What is Time? Stephen Wolfram’s Groundbreaking New Theory

Time is really not just like space. Time is a very different phenomenon from space. The fact that relativity emerges as this connection between space and time is something that is kind of an emergent thing; it's not something that is intrinsic to the nature of space or the nature of time. Time, I think, can be thought of as the sort of inexorable progress of computation in the universe.

Stephen, the thing that always comes up, uh, when we talk about these three subjects—time, life, and consciousness—nobody can define it. Nobody ever gives me a satisfactory definition that those three, you know, people in those fields can agree upon, and therefore I think it's kind of bunk. But today we're going to delve into how we can actually understand what time is intrinsically, as you say, but also apply it to our field—my field, cosmic microwave background—its temperature and polarization. So Stephen, how are you doing today?

I'm doing well, thank you. The first thing I want to ask you about is, uh, is, is what time is to you versus what it is to the general listening lay person. Have the brightest audience in the known Multiverse, but the question is we all sort of—it's it's kind of like the old Supreme Court definition of pornography: you know it when you see it. But I'd like to connect it both with your physics project and with my Simon Ray project. That's for you to actually do what you do uniquely well, which is to make things that are very complex utterly understandable, but preserve the fascination.

So Stephen, the recent article starts with this deceptively simple but really profound question: Time is a central feature of human experience, but what actually is it? What are you suggesting in this, to me, revolutionary new monograph, “What is Time?” People will say, well, we can say it's now, it's sometime in the future. We think of time as like a position; we say, you know, we have a clock, and we're looking at our smartphone or whatever, and it reads a certain time, and it feels a lot like we're just saying where we are in some thing where we can be moving through it. The thing that's a bit odd about time immediately is, unlike space, where most of the time we're just in one place in space, or we think of ourselves as being in one place in space, and we kind of have to decide to move to another place in space, time doesn't work that way. Time inexorably moves forward for us; so that's that's the first kind of thing which kind of distinguishes it from space.

I think one of the things that sort of happened in 20th-century physics, as a result of some of the technicality of Relativity, is people got the idea space and time are the same kind of thing, and that was a, uh, kind of—actually Einstein, I don't think really thought that. I think Minkowski, a mathematician who kind of came to sort of, uh, clean up the mathematics of special RS, uh, by 1909 or so, was saying, well, we notice that we have these expressions for proper time, for space-time distance; it's x² - t², and that reminds him of these things in mathematics—quadratic forms—and so we let's just think of time as being a coordinate just like space, and that's kind of where the whole notion of time is just like space came from. I think that time is really not just like space; time is a very different phenomenon from space, and the fact that relativity emerges as this connection between space and time is something that is kind of an emergent thing; it's not something that is intrinsic to the nature of space or the nature of time.

The place to start in understanding time, and it's in a sense very unsurprising once you kind of see what what's going on, is time, I think, can be thought of as the sort of inexorable progress of computation in the universe. So what does that mean? Well, let's say we just define rules for some system—might be a system of black and white squares, might be some set of graphs that connect different different nodes together—but it's just some rule: says whenever you see a configuration that looks like this, replace it by a configuration that looks like that. Can be a very simple rule, but you keep applying it wherever it might apply; you apply it, you keep on doing that, and the thing that then happens—the big surprise that I kind of discovered in the early 1980s—is even when the rules that you put in are very simple, the behavior that you get out may be very complicated. It's something that's really not—it it took took me a while to kind of adapt to that intuition that you know you think from doing engineering things like that: if you want to make a complicated thing, you have to have complicated rules to set that thing up, but it turns out that in the computational universe that's just not true. It's kind of like you can take sort of a computation and use it as kind of a telescope to look into this computational universe, and sort of the first thing you see is this phenomenon that even when your rules—your program—is very simple, the behavior you get maybe very complicated.

Okay, how does that relate to time? Well, there's a very important phenomenon that's the result of this fact that even very simple rules lead to very complicated behavior, and in the end it's this phenomenon I call computational irreducibility. So here's how this works: So in traditional science, particularly physics, one's used to the idea, oh, let's find the fundamental laws, the fundamental rules by which some system operates, and then we're kind of done because we kind of imagine once we've got those laws, we might represent them mathematically; we can just essentially write down a formula for what the system is going to do. So we can just say immediately this is what's going to happen in the system; we can make predictions about what's going to happen in the system where we can use our formula to see what the system is going to do, and that's much easier than the sort of computational effort the system has to go to to do what it does. So typical example of this: the two-body problem in Celestial mechanics. You have an idealized Sun, an idealized Earth, and you have these equations that describe the motion of the idealized Earth around the idealized Sun, and those equations we can just write down a formula for the solution to those equations. So if you want to know where's the Earth going to be a million years from now, you don't have to trace a million orbits; you can just say I'm going to plug the number of million into my formula and immediately get the answer. That's been the thing that we sort of hoped for in a lot of kind of traditional science; we hope for these kinds of computational reducibility predictions.

Well, turns out that out in the computational universe there's a lot of systems that don't show that kind of reducibility; they show computational irreducibility; they show a phenomenon where you can, if if you want to say what's the system going to do after a million applications of this rule, well, you can run those million applications of the rule and see what the system does, but it turns out that's sort of an irreducible computation; you can't find a way to kind of jump ahead and say I know what's going to happen—it's going to come out with answer 34 or something—you just have to follow the steps to see what happens. And so that's kind of a—it's a from sort of the point of view of of kind of how to think about science—it's a significant thing because it kind of says that there are limitations to science that arise kind of within science itself; there are things where you can't just say we've got it—we know the answer immediately—and you know I think one thing to understand about computational irreducibility, which um is you might say well that's really a downer, that means you know science has limitations, but it also means something else: it means that the passage of all of these applications of rules and so on, which we'll talk about as being corresponding to the passage of time, that passage of time actually in a sense achieves something. It's not the case that we can kind of lead our lives for however many years and say we can we we say we don't need to lead our lives for all those years; we can already predict in advance the answer is going to be 42, so to speak. The computational irreducibility means that that sequence of steps has a definite meaning; it has an irreducible content, so to speak.

So okay, so what is time? Time is this irreducible process of computation—of sort of next states of the universe. So the universe has some particular configuration, and then this these rules will be applied to figure out what's the configuration of the universe going to be next, so to speak. If you had the idea that those rules would be mathematical rules that have computational reducibility, you would just say, well, you know, yes, there are these rules being applied, but we don't really need to apply those rules; we can just work out a formula, jump ahead, and say what the answer is. But what computational irreducibility implies is that actually no, we really do have to follow those rules; we have to explicitly run, we have to explicitly apply these rules over and over again. And so this experience of time, this this notion of time—time is this sort of inexorable application of rules to the things that are the structure of the universe. Now, one reason it's been sort of confusing and one one hasn't been able to see that is because traditional models of physics have tended to be based on mathematical equations which have the feature that you kind of are always hoping you're going to get this kind of computationally reducible solution; you're always kind of—and there are even in in the way equations are set up, like differential equations and so on, there really is very little distinction made between initial value equations where you say this is the initial condition and it's going to have to work out what happens after that, and things like boundary value equations where you say this is this is what happens at the sort of two ends of the application of this equation, and now we're going to fill in what's in the middle. In traditional mathematical formulations of physics, there isn't much distinction made between those things. When you think about physics as this thing based on what one can think of as computational rules, there's a big distinction between those things because of computational irreducibility. We have these underlying rules; we can apply them step by step by step and see what happens, but we can't expect to jump ahead; we can't expect to say, oh, we know these two ends, let's fill in the middle, and so on. We have to just sort of follow the steps and see what comes out. And so this this phenomenon of time is the phenomenon of the sort of progressive computation of next states of the universe, and it's the fact that there is computational irreducibility that makes there be some kind of rigid structure to time, that makes there be something where time doesn't just crumble when you when you say let's just figure out what's going to happen; you kind of have to live through those steps, live through that that time.

Now, there there are many many pieces of this; for example, one of the issues is if you look at different kinds of things, whether you look at experience of of us humans, whether you look at sort of things happening in nature, there's this question of sort of is the way that time is running in those cases—is it is it the same or is it somehow time is different? There there are many pieces to this whole story, but sort of the the first step is this idea that the progress of time is the inexorable progress of computation. Now, there are many pieces that we have to talk about; I mean, for example, one thing is is there only one kind of time or are there different kinds of times for different systems? It's kind of a little bit like what happened with temperature back in the day; people wondered, you know, there was temperature measured by the the expansion of mercury; there was temperature measured by, you know, change of electric resistance of this or that thing, and and then it became realized that there was an absolute scale of temperature—that there was some there was some intrinsic thing which we later learned was the motion of molecules that gave us kind of an absolute notion of temperature. Well, so it is with time, and the thing which is kind of the analog of that is computational irreducibility—the fact that there is the same phenomenon of computational irreducibility across all these different kinds of systems, and that there is the sort of the same ultimate kind of scale of application of computation across all these different kinds of systems that leads to some kind of absolute notion of time that isn't doesn't depend just on the particular system that you're you're kind of studying time with, so to speak. It doesn't depend on whether you're using a pendulum clock or some, you know, modern, uh, uh, you know, quantum, uh, time-measuring device or or whatever. So it's so that's another piece to the story. I mean, the, uh, there's a lot to say about kind of the relationship between time and space; there's, uh, a lot to say about kind of our experience of time; so things get—let's see—I I mean we there there are many different directions to go here, but let's talk a little bit about time versus space and the in kind of one of the things that's been sort of one of my big excitements last four or five years has been these discoveries we've made in fundamental physics which just with every passing month, every passing year, it's kind of like, Yep, this is it, this is the story, and it's pretty neat, you know. It's the last really big kind of, uh, paradigmatic change in physics was basically 100 years ago, and we've been sort of operating out of the same playbook for 100 years, and 100 years ago people kind of suspected some of the things that we've now seen to be the case, although they didn't have kind of the machinery to understand what was going on. I mean, I I think probably a starting point for all of this is kind of we go back to, you know, ancient Greek times; people were discussing, you know, is the universe discrete or continuous? Are there atoms or does everything in the universe kind of flow like water? Well, it took a really long time to resolve that question; it wasn't until the end of the 19th century that it became clear that yes, molecules exist. We were lucky enough that the scale of our microscopes and so on relative to the scale of molecules was such that we could actually see Brownian motion happening, and we could tell, yes, there really are discrete molecules. Then we found out there are also discrete photons of light and so on, and actually in the in the first few decades of the 20th century, most physicists believed that space was discrete as well. I hadn't really realized this until recently; I've been finding all of this stuff which was never really published because they never managed to make a model like that work. Einstein, Bohr, Heisenberg—they all thought that space was discrete, and as they tried to make models where that would happen, they couldn't make those models consistent with relativity; they always ended up with things where they put down some some rigid lattice in space, for example, and then they say, well, you know, but we know that relativity says it doesn't matter what what frame, you know, what what how we're traveling relative to this lattice; they could never make that work. So 100 years later we can make that work, partly because we have this much more computational kind of infrastructure to think about what we build space and everything in the universe out of, and kind of the underlying idea of what what we've done is to think about space—the universe—everything in space as being represented by this giant network. And so what are the things in this network? The things in this network are what we can think of as atoms of space—these kind of point objects whose only feature is that they're distinct from each other. These atoms of space are related by this network that says this atom of space is related to these other atoms of space; that's kind of the the the whole—that's kind of the data structure of the universe. And the the really surprising thing—I mean, the first really surprising thing—is you say, well, okay, if you have zillions of these atoms of space and you have this network and it's being continuously rewritten as pieces of it follow these rules and change into other pieces of network, what does that look like when you've got 10¹⁰⁰ atoms of space? What what is the aggregate behavior of such a system? Well, there's an analogous problem when you think about a fluid, for example; you've got all these molecules bouncing around, and you ask what's the aggregate behavior of all the molecules in a fluid, and we know, well, that's fluid mechanics—it's the equations of fluid mechanics, the Navier-Stokes equations and so on. So the question is what's the analogous limit of this graph being rewritten and so on, where it turns out the analogous limit is the Einstein equations—so the equations of of spacetime that you're very familiar with. That's kind of the first big clue that something interesting is happening is you kind of inexorably dealing with the fact that from that microscopic structure of just atoms of space and rewrites and graphs and so on, you end up getting the Einstein equations. And you know we can see a lot of detail; actually, we have decent simulations of things like black hole mergers. Black holes are very convenient because a really tiny black hole that is just a small number of sort of, uh, atoms of space across, so to speak, a really tiny black hole behaves in the same way as a big observable black hole, and so we can kind of do something where we're kind of just simulating these really tiny black holes, and we can see them merge and produce gravitational radiation and all sorts of good things like that. That's kind of a notion of what space is. There are then questions about about relativity and, uh, how relativistic invariance occurs, things like that; this is a slightly slightly deeper rabbit hole, um, but, uh, the the key idea is you've got this notion of space—space is this hypergraph that's laid out with all these atoms of space—time is the inexorable rewriting of that hypergraph by these computational rules. But the thing to understand is what does an observer like us observe of what's going on in the system, remembering that an observer like us must be embedded within the system—we we are part of that system—and the thing we realize is that all that we can observe is the causal relationships between these updating events. So one way to think about it is imagine that we were not being updated; then whatever is happening in the universe we're not going to know what happened; we're only going to know what happened when we've also been updated. So in a sense what what ends up being the case is that all we can really be sensitive to is this network of of relationships—the causal relationships between updating events. So for example, let's say you have this little update that happens and it produces certain output; well, then you can ask, well, what other update events depend on the output from that first update event, and from that you can build up this causal graph of what what effects what, and it's that causal graph that is the the real sort of substance of what's going on in these models, and that causal graph is in a sense a graph that connects both space and time. These events—one can think of them as—in the end we will perceive them as being as occurring at certain places in space and time—and what's happening in this this graph—the graph is the only sort of reality to this system—and the question is then how do we parse that graph as observers? And what ends up happening—so key fact about us as observers—there are many things about what goes on that depend on our nature as observers. So one thing about us as observers that's not obvious is that we can parse the universe as consisting of states of space at successive moments of time. When you say parse, you mean to measure the unit; we can make observations; we observe the universe; we we understand the universe to consist of—there's this state of space at this moment in time, then there's another state of space at a separate at a subsequent moment in time. So in our everyday experience, that's what happens: you know, if you look around the room, you know, maybe you know you see something that's 10 m away; well, the light from something 10 m away…

Gets to your eye in a microsc, but your brain takes milliseconds to process that signal. And so, to you, all the photons arrive simultaneously; from that, from all the photons from your local environment, arrive as far as you're concerned in a blink of an eye, so to speak—in the time it takes neurons to respond. So for your brain, it's as if the the the is a state of space at a certain moment in time, and then there's another state of space at a subsequent moment of time.

Now you know, in your day job, so to speak, you're dealing with things that aren't 10 m away; you're dealing with things that are, you know, 10 to the 25 m away or something, 10 to the 26 m away. And when in in that case, this kind of idea that we have that there's sort of space separate from time and we can just think of an instantaneous state of space doesn't work anymore. It wouldn't work for us if our brains worked a million times faster than they do and we were still, you know, living in rooms the same size as we live in now. Then we would be a brain like a piece of digital electronics that can see the photons that it will see the individual photons. And the fact that we will decide to think of space as being this, you know, this state of space at successive moments of time—that's that's a feature of the particular scale we're at and the particular characteristics we have as observers. It's not, in a sense, the intrinsic nature of what's going on.

And so, for example, in these models, what's more intrinsic is this causal graph of little tiny updating events that are happening all over the universe. That's the thing where we have to parse that graph; we have to we have to say we're going to we're going to choose to slice that graph so that we have the states of space at successive moments of time. In the jargon of Relativity, that would be space-like hypersurfaces; we are defining simultaneity surfaces. So what we can say is if we've got these updating events—one update event follows from another, follows from another—those we can say are time-like separated events; one event affects another event at a later time. But then the big thing that's sort of a big story of Relativity is this idea that different events, they may not be time-like separated. The thing that's happening on Mars and the thing that's happening on Earth are not; they they can happen at the same time. We can we have to define what this what the surface of simultaneity looks like. In other words, we say, you know, it's noon on Earth; when is it noon on Mars? Is it noon on Mars, you know, when a light signal from Earth from the, you know, the noon light signal from Earth reaches Mars, or is it noon on Mars at a different time? And so so we end up with this kind of a space-like hypersurface, this simultaneity surface where we where and what what's happening in this causal graph story is we're simply taking this slice of the causal graph and we're saying these events we consider to be simultaneous in time. And there is a consistency that we can we we want events to be in these successive slices representing events that are sort of at successive moments of time, and there's a consistency that we have to have that those events in successive space-like hypersurfaces can never be time-like connected to each other. It has to be the case that within one simultaneity surface those events are never time-like related to each other; they they they have to be they're not accessible; you cannot access them.

And right, you you mention in the towards the end of the essay, time remains that computational process by which successive states of the world are produced. Then you say, computational irreducibility gives time a certain rigid character, at least for computationally bounded observers like us. That gave me chills, Stephen, because it suggests that maybe there aren't bounded computationally at least observers. What would those observers be like?

One of the biggest things that's emerged in in my kind of thinking about sort of uh the universe and everything in the last couple of years has been the fact that the reason we observe the laws of physics we do is because we are observers of the kind we are. I never imagined that it would be possible to derive the laws of physics; I always assumed that the laws of physics were just like, well, we we got this universe; this is how it works, right? The instruction manual, right? I never thought they they would be derivable. The first kind of clue that they might be is the second law of Thermodynamics. So the second law of Thermodynamics, which was first talked about in the in the mid-1800s, is this thing that says, well, you got all these molecules, for example, in a gas; they're bouncing around; they're colliding with each other according to laws of mechanics, which we know, but yet in the aggregate gases tend to get more random in the configurations of molecules, and we can say things like that entropy increases. And it kind of seems like it was very tantalizing in the 19th century, particularly very tantalizing trivia fact actually in the invention of—so in 1905, you know, Einstein wrote three very famous papers—relativity, the photoelectric effect, Brownian Motion. In 1904, he wrote a couple of papers, and they were supposed proofs of the second law of Thermodynamics, and they were wrong. And so and I don't think Einstein ever returned to the second law of Thermodynamics, but what was really interesting to me in terms of History of Science, those papers were really a follow on to the work of Boltzmann, who was sort of the person who really pioneered kind of the atomic theory of gases and things like this and kind of had the idea that matter is made of discrete atoms and that you could build physics and theory of heat and so on from that. But it's sort of interesting that Einstein had a similar kind of—you can derive this notion in 1904 for the second law of Thermodynamics; it didn't work; in the case of Relativity in 1905 it did work; same kind of methodological idea.

Well, the thing that's really a surprise now is it looks like we really can derive these laws of physics. So second law of Thermodynamics—what really is it? It's actually a story of computational irreducibility, because here's what happens: You start off with these molecules, let's say they're all in one corner of a box; they're in a very orderly configuration. Then you let them collide and and follow the laws and mechanics; what they are doing is performing a computation; it's an irreducible computation. So what comes out of that is something which no longer has a trace of the what happened at the beginning of the fact that these molecules were all in a very organized state, because that initial condition has been essentially encrypted by the progress of computation in the system; it's been encrypted by this irreducible computation. Okay, so then we come along and we look at the results of that computation, and we say, "Looks kind of random to us," because we can't invert that irreducible computation, because we with our brains, with our measuring devices, we are computationally bounded observers; we can only do a limited amount of computation. And so when that's compared to the irreducible computation that the gas has done, we come up short, and we just say, "Looks random to us," and that's basically the second law of Thermodynamics. And so, in other words, the second law of Thermodynamics is a consequence of the fact that there is underlying computational irreducibility sort of interacting with us as computationally bounded observers. If you go down to the scale of inter-molecules and you can do a little bit of computation about what's going on, then in a gas with only 20 molecules in it or something, you can break the second law of Thermodynamics, because you can break computational irreducibility, because with a sensitive enough measuring device that can look at individual molecules and with good simulation and so on, you can say, "I know what's going to happen; I know what happened before." So that's a case where the computational capability of the Observer is strong enough relative to the system that you break the second law of Thermodynamics. But for an actual typical gas with all the, you know, billion billion billion molecules that might be in a little small region of gas, then the the kind of computational capabilities of us as observers or our measuring devices is no match for that, so we just say, for us, we observe the second law of thermodynamics. If we were observers who were not computationally bounded, we would not believe in the second law of thermodynamics. So that could be used to detect, you know, whether or not something is a computationally limited or yeah, Observer—uh, just like a bounded Observer like us.

Well, to some extent, yeah. So so here's the fun thing: Back in the 1860s, when people were first talking about the second law of thermodynamics, one thing that people said is, "Oh, the universe will sort of have a miserable end in the heat death of the universe." What they meant was just like, you know, you start off with all sorts of mechanical motion and things are very organized, and eventually there's friction and heat is generated, and eventually everything kind of runs down to just be a whole bunch of heat. What is heat? Heat is the supposedly random motion of molecules. So people were saying that's a terrible situation—at, you know, a trillion years in the future or something, there won't be anything in the universe other than random heat. That's a really bad end, but that end depends on what kind of Observer is observing what happens, because a computationally bounded Observer—to that computationally bounded Observer, yes, all those molecules bouncing around just seem completely random, but to an observer that's more computationally sophisticated, they're capable of seeing actually that configuration of molecules—that's the trillion-year future of, you know, Brian and Stephen having their conversation, so to speak—and there are details there that can be seen by a computationally unbounded Observer, but to us as we are right now, as observers of the kind we are right now, it would look as if there's a heat death of the universe; everything has just turned into random heat. But if we were not computationally bounded observers, we wouldn't think that; we would say, "Oh, look at all these amazing molecules which uh have this complicated motion that comes from this very meaningful thing that happened a trillion years ago." So that's kind of how how that works.

Now the thing that's really remarkable to me is that both general relativity and quantum mechanics turn out—it seems—to be derivable in the same way. So General Relativity ends up being the interplay between computational irreducibility of all of these underlying processes and all these hypergraph writings and so on, and the fact that we as observers of that are computationally bounded. So space at the smallest scale consists of all this complicated stuff going on, but to us at the scale we're at, space just seems continuous; it seems like we can move from one place in space to another, and and that's a feature of the fact that we are we're computationally bounded observers of that. If we were able to just detect exactly what's going on, we wouldn't believe in simple continuous space. So I'll give a couple of examples of that. So, for example, the possibility of motion is non-trivial. So the fact that you can take a thing and move it in space and it's still the same thing is not obvious, even in traditional general relativity. You know, if you're right next to a spacetime singularity, you you can end up that your thing, your spacecraft, whatever else it is, can't just move there, because kind of space is torn apart at that point, and there can't be sort of a a coherent spacecraft there, right? And moving into space means you're moving in time, right? The time and space axes get inverted.

Well, yes, and that that that's that's an even even different issue, but but but the the thing is the possibility of pure motion is not a trivial thing, and it's a consequence of essentially computational boundedness that we end up believing in pure motion. For example, the fact that, you know, black holes—we think of those as just being characterized by what's outside the black hole, and we're not we're not kind of looking at all of the details of what's, you know, the the crinkling of the Event Horizon and so on; we just say it looks to observers like us, it looks like it's just a black hole, even though there might have been a whole civilization crushed inside the black hole; it just looks like a black hole. It's the same with electrons; we think that from the outside, so to speak, all electrons look the same; that's always been kind of mysterious. I think that in the end the story will end up being electrons will end up being very much like black holes, and it will turn out to be the case that from sort of outside the electron and when we look at it as observers like us, the electron just seems to be able to move without change; it's like an eddy in a fluid; you have this little swirl in in a in water, for example; that swirl can kind of move through the water, but as it moves it's it's using different molecules in the water to make itself, and it's the same thing with an electron or a black hole; it's using different atoms of space to make itself as it moves.

By the way, there's a there's a kind of interesting consequence to this, which is something that comes up in relativity, which is if you think about kind of—it's moving in space, and it is essentially as it moves it has to reconstruct its structure at a different place in space, and that process takes some kind of computational work. The actual process of the kind of progression through time of the thing—let's say the thing is some kind of clock—that progression through time is using computational steps to make the ticks of the clock. And so what happens is if the thing is moving, then the the motion takes some amount of computation to achieve; reconstructing the thing at a different place in space takes a certain amount of computation to achieve. So if the thing has a limited amount of computation, a fixed amount of computation, it has a trade-off between using its computation to sort of evolve for itself through time and using its computation to reconstruct itself at different places in space. And so if you're moving faster in space, you are progressing—you're evolving more slowly in time, and that that's basically the story of time dilation. I mean, the the the detail which is really cool that there's sort of a mechanical explanation of time dilation now—it gets, you know, the full story there in because you're really dealing with these causal graphs, not with just sort of a fixed structure of space—that's how you end up getting into uh sort of traditional Riemann variants and things like this. I mean, it's it's a uh I think, you know, the the the thing just to sort of finish this thought of of this really remarkable fact, as far as I'm concerned, that the kind of what we perceive in the universe is really just a consequence of the fact that there's computational irreducibility underneath, and we are observers who are computationally bounded. And actually, there's one more characteristic that we have to have to get general relativity and quantum mechanics, which is we have to believe that we're persistent in time, even though at every moment in time we're made of different atoms of space. You and I both believe that it's the same us now as it was a second ago; that's a a way that we in sense in a sense parse the universe by that assumption that it's the same us at successive moments in time.

Persistence of memory, right? Yeah, right. I mean, it's it's it's not obvious that the fact that we treat it as being the same us—we don't say it's a—and that's very important in well both in general relativity and in quantum mechanics. In quantum mechanics, the key thing that happens, and this relates again to time in this rewriting, this hypergraph and all these kinds of things, it turns out there are many different ways that rewriting can happen, and each different set of rewritings essentially defines a different thread of history, a different sort of thread of time. Each each one of those different sequences of rewritings corresponds to a different history for the universe, and the thing that is non-trivial is because we believe we are persistent in time and we believe we have the single thread of experience in time, we have to conflate all those different threads of history into a single kind of into the single thread of experience that we have. It's deeply analogous to what happens in both in thermodynamics and in spacetime that we are kind of aggregating a large number of those independent threads of time, just like we're aggregating the effect of lots of different molecules in a gas or lots of different atoms of space in spacetime; we're aggregating the effects of many different threads of time. So the kind of strange setup is our minds are are operating on many threads of time, and those threads of time are continuously branching and merging and so on, but our minds essentially are large—just as we're large compared to individual molecules, we're large compared to the atoms of space; we're also large in what we call branchial space, the space of these possible branches of history; we we span many branches of history, and it is our kind of belief about the world that we can just aggregate those branches of history and say something definite happened. And when we see the the edges of that that's when we see quantum effects. Quantum effects are sort of where where it doesn't quite—it hasn't quite had time to match up; we don't quite get to do that conflation of all those different threads of history. And and for example, one of the things that I actually understood only quite recently is sort of one of the features of quantum mechanics is one's always saying, "Oh, there's randomness in quantum mechanics; you kind of don't know what's going to happen; it's probabilistic." The cause of that in these models is is kind of the same thing as the cause of the fact that the view that we have of the universe is a consequence of the fact that sitting here on this planet—if we were somewhere else in the universe, we would have a different view of what was happening in the universe; same physical laws, but the sky would have different things in it from some other part of the universe. Well, in branchial space, in the space of possible histories, it's the same thing; we I mean we agree on things about the night sky because we're all sitting on this one planet; well, we agree about things that happen in quantum mechanics because we are all sitting very close together in branchial space; there's a just like there is—we could imagine that some, you know, some alien critter sitting on some star at the opposite side of the galaxy has a different view of the details, not of the laws of physics necessarily, but of what's actually happening in the universe. So similarly, the fact that there is this apparent randomness in quantum mechanics is a consequence of the fact that we we don't know—know—sort of from a priori where we are in branchial space, just like the fact that we're on this planet rather than some other planet is—you know, we can trace back the history of that, but there's no kind of theorem; there's no theory that says we've got to be on this planet, not on some other planet, and that's kind of the the source of this kind of lack of—there's there's this kind of lack of knowledge, this kind of randomness about what happens that comes from the fact that we are in a random place in branchial space, so to speak.

Speaking of random randomness, uh, I immediately could not be dissuaded from thinking about Boltzmann brains and sort of this random fluctuation that could be maybe the simplest imaginable conscious Observer or computationally possible Observer. Is that true? I mean, I think of them as even more simple than electrons, which, you know, there's this whole controversy of whether or not inanimate objects are conscious or participate in the Consciousness project, so to speak, called panpsychism, and there are many people that do believe that—many eminent uh philosophers, for example. I find it kind of absurd, but but I want to ask you, Boltzmann brains—are they the atoms of of Consciousness? The whole idea of sort of what is capable of intelligence is something I've I mean I sort of talked about for 40 years or so, and it's it's it's found its way into a bunch of philosophy of science as well. So the key thing to realize is there's this thing I call the principle of computational equivalence. You might have thought that if you had a system with very simple rules, it would not be capable of doing anything as sophisticated as something like a brain does, but it isn't true; the sort of sophistication of the computation that

Can happen even in a system of very simple rules is just as great as what can happen in a brain. And in fact, we've kind of got a a lesson in that from looking at AI and large language models and so on; that they're just kind of computational systems, and yet they do very brain-like things. That's just an example of that phenomenon, so to speak.

So getting the capability of sophisticated computation, of intelligence, is not difficult. The issue is, is that intelligence aligned with our intelligence? So I like to think about it in terms of what I call Ral space. It's it's essentially the space of all possible kinds of Rules by which you could describe what's going on in the universe. Different human brains are pretty close together in Ral space. The details of how we think about about modeling the universe are different, but it's close enough we can communicate. We can package up our thoughts by doing the analog of making particles; we we make up words and Concepts. We use human language to take all those complicated neuron firings in in one brain, package it up, transmit it to another brain, be able to unpack it in that other brain and have something which is reasonably aligned with what the first brain was thinking, so to speak.

So the way to think about it is sort of human brains, human minds are pretty close together in Ral space. Then you've got the cats and dogs and things like that; they're further away. There are a few things sort of, you know, features of sort of emotional response that are that are in in common. Then we get to things like the weather, which people, you know, will sometimes quip, you know, the weather has a mind of its own. But the fact is that the sort of the Dynamics of fluid of of air and and clouds in the atmosphere and so on is just as computationally sophisticated as the things that are going on in the neuron firings in our brains; it's just that what happens in the weather is pretty far away in Ral space from where we are. It's not well aligned; we can't sort of say, oh, we understand the purpose of the weather and so on.

Now, when it comes to kind of what is consciousness, so to speak, I think for me one of the things that's been important in in kind of nailing that down is to say, well, why do we care? Well, one reason we care is that Consciousness is sort of a feature of observers like us, and it seems that things like this this kind of single thread of experience that's all very tied up with observers like us. I mean, I just to explain, you know, I' I've tried to develop what I call Observer Theory, which is kind of a general theory of observers analogous to the general theory of computation that one has about computational systems. And sort of the key thing about observers is they filter all the data that's coming into them to kind of take all the complexity of what's out there in the world and kind of compress it to the point where it can be stuffed into a finite mind.

So, for example, when you are doing, you know, we're we're looking around at at, you know, this scene of of uh whatever we're looking at, and maybe there are, you know, I don't know, I don't know what it is, 100 million photons that uh you know, affect the The receptors in our eyes every second, but yet we don't pay attention to all of those details. We just pay attention to some overall thing about, well, there's a you know, there's this object in front of me and things like this. So we are deeply compressing the sort of raw data of the universe to stuff it into our finite minds, and that's kind of the essential feature of observers. Observers have this feature that they equivalents together many states of the world, and they care about only certain aggregate states of the world. So there are many systems that do that kind of equivalencing, and what the inner experience of such a system is is I mean, that that's a that's sort of a complicated philosophical thing to untangle, but essentially the, you know, the operationally the key feature of observers like us: we're computationally bounded, we have finite minds, and we believe we're persistent in time. And I think that notion of kind of that single aggregated thread of experience, you know, operationally is important. You know, when you say, is that person conscious, you know, you're doing a neurophysiological assessment of of a neur neurological assessment of is that person conscious; a lot of it has to do with do they do they kind of aggregate together all those sensory inputs and have a definite sort of thread of experience, a definite sort of thread of attention and so on.

This question of what does it take to have a thing that doing equivalencing, it's a little bit of a complicated Turtles all the way down story, because to know that you have a thing that's doing equivalent sing, you have to have an observer of that equivalent thinging, and so you end up with this kind of chain of observers kind of all the way down. And that's a at some point you're kind of asking, you know, is there does there emerge a thing in some particular kind of system that does this kind of equivalence thing? Can you notice that there's a thing with this kind kind of equivalent thing for which you have to have another level of Observer and so on. But one of the things we we I'm been working on actually recently is the following things. So so one of the things we didn't quite talk about is the the deepest part of the rabbit hole as far as as far as I'm concerned is this thing we call the ruad, which is kind of this entangled limit of all possible computations. It's what you get if the universe is running all possible rules at the same time, so to speak. It's the it's this thing that is sort of the unique object that is the result of running all these rules and running them in all possible ways. And that thing, it's very interesting because that thing sort of inevitably exists; that thing is just a formal object that must exist. And so when we are we have to be embedded within that object, and what we are asking is how does an observer like us perceive what's going on in the ruad? And the whole big point is that given those characteristics of us as an observer, we necessarily see the laws of physics that we have, you know, discovered in the 20th century and so on, which is pretty amazing that it's possible to say you can now if you say what does an observer not like us perceive in the universe, well, that's could perceive very different things, even as I mentioned, you know, an observer thinking a million times faster than we do, but in a in a in a region of space so of the same scale that we're at will perceive a very different kind of set of things to be happening. And I think that the um uh it's very hard; I I put some considerable effort into this to imagine what it is like to be an observer not like us.

And in fact, here's one way to think about it. So I have some some fun pictures of what happens if you just use generative AI and you say, here's generative AI set up to be just like us; you tell it make a picture of a cat, and it'll make a nice picture of a cat. And then you'd say, make a picture of a dog; it makes a picture of a dog. But there is an interc concept space between the picture of the cat and the picture of the dog; there is a a set of kind of pictures that in a sense this abstract mind can imagine; they're the mental images of an alien mind. Those mental images, those those things between the cat and dog and so on are are things that are constructible for a mind, but not what our human minds are used to. And I've been referring to that as interc concept space. So we have Concepts like cat and dog, and in between there is interc concept space, and the space that we have populated with concepts with the 50,000 words in typical human languages and so on, the the the region that we have populated effectively in the ruad is absolutely infinitesimal. In other words, there's a there's a huge huge kind of interc concept space relative to kind of the tiny places where we have sort of colonized an interc concept space. That's one little way of getting a little tiny peak of what it's like to be an observer not like us.

Actually, some of what I've done in longtime work in what I call rology, the study of sort of arbitrary simple rules in the computational universe, gives one other views of kind of what rules that are not like rules we attribute to the universe, what they do. That's sort of another way to get a sense of what observers not like us uh will will we'll see. But um, I mean, one of the questions, I mean, coming back to time for a second, one of the things that may be a bit confusing is in this ruad object, it we talk about it's the limit of all possible computations; it's this thing that represents the progress of all possible computations. So you say, well, that's just a thing; it exists; so that means that all of time has already happened. In other words, we have this object that represents the whole history of the universe, all of space, all of time, everything that happens in the universe is inside this ruad object. So you might say, why then do we experience sort of time as a progression? Why why isn't it just we've got this big gulp; all of time is right there? The reason is because we are computationally bounded; we are only able to explore this ruad kind of one step at a time. For observers like us, we can't take a Big Gulp of the ruad; it's just not; it doesn't fit in our finite Minds. If if we had infinite Minds, we could fit the whole ruad in our minds, but because we have finite Minds, we're stuck kind of walking through the ruad kind of one tiny step at a time, and that's why we perceive there to be a progression in time rather than just it's it's this way; that's that's all of what there is in time.

Hey, I know if you're enjoying this conversation, you'll love my Monday magic mailing list where I send out the greatest information in the known universe about everything that's fascinating to me, your friendly neighborhood cosmologist. I'll even be writing about this episode, so go to brian.com/list. You'll also be entered to win a real live meteorite; I give them out to one or two lucky winners every month. But if you have a .edu email address, you're guaranteed to win. Go to brian.com if you're are blessed with a .edu email address. Now back to the episode. I wonder if we could pivot to away from The Observers into a realm that both thermodynamics, temperature, and time play a big role, and that's the way the bread gets buttered around the keing household, which involves the cosmic microwave background radiation. Good. And I thought, yes, yeah. So I thought we'd take a quick detour and explain the role of of gravity, the role that gravity plays in the ruad in in computational universe. So talk about what will be familiar to my physics uh physics audience, physically uh inclined audience, shall we say, will be most understandable, Stephen, if you explain it in terms of the way that the hypergraphs activities depend on energy and momentum, then we'll get into gravity and how it emerges, and then we'll look at two specific cases: black holes and the possible Singularity at the origin of the universe, and that'll be a Prelude to talk about time and the evolution of the CMB. So please, Steven, hypergraphs and energy momentum, how are they connected?

So we've got this graph, and the graph connects atoms of space. These atoms of space are not laid out in space; there isn't any space yet. This network defines space. So it's as if all we know is what the friend network of the atoms of space says; all we know is who's friends with who. We don't the social gra; what's that? Yeah, the social graph of the atoms of space. And what then happens is when you have a efficiently large such graph, you can start saying, well, actually we can think of this as as we can we can imagine laying out all these atoms of space in a way that is like our familiar structure of space. So, for example, one of the things that's quite non-trivial is the dimension of space is something; it's not defined by this graph. The dimension of space has to emerge by looking at something like you start from one place in the graph, and let's say let's say you've got all your friends, and all your friends live in a city which is arranged on a grid, then it will be the case that if you start with one person and you say how many friends do they have one mile away, two miles away, three miles away, the number of friends will go up like the square of the distance, just because it's the area in two Dimensions. If instead these were, you know, if instead I don't know, the this was plankton in the ocean where it's three-dimensional and um it was kind of like friends in plankton in the in the Plankton Village, so to speak, then this this sort of how many friends do you get to a certain distance away would go up like the volume of a of a sphere, R cubed. And so that's the way that you start getting from this from the structure of this graph; you start getting things like what's the effective dimension of this graph. And by the way, one of the big predictions of our models is that there will be Dimension fluctuations; in other words, that dimension of space is not exactly three. In fact, our strong suspicion is that in the beginning of the universe the dimension of space was infinity, and that only as as sort of the universe in effect progressed did the effective uh dimension of space end up cooling down to be roughly three. And there's a big question of whether there are Dimension fluctuations left over from the other universe; that will be a spectacular thing to see in the CMB, and I'd love to know details where we can we we we'll get to that in a minute. Let's talk about about um energy momentum. So we're talking about kind of space; we can Define things like what's a straight line in space; we're kind of going through this graph looking at the shortest path from one friend, let's say to another, from one atom of space to another, and that defines So-Cal jisc a shortest path in the graph, the shortest path in space. Okay, so so now what's energy? You know, I have to say I was really surprised by how simple it ends up being. Energy is basically the amount of activity in the graph; it's the number of rewrites that are happening in a particular region of the graph. Now that's a slippery concept because we don't have a notion of space yet, so the notion of what's the density of rewrites depends on how much space there is there, and so there's a slightly more the the more formal thing is to look at this causal graph that I mentioned before and to ask as you look at that causal graph and you have a space like hypersurface that's defined a slice through the causal graph that defines a simultaneity surface; the energy is the Flux Of causal edges that poke through that space-like hypersurface, and momentum is the Flux Of causal edges that poke through a Tim like hypersurface which is orthogonal to that. And so as you change your reference frame, which is as you change how you define simultaneity surfaces, as you change your reference frame in relativity, you are changing the the way that those those causal edges poke through the space like hypersurfaces. So one very non-trivial fact, which is not explained in standard relativity theory, is that the relativistic transformation of space and time is the same as the relativistic transformation of energy and momentum. In our models, that's something that necessarily falls out from the fact that we think about space as this G6 in the hypergraph and time as the sequence of events, and that then the the uh this density of of of causal edges is energy and and so so then what happens is here's how gravity Works, which is again totally remarkable that there's an almost mechanical description of this. So you have a shortest path in the graph, and that's defined by just looking at the graph and just saying how do I go from from atom of space to atom of space in in the shortest path. Well, when there is activity in the graph that deflects that shortest path, it changes the shortest path; it's changing the structure of the graph; it changes where the shortest path is; it changes it according to the Einstein equations, basically; that basically the presence of energy momentum deflects these gd6 in the graph. I mean, just as a as a fun fact, okay, the um one thing you might ask is is uh I years ago when I was when I was first working on on sort of the precursors of this physics project, there's a person, mathematician who worked with me, and uh he would tell people from time to time, oh, I'm working on, you know, fundamental Theory of physics and so on, and they would think, ah, you're kind of nuts, and and they would say things like, and so are you going to invent warp drive? So now the question is, now that we think we really do understand the sort of machine code of physics, is warp drive possible? You in other words, is it possible to go faster than light? And turns out that in some sense it is. So here's how this works; it's actually deeply related to things like the second row of thermodynamics. Again, let's tell a story about the second row of thermodynamics; we've got all these gas molecules bouncing around in this room; they're going at about the speed of sound, but yet if I were to, you know, release some some scent, you know, in at this place in the room, it would diffuse very slowly to the other side of the room because it's being sort of carried on one molecule then the next then the next or being kicked around by one molecule then the next then the next. But if we could figure out at a microscopic level, I want a hitchhike on this molecule now, then that's going to collide with another molecule; I'm going to jump to that other molecule; then I'm going to jump to this other molecule, and I could figure out that path; I could go at the speed of sound across the room. So, in other words, I could beat the usual structure of the gas; I could make instead of going at sort of the speed of diffusion in the gas, I could go at the speed of sound. The same thing happens in SpaceTime; if you could jump to exactly the right event in the structure of of this hypergraph, the exactly the right rewrite event, you would be able to kind of surf through space faster than the speed of light. However, there's a problem; the problem is that you talked about, you know, an observer, a Consciousness, for example, that the very phenomenon of computational irreducibility tells you that things are so scrambled up that you will never be able to get a big thing through that you know that that sort of Surfing Expedition; you'll, you know, at best if you were a computationally unbounded Observer able to operate at the level of atoms of space, you could do that whole surfing thing, but as soon as you're a computationally bounded Observer or an observer that has any the attributes of us as as observers of the kind we are, we just don't fit through that very tiny kind of possibility of Surfing between atoms of space. And so the fact that faster than light travel is impossible is the same statement as that the second law of Thermodynamics follows and that you can't turn heat systematically into mechanical work. So in so far as you can turn heat into mechanical work, so similarly you can turn turn sort of the details of what's happening in this hypergraph into being able to go at, you know, faster than light. So that that was sort of a a side thing, but but the main the main thing, and by the way, I want to say something about the structure of the of of this hypergraph and the relationship to heat. One of the things that I'm guessing right now, so one of the questions is are we going to be able to see the discreetness of space? 100 years ago, 120 years ago, people were really lucky that molecules were big enough that Brownian motion you could see Brownian motion through a microscope, and that wasn't obvious; molecules could have been, you know, a million times smaller, in which case you wouldn't have been able to make that measurement, but we were lucky with molecules. So now the question is

What about the discreetness of space? What effect, what phenomenon could we look at that would reveal the discreetness of space? And one of the things that I kind of suspect is that there's already a phenomenon that's been known for a long time, which, once we understand it, will say, "Oh, okay, it's obvious space has to be discreet." So, just to tell an analogy to that: in the 1800s, people were wondering what is heat. And people said, "Well, heat flows from one thing to another. What flows from one thing to another? Well, it's a fluid, it's something like caloric fluid," they defined, and that that was the, you know, that was their notion of what what heat was. Well, turns out heat was actually the microscopic motion of molecules. Heat, the very phenomenon of heat, basically should have told one that matter is discreet, that that it isn't like a fluid flowing from here to there; it's the features of that microscopic structure. So now the question is, what is the phenomenon now that we already know that might reveal kind of the space-time heat that might reveal the similar features of the discreetness of space as the phenomenon of heat reveals the discreetness of matter? So I'm not sure, but my my current sort of thing hypothesis to investigate is dark matter and possibly a little bit Dark Energy, but I think dark matter is really the really the story.

And it's kind of amusing because when you say—I mean the phenomenon of rotation curves of galaxies not being what you expected—that's been known for nearly 100 years, and um, it's been something where the—what is it? Well, just like caloric fluid was thought of as a fluid because nobody could think of anything else that heat could be other than a fluid, so dark matter got the name matter 'cause nobody could think of what it could be other than something, some kind of matter made of particles. I doubt that it's that; my strong guess is it's a feature of the structure of space, and my strong guess is that it's actually a it's a it's a symptom of essentially space-time heat, and it is possibly related to to Dimension fluctuation. In general relativity, we usually think of space as being curved; we don't think of it as changing its Dimension, but that's actually surprisingly equivalent to the notion of changing Dimension. It's that there's there's probably a duality between formulating general relativity in terms of curvature and in terms of Dimension change.

The only push back I I would put on that, Stephen, is that we do know dark matter in particulate form that's been detected; it's known as neutrinos. They every characteristic of of dark matter: they're weakly interacting, they're massive, they don't produce light, they don't interact with light or charge, so they would have to be simult—I'm not saying it's impossible to accommodate them in SpaceTime heat, but you'd have to accommodate neutrinos. No, no, neutrinos is a very different kind of thing. I mean neutrinos, you know, we don't yet know about the neutrino background radiation; you know, it probably has—um, I remember working this out long ago; I think it's 1.6 Kelvin was what was uh the temperature—and I I for some brief time in the early 1980s I thought maybe I had a way to detect low energy neutrinos using coherent scattering in helium, in in superfluid helium in the a phase of superfluid helium 3, and that was actually—it was a very traumatic thing because at the time if one had been able to detect that, one would have been able to detect nuclear reactors anywhere in the ocean from orbit, and this was the middle of the Cold War, and it wasn't obvious what you do with the knowledge that there's a physics way to detect where all the nuclear submarines are. Was one of those cases is where I was actually pretty happy that the science didn't work out, so I didn't have to solve the problem of what do you do with that kind of information. But yeah, know, I think neutrinos are are, you know, they have all the characteristics of particles like photons and so on; they just have somewhat different interaction uh features of interaction. I mean, in fact, okay, fun fact: when I was a kid, aged probably 16 or so, one of my first um, it's paper that I never ended up publishing was about um neutrino background radiation, and it was about the possibility of a high density of neutrino background radiation because neutrinos, unlike photons, um, if you pack enough neutrinos, have the Exclusion Principle because they're Fermions, they have spin half, and so if you try and sort of pack too many neutrinos in, they form this kind of like like the electrons in an atom; they they kind of can only be a certain number of neutrinos in those States, so you end up with this kind of packed collection of neutrinos in the universe, and so I was wondering how could you detect that and if if that happened, you're absolutely right, they have huge gravitational effect.

So then I can, another trivia thing which led to my all-time favorite nuclear isotope: so in those days, this was long before the web, long before Wolfram Alpha, long before all those kinds of things, I wanted to find out what—well, in in nuclear Decay when there's beta Decay, it produces neutrinos, and if you have this sea of neutrinos all filled up, the beta Decay can't happen because you can't have a neutrino that that uh that pokes its way into that sea, and so the the the beta Decay gets that gets cut off, and so my question was, what is the the beta Decay which has the smallest energy difference, so it has the kind of lowest energy, the neutrinos that will be most likely to sort of fall into this neutrino sea? And so that that caused me—I still remember it—actually leafing through every page of the table of Isotopes trying to find the beta decay with the smallest Q value, the smallest energy difference, and the answer, at least in those days, was rhenium 187. Rhenium 187 became my favorite isotope; it's something which has tiny Q value, and so it it it is sensitive to the presence of degenerate neutrinos in the universe. But but I don't think that—um, I mean I think the story of of neutrinos, I don't think that's a uh, so far as I know, that's not a plausible hypothesis for—well, their masses are insufficient to make the closure density, you know, equal to Omega matter that we observe. But so so that's true, but they but they do fulfill—in other words, a lot of people say, "Well, we we need MOND, we need modified Newtonian Dynamics, we need some uh relativistic version thereof." There's not just one type of particle, right? I mean, we have 114 elements in the periodic table; there's not just one form of matter, right? All I'm saying is that if you could identify the dark matter as this space-time heat, which you know we can we can discuss, it would also simultaneously have to, you know, interact with or explain how neutrinos do behave as, you know, as you say, Fermions, but they have mass, but they also do not interact with ordinary matter as does, you know, hypothesized WIMPs.

No, no, I mean the thing is, in our models, kind of particles like electrons, neutrinos, and so on, they are kind of topological topologically stable objects moving sort of without change through this hypograph, or without much change through the hypergraph. It's like kind of an eddy in water; the eddy can move without change; it can keep swirling as it as it moves; it's the same kind of thing I think with electrons and neutrinos and all things where you can talk about them as being identifiable particles, where the particle moves without change through space and time. It's a different thing if you have something which is associated with the structure of space, so it would be like saying, "Oh, we've got uh, let's say we're dealing with with let's say sound waves, okay? We've got sound waves in air, and sound waves are this definite kind of big effect in, you know, moving through air, compression, rarefraction, and so on, moving through air, then we have the underlying molecules just bouncing around doing their thing at a certain temperature with a certain kinetic energy and so on. So I think the analogy—it's not quite Perfect Analogy, but roughly the analogy is things that are identifiable particles, but we can pick it up and we can say this thing moves without change through space; those are kind of like the sound waves, and what we're talking about in space-time heat is really much like the heat that we see in, for example, a gas, where it really is the individual microscopic motion of molecules. So it's really a lower level object; it's a lower level construct. Now, interesting question: whether modified Newtonian Dynamics has any relation to this; that is a Hot Topic. And if there people watching this who are physicists who are interested in this, please contact us; we're we're—the real thing we want to know, the challenge is this: we have I think a very good candidate for what the machine code of the universe say, but going from that machine code to observable features of what you can look at with your telescope or whatever, that's a lot of physics work, and it needs an army of physicists to do it. That's why I reached out to you to to try to solicit and elicit information and interest from my students, your students, and people that want to interact with us. But you know, we're we're running a little low on time, Stephen, but so we're going to have to do a Part A, Part Two about just this work alone, and I also want to, you know, just encourage my colleagues and so forth to to consider take Seriously these predictions because these are some of the, you know, foundational issues.

Sometimes I feel like, Stephen, you don't get the attention, you know, that that you're, you know, deserving because you're you're you're sort of solving so many things at once; there's there's sort of a a bandwidth limitation on the receiving end that that's just a natural, you know, consequence; we're all absorbed in our own research, and there's very little time to pay attention to—well, now we have origin of time, explanation of the second law of Thermodynamics, predictions of what dark matter is—it's it's as to say overwhelming, but that doesn't mean that it's it's in any way detracting from it. But I do want to point out—let me let me just say something about that—it is the, you know, I've been lucky enough to kind of be involved in sort of changes of Paradigm, and when you change the Paradigm, lots of stuff can come out in science. Kind of the biggest kind of Paradigm change that sort of already happened was something that I was much involved in initiating in the in the early 1980s, which is: model things in nature with programs, not with equations. And so for 300 years there was kind of this tradition that, you know, you want to make a model in science that's an exact model, write down a mathematical equation. People don't do that anymore in most areas of science; people are writing down sort of rules and programs and using that as their underlying model, and that's a transformation that's taken basically 40 years to happen, and it's kind of interesting to me because I knew this was going to happen; this was uh, it, but it's very silent because it just, you know, it slowly happens, then people take it for granted. I mean, for example, this phenomenon of computational irreducibility, I kind of discovered that in 1984, so so 40 years ago, and to many people it's like, "Oh my gosh, this is a this is a crazy thing; how can this possibly be right?" But what's really nice for me to see is among young scientists, many of them, it's obvious the world couldn't be any different way, and it's it's it's kind of fun to see this transition from what seems impossible to what becomes obvious. The thing that you see in in what's happened in our physics project and so on, it's really a remarkable thing that I didn't see coming; I didn't think was going to happen in my lifetime. It's it's something where, you know, we had this burst of activity in physics roughly 100 years ago with a bunch of methodology that was both kind of the the almost philosophical methodology of kind of reasoning about relativity, about photons, things like that, together with kind of the mathematics that was developed in the in the 19th century with differential geometry and things of this kind being able to sort of merge with that and and things like matrices and so on merging with that and giving us this moment when we could really make paradigmatic progress in physics. We finally have another such moment, and the sort of the underlying Paradigm is all things about computation and about these phenomena of computation, and those are very alien; those have been very alien to people who have been sort of steeped in traditional physics.

Now I have to say, say the good news in recent times has been both that a lot of different approaches in mathematical physics seem to plug in very beautifully with the kind of computational infrastructure that we have, point one, and point two, through things like Quantum information and so on, people who think about physics have become much more familiar with kind of computational ideas, and so it's a lot less alien to think of physics as a fundamentally computational phenomenon. But yes, it's a it's a thing where, you know, I think the um, kind of—well, I was saying when we started doing the physics project uh five years ago or so now, it's such a short time—is um, you know, I was saying this won't have applications for 200 years; I was wrong. There are a bunch of applications now that make use of the fact that there are other areas—biology, distributed computing, mathematics and so on—which can use the formalism of the physics project to say things about their fields, but use the achievements of physics and the fact that it's sort of the same formalism to import ideas from physics, you know, black holes in metamathematics or things about computational irreducibility in biological evolution and so on. It is a feature of the history of science that when there are new paradigms, there is low-hanging fruit to be picked, and there's a lot of low-hanging fruit to be picked, a lot of different areas. I mean, I'm I'm I'm sort of sorry that we didn't have a chance to talk in more detail about what you can observe in the cosmic microwave background. Hey there, I know you're enjoying this episode, and I just want one thing from you, which is to subscribe or follow the podcast, whether on YouTube or on audio channels. I know you love it; I know you don't want to miss the next great episode. We have phenomenal broadcasts coming up with Yan LeCun, the father of Meta's AI systems; we have conversations with Neil deGrasse Tyson, Brian Greene, and many many more coming up; it's going to be a blast; the end of 2024 is going to be lit, and so is the beginning of 25, so do me that favor, won't you? Now, back to the episode.

Well, yeah, I just want to leave it as sort of an exercise to the to the viewer, uh, but no, in seriousness, I'd love to come back and and do a second part. I mean, we already, you know, kind of deserve four or five parts, but but I know your time is is very valuable. But I do want to point this out: you mentioned it, and and I say this with love and respect as usual, but you mentioned dark matter, but dark matter, you know, the Paradigm, as your words suggest, is cold dark matter; it's it's it's sterile neutrinos; it's it's Axion things that are very low temperature, pH, whereas whereas we have access with our telescopes, Simon's Array and other telesc—what you—what are you show—show me what you're—what is one of Galileo—I thought you were—I thought you showing me a piece of of uh of the Simon's telescope, but no—oh no, I have that uh the other room over here. But in reality, the the origin of the universe to me suggests the the best uh and most fertile playground to investigate the history of the early universe computationally, and I I just sketched out some ideas that I had, and I'm not even a, you know, a theoretical astrophysicist, but but the fact that the CMB is is sort of the the—it's—well, it is the oldest possible light in the universe; it's the oldest possible light; it's a heat left over from the formation, the fusion of the very first elements and the and the very earliest nuclei on the periodic table, small, lightest nuclei on the periodic table, and it is intimately related—there's a direct correlation between temperature and redshift—and then, given a couple of very modest assumptions, connect redshift to time. So here we have temperature and time, and it's because it's the oldest light in the universe; it's the most pristine Relic that we have, and therefore it behooves us to pick that low-hanging fruit that you just said. So again, leaving this for an exercise, but but I do want to come back to this in the in the near future, and I do want to send some of my—this—I'm sorry, this is too much of a cliffhanger for me; I insist on talking about this just for a few minutes. Let's do it. So yeah, so I do want to ask you this: the fundamental observable in the CMB that's been measured to extremely high Precision is its temperature and isotropy spectrum, and the fundamental, the largest scale and therefore the most pristine massive fossils on the microwave sky, in the beach ball behind me on my shelf over there, are relics of the gravitational potential Wells that were laid down in most models of cosmology by inflation. Now, inflation gives us an opportunity to probe even more tiny scales, close to the Planck scale, and so it seemed to me to be the ideal laboratory. So so Stephen, let me let me just ask you a couple of things: if we were to apply this, how would we—what could we expect from you? I can give you the data; I can give you the Spectrum; I can give you correlation functions; I can give you a power Spectrum; can you predict the temperature and isotropy Spectrum on this beach ball? Can you—does it emerge, given a modest amount of assumptions, could we get a prediction of that? And then, eventually, we'll need to get the polarization because only by getting the polarization can we see the tensor perturbations thought to be harbingers of inflation. So first, can you predict the temperature Spectrum?

Not yet; that's a that's a hard ask. I mean, it's it's like asking, you know, it's like given, you know, what we know about quarks and gluons, tell me about the the the fission of a uranium nucleus. There's a a depth of computational irreducibility; we can be lucky and find certain kind of paths through that. Now, having said that, I can tell you what some of the steps are. What we really want to find first is an analog of the Freedman-Robertson-Walker metric; that is the, you know, the homogeneous Universe metric that describes an expanding universe, but the usual such metric, you know, defines such a universe with only one parameter, which is its radius, its effective radius so to speak; we need another parameter, which is its effective Dimension. We need to a version of that that has Dimension change, so that's—if we can get that first, we get for the homogeneous case, then we look at inhomogeneities in Dimension, and the most exciting thing there is the possibility of Dimension fluctuations left over from the early universe, and the question then is, what is the effect of a dimension fluctuation on the CMB? And that to me is is the most likely kind of very bizarre thing that we'll see. Okay, and I don't know—you know, when you ask—there are photons, so so how do photons propagate if we have a plane wave of photons? So we have we have just a sort of a source an infinite distance away, and what was a circle we've now just seeing a, you know, a single piece of it; that's a plane wave. Well, a way to think about that plane wave is it's made up of of a large number of little spherical wavelets; at every point on the plane wave it makes a new plane Wave by having these little spherical pieces on the first plane wave. And so I think there's a way to think about that when you have a dimension fluctuation, those little spherical wavelets become hyperspherical wavelets, and the structure of the plane wave has changed, and so—but exactly how we don't know. My guess would be that it is uh, if you propagate a plane wave through a dimension fluctuation, you will get something which is a weird form of gravitational lensing; my guess is that it will shatter the plane wave basically, whereas a gravitational lensing uh just concentrates it, just focuses it; my guess is that dimension fluctuations will essentially shatter that plane wave, giving it like a caustic, a caustic well.

No, atic is is is concentrating energy in a particular. So I don't know what I mean. This is one of the things we need to figure out: what happens when an electromagnetic wave propagates through a region that has variable dimension? What happens in the early Universe when dimension is a dynamical parameter? Where you have, oh, there's this region of space that has dimension 3.01; there's this neighboring one that has dimension 2.98. And how does that, how does that, you know, when you when you start off in the early Universe with, let's say, infinite dimension, infinite-dimensional space, and you end up with something that's sort of cooling down to this lower-dimensional space, what kind of spectrum of fluctuations gets left over? We don't know, but that's something that is is within the realm. I mean, okay, here's here's the foundational problem: the mathematics you need is completely unknown, and we're trying to build it. But here's how it works. So you know, if you study calculus, you'll study univariate calculus, calculus of one variable; you'll study multivariate calculus, calculus where there's variables X, Y, Z, and so on. What we need is calculus where there are fractional numbers of variables, and nobody's ever figured that out; nobody's even tried to study that. And that's what, when you look at the kind of geometry that emerges from these hypergraphs and things, you end up needing to know about things like calculus in 3.1 dimensions. And that's simply a mathematical structure that hasn't been built. We're we're in the process of building it, but it's a fairly heavy lift. I mean, that's a that's a deep foundational piece of mathematics that has to be built to be able to, you know, have a a place where we can really talk about things like propagation of electromagnetic waves and fractional dimensional space and so on.

But so if you were to, you know, if if I were to guess what the kind of thing that you will see will be something that is very bizarre that you never expected. It's not something where, you know, my experience, spherical harmonics, yeah, it's not going to be. So you know, the thing that is a very good intuition builder is, which I've been sort of doing for for well, 45 years now, is just doing experiments in the computational universe. You set up these rules; you see what they do. The thing that is really shocking is pretty much every every week when I'm working on this kind of thing, there'll be something where I say, "I know what this is going to do. I've been doing this for 45 years. I know what this is going to do," and it does something bizarre and unexpected. And that's a piece of intuition one doesn't usually have. One usually thinks once you kind of sort of know what this general kind of thing, how this general kind of thing works, you kind of know what's going to happen. What one sees in these computational systems is bizarre phenomena that were never expected. Like dimension fluctuations are an example of something that, you know, if if you just live in standard general relativity, you would never imagine a phenomenon like dimension fluctuations.

So I I think that the, you know, the thing is, you know, this is a sort of, you know, when you make measurements, you know, I would say my one sort of piece of experimental advice, so to speak, is keep all the data. By which I mean, if you're using, you know, the analog of sort of software radio to collect things and you're and you're kind of, you know, picking out, you're doing Fourier analysis of it to pick out particularly frequency spectra and things like this, keep all the data. Don't just keep the thing that was the result of the Fourier analysis; keep the raw data. That's a massive that's a massive challenge, and we are we are doing that. The Simons Observatory will get of order a terabyte of data every day from four telescopes sampling uh 100,000 detectors 100 times per second in two different polarization states and six frequency bands. Uh, we just started to get first light data just a few months ago. Jim Simons got to see it before he passed away. But Stephen, this has been so fascinating. I it's always, you know, parting is such sweet sorrow, but but you know, the time has come around here in the keing to put the king kids to bed. But before I go, I want to read you a quote, and it's uh 1700 years old from St. Augustine. He said, "What is time? If no one asks me, I know; but if I try to explain it, I cannot." And he discovered something very interesting as he finally mused at the end of his essays. He said, "What we measure is not it." It's very evocative to me of what you're doing, because in a large sense, as you as you conclude, you know, this principle of computational equivalence allows there to be a robust notion of time independent of the substrate that's involved, whether it's us as observers, the everyday physical world, or for that matter, the whole universe. I think St. Augustine would be quite pleased to see what you're doing. You could have allayed a lot of his questions, Stephen.

And and I do hope I'm going to send uh my undergraduates this this uh essay. And we have been doing some stuff quite unsuccessfully, unfortunately. We tried to ask a quick question: what would a—we had ChatGPT. If we had the the uh Mathematica in the year uh let's let's call it 1877, and we had all of Mercury's orbits uh for the previous, you know, tens of thousands of years, could a computational system have derived the laws of what we call general relativity? And it turns out we we can't. We we we know for sure we can't do it with LLMs. We can't effectively do it with. Hopeless, hopeless. No, no, but we use some of your symbolic regression uh techniques, um and we basically have to insert by hand the curvature of SP. We make these gravitomagnetic effects. Um, I'll I'll bring that up to you sometime. So I will make one comment: it's in the um yeah, in the version of of Wolfram Language which will come out in uh beginning of next year, we can actually compute the per the advance of the perihelion of Mercury. It's kind of cool. We have enough enough uh capability in uh astrodynamics and so on to be able to do that. It is, if you if you didn't believe in relativity before, after you've dealt with all these crazy coordinate systems in the solar system and all of their different time bases and so on, you have no choice but to to really, you know, feel relativity, so to speak. But I I don't think I think this idea of going from the what we see in the world to deduce its underlying laws, that's a whole another discussion, but that's a that's a that's all of these ideas about computational irreducibility and so on kind of say that doesn't really work; that doesn't that doesn't really it's not really the thing. That's a whole another story. But I but I like your your quote from St. Augustine. That's nice. I you know, one of the things, the meta-comment to make, is a lot of what we are now able to start talking about from some of these things from the physics project, the ru ad things like this, are foundational questions in science that actually predate modern science. People like, you know, the the theologians of of a thousand years ago or whatever had things to say about these these questions, and what they said was often quite interesting, and it got kind of swept away by the advance of mathematical science. It's really kind of dramatic that at this point we're able to kind of dig deep enough that we can get back to some of those foundational questions as well. We should, you know, because these are the most basic questions, as we started off: what is life? What is consciousness? What is time? It seems to me you're addressing all three of these uh questions, and I couldn't be more excited. Uh, for I'm working on the what is life question. I've been working recently on the foundations of biology. I only know the direction to go for the answer to the what is life question, but we'll get there. We'll get get there. From than thank you so much. We'll be in touch, and we'll do it again hopefully very soon. Thank you. Hey there. I know if you're listening to this podcast, you're going to love this conversation with Stephen Wolfram from earlier this year where he claims to have solved the second law of thermodynamics. Click here for that, and don't forget to subscribe.