Stephen Wolfram: Cellular Automata, Computation, and Physics | Lex Fridman Podcast #89

1. 0:00 – 4:16

   Introduction

   1. LFLex Fridman0:00

      The following is a conversation with Stephen Wolfram, a computer scientist, mathematician, and theoretical physicist who is 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, which, on a personal note, was one of the most influential books in my journey in computer science and artificial intelligence. It made me fall in love with the mathematical beauty and power of cellular automata. It is true that perhaps one of the criticisms of Stephen is on a human level, that he has a big ego, which prevents some researchers from fully enjoying the content of his ideas. We talk about this point in this conversation. To me, ego can lead you astray, but can also be a superpower, one that fuels bold, innovative thinking that refuses to surrender to the cautious ways of academic institutions. And here, especially, I ask you to join me in looking past the peculiarities of human nature and opening your mind to the beauty of ideas in Stephen's work and in this conversation. I believe Stephen Wolfram is one of the most original minds of our time, and at the core is a kind, curious, and brilliant human being. This conversation was recorded in November 2019 when the Wolfram Physics Project was underway, but not yet ready for public exploration as it is now. We now agreed to talk again, probably multiple times in the near future, so this is round one, and stay tuned for round two soon. This is the Artificial Intelligence podcast. If you enjoy it, subscribe on YouTube, review it with five stars on Apple Podcast, support it on Patreon, or simply connect with me on Twitter @lexfridman, spelled F-R-I-D-M-A-N. As usual, I'll do a few minutes of ads now and never any ads in the middle that can break the flow of the conversation. I hope that works for you and doesn't hurt the listening experience. Quick summary of the ads. Two sponsors, ExpressVPN and Cash App. Please consider supporting the podcast by getting ExpressVPN at expressvpn.com/lexpod and downloading Cash App and using code LEXPODCAST. This show is presented by Cash App, the number one finance app in the App Store. When you get it, use code LEXPODCAST. Cash App lets you send money to friends, buy Bitcoin, and invest in the stock market with as little as $1. Since Cash App does fractional share trading, let me mention that the order execution algorithm that works behind the scenes to create the abstraction of fractional orders is an algorithmic marvel. So big props to the Cash App engineers for solving a hard problem that in the end provides an easy interface that takes a step up to the next layer of abstraction over the stock market. This makes trading more accessible for new investors and diversification much easier. So again, if you get Cash App from the App Store or Google Play and use the code LEXPODCAST, you get $10 and Cash App will also donate $10 to FIRST, an organization that is helping to advance robotics and STEM education for young people around the world. This show is presented by ExpressVPN. Get it at expressvpn.com/lexpod to get a discount and to support this podcast. I've been using ExpressVPN for many years. I love it. It's really easy to use. Press the big power on button and your privacy is protected. And if you like, you can make it look like your location is anywhere else in the world. This has a large number of obvious benefits. Certainly it allows you to access international versions of streaming websites like the Japanese Netflix or the UK Hulu. ExpressVPN works on any device you can imagine. I use it on Linux. Shout out to Ubuntu. New version coming out soon actually. Uh, Windows, Android, but it's available anywhere else too. Once again, get it at expressvpn.com/lexpod to get a discount and to support this podcast. And now here's my conversation with Stephen Wolfram.

2. 4:16 – 12:11

   Communicating with an alien intelligence

   1. LFLex Fridman4:17

      You and your son Christopher helped create the alien language in the movie Arrival. So let me ask maybe a, a bit of a crazy question, but if aliens were to visit us on earth, do you think we would be able to find a common language?

   2. SWStephen Wolfram4:32

      Well, by the time we're saying aliens are visiting us, we've already prejudiced the whole story (laughs) . Because the, you know, the concept of an alien actually visiting, so to speak, we already know their kind of, uh, things that make sense to talk about visiting. So we already know they exist in the same kind of physical setup that we do. Uh, they're not, uh, uh, you know, uh, it's not just radio signals. It's an actual thing that shows up and so on. Um, so I think in terms of, you know, can one find ways to communicate well, the best example we have of this right now is AI. I mean, that's our first sort of example of alien intelligence. And the question is, how well do we communicate with AI? You know, if you were to say, if you were in the middle of a neural net and you open it up and it's like, "What are you thinking?" Can you discuss things with it? It's not easy, but it's not absolutely impossible. So I think, I think by the time by given the setup of your question, aliens visiting, I think the answer is yes. One will be able to find some form of communication. Whatever communication means, communication requires notions of purpose and things like this. It's a kind of philosophical quagmire.

   3. LFLex Fridman5:47

      So if AI is a kind of alien life form, what do you think visiting looks like? So if we look at aliens visiting and, and we'll get to discuss computation and, and the world of computation, but if you were to imagine, you said you already prejudiced something by saying you visit, but what, how would aliens visit?

   4. SWStephen Wolfram6:09

      ... by visit, there's kind of an implication, and here we're using the imprecision of human language, you know. In a world of the future in- if that's represented in computational language, we might be able to take the, uh, the concept visit and go look in the documentation basically and find out exactly what does that mean, what properties does it have and so on. But by visit, in ordinary human language, I'm kind of taking it to be there's, you know, something, a physical embodiment that shows up in a spacecraft, since we kinda know that that's necessary. Um, we're not imagining it's, uh, just, you know, photons showing up on a radio signal that, um, uh... you know, photons in some very elaborate pattern. We're imagining it's- it's physical things made of atoms and so on that- that show up.

   5. LFLex Fridman6:59

      Can it be photons in a pattern?

   6. SWStephen Wolfram7:01

      Well, that's good question. I mean, whether there is the possibility, you know, what counts as intelligence? Good question.

   7. LFLex Fridman7:08

      (laughs) . Yes.

   8. SWStephen Wolfram7:08

      I mean, they- it's some... You know, and I used to think there was sort of a, "Oh, there'll be, you know, it'll be clear what it means to find extraterrestrial intelligence," et cetera, et cetera, et cetera. I've- I've increasingly realized as a result of science that I've done, that there really isn't a- a bright line between the intelligent and the merely computational, so to speak. So, you know, in our kind of everyday sort of discussion, we'll say things like, you know, "The weather has a mind of its own." Well, we- let's unpack that question. You know, we realize that there are computational processes that go on that determine the fluid dynamics of this and that in the atmosphere, et cetera, et cetera, et cetera. How do we extinguish- distinguish that from the processes that go on in our brains of, you know, the physical processes that go on in our brains? How do we- how do we- how do we separate those? How do we say the- the physical processes going on that represent sophisticated computations in the weather, oh, that's not the same as the physical processes that go on that represent sophisticated computations in our brains? The answer is, I don't think there is a fundamental distinction. I think the distinction for us is that there's kind of a- a thread of- of history and so on that connects, uh, kind of what happens in different brains to each other, so to speak, and it's a... You know, what happens in the weather is something which is not connected by sort of a- a thread of- of, uh, civilizational history, so to speak, to what we're used to.

   9. LFLex Fridman8:33

      In our stor- in the stories that the human brain has told us, but maybe the weather has its own stories that it tells itself.

   10. SWStephen Wolfram8:39

       Absolutely. Absolutely. And that's- and that's where we run into trouble thinking about extraterrestrial intelligence because, you know, it's like that pulsar magnetosphere that's generating these very elaborate radio signals, you know, is that something that we should think of as being this whole civilization that's developed over the last however long, you know, millions of years of- of, uh, of processes going on in the, in the neutron star or whatever, um, versus what, uh, you know, what we're used to in human intelligence. I mean, I think it's a... I think in the end, you know, when people talk about extraterrestrial intelligence and where is it and the whole, you know, Fermi Paradox of how come there's no other for- signs of intelligence in the universe?

   11. LFLex Fridman9:19

       Mm-hmm.

   12. SWStephen Wolfram9:19

       My guess is that we've got sort of two, uh, alien forms of intelligence that we're dealing with. Eh, uh, artificial intelligence and sort of physical or extraterrestrial intelligence. And my guess is people will sorta get comfortable with the fact that both of these have been achieved around the same time. And, um, in other words, people will say, "Well yes, we're used to computers, things we've created, digital things we've created being sort of intelligent like we are." And they'll say, "Oh, we're kind of also used to the idea that there are things around the universe that are kind of intelligent like we are, except they don't share the sort of civilizational history that we have. And so we don't... uh, they're- they're, you know, they're a- they're a different branch." I mean, it's similar to when you talk about life, for instance. I mean, you- you- you kinda said life form, I think, almost synonymously with intelligence, which I don't think is- is, um... You know, I- th- the- the AIs would be upset to hear you, uh, (laughs) equate those two things.

   13. LFLex Fridman10:19

       Because they really probably implied biological life.

   14. SWStephen Wolfram10:23

       Right. Right, right.

   15. LFLex Fridman10:24

       But you're saying, I mean, we'll explore this more, but you're saying it's really a spectrum and it's all just a kind of computation, and so it's- it's a full spectrum and, uh, we just make ourselves special by weaving a narrative around our particular kinds of computation.

   16. SWStephen Wolfram10:40

       Yes. I mean, well, th- the thing that I think I've kind of come to realize is, you know, at some level it's a little depressing to realize that-

   17. LFLex Fridman10:47

       (laughs) .

   18. SWStephen Wolfram10:47

       ... there's- there's so little that's special about us.

   19. LFLex Fridman10:48

       Or liberating. (laughs) .

   20. SWStephen Wolfram10:50

       Well, yeah, but I mean, it's, you know, it's the story of science, right? In- in, you know, from Copernicus on, it's like, you know, first we were like convinced our planet's at the center of the universe.

   21. LFLex Fridman11:00

       Yes.

   22. SWStephen Wolfram11:00

       No, that's not true. Well, then we were convinced there's something very special about the chemistry that we have, uh, as biological organisms. No, that's not really true. And then we're still holding out that hope, "Oh, this intelligence thing we have, that's really special."

   23. LFLex Fridman11:13

       Yeah.

   24. SWStephen Wolfram11:14

       Um, I don't think it is. However, in a sense, as you say, it's kind of liberating for the following reason, that you realize that what's special is the details o- of us, not some abstract attribute that, you know, we could wonder, "Oh, is something else gonna come along and, you know, also have that abstract attribute?" Well, yes, every abstract attribute we have, something else has it. But the full details of our kind of, uh, history of our civilization and so on, nothing else has that. That's what, you know, that's our story, so to speak. And that's sort of almost by definition special. So I- I- I view it as not being such a... I mean, I was... I- initially I was like, "This is bad. This is (laughs) - this is kind of, you know, how can we have self-respect about, um, about the things that we do?" Then I realized the details of the things we do, they are the story. Everything else is kind of a blank canvas.

3. 12:11 – 29:06

   Monolith in 2001: A Space Odyssey

   1. LFLex Fridman12:11

      So, maybe on a small tangent, you just made me think of it, but what do you make of the monoliths in 2001 Space Odyssey in terms of aliens communicating with us and sparking the, the kind of particular intelligent computation that we humans have? Is there anything interesting to get from that sci-fi-

   2. SWStephen Wolfram12:36

      Yeah. I mean-

   3. LFLex Fridman12:36

      ... element?

   4. SWStephen Wolfram12:36

      ... what's, what's fun about that is, you know, the monoliths are these, you know, one to four to nine perfect cuboid things.

   5. LFLex Fridman12:43

      Mm-hmm.

   6. SWStephen Wolfram12:44

      And in the, you know, Earth of a million years ago or whatever they were portraying with a, with a bunch of apes and so on, a thing that has that level of perfection seems out of place.

   7. LFLex Fridman12:54

      Right.

   8. SWStephen Wolfram12:55

      It seems very kind of, uh, uh, constructed, very engineered. So that's an interesting question. What is the... You know, what's the techno signature, so to speak? What is it that you see it somewhere and you say, "My gosh, that had to be engineered?"

   9. LFLex Fridman13:10

      Mm.

   10. SWStephen Wolfram13:10

       Um, now, the fact is, we see crystals, which are also very perfect and, uh, you know, the, the perfect ones are very perfect, they're a nice polyhedra or whatever. Um, and so in that sense if you say, "Well, it's a sign of sort of... It's a techno signature-

   11. LFLex Fridman13:26

       Mm-hmm.

   12. SWStephen Wolfram13:27

       ... that it's a perfect, you know, a perfect polygonal shape, polyhedral shape," that's not true. Um, and so then it's, it's an interesting question, what, what is the... you know, what is the right signature? I mean, like, you know, Gauss, famous mathematician, you know, he had this idea you should cut down the Siberian forest in the shape of sort of a typical, um, image of the proof of the Pythagorean theorem.

   13. LFLex Fridman13:49

       Hm. Nice.

   14. SWStephen Wolfram13:50

       On the grounds that, um... It was a kind of cool idea.

   15. LFLex Fridman13:52

       Yeah.

   16. SWStephen Wolfram13:52

       It didn't get done, but, um, uh, you know, it was on the grounds that the Martians would see that and realize, "Gosh, there are mathematicians out there." (laughs) Um, it's kind of... You know, it's the... I- in his theory of the world, that was probably the best advertisement for the cultural achievements of our species. Um, but, you know, it's a, it's a, it's a reasonable question. What do you... Uh, what can you send or create that is a sign of intelligence in its creation or even intention in its creation?

   17. LFLex Fridman14:21

       Yeah, you talk about if we were to send a beacon. Can you, can you... What, what should we send? Is math our greatest creation? Is, uh... What is our greatest creation?

   18. SWStephen Wolfram14:31

       I think, I think... And it's a, it's a philosophically doomed issue to-

   19. LFLex Fridman14:35

       (laughs)

   20. SWStephen Wolfram14:35

       I mean, in other words, you send something, you think it's fantastic, but it's kind of like we are part of the universe. We make things that are... you know, things that happen in the universe. Computation, which is sort of the thing that we are in some abstract sen- u- and sense using to create all these elaborate things we create, is surprisingly ubiquitous. In other words, we might have thought that, you know, we've built this whole giant, uh, engineering stack that's led us to microprocessors, that's led us to be able to do elaborate computations. But this idea the, the computations are happening all over the place.

   21. LFLex Fridman15:14

       Yeah.

   22. SWStephen Wolfram15:15

       The only question is whether, whether there's a thread that connects our human intentions to what those computations are.

   23. LFLex Fridman15:22

       Mm-hmm.

   24. SWStephen Wolfram15:22

       And so I think, I think this question of what do you send to kind of show off our civilization, uh, in the best possible way, I think any kind of almost random slab of stuff we've produced is about equivalent to everything else. I think it's one of these things where-

   25. LFLex Fridman15:40

       Such a non-romantic, uh, way of (laughs) phrasing it. I just, uh... Sorry to interrupt, but I just talked to, uh, Ann Druyan, who's, uh, the wife of Carl Sagan.

   26. SWStephen Wolfram15:49

       Uh-huh.

   27. LFLex Fridman15:49

       And so I don't, I don't know if you're familiar with the Voyager. I mean, she was part of-

   28. SWStephen Wolfram15:53

       Oh, yeah.

   29. LFLex Fridman15:53

       ... s- sending, I think, brain waves of, you know, uh, when she was-

   30. SWStephen Wolfram15:58

       Wasn't it hers?
4. 29:06 – 44:54

   What is computation?

   1. LFLex Fridman29:06

      back. What is computation?

   2. SWStephen Wolfram29:09

      That's a good question. Operationally, computation is following rules. That's kind of it. I mean, computation is the result, is the process of systematically following rules, and it is the thing that happens when you do that.

   3. LFLex Fridman29:24

      So taking initial conditions and taking inputs and following rules.

   4. SWStephen Wolfram29:29

      Yeah.

   5. LFLex Fridman29:29

      I mean, what are you following rules on? So there has to be some data, some-

   6. SWStephen Wolfram29:34

      Not necessarily. It can be something where the- there's a, a, you know, very simple input and then you're following these rules and you'd say there's not really much data going into this. It's... You could actually pack the initial conditions into the rule if you want to. Um, so I think the, the, the question is, is there a robust notion of computation? That is, does-

   7. LFLex Fridman29:54

      What does robust mean?

   8. SWStephen Wolfram29:56

      What I mean by that is something like this. So, so one of the things in a different... in another physics, uh, something like energy, okay? There are different forms of energy. There's... Uh, but somehow energy is a robust concept that doesn't... isn't particular to kinetic energy or, you know, nuclear energy or whatever else. There's a robust idea of energy. So one of the things you might ask is, does the robust idea of computation-... or does it matter that this computation is running on a touring machine, this computation is running in a S- you know, CMOS silicon CPU, this computation is running in a- in a fluid system in the weather, those kinds of things, or is there a robust idea of computation that transcends the sort of detailed framework that it's running in? Okay. And that-

   9. LFLex Fridman30:42

      Is there?

   10. SWStephen Wolfram30:43

       Yes. I mean, it wasn't obvious that there was, so it's worth understanding the history and how we got to where we are right now, because, you know, to say that there is, is a statement in part about our universe. It's not a statement about what is mathematically conceivable. It's about what actually can exist for us.

   11. LFLex Fridman31:03

       Maybe you can also comment, because energy as a concept is robust, but there's also... E- it's intricate, complicated relationship with matter, with mass, is- is very interesting, of particles that carry force and particles that s- sort of... Particles that carry force and particles that have mass. Th- these kinds of ideas, they seem to map to each other, at least in the- in the mathematical sense. Is there a connection between energy and mass and computation, or are these completely disjoint ideas?

   12. SWStephen Wolfram31:44

       We don't know yet. The things that I'm trying to do about fundamental physics, uh, may well lead to such a connection, but there is no known connection at this time.

   13. LFLex Fridman31:55

       So c- can you elaborate a little bit more on what... How do you think about computation? What is computation?

   14. SWStephen Wolfram32:02

       Yeah. So, I mean, let's- let's tell a little bit of a historical story.

   15. LFLex Fridman32:05

       Yes.

   16. SWStephen Wolfram32:05

       Okay? So, you know, back, go back 150 years, people were making mechanical, uh, calculators of various kinds. And, you know, the typical thing was you want an adding machine, you go to the adding machine store, basically. You want a multiplying machine, you go to the multiplying machine store. There are different pieces of hardware. And so that means that, at least at the level of that kind of computation and those kinds of pieces of hardware, there isn't a robust notion of computation. There's the adding machine kind of computation, there's the multiplying machine comp- notion of computation, and they're disjoint. So what happened in around 1900, people started imagining, particularly in the context of mathematical logic, could you have something which would be- represent any reasonable function, right? And they came up with things, this idea of primitive recursion was one of the early ideas, and it didn't work. There were reasonable functions that people could come up with that were not represented using the primitives of primitive recursion. Okay. So then, then along comes 1931 and Gödel's theorem and so on. And as, uh, in- in looking back, one can see that as part of the process of establishing Gödel's theorem, uh, Gödel basically showed how you could compile arithmetic, uh, how, how you could basically compile, uh, logical statements, like this statement is unprovable, into arithmetic. So what he essentially did was to show that arithmetic, uh, can be a computer in a sense that's capable of representing all kinds of other things. And then Turing came along 1936, came up with Turing machines. Meanwhile, Alonzo Church had come up with lambda calculus. And the surprising thing that was established very quickly is the Turing machine idea about what might be... What computation might be is exactly the same as the lambda calculus idea of what computation might be. And so... And then there started to be other ideas, you know, register machines, other kinds of, other kinds of representations of computation. And the big surprise was they all turned out to be equivalent. So in other words, it might have been the case, like those old adding machines and multiplying machines, that, you know, Turing had his idea of computation, Church had his idea of computation, and they were just different. But it isn't true. They're actually all equivalent. So then by, I would say the, the, uh, oh, 1970s or so, in, in sort of the computation, computer science, computation theory area, people had sort of said, "Oh, Turing machines are kind of what computation is." Physicists were still holding out saying, "No, no, no, that's just not how the universe works. We've got all these differential equations. We've got all these real numbers that have infinite numbers of digits."

   17. LFLex Fridman34:43

       Yeah. The universe is not a Turing machine.

   18. SWStephen Wolfram34:45

       Right. The, you know, the Turing machines are a, a small subset of, of the, uh, the things that we make in microprocessors and engineering structures and so on. So probably, actually through my work in the 1980s about sort of, uh, the relationship between computation and models of physics, it became a little less clear that there would be... That there was this big sort of dichotomy between, uh, what can happen in physics and what happens in things like Turing machines. And I think probably by now, uh, people would mostly think... Uh, and- and- and by the way, brains were another kind of element of this. I mean, you know, Gödel didn't think that his notion of computation or what amounted to his notion of computation would cover brains. And, um, uh, Turing wasn't sure either. Um, but, uh, although he was a little bit... He got to be a little bit more convinced that it should cover brains. Um, but, uh, so, you know, by... I would say by probably sometime in the 1980s, there was beginning to be sort of a general belief that, yes, this notion of computation that could be captured by things like Turing machines was reasonably robust. Now, the next question is, okay, you can have a universal Turing machine that's capable of being programmed to do anything that any Turing machine can do. Um, and, uh, you know, this idea of universal computation, it's an important idea. This idea that you can have one piece of hardware and program it with different pieces of software, um, you know, that's kind of the idea that launched most modern technology. I mean, that's kind of the- that's the idea that launched computer revolution, software, et cetera. So, important idea.

   19. LFLex Fridman36:25

       Yeah.

   20. SWStephen Wolfram36:25

       But, but the thing that still-... kind of holding out from that idea is, okay, there is this universal computation thing, but seems hard to get to. Seems like you wanna make a universal computer, you have to kind of have a microprocessor with, you know, a million gates in it, and you have to go to a lot of trouble to make something that achieves that level of computational sophistication. Okay, so the surprise for me was that stuff that I discovered in the early '80s, um, looking at these things called cellular automata, which are really simple computational systems. Um, the thing that was a big surprise to me was that even when their rules were very, very simple, they were doing things that were as sophisticated as they did ev- when their rules were much more complicated. So it didn't look like, you know, this idea, oh, to get sophisticated computation, you have to build something with very sophisticated rules, that idea didn't seem to pan out and instead, it seemed to be the case that sophisticated computation was completely ubiquitous, even in systems with incredibly simple rules. And so that led to this thing that I call the principle of computational equivalence, which basically says when you have a system that follows rules of- of- of any kind, then whenever the system isn't doing things that are in some sense obviously simple, they- then the computation that the behavior of the system corresponds to is of equivalent sophistication. So that means that when you kinda go from the very, very, very simplest things you can imagine, then quite quickly, you hit this kind of threshold above which everything is equivalent in its computational sophistication. Not obvious that would be the case. I mean, that's a- a science fact. Well-

   21. LFLex Fridman38:10

       No, no, no, hold on a second. You- so this- you've opened with a new kind of science. I- I mean, I remember it was a huge eye-opener that s- such simple things can create such complexity, and yes, there's an equivalence, but it's not a fact. It just appears to... I mean, it's as much as a f- fact as sort of these, uh, theories are so elegant that it- it seems to be the way things are. But let me ask sort of- you just brought up, uh, previously kinda, like, the communities of computer scientists with their Turing machines, the physicists with their universe, and the- the- whoever the heck, maybe neuroscientists looking at the brain. What's your sense in the equivalence? Y- you've shown through your work that simple rules can create, uh, equivalently complex Turing machine systems, right? Is the universe equivalent to the kinds of, uh, to Turing machines? Is the human brain a kind of Turing machine? Do you see those things basically blending together? Or is there still a mystery about how disjoint they are?

   22. SWStephen Wolfram39:25

       Well, my guess is that they all blend together. But we don't know that for sure yet. I mean, this- I- you know, I should say, I- I said rather glibly that the principle of computational equivalence is sort of a science fact, and I-

   23. LFLex Fridman39:37

       Yes.

   24. SWStephen Wolfram39:37

       ... I was using air quotes-

   25. LFLex Fridman39:39

       In quotes. Yes, yes.

   26. SWStephen Wolfram39:39

       ... air quotes for the- for the- for the science fact, because when you- it is a, uh... I mean, just to talk about that for a second and then we'll-

   27. LFLex Fridman39:47

       Yes.

   28. SWStephen Wolfram39:47

       ... we'll- we'll, um, um... The thing is that it is- it has a complicated p- epistemological character, similar to things like the second law of thermodynamics, law of entropy increase. Um, the- you know, what is the second law of thermodynamics? It is- is it a law of nature? Is it a thing that is true of the physical wor- is it- is it something which is mathematically provable? Is it something which happens to be true of the systems that we see in the world? Is it, uh, in some sense a definition of heat perhaps? Well, it's a combination of those things. And, uh, it's the same thing with the principle of computational equivalence. And in some sense, the principle of computational equivalence is at the heart of the definition of computation, because it's telling you there is a thing, there is a robust notion that is equivalent across all these systems and doesn't depend on the details of each individual system. And that's why we can meaningfully talk about a thing called computation and we're not stuck talking about, "Oh, there's computation in Turing machine number 3785." And et cetera, et cetera, et cetera. That's- that's why there is a- a robust notion like that. Now, on the other hand, can we prove the principle of computational equivalence? Can we- can we prove it as a mathematical result? Well, the answer is, uh, actually we've got some nice results along those lines that say, you know, throw me a random system with very simple rules. Well, in a couple of cases, we now know that even the very simplest rules we can imagine of a certain type are universal and do sort of follow what you would expect from the principle of computational equivalence, so that's a nice piece of sort of mathematical evidence for the principle of computational equivalence.

   29. LFLex Fridman41:28

       Just to linger on that point, the simple rules creating sort of these complex behaviors, but i- is there a way to mathematically say that this behavior is complex, that you've gr- you mentioned that you cross a threshold?

   30. SWStephen Wolfram41:47

       Right.
5. 44:54 – 1:14:10

   Physics emerging from computation

   1. SWStephen Wolfram44:54

   2. LFLex Fridman44:54

      (laughs) What kind of computation do you think the fundamental laws of physics might emerge from? So just to clarify, so there, you've, you've done a lot of fascinating work with kind of discrete kinds of computation that, uh, you know, the c- 'cause cellular automata, and we'll talk about it, have this very clean structure. It's, it's such a nice way to demonstrate that simple rules can create immense complexity. But what ki- y- you know, is that actually, are cellular automata sufficiently general to describe the kinds of computation that might create the laws of physics? Just to give, can you give a sense of-

   3. SWStephen Wolfram45:36

      Yeah.

   4. LFLex Fridman45:36

      ... what kind of computation do you think, uh, would-

   5. SWStephen Wolfram45:39

      Right, go ahead.

   6. LFLex Fridman45:40

      ... create the laws-

   7. SWStephen Wolfram45:40

      Well, so-

   8. LFLex Fridman45:40

      ... of physics?

   9. SWStephen Wolfram45:40

      So this is a slightly complicated issue.

   10. LFLex Fridman45:42

       Yes.

   11. SWStephen Wolfram45:42

       Because as soon as you have universal computation, you can, in principle, simulate anything with anything.

   12. LFLex Fridman45:48

       Right.

   13. SWStephen Wolfram45:48

       But it is not a natural thing to do, and if you're asking, were you to try to find our physical universe by looking at possible programs and the computational universe of all possible programs, would the ones that correspond to our universe be small and simple enough that we might find them by searching that computational universe, we gotta have the right basis, so to speak. We have, we gotta have the right language in effect for describing computation for that to be feasible. So the thing that I've been interested in for a long time is, what are the most structureless structures that we can create with computation? So in other words, if you say a cellular automaton has a bunch of cells that are arrayed on a grid, and it's very, you know, and, and every cell is updated in synchrony at the c- at a particular, you know, when there's a, there's a, a click of a, of a clock, so to speak, and it, it goes, a tick of a clock, and it, every cell gets updated at the same time. That's a very specific, very rigid kind of thing. But my guess is that when we look at physics and we look at things like space and time, that what's underneath space and time is something as structureless as possible, that what we see, what emerges for us as physical space, for example, comes from something that is sort of arbitrarily unstructured underneath. And so I've been, for a long time, interested in kind of what, what are the most structureless structures that we can set up? And, uh, actually, what I had thought about f- for ages is using graphs, um, networks, where essentially ... So, so let's talk about space, for example.

   14. LFLex Fridman47:20

       Mm-hmm.

   15. SWStephen Wolfram47:21

       So "What is space?" is a kind of a question one might ask. Back in the early days of quantum mechanics, for example, people said, "Oh, for sure, space is gonna be discrete 'cause all these other things we're finding are discrete." But that never worked out in physics. And so space and physics today is always treated as this continuous thing, just like Euclid imagined it.

   16. LFLex Fridman47:40

       Mm-hmm.

   17. SWStephen Wolfram47:41

       I mean, the, the very first thing Euclid says in his sort of common notions is, you know, "A point is something which has no part." In other words, there are, there are points that are arbitrarily small.

   18. LFLex Fridman47:51

       Mm-hmm.

   19. SWStephen Wolfram47:51

       And there's a continuum of possible positions of points. And the question is, is that true? And so for example, if we look at, I don't know, a fluid, like air or water, we might say, "Oh, it's a continuous fluid. We can pour it, we can do all kinds of things continuously." But actually, we know, 'cause we know the physics of it, that it consists of a bunch of discrete molecules bouncing around, and only in the aggregate is it behaving like a continuum. And so the possibility exists that that's true of space too. People haven't managed to make that work with existing frameworks in physics, um, but I've been interested in whether one can imagine that underneath space, and also underneath time, is something more structureless. And the question is, is it computational?... so, there are a couple of possibilities. It could be computational, somehow fundamentally equivalent to a Turing machine, or it could be fundamentally not. So, how could it not be? It could not be... So, a Turing machine essentially deals with integers, whole numbers at some level, and, you know, it can do things like it can add one to a number. It can do things like this.

   20. LFLex Fridman48:52

       It can also store whatever the heck it did, right?

   21. SWStephen Wolfram48:55

       Yes. It can... Has an infinite store, uh, storage.

   22. LFLex Fridman48:58

       Yeah.

   23. SWStephen Wolfram48:58

       But what, um, uh, when one thinks about doing physics or sort of idealized physics or idealized mathematics, one can deal with real numbers, numbers with an infinite number of digits-

   24. LFLex Fridman49:10

       Yeah.

   25. SWStephen Wolfram49:10

       ... numbers which are absolutely precise. Someone can say, "We can take this number, and we can multiply it by itself."

   26. LFLex Fridman49:16

       Are you comfortable with infinity in this context?

   27. SWStephen Wolfram49:19

       Uh-

   28. LFLex Fridman49:19

       Are you comfortable in, in the context of computation, do you think infinity plays a part?

   29. SWStephen Wolfram49:24

       I think that the role of infinity is complicated. Infinity is useful in conceptualizing things. It's not actualizable. Almost by definition, it's not actualizable.

   30. LFLex Fridman49:35

       But do you think infinity is part of the thing that might underlie the laws of physics?
6. 1:14:10 – 1:19:23

   Simulation

   1. SWStephen Wolfram1:14:11

   2. LFLex Fridman1:14:11

      If, indeed, we are in such a simp- (laughs) the universe is such a simple rule, is it possible that there is something outside of this that we are in a kind of what people call s- the simulation, right? That we're just part of a computation that's being explored by a graduate student in an alternate universe?

   3. SWStephen Wolfram1:14:31

      Well, you know, the problem is, we don't get to say much about what's outside our universe because by definition, our universe is what we exist within.

   4. LFLex Fridman1:14:39

      Yeah.

   5. SWStephen Wolfram1:14:39

      Now, can we make a sort of almost theological conclusion from being able to know how our particular universe works? Interesting question. I don't think that i- if you ask the question, could we... and it relates again to this question about extraterrestrial intelligence-

   6. LFLex Fridman1:14:56

      Mm-hmm.

   7. SWStephen Wolfram1:14:57

      ... you know, we've got the rule for the universe. Was it built in on purpose? Hard to say. That's the same thing as saying we see a signal from, you know, that we're s- uh, you know, receiving from some, you know, random star somewhere, and it's a- a series of pulses and, you know, it's a periodic series of pulses, let's say. Was that done on purpose? Can we conclude something about the origin of that series of pulses?

   8. LFLex Fridman1:15:21

      Just because it's elegant does not necessarily mean that somebody created it or that we can even comprehend-

   9. SWStephen Wolfram1:15:29

      Yeah. I mean, I- I think-

   10. LFLex Fridman1:15:30

       ... what was created.

   11. SWStephen Wolfram1:15:30

       ... it's- it's the ultimate version of the sort of identification of- of the techno-signature question. It's the ultimate version of that, is, was our universe a piece of technology, so to speak? And how on earth would we know? Because... But I mean, it'll be... It's, um... I mean, you know, in the- in the kind of crazy science fiction thing you could imagine, you could say, "Oh, somebody's going to have, um..." You know, there's gonna be a signature there. It's gonna be, you know, made by so-and-so. But there's no way we could understand that, so to speak, and it's not clear what that would mean, because the universe simply, uh... You know, this... If we find a rule for the universe, we're not... We're simply saying that rule represents what our universe does. We're not saying that that rule is something running on a big computer and making our universe. It's just saying that represents what our universe does, in the same sense that, you know, laws of classical mechanics, differential equations, whatever they are, represent what mechanical systems do. It's not that the mechanical systems are somehow running solutions to those differential equations. Those differential equations are just representing the behavior of those systems.

   12. LFLex Fridman1:16:39

       So what's the gap, in your sense, to linger on the fascinating, perhaps slightly sci-fi question, what's the gap between understanding the fundamental rules that create a universe and engineering a system, actually creating a simulation ourselves? So you've talked about sort of... You've talked about, you know, um, nano-engineering, kind of ideas that are kind of exciting, actually creating some ideas of computation in the physical space. How hard is- is it, as an engineering problem, to create the universe once you know the rules that create it?

   13. SWStephen Wolfram1:17:12

       Well, that's an interesting question. I think the substrate on which the universe is operating is not a substrate that we have access to. I mean, the only substrate we have is that same substrate that the universe is operating in. So if the universe is a bunch of hypergraphs being rewritten, then we get to attach ourselves to those same hypergraphs being rewritten. We don't get to, um, uh... And- and if you ask the question, you know, is the code clean? You know, is... You know, can we write nice, elegant code with- with efficient algorithms and so on? Um, well, that's an interesting question. How- how... You know, that's this question of how much computational reducibility there is in the system.

   14. LFLex Fridman1:17:51

       But... So I've seen some beautiful cellular automata that basically create copies of itself within itself, right?

   15. SWStephen Wolfram1:17:57

       Uh-huh.

   16. LFLex Fridman1:17:57

       So that's the question, whether it's possible to create... like whether you need to understand the substrate or whether you can just-

   17. SWStephen Wolfram1:18:04

       Yeah. Well, right. I mean, so-

   18. LFLex Fridman1:18:05

       ... k-

   19. SWStephen Wolfram1:18:05

       ... so one of the things that is sort of one of my slightly sci-fi thoughts about the future, so to speak, is, you know, right now, if you poll typical people who say, "Do you think it's important to find the fundamental theory of physics?" Um, you get... 'Cause I've done this poll, informally at least, it's curious actually. You get a decent fraction of people saying, "Oh yeah, that would be pretty interesting."

   20. LFLex Fridman1:18:27

       I think that's becoming, surprisingly enough, more... I mean, th- there- there's a lot of people are interested in physics in a way that... like without understanding it, just-

   21. SWStephen Wolfram1:18:38

       Right.

   22. LFLex Fridman1:18:38

       ... kind of watching scientists, a very small number of them, struggle to understand the nature of our reality.

   23. SWStephen Wolfram1:18:46

       Right.

   24. LFLex Fridman1:18:46

       I mean-

   25. SWStephen Wolfram1:18:46

       I- I mean, I- I think that's somewhat true. And in fact, in this project that I'm, uh, launching into to try and find the fundamental theory of physics, I'm going to do it as a very public project. I mean, it's gonna be live-streamed and all this kind of stuff.

   26. LFLex Fridman1:18:59

       Awesome.

   27. SWStephen Wolfram1:18:59

       And I don't know what will happen. It'll be kind of fun. Um, I mean, I think that it- it's, uh, the interface to the world of this project... I mean, I- I figure one feature of this project is... You know, unlike technology projects that basically are what they are, this is a project that might simply fail, because it might be the case that it generates all kinds of elegant mathematics, but it has absolutely nothing to do with the physical universe that we happen to

7. 1:19:23 – 1:28:01

   Fundamental theory of physics

   1. SWStephen Wolfram1:19:23

      live in. Well, okay, so- so we're talking about...... kind of the quest to find a fundamental theory of physics. First point is, you know, it's turned out it's kinda hard to find the fundamental theory of physics. People weren't sure that that would be the case. Back in the early days of applying mathematics to science, 1600s and so on, people were like, "Oh, in 100 years we'll know everything there is to know about how the universe works." Turned out to be harder than that, and people got kinda humble at some level, 'cause every time we got to sort of a greater level of smallness in studying the universe, it seemed like the math got more complicated and everything got, got harder.

   2. LFLex Fridman1:19:59

      Mm-hmm.

   3. SWStephen Wolfram1:20:00

      The, you know, when I, I, when I was a kid basically, I started doing particle physics, and, um, you know, when I was doing particle physics, I always thought finding the fundamental, fundamental theory of physics, that's a kooky business, we'll never be able to do that. Um, but we can operate within these frameworks that we built for doing quantum field theory and general relativity and things like this. And it's all good, and we can figure out a lot of stuff.

   4. LFLex Fridman1:20:26

      D- did you even at that time have a sense that there's something behind that too?

   5. SWStephen Wolfram1:20:30

      Sure, sure. I just didn't expect that... I thought in some rather un... It's actually kind of crazy, thinking back on it, because it's kinda like there was this long period in civilization where people thought the ancients had it all figured out and will never figure out anything new.

Episode duration: 3:11:08