Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist. Please check out our sponsors to get a discount and to support this podcast:
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EPISODE LINKS:
Wolfram Physics Project: https://www.wolframphysics.org/
Stephen's Twitter: https://twitter.com/stephen_wolfram
Stephen's Blog: https://writings.stephenwolfram.com
Books:
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- A Project to Find the Fundamental Theory of Physics: https://amzn.to/3mA3OaS

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OUTLINE:
0:00 - Introduction
7:14 - Key moments in history of physics
12:43 - Philosophy of science
14:37 - Science and computational reducibility
22:08 - Predicting the pandemic
38:58 - Sunburn moment with Wolfram Alpha
39:46 - Computational irreducibility
46:45 - Theory of everything
52:41 - General relativity
1:01:16 - Quantum mechanics
1:06:46 - Unifying the laws of physics
1:12:01 - Wolfram Physics Project
1:29:53 - Emergence of time
1:34:11 - Causal invariance
1:53:03 - Deriving physics from simple rules on hypergraphs
2:07:24 - Einstein equations
2:13:04 - Simulating the physics of the universe
2:17:28 - Hardware specs of the simulation
2:24:37 - Quantum mechanics in Wolfram physics model
2:42:46 - Double-slit experiment
2:45:13 - Quantum computers
2:53:21 - Getting started with Wolfram physics project
3:14:46 - The rules that created our universe
3:24:22 - Alien intelligences
3:32:29 - Meta-mathematics
3:37:58 - Why is math hard?
3:52:55 - Sabine Hossenfelder and how beauty leads physics astray
4:01:07 - Eric Weinstein and Geometric Unity
4:06:17 - Travel faster than speed of light
4:16:59 - Why does the universe exist at all

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The following is a conversation with Stephen Wolfram, his second time on

He's a computer scientist, mathematician, theoretical physicist, and the founder and CEO of Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the New Wolfram Physics Project.

He's the author of several books, including A New Kind of Science, and the new book, A Project to Find the Fundamental Theory of Physics.

The second round of our conversation is primarily focused on this latter endeavor of searching for the physics of our universe in simple rules that do their work on hypergraphs and eventually generate the infrastructure from which space, time, and all of modern physics can emerge.

Quick summary of the sponsors, SimpliSafe, SunBasket, and Masterclass.

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As a side note, let me say that to me, the idea that seemingly infinite complexity can arise from very simple rules and initial conditions is 1 of the most beautiful and important mathematical and philosophical mysteries in science.

I find that both cellular automata and the hypergraph data structure that Stephen and team are currently working on to be the kind of simple, clear mathematical playground within which fundamental ideas about intelligence, consciousness, and the fundamental laws of physics can be further developed in totally new ways.

In fact, I think I'll try to make a video or 2 about the most beautiful aspects of these models in the coming weeks.

Especially, I think, trying to describe how fellow curious minds like myself can jump in and explore them, either just for fun or potentially for publication of new innovative research in math, computer science, and physics.

But honestly, I think the emerging complexity in these hypergraphs can capture the imagination of everyone, even if you're someone who never really connected with mathematics.

That's my hope at least, to have these conversations that inspire everyone to look up to the skies and into our own minds in awe of our amazing universe.

Let me also mention that this is the first time I ever recorded a podcast outdoors as a kind of experiment to see if this is an option in times of COVID.

I did my best and promise to keep improving and learning as always.

If you enjoy this thing, subscribe on YouTube, review it with 5 Stars on Apple Podcast, follow on Spotify, support on Patreon, or connect with me on Twitter, Alex Friedman.

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And now, finally, here's my conversation with Steven Wolfram.

are moments in history of physics and maybe mathematical physics or even mathematics where breakthroughs happen and then a flurry of progress follows.

So if you look back through the history of physics, what moments stand out to you as important such breakthroughs where a flurry of progress follows.

So the big famous 1 was 1920s, the invention of quantum mechanics, where, you know, in about 5 or 10 years, lots of stuff got figured out.

Yeah, it was kind of Schrodinger, Heisenberg, Einstein had been a key figure, originally Planck, then Dirac was a little bit later.

That was something that happened at that time, that sort of before my time, right?

In my time was in the 1970s there was this sort of realization that quantum field theory was actually going to be useful in physics and QCD quantum carbon dynamics theory of quarks and gluons and so on was really getting started and There was again sort of big flurry of things happened then I happened to be a teenager at that time and happened to be really involved in physics.

And so I got to be part of that, which was really cool.

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

People, David Gross, Frank Wilczek, David Politzer.

The people who are the slightly older generation, Dick Feynman, Murray Gell-Mann, people like that who were Steve Weinberg, Gerhard Hoft.

But these are all, you know, characters who were involved.

I mean, it was, you know, It's funny because those are all people who are kind of in my time and I know them and they don't seem like sort of these historical iconic figures.

They seem more like everyday characters, so to speak.

And so it's always when you look at history from long afterwards, it always seems like everything happened instantly.

There was usually a long buildup, but usually there's, you know, there's some methodological thing happens, And then there's a whole bunch of low-hanging fruit to be picked.

We see it today with machine learning and deep learning neural nets and so on.

Methodological advance, things actually started working in 2011, 2012 and so on.

And there's been this sort of rapid picking of low-hanging fruit, which is probably some significant fraction of the way done, so to speak.

Like if I had to really introspect, like what was the key moment for the deep learning quote unquote revolution?

So is there something like that with physics where, So deep learning neural networks have been around for a long time.

There's a bunch of little pieces that came together and then all of a sudden everybody's eyes lit up.

Like even just looking at your own work, just your thinking about the universe, that there's simple rules can create complexity, you know, at which point was there a thing where your eyes light up?

It's like, wait a minute, there's something here.

Is it the very first idea or is it some moment along the line of implementations and experiments and so on?

There's a couple of different stages to this.

I mean, 1 is the think about the world computationally.

You know, can we use programs instead of equations to make models of the world?

That's something that I got interested in in the beginning of the 1980s.

You know, I did a bunch of computer experiments.

You know, when I first did them, I didn't really, I could see some significance to them, but it took me a few years to really say, wow, there's a big, important phenomenon here that lets sort of complex things arise from very simple programs.

That kind of happened back in 1984 or so.

Then, you know, a bunch of other years go by, then I start actually doing a lot of much more systematic computer experiments and things and find out that this phenomenon that I could only have said occurs in 1 particular case is actually something incredibly general.

And then that led me to this thing called principles of computational equivalence.

And then, you know, as part of that process, I was like, OK, you can make simple programs, can make models of complicated things.

That's our sort of ultimate example of a complicated thing.

And so I got to thinking, could we use these ideas to study fundamental physics?

I happen to know a lot about traditional fundamental physics.

I had a bunch of ideas about how to do this in the early 1990s.

I figured out a bunch of things I thought were pretty interesting.

With the new kind of science and the cellular automata world and there's echoes in the cellular automata world with your new Wolfram physics project.

Allow me to sort of romanticize a little more on the philosophy of science.

So Thomas Kuhn, a philosopher of science, describes that the progress in science is made with these paradigm shifts.

And so to link on the original line of discussion, do you agree with this view that there is revolutions in science that just kind of flip the table?

What happens is it's a different way of thinking about things.

It's a different methodology for studying things and that opens stuff up.

There's this idea of, He's a famous biographer, but I think it's called The Innovators.

The biographer of Steve Jobs, of Albert Einstein.

He also wrote a book, I think it's called The Innovators, where he discusses how a lot of the innovations in the history of computing has been done by groups.

There's a complicated group dynamic going on.

But there's also a romanticized notion that the individual is at the core of the revolution.

Is ultimately like 1 person responsible for these revolutions that creates the spark, or 1 or 2, whatever, but, or is it just the big mush and mess and chaos of people interacting, of personalities interacting?

I think it ends up being like many things, there's leadership and there ends up being, it's a lot easier for 1 person to have a crisp new idea than it is for a big committee to have a crisp new idea.

And I think, you know, but I think it can happen that, you know, you have a great idea, but the world isn't ready for it.

And you can, I mean, this has happened to me plenty, right?

It's, you have an idea, it's actually a pretty good idea, but things aren't ready, either you're not really ready for it, or the ambient world isn't ready for it, and it's hard to get the thing to get traction.

I mean, when I look at a new kind of science, you're now living inside the history, so you can't tell the story of these decades, but it seems like the new kind of science has not had the revolutionary impact I would think it might.

Like, it feels like at some point, of course it might be, but it feels at some point people will return to that book and say there was something special here.

Oh yeah, it's happened except that People aren't, you know, the sort of the heroism of it may not be there, but what's happened is, for 300 years, people basically said, if you want to make a model of things in the world, mathematical equations are the best place to go.

You know, new models that get made of things most often are made with programs, not with equations.

Now, you know, was that sort of going to happen anyway?

Was that a consequence of, you know, my particular work and my particular book?

I mean, I am always amazed at the amounts of feedback that I get from people where they say, oh, by the way, you know, I started doing this whole line of research because I read your book, blah, blah, blah, blah, blah.

It's like, well, can you tell that from the academic literature?

You know, was there a chain of, you know, academic references?

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

It's had plenty of citations, but it's, you know, I think that the, people think of it as probably more conceptual inspiration than kind of a, this is a line from here to here to here in our particular field.

I think that the thing which I am disappointed by, and which will eventually happen, is this kind of study of the sort of pure computationalism, this kind of study of the abstract behavior of the computational universe.

That should be a big thing that lots of people do.

You mean in mathematics purely, almost like.

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

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

That's why the book is called that, right?

It's interesting that I haven't seen really rigorous investigation by thousands of people of this idea.

I mean, you look at your competition around Rule 30, I mean, that's fascinating.

If you can say something, is there some aspect of this thing that could be predicted?

That's the fundamental question of science.

Well, that has been a question of science.

I think that is some people's view of what science is about.

And it's not clear that's the right view.

In fact, as we live through this pandemic full of predictions and so on, it's an interesting moment to be pondering what science's actual role in those kinds of things is.

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

I think that question is answered, and the answer is no.

The answer could be just humans are not smart enough yet.

I mean, that's sort of the big discovery of this principle of computational equivalence of mine.

And this is something which is kind of a follow-on to Godel's theorem, to Turing's work on the halting problem, all these kinds of things, that there is this fundamental limitation built into science, this idea of computational irreducibility that says that, you know, even though you may know the rules by which something operates, that does not mean that you can readily sort of be smarter than it and jump ahead and figure out what it's going to do.

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

And then a set of tools and mathematics that help you discover such pockets.

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

That's why, and this is 1 of the things that sort of come out of this physics project and actually something that again, I should have realized many years ago, but didn't, is it could very well be that everything about the world is computationally irreducible and completely unpredictable.

But in our experience of the world, there is at least some amount of prediction we can make.

And that's because we have sort of chosen a slice of, probably talk about this in much more detail, but I mean, we've kind of chosen a slice of how to think about the universe in which we can kind of sample a certain amount of computational reducibility.

And it may not be the whole story of how the universe is, but it is the part of the universe that we care about and we sort of operate in.

And that's, you know, in science, that's been sort of a very special case of that.

That is, science has chosen to talk a lot about places where there is this computational reducibility that it can find, you know, the motion of the planets can be more or less predicted.

You know, the, Something about the weather is much harder to predict.

Something about other kinds of things are much harder to predict.

And it's, these are, but science has tended to concentrate itself on places where its methods have allowed successful prediction.

So you think rule 30, if we could linger on it, because it's just such a beautiful, simple formulation of the essential concept underlying all the things we're talking about.

Do you think there's pockets of reducibility inside rule

Yes, but it's a question of how big are they what will they allow you to say and so on and that's and figuring out where those pockets are I mean in a sense that's the that sort of a you know that is an essential thing that 1 would like to do in science.

But it's also the important thing to realize that has not been, is that science, if you just pick an arbitrary thing, you say, what's the answer to this question?

That question may not be 1 that has a computationally reducible answer.

That question, if you choose, you know, if you walk along the series of questions and you've got 1 that's reducible and you get to another 1 that's nearby and it's reducible too, if you stick to that kind of, stick to the land, so to speak, then you can go down this chain of sort of reducible, answerable things.

But if you just say, I'm just going to pick a question at random, I'm going to have my computer pick a question at random.

And what we're throwing in the world, so to speak, we, you know, when we engineer things, we tend to engineer things to sort of keep in the zone of reducibility.

When we're throwing things by the natural world, for example, not at all certain that we will be kept in this kind of zone of reducibility.

Is this, so how do we, there's obviously huge amount of economic pain that people are feeling.

There's a huge incentive and medical pain, health, just all kinds of psychological.

There's a huge incentive to figure this out, to walk along the trajectory of reducibility.

You know, people understand generally how virus is spread, but it's very complicated because there's a lot of uncertainty.

There could be a lot of variability, a lot of, like, so many, obviously, a nearly infinite number of variables that represent human interaction.

And so you have to figure out, from the perspective of reducibility, figure out which variables are really important in this kind of, from an epidemiological perspective.

So why aren't we, you kind of said that we're clearly failing.

So, I mean, you know, when this pandemic started up, you know, I happened to be in the middle of being about to release this whole physics project thing.

But, you know, but I thought, you know, I should do the public service thing of trying to understand what I could about the pandemic.

And we've been curating data about it and all that kind of thing.

But so I started looking at the data and started looking at modeling and I decided it's just really hard.

You need to know a lot of stuff that we don't know about human interactions.

It's actually clear now that there's a lot of stuff we didn't know about viruses and about the way immunity works and so on.

And it's, you know, I think what will come out in the end is there's a certain amount of what happens that we just kind of have to trace each step and see what happens.

There's a certain amount of stuff where there's gonna be a big narrative about, this happened because, you know, of T cell immunity.

This happened because there's this whole giant sort of field of asymptomatic viral stuff out there.

You know, there will be a narrative, and that narrative, whenever there's a narrative, that's kind of a sign of reducibility.

But when you just say, let's from first principles figure out what's going on, then you can potentially be stuck in this kind of mess of irreducibility, where you just have to simulate each step, and you can't do that unless you know details about human interaction networks and so on and so on and so on.

The thing that has been very sort of frustrating to see is the mismatch between people's expectations about what science can deliver and what science can actually deliver, so to speak.

Because people have this idea that, you know, it's science.

So there must be a definite answer and we must be able to know that answer.

And, you know, this is, it is both, you know, when you've, after you've played around with sort of little programs in the computational universe, you don't have that intuition anymore.

You know, it's, I always, I'm always fond of saying, you know, the computational animals are always smarter than you are.

That is, you look at 1 of these things and it's like, it can't possibly do such and such a thing.

Then you run it and it's like, wait a minute, it's doing that thing, how does that work?

Okay, now I can go back and understand it.

But that's the brave thing about science, is that in the chaos of the irreducible universe, we nevertheless persist to find those pockets, that's kind of the whole point.

That's, like you say that the limits of science, but that, you know, Yes, it's highly limited, but there's a hope there.

And there's so many questions I wanna ask here.

So 1, you said narrative, which is really interesting.

So obviously, at every level of society, you look at Twitter, everybody's constructing narratives about the pandemic, about not just the pandemic, but all the cultural tension that we're going through.

So there's narratives, but they're not necessarily connected to the underlying reality of these systems.

So our human narratives, I don't even know if they're, I don't like those pockets of reducibility because we're, it's like constructing things that are not actually representative of reality.

And thereby not giving us good solutions to how to predict the system?

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

But I mean, it's similar to sort of explaining things in AI or in any computational system.

Well, it could just be this happened because of this detail and this detail and this detail and a million details.

There's no kind of big arc of the story that says, oh, it's because, you know, there's a viral field that has these properties and people start showing symptoms.

You know, when the seasons change, people will show symptoms and people don't even understand, you know, seasonal variation of flu, for example.

It's something where, you know, there could be a big story or it could be just a zillion little details that mount up.

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Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe | Lex Fridman Podcast #124