Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist. Please support this podcast by checking out our sponsors:
- ROKA: https://roka.com/ and use code LEX to get 20% off your first order
- FightCamp: https://joinfightcamp.com/lex to get free shipping
- Onnit: https://lexfridman.com/onnit to get up to 10% off
- Indeed: https://indeed.com/lex to get $75 credit
- Fundrise: https://fundrise.com/lex

EPISODE LINKS:
Stephen's Twitter: https://twitter.com/stephen_wolfram
Stephen's Blog: https://writings.stephenwolfram.com
Wolfram Physics Project: https://www.wolframphysics.org
A New Kind of Science (book): https://amzn.to/30XoEun
Fundamental Theory of Physics (book): https://amzn.to/30XbAoT

PODCAST INFO:
Podcast website: https://lexfridman.com/podcast
Apple Podcasts: https://apple.co/2lwqZIr
Spotify: https://spoti.fi/2nEwCF8
RSS: https://lexfridman.com/feed/podcast/
Full episodes playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Clips playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41

OUTLINE:
0:00 - Introduction
0:57 - What is complexity
13:58 - Randomness in the universe
18:19 - The Wolfram Physics Project
30:21 - Space and time are discrete
42:26 - Quantum mechanics and hypergraphs
51:40 - What is intelligence
1:02:23 - Computational equivalence
1:10:43 - What it is like to be a cellular automata
1:25:07 - Making prediction vs explanations
1:38:27 - Why does the universe exist
1:44:08 - The universe and rulial space
1:52:51 - Does an atom have consciousness
2:03:17 - Why does our universe exist
2:11:48 - What is outside the ruliad
2:22:22 - Automated proof systems
2:38:17 - Multicomputation for biology
2:56:48 - Cardano NFT collaboration with Wolfram Alpha
3:03:48 - Global theory of economics

SOCIAL:
- Twitter: https://twitter.com/lexfridman
- LinkedIn: https://www.linkedin.com/in/lexfridman
- Facebook: https://www.facebook.com/lexfridman
- Instagram: https://www.instagram.com/lexfridman
- Medium: https://medium.com/@lexfridman
- Reddit: https://reddit.com/r/lexfridman
- Support on Patreon: https://www.patreon.com/lexfridman

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.

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.

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

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

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 really embarrassingly long time ago.

And, you know, I was, you know, how does snowflakes get to have complicated forms?

How do galaxies get to have complicated shapes?

How does, you know, how do living systems get produced?

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've 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.

This was like early, maybe 1980-ish time frame.

And it's like, OK, what can 1 do to understand the sort of basic secret that nature seems to have?

Because it seems like nature, you look around in 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, we got sort of circles and lines and things like this.

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?

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, a model is some abstract representation of the system, some formal representation of the system.

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, to me that seemed really obvious.

And the reason it seemed really obvious is because I just spent several years building this big piece of software that was sort of a predecessor to Mathematica and Morphine 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 1 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 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 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.

Actually, I didn't know at first they were called cellular automata, but I found that out subsequently.

But it's just a line of cells, you know, each 1 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 2 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.

I mean, it probably took a few hours originally.

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, 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 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 do that, so to speak.

But the big thing is, even with very simple rules of that type, sort of the minimal, tiniest program, sort of the 1 line program or something, it's possible to get very complicated behavior.

My favorite example is the thing called rule 30, which is a particular cellular automaton rule.

You just start it off from 1 black cell and it makes this really complicated pattern.

And so that for me was sort of a critical discovery that then kind of said, playing back onto, 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.

And that was, so for me, that was the kind of the story of kind of how, that was sort of the indication that 1 had got an idea of what the sort of secret that nature uses to make complexity and how complexity can be made in other places.

Complexity is, it's not easy to tell what's going on.

That's the informal version of what is complexity.

Well, no, the rules can generate just randomness,

It's not what people's intuition had been and has been for a long time.

That is, 1 might think you have a rule, you can tell there's a rule behind it.

I mean, it's just like the early robots in science fiction movies, right?

You can tell it's a robot because it does simple things, right?

Turns out that isn't actually the right story, but it's not obvious that isn't the right story because people assume simple rules, simple behavior.

And the key discovery about the computational universe is that isn't true.

And that discovery goes very deep and relates to all kinds of things that I've spent years and years studying.

But in the end, the sort of 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, show me the rule.

And you know, 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.

By the way, has anybody succeeded at that?

For predicting the middle column of rule 30?

A number of people have sent things in and sort of people are picking away at it, but it's hard.

I mean, I've been actually even proving that the center column of rule 30 doesn't repeat.

That's something I think might be doable, okay?

Yes, and so that's analogous to a similar kind of thing is like the digits of pi, which are also generated in this very deterministic way.

And so a question is how random are the digits of pi?

For example, does every, first of all, do the digits of pi ever repeat?

This was proved in the 1800s that pi is not a rational number.

So that means only rational numbers have digit sequences that repeat.

So we know the digits of pi don't repeat.

So now the question is, does, you know, 0123, or whatever, do all the digits base 10 or base 2, or however you work it out, do they all occur with equal frequency?

That's far away from what can be understood mathematically at this point.

And that's kind of, but I'm even looking for step 1, which is prove that the center column doesn't repeat and then prove other things about it like equidistribution of equal numbers of zeros and ones.

And those are things which I, you know, I kind of set up this little prize thing because I thought those were not too out of range.

Those are things which are within, you know, a modest amount of time, it's conceivable that those could be done.

They're not far away from what current mathematics might allow.

They'll require a bunch of cleverness and hopefully some interesting new ideas that will be useful other places.

started in 1980 with this idea before I think you realized this idea of programs.

You thought that there might be some kind of thermodynamic like randomness and then complexity comes from a clever filter that you kind of, like I don't know, spaghetti or something.

You filter the randomness and outcomes complexity, which is an interesting intuition.

How do we know that's not actually what's happening?

So just because you were then able to develop, look, you don't need this like incredible randomness, you can just have very simple, predictable, initial conditions and predictable rules.

Still, there might be some systems where it's filtering randomness in the inputs.

Well, the point is, when you have quotes randomness in the input, that means there's all kinds of information in the input.

And in a sense, what you get out will be maybe just something close to what you put in.

Like people are very in dynamical systems theory, sort of big area of mathematics that developed from the early 1900s and really got big in the 1980s.

You know, an example of what people study there a lot and it's popular version is chaos theory.

An example of what people study there a lot, and it's popular version is chaos theory.

An example of what people study a lot is the shift map, which is basically taking 2X mod 1, the fractional part of 2X, which is basically just taking digits in binary and shifting them to the left.

So at every step, you get to see, if you say, how big is this number that I got out?

Well, the most important digit in that number is whatever ended up at the left-hand end.

But now if you start off from an arbitrary random number, which is quotes randomly chosen, so all its digits are random, then when you run that sort of chaos theory shift map, all that you get out is just whatever you put in.

You just get to see what you, it's not obvious that you would excavate all of those digits.

And if you're, for example, making a theory, I don't know, fluid mechanics, for example, if there was that phenomenon in fluid mechanics, then the equations of fluid mechanics can't be right.

Because what that would be saying is, the equations of that it matters to the fluid, what happens in the fluid at the level of the, you know, millionth digit of the initial conditions, which is far below the point at which you're hitting kind of sizes of molecules and things like that.

So it's kind of almost explaining if that phenomenon is an important thing, it's kind of telling you that the fluid dynamics, which describes fluids as continuous media and so on, isn't really right.

But so, you know, so this idea that, you know, there's a, it's a tricky thing, because as soon as you put randomness in, you have to know, you know, how much of what's coming out is what you put in versus how much is actually something that's being generated.

And what's really nice about these systems where you just have very simple initial conditions and where you get random stuff out or seemingly random stuff out is you don't have that issue.

You don't have to argue about, was there something complicated put in?

Because it's plainly obvious there wasn't.

Now, as a practical matter in doing experiments, the big thing is, if the thing you see is complex and reproducible, then it didn't come from just filtering some quotes randomness from the outside world.

It has to be something that is intrinsically made because it wouldn't otherwise be, I mean, you know, it could be the case that you set things up and it's always the same each time and you say, well, it's kind of the same, but it's not random each time because it's kind of the definition of it being random is it was kind of picked at random each time, so to speak.

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?

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.

Now, could you add that in as an extra little featureoid without breaking the universe?

Probably, but in fact, almost certainly yes.

But is it necessary for understanding the universe?

No, and I think actually from a more fundamental point of view, I think I might be able to argue, so 1 of the things that I've been interested in, I've been pretty surprised that I've had anything sentient to say about, is the question of why does the universe exist?

I didn't think that was a question that I would, I thought that was a far out there metaphysical kind of thing.

Even the philosophers have stayed away from that question for the most part.

It's so such a kind of, 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 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.

How does the irrelevance of randomness connect to the big why question

So, okay, so I mean, why does the universe exist?

So you may be, which 1, which of these topics is better to enter first?

Why does the universe exist and why you think it's the only 1 that exists?

Well, I think they're very closely related.

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.

Because if you wanna know why the universe exists, you kind of have to know what the universe is made of.

And I think the, Well, let me 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 program or something and you run it and you make the universe.

Now you say, well, how do you actually, why is that program actually running?

And people say, you've got this program that makes the universe, what computer is it running on?

2 plus 2 equals 4, but that's different from saying there's a pile of 2 rocks, another pile of 2 rocks, and somebody moves them together and makes 4, 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, 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.

So in a sense, if we say, 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.

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

And maybe I should start off by saying something about the consciousness story, because that's- Yes.

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.

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

Where, what are all the beautiful ideas you have come across?

What are the interesting things you can mention?

I mean, it's a frigging Cambrian explosion.

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.

And I really did not see, 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 the sort of multi-computational model.

And that that kind of model is applicable not only to physics, but also to lots of other kinds of things.

And 1 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 pretty exciting and very surprising to me.

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, there's a lot we can't know about what's going to happen.

It's kind of a very confusing thing for people who say, science has nailed everything down.

Based on science, we can know everything.

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 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 in all these other areas.

So that's been sort of an exciting thing.

But I would say that in general for our project, it's been going spectacularly well.

I mean, you know, 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 it's, And in fact, 1 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.

And in a major area in meta-mathematics, I'd be realizing that something I've long believed, we can talk about it later, that just really isn't right.

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

We can maybe ask you the following question.

So it's easy through words to describe how cellular automata works.

And it's the fundamental mechanism by which you, in your book, a new kind of science explored the idea of complexity and how to do science in this world of irreducible islands and irreducible, generally irreducibility.

Okay, so how does the model of hypergraphs differ from cellular automata?

And how does the idea of multi-computation differ?

This is a, you know, my life is like all of our lives, something of a story of computational irreducibility.

And, you know, it's been going for a few years now.

So it's always a challenge to kind of find these appropriate pockets of reducibility.

So, I mean, first of all, let's talk about physics, first of all.

And a key observation, 1 of the starting point of our physics project is things about what is space?

And ever since Euclid, people just sort of say space is just this thing where you can put things at any position you want.

And they're just points and they're just geometrical things that you can just arbitrarily put at different coordinate positions.

So the first thing in our physics project is the idea that space is made of something.

Just like water is made of molecules, space is made of kind of atoms of space.

And the only thing we can say about these atoms of space is they have some identity.

There's a, there is, it's this atom as opposed to this atom.

See all Lex Fridman transcripts on Youtube

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