Stephen Wolfram | My Discovery Changes Everything

I think I now finally am beginning to understand quantum mechanics today. On the "Into the Impossible" podcast, we welcome for the third time the world-renowned computer scientist Dr. Steven Wolfram. Steven's been responsible for many breakthroughs in computer science, including many inventions that you may even have on your phone right now. He's been a pioneer in developing and applying computational thinking, going as far as to develop his own programming language. Computational reducibility says you can't cheat the passage of time. Most recently, he claims to have solved the mystery behind the most perplexing law of nature, the Second Law of Thermodynamics, and it's doing all the things that the Second Law of Thermodynamics says you shouldn't be able to do. Tune in and find out if you agree that Steven's unlocked the mysteries of the thermodynamic universe. Today, he's here to prove what many who have come before him have failed to do. And along the way, we'll go into a fascinating journey into the dark side of the universe, a way that only Steven Wolfram and I can take you. So let's tune in.

Well, welcome everybody to the third round of my conversational uh dialogization with this uh phenomenal guest today. This is Stephen Wolfram, as I say, third, third-time guest on the podcast. Uh, Dr. Stephen Wolfram joining us from the East Coast. How are you tonight, Stephen?

Just fine. It's late for, for, for me, so it's even later for you. I really appreciate you staying up so late.

On the E, I'm a, I'm a late worker. You're a night owl. Of my day, you were on first time three years ago when I first started the podcast. And in the intervening three years since we've had our conversation, you have written many books. But the two books that have really piqued my interest and millions of people around the world are the books you wrote this year. And those are "What is GPT Doing?" and we'll talk about that, uh, briefly. And we'll talk primarily, I believe, about the Second Law. And you're, you're kind of lots of things. You know, I realized you, you said you want to talk about these books. So I went to my bookshelf and I realized, this is my, um, that's, those are the books that I wrote during the pandemic. It's kind of a, a big pile.

It is. Some, no, it's very productive. I'm, I'm impressed with myself. I think, uh, yeah, I think my audience will want to know, are you writing a book as we speak with one of your hands? It would not surprise me.

But Stephen, since you came on three years ago, I added a new segment on the podcast called "Judging Books by Their Covers." And so I'd like you to take, uh, either one of the books. Let's start with the ChatGPT book, maybe. And I want you to explain, uh, the cover, the title, the design, and, uh, the any of the artwork. Yes. So can you please explain what gave you the idea for the title and cover?

I wrote this little book because ChatGPT came out. I know something about these kinds of things, and lots of people asked, "What is ChatGPT doing?" and "Why does it work?" So I decided to write a book with that title. And actually, it was originally a blog post, and then, then a chap. I know, actually, the person called Paul Graham, who's the founder of Y Combinator, sent me mail saying, "You know, this was a really good blog post. You should turn it into a book." And I, I said, "It's too small to be a book. It's, uh, uh, it's too short." They said, "You should turn it into a book anyway." So we, so I told my publishing team, "We're going to make a book in the next couple of weeks." This was a book made very quickly. It was, uh, you know, it's, it's about what it says, you know, "What is ChatGPT doing?" "Does it work?" This kind of large-scale overview of, of, uh, how an AI system like this works. It's, it was rather easy for me to write. I, it took me a very short amount of time to write this, but it's something which still, I, I believe, it's really quite unique, and a lot of people read it, um, in both, particularly in the, in the technology world, uh, sort of the, the execs in the technology world, widely read by, by those people. Kind of a, a, you know, it's, it's kind of the, the high-level overview of, uh, of what ChatGPT is doing. And the question that I was really interested in is, why does it work? And that's really a, a thing that I realized that it's really telling us a science fact. It's telling us human language, which is sort of a pinnacle of our achievement, is in some sense not as complicated as we thought. There are regularities in human language which ChatGPT, the LLM, this, the large language model, discovered that we kind of should have known were there for the last couple of thousand years, but we didn't. You know, we kind of knew that that language was made up in kind of sentences that went, you know, noun, verb, noun, and so on. But what ChatGPT and so on is showing us is something about the kind of the further structure, the kind of the way that you put together sentences based on the, the kinds of combinations of words that can mean things. And, and the cover, in this particular case, is a, is a piece of the internals of, um, uh, of ChatGPT, showing kind of the, the flow of information through the neural net that, uh, is the, it's kind of, it's this neural net is kind of like a giant mathematical function with, uh, in the case of, of ChatGPT, hundreds of billions of parameters. And you feed in a piece of text that you've given so far, and out comes its statement of what it thinks the next word should be in the piece of text that you're generating. Actually, it's kind of fun to see the, you know, we, uh, the translations of this book into different languages have lots of different covers, including some very wild, no doubt AI-generated covers that, uh, I kind of wonder what the prompt was, um, that led to those, led to those covers.

Try to reverse engineer the prompt. Yeah. I'm always worried about, you know, they had mad cow disease back in the '90s, and now that bots are training other bots, I'm kind of worried about mad bot disease. But maybe we'll get into that after you describe the, uh, the Second Law book that really has captivated me, and I have a lot of questions, not only just from me, but for my audience is dying to ask you questions. And I've taken some on Twitter and from YouTube comment section. So explain what we're looking at there, the Second Law.

Right, right, right. So, I mean, and, you know, what's, what's this cover has an interesting story. Okay. So it begins 51 years ago. So I was a 12-year-old kid, and I'd gotten interested in physics. I'd originally been interested in space, but, um, that kind of segued into an interest in physics. And I'd been, you know, starting to read physics books and so on. And I was graduating from English Elementary School, more or less, as that's the English system, that's sort of an age 12 thing. And I kind of, as a sort of pseudo graduation gift, I suppose, that translated into modern American culture would be, I'm, I'm going to get these, these books. And there was a series of five books about physics, uh, the, actually the Berkeley Physics Course series, undergraduate physics textbook series. And so I got these books. And, um, uh, it was in June of 1972. And, uh, I kind of, in those days, I used to write my name and the date when I got books. And the books, I stopped doing that at some point, which was a shame. But so I, I kind of know when I got these books. So it turns out that book, well, the, the fifth book in that series was about statistical physics, was about kind of the physics of systems that have so many components, you have to use statistics to say how they work. So, for example, molecules in a gas, things like this. And the cover of that book, if I can, uh, can hold up, that's, um, that's the, uh, book cover that, that, um, um, that show. Was that Caltech? Was that a Caltech book?

Yes, that's, that's, that's, um, the person who made that cover was a chap called Bernie Aller. And, uh, Fred R. R. was the guy who wrote the book, but it was, it was kind of connected with Caltech and, and that whole crowd. That book cover was kind of a claimed to be a simulation of kind of gas molecules in a box, starting off in this kind of very, on one side of the box, kind of ordered, on one side of the box, and then progressively with time, becoming more disordered, and eventually kind of randomly filling the box. And that was, uh, was kind of a, a thing that was sort of a core feature of statistical physics, the Second Law of Thermodynamics, the law of entropy increase, and so on, illustrated on this, on this book cover. I got really interested in this partly because this was a case where the book was claiming you could derive a law of physics from, not just be told, "Oh, relativity works," or, "Quantum mechanics works." It was, you can actually derive the law of physics from something that is more fundamental, just something essentially mathematical, something formal. You could derive this law of physics, this law of entropy increase, this idea that things tend to get more random over time. I thought that was pretty interesting. Uh, I didn't fully, at that time, at age 12 or whatever, I don't think I fully understood the math that was in this book, and I didn't fully believe it, actually. And I said, "I'm going to simulate this, this thing that's on this book cover." And at that time, I had access to a computer, very primitive computer by today's standards. It was about the size of a large desk, and it was, you know, programmed with paper tape, things like this. And I'm like, "I'm going to simulate this thing and see whether I can get the same results as are on the book cover." Well, I didn't succeed. And, you know, as it turns out, years later, I realize the fact that I didn't succeed was actually showing me something very interesting. But at the time, I kind of wasn't ready to understand that point. Anyway, so the, the end result of that, I was interested in the Second Law of Thermodynamics. Second Law of Thermodynamics has this funny history. You know, it was, it was kind of first mentioned in the 1820s, and then kind of really, uh, people started talking a lot about it in the 1860s. And people said, "Well, you know, we're not even sure molecules exist." So the Second Law of Thermodynamics is about sort of randomization of molecules. We don't even know molecules exist. And so it was all very confused. And, uh, by the beginning of the 1900s, when people realized molecules do exist, it was kind of like, "Oh, and by the way, the Second Law was proved mathematically back in the past." Well, it never had been. And this led to many confusions over the years of people saying, "You know, is the Second Law really true? Is it, you know, what, what is the cause of it? How does it work?"

We can talk about this more. Or Stephen, how about this quote from your fellow countryman, Sir Arthur Eddington? He said, uh, in 1915, the year of Einstein's, you know, one of his miracle years, "If your theory is found to be against the Second Law of Thermodynamics, I can give you no hope. There is nothing for it but to collapse in deepest humiliation." And yet, you're right, nobody had proven it, I think, by that point, right?

I mean, that it was so, I know, nobody. The stuff I've done recently is the closest we've got to kind of proving the Second Law of Thermodynamics and understanding what its real origins are. Yes. I, I'm not, I was never very impressed with Eddington, I have to say. And, uh, that was not, you know, I'm, I'm aware of that quote. I mean, you know, in, in fact, in, this book, one part of the book is devoted to my efforts to trace the history of the Second Law of Thermodynamics, which I, I have to say, I was very surprised nobody had written a definitive history of the Second Law of Thermodynamics. After I worked on it, I understood why they hadn't. It's really complicated, and you have to know a whole bunch of stuff about, kind of, the technical side of what's going on to be able to untangle what's happening. But, yeah, Eddington was a late-stage person because really, by the beginning of the 20th century, people had sort of said, "We know the Second Law is true." Actually, I'll tell you a story about about the Second Law and proving the Second Law. So, you know, Einstein, you mentioned 1915, General Relativity. 1905 was Einstein's kind of miracle year, where he introduced, you know, photons, and he introduced, uh, kind of Brownian motion that proved molecules existed, and relativity. Okay, so big, big year. Okay. So I was studying the Second Law, and I was interested in who had worked on trying to prove the Second Law. Well, it turns out one name I didn't know was going to be on there is Albert Einstein. So in 1902, 1903, 1904, he wrote three papers. They were all on the Second Law, and they all purported to be essentially proofs of the Second Law, and they were all wrong. He had actually been working on the Second Law right up to the time when, and he never worked on the Second Law again after 1905. But what was really interesting to me was the kind of thinking that went into his attempts to prove the Second Law was this kind of philosophical way of thinking about science that he kind of got a little bit from Boltzmann. Boltzmann had been the person who had who had, um, uh, been, um, uh, very much involved in, kind of, understanding the idea of molecules, understanding the, the sort of foundations of the Second Law, and had had this very philosophical approach to, to thinking about science. And this kind of idea of thought experiments, the idea that you can figure things out just by, kind of, logical reasoning, was a very Boltzmann-type idea, which Einstein picked up on and first of all tried to apply it to the Second Law and failed. It kind of had that, that strange history. But, but, um, by the time of people like Eddington, it was like, "Yep, it's true. You know, we're sure it's true." You know, in, in textbooks, you know, when I was a kid, by, by sort of, in, nowadays, I would say one of my favorite things is some, some book that explains the Second Law. One of the mysteries of the Second Law is that you can kind of prove this thing called Boltzmann's H-theorem that says that, oh, the entropy will increase with time. But you can take that same proof, you can reverse it, and you can say that also proves the entropy decreases with time. And so there's a well-known textbook which ends its chapter on this saying, "This point is often puzzling to the student." Well, it was puzzling to everybody else as well, for about 100 years. Um, and, uh, we can kind of unravel how that really works.

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I would like to go there. I would like to also, though, I mean, I've had many great conversations, including those with you. But, you know, encoded in the Second Law is a, is a notion of time. And I wonder if we could start there. In the kind of, the most, most primitive essence, what, how do you conceptualize time? Or how, how can you define time? What is time? What is time, and how does it emerge in, in, in Wolfram physics? I understand not only time but space emerges. So talk us through, what is time?

So as far as I'm concerned, time is the inexorable progress of computation. If we think about things in the world as being governed by rules, then what happens in the course of time is those rules get applied. And that's a, that's a process. The, the sort of, what the, the thing that changes through time is that we've applied these rules more and more and more times. And it's sort of an interesting thing because one had imagined when one thinks about time in mathematics, uh, usually time is a parameter in an equation. You get some formula, it says, you know, the planet will be at this position at this time. You can pick any value for that time, you just dial in the time, you say what the answer is. Well, that's kind of a view of time that came from, sort of, the mathematical way of thinking. From a computational way of thinking, it's more, you have these rules, and then you run the rules, and you run them this step, this step, this step, and you see what happens. And one of the important phenomena that I kind of first started identifying in the 1980s is this phenomenon of computational irreducibility. This question of when the computations happen, you do this step, this step, this step, is there a way to jump ahead? Is there a way to do what kind of mathematics says you can do and just dial in the value of time and say, "This is what's going to happen?" Or do you have to follow every step, follow this sort of irreducible computation to see what's going to happen? And the thing that was sort of a discovery of mine in the 1980s is that it's very common to have systems which are computationally irreducible, where the only way to work out what will happen in them is just to run every step and see what happens. And that's kind of the, the sense in which that that process of running the steps, that is the passage of time. And it's sort of an interesting thing that computational irreducibility says you can't cheat the passage of time. You can't jump ahead and say, "I'm going to figure out by being a smarter computer," so to speak, "what's going to happen by being a smarter brain, whatever, I can figure out what's going to happen." That doesn't work. There's this sort of irreducible process you have to go through. That's a limitation on science, in a sense. For us feeling good about ourselves, it's, it's a big positive because it means that sort of you have to live the time, so to speak. There's no way to just say the answer to life, the universe, everything, whatever, is 42 or whatever. You, you have to actually live through it to get to the answer. There's no kind of way to jump ahead.

Can't shortcut. Cannot shortcut. Yeah. Right. It's an irreducible process. So for me, kind of time is this computational process of the, the sort of progression of the universe figuring, applying these rules to see what comes next, so to speak.

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Can computation occur at zero temperature?

It has nothing to do with temperature. I mean, temperature is an overlay far above that, that kind of issue. So computation is, is just the following of rules that you specify. There might be rules that you could specify for, you know, a line of black and white cells. You can talk about temperature. Let's talk about temperature for a minute. There's a very different kind of thing. So, you know, actually, it's a very interesting story because in the, in the early 1800s, people knew about heat. They knew heat flowed from hotter bodies to colder bodies and things like this. And they said, "What is heat?" They said, "Well, heat must be the, you know, it must be like a fluid. The only thing we know that flows is a fluid like water." So they called it caloric. Caloric fluid was what was the embodiment of heat and flowed from sort of a hotter body to a colder body. And temperature was a sort of characterization of amounts of, was related to sort of this characterization of how much heat was there, more or less. Well, so this theory of what heat was turned out to be completely wrong. Because what is heat? Heat is the randomized motion of molecules. Heat is a feature of the microscopic structure of matter. If, if matter wasn't made of molecules, there wouldn't be heat in the same sense. And so the concept of temperature is a feature of, of a characterization of, sort of, the amount of randomness in these molecules. It's, it's, it's really the, you know, it's just the average energy. The average energy of motion, the average kinetic energy of molecules, is just, that's what defines temperature. Is this average kinetic energy of molecules? That level of description of talking about molecules and moving around and so on, the Second Law is vastly more general than that. The Second Law is a, is essentially a computational statement of the fact that systems that start simple to describe will typically become complicated to describe. It's kind of like encryption. You're saying you start with that, that simple, uh, initial seed, and then you run this thing, and you get something which, for all practical purposes, looks random. That's what's happening in these systems. It doesn't have to do with molecules running around. It doesn't have to do with the specifics of temperature and so on. It really is a, a fair, a very basic computational phenomenon that actually is a consequence of this phenomenon of computational irreducibility.

I do want to say one thing about temperature and heat, he, and so on, which is something, you know, close perhaps to your interests. So one of the questions is, in, actually, I should say more about about our theory, but I want, I want to make sure to come back to this question of caloric fluid, because I have a, I'm going to give you an aphorism, okay? My aphorism is, is dark matter is the caloric of our times, and that it will be in the fistin and the fren phenological approach. The reason I want to say that, I brought up temperature, is because as you know, in all the Maxwell relations, in the Gibbs, Helmholtz, you know, entropy, enthalpy, you always have temperature and entropy interrelated. They're coming in and derivative pairs. And so the reason that I'm, I'm sort of asking about that is because it would seem that, you know, there is from things like Lauer entropy and and so forth, there is a minimum amount of of of heat is tangible to a human being, unlike entropy, which is abstract and and mathematical. It doesn't mean it's any less real. But I guess the question I have is, is you're saying computation is fundamental, and it may be more fundamental than than even these the Maxwell relations themselves, right? It may be that the, the actual operations themselves, which don't have time in them, right? They're these kind of abstract things, differentials. But I always, you know, kind of feel like there's an a little interlocutor saying, "Well, it's changing with respect to time." The differential is changing with respect to time. But so it's interesting to say that it's not necessary to consider temperature even to have computation.

Yeah, no, temperature is a very derived concept that has to do with energy and so on. The fundamental phenomenon of the Second Law has nothing to do with energy, temperature, those kinds of things. To talk about entropy, entropy is in a sense a lower-level concept. So what is entropy? Entropy is, you know, a certain number of things about a system, a certain amount about a system. Like you say, there are gas molecules and they're all in this box, and there are a billion of them, and that's all you know. Then the question is, well, how many possible configurations of the system could there be that are consistent with those constraints that we know? And it's a bit easier to figure that out if you don't let the gas molecules be in any position, but you just say, as Boltzmann actually originally did, that it's sort of quantized, and that the gas molecules are just in some grid of possible positions. You just say how many possible positions are they in? Oh, it may be, you know, two to some very big power. Okay. So entropy is just the logarithm, the power, the exponent there, of how many possible configurations are consistent with these constraints that you know about the system. That's, that's the, the definition of entropy. In the original formulations of entropy, it was all kind of complicated to understand because it involved continuous variables, and you have to kind of discretize the continuous variables to figure out what's happening. It's just a mathematically complicated thing. But this question about, "Does entropy increase?" which is sort of the, for the Second Law of Thermodynamics, the question is, if you are saying, "I've got this way of describing the system," and I can describe it, I can sort of immediately say, "Oh, I'm looking at this pattern of molecules, and I can immediately say every molecule is on an even-numbered square," let's say, that's a very sort of short description. Now, if I let the system run, and it's this irreducible computation happens, the thing that will happen is those molecules will be sort of computationally scrambled up. And then we ask the question, when we look at them later, "Can we similarly sort of say very easily what constraints they satisfy?" And the answer will be no. In a sense, the configuration of molecules was encrypted relative to how it started. And it's this phenomenon. So the Second Law is really a story of the interplay between computational irreducibility of these underlying processes and the fact that when we observe these systems, we are computationally bounded in what we can notice about these systems. If we were computationally very sophisticated, we could just say about these molecules, "Well, I know," and by the way, one, one feature of molecular dynamics is it's reversible in the sense that if you see a collision between two molecules, and you're just seeing that collision, it's like the billiard balls bounce. They bounce off. If you ran that movie in reverse, it would be an equally valid movie of the billiard balls, you know, moving back the way they came and so on. At the level of individual billiard balls, at the level of individual molecules, everything is reversible in that sense. And so you could say, "Well, if I know exactly where all the molecules are, then I could just run this computation in reverse." People have have concentrated a lot on knowing where the molecules are. It's also important to be able to compute what will actually happen when these molecules sort of do their thing and have all their collisions and so on. And the point is that to know sort of where the thing came from, you have to be able to do that computation. But that computation is an irreducible computation. And if we, as observers of the system, are bounded in the computations we can do, we don't get to be able to do that irreducible computation. So we have to kind of just throw up our hands and say, "What looks random to us?" And that's, that's why we say it appears that the entropy increases because we say, "We can't decode this sort of encryption. We can't say, 'Well, actually, it came from this very simple initial condition.'" That's at the level of, of sort of how things with entropy work. When it comes to dealing with, um, with with energy, for example, in, in the case of molecular dynamics, it's a sort of a separate overlay. And essentially, what you're saying is, "Well, it doesn't just, these, these squares that are bouncing around, we're also going to assign a number to every square, and we're going to say that the energy is conserved when there are interactions between these squares." It's kind of a slightly higher level of, uh, uh, of kind of detail that isn't really part of the core point of the Second Law of Thermodynamics. But it turns out when you do that, you, you end up with this exponential distribution of energies that, um, where the scaling for that exponential is temperature. And then you get the Maxwell distribution, and you get, um, all the various properties of statistical mechanics and so on. And, and in fact, the, you know, in the end, I mean, it's a bit technical and mathematical. What confused people back in the day was this, when I say back in the day, I mean back in the 1860s, 1870s, um, was before our time, um, the, uh, uh, you know, what confused people was there was sort of an elegant mathematical structure that James Clerk Maxwell and other people noticed in connection with all these different parameters that define thermodynamics. And some people, like, actually, Josiah Willard Gibbs, early American physicist at Yale, was, you know, his first big work in the, in the 1870s was, was about about kind of, seeing what the consequences of, kind of, the mathematical structure, the geometrical structure of the relations between all these things about temperature and free energy and entropy and so on were. Those are things which have their own kind of life that are very relevant for for practical thermodynamics, practical chemical thermodynamics, things like that. It's a separate thing from the foundational question of, kind of, how does, how do things end up tending to get more random? And that, that doesn't depend on, on that kind of overlay of energy and temperature and so on.

Yeah, no, it's more fundamental. I guess the thing that, you know, is most striking to me, and the question I have for you now is, you know, could this have come, you know, in an alternate universe, could this book have come 30 years ago? In other words, were there things that you needed to discover through the Wolfram Physics Project, through things like the Rulead, which I hope we're going to get into, and, and the colonization thereof? But, could this have been discovered? You know, could Hawking, Beckenstein, could Gibbs, if he were still alive, could Maxwell have discovered what you have proven in this book in 2023? Or did it require the work of the Wolfram Physics Project in order to instantiate it into the world?

I was pretty close to this book back in the mid-1980s when I figured out computational irreducibility. I kind of knew that something like this was there. I didn't work out the details. And there was one important piece that had to do with the role of the observer and thinking about the observer as an important participant in the creation of physics, so to speak. And, you know, again, to, to kind of skip ahead a little bit, the thing that to me is, you know, we have these three big theories of 20th-century physics: statistical mechanics, Second Law of Thermodynamics is sort of the big shining piece of that, general relativity, and quantum mechanics. And it's always seemed that, well, the Second Law is almost something you just prove from pure thought. You know, general relativity, it's like, no, you know, general relativity is something you kind of have to wheel in from the outside and say, "Well, the universe happens to work this way." Quantum mechanics, the same thing. The thing that has been truly remarkable, and that's really emerged in the last couple of years in the things I've been doing, we've been doing, is all three of those theories of 20th-century physics seem to be derivable. And it's remarkable that laws of physics could be derivable. You know, that was the thing that first got me really interested in statistical mechanics, that there might be a fundamental fact about physics that was somehow derivable rather than merely something you have to be told. That's kind of the, the story. And that, that idea that these things might be derivable, that's all sort of come together. And that's been a thing that that made this kind of this the story of the Second Law much more poignant for me, much more something where I where I thought I could characterize, because what happens is the characterization of the observer necessary to derive the Second Law, general relativity, and quantum mechanics, it's the same characterization. And so that gives a, that, that sort of gives more strength to saying, "Well, I'm going to pick an observer that works like this." It's kind of like that, that's a, that's a bigger pivot point for for that.

My audience is used to hearing interpretations of quantum mechanics. But if I understand correctly, you're essentially saying a classical theory like thermodynamics also needs interpretations and also needs to have a very well-defined notion of what an observer is or is not.

Absolutely. And, and what, you know, for example, the fact that the molecules seem to become more random in their motions is something that if you were an observer who could untangle all the details of how all the molecules work, you wouldn't believe the Second Law. And actually, one of the things that's kind of interesting, there's this idea of a Maxwell's demon, a kind of little, little creator that is operating down at the level of molecules, and it's opening and closing doors, and it's doing all the things that the Second Law of Thermodynamics says you shouldn't be able to do, of being able to sort of untangle the randomness and unweave the randomness, right? And so one of the funny things is that if you look at the physics journals these days, pretty much every week somebody reports the creation of a Maxwell's demon. And how can that be? You know, we still believe in the Second Law, don't we? Well, what's happening is these are things which are making doing sensors at the level of individual molecules, and at the level of small numbers of molecules, you can untangle the Second Law. The Second Law isn't true for small numbers of molecules. The Second Law is a feature of observers like us, who observe these molecules in a computationally bounded way, on a large scale, and so on. So the Second Law is also a story of the way that we are observing the universe, rather than just the way the universe is. And, and again, this, the sort of the key phenomenon is this interplay between computational irreducibility underneath and the computational boundedness of us as observers of that system.

One of the things that that, uh, I would say, sort of a wrong turn in science that kind of started a couple of thousand years ago is this idea that space is continuous. That you can just put things anywhere you want in space. This is sort of a foundational idea in Euclid, for example. The very first postulate, a common notion, actually, of Euclid, is a point is that which has no part. That's saying there are infinitesimal points. You can have, uh, there's no shortest distance in space. Space is just a continuous thing. Well, now you run forward in time, you get to the end of the 19th century, and, uh, people were wondering, people were discovering quantum mechanics, for example. People were wondering whether molecules existed. The, uh, sort of the big question that had existed at that up to that time was, is matter discrete or continuous? That had been argued about since since ancient Greek times. And people have been, you know, some people said, "Oh, matter is continuous. It's, uh, everything's like a fluid that's just going to continuously flow." Other people said, "It's made of molecules." Well, that didn't get resolved until the first decade of the 20th century. Brownian motion was the thing that probably really, really clinched that, that particular issue. You could actually see under a microscope, uh, little pollen grains being kicked around by by individual water molecules. So that was kind of, Brownian motion showed matter was, was discrete. Then your friend and mine, you know, Einstein, uh, in 1905, basically said, "Well, light is discrete as well. That has photons." And then next thing was discrete. So the next question was, is space discrete? And actually, I've been, been finding more and more that at that time, for the first 20 years, 20, 30 years of the 20th century, the typical physicist believed space was discrete. And I'm sorry to interrupt. I'm sorry, but people nowadays make, uh, assertions that space is discretized, including our friend Elon Musk, that there is a fundamental physics attribute called the Planck length, which obviously you can define it, but there's nothing as fundamental about the Planck length as I understand it as the discretization that you're going to explain to us, correct?

Yeah, I mean, the Planck length is more a question of units. It's a question of how you combine, you know, the different units that we use to measure, you know, what do we mean by time? What do we mean by length relative to time? What do we mean? Absolutely not fundamental in the way that you are going to describe.

Okay, please continue.

Right. No, so, so I mean, you know, back, I think 1916, for example, Einstein had a nice little quote that said, you know, "In the end, space will turn out to be discrete, but we don't have the tools we need to study that yet." So 100 years later, we do. And, uh, and so, sort of, the first thing that's sort of a foundation of, of our physics project from, uh, from 2020 is, this idea that space is, in fact, discrete. And it's made of things, just like, you know, matter is made of molecules. Space is made of atoms of space. Atoms of space. There's nothing an atom of space is just a discrete element. There is nothing to say about it other than that it has a certain identity, that it exists. The other thing you can say is how it's related to other atoms of space. So you can kind of represent that by this giant kind of friend network of the atoms of space, this giant network that says how the atoms of space are related. And so then it turns out that when we talk about, you know, how does, how does time operate on this, where we've got this big network of all these atoms of space, and all we know is how they're related to each other, and then what, what's happening is that there's a rule that gets applied that says, if here's a little configuration of atoms of space that corresponds to this collection of relations, then it will be transformed to a collection of atoms of space with this other collection of relations. It's this sequence of transformations between little clumps of atoms of space. And that process, you run that process many, many, many times. And it's kind of like, it's a little bit like the process of looking at water molecules. You know, the water molecules are colliding, and they're, they're doing their thing. And on a large scale, when you look at water, it flows, you can pour it, it's continuous, it obeys the equations of fluid mechanics and so on. But at a small scale, it's just a bunch of molecules bouncing around. So you apply the same thing in the case of these graphs, hypergraphs that are the relations between the atoms of space. You do the same kind of thing that you do in fluid mechanics, saying, "Well, what's the large-scale behavior of such a system?" And instead of getting the equations of fluid mechanics, you get the equations of spacetime. You get the Einstein equations for spacetime as something which is derived as the large-scale limit of the dynamics of these atoms of space. There are a bunch of footnotes to that statement. U, among the things that gets complicated very quickly is this network that represents atoms of space. It's not in any particular number of dimensions. It's not like we can say it's a three-dimensional thing, a substrate. It's not a substrate. It's not. Well, it is everything in the universe. I mean, just like imagine that the whole world was made of water, and all that we could do to make sort of persistent things like us was have little eddies in the water that sort of persist through the water, even though underneath there are a bunch of kind of, uh, um, sort of, you know, molecules of water that are bouncing around. For us, that the kind of the concept of our models is there's nothing in the universe except space, and the features of space are the things that we notice. What might be an eddy in water would be an electron in the structure of space. And actually, the one thing we, we don't know how electrons work yet in our models. We do know how black holes work in our models. And, um, so we can, you know, we can see how this black hole exists in the structure of of spacetime. And what you see is that spacetime, space is very dynamic. In order for space to be held together, so to speak, it's continually having to get sort of knitted together by these by these rules that, uh, uh, that relate different atoms of space. A black hole is this region of space that has this event horizon, where, well, in the, in the formal setup of our models, it's a causal graph that has certain kinds of disconnection in it. But anyway, you can, you can set up these black holes. And so, for example, we just made a few weeks ago a video of two little tiny black holes and what happens in our models. And it's pretty neat because you see kind of that there's space is bubbling around. These are very, very tiny black holes, so they're black holes down at length scales comparable to the, to the elementary length, comparable to the discretization length for space. See these two black holes, they're just there, and they feel the force of gravity, so they attract each other, and they come together, and they merge, and they produce little gravitational wave ripples. And so far as we can tell, it's a pretty accurate rendition of what general relativity says should happen. In fact, it's accurate enough that there are a bunch of groups that study kind of the numerical versions of the Einstein's equations that are sort of taking on this model as far as they're concerned, as a way to think about a discretization of the Einstein equations. So, in other words, for them, what we've done is we've made this.

A discrete network thing, which on a large scale is like the Einstein equations. Now, normally when they deal with the Einstein equations, they're typically, you know, they start with these mathematical equations, and then they usually use our, our product Mathematica to kind of, uh, grind through and understand how those equations are set up. And then eventually, they'll get sort of simplified equations, and then they'll say, "Okay, now we're going to put this on a computer."

But the way they do those solutions is to assume that space is kind of broken into all pieces, just for the sake of the computer. They don't imagine that space really works that way, for the sake of the computer, right? And, and but so in our models, space really works that way. And what's, what's kind of neat is that our models are actually a good method for doing numerical General Relativity. And that's, um, so.

And now, the thing that I find really fun is there's starting to be some groups using these. And I think for them, if there's something that is a deviation between our models and General Relativity, it's like, "Oh, this is really terrible for us." It's like, "Fantastic! Now we can see the discreteness of space." And so one of the things that's pretty interesting is we're starting to see, we're starting to try and tease out effects that are the, the, that allow one to, to detect the discreteness of space.

So the way, one way to put it is, Brownian motion was the thing that clinched it for molecules. We want to find the analog of Brownian motion for physical space. What is that thing? Is it some shot noise? Is it the gravitational radiation from emerging black holes? What is that difference in the ring-down speed when black holes merge that's associated with discreteness? What's the difference in the way frame dragging works around a black hole associated with discreteness of space?

We don't know the length scale for the discreteness of space, just like people didn't know how big molecules were. So it's a lot smaller than the Planck length, we know that, um, but we don't know how much smaller. And we don't know, you know, it could be that it's out of the range of what we can experimentally detect. It's looking like there are effects in, for example, critical black holes that are spinning right at the sort of the limit of how fast they can. They don't actually spin, it's just a parameter in the equations, but, but, um, they, they, they drag things around as if they were spinning. But, um, right at the, at the edge, the, the structure of space is held together by a small number of, of relations in this, in this graph. And so if the, if the black hole kind of spun faster, a piece of space would essentially break off. And at that moment, at that point where you have this critical black hole, there is probably a, that's a moment where you kind of have a gravitational microscope. You can start to see effects that, that probe down to this, down to the discreteness length. Maybe we don't know exactly how that works.

So I just, I, I can explain my aphorism about dark matter is the caloric of our, yeah. And just to, to refresh the, the, the viewers or listeners, you know, kind of memory. I mean, caloric is a fictitious property attributed, thought to be attributed to matter that was storing heat, and it's gone to the dustbin of history now. What's interesting about what you're saying is that, uh, it may be, uh, the, the analog of that in the 21st century might be dark matter. And we have abundant, you know, so, so to push back with respect, you know, we physicists are, you know, debating now between the various candidates for dark matter. It's not only that dark matter exists, we have abundant evidence for, you know, from the CMB anisotropies that I study, to my colleagues who look for direct detection experiments, to galaxy clusters from Zwicky back in Pasadena, where you used to spend some of your time, and it goes all the way through Vera Rubin, who spent time here in San Diego. So for you to say, uh, it's going to rankle some people because the, well, let me explain what I mean, because it's, there's more to it than just that statement, okay? So, so, uh, and maybe I should have, maybe I should state it slightly differently for these purposes, but, but, you know, first of all, what is dark matter? So, you know, it's, you see a galaxy, it's got a bunch of stars, you know, 100 billion stars in it, and there's a certain amount of gravity that should be associated with all of those stars. The way galaxies rotate, it's as if there's a whole bunch more gravitational mass than you can see in the stars, in the, in the light matter, so to speak, of, of the stars that are lit up. So there's something there that has a gravitational effect, but is not, uh, like a star where you're seeing light and so on. And, uh, so what do I mean by my statement? Caloric was an interpretation of what heat was. Nobody was, nobody was disputing, you know, we still talk about calories today. Heat is a thing. Nobody is disputing whether heat existed. The question is, what was heat? And at the time, people assumed that heat was this kind of fluid that matter was kind of had, had heat inside it. There was sort of a, like a fluid that had, had worked its way into the pores of the matter, so to speak, to be the heat that was there, because the only thing that was, the only thing people could imagine heat was, turns out what heat actually is, is the microscopic motion of molecules. So now the question is, in modern times, what is this thing that produces a gravitational effect that isn't kind of like the matter we know? Well, the immediate thing for people to say is, well, the only thing we know is particles. It must be something, some kind of particles. So just like people said in the past, heat must be some kind of fluid, because that's the only kind of thing we know. When we're confronted with dark matter and this thing that happens, a gravitational effect, the immediate thing for people to say is, it must be some, some other kind of matter that we've never seen, some kind of, you know, some particles, you know, this kind of particle, that kind of particle. I don't think that's right. I think it's actually a feature of the structure of space, just like it turned out heat was this feature of the microscopic structure of matter. I suspect dark matter is a feature of the microscopic structure of space. So, in fact, and the most ironic thing is that when you look at the structure of space in our models, there is at the most microscopic level, there's all this randomness, all this computational irreducibility, all these different sort of rewrites of this kind of relations that knit together the structure of space. It's kind of like heat. And so it could turn out to be the case that dark matter is basically space-time heat. That it's basically that there exists a, a feature of the structure of space-time, just like heat in matter is these motional molecules, that there's kind of a space-time analog of that that is associated with kind of activity in the structure of these networks that make up space. And so that would be kind of an ironic thing for it to turn out that, um, you know, it's, that what we're missing is something this exactly. It's just, you know, science has this habit of sometimes repeating itself, as history does, that, uh, uh, that will turn out that the thing we don't know what on earth it is, is actually something that is a direct analog of that molecular process that we saw in matter, but now applied to the atoms of space that are not, that are much more idealized structures than the kind of molecules, atoms that we have in, in matter. So, you know, the challenge. So now the question is, okay, you're an experimentalist. How do you detect this? And, uh, what can you actually look for? And, uh, stay tuned, because we're trying to figure this out.

Well, I just want to again, you know, push back with respect and affection, but to say that, um, you know, dark matter doesn't have any instantiations right now that we understand very well. It wouldn't be true. In other words, we know neutrinos are dark matter. They interact weakly, they have a tiny mass. We know what their mass bound is. We are actually going to measure that with the Simon Observatory, going to measure it from an upper limit plus a lower limit into a detection at several, uh, sigma, and other experiments as well. Weak gravitational lensing will do that. And we know of another candidate that you just mentioned a few minutes ago, black holes. Black holes. Now, there may not be enough of them to make up the critical closure density, but we know two of these things exist in particulate form. And I'm wondering how, how do you react to that? In other words, do we need another candidate now to explain the peculiar property of galaxies and Zwicky clusters of galaxies where he derived it from the Virial theorem? Why do we need, why do we need to discretize space? We just need to find an axion, which we're gonna also look for, um, and some of the, uh, detections of already. So why do we need to add in another ingredient into the mix, namely discretization of clumping of space-time?

You don't, just like you can go look for features of caloric fluid. It turns out you won't find them. I mean, that's the, you know, this is one of these things where it is a model, really has, well, has one parameter, which is the, the size of the elementary length. Beyond that, it has no freedom. There's, you know, it, whatever it predicts is what it predicts. We're not, you know, there's no wiggle room, which is not the case in most current models in particle physics or something like that. It's like, "Oh, we can tune this parameter, we can do this, we can do that." We don't have any of that freedom. To me, what's, what's really exciting about what's happened the last few years is if you have a model that has no parameters, it's kind of like, it's either right or it's wrong. And what's happened is more and more things have kind of lined up. Yep, it explains that. Yep, it explains that. And so on. And so that's very encouraging. You know, I don't know yet whether the dynamics of our models will lead to a phenomenon that corresponds to dark matter. We don't know that yet. We probably will know that quite soon. It's really a detailed question, doing these simulations and so on. But, you know, if it does lead to that, then we're just going to say, this is, this is what we think is happening. I mean, you know, and if it turns out it doesn't lead to that, well, we're stuck with axions and things, and we have to see whether we can find those. The question is really, is dark matter a clue to a bigger phenomenon, or is it just a detail of something that is kind of like the particle physics we already knew and so on? I don't know. I mean, I, I, I, I say that, um, I, I've been very sort of, my own, if I were to guess, I would guess that it's something out of left field. It's not a, oh, you know, I mean, I used to think dark matter was probably small black holes, and, you know, then people said, "Oh, no, it couldn't possibly be that," and etc., etc., etc. It's gone through, I think neutrinos are not very promising for that, but, but in, you know, different kinds of, uh, and it's not, we don't know yet whether our model says you should have a phenomenon that corresponds to dark matter, but, uh, you know, I think it is, it is kind of an interesting thing to think about, and it's, it's a, I think there's a certain kind of, um, I would say intellectual charm to this idea that the thing we might be missing is the same thing that people missed in the 1800s with respect to the structure of matter and the nature of heat. And, and so it's, it's a, um, but I mean, there are, you know, for us, one of the things that happens is there are dimension fluctuations in the universe. The universe starts infinite dimensional and gradually cools down. We don't know why it ends up at three. My guess is that the three is a feature of us as observers, and that we could describe the universe not as three-dimensional. It is a feature of the way that we, we are as observers that makes us think that we should parse the universe as a three-dimensional thing. But in any case, the, but one of the predictions of our model is that there will be dimension fluctuations. We don't know how big, but we know that there will be places where space is not three-dimensional, but it's, you know, 3.01 dimensional, etc.

And there are limits. There are limits from the similar phenomena that we discussed earlier, black hole coalescence, and also black hole-neutron star coalescences. And I want to get back to, to black holes, because I think they do unify your interest in, in the second law and, and also with gravitational collapse and the phenomena of observer and system. So obviously, my, my viewers and listeners are familiar with things like Hawking radiation, Bekenstein entropy, and another thing. Things, I think it would be a treat if we could, if you could kind of work an example. Can you derive, you know, Hawking radiation or the Bekenstein entropy for black holes from, you know, from these irreducibly computational, uh, framework in a way that we can, and, you know, note the second law's importance? And as I say, a worked example in sort of words. I don't expect you to have a whiteboard nearby. It wouldn't surprise me if you do, but, but, um, can we go through that? Let's derive, let's talk about, uh, Hawking radiation and Bekenstein entropy. Um, and can we get that?

This is, this is, okay, my young collaborator Jonathan Gorard has just been working on this, and I think he has some paper which maybe is already out or maybe is about to be out about this exact very topic. It's, it's a bit of a complicated story, and there are pieces to it that are a bit alien from the way people have thought about this before. Let me say that to get to Hawking radiation, things like that, we have to talk about, about quantum mechanics. We didn't talk about quantum mechanics yet. But let me say something even before we get to quantum mechanics. Let's talk about the intrinsic entropy of space-time, which is not what one's talking about in black hole entropy. But in this model where there is a discrete structure of space-time, you can say, I've got a lump of space-time, and how many different configurations, given that I know that there's a certain curvature to the space in this region of, of the universe, how many possible configurations are there of this underlying space-time structure that are consistent with that overall curvature? That's something we've never been able to address. We've never been able to talk about with traditional approaches to general relativity and quantum mechanics. We now can talk about that. You can actually start working out the intrinsic entropy of space-time. And, given constraints, you can say, given these constraints, given that we know we have, for example, a black hole with certain, sort of external metric, external gravitational field, and so on, we can say, well, let's actually count how many possible configurations of space-time there are consistent with that. That's something we can imagine doing. We haven't successfully done that yet. I think Jonathan has made progress recently in doing some of those kinds of things. But, but let's talk about, well, let's talk about it gets a little bit more complicated when we talk about quantum mechanics. We have to talk about what quantum mechanics is first of all. But let me say something about, about general relativity and the derivation of general relativity. You've got this underlying network, it's flopping around in all kinds of different ways. The fact that we even believe that space is continuous, the fact that we've even had that idea, is a consequence of the way we are as observers. The fact that we don't say, "Oh, space is made of all these atoms of space." We say, "Space seems to us like it's continuous." That's because we're pretty big compared to the atoms of space. The atoms of space might be, you know, 10 to the minus 100 meters apart, so to speak, in some sense, and we're very big compared to that. And by the way, there are many aspects of the way we parse the universe that are specific, detailed consequences of the way we are as observers. Let me give another example. So, you know, we usually think there is a state of the universe at successive moments in time. We look around the room, we say, "That's the state of the room now." At a later time, the room will look different. Okay? The reason we think that is because as we look around, we're seeing a few tens of meters away. The speed of light is taking information from tens of meters away to us in milliseconds, but our brains take milliseconds to update and know what we saw. So it's the fact that the speed of light relative to our speed of brain operation is the way it is that makes us parse space-time as there's the complete structure of space at successive moments in time. So, sort of a thought experiment: imagine that our brains worked a million times faster. Imagine we replaced our neural hardware with semiconductor hardware, which runs a million times faster. What would we think about the structure of space and space-time? Because it'd be very different. We'd be, we'd be continuously seeing sort of the things that are, you know, relativistic effects, individual photons. We'd be seeing, you know, just like we have echoes from sound, we'd be seeing all these echoes of light and so on. Very different experience. And we wouldn't necessarily piece together this, you know, its space at successive moments in time. Same thing if we were much bigger than we are. If we were the size of the solar system or something. We would have a very different view of the relationship of space and time. So the thing to realize is the fact that we perceive General Relativity is a consequence of the fact that we're observers of the kind we are. And it turns out that this idea of computational boundedness, we can't untangle the computational irreducibility of underlying processes together with another condition, which is actually also needed in, in second law, but it's slightly more subtle. The second condition that we need is that we believe we are persistent in time. And you might say, "That's totally obvious. We're obviously the same us at the next moment in time as we were at the previous moment in time." But it's not obvious because we're made of different atoms of space at successive moments in time. So the fact that we have this belief that it's the same us is a non-trivial thing. And that is a feature of us as observers of the universe, that we believe we have this thread of experience that continues. And so those two things turn out to inevitably give us General Relativity. So the, the, the feature of us as observers, the same features as us as observers that gives us a second law of thermodynamics, also gives us General Relativity.

Okay, so we should talk about quantum mechanics. So we talked about this, this, uh, network, and it's all these rewrites are happening, and we say, well, the network progresses from this state to this state, and so on. But actually, there's a little bit more to it, because it's, what we say is there are these rewrites that can happen. Well, now we can say, well, just run all possible rewrites. What we'll get is many different paths of history. There's one sequence of rewrites that give you this sequence of states of the universe, this thread of history. Another sequence of rewrites that give you another thread of history. And what we end up with is what we call the multi-way system, where you've got these different threads of history that are branching and merging. And that's a thing that's, that's continually happening. There are different threads of history that are branching and merging. And it's that phenomenon that essentially inevitably gives us quantum mechanics. Because sort of the core idea of quantum mechanics is that it isn't definite, things don't happen in the universe. Instead, there are many parts of history, and we just get to observe certain probabilities of different parts having happened. And what, what happens in our models is there's this multi-way graph that represents all these different parts of history. And then the, then the thing is, well, well, why do we even believe that definite things happen? Why do we believe that we have, we, we believe that we have a single thread of experience? Yet quantum mechanics has all these different branches that are, that are going. So it is an assumption of us as observers that we can say that we can aggregate these things into saying there is a definite thing that happens. Very similar to what happens in thermodynamics, where we say there's a definite pressure to this gas. Well, pressure from a gas is made up of lots of little individual molecules, you know, hitting our pressure measuring device. And it's the fact that we aggregate those to say, "Oh, there's just a definite pressure." That's why we believe that there's a pressure in the gas, and the gas obeys the gas laws and so on. So similarly, with respect to quantum mechanics, the reason that we believe that definite things happen is because we are essentially extended objects in this kind of space of quantum branches. We, we talk about this thing we call branchial space, the space of quantum branches, just like we can talk about physical space as being the extension of this hypergraph. So similarly, in this, in this multi-way graph, you can kind of slice the multi-way graph, you get all these different ends, and they have certain relations that define kind of another type of space that has distances between things that are distances between different parts of history for the universe. And the, the sort of the big point is that we are extended with respect to that. We are, we are in that system, and we are, uh, we're kind of, we're observing that by aggregating across many branches of history. So that, that's kind of the, the very rough idea of how quantum mechanics emerges. Now, when you talk about black holes...

Oh, sorry, Stephen. Could be before we go there, because I think it's a natural point to just break. One thing that's always kind of flabbergasted me is you start with something in classical mechanics, a Poisson bracket, and you have commutation relations, and the exact same language and mathematics transmutes exactly over, you know, into quantum mechanics, except these things are non-vanishing, and in fact, they also involve the square root of negative one. Um, and it's completely, you know, almost as mind-blowing a fact as there is. You know, uh, Feynman used to say, as you knew Feynman personally, but, you know, the most remarkable relation is, you know, Euler's relation between E and pi and i and so forth. But this to me is almost even more remarkable, that you get a physical, I mean, that's just, just in the laws of mathematics. I'm not minimizing it, but now you've got this thing in classical mechanics that ports one to one, except for the square root. What, what do you make of this? I mean, is this something, you know, that is just a fact? It's okay. How does that work?

I, I mean, it's always sort of fun because Vic Fan always used to say he'd worked on quantum mechanics his own life, his whole life, and he always used to say, "Nobody understands quantum mechanics." And I, I talked to him about that at great, great length. Okay. It's a shame he isn't still alive because I think I now finally am beginning to understand quantum mechanics. And so one question is, like, where does the i come from in quantum mechanics? I think it's a, I think it's a confusion, actually. I think that one of the things that was sort of a wrong turn that was taken in studying space-time, actually, was what was done not by Einstein, but by Minkowski in 1919, when he said, "Oh, space and time are really the same kind of thing. Let's package them together into this thing we call space-time." And he did that. Minkowski was a number theorist, a mathematician, and he said, "It's very elegant. We can make these quadratic forms that are x squared for space and t squared for time, and it's x squared minus t squared. It's all very beautiful. We can package together space and time as being the single space-time thing." I think that was a mistake. I think space is a thing that's very different from time. Space is this extension of this hypergraph. Time is the inexorable progress of computation. It is an emergent fact that space and time sort of work together in the ways that give relativity. That's an emergent fact. That's not something that's built into the underlying model. In quantum mechanics, I think a similar wrong turn was taken. So in quantum mechanics, one of the things that one does when formulating quantum mechanics in terms of wave functions in the Schrödinger equation or a whole variety of other, other versions of that formalism, what one's doing is one's saying, there are these quantum amplitudes. There these things that, uh, we will be able to represent, kind of the quantum world in terms of. And quantum amplitudes are complex numbers. They have a magnitude, the, the, the overall, you know, complex numbers can be represented in, you can sort of plot them in two dimensions, and they have a distance from the origin and an angle from the origin. So the, the magnitude and the phase. In quantum mechanics, one packages together the magnitude and the phase. In our models, they come from completely different places. The magnitude comes from the counting of the number of paths in this multi-way system. The phase is basically the position in branchial space. There's a bunch of mathematics we have not yet worked out, and that's quite difficult, I would say. But what seems to be the case is that what's happening is in quantum mechanics, you are, you're, well, okay, so I should say another thing. In space-time, one of the key things that happens is that the presence of energy, momentum, or mass deflects shortest paths. So as you know very well, the, um, there are geodesic paths, shortest paths in space-time. And you know, when you just are dealing with everything on a plane, for example, the shortest path between two points is a straight line. If you distort that plane, the shortest path between two points won't be a straight line anymore. And the kind of original idea of general relativity was the structure of space-time is being distorted by the presence of mass. And that distortion is causing shortest paths to no longer be straight lines. Shortest paths are deflected, and that's the deflection associated with the force of gravity. And that was kind of, that's kind of the basic idea of General Relativity. And so what happens in our models is, well, you can have shortest paths, same kind of deal in this graph. You can just say, what's the shortest path on the graph going through edges of the graph? How do you get from this place to that place going through the smallest number of edges on the graph? So now you can say, well, the next question is, what's energy momentum? This is something that really surprised me, actually. I thought it was going to be very difficult to understand what energy momentum is. Turns out it's not. Turns out energy momentum is essentially just the amount, the density of activity in the network. So we've got all this network is being rewritten in all these different ways. We can represent that slightly more formally by a causal graph that says there are these little rewrite events, and every rewrite event can is producing output that will be the input to subsequent rewrite events. And we can make this graph that represents the, the sort of causal connections between these things. And energy is simply, if we look at, well, we have to define, in, in relativity, as you well know, we're talking about space-like hypersurfaces. These things. So, so events can be related in a time-like way, in the sense that one event is followed by another event in a sequence in time. But there are also events that can be space-like separated, where those events can happen simultaneously in time. If you're time-like separated, you better not be space-like separated, because one event is follows from another event, and they couldn't be simultaneous. But there are events that are sort of orthogonal to the, the time-like directions or space-like directions. There are many different choices of space-like directions that what's what gives the reference frames in relativity and so on. But in any case, if you look at these space-like hypersurfaces, energy in our models is simply the flux of these causal edges through space-like hypersurfaces. Momentum is flux through time-like hypersurfaces. Okay, so then you can derive the presence of the existence of gravity. And you can derive the fact that there is, when there is this density of activity in the network, it deflects shortest paths in the network. That's a pretty neat thing that you can give an intuitive definition.

Intuitive happens, right? Yeah. So actually, to give another one of these intuitive things. So time dilation is a phenomenon of, of special relativity, that, you know, things that are going fast, things that are moving a lot, time seems to go slower for them. Well, in our models, you can kind of see why that happens, because what is time? Time is this inexorable process of executing computations. Motion is, you get to recreate yourself at a different place in space. That, that phenomenon of motion, the fact that you're recreating yourself at a different place in space, that takes computational effort. So, you know, have this trade-off. What are you going to spend your computational effort on? You're going to spend your computational effort on moving in space, or you're going to use it on progressing in time? And so when you're moving in space, you're using up your computation on motion, so you don't have as much left over to progress in time. So that means you effectively, time goes slower for you. And that's what time dilation comes from. And, and the math works out. And that's, that's really how it works. And, and it's, it's really quite, to me, it's really amazing that you can give what is essentially a mechanistic explanation of what seemed to be a purely kind of, the math happens to work out that way kind of phenomenon. But, okay, so that's how this works in, in physical space. In branchial space, there's a similar phenomenon. You have these geodesics, these shortest paths, things travel on shortest paths. But now energy momentum also deflects shortest paths in branchial space. And then what's the consequence of that? Well, it's, there's this, something is, is, is, is deflecting shortest paths and it's moving where you are in branchial space. The fundamental law of quantum mechanics, one way to state it, is the Feynman path integral. The Feynman path integral says you have this thing that is what's called the action, kind of this relativistically invariant version of energy. Um, and that the presence of action, effectively energy momentum, is the thing that changes the phase of your, of the, of your description of the quantum system. So, in other words, the presence of energy momentum is making this change. So in our models, the presence of energy momentum is deflecting geodesics. It's moving things, but it's moving things not in physical space, but in branchial space. So now the question is, what, what is motion in branchial space? Well, motion in branchial space appears to be change of quantum phase. And so what's happening is, what in the, the phenomenon that is general relativity, that is deflection due to gravity in physical space, that same phenomenon, the deflection in branchial space, is a change of quantum phase. And that change of quantum phase is what the path integral says should happen in quantum mechanics. So, in other words, what one's saying is quantum mechanics is the same phenomenon as gravity and general relativity. What is general relativity in physical space is quantum mechanics in branchial space. They're the same thing.

Does that imply it's a simple geometrical, that branchial space is also symplectic, uh, space? In other words, that manifold, uh, it's essentially an abstract manifold on which these things can take, take place, or am I misinterpreting that?

So it's a little complicated because momentum is this flux of causal edges through time-like hypersurfaces. And so when you look at a commutation relation that's about, uh, this flux of causal edges as compared to position, I don't know the answer. It's quite possible that it's, it's not mathematically trivial to figure that out. Um, it, uh, an interesting question about these commutators and anti-commutators is the presence of, you know, there are two very different kinds of particles, bosons and fermions. Things like photons, where you can cram as many photons as you want into something, they really like to hang out together, which is why lasers work. Or electrons, but they really don't like to hang out together. You can only get one electron in a given state, and that's why, you know, matter doesn't collapse and things like this. And that's, that's, um, and so this distinction between fermions and bosons is the distinction between commutators and anti-commutators in quantum mechanics. And it looks like there is, in these multi-way graphs, it looks like we don't know exactly how this works, but it looks like there is a relationship between, kind of, the structure of these multi-way graphs and whether when you have a branch in the multi-way graph, it immediately recombines or not. That, that's related to the presence of that, that the, the branching and recombining is a commutator being equal to zero. And so the, uh, um, it seems like bosons are that case, and fermions are the case where things sort of tree out and don't recombine. How that relates to the symplectic structure in, uh, in phase space, let me think about that for a second. We should come back to it, maybe in a, in a separate conversation at a later time.

But, um, uh, because I think it's imperative for me as an experimental physicist, you know, I'd be, I'd be, uh, shirking my duties if I, if I didn't ask about some consequences that my colleagues potentially can investigate, you know, not not on your behalf, but on our behalf, right? Because these could be pointing in new directions, newer interpretations, but also new physical observables. So we talked a lot about black bodies, we talked a lot about the second law, we talked about, uh, so I studied the CMB, the most perfect black body known to exist in the universe. Uh, there are aspects of it that can be used to synchronize clocks or to synchronize, uh, coordinate systems within our local frame of motion, which is caused by our dark matter-driven, at least in some conceptions, motion towards the Virgo supercluster. So my question for you is, are there observables? Are there distortions, say, there common spectral distortions to a black body that are, I wouldn't say easy to observe, I mean, it's not exactly what I do, but the technology's been there for, for some time to measure very minute parts per million, parts per hundreds of a million distortions to black bodies. Are there, are there kind of queries that you can set me and my colleagues off on to look for that would lead to an interpretation or perhaps a measurement of some fundamental length scale, computational?

We think so. We don't yet know. I mean, this is one of the challenges is you have a fundamental theory, and you have to build up from that to something you can actually point a telescope there and see it. I mean, you know, cautionary tale from General Relativity that you probably know well is, uh, you know, the, one of the predictions of General Relativity is that the bending of light around the sun will be twice as great as it was in the, in the Newtonian theory. In 1916, so the theory was proposed in 1915. In 1916, there was a total eclipse, uh, was visible from Crimea. And, uh, there was an expedition that went to go and observe where light was bent more around the sun than it would have otherwise been. At that time, well, at that point, Einstein had calculated it wrong. So he had a prediction, and these guys went to go and measure the prediction, and they almost measured it, except the US entered World War I, and these American physicists with all their equipment were told by the Russians, I guess at that time, "No, you know, this is off limits. Go away." Oh, they, they imprisoned them. Yeah, that's right. So, so the experiment didn't get done. Then your friend Eddington in 1919 went to South Africa, redid the experiment. I suspect he cooked the books on that experiment, but that's a different issue. And by that time, Einstein had corrected the, the calculation of the bending of light around the sun, and Eddington claimed to have observed exactly that phenomenon. So, you know, it is a difficult thing to go from the fundamental physics to an experimental prediction. I've seen this. I used to do particle physics where one could, at the, in the late 1970s, which was a very golden age for particle physics, and I saw this multiple times of, you know, for example, one of my experiences in, as a young physicist when I was 17 years old, actually, was I, I worked out in QCD theory of quarks and gluons, how many charm particles should be produced in proton-proton collisions. So I had this calculation. I said, "The number should be this." Okay. There was an experiment that said, "No, it's not that. The number is 10 times smaller. Is less than 10 times smaller than that." And it's like, "What's going on?" I didn't know what to do. So I published this paper where I said, "This is the calculation from QCD, and then half the paper is, but the experiment says it isn't true. Here's why it might be wrong, even though QCD really said that's how it should work." Well, it turns out the experiment was wrong. That was the last time I didn't visit an experiment whose, uh, you know, after that time, I always made it a principle, I'm going to go visit the experiment, going to ask all kinds of questions, I'm going to, you know, it was a, it was one of these experiments where they're looking for something where they didn't find anything. And that's always suspicious because, you know, when you find nothing, it's kind of, you don't really know that you were looking to trying to detect it correctly. But so, so, you know, with that cautionary statement, what kinds of things might one look for? Well, I think the, the, you know, I think dimension fluctuations are a big thing. I think that, uh, there are a bunch of, um, bunch of effects. Actually, it was just, um, uh, my young colleague Jonathan Gorard was just at a, a, um, uh, gravitational wave background conference, and I think and some other people there cooked up a whole bunch of things that are possible effects that you could look for. The challenge in all of these is just doing the physics that goes between this very small length scale. So, for example, one really cool effect would be gravitational lensing around the dimension fluctuation. In ordinary gravitational lensing, you know, you're, you're looking at some galaxy or something, and the light is being bent by the presence of, of, uh, of mass. Um, in this case, we expect that the light will be bent by the presence of a dimension fluctuation. If, if, if the universe isn't exactly three-dimensional, then the, the kind of the, you know, if you even have the electric field from a point charge, usually just streams out in all directions and has an inverse square law kind of, uh, fall off. But if you're not in three dimensions, it's not an inverse square law. And there's an effective, there's an effective kind of refractive index type thing that seems to happen when you go through a dimension fluctuation. So the, the coolest experiment, which I don't think is going to work out this way, but it would be super cool if it did, is that we don't know how this works yet. We don't know what actually happens to a bundle of photons that go through a, a dimension fluctuation. But, you know, in, in a very fanciful way, one could imagine they're shattered into some kind of fractal distribution, uh, in the imaging plane. And then the, the, the thing that would be spectacular, which which I think is very fanciful so far, is we'd be able to say, use the Space Telescope, look at this thing, you've got this thing that looks like noise, you make this transform on it, and you got a picture of a galaxy. If that happened, we really know we're seeing dimension fluctuations. I don't think it's going to be as simple as that. I think that the likelihood is, in terms of CMB, I think the, the potential is relic dimension fluctuations from the early universe. And the question is, what are their signatures? And, you know, in our models, there's no inflation story. The reason that different parts of the universe are in causal contact is because the universe was originally infinite dimensional, where causal contact is trivial, because the, you know, the different parts of the graph, everything is connected to everything. So, so then what happens?

So there are no doubt predictions about, actually, that brings up something very concrete, Stephen, because if we, on the Simons Observatory, or our competitor, and BICEP, and others, if we detect a primordial gas of gravitational waves resulting from primordial curvature perturbations and fluctuations in the inflaton, that would seem to falsify this, at least the notion, as I understand it, of of the infinite dimensional space cleaving into a finite number of dimensions. So it's, by virtue of what you're saying, because it's falsifiable in the Popperian sense, is it not?

The calculation of what the gravitational wave spectrum is from, you know, our models is a difficult thing. I mean, it hasn't yet been done. We don't know how to do that yet. We've, there's no, there's no inflaton. There's nothing to fluctuate. There's no multiverse, right? In your model. No, that's right. But, but there will be, there will absolutely be relic gravitational waves from the beginning of the universe. Right, but their spectrum would be probably very different from what inflation would predict. In other words, I'm looking for is a big messy story. I mean, inflation has a thousand, well, not a thousand, but at least 20 parameters that you can tweak. We don't have those parameters. So whatever we predict, we're stuck with predicting that. We don't know what. I would encourage you, I would encourage you at great haste, Stephen, because this is something that over a billion dollars is being planned, devoted to in the field of cosmic microwave background, so-called B-mode experiments, that are not only looking for the presence of these primordial gravitational waves, but eventually their power spectrum, if indeed they exist. Now, if we discover them, and you know, in other words, it's a crisp test, it's a decisive test, to use Popper's language. But, Stephen, I have to go put some kids to bed in about 10 minutes, but I have a billion more questions to ask you. I'd love it if you would beg, beg your forbearance to have a part two at some part, four at some time. But I do have some questions from the audience that they're dying to ask you.

Yes, please. So, okay, these will be, maybe yes or no or quick short answers, so we can get through as many.

I'm really bad at short answers. I apologize.

I haven't noticed, Stephen. I never noticed. Okay, so you mentioned, according to, uh, my listener, Sean Shader, Steph mentioned that he had realized AdS/CFT is related to, do with something to do with branchial space. Can you give any details or implications about that?

So what happens is, and again, the details are not fully known yet, but this is not a yes/no question. Okay. In the simplest way of thinking about it, every branch in the multi-way graph has a complete universe, has a complete state of the universe. But that's a very inefficient way to think about it. Rather, those states of the universe, most aspects of them are the same. It's only a small part that's different. So you end up, you end up with this thing we call a multi-way causal graph that relates the different events that happen at different places in physical space and on different branches in this multi-way graph. And you've got this multi-way causal graph that contains information both on the relationship between events at different places in space and the events at.

different places in branchial space. It's the fact that there is a single object that contains information about both branchial space, which is related to quantum mechanics, and physical space, that's related to general relativity. That's what knits those two things together.

And so the adfc of key correspondence is almost certainly two different projections of this multi-way causal graph: a projection in the branchial direction giving you the CFT part, a projection in the in the space spatial direction giving you the the ads part. And again, there's the bunch of people have been working on this. And um, it's uh uh, you know, that that seems to be what's going on. That's the intuition about what's going on. U you know, there's this ER equals epr kind of conjecture that comes out of ads CFT, which it looks like we can reproduce in our models. But there are many details to be filled in.

I mean, this is a, you know, what what what's happened with these models basically is there's a big burst of activity in physics 100 years ago. Lots of of things got figured out. There's a certain paradigm that existed in mathematical physics at that time. We kind of have a new paradigm, and there's a lot of new stuff that could be figured out. But it's complicated, and it's it's going to take, you know, it's going to take the work of lots of people and some time to know all these consequences. But we we've, you know, kind of the way we see it is it looks like we've really, you know, we know how the machine code works now. We kind of have to see what the consequences of that are.

Hey guys, I'm so sorry to interrupt this amazing deep with my friend Stephen Wolfram, but I know that you're going to want to catch this special offer that I make once a month. I select a winner of one of you out there to win a piece of space dust, a real 4.3 billion year old space rock. Just visiting my website Brian King.com and by joining my mailing list, you get the freshest space news and access to my guest. I always send out information so you guys can communicate with great guests just like Stephen Wolfram, ask him questions as you saw that we did on this episode. So do it now, now before you forget. Go to Brian King.com, list, if you're not already subscribed and join the mailing list and every Monday you'll get the most magical message delivered straight to your inbox. Okay, now back to the episode.

So this is a question I'm going to kind of pervert it to my purposes. But uh, someone named uh G Tyro, uh maybe, uh asked the question of your thoughts on the future of Science in the age of LLMs. And I want to augment that, Stephen, with my host prerogative by uh stating a fact that you're probably aware of. Uh, you do you recall what Einstein's happiest thought was that gave him palpitations, Stephen? Do you remember what Einstein said? The fact that the universe is is is understandable to us is is remarkable. I mean, that not that one. I'll give you a hint. There's old Albert. Okay, what was here's Albert? He's in free fall. He's in free fall. Okay, so an observer in free fall experiences no gravitational force. I want to use that as a springboard to ask you about about AI and and its potential as a scientist uh to do scientific uh for us as scientists, but to generate new scientific ideas. And the way I like to say it is, can a computer have a happiest thought like Albert? And can it do science the way he did without a body, without the sensation of what it means to free fall, perhaps in a visceral sense? Are you optimistic that there'll be an AI Galileo or AI e, you know, Einstein? To what extent are you optimistic or pessimistic about scientist scientific breakthroughs coming from AIs and LLMs?

Well, this is a complicated story. The the basic thing is, in the computational universe of all possible computations, there's lots of stuff that goes on. Only some tiny sliver of it is stuff that we humans care about. There's only some tiny sliver of it that we even have sensory apparatus to detect. And so we've, you know, we've pulled out these things that we care about that are the the the aspects of the universe, the natural laws that we want to talk about in the universe. There's a lot more besides. So the challenge is not to go out and find natural laws. It's kind of like in mathematics, we can go out and generate theorems. I wrote this whole book about the physicalization of meta mathematics about, you know, in us humans, we've written down about three or four million theorems in the history of mathematics, but there's an infinite number of possible theorems. You can just go out and generate them. You can have a computer go generate all these theorems. The issue is, which of these theorems are we humans going to care about? And this question of sort of what is there to discover, there's a, there's a big piece to that, which is there are all these prongs we can we can kind of pursue. There are all these directions we can pursue. Which ones are ones that that sort of uh kind of merge with the narratives that we humans care about?

So this question about, uh, what does it mean for, you know, I've spent large part of my life trying to formalize the world in computational terms. And that's what our computational language, Wolfram Language, that you know, millions of people use every day, uh, is all about. It's about kind of, you know, we had these different kinds of formalization. We used human language to formalize things. We could say, you know, the concept of a rock, rather than individually pointing at every rock. We have logic that kind of, you know, sort of gives us the structure of arguments independent of individual arguments. We have mathematics, gives us a type of formalization. Computation is, I think, a much more powerful type of formalization that is the defining kind of paradigmatic idea of our century, actually. And I think that, uh, the kind of that's kind of the big, the big thing is, can you represent the world computationally? And then the question of, in which direction do you want to go? This this comp, this thing you can represent computationally has lots of directions, lots of richness. The question of which way you want to go is really a much more human question.

Did we do? This is a long story. I mean, I've I've I've uh I've I've talked about, written about a lot this this these kinds of issues. I think this is a, um, uh, you know, bottom line, sort of, uh, you know, in a sense, people would have said a lot of the things I built in my life a sort of AI doing science. But this question about, you know, do you just say, okay, AI, I want to detect features of the of the cosmic microwave background, you know, tell me what experiment I should build, tell me what, um, those are things where if you define your objectives carefully enough, then there is a chance that you can search for solutions to, you know, I've got this engineering problem, I want to have this particular strut that, you know, is is organized in this way and is is, you know, minimum weight or whatever else. And, you know, you can absolutely imagine computationally kind of searching the set of possibilities and finding the one that works.

I think there's much more to say about this. I mean, there's there's some, and actually, I'm I'm currently doing some experiments that have to do with the question of just what can things like LLMs predict. You know, they do a good job of predicting, uh, sort of what you might say in an essay to follow what is typical of what has been said in the essays on on a few billion web pages. And the question would be, in the natural world, to what extent can an LLM predict things that happen in the natural world? There's no reason they should be able to. For example, an LLM trained on human natural language, I don't think it's going to do it. We actually just, in fact, I probably get right after this to see the results of one of those experiments. We've been training some LLMs, LLM like technology, to to make predictions of idealized natural systems and trying to understand, uh, to what extent to my guess about what's going to happen. This is a very dangerous thing in doing science because I have a guess about what's going to happen, but I've been doing science long enough to know that the most one of the most important things is not to take your guesses that seriously because the chips are going to fall as they fall, and you have to be ready for that. And it's a mistake. You know, scientists make this mistake all the time. You have a hypothesis and you just keep going doing things until you verify that hypothesis. And you know, that's you have to not do that. So but I'm going to tell you what I think is going to happen, and then I'll go look at my computer and it will have not happened. So that that's, um, the humility.

Yeah, right. No, it's an important feature of of, um, you know, I think it's it's it's critical if you actually want to get the science right. I mean, it's kind of, um, um, you know, but I think the what I think is going to happen is that it's going to be possible to predict things that when we as humans look at them, we say, oh yeah, I know how that's going to continue. As soon as you're hitting kind of computational irreducibility, and as soon as you can't tell as a human what's going to happen, the AI is going to fail as well. We'll see if if if we're chatting again in another episode, you can ask me about that again, and I'll tell you what the answer was.

I would love that. And I, I just to just to reiterate how grateful I am for your time and staying up late. And I want you to get to look at those experiments. And I got to put some little experiments to bed. But we got through about two of the 11 pages of notes and questions that I had. So I'll beg your forbearance in the New Year perhaps, uh, to do a, a part four, because, uh, there's there's so much deep interest in what you're doing. And, you know, from a venal self-interested perspective too, I want to know what, you know, possible ways to prospect in the CMB sky and in the underground particle accelerators, so forth, that my colleagues and I can do to get a deeper, a deeper glimpse into the nature of reality.

I want that too. We're we're, you know, the problem is, we're building a bridge from two sides. Right? We have an underlying theory, you have experimental equipment that can measure things. And now it's a question of, we got to, you know, in the end, we've got to, in the end, there's a lot of physics work of building that bridge. And, you know, I think that's, uh, we're we're kind of just trying to get that started. And, you know, I I might, I might grill you for information about, um, the details of, you'll know that we're getting close when I'm grilling you for information about your detectors and exactly what they can detect and so on. But we're not yet there. I'm not, I'm not yet ready for that.

No, I'm more than happy to oblige. And and I have brilliant students that can assist. But yeah, I've been thinking about, we need sort of a Rosetta Stone, you know, to transmit between the language of mathematics, the Wolfram Alpha language, and, uh, the the physics project, the theoretical space. We need to map that to the hardcore observer space, because that's what I love to do. And, uh, there's nothing more fun than making a decisive measurement.

So Stephen, uh, Wolfram, Dr. Stephen Wolfram, thank you so much for sharing your time. I hope, uh, the experiments that you're running tonight will bring you great joy, but also allow you to get some sleep whenever it is that you turn in, turn in for the evening. Thank you so much, Stephen. Have a great rest of your year, and I'll be in touch in early, uh, early next year, and we'll hopefully do another part.

Sounds good.