#124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe

Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist. This is our second conversation on the podcast. Please check out our sponsors to get a discount and to support this podcast: – SimpliSafe: https://simplisafe.com/lex – Sun Basket, use code LEX: https://sunbasket.com/lex – MasterClass: https://masterclass.com/lex If you would like to get more information about this podcast go to https://lexfridman.com/podcast or connect with @lexfridman on Twitter https://twitter.com/lexfridman, LinkedIn https://www.linkedin.com/in/lexfridman/, Facebook https://www.facebook.com/lexfridman, Medium https://medium.com/@lexfridman, or YouTube https://www.youtube.com/lexfridman where you can watch the video versions of these conversations. If you enjoy the podcast, please rate it 5 stars on Apple Podcasts https://podcasts.apple.com/us/podcast/id1434243584, follow on Spotify https://open.spotify.com/show/2MAi0BvDc6GTFvKFPXnkCL, or support it on Patreon https://www.patreon.com/lexfridman. Here’s the outline of the episode. On some podcast players you should be able to click the timestamp to jump to that time. OUTLINE: 00:00 – Introduction 07:14 – Key moments in history of physics 12:43 – Philosophy of science 14:37 – Science and computational reducibility 22:08 – Predicting the pandemic 38:58 – Sunburn moment with Wolfram Alpha 39:46 – Computational irreducibility 46:45 – Theory of everything 52:41 – General relativity 1:01:16 – Quantum mechanics 1:06:46 – Unifying the laws of physics 1:12:01 – Wolfram Physics Project 1:29:53 – Emergence of time 1:34:11 – Causal invariance 1:53:03 – Deriving physics from simple rules on hypergraphs 2:07:24 – Einstein equations 2:13:04 – Simulating the physics of the universe 2:17:28 – Hardware specs of the simulation 2:24:37 – Quantum mechanics in Wolfram physics model 2:42:46 – Double-slit experiment 2:45:13 – Quantum computers 2:53:21 – Getting started with Wolfram physics project 3:14:46 – The rules that created our universe 3:24:22 – Alien intelligences 3:32:29 – Meta-mathematics 3:37:58 – Why is math hard? 3:52:55 – Sabine Hossenfelder and how beauty leads physics astray 4:01:07 – Eric Weinstein and Geometric Unity 4:06:17 – Travel faster than speed of light 4:16:59 – Why does the universe exist at all

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

• 0:00Lex Fridman?

  The following is a conversation with Stephen Wolfram, his second time on the podcast. He's a computer scientist, mathematician, theoretical physicist, and the founder and CEO of Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the new Wolfram Physics Project. He's the author of several books, including A New Kind of Science and the new book, A Project to Find the Fundamental Theory of Physics. The second round of our conversation is primarily focused on this latter endeavor of searching for the physics of our universe in simple rules that do their work on hypographs and eventually generate the infrastructure from which space, time, and all of modern physics can emerge.

• 0:45Lex Fridman?

  Quick summary of the sponsors: SimpliSafe, Sun Basket, and MasterClass. Please check out these sponsors in the description to get a discount and to support this podcast. As a side note, let me say that, to me, the idea that seemingly infinite complexity can arise from very simple rules and initial conditions is one of the most beautiful and important mathematical and philosophical mysteries in science. I find that both cellular automata and the hypograph data structure that Stephen and team are currently working on to be the kind of simple, clear mathematical playground within which fundamental ideas about intelligence, consciousness, and the fundamental laws of physics

• 1:28Lex Fridman?

  can be further developed in totally new ways. In fact, I think I'll try to make a video or two about the most beautiful aspects of these models in the coming weeks, especially, I think, trying to describe how fellow curious minds like myself can jump in and explore them, either just for fun or potentially for publication of new innovative research in math, computer science, and physics. But honestly, I think the emerging complexity in these hypographs can capture the imagination of everyone, even if you're someone who never really connected with mathematics. That's my hope, at least, to have these conversations that inspire everyone to

• 2:08Lex Fridman?

  look up to the skies and into our own minds in awe of our amazing universe. Let me also mention that this is the first time I ever recorded a podcast outdoors as a kind of experiment to see if this is an option in times of COVID. I'm sorry if the audio is not great. I did my best and promised to keep improving and learning as always. If you enjoy this thing, subscribe on YouTube, review it with five stars and Apple Podcast, follow on Spotify, support on Patreon, or connect with me on Twitter at Lex Fridman. As usual, I'll do a few minutes of ads now and no ads in the middle. I tried to make these interesting, but I do give you timestamps, so you're welcome

• 2:51Lex Fridman?

  to skip, but still, please do check out the sponsors by clicking the links in the description. It's the best way to support this podcast. Also, let me say, even though I'm talking way too much, that I did a survey and it seems like over 90% of people either enjoy these ad reads somehow magically, or don't mind them at least. That honestly just warms my heart that people are that supportive. This show is sponsored by SimpliSafe, a home security company. Go to simplisafe.com to get a free HD camera. It's simple, no contracts, 15 bucks a month, easy setup. Even I figured it out. I have it set up in my apartment. Of course, I also welcome intruders.

• 3:34Lex Fridman?

  One of my favorite movies is Leon or The Professional with Jean Reno, Gary Oldman, and the brilliant young Natalie Portman. If you haven't seen the movie, he's a hitman with a minimalist life that resembles my own. In fact, when I was younger, the idea of being a hitman or targeting evil in a skilled way, which is how I thought about it, really appealed to me. The skill of it, the planning, the craftsmanship. In another life, perhaps, if I didn't love engineering and science so much, I could see myself being something like a Navy SEAL. And in general, I love the idea of serving my country, of serving society by contributing my skill in some small way.

• 4:18Lex Fridman?

  Anyway, go to simplisafe.com/lex to get a free HD camera and to support this podcast. They're a new sponsor, and this is a trial run, so you know what to do. This show is also sponsored by Sun Basket, a meal delivery service. Visit sunbasket.com/lex and use code Lex to get $30 off your order and to support this podcast. This is the last read of the trial they're doing, so this is the time to get them if you're considering it. And if you do, it'll help ensure that they decide to support this podcast long term. Their meals are healthy and delicious, a nice break from the minimalist meals of meat and vegetables that I usually eat. Maybe on a personal note, one of my favorite things to do is watch people cook,

• 5:03Lex Fridman?

  especially people who love cooking, and hang out with people over amazing meals. I still tend to be strict in my diet, no matter what, even in fancy restaurants, but it brings me joy to see friends and family indulge something like a cake that has way too many calories, or ice cream, or whatever. My mom, in fact, for much of my life, made this cake called an anthill on my birthday that brings me a lot of joy and way too many calories. I was thinking of doing a video with my mom as she makes it. I thought it'd be a fun thing to do together. Anyway, go to sunbasket.com/lex and use code Lex. Do it now, so they sign a long-term contract for this podcast.

• 5:48Lex Fridman?

  This show is also sponsored by MasterClass. Sign up at masterclass.com/lex. $180 a year, you get an all-access pass to watch lessons from Chris Hadfield, Neil deGrasse Tyson, Tony Hawk, Carlos Santana, Garry Kasparov, Daniel Negrono, and many more brilliant world experts.

• 6:07Lex Fridman?

  MasterClass has been a really special sponsor. They believe in this podcast in a way that gives me strength and motivation to take intellectual risks. I'm thinking of doing a few solo podcast episodes on difficult topics, especially in history, like the rise and fall of the Reich or Stalin, Putin, and many other difficult topics that I'm fascinated by. I have a worldview that seeks inspiring, positive insights, even and perhaps especially from periods of tragedy and evil that perhaps some folks may find value in, if I can only learn to convey the ideas in my mind as clearly as I think them.

• 6:45Lex Fridman?

  I think deeply and rigorously and precisely, but to be honest, have trouble speaking in a way that reflects that rigor of thought. So it really does mean a lot, the love and support I get as I try to get better at this thing, at this talking thing. Anyway, go to masterclass.com/lex to get a discount and to support this podcast. And now, finally, here's my conversation with Stephen Wolfram.

• 7:32Lex Fridman?

  You said that there are moments in history of physics, and maybe mathematical physics or even mathematics, where breakthroughs happen and then a flurry of progress follows. So if you look back through the history of physics, what moment stand out to you as important such breakthroughs where a flurry of progress follows?

• 7:52Stephen Wolfram?

  So the big famous one is 1920s, the invention of quantum mechanics, where, you know, in about five or 10 years, lots of stuff got figured out. That's now quantum mechanics.

• 8:02Lex Fridman?

  Can you mention the people involved?

• 8:04Stephen Wolfram?

  Yeah, that was kind of the... Schrödinger, Heisenberg, Einstein had been a key figure, originally Planck, then Dirac was a little bit later. That was something that happened at that time, that's sort of before my time, right? In my time was in the 1970s, there was this sort of realization that quantum field theory was actually going to be useful in physics and QCD, quantum gravity dynamics, theory of quarks and gluons and so on, was really getting started. And there was again, sort of, big flurry of things happened then. I happened to be a teenager at that time and happened to be really involved in physics. And so I got to be part of that, which was really cool.

• 8:47Lex Fridman?

  Who were the key figures, aside from your young selves at that time?

• 8:51Stephen Wolfram?

  You know, who won the Nobel Prize for QCD, okay? People, David Gross, Frank Wilczek, you know, David Paulitzer, the people who were the sort of the slightly older generation, Dick Feynman, Murray Gell-Mann, people like that, who were Steve Weinberg, Garrett Hofd, he's younger, he's in the younger group, actually. But these are, these are all, you know, characters who were involved. I mean, it was, you know, it's funny, because those are all people who are kind of in my time, and I know them, and they don't seem like sort of these historical, you know, iconic figures. They seem more like everyday characters,

• 9:30Stephen Wolfram?

  so to speak. And so it's always, you know, when you look at history from long afterwards, it always seems like everything happened instantly. And that's usually not the case. There was usually a long buildup. But usually there's, you know, there's some methodological thing happens, and then there's a whole bunch of low hanging fruit to be picked. And that usually lasts five or 10 years. You know, we see it today with machine learning and, you know, deep learning, neural nets and so on, you know, methodological advance, things actually started working in, you know, 2011, 2012 and so on. And, you know, there's been this sort of rapid picking of low hanging fruit, which is probably, you know, some

• 10:14Stephen Wolfram?

  significant fraction of the way, way done, so to speak.

• 10:17Lex Fridman?

  Do you think there's a key moment, like if I had to really introspect, like what was the key moment for the deep learning, quote unquote, revolution?

• 10:25Stephen Wolfram?

  I mean, it's probably the AlexNet business.

• 10:27Lex Fridman?

  AlexNet with ImageNet. So is there something like that with physics where?

• 10:33Lex Fridman?

  So deep learning neural networks have been around for a long time.

• 10:37Stephen Wolfram?

  Absolutely, it's nineteen forties, yeah.

• 10:39Lex Fridman?

  There's a bunch of little pieces that came together and then all of a sudden, everybody's eyes lit up. Like, wow, there's something here. Like even just looking at your own work, just your thinking about the universe, that there's simple rules can create complexity. You know, at which point was there a thing where your eyes light up? It's like, wait a minute, there's something here. Is it the very first idea? Or is it some moment along the line of implementations and experiments and so on?

• 11:12Stephen Wolfram?

  There's, there's a couple of different stages to this. I mean, one is the think about the world computationally. You know, can we use programs instead of equations to make models of the world? That's something that I got interested in in the, at the beginning of the nineteen eighties. You know, I did a bunch of computer experiments. Uh, you know, when I first did them, I didn't really, I, I could see some significance to them, but it took me a few years to really say, wow, there's a big important phenomenon here that lets sort of complex things arise from very simple programs. Um, that kind of happened back in nineteen eighty-four or so. Then, you know, a bunch of other years go by, then I start actually doing a, a lot of much more systematic computer experiments and things and find out that the,

• 11:56Stephen Wolfram?

  you know, this phenomenon that I could only have said occurs in one particular case is actually something incredibly general. And then that led me to this thing called principle of computational equivalence. And that was a, a long story. And then, you know, as part of that process, I was like, okay, you can make simple programs can make models of complicated things. What about the whole universe? That's our sort of ultimate example of a complicated thing.

• 12:20Lex Fridman?

  Yeah.

• 12:21Stephen Wolfram?

  And so I got to thinking, you know, could we use these ideas to, to study fundamental physics? Uh, you know, I happen to know a lot about, you know, traditional fundamental physics. My, um, uh, my first, you know, I, I had a bunch of ideas about how to do this in the early nineteen nineties. I made a bunch of technical progress. I figured out a bunch of things I thought were pretty interesting. You know, I wrote about them back in two thousand and two.

• 12:44Lex Fridman?

  With a new kind of science in the cellular atomic world and

• 12:47Stephen Wolfram?

  Right.

• 12:47Lex Fridman?

  there's echoes in the cellular atomic world with your New Wolfram Physics Project. We'll get to all that. Allow me to sort of romanticize a little more on the philosophy of science. So Thomas Kuhn, philosopher of science, describes that, you know, the progress in science is made with these paradigm shifts. And so to linger on the sort of original line of discussion, do you agree with this view that there is revolutions in science that just kind of flip the table?

• 13:20Stephen Wolfram?

  What happens is it's a different way of thinking about things. It's a different methodology for studying things and that opens stuff up.

• 13:29Lex Fridman?

  There's this idea of, he's a famous biographer, but I think it's called The Innovators. The biographer Steve Jobs of Albert Einstein.

• 13:39Stephen Wolfram?

  Oh, yeah.

• 13:40Lex Fridman?

  He also wrote a book, I think it's called The Innovators, where he discusses how a lot of the innovations in the history of computing has been done by groups. There's a complicated group dynamic going on. But there's also a romanticized notion that the individual is at the core of the revolution. Like, where does your sense fall? Is ultimately like one person responsible for these revolutions that creates the spark? Or one or two, whatever, but or is it just the big mush and mess and chaos of people interacting, of personalities interacting?

• 14:18Stephen Wolfram?

  I think it ends up being like many things, there's leadership and there ends up being, it's a lot easier for one person to have a crisp new idea than it is for a big committee to have a crisp new idea. And I think, you know, but I think it can happen that, you know, you have a great idea, but the world isn't ready for it. And, you know, you can, you can, I mean, this has happened to me plenty, right? It's, you know, you have an idea, it's actually a pretty good idea, but things aren't ready. Either you're not really ready for it or the ambient world isn't ready for it and it's hard to get the thing to get traction.

• 14:55Lex Fridman?

  It's kind of interesting. I mean, when I look at a new kind of science, you're now living inside the history, so you can't tell the story of these decades. But it seems like the new kind of science has not had the revolutionary impact I would think it might. Like, it feels like at some point, of course, it might be, but it feels at some point, people will return to that book and say, that was something special here. This is incredible.

• 15:28Stephen Wolfram?

  What happened?

• 15:29Lex Fridman?

  Or do you think that's already happened?

• 15:31Stephen Wolfram?

  Oh, yeah, it's happened, except that people aren't, you know, the sort of the heroism of it may not be there. But what's happened is, for 300 years, people basically said, if you want to make a model of things in the world, mathematical equations are the best place to go. Last 15 years, doesn't happen. You know, new models that get made of things most often are made with programs, not with equations. Now, you know, was that sort of going to happen anyway? Was that a consequence of, you know, my particular work and my particular book? It's hard to know for sure. I mean, I am always amazed at the amount of feedback that I get from people where they say, oh, by the way, you know, I started doing this whole line of research because I read your book, blah, blah, blah, blah, blah. It's

• 16:16Stephen Wolfram?

  like, well, can you tell that from the academic literature? You know, was there a chain of, you know, academic references? Probably not.

• 16:23Lex Fridman?

  One of the interesting side effects of publishing in the way you did this tome is it serves as an education tool and an inspiration to hundreds of thousands, millions of people. But because it's not a single, it's not a chain of papers with piffy titles, it doesn't create a splash of citations.

• 16:46Stephen Wolfram?

  It's had, it's had plenty of citations, but it's, you know, I think that the, people think of it as probably more, you know, conceptual inspiration than, than kind of a, you know, this is a line from here to here to here in our particular field. I think that the, you know, the thing which I am disappointed by, and which will eventually happen, is this kind of study of the, this sort of pure computationalism, this kind of study of the abstract behavior of the computational universe. That should be a big thing that lots of people do.

• 17:21Lex Fridman?

  You mean in mathematics purely, almost like.

• 17:23Stephen Wolfram?

  It's like pure mathematics, but it isn't mathematics.

• 17:26Lex Fridman?

  But it isn't, it isn't. It's a new kind of mathematics.

• 17:30Stephen Wolfram?

  A new kind of science. Yeah, right. That's why the book is called that. Right. That's not coincidental.

• 17:36Lex Fridman?

  Yeah. It's interesting that I haven't seen really rigorous investigation by thousands of people of this idea. I mean, you look at your competition around rule thirty. I mean, that's fascinating. If you, if you can say something.

• 17:51Stephen Wolfram?

  Right.

• 17:52Lex Fridman?

  Is there some aspect of this thing that could be predicted? That's the fundamental question of science. That's the core.

• 17:59Stephen Wolfram?

  That has been a question of science. I think that's a, that is a, some people's view of what science is about. And it's not clear that's the right view. In fact, as we, as we live through this pandemic full of predictions and so on, it's an interesting moment to be pondering what, what science's actual role in those kinds of things is.

• 18:15Lex Fridman?

  Oh, you think it's possible that in science, clean, beautiful, simple prediction may not even be possible in real systems? That's the open.

• 18:25Stephen Wolfram?

  Right. I don't think it's open. I think that question is answered and the answer is no.

• 18:29Lex Fridman?

  Well, no, no, the answer could be just humans are not smart enough yet. Like, we don't have the tools yet.

• 18:35Stephen Wolfram?

  No, that's, that's the whole point. I mean, that's, that's sort of the big discovery of this principle of computational equivalence of mine. And the, you know, this is something which is kind of a follow on to Gödel's theorem, to Turing's work on the halting problem, all these kinds of things, that there is this fundamental limitation built into science, this idea of computational irreducibility that says that, you know, even though you may know the rules by which something operates, that does not mean that you can readily sort of be smarter than it and jump ahead and figure out what it's going to do.

• 19:09Lex Fridman?

  Yes, but do you think there's a hope for pockets of computational reducibility, computational re.

• 19:16Stephen Wolfram?

  Reducibility.

• 19:16Lex Fridman?

  Reducibility. Yes. That's, yes. So, and then, and then a set of tools and mathematics that help you discover such pockets.

• 19:24Stephen Wolfram?

  That's where we live, is in the pockets of reducibility.

• 19:27Lex Fridman?

  Right.

• 19:27Stephen Wolfram?

  That's why, you know, and this is one of the things that sort of come out of this physics project and actually something that, again, I should have realized many years ago, but didn't, is, you know, the, it, it could very well be that everything about the world is computationally irreducible and completely unpredictable. But, you know, in our experience of the world, there is at least some amount of prediction we can make. And that's because we have sort of chosen a slice of, probably talk about this in much more detail, but I mean, we've kind of chosen a slice of how to think about the universe in which we can kind of sample a certain amount of computational reducibility. And that's, that's sort of where we, where we exist.

• 20:09Stephen Wolfram?

  And it may not be the whole story of how the universe is, but it is the part of the universe that we care about and we sort of operate in. And that's, you know, in science, that's been sort of a very special case of that. That is, science has chosen to talk a lot about places where there is this computational reducibility that it can find. You know, the motion of the planets can be more or less predicted. You know, the, uh, something about the weather is much harder to predict. Something about, you know, other kinds of things, the, the, are much harder to predict. And it's, um, uh, these are, but science has tended to, you know, concentrate itself on places where its methods have allowed successful prediction.

• 20:52Lex Fridman?

  So you think Rule 30, if I could linger on it? Because it's just such a beautiful, simple formulation of the essential concept underlying all the things we're talking about. Do you think there's pockets of reducibility inside Rule 30?

• 21:06Stephen Wolfram?

  Yes. That is a question of how big are they? What will they allow you to say? And so on. And that's, and figuring out where those pockets are, I mean, in a sense, that's the, that's sort of a, uh, uh, you know, that is an essential thing that one would like to do in science. But it's, it's also, the, the important thing to realize that, that has not been, you know, is, is that science, if you just pick an arbitrary thing, you say, what's the answer to this question? That question may not be one that has a computationally reducible answer. That question, if you, if you choose, you know, if, if you walk along the series of questions and you've got one that's reducible and you get to another one that's nearby and it's reducible too.

• 21:50Stephen Wolfram?

  If you stick to that kind of, stick to the land, so to speak.

• 21:54Lex Fridman?

  Yeah.

• 21:54Stephen Wolfram?

  Then you can go down this chain of sort of reducible, answerable things. But if you just say, I'm just pick a question at random, I'm gonna have my computer pick a question at random.

• 22:04Lex Fridman?

  Yeah, most likely it's gonna be reducible.

• 22:06Stephen Wolfram?

  Most likely it will be reducible. And, and what we're throwing in the world, so to speak. Uh, we, you know, when we engineer things, we tend to engineer things to sort of keep in the zone of reducibility. When we're throwing things by the natural world, for example, not, not at all certain that we will be kept in this kind of zone of reducibility.

• 22:26Lex Fridman?

  Can we talk about this pandemic then?

• 22:28Stephen Wolfram?

  Sure.

• 22:30Lex Fridman?

  For a second? Is, uh, so how do we, there's obviously huge amount of economic pain that people are feeling. There's a huge incentive and medical pain, uh, health, just all psychological. There's a huge incentive to figure this out, to walk along the trajectory of reducible, of reducibility. Uh, there's, there's a, a lot of disparate data. You know, people understand generally how viruses spread, but it's very complicated because there's a lot of uncertainty, uh, there's a, uh, there could be a lot of variability, like so many, obviously a nearly infinite number of variables that, uh, that represent human interaction.

• 23:15Lex Fridman?

  And so you have to figure out, in terms, from the perspective of reducibility, figure out which variables are really important in this kind of, uh, from an epidemiological perspective. So why aren't we? You kind of said that we're clearly failing.

• 23:33Stephen Wolfram?

  Well, I think it's a complicated thing. So I mean, you know, when this pandemic started up, you know, I happened to be in the middle of being about to release this whole physics project thing. But I thought, you know.

• 23:43Lex Fridman?

  The timing is just cosmically absurd.

• 23:45Stephen Wolfram?

  A little bit bizarre, but you know, but I thought, you know, I should do the public service thing of, you know, trying to understand what I could about the pandemic. And, you know, we'd been curating data about it and all that kind of thing. But, but, you know, so I started looking at the data and started looking at modeling. And I decided it's just really hard. You need to know a lot of stuff that we don't know about human interactions. It's actually clear now that there's a lot of stuff we didn't know about viruses and about the way immunity works and so on. And it's, you know, I think what will come out in the end is there's a certain amount of of what happens that we just kind of have to trace each step and see what happens. There's a certain amount of stuff where there's going to be a big narrative about this happened because,

• 24:28Stephen Wolfram?

  you know, of T cell immunity. This happened because there's this whole giant sort of field of asymptomatic viral stuff out there. You know, there will be a narrative and that narrative, whenever there's a narrative, that's kind of a sign of reducibility. But when you just say, let's from first principles, figure out what's going on, then you can potentially be stuck in this kind of mess of irreducibility. We just have to simulate each step and you can't do that unless you know details about, you know, human interaction networks and so on and so on and so on. The thing that has has been very sort of frustrating to see is the mismatch between people's expectations about what science can deliver and what science can actually deliver, so to speak.

• 25:11Stephen Wolfram?

  Because people have this idea that, you know, it's science. So there must be a definite answer and we must be able to know that answer. And, you know, this is, it is both, you know, that when you've, after you've played around with sort of little programs in the computational universe, you don't have that intuition anymore. You know, it's, I was, I'm always fond of saying, you know, the computational animals are always smarter than you are. That is, you know, you look at one of these things and it's like, it can't possibly do such and such a thing. Then you run it and it's like, wait a minute, it's doing that thing. How does that work? Okay, now I can go back and understand it.

• 25:46Lex Fridman?

  But that's the brave thing about science is that in the chaos of the irreducible universe, we nevertheless persist to find those pockets. That's kind of the whole point. That's like you say that the limits of science, but that, you know, yes, it's highly limited, but there's a hope there. And like, there's so many questions I want to ask here. So one, you said narrative, which is really interesting. So obviously from a, at every level of society, you look at Twitter, everybody's constructing narratives about the pandemic, about not just the pandemic, but all the cultural tension that we're going through. So there's narratives, but they're not necessarily connected to

• 26:29Lex Fridman?

  the underlying reality of these systems. So our human narratives, I don't even know if they're,

• 26:40Lex Fridman?

  I don't like those pockets of reducibility because we're, it's like constructing things that are not actually representative of reality. Well, and thereby not giving us like good solutions to how to predict the system.

• 26:57Stephen Wolfram?

  Look, it gets complicated because, you know, people want to say, explain the pandemic to me, explain what's going to happen.

• 27:02Lex Fridman?

  In the future, like.

• 27:03Stephen Wolfram?

  Yes, but also can you explain it? Is there a story to tell?

• 27:07Lex Fridman?

  What already happened in the past?

• 27:09Stephen Wolfram?

  Yeah, or what's going to happen. But I mean, and, you know, it's similar to sort of explaining things in AI or in any computational system. It's like, like, you know, explain what happened. Well, it could just be this happened because of this detail and this detail and this detail and a million details. And there isn't a big story to tell. There's no kind of big arc of the story that says, oh, it's because, you know, there's a viral field that has these properties and people start showing symptoms. You know, when, when the seasons change, people will show symptoms and people don't even understand, you know, seasonal variation of flu, for example. It's a, it's a, it's something where, where, you know, that that could be a big story or it could be just a zillion little details that that mount up.

• 27:51Lex Fridman?

  See, but okay, let's, let's pretend that this pandemic, like the coronavirus, resembles something like the 1D rule 30 cellular automata. Okay, so I mean, that's how epidemiologists model virus spread.

• 28:09Stephen Wolfram?

  Indeed, yes. Sometimes use cellular automata, yes.

• 28:11Lex Fridman?

  Yeah, so, and okay, so you could say it's simplistic, but okay, let's say it is, it's representative of actually what happens. You know, the, the dynamic of you have a graph, it probably is closer to the hypergraph.

• 28:26Stephen Wolfram?

  It is, yes. It's actually, that's, that's another funny thing.

• 28:30Lex Fridman?

  Yeah.

• 28:30Stephen Wolfram?

  As, as we were getting ready to release this physics project, we realized that a bunch of things we'd worked out about, about foliations of causal graphs and things were directly relevant to thinking about contact tracing.

• 28:41Lex Fridman?

  Yeah.

• 28:41Stephen Wolfram?

  And interactions of cell phones and so on, which is really weird.

• 28:44Lex Fridman?

  But like, it just feels like, uh, it feels like we should be able to get some beautiful core insight about the spread of this particular virus on the hypergraph of human civilization. Right?

• 28:57Stephen Wolfram?

  I tried, I didn't, I didn't manage to figure it out.

• 29:00Lex Fridman?

  But you're one person.

• 29:01Stephen Wolfram?

  Yeah, but I mean, I think actually it's, it's a funny thing because it turns out the, um, the main model, you know, this SIR model, I, I only realized recently was invented by the, the grandfather of a good friend of mine from high school. So that was just a, you know, it's a weird thing, right? The question is, you know, okay, so you know, you know, on this graph of how humans are connected, you know, something about what happens if this happens and that happens. That graph is made in complicated ways that depends on, on all sorts of issues that, where we don't have the data about how human society works well enough to be able to make that graph. There's actually, uh, uh, one of my kids did a study of sort of what happens on different kinds of graphs and how robust are the results?

• 29:43Stephen Wolfram?

  Okay, his basic answer is there are few general results that you can get that are quite robust, like, you know, a small number of big gatherings is worse than a large number of small gatherings. Okay, that's quite robust. But when you ask more detailed questions, it seemed like it just depends. It depends on details. In other words, it's kind of telling you in that case, you know, the irreducibility matters, so to speak. It's not, there's not going to be this kind of one sort of master theorem that says, and therefore this is how things are going to work.

• 30:15Lex Fridman?

  Yeah, but there's a certain kind of, from a graph perspective. The certain kind of dynamic to human interaction. So like, large groups and small groups. I think it matters who the groups are. For example, you could imagine large, depends how you define large, but you can imagine groups of thirty people. As lo- like, as long as they are cliques or whatever.

• 30:39Stephen Wolfram?

  Right.

• 30:40Lex Fridman?

  As, as long as the outgoing degree of that graph is small or something like that. Like, you can imagine some beautiful underlying rule of

• 30:49Stephen Wolfram?

  Right.

• 30:49Lex Fridman?

  Human dynamic interaction where I can still be happy, where I can have a conversation with you and a bunch of other people that mean a lot to me in my life and then stay away from the bigger, I don't know, not going to a Miley Cyrus concert or something like that and, and figuring out mathematically some nice.

• 31:07Stephen Wolfram?

  See, this is an interesting thing. So I mean, in, you know, this is the question of what you're describing is kind of, uh, the problem of uh, the many situations where you would like to get away from computational irreducibility. A classic one in physics is thermodynamics. The, you know, the second law of thermodynamics, the law that says, you know, entropy tends to increase things that, you know, start orderly tend to get more disordered. Or, which is also the thing that says, given that you have a bunch of heat, it's hard, heat is, you know, the microscopic motion of molecules, it's hard to turn that heat into systematic mechanical work. It's hard to, you know, just take something being hot and turn that into, oh, the, the, you know, the, all the atoms are going to line up in the bar of metal and the piece of metal is going to shoot in some direction.

• 31:51Stephen Wolfram?

  That's essentially the same problem as how do you go from this, this computationally irreducible mess of things happening and get something you want out of it.

• 32:00Lex Fridman?

  That's right.

• 32:01Stephen Wolfram?

  It's kind of mining, you know, you're, you're kind of, now, you know, actually I've, I've understood in recent years that, that the story of, of thermodynamics is actually precisely a story of computational irreducibility. But it is a, um, it is already, uh, an analogy, you know, you can, you can kind of see that is can you take the, um, you know, what you're asking to do there is you're asking to go from the, um, uh, the kind of, um, the mess of all these complicated human interactions and all this kind of computational processes going on. And you say, I want to achieve this particular thing out of it. I want to kind of extract from the heat of what's happening. I want to kind of extract this useful piece of sort of mechanical work that I find helpful. I mean.

• 32:43Lex Fridman?

  Do you have a hope for the pandemic? So we'll talk about physics, but for the pandemic, can that be extracted? Do you think?

• 32:49Stephen Wolfram?

  Well, I think.

• 32:49Lex Fridman?

  What's your intuition?

• 32:50Stephen Wolfram?

  The the good news is the curves, basically, you know, for reasons we don't understand. The curves, you know, the the the clearly measurable mortality curves and so on for the northern hemisphere have gone down.

• 33:03Lex Fridman?

  Yeah, but the bad news is that it could be a lot worse for future viruses. And what this pandemic revealed is we're highly unprepared for the this discovery of the pockets of reducibility within a pandemic that's much more dangerous.

• 33:20Stephen Wolfram?

  Well, my my guess is the specific risk of, you know, viral pandemics, you know, that the pure virology and, you know, immunology of the thing. This will cause that to advance to the point where this particular risk is probably considerably mitigated. But, you know, it's, you know, does, is is the structure of modern society robust to all kinds of risks? Well, the answer is clearly no. And, you know, it's it's surprising to me the extent to which people. Uh, you know, as I say, it's it's it's a, it's kind of scary, actually, how much people believe in science. That is, people say, oh, you know, because the science says this, that and the other will do this and this and this, even though from a sort of common sense point of view, it's a little bit crazy.

• 34:06Stephen Wolfram?

  And and people are not prepared and it doesn't really work in in society as it is for people to say, well, actually, we don't really know how the science works. People say, well, tell us what to do.

• 34:16Lex Fridman?

  Yeah, because then, yeah, what's the alternative? The for the masses, it's difficult to sit. It's difficult to meditate on computational reducibility. It's difficult to sit.

• 34:27Stephen Wolfram?

  Right.

• 34:27Lex Fridman?

  To it's.

• 34:28Stephen Wolfram?

  No, you have to know what to do.

• 34:29Lex Fridman?

  Enjoy a good dinner meal while while knowing that you know nothing about the world.

• 34:33Stephen Wolfram?

  I think this is a, this is a place where, you know, this is, this is what politicians, you know, and political leaders do for a living, so to speak, because you got to make some decision about what to do. And it's some.

• 34:43Lex Fridman?

  Tell some narrative that, uh, while amidst the mystery and knowing not much about the the past or the future, still telling a narrative that somehow gives people hope that we know what the heck we're doing.

• 34:56Stephen Wolfram?

  Yeah, get society through the issue, you know, even even though, you know, the idea that we're just gonna, you know, sort of be able to get the definitive answer from science and it's gonna tell us exactly what to do. Unfortunately, you know, uh, that it it's interesting because let me point out that if that was possible, if science could always tell us what to do, then in a sense, our, you know, that would be a big downer for our lives. If science could always tell us what the answer is gonna be, it's like, well, you know, it's kind of fun to live one's life and just sort of see what happens. If one could always just say, let me, let me check my science. Oh, I know, you know, the result of everything is gonna be forty two. I don't need to live my life and do what I do. It's just, we already know the answer.

• 35:40Stephen Wolfram?

  It's actually good news in a sense that there is this phenomenon of computational irreducibility that doesn't allow you to just sort of jump through time and say, this is the answer, so to speak. Um, and that's, so that's a good thing. The bad thing is it doesn't allow you to jump through time and know what the answer is.

• 35:57Lex Fridman?

  It's scary. Do you think we're gonna be okay as a human civilization? You said, we don't know.

• 36:03Stephen Wolfram?

  Absolutely.

• 36:04Lex Fridman?

  Yeah. Do you think it's, do you think we'll prosper or destroy ourselves as a?

• 36:11Stephen Wolfram?

  In general?

• 36:12Lex Fridman?

  In general.

• 36:13Stephen Wolfram?

  I'm an optimist. The, no, I think that the, you know, it'll be interesting to see, for example, with this, you know, pandemic. I, you know, to me, uh, you know, when you look at like organizations, for example, you know, having some kind of perturbation, some kick to the system, usually the end result of that is actually quite good. You know, unless it kills the system, it's actually quite good usually. And I think in this case, you know, people, I mean, my impression, you know, it's it's a little weird for me because, you know, I've been a remote tech CEO for thirty years. It doesn't, you know, this is bizarrely, uh, you know, and the fact that, you know, like this coming to see you here is is

• 36:52Lex Fridman?

  One of the rare moments.

• 36:53Stephen Wolfram?

  Is the first time in six months that I've been like, you know, in a building other than my house. Okay, so, so, so, you know, uh, it's, I'm, I'm a kind of ridiculous outlier and these kinds of things.

• 37:04Lex Fridman?

  But overall, your sense is when you shake up the system and throw in chaos that you you uh, challenge the system, we humans emerge better.

• 37:15Stephen Wolfram?

  Seems to be that way. Who's to know? But I think that, you know, people, you know, my, my sort of vague impression is that people are sort of, you know, oh, what's actually important? You know, what's, what, what is worth caring about and so on? And that seems to be something that perhaps is, is more, you know, emergent in this kind of situation.

• 37:34Lex Fridman?

  It's so fascinating that on the individual level, we have our own complex cognition, we have consciousness, we have intelligence, we're trying to figure out little puzzles. And then that somehow creates this graph of collective intelligence, where we figure out, and then you throw in these viruses, of which there's millions of different, you know, this entire taxonomy, and the viruses are thrown into the system of collective human intelligence, and the little humans figure out what to do about it. We get like, we tweet stuff about information, there's doctors, there's conspiracy theorists, and then we play with different information. I mean, the whole of it is fascinating. I, I'm like

• 38:14Lex Fridman?

  you, also very optimistic, but there's a few, just, you said, the computational reducibility. There's always a fear of the darkness of the uncertainty before us. It's scary.

• 38:28Stephen Wolfram?

  I mean, the thing is, if you knew everything, it would be boring. And it would be, and, and then, and worse than boring, so to speak. It would be, you, it would reveal the pointlessness, so to speak. And in a sense, the, the fact that there is this computational reducibility, it's like, as we live our lives, so to speak, something is being achieved. We're computing what our lives, you know, you know, what happens in our lives.

• 38:54Lex Fridman?

  That's funny. So the, the computation reducibility is kind of like, it gives the meaning to life. It is the meaning of life. Computation reducibility is the meaning of life. There you go.

• 39:03Stephen Wolfram?

  It gives it meaning. Yes. I mean, it, it, it's what, it's what causes it to not be something where you can just say, you know, you went through all those steps to live your life, but we already knew what the answer was.

• 39:15Lex Fridman?

  Right.

• 39:16Stephen Wolfram?

  Hold on one second. I'm going to use my handy WolframAlpha sunburn computation thing, so long as I can get network here. There we go. Oh, actually, you know what? It says sunburn unlikely. This is a QA moment.

• 39:33Lex Fridman?

  This is a good moment. Okay.

• 39:34Stephen Wolfram?

  Okay, well, let me just check what it thinks. See why it thinks that. It doesn't seem like my intuition. This is one of these cases where we can. The question is, do we do? Do we trust the science or do we use common sense?

• 39:47Lex Fridman?

  Do you think it's cool?

• 39:49Stephen Wolfram?

  Yeah, yeah, well, we'll see. This is a QA moment, as I say. It's, do we trust the product? Yes, we trust the product, so.

• 39:57Lex Fridman?

  And then there'll be a data point either way.

• 39:59Stephen Wolfram?

  If if I'm desperately sunburned, I will send in a angry feedback.

• 40:04Lex Fridman?

  Because we mentioned the concept so much and a lot of people know it. But can you say what computation reducibility is?

• 40:12Stephen Wolfram?

  Yeah, right. So it's only the question is, if you think about things that happen as being computations, you think about the some process in physics, something that you compute in mathematics, whatever else, it's a computation in the sense it has definite rules. You follow those rules. You follow them many steps and you get some result. So then the issue is, if you look at all these different kinds of computations that can happen, whether they're computations that are happening in the natural world, whether they're happening in our brains, whether they're happening in our mathematics, whatever else, the big question is, how do these computations compare? Is are there dumb computations and smart computations? Or are they somehow all equivalent?

• 40:55Stephen Wolfram?

  And the thing that I kind of was sort of surprised to realize from a bunch of experiments that I did in the early 90s, and now we have tons more evidence for it. This thing I call the principle of computational equivalence, which basically says, when one of these computations, one of these processes that follows rules, doesn't seem like it's doing something obviously simple, then it has reached the sort of equivalent level of sophisticated computational sophistication of everything. So what does that mean? That means that, you know, you might say, gosh, I'm studying this little tiny, you know, tiny program on my computer. I'm studying this little thing in in nature, but I have my brain and my brain is surely much smarter than that thing. I'm going to be able to systematically outrun the computation that it does because I have

• 41:40Stephen Wolfram?

  a more sophisticated computation. That I can do, but what the principle of computational equivalence says is that doesn't work. Our, our brains are doing computations that are exactly equivalent to the kinds of computations that are being done in all these other sorts of systems. And so what consequences that have? Well, it means that we can't systematically outrun these systems. These systems are computationally irreducible in the sense that there's no sort of shortcut that we can make that jumps to the answer.

• 42:08Lex Fridman?

  In a general case.

• 42:09Stephen Wolfram?

  Right, right. But, but the, so what has happened, you know, what science has become used to doing is using the little sort of pockets of computational reducibility, which by the way are an inevitable consequence of computational irreducibility, that there have to be these pockets scattered around of computational reducibility to be able to find those particular cases where you can jump ahead. I mean, one, one thing, sort of a little bit of a parable type thing that I think is, is fun to tell you. And if you look at ancient Babylon, they were trying to predict three kinds of things. They tried to predict, you know, where the planets would be, what the weather would be like, and who would win or lose a certain battle. And they had no idea which of these things would be more predictable than the other.

• 42:54Lex Fridman?

  That's funny.

• 42:54Stephen Wolfram?

  And, and you know, it turns out, you know, where the planets are is a, is a piece of computational reducibility that, you know, three hundred years ago or so, we pretty much cracked. I mean, it's been technically difficult to get all the details right, but it's basically, we, we got that, you know, who's going to win or lose the battle? No, we didn't crack that one, that one, that one. Right.

• 43:15Lex Fridman?

  Game theorists are trying. And then the weather.

• 43:18Stephen Wolfram?

  It's kind of halfway on that.

• 43:20Lex Fridman?

  Halfway?

• 43:20Stephen Wolfram?

  Yeah, I think we're, we're doing okay at that one. I, you know, long term climate, different story, but, but the weather, you know, we're, we're much closer on that.

• 43:27Lex Fridman?

  But do you think eventually we'll figure out the weather? So do you think eventually most think we'll figure out the local pockets in everything? Essentially, the local pockets of reducibility?

• 43:37Stephen Wolfram?

  No, I think that the, it's a, it's an interesting question, but I think that the, you know, there is an infinite collection of these local pockets. We'll never run out of local pockets. And by the way, those local pockets are where we build engineering, for example. That's how. You know, when we, if we want to have a predictable life, so to speak, then, you know, we have to build in these sort of pockets of reducibility. Otherwise, you know, if we were, if we were sort of existing in this kind of irreducible world, we'd never be able to, you know, have definite things to know what's going to happen. You know, I, I have to say, I think one of the features, you know, when we look at a sort of today from the future, so to speak. I suspect one of the things where people will say, I can't believe they didn't see that

• 44:22Stephen Wolfram?

  is stuff to do with the following kind of thing. So, so, you know, if we describe, oh, I don't know, something like um, heat, for instance, we say, oh, you know, the air in, in here, it's, you know, it's this temperature, this pressure. That's as much as we can say. Otherwise, just a bunch of random molecules bouncing around. People will say, I just can't believe they didn't realize that there was all this detail and how all these molecules were bouncing around, and they could make use of that. And actually, I realized, there's a thing I realized last week, actually, was um, was a thing that people say, you know, one of the scenarios for the very long-term history of our universe is a so-called heat death of the universe, where basically, everything just becomes thermodynamically boring. Everything's just this big kind of gas and thermal equilibrium.

• 45:08Stephen Wolfram?

  People say, that's a really bad outcome. But actually, it's not a really bad outcome. It's an outcome where there's all this computation going on, and all those individual gas molecules are all bouncing around in very complicated ways, doing this very elaborate computation. It just happens to be a computation that, right now, we haven't found ways to understand. We haven't found ways, you know, our brains haven't, you know, and our mathematics and our science and so on, haven't found ways to tell an interesting story about that. It just looks boring to us.

• 45:37Lex Fridman?

  There's a, you're saying there's a hopeful view of the heat death? Quote unquote of the universe where there's actual beautiful complexity.

• 45:47Stephen Wolfram?

  Absolutely.

• 45:48Lex Fridman?

  Similar to the kind of complexity we think of. That creates rich experience in human life and life on earth.

• 45:55Stephen Wolfram?

  Yes.

• 45:56Lex Fridman?

  So those little molecules interact in complex ways that that could be intelligence in that there could be.

• 46:01Stephen Wolfram?

  Absolutely. I mean, this is this is what you learn.

• 46:03Lex Fridman?

  Wow, that's a hopeful message.

• 46:05Stephen Wolfram?

  Right. I mean, this is what you kind of learn from this principle of computational equivalence.

• 46:09Lex Fridman?

  Yeah.

• 46:09Stephen Wolfram?

  You learn it's both a a message of of sort of hope and a message of kind of. You know, there's you're not as special as you think you are, so to speak. I mean, because, you know, we. We imagine that with sort of all the things we do with with human intelligence and all that kind of thing. And all of the stuff we've constructed in science, it's like we're very special. But actually, it turns out, well, no, we're not. We're just doing computations like things in nature do computations like those gas molecules do computations like the weather does computations. The only the only thing about the computations that we do that's really special. Is that we understand what they are, so to speak. In other words, we have a, you know, to us, they're special because.

• 46:52Stephen Wolfram?

  Kind of they're connected to our purposes, our ways of thinking about things and so on. And that's some but so.

• 46:58Lex Fridman?

  That's very human centric. That's we're just attached to this kind of thing. So let's talk a little bit of physics. Maybe let's ask the the biggest question. What is a theory of everything? In general, what does that mean?

• 47:13Stephen Wolfram?

  Yeah. So I mean, the question is, can we kind of reduce what has been physics as a. Something where we have to sort of pick away and say, do we roughly know what how the world works? To something where we have a complete formal theory. Where we say, if we were to run this program for long enough, we would reproduce everything. You know, down to the fact that we're having this conversation at this moment, et cetera, et cetera, et cetera.

• 47:40Lex Fridman?

  Any physical phenomena, any phenomenon in this world.

• 47:42Stephen Wolfram?

  Any phenomenon in the universe.

• 47:44Lex Fridman?

  Yeah.

• 47:44Stephen Wolfram?

  But the, you know, because of computational irreducibility, it's not, you know, that's not something where you say, okay, you've got the fundamental theory of everything, then, you know, tell me whether, you know, uh, lions are going to eat tigers or something, you know, that's a, no, you have to run this thing for, you know, ten to the five hundred steps or something to know something like that. Okay? So at some moment, potentially, you say, this is a rule and run this rule enough times and you will get the whole universe. Right? That's, that's what it means to kind of have a fundamental theory of physics, as far as I'm concerned, is you've got this rule. It's potentially quite simple. We don't know for sure it's simple, but we have various reasons to believe it might be simple.

• 48:30Stephen Wolfram?

  And then you say, okay, I'm showing you this rule. You just run it only ten to the five hundred times and you'll get everything. In other words, you've, you've kind of reduced the problem of physics to a problem of mathematics, so to speak. It's like, it's as if, you know, you'd like, you generate the digits of pi. There's a definite procedure. You just generate them. And it'd be the same thing. If you have a fundamental theory of physics of the kind that, that I'm imagining, you, you know, you get a, this rule and you just run it out and you get everything that happens in the universe.

• 49:03Lex Fridman?

  So a theory of everything is a mathematical framework within which you can explain everything that happens in a universe, kind of in a unified way. It's not, there's a bunch of disparate modules of...

• 49:21Lex Fridman?

  Does it feel like if you create a rule, and we'll talk about the Wolfram physics model, which is fascinating, but if you, if you have a simple set of rules with a, with a data structure like a hypograph.

• 49:39Lex Fridman?

  Does that feel like a satisfying theory of everything? Because then you really run up against the irreducibility, computational irreducibility.

• 49:49Stephen Wolfram?

  Right, so that's a really interesting question. So I, I, you know, what I thought was gonna happen is I thought we, you know, I thought we had a pretty good, I had a pretty good idea for what the structure of this sort of theory that's sort of underneath space and time and so on might be like. And I thought, gosh, you know, in my lifetime, so to speak, we might be able to figure out what happens in the first 10 to the minus 100 seconds of the universe. And that would be cool, but it's pretty far away from anything that we can see today and it will be hard to test whether that's right and so on and so on and so on. To my huge surprise, although it should have been obvious, and it's embarrassing that it wasn't obvious to me, but, but to my huge surprise,

• 50:33Stephen Wolfram?

  we managed to get unbelievably much further than that. And basically what happened is that it turns out that even though there's this kind of bed of computational irreducibility that sort of these, all these simple rules run into, there is a, there are certain pieces of computational reducibility that quite generically occur for large classes of these rules. And, and this is the really exciting thing as far as I'm concerned, the, the, the big pieces of computational reducibility are basically the pillars of 20th century physics. That's the amazing thing, that general relativity and quantum field theory, the sort of, the pillars of 20th century physics turn out to be precisely the stuff you can say.

• 51:17Stephen Wolfram?

  There's a lot you can't say, there's a lot that's kind of at this irreducible level where you kind of don't know what's going to happen, you have to run it, you know, you can't run it within our universe, et cetera, et cetera, et cetera, et cetera, et cetera. But the thing is, there are things you can say, and the things you can say turn out to be, very beautifully, exactly the structure that was found in 20th century physics, namely general relativity and quantum mechanics.

• 51:41Lex Fridman?

  And general relativity and quantum mechanics are these pockets of reducibility that we think of as That 20th century physics is essentially pockets of reducibility. And then it is incredibly surprising that any kind of model that's generative from simple rules would have would have such pockets.

• 52:05Stephen Wolfram?

  Yeah, well, I think what's surprising is we didn't know where those things came from. It's like general relativity, it's a very nice mathematically elegant theory. Why is it true? You know, quantum mechanics, why is it true? What we realized is that from this, that they are, these theories are generic to a huge class of systems that have these particular, very unstructured underlying rules. And that's the, that's the thing that is sort of remarkable. And that's the thing to me, that's just, it's really beautiful. I mean, it's, and the thing that's even more beautiful is that it turns out that, you know, people have been struggling for a long time. You know, how does general relativity, theory of gravity relate to quantum mechanics? They seem to have all kinds of incompatibilities.

• 52:50Stephen Wolfram?

  It turns out what we realized is at some level, they are the same theory. And this is, it's, it's just great as far as I'm concerned.

• 52:58Lex Fridman?

  So maybe like taking a little step back from your perspective, not from the low, not from the beautiful hypergraph well, from physics model perspective, but from the perspective of 20th century physics, what is general relativity? What is quantum mechanics? How do you think about these two theories? From the context of the theory of everything? Like, is just even definitions?

• 53:23Stephen Wolfram?

  Yeah, yeah, yeah, right. So, so I mean, you know, a little bit of history of physics, right? So, so I mean, the, the, you know, okay, very, very quick history of physics, right? So, so I mean, you know, physics, you know, in ancient Greek times, people basically said, we can just figure out how the world works. As, you know, we're philosophers, we're going to figure out how the world works. You know, some philosophers thought there were atoms. Some philosophers thought there were, you know, continuous flows of things. People had different ideas about how the world works. And they tried to just say, we're going to construct this idea of how the world works. They didn't really have sort of notions of doing experiments and so on, quite the same way as developed. So that was sort of an early tradition for thinking about sort of models of the world.

• 54:04Stephen Wolfram?

  Then by the time of sixteen hundreds, time of Galileo and then Newton, sort of the big, the big idea there was, you know, you know, title of Newton's book, you know, Principia Mathematica, Mathematical Principles of Natural Philosophy. We can use mathematics to understand natural philosophy, to understand things about the way the world works. And so that then led to this kind of idea that, you know, we can write down a mathematical equation and have that represent how the world works. So Newton's, one of his most famous ones is his universal law of gravity, inverse square law of gravity, that allowed him to compute all sorts of features of, of the planets and so on, although some of them he got wrong and it was, took another hundred years for people to actually be able to do the math

• 54:47Stephen Wolfram?

  uh to the level that was needed. But, but, but so that, that had been, this sort of tradition was we write down these mathematical equations. We don't really know where these equations come from. We write them down. Then we figure out, we work out the consequences and we say, yes, that agrees with what we actually observe in astronomy or something like this. So that tradition continued. And then the first of these two sort of great twentieth century innovations was, well, the history is actually a little bit more complicated, but let's, let's say that the, the, the, the, there were two. Quantum mechanics and general relativity. Quantum mechanics, the kind of nineteen hundred was kind of the very early uh stuff done by Planck that led to the idea of photons, particles of light. Um but let's, let's take general relativity first.

• 55:32Stephen Wolfram?

  One, one feature of the story is that special relativity thing Einstein invented in nineteen oh five was something which surprisingly was a kind of logically invented theory. It was not a theory where, was something where, given these ideas that were sort of axiomatically thought to be true about the world, it followed that such and such a thing would be the case. It was a little bit different from the, the kind of methodological structure of some, of some existing theories in more, in the more recent times, or it's just been, we write down an equation and we find out that it works. So what happened there? So there's some reasoning about the light? The basic idea was, you know, the speed of light is, appears to be constant.

• 56:17Stephen Wolfram?

  Uh, you know, even if you're traveling very fast, you shine a flashlight, the light will come out. Even if you're going at half the speed of light, the light doesn't come out of your flashlight at one and a half times the speed of light. Um, it's still just the speed of light. And to make that work, you have to change your view of how space and time work. Um, to be able to account for the fact that when you're going faster, it appears that, you know, uh, length is foreshortened and time is dilated and things like this. And that's special relativity. That's special relativity. So then Einstein went on with sort of vaguely similar kinds of thinking. In nineteen fifteen, invented general relativity, which is a theory of gravity.

• 56:57Stephen Wolfram?

  And the basic point of general relativity is, is it's a theory that says when there is mass in space, space is curved. And what does that mean? You know, you, usually you think of, uh, what's the shortest distance between two points? Like in a, ordinarily in, on a plane in space, it's a straight line. You know, photons, light goes in straight lines. Well, then the question is, is if, if you have a curved surface, a straight line is no longer straight. On the surface of the earth, the shortest distance between two points is a great circle. It's a circle. Um, it's, uh, so, you know, Einstein's observation was maybe the physical, uh, structure of space

• 57:42Stephen Wolfram?

  is such that space is curved. So the shortest distance between two points, the, the path, the straight line in quotes, won't be straight anymore. And in particular, if a, if a photon is, is, you know, traveling near, near the sun or something, or if a particle is going, something is traveling near the sun, maybe the shortest path will be one that is, is, uh, is, is something which looks curved to us because it seems curved to us because space has been deformed by the presence of mass associated with that, that, uh, massive object. So, so the kind of the idea, uh, there is, um, think of the structure of space as being a dynamical, changing kind of thing. But then what Einstein did was he wrote down these differential equations that basically

• 58:25Stephen Wolfram?

  represented the curvature of space and its response to the presence of mass and energy.

• 58:30Lex Fridman?

  And that ultimately is connected to the force of gravity, which is one of the forces that seems to, based on a strength, operate on a different scale than some of the other forces. So it operates in a scale that's very large.

• 58:45Stephen Wolfram?

  What happens there is just this curvature of space, which causes, you know, the paths of objects to be deflected. That's what gravity does. It causes the paths of objects to be deflected. And this is an explanation for gravity, so to speak. And the surprise is that from 1915 until today, everything that we've measured about gravity precisely agrees with general relativity. And that's, and that, you know, it wasn't clear black holes were sort of a predict- well, actually, the expansion of the universe was an early potential prediction, although Einstein tried to sort of patch up his equations to make it not cause the universe to expand, because it was kind of so obvious the universe wasn't expanding. And, you know, it turns out it was expanding and he should have just trusted the equations.

• 59:29Stephen Wolfram?

  And that's a lesson for those of us interested in making fundamental theories of physics is you should trust your theory and not try and patch it because of something that you think might be the case, that might turn out not to be the case.

• 59:42Lex Fridman?

  Even if the theory says something crazy is happening?

• 59:45Stephen Wolfram?

  Yeah, right.

• 59:46Lex Fridman?

  Like the universe is expanding?

• 59:47Stephen Wolfram?

  Like the universe is expanding, right, which is, but, but, you know, then it took until the 1940s, probably even really until the 1960s, until people understood that black holes were a consequence of general relativity and so on. But that's, you know, the big surprise has been that so far, this theory of gravity has perfectly agreed with, you know, these collisions of black holes seen by the gravitational waves. You know, it all just works. So that's been kind of one pillar of the story of physics. It's mathematically complicated to work out the consequences of general relativity, but it's not, there's, there's no, I mean, and, and, and some things are kind of squiggly and complicated. Like people believe, you know, energy is conserved. Okay, well,

• 1:00:30Stephen Wolfram?

  energy conservation doesn't really work in general relativity in the same way as it ordinarily does. And it's all a big mathematical story of how you actually nail down something that is definitive, that you can talk about and not specific to the, you know, reference frames you're operating in and so on and so on and so on. But fundamentally, general relativity is a straight shot in the sense that you have this theory, you work out its consequences.

• 1:00:52Lex Fridman?

  And that that theory is useful in terms of basic science and trying to understand the way black holes work, the way the creation of galaxies work, sort of all of these kind of cosmological things, understanding what happened, like you said, at the Big Bang.

• 1:01:06Stephen Wolfram?

  Yeah.

• 1:01:06Lex Fridman?

  Like all those kinds of, well, no, not at the Big Bang, actually, right, but.

• 1:01:11Stephen Wolfram?

  Well, features of the expansion of the universe, yes. I mean, and there are, there are lots of details where we don't quite know how it's working, you know, is there, you know, where's the dark matter, is there dark energy, you know, et cetera, et cetera, et cetera. But, but fundamentally, the, the, you know, the testable features of general relativity, it all works very beautifully. And it's, it's in a sense, it is mathematically sophisticated, but it is not conceptually hard to understand in some sense.

• 1:01:34Lex Fridman?

  Okay, so that's general relativity. And what's its friendly neighbor? Like you said, there's two theories, quantum mechanics.

• 1:01:40Stephen Wolfram?

  Right. So quantum mechanics, the, the, the sort of, the way that that originated was, one question was, is the world continuous or is it discrete? You know, in ancient Greek times, people have been debating this. People debated it, you know, throughout history. Is light made of waves? Is it continuous? Is it discrete? Is it made of particles, corpuscles, whatever? You know, what had become clear in the 1800s is that atoms, that, you know, materials are made of discrete atoms. You know, when you take some water, the water is not a continuous fluid, even though it seems like a continuous fluid to us at our scale. But if you say, let's look at it smaller and smaller and smaller and smaller scale, eventually you get down to these,

• 1:02:21Stephen Wolfram?

  you know, these molecules and then atoms, it's made of discrete things. The question is sort of, how important is this discreteness? Just what's discrete, what's not discrete? Is energy discrete? Is, you know, is, what's discrete, what's not? And so.

• 1:02:35Lex Fridman?

  Does it have mass? Those kinds of questions?

• 1:02:38Stephen Wolfram?

  Yeah, yeah, right. Well, there's question, I mean, for example, is mass discrete is an interesting question, which is now something we can address. But, but, you know, what, what happened in the, in, in the, coming up to the 1920s, there was this kind of mathematical theory developed that could explain certain kinds of discreteness in, in particularly in, in features of atoms and so on. And. You know, what developed was this mathematical theory that was the theory, the theory of quantum mechanics, theory of wave functions, Schrodinger's equation, things like this. That's a mathematical theory that allows you to calculate lots of features of the microscopic world, lots of things about how atoms work, et cetera, et cetera, et cetera. Now, the calculations all work just great.

• 1:03:23Stephen Wolfram?

  The, um, uh, the question of what does it really mean is a complicated question. Now, I mean, to, to just explain a little bit historically, the, you know, the early calculations of things like atoms worked great in nineteen twenties, nineteen thirties and so on. There was always a problem, there were, uh, in quantum field theory, which is a theory of, uh, uh, in quantum mechanics, you're dealing with a certain number of at, a certain number of electrons, and you fix the number of electrons. You say, I'm dealing with a two-electron thing. Um, in quantum field theory, you allow for particles being created and destroyed. So you can emit a photon that didn't exist before, you can absorb a photon, things like that. That's a more complicated, mathematically complicated theory, and it had all kinds of mathematical issues and all kinds of infinities that cropped up.

• 1:04:07Stephen Wolfram?

  And it was finally figured out more or less how to get rid of those. But there were only certain ways of doing the calculations, and those didn't work for atomic nuclei, among other things. Um, and that led to a lot of developments up until the nineteen sixties of alternative ideas for how, how one could understand what was happening in atomic nuclei, et cetera, et cetera, et cetera. End result, in the end, the kind of most, quote, obvious mathematical structure of quantum field theory seems to work, although it's mathematically difficult to deal with. But you can calculate all kinds of things. You can calculate to, you know, a dozen decimal places, certain, certain things, you can measure them, it all works, it's all beautiful.

• 1:04:47Lex Fridman?

  The underlying fabric is, the model of that particular theory is fields, like you keep saying fields.

• 1:04:53Stephen Wolfram?

  Those are quantum fields. Those are different from classical fields. A field is something like you say, there's like you say, the temperature field in this room. It's like there is a value of temperature at every point around the room. That's some, or you can say the wind field would be the the vector direction of the wind at every point.

• 1:05:14Lex Fridman?

  It's continuous.

• 1:05:15Stephen Wolfram?

  Yes, and it's a, that's a classical field. The quantum field is a much more mathematically elaborate kind of thing. And I should explain that that one of the pictures of quantum mechanics that's really important is, you know, in classical physics, one believes that sort of definite things happen in the world. You pick up a ball, you throw it, the ball goes in a definite trajectory that's, that has certain equations of motion, it goes in a parabola, whatever else. In quantum mechanics, the picture is definite things don't happen. Instead, sort of what happens is this whole sort of structure of of all, you know, many different paths being followed. And we can calculate certain aspects of what happens, certain probabilities of different outcomes and so on.

• 1:05:58Stephen Wolfram?

  And you say, well, what really happened? What's really going on? What's the sort of, what's the underlying, you know, what's the underlying story? What, how do we, how do we turn this this mathematical theory that we can calculate things with into something that we can really understand and have a narrative about? And that's been really, really hard for quantum mechanics. My, my friend Dick Feynman always used to say, nobody understands quantum mechanics, even though he'd made his, you know, whole career out of calculating things about quantum mechanics. And, you know, so, so it's a little.

• 1:06:29Lex Fridman?

  But nevertheless, it's what the quantum field theory is very, very accurate at predicting a lot of the physical phenomena. So it works.

• 1:06:39Stephen Wolfram?

  Yeah, and but there are things about it, you know, it has certain, when we apply it, the standard model of particle physics, for example, we, you know, which we apply to calculate all kinds of things, it works really well. And you say, well, it has certain parameters, it has a whole bunch of parameters, actually. You say, why is the, you know, why does the muon particle exist? Why is it 206 times the mass of the electron? We don't know, no idea.

• 1:07:04Lex Fridman?

  But so the standard model of physics is is is one of the models that's very accurate for describing three, three of the fundamental forces of physics. And it's looking at the the world of the very small.

• 1:07:15Stephen Wolfram?

  Right.

• 1:07:16Lex Fridman?

  And then there's back to the neighbor of uh gravity, of general relativity. So and in the context of a theory of everything. What's traditionally the task of the unification of these theories?

• 1:07:32Stephen Wolfram?

  Well, I mean, the issue is you try to use the methods of quantum field theory to talk about gravity and it doesn't work, just like there are photons of light. So there are gravitons, which are sort of the particles of gravity. And when you try and compute sort of the properties of the of the particles of gravity, the kind of mathematical tricks that get used um in working things out in quantum field theory don't work. And um that's um so that's been a sort of fundamental issue. And when you think about black holes, which are a place where uh sort of the the the structure of space is um uh you know, has has sort of rapid variation and you get kind of quantum effects mixed in with effects from general relativity, things get very complicated

• 1:08:16Stephen Wolfram?

  and there are apparent paradoxes and things like that. And people have, you know, there have been a bunch of mathematical developments in in physics over the last, I don't know, thirty years or so, which have kind of picked away at those kinds of issues and got hints about how things might work. Um and but it hasn't been uh uh you know, and the other thing to realize is, as far as physics is concerned, it's just like, here's general relativity, here's quantum field theory, you know, be happy.

• 1:08:43Lex Fridman?

  Yeah, so do you think there's a quantization of gravity, of quantum gravity? What do you think of efforts that people have tried to? Yeah, what do you think in general of the efforts of the physics community to try to unify these laws?

• 1:08:57Stephen Wolfram?

  So I think what's it's interesting. I mean, I would have said something very different before what's happened with our physics project. Um, I mean, you know, the remarkable thing is what we've been able to do is to make from this very simple structure. Literally simple, underlying set of ideas. We've been able to build this, this, you know, very elaborate structure that's both very abstract and very sort of mathematically rich. And the big surprise, as far as I'm concerned, is that it touches many of the ideas that people have had. So in other words, things like string theory and so on, twister theory. It's like the, you know, we might have thought, I had thought, we're out on a prong. We're building something that's computational. It's completely different from what other people have done.

• 1:09:42Stephen Wolfram?

  But actually, it seems like what we've done is to provide essentially the machine code that, you know, these things are of various features of domain-specific languages, so to speak, that talk about various aspects of this machine code. And I think there's a, this is something that to me is, is, is very exciting because it allows one both for us to provide sort of a new foundation for what's been thought about there and for the, all the work that's been done in those areas to, you know, to give us, you know, more, more momentum to be able to figure out what's going on. Now, you know, people have sort of hoped, oh, we're just going to be able to get, you know, string theory to just answer everything. That hasn't worked out.

• 1:10:22Stephen Wolfram?

  And I think we now kind of can see a little bit about just sort of how far away certain kinds of things are from being able to explain things. Some things, one of the big surprises to me, actually, I literally just got a message about one aspect of this is, um, uh, the, uh, uh, you know, it's turning out to be easier. I mean, this project has been so much easier than I could ever imagine it would be. That is, I thought we would be, you know, just about able to understand the first 10 to minus 100 seconds of the universe. And, um, you know, it would be 100 years before we get much further than that. It's just turned out, it actually wasn't that hard. And we're not finished, but, you know.

• 1:11:00Lex Fridman?

  So you're, you're, you're seeing echoes of all the disparate theories of physics in this framework.

• 1:11:04Stephen Wolfram?

  Yes. Yes, I mean, it's a very interesting, you know, sort of history of science-like phenomenon. I mean, the best analogy that I can see is what happened with the early, early days of, of computability and computation theory. You know, Turing machines were invented in nineteen thirty-six. People sort of understand computation in terms of Turing machines, but actually, there had been pre-existing theories of computation, combinators, general recursive functions, lambda calculus, things like this. But people hadn't, those hadn't been concrete enough that people could really wrap their arms around them and understand what was going on. And I think what we're going to see in this case is that a bunch of these mathematical theories, including some very, and one of the things that's really interesting is, one

• 1:11:47Stephen Wolfram?

  of the most abstract things that's come out of, of sort of mathematics, higher category theory, things about infinity groupoids, things like this, which to me always just seemed like they were floating off into the stratosphere, ionosphere of mathematics, turn out to be things which our sort of theory anchors down to something fairly definite and says are super relevant to the way that we can understand how physics works.

• 1:12:16Lex Fridman?

  Give me a sec. By the way, I just threw a hat on. You've said that, um, with this metaphor analogy, that the theory of everything is a big mountain. And you have a sense that however far we are up the mountain, that the, the Wolfram Physics model, a view of the universe is at least the right mountain.

• 1:12:43Stephen Wolfram?

  We're the right mountain, yes, without question.

• 1:12:45Lex Fridman?

  So which aspect of it is the right mountain? So, for example, I mean, so there's so many aspects to just the way of the Wolfram Physics project, the way it approaches the world, that's, um, that's clean, crisp, and unique and powerful. So, you know, there's a, there's discreet nature to it, there's a hypograph, there's a computational nature, there's a generative aspect, you start from nothing, you generate everything.

• 1:13:15Lex Fridman?

  Which, do you think the actual model is actually a really good one? Or do you think this general principle of from simplicity generating complexity is the right? Like, what aspect of the mountain?

• 1:13:25Stephen Wolfram?

  Yeah, right. I, I think that the, the kind of the meta idea about using simple computational systems to do things, that's, you know, that's the ultimate big paradigm that is, you know, sort of super important. The details of the particular model are very nice and clean and allow one to actually understand what's going on. They are not unique. And in fact, we know that. We know that there's a, there's a large number of different ways to describe essentially the same thing. I mean, I can describe things in terms of hypergraphs. I can describe them in terms of higher category theory. I can describe them in a bunch of different ways. They are in some sense, all the same thing, but our sort of story about what's going on and, and the kind

• 1:14:08Stephen Wolfram?

  of, kind of cultural mathematical resonances are a bit different. And I think it's, it's, it's perhaps worth sort of saying a little bit about kind of the, the, you know, foundational ideas of, of, of, you know, of these, of these models and things.

• 1:14:22Lex Fridman?

  Great. So can you maybe, can we like rewind? We've talked about it a little bit, but can you say like what the central idea is of the Wolfram Physics project?

• 1:14:34Stephen Wolfram?

  Right. So, so the question is, we're interested in finding sort of simple computational rule that describes our whole universe.

• 1:14:41Lex Fridman?

  Can we just pause on that? It's just so beautiful. That's such a beautiful, that's such a beautiful idea, that we can generate our universe from a, from a, from a data structure, a simple structure, a simple set of rules, and we can generate our entire universe.

• 1:15:00Stephen Wolfram?

  Yes.

• 1:15:01Lex Fridman?

  That's awe inspiring.

• 1:15:02Stephen Wolfram?

  Right. But, but so, so, you know, the question is, how do you actualize that? What might this rule be like? And so one thing you quickly realize is, if you're going to pack everything about a universe into this tiny rule, not much that we are familiar with in our universe will be obvious in that rule. So you don't get to fit all these parameters of the universe, all these features of, you know, this is how space works, this is how time works, et cetera, et cetera, et cetera. You don't get to fit that all, and it all has to be sort of packed in to this, this thing, something much smaller, much more basic, much lower level machine code, so to speak, than that. And all the stuff that we're familiar with has to kind of emerge from the operation of.

• 1:15:43Lex Fridman?

  So the rule in itself, because of the computational reducibility, is not going to tell you the story. It's not going to give you the answer to, uh, it's not going to let you predict what you're going to have for lunch tomorrow. And it's not going to let you predict basically anything about your life, about the universe.

• 1:16:02Stephen Wolfram?

  Right, but, and you're not going to be able to see in that rule, oh, there's the three for the number of dimensions of space and so on.

• 1:16:08Lex Fridman?

  Right.

• 1:16:08Stephen Wolfram?

  That's not going to be the.

• 1:16:09Lex Fridman?

  Space-time is not going to be obviously.

• 1:16:12Stephen Wolfram?

  Right, so the question is then, what, what is the universe made of? That's, that's a, it's a basic question. And we've had some assumptions about what the universe is made of for the last few thousand years, that I think in some cases, it just turned out not to be right. And, you know, the most important assumption is that space is a continuous thing. That is, that you can, if you say, let's pick a point in space, we're going to do geometry, we're going to pick a point, we can pick a point absolutely anywhere in space. Precise numbers, we can specify of where that point is. In fact, you know, Euclid, who kind of wrote down the original kind of axiomatization of geometry, back in 300 B.C. or so, um, you know, his, his very first definition, he says, "A point is that which has no part."

• 1:16:58Stephen Wolfram?

  A point is this, is this, you know, uh, this indivisible, you know, infinitesimal thing. Okay, so we might have said that about material objects, we might have said that about water, for example. We might have said water is a continuous thing that we can just, uh, you know, pick any point we want in, in, in some water, but actually we know it isn't true. We know that water is made of molecules that are discrete. And so the question, one fundamental question is, what is space made of? And so one of the things that's sort of a starting point for what I've done is to think of space as a discrete thing. To think of there being sort of atoms of space, just as there are atoms of material things, although very different kinds of atoms.

• 1:17:40Stephen Wolfram?

  And by the way, I mean, this idea, you know, there were ancient Greek philosophers who had this idea. There were, you know, Einstein actually thought this is probably how things would work out. I mean, he said, you know, repeatedly, he thought that's the way it would work out. We don't have the mathematical tools in our time, which was nineteen forty's, nineteen fifty's and so on, to explore this.

• 1:17:59Lex Fridman?

  Like the way he thought, you mean that there is something very, very small and discrete that's underlying?

• 1:18:08Stephen Wolfram?

  Space.

• 1:18:09Lex Fridman?

  Space.

• 1:18:09Stephen Wolfram?

  Yes. And that that means that, so, you know, the mathematical theory, mathematical theories in physics assume that space can be described just as a continuous thing. You can just pick coordinates and the coordinates can have any values. And that's how you define space. Space is this just sort of background, uh, sort of theater on which the universe operates.

• 1:18:31Lex Fridman?

  But can we draw a distinction between space as a thing that could be described by, uh, three values, coordinates? And how you're, are you, are you using the word space more generally when you say?

• 1:18:46Stephen Wolfram?

  No, I'm, I'm just talking about space as in what we experience in, in, in the universe.

• 1:18:51Lex Fridman?

  So you think this three D aspect of it is fundamental?

• 1:18:55Stephen Wolfram?

  No, I don't think a three D is fundamental at all, actually. I think that the, what's the, the, the thing that has been assumed is that space is this continuous thing where you can just describe it by, let's say, three numbers, for instance. But most important thing about that is that you can describe it by precise numbers. Because you can pick any point in space and you can talk about motions, any infinitesimal motion in space.

• 1:19:19Lex Fridman?

  And that's what continuous means.

• 1:19:20Stephen Wolfram?

  That's what continuous means. That's what, you know, Newton invented calculus to describe these kind of continuous, small variations and so on. That was, that's kind of a fundamental idea from Euclid on. That's been a fundamental idea about space. And so.

• 1:19:33Lex Fridman?

  Is that right or wrong?

• 1:19:35Stephen Wolfram?

  It's not right. It's not right. It's right at the level of our experience, most of the time. It's not right at the level of the machine code, so to speak. And so

• 1:19:46Lex Fridman?

  Machine code? Yeah, of the simulation. That's right. That's right. The very lowest level of the fabric of the universe, at least under the the the Wolfram physics model, is your senses is discrete.

• 1:20:01Stephen Wolfram?

  Right. So now, what does that mean? So it means, what is space then? So in in our models, the basic idea is, you say, there are these sort of atoms of space. There are these points that represent, you know, represent places in space. But they're just discrete points. And the only thing we know about them is how they're connected to each other. We don't know where they are. They don't have coordinates. We don't get to say this is a position such and such. It's just, here's a big bag of points. Like in our universe, there might be 10 to the 100 of these points. And all we know is this point is connected to this other point. So it's like, you know, all we have is the friend network, so to speak. We don't, we don't have, you know, people's, you know, physical addresses.

• 1:20:46Stephen Wolfram?

  All we have is the friend network of these points.

• 1:20:49Lex Fridman?

  Yeah. The underlying nature of reality is kind of like a Facebook. We don't know their location, but we have the friends.

• 1:20:54Stephen Wolfram?

  Yeah, yeah, right. We know which point is connected to which other points. And and that's all we know. And so you might say, well, how on earth can you get something which is like our experience of, you know, what seems like continuous space? Well, the answer is, by the time you have 10 to the 100 of these things, there they those connections can work in such a way that on a large scale, it will seem to be like continuous space in, let's say, three dimensions or some other number of dimensions, or 2.6 dimensions, or whatever else.

• 1:21:25Lex Fridman?

  Because they're much, much, much, much larger. So like the Uh, the number of relationships here we're talking about is just a humongous amount. So the, the kind of thing you're talking about is very, very, very small relative to our experience of daily life.

• 1:21:40Stephen Wolfram?

  Right. So I mean, you know, we don't know exactly the size, but maybe, maybe uh, uh, ten to the minus, uh, maybe around ten to the minus one hundred meters. So, you know, the size of, to give a comparison, you know, size of a, of a proton is ten to the minus fifteen meters. And so this is something incredibly tiny compared to that.

• 1:21:59Lex Fridman?

  And, and the, the idea that from that would emerge the experience of continuous space is mind blowing. Well, what's your intuition? Why that's possible? Like, first of all, I mean, we'll get in, into it, but I don't know if we will through the medium of conversation. But the construct of hypographs is just beautiful.

• 1:22:23Stephen Wolfram?

  Right.

• 1:22:24Lex Fridman?

  Uh, cellular automaton are beautiful. We'll talk about it, but.

• 1:22:26Stephen Wolfram?

  Right. But, but, but this thing about, you know, continuity arising from discrete systems is in today's world is actually not so surprising. I mean, you know, your average computer screen, right? Every computer screen is made of discrete pixels. Yet we have the, you know, we have the idea that we're seeing these continuous pictures. I mean, it's, you know, the fact that on a large scale continuity can arise from lots of discrete elements. This is at some level unsurprising now.

• 1:22:53Lex Fridman?

  But whoa, whoa, whoa, whoa, wait. But the pixels have a, a very definitive structure of neighbors uh, on, on a computer screen.

• 1:23:03Stephen Wolfram?

  Right.

• 1:23:04Lex Fridman?

  There is no concept of spatial, of space inherent in the underlying fabric of reality.

• 1:23:13Stephen Wolfram?

  Right, right, right. So, so the, the, the point is, but there are cases where there are. So for example, let's just imagine you have a square grid. Okay. And at every point on the grid, you have one of these atoms of space. And it's connected to four other, four other atoms of space on the, you know, northeast, southwest corners, right? Um, there you have something where if you zoom out from that, it's like a computer screen.

• 1:23:36Lex Fridman?

  Yeah. So the relationship creates the, the spatial, like the relationship creates a constraint.

• 1:23:44Lex Fridman?

  Which then in an emergent sense creates a like, yeah, like a uh basically a spatial coordinate.

• 1:23:54Stephen Wolfram?

  Yes.

• 1:23:54Lex Fridman?

  That thing.

• 1:23:55Stephen Wolfram?

  Yeah, right.

• 1:23:55Lex Fridman?

  Even though the individual point doesn't have a spatial.

• 1:23:58Stephen Wolfram?

  Even though the individual point doesn't know anything, it just knows what its, you know, what its neighbors are. They, on a large scale, it can be described by saying, oh, it looks like it's a, you know, this grid, zoomed out grid. You can say, well, you can describe these different points by saying they have certain positions, coordinates, et cetera. Now, in the, in the sort of real setup, it's more complicated than that. It isn't just a square grid or something. It's something much more dynamic and complicated, which we'll talk about. But um, uh, so, you know, first, the first idea, the first key idea is, you know, what's the universe made of? It's made of atoms of space, basically, with these connections between them. What kind of connections do they have? Well, so a, the simplest kind of thing you might say is we've got something like a graph

• 1:24:42Stephen Wolfram?

  where every, uh, every atom of space, uh, where, where we have these edges that go between atoms, these connections that go between atoms of space. We're not saying how long these edges are, we're just saying there is a connection from, from this place to the, from this atom to this atom.

• 1:24:56Lex Fridman?

  Just a quick pause, cause there's a lot of varied people that listen to this. Just to clarify, cause I did a poll, actually, what do you think a graph is a long time ago? And it's kind of funny how few people know the term graph, uh, outside of computer science.

• 1:25:13Stephen Wolfram?

  So it's. Let's call it a network. I think.

• 1:25:15Lex Fridman?

  Let's call it a network is better. So, but every time, I like the word graph though, so let's define, let's just say that a gra- graph. We'll use terms nodes and edges maybe, and it's just the nodes represent some abstract entity and then the edges represent relationships between those entities.

• 1:25:32Stephen Wolfram?

  Right, exactly.

• 1:25:33Lex Fridman?

  So that's what a graph, sorry. So, so there you go. So that's the basic structure.

• 1:25:38Stephen Wolfram?

  That is, that is the simplest case of a basic structure. Actually, uh, it tends to be better to think about hypergraphs. Uh, so a hypergraph is just, instead of saying, uh, there are connections between pairs of things, we say there are connections between any. Number of things, so there might be ternary edges. So instead of instead of just having two points are connected by an edge, you say three points are all associated with a hyperedge, are all connected by a hyperedge. That's just, at some level, that's, at some level, that's a detail. It's a detail that happens to make the, for me, you know, sort of in the history of this project, the realization that you could do things that way,

• 1:26:19Stephen Wolfram?

  broke out of certain kinds of arbitrariness that I felt that there was in the model before I had seen how this worked.

• 1:26:25Lex Fridman?

  I mean, all, a hypergraph can be mapped to a graph. It's just a convenient representation mathematically.

• 1:26:32Stephen Wolfram?

  Right, that's correct, that's correct. But so then, so, okay, so the, the first question, the first idea of these models of ours is space is made of these, you know, connected sort of atoms of space. The next idea is, space is all there is. There's nothing except for this space. So in traditional ideas in physics, people have said, the space, it's kind of a background, and then there's matter, all these particles, electrons, all these other things, which exist in space, right? But in this model, one of the key ideas is, there's nothing except space. So in other words, everything that has, that exists in the universe is a feature of this hypergraph. So how can that possibly be? Well, the way that works is that there are certain

• 1:27:17Stephen Wolfram?

  structures in this hypergraph where you say, that little twisty knotted thing, we don't know exactly how this works yet, but, but we, we have sort of idea about how it works mathematically. This sort of twisted knotted thing, that's the core of an electron. This thing over there, that has this different form, that's something else.

• 1:27:36Lex Fridman?

  So the different peculiarities of the structure of this graph are the very things that we think of as the particles inside the space, but in fact, it's just a property of the space. Mind blowing, first of all, that. It's mind blowing, and we'll probably talk in its simplicity and beauty.

• 1:27:56Stephen Wolfram?

  Yes, I think it's very beautiful. I mean, this is I'm.

• 1:27:58Lex Fridman?

  But okay, so that but that's space. And then there's another concept we didn't really kind of mention. But you think of computation as a like a transformation.

• 1:28:08Stephen Wolfram?

  Let's talk about time in a second. Let's let's just let's just, I mean, on the subject of space that, you know, there's this question of kind of what? You know, there's this idea, there is this hypergraph. It represents space and it represents everything that's in space. The features of that hypergraph. You can say certain features in this part, we do know. Certain features of the hypergraph represent the presence of energy, for example, or the presence of mass or momentum. And we know what the features of the hypergraph that represent those things are. But it's all just the same hypergraph. So one thing you might ask is, you know, if you just look at this hypergraph and you say, and we're going to talk about sort of what the hypergraph does. But if you say, you know, how much of what's going on in this hypergraph is?

• 1:28:49Stephen Wolfram?

  Things we know and care about, like particles and atoms and electrons and all this kind of thing. And how much is just the background of space? So it turns out so far as in one rough estimate of this. Or everything that we care about in the universe is only one part in 10 to the 120 of what's actually going on. The vast majority of what's happening is purely things that maintain the structure of space. That in other words, that the things that are the features of space. That are the things that we consider notable, like the presence of particles and so on. That's a tiny little piece of froth on the top of all this activity. That mostly is just intended to, you know, mostly I can't say intended.

• 1:29:32Stephen Wolfram?

  There's no intention here that just maintains the structure of space.

• 1:29:37Lex Fridman?

  Let me let me load that in. It's a it just makes me feel so good as a human being. Well, to be the froth on the one in the 10 to the.

• 1:29:48Stephen Wolfram?

  120 or something of well.

• 1:29:50Lex Fridman?

  And also just humbling. Um, how in this mathematical framework? How much work needs to be done on the infrastructure?

• 1:30:00Stephen Wolfram?

  Right, yes.

• 1:30:01Lex Fridman?

  Our universe.

• 1:30:02Stephen Wolfram?

  Right, to maintain the infrastructure of our universe is a lot of work. We are we are merely writing a little tiny things on top of that infrastructure. But. But you know, you were just starting to talk a little bit about, you know, we talked about, you know, space that represents all the stuff that's in the universe. The question is, what does that stuff do? And for that, we have to start talking about time and what is time and so on. And, you know, one of the, the basic idea of this model is time is the progression of computation. So in other words, we have a, a structure of space. And there is a rule that says how that structure of space will change.

• 1:30:42Stephen Wolfram?

  And it's the application, the repeated application of that rule that defines the progress of time.

• 1:30:49Lex Fridman?

  And what does the rule look like in a, in a space of hypergraph?

• 1:30:53Stephen Wolfram?

  Right. So what the rule says is something like, if you have a little tiny piece of hypergraph that looks like this, then it will be transformed into a piece of hypergraph that looks like this. So that's all it says. It says you pick up these elements of space. And you can think of these, these edges, these hyper edges as being relations between elements in space. You might pick up these two relations between elements in space. And we're not saying where those elements are or what they are, but every time there's a certain arrangement of elements in space, then arrangement in the sense of the way they're connected, then we transform it into some other arrangement.

• 1:31:32Lex Fridman?

  So there's a little tiny pattern and you transform it into another little pattern?

• 1:31:36Stephen Wolfram?

  That's right.

• 1:31:36Lex Fridman?

  And then because of this, I mean, again, it's kind of similar to cellular automaton that like,

• 1:31:41Stephen Wolfram?

  Yes.

• 1:31:42Lex Fridman?

  on paper, the rule looks like super simple. It's like, uh, yeah, okay.

• 1:31:48Lex Fridman?

  Yeah, like, yeah, right. From this, the universe can be born. Uh, but like, once you start applying it, beautiful structure starts being, potentially can be created. And what you're doing is you're applying that rule to different parts. Like anytime you match it within the hypergraph.

• 1:32:06Stephen Wolfram?

  Exactly.

• 1:32:06Lex Fridman?

  And then one of the like incredibly beautiful and interesting things to think about is the order in which you apply that rule.

• 1:32:16Stephen Wolfram?

  Yes.

• 1:32:16Lex Fridman?

  Because that pattern appears all over the place.

• 1:32:19Stephen Wolfram?

  Right, so this is a big, complicated thing, very hard to wrap one's brain around. Okay, so, so you, you say, the rule is, every time you see this little pattern, transform it in this way. But yet, you know, as you look around the space that represents the universe, there may be zillions of places where that little pattern occurs. So, so what, what, what it says is, just do this, apply this rule wherever you feel like. And what, what is extremely non-trivial is, well, okay, so, so this is happening sort of in, in computer science terms, sort of asynchronously, you're just doing it wherever, wherever you feel like doing it. And the only constraint is, that if you're going to apply the rule somewhere,

• 1:33:01Stephen Wolfram?

  the, the things to which you apply the rule, the, the little, you know, elements to which you apply the rule, if they, if they have to be, okay, well, you can think of each application of the rule as being kind of an event that happens in the universe.

• 1:33:16Lex Fridman?

  Yep.

• 1:33:17Stephen Wolfram?

  And these, the input to an event has to be ready for the event to occur. That is, if one event occurred, if one transformation occurred, and it produced a particular atom of space, then that atom of space has to already exist before another transformation that's going to apply to that atom of space can occur.

• 1:33:40Lex Fridman?

  Yeah, so that's like the prerequisite for the event.

• 1:33:43Stephen Wolfram?

  That's right, that's right. So it, it, that defines a kind of, uh, this sort of set of causal relationships between events. It says, this event happens, has to have happened before this event. But that is, um...

• 1:33:57Lex Fridman?

  But that's, that's not a very limiting constraint.

• 1:34:00Stephen Wolfram?

  No, it's not. And what's interesting-

• 1:34:02Lex Fridman?

  You still get the zillion, uh, that's a technical term, options.

• 1:34:07Stephen Wolfram?

  That's correct. But, but, okay, so this, this is where things get a little bit more elaborate, but-

• 1:34:12Lex Fridman?

  But they're mind-blowing, so...

• 1:34:14Stephen Wolfram?

  Right, but so, so what, what, what happens is, so the first thing you might say is, you know, let's, well, okay, so, so this question about the freedom of which, which event you do when, well, let me, let me sort of state an answer and then explain it, okay? The, the, um, the validity of special relativity is a consequence of the fact that in some sense, it doesn't matter in what order you do these underlying things, so long as they respect this kind of set of causal relationships.

• 1:34:42Lex Fridman?

  And that's, that's a, in a, the, the part that's in a certain sense is a really important one, but the fact that it, it sometimes doesn't matter, that's a, I don't know, that's another like beautiful thing.

• 1:34:56Stephen Wolfram?

  So, so there's this idea of what I call causal invariance.

• 1:35:00Lex Fridman?

  Causal invariance, exactly.

• 1:35:01Stephen Wolfram?

  So, so that's a-

• 1:35:02Lex Fridman?

  Really, really powerful, powerful idea.

• 1:35:04Stephen Wolfram?

  Powerful idea, which has actually arisen in different forms many times in the history of mathematics, mathematical logic, even computer science, has many different names. Um, I mean, our particular version of it is a little bit tighter than other versions, but it's basically the same idea. Here's, here's how to think about that idea. So imagine that, well, let's talk about it in terms of math for a second. Let's say you're doing algebra and you're told, you know, multiply out this series of polynomials that are, that are multiplied together, okay? You say, well, which order should I do that in? Say, well, do I multiply the third one by the fourth one and then do it by the first one? Or do I do the fifth one by the sixth one and then do that? Well, it turns out it doesn't matter. You can, you can multiply them out in any order, you'll always get the same answer.

• 1:35:49Stephen Wolfram?

  That's a, that's a, a property, if you think about kind of making a kind of network that represents in what order you do things, you'll get different orders for different ways of multiplying things out, but you'll always get the same answer. Same thing if you, let's say you're sorting, you've got a bunch of As and Bs, they're in random, some random order, you know, BAA, BBBAA, whatever. And you have a little rule that says every time you see BA, flip it around to AB, okay? Eventually, you apply that rule enough times, you'll have sorted the string so that it's all the As first and then all the Bs. Again, you, there are many different orders in which you can do that, that, many different sort of places

• 1:36:30Stephen Wolfram?

  where you can apply that update. In the end, you'll always get the string sorted the same way.

• 1:36:36Lex Fridman?

  I know, I know with sorting a string, it's, it sounds obvious. That's to me surprising. That that there is in complicated systems, obviously with a string, but in a hypergraph that the application of the rule asynchronous rule can lead to the same results sometimes.

• 1:36:54Stephen Wolfram?

  Yes, yes, that is, it is not obvious. And it was something that, you know, I, I sort of discovered that idea for these kinds of systems and back in the 1990s. And for various reasons, I, I, I was not, I was not satisfied by how sort of fragile finding that particular property was. And let me, let me just make another point, which is that, that it turns out that even if the underlying rule does not have this property of causal invariance, it can turn out that every observation made by observers of the rule can, they can impose what amounts to causal invariance on the rule. We can explain that. It's a little bit more complicated. I mean, technically that has to do with this idea of completions, which

• 1:37:36Stephen Wolfram?

  is something that comes up in term rewriting systems, automated theorem proving systems and so on. But that, let's, let's ignore that for a second. We can come to that later.

• 1:37:45Lex Fridman?

  Is it useful to talk about observation?

• 1:37:47Stephen Wolfram?

  Not yet, not yet.

• 1:37:49Lex Fridman?

  Okay, so great. So there's some concept of causal invariance as you apply these rules and in asynchronous way, you can think of those transformations as events. So there's this hypergraph that represents space and all of these events happening in the space and the graph grows in interesting complicated ways. And eventually the farth arises to of what we experience as human existence. So

• 1:38:13Stephen Wolfram?

  That's, that's, that's some version of the picture, but, but let's explain a little bit more.

• 1:38:18Lex Fridman?

  Exactly. What's a little, a little more detail like?

• 1:38:21Stephen Wolfram?

  Right. Well, so, so one thing that is sort of surprising in this, in this theory is one of the sort of achievements of 20th century physics was kind of bringing space and time together. That was, you know, special relativity, people talk about spacetime, this sort of unified thing where space and time kind of are mixed. And there's a nice mathematical formalism that in which, you know, space and time sort of appear as part of the spacetime continuum, the spacetime, you know, four vectors and things like this. Um, you know, we talk about time as the fourth dimension and all these kinds of things. It's, you know, and it seems like the theory of relativity sort of says space and time are fundamentally the same kind of thing.

• 1:39:03Stephen Wolfram?

  So one of the things that took a while to understand in this approach of mine is that in my kind of approach, space and time are really not fundamentally the same kind of thing. Space is the extension of this hypergraph. Time is the kind of progress of this inexorable computation of these rules getting applied to the hypergraph. So it's, they seem like very different kinds of things. And so that at first seems like, how can that possibly be right? How can that possibly be Lorentz invariant? That's the term for things being, you know, following the rules of special relativity. Well, it turns out that when you have causal invariance, that, and let's see, we can, it's worth, it's worth explaining a little bit how this works.

• 1:39:48Stephen Wolfram?

  It's a little bit, little bit elaborate, but, but the basic point is that the, even though space and time sort of come from very different places, it turns out that the rules of sort of space-time that special relativity talks about come out of this model when you're looking at large enough systems. So, so a way to think about this, you know, in terms of the, when you're looking at large enough systems,

• 1:40:17Stephen Wolfram?

  the part of that story is when you look at some fluid like water, for example, there are equations that govern the flow of water. Those equations are the things that apply on a large scale. If you look at the individual molecules, they don't know anything about those equations. It's just the, the, the sort of the large scale effect of those molecules turns out to follow those equations. And it's the same kind of thing happening in our models.

• 1:40:43Lex Fridman?

  I know this might be a small point, but it may be a very big one. We've been talking about space and time at the lowest level of the model, which is space, the hypergraph, time is the evolution of this hypergraph. But there's also space-time that we think about in general relativity, for special relativity.

• 1:41:04Lex Fridman?

  Like what, how does, how do you go from the lowest source code of space and time we're talking about to the more traditional terminology of space and time?

• 1:41:16Stephen Wolfram?

  Yeah, right. So the key thing is this thing we call the causal graph. So the causal graph is the graph of causal relationships between events. So every one of these little updating events, every one of these little transformations of the hypergraph, happens, somewhere in the hypergraph, happens at some stage in the computation. That's an event. That event is, has a causal relationship to other events, in the sense that if the, if another event needs as its input, the output from the first event, there will be a causal relationship of the, the, the future event will depend on the past event. So you can say, it's, it has a causal connection. And so you can make this graph of causal relationships between events.

• 1:42:00Stephen Wolfram?

  That graph of causal relationships, causal invariance implies that that graph is unique. It doesn't matter, even though you think, oh, I'm, I'm, you know, let's say we were sorting a string, for example, I did that particular transposition of, of characters at this time, and then I did that one, then I did this one. Turns out if you look at the network of, of connections between those updating events, that network is the same. It's, it's the, if, if you were to

• 1:42:26Lex Fridman?

  I see.

• 1:42:27Stephen Wolfram?

  The, the, the structure, so in other words, if you were to draw that, that, if you were to put that network on a picture of where you're doing all the updating, the places where you put the, the nodes of the network will be different, but the way the nodes are connected will always be the same.

• 1:42:41Lex Fridman?

  So, but the causal graph is a, is, I don't, it's kind of an observa, it, it's not a enforced, it's just emergent from a set of events.

• 1:42:51Stephen Wolfram?

  Well, it's a, it's a feature of, of, okay, so what it is

• 1:42:53Lex Fridman?

  The characteristic, I guess, of the way events happen.

• 1:42:56Stephen Wolfram?

  Right, it's, an event can't happen until its input is ready.

• 1:42:59Lex Fridman?

  Right.

• 1:43:00Stephen Wolfram?

  And so that creates this, this network of causal relationships, and that's, that's the causal graph. And the thing, the, the next thing to realize is, okay, we, when you're going to observe what happens in the universe, you have to sort of make sense of this causal graph. So, and you are an observer who yourself is part of this causal graph. And so that means, so let me give you an example of how that works. So, so imagine we have a really weird theory of physics of the world where it says that this updating process, there's only going to be one updated every moment in time. And there's just going to be like a touring machine that has a little head that runs around and just is always just updating one thing at a time. So you say, you know, I have a theory of physics and the theory of physics says

• 1:43:45Stephen Wolfram?

  there's just this one little place where things get updated. You say that's completely crazy because, you know, it's plainly obvious that things are being updated sort of, you know.

• 1:43:54Lex Fridman?

  Synchronously, yeah.

• 1:43:55Stephen Wolfram?

  Right, but, but, but, but the fact is that the thing is that if I'm, you know, talking to you and you seem to be being updated as I'm being updated. But, but if there's just this one little head that's running around updating things, I will not know whether you've been updated or not until I'm updated. So in other words.

• 1:44:13Lex Fridman?

  Right.

• 1:44:14Stephen Wolfram?

  Draw this causal graph of the causal relationship between the updating's in you and the updating's in me, it'll still be the same causal graph. Whether even though the underlying sort of story of what happens is, oh, there's just this one little thing and it goes and updates in different places in the universe. So.

• 1:44:30Lex Fridman?

  Is that, is that clear or is that a hypothesis? Is that, is that clear that there's a unique causal graph?

• 1:44:39Stephen Wolfram?

  If there's causal invariance, there's a unique causal graph.

• 1:44:42Lex Fridman?

  So it's okay to think of what we're talking about as a hypergraph and the operations on it as a kind of touring machine with a single head, like a single guy running around updating stuff.

• 1:44:53Stephen Wolfram?

  Um.

• 1:44:54Lex Fridman?

  Is that safe to intuitively think of it this way?

• 1:44:57Stephen Wolfram?

  Um, let me think about that for a second. Yes, I think so. I think that, I think there's nothing, it doesn't matter. I mean, you, you can, you can say, okay, there is one, the, the reason I'm pausing for a second is that, um, I'm wondering, well, when you say running around.

• 1:45:13Stephen Wolfram?

  Depends how far it jumps every time it runs.

• 1:45:15Lex Fridman?

  Yeah, yeah, that's right. But I mean, like, one operation.

• 1:45:19Stephen Wolfram?

  Yeah, you can think of it as one operation.

• 1:45:21Lex Fridman?

  It's easier for the human brain to think of it that way as opposed to simultaneous.

• 1:45:26Stephen Wolfram?

  Well, maybe. It's not. Okay, but the thing is, that's not how we experience the world. What we experience is, we look around, everything seems to be happening at successive moments in time everywhere in space.

• 1:45:38Lex Fridman?

  Yes.

• 1:45:38Stephen Wolfram?

  That is, and that's partly a feature of our particular construction. I mean, that is, the speed of light is really fast compared to, you know, we look around, you know, I can see maybe a hundred feet away right now. You know, it's, the, my brain does not process very much in the time it takes light to go a hundred feet.

• 1:45:59Lex Fridman?

  The brain operates at a scale of hundreds of milliseconds or something like that. I don't know.

• 1:46:03Stephen Wolfram?

  Right.

• 1:46:03Lex Fridman?

  And, and the speed of light is much faster.

• 1:46:05Stephen Wolfram?

  Right. You know, light goes, in a billionth of a second, light has gone a foot. So it goes a billion feet every second.

• 1:46:11Lex Fridman?

  There's certain moments through this conversation where I, I imagine the absurdity of the fact that there's two descendants of apes modeled by a hypergraph that are communicating with each other and experiencing this whole thing as a real-time simultaneous update with, I'm taking in photons from you right now, but there's something much, much deeper going on.

• 1:46:36Stephen Wolfram?

  Right.

• 1:46:36Lex Fridman?

  Here.

• 1:46:36Stephen Wolfram?

  It, it does have a.

• 1:46:37Lex Fridman?

  It's paralyzing sometimes to just.

• 1:46:40Stephen Wolfram?

  Yes.

• 1:46:40Lex Fridman?

  To remember that.

• 1:46:41Stephen Wolfram?

  Right. No, I mean, you know, but, but, you know, yes, yes.

• 1:46:45Lex Fridman?

  As a small, little tangent, I just remembered that we're talking about, I mean, this, about the fabric of reality.

• 1:46:54Stephen Wolfram?

  Right. So we've, we've got this causal graph that represents the sort of causal relationships between all these events in the universe.

• 1:47:01Lex Fridman?

  Yeah.

• 1:47:01Stephen Wolfram?

  That causal graph kind of is a representation of space-time, but our experience of it requires that we pick reference frames. This is kind of a key idea. Einstein had this idea. That what that means is, we have to say, what are we going to pick as being the, sort of what we define as simultaneous moments in time?

• 1:47:25Stephen Wolfram?

  So for example, we can say, um, you know, we, we, how do we set our clocks? You know, if we've got a spacecraft landing on Mars, you know, do we say that it, you know, what, what time is it landing at? Was it, you know, even though there's a 20 minute speed of light delay or something, you know, what time do we say it landed at? How do we, how do we set up sort of time coordinates for, for the world? And that turns out to be that there's kind of this arbitrariness to how we set these reference frames that define sort of what counts as simultaneous. And what is the, the essence of special relativity is to think about reference frames going at different speeds and to think about sort of how they assign what counts as space, what counts as time and so on.

• 1:48:09Stephen Wolfram?

  Um, that's all a bit technical, but the basic bottom line is that the, this causal invariance property that means that it's always the same causal graph, independent of how you slice it with these reference frames, you'll always sort of see the same physical processes go on. And that's basically why special relativity works.

• 1:48:27Lex Fridman?

  So there's something like special relativity, uh, like everything around space and time that, uh, that fits this idea of the causal graph.

• 1:48:40Stephen Wolfram?

  Right, well, you know, one way to think about it is given that you have a, a basic structure that just involves updating things in, in these, you know, connected updates and looking at the causal relationships between connected updates, that's enough. When you unravel the consequences of that, that together with the fact that there are lots of these things and that you can take a continuum limit and so on, implies special relativity. And, um, so that, uh, it's kind of a, not a big deal because it's kind of a, it's kind of a, you know, it was completely unobvious when you started off with saying, we've got this graph, it's being updated in time, et cetera, et cetera, et cetera. That just looks like nothing to do with special relativity. And yet you get that.

• 1:49:22Stephen Wolfram?

  And, and what, I mean, then the thing, I mean, this was stuff that I figured out back in the 1990s. The, um, the, the next big thing you get is general relativity. Um, and so the, in this hypergraph, the, this sort of limiting structure, when you have a very big hypergraph, you can think of as being just like, you know, water seems continuous on a large scale. So this hypergraph seems continuous on a large scale. One question is, you know, how many dimensions of space does it correspond to? So one question you can ask is if you've just got a bunch of points and they're connected together, how do you deduce what effective dimension of space that bundle of points corresponds to? And that's, that's pretty easy to explain.

• 1:50:05Stephen Wolfram?

  So basically, if you say you've got a point and you look at how many neighbors does that point have? Okay, imagine it's on a square grid, then it'll have four neighbors. Go another level out, how many neighbors do you get then? What you realize is as you go more and more levels out, as you go more and more distance on the graph out, you're, you're capturing something which is essentially a circle in two dimensions. So that, you know, the, the number of, the area of a circle is pi r squared. So the, it's the number of points that you get to goes up like the distance you've gone squared. And in general, in d-dimensional space, it's r to the power d. It's the, the number of points you get to, if you go r steps on the graph, grows like

• 1:50:50Stephen Wolfram?

  the number of steps you go to the power of the dimension. And that's a, that's a way that you can estimate the effective dimension of one of these graphs.

• 1:50:57Lex Fridman?

  So what does that grow to? So how does the dimension grow? Cause uh, I mean, obviously the visual aspect of these hypergraphs, they're often visualized in three dimensions.

• 1:51:07Stephen Wolfram?

  Right.

• 1:51:07Lex Fridman?

  And then there's a certain kind of structure. Uh, like you said, there's the, I mean, a circle, the, the, a sphere, uh, there, there's a planar aspect to it.

• 1:51:18Stephen Wolfram?

  Right.

• 1:51:19Lex Fridman?

  To this graph, to where it kinda, it almost starts creating a surface, like a complicated surface, but a surface. So how does that connect to effective dimension?

• 1:51:29Stephen Wolfram?

  Okay. So I mean, if you can lay out the graph in such a way that the, that the points in the graph, that, uh, you know, the, the points that are neighbors on the graph are neighbors as you lay them out.

• 1:51:40Lex Fridman?

  Hmm.

• 1:51:41Stephen Wolfram?

  And you can do that in two dimensions, then it's going to approximate a two-dimensional thing. If you can't do that in two dimensions, if everything would have to fold over a lot in two dimensions, then it's not approximating a two-dimensional thing. Maybe you can lay it out in three dimensions. Maybe you have to lay it out in five dimensions to have it be the case that it sort of smoothly lays out like that.

• 1:51:59Lex Fridman?

  Well, but okay, since, uh, I apologize for the different tangent questions, but you know, there's an infinity number of possible rules.

• 1:52:08Lex Fridman?

  So we have to look for rules that uh that create the kind of structures that are reminiscent for uh that have echoes of the different physics theories in them. So what kind of rules, is there something simple to be said about the kind of rules that you have found beautiful, that you have found powerful?

• 1:52:31Stephen Wolfram?

  Right, so I mean, what, you know, one of the features of computational irreducibility is it's very, you can't say in advance what's going to happen with any particular, you can't say, I'm going to pick these rules from this part of rule space, so to speak, because they're going to be the ones that are going to work. That's, you can make some statements along those lines, but you can't generally say that. Now, you know, the state of what we've been able to do is, you know, different properties of the universe, like dimensionality, you know, integer dimensionality, features of other features of quantum mechanics, things like that. At this point, what we've got is, we've got rules that, that any one of those features, we can get a rule that has that feature.

• 1:53:15Lex Fridman?

  Yeah, so the

• 1:53:16Stephen Wolfram?

  We don't have the sort of, the final, here's a rule which has all of these features. We do not have that yet.

• 1:53:21Lex Fridman?

  So if I were to try to summarize the Wolfram Physics project, which is, you know, something that's been in your brain for a long time, but really has just exploded in activity, you know, only just months ago.

• 1:53:36Stephen Wolfram?

  Yes.

• 1:53:37Lex Fridman?

  So it's an evolving thing, and next week, I'll try to publish this conversation as quickly as possible, because by the time it's published, already new things will probably have come out. So if I were to summarize it, we've talked about the basics of, there's a hypergraph that represents space, there is uh transformations on the hypergraph that represents um

• 1:54:01Stephen Wolfram?

  Time, that progress of time.

• 1:54:04Lex Fridman?

  There's a causal graph that's a characteristic of this. And the basic process of science of, yeah, of science within the Wolfram Physics model is to try different rules and see which properties of physics that we know of, known physical theories are, appear within the graphs that emerge from that rule.

• 1:54:28Stephen Wolfram?

  That's what I thought it was going to be.

• 1:54:29Lex Fridman?

  Oh, okay. So what?

• 1:54:32Stephen Wolfram?

  It turns out we can do a lot better than that. It turns out that using kind of mathematical ideas, we can say, and computational ideas, we can, we can make general statements. And those general statements turn out to correspond to things that we know from 20th century physics. In other words, the idea of you just try a bunch of rules and see what they do. That's what I thought we were going to have to do. Um, but in, in fact, we can say, given causal invariance and computational irreducibility, we can derive, and this is where it gets really pretty interesting. We can derive special relativity, we can derive general relativity, we can derive quantum mechanics. And that's where things really start to get exciting is, you know,

• 1:55:16Stephen Wolfram?

  it wasn't at all obvious to me that even if we were completely correct, and even if we had, you know, this is the rule, you know, even if we found the rule, to be able to say, yes, it corresponds to things we already know. I did not expect that to be the case. And

• 1:55:30Lex Fridman?

  So for somebody who is a, a simple mind and definitely not a physicist, not even close, what does derivation mean in this case?

• 1:55:40Stephen Wolfram?

  Okay, so, so let me, this is an interesting question. Okay, so there's, so one, one thing.

• 1:55:46Lex Fridman?

  In the context of computational reducibility.

• 1:55:49Stephen Wolfram?

  Yeah, yeah, right, right. So what you have to do, let me get, let me go back to again, the mundane example of fluids and water and things like that, right? So, so you have a bunch of molecules bouncing around. You can say, uh, just as a piece of mathematics, I happen to do this from cellular automata back in the mid 1980s. You can say, just as a matter of mathematics, you can say, the continuum limit of these little molecules bouncing around is the Navier-Stokes equations. That's just a piece of mathematics. It's not, it doesn't rely on, uh, you have to make certain assumptions that you have to say, there's enough randomness in the way the molecules bounce around that certain statistical averages work, et cetera, et cetera, et cetera.

• 1:56:33Stephen Wolfram?

  Okay, it is a very similar derivation to derive, for example, the Einstein equations. Okay, so the way that works roughly, the Einstein equations are about curvature of space. curvature of space, I talked about sort of how you can figure out dimension of space. There's a similar kind of way of figuring out if you if you just sort of say, you know, you're making a larger and larger ball or larger and larger. If you draw a circle on the surface of the earth, for example, you might think the area of a circle is pi r squared. But on the surface of the earth, because it's a sphere, it's not flat. The the area of a circle isn't precisely pi r squared. As the circle gets bigger, the area is slightly smaller than you would expect from the formula pi r squared has a little correction term

• 1:57:17Stephen Wolfram?

  that depends on the the ratio of the size of the circle to the radius of the earth. Okay, so it's the same basic thing allows you to measure from one of these hypergraphs. What is its effective curvature?

• 1:57:28Lex Fridman?

  And that's so the little piece of mathematics that explains special general relativity is can map nicely to describe fundamental property of the hypergraphs, the curvature of the hypergraphs.

• 1:57:45Stephen Wolfram?

  So so special relativity is about the relationship of time to space. General relativity is about curvature in in this space represented by this hypergraph.

• 1:57:56Lex Fridman?

  So what is the curvature of a hypergraph?

• 1:57:58Stephen Wolfram?

  Okay, so first I have to explain, what was explaining is first thing you have to have is a notion of dimension. You you don't get to talk about curvature of things. If you say, oh, it's a curved line, but I don't know what a line is yet.

• 1:58:11Lex Fridman?

  So yeah, what is the dimension of a hypergraph then? Where from where we've talked about effective dimension, but.

• 1:58:18Stephen Wolfram?

  Right, that's what that's what this is about. That's what this is about is you have your hypergraph. It's got a trillion nodes in it. What is it roughly like? Is it roughly like a grid, a two dimensional grid? Is it roughly like all those all those nodes are arranged online? What's it roughly like? And there's a pretty simple mathematical way to estimate that by just looking at the the this thing I was describing, this sort of the size of a ball that you construct in the hypergraph. That's a you just measure that. You can just, you know, compute it on a computer for a given hypergraph. And you can say, oh, this thing is wiggling around, but it's it's rough. Roughly corresponds to two or something like that, or roughly corresponds to two point six or whatever. So that's how you, that's how you have a notion of dimension in these hypergraphs.

• 1:59:03Stephen Wolfram?

  Curvature is something a little bit beyond that. It's if you look at the, how the size of this ball increases as you increase its radius. Curvature is a correction to the si- size increase associated with dimension. It's a sort of a second order term in, in the, in determining size, just like the area of a circle is roughly pi r squared. So it goes up like r squared. The two is because it's in two dimensions. But when that circle is drawn on a big sphere, the, the actual formula is pi r squared times one minus uh r squared over a squared and some coefficient. So in other words, there's a correction to, and that correction term, that gives you curvature.

• 1:59:45Stephen Wolfram?

  And that correction term is what makes this hypergraph correspond, have the potential to correspond to curved space. Now, the next question is, is that curvature, is the way that curvature works, the way that Einstein's equations for general relativity, you know, is it the way they say it should work? And the answer is, uh, yes.

• 2:00:06Lex Fridman?

  Really?

• 2:00:07Stephen Wolfram?

  And so how does that work? The, I mean, you're the-

• 2:00:12Lex Fridman?

  The calculation of the curvature of this hypergraph for, for some, some set of rules?

• 2:00:17Stephen Wolfram?

  No, it doesn't matter what the rules are. It doesn't, so long as they have causal invariance and computational irreducibility. And, and they lead to finite dimensional space. Fine, non-infinite dimensional space.

• 2:00:28Lex Fridman?

  Or all dimension-

• 2:00:30Stephen Wolfram?

  Dimensional. It can grow infinitely, but it can't be infinite dimensional. So-

• 2:00:34Lex Fridman?

  What does a infinitely dimensional hypergraph look like? So that means-

• 2:00:38Stephen Wolfram?

  For example, so in a tree, you start from one root of the tree. It doubles, doubles again, doubles again, doubles again. And that means if you ask the question, starting from a given point, how many points do you get to? Remember, in like a circle, you get to r squared with the two there. On a tree, you get to, for example, two to the r. It's exponential dimensional, so to speak, or infinite dimensional.

• 2:01:01Lex Fridman?

  Do you have a sense of, in the space of all possible rules, how many uh lead to uh infinitely dimensional hypergraphs?

• 2:01:11Stephen Wolfram?

  Uh, no.

• 2:01:12Lex Fridman?

  Okay. Is that an important thing to know?

• 2:01:15Stephen Wolfram?

  Yes, it's an important thing to know. I would love to know the answer to that. And but but you know, it gets a little bit more complicated because, for example, it's very possible the case that in our physical universe, that the universe started infinite dimensional. And it only, as it, as the, you know, at the big bang, it was very likely infinite dimensional. And as, as the universe sort of expanded and cooled, its dimension gradually went down. And so one of the bizarre possibilities, which actually there are experiments you can do to try and look at this, the universe can have dimension fluctuations. So in other words, we think we live in a three dimensional universe, but actually there may be places where it's actually 3.01 dimensional, or where it's, you know, 2.99 dimensional.

• 2:01:58Stephen Wolfram?

  And it may be that in the, in the very early universe, it was actually infinite dimensional, and it's only a late stage phenomenon that we end up getting three dimensional space.

• 2:02:06Lex Fridman?

  But from your perspective of the hypergraph, the, one of the underlying assumptions kind of implied, but you have a sense, a hope, set of assumptions that the, the rules that underlie our universe, or the rule that underlies our universe, is static. Is that the, one of the assumptions you're currently operating under?

• 2:02:29Stephen Wolfram?

  Uh, yes, but there's a, there's a footnote to that, which we should get to, because it requires a few more steps.

• 2:02:34Lex Fridman?

  Okay, well, actually then, but let's backtrack to the curvature, because we're talking about, as long as it's finite dimensional, uh, finite dimensional, computational irreducibility, and causal invariance, then it follows that, uh, the, uh, that the large scale structure will follow Einstein's equations.

• 2:02:55Stephen Wolfram?

  And now let me again qualify that a little bit more, there's a little bit more complexity to it. The, um, uh, okay, so.

• 2:03:04Stephen Wolfram?

  Einstein's equations in their simplest form apply to the vacuum. No matter, just the vacuum. And they say, in particular, what they say is if you have, so there's this term jedesik. That's a term that means shortest path. Comes from measuring shortest paths on the earth. So you, you look at a bunch of, a, a, a bundle of jedesiks, a bunch of shortest paths. It's like the paths that photons would take between two points. Then the statement of Einstein's equations is basically a statement about a certain, the, that as you look at a bundle of jedesiks, the structure of space has to be such that although the, the cross-sectional area of this bundle may, although the actual shape of the cross-section may change, the cross-sectional area does not.

• 2:03:49Stephen Wolfram?

  That's a version, that's a, that's the most simple minded version of mu nu minus a half R g mu nu equals zero, which is the, the more mathematical version of Einstein's equations. It's a statement, it's a statement of the thing called the Ricci tensor is equal to zero. And that's, that's Einstein's equations for the vacuum. Okay, so we get that in, as a result of this model. But footnote, big, you know, big footnote, because all the matter in the universe is the stuff we actually care about. The vacuum is not stuff we care about. So the question is, how does matter come into this? And for that, you have to understand what energy is in these models.

• 2:04:29Stephen Wolfram?

  And one of the things that we realized, you know, last, late last year was that there's a very simple interpretation of energy in these models. Okay. And energy is basically, well intuitively, it's the amount of activity in these hypergraphs and the way that that remains over time. So a little bit more formally, you can think about this causal graph as having these edges that represent causal relationships. You can think about, oh boy, there's one more concept that we didn't get to. There's that. The notion of spacelike hypersurfaces. So this is, this is, is not as scary as it sounds.

• 2:05:13Stephen Wolfram?

  The, the, it's a, it's a common notion in general relativity. It's a, the notion is you are, you're defining what is a possibly, what is, what?

• 2:05:24Stephen Wolfram?

  Um, where in spacetime might be a particular moment in time? So in other words, what, what is a consistent set of places where you can say this is happening now? So to speak, and you make this series of, of, of sort of slices through the spacetime, uh, through this causal graph to re- represent sort of what we consider to be successive moments in time.

• 2:05:51Lex Fridman?

  Okay.

• 2:05:52Stephen Wolfram?

  It's somewhat arbitrary because you can, you can deform that if you're going at a different speed and special activity. You tip those things if you're, you can, you know, there, there are different kinds of deformations, but only certain deformations are allowed by the structure of the causal graph. Anyway, be as it may, the, the, the, the basic point is there is a way of figuring out, you know, you say, what is the energy associated with what's going on in this, in this hypergraph? And the answer is there is a precise definition of that. And it is, the formal way to say it is it's the flux of causal edges through space like hypersurfaces. The slightly less formal way to say it, it's basically the amount of activity, the, the,

• 2:06:33Stephen Wolfram?

  see, the reason it gets tricky is you might say it's the amount of activity per unit volume in, in this hypergraph, but you haven't defined what volume is. So it's, it's, it's a little bit that you have to be.

• 2:06:44Lex Fridman?

  But this hypersurface gives some more formalism to that.

• 2:06:48Stephen Wolfram?

  Yeah, yeah, it gives a way to connect that.

• 2:06:50Lex Fridman?

  But intuitively, we should think about as the just.

• 2:06:52Stephen Wolfram?

  The amount of activity. Right. So, so the amount of activity that kind of remains in one place in the hypergraph corresponds to energy. The amount of activity that is kind of where an activity here affects an activity somewhere else cause corresponds to momentum. And, um, and so one of the things that's kind of cool is that, I'm trying to think about how to say this intuitively, the mathematics is easy, but the, the intuitive version, I'm not sure. But basically the way that things sort of stay in the same place and have activity is associated with rest mass. And so one of the things that you get to derive is E equals mc squared. Um, that is a consequence of this interpretation of energy in terms of the way the causal graph works,

• 2:07:35Stephen Wolfram?

  which is a, the whole thing is sort of a consequence of this whole story about updates and hypergraphs and so on.

• 2:07:41Lex Fridman?

  So. Can you linger on that a little bit? How do we get E equals mc squared? So where does the mass come from?

• 2:07:48Stephen Wolfram?

  Okay, okay.

• 2:07:49Lex Fridman?

  I mean, is there an intuitive? So, okay, first of all, you're pretty deep in the mathematical explorations of this thing right now. We're in a very, we're in flux currently. So maybe you haven't even had time to think about intuitive explanations. But.

• 2:08:09Stephen Wolfram?

  Yeah, I mean, this one, this one is, is look, roughly what's happening. That derivation is actually rather easy.

• 2:08:15Lex Fridman?

  Yeah.

• 2:08:16Stephen Wolfram?

  And everybody, and I've been saying we should pay more attention to this derivation because it's such, you know, because people care about this point. But everybody says, it's just easy.

• 2:08:23Lex Fridman?

  It's easy. So there's some concept of energy that's, it can be too easily thought of as the activity, the flux, the level, the level of changes that are occurring based on the transformations within a certain volume, however the heck do you find the volume? Okay, so, and then mass?

• 2:08:41Stephen Wolfram?

  Well, mass is.

• 2:08:42Lex Fridman?

  What?

• 2:08:43Stephen Wolfram?

  Mass is associated with kind of the energy that does not cause you to, that does not somehow propagate through time. Yeah, I mean, one of the things that was not obvious in the usual formulation of special relativity is that space and time are connected in a certain way. Energy and momentum are also connected in a certain way. The fact that the connection of energy to momentum is analogous to the connection to space between space and time is not self-evident in ordinary relativity. It is a consequence of this, of the way this model works. It's an intrinsic consequence of the way this model works. And it's all to do with that, with unraveling that connection

• 2:09:23Stephen Wolfram?

  that ends up giving you this, this relationship between energy and, and, well, it's energy, momentum, mass, they're all connected.

• 2:09:31Lex Fridman?

  And, and so like, that's hence the general relativity. You have a sense that it appears to be baked in. To the fundamental properties of the way these hypergraphs are evolved.

• 2:09:47Stephen Wolfram?

  Well, I didn't yet get to. So I got as far as special relativity and E equals mc squared. The one last step is, in general relativity, the the final connection is energy, mass, cause, curvature in space. And that's something that when you understand this interpretation of energy and you kind of understand the correspondence to curvature and hypergraphs, then you can finally sort of the the big final answer is you derive the full version of Einstein's equations for spacetime and matter. And that's.

• 2:10:22Lex Fridman?

  So is that, have you, that last piece with curvature? Have, is that, have you arrived there yet?

• 2:10:30Stephen Wolfram?

  Oh, yeah, we're with her. Yes. And here's the, here's the way that we, here's how we're really, really going to know we've arrived. Okay? So, you know, we have the mathematical derivation. It's all fine. But, but, you know, mathematical derivations. Okay, so one thing that's sort of a, a, you know, we're taking this limit of what happens when you, the limit, you have to look at things which are large compared to the size of an elementary length, small compared to the whole size of the universe, large compared to certain kinds of fluctuations, blah, blah, blah. There's a, there's a, there's a tower of many, many of these mathematical limits that have to be taken. So if you're a pure mathematician saying, where's the precise proof? It's like, well, there are all these limits. We can, you know, we can try each one of them computationally, and we could say, yeah, it really works.

• 2:11:15Stephen Wolfram?

  But the formal mathematics is really hard to do. I mean, for example, in the case of deriving the equations of fluid dynamics from molecular dynamics, that derivation has never been done. There is no rigorous version of that derivation. So.

• 2:11:29Lex Fridman?

  Because you can't do the limits?

• 2:11:31Stephen Wolfram?

  Yeah, because you can't do the limits.

• 2:11:32Lex Fridman?

  But so the limits allow you to try to describe something general about the system and very, very particular kinds of limits that you need to take with these very.

• 2:11:41Stephen Wolfram?

  Right, and, and the limits will definitely work the way we think they work and we can do all kinds of computer experiments.

• 2:11:46Lex Fridman?

  It's just a hard derivation.

• 2:11:47Stephen Wolfram?

  Yeah, it's just, it's just the mathematical structure kind of, you know, ends up running right into computational irreducibility and you end up with a bunch of, a bunch of difficulty there. But here's the way that we're getting really confident that we know completely what we're talking about, which is when people study things like black hole mergers using Einstein's equations, what do they actually do? Well, they actually use mathematics or a whole bunch to analyze the equations and so on, but in the end, they do numerical relativity, which means they take these nice mathematical equations and they break them down so that they can run them on a computer and they break them down into something which is actually a discrete approximation to these equations. Then they run them on a computer, they get results, then you look at the gravitational waves and you see if they match. Okay? Turns

• 2:12:32Stephen Wolfram?

  out that our model gives you a direct way to do numerical relativity. So in other words, instead of saying you start from these continuum equations from Einstein, you break them down into these discrete things, you run them on a computer, you say, we're doing it the other way around. We're starting from these discrete things that come from our model and we're just running big versions on, on a computer. And, uh, you know, what we're saying is, and this is, this is how things will work. So what I'm, the way I'm calling this is, is proof by compilation, so to speak. That is, in other words, you're, you're taking, um, something where, you know, we've got this description of a black hole system and what we're doing is we're, we're showing that the, you know, what we get by just running

• 2:13:15Stephen Wolfram?

  our model agrees with what you would get by doing the computation from the Einstein equations.

• 2:13:21Lex Fridman?

  As a small tangent, or actually a very big tangent, but, uh,

• 2:13:28Lex Fridman?

  Proof compilation is a beautiful concept. In a sense, the way of doing physics with this model is by running it or compiling it.

• 2:13:43Stephen Wolfram?

  Some level, yes.

• 2:13:45Lex Fridman?

  Have you thought about, and these things can be very large, is there totally new possibilities of computing hardware and computing software, which allows you to perform this kind of compilation?

• 2:14:00Stephen Wolfram?

  Well.

• 2:14:01Lex Fridman?

  Algorithms, software, hardware?

• 2:14:03Stephen Wolfram?

  So first comment is, these models seem to give one a lot of intuition about distributed computing, a lot of different intuition about how to think about parallel computation. And that particularly comes from the quantum mechanics side of things, which we didn't talk about much yet. But the question of what, you know, given our current computer hardware, how can we most efficiently simulate things?

• 2:14:27Lex Fridman?

  Yeah.

• 2:14:27Stephen Wolfram?

  That's actually partly a story of the model itself, because the model itself has deep parallelism in it.

• 2:14:33Lex Fridman?

  Yes.

• 2:14:33Stephen Wolfram?

  The ways that we are simulating it, we're just starting to be able to use that deep parallelism to be able to be more efficient in the way that we simulate things. But in fact, the structure of the model itself allows us to think about parallel computation in different ways. And one of my realizations is that, you know, so it's very hard to get in your brain how you deal with parallel computation. And you're always worrying about, you know, if multiple things can happen at different, on different computers at different times, oh, what happens if this thing happens before that thing? And we've really got, you know, we have these race conditions where something can race to get to the answer before another thing, and you get all tangled up because you don't know which thing is going to come in first. And usually, when you do parallel computing, there's a big obsession to lock things down

• 2:15:18Stephen Wolfram?

  to the point where you've, you've had locks and mutaxes and god knows what else, where, where you've, you've, you've arranged it so that there can only be one sequence of things that can happen. So you don't have to think about all the different kinds of things that can happen. Well, in these models, physics is throwing us into forcing us to think about all these possible things that can happen. But these models, together with what we know from physics, is giving us new ways to think about all possible things happening, about all these different things happening in parallel. And so I'm guessing-

• 2:15:49Lex Fridman?

  They have built-in protection for some of the parallelism.

• 2:15:52Stephen Wolfram?

  Well, causal invariance is the built-in protection. Causal invariance is what means that even though things happen in different orders, it doesn't matter in the end.

• 2:16:00Lex Fridman?

  As a person who struggled with concurrent programming in like Java, with all the basic concepts of concurrent programming, that if there could be built up a strong mathematical framework for causal invariance, that's so liberating. And that could be not just liberating, but really powerful for massively distributed computation.

• 2:16:26Stephen Wolfram?

  Absolutely. No, I mean, you know, what's eventual consistency in distributed databases is essentially the causal invariance idea.

• 2:16:33Lex Fridman?

  Yeah.

• 2:16:34Stephen Wolfram?

  Okay, so that's, but-

• 2:16:35Lex Fridman?

  But have you thought about, you know, like really large simulations?

• 2:16:42Stephen Wolfram?

  Yeah, I mean, I'm also thinking about, look, the fact is, you know, I've spent much of my life as a language designer, right? So I can't possibly not think about, you know, what does this mean for designing languages for parallel computation? In fact, another thing that's one of these, you know, I'm always embarrassed at how long it's taken me to figure stuff out. But, you know, back in the 1980s, I worked on trying to make up languages for parallel computation. I thought about doing graph rewriting. I thought about doing these kinds of things, but I couldn't see how to actually make the connections to actually do something useful. I think now physics is kind of showing us how to make those things useful. And so my guess is that in time, we'll be talking about, you know, we do parallel programming,

• 2:17:26Stephen Wolfram?

  we'll be talking about programming in a certain reference frame, just as we think about thinking about physics in a certain reference frame. It's a certain co-ordinatization of what's going on. We say, we're going to program in this reference frame, or let's change the reference frame to this reference frame, and then our program will seem different and we'll have a different way to think about it, but it's still the same program underneath.

• 2:17:46Lex Fridman?

  So let me ask on this topic, because I put out that I'm talking to you. I got way more questions than I can deal with. But what pops to mind is a question somebody asked on Reddit, I think, is, please ask Dr. Wolfram, what are the specs of the computer running the universe? So we're talking about specs of hardware and software for simulations of a large scale thing. What about a scale that is comparative to something that eventually leads to the two of us talking and about?

• 2:18:19Stephen Wolfram?

  Right, right, right. So actually, I did try to estimate that. And we had to go a couple more stages before we can really get to that answer, because we're talking about this thing. You know, this is what happens when you build these abstract systems and you're trying to explain the universe. They're quite a number of levels deep, so to speak. But the...

• 2:18:42Lex Fridman?

  You mean conceptually or like literally? Because you're talking about very small objects and there's 10 to the 120 something.

• 2:18:49Stephen Wolfram?

  Yeah, right. It is conceptually deep. And one of the things that's happening sort of structurally in this project is, you know, there were ideas. There's another layer of ideas, there's another layer of ideas to get to the different things that correspond to physics. They're just different layers of ideas. And they are, you know, it's actually probably, if anything, getting harder to explain this project. Because I'm realizing that the fraction of way through that I am so far in explaining this to you is less than, than, you know, it might be because we know more now, you know, every week, basically, we know a little bit more.

• 2:19:23Lex Fridman?

  And like, those are just layers on the initial fundamental.

• 2:19:28Stephen Wolfram?

  Yes, but the layers are, you know, you might be asking me, you know, how do we get, you know, the difference between fermions and bosons, the difference between particles that can be all in the same state and particles that exclude each other, okay? Last three days, we've kind of figured that out, okay? But, and it's very interesting. It's very cool. And it's very...

• 2:19:49Lex Fridman?

  And those are some kind of properties at a certain level, layer of abstraction on the holograph.

• 2:19:55Stephen Wolfram?

  Yes, yes. And there's... But the layers of abstraction are kind of, they're compounding.

• 2:20:00Lex Fridman?

  Stacking up, so it's difficult, but.

• 2:20:02Stephen Wolfram?

  But okay, but.

• 2:20:03Lex Fridman?

  But the specs nevertheless remain the same.

• 2:20:05Stephen Wolfram?

  The specs underneath, so I have an estimate. So the question is, what are the units? So we've got these different fundamental constants about the world. So one of them is the speed of light, which is the, so the thing that's always the same in all these different ways of thinking about the universe is the notion of time, because time is computation. And so there's an elementary time, which is sort of the, the, the amount of time that we ascribe to elapsing in a, in a single computational step.

• 2:20:33Lex Fridman?

  Yeah.

• 2:20:34Stephen Wolfram?

  Okay, so that's the elementary time. So then there's an elementary.

• 2:20:37Lex Fridman?

  Parameter or whatever, that's a constant.

• 2:20:39Stephen Wolfram?

  It's whatever we define it to be, because I mean, we, we don't, you know.

• 2:20:42Lex Fridman?

  I mean, it's all relative, right? It doesn't matter.

• 2:20:45Stephen Wolfram?

  It doesn't matter what it is, because we could be, it could be slower. It's just a number which, which we use to convert that to seconds, so to speak, because we are experiencing things and we say, this amount of time has elapsed.

• 2:20:57Lex Fridman?

  But we're within this thing, so it doesn't, yeah.

• 2:21:00Stephen Wolfram?

  It doesn't matter, right? But what does matter is the ratio, what, what we can, the ratio of the spatial distance in this hypergraph to this, to this moment of time. Again, that's an arbitrary thing, but we measure that in meters per second, for example, and that ratio is the speed of light. So the ratio of the elementary distance to the elementary time is the speed of light. Okay?

• 2:21:24Lex Fridman?

  Perfect.

• 2:21:24Stephen Wolfram?

  And so there's another, there are two other levels of this. Okay, so there is a thing which we can talk about, which is the maximum entanglement speed, which is a thing that happens at another level in this whole sort of story of how these things get constructed. That's a sort of maximum speed in quantum, in the space of quantum states. Just as the speed of light is a maximum speed in physical space, this is a maximum speed in the space of quantum states. There's another level which is associated with what we call rulial space, which is a, another one of these maximum speeds, we'll get to this.

• 2:21:57Lex Fridman?

  So these are limitations on the system that are able to capture the kind of physical universe which we live in. The quantum mechanical.

• 2:22:04Stephen Wolfram?

  They are inevitable features of having a, a rule that has only a finite amount of information in the rule. So long as you have a rule that only involves a bounded amount, a limited amount of only involving a limited number of elements, limited number of relations, it is inevitable that there are these speed constraints. We knew about the one for speed of light. We didn't know about the one for maximum entanglement speed, which is actually something that is possibly measurable, particularly in black hole systems and things like this. But anyway, this is long, long story short. You're asking what the processing specs of the universe, of the sort of computation of the universe. There's a question of even what are the units of some of these measurements?

• 2:22:46Stephen Wolfram?

  Okay, so the units I'm using are Wolfram Language instructions per second. Okay, because you've got to have some, you know, what computation are you doing?

• 2:22:54Lex Fridman?

  There's got to be some kind of frame of reference.

• 2:22:55Stephen Wolfram?

  Right, right. So because it turns out in the end, there will be, there's sort of an arbitrariness in the language that you use to describe the universe. So in those terms, I think it's like 10 to the 500 Wolfram Language operations per second, I think, is the, I think it's of that order.

• 2:23:14Lex Fridman?

  So that's the scale of the computation. What about memory? If there's an interesting thing to say about storage and memory?

• 2:23:20Stephen Wolfram?

  Well, there's a question of how many sort of atoms of space might there be? You know, maybe 10 to the 400. We don't know exactly how to estimate these numbers. I mean, this is, this is based on some, some, I would say somewhat rickety way of estimating things. You know, when they start to be able to be experiments done, if we're lucky, there will be experiments that can actually nail down some of these numbers.

• 2:23:41Lex Fridman?

  And because of computation reducibility, there's not much hope for very efficient compression, like very efficient representation of this.

• 2:23:52Stephen Wolfram?

  Question, good question. I mean, there's probably certain things, you know, the fact that we can deduce anything. Okay, the question is how deep does the reducibility go?

• 2:24:02Lex Fridman?

  Right.

• 2:24:02Stephen Wolfram?

  Okay, and I keep on being surprised that it's a lot deeper than I thought. Okay, and so one of the things is that. That there's a question of sort of how much of the whole of physics do we have to be able to get in order to explain certain kinds of phenomena like for example if we want to study quantum interference do we have to know what an electron is turns out I thought we did turns out we don't I thought to know what energy is we would have to know what electrons were we don't

• 2:24:30Lex Fridman?

  You can get a lot of really powerful shortcuts

• 2:24:33Stephen Wolfram?

  Right there's a there's a bunch of sort of bulk information about the world the the thing that I'm excited about last few days okay is um uh the idea of fermions versus bosons fundamental idea that I mean it's the the reason we have matter that doesn't just self-destruct is because of the exclusion principle that means that two electrons can never be in the same quantum state

• 2:24:55Lex Fridman?

  Is it useful for us to maybe first talk about how quantum mechanics fits

• 2:25:00Stephen Wolfram?

  Let's talk about quantum mechanics

• 2:25:01Lex Fridman?

  Into the Wolfram physics model

• 2:25:04Stephen Wolfram?

  Yes

• 2:25:04Lex Fridman?

  Let's go there so we talked about general relativity now what uh what have you found

• 2:25:12Stephen Wolfram?

  What's the story of quantum mechanics right

• 2:25:14Lex Fridman?

  Within and outside of the Wolfram physics

• 2:25:17Stephen Wolfram?

  Right so I mean the the the key idea of quantum mechanics that sort of the the the typical interpretation is classical physics says a definite thing happens quantum physics says there's this whole set of paths of things that might happen and we are just observing some overall probability of of how those paths work okay so when you think about our hypergraphs and all these little updates that are going on there's a very remarkable thing to realize which is if you say well which particular sequence of updates should you do say well it's not really defined you can do any of a whole collection of possible sequences of updates okay that set of possible

• 2:25:57Stephen Wolfram?

  sequences of updates defines yet another kind of graph that we call a multiway graph and a multiway graph just is a graph where at every node there is a choice of several different possible things that could happen so for example you go this way you go that way those are two different edges in the multiway graph and you're building up Set of possibilities. So actually, like, for example, I just made the one, the multi-way graph for tic-tac-toe. Okay, so tic-tac-toe, you start off with some, some board that, you know, is everything is blank, and then somebody can put down a an X somewhere, an O somewhere, and then there are different possibilities. At each stage, there are different possibilities.

• 2:26:37Stephen Wolfram?

  And so you build up this multi-way graph of all those possibilities. Now, notice that even in tic-tac-toe, you have the feature that there can be something where you have two different things that happen, and then those branches merge because you end up with the same shape, you know, the same configuration of the board, even though you got there in two different ways. So, the thing that's sort of an inevitable feature of our models is that, just like quantum mechanics suggests, definite things don't happen. Instead, you get this whole multi-way graph of all these possibilities. Okay, so then, the question is, so, okay, so that's sort of a picture of what's going on. Now you say, okay, well, quantum mechanics has all these features of, you know, all this mathematical structure and so on.

• 2:27:22Stephen Wolfram?

  How do you get that mathematical structure? Okay, couple of, couple of things to say. So, quantum mechanics is actually, in a sense, two different theories glued together. Quantum mechanics is the theory of how quantum amplitudes work, that more or less give you the probabilities of things happening. And it's the theory of quantum measurement, which is the theory of how we actually conclude definite things. Because the mathematics just gives you these quantum amplitudes, which are more or less probabilities of things happening. But yet, we actually observe definite things in the world. Quantum measurement has always been a bit mysterious. It's always been something where people just say, well, the mathematics says this, but then you do a measurement and the philosophical arguments about what the measurement is. But it's not something where there's a theory of the measurement.

• 2:28:07Lex Fridman?

  Somebody on Reddit also asked, please ask Steven to tell his story of this, the double slit experiment.

• 2:28:17Stephen Wolfram?

  Okay, yeah, I can.

• 2:28:18Lex Fridman?

  Is that, does that make sense?

• 2:28:20Stephen Wolfram?

  Oh yeah, it makes sense. Absolutely makes sense.

• 2:28:22Lex Fridman?

  Why, is this like a good way to discuss?

• 2:28:25Stephen Wolfram?

  Little bit. Let me, let me go, let me explain a couple of things first. So, so. The structure of quantum mechanics is mathematically quite complicated. One of the features, let's see, well, how to how to describe this? Okay, so first point is there's this multiway graph of all these different paths of of things that can happen in the world. And the important point is that that these you can have branchings and you can have mergings. Okay, so this property turns out causal invariance is the statement that the number of mergings is equal to the number of branchings.

• 2:29:03Lex Fridman?

  Yeah.

• 2:29:03Stephen Wolfram?

  So in other words, every time there's a branch, eventually there will also be a merge. In other words, every time there were two possibilities for what might have happened, eventually those will merge.

• 2:29:12Lex Fridman?

  Beautiful concept, by the way, but yeah, yeah, yeah.

• 2:29:14Stephen Wolfram?

  So so that so that idea, okay, so then.

• 2:29:20Stephen Wolfram?

  So that's that's one thing, and that's closely related to the the sort of objectivity in quantum mechanics. The fact that we believe definite things happen. It's because although there are all these different paths, in some sense, because of causal invariance, they all imply the same thing. That's I'm cheating a little bit in saying that, but that's roughly the essence of what's going on. Okay, next next thing to think about is. You have this multiway graph. It has all these different possible things that are happening. Now, we ask this multiway graph is sort of evolving with time. Over time, it's branching, it's merging, it's doing all these things. Okay.

• 2:29:57Stephen Wolfram?

  Question we can ask is if we slice it at a particular time, what do we see? And that slice represents, in a sense, something to do with the state of the universe at a particular time. So in other words, we've got this multiway graph of all these possibilities. And then we're asking, and and, okay, we take this slice. This slice represents a sense, okay, each of these different paths corresponds to a different quantum possibility for what's happening.

• 2:30:26Lex Fridman?

  Right.

• 2:30:26Stephen Wolfram?

  When we take the slice, we're saying, what is the set of quantum possibilities that exist at a particular time?

• 2:30:32Lex Fridman?

  And when you say slice, are these you slice the graph and then there's a bunch of leaves?

• 2:30:37Stephen Wolfram?

  A bunch of leaves.

• 2:30:37Lex Fridman?

  And those represent the state of things.

• 2:30:41Stephen Wolfram?

  Right, but then, okay, so the important thing that you are quickly picking up on is that what what matters is kind of how these leaves are related to each other. So a good way to tell how leaves are related is just to say, on the step before, did they have a common ancestor? So two leaves might be, they might have just branched from one thing, or they might be far away, you know, way far apart in this graph, where to get to a common ancestor, maybe you have to go all the way back to the beginning of the graph, all the way back to the beginning.

• 2:31:12Lex Fridman?

  So there's some kind of measure of distance.

• 2:31:14Stephen Wolfram?

  Right, and that, but what you get is by making this slice, we call it branchial space, the space of branches, and in this branchial space, you have a graph that represents the relationships between these quantum states in branchial space. You have this notion of distance in branchial space. Okay.

• 2:31:35Lex Fridman?

  It's connected to quantum entanglement.

• 2:31:38Stephen Wolfram?

  Yes, yes, it's, it's, it's basically, the, the distance in branchial space is kind of an entanglement distance. So.

• 2:31:45Lex Fridman?

  That's a very nice model.

• 2:31:47Stephen Wolfram?

  Right, it is very nice, it's very beautiful, it's, it's, I mean, it's, it's so clean, I mean, it's, it's really, you know, and it, it tells one, okay, so anyway, so then, then this, this branchial space has this sort of map of the, the entanglements between quantum states. So in physical space, we have, so, so you know, you can say, take, let's say, the causal graph, and we can slice that at a particular time, and then we get this map of how things are laid out in physical space. When we do the same kind of thing, there's a thing called the multiway causal graph, which is the analog of a causal graph for the multiway system, we slice that, we get essentially the relationships between things,

• 2:32:29Stephen Wolfram?

  not in physical space, but in the space of quantum states. It's like which quantum state is similar to which other quantum state. Okay, so now, I think, next thing to say is just to mention how quantum measurement works. So quantum measurement has to do with reference frames in branchial space. So, okay, so, measurement in, in physical space, it matters whether, how we assign. Spatial position and how we how we define coordinates in space and time. And that's that's how we make measurements in ordinary space. So are we making a measurement based on us sitting still here? Are we traveling at half the speed of light and making measurements that way? These are different reference frames in which we're making our measurements.

• 2:33:12Stephen Wolfram?

  And the relationship between different events and different points in space and time will be different depending on what reference frame we're in. Okay, so then we have this idea of quantum observation frames, which are the analog of reference frames, but in branchill space. And so what happens is what we realize is that a quantum measurement is the the observer is sort of arbitrarily determining this reference frame. The observer is saying, I'm going to understand the world by saying that space and time are coordinated this way. I'm going to understand the world by saying that quantum states and time are coordinated in this way.

• 2:33:54Stephen Wolfram?

  And essentially, what happens is that, you know, the process of quantum measurement is a process of deciding how you slice up this multi-way system in these quantum observation frames. So in a sense, the observer, the way the observer enters is by their choice of these quantum observation frames. And what happens is that the observer, because, okay, this is again another stack of other concepts, but anyway, because the observer is computationally bounded, there is a limit to the type of quantum observation frames that they can construct.

• 2:34:27Lex Fridman?

  Interesting. Okay, so there's, okay, so there's some constraints, some limit on on the choice of observation frames.

• 2:34:35Stephen Wolfram?

  Right, and by the way, I just want to mention that there's a, I mean, it's bizarre, but there's a hierarchy of these things. So in in in thermodynamics, the the fact that we believe entropy increases, we believe things get more disordered is a consequence of the fact that we can't track each individual molecule. If we could track every single molecule, we could run every movie in reverse, so to speak, and we would, you know, that we would not see that things are getting more disordered. But it's because we are computationally bounded, we can only look at these big blobs. Of what all these molecules collectively do that we think that things are that we describe it in terms of of entropy increasing and so on. And it's the same phenomenon, basically, also a consequence of computational irreducibility.

• 2:35:19Stephen Wolfram?

  That causes us to basically be forced to conclude that definite things happen in the world. Even though there's this quantum, you know, this set of all these different quantum processes that are going on. So, I I mean, I'm I'm I'm skipping a little bit and the the but that's a that's a rough picture.

• 2:35:36Lex Fridman?

  And in the evolution of the Wolf and Physics Project, where do you feel you stand on some of the puzzles that are along the way? See, you're skipping along a bunch of.

• 2:35:45Stephen Wolfram?

  It's amazing how much these things are unraveling. I mean, you know, these things, look, it used to be the case that I would. Agree with Dick Feynman, nobody understands quantum mechanics, including me. Okay, I'm getting to the point where I think I actually understand quantum mechanics. My my exercise, okay? Is can I explain quantum mechanics for real at the level of kind of middle school type explanation? And I'm getting closer. It's getting it's getting there. I'm not quite there. I've tried it a few times. And I realized that there are things that um where I have to start talking about elaborate mathematical concepts and so on. But I think, and and you've got to realize that it's not self evident that we can explain, you know, at an intuitively graspable level.

• 2:36:26Stephen Wolfram?

  Something which, uh, you know, about the way the universe works, the universe wasn't built for our understanding, so to speak. But but I think then then, um, okay, so another important important idea is um. This idea of branchial space, which I mentioned, this sort of space of quantum states. It is, okay, so I mentioned Einstein's equations describing, you know, the effect of. The effect of mass and energy on trajectories of particles, on geodesics. The curvature of of a physical space is associated with the presence of energy according to Einstein's equations.

• 2:37:06Stephen Wolfram?

  Okay, so it turns out that rather amazingly, the same thing is true in branchial space. So it turns out the presence of. Or more accurately Lagrangian density, which is a kind of relativistic invariant version of energy. The presence of that causes essentially deflection of judis six in this branchial space. Okay, so you might say, so what? Well, turns out that the sort of the best formulation we have of quantum mechanics. This the Feynman path integral is a thing that describes quantum processes in terms of mathematics.

• 2:37:46Stephen Wolfram?

  That can be interpreted as, well, in quantum mechanics, the the big thing is you get these quantum amplitudes, which are complex numbers that represent. When you combine them together, represent probabilities of things happening. And so the big story has been, how do you derive these quantum amplitudes? And people think these quantum amplitudes, they have a complex number has, you know, real part and imaginary part. You can also think of it having a magnitude and a phase. And it people have sort of thought these quantum amplitudes have magnitude and phase, and you compute those together. Turns out that magnitude, the magnitude and the phase come from completely different places. The magnitude comes, okay, so what do you, how do you compute things in quantum mechanics roughly?

• 2:38:30Stephen Wolfram?

  I'm I'm telling you, I'm I'm getting there to be able to do this at a middle school level, but I'm not there yet. The the roughly what happens is you're asking, does this state in quantum mechanics? Evolved to this other state in quantum mechanics? And you can think about that like a particle traveling or something traveling through physical space. But instead it's traveling through branchial space. And so what's happening is, does this quantum state evolve to this other quantum state? It's like saying, does this object move from this place in space to this other place in space? Okay, now, the way that you that these quantum amplitudes characterize kind of.

• 2:39:10Stephen Wolfram?

  To what extent the thing will successfully reach some particular point in branchial space, just like in physical space, you could say, oh, it had a certain. Velocity and it went in this direction. In branchial space, there's a similar kind of concept.

• 2:39:22Lex Fridman?

  Is there a nice way to visualize for me now mentally branchial space?

• 2:39:28Stephen Wolfram?

  It's just you have this hypergraph, it's, I'm sorry, you have this multiway graph. It's this big branching thing, branching and merging thing.

• 2:39:36Lex Fridman?

  But I mean, like moving through that space, I I'm just trying to understand what that looks like.

• 2:39:43Stephen Wolfram?

  You know, that space is probably exponential dimensional, which makes it, again, another can of worms in understanding what's going on. That space, as in in ordinary space, this hypergraph, the spatial hypergraph, limits to something which is like a manifold, like a, like something like three dimensional space. Almost certainly, the multiway graph limits to a Hilbert space, which is something that, I mean, it's, it's just a weirder exponential dimensional space. And by the way, you can ask, I mean, there are much weirder things that go on. For example, one of the things I've been interested in is the expansion of the universe in branchill space. So we know the universe is expanding in physical space, but the universe

• 2:40:25Stephen Wolfram?

  is probably also expanding in branchill space. So that means the, the number of quantum states of the universe is increasing with time.

• 2:40:33Lex Fridman?

  The diameter of the thing is growing.

• 2:40:35Stephen Wolfram?

  Right. So that means that the, and, and by the way, uh, this is related to whether quantum computing can ever work. Um, and

• 2:40:45Lex Fridman?

  Why?

• 2:40:46Stephen Wolfram?

  Okay, so let me explain why. So, so let's talk about, okay, so first of all, just, just to finish the thought about quantum amplitudes, the, the incredibly beautiful thing, but I've just, this is just, I'm just very excited about this. The, the, um, the Feynman path integral is, is this formula, it says that the amplitude, the quantum amplitude is e to the i s over h bar, where s is this thing called the action. And, um, it, uh, okay, so that can be thought of as representing a deflection of the angle of this path in the multiway graph. So it's a deflection of a geodesic in the multiway path that is caused by this thing called the action, which is essentially associated with the energy. Okay. And so this is a deflection

• 2:41:29Stephen Wolfram?

  of a path in branchill space that is described by this path integral, which is the thing that is the mathematical essence of quantum mechanics. Turns out that deflection is the deflection of geodesics in branchill space follows the exact same mathematical setup as the deflection of geodesics in physical space, except the deflection of geodesics in physical space is described with Einstein's equations, the deflection of geodesics in branchill space is defined by the Feynman path integral, and they are the same. In other words, they are mathematically the same. So that means that general relativity is a story of essentially motion in physical space. Quantum mechanics is a story of essentially motion in branchial space.

• 2:42:14Stephen Wolfram?

  And the underlying equation for those two things, although it's presented differently because one's interested in different things in branchial space than in physical space, but the underlying equation is the same. So in other words, it's the, it's just, you know, these two theories, which are the two sort of pillars of 20th century physics, which have seemed to be off in different directions, are actually facets of the exact same theory. And this, I mean.

• 2:42:41Lex Fridman?

  That's exciting to see, to see where that evolves and exciting that that just is there.

• 2:42:46Stephen Wolfram?

  Right. I mean, to me, you know, look, I, having spent some part of my early life, you know, working in these, in the context of these theories of, of, you know, 20th century physics, it's, they just, they seem so different. And the fact that they're really the same is just really amazing. Actually, let me, you, you mentioned double slit experiment. Okay. So the double slit experiment is a, is an interference phenomenon where you say there are, you know, you can have a photon or an electron, and you say there are these two slits, it could have gone through either one, but there is this interference pattern where it's, there's destructive interference where you might have said in classical physics, oh, well, if, if there are two slits, then there's a better chance that it gets through one or the other of them.

• 2:43:29Stephen Wolfram?

  But in quantum mechanics, there's this phenomenon of destructive interference that means that even though there are two slits, two can lead to nothing as opposed to two leading to more than, than, for example, one slit. And in what happens in this model, and we've just been understanding this in the last few weeks, actually, is that the.

• 2:43:50Stephen Wolfram?

  What essentially happens is that the the double slit experiment is a story of the interface between branchial space and physical space. And what's essentially happening is that the destructive interference is the result of the two possible paths associated with photons going through those two slits, winding up at opposite ends of branchial space. And so they don't, and so that's why there's sort of nothing there when you look at it, is because these two different sort of branches couldn't get merged together to produce something that you can measure in physical space.

• 2:44:24Lex Fridman?

  Is there a lot to be understood about branchial space, I guess?

• 2:44:28Stephen Wolfram?

  Yes.

• 2:44:29Lex Fridman?

  Mathematically speaking?

• 2:44:31Stephen Wolfram?

  Yes, it's a very beautiful mathematical thing, and it's very, I mean, by the way, this whole theory is just amazingly rich in terms of the mathematics that it says should exist. Okay, so for example, calculus, you know, is a story of infinitesimal change in integer dimensional space, one dimensional, two dimensional, three dimensional space. We need a theory of infinitesimal change in fractional dimensional and dynamic dimensional space. No such theory exists.

• 2:45:00Lex Fridman?

  So there's tools of mathematics that are needed here.

• 2:45:02Stephen Wolfram?

  Right.

• 2:45:03Lex Fridman?

  And this is the motivation for that, actually.

• 2:45:04Stephen Wolfram?

  Right, and it's, you know, there are, there are indications, and we can do computer experiments, and we can see how it's going to come out, but we need to, you know, the the actual mathematics is, doesn't, doesn't exist. And in branchial space, it's actually even worse. There's, there's even more sort of layers of mathematics that are, you know, we can see how it works roughly by doing computer experiments, but to really understand it, we need more, more sort of mathematical sophistication.

• 2:45:30Lex Fridman?

  So, quantum computers.

• 2:45:32Stephen Wolfram?

  Okay, so the basic idea of quantum computers, the, the promise of quantum computers is quantum mechanics does things in parallel, and so you can sort of intrinsically do computations in parallel, and somehow that can be much more efficient than just doing them one after another. And, you know, I actually worked on quantum computing a bit with Dick Feynman back in 1981, 2, 3, that kind of timeframe, and, and we-

• 2:45:59Lex Fridman?

  Fascinating image, you, you and Feynman working on quantum computers.

• 2:46:04Stephen Wolfram?

  Well, we, we tried to work, the, the big thing we tried to do was invent a randomness chip. That would generate randomness at a high speed using quantum mechanics. And the discovery that that wasn't really possible was part of the the story of. We never really wrote anything about it. I think maybe he wrote some stuff, but I we didn't. We didn't write stuff about what we figured out about sort of the fact that it really seemed like the measurement process in quantum mechanics was a serious damper on what was possible to do in sort of, you know, the possible advantages of quantum mechanics and for computing. But anyway, so so the the sort of the promise of quantum computing is, let's say you're trying to, you know, factor an integer. Well, you can instead of, you know, when you factor an integer, you might say, well,

• 2:46:49Stephen Wolfram?

  does this factor work? Does this factor work? Does this factor work? In ordinary computing, it seems like we pretty much just have to try all these different factors, you know, kind of one after another. But in quantum mechanics, you might have the idea, oh, you can just sort of have the physics try all of them in parallel. Okay. And the, you know, and there's this algorithm, Shor's algorithm, which which allows you, according to the formalism of quantum mechanics, to do everything in parallel and to do it much faster than you can on a classical computer. Okay. The only little footnote is you have to figure out what the answer is. You have to measure the result. So the quantum mechanics internally has figured out all these different branches.

• 2:47:33Stephen Wolfram?

  But then you have to pull all these branches together to say, and the classical answer is this. Okay. The standard theory of quantum mechanics does not tell you how to do that. It tells you how the branching works, but doesn't tell you the process of corralling all these things together. And that process, which intuitively you can see is going to be kind of tricky, but our model actually does tell you how that process of pulling things together works. And the answer seems to be, we're not absolutely sure. We've only got to two times three so far in in, you know, which is kind of in in in this in this factorization in quantum computers. But we can, the, you know, what seems to be the case is that the advantage you get

• 2:48:14Stephen Wolfram?

  from the parallelization from quantum mechanics is lost from the amount that you have to spend pulling together all those parallel threads to get to a classical answer at the end. Now, that phenomenon is not unrelated to various decoherence phenomena that are seen in practical quantum computers and so on. I mean, I should say, as a very practical point, I mean, it's like, should people stop bothering to do quantum computing research? No, because what they're really doing is they're trying to use physics to get to a new level of what's possible in computing. And that's a completely valid activity. Whether, whether you can really put, you know, whether you can say, oh, you can solve an NP-complete problem, you can reduce exponential time to polynomial time, you know, we're not sure.

• 2:48:58Stephen Wolfram?

  And, and I'm suspecting the answer is no, but that's not relevant to the practical speed ups you can get by using different kinds of technologies, different kinds of physics to do basic computing.

• 2:49:09Lex Fridman?

  So you're, you're saying, I mean, some of the models you're playing with, the indication is that to get all the sheet back together and, you know, to, to corral everything together to get the actual solution to the algorithm is.

• 2:49:27Stephen Wolfram?

  You lose all the.

• 2:49:28Lex Fridman?

  You lose, use all of the.

• 2:49:29Stephen Wolfram?

  By the way, I mean, so, so again, this question, do we actually know what we're talking about, about quantum computing and so on? So again, we're doing proof by compilation. So we have a quantum computing framework.

• 2:49:42Lex Fridman?

  Yeah.

• 2:49:43Stephen Wolfram?

  In Wolfram Language, which is, you know, a standard quantum computing framework that represents things in terms of the standard, you know, formalism of quantum mechanics. And we have a compiler that simply compiles the representation of quantum gates into multiway systems.

• 2:49:58Lex Fridman?

  Hmm.

• 2:49:59Stephen Wolfram?

  So, and in fact, the message that I got was from somebody who's working on the project who has managed to compile one of the sort of a core formalism based on category theory and of core quantum formalism into multiway systems.

• 2:50:14Lex Fridman?

  When you say multiway system, these multiway graphs?

• 2:50:17Stephen Wolfram?

  Yes.

• 2:50:18Lex Fridman?

  So you're, you're, yeah, okay, that's awesome. And then you can do all kinds of experiments on that multiway graph.

• 2:50:23Stephen Wolfram?

  Right, well, but the point is that what we're saying is the thing, we've got this representation of, let's say, Shaw's algorithm in terms of standard quantum gates. And it's just a pure matter of sort of computation to just say that is equivalent. We will get the same result as running this multiway system.

• 2:50:40Lex Fridman?

  Can you do complexity analysis on that multiway system?

• 2:50:44Stephen Wolfram?

  Well, that's what we've been trying to do. Yes, we're getting there. We haven't done that yet. I mean, we, we, there's a pretty good indication of how that's going to work out. And we've done it, as I say, our computer experiments, we've unimpressively gotten to about two times three in terms of factorization, which is kind of about how far people have got with physical quantum computers as well. But, but that's, um, but yes, we will be able to, we definitely will be able to do complexity analysis and we will be able to know. So the one remaining hope for quantum computing really, really working at this formal level of, you know, quantum brand exponential stuff being done in polynomial time and so on. The one hope, which is very bizarre, is that you can kind of piggyback on the expansion of branchill space.

• 2:51:28Stephen Wolfram?

  So here's, here's how that might work. So you think, you know, energy conservation, standard thing in high school physics, energy is conserved, right? But now you imagine, you think about energy in the context of cosmology and the context of the whole universe. It's a much more complicated story. The expansion of the universe kind of violates energy conservation. And so, for example, if you imagine you've got two galaxies, they're receding from each other very quickly. They've got two big central black holes. You connect a spring between these two central black holes. Not easy to do in practice, but let's imagine you could do it. Now that spring is being pulled apart. It's getting, getting more potential energy in the spring as a result of the expansion of the universe.

• 2:52:12Stephen Wolfram?

  So in a sense, you are, you are piggybacking on the expansion that exists in the universe and the sort of violation of energy conservation that's associated with that cosmological expansion to essentially get energy. You're essentially building a perpetual motion machine by using the expansion of the universe. And that is a physical version of that. It is conceivable that the same thing can be done in branchial space to essentially mine the expansion of the universe in branchial space as a way to get sort of quantum computing for free, so to speak, just from the expansion of the universe in branchial space. Now, the physical space version is kind of absurd and involves, you know, springs between black holes and so on.

• 2:52:57Stephen Wolfram?

  It's conceivable that the branchial space version is not as absurd and that it's actually something you can reach with physical things you can build in labs and so on. We don't know yet.

• 2:53:07Lex Fridman?

  Okay, so yeah, like you were saying, the branch of space might be expanding and there might be some, something that could be exploited.

• 2:53:15Stephen Wolfram?

  Right, in the same kind of way that, that, that you can exploit the, you know, that expansion of the universe in principle, in physical space.

• 2:53:24Lex Fridman?

  You just have like a glimmer of hope.

• 2:53:26Stephen Wolfram?

  Right, I think that the, look, I think the real answer is going to be that for practical purposes, you know, the official brand that says you can, you can, you know, do exponential things in polynomial time is probably not going to work.

• 2:53:38Lex Fridman?

  For people curious to kind of learn more, so this is more like, this is not middle school. We're gonna go to elementary school for a second. Maybe middle, let's go to middle school. So if I were to try to maybe write a, write a pamphlet of like Wolfram Physics project for dummies, AKA for me, or maybe make a video on the basics, but not just the basics of the physics project, but the basics plus the most beautiful central ideas. How would you go about doing that? Could you help me out a little bit?

• 2:54:20Stephen Wolfram?

  Yeah, yeah, I mean, you know, as a really practical matter, we have this kind of visual summary picture that we made.

• 2:54:26Lex Fridman?

  That's right.

• 2:54:27Stephen Wolfram?

  Which I think is a pretty good, you know, when I've tried to explain this to people and, you know, it's a pretty good place to start. Is you got this rule, you know, you apply the rule, you're building up this, this big hypergraph. You've got all these possibilities. You're kind of thinking about that in terms of quantum mechanics. I mean, that's a, that's a, that's a decent place to start.

• 2:54:48Lex Fridman?

  So basically, the things we've talked about, which is space represents a hypergraph.

• 2:54:54Lex Fridman?

  Transformation of that space is kind of time.

• 2:54:58Stephen Wolfram?

  Yes.

• 2:54:58Lex Fridman?

  And then.

• 2:55:00Stephen Wolfram?

  Structure of that space, the curvature of that space has gravity. That's, that can be explained without going anywhere near quantum mechanics. I would say that's actually easier to explain than special relativity.

• 2:55:12Lex Fridman?

  Oh, so going into general, so going to curvature.

• 2:55:15Stephen Wolfram?

  Yeah, I mean, special relativity, I, I think is, it's a little bit elaborate to explain.

• 2:55:20Lex Fridman?

  Yeah.

• 2:55:21Stephen Wolfram?

  And honestly, you only care about it if you know about special relativity. If you know how special relativity is ordinarily derived and so on.

• 2:55:27Lex Fridman?

  So general relativity is easier.

• 2:55:29Stephen Wolfram?

  Is easier, yes.

• 2:55:30Lex Fridman?

  And what about quantum, what's the easiest way to reveal?

• 2:55:33Stephen Wolfram?

  I think the, the basic point is just this, this fact that there are all these different branches, that there's this kind of map of how the branches work. And that, I mean, I think, I think actually the recent things that we have about the double slit experiment are pretty good. Cause you can actually see this, you can see how the double slit, you know, phenomenon arises from just features of these graphs. Now, you know, having said that, right, there is a little bit of, of sleight of hand there. Because the, the true story of the way that double slit thing works, depends on the co-ordinatization of branchial space. That, for example, in our internal team, there is still a vigorous battle going on about how that works.

• 2:56:19Stephen Wolfram?

  And it's, it's what's becoming clear is, I mean, what's becoming clear is that it's mathematically really quite interesting. I mean, that is that there's a, you know, it involves essentially putting space filling curves. You'll basically have a thing which is naturally two dimensional. And you're sort of mapping it into one dimension with a space filling curve. And it's like, why is it this space filling curve and another space filling curve? And that becomes a story about Riemann surfaces and things. And it's quite elaborate. And, but, but the, there's a more, a little bit sleight of hand way of doing it. Where it's, you know, it's surprisingly direct.

• 2:56:54Lex Fridman?

  It's so, a question that might be difficult to answer. But for several levels of people, could you give me advice on how we can learn more? Specifically. There is people that are completely outside and just curious and are captivated by the beauty of hypergraphs, actually. So people that just want to explore, play around with this. Second level is people from, say, people like me, who somehow got a PhD in computer science, but are not physicists. And but fundamentally, the work you're doing is of computational nature. So it feels very accessible.

• 2:57:38Stephen Wolfram?

  Yes.

• 2:57:39Lex Fridman?

  So what are, what can a person like that do to learn enough physics? Or not, to be able to, uh, one, explore the beauty of it? And two, the final level of contribute something

• 2:57:55Stephen Wolfram?

  Right.

• 2:57:55Lex Fridman?

  of a level of even publishable.

• 2:57:58Stephen Wolfram?

  Right.

• 2:57:59Lex Fridman?

  Like, strong, interesting ideas.

• 2:58:01Stephen Wolfram?

  Right.

• 2:58:02Lex Fridman?

  At all those layers, complete beginner.

• 2:58:04Stephen Wolfram?

  Yeah, right.

• 2:58:05Lex Fridman?

  A CS person and a CS person that wants to publish.

• 2:58:08Stephen Wolfram?

  Right. I mean, I think that, you know, I've written a bunch of stuff. A person called Jonathan Gorad, who's been a key person working on this project, has also written a bunch of stuff. And some other people started writing things, too.

• 2:58:19Lex Fridman?

  And he's a physicist.

• 2:58:21Stephen Wolfram?

  Physicist. Well, he's, I would say, a mathematical physicist. He's pretty mathematically sophisticated. He's, he regularly outmathematicizes me.

• 2:58:29Lex Fridman?

  Yeah. This strong, yeah, strong mathematical physicist. Yeah, I looked at some of the papers.

• 2:58:34Stephen Wolfram?

  Right. But, but so, so, I mean, you know, I wrote this kind of original announcement, blog post about this project, which people seem to have found. I've been really happy, actually, that people who, uh, you know, people seem to have grocked key points from that. Much deeper key points, people seem to have grocked than I thought they would grok.

• 2:58:57Lex Fridman?

  And that's a kind of a long blog post. They explain some of the things we talked about, like the hypergraph and the basic rules. And I don't, does it, I forget, it doesn't have any quantum mechanics in it?

• 2:59:07Stephen Wolfram?

  It does. Quantum mechanics, yes, it does. But we, we know a little bit more since that blog post. That probably clarifies, but that blog post is, does a pretty decent job. And, you know, talking about things like, again, something we didn't mention, the fact that the uncertainty principle is a consequence of curvature in branchial space.

• 2:59:25Lex Fridman?

  How much physics should a person know to be able to understand? The beauty of this framework and to contribute something novel.

• 2:59:34Stephen Wolfram?

  Okay, so I think that those are different questions. So, I mean, I think that the why does this work? Why does this make any sense?

• 2:59:45Stephen Wolfram?

  To really know that, you have to know a fair amount of physics. Okay. And for example, have a

• 2:59:51Lex Fridman?

  When you say, why does this work? You're referring to the connection between this model and

• 2:59:56Stephen Wolfram?

  General relativity, for example. You have to understand something about general relativity.

• 3:00:00Lex Fridman?

  There's also a side of this where just as the pure mathematical framework is fascinating.

• 3:00:05Stephen Wolfram?

  Yes.

• 3:00:05Lex Fridman?

  If you throw the physics out.

• 3:00:07Stephen Wolfram?

  Right, then it's quite accessible to, I mean, you know, I wrote this sort of long technical introduction to the project, which seems to have been very accessible to people who are, you know, who understand computation and formal abstract ideas, but are not specialists in physics or other kinds of things. I mean, the thing with the physics part of it is, you know, it's, there's both a way of thinking and a, literally a mathematical formalism. I mean, it's like, you know, to know that we get the Einstein equations, to know we get the energy momentum tensor, you kind of have to know what the energy momentum tensor is. And that's physics. I mean, that's kind of graduate level physics, basically.

• 3:00:46Stephen Wolfram?

  And so that, you know, making that final connection is, requires some depth of physics knowledge.

• 3:00:55Lex Fridman?

  I mean, that's the unfortunate thing, the difference in machine learning and physics in the 21st century. Is it really out of reach of a year or two worth of study?

• 3:01:05Stephen Wolfram?

  No, you could get it in a year or two. But you can't get it in a month.

• 3:01:09Lex Fridman?

  Right.

• 3:01:09Stephen Wolfram?

  I mean,

• 3:01:10Lex Fridman?

  So, but it doesn't require necessarily like 15 years?

• 3:01:13Stephen Wolfram?

  No, it does not. And in fact, a lot of what has happened with this project makes a lot of this stuff much more accessible. There are things where it has been quite difficult to explain what's going on and it requires much more, you know, having the concreteness of being able to do simulations, knowing, knowing that this thing that you might have thought was just an analogy is really actually what's going on, makes one feel much more secure about just sort of saying, this is how this Works. And I think it will be, you know, the, I'm hoping the textbooks of the future, the physics textbooks of the future. There will be a certain compression. There will be things that used to be very much more elaborate because, for example, even doing continuous mathematics versus this discrete mathematics.

• 3:01:56Stephen Wolfram?

  That, you know, to know how things work in continuous mathematics, you have to be talking about stuff and waving your hands about things. Whereas with discrete, the discrete version, it's just like, here is a picture. This is how it works. And there's no, oh, did we get the limit right? Did this, you know, did this thing that is of, you know, uh, zero, you know, measure zero object, you know, interact with this thing in the right way? You don't have to have that whole discussion. It's just like, here's a picture, you know, this is what it does. And, you know, you can, then it takes more effort to say, what does it do in the limit when the picture gets very big?

• 3:02:29Lex Fridman?

  But you can do experiments to build up an intuition, actually.

• 3:02:31Stephen Wolfram?

  Yes, right. And you, you can get sort of core intuition for what's going on. Now, in terms of contributing to this, the, you know, I would say that the study of the computational universe and how all these programs work in the computational universe, there's just an unbelievable amount to do there. And it is very close to the surface. That is, you know, high school kids, you can do experiments. It's not, um, you know, and you can discover things. I mean, you know, we, you can discover stuff about, I don't know, like this thing about expansion of branchill space. That's an absolutely accessible thing to look at. Now, you know, the main issue with doing these things is not, there isn't a lot of technical depth difficulty there.

• 3:03:13Stephen Wolfram?

  The actual doing of the experiments, you know, all the code is all on our website to do all these things. The real thing is sort of the judgment of what's the right experiment to do? How do you interpret what you see? That's the part that, you know, people will do amazing things with. And that's the part that, but, but it isn't like you have to have done 10 years of, of study to get to the point where you can do the experiments.

• 3:03:36Lex Fridman?

  That's a cool thing. You can do experiments day one, basically. It's that, that, that, that's the amazing thing about, and you've actually put the tools out there. It's, it's beautiful. It's mysterious. Uh, there's still, I would say, maybe you can correct me. It feels like there's a huge number of log hanging fruit.

• 3:03:53Stephen Wolfram?

  Oh, there is.

• 3:03:54Lex Fridman?

  On the mathematical side at least, not the, not the physics side perhaps.

• 3:03:57Stephen Wolfram?

  No, there's, look, on the, on the, okay, on the physics side, we are, we're definitely in harvesting mode.

• 3:04:06Lex Fridman?

  Of which which fruit the low hanging ones or?

• 3:04:08Stephen Wolfram?

  The low hanging.

• 3:04:09Lex Fridman?

  All right.

• 3:04:09Stephen Wolfram?

  Yeah, right. I mean, basically, here's the thing. There's a certain list of, you know, here are the effects in quantum mechanics. Here are the effects in general activity. It's just like industrial harvesting. It's like, can we get this one, this one, this one, this one, this one? And and the thing that's really, you know, interesting and satisfying. And it's like, you know, is one climbing the right mountain? Does one have the right model? The thing that's just amazing is, you know, we keep on like, are we going to get this one? How hard is this one? It's like, oh, you know, it looks really hard. It looks really hard. Oh, actually, we can get it. Um, and.

• 3:04:44Lex Fridman?

  And you're you're continually surprised. I mean, it seems like I've been following your progress. It's kind of exciting. All the in harvesting mode, all the things you're picking up along the way.

• 3:04:53Stephen Wolfram?

  Right, right. No, I mean, it's it's the thing that is. I keep on thinking it's going to be more difficult than it is. Now, that's a, you know, that's a, who knows what? I mean, the one thing, so the the the um, the thing that's been a was a big thing that I think we're we're pretty close to. I mean, I can give you a little bit of the roadmap. It's sort of interesting to see. It's like, what are particles? What are things like electrons? How do they really work?

• 3:05:15Lex Fridman?

  Are you close to get like what? What's a are you close to trying to understand like the atom, the electrons, the electrons, protons?

• 3:05:24Stephen Wolfram?

  Okay, so this is this is the stack. So the first thing we want to understand is uh, the quantization of spin. So particles, they they kind of spin. They have a certain angular momentum. That angular momentum, even though the masses of particles are all over the place. You know, the electron has a mass of point five one one M V. The but you know, the proton is nine thirty eight M V, et cetera, et cetera, et cetera. They're all kind of random numbers. The the spins of all these particles are either integers or half integers. And that's a fact that was discovered in the nineteen twenties, I guess. The uh, I think that we are close to understanding why spin is quantized.

• 3:06:03Stephen Wolfram?

  Um, and that's a, and it it appears to be a quite elaborate mathematical story about homotopy groups in twister space and all kinds of things. But bottom line is that seems within reach. And that's that's a big deal because that's a very core feature of understanding how particles work in quantum mechanics. Another core feature is this difference between particles that obey the exclusion principle and sort of stay apart that leads to the stability of matter and things like that. And particles that love to get together and be in the same state, things like photons that and that's what leads to phenomena like lasers, where you can get sort of coherently everything in the same state. That difference is the particles of integer spin are bosons like to get together in the

• 3:06:48Stephen Wolfram?

  same state, the particles of half integer spin are fermions, like electrons, that they tend to stay apart. And so the question is, can we can we get that in our models? And oh, just the last few days, I think we made, I mean, I think the story of, I mean, it's it's it's one of these things where we're really close.

• 3:07:08Lex Fridman?

  It's it's It's just connected fermions and bosons.

• 3:07:11Stephen Wolfram?

  Yeah, yeah, yeah. So this was what what happens is what seems to happen. Okay. It's, you know, subject to revision next even next few days. But what seems to be the case is that bosons are associated with essentially merging in multiway graphs and fermions are associated with branching in multiway graphs. And that essentially the exclusion principle is the fact that in branchial space, things have a certain extent in branchial space that in which things are being sort of forced apart in branchial space, whereas the case of bosons, they get they they come together in branchial space. And the real question is, can we explain the relationship between that and these things called spinners, which are the representation of half integer spin particles that have

• 3:07:55Stephen Wolfram?

  this weird feature that usually when you go around 360 degree rotation, you get back to where you started from. But for a spinner, you don't get back to where you started from. It takes 720 degrees of rotation to get back to where you started from. And we are just, it feels like we are, we're just incredibly close to actually having that, understanding how that works. And it turns out it it looks like, my current speculation is, that it's as simple as the directed hypergraphs versus undirected hypergraphs.

• 3:08:24Lex Fridman?

  Interesting.

• 3:08:25Stephen Wolfram?

  The relationship between spinners and vectors. So which is just.

• 3:08:28Lex Fridman?

  Interesting. Yeah, that'll be interesting if these are all these kind of uh nice properties of this multiway graphs of branching and.

• 3:08:36Stephen Wolfram?

  Right, but spinners have been very mysterious. And if that's what they turn out to be, there's going to be an easy explanation.

• 3:08:42Lex Fridman?

  Yeah, it's directed versus undirected.

• 3:08:44Stephen Wolfram?

  It's just, and that's why there's only two different cases. It's.

• 3:08:48Lex Fridman?

  Well, why are spinners important in quantum mechanics? Can you just give a?

• 3:08:53Stephen Wolfram?

  Yeah, so spinners are important because they are um they're the representation of of electrons which have half hundred spin. They are the the wave functions of electrons are spinners. Just like the wave functions of photons are vectors, the wave functions of electrons are spinners. And and they have this property that when you rotate by by three hundred and sixty degrees, they come back to minus one of themselves and it takes seven hundred and twenty degrees to get back to the original value. And and they are a consequence of of um uh and we usually think of of of rotation in space as being, you know, when you have this notion of rotational invariance.

• 3:09:36Stephen Wolfram?

  And rotational invariance, as we ordinarily experience it, doesn't have the feature, you know, if you go through three hundred and sixty degrees, you go back to where you started from. But that's not true for electrons. And so that's that's why understanding how that works is important.

• 3:09:50Lex Fridman?

  Yeah, I've been playing with Mobius strip quite a bit lately, just for fun.

• 3:09:54Stephen Wolfram?

  Yes, yes.

• 3:09:55Lex Fridman?

  It adds some funk. It has the same kind of funky properties.

• 3:09:58Stephen Wolfram?

  Yes, right, exactly. You can have this, the so-called belt trick, which is this way of taking an extended object. And you can see properties like spinners with that kind of extended object that um.

• 3:10:07Lex Fridman?

  Yeah, it would be very cool if there's it somehow connects the directed versus undirected.

• 3:10:11Stephen Wolfram?

  I think that's what it's going to be. I think it's going to be as simple as that, but we'll see. I mean, this is this is the thing that that, you know, this is the big sort of bizarre surprise is that, you know, uh because, you know, I I I learned physics is probably, let's say, let's say, a fifth generation in the sense that, you know, if you go back to the nineteen twenties and so on, there were the people who were originating quantum mechanics and so on. Maybe it's a little less than that. Maybe I was like a. A a third generation or something, I don't know, but but you know, the people from whom I learnt physics were the people who were, you know, who have been students of the students of the the people who originated the the current understanding of physics. And we're now at, you know, probably the seventh generation of physicists or something from the from the early days of twentieth century physics.

• 3:10:55Stephen Wolfram?

  And, you know, whenever a field gets that many generations deep, it seems the foundations seem quite inaccessible. And they seem, you know, it seems like you can't possibly understand that. We've gone through, you know, seven academic generations and that's been, you know, that's been this thing that's been difficult to understand for for that long. It just can't be that simple.

• 3:11:18Lex Fridman?

  But in a sense, maybe that journey takes you to a to a simple explanation that was there all along.

• 3:11:25Stephen Wolfram?

  Right, right, right. I mean, you know, and the thing for me personally, the thing that's been quite interesting is, you know, I didn't expect this project to work in this way. And I, you know, but I had this sort of weird piece of personal history that I used to be a physicist.

• 3:11:39Lex Fridman?

  Yeah.

• 3:11:39Stephen Wolfram?

  And I used to do all this stuff and I know, you know, the the standard canon of physics. I knew it very well. And, um, you know, but then I'd been working on this kind of computational paradigm for basically forty years. And uh the fact that, you know, I'm sort of now coming back to to, you know, trying to apply that in physics, it kind of felt like that journey was necessary.

• 3:12:02Lex Fridman?

  Was this uh, when did you first try to play with a hypergraph?

• 3:12:06Stephen Wolfram?

  So I, what happened is, yeah, so so what I had was, okay, so this is again, you know, one one always feels dumb after the fact. It's it's um, it's obvious after the fact. But but so back in the early nineteen nineties, I realized that using graphs as a sort of underlying thing underneath space and time was going to be a useful thing to do. I figured out about multiway systems. I figured out the things about general relativity I'd figured out by the end of the nineteen nineties. But I always felt there was a certain inelegance because I was using these graphs and there were certain constraints on these graphs that seemed like they were, they were kind of awkward. It was kind of like. You can pick, it's like you couldn't pick any rule. It was like, pick any number, but the number has to be prime.

• 3:12:50Stephen Wolfram?

  It was kind of like you couldn't, it was kind of an awkward special constraint. I had these trivalent graphs, graphs with just three connections from every node. Okay, so, but, but I discovered a bunch of stuff with that, but I thought it was kind of inelegant. And, you know, the other piece of sort of personal history is obviously I spent my life as a language, computational language designer. And so the story of computational language design is a story of how do you take all these random ideas in the world? And kind of grind them down into something that is computationally as simple as possible. And so, you know, I've been very interested in kind of simple computational frameworks for representing things. And have, you know, ridiculous amounts of experience in, in trying to do that.

• 3:13:33Lex Fridman?

  And actually, all of those trajectories of your life kind of came together. So you, you make it sound like you could have come up with everything you're working on now decades ago, but in reality.

• 3:13:44Stephen Wolfram?

  Look, two things slowed me down. I mean, one thing that slowed me down was I couldn't figure out how to make it elegant. And, and that turns out hypergraphs were the key to that, and that I figured out about, about less than two years ago now. Um, and, um, the other, I mean, I, I think, so that was, that was sort of a, a key thing. Well, okay, so the real embarrassment of this project, okay, is that the final structure that we have that is the foundation for this project is basically a, a kind of an idealized version, a formalized version of the exact same structure that I've used to build computational languages for more than forty years.

• 3:14:24Lex Fridman?

  Yeah.

• 3:14:24Stephen Wolfram?

  But it took me, but I didn't realize that. And, and, you know.

• 3:14:28Lex Fridman?

  And there, yep, may be other, so we're focused on physics now, but I mean, that's what the new kind of science is about, same kind of stuff. And this, in terms of mathematically, um, the, the beauty of it, so, so there could be entire other kind of objects. They're useful for, like, we, we're not talking about, you know, machine learning, for example. Maybe there is other variants of the hypergraph that are very useful for reasoning.

• 3:14:53Stephen Wolfram?

  We'll, we'll see whether the multi-way graph for a machine learning system is interesting. Okay?

• 3:14:59Lex Fridman?

  Let's leave it at that. That's conversation number three.

• 3:15:01Stephen Wolfram?

  That's, that's, that's, uh, we're not going to go there right now, but.

• 3:15:05Lex Fridman?

  One of the things you've mentioned is um the space of all possible rules that we kind of discussed a little bit uh that you know, there could be, I guess, the set of possible rules is infinite.

• 3:15:18Stephen Wolfram?

  Right. Well, so here's here's the big sort of one of the conundrums that that I'm kind of trying to deal with is let's say we think we found the rule for the universe. And we say, here it is, you know, write it down. It's a little tiny thing. And then we say, gosh, that's really weird. Why did we get that one? Right? And then we're in this whole situation, because let's say it's fairly simple. How did we come up the winners getting one of the simple possible universe rules? Why didn't we get what some incredibly complicated rule? Why do we get one of the simpler ones? And and that's the thing which, you know, in the history of science, you know, the whole sort of story of Copernicus and so on was, you know, we used to think the earth was the center of the universe, but now we find out it's not.

• 3:16:03Stephen Wolfram?

  And we're actually just in some, you know, random corner of some random galaxy out in this big universe. There's nothing special about us. So if we get, you know, universe number three hundred and seventeen out of all the infinite number of possibilities, how do we get something that's small and simple? Right? So I was very confused by this. And it's like, what are we going to say about this? How are we going to explain this? And I thought it was might be one of these things where you just, you know, you can get it to the threshold. And then you find out it's rule number such and such, and you just have no idea why it's like that.

• 3:16:34Lex Fridman?

  Yeah.

• 3:16:35Stephen Wolfram?

  Okay, so then I realized it's actually more bizarre than that. Okay. So we talked about multiway graphs. We talked about this idea that you take these underlying transformation rules on these hypergraphs. And you apply them wherever the rule can apply, you apply it. And that makes this whole multiway graph of possibilities. Okay, so let's go a little bit weirder. Let's say that at every place, not only do you apply a particular rule in all possible ways it can apply, but you apply all possible rules in all possible ways they can apply. As you say, that's just crazy. That's way too complicated. You're never going to be able to conclude anything. Okay, however, turns out

• 3:17:17Lex Fridman?

  Uh oh.

• 3:17:17Stephen Wolfram?

  That

• 3:17:18Lex Fridman?

  Don't tell me there's some kind of invariance.

• 3:17:20Stephen Wolfram?

  Yeah, yeah. So what happens is

• 3:17:24Lex Fridman?

  And that would be amazing.

• 3:17:25Stephen Wolfram?

  Right, so, so this thing that you get is this kind of ruleal multiway graph. This multiway graph that is a branching of rules as well as a branching of possible applications of rules. This thing has causal invariance. It's a, it's an inevitable feature that it shows causal invariance. And that means that you can take different reference frames, different ways of slicing this thing. And they will all in some sense be equivalents. If you, if you make the right translation, they will be equivalents. So, okay, so the, the, the basic point here is

• 3:17:57Lex Fridman?

  If that's true, that would be beautiful.

• 3:18:00Stephen Wolfram?

  It is true and it is beautiful.

• 3:18:02Lex Fridman?

  So you, you, it's not just an intuition, there is some

• 3:18:05Stephen Wolfram?

  No, no, no, there's, there's real mathematics behind this and it, and it's, it is, it is, okay, so here's

• 3:18:11Lex Fridman?

  Yeah, that, that would be, that's amazing.

• 3:18:14Stephen Wolfram?

  Right, so, so by the way, I mean, the mathematics that's connected to is the mathematics of higher category theory and groupoids and things like this, which I've always been afraid of. But now I'm, I'm, I'm finally wrapping my arms around it. But um, um, it's also related to, uh, it also relates to computational complexity theory. Um, it's also deeply related to the P versus NP problem and other things like this. Again, seems completely bizarre that these things are connected, but here's why it's connected. The, this space of all possible, okay, so a Turing machine, very simple model of computation, you know, you just got a, a, this tape where you write down, you know, ones and zeros or something on the tape.

• 3:18:55Stephen Wolfram?

  And you have this, this rule that says, you know, you, you change the number, you move the head of the, uh, on the tape, et cetera. You have a definite rule for doing that. A deterministic Turing machine just does that deterministically. Given the configuration of the tape, it will always do the same thing. A non-deterministic Turing machine can have different choices that it makes at every step.

• 3:19:16Lex Fridman?

  Yeah.

• 3:19:16Stephen Wolfram?

  And so, you know, um, you know, this stuff, you probably teach this stuff, the, um, it, um, Uh, you know, so a non deterministic Turing machine has the set of branching possibilities, which is in fact, one of these multi way graphs. And in fact, if you say, imagine the extremely non deterministic Turing machine, the Turing machine that can just do, uh, that takes any possible rule at each step. That is this ruleal multi way graph. The set of, the set of, the set of possible histories of that extreme non deterministic Turing machine is a ruleal multi way graph.

• 3:19:53Lex Fridman?

  And you're, uh, what term are you using? Ruleal?

• 3:19:56Stephen Wolfram?

  Ruleal.

• 3:19:56Lex Fridman?

  Ruleal, I like.

• 3:19:57Stephen Wolfram?

  Weird word. Yeah, it's a weird word.

• 3:19:59Lex Fridman?

  Ruleal.

• 3:20:00Stephen Wolfram?

  Multi way graph. Okay, so this, so that.

• 3:20:03Lex Fridman?

  I, I'm trying to think of, I'm trying to think of the space of rules. Uh, so these are basic transformations.

• 3:20:11Stephen Wolfram?

  So in a Turing machine, it's like it says, move left, move, you know, if it's a one, if it's a black square under the head, move left and right a green square. That's a rule.

• 3:20:23Lex Fridman?

  That's a very basic rule, but I'm trying to see the rules on the hypergraphs. How rich of the programs can they be? Or do they all ultimately just map into something simple?

• 3:20:33Stephen Wolfram?

  Yeah, they're all, I mean, hypergraphs, that's another layer of complexity on this whole thing. You can, you can think about these in transformations of hypergraphs, but Turing machines are a little bit simpler.

• 3:20:42Lex Fridman?

  Stick up with Turing machines, okay?

• 3:20:43Stephen Wolfram?

  Right, they're a little bit simpler. So if you look at these extreme non deterministic Turing machines, you're mapping out all the possible non deterministic paths that the Turing machine can follow.

• 3:20:54Lex Fridman?

  Yeah.

• 3:20:54Stephen Wolfram?

  And, and if you ask the question, uh, can you reach? Okay, so, so a deterministic Turing machine follows a single path. The non deterministic Turing machine fills out this whole, uh, sort of ball of possibilities. And so then the P versus NP problem ends up being questions about, and we haven't completely figured out all the details of this, but it's basically, has to do with questions about the, the growth of that ball relative to what happens with individual paths and so on. So essentially, there's a geometrization of the P versus NP problem that comes out of this. That's a sideshow, okay? The main, the main event here is the statement that.

• 3:21:33Stephen Wolfram?

  You can look at this multiway graph where the branches correspond not just to different applications of a single rule, but to different applications, to applications of different rules, okay? And that then, that when you say, I'm going to be an observer embedded in that system, and I'm going to try and make sense of what's going on in the system. And to do that, I essentially am picking a reference frame. And that turns out to be, uh, well, okay, so the way this comes out essentially is the reference frame you pick is the rule that you infer is what's going on in the universe.

• 3:22:12Stephen Wolfram?

  Even though all possible rules are being run, although all those possible rules are in a sense giving the same answer because of causal invariance. But what you see will be, could be completely different. If you pick different reference frames, you essentially have a different description language for describing the universe. Okay, so how does, what does this really mean in practice? So imagine there's us. We think about the universe in terms of space and time, and we have various kinds of description models and so on. Now let's imagine the friendly aliens, for example, right? How do they describe their universe? Well, you know, our description of the universe probably is affected by the fact that, you know, we are about the size we are, you know, a meter-ish tall, so to speak.

• 3:22:57Stephen Wolfram?

  We have brain processing speeds of about the speeds we have. We're not the size of planets, for example, where the speed of light really would matter. You know, in our everyday life, the speed of light doesn't really matter. Everything can be, you know, the fact that the speed of light is finite is irrelevant. It could as well be infinite. We wouldn't, wouldn't make any difference. You know, it affects the, the ping times on the internet.

• 3:23:18Lex Fridman?

  Yeah, that's right.

• 3:23:19Stephen Wolfram?

  That's about the level of, of, um, of how we notice the speed of light. In our sort of everyday existence, we don't really notice it. Um, and so we have a way of describing the universe that's based on our sensory, you know, our senses are, uh, these days also on the mathematics we've constructed and so on. But the realization is, it's not the only way to do it. There will be completely, completely utterly incoherent descriptions of the universe, which correspond to different reference frames in this sort of rulial space.

• 3:23:51Lex Fridman?

  In the rulial space, that's fascinating. So we're, we have some kind of reference frame in this rulial space.

• 3:23:56Stephen Wolfram?

  Right.

• 3:23:57Lex Fridman?

  And from that.

• 3:23:59Stephen Wolfram?

  That's why we are attributing this rule to the universe. So in other words, when we say, why is it this rule and not another? The answer is just, you know, shine the light back on us, so to speak. It's because of the reference frame that we've picked in our way of understanding what's happening in this sort of space of all possible rules and so on.

• 3:24:19Lex Fridman?

  But also in the space from this reference frame, because of the royal, the, the, the invariance, that's simple, that the rule on which the universe, with which you can run the universe, might as well be simple.

• 3:24:38Stephen Wolfram?

  Yes, yes, but okay, so here's another point. So this is again, these are a little bit mind twisting in some ways, but, but the, the, um, okay, another thing that's sort of we know from computation is this idea of computation universality. The fact that, given that we have a program that runs on one kind of computer, we can as well, you know, we can convert it to run on any other kind of computer. We can emulate one kind of computer with another. So that might lead you to say, well, you think you have the rule for the universe, but you might as well be running it on a Turing machine because we know we can emulate any computational rule on any kind of machine. And that's essentially the same thing that's being said here.

• 3:25:21Stephen Wolfram?

  That is, that what we're doing is we're saying, these different interpretations of physics corresponds to essentially running physics on different underlying, you know, thinking about the physics as running in different, with different underlying rules, as if different underlying computers were running them. And but because of computation universality, or more accurately, because of this principle of computational equivalence thing of mine, there's, they are.

• 3:25:51Stephen Wolfram?

  These things are ultimately equivalent. So the only thing that is the ultimate fact about the universe, the ultimate fact that doesn't depend on any of these, you know, we don't have to talk about specific rules, et cetera, et cetera, et cetera. The ultimate fact is the universe is computational. And it is the, the things that happen in the universe are the kinds of computations that the principle of computational equivalence says should happen. Now, that might sound like you're not really saying anything there, but you are because you can, you could in principle have a hypercomputer that things that take an ordinary computer an infinite time to do, the hypercomputer can just say, oh, I know the answer. It's this immediately.

• 3:26:33Stephen Wolfram?

  What this is saying is the universe is not a hypercomputer. It's not simpler than a, an ordinary Turing machine type computer. It's exactly like an ordinary Turing machine type computer. And so that's the, that's in the end, the sort of net, net conclusion is that's the thing that is the sort of the hard immovable fact about the universe. That's sort of the, the fundamental principle of the universe is that it is computational and not hypercomputational and not sort of infracomputational. It is this level of computational ability. And it's, um, it kind of has, and that's sort of the, the, the core fact. But now, you know, this, this idea that you can have these different kind of

• 3:27:18Stephen Wolfram?

  rulial reference frames, these different description languages for the universe, it, it makes me, you know, I, I used to think, okay, you know, imagine the aliens, imagine the extraterrestrial intelligence thing. You know, at least they experience the same physics.

• 3:27:32Lex Fridman?

  Right.

• 3:27:33Stephen Wolfram?

  And now I've realized it isn't true.

• 3:27:35Lex Fridman?

  They could have a different rulial frame. That's fascinating.

• 3:27:38Stephen Wolfram?

  That they can end up with a, a, a, a description of the universe that is utterly, utterly incoherent with ours. And, and that's also interesting in terms of how we think about, well, intelligence, the nature of intelligence and so on. You know, I'm, I'm fond of the quote, you know, the weather has a mind of its own. Because these are, you know, these are sort of computationally, that, that system is computationally equivalent to the system that is our brains and so on. And what's different is we don't have a way to understand, you know, what the weather is trying to do, so to speak. We have a story about what's happening in our brains. We don't have a sort of connection to what's happening there.

• 3:28:15Lex Fridman?

  So we actually, it's funny, last time. We talked maybe over a year ago, uh, we talked about how it was more based on your work with a rival. Uh, we talked about how would we communicate with alien intelligences. Can you maybe comment on? How we might, how the Wolf from Physics Project changed your view, how we might be able to communicate with alien intelligence? Like if they showed up, is it possible that because of our comprehension of the physics of the world might be completely different? We would just not be able to communicate.

• 3:28:53Stephen Wolfram?

  Here's, here's the, here's the thing, you know, intelligence is everywhere. The fact, this idea that there's this notion of, oh, there's going to be this amazing extraterrestrial intelligence and it's going to be this unique thing. It's just not true. It's the same thing, you know, I, I think people will realize this about the time when people decide that artificial intelligences are kind of just natural things that are like human intelligences. They'll realize that, that extraterrestrial intelligences or intelligences associated with physical systems and so on. It's all the same kind of thing.

• 3:29:27Lex Fridman?

  It's ultimately computation.

• 3:29:28Stephen Wolfram?

  It's all the same, it's all just computation and the issue is, can you, are you sort of inside it? Are you, are you thinking about it? Do you have sort of a story you're telling yourself about it? And, you know, the weather could have a story, it's telling itself about what it's doing. We just, it's utterly incoherent with the stories that we tell ourselves based on how our brains work.

• 3:29:51Lex Fridman?

  I mean, ultimately it must be a, a question whether we can align.

• 3:29:56Stephen Wolfram?

  Exactly.

• 3:29:57Lex Fridman?

  Align with the kind of intelligences.

• 3:29:59Stephen Wolfram?

  Right, right, right.

• 3:30:00Lex Fridman?

  If there's a systematic way of doing it.

• 3:30:01Stephen Wolfram?

  Right, so the question is in the space of all possible intelligences, what's the, how do you think about the distance between description languages? For one intelligence versus another? And needless to say, I have thought about this and, um, you know, I, I don't, I don't have a great answer yet, but, but I think that's a, that's a thing where there will be things that can be said. And there'll be things that where you can sort of start to characterize, you know, what is the translation distance? Between this, you know, version of the universe or this, you know, kind of set of computational rules and this other one. In fact, okay, so this is a, you know, there's this idea of algorithmic information theory.

• 3:30:41Stephen Wolfram?

  There's this question of sort of what is the, uh, when you have some, something, what is the sort of shortest description you can make of it? Where that description could be saying, run this program to get the thing, right? So I'm pretty sure that, that the, um, uh, that

• 3:31:01Stephen Wolfram?

  there will be a physicalization of the idea of algorithmic information. And that, okay, this is again, a little bit bizarre, but so I mentioned that there's the speed of light, maximum speed of information transmission in physical space. There's a maximum speed of information transmission in branchill space, which is a maximum entanglement speed. There's a maximum speed of information transmission in rulial space, which is, has to do with a maximum speed of translation between different, uh, description languages. And again, I'm, I'm not fully wrapped my brain around this one.

• 3:31:35Lex Fridman?

  Yeah, that one just blows my mind to think about that, but that starts getting closer to the, yeah, the.

• 3:31:41Stephen Wolfram?

  It's kind of a physicalization, right, it's, it's a, and it's also a physicalization of, of algorithmic information. And I think there's probably a connection between, I mean, there's probably a connection between the notion of energy and some of these things, which again, I, I, you know, hadn't seen all this coming. I, I've always been a little bit resistant to the idea of connecting physical energy to things in, in, in computation theory, but I think that's probably coming.

• 3:32:04Lex Fridman?

  And that's essentially at the core with the, the physics project is that you're connecting information theory with physics.

• 3:32:13Stephen Wolfram?

  Yeah, it's computation.

• 3:32:14Lex Fridman?

  Computation with our physical universe.

• 3:32:17Stephen Wolfram?

  Yeah, right. I mean, the fact that our physical universe is, is right, that we can think of it as a computation and that we can have discussions like, you know, the theory of the physical universe is the same kind of a theory as the P versus NP problem and so on, is, is really, uh, you know, I think that's really interesting and, and the fact that, well, uh, okay. So this, this kind of brings me to one, one more thing that I have to, in terms of this sort of unification of different ideas, which is meta mathematics.

• 3:32:47Lex Fridman?

  Yeah, let's talk about that. You mentioned that earlier. What the heck is mathematics?

• 3:32:51Stephen Wolfram?

  And uh. Okay, so here's, here's what, here's, okay. So what is mathematics? Mathematics, uh, sort of at a, at a lowest level, one thinks of mathematics as you have certain axioms. You say, you know, you say things like X plus Y is the same as Y plus X. That's an axiom. Um, about addition. And then you say, we've got these axioms. And we, and, and from these axioms, we derive all these theorems that fill up the literature of mathematics. The, the, the activity of mathematicians is to derive all these theorems. Actually, the axioms of mathematics are very small. You can fit, you know, when I did my new kind of science book, I fit all of the standard axioms of mathematics on basically a page and a half.

• 3:33:35Stephen Wolfram?

  Um, it's not much stuff. It's like a very simple rule from which all of mathematics arises. Um, the way it works, though, is a little different from the way things work in, in sort of, uh, of a computation. Because in mathematics, what you're interested in is a proof. And the proof says, from here, you can use, from this expression, for example. You can use these axioms to get to this other expression. So that proves these two things are equal. Okay, so we can, we can begin to see how this is going to work. What, what's gonna, what happened is there are paths in meta mathematical space. So what happens is each, um, two different ways to look at it.

• 3:34:15Stephen Wolfram?

  You can just look at it as a mathematical expressions, or you can look at it as mathematical statements, postulates or something. But either way, you think of these things and they are connected, uh, by these axioms. So in other words, you have some fact, you, or you have some expression, you apply this axiom, you get some other expression. And in general, given some expression, there may be many possible different expressions you can get. You basically build up a multi-way graph. And a proof is a path through the multiway graph that goes from one thing to another thing. The path tells you, how did you get from one thing to the other thing? It's the, it's the story of how you got from this to that.

• 3:34:58Stephen Wolfram?

  The theorem is, the thing at one end is equal to the thing at the other end. The proof is, the path you go down to get from one thing to the other.

• 3:35:06Lex Fridman?

  You mentioned that Gödel's incompleteness theorem is that natural, it fits naturally there. How, how does it fit?

• 3:35:12Stephen Wolfram?

  So what happens there is that the Gödel's theorem is basically saying that there are paths of infinite length. That is, that there's no upper bound. If you know these two things, you say, I'm trying to get from here to here. How long do I have to go? You say, well, I've looked at all the paths of length 10. Somebody says, that's not good enough. That path might be of length a billion. And, and you, there's no upper bound on how long that path is. And that's, that's what leads to the incompleteness theorem. So, I mean, the, the thing that is kind of an emerging idea is you can start asking, what's the analog of Einstein's equations in metamathematical space? What's the analog of a black hole in metamathematical space?

• 3:35:50Lex Fridman?

  What's the hope of this? So, yeah, it's fascinating to model all the mathematics in this way.

• 3:35:54Stephen Wolfram?

  So here's, here's what it is. This is mathematics in bulk. So, human mathematicians have made a few million theorems. They've published a few million theorems. But imagine the infinite future of mathematics. Apply something to mathematics that mathematics likes to apply to other things. Take a limit. What is the limit of the infinite future of mathematics? What does it look like? What is the continuum limit of mathematics? What is the, as you just fill in more and more and more theorems? What does it look like? What does it do? How does, what kinds of conclusions can you make? So, for example, one thing I've just been doing is taking Euclid. So Euclid, very impressive. He had 10 axioms. He derived 465 theorems. Okay?

• 3:36:34Stephen Wolfram?

  His book, you know, that was, was the sort of defining book of mathematics for 2,000 years. Um, so you can actually map out, and I, I, I actually did this. Twenty years ago, but I've done it more seriously now. You can map out the theorem dependency of those 465 theorems. So from the axioms, you grow this graph. It's actually a multiway graph of how all these theorems get proved from other theorems. And so you can ask questions about, you know, well, you can ask things like, what's the hardest theorem in Euclid? The answer is the hardest theorem is that there are five platonic solids. That turns out to be the hardest theorem in Euclid. That's actually his, his last theorem in all his books. That's the final.

• 3:37:13Lex Fridman?

  What's the hardness, the, the distance you have to travel?

• 3:37:16Stephen Wolfram?

  Yeah, that's it's 33 steps from the, the longest path in the graph is 33 steps. So that's the, there, there's a 33 step path you have to follow to go from the axioms according to Euclid's proofs to the statement there are five platonic solids. So, so, okay, so then, then, then the, the question is, in, uh, what does it mean? If you have this map, okay, so in a sense, this meta mathematical space is the infrastructural space of all possible theorems that you could prove in mathematics. That's the geometry of meta mathematics. There's also the geography of mathematics. That is, where did people choose to live?

• 3:37:56Lex Fridman?

  Right.

• 3:37:57Stephen Wolfram?

  In space. And that's what, for example, exploring the sort of empirical meta mathematics.

• 3:38:01Lex Fridman?

  See, you could put each individual, like, human mathematician, you can embed them into that space. I mean, they, they kind of live.

• 3:38:08Stephen Wolfram?

  They, they represent a path, the little things they do.

• 3:38:11Lex Fridman?

  Maybe a set of paths.

• 3:38:12Stephen Wolfram?

  Right.

• 3:38:12Lex Fridman?

  So like, and a set of axioms that are chosen.

• 3:38:16Stephen Wolfram?

  Right, so, so for example, here's an example of, of a thing that I realized. So one of the surprising things about, well, the two surprising facts about math. One is that it's hard and the other is that it's doable. Okay, so first question is, why is math hard? You know, you've got these axioms, they're very small. Why can't you just solve every problem in math easily?

• 3:38:35Lex Fridman?

  Yeah, it's just logic.

• 3:38:36Stephen Wolfram?

  Right, yeah, well, logic happens to be a particular special case that does have certain simplicity to it. But general mathematics, even arithmetic, already doesn't have the simplicity that logic has.

• 3:38:47Lex Fridman?

  So why is it hard?

• 3:38:49Stephen Wolfram?

  Because of computational irreducibility.

• 3:38:51Lex Fridman?

  Right.

• 3:38:53Stephen Wolfram?

  Because what happens is to know what's true. And this is this whole story about the path you have to follow and how long is the path? And Gödel's theorem is the statement, there could be an inf- that the path is not a bounded length. But the fact that the path is not always compressible to something tiny is a story of computational irreducibility. So that's, that's why math is hard. Now, the next question is, why is math doable? Because it might be the case that most things you care about don't have finite length paths. Most things you care about might be things where you get lost in the sea of computational irreducibility. And worse, undecided ability. That is, there's just no finite length path that gets you there. You know, why is mathematics doable?

• 3:39:36Stephen Wolfram?

  You know, Gödel proved his incompleteness theorem in 1931. Most working mathematicians don't really care about it. They just go ahead and do mathematics, even though it could be that the questions they're asking are undecided. It could have been that Fermat's Last theorem is undecided. It turned out it had a proof, it's a long, complicated proof. The twin prime conjecture might be undecided. The Riemann hypothesis might be undecided. These things might be, the axioms of mathematics might not be strong enough to reach those statements. It might be the case that depending on what axioms you choose, you can either say that's true or that's not true. And, and by the way, Fermat's Last theorem, there could be a shorter path. Absolutely.

• 3:40:17Stephen Wolfram?

  Yeah, so that the, the notion of geodesics in metat mathematical space is a notion of shortest proofs in metat mathematical space. And that's a, you know, human mathematicians do not find shortest paths, nor do automated theorem provers. But the fact, and, and by the way, the, I mean, this stuff is so bizarrely connected. I mean, if you, if you're into automated theorem proving, there are these so-called critical pair lemmas in automated theorem proving. Those are precisely the branch pairs in our, that in multi-weighted graphs. Let me just finish on the why mathematics is doable. Oh, yes, the second part. So you know why it's hard, why is it doable? Right, why do we not just get lost in undecided ability all the time? Yeah.

• 3:40:58Stephen Wolfram?

  So, and, and here's another fact, is in doing computer experiments and doing experimental mathematics, you do get lost in that way. When you just say, I'm picking a random integer equation.

• 3:41:11Stephen Wolfram?

  How do I, does it have a solution or not? And you just pick it at random without any human sort of path getting there. Often, it's really, really hard. It's really hard to answer those questions. We just pick them up random from the space of possibilities. But what's, what I think is happening is, and that's a case where you just fell off into this ocean of sort of irreducibility and so on. What's happening is, human mathematics is a story of building a path. You, you started off, you're, you're always building out on this path where you are proving things. You, you, you've got this proof trajectory and you're basically, the human mathematics is the sort of, the exploration of the world along this proof tra- trajectory, so to speak.

• 3:41:54Stephen Wolfram?

  You're not, you're not just, you know, parachuting in from, from, you know, from, from anywhere. You're following, you know, Lewis and Clark or whatever. You're actually, you're actually going, you know, doing the path. And the fact that you are constrained to go along that path is the reason you don't end up with lot. Every so often, you'll see a little piece of undecided ability and you'll avoid that, that part of the path. But that's basically the story of why human mathematics has, has seemed to be doable. It's a story of exploring these paths that, that are by their nature, they have been constructed to be paths that can be followed. And so you can follow them further. Now, you know, what, why is this relevant to anything? So, okay, so here's the, the, my, my, my belief.

• 3:42:37Stephen Wolfram?

  The fact that human mathematics works that way is, I think there's some sort of connections between the way that observers work in physics and the way that the axiom systems of mathematics are set up to make mathematics be doable in that kind of way. And so, in, in other words, in particular, I think there is an analog of causal invariance, which I think is, and this is again, it's sort of the upper reaches of mathematics and, and stuff that, um, uh. It's a thing, there's this thing called homotopy type theory, which is an abstract, it's came out of category theory, and it's sort of an abstraction of mathematics. Mathematics itself is an abstraction, but it's an abstraction of the abstraction of mathematics.

• 3:43:21Stephen Wolfram?

  And there is a thing called the univalence axiom, which is a sort of a, a, a, a, a key axiom in that set of ideas. And I'm pretty sure the univalence axiom is equivalence, causal and variance.

• 3:43:33Lex Fridman?

  What was the term used again, you know?

• 3:43:35Stephen Wolfram?

  Univalence.

• 3:43:36Lex Fridman?

  Is that something for somebody like me accessible?

• 3:43:39Stephen Wolfram?

  Um.

• 3:43:40Lex Fridman?

  Or is this?

• 3:43:40Stephen Wolfram?

  There's a statement of it that's fairly accessible. I mean, the statement of it is, um, uh, basically it says, things which are equivalent can be considered to be identical.

• 3:43:53Lex Fridman?

  In which, but in which space?

• 3:43:55Stephen Wolfram?

  Yeah, it's, it's in, in higher category.

• 3:43:58Lex Fridman?

  In category theory.

• 3:43:59Stephen Wolfram?

  Okay, so it's, it's a, it's a, but I mean, the, the, the thing, just to give a sketch of how that works. So category theory is an attempt to idealize, it's an attempt to sort of have a formal theory of mathematics that is at a sort of higher level than mathematics. It's where, where you just think, think about these mathematical objects and these categories of objects and these, these morphisms, these connections between categories. Okay, so it turns out the morphisms in categories, at least weak categories, are very much like the paths in our hypergraphs and things. And it turns out, again, this is, this is where it all gets, gets crazy. I mean, it's, it's, the fact that these things are connected is just bizarre.

• 3:44:39Stephen Wolfram?

  So category theory, uh, the, our causal graphs are like second order category theory. And it turns out you can take the limit of infinite order category theory. So just, just give roughly the idea. This is a, this is a roughly explainable idea. So a mathematical proof will be a path that says you can get from this thing to this other thing. And here's the path that you get from this thing to this other thing. But in general, there may be many paths, many proofs that get you many different paths that all successfully go from this thing to this other thing. Okay, now you can define a higher order proof, which is a proof of the equivalence of those proofs. Okay, so you're saying there's a.

• 3:45:22Lex Fridman?

  A path between those proofs essentially.

• 3:45:24Stephen Wolfram?

  Yes, a path between the paths.

• 3:45:26Lex Fridman?

  Yeah.

• 3:45:26Stephen Wolfram?

  Okay, and so you do that, that's the sort of second order thing. That path between the paths is essentially related to our causal graphs.

• 3:45:35Stephen Wolfram?

  Then you take the limit.

• 3:45:37Lex Fridman?

  Ah, wow, okay.

• 3:45:37Stephen Wolfram?

  Path between path between path between path. The infinite limit. That infinite limit turns out to be our Ruleal multiway system.

• 3:45:46Lex Fridman?

  Yeah, the Ruleal, the, the Ruleal multiway system, that's a fascinating thing, both in the physics world and, and as you're saying.

• 3:45:52Stephen Wolfram?

  Yeah, yeah.

• 3:45:53Lex Fridman?

  That's, that's fascinating. I'm not sure I've loaded it all in completely, but.

• 3:45:56Stephen Wolfram?

  Well, I'm not sure I have either, and it may be one of these things where, where, you know, in another, another five years or something, it's like, this was obvious, but I didn't see it. No, but the thing which is sort of interesting to me is that there's sort of an upper reach of, of mathematics, of the abstraction of mathematics. Um, this thing, there's this mathematician called Grothendieck, who's generally viewed as being sort of one of the most abstract, sort of creator of the most abstract mathematics of nineteen seventies-ish timeframe. Um, and one of the things that he constructed was this thing he called the infinity groupoid. Um, and he has this sort of hypothesis about the inevitable appearance of geometry from essentially logic in the structure of this thing.

• 3:46:39Stephen Wolfram?

  Well, it turns out this Ruleal multiway system is the infinity groupoid. So it's a, it's this limiting object, and this is an, this is an instance of that limiting object. So what to me is, I mean, again, I, I've been always afraid of this kind of mathematics because it seemed incomprehensibly abstract to me. Um, but what's, what's, what I'm sort of excited about with this is that, that we've sort of concretified the way that you can reach this kind of mathematics, which makes it, uh, well, both seem more relevant and also the fact that that, you know, I, I don't yet know exactly what mileage we're going to get from using the sort of the apparatus that's been built in those areas of mathematics to analyze what we're doing. But the thing that's.

• 3:47:24Lex Fridman?

  So both ways, so using the mathematics to understand what you're doing and using.

• 3:47:28Stephen Wolfram?

  Right.

• 3:47:28Lex Fridman?

  What you're doing computationally to understand that.

• 3:47:30Stephen Wolfram?

  Right, so, so for example, the, the understanding of, uh, metamathematical space. One of the reasons I really want to do that is because I want to understand quantum mechanics better. And, and that, what you see, you know, we live that.

• 3:47:45Stephen Wolfram?

  Uh, kind of the multiway graph of mathematics, because we actually know this is a theorem we've heard of. This is another one we've heard of. We can actually say these are actual things in the world that we relate to, which we can't really do as as readily for the the physics case. And so it's kind of a way to help my intuition. It's also, you know, there are bizarre things like the, what's the analog of Einstein's equations in metamathematical space? What's the analog of a black hole? You know, it turns out it looks like, not completely sure yet, but there's this notion of non-constructive proofs in mathematics. And I think those relate to, well, actually, the the there are, they relate to things and related to event horizons.

• 3:48:27Stephen Wolfram?

  Um, so the fact that you can take ideas from physics like event horizon.

• 3:48:31Lex Fridman?

  And map them into the same kind of space.

• 3:48:34Stephen Wolfram?

  It's it's really.

• 3:48:35Lex Fridman?

  Do you think there'll be, do you think you might stumble upon some breakthrough ideas in theorem proving? Like for from the the other direction?

• 3:48:46Stephen Wolfram?

  Yeah, yeah, yeah. No, I mean, what what's really nice is that we are using. So this this absolutely directly maps to theorem proving. So paths and multiway graphs, that's what a theorem prover is trying to.

• 3:48:56Lex Fridman?

  But I also mean like like automated theorem.

• 3:48:58Stephen Wolfram?

  Yeah, yeah, yeah, that that's what, right. So the finding of paths, the finding of shortest paths or finding of paths at all is what automated theorem provers do. And actually, what what we've been doing, so we've, you know, we've actually been using automated theorem proving, both in the physics project to prove things and using that as a way to understand multiway graphs. And because what an automated theorem prover is doing is it's trying to find a path through a multiway graph. And its critical pair lemmas are precisely little stubs of branch pairs going off into branchill space. And that's, I mean, it's really weird. And, you know, we have these visualizations in Wolfram Language of our of of proof graphs from our automated theorem proving system.

• 3:49:41Lex Fridman?

  And they look reminiscent of.

• 3:49:43Stephen Wolfram?

  Well, it's just bizarre because we made these up a few years ago. And they have these little triangle things and they are, they are, we we didn't quite get it right. We didn't quite get the analogy perfectly right, but it's very close. You know, just to say in terms. Of the how these things are connected. So there's another bizarre connection that I have to mention because because um um. Which is uh which again, we don't fully know, but it's a connection to uh uh. Something else you might not have thought was in the slightest bit connected, which is distributed blockchain like things. Now, you might figure out that's you you would figure out that that's connected because because it's a story of distributed computing.

• 3:50:20Lex Fridman?

  Yeah.

• 3:50:20Stephen Wolfram?

  And the issue, you know, with a blockchain, you're saying there's going to be this one ledger that that globally says this is what happened in the world. But that's a bad deal if you've got all these different transactions that are happening and, you know, this transaction in country A. Doesn't have to be reconciled with the transaction in country B, at least not for a while. And that story is just like what happens with our causal graphs. That whole reconciliation thing is just like what happens with light cones and.

• 3:50:52Lex Fridman?

  Yeah, so that that's where the causal variance comes into play. I mean, that that's, you know, most of your conversations are about physics, but it's kind of funny that. This probably and possibly might have even bigger impact and uh revolutionary ideas and totally other disciplines.

• 3:51:11Stephen Wolfram?

  Right, we see, see, yeah, right. So the question is, why is that happening, right?

• 3:51:14Lex Fridman?

  Yeah.

• 3:51:15Stephen Wolfram?

  And and the reason it's happening, I I've thought about this, obviously, because I like to think about these meta questions of, you know, what's happening is this model that we have. Is an incredibly minimal model.

• 3:51:25Lex Fridman?

  Yeah.

• 3:51:26Stephen Wolfram?

  And once you have an incredibly minimal model, and this happened with cellular automata as well, cellular automata are an incredibly minimal model. And so it's inevitable that it gets you it's sort of an upstream thing that gets used in lots of different places. And it's like, you know, the fact that it gets used, you know, cellular automata is sort of a minimal model of, let's say, road traffic flow or something. And they're also a minimal model of something in, you know, chemistry, and they're also a minimal model of something in in epidemiology, right? It's because they're such a simple model that they can that they use apply to all these different things. Similarly, this model that we have at the physics project is a is a is another. It's a cellular automata or a minimal model of parallel of of basically of parallel computation where you've defined space and time.

• 3:52:10Stephen Wolfram?

  These models are minimal models where you have not defined space and time. And they have been very hard to understand in the past. But the, I think the, perhaps the most important breakthrough there is the realization that these are models of physics. And therefore, that you can use everything that's been developed in physics to get intuition about how things like that work. And that's why you can potentially use ideas from physics to get intuition about how to do parallel computing. And because the underlying model is the same.

• 3:52:41Lex Fridman?

  Yeah.

• 3:52:42Stephen Wolfram?

  And but but we have all of this achievement in physics. I mean, you know, you might say, oh, you've come up with the fundamental theory of physics that throws out what people have done in physics before. Well, it doesn't. But also, the real power is to use what's been done before in physics to apply it in these other places.

• 3:52:57Lex Fridman?

  Yes.

• 3:52:57Stephen Wolfram?

  And.

• 3:52:57Lex Fridman?

  Absolutely. This kind of brings up, I know you probably don't particularly love commenting on the work of others. But let me, let me bring up a couple of personalities, just because it's fun and people are curious about it. So there's a, Sabine Hossenfelder. I don't know if you're familiar with her. She, she, she wrote this book that I need to read. But it basically, I forget what the title is, but it's Beauty Leads Us astray in Physics is the subtitle, something like that. Which so much about what we're talking about now, like this simplification is a, to us, humans seems to be beautiful.

• 3:53:38Lex Fridman?

  Like, there's a certain intuition with physicists, with people, that a simple theory, like this reducibility, pockets of reducibility is the ultimate goal. And I think what she tries to argue is, no, we just need to come up with theories that are just really good at predicting physical phenomena. It's okay to have a bunch of disparate theories as opposed to trying to chase this beautiful.

• 3:54:05Lex Fridman?

  Theory of everything is the ultimate beautiful theory, a simple one.

• 3:54:09Stephen Wolfram?

  You know, it's always.

• 3:54:10Lex Fridman?

  What's your response to that?

• 3:54:12Stephen Wolfram?

  Well, so what you're quoting, I don't know the Sabine Hossenfelder's, you know, exactly what she said.

• 3:54:18Lex Fridman?

  Yeah, I might be misquoting the title. I'm quoting the title of her book.

• 3:54:21Stephen Wolfram?

  Okay, let me, let me, let me respond to what you are describing. Which may or may not have anything to do with what, you know, what Sabine Hossenfelder says.

• 3:54:30Lex Fridman?

  Yeah.

• 3:54:30Stephen Wolfram?

  Or thinks.

• 3:54:32Lex Fridman?

  Sorry, Sabine.

• 3:54:33Stephen Wolfram?

  Right.

• 3:54:34Lex Fridman?

  Sorry for misquoting.

• 3:54:37Stephen Wolfram?

  But I mean, the question is, you know, does, is beauty a guide to whether something is correct?

• 3:54:43Lex Fridman?

  That's right.

• 3:54:44Stephen Wolfram?

  Which is kind of also the story of Occam's razor.

• 3:54:46Lex Fridman?

  Right.

• 3:54:46Stephen Wolfram?

  You know, if you've got a bunch of different explanations of things, you know, is the thing that is the simplest explanation likely to be the correct explanation? And there are situations where that's true and there are situations where it isn't true. Sometimes in human systems, it is true because people have kind of, you know, in evolutionary systems, sometimes it's true because it's sort of been kicked to the point where it's minimized. But, you know, in physics, does Occam's razor work? You know, is there a simple, quotes, beautiful explanation for things or is it a big mess? You know, we don't intrinsically know. You know, I think that the, I wouldn't, before I worked on the project in recent times, I would have said, we do not know how complicated the rule for the universe will be.

• 3:55:29Stephen Wolfram?

  And, and I would have said, you know, the one thing we know, which is a fundamental fact about science, that's the thing that makes science possible, is that there is order in the universe. I mean, you know, early theologians would have used that as an argument for the existence of God. Because it's like, why is there order in the universe? Why doesn't every single particle in the universe just do its own thing?

• 3:55:50Lex Fridman?

  Yeah.

• 3:55:51Stephen Wolfram?

  You know, something must be making there be order in the universe. We, you know, in, in the sort of early theology point of view, that's, you know, the role of God is to do that, so to speak. In our, you know, we might say it's the role of a formal theory to do that. And then the question is, but how simple should that theory be? And should that theory be one that, that, you know, where? I think the point is if it's simple, it's almost inevitably somewhat beautiful in the sense that because all the stuff that we see has to fit into this little tiny theory. And the way it does that has to be, you know, it depends on your notion of beauty.

• 3:56:30Stephen Wolfram?

  But I mean, and for me, the the sort of the surprising connectivity of it is at least in my aesthetic, that's something that responds to my aesthetic.

• 3:56:42Lex Fridman?

  But the question is, I mean, you're you're you're a fascinating person in the sense that you're at once talking about computational, the fundamental computational reducibility of the universe. And on the other hand, trying to come up with a theory of everything, which simply describes the the the simple origins of that computational reducibility.

• 3:57:08Stephen Wolfram?

  Right.

• 3:57:08Lex Fridman?

  I mean, both of those things are kind of it's paralyzing to think that we can't make any sense of the universe in the general case. But it's hopeful to think like, one, we can think of a rule and that generates this whole complexity. And two, we can find pockets of reducibility that are powerful for our everyday life to do different kinds of predictions. I suppose Sabine wants to find focus on the finding of small pockets of reducibility versus the theory of everything.

• 3:57:44Stephen Wolfram?

  You know, it's a funny thing because because, you know, a bunch of people have started working on this, this, you know, physics project, people who are, you know, physicists, basically. And it is really a fascinating sociological phenomenon because what, you know, when I was working on this before in the 1990s, you know, wrote it up, put it, it's 100 pages of this 1,200 page book that I wrote, New Kind of Science, is, you know, 100 pages of that is about physics. But I I saw it at that at that time, not as a pinnacle achievement, but rather as a use case, so to speak. I mean, my main point was this new kind of science. And it's like, you can apply it to biology, you can apply it to, you know, other kinds of physics, you can apply it to fundamental physics.

• 3:58:27Stephen Wolfram?

  It's just, it's just an application, so to speak. It's not the core thing. But but then. You know, one of the things was interesting with that with that book was, you know, book comes out. Lots of people think it's pretty interesting and lots of people start using what it has in different kinds of fields. The one field where there was sort of a a heavy pitchforking was from my friends, the fundamental physics people.

• 3:58:53Lex Fridman?

  Yeah.

• 3:58:53Stephen Wolfram?

  Which was, it's like, no, this can't possibly be right. And, you know, it's like, you know, if what you're doing is right, it'll overturn fifty years of what we've been doing. And it's like, no, it won't, was what I was saying. And it's like, um, but, uh, you know, for a while, when I started, you know, I I was going to go on back in two thousand two. Well, two thousand four, actually, I was going to go on working on this project. And I actually stopped partly because it's like, why am I, you know, this is like, I've been in business a long time, right? I'm I'm building a product for a target market that doesn't want the product. And it's like.

• 3:59:28Lex Fridman?

  Why work? Yeah, yeah. Why the why work against the swim against the current or whatever?

• 3:59:32Stephen Wolfram?

  But but you see what's happened, which is sort of interesting is is that so a couple of things happened and it was it was like, uh. You know, it was like I I I don't want to do this project because I can do so many other things, which I'm really interested in. Where, you know, people say, great, thanks for those tools. Thanks for those ideas, et cetera. Whereas, you know, if you're dealing with kind of a a, uh, you know, a a sort of a structure where people are saying, no, no, we don't want this new stuff. We don't need any new stuff. We're really fine with what what.

• 4:00:04Lex Fridman?

  Yeah, there's like literally like, I don't know, millions of people who are thankful for Wolfram Alpha. A bunch of people wrote to me how thankful they are. They are a different crowd than the theoretical physics community, perhaps.

• 4:00:15Stephen Wolfram?

  Yeah, well, right. But, you know, the theoretical physics community pretty much uniformly uses our Wolfram language and Mathematica, right? And so it's it's kind of like, like, um.

• 4:00:24Lex Fridman?

  Yeah.

• 4:00:25Stephen Wolfram?

  You know, and that that's, but the thing is, what happens, you know, this is what happens. Mature fields do not. You know, it's like we're doing what we're doing. We have the methods that we have and we're we're just fine here. Now, what's happened in the last eighteen years or so, I think, is a couple of things have happened. First of all, the the hope that, you know, string theory or whatever would would deliver the fundamental theory of physics, that hope has disappeared. That the another thing that's happened is the the sort of the interest in computation around physics has been greatly enhanced by the whole quantum information, quantum computing story. People, you know, the idea there might be something sort of computational related to physics has somehow somehow grown.

• 4:01:10Stephen Wolfram?

  And I think, you know, it's it's sort of interesting. I mean, right now, if we say, you know, it's like if you're like, who else is trying to come up with the fundamental theory of physics? It's like there aren't professional, no professional, no professional physicists.

• 4:01:25Lex Fridman?

  What are your, I mean, you've talked with him, but just as a matter of personalities, because it's a beautiful story. What are your thoughts about Eric Weinstein's work?

• 4:01:33Stephen Wolfram?

  You know, I I think his his, I mean, he did a PhD thesis in mathematical physics at Harvard.

• 4:01:41Lex Fridman?

  Mathematical physicist.

• 4:01:42Stephen Wolfram?

  And and, you know, it's it it seems like it's kind of, you know, it's it's in that framework and it's kind of like, I I'm not sure how much further it's got than his PhD thesis, which was 20 years ago or something. And I think that, you know, the the, you know, it's a fairly specific piece of mathematical physics that's quite nice and.

• 4:02:03Lex Fridman?

  What trajectory do you hope it takes? I mean.

• 4:02:06Stephen Wolfram?

  Well, I think in his particular case, I mean, from what I understand, which is not everything at all, but, you know, I think I know the rough tradition, at least, is operating in is sort of theory of gauge theories.

• 4:02:16Lex Fridman?

  Gauge theories.

• 4:02:17Stephen Wolfram?

  Local gauge invariance and so on. Okay, we are very close to understanding how local gauge invariance works in our models, and it's very beautiful. And it's very, and, you know, does some of the mathematical structure that he's enthusiastic about fit? Quite possibly, yes.

• 4:02:33Lex Fridman?

  So there might be a possibility of trying to understand how those things fit, how gauge theory fits.

• 4:02:37Stephen Wolfram?

  Right, very well. I mean, the question is, you know, so there are a couple of things one might try to get in the world. So, for example, it's like, can we get three dimensions of space? We haven't managed to get that yet. Gauge theory, the standard model of particle physics says that it's SU3 cross SU2 cross U1. Those are the designations of these Lie groups. It doesn't, but but anyway, so those are those are sort of representations of symmetries of the theory. And so, you know, it is conceivable that it is generically true. Okay, so all those are subgroups of a group called E8, which is a weird. Exceptional Li Group, okay? It is conceivable, I don't know whether it's the case, that that will be generic in these models.

• 4:03:22Stephen Wolfram?

  That it will be generic, that the gauge invariance of the model has this property. Just as things like general relativity, which corresponds to a thing called general covariance, which is another gauge-like invariance. It could conceivably be the case that the kind of local gauge invariance that we see in particle physics is somehow generic. And that would be a, you know, the thing that's really cool, I think, you know, sociologically, although this hasn't really hit yet, is that all of these different things, all these different things people have been working on, in these, in some cases, quite abstruse areas of mathematical physics, an awful lot of them seem to tie into what we're doing.

• 4:04:07Stephen Wolfram?

  And, you know, it might not be that way.

• 4:04:09Lex Fridman?

  Yeah, absolutely. That's a beautiful thing that they, I mean, but the reason I, so the reason Eric Weinstein's important is to the point that you mentioned before, which is, it's strange that the theory of everything is not at the core of the passion, the dream, the focus, the funding of the physics community.

• 4:04:32Stephen Wolfram?

  It's too hard. It's too hard and people gave up. I mean, basically what happened is, ancient Greece, people thought we're nearly there. You know, the world is made of platonic solids, it's, you know, water is a tetrahedron or something.

• 4:04:46Lex Fridman?

  Yes.

• 4:04:46Stephen Wolfram?

  We're almost there, okay? Long period of time where people were like, no, we don't know how it works. You know, time of Newton, you know, we're almost there, everything is gravitation. You know, time of Faraday and Maxwell, we're almost there, everything is fields, everything is the ether, you know, then.

• 4:05:04Lex Fridman?

  And the whole time we're making big progress, though.

• 4:05:07Stephen Wolfram?

  Oh, yes, absolutely. But the fundamental theory of physics is almost a footnote, because it's like, it's the machine code. It's like we're operating in the high-level languages.

• 4:05:17Lex Fridman?

  Yeah.

• 4:05:18Stephen Wolfram?

  Um, you know, that's what we really care about, that's what's relevant for our everyday physics.

• 4:05:22Lex Fridman?

  You talked about different centuries, and the 21st century will be, uh, everything's computation.

• 4:05:27Stephen Wolfram?

  Yes.

• 4:05:27Lex Fridman?

  If that takes us all the way, we don't know, but it might take us pretty far.

• 4:05:31Stephen Wolfram?

  Yes, right, that's right. And I, but I think the point is that it's like, you know, if you're doing biology, you might say, how can you not be really interested in the origin of life and the definition of life? Well, it's irrelevant. You know, you're studying the properties of some virus. It doesn't matter, you know, where, you know, you're, you're operating at some much higher level. And it's the same, what's, what's happened with physics is, I was sort of surprised, actually, I was sort of mapping out this history of, of people's efforts to understand the fundamental theory of physics. And it's remarkable how little has been done on this question. And it's, you know, because, you know, there've been times when there's been bursts of enthusiasm, oh, we're almost there. And, and then it decays and, and people just say, oh, it's too hard, but it's not relevant anyway.

• 4:06:15Stephen Wolfram?

  And I think that the, um, the thing that, um,

• 4:06:19Stephen Wolfram?

  you know, so, so the question of, of, you know, one question is, why does anybody, why should anybody care? Right? Why should anybody care what the fundamental theory of physics is? I think it's intellectually interesting, but what will be the sort of, what will be the impact of this?

• 4:06:34Lex Fridman?

  What, I mean, this is the key question. What do you think will happen if we figure out the fundamental theory of physics?

• 4:06:42Stephen Wolfram?

  Right.

• 4:06:43Lex Fridman?

  Outside of the intellectual curiosity of us.

• 4:06:46Stephen Wolfram?

  Okay, so here's what, here's my best guess. Okay? So if you look at the history of science, I think a very interesting analogy is Copernicus. Okay, so what did Copernicus do? There'd been this Ptolemaic system for working out the motion of planets. It did pretty well. It used epicycles, et cetera, et cetera, et cetera. It had all this computational ways of working out where planets will be. When we work out where planets are today, we're basically using epicycles. But Copernicus had this different way of formulating things in which he said, you know, and the earth is going around the sun. And that had a consequence. The consequence was you can use this mathematical theory to conclude something which is absolutely not what we can tell from common sense.

• 4:07:31Stephen Wolfram?

  Right, so it's like, trust the mathematics, trust the science. Okay, now, fast forward four hundred years. And, you know, and now we're in this pandemic. And it's kind of like, everybody thinks the science will figure out everything. It's like, from the science, we can just figure out what to do. We can figure out everything. That was before Copernicus. Nobody would have thought, if the science says something that doesn't agree with our everyday experience, where we just have to, you know, compute the science and then figure out what to do. People would say that's completely crazy.

• 4:08:03Lex Fridman?

  And so your sense is, once we figure out the framework of computation that can basically do any, understand the fabric of reality, we'll be able to derive totally counterintuitive things?

• 4:08:16Stephen Wolfram?

  No, the, the, the point, I think, is the following, that, that right now, you know, I talk about computational irreducibility. People, you know, I was, I was very proud that I managed to get the term computational irreducibility into the Congressional Record last year.

• 4:08:30Lex Fridman?

  That's right, by the way, that's a whole nother topic we're talking about.

• 4:08:33Stephen Wolfram?

  Different, different topic. Different, different, different topic. But, but, um, in any case, you know, but, so computational irreducibility is one of these sort of concepts that I think is important in understanding lots of things in the world. But the question is, it's only important if you believe the world is fundamentally computational. Right? And, but if you, if you know the fundamental theory of physics and it's fundamentally computational, then you've rooted the whole thing. That is, you know, the world is computational. And while you can discuss whether, you know, uh, it, it's not the case that people would say, well, you have this whole computational irreducibility, all these features of computation. We don't care about those, because after all, the world isn't computational, you might say.

• 4:09:14Stephen Wolfram?

  But if you know, you know, base, base, base thing, physics is computational, then you know that that stuff is, you know, that, that's kind of the grounding for that stuff. Just as, in a sense, Copernicus was the grounding for the idea that you could figure out something with math and science that was not what you would intuitively think from your senses. So now, we've got to this point where, for example, we say, you know, once we have the idea that computation is the foundational thing that explains our whole universe. Then we have to say, well, what does it mean for other things? Like, it means there's computational irreducibility. That means science is limited in certain ways. That means this, that means that.

• 4:09:57Stephen Wolfram?

  But the fact that we have that grounding means that, you know, and I think, for example, for Copernicus, for instance, the implications of his work on the sort of mathematics of astronomy were cool, but they involved a very small number of people. The implications of his work for sort of the philosophy of how you think about things were vast and involved, you know, everybody, more or less.

• 4:10:20Lex Fridman?

  But do you think so that's actually the way scientists and people see the world around us, so it has a huge impact in that sense? Do you think it might have an impact more directly to engineering derivations from physics? Like propulsion systems, our ability to colonize the world? Like, for example, okay, this is like sci fi, but if you if you understand the computational nature, say, of of the different forces of physics, you know, there's there's a notion of being able to, you know, warp gravity, things like this.

• 4:10:56Stephen Wolfram?

  Yeah, can we make warp drive?

• 4:10:58Lex Fridman?

  Warp drive, yeah. So like, would we be able to, will it, will, you know, will like Elon Musk start paying attention? Like, it's awfully costly to launch these rockets. Do you think we'll be able to, yeah, create warp drive and?

• 4:11:10Stephen Wolfram?

  Right, you know, I I set myself some homework. I agreed to give a talk at some NASA workshop in a few weeks about faster than light travel. So I I haven't figured it out yet, but but no, but.

• 4:11:20Lex Fridman?

  You got two weeks.

• 4:11:21Stephen Wolfram?

  Yeah, right.

• 4:11:21Lex Fridman?

  But do you think that kind of understanding of fundamental theory of physics can lead to those engineering breakthroughs?

• 4:11:27Stephen Wolfram?

  Okay, I think it's far away, but I'm not certain. I mean, and, you know, this is the thing that that I set myself an exercise when gravity waves, gravitational waves were discovered, right? I set myself the exercise of what would black hole technology look like? In other words, right now, you know, black holes are far away there. You know, how on earth can we do things with them? But just imagine that we could get, you know, pet black holes right in our backyard. You know, what kind of technology could we build with them? I got a certain distance, not that far. But I think in in, you know, so there are ideas. You know, I have this, one of the weirder ideas is things I'm calling space tunnels, which are higher dimensional pieces of of of spacetime, where basically you can, you know, in in our three dimensional space, there might be a five dimensional,

• 4:12:11Stephen Wolfram?

  you know, a region which actually will appear as a white hole at one end and a black hole at the other end. You know, who knows whether they exist? And then the question's another one, okay, this is another crazy one, is the thing that I'm calling a vacuum cleaner. Okay, so, so, so I I I mentioned that, you know, there's all this activity in the universe, which is maintaining the structure of space.

• 4:12:32Lex Fridman?

  Yes.

• 4:12:32Stephen Wolfram?

  And that leads to a certain uh energy density effectively in space. And so the question, in fact, dark energy is a story of essentially negative mass produced by uh the absence of energy you thought would be there, so to speak. And we don't know exactly how it works in in our either our model or the physical universe. But this notion of a vacuum cleaner is a thing where, you know, you have all these things that are maintaining the structure of space. But what if you could clean out some of that stuff that's maintaining the structure of space?

• 4:13:06Lex Fridman?

  Interesting.

• 4:13:07Stephen Wolfram?

  And make a simpler vacuum somewhere.

• 4:13:09Lex Fridman?

  Yeah.

• 4:13:09Stephen Wolfram?

  You know, what would that do?

• 4:13:10Lex Fridman?

  A totally different kind of vacuum.

• 4:13:11Stephen Wolfram?

  Right, and that that would lead to negative energy density, which would need to, so gravity is is usually a purely attractive force, but negative mass would lead to repulsive gravity um and uh lead to all kinds of weird things. Now, can it be done in our universe? Um, you know, my immediate thought is no, but but, you know, the the fact is that, okay, so so.

• 4:13:35Lex Fridman?

  And once you understand the fact, because you're saying like, at this level abstraction, can we reach to the lower levels and mess with it?

• 4:13:42Stephen Wolfram?

  Uh, yes.

• 4:13:43Lex Fridman?

  Once you understand the levels, I think.

• 4:13:45Stephen Wolfram?

  I I know, and I'm, I'm, you know, I have to say that that this reminds me of people telling one years ago that, you know, you'll never transmit data over a copper wire at more than a thousand, you know, a thousand board or something, right? And and this is, why did that not happen? You know, why why did, why do we have these much, much faster data transmission? Because we've understood many more of the details of what's actually going on. And and it's the same exact story here and it's the same, you know, I think that this, as I say, I I think one of the features of sort of, one of the things about our time that will seem incredibly naive in the future is the belief that, you know, things like heat is just random motion of molecules, that that that is just, just throw up your

• 4:14:28Stephen Wolfram?

  hands, it's just random, we can't say anything about it, that will seem naive.

• 4:14:33Lex Fridman?

  Yeah, the, at the heat death of the universe, those particles would be laughing at us humans thinking.

• 4:14:38Stephen Wolfram?

  Yes, right.

• 4:14:39Lex Fridman?

  That life is not beautiful.

• 4:14:41Stephen Wolfram?

  Civilization, you know.

• 4:14:43Lex Fridman?

  Humans used to think they're special with their little brains.

• 4:14:46Stephen Wolfram?

  Well, right, but but also, but but and they used to think that this would just be random and uninteresting, but that's, but so, so this question about whether you can, you know, mess with the underlying structure and how you find a way to mess with the underlying structure, that's a, you know, I have to say, you know, my immediate thing is, boy, that seems really hard, but then, and and, you know, possibly computational irreducibility will bite you, but then there's always some path of computational reducibility, and that path of computational reducibility is the engineering invention.

• 4:15:18Lex Fridman?

  Exactly.

• 4:15:19Stephen Wolfram?

  That has to be made.

• 4:15:20Lex Fridman?

  Those little pockets can have huge engineering impact.

• 4:15:23Stephen Wolfram?

  Right, and I and I think that that's right, and I mean, we live in, you know, we make use of so many of those pockets, and the fact is, you know, I, I, you know, this, this is, yes, it's, it's a, you know, it's one of these things where, where, you know, I'm a person who likes to figure out ideas and so on, and the sort of tests of my level of imagination, so to speak, and so, a couple of places where there's sort of serious humility in terms of my level of imagination, one is this thing about different reference frames for understanding the universe, where like, imagine the physics of the aliens, what will it be like, and I'm like, that's really hard, I don't know, you know, and and and I mean.

• 4:16:06Lex Fridman?

  But once you have the framework in place, you can at least. Reason about the things you don't know.

• 4:16:11Stephen Wolfram?

  Yes.

• 4:16:11Lex Fridman?

  Maybe can't know, or like it's too hard for for you to know. But then the the mathematics can, that's exactly it. Allow you to reach beyond where you can reason.

• 4:16:22Stephen Wolfram?

  Right, so so I'm, you know, I'm, I'm, I'm trying to not have. You know, if you think back to Alan Turing, for example, and, you know, when he invented Turing machines, you know, and and imagining what computers would end up doing, so to speak.

• 4:16:35Lex Fridman?

  Yeah.

• 4:16:35Stephen Wolfram?

  Um, you know, and it's

• 4:16:36Lex Fridman?

  Very difficult.

• 4:16:37Stephen Wolfram?

  It's difficult, right, and it's it's.

• 4:16:39Lex Fridman?

  Made a few reasonable predictions, but most of it, he couldn't predict possibly.

• 4:16:43Stephen Wolfram?

  By the time, by 1950, he was making reasonable predictions about some things.

• 4:16:46Lex Fridman?

  But not the 30s.

• 4:16:47Stephen Wolfram?

  Right, not, not, not in the, not when he first, you know, conceptualized, you know, and he conceptualized universal computing for a very specific mathematical reason that wasn't um, uh, wasn't as general, but but yes, it's a, it's a good sort of exercise in humility to realize that that it's kind of like, it's, it's really hard to figure these things out. The engineering of of um, the universe, if we know how the universe works, how can we engineer it?

• 4:17:13Lex Fridman?

  That's such a beautiful vision, that's such a beautiful.

• 4:17:15Stephen Wolfram?

  By the way, I have to mention one more, which is the the ultimate question of of from physics is, okay, so we have this abstract model of the universe. Why does the universe exist at all? Right, so, you know, we might say there is a a formal model that if you run this model, you get the universe.

• 4:17:35Lex Fridman?

  Yeah.

• 4:17:35Stephen Wolfram?

  Or the model gives you, you know, a model of the universe, right? You, you, you, you run this mathematical thing and the mathematics unfolds in the way that corresponds to the universe. But the question is, why was that actualized? Why does the actual universe actually exist? And um, so this is, this is another one of these humility and and um, uh, is like, can you figure this out? I have a guess, okay, about the answer to that. And um, my guess is somewhat unsatisfying, but my guess is that it's a little bit similar to Gödel's second incompleteness theorem, which is the statement that from within, as an axiomatic theory like Peano arithmetic, you cannot from within that theory prove the consistency of the theory.

• 4:18:19Stephen Wolfram?

  So my guess is that for entities within the universe, there is no finite determination that can be made of the the the statement the universe exists is essentially undecidedable to any entity that is embedded in the universe.

• 4:18:37Lex Fridman?

  Within that universe, how does that make you feel? Is that is that? Does that put you at peace that it's impossible? Or is it really ultimately frustrating?

• 4:18:48Stephen Wolfram?

  Well, I think it just says that it's not a kind of question that, you know, it's there are things that it is reasonable. I mean, there's kinds of, you know, you can talk about hyper computation as well. You can say, imagine there was a hypercomputer, here's what it would do. It's okay, great, it would be lovely to have a hypercomputer, but unfortunately, we can't make it in the universe. Like, it would be lovely to answer this, but unfortunately, we can't do it in the universe. Um, and, you know, this is all we have, so to speak. Um, and I think it's it's really just a a statement. It's sort of, in the end, it'll be a kind of a logical, logically inevitable statement, I think. I think it will be something where it is, as you understand what it means to have, what it means to have a sort of predicate of existence,

• 4:19:33Stephen Wolfram?

  and what it means to have these kinds of things, it will sort of be inevitable that this has to be the case, that from within that universe, you can't establish the reason for its existence, so to speak. You can't prove that it exists and so on.

• 4:19:44Lex Fridman?

  And nevertheless, because of computation or reducibility, the future is ultimately not predictable for a mystery, and that's what makes life worth living.

• 4:19:54Stephen Wolfram?

  Right, I mean, right, and, you know, it's funny for me, because as a as a pure sort of human being doing what I do, it's, you know, I'm I'm a, you know, I like, I'm interested in people. I like sort of, you know, the whole human experience, so to speak. And yet, it's a little bit weird when I'm thinking, you know, it's all hypergraphs down there, and it's all just.

• 4:20:15Lex Fridman?

  Hypergraphs all the way down.

• 4:20:17Stephen Wolfram?

  Right.

• 4:20:17Lex Fridman?

  It's like turtles all the way down.

• 4:20:18Stephen Wolfram?

  Yeah, yeah, right. And and it's kind of, you know, it's to me, it is a funny thing, because every so often I get this, you know, as I'm thinking about, I think we've really gotten, you know, we've really figured out kind of the essence of how physics works. And I'm like, thinking to myself, you know, here's this physical thing, and I'm like. You know, this feels like a very definite thing. How can it be the case that this is just some ruleal reference frame of, you know, this infinite creature that that is so abstract and so on. And I kind of, it is a, it's a, it's a funny sort of feeling that, that, you know, we are, we're sort of, it's like, it's, in the end, it's just sort of, we're just be happy, we're just humans type thing.

• 4:20:59Stephen Wolfram?

  And, and it's kind of like, but, but we're making, we make things as, it, it's not like we're just a tiny speck. We are, in a sense, the, we are more important by virtue of the fact that, in a sense, it, it's not like there's, there is no ultimate, you know, it's like, we're important because, because, you know, we're here, so to speak, and we're not, it's not like there's a thing where we're saying, you know, we are just but one sort of intelligence out of all these other intelligences. And so, you know, ultimately, there'll be the superintelligence, which is all of these put together and it'll be very different from us.

• 4:21:42Stephen Wolfram?

  No, it's actually going to be equivalent to us. And the thing that makes us a sort of special is just the details of us, so to speak. It's not something where we can say, oh, there's this other thing, you know, just, you think humans are cool, just wait until you've seen this. You know, it's going to be much more impressive. Well, no, it's all going to be kind of computationally equivalent. And the thing that, you know, it's, it's not going to be, oh, this thing is amazingly much more impressive and amazingly much more meaningful, let's say. No, we're it. I mean, that's, that's, that, that's the.

• 4:22:19Lex Fridman?

  And, and the symbolism of this particular moment. So this has been one of the, one of the favorite conversations I've ever had, Stephen. It's a huge honor to talk to you, to talk about a topic like this for four plus hours on the fundamental theory of physics. And yet, we're just two finite descendants of apes that have to end this conversation because darkness have come up. On us.

• 4:22:45Stephen Wolfram?

  Right, and we're gonna get bitten by mosquitoes and all kinds of terrible things.

• 4:22:48Lex Fridman?

  Symbolism of that, we're talking about the most basic fabric of reality and having to end because of the fact that things end. It's tragic and beautiful, Stephen. Thank you so much. Huge honor. I can't wait to see what you do in the next couple of days and next week, a month. We're all watching with excitement. Thank you so much.

• 4:23:09Stephen Wolfram?

  Thanks.

• 4:23:10Lex Fridman?

  Thanks for listening to this conversation with Stephen Wolfram. And thank you to our sponsors, Simply Safe, Sun Basket, and Masterclass. Please check out our sponsors in the description to get a discount and to support this podcast. If you enjoy this thing, subscribe on YouTube, review it with five stars on Apple Podcasts, follow on Spotify, support on Patreon, or connect with me on Twitter at Lex Fridman. And now, let me leave you with some words from Richard Feynman. Physics isn't the most important thing. Love is.

• 4:23:44Lex Fridman?

  Thank you for listening and hope to see you next time.