What is Time? Stephen Wolfram’s Groundbreaking New Theory [Ep. 468]

Please join my mailing list here 👉 https://briankeating.com/list to win a meteorite 💥 What is time? Is it just a ticking clock, or is it something more profound? In this thought-provoking episode of Into the Impossible, Stephen Wolfram challenges everything we know about time, offering a revolutionary computational perspective that could forever change how we understand the universe. Stephen Wolfram is a computer scientist, physicist, and businessman. He is the founder and CEO of Wolfram Research and the creator of Mathematica, Wolfram Alpha, and Wolfram Language. Over the course of 4 decades, he has pioneered the development & application of computational thinking. He has been responsible for many discoveries, inventions & innovations in science, technology, and business. He argues that time is the inevitable progress of computation in the universe, where simple rules can lead to complex behaviors. This concept, termed computational irreducibility, implies that time has a rigid structure and that our perception of it is limited by our computational capabilities. Wolfram also explores the relationship between time, space, and gravity, suggesting that dark matter might be a feature of the structure of space. Tune in to discover the true nature of time. Key Takeaways: 00:00:00 Intro 00:01:06 The true nature of time 00:24:57 The role of computational irreducibility in thermodynamics 00:30:07 The Ruliad and the nature of observers 00:53:40 The role of gravity in the computational universe 01:06:27 Dark matter and the discreteness of space 01:13:06 Paradigm shifts in science and technology 01:20:33 Exploring the cosmic microwave background (CMB) 01:31:47 Outro Additional resources: ➡️ Check out Stephen Wolfram: 💻 Website: https://www.stephenwolfram.com/ ✖️ Twitter: https://twitter.com/stephen_wolfram ➡️ Follow me on your fav platforms: ✖️ Twitter: https://twitter.com/DrBrianKeating 🔔 YouTube: https://www.youtube.com/DrBrianKeating?sub_confirmation=1 📝 Join my mailing list: https://briankeating.com/list ✍️ Check out my blog: https://briankeating.com/cosmic-musings/ 🎙️ Follow my podcast: https://briankeating.com/podcast Into the Impossible with Brian Keating is a podcast dedicated to all those who want to explore the universe within and beyond the known. Make sure to follow/subscribe so you never miss an episode! Learn more about your ad choices. Visit megaphone.fm/adchoices

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Speaker 00

  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.

• 0:22Brian Keating?

  Stephen, the thing that always comes up 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?

• 0:50Speaker 00

  I'm doing well, thank you.

• 0:51Brian Keating?

  The first thing I want to ask you about is, is, is what time is to you versus what it is to the general listening layperson. We have the brightest audience in the known multiverse. But the question is, we all sort of, it's kind of like the old Supreme Court definition of pornography. You know, you know it when you see it. But I'd like to connect it both with your physics project and with my Simons Array 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.

• 1:22Speaker 00

  All right.

• 1:23Brian Keating?

  Yes. Your 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?

• 1:36Speaker 00

  What is time? People, 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 a 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. Some 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.

• 2:19Speaker 00

  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 kind of actually Einstein, I don't think really thought that. I think Minkowski, a mathematician who kind of came to sort of clean up the mathematics of special relativity by 1909 or so. Was saying, well, we noticed that we have these expressions for proper time for for space time distance. It's X squared minus T squared. And that reminds him of these things in mathematics, quadratic forms.

• 3:01Speaker 00

  And so 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?

• 3:45Speaker 00

  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 that 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 nineteen eighties, 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...

• 4:29Speaker 00

  It 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 may be 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.

• 5:12Speaker 00

  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.

• 5:57Speaker 00

  So typical example of this, the two-body problem in celestial mechanics. You have an idealized sun and 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 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 hope 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,

• 6:40Speaker 00

  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 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 thirty four 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.

• 7:24Speaker 00

  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 reducibility, 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 forty two, so to speak.

• 8:07Speaker 00

  The computational reducibility 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.

• 8:49Speaker 00

  We can just work out a formula, jump ahead and say what the answer is. But what computational reducibility 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.

• 9:34Speaker 00

  You're always kind of, and there are even in in the way equations are set up, like partial 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 reducibility, we have these underlying rules, we can apply

• 10:19Speaker 00

  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. There ma- 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

• 11:04Speaker 00

  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? Kind of a little bit like what happened with temperature back in the day.

• 11:49Speaker 00

  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 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

• 12:33Speaker 00

  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 There's a lot to say about kind of the relationship between time and space. There's a lot to say about kind of our experience of time. So things get, let's see, I mean, there are many different directions to go here. But let's talk a little bit about time versus space.

• 13:18Speaker 00

  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 paradigmatic change in physics was basically a hundred years ago. And we've been sort of operating out of the same playbook for a hundred years. And a hundred 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.

• 14:01Speaker 00

  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.

• 14:42Speaker 00

  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'd 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, how we're traveling relative to this lattice, they could never make that work.

• 15:27Speaker 00

  So, a hundred 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 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.

• 16:12Speaker 00

  That's kind of the whole, that's kind of the data structure of the universe. And 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 10 to the 100 atoms of space? 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.

• 16:55Speaker 00

  So the question is, what's the analogous limit of this graph being rewritten and so on? Well, it turns out the analogous limit is the Einstein equations. So, the equations of spacetime that you're very familiar with, that's kind of the first big clue that something interesting is happening, is you're 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

• 17:38Speaker 00

  that is just a small number of sort of 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 then questions about about relativity and how relativistic invariance occurs, things like that. This is a slightly, slightly deeper rabbit hole. Um, but the, the key idea is you've got this notion of space.

• 18:19Speaker 00

  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.

• 19:03Speaker 00

  Then whatever's 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 events? And from that, you can build up this causal graph of what, what affects what. And it's that causal graph that is the the real sort of substance of what's going on in these models.

• 19:44Speaker 00

  And that causal graph is, in a sense, a graph that can connects both space and time. These events, one can think of them as, in the end, we will perceive them as be 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

• 20:25Speaker 00

  is that we can parse the universe as consisting of states of space at successive moments of time.

• 20:34Brian Keating?

  When you say parse the universe, you mean to measure the universe? We can make observational measures.

• 20:38Speaker 00

  Yeah, 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 the subsequent moment of 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 meters away. Well, the light from something 10 meters away gets to your eye in a microsecond, 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.

• 21:23Speaker 00

  So, for your brain, it's as if the there 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 meters away, you're dealing with things that are, you know, 10 to the 25 meters away or something, 10 to the 26 meters. is 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

• 22:06Speaker 00

  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, the 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.

• 22:50Speaker 00

  We have to, we have to say, we're gonna, we're gonna choose to slice that graph so that we have these states of space at successive moments of time. In the jargon of relativity, that will be spacelike 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

• 23:35Speaker 00

  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? And 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 the slice of the causal graph and we're saying these events we consider to be simultaneous in time.

• 24:15Speaker 00

  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.

• 24:42Brian Keating?

  They're not accessible. You cannot access them in all right. You you mentioned 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?

• 25:12Speaker 00

  One of the biggest things that's emerged in in my kind of thinking about sort of 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 will be possible to derive the laws of physics. I always assumed that the laws of physics were just like, well, we we've got this universe. This is how it works.

• 25:37Brian Keating?

  Right. The instruction model.

• 25:39Speaker 00

  Right. I never thought they they will 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 nineteenth century, particularly very tantalizing. Trivia fact, actually.

• 26:19Speaker 00

  In the invention of, so in nineteen oh five, you know, Einstein wrote three very famous papers. Relativity, the photoelectric effect, Brown in motion. In nineteen oh four, 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.

• 27:05Speaker 00

  You can derive this notion in nineteen oh four for the second law of thermodynamics. It didn't work. In the case of relativity in nineteen oh five, it did work. And 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 very orderly configuration. Then you let them collide and and follow the laws of mechanics. What they are doing is performing a computation. It's an irreducible computation.

• 27:50Speaker 00

  So what comes out of that is something which no longer has a trace. Of 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,

• 28:35Speaker 00

  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 individual 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 gonna happen. I know what happened before." So, that's a case where

• 29:20Speaker 00

  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 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.

• 29:53Brian Keating?

  So, it could be used to detect, you know, whether or not something is a computationally limited observer, just like a bounded observer like us?

• 30:01Speaker 00

  Well, to some extent, yeah. So, here's a fun thing. Back in the 1860s, when people were first talking about 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 this supposedly random motion of molecules. So people were saying, "That's a terrible situation, you know, 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."

• 30:45Speaker 00

  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 conversations, 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

• 31:26Speaker 00

  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 have this complicated motion that comes to 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 hypography writings and so on, and the fact that we, as observers of that, are computationally bounded.

• 32:11Speaker 00

  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,

• 32:54Speaker 00

  you know, if you're right next to a space-time singularity, 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 coherent spacecraft there.

• 33:10Brian Keating?

  Right, and moving into space means that you're moving in time, right? The time and space axes get inverted.

• 33:16Speaker 00

  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. Just looks like a black hole. It's the same with electrons.

• 34:00Speaker 00

  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 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.

• 34:45Speaker 00

  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.

• 35:25Speaker 00

  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 detail, which is really cool, that there's sort of a mechanical explanation of time dilation.

• 36:09Speaker 00

  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 sort of traditional Rensenvarian and things like this. I mean, it's, it's a, I think. You know, the thing, just to sort of finish this thought 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

• 36:54Speaker 00

  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 way that we, in a sense, parse the universe by that assumption that it's the same us at successive moments in time.

• 37:18Brian Keating?

  And persistence of memory, right?

• 37:19Speaker 00

  Yeah, right. I mean, 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.

• 37:59Speaker 00

  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 effect. Of many different threads of time.

• 38:40Speaker 00

  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.

• 39:23Speaker 00

  Quantum effects are sort of where where it doesn't quite, we 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 we're 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

• 40:08Speaker 00

  of the universe. Well, in branchial space and 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.

• 40:48Speaker 00

  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 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 the 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.

• 41:26Brian Keating?

  Speaking of those random randomness, 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 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?

• 42:08Speaker 00

  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 with 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

• 42:53Speaker 00

  very brain-like things. That's just an example of that. 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 ruleal space. It's essentially the space of all possible kinds of rules by which you could describe what's going on in the universe. And different human brains are pretty close together in ruleal space. The details of how we think 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.

• 43:37Speaker 00

  We make up words and concepts. We use human language to take all those complicated neuron firings 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 ruleal space. Then you've got to 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 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.

• 44:18Speaker 00

  But the fact is that the sort of the dynamics of fluid, of air 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 ruleal 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 trying to nail 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.

• 45:02Speaker 00

  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, just to explain, you know, 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,

• 45:44Speaker 00

  you know, this scene of, of whatever we're looking at, and maybe there are, you know, I don't know, I don't know what it is, a hundred million photons that, 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 equivalence together many states of the world, and they care about only certain aggregate states of the world.

• 46:29Speaker 00

  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, a neurological assessment of, is that person conscious?

• 47:11Speaker 00

  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's 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 equivalencing, you have to have an observer of that equivalencing. 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 equivalencing?

• 47:54Speaker 00

  Can you notice that there's a thing with this kind of equivalencing for which you have to have another level observer and so on? But one of the things we, we, I've been working on actually recently is the following thing. 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 ruliad, 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 this, 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.

• 48:36Speaker 00

  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 ruliad? 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.

• 49:20Speaker 00

  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 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, uh, it's very hard, I've, I've 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 had 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.

• 50:03Speaker 00

  But there is an interconcept 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 that 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 constructable for a mind, but not what our human minds are used to. And I've been referring to that as interconcept space. So we have concepts like cat and dog, and in between there is interconcept space. And the space that we have populated with concepts, with the 50,000 words in typical

• 50:46Speaker 00

  human languages and so on, the, the, the region that we have populated effectively in the ruliad is absolutely infinitesimal. In other words, there's a, there's a huge kind of interconcept space relative to kind of the tiny places where we have sort of colonized an interconcept space. That's one little way of getting a little tiny peek of what it's like to be an observer not like us. Actually, some of what I've done in long time work in what I call ruliology, 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 the rules we attribute to the universe, what

• 51:29Speaker 00

  they do, that's sort of another way to get a sense of what observers not like us will, will, will see. But 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 ruliad object... 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 ruliad object.

• 52:11Speaker 00

  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 ruliad kind of one step at a time. For observers like us, we can't take a big gulp of the ruliad. It's just not, it doesn't fit in our finite minds. If, if we had infinite minds, we could fit the whole ruliad in our minds. But because we have finite minds, we're stuck kind of walking through the ruliad kind of one tiny step at a time.

• 52:51Speaker 00

  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.

• 53:00Speaker 02

  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 briankeating.com/list. You'll also be entered to win real live meteorite. I give them out to one or two lucky winners every month. But if you have a dot edu email address, you're guaranteed to win. Go to briankeating.com/edu if you're blessed with a dot edu email address. Now back to the episode.

• 53:28Brian Keating?

  I wonder if we could pivot to now 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 Keating household, which involves the cosmic microwave background radiation.

• 53:42Speaker 00

  Good subject.

• 53:42Brian Keating?

  And I thought we'd.

• 53:43Speaker 00

  Yes.

• 53:43Brian Keating?

  Yeah, so I thought we'd take a quick detour and explain the role of, of gravity, the role that gravity plays in the ruliad, in, in computational universe.

• 53:55Brian Keating?

  So talk about what will be familiar to my physics, physics, audience, physically inclined audience, shall we say, will be most understandable, Stephen, if you explain it in terms of the way that the hypergraph's 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, Stephen, hypergraphs and energy momentum, how are they connected?

• 54:27Speaker 00

  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 is. All we know is who's friends with who?

• 54:48Brian Keating?

  The social graph.

• 54:49Speaker 00

  What's that? Yeah, the social graph of the atoms of space. And what then happens is when you have a sufficiently 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 that'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,

• 55:34Speaker 00

  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 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 are 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?

• 56:17Speaker 00

  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 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 early universe. That will be a spectacular thing to see in the CMB. And I'd love to know details where we can, we we'll get to that in a minute. Let's talk about. Yeah. About some energy momentum. So we're talking about kind of space.

• 57:02Speaker 00

  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-called geodesic, a shortest path in the graph, a 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.

• 57:46Speaker 00

  And so there's a slightly more that 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 spacelike 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 spacelike hypersurface.

• 58:08Speaker 00

  And momentum is the flux of causal edges that poke through a time-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 way that those causal edges poke through the spacelike 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

• 58:50Speaker 00

  from the fact that we think about space as this geodesics in the hypergraph and time as the sequence of events, and that then this density of causal edges is energy. And 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 atom of space to atom of space in the shortest path?" Well, when there is activity in the graph, that deflects that shortest path, it changes the shortest path.

• 59:35Speaker 00

  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 geodesics in the graph. I mean, just as a fun fact, okay? The one thing you might ask is, years ago, when I was first working on the precursors of this physics project, there was a person, mathematician, who worked with me, and 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 they would say things like, "And so, are you going to invent warp drive?" So now, the question is,

• 1:00:19Speaker 00

  now that we think we really do understand the sort of machine code of physics, is warp drive possible? 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 orthonamics again. Let's tell a story about second orthonamics. 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 scent, you know, in 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,

• 1:01:02Speaker 00

  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 to 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 this hypergraph, exactly the right rewrite event,

• 1:01:42Speaker 00

  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 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

• 1:02:24Speaker 00

  or an observer that has any of 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 insofar as you can turn heat into mechanical work, so similarly, you can turn sort of the details of what's happening in this hypergraph into being able to go, you know, faster than light. So that was sort of a side thing, but the main, the main thing, and by the way, I want

• 1:03:06Speaker 00

  to say something about the structure 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 discreteness of space? A hundred 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 discreteness of space? What effect, what phenomenon could we look at that would reveal the discreteness of space?

• 1:03:47Speaker 00

  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, we'll say, oh, okay, it's obvious, space has to be discrete. 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, it turns out, heat was actually the microscopic motion of molecules. Heat, the very phenomenon of heat, basically should have told one that matter is discrete.

• 1:04:30Speaker 00

  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 spacetime heat? That might reveal the similar features of the discreteness of space? As the phenomenon of heat reveals the discreteness 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 a hundred years.

• 1:05:15Speaker 00

  And 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. Because 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 spacetime heat. And it is possibly related to to dimension fluctuations. And we usually think of in general relativity, we usually think of space as being curved.

• 1:06:00Speaker 00

  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.

• 1:06:15Brian Keating?

  The only pushback I would put on that, Stephen, is that we do know dark matter in particular form that's been detected. It's known as neutrinos. They're 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 simultaneous. I'm not saying it's impossible to accommodate them in spacetime heat. But you'd have to accommodate neutrinos.

• 1:06:36Speaker 00

  No, no, neutrinos are very different kind of thing. I mean, neutrinos, you know. We don't yet know about neutrino background radiation. You know, it probably has, I remember working this out long ago. I think it's 1.6 kelvins was what was the temperature. And 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 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

• 1:07:21Speaker 00

  that there's a physics way to detect where all the nuclear submarines are. It was one of those cases 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, no, I think neutrinos are, you know, they have all the characteristics of particles like photons and so on. They just have somewhat different interaction, features of interaction. I mean, in fact, okay, fun fact, when I was a kid, age probably 16 or so, one of my first papers that I never ended up publishing was about neutrino background radiation. And it was about the possibility of high density of neutrino background radiation. Because neutrinos, unlike photons, if you pack enough, neutrinos have the exclusion principle

• 1:08:06Speaker 00

  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 the electrons in an atom, 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 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 nuclear decay, when there's beta decay, it produces neutrinos.

• 1:08:51Speaker 00

  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 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 emitter 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.

• 1:09:36Speaker 00

  It's something which has tiny Q value, and so it it is sensitive to the presence of degenerate neutrinos in the universe. But but I don't think that, I mean, I think the story of of neutrinos, I don't think that's a, so far as I know, that's not a plausible hypothesis for.

• 1:09:55Brian Keating?

  Well, their their masses are insufficient to make the closure density, you know, equal to omega matter that we observe. But so that's so that's true, but they but they do fulfill. In other words, a lot of people will say, well, we we need Mond or we need modified Newtonian dynamics, we need some relativistic version there. I mean, it'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 spacetime 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.

• 1:10:39Speaker 00

  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 hypergraph, 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.

• 1:11:23Speaker 00

  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, rarefaction, 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, where we can pick it up and we can say, this thing moves without change through space. Those are kind of like the sound waves.

• 1:12:05Speaker 00

  And what we're talking about in spacetime 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 neutronian dynamics has any relation to this? That is a hot topic, and if there are people watching this who are physicists who are interested in this, please contact us. We're, we're, um, 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 is, but going from that machine code to observable features of what you can look at with your telescope

• 1:12:48Speaker 00

  or whatever, that's a lot of physics work and it needs an army of physicists to do it.

• 1:12:54Brian Keating?

  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, 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 Big series, these predictions, because these are some of the foundational issues. Sometimes I feel like, Stephen, you don't get the attention that you're deserving because you're sort of solving so many things at once. There's sort of a bandwidth limitation on the receiving end. That's just a natural consequence. We're all absorbed in our own research and there's very little time to pay attention to.

• 1:13:38Brian Keating?

  Well, now we have origin of time, explanation of the second law of thermodynamics, predictions of what dark matter is. It's as to say overwhelming, but that doesn't mean that it's in any way detracting from it. But I do want to point out.

• 1:13:50Speaker 00

  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 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.

• 1:14:34Speaker 00

  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, 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 40 years ago. And to many people, it's like, oh my gosh, 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 kind of fun to see this transition from what seems impossible to what becomes obvious.

• 1:15:19Speaker 00

  The thing that you see 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 a hundred 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 nineteenth 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.

• 1:16:01Speaker 00

  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. 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.

• 1:16:41Speaker 00

  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 kind of, well, I was saying when we started doing the physics project. Five years ago or so now, it's such a short time. Is, you know, I was saying this won't have applications for two hundred 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

• 1:17:24Speaker 00

  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 mathematics. Mathematics, or things about computational irreducibility and 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 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.

• 1:17:57Speaker 02

  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 Jan LaKoon, 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.

• 1:18:26Brian Keating?

  Well, yeah, I just want to leave it as sort of an exercise to the, to the viewer. But no, in seriousness, I'd love to come back 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 very valuable. But I do want to point this out. You mentioned it, 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 sterile neutrinos, it's, it's axions, things that are very low temperature phenomena. Whereas, whereas, we have access with our telescopes, Simon's Array and other telescopes.

• 1:19:00Speaker 00

  What are you showing? What are you showing? Show, show me what you're showing.

• 1:19:02Brian Keating?

  Going to Galileo's.

• 1:19:04Speaker 00

  Oh, okay. That's, that's, I thought you were, I thought you were showing me a piece of, of, of the Simon's telescope, but no.

• 1:19:09Brian Keating?

  Oh, no, I have that, the other room over here. But in reality, the, the origin of the universe, to me, suggests the, the best and most fertile playground to investigate the history of the early universe computationally. And I just sketched out some ideas that I had. And I'm not even a, you know, theoretical astrophysicist, but, but the fact that the CMB is sort of the, the, it's, well, it is the oldest possible light in the universe. It's the oldest possible light to heat left over from the formation, the fusion of the very first elements and the, and the very earliest nuclei on the periodic table, a small light. Is nuclear 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 can

• 1:19:54Brian Keating?

  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

• 1:20:13Speaker 00

  I'm sorry, this is too much of a cliffhanger for me. I insist on talking about this just for a few minutes.

• 1:20:18Brian Keating?

  Let's do it. So yeah, 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?

• 1:21:00Brian Keating?

  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?

• 1:21:26Speaker 00

  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 fission of a uranium nucleus. There's 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 Friedman 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 radius, its effective radius, so to speak.

• 1:22:10Speaker 00

  We need another parameter, which is its effective dimension. We need 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

• 1:22:55Speaker 00

  an infinite distance away. And what was a circle, we've now just seen a, you know, a, 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 a, 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 is changed. And so, but exactly how we don't know. My guess would be that it is, if you propagate a plane wave

• 1:23:38Speaker 00

  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 just concentrates, it just focuses it. My guess is that dimension fluctuations will essentially shatter that plane wave.

• 1:23:57Brian Keating?

  Giving it like a caustic, a caustic.

• 1:23:59Speaker 00

  Well, no, acoustic 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. It's 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 three point oh one. There's this neighboring one that has dimension two point nine eight. 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?

• 1:24:44Speaker 00

  We don't know, but that's something that is, is within the realm. I mean, okay. Here's, here's the foundational problem there. 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 number 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 three point one dimensions.

• 1:25:27Speaker 00

  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.

• 1:26:01Brian Keating?

  Spherical harmonics and.

• 1:26:03Speaker 00

  Yeah, it's, 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, forty five 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 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 forty five 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.

• 1:26:45Speaker 00

  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 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 particular frequency spectra and things like this.

• 1:27:29Speaker 00

  Keep all the data. Don't just keep the thing that was the result of the Fourier analysis. Keep the raw data.

• 1:27:36Brian Keating?

  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 telescope sampling, a hundred thousand detectors, a hundred times per second in two different polarization states and six frequency bands. And 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 Keating to put the Keating kids to bed. But before I go, I want to read you a quote. And it's 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.

• 1:28:22Brian Keating?

  And he discovered something very interesting as he finally mused at the end of his essays. He said, what we measure not is not. 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 I do hope I'm going to send my undergraduates this, this essay. And we have been doing some stuff quite unsuccessfully, unfortunately. We tried to ask a quick question.

• 1:29:07Brian Keating?

  What would a, if we had ChatGPT, if we had the, the Mathematica in the year, uh, let's, let's call it 1877, and we had all of Mercury's orbits 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 L L M's. We can't effectively do it with this.

• 1:29:35Speaker 00

  Hopeless, hopeless.

• 1:29:36Brian Keating?

  No, no, but we use some of your symbolic regression techniques and we basically have to insert by hand the curvature of space. We make these gravito magnetic effects. I'll, I'll bring that up to you sometime.

• 1:29:48Speaker 00

  So I, I will make one comment. It's in the, um, yeah, in the version of, of Wolfram Language, which will come out in beginning of next year, we can actually compute the period, the, the advance of the period in Mercury. It's kind of cool. We have enough, enough capability in 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.

• 1:30:33Speaker 00

  That's a whole nother discussion, but that's a, that's, 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 nother story, but I, but I like your, your quote from Saint 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 ruli 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, whatever, had things to say about these, these questions. And what they said was often quite

• 1:31:18Speaker 00

  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.

• 1:31:32Brian Keating?

  As well we should, you know, because these are the most basic questions that'll be started off. What is life? What is consciousness? What is time? It seems to me you're addressing all three of these questions, and I couldn't be more excited.

• 1:31:43Speaker 00

  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.

• 1:31:53Brian Keating?

  We'll get there. Stephen Wolfram, thank, thank you so much. We'll be in touch and we'll do it again, hopefully very soon. Thank you.

• 1:32:00Speaker 02

  Hey there. I know if you're listening to this podcast, you're gonna 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.