Stephen Wolfram: Complexity and the Fabric of Reality | Lex Fridman Podcast #234

1. 0:00 – 0:57

   Introduction

   1. LFLex Fridman0:00

      The following is a conversation with Stephen Wolfram, his third time on the podcast. He's a computer scientist, mathematician, theoretical physicist, and the founder of Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the new Wolfram Physics project. This conversation is a wild, technical rollercoaster ride through topics of complexity, mathematics, physics, computing, and consciousness. I think this is what this podcast is becoming, a wild ride. Some episodes are about physics, some about robots, some are about war and power, some are about the human condition and our search for meaning, and some are just what the comedian Tim Dillon calls fun. This is the Lex Fridman Podcast. To support it, please check out the sponsors in the description, and now, here's my conversation with Stephen Wolfram.

2. 0:57 – 13:58

   What is complexity

   1. LFLex Fridman0:57

      Almost 20 years ago, you published A New Kind of Science, where you presented a study of complexity, and an approach for modeling of complex systems. So, let us return again to the core idea of complexity. What is complexity?

   2. SWStephen Wolfram1:15

      I don't know. I think that's not the most interesting question.

   3. LFLex Fridman1:18

      (laughs)

   4. SWStephen Wolfram1:18

      It's like, you know, if you ask a biologist, "What is life?"

   5. LFLex Fridman1:22

      Yeah.

   6. SWStephen Wolfram1:22

      That's not the question they care the most about. What I was interested in is how does something that we would usually identify as complexity arise in nature, and I got interested in that question like 50 years ago, which is a really embarrassingly long time ago, and, you know, I- I was, uh, you know, how do snowflakes get to have complicated forms? How do galaxies get to have complicated shapes? How does, you know, how do living systems get produced? Things like that. And the question is, what's the sort of underlying scientific basis for those kinds of things? And the thing that I was, at first, very surprised by, because I'd been doing physics and particle physics and fancy mathematical physics and so on, and it's like, I know all this fancy stuff. I should be able to solve this sort of basic science question, and I couldn't. This was like early, maybe 1980-ish timeframe, and it's like, okay, what can one do to understand the sort of basic secret that nature seems to have, because it seems like nature, you know, you look around at the natural world, it's full of incredibly complicated forms. You look at sort of most engineered kinds of things, for instance. They tend to be, you know, we got just sort of circles and- and lines and things like this, and the question is what secret does nature have that lets it make all this complexity that we, in doing engineering, for example, don't naturally seem to have? And so, that was the kind of the thing that I got interested in, and then the question was, you know, could I understand that with things like mathematical physics? Well, it didn't work very well. So then I got to thinking about, okay, is there some other way to try to understand this? And then the question was, if you're going to look at some system in nature, how do you make a model for that system, for what that system does? So, you know, a model is some abstract representation of the system, some formal representation of the system. What are- what is the raw material that you can make that model out of? And so, what I realized was, well, actually, programs are a really good source of raw material for making models of things, and, you know, in terms of my personal history, the- to me, that seemed really obvious, and the reason it seemed really obvious is just because I'd just spent several years building this big piece of software that was sort of a predecessor to Mathematica and Wolfram Language, thing called SMP, Symbolic Manipulation Program, which was something that had this idea of starting from just these computational primitives and building up everything one had to build up. And so, kind of the notion of, well, let's just try and make models by starting from computational primitives and seeing what we can build up, that seemed like a totally obvious thing to do. In, uh, in retrospect, it might not have been externally quite so obvious, but it was obvious to me at the time, given the path that I happened to have been on. So, you know, so that got me into this question of, let's use programs to model what happens in nature, and the question then is, well, what kind of programs? And, you know, we're used to programs that you write for some particular purpose and it's a big, long piece of code and it does some specific thing, but what I got interested in was, okay, if you just go out into the sort of computational universe of possible programs, you say, take the simplest program you can imagine, what does it do? And so, I started studying these things called cellular automata, um, actually, I didn't know at first they were called cellular automata, but I found that out, um, subsequently, but it's just a- a line of cells, you know, each one is black or white, and it's just some rule that says the color of the cell is determined by the color that it had on the previous step and its two neighbors on the previous step. And I had initially thought that's, you know, sufficiently simple setup, it's not gonna do anything interesting, it's always gonna be simple, no complexity, simple rules, simple behavior. Okay, but then I actually ran the computer experiment, which was pretty easy to do, um, I mean, it probably took a few hours, um, originally, and, um, the, uh, and the results were not what I'd expected at all. Now, needless to say, in the way that science actually works, the results that I got had a lot of unexpected things which I thought were really interesting, but the really strongest result, which was already right there in the printouts I made, I didn't really understand for a couple more years. So it was- it was not... You know, the compressed version of the story is, you run the experiment and you immediately see what's going on, but I wasn't smart enough to- to do that, so to speak. But the big- the big thing is, even with very simple rules of that type, sort of the minimal, tiniest program, sort of the- the- the one-line program or something, it's possible to get very complicated behavior. My- my favorite example is this thing called Rule 30, which is a particular cellular automata rule, you just start it off from one black cell and it makes this really complicated pattern, and so that, for me, was sort of a- a critical discovery that then kind of said......playing back onto, you know, how does nature make complexity? I sort of realized that might be how it does it. That might be kind of the secret that it's using, is that in this kind of computational universe of possible programs, it's actually pretty easy to get programs where even though the program is simple, the behavior when you run the program is not simple at all.

   7. LFLex Fridman6:25

      Mm-hmm.

   8. SWStephen Wolfram6:25

      And that was... So for me, that was the, the kind of the, the story of kind of how... That, that was sort of the, the indication that one had got an idea of what the sort of secret that nature uses to make complexity and that complexity, how complexity can be made in other places. Now, if you say, "What is complexity?" You know, it's, it's... Complexity is, it's not easy to tell what's going on. That's the informal version of what is complexity.

   9. LFLex Fridman6:53

      But there is something going on-

   10. SWStephen Wolfram6:55

       But there's a rule.

   11. LFLex Fridman6:55

       ...but it's not easy to know what-

   12. SWStephen Wolfram6:56

       Right.

   13. LFLex Fridman6:57

       Well, no. The ru- rules can generate just randomness, right?

   14. SWStephen Wolfram7:01

       Well, that, that's not obvious. In other words-

   15. LFLex Fridman7:04

       That's not obvious, that's right.

   16. SWStephen Wolfram7:05

       ...it's not obvious at all.

   17. LFLex Fridman7:06

       Right.

   18. SWStephen Wolfram7:06

       And it wasn't what I expected, it's not what people's intuition had been, and, and has been, uh, for, you know, for a long time. That is, one might think you have a rule, you can tell there's a rule behind it. I mean, it's just like, you know, the early, you know, robots in science fiction movies, right? You can tell it's a robot 'cause it does simple things, right?

   19. LFLex Fridman7:27

       Right.

   20. SWStephen Wolfram7:27

       Turns out that isn't actually the right story, but it's not obvious that isn't the right story, 'cause people assume simple rules, simple behavior. And that, the, the sort of the key discovery about the computational universe is that isn't true.

   21. LFLex Fridman7:40

       Mm-hmm.

   22. SWStephen Wolfram7:40

       And that discovery goes very deep and relates to all kinds of things that I've spent years and years studying. But, um, you know, that, that... In the end, the sort of the, the what is complexity is, well, you can't easily tell what it's going to do. You could just run the rule and see what happens, but you can't just say, "Oh, you know, show me the rule. Great, and now I know what's gonna happen." And, you know, the, the key phenomenon around that is this thing I call computational irreducibility. This fact that in something like Rule 30, you might say, "Well, what's it gonna do after a million steps?" Well, you can run it for a million steps and just do what it does to find out, but you can't compress that. You can't reduce that and say, "I'm gonna be able to jump ahead and say, 'This is what it's gonna do after a million steps,' but I don't have to go through anything like that computational effort."

   23. LFLex Fridman8:29

       By the way, has anybody succeeded at that? You had a challenge, a competition-

   24. SWStephen Wolfram8:33

       Right. Right.

   25. LFLex Fridman8:34

       ...uh, for predicting the middle column of Rule 30. Anybody-

   26. SWStephen Wolfram8:36

       Indeed.

   27. LFLex Fridman8:37

       ...anybody?

   28. SWStephen Wolfram8:38

       Oh, uh, a number of people have sent things in and, and sort of people are picking away at it, but it's hard. I mean, it's, it's, uh... I've been, I've been actually, uh, even proving that the center column of Rule 30 doesn't repeat.

   29. LFLex Fridman8:51

       Mm-hmm.

   30. SWStephen Wolfram8:51

       That's something I think might be doable, okay? I think-
3. 13:58 – 18:19

   Randomness in the universe

   1. SWStephen Wolfram13:58

      speak.

   2. LFLex Fridman13:58

      So, is it possible to for sure know that our universe does not, at the fundamental level, have randomness? Is it possible to conclusively say there's no randomness at the bottom?

   3. SWStephen Wolfram14:11

      Well, it's an interesting question. I mean, you know, science, natural science is an inductive business, right? You observe a bunch of things and you say, "Can we fit these together? What is our hypothesis for what's going on?" The thing that I think I can say fairly definitively is, at this point, we understand enough about fundamental physics that there is... If there was sort of an extra dice being thrown, it's something that doesn't need to be there. We can get what we see without that. Now, you know, could you add that in as an extra little featuroid, um, you know, without breaking the universe? Uh, probably. But, in fact, almost certainly yes. But is it necessary for understanding the universe? No. And I think actually from a- a more fundamental point of view, it's- it's, uh, I think I might be able to argue... So, so one of the things that I've been interested in and been pretty surprised that I've had anything sentient to say about is the question of why does the universe exist?

   4. LFLex Fridman15:12

      Mm-hmm.

   5. SWStephen Wolfram15:13

      I didn't think that was a question that I would... You know, I thought that was a far out there metaphysical kind of, um, thing. Uh, even the philosophers have stayed away from that question for the most part. It's so... Such a kind of, uh, you know, difficult to address question. But I actually think, to my great surprise, that from our physics project and so on, that it is possible to actually, uh, address that question and explain why the universe exists. And I kind of have a suspicion. I've not thought it through. I kind of have a suspicion that that explanation will eventually show you that in no meaningful sense can there be randomness underneath the universe. That is that if there is, it's something that is necessarily irrelevant to our perception of the universe. That is that it could be there, but it doesn't matter because, in a sense, we've already... You know, whatever it would do, whatever extra thing it would add is not relevant to our perception of what's going on.

   6. LFLex Fridman16:09

      So why does the universe exist? How does, uh, the irrelevance of randomness connect to, uh, the big why question of the universe?

   7. SWStephen Wolfram16:19

      So- so, okay, so I mean, why does the universe exist? Well, let's see. I mean-

   8. LFLex Fridman16:23

      And, uh, is this the only universe we got?

   9. SWStephen Wolfram16:25

      It's the only one. That, about that I'm pretty sure. Now-

   10. LFLex Fridman16:29

       So can you maybe... Which one i- which- which of these topics is better to enter first? Why does the universe exist and, uh, why you think it's the only one that exists?

   11. SWStephen Wolfram16:39

       Well, I think they're very closely related.

   12. LFLex Fridman16:41

       Okay.

   13. SWStephen Wolfram16:41

       Okay? So I mean, the first thing, let's see. I mean, this why does the universe exist question is built on top of all these things that we've been figuring out about fundamental physics 'cause if you wanna know why the universe exists, you kinda have to know what the universe is made of. And, uh, I think the, um... Well, let- let me, let me, uh, describe a little bit about the why does the universe exist question. So the main issue is, let's say you have a model for the universe and you say, "I've got this- this program or something," and you run it and you make the universe. Now you say, "Well, how do you actua- why is that program actually running?" And people say, "You've got this program that makes the universe, what computer is it running on?"

   14. LFLex Fridman17:21

       Mm-hmm.

   15. SWStephen Wolfram17:22

       Right? What- what does it mean? What- what actualizes something? You know, two plus two equals four, but that's different from saying there's two... A pile of two rocks and another pile of two rocks and somebody moves them together and makes four, so to speak. And so what is it that kind of turns it from being just this formal thing to being something that is actualized? Okay, so there we have to start thinking about, well- well, what do we actually know about what's going on in the universe? Well, we are observers of this universe.... but confusingly enough, we're part of this universe.

   16. LFLex Fridman17:54

       Mm-hmm.

   17. SWStephen Wolfram17:54

       So, in a sense, we, what, what, what, if, if we say, what do we, what do we know about what's going on in the universe? Well, what we know is what, sort of, our consciousness records about what's going on in the universe.

   18. LFLex Fridman18:06

       Mm-hmm.

   19. SWStephen Wolfram18:06

       And so-

   20. LFLex Fridman18:06

       Consciousness is part of the fabric of the universe, so we're in it.

   21. SWStephen Wolfram18:10

       Yes, we're in it. And, and, and maybe I should, maybe I should start off by saying something about the consciousness story, because that, that's, um-

   22. LFLex Fridman18:18

       Yes.

   23. SWStephen Wolfram18:18

       ... uh-

4. 18:19 – 30:21

   The Wolfram Physics Project

   1. SWStephen Wolfram18:19

      (laughs)

   2. LFLex Fridman18:19

      May- maybe we should begin even before that, at the very base layer of the Wolfram Physics Project. Maybe you can give a broad overview, once again, really quick, about this hypergraph model.

   3. SWStephen Wolfram18:33

      Yes.

   4. LFLex Fridman18:33

      And also, what is it, a year and a half ago since you've brought this project to the world?

   5. SWStephen Wolfram18:39

      Yeah.

   6. LFLex Fridman18:39

      What is the status update? Where, what are all the beautiful ideas you have come across? Uh, what are the interesting things you can sort of mention?

   7. SWStephen Wolfram18:47

      Oh, it's, it's, I mean, it's a, it's a frigging Cambrian explosion.

   8. LFLex Fridman18:51

      (laughs)

   9. SWStephen Wolfram18:51

      (laughs) I mean, it's, it's crazy. I mean, there are all these things which I've kind of wondered about for years, and suddenly, there's actually a way to think about them.

   10. LFLex Fridman19:00

       Mm-hmm.

   11. SWStephen Wolfram19:00

       And I really did not see, uh, I mean, the real strength of what's happened, I absolutely did not see coming. And the real strength of it is, we've got this model for physics, but it turns out, it's a foundational kind of model that's a different kind of computation-like model that I'm kind of calling this, sort of, multi-computational model.

   12. LFLex Fridman19:18

       Mm-hmm.

   13. SWStephen Wolfram19:18

       Um, and that, that kind of model is applicable not only to physics, but also to lots of other kinds of things. And one reason that's extremely powerful is because physics has been very successful, so we know a lot based on what we figured out in physics. And if we know that the same model governs physics and governs, I don't know, economics, linguistics, immunology, whatever, we know that the same kind of model governs those things, we can start using things that we've successfully discovered in physics and applying those intuitions in all these other areas. And that's, that's pretty exciting, and, and, and very surprising to me. Um, and in fact, it's kind of like, in the original story of, sort of, you go and you explain why is there complexity in the natural world? Then you realize, well, there's all this complexity, there's all this computational irreducibility, you know, there's a lot we can't know about what's going to happen. It's, it's kind of, it's kind of a very confusing thing for people who say, you know, "Science has nailed everything down. We're gonna, you know, based on science, we can know everything."

   14. LFLex Fridman20:17

       Mm-hmm.

   15. SWStephen Wolfram20:17

       Well, actually, there's this computational irreducibility thing right in the middle of that, thrown up by science, so to speak. And then the question is, well, given computational irreducibility, how can we actually figure out anything about what happens in the world? Why aren't we, why are we able to predict anything? Why are we able to sort of operate in the world? And the answer is that we sort of live in these slices of computational reusability that exists in this kind of ocean of computational irreducibility. And it turns out that it seems that it's a very fundamental feature of the kind of model that seems to operate in physics, and perhaps in a lot of these other areas, that there are these particular slices of computational reducibility that are relevant to us. And those are the things that both allow us to operate in the world-

   16. LFLex Fridman21:03

       Mm-hmm.

   17. SWStephen Wolfram21:03

       ... and not just have everything be completely unpredictable, but they're also things that potentially give us what amount to sort of physics-like laws-

   18. LFLex Fridman21:11

       Mm-hmm.

   19. SWStephen Wolfram21:11

       ... in all these other areas. So that's, that's been sort of an exciting thing, but, but I would say that, in general, for our project, it's been going spectacularly well. I mean, I, you know, I, it's very, honestly, it wasn't something I expected to happen in my lifetime. I mean, it's, you know, it's something where, where it's, it's, and in fact, one of the things about it, some of the things that we've discovered are things where I was pretty sure that wasn't how things worked.

   20. LFLex Fridman21:38

       Mm-hmm.

   21. SWStephen Wolfram21:38

       And turns out I'm wrong, and, you know, I, uh, in a major area in meta-mathematics, I've, I've been realizing that I, something I've long believed, we can talk about it, uh-

   22. LFLex Fridman21:47

       Mm-hmm.

   23. SWStephen Wolfram21:47

       ... later, that, that, that, uh, just, just really isn't right.

   24. LFLex Fridman21:51

       Mm-hmm.

   25. SWStephen Wolfram21:51

       But, but I think that, um, the, um, the thing that, uh... So, so what's happened with the physics project, I mean, you know, it's a, can explain a little bit about how the, how the model works, but basically-

   26. LFLex Fridman22:02

       Well, can maybe ask you, uh, the following question. So it's easy through words to describe how cellular automata works, you've, you've explained this. And, uh, it's the fundamental mechanism by which you, in your book, A New Kind of Science, explored the idea of complexity and-

   27. SWStephen Wolfram22:20

       Mm-hmm.

   28. LFLex Fridman22:20

       ... how to do science in this world of island, reducible islands and irreduc- and general irreducibility. Okay, so how does the model of hypergraphs differ from cellular automata, and how does the idea of multi-computation differ? Like, maybe that's a way to describe it.

   29. SWStephen Wolfram22:39

       All right. We're, we're, yeah, right. This is a, you know, my life is, like all of our lives, something of a story of computational irreducibility.

   30. LFLex Fridman22:46

       Yes.
5. 30:21 – 42:26

   Space and time are discrete

   1. SWStephen Wolfram30:21

   2. LFLex Fridman30:21

      So, you... Can you maybe elaborate a little bit deeper how a microscope that can see to 10 to the minus 100, how rotating black holes and, uh, presumably the, the detailed, accurate detection of gravitational waves from such black holes can reveal the discreteness of space?

   3. SWStephen Wolfram30:42

      Okay, first thing is, what is a black hole? Uh, actually, we, we, we need to go a little bit further in the, in the story of what spacetime is-

   4. LFLex Fridman30:48

      Sure.

   5. SWStephen Wolfram30:48

      ... because I explained a little bit about what space is, but I didn't talk about what time is, and that's sort of important in, in understanding spacetime, so to speak.

   6. LFLex Fridman30:56

      Mm-hmm. And your sense is both space and time in this story are discrete.

   7. SWStephen Wolfram31:00

      Absolutely. Absolutely. But it's a complicated story.

   8. LFLex Fridman31:03

      Yes.

   9. SWStephen Wolfram31:03

      And, um, needless to say.

   10. LFLex Fridman31:05

       Well, it's simple at the bottom.

   11. SWStephen Wolfram31:07

       It's-

   12. LFLex Fridman31:07

       (laughs)

   13. SWStephen Wolfram31:07

       ... it's very simple at the bottom (laughs) . It's, uh, it's very... In the end, it's simple but deeply abstract.

   14. LFLex Fridman31:13

       Yeah.

   15. SWStephen Wolfram31:14

       And, um, and something that is simple in conception but kind of wrapping one's head around what's going on is pretty hard.

   16. LFLex Fridman31:22

       Mm-hmm.

   17. SWStephen Wolfram31:22

       Um, but so, so first of all we have this... So, you know, I've described these kind of atoms of space and their connections. You can think about these things as a hypergraph. You know, a graph is just, you connect nodes to nodes, but a hypergraph, you can have, you know, uh, you can have sort of not just friends, individual friends to friends, but you can have these triplets of, of friends or whatever else. It's, it's, um... And so we're just saying... And that, that's just the relations between atoms of space are the hyper-edges of the hypergraph. And so we got some big collection of, of these atoms of space, maybe 10 to the 400 or something in our, in our universe, um, and that's the structure of space. That's... And every feature of what we experience in the world is a feature of that, that hypergraph, that spatial hypergraph. So then the question is, well, how does... What, what does that spatial hypergraph do? Well, the idea is that there are rules that, that update that spatial hypergraph. And, you know, in a cellular automaton you've just got this line of cells and you just say, "At every step, at every timestamp... You've got fixed timestamps, fixed array of cells, at every step, uh, every cell gets updated according to a certain rule."

   18. LFLex Fridman32:31

       Mm-hmm.

   19. SWStephen Wolfram32:31

       And that's, um, that's kind of the, uh, that's the way it works. Now in this hypergraph, it's sort of vaguely the same kind of thing. We say, "Every time you see a little piece of hypergraph that looks like this, update it to one that looks like this."

   20. LFLex Fridman32:44

       Mm-hmm.

   21. SWStephen Wolfram32:45

       So it's... Just keep rewriting this hypergraph. Every time you see something that looks like that, anywhere in the universe, it gets rewritten. Now, one thing that's tricky about that, which we'll come to, is this multi-computational idea which has to do with, you're not saying in, in some kind of lockstep way, "Do this one, then this one, then this one." It's just whenever you see one you can do, you can go ahead and do it. And that leads one not to have a single thread of time in the universe. Because if you knew which one to do, you would just say, "Okay, we do this one, then we do this one, then we do this one." But if you say, "Just do whichever one you feel like," you end up with these multiple threads of time, these kind of multiple histories of the universe depending on which order you happen to do the things you could do in.

   22. LFLex Fridman33:27

       So it's fundamentally asynchronous and parallel.

   23. SWStephen Wolfram33:30

       Yes. Yes.

   24. LFLex Fridman33:31

       Which is very uncomfortable for the human brain that seeks for things to be sequential-

   25. SWStephen Wolfram33:36

       Yes.

   26. LFLex Fridman33:36

       ... and synchronous.

   27. SWStephen Wolfram33:37

       Right. Well, I think that this is, this is part of the story of consciousness is, I think the key aspect of consciousness that is important for sort of parsing the universe is this point that we have a single thread of experience.

   28. LFLex Fridman33:52

       Okay.

   29. SWStephen Wolfram33:52

       We have a memory of what happened in the past. We can say something, predict something about the future. But there's a single thread of experience. And, you know, it's not obvious it should work that way. I mean, we've got 100 billion neurons in our brains and they're all firing in all kinds of different ways, but yet our experience is that there is this single thread of, of, of time that, that goes, that, that goes along.

   30. LFLex Fridman34:12

       Mm-hmm.
6. 42:26 – 51:40

   Quantum mechanics and hypergraphs

   1. LFLex Fridman42:26

      I guess, from, on a human level, what is the cost you're paying? What are you missing from not getting an updated picture all the time? Okay, I got, I- I understand what you're just saying-

   2. SWStephen Wolfram42:35

      Yeah, yeah. Right.

   3. LFLex Fridman42:36

      ... but like, what, like how does consciousness emerge from that? Like h- how, (laughs) like w- what are the limitations of that observer?

   4. SWStephen Wolfram42:44

      Okay.

   5. LFLex Fridman42:44

      I understand you're getting a, a delayed picture-

   6. SWStephen Wolfram42:46

      Well, there's, there's a... Okay, so there's, there's m- bunch of limitations to the observer, I think.

   7. LFLex Fridman42:50

      Yeah.

   8. SWStephen Wolfram42:51

      Maybe just explain something about quantum mechanics, 'cause that maybe is a, is an extreme version of some of these issues-

   9. LFLex Fridman42:57

      Mm-hmm.

   10. SWStephen Wolfram42:57

       ... which helps to kind of motivate why one should sort of think things through a little bit more carefully. So, one feature of the, of this... Okay, so in standard physics, like high school physics, you learn, you know, the equations of motion for a ball, and the, the, you know, it says, "You throw the ball this angle, this velocity, things will move in this way," and there's a definite answer, right? The story, the, the key story of quantum mechanics is there aren't definite answers to, where does the ball go? There's kind of this whole sort of bundle of possible paths, and all we say we know from quantum mechanics is certain probabilities for where the ball will end up, okay? So that's kind of the, the core idea of quantum mechanics. So in our models, you... Quantum mechanics is not some kind of plug-in, add-on type thing.

   11. LFLex Fridman43:44

       Mm-hmm.

   12. SWStephen Wolfram43:44

       You absolutely cannot get away from quantum mechanics, because as you think about updating this hypergraph, there isn't just one sequence of things, one definite sequence of things that can happen. There are all these different possible update sequences that can occur. You could do this, you know, piece of the hypergraph now, and then this one later, and et cetera, et cetera, et cetera. All those different paths of history correspond to these quantum, quantum paths in, in quantum mechanics, these different possible quantum histories. And one of the things that's kind of surprising about it is, they, they branch, you know? There can be a certain state of the universe, and it could do this or it could do that, but they can also merge. There can be two states to the universe which their next state, the next state they produce is the same for both of them.

   13. LFLex Fridman44:27

       Mm-hmm, yeah.

   14. SWStephen Wolfram44:28

       And that process of branching and merging is kind of critical, and the idea that they can be merging is critical, and somewhat non-trivial for these hypergraphs because there's a whole graph isomorphism story, and there's a whole very elaborate set of mathematics-

   15. LFLex Fridman44:40

       And that's where the causal invariance comes in, and it's kind of merging-

   16. SWStephen Wolfram44:42

       Yes, among, among other things, right, yes.

   17. LFLex Fridman44:44

       Okay.

   18. SWStephen Wolfram44:44

       That, that's... But, but so, so then what happens is that what, what one's seeing... Okay, so we've got this thing, it's branching, it's merging, et cetera, et cetera, et cetera. Okay, so now the question is, how do we perceive that? What do, you know... How do we, do we, why don't we notice that the universe is branching and merging?

   19. LFLex Fridman45:03

       Mm-hmm.

   20. SWStephen Wolfram45:03

       Why, you know, why is it the case that we just think a definite set of things happen?

   21. LFLex Fridman45:06

       Mm-hmm.

   22. SWStephen Wolfram45:07

       Well, the answer is, we are embedded in that universe, and our brains are branching and merging too.

   23. LFLex Fridman45:13

       Mm-hmm.

   24. SWStephen Wolfram45:13

       And so what quantum mechanics becomes a story of is how does a branching brain perceive a branching universe?

   25. LFLex Fridman45:19

       Mm-hmm.

   26. SWStephen Wolfram45:20

       And the key thing is, as soon as you say, "I think definite things happen in the universe," that means you are essentially conflating lots of different parts of history. You're saying, actually, as far as I'm concerned, because I'm convinced that definite things happen in the universe, all these parts of history must be equivalent. Now, it's not obvious that that would be a consistent thing to do. It might be you say, "All these parts of history are equivalent," but by golly, moments later, that would be a completely inconsistent point of view. Everything would have, you know, gone to hell in different ways. The fact that that doesn't happen is, well, that's a consequence of this causal invariance thing, but that's... And the fact that that does happen a little bit is what causes little quantum effects, and that, um... If that didn't happen at all, there wouldn't be anything that sort of is like quantum mechanics. It would be, uh... Quantum mechanics is kind of like in this, uh, in, in this kind of, this bundle of paths, it's a little bit like what happens in statistical mechanics and fluid mechanics, whatever, that most of the time you just see this continuous fluid, you just see the world just progressing in this kind of way that's like this continuous fluid. But every so often, if you look at the exact right experiment, you can start seeing, well, actually, it's made of these molecules where they might go that way or they might go this way, and that's kind of quantum effects.

   27. LFLex Fridman46:36

       Mm-hmm.

   28. SWStephen Wolfram46:36

       And, and so that's, so the, the, this kind of idea of we're, we're sort of embedded in the universe, this branching brain is perceiving this branching universe, and that ends up being sort of a story of quantum mechanics. That's, that's part of the, the whole picture of what's going on. But I think, I mean, to come back to sort of where does conscious- what is, what is the story of consciousness? So in the universe, we've got, you know, whatever it is, 10 to the 400 atoms of space, they're all doing these complicated things. It's all a big, complicated, irreducible computation. The question is, what do we perceive from all of that?

   29. LFLex Fridman47:11

       Mm-hmm.

   30. SWStephen Wolfram47:11

       And the answer is that we are, we are parsing the universe in a particular way. Let me again go back to the, the gas molecules analogy. You know, in the gas in this room, there are molecules bouncing around in all kinds of complicated patterns.
7. 51:40 – 1:02:23

   What is intelligence

   1. SWStephen Wolfram51:40

   2. LFLex Fridman51:40

      So, in that sense, intelligence as computational sophistication is much broader than, uh-

   3. SWStephen Wolfram51:47

      Yes.

   4. LFLex Fridman51:47

      ... than the, the computational constraints which consciousness operates under, and also the sequent- like, the sequential thing.

   5. SWStephen Wolfram51:56

      Yes, right.

   6. LFLex Fridman51:56

      Like the, the notion of time. That's, that's kind of interesting, but then the, the followup question is like, okay, starting to get a sense of what is intelligence, and how does that connect to our, our human brain? 'Cause you're saying, um, intelligence is almost like a fabric. Like, what, we like plug into it or something? Like-

   7. SWStephen Wolfram52:15

      Yeah, I think, you know, people, peop-

   8. LFLex Fridman52:16

      ... our consciousness plugs into it?

   9. SWStephen Wolfram52:18

      Yeah, I mean, the ... Intelligence, I think, the core ... I mean, you know, intelligence at some level is just a word, but we're asking, you know, what is the, the notion of intelligence as we generalize it beyond the bounds of humans, beyond the bounds of even the AIs that we humans have built and so on? You know, what, what is intelligence, you know? Is the weather ... You know, people say the weather has a mind of its own. What does that mean, you know? Can the weather be intelligent?

   10. LFLex Fridman52:44

       (inhales) Yeah.

   11. SWStephen Wolfram52:44

       You know?

   12. LFLex Fridman52:44

       What does agency have to do with intelligence here? So, is intelligence just like your conception of computation? Just intelligence is a, is the capacity to perform computation in the sea of ...

   13. SWStephen Wolfram52:57

       Yeah, I think so. I mean, I think that's right, and I, I think that, you know, this question of, of, is it for a purpose, okay?

   14. LFLex Fridman53:04

       Mm-hmm.

   15. SWStephen Wolfram53:04

       That quickly degenerates into-

   16. LFLex Fridman53:06

       Yeah.

   17. SWStephen Wolfram53:06

       ... a horrible philosophical mess, because, you know, whenever you say, "Did the weather do that for a purpose?"

   18. LFLex Fridman53:13

       Yeah.

   19. SWStephen Wolfram53:13

       Right? Well, yes, it did. It was trying to move a bunch of hot air from the equator to the poles or something. That's its purpose.

   20. LFLex Fridman53:19

       But w- why ... 'Cause I, I seem to be equally as dumb today as I was yesterday, so there's some persistence or like a consistency over time that the intelligence I've plugged into. So like, what's ... It seems like there's a hard constraint-

   21. SWStephen Wolfram53:36

       Well, that's the matter.

   22. LFLex Fridman53:36

       ... between the amount of computation I can perform and my consciousness. Like, they seem to be really closely connected somehow.

   23. SWStephen Wolfram53:43

       Well, I think the point is that the thing that gives you kind of the ability to have kind of conscious intell- intelligence ... You, you can have kind of this ... Okay, so, so one thing is we don't know intelligences other than the ones that are very much like us.

   24. LFLex Fridman54:00

       Yes.

   25. SWStephen Wolfram54:01

       Right? And the ones that are very much like us, I think have this feature of single thread of time, bounded, you know, computationally bounded. Now, that ... But you also need computational sophistication. Having a single thread of time and being computationally bounded, you could just be a clock going tick-tock. You know? That would satisfy those conditions. But the fact that we have this ...... uh, sort of, uh, irreducible, you know, computational ability, that's- that's an important feature. That's- that's the sort of the- the bedrock on which we can construct the things we construct. Now, the fact that we have this experience of the world that has a single thread of time and computational boundedness, the thing that I sort of realized is, it's that that causes us to deduce from this irreducible mess of what's going on in the physical world the laws of physics that we think exist. So, in other words, if we say, "Why do we believe that there is, you know, uh, continuous space?" Let's say. "Why do we believe that gravity works the way it does?"

   26. LFLex Fridman55:07

       Mm-hmm.

   27. SWStephen Wolfram55:07

       Well, in principle, we could be kind of parsing details of the universe that were, uh, you know, that inv- Uh, okay, the analogy is, uh, again, with, uh, the, you know, statistical mechanics and molecules in a box. We could be sensitive to every little detail of the swirling around of those molecules-

   28. LFLex Fridman55:27

       Right.

   29. SWStephen Wolfram55:27

       ... and we could say, "What really matters is the, you know, the wiggle effect."

   30. LFLex Fridman55:31

       Yes.
8. 1:02:23 – 1:10:43

   Computational equivalence

   1. SWStephen Wolfram1:02:23

      scientific principle."

   2. LFLex Fridman1:02:24

      Can you, can you maybe elaborate how the principle of computational equivalence can save a planet?

   3. SWStephen Wolfram1:02:33

      That would, that would be a v- I have a terrible spoiler for Rudi's book.

   4. LFLex Fridman1:02:35

      It... That would be a spoiler, okay.

   5. SWStephen Wolfram1:02:36

      Yeah, yeah. But, but, no, but I, uh, let me say what the principle of computational equivalence is.

   6. LFLex Fridman1:02:40

      Mm-hmm.

   7. SWStephen Wolfram1:02:41

      Um, so the question is, you are... You have a system, you have some rule, you can think of its behavior as corresponding to a computation. The question is, how sophisticated is that computation?

   8. LFLex Fridman1:02:53

      Mm-hmm.

   9. SWStephen Wolfram1:02:53

      The statement of the principle of computational equivalence is, as soon as it's, it's not obviously simple, it will be as sophisticated as anything.

   10. LFLex Fridman1:03:01

       Mm-hmm.

   11. SWStephen Wolfram1:03:01

       And so that has the implication that, you know, Rule 30, uh, you know, our brains, other things in physics, they're all ultimately equivalent in the computations they can do, and that's what leads to this computational irreducibility idea. Because the reason we don't get to jump ahead, you know, and, and out-think Rule 30 is because we're just computationally equivalent to Rule 30, so we're kind of just both just running computations that are the same sort of raw... The same level of computation, so to speak.

   12. LFLex Fridman1:03:30

       Mm-hmm.

   13. SWStephen Wolfram1:03:31

       So that's kind of the, the idea there, and the question... I mean, it's, it's like, uh, the... You know, in, in the... The science fiction version would be, okay, somebody says, "We just need more servers. Get us more servers." The way to get even more servers is turn the whole planet into a bunch of micro-servers.

   14. LFLex Fridman1:03:49

       Mm-hmm.

   15. SWStephen Wolfram1:03:50

       And that, that's, uh, that's where it starts, and so the question of, you know, computational equivalence, principle of computational equivalence is, well, actually, you don't need to build those custom servers. Actually, you can, uh, you can just, um, use natural computation to compute things, so to speak. You can use nature to compute. You don't need to have done all that engineering, and it's kind of the... It's, it's kind of feels a little disappointing that you say, "We're gonna build all these servers, we're gonna do all these things, we're gonna make... You know, maybe we're going to have human consciousness uploaded into, you know, some elaborate digital environment." And then you look at that thing and you say, "It's got electrons moving around just like in a rock." And then you say, "Well, what's the difference?" And the principle of computational equivalence says there isn't, at some level, a fundamental... You know, you can't say mathematically there's a fundamental difference between the rock that is the future of human consciousness and the rock that's just a rock.

   16. LFLex Fridman1:04:48

       Mm-hmm.

   17. SWStephen Wolfram1:04:48

       Now, what I've sort of realized with this kind of consciousness thing is there is a, a... there is an aspect of this that seems to be more special, that isn't... And, and for example, something I, I haven't really teased apart properly is when it comes to something like the weather and the weather having a mind of its own or whatever, or your average, you know, pulsar magnetosphere acting like a sort of intelligent thing, how does that relate to... You know, how, how do... How is that, that entity related to the kind of consciousness that we have and sort of what would the world look like, you know, to the weather? If we think about the weather as a mind, what will it perceive? What will it laws of... its laws of physics be? I don't really know. Um-

   18. LFLex Fridman1:05:31

       'Cause it's very parallel.

   19. SWStephen Wolfram1:05:33

       It's very parallel, among other things, and it, it, it's not obvious. I mean, this is a, a, a really kind of mind-bending thing, because we've got to try and imagine where, uh... You know, we've got to try and imagine a parsing of the universe different from the one we have. And by the way, when we think about extraterrestrial intelligence and so on, I think that's kind of the key thing is, you know, we've always assumed... I've always assumed, okay, the extraterrestrials, at least they have the same physics. We all live in the same universe, they've got the same physics. But actually, that's not really right, because the extraterrestrials could have a completely different way of parsing...... that, the universe. So it's as if, you know, there could be, for all we know, right here in this room, you know, in the, in the details of the motion of these gas molecules-

   20. LFLex Fridman1:06:18

       Mm-hmm.

   21. SWStephen Wolfram1:06:18

       ... there could be an amazing intelligence that we wi- like, but we have no way of, w- we're not parsing the universe in the same way. If only we could parse the universe in the right way, you know, immediately this amazing thing that's going on and this, you know, huge culture that's developed and all that kind of thing would be obvious to us. But it's not, because we have our particular way of parsing the universe.

   22. LFLex Fridman1:06:39

       Would that thing also have a s- agency? I don't know the right word to use, but something like consciousness, but a different kind of consciousness?

   23. SWStephen Wolfram1:06:48

       I think it's a question of just what you mean by the word, because I think that the, you know, this notion of consciousness and the... Okay, so some people think of consciousness as, sort of a key aspect of it is that we feel that, the, the sort of a feeling of that we exist in some way, that we have this-

   24. LFLex Fridman1:07:05

       Yeah.

   25. SWStephen Wolfram1:07:05

       ... intrinsic feeling about ourselves.

   26. LFLex Fridman1:07:08

       Mm-hmm.

   27. SWStephen Wolfram1:07:08

       You know, I, I suspect that any of these things would also have an intrinsic feeling about themselves. I've been sort of trying to think recently about constructing an experiment about what if you were just a piece of a cellular automaton, let's say.

   28. LFLex Fridman1:07:21

       Mm-hmm.

   29. SWStephen Wolfram1:07:21

       You know, what would your feeling about yourself actually be? And, you know, can we put ourselves in the, in the shoes, in the cells of the cellular automaton, so to speak? Can we, can we get ourselves close enough to that, that we could have a sense of what the world would be like if you were operating in that way? And it's a little difficult, because, you know, you have to not only think about what are you perceiving, but also what's actually going on in your brain.

   30. LFLex Fridman1:07:48

       Mm-hmm.
9. 1:10:43 – 1:25:07

   What it is like to be a cellular automata

   1. LFLex Fridman1:10:43

      about, just, uh, to backtrack a little bit, about cellular automata, being able to, uh... What's it like to be a cellular automata in a way that's equivalent to what it's like to be a conscious human being?

   2. SWStephen Wolfram1:10:58

      Mm-hmm.

   3. LFLex Fridman1:11:01

      H- w- how do you approach that? So is it looking at some subset of the cellular automata, asking questions of that subset, like how the world is perceived, how y- you-

   4. SWStephen Wolfram1:11:12

      Yeah, something like that.

   5. LFLex Fridman1:11:13

      ... as that subset, like for that-

   6. SWStephen Wolfram1:11:15

      Yeah.

   7. LFLex Fridman1:11:15

      ... local pocket of computation, what are you able to say about the broader set of terms?

   8. SWStephen Wolfram1:11:20

      Something like that.

   9. LFLex Fridman1:11:21

      And that somehow then can give you a sense of how to step outside of that cellular automata.

   10. SWStephen Wolfram1:11:26

       Right, but, but the tricky part is that that little subset, it's, what it's doing is it has a view of itself.

   11. LFLex Fridman1:11:35

       Yeah.

   12. SWStephen Wolfram1:11:35

       And the question is, how do you get inside it? It's like, you know, when we, with humans, right, it's like we can't get inside each other's consciousness.

   13. LFLex Fridman1:11:44

       Mm-hmm.

   14. SWStephen Wolfram1:11:44

       That doesn't really, um, you know, that doesn't really even make sense. It's like there is an experience that somebody is having, but you can perceive things from the outside, but sort of getting inside it, it, it doesn't, it doesn't quite make sense. And I, you know, for me, these sort of philosophical issues, and this one I have not untangled, so let's, let's be, um-

   15. LFLex Fridman1:12:03

       Sure.

   16. SWStephen Wolfram1:12:04

       ... um, the, you know... For me, the thing that has been really interesting in thinking through some of these things is, you know, when it comes to questions about consciousness or whatever else, it's like, when I can run a program and actually see pictures and, you know, make things concrete, I have a much better chance to understand what's going on than when I'm just trying to reason about things in a very abstract way.

   17. LFLex Fridman1:12:24

       Yeah, but there, there may be a way to, uh, map...... the program to your conscious experience. So for example, when you play a video game, you do a first person shooter-

   18. SWStephen Wolfram1:12:35

       Mm-hmm.

   19. LFLex Fridman1:12:35

       ... you walk around inside this entity.

   20. SWStephen Wolfram1:12:39

       Yep.

   21. LFLex Fridman1:12:39

       It's a very different thing than watching this entity. So if you can somehow-

   22. SWStephen Wolfram1:12:44

       Yeah, yeah.

   23. LFLex Fridman1:12:44

       ... connect more and more, connect this, this full conscious experience to this subset of the cellular automata, right?

   24. SWStephen Wolfram1:12:51

       Yeah, it's something like that, but the difference in the first person shooter thing is there's still... Your brain and your memory is still remembering, you know. You, you still have... It's, it's hard to... I mean, again, what one's gonna get. One is not going to actually be able to be the cellular automaton. One's going to be able to watch what the cellular automaton does, but this is the frustrating thing that I'm trying to understand. You, you know, how to, how to think about being it, so to speak.

   25. LFLex Fridman1:13:18

       Okay, so like in virtual reality, there's a concept of immersion, like with anything, with video game, with books-

   26. SWStephen Wolfram1:13:23

       Mm-hmm.

   27. LFLex Fridman1:13:23

       ... there's a concept of immersion. It feels like over time, if the virtual reality experience is, is well done, and maybe in the future it will be extremely well done, the immersion leads you to feel like... Y- you mentioned memories. You forget that you even ever existed outside that experience.

   28. SWStephen Wolfram1:13:43

       Yeah.

   29. LFLex Fridman1:13:43

       It's so immersive, I mean, you could argue sort of mathematically that you can never truly become immersed, but maybe you can. I mean-

   30. SWStephen Wolfram1:13:51

       Well, yeah, I mean-

Episode duration: 3:38:42