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

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. 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?

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

(laughs)

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

Yeah.

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.