And he got the book. He ran over to his mom. Christmas shopping season. And the kid says to his mommy says, Mom, Mom, Mom, Mom, look, we got to get this for Dad. It's the elegant universe. He'll love it. It's about string theory. And that was the moment when

I knew that Super String Theory, or just String Theory, for short, had entered the popular imagination. In large part, thanks to Brian's excellent book, The Elegant Universe, and the Nova TV special that followed it, which is a weird thing to have a theory of quantum gravity, or a theory of everything, which is perhaps what string theory could be, to be out there in the public debated, right? Not just, you know, told to people and they go, huh, that's interesting. People out there on the streets have really strong opinions about string theory. Some love it. Some are very disdainful of it. That's a weird state of being for a speculative, highly technical theory in theoretical physics. For some reason, string theory captures the imagination. One of my fellow

postdocs at the ITP back in those days was Clifford Johnson, who is today's guest on the Mindscape podcast. Clifford is an official card-carrying string theorist. He's written many papers on various different aspects of string theory. He's even authored a book called D-Brains. D-Brains are part of the string theory toolbox, and it's a highly technical book. I do not necessarily encourage you to buy it unless you were a professional physicist.

I do encourage you to buy Clifford's more recent book called simply The Dialogues. It is a graphic novel that Clifford both wrote the text for and illustrated. It's a novel about people talking about science, talking about physics, and suggesting the idea that sitting over coffee and talking about science is something we should all be doing. That's an idea that I'm extremely sympathetic with. So mostly today we'll be talking about string theory, where it came from, why physicists invented it, why so many physicists, so many very, very smart cookies, had become incredibly entranced by string theory. What is the origin of some of the criticisms of string theory out there and the state of the field today.

So let's go. Free is great, but only if it's useful. Free credit scores from some apps can differ by as much as 100 points from your actual FICO score that 90% of top lenders use when you apply for a credit card, personal loan, car loan, or mortgage. That can mean a higher interest rate, a bigger monthly payment, or worse. Denied. My FICO gives you your actual FICO score.

The score lenders use straight from the company that created it. For the moments that matter, get the score that matters, your FICO score. Visit myfico.com and get started for free today. Clifford Johnson, welcome to the Minescape podcast. Pleasure. Now, you're a physicist, theoretical physicist, and a string theorist. I know some string theorists, as soon as you describe them as a string theorist, they say, no, no, no, that's not what I am, I'm this other thing.

So, like, how do you label yourself? I suppose string theory takes up a lot of my time. least a lot of the things I work on have their origins in the string theory context. And yes, I'm probably one of those who pushes back against being called a string theorist. I think maybe the issue is that we're, we like to be defined by the questions we're working on rather than the tools we're using to answer those questions. So you're not technology-driven. Exactly.

Knowledge-driven. Right, right. But nevertheless, there have been strings in your papers you write, right? I mean, sort of what fraction of the papers you've actually written, let's say, in last 10 years, have been about string theory one way or the other? Probably in some sense, probably 99% of them. We're not going to quibble about that. So what is string theory, and why should we hear about it?

That's probably another thing you hear lots of. different answers from different string theorists. I tend to think of string theory as primarily our best shot right now at understanding a theory of quantum gravity, the old problem of trying to understand how to put together quantum physics and gravity. And one of the things about string theory that's very tantalizing is that it seems within the way it does that, it also gives you a chance of describing all the other. other forces of nature that we know of as well.

And that's something that distinguishes string theory from other approaches to quantum gravity. Yeah, there are other approaches of quantum gravity that regardless of what you think of them, and how successful they are, they really do seem to be mostly just a framework that is to do with the gravity and the quantum and not much else.

Although, you know, discoveries may be made. Yeah, you can always learn things. but what does quantum mean? What does gravity mean? Why is it a whole thing to get them together? Shouldn't it be easy? Now, veteran mindscape listeners have listened to Carlo Rovelli talk about these things,

but that comes from a very different place than string theory, but the motivation is similar. Yeah. The motivation is really very much to do with our understanding of the observed universe, which is that you will be pushed into, regimes where the quantum and the gravitational inevitably have to talk to each other.

So to take a step back, the quantum stuff is traditionally to do with the rules that seem to apply for the very, very small. The devices we use, computers, phones, things like that. They all use the rules of quantum mechanics to move fundamental particles like the electron around, and you know, you can use it to make cool things and understand how atoms work, the structure of matter, things like that. And that seems to be all about the very small, more or less.

But then there's this other regime which is to do with astrophysics and cosmology and so on and so forth, which is to do with, where the dominant physics seems to be about gravity. And Einstein taught us how to understand that sort of physics with what's called general relativity.

And it's all to do with, the curvature of space time, which you may have heard of. And whereas the description of quantum stuff seems to be more in terms of fundamental particles interacting with each other in various ways. And so they're very, very different pictures. But these pictures get driven together when you realize that, for example, the universe is expanding.

The universe is expanding, it's observable fact. And if you run that backwards, if you go to earlier epochs of the universe, in some sense the gravitational stuff that dominates the shape of the universe has to be understood in terms of

the particle physics type stuff, the small stuff, because the scales on which the physics is happening are those same scales, those very small scales I talked about. So the quantum physics has to talk to the gravitational physics in ways that we don't know yet because we

don't have a theory of quantum gravity that we know works for nature. String theory is... Sorry, just to get it... So as a relatively practical matter, as these things go, what you're saying is if we want to understand things like the Big Bang or presumably black holes, we need both quantum mechanics and gravity at once, and we don't yet have that. Yeah, in fact, I was going to get to black holes.

That's another region where when you think of the black hole as a thing that pops out of, for example, worrying about gravity, you end up with, famously, this thing called the Black Hole Horizon, which is sort of this one-way membrane, this place after which you pass, you cannot go back out.

And it's the famous Black Hole Horizon. It turns out when you apply quantum physics to that, no matter what the size of the black hole is, it turns out quantum physics doesn't like to play that, game of one-way barriers. And it tells you that there's actually a mechanism by which quantum mechanically that one-way barrier

will generate ways of stuff getting back out. That'll actually leak energy and mass from the black hole and make the black hole begin to shrink. And ultimately, in principle, the black hole

would disappear. And that leads you into a whole bunch of paradoxes that famously due to people like Stephen Hawking who came up with that shrinking mechanism that tell you that you need to understand

again this quantum and gravity stuff better in order to understand the fate of black holes and in some sense the fate of our understanding of quantum mechanics itself and so there are all sorts of interesting issues that begin to not go away and become

more and more annoying if you don't have a theory of quantum gravity to explain So at some very simple level of principle, the world is quantum mechanical. The world has gravity. So of course you need quantum gravity, but you're saying also as a relatively, I keep wanting to say straightforward or down to earth, but it's really not because we're talking about the big bang of black holes. But as a concrete matter, there are phenomena in our universe that can't be understood

without understanding quantum gravity. Absolutely. There are ways, just to blur it a little bit, there are. always, people do propose that maybe there are some get-out clauses and you could have gravity in a quantum mechanical world without it being quantum.

But that in some ways can often end you up in a place that's harder to explain than just quantizing the thing. That's just going to end in tears. I don't see anything good coming out of that. So that's fine and probably the motivation people are willing to accept. But now, why in the world would we

say the right way to address this is to replace particles with little loops of string if indeed that's what we're doing in string theory. Well, so the answer is that no one can tell you a good principled reason why you do that. It really was discovered by accident that that is at all the right thing to do or a right thing to do because we don't know if it's the right thing to do. When you think from a particle physics perspective about what a quantum theory of gravity should look like or a quantum theory of any... interaction, any interaction between objects.

The particle perspective is that there is a particle whose job it is to communicate the effects of that force. And so the famous, you know, the electromagnetism, that force, the force that governs all of chemistry and, you know, so is responsible for electricity and magnetism, things like that, that is communicated by the exchange of photons. So the particle we're very familiar with, it's the particle of light. And so every different kinds of force, the nuclear forces have their own exchange particles. And you can actually work out what the properties of the exchange force should be for gravity

if you did have a quantum theory of gravity, and it's called the graviton. The graviton, yes. And everyone always says, well, have you discovered gravitons yet? And I say no, and we never will because they're too hard to detect. But the principles of quantum mechanics and general relativity convince us that there are something called graviton. Yeah. And so what you could start doing is you could write down a theory. that is interacting gravitons.

And you can just write down the properties of the graviton how they should interact on general principles. And the theory just resists making sense on its own for various technical reasons, which we don't need to go into it. It just stops working pretty soon. You try and calculate anything sensible with it. Completely for other reasons,

people were playing around with the idea of what if you were not looking at fundamental particles interacting quantum mechanically, but you were looking at loops of strain. When are we thinking then now? Sorry? When were they playing? This is actually back in the 60s.

And the late 60s going into the 70s for reasons to do with trying to understand nuclear physics, they were thinking about this. There are actual mechanisms by which in nuclear interactions you effectively make these things that look like strings they're called flux tubes

and then they move like real physical objects and can interact and split and join and things like that so people thought it would actually be useful to write down a theory just in principle what would such a theory look like and so if you work it all out it actually works rather nicely and out pops something very interesting

which actually at the time was a bug in the whole description right which is that these loops of string tend to want to join their ends and become little closed loops of string. So the loops you were thinking of to start are just line segments.

Yeah, they were sort of lines. They had ends at the other. Actually, the fundamental particles called quarks that are very important in nuclear physics would be joined by these things called flux tubes and there'd be the description

and it was thought to be a candidate for the theory of the strong interactions that bind these quarks together but there were mechanisms by which these strings just the theory tells you that they have to be allowed to do that to join those ends and become loops of string that are closed and if you if you follow that you find that those loops of string the different vibrations they can do the most basic vibration

if you if you sort of squint and don't realize it's a string it's sort of it's small enough that it looks like a particle It looks just like that particle that you would have associated with gravity, what's called a spin-to massless boson, the graviton, the graviton. And sorry, I want to, you know, because I think that to the people who don't do this for a living, it's kind of a remarkable thing, the theory forces it on it. Like, you invented the theory, and it forces you to do something you didn't want to do. How often is that happening in physics? Exactly. So you often get requirements of the theory has to be consistent, and you realize, oh, I forgot this thing, so I need to add that in, or I don't have the right number of this bit compared, you know, the right ingredients weren't put together in the right way, and then you're done. one of the remarkable things

and I talk about this very fact quite a bit which is that it's unusual historically and I think has few such striking precedents that you write down a theory and it says I'm going to work but here's a list of demands for why

what I need in order to work and that list of demands and sends you off in this completely different direction and one of them was that it has to if you write down these these loops of string, it has to have this spin two particle that people then realized

later on with the graviton. The reason it was a problem is because there was no such particle in the strong interactions that they were trying to describe. They didn't want that. So it looked like a big fail. And it was. But the particle, the theory

did some other things as well. Really unprecedented says it doesn't actually work very well if you try and have it in our three spatial plus one time dimensions. It actually starts telling you that actually I'm going to work really well if I work in, I actually started out being in 26 dimensions, and then there are better versions of it that work in 10 dimensions, which is another obvious bug.

So, Street Theory has very strong union representation, and they have a lot of demands before they get to work. So 26 dimensional space time, and you need to have gravity in it. Yeah. And weaker minds than ours would have said, well, let's do something else. Exactly. And, well, not only let's do something else, but something else did come along. A better theory for describing the strong interactions called quantum chromodynamics came along. And so people were very happy to not have to deal with this list of demands.

It turns out that there were some people who thought this was really interesting. Notably, John Schwartz and Joel Scherck, they said, hey, maybe this theory is good for something else. These bugs are actually a feature and we've been using this thing for something else and this is a great example of something that I actually think is really important in not just in physics but generally speaking if people are working on a thing

with as much integrity as possible just trying to do an interesting thing and develop an idea it may often turn out that it's not necessarily good for the thing they thought it was going to be for but it often can have uses elsewhere and certainly in science we see that a lot in various other ways. There are many ideas that get recycled in various parts

and have their home in places other than where they were first invented. And certainly string theory seems to be an example of that. Yeah, it's definitely motivation for letting smart people pursue their interests in what they think is interesting without an immediate obvious payoff in the quarterly report, right? Because we're going to eventually get someplace big. So John Schwartz, my case. Caltech colleague Joel Schirk who passed away a few years ago as I recall.

So they said look gravity exists string theory seems to predict gravity so what did they do about this difficulty about making it match onto the real world? So they then said well maybe this whole string theory thing is a theory of gravity. The the higher dimensional part is a suggestion that there are large observable dimensions in which we live, the three spatial dimensions plus time, and they and others that came after them, came up with mechanisms by which the extra dimensions

that the string theory suggests need to be there for the consistency of the theory turn out to be internal degrees of freedom, extra decorations that, that the physics has. So it looks to us, if you write it the right way, it looks to us like a three-dimensional theory

plus some extra labels, if you like, that some would describe as positions in these higher dimensional spaces, and others would say it's just different flavors of particle and things like that. And indeed, you can work out models

if you're a string phenomenologist, someone who builds models of string theory that our attempts at representing our real world, our observed world. There are very well understood mechanisms by which the higher dimensions of the string theory end up reflect, sorry, they end up making themselves known, for example, by being some of the unexplained patterns that we actually do see in the standard model of, of, of, of, of, of, of, of, of, of, of, of, physics. So if you work out the list of particles that we've discovered, they assemble

themselves into some very interesting electrons. The electron and the muon and the tau and all the neutrinos and the quarks. There are various families of particles that don't really have any explanation. The standard model of particle physics describes it but does not explain where those patterns

come from. One thing that higher dimensions can do is in fact give you reasons why those patterns exist. They turn out, yeah. So there's, we have to get rid of, well, we went from 26, I think we need to mention 10 at some point, but we had to get rid of a lot of dimensions and roughly speaking we

curl them up into a little tiny ball, right? That's basically what we do. That's one way of doing it. It's not the only way, but that's the way people often describe it. Off the shelf. Yeah, standard package way of getting rid of the extra dimensions. But there's more than one way of doing that and therefore there's different, there's one string theory, or we'll get to that too maybe, but there's not that many flavors of string

theory at the most fundamental level, but there are many ways that it could manifest itself as three plus one dimensional space time. Yeah, the mechanism by which those hidden dimensions become hidden, the shape of that space, as it were, seems to have many, many choices. and even amongst the choices that end up resembling to a sort of first pass our world, there are many, many choices within that. From a pragmatic perspective, that ends up looking like you have a theory with a lot of unexplained parameters. And so that's one of the things we're still struggling with in string theory. Is that really true or have we not understood the theory well enough to see how to fix those parameters?

and the answer is we don't know. Yeah, it's very hard to do experiments, right? You're talking about energy scales far beyond what we can probe at the large Hadron Collider, for example. Yeah, yeah. It would be nice if there was experimental guidance to help us fix those parameters. And it could be, you know, the pessimistic view is that those parameters aren't fixed and you do some experiment to figure out what those parameters are.

and there's just any number of different ways of designing a string theory to fit those parameters and see you lose predictive ability. And that's a big discussion. Yeah, I mean, as I recall, there was a hope back in the 80s. I know that the theory came online in the 60s and it was developed, but only by a small number of people in the 70s. And it exploded in popularity in the 80s.

And there was hope that it was... be unique, right? Like the string theory would just predict the ratio of masses of all these different particles. And so as of 2018, that seems to be unlikely, right? Is that fair? It seems to be, how is the best way of putting it? It hasn't come true yet.

I would say it hasn't come true yet. Well, unlikely says something more than it hasn't come true yet. It's talking about whether or not it will come true. The answer is we don't know, but So the question is, what are the prospects for the theory? Is it that there's some mechanism that will teach us that there's a unique answer that string theory will produce? And I think no one has or feels that we're necessarily close to a good idea that will tell us if there's some big principle we're missing. But clearly from the way you're phrasing this, you're still holding out the prospect.

I think it is a possibility that that old idea could work in some shape or form. my gut feeling says that by time we figure out something like that, we may not even be doing something that's even recognizably string theory anymore. Good, right. So we'll get to that.

But first, we skipped over the whole 10-dimensional thing. Because you said 26. I said 26. Ryan Green tells me it's 10-dimensional. Are you guys disagreeing? No, no. It's not this new math at all. There really is a 16 to be understood.

Again, depending upon how you think, about it, there are different ways of going from that 26 to 10. But the short version of the story is that the theory that's 26th dimension was really the first thing you write down. And you basically, in nature, in particle physics, there are two broad kinds of particle. The things called fermions, things called bosons. It has to do with what's called the spin. of these particles and,

but roughly speaking, the stuff, everything that you think of as a matter particle is actually a fermion. It has what's called spin half or some fractional spin,

sorry, some multiple of a half spin. Yeah, thank you. So electron's between those parts of, yeah, I wasn't sure whether I was supposed to say,

integer or not, right now. Check it up. So, So, yes, electrons, quarks and things like that. Whereas the particles they exchange that give rise to force that we recognize as force exchange particles are actually bosons. So the original string theories that were written down that are 26th dimensional are bosonic string theories. They just have that one kind, but nature has these two kinds.

So if you start trying to write down theories that have both kinds of particles, fermions and boson, as an attempt to understand nature, what you find is that the theory, again, doesn't work very well unless you work in 10 dimensions. So the 26th dimensional theory has forces but not matter. If you like, yes. And if we want both, 10 dimensions seems to be the way to go. Yeah.

And so that was what triggered the big explosion, what's called the first super string revolution, which was, so John Schwartz and, Michael Green found that the things that were failing to work when you had both bosons and fermions in the theory go away precisely in ten dimensions. There's a big internal consistency thing called an anomaly which you need to which comes up in quantum theories when you have fermions and those go away precisely in those dimensions for very very beautiful and interesting from a technical perspective reasons,

which meant that people really began to pay attention because it was a consistency that was so delicate and so intricately put together that it told you something very deep was going on. So in some sense, again, the theory is telling you what its demands are, right? It wasn't even obvious that it would work in any number of dimensions.

Indeed. Yeah. And this is where the word super, gets attached to super string theory, right? Right. And that's because the presence of fermions and bosons actually have to come in a certain kind of balance.

It turns out there's a symmetry relating the bosons and fermions which got called supersymmetry. And that was a kind of symmetry that had not been thought of before that actually was discovered in the context of string theory. and turns out to be, again, in its own right, very interesting,

and we can probably talk about that too. So supersymmetry was combined with string theory, and so the term super string theory was born. Some of the real sort of big shots in the field started paying attention then and started making some remarkable contribution. So famously, that's when Witten came into the field. Ed Witton, yes. and started showing how these internal spaces

where there's hidden six dimensions, because six plus four is ten, those hidden six dimensions would be had certain important properties that he was able to characterize and then it turned out to lead to an explosion of activity in mathematics as well because those spaces turn out to have

very important mathematical properties. This is actually the birth of string theory as this other thing. thing, which is a unifier of ideas in theoretical physics and mathematics and some other fields, because it turns out that those tight consistencies begin to generate new knowledge about the mathematical possibilities that you can have. And then yet another thing that the theory ended up telling us that we didn't put into it is that string theory is not just a theory of strings.

Yeah. There's other stuff. Why couldn't we just stop with the string? Exactly. And so historically that's really interesting because people were asking that question very early on. Well, if you go from points to lines, why stop there? And people were coming up with all kinds of reasons why you should stop there, which were not very well motivated, but mostly due to, you know, failure of imagination

and no good evidence that the other stuff would work. I remember in the early 90s being in a lecture hall at a summer school and a student asked, well, why aren't there two-dimensional membranes and an extremely famous string thing? who's name I will suppress was extremely scoffing of the idea that we should go anywhere beyond Strings. Yeah, I remember being in some of those rooms and hearing some of those answers and questions as well. And what actually happened is the theory began to cry out for the inclusion of those sorts of things itself. So there were hints

by a number of people working but I think some of the most compelling hints were done in this beautiful paper by Paul Townsend and Chris Hull and then Edward Witten very famously actually at a conference that was here at USC where I'm based in 1995 put it all together and triggered what we now call

the second super string revolution. The idea was that if you start considering regimes which are, if you like, called strongly interacting regimes where the strings are not just interacting with each other weekly

but really, really strongly you start getting into difficulties. This actually happens more broadly than just in string theory or particle physics, what have you. Typically, anything we calculate in theoretical

physics is in a regime. usually starts out in a regime with a that's called perturbation theory, where you start out with the theory where nothing is interacting, and then you add in... Just a bunch of particles going right by each other, never bumping into each other.

That's easy, we can do that. Yeah, and so you get that all right, and then you go, okay, now let's get these guys to interact, but we do it first, very weakly. We say that it's the non-interacting theory plus some small corrections, the interactions. Tiny glancing blows. Yeah, and actually that turns out to be incredibly

powerful. Much of theoretical physics is based on just doing that. But there are regimes, again, you're often driven to them by the necessity to understand experiments and things like that, where you actually need to understand regimes where those constituents are interacting with each other strongly. And if you ask that question about string theory, you find that a lot of the descriptions that you first thought of in terms of strings interacting with each other are not very good descriptions at all. And they begin to break down in a way that leaves you wondering what to do.

And so one possibility is that eventually you just find, sure, we're lucky maybe in some regime and we find a strong couple description and then you work out the answers and you're done. What actually happened in this case is that we started understanding it first in these extremes where if you try and understand strong coupling but sort of at some intermediate level, the whole theory looks like a mess. The basic players begin to...

It's hard to tell who's what. You lose track of who the basic players are, the basic degrees of freedom, as we would say, technically. It's not clear what they are anymore. But if you just in your mind extrapolate to an extremely strongly coupled regime, the theory begins to simplification. again, strangely.

And it turns out that there's a way of rewriting all of that horrible mess in terms of a weekly coupled theory again, which sounds bizarre. But it says that what you can do is identify new players in this

horrible mathematical mess, that if you describe things from their perspective, the theory simplifies again. So it's like if two people have never met, they are just individuals and we treat them that way. If they are long fallen in love and are married,

then they're a couple and we treat them that way. But it's when they know each other a little bit and there's sexual tension that things are complicated and we're not quite sure how to treat them. Right. But if you go to the other extreme and I'm trying to see where this analogy is going to go. The married couple is strongly coupled.

Yes, but I'm wondering what the dual weekly couple limit. Weekly coupled are misanthropic people who don't want to have any. But indeed, yes, it's hard to sort of pull these things apart. The whole is greater than some of its parts. But finishing the story, what we found is, and this is something that is sort of where I came in in terms of that stage in my career,

where I was very interesting and strongly coupled problems, you find in some of these regimes that the new players sometimes are strings again, but in some cases they're not strings. actually extended objects, higher dimensional membranes. So they either have, they're either like a sheet of paper, which is a two-dimensional membrane, or higher dimensions. And because you have ten dimensions, you have many, many different possibilities.

And it turns out when you sit down and work it all out, basically all the possibilities are in play. The full description of string theory is not as a theory of strings at all. it's a theory of all possibilities of extended objects interacting in some way it just so happens that strings are privileged

by being the things that carry because of that that closed loop that carry the quantum of gravity but there's more than just gravity going on right and this relationship between

weakly coupled strings and strongly coupled other things that may be strings or other things this is an example of a duality? Yeah, so the phrase duality is used all over our culture, of course. In this context, it has some of that same character, which is that there are two or more aspects to this ways of looking at this whole thing. And so duality in this case is saying there's some physics,

and in one way of looking at it, it can be described in terms of interacting strings, but there's a different way of looking at it in which it may be interacting membranes or an interacting set of strings that are very different from the other perspective. And so these dual natures are considered both essential to understanding what the whole thing is. So it's one theory that we can talk about in two different ways.

Yes, yes. You know, in some ways, well, actually I would say it differently. I would say it's one set of phenomena and we have different theories that describe parts of those phenomena that sort of fit together in a patchwork to give us an understanding of the whole thing. Sometimes I say, tell me if I've been making mistake here,

sometimes I say it's that we have two different classical limits of the same underlying quantum theory? Not perfectly happy. I'm not 100% happy with that, but, sure, sure. Okay, that made you happy.

You know, it's fine. I mean, there can be other limits that are sort of intrinsically quantum. Yeah, this is good enough. All right, you know, good enough for a podcast. I think, you know. There's another dual podcast in which I disagree. The dual podcast is much more strongly coupled

than this one is. And this is all part of this whole business with the brains, B-R-A-N-E-S, that's constructed from membrane. So we have one brains or just strings. two brains, three brains, four brains, five brains, et cetera. And this all came in the 1990s. So the early 80s were the first super string revolution.

The 1990s were the second super string revolution. And the most famous duality of them all came on the scene in the 1990s, thanks to Juan Maldesana. Yeah. So in, so 1995 was the revolution where we realized that brains were crucial. And the many different string theories, the four different string theories that we did that we did know about were actually parts of this big hole. And people were bandying about this term that the whole thing should be called M theory, but no one knew what M stood for. And every possible pun on the word brain appeared in a paper title. Exactly, yeah.

You're responsible for some of those. I'm responsible for some of those puns, yes. but then and I will get to to Mal the Center in a moment but it's worth mention the really key thing I would say that stopped this from all being

just nice words was that people began to find these very very sharp computational tools that allowed you to really handle because previously we didn't have the technical ability to handle the dynamics of these higher dimensional objects, which is I think why a lot of people said, well, they just don't make sense

because the previous attempts just meant that it wasn't working. And so famously, Joe Polchinsky, who sadly passed away this year, was responsible for coming up with the technology, the calculational technology that told you, at least in some regimes, how to handle these different kinds. of higher dimensional extended objects and describe their shapes, how they intersect. It was just an amazingly powerful technology.

By the way, just because I know we use the word, but this is a different use of the word technology than some of our listeners might be familiar with. Technical know-how and ability. So not a device in terms of a physical device, but a means by which you can calculate things and get answers, which is the meat and drink of... or the tofu of the theorist.

And so this calculational technology then began to be applied to many different things, whether you were interested in better models of how to get the standard model, particle physics out one heavy, but also understanding questions about black holes, real quantum gravity questions. And so there's a whole story there. But this amazingly is happening in two years. From 1995, by 1997, we have a very nice detailed picture of how to do a lot of things with black holes and string theory.

There's a seminal paper in 96 by Strominger and Vaffer, and then there's a host of other papers. And what was beginning to emerge was this idea that there's another kind of duality called, okay, well, for technical reasons, called gauge gravity duality, which is that there are calculations you could do using gravity that will teach you things about what are called gauge theories. Gage theories are certain kinds of particle physics type theories that you use in particle physics to calculate things. They don't have gravity in them.

Yeah, that's the important thing. So when we say gauge theory, we're not going to define what a gauge theory is, but it's a certain kind of theory that just lives in the world where you ignore gravity, but you still have particles interacting with each other. So the standard meat and potatoes, as you just said, of a particle physicist that daily left. And the prototype example of that is the theory of electromagnetism. That is the original and arguably the best gauge theory. And going back to Maxwell's description of electromagnetism in the 19th century.

So you have this powerful tool that we know works really well for particle physics. It is still the thing we use to get the answers right about what's coming out of the large hydro and collider and what, These are Gaysheries. So all the Feynman diagrams that we see. Yeah, Feynman diagrams, all those things come from working on Gayshiries. So Gay Sheries turn out to be a key piece of the tool that describes these extended objects, these brains of different kinds called Debrains that Joe had found with collaborators. Anyway, so what was beginning to emerge when you started applying them to things like Black Hulls, etc.,

was that there are calculations you can do just using theories with no gravity, these gase theories, and they will tell you about things that have to do with gravity. And that was unprecedented. That was really unprecedented. If you follow how string theory is built, it follows from some of those very early things

I was telling you about those closed loops coming from the joining of open loops. But just to, I think we were, We had to catch our breath here. This is a lot to take in. So we were starting with gauge theories, which is just a fancy way of saying, we're doing particle physics without gravity,

which means, because you said before, that string theory predicts gravity, these aren't even string theories. These are just particle physics theories, right? Yeah. And we look at them closely enough in the right circumstances, and we realize they're secretly telling us something about gravity,

even though gravity wasn't there. So that's mind-blowing. It is mind-blowing. But it is all traceable back to the fact that when you embed these things called gauge theories, when you embed them in string theory, which is to say when you, because string theory contains a lot of stuff, as I said, coming from the vibrations of these different kinds of strings and what have you.

And so there's some kinds of string that when you describe their vibrations, and again, you look at them sort of far away enough that you don't realize that their loops of string, they just look like little particles, they will give you gays theories. And those are really the things, the things I referred to earlier as open strings, the strings that have ends.

Right. And so, but because string theories tell you that, sorry, because the dynamics of, you know, just the laws of motion of these things tell you that they have to close up eventually, they will tell you even if you don't put it in that they also know about gravity. And so it comes out of the theory at you. Again, that was not something we weren't looking for. It came out of the theory.

And so people were beginning to understand how to handle that on a technical level better and better. and so the idea of these dualities, different pictures you could use, where sometimes I'm studying the physics in terms of gravitational physics or sometimes I'm studying it in terms of non-gravitational physics and I can get sometimes useful answers from both perspectives. That was beginning to emerge. And then, by late 1997, an example of very, very clean and beautiful example of this was put forward by Juan Mal de Sena,

which is now called the ADS-CFT correspondence. And that is just a version, but a very, very powerful and sharp version of this larger picture of this duality between gravity and Gay-Sheri. And so the ADS-C-F-T correspondence and the ADS and the CFT are technical terms, but it's really telling you that I do gravity in a certain kind of space or space-time, which is actually called anti-de-sitter. Basically, it's a space-time that is a, has a cosmological constant, it has an energy density to the space time that turns out to be

negative, and you can write it down and do things with it. It's a model, it doesn't have necessarily anything to do with our world. It's a place in which you can do certain kinds of quantum gravity calculations, and that's always a healthy thing to be able to do. But when you do those calculations, including sometimes the black holes are present, they may form, they may disappear, all the sorts of things they can do, there's a completely different description of that in a theory that has no gravity in one dimension fewer,

and that's an important clue, I think, that we ought to get back to, in one dimension fewer, which just looks like a somewhat difficult, but in principle possible particle physics calculation. And so this gives you this amazing insight, into what gravity may or may not be, but it also gives you this amazing toolbox.

Because one of the things that comes along with these dualities is that it tells you that sometimes the easy calculations on one side of the duality turn out to be the hard calculation on the other side. So for pragmatic reasons, we like dualities because usually they tell us, they give us ways of calculating things that we normally can't get at.

So there's a piece of physics you're trying to describe, which is a really hard particle physics computation, and it tells you, do this gravity computation, and you'll get the answer. Or there's a really hard gravity computation, and it says, do this particle physics calculation, you'll get the answer. This amazingly gives you insight

into a whole bunch of interesting problems that were sort of held up for decades. So let's see if we can't make sure we understand what ADS means, anti-Dissiter space. So tell us a little about, remind us the sense in which it's not the real world. We live in the real world,

And the real world seems to have a positive energy in empty space, a positive cosmological constant. Indeed. And so the cosmological constant, there are different ways of thinking about. One way to thinking about it is that there's just some intrinsic, it just comes with the territory, amount of energy associated where if you take a chunk of space time and you were to look at its energy content, you would find that it has some. And there are three possibilities. It can either be positive, negative, or zero.

even in empty space. Even in empty space. Space itself has this energy density associated with it. And so for a long time, we thought that it was zero for our world. We didn't notice any, right? We didn't notice any. And theorists being theorist then wrote many, many papers saying, well, of course it's zero.

Here's my theory. It must be zero. Exactly. And the, so there have been observations that suggest at least among the simplest explanations is that our universe actually has a small positive cosmortical

constant. You can also pushing the universe apart, accelerating galaxy. Indeed, one way of thinking about it is that it really sort of accelerates expansion of the universe. The negative cosmotic constant is the other possibility and so like I said

it doesn't necessarily seem to have anything to do with our universe, but because of this duality I was telling you about it tells you about how to do because calculations in such negative cosmological constant spaces secretly are calculating for you

strongly coupled particle physics question there are ways in which people have been using that forgetting about the whole whether or not this is anything to do with theories of everything or anything like that it's just an issue of I now have this toolbox that tells me how to do these strongly cup of calculations,

which are really important for understanding things in nuclear physics, really important things for understanding things in condensed matter physics. There are phases of particle physics, whether it's lots of electrons interacting with each other in a certain kind of medium, or whether it's the core of a neutron star, or whether it's just the nuclei of our atoms. atoms, those actually are intrinsically strongly coupled systems that nature tells us are there, and we can experiment on them.

And they have phenomena that we don't understand in terms of doing weekly coupled calculations. So you need a tool that can tell you how to do some of these strongly coupled calculations. And there are many different kinds of tools, but among the tools are now thinking about them in terms of these dual theories of gravity. Right. So I'm still not completely convinced that we all know what ADS is. So I'm going to keep counting on this. Sorry.

That's fine. So ADS is, we say it's a space time with a negative cosmological constant. So it's not like a place you can go. It's not like a location in our universe. This is a hypothetical universe, right, that we physicists can write down the equations for. And it's basically an empty universe except that there's a negative energy in empty space itself. That's what anti-Dissider space is. Yes, right?

There's a person named DeSitter a hundred years ago, and he invented DeSitter space, and now we just changed the sign. You change the sign, and a whole lot of things change when you change that simple sign. Exactly. And this might even be dangerous to say, but maybe it's better to bring up the confusions

and fix them to pretend that they're not there. If a positive cosmological constant accelerates things apart, why wouldn't a negative cosmological constant just cause the universe to recalapse into a big crunch? Oh, that's a good question. I have to think about... I think about a good way of thinking about that.

I mean, the short answer is that it does if there's other stuff in the universe. Yeah, yeah, I'm trying to think... Sort of famously, when you start adding... When you start adding things, you will get instabilities. Right. I'm trying to think in some ways

why the pure case is still quite robust. There's kind of nothing to crunch. Yeah, I guess there's nothing to crunch. Yeah, that's a good way of putting it. Yeah, yeah, yeah. So we have an infinitely big space with negative energy everywhere,

and you're saying that a theory of gravity, of quantum gravity, in that space, is dual-to, which is done the way of saying, is sort of physically the same, but written in a different way as a theory with no gravity at all

in one less dimension. So if we had a four-dimensional anti-decider space, that will be dualed to a three-dimensional quantum field theory. And problems that are hard in one theory

might be easy and the other one and vice versa. And now we have this way of taking hard problems and mapping them on to easy problems so this is full employment for theoretical physicists. Yeah. I mean, ultimately that's really all we do.

We find tools for answering you know being able to calculate in various regimes and understand things and much of the rest is you know decoration

so the word holography also yeah so I was going to get to that because one of the things it also tells us is that worrying about the dimension

of space time itself may be a red herring I personally think it's this is all a clue that, you know, when we start going, oh, string theory has this number of dimensions and you hit a bunch of them what have you,

I think one day we'll understand that that's all the red herring. It's overrated. Space time is overrated. Well, dimension itself is something that is going to be somewhat in the eye of the beholder. And we already see it in this context. You do these calculations in one of these gays series. So you start out, for example, trying to understand certain phenomena in

three plus one dimensional space time you think surely that's the right way because we live in three plus one dimensions and you do the calculation and it goes off to strong coupling and you have good experimental reason to want to know what the answers are in strong coupling and then someone comes along and says well for that particular phenomenon here is a way of understanding it but you've got to work with a

five dimensional theory of gravity and not what anyone ordered right and you know you might go well that's just nonsense or you might go, I just want something that can tell me what the answers are. And so you just hold your nose. It's the wrong number of dimensions and it's the theory of gravity, which isn't where I started. But from a pragmatic perspective, that's telling you that you can get answers to physical phenomena. Nature doesn't care whether you label it with this number of dimensions and whether this is gravity or not.

And nature is just nature. And I think that's where we're being led. And we saw that also with the, is it particles, is it strings? is it membranes, is what have you. Nature doesn't care. And this is part of why, and I think this is the single hardest thing

for people in the public to get as to why string theorists are so excited. I mean, there's been an anti-string theory backlash. There was a pro-string theory, you know, counter-backer. The elegant universe came along.

People were very, very excited, Nova Special, et cetera. And then there were these books against it and people got upset. But when you're in the trenches doing string theory, this theory that you wrote in the 1960s keeps pushing us in interesting directions that we didn't even anticipate it.

It smells like something right is going on, and maybe that's, maybe it's not right. You know, it's always possible because at the end of the day, it's going to be experiments that decide, but there are really good reasons to think that it's not just all an accident that all this is working out. Yeah, not only is it not an accident. It's not that we're being misled by, you know, a, a, a, a vocal set of senior people or what have you, because the point is that this is theoretical physics.

So you can do those calculations, and the calculations themselves are telling you what's going on. Some visionary senior people may tell you to look at those calculations, but then very rapidly you get up to speed and you see, oh, this really is interesting. And then for your own reasons, depending upon your own flavor of physics that led you to where you are, you go, oh, there's something really interesting in here

and there's more than meets the eye. And so I think historically, this is an interesting time because I think we really are sort of chipping away at corners of something that I think is much larger, much more interesting, and none of us know where it's going to go. And yes, but it is certainly the case

that it could turn out all to be wrong. But I suspect even if it turns out to be wrong in the sense of it isn't, good for the thing that we thought it was going to be good for, I'd be surprised if it wasn't going to be good for something. Well, you made the point that we've developed technology in this sense, and it can now be applied to problems that are other than the Big Bang or quantum gravity, right? And so give us just one example for us to fix our minds, either from your work or from

somewhere else, about how we can use, let's say, ADS-C-F-T, this duality between particle physics and gravity to answer some tangible questions about physics. Yeah, well, so there are a number of regions where I think a lot of the work is, you know, just that one step further than maybe sort of qualitative in the sense that there are kinds of behavior that you would like to classify, you'd like to understand at least what the possibilities are, that you see in strongly coupled systems in real experiments. So people actually make condensed matter

people who worry about clumps of material where the electrons are doing stuff in some strange way and there's some new kind of way they behave as a result of them interacting strongly that you'd like to understand. But we're talking about real people in real labs

not five-dimensional fake dimensionary These are real people in real labs building stuff that may be in your phone one day or something like that. And then on the other hand, there are questions to do with the kinds of things that can happen when you take lots of nuclear material quarks interacting strongly and clump them together. Now, one example is just nuclei themselves, the nuclei of atoms. But you also have nuclear material doing interesting things in astrophysics.

You get entire, you know, 10 miles across lumps of nuclear material condensed together called neutron stars, that we now actually observe them colliding in real physics. And that may be the place where a huge amount of the heavy elements, you know, gold famously and what have you, that we see here on earth actually came from, all of those have to do with phases of strongly coupled matter that we know take place in nature and we don't have good descriptions of.

So there are many, many different kinds of possibilities. and the working with these dual theories at least help you enumerate the kinds of possibilities. They don't get the answers right on the nose because these systems are typically very complicated and have many more components than we can handle computationally. But there are broad brushstrokes you want to get right initially like what is even possible, what kinds of phases

of these different kinds of matter, exotic matter, if you like, can you get? And previously we had no good tools for enumerating those phases very nicely. That's one thing that you do get out of these kinds of strongly coupled models. Didn't I see that you wrote a paper with neutron stores in the title?

Have I written a paper with neutron stars? I don't know. I can't remember. I mean, I have been thinking about neutron stars. I plan to write some papers on neutrons. But this is the kind of thing But literally using the tools we learn from string theory to understand the neutron stars out there in the eye. Yeah, yeah. So some of my earliest work was very early on when this ADS-CFT stuff came out.

I figured out ways with some colleagues of working out what the physicists would call the phase diagram, which is essentially a diagram of the possibilities, the kinds of phases. So famously, phases, water, it has a solid form, it has a solid form, it has a liquid form, he has a gaseous form. You can actually work out the phase diagram of water under various, you know, this pressure and this temperature, what form is it in? So you can work that out.

You need to know that to understand water if you really claim to understand water. So you need to understand that for nuclear physics as well. So some of the very earliest work was the stuff I was involved with in showing that this in principle could help you get the phase diagram of the core of a neutron star right in principle.

You know, this was, again, broad brush strokes. because I was convinced that that would be a really great application for some of this stuff. Now, as I said, this is broad brushstrokes. There's a lot to be done. What's been happening really very recently, which I think is very exciting, is the whole business of being able to calculate very difficult quantum mechanical, sorry, quantum mechanical diagnostic tools, as it were. in field theories.

Again, our colleagues in the experimental world of various kinds want to know when these different phases are happening or about to happen or about to be changed from one phase to another, what do you keep track off to figure out what's going on? How do you characterize these things? A lot of the traditional phases of matter are typically that we learn about in school and what have you have to do with things being driven by very classical sorts of things that are going on.

Now, a lot of these new phases are driven by quantum effects. Right. So it's harder. It's harder and it's harder to calculate. Yeah. And so there are very important quantities called entanglement that are the things that we like to keep track. We think it would be good to keep track of. It turns out these are really hard things to calculate in field theories outside two-dimensional field theories where it turns out there are tricks you can use.

one of the really big things that's been happening in the last just a few years I would say has been the explosion of methods using gravity duels of calculating these quantum diagnostic things things like entanglement entropy and various cousins of entanglement entropy and you use these now as the things you track

to see when the degrees of freedom are rearranging themselves and a new phase is coming up. That's going to be hugely important, I think, as an application on the quantum side, but then we've also been turning it on its head because I think people are beginning to realize that keeping track of quantum degrees of freedom may be a more arguably fundamental way

of keeping track of what's going on on the spacetime side, what's gravity actually doing. Right. And so it's becoming also important in understanding what truly are black holes in string theory and hopefully what truly black holes are quantum mechanically and things like that. Fuzz balls are in the news. The black holes might be fuzzy balls of string. Yeah. So this is again something is hugely important. I think going back to 1996 where we embedded black holes and string theory now with the new knowledge that strings is more than strings

it's all of these other kinds of things and we realized that we could understand a number of the fundamental things that Beckenstein and Hawking had said about black holes and quantum mechanics back in the 70s. We understood how to actually prove some of those things they said in 1996. And that was started with Strominger and Vaff

that's a beautiful paper. And then what happens is that we sort of forgot some of the lessons that we learned from that paper and some of the follow-up papers. And then we started revisiting black holes and quantum mechanics again, what are black holes, quantum information paradox? And Samir Mathur pointed out that actually if we go back to that original picture of strontmenter and Vaffer and just follow what the string theory tells you, it tells you something quite remarkable, which is that all of that stuff you use to build the blackboard, holes out of these strings interacting with membranes, what have you. If you follow what those things do, it tells you that black holes really in some sense are themselves emergent phenomena. They're not really real. They are the result of taking the classical limit and going to general relativity in some sense.

I think emerging phenomena are real. But I'm fundamental. Yes. I tried to shy away from the word fundamental. You went 59 minutes without using the word. using the word real. Yeah.

And so that all sounds a bit woolly, but the pragmatic result is that, again, in a way, it's maybe again a kind of a duality.

If you're interested in astrophysical problems that are far away from the business of quantum effects, sure, use Einstein's general relativity and that solution

that Schwartzhild taught us is the black hole with a horizon, and that'll do a good job. if you're interested in understanding the internal structure of the black hole from a quantum mechanical perspective that's not good enough

and what this picture coming from string theory tells you is that you build black holes out of these fuzzy kinds of domains that you can actually describe in string theory in a way the stringiness makes it all very fuzzy

and when you put lots of them together and sort of squint a little bit, it effectively looks like the thing you call a black hole with a sharp horizon. But if you look closely enough, you'll see that actually there is no horizon. The horizon is just to this effective thing

that describes the collective phenomena coming from all of those things interacting together. And in some ways, it immediately tells you that the black hole information paradox isn't a paradox at all. It's just a paradox that is forced upon you by taking that approximation of pretending there's a horizon effectively where there really isn't. So speaking of the real world, we're in it.

And you're a professor and you have to go teach a class. So I really wanted to talk about the fact that you wrote a graphic novel. I have a little more time. Oh, you do have a little more time. I'm not too far away. And students don't start turning up for at least another few minutes after class. You know how much time you have. So I'll mention it in the intro.

But tell us a little bit, because it comes out of your desire to have everyone be enthusiastic about physics and string theory, but you wrote a graphic novel and you illustrated it. Yeah. And, you know, in some ways, the illustrated and graphic part of it wasn't the driving force so much as my frustration with the fact that, you know, the kind of books we write, you know, as sort of professional theorists who want to tell you exciting things about what we're, doing, aren't always inviting you to be part of the conversation. And what I really wanted to do was have something that was more conversational. And in some ways, that it didn't see, I didn't want it to just be the voice of the expert

telling you what to think about stuff. And there's nothing wrong with that kind of book. You've written several. I'll probably write some. I'm going to talk and you're going to listen. Do not read the comments. And so, and so I wanted to. revisit, in some ways I realize

that it would be fun to revisit this ancient form which is the dialogue form where you actually as a reader you end up eavesdropping on a conversation between people about ideas and in some sense that gives you multiple voices and different points of view

and it helps you unpack the concepts in a way that I think is not done as much as I think would be nice in sort of contemporary writing. So that was the idea I've long had the ambition of writing a book in dialogue form. My publisher does not want me to do it.

I think I'm working on him. It would not be illustrated, but you pulled it off, so I'm jealous. Well, you know, thank you. And yes, a lot of publishers, in fact, most of them just didn't get it. They didn't get what I was trying to do. And then worse, it had all these pictures. Because then I thought, because I was thinking, actually, would be really great, would be to see that these conversations aren't, you know,

when we do think of the dialogues going back to the ancients, we think of people in togas on mountaintops, having deep conversations about philosophy. And I want us to go, well, you can have conversations, but they're taking place in the contemporary world, you know, in cafes and museums and on buses and trains, where we all are. And science isn't just taking place in labs and conference rooms and what have you.

And then the other thing was it would be ordinary people, and it would be great if you could see these people in these places. So that was the whole package. And I thought, oh, clearly this would be narrative art. It would be a graphic novel style book. And are they talking about string theory? And so the string theory is in there, but it isn't a book about string theory. It is one of many things that people talk about in these conversations.

The other great thing about conversations is that conversations don't have a signpost telling you what it's about. So one of the great things about science is that it's interconnected. And you start talking about one thing and you end up. in this other place and it's all been interesting. I mean, hopefully. The jacket copy claimed. And so that messiness of conversation, I also thought would be fun to have.

And then the final thing, because I'm sort of babbling, is the fact that I think these conversations really do happen. I'm a big people watcher. I sit in cafes and I end up listening to people. And science does come up. And you hear people, you know, neither of them are experts, but they want to engage with this stuff.

They saw a TV show or they read a book and they want to talk more about these ideas. And so one of the things that's frustrating is that no one celebrates that these conversations are taking place. So I wanted the book that really celebrates the spirit of those conversations, invites people to have their own and gives you a snapshot of some of those conversations through, you know, thumbing through and seeing what's going on. So that was the idea. And people seem to like it. They do happen these conversations, and they don't happen enough, and we can encourage them a little bit more. And so it's called The Dialogues.

Yes, Dialogs, subtitle Conversations About the Nature of the Universe. Available, wherever books are available? Where other books are available, and you'll find some bookstores where it's in the science section, and some bookstores where it's in the graphic novel section. Just ask for it. And if they don't have it, tell them to order a bunch, because other people will find them and usually really, really love it once they find it. All right, Clifford Johnson.

Thanks so much for being on the podcast. It's a real pleasure.