The following is a conversation with Stephen Wolfram, his second time in the podcast.

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.

This 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.

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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 one 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 two 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'm sorry if the audio is not great. I did my best and promise to keep improving

and learning as always. If you enjoy this thing, subscribe on YouTube, review it with 5,000 up a podcast, follow on Spotify,

support on Patreon, or connect with me on Twitter, Alex Freedman. As usual, I'll do a few minutes of ads now and no ads in the middle.

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seen the movie, he's a hitman with a minimalist life that resembles my own. In fact, when I was younger, the idea of being a hitman or targeting evil in a

skilled way, which is how I thought about it, really appealed to me. The skill of it, the planning, the craftsmanship. In another life,

perhaps if I didn't love engineering and science so much, I could see myself being something like a Navy SEAL. And in general, I love the idea of

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Lex to get a discount and to support this podcast. And now finally, here's my conversation with Steven Wolfram. You said that there 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 flurry of progress follows? So the big famous

one was 1920s, the invention of quantum mechanics, where, you know, in about five or 10 years, lots of stuff got figured out. That's now quantum

mechanics. Can you mention the people involved? Yeah, it was kind of the Schrodinger, Heisenberg, you know, Einstein had been a key figure originally

Plank, then Dirac was a little bit later. That was something that happened at that time. That's 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? You know, who won the Nobel Prize for QCD? Okay, people, David Gross, Frank Wilczak,

you know, David Pollitzer, the people who are the sort of the slightly older generation, Dick Feynman, Murray Gellman, people like that, who were Steve

Weinberg, Gadot Hoft, he's younger. He's in the younger group, actually. 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 historical, you know, iconic figures.

They seem more like everyday characters, so to speak. And so it's always, you know, when you look at history from long afterwards, it always seems like everything happened instantly.

And that's usually not the case. There was usually a long build up. 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.

And that usually lasts five or 10 years. You know, we see it today with machine learning and, you know, deep learning neural nets and so on, you know, methodological advance, things actually started working in, you know, 2011, 2012 and so on.

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

Do you think there's a key moment? Like, if I had to really introspect, like, what was the key moment for the deep learning, quote unquote, revolution?

It's probably the AlexNet business.

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

Absolutely, it's the 1940s.

There's a bunch of little pieces that came together, and then all of a sudden everybody's eyes lit up, like, wow, there's something here.

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, one 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 at 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 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 the,

you know, this phenomenon that I could only have said occurs in one particular case is actually something incredibly general.

And then that led me to this thing called Principled Computational Equivalence, and that was a long story.

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

What about the whole universe? That's our sort of ultimate example of a complicated thing.

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

You know, I happen to know a lot about, you know, traditional fundamental physics.

My first, you know, I had a bunch of ideas about how to do this in the early 1990s.

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

You know, I wrote about them back in 2002.

With the new kind of science and the cellular autometer world.

Right.

And there's echoes in the cellular autometer world with your new Wolfram physics project world.

We'll get to all that. Allow me to sort of romanticize a little more on the philosophy of science.

So Thomas Kuhn, a philosopher of science, describes that, you know, 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.

This is this idea of, he's a famous biographer, but I think it's called the innovators, the biographer 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.

Like where does your sense fall?

Is ultimately like one person responsible for these revolutions that creates the spark or one or two, whatever.

But or is it just the big mush and mess and chaos of people interacting or 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 one person to have a crisp new idea than it is for a big committee to have a crisp new idea.

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

And this has happened to me plenty.

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.

It's kind of interesting.

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.

It seems like the new kind of science has not had the revolutionary impact. I would think it might.

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 that was something special here.

This was incredible.

What happened?

Or do you think that's already happened?

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.

Last 15 years doesn't happen.

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?

It's hard to know for sure.

I mean, I am always amazed at the amount 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.

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

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

Probably not.

One 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 of millions of people.

But because it's not a single, it's not a chain of papers with piffy 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, you know, conceptual inspiration than kind of a, you know, this is a line from here to here to here in our particular field.

I think that the, you know, the thing which I am disappointed by and which will eventually happen is this kind of study of the, 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 isn't.

It's a new kind of mathematics.

It's a new kind of mathematics.

Yeah, right.

That's why the book is called that.

Right.

That's not coincidental.

Yeah.

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, if you can say something.

Right.

Is there some aspect of this thing that could be predicted?

That's the fundamental question of science.

That's the core.

Well, that has been a question of science.

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

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

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

That's the open question.

Right.

I don't think it's open.

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

I mean, no, no, the answer could be just humans are not smart enough yet.

We don't have the tools yet.

No, that's, that's the whole point.

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

And the, you know, this is something which is kind of a follow on to Goethe'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, computational reducibility?

Yes.

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.

Right.

That's why, you know, and this is one 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, you know, the, it could very well be that everything about the world is computationally reducible and completely unpredictable.

But, you know, 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 that's that's sort of where we where we exist. 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, you know, other kinds of things that the are much harder to predict.

And it's some, these are but science has tended to, you know, 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 central concept underlying all the things we're talking about.

Do you think there's pockets of reducibility inside rule 30?

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 one would like to do in science.

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

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

That question, if you, if you choose, you know, if you walk along the series of questions and you've got one that's reducible and you get to another one 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 pick a question at random, I'm going to have my computer pick a question at random.

Most likely it's going to be reducible.

Most likely it will be irreducible. 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, not at all certain that we will be kept in this kind of zone of reducibility.

Can we talk about this pandemic then?

Sure.

For a second.

So how do we, there's obviously a huge amount of economic pain that people are feeling.

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

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

There's, there's a lot of disparate data.

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

There's a, there could be a lot of variability also, like so many, obviously a nearly infinite number of variables that, 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.

Well, I think it's a complicated thing.

So, 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.

Yes.

But I thought, you know,

The timing is just cosmically absurd.

A little bit bizarre.

But, but, but, you know, but I thought, you know, I should do the public service thing of, you know, trying to understand what I could about the pandemic and, you know, we've been curating data about and all that kind of thing.

But, you know, 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 going to be a big narrative about this happened because, you know, of T cell immunity.

This has 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.

We just have to simulate each step and you can't do that unless you know details about, you know, human interaction networks and so on and so on and so on.

The thing that has 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, that 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 know, you look at one 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 like, there's so many questions I want to ask here.

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

So obviously from 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.

Well, and thereby not giving us like good solutions to how to predict the system.

Look, it gets complicated because, you know, people want to say, explain the pandemic to me, explain what's going to happen in the future.

Yes, but also, can you explain it?

Is there a story to tell?

What already happened in the past?

Yeah, or what's going to happen.

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

It's like, like, you know, explain what happened.

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

And there isn't a big story to tell.

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

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

See, but okay, let's, let's pretend that this pandemic, like the coronavirus resembles something like the one D rule 30 cellular automata.

Okay.

So, I mean, that's how epidemiologists model virus spread.

Indeed.

Yes.

Sometimes you sell your automata.

Yes.

And okay, so you can say it's simplistic, but okay, let's say it is it's representative of actually what happens.

You know, the, the dynamic of you have a graph.

It's probably as closer to the hypergraph.

Yes.

That's another funny thing.

Yeah.

As we were getting ready to release this physics project, we realized that a bunch of things we'd worked out about, about foliations of causal graphs and things were directly relevant to thinking about contact tracing.

Yeah, exactly.

And interactions of cell phones and so on, which is really weird.

But like, it just feels like, it feels like we should be able to get some beautiful core insight about the spread of this particular virus on the hypergraph of human civilization, right?

I tried.

I didn't, I didn't manage to figure it out.

But you're one person.

Yeah.

But I mean, I think actually it's, it's a funny thing because it turns out the, the main model, you know, this SIR model, I only realized recently was invented by the grandfather of a good friend of mine from high school.

So that was just a, you know, it's a weird thing.

Right.

The question is, you know, okay, so you know, you know, on this graph of how humans are connected, you know, something about what happens if this happens and that happens.

That graph is made in complicated ways that depends on all sorts of issues that where we don't have the data about how human society works well enough to be able to make that graph.

There's actually one of my kids did a study of sort of what happens on different kinds of graphs and how robust are the results.

Okay.

His basic answer is there are a few general results that you can get that are quite robust, like, you know, a small number of big gatherings is worse than a large number of small gatherings.

Okay.

That's quite robust.

But when you ask more detailed questions, it seemed like it just depends.

It depends on details.

In other words, it's kind of telling you in that case, you know, the irreducibility matters, so to speak.

It's not, there's not going to be this kind of one sort of master theorem that says, and therefore this is how things are going to work.

Yeah, but there's a certain kind of from a graph perspective, the certain kind of dynamic to human interaction.

So like large groups and small groups, I think it matters who the groups are.

For example, you can imagine large depends how you define large, but you can imagine groups of 30 people as long, like, as long as they are cliques or whatever.

Right.

As long as the outgoing degree of that graph is small or something like that.

Like you can imagine some beautiful underlying rule of human dynamic interaction where I can still be happy, where I can have a conversation with you and a bunch of other people that mean a lot to me in my life.

And then stay away from the bigger, I don't know, not going to a Miley Cyrus concert or something like that and figuring out mathematically some nice rule of behavior.

See, this is an interesting thing.

So I mean, in, you know, this is the question of what you're describing is kind of the problem of many situations where you would like to get away from computational irreducibility.

A classic one in physics is thermodynamics.

The, you know, the second law of thermodynamics, the law that says, you know, entropy tends to increase things that, you know, start orderly tend to get more disordered.

Or which is also the thing that says, given that you have a bunch of heat, it's hard heat is, you know, the microscopic motion of molecules, it's hard to turn that heat into systematic mechanical work.

It's hard to, you know, just take something being hot and turn that into, oh, the, you know, the, all the atoms are going to line up in the bar of metal and the piece of metal is going to shoot in some direction.

That's essentially the same problem as how do you go from this, this computationally irreducible mess of things happening and get something you want out of it.

It's kind of mining, you know, you're kind of now, you know, actually, I've, I've understood in recent years that, that the story of, of thermodynamics is actually precisely a story of computational irreducibility.

But it is a, it is already an analogy.

You know, you can, you can kind of see that as can you take the, you know, what you're asking to do there is you're asking to go from the kind of the mess of all these complicated human interactions and all this kind of computational processes going on.

And you say, I want to achieve this particular thing out of it.

I want to kind of extract from the heat of what's happening.

I want to kind of extract this useful piece of sort of mechanical work that I find helpful.

I mean, do you have a hope for the pandemic?

So we'll talk about physics, but for the pandemic, can that be extracted?

Do you think?

Well, I think the good news is the curves, basically, you know, for reasons we don't understand the curves, you know, the, the, the clearly measurable mortality clouds and so on for the northern hemisphere have gone down.

Yeah, but the bad news is that it could be a lot worse for future viruses and what this pandemic revealed is we're highly unprepared for the discovery of the pockets of reducibility within a pandemic that's much more dangerous.

Well, my guess is the specific risk of, you know, viral pandemics, you know, that the pure virology and, you know, immunology of the thing.

This will cause that to advance to the point where this particular risk is probably considerably mitigated.

But, you know, it's, you know, does, is the structure of modern society robust to all kinds of risks?

Well, the answer is clearly no.

And, you know, it's surprising to me the extent to which people, you know, as I say, it's a, it's a, it's kind of scary actually how much people believe in science.

That is, people say, oh, you know, because the science says this, that and the other will do this and this and this, even though from a sort of common sense point of view, it's a little bit crazy.

And people are not prepared and it doesn't really work in society as it is for people to say, well, actually we don't really know how the science works.

People say, well, tell us what to do.

Yeah, because then, yeah, what's the alternative?

The, for the masses, it's difficult to sit, it's difficult to meditate on computational reducibility.

It's difficult to sit, it's difficult to enjoy a good dinner meal while, while knowing that you know nothing about the world.

I think this is a, this is a place where, you know, this is, this is what politicians, you know, and political leaders do for a living, so to speak, because you got to make some decision about what to do.

And it's some.

Tell some narrative.

Right.

While amidst the mystery and knowing not much about the, the past or the future, still telling a narrative that somehow gives people hope that we know what the heck we're doing.

Yeah, and get society through the issue.

You know, even, even though, you know, the idea that we're just going to, you know, sort of be able to get the definitive answer from science and it's going to tell us exactly what to do.

Unfortunately, you know, that it's interesting because let me point out that if that was possible, if science could always tell us what to do, then in a sense, our, you know, that will be a big downer for our lives.

If science could always tell us what the answer is going to be.

It's like, well, you know, it's kind of fun to live one's life and just sort of see what happens.

If one could always just say, let me, let me check my science.

Oh, I know, you know, the result of everything is going to be 42.

I don't need to live my life and do what I do.

It's just, we already know the answer.

It's actually good news in a sense that there is this phenomenon of computational irreducibility that doesn't allow you to just sort of jump through time and say this is the answer, so to speak.

And that's, so that's a good thing.

The bad thing is it doesn't allow you to jump through time and know what the answer is.

It's scary.

Do you think we're going to be okay as a human civilization?

He said, we don't know.

Absolutely.

Do you think we'll prosper or destroy ourselves as a...

In general?

In general.

I'm an optimist.

No, I think that, you know, it'll be interesting to see, for example, with this, you know, pandemic.

You know, to me, you know, when you look at like organizations, for example, you know, having some kind of perturbation, some kick to the system, usually the end result of that is actually quite good.

You know, unless it kills the system, it's actually quite good usually.

And I think in this case, you know, people, I mean, my impression, you know, it's a little weird for me because, you know, I've been a remote tax CEO for 30 years.

It doesn't, you know, this is bizarrely, you know, and the fact that, you know, like this coming to see you here is the first time in six months that I've been like, you know, in a building other than my house.

Okay, so, you know, I'm a kind of ridiculous outlier in these kinds of things.

But overall, your sense is when you shake up the system and throw in chaos that you challenge the system, we humans emerge better.

Seems to be that way.

Who's to know?

But I think that, you know, people, you know, my sort of vague impression is that people are sort of, you know, oh, what's actually important?

You know, what's, what, what is worth caring about and so on?

And that seems to be something that perhaps is, is more, you know, emergent in this kind of situation.

It's so fascinating that on the individual level, we have our own complex cognition, we have consciousness, we have intelligence with trying to figure out little puzzles.

And then that somehow creates this graph of collective intelligence.

Well, we figure out, and then you throw in these viruses of which there's millions different, you know, there's entire taxonomy.

And the viruses are thrown into the system of collective human intelligence and little humans figure out what to do about it.

We get like, we tweet stuff about information, there's doctors as conspiracy theorists, and then we play with different information.

I mean, the whole of it is fascinating.

I like you also very optimistic, but there's a few just you said the computation or reducibility.

There's always a fear of the darkness of the uncertainty before us.

Yeah, no, I mean, the thing is, if you knew everything, it will be boring.

And it would be and then and worse than boring, so to speak, it would be you, it would reveal the pointlessness, so to speak.

And in a sense, the fact that there is this computational reducibility, it's like as we live our lives, so to speak, something is being achieved.

We're computing what our lives, you know, what happens in our lives.

That's funny.

So the computation or reducibility is kind of like, it gives the meaning to life.

It is the meaning of life.

Computation or reducibility is the meaning of life.

There you go.

It gives it meaning.

Yes, I mean, it's what it's what causes it to not be something where you can just say, you know, you went through all those steps to live your life, but we already knew what the answer was.

Hold on one second.

I'm going to use my handy Wolf Malphur sunburn computation thing so long as I can get network here.

There we go.

No, actually, you know what?

It says sunburn unlikely.

This is a QA moment.

This is a good moment.

Okay.

Well, let me just check what it thinks.

I would see why it thinks that it doesn't seem like my intuition.

This is one of these cases where we can, the question is, do we, do we trust the science or do we use common sense?

The UV thing is cool.

Yeah.

Yeah.

Well, we'll see.

This is a QA moment, as I say, and so we trust the product.

Yes.

We trust the product.

And then there'll be a data point.

Either way.

If I'm desperately sunburned, I will send in an angry feedback.

Because we mentioned the concept so much, and a lot of people know it, but can you say what computation or usability is?

Yeah, right.

So the question is, if you think about things that happen as being computations, you think about the, some process in physics, something that you compute in mathematics, whatever else.

It's a computation in the sense it has definite rules.

You follow those rules.

You follow them many steps and you get some result.

So then the issue is, if you look at all these different kinds of computations that can happen, whether they're computations that are happening in the natural world, whether they're happening in our brains, whether they're happening in our mathematics, whatever else.

The big question is, how do these computations compare?

Is, are there dumb computations and smart computations?

Or are they somehow all equivalent?

And the thing that I kind of was sort of surprised to realize from a bunch of experiments that I did in the early 90s, and now we have tons more evidence for it, this thing I call the principle of computational equivalence.

Which basically says, when one of these computations, one of these processes that follows rules, doesn't seem like it's doing something obviously simple, then it has reached the sort of equivalent level of computational sophistication of everything.

So what does that mean?

That means that you might say, gosh, I'm studying this little tiny program on my computer.

I'm studying this little thing in nature, but I have my brain and my brain is surely much smarter than that thing.

I'm going to be able to systematically outrun the computation that it does because I have a more sophisticated computation that I can do.

But what the principle of computational equivalence says is that doesn't work.

Our brains are doing computations that are exactly equivalent to the kinds of computations that are being done in all these other sorts of systems.

And so what consequences does that have?

Well, it means that we can't systematically outrun these systems.

These systems are computationally irreducible in the sense that there's no sort of shortcut that we can make that jumps to the answer.

In a general case.

Right.

But so what has happened, what science has become used to doing is using the little sort of pockets of computational reducibility, which, by the way, are an inevitable consequence of computational irreducibility,

that there have to be these pockets scattered around of computational reducibility to be able to find those particular cases where you can jump ahead.

I mean, one thing sort of a little bit of a parable type thing that I think is fun to tell.

If you look at ancient Babylon, they were trying to predict three kinds of things.

They tried to predict where the planets would be, what the weather would be like, and who would win or lose a certain battle.

And they had no idea which of these things would be more predictable than the other.

That's funny.

And it turns out where the planets are is a piece of computational reducibility that 300 years ago or so we pretty much cracked.

I mean, it's been technically difficult to get all the details right, but it's basically, we got that.

You know, who's going to win or lose the battle?

No, we didn't crack that one.

That one.

Right.

Game theorists are trying.

And then the weather.

It's kind of halfway.

Halfway.

Yeah, I think we're doing okay with that one.

Long term climate, different story.

But the weather, you know, we're much closer on that.

But do you think eventually we'll figure out the weather? So do you think eventually most think we'll figure out the local pockets in everything?

Essentially, the local pockets of reducibility?

No, I think that it's an interesting question.

But I think that the, you know, there is an infinite collection of these local pockets will never run out of local pockets.

And by the way, those local pockets are where we build engineering, for example.

That's how we, you know, when we, if we want to have a predictable life, so to speak, then, you know, we have to build in these sort of pockets of reducibility.

Otherwise, you know, if we were, if we were sort of existing in this kind of irreducible world, we'd never be able to, you know, have definite things to know what's going to happen.

You know, I have to say, I think one of the features, you know, when we look at sort of today from the future, so to speak, I suspect one of the things where people will say,

I can't believe they didn't see that is stuff to do with the following kind of thing.

So, you know, if we describe, oh, I don't know, something like heat, for instance, we say, oh, you know, the air in here, it's, you know, it's this temperature, this pressure.

That's as much as we can say.

Otherwise, just a bunch of random molecules bouncing around.

People will say, I just can't believe they didn't realize that there was all this detail in how all these molecules were bouncing around, and they could make use of that.

And actually, I realized there's a thing I realized last week, actually, was a thing that people say, you know, one of the scenarios for the very long term history of our universe is the so called heat death of the universe,

where basically everything just becomes thermodynamically boring.

Everything's just this big kind of gas and thermal equilibrium, people say, that's a really bad outcome.

But actually, it's not a really bad outcome.

It's an outcome where there's all this computation going on, and all those individual gas molecules are all bouncing around in very complicated ways, doing this very elaborate computation.

It just happens to be a computation that right now, we haven't found ways to understand.

We haven't found ways, you know, our brains haven't, you know, and our mathematics and our science and so on, haven't found ways to tell an interesting story about that.

It just looks boring to us.

You're saying there's a hopeful view of the heat death, quote unquote, of the universe where there's actual beautiful complexity going on.

Similar to the kind of complexity we think of that creates rich experience in human life and life on Earth.

Yes.

And those little molecules interacting complex ways that could be intelligence in that there could be.

Absolutely.

I mean, this is what you learn from this principle.

That's a hopeful message.

Right.

I mean, this is what you kind of learn from this principle of computational equivalence.

You learn it's both a message of sort of hope and a message of kind of, you know, you're not as special as you think you are, so to speak.

You know, we we imagine that with sort of all the things we do with with human intelligence and all that kind of thing and all of the stuff we've constructed in science.

It's like, we're very special.

But actually, it turns out, well, no, we're not.

We're just doing computations like things in nature do computations like those gas molecules do computations like the weather does computations.

The only the only thing about the computations that we do that's really special is that we understand what they are, so to speak.

In other words, we have a, you know, to us, the special because kind of they're connected to our purposes, our ways of thinking about things and so on.

And that's some but so that's very human centric.

That's we're just attached to this kind of thing.

So let's talk a little bit of physics.

Maybe let's ask the biggest question.

What is a theory of everything in general?

What does that mean?

Yeah, so I mean, the question is, can we kind of reduce what has been physics as a something where we have to sort of pick away and say, do we roughly know how the world works to something where we have a complete formal theory where we say if we were to run this program for long enough, we would reproduce everything, you know, down to the fact that we're having this conversation at this moment, et cetera, et cetera, et cetera.

Any physical phenomena, any phenomena in this world.

Phenomenon in the universe.

But the, you know, because of computational irreducibility, it's not, you know, that's not something where you say, okay, you've got the fundamental theory of everything.

Then, you know, tell me whether, you know, lions are going to eat tigers or something.

You know, that's a, no, you have to run this thing for, you know, 10 to the 500 steps or something to know something like that.

Okay, so at some moment, potentially, you say, this is a rule and run this rule enough times and you will get the whole universe.

Right.

That's, that's what it means to kind of have a fundamental theory of physics as far as I'm concerned is you've got this rule.

It's potentially quite simple.

We don't know for sure it's simple, but we have various reasons to believe it might be simple.

And then you say, okay, I'm showing you this rule, you just run it only 10 to the 500 times and you'll get everything.

In other words, you've kind of reduced the problem of physics to a problem of mathematics, so to speak.

It's like, it's as if, you know, you'd like to generate the digits of pi.

There's a definite procedure, you just generate them.

And it'd be the same thing if you have a fundamental theory of physics of the kind that I'm imagining.

You, you know, you get a, this rule and you just run it out and you get everything that happens in the universe.

So a theory of everything is a mathematical framework within which you can explain everything that happens in a universe.

It's kind of in a unified way.

It's not.

There's a bunch of disparate modules.

Right.

Does it feel like if you create a rule and we'll talk about the Wolfram physics model, which is fascinating.

But if you, if you have a simple set of rules with a, with a data structure, like a hypograph, does that feel like a satisfying theory of everything?

Because then you really run up against the irreducibility, computational reducibility.

Right. So that's a really interesting question.

So I, I, you know, what I thought was going to happen is I thought we, you know, I thought we had a pretty good, I had a pretty good idea for what the structure of this sort of theory that's sort of underneath space and time and so on might be like.

And I thought, gosh, you know, in my lifetime, so to speak, we might be able to figure out what happens in the first 10 to the minus 100 seconds of the universe.

And that would be cool, but it's pretty far away from anything that we can see today and it will be hard to test whether that's right and so on and so on and so on.

To my huge surprise, although it should have been obvious and it's embarrassing that it wasn't obvious to me, but, but to my huge surprise, we managed to get unbelievably much further than that.

And basically what happened is that it turns out that even though there's this kind of bed of computational irreducibility, that sort of these, all these simple rules run into.

There is a, there are certain pieces of computational reducibility that quite generically occur for large classes of these rules.

And, and this is the really exciting thing as far as I'm concerned, the, the, the big pieces of computational reducibility are basically the pillars of 20th century physics.

That's the amazing thing that general relativity and quantum field theory, the sort of the pillars of 20th century physics turn out to be precisely the stuff you can say.

There's a lot you can't say there's a lot that's kind of at this irreducible level where you kind of don't know what's going to happen.

You have to run it, you know, you can't run it within our universe, et cetera, et cetera, et cetera, et cetera, et cetera.

But the thing is there are things you can say, and the things you can say turn out to be very beautifully exactly the structure that was found in 20th century physics, namely general relativity and quantum mechanics.

And general relativity and quantum mechanics are these pockets of reducibility that we think of as that, that 20th century physics is essentially pockets of reducibility.

And then it's, it is incredibly surprising that any kind of model that's generative from simple rules would have, would have such pockets.

Yeah, well, I think what's surprising is we didn't know where those things came from. It's like general relativity, it's a very nice mathematically elegant theory.

Why is it true? You know, quantum mechanics, why is it true?

What we realized is that from this, that they are, these theories are generic to a huge class of systems that have these particular very unstructured underlying rules.

And that's the, that's the thing that is sort of remarkable. And that's the thing to me that's just, it's really beautiful.

I mean, it's, and the thing that's even more beautiful is that it turns out that, you know, people have been struggling for a long time.

You know, how does general relativity theory of gravity relate to quantum mechanics?

They seem to have all kinds of incompatibilities.

It turns out what we realized is at some level they are the same theory.

And that's just, it's, it's just great as far as I'm concerned.

Maybe like taking a little step back from your perspective, not from the low, not from the beautiful,

hypergraph, well, from physics model perspective, but from the perspective of 20th century physics.

What is general relativity? What is quantum mechanics?

How do you think about these two theories from the context of the theory of everything?

It's just even definitions.

Yeah, yeah, yeah, right. So I mean, you know, a little bit of history of physics, right?

So, so I mean the, the, you know, okay, very, very quick history.

Yes. Right. So, so I mean, you know, physics, you know, in ancient Greek times, people basically said,

we can just figure out how the world works as, you know, we're philosophers, we're going to figure out how the world works.

You know, some philosophers thought there were atoms, some philosophers thought there were, you know, continuous flows of things.

People had different ideas about how the world works.

And they tried to just say, we're going to construct this idea of how the world works.

They didn't really have sort of notions of doing experiments and so on quite the same way as developed later.

So that was sort of an early tradition for thinking about sort of models of the world.

Then by the time of 1600s, time of Galileo and then Newton, sort of the big, the big idea there was, you know,

you know, title of Newton's book, you know, Principia Mathematica,

Mathematical Principles of Natural Philosophy.

We can use mathematics to understand natural philosophy, to understand things about the way the world works.

And so that then led to this kind of idea that, you know, we can write down a mathematical equation

and have that represent how the world works.

So Newton's one of his most famous ones is his universal law of gravity,

inverse square law of gravity that allowed him to compute all sorts of features of the planets and so on,

although some of them he got wrong and it took another 100 years for people to actually be able to do the math to the level that was needed.

But so that had been, this sort of tradition was we write down these mathematical equations.

We don't really know where these equations come from.

We write them down, then we figure out, we work out the consequences and we say,

yes, that agrees with what we actually observe in astronomy or something like this.

So that tradition continued and then the first of these two sort of great 20th century innovations was,

well, the history is actually a little bit more complicated, but let's say there were two, quantum mechanics and general relativity.

Quantum mechanics, kind of 1900 was kind of the very early stuff done by Planck that led to the idea of photons, particles of light.

But let's take general relativity first.

One feature of the story is that special relativity thing Einstein invented in 1905 was something which surprisingly was a kind of logically invented theory.

It was not a theory where it was something where, given these ideas that were sort of axiomatically thought to be true about the world,

it followed that such and such a thing would be the case.

And it was a little bit different from the kind of methodological structure of some existing theories in the more recent times.

Or it had just been, we write down an equation and we find out that it works.

So what happened there?

So there's some reasoning about the light.

The basic idea was the speed of light appears to be constant.

Even if you're traveling very fast, you shine a flashlight, the light will come out, even if you're going at half the speed of light,

the light doesn't come out of your flashlight at one and a half times the speed of light.

It's still just the speed of light.

And to make that work, you have to change your view of how space and time work to be able to account for the fact that when you're going faster,

it appears that, you know, length is foreshortened and time is dilated and things like this.

And that's special relativity.

That's special relativity.

So then Einstein went on with sort of vaguely similar kinds of thinking in 1915 invented general relativity, which is a theory of gravity.

And the basic point of general relativity is it's a theory that says when there is mass in space, space is curved.

And what does that mean?

You know, usually you think of what's the shortest distance between two points, like, you know, ordinarily on a plane in space, it's a straight line.

You know, photons, light goes in straight lines.

Well, then the question is, if you have a curved surface, a straight line is no longer straight.

On the surface of the earth, the shortest distance between two points is a great circle.

It's a circle.

So, you know, Einstein's observation was maybe the physical structure of space is such that space is curved.

So the shortest distance between two points, the path, the straight line in quotes won't be straight anymore.

And in particular, if a photon is, you know, traveling near the sun or something or if a particle is going, something is traveling near the sun,

maybe the shortest path will be one that is something which looks curved to us because it seems curved to us because space has been deformed by the presence of mass,

associated with that massive object.

So the kind of the idea there is think of the structure of space as being a dynamical changing kind of thing.

But then what Einstein did was he wrote down these differential equations that basically represented the curvature of space

and its response to the presence of mass and energy.

And that ultimately is connected to the force of gravity, which is one of the forces that seems to, based on its strength, operate on a different scale than some of the other forces.

So it operates in a scale that's very large.

What happens there is just this curvature of space, which causes, you know, the paths of objects to be deflected.

That's what gravity does.

It causes the paths of objects to be deflected.

And this is an explanation for gravity, so to speak.

And the surprise is that from 1915 until today, everything that we've measured about gravity precisely agrees with General Altsoverty.

And that, you know, it wasn't clear black holes were sort of a predict, well actually the expansion of the universe was an early potential prediction,

although Einstein tried to sort of patch up his equations to make it not cause the universe to expand because it was kind of so obvious the universe wasn't expanding.

And, you know, it turns out it was expanding and he should have just trusted the equations.

And that's a lesson for those of us interested in making fundamental theories of physics is you should trust your theory and not try and patch it because of something that you think might be the case that might turn out not to be the case.

Even if the theory says something crazy is happening.

Yeah, right.

Like the universe is expanding.

Right, which is, but you know, then it took until the 1940s, probably even really until the 1960s until people understood that black holes were a consequence of General Altsoverty and so on.

But that's, you know, the big surprise has been that so far this theory of gravity has perfectly agreed with, you know, these collisions of black holes seen by their gravitational waves, you know, it all just works.

So that's been kind of one pillar of the story of physics. It's mathematically complicated to work out the consequences of General Altsoverty, but it's not.

There's no, I mean, and some things are kind of squiggly and complicated, like people believe, you know, energy is conserved.

Okay, well, energy conservation doesn't really work in General Altsoverty in the same way as it ordinarily does.

And it's all a big mathematical story of how you actually nail down something that is definitive that you can talk about it and not specific to the, you know, reference frames you're operating in and so on and so on and so on.

But fundamentally, General Altsoverty is a straight shot in the sense that you have this theory, you work out its consequences.

And that theory is useful in terms of basic science and trying to understand the way black holes work, the way the creation of galaxies work, sort of all of these kind of cosmological things.

Understanding what happened, like you said, at the Big Bang, like all those kinds of, oh no, not at the Big Bang actually, right?

Well, features of the expansion of the universe, yes. I mean, and there are lots of details where we don't quite know how it's working, you know, is there, you know, where's the dark matter?

Is there dark energy, you know, et cetera, et cetera, et cetera. But fundamentally, the, you know, the testable features of General Altsoverty, it all works very beautifully.

And it's, in a sense, it is mathematically sophisticated, but it is not conceptually hard to understand in some sense.

Okay, so that's General Altsoverty. And once it's friendly neighbor, like you said, there's two theories, quantum mechanics.

Right. So quantum mechanics, the sort of, the way that that originated was, one question was, is the world continuous or is it discrete?

You know, in ancient Greek times, people have been debating this. People debated it in, you know, throughout history as light made of waves.

Is it continuous? Is it discrete? Is it made of particles, corpuscles, whatever?

You know, what had become clear in the 1800s is that atoms, that, you know, materials are made of discrete atoms.

You know, when you take some water, the water is not a continuous fluid, even though it seems like a continuous fluid to us at our scale.

But if you say, let's look at it, smaller and smaller and smaller and smaller scale, eventually you get down to these, you know, these molecules and then atoms.

It's made of discrete things. So the question is sort of how important is this discreteness, just what's discrete, what's not discrete?

Is energy discrete? Is, you know, what's discrete, what's not?

And so...

Does it have mass, those kinds of questions?

Yeah, yeah, right. Well, there's question, I mean, for example, is mass discrete is an interesting question, which is now something we can address.

But, you know, what happened in the coming up to the 1920s?

There was this kind of mathematical theory developed that could explain certain kinds of discreteness in particularly in features of atoms and so on.

And, you know, what developed was this mathematical theory that was the theory of quantum mechanics, theory of wave functions, Schrodinger's equation, things like this.

That's a mathematical theory that allows you to calculate lots of features of the microscopic world, lots of things about how atoms work, et cetera, et cetera, et cetera.

Now, the calculations all work just great.

The question of what does it really mean is a complicated question.

Now, I mean, to just explain a little bit historically, the, you know, the early calculations of things like atoms worked great in the 1920s and 1930s and so on.

There was always a problem there were in quantum field theory, which is a theory of in quantum mechanics, you're dealing with a certain number of certain number of electrons, and you fix the number of electrons, you say, I'm dealing with a two electron thing.

In quantum field theory, you allow for particles being created and destroyed.

So you can emit a photon that didn't exist before you can absorb a photon, things like that.

That's a more complicated, mathematically complicated theory, and it had all kinds of mathematical issues and all kinds of infinities that cropped up.

And it was finally figured out more or less how to get rid of those.

But there were only certain ways of doing the calculations, and those didn't work for atomic nuclei, among other things.

And that led to a lot of development up until the 1960s of alternative ideas for how, how one could understand what was happening in atomic nuclei, et cetera, et cetera, et cetera.

And result in the end, the kind of most, quote, obvious mathematical structure of quantum field theory seems to work, although it's mathematically difficult to deal with.

But you can calculate all kinds of things.

You can calculate, you know, a dozen decimal places, certain things, you can measure them, it all works.

It's all beautiful.

Now you say...

The underlying fabric is the model of that particular theory is fields, like you keep saying fields.

Those are quantum fields, those are different from classical fields.

A field is something like you say the temperature field in this room.

It's like there is a value of temperature at every point around the room.

Or you can say the wind field would be the vector direction of the wind at every point.

It's continuous.

Yes.

And that's a classical field.

The quantum field is a much more mathematically elaborate kind of thing.

And I should explain that one of the pictures of quantum mechanics that's really important is, you know, in classical physics, one believes that sort of definite things happen in the world.

You pick up a ball, you throw it, the ball goes in a definite trajectory that has certain equations of motion, it goes in a parabola, whatever else.

In quantum mechanics, the picture is definite things don't happen.

Instead, sort of what happens is this whole sort of structure of all, you know, many different paths being followed.

And we can calculate certain aspects of what happens, certain probabilities of different outcomes and so on.

And you say, well, what really happened?

What's really going on?

What's the sort of, what's the underlying, you know, what's the underlying story?

How do we turn this mathematical theory that we can calculate things with into something that we can really understand and have a narrative about?

And that's been really, really hard for quantum mechanics.

My friend, Dick Feynman, always used to say, nobody understands quantum mechanics, even though he'd made his, you know, whole career out of calculating things about quantum mechanics.

And, you know, so it's a little...

But nevertheless, it's what the quantum field theory is very, very accurate at predicting a lot of the physical phenomena.

So it works.

Yeah.

But there are things about it, you know, it has certain, when we apply it, the standard model of particle physics, for example, we, you know, which we apply to calculate all kinds of things.

It works really well.

And you say, well, it has certain parameters.

It has a whole bunch of parameters, actually.

You say, why is the, you know, why does the Muon particle exist?

Why is it 206 times the mass of the electron?

We don't know.

No idea.

But so the standard model of physics is one of the models that's very accurate for describing three, three of the fundamental forces of physics.

And it's looking at the world of the very small.

Right.

And then there's back to the neighbor of gravity, of general relativity.

So, and in the context of a theory of everything, what's traditionally the task of the unification of these theories?

Well, I mean, the issue is, you try to use the methods of quantum field theory to talk about gravity, and it doesn't work.

Just like there are photons of light.

So there are gravitons, which are sort of the particles of gravity.

And when you try and compute sort of the properties of the, of the particles of gravity, the kind of mathematical tricks that get used in working things out in quantum field theory don't work.

And that's, so that's been a sort of fundamental issue. And when you think about black holes, which are a place where sort of the, the structure of space is, you know, has, has sort of rapid variation and you get kind of quantum effects mixed in with effects from general

relativity, things get very complicated and there are apparent paradoxes and things like that. And people have, you know, there have been a bunch of mathematical developments in, in physics over the last, I don't know, 30 years or so, which have kind of picked away at those kinds of issues, and

got hints about how things might work.

And, but it hasn't been, you know, and the other thing to realize is, as far as physics is concerned, it's just like his general relativity, his quantum field theory, you know, be happy.

Professor, do you think there's a quantization of gravity to quantum gravity? What do you think of efforts that people have tried to? Yeah, what do you think in general of the efforts of the physics community to try to unify these laws?

So I think what's, it's interesting. I mean, I would have said something very different before what's happened with our physics project.

I mean, you know, the remarkable thing is what we've been able to do is to make from this very simple, structurally simple underlying set of ideas, we've been able to build this, this, you know, very elaborate structure that's both very abstract,

and very sort of mathematically rich. And the big surprise as far as I'm concerned is that it touches many of the ideas that people have had.

So in other words, things like string theory and so on, twister theory, it's like the, you know, we might have thought I had thought we're out on a prong, we're building something that's computational, it's completely different from what other people have done.

But actually, it seems like what we've done is to provide essentially the machine code that, you know, these things are of various features of domain specific languages, so to speak, that talk about various aspects of this machine code.

And I think there's a, this is something that to me is very exciting because it allows one both for us to provide sort of a new foundation for what's been thought about there, and for the all the work that's been done in those areas to, you know, to give us, you know,

more momentum to be able to figure out what's going on. Now, you know, people have sort of hoped, oh, we're just going to be able to get, you know, string theory to just answer everything that hasn't worked out.

And I think we now kind of can see a little bit about just sort of how far away certain kinds of things are from being able to explain things.

Some things, one of the big surprises to me, actually, I literally just got a message about one aspect of this is the, you know, it's turning out to be easier.

I mean, this project has been so much easier than I could ever imagine it would be.

Because I thought we would be, you know, just about able to understand the first 10 to the minus 100 seconds of the universe. And, you know, it would be 100 years before we get much further than that.

It's just turned out it actually wasn't that hard. I mean, we're not finished, but, you know,

So you're, you're, you're seeing echoes of all the disparate theories of physics in this framework.

Yes. Yes. I mean, it's a very interesting, you know, sort of history of science like phenomenon.

The first analogy that I can see is what happened with the early, early days of, of computability and computation theory.

You know, Turing machines were invented in 1936.

People sort of understand computation in terms of Turing machines, but actually there had been preexisting theories of computation,

combinators, general recursive functions, lambda calculus, things like this.

But people hadn't, those hadn't been concrete enough that people could really wrap their arms around them and understand what was going on.

And I think what we're going to see in this case is that a bunch of these mathematical theories, including some very,

and one of the things that's really interesting is one of the most abstract things that's come out of, of sort of mathematics,

higher category theory, things about infinity group voids, things like this,

which to me always just seemed like they were floating off into the stratosphere ionosphere of mathematics,

turn out to be things which our sort of theory anchors down to something fairly definite and says are super relevant to the way that we can understand how physics works.

Give me a second. By the way, I just threw a hat on.

You've said that this metaphor analogy that theory of everything is a big mountain.

And you have a sense that however far we are up the mountain, that the Wolfram physics model of the universe is at least the right mountain.

We're the right mountain.

Yes, without question.

So which aspect of it is the right mountain?

So for example, I mean, so there's so many aspects to just the way of the Wolfram physics project, the way it approaches the world.

That's clean, crisp and unique and powerful.

So, you know, there's a discrete nature to it.

There's a hypergraph.

There's a computation nature.

There's a generative aspect.

You start from nothing.

You generate everything.

Do you think the actual model is actually a really good one?

Or do you think this general principle of from simplicity generating complexity is the right?

Like what aspect of the mountain?

I think that the kind of the meta idea about using simple computational systems to do things, that's, you know, that's the ultimate big paradigm that is, you know, sort of super important.

The details of the particular model are very nice and clean and allow one to actually understand what's going on.

They are not unique.

And in fact, we know that.

We know that there's a large number of different ways to describe essentially the same thing.

I mean, I can describe things in terms of hypergraphs.

I can describe them in terms of higher category theory.

I can describe them in a bunch of different ways.

They are in some sense all the same thing, but our sort of story about what's going on and the kind of cultural mathematical resonances are a bit different.

I think it's perhaps worth sort of saying a little bit about kind of the foundational ideas of these models and things.

Great.

So can we rewind?

We've talked about it a little bit, but can you say like what the central idea is of the Wolfram Physics Project?

Right.

So the question is we're interested in finding sort of simple computational rule that describes our whole universe.

Can we just pause on that?

It's just so beautiful.

That's such a beautiful idea that we can generate our universe from a data structure, a simple set of rules, and we can generate our entire universe.

Yes.

That's all inspiring.

Right.

But so the question is how do you actualize that?

What might this rule be like?

And so one thing you quickly realize is if you're going to pack everything about our universe into this tiny rule, not much that we are familiar with in our universe will be obvious in that rule.

So you don't get to fit all these parameters of the universe, all these features of, you know, this is how space works, this is how time works, et cetera, et cetera, et cetera.

You don't get to fit that all in, it all has to be sort of packed in to this thing, something much smaller, much more basic, much lower level machine code, so to speak, than that.

And all the stuff that we're familiar with has to kind of emerge from the operation.

So the rule in itself because of the computational reducibility is not going to tell you the story.

It's not going to give you the answer to, it's not going to let you predict what you're going to have for lunch tomorrow.

Right.

It's not going to let you predict basically anything about your life, about the universe.

Right.

And you're not going to be able to see in that rule, oh, there's the three for the number of dimensions of space and so on.

Right.

That's not going to be just...

Space time is not going to be obviously...

Right.

So the question is then what is the universe made of?

That's a basic question.

And we've had some assumptions about what the universe is made of for the last few thousand years that I think in some cases just turned out not to be right.

And the most important assumption is that space is a continuous thing.

That is that you can, if you say, let's pick a point in space.

We're going to do geometry.

We're going to pick a point.

We can pick a point absolutely anywhere in space.

Precise numbers we can specify of where that point is.

In fact, Euclid who kind of wrote down the original kind of axiomatization of geometry back in 300 BC or so, his very first definition, he says,

a point is that which has no part.

A point is this indivisible infinitesimal thing.

So we might have said that about material objects.

We might have said that about water, for example.

We might have said water is a continuous thing that we can just pick any point we want in some water.

But actually we know it isn't true.

We know that water is made of molecules that are discreet.

And so the question, one fundamental question is what is space made of?

And so one of the things that sort of a starting point for what I've done is to think of space as a discreet thing.

To think of there being sort of atoms of space, just as there are atoms of material things, although very different kinds of atoms.

And by the way, I mean, this idea, you know, there were ancient Greek philosophers who had this idea.

There were, you know, Einstein actually thought this is probably how things would work out.

I mean, he said, you know, repeatedly, he thought that's where it would work out.

We don't have the mathematical tools in our time, which was 1940s, 1950s and so on, to explore this.

Like the way he thought, you mean that there is something very, very small and discreet that's underlying space?

Yes.

And that means that, so, you know, the mathematical theory, mathematical theories in physics assume that space can be described

just as a continuous thing.

You can just pick coordinates and the coordinates can have any values.

And that's how you define space.

Space is just sort of background sort of theater on which the universe operates.

But can we draw a distinction between space as a thing that could be described by three values, coordinates,

and how you're, are you using the word space more generally when you say?

No, I'm just talking about space as what we experience in the universe.

So you think this 3D aspect of it is fundamental?

No, I don't think that 3D is fundamental at all, actually.

I think that the thing that has been assumed is that space is this continuous thing where you can just describe it by, let's say, three numbers, for instance.

But the most important thing about that is that you can describe it by precise numbers, because you can pick any point in space.

And you can talk about motions, any infinitesimal motion in space.

And that's what continuous means.

That's what continuous means.

That's what, you know, Newton invented calculus to describe these kind of continuous small variations and so on.

That was, that's kind of a fundamental idea from Euclid on.

That's been a fundamental idea about space.

Is that right or wrong?

It's not right. It's not right.

It's right at the level of our experience most of the time.

It's not right at the level of the machine code, so to speak.

Machine code?

Yeah, of the simulation. That's right. That's right.

The very lowest level of the fabric of the universe, at least under the Wolfram physics model, is your senses discreet?

Right. So now, what does that mean?

So it means what is space then?

So in models, the basic idea is you say there are these sort of atoms of space.

They're these points that represent, you know, represent places in space.

But they're just discrete points.

And the only thing we know about them is how they're connected to each other.

We don't know where they are. They don't have coordinates.

We don't get to say this is a position such and such.

It's just, here's a big bag of points.

Like in our universe, there might be 10 to the 100 of these points.

And all we know is this point is connected to this other point.

So it's like, you know, all we have is the friend network, so to speak.

We don't have, you know, people's physical addresses.

All we have is the friend network of these points.

Yeah. The underlying nature of reality is kind of like a Facebook.

We don't know their location, but we have the friends.

Yeah, right. We know which point is connected to which other points.

And that's all we know.

And so you might say, well, how on earth can you get something which is like our experience

of, you know, what seems like continuous space?

Well, the answer is by the time you have 10 to the 100 of these things,

those connections can work in such a way that on a large scale,

it will seem to be like continuous space in, let's say, three dimensions

or some other number of dimensions or 2.6 dimensions or whatever else.

Because they're much, much, much, much larger.

So like the number of relationships here we're talking about is just a humongous amount.

So the kind of thing you're talking about is very, very, very small relative to our experience of daily life.

Right. So, I mean, you know, we don't know exactly the size,

but maybe 10 to the minus, maybe around 10 to the minus 100 meters.

So, you know, the size of, to give a comparison, the size of a proton is 10 to the minus 15 meters.

And so this is something incredibly tiny compared to that.

And the idea that from that would emerge the experience of continuous space is mind blowing.

Well, what's your intuition? Why that's possible?

Like, first of all, I mean, we'll get into it, but I don't know if we will through the medium of conversation,

but the construct of hypergraphs is just beautiful.

Right.

Tell you're a domino or beautiful. We'll talk about it.

But this thing about, you know, continuity arising from discrete systems is in today's world is actually not so surprising.

I mean, you know, your average computer screen, right?

Every computer screen is made of discrete pixels.

Yet we have the, you know, we have the idea that we're seeing these continuous pictures.

I mean, it's, you know, the fact that on a large scale, continuity can arise from lots of discrete elements.

This is at some level unsurprising now.

Wait, wait, wait, wait, wait. But the pixels have a very definitive structure of neighbors on a computer screen.

Right.

There's no concept of spatial, of space inherent in the underlying fabric of reality.

Right, right, right. So the point is, but there are cases where there are.

So for example, let's just imagine you have a square grid.

Okay. And at every point on the grid, you have one of these atoms of space.

And it's connected to four other, four other atoms of space on the, you know, northeast, southwest corners, right?

There you have something where if you zoom out from that, it's like a computer screen.

Yeah. So the relationship creates the spatial.

Right.

The relationship creates a constraint, which then in an emergent sense creates a, like, yeah, like a, basically a spatial coordinate for that thing.

Yeah, right.

Even though the individual point doesn't have a spatial.

Even though the individual point doesn't know anything, it just knows what it's, you know, what its neighbors are.

Basically on a large scale, it can be described by saying, oh, it looks like it's a, you know, this grid is zoomed out grid.

You can say, well, you can describe these different points by saying they have certain positions, coordinates, et cetera.

Now, in the, in the sort of real setup, it's more complicated than that.

It isn't just a square grid or something.

It's something much more dynamic and complicated, which we'll talk about.

So, you know, first, the first idea, the first key idea is, you know, what's the universe made of, it's made of atoms of space, basically, with these connections between them.

What kind of connections do they have?

Well, so a, the simplest kind of thing you might say is we've got something like a graph where every, every atom of space where we have these edges that go between out of these connections that go between atoms of space.

We're not saying how long these edges are, we're just saying there is a connection from, from this place to the, from this atom to this atom.

Just a quick pause, because there's a lot of varied people that listen to this.

Just to clarify, because I did a poll actually, what do you think a graph is a long time ago?

And it's kind of funny how few people know the term graph outside of computer science.

Let's call it a network.

I think that's called a network is better.

But every time I like the word graph though, so let's define, let's just say that a graph will use terms nodes and edges, maybe, and it's just nodes represent some abstract entity, and then the edges represent relationships between those entities.

Right, exactly.

So that's what graphs.

Sorry.

So there you go.

So that's the basic structure.

That is, that is the simplest case of a basic structure.

Actually, it tends to be better to think about hypergraphs.

So a hypergraph is just instead of saying there are connections between pairs of things, we say there are connections between any number of things.

So there might be ternary edges.

So instead of, instead of just having two points are connected by an edge, you say three points are all associated with a hyper edge are all connected by a hyper edge.

That's just at some level, that's, at some level, that's a detail.

It's a detail that happens to make the, for me, you know, sort of in the history of this project, the realization that you could do things that way broke out of certain kinds of arbitrariness that I felt that there was in the model before I had seen how this worked.

I mean, all a hypergraph can be mapped to a graph.

It's just a convenient representation, mathematical.

Right.

That's correct.

That's correct.

So, okay, so the, the first question, the first idea of these models of ours is space is made of these, you know, connected sort of atoms of space.

The next idea is space is all there is.

There's nothing except for this space.

So in traditional ideas in physics, people have said there's space, it's kind of a background.

And then there's matter, all these particles, electrons, all these other things, which exist in space.

But in this model, one of the key ideas is there's nothing except space.

So in other words, everything that has that exists in the universe is a feature of this hypergraph.

So how can that possibly be?

Well, the way that works is that there are certain structures in this hypergraph where you say that little twisty knotted thing.

We don't know exactly how this works yet, but we have sort of idea about how it works mathematically.

This sort of twisted knotted thing, that's the core of an electron.

This thing over there that has this different form, that's something else.

So the different peculiarities of the structure of this graph are the very things that we think of as the particles inside the space,

but in fact, it's just the property of the space.

Mind blowing, first of all, that it's mind blowing.

And we'll probably talk in its simplicity and beauty.

Yes, I think it's very beautiful.

But that's space, and then there's another concept we didn't really kind of mention,

but you think it of computation as like a transformation.

Let's talk about time in a second.

Let's just, I mean, on the subject of space, there's this question of kind of what, there's this idea,

there is this hypergraph, it represents space and it represents everything that's in space.

The features of that hypergraph, you can say certain features in this part we do know,

certain features of the hypergraph represent the presence of energy, for example,

or the presence of mass or momentum.

And we know what the features of the hypergraph that represent those things are,

but it's all just the same hypergraph.

So one thing you might ask is, you know, if you just look at this hypergraph and you say,

and we're going to talk about sort of what the hypergraph does,

but if you say, you know, how much of what's going on in this hypergraph is things we know and care about,

like particles and atoms of electrons and all this kind of thing, and how much is just the background of space.

So it turns out, so far as in one rough estimate of this,

or everything that we care about in the universe is only one part and 10 to the 120 of what's actually going on.

The vast majority of what's happening is purely things that maintain the structure of space.

In other words, the things that are the features of space that are the things that we consider notable,

like the presence of particles and so on, that's a tiny little piece of froth on the top of all this activity

that mostly is just intended to, you know, mostly it can't say intended.

There's no intention here that just maintains the structure of space.

Let me load that in. It just makes me feel so good as a human being.

To be the froth on the one in the 10 to the 120 or something.

And also just humbling how in this mathematical framework, how much work needs to be done on the infrastructure of our universe.

Right. To maintain the infrastructure of our universe is a lot of work.

We are merely writing a little tiny things on top of that infrastructure.

But you were just starting to talk a little bit about space.

That represents all the stuff that's in the universe.

The question is, what does that stuff do?

And for that, we have to start talking about time and what is time and so on.

And, you know, one of the basic idea of this model is time is the progression of computation.

So in other words, we have a structure of space and there is a rule that says how that structure of space will change.

And it's the application, the repeated application of that rule that defines the progress of time.

Then what does the rule look like in the space of hypergraphs?

Right. So what the rule says is something like if you have a little tiny piece of hypergraph that looks like this,

then it will be transformed into a piece of hypergraph that looks like this.

So that's all it says.

It says you pick up these elements of space.

And you can think of these edges, these hyper edges as being relations between elements in space.

You might pick up these two relations between elements in space.

And we're not saying where those elements are or what they are, but every time there's a certain arrangement of elements in space,

then arrangement in the sense of the way they're connected, then we transform it into some other arrangement.

So there's a little tiny pattern and you transform it into another little pattern.

That's right.

And then because of this, I mean, again, it's kind of similar to cellular automata in that, like, on paper, the rule looks like super simple.

It's like, yeah, okay. Yeah, right. From this, the universe can be born.

But like, once you start applying it, beautiful structure starts being potentially can be created.

And what you're doing is you're applying that rule to different parts, like any time you match it within the hypergraph.

Exactly.

And one of the, like, incredibly beautiful and interesting things to think about is the order in which you apply that rule.

Yes.

Because that pattern appears all over the place.

Right.

So this is a big, complicated thing, very hard to wrap one's brain around.

Okay.

So you say the rule is every time you see this little pattern, transform it in this way.

But yet, you know, as you look around the space that represents the universe, there may be zillions of places where that little pattern occurs.

Yeah.

So what it says is just do this, apply this rule wherever you feel like.

And what is extremely non trivial is, well, okay, so this is happening sort of in computer science terms sort of asynchronously.

You're just doing it wherever you feel like doing it.

And the only constraint is that if you're going to apply the rule somewhere, the things to which you apply the rule,

the little, you know, elements to which you apply the rule, if they have to be, okay,

well, you can think of each application of the rule as being kind of an event that happens in the universe.

Yep.

And the input to an event has to be ready for the event to occur.

That is, if one event occurred, if one transformation occurred, and it produced a particular atom of space,

then that atom of space has to already exist before another transformation that's going to apply to that atom of space can occur.

Yeah.

So that's like the prerequisite for the event.

That's right.

That's right.

So that defines a kind of this sort of set of causal relationships between events.

It says this event has to happen before this event.

But that is.

But that's not a very limited constraint.

No, it's not.

And what's interesting.

You still get the zillion, that's the technical term, options.

That's correct.

But okay, so this is where things get a little bit more elaborate.

But they're mind blowing.

Right.

So what happens is, so the first thing you might say is, you know, let's, well, okay,

so this question about the freedom of which event you do when.

Well, let me, let me sort of state an answer and then explain it.

Okay.

The validity of special relativity is a consequence of the fact that in some sense it doesn't matter in what order you do these underlying things so long as they respect this kind of set of causal relationships.

And that's, that's in the part that's in a certain sense is a really important one but the fact that it sometimes doesn't matter.

That's a, I don't know, that's another like beautiful thing.

Okay, so there's this idea of what I call causal invariance.

Causal invariance, exactly.

So that's a really, really powerful, powerful idea.

Which has actually arisen in different forms many times in the history of mathematics, mathematical logic, even computer science has many different names.

I mean, our particular version of it is a little bit tighter than other versions, but it's basically the same idea.

Here's, here's how to think about that idea.

So imagine that, well, let's talk about it in terms of math for a second.

Let's say you're doing algebra and you're told, you know, multiply out this series of polynomials that are, that are multiplied together.

Okay, you say, well, which order should I do that in?

Say, well, do I multiply the third one by the fourth one and then do it by the first one?

Or do I do the fifth one by the sixth one and then do that?

Well, it turns out it doesn't matter.

You can, you can multiply them out in any order.

You'll always get the same answer.

That's a, that's a property.

If you think about kind of making a kind of network that represents in what order you do things, you'll get different orders for different ways of multiplying things out, but you'll always get the same answer.

Same thing if you, let's say you're sorting, you've got a bunch of A's and B's, then random, some random order, you know, B, A, A, B, B, B, A, A, A, whatever.

And you have a little rule that says, every time you see B, A, flip it around to A, B.

Okay, eventually you apply that rule enough times, you'll have sorted the string so that it's all the A's first and then all the B's.

Again, you, there are many different orders in which you can do that, that many different sort of places where you can apply that update.

In the end, you'll always get the string sorted the same way.

I know, I know with sorting the string, it sounds obvious.

That's to me surprising that, that there is in complicated systems, obviously with the string, but in the hypergraph that the application of the rule, asynchronous rule can lead to the same results sometimes.

Yes, yes, that is, it is not obvious.

And it was something that, you know, I sort of discovered that idea for these kinds of systems in back in the 1990s.

And for various reasons, I was not satisfied by how sort of fragile finding that particular property was.

And let me just make another point, which is that it turns out that even if the underlying rule does not have this property of causal invariance,

it can turn out that every observation made by observers of the rule can, they can impose what amounts to causal invariance on the rule.

We can explain that.

It's a little bit more complicated.

I mean, technically that has to do with this idea of completions, which is something that comes up in term rewriting systems, automated theorem proving systems and so on.

But that, let's ignore that for a second.

We can come to that later.

Is it useful to talk about observation?

Not yet.

Not yet.

Okay.

So great.

So there's some concept of causal invariance as you apply these rules in an asynchronous way.

You can think of those transformations as events.

So there's this hypergraph that represents space and all of these events happening in the space and the graph grows in interesting, complicated ways.

And eventually the froth arises of what we experience as human existence.

That's some version of the picture, but let's explain a little bit more.

Exactly.

What's a little more detail?

Right.

So one thing that is sort of surprising in this theory is one of the sort of achievements of 20th century physics was kind of bringing space and time together.

That was, you know, special relativity.

People talk about space time, this sort of unified thing where space and time kind of a mixed and there's a nice mathematical formalism that in which, you know, space and time sort of appear as part of the space time continuum.

The space time, you know, four vectors and things like this.

You know, we talk about time as the fourth dimension and all these kinds of things.

It's, you know, and it seems like the theory relativity sort of says space and time are fundamentally the same kind of thing.

So one of the things that took a while to understand in this approach of mine is that in my kind of approach, space and time are really not fundamentally the same kind of thing.

Space is the extension of this hypergraph.

Time is the kind of progress of this inexorable computation of these rules getting applied to the hypergraph.

So they seem like very different kinds of things.

And so that at first seems like how can that possibly be right?

How can that possibly be Lorentz invariant?

That's the term for things being, you know, following the rules of special relativity.

Well, it turns out that when you have causal invariance that, and let's see, we can, it's worth, it's worth explaining a little bit how this works.

It's a little bit, a little bit elaborate.

But the basic point is that the, even though space and time sort of come from very different places, it turns out that the rules of sort of space time that special relativity talks about come out of this model.

When you're looking at large enough systems.

So, so a way to think about this, you know, in terms of the, when you're looking at large enough systems, the part of that story is when you look at some fluid like water, for example, there are equations that govern the flow of water.

Those equations are things that apply on a large scale.

If you look at the individual molecules, they don't know anything about those equations.

It's just the, the, the sort of the large scale effect of those molecules turns out to follow those equations.

And it's the same kind of thing happening in our models.

I know this might be a small point, but maybe a very big one.

We've been talking about space and time at the lowest level of the model, which is space, the hypergraph time is the evolution of this hypergraph.

But there's also space time that we think about in general relativity for your special relativity.

Like what, how does, how do you go from the lowest source code of space and times we're talking about to the more traditional terminology of space and time?

Yeah, right.

So the key thing is this thing we call the causal graph.

So the causal graph is the graph of causal relationships between events.

So every one of these little updating events, every one of these little transformations of the hypergraph happens somewhere in the hypergraph happens at some stage in the computation.

That's an event.

That event is, has a causal relationship to other events in the sense that if the, if another event needs as its input, the output from the first event, there will be a causal relationship of the, the, the future event will depend on the past event.

So you can say it's, it has a causal connection.

So you can make this graph of causal relationships between events.

That graph of causal relationships, causal invariance implies that that graph is unique.

It doesn't matter.

Even though you think, oh, I'm, I'm, you know, let's say we were sorting a string, for example, I did that particular transposition of characters at this time.

And then I did that one.

Then I did this one.

Turns out if you look at the network of, of connections between those updating events, that network is the same.

It's, it's the, if, if you were to, the, the, the structure.

So in other words, if you were to draw that, that, if you were to put that network on a picture of where you're doing all the updating, the places where you put the, the nodes of the network will be different.

But the way the nodes are connected will always be the same.

So the causal graph is a, is, I don't know, it's kind of an observation. It's not enforced.

It's just emergent from a set of events.

Well, it's a, it's a feature of, of, of, okay.

So what it is.

The characteristic, I guess, is the way events happen.

Right.

It's an event can't happen until its input is ready.

Right.

And so that creates this, this network of causal relationships.

And that's, that's the causal graph.

And the thing that the next thing to realize is, okay, we, when you're going to look at,

when you're going to observe what happens in the universe, you have to sort of make sense

of this causal graph.

So, and you are an observer who yourself is part of this causal graph.

And so that means, so let me give you an example of how that works.

So, so imagine we have a really weird theory of physics of the world where it says this

updating process, there's only going to be one updated every moment in time.

And there's just going to be like a Turing machine.

A little head that runs around and just is always just updating one thing at a time.

So you say, you know, I have a theory of physics and the theory of physics says there's just

this one little place where things get updated.

You say, that's completely crazy because, you know, it's plainly obvious that things are

being updated sort of, you know, at the same time.

But, but, but the fact is that the thing is that if I'm, you know, talking to you and

you seem to be being updated as I'm being updated, but, but if there's just this one

little head that's running around updating things, I will not know whether you've been

updated or not until I'm updated.

So in other words, when you draw this causal graph of the causal relationship between the

updating and you and the updating and me, it'll still be the same causal graph, whether

even though the underlying sort of story of what happens is, oh, there's just this one

little thing and it goes and updates in different places in the universe.

So is that, is that clear or is that a hypothesis?

Is that, is that clear that there's a unique causal graph?

If there's causal invariance, there's a unique causal graph.

So we, so it's okay to think of what we're talking about as a hyper graph and the operations

on it as a kind of a touring machine with a single head, like a single guy running around

updating stuff.

Is that safe to intuitively think of it this way?

Let me think about that for a second.

Yes, I think so.

I think that, I think there's nothing, it doesn't matter.

I mean, you can say, okay, there is one, the reason I'm pausing for a second is that I'm

wondering, well, when you say running around depends how far it jumps every time it runs.

Yeah, yeah, that's right.

But I mean like one operation at a time.

Yeah, you can think of it as one operation at a time.

It's easier for the human brain to think of it that way as opposed to simultaneously.

Well, maybe it's not, okay, but the thing is that's not how we experience the world.

What we experience is we look around, everything seems to be happening at successive moments

in time, everywhere in space.

Yes.

That is the, and that's partly a feature of our particular construction.

I mean, that is the speed of light is really fast compared to, you know, we look around,

you know, I can see maybe a hundred feet away right now.

You know, it's the, my brain does not process very much in the time it takes light to

cover a hundred feet. The brain operates at a scale of hundreds of milliseconds or

something like that.

I don't know.

Right.

And speed of light is much faster.

Right.

You know, light goes in a billionth of a second, light has gone a foot.

So it goes a billion feet every second.

There's certain moments through this conversation where I imagine the absurdity of the fact that

there's two descendants of apes modeled by a hypograph that are communicating with each

other and experiencing this whole thing as a real time simultaneous update with, I'm

taking in photons from you right now, but there's something much, much deeper going on

here.

Right.

It does have a...

It's paralyzing sometimes to just...

Yes.

To remember that.

Right.

No, I mean, you know...

Sorry.

Yes, yes.

As a small little tangent, I just remembered that we're talking about, I mean, this, about

the fabric of reality.

Right.

So we've got this causal graph that represents the sort of causal relationships between all

these events in the universe.

That causal graph kind of is a representation of space time, but our experience of it requires

that we pick reference frames.

This is kind of a key idea.

Einstein had this idea that what that means is we have to say, what are we going to pick

as being the sort of what we define as simultaneous moments in time?

So for example, we can say, how do we set our clocks?

If we've got a spacecraft landing on Mars, do we say that...

What time is it landing at?

Was it...

Even though there's a 20 minute speed of light delay or something, what time do we say it

landed at?

How do we set up sort of time coordinates for the world?

And that turns out to be that there's kind of this arbitrariness to how we set these

reference frames that define sort of what counts as simultaneous.

And what is the essence of special relativity is to think about reference frames going at

different speeds and to think about sort of how they assign what counts as space, what

counts as time and so on.

That's all a bit technical, but the basic bottom line is that this causal invariance

property that means that it's always the same causal graph, independent of how you slice

it with these reference frames, you'll always sort of see the same physical processes go

on.

And that's basically why special relativity works.

So there's something like special relativity, like everything around space and time that

fits this idea of the causal graph.

Right.

Well, one way to think about it is given that you have a basic structure that just

involves updating things in these connected updates and looking at the causal relationships

from connected updates, that's enough when you unravel the consequences of that.

That together with the fact that there are lots of these things and that you can take

a continuum limit and so on, implies special relativity.

And so that, it's kind of a big deal because it's kind of a, it was completely unobvious

when you started off with saying, we've got this graph, it's being updated in time, et

cetera, et cetera, et cetera, that just looks like nothing to do with special relativity.

And yet you get that.

And what, I mean, then the thing, I mean, this was stuff that I figured out back in

the 1990s, the next big thing you get is general relativity.

And so in this hypergraph, the sort of limiting structure, when you have a very big hypergraph,

you can think of as being just like, water seems continuous on a large scale.

So this hypergraph seems continuous on a large scale.

One question is, how many dimensions of space does it correspond to?

So one question you can ask is if you've just got a bunch of points and they're connected

together, how do you deduce what effective dimension of space that bundle of points corresponds

to?

And that's pretty easy to explain.

So basically, if you say, you've got a point and you look at how many neighbors does that

point have?

Imagine it's on a square grid, then it'll have four neighbors.

Go another level out, how many neighbors do you get then?

What you realize is, as you go more and more levels out, as you go more and more distance

on the graph out, you're capturing something which is essentially a circle in two dimensions

so that the area of a circle is pi r squared.

So the number of points that you get to goes up like the distance you've gone squared.

And in general, in d dimensional space, it's r to the power d.

It's the number of points you get to if you go r steps on the graph, grows like the number

of steps you go to the power of the dimension.

And that's a way that you can estimate the effective dimension of one of these graphs.

So what does that grow to?

So how does the dimension grow?

Because, I mean, obviously, the visual aspect of these hypergraphs, they're often visualized

in three dimensions.

And then there's a certain kind of structure, like you said, there's a sphere, there's a

planar aspect to it, to this graph, to where it kind of almost starts creating a surface,

like a complicated surface, but a surface.

So how does that connect to effective dimension?

I was supposed to think about that.

I mean, if you can lay out the graph in such a way that the points in the graph that are

neighbors on the graph are neighbors as you lay them out, and you can do that in two dimensions,

then it's going to approximate a two dimensional thing.

If you can't do that in two dimensions, if everything would have to fold over a lot in

two dimensions, then it's not approximating a two dimensional thing.

Maybe you can lay it out in three dimensions.

Maybe you have to lay it out in five dimensions to have it be the case that it sort of smoothly

lays out like that.

Well, but okay, so I apologize for the different tangent questions, but you know, there's an

infinity number of possible rules.

So we have to look for rules that create the kind of structures that are reminiscent for,

that have echoes of the different physics theories in them.

So what kind of rules, is there something simple to be said about the kind of rules

that you have found beautiful, that you have found powerful?

So I mean, one of the features of computational reducibility is it's very, you can't say in

advance what's going to happen with any particular, you can't say, I'm going to pick these rules

from this part of rule space, so to speak, because they're going to be the ones that

are going to work.

You can make some statements along those lines, but you can't generally say that.

Now, you know, the state of what we've been able to do is, you know, different properties

of the universe, like dimensionality, you know, integer dimensionality, features of

other features of quantum mechanics, things like that.

At this point, what we've got is we've got rules that any one of those features, we can

get a rule that has that feature, but we don't have the sort of the final, here's a rule

which has all of these features, we do not have that yet.

So if I were to try to summarize the Wolfram Physics Project, which is, you know, something

that's been in your brain for a long time, but really has just exploded in activity,

you know, only just months ago.

So it's an evolving thing, and next week, I'll try to publish this conversation as quickly

as possible, because by the time it's published, already new things will probably have come

out.

So if I were to summarize it, we've talked about the basics of, there's a hypergraph

that represents space, there is transformations in the hypergraph that represents time, that

progress of time, there's a cause of graph that's a characteristic of this.

And the basic process of science, of science within the Wolfram Physics Model is to try

different rules and see which properties of physics that we know of, known physical theories,

are appear within the graphs that emerge from that rule.

That's what I thought it was going to be.

Oh, okay.

So what?

So what is it?

It turns out we can do a lot better than that.

It turns out that using kind of mathematical ideas, we can say, and computational ideas,

we can make general statements, and those general statements turn out to correspond to things

that we know from 20th century physics.

In other words, the idea of you just try a bunch of rules and see what they do, that's

what I thought we were going to have to do.

But in fact, we can say, given causal invariance and computational irreducibility, we can derive,

and this is where it gets really pretty interesting, we can derive special relativity, we can derive

general relativity, we can derive quantum mechanics.

And that's where things really start to get exciting, is it wasn't at all obvious to

me that even if we were completely correct, and even if we had, this is the rule, even

if we found the rule, to be able to say, yes, it corresponds to things we already know,

I did not expect that to be the case.

So for somebody who is a simple mind and definitely not a physicist, not even close, what does

derivation mean in this case?

So let me, this is an interesting question, okay, so there's, so one thing.

In the context of computational irreducibility.

Yeah, yeah, right, right, so what you have to do, let me go back to, again, the mundane

example of fluids and water and things like that, right?

So you have a bunch of molecules bouncing around.

You can say, just as a piece of mathematics, I happen to do this from cellular automata

back in the mid 1980s, you can say, just as a matter of mathematics, you can say the continuum

limit of these little molecules bouncing around is the Navier Stokes equations.

That's just a piece of mathematics, it's not, it doesn't rely on, you have to make certain

assumptions that you have to say, there's enough randomness in the way the molecules

bounce around that certain statistical averages work, etc, etc, etc.

Okay, it is a very similar derivation to derive, for example, the Einstein equations.

Okay, so the way that works, roughly, Einstein equations are about curvature of space.

Coverture of space, I talked about sort of how you can figure out dimension of space.

There's a similar kind of way of figuring out, if you just sort of say, you know, you're

making a larger and larger ball or larger and larger, if you draw a circle on the surface

of the earth, for example, you might think the area of a circle is pi r squared, but

on the surface of the earth, because it's a sphere, it's not flat, the area of a circle

isn't precisely pi r squared, as the circle gets bigger, the area is slightly smaller

than you would expect from the formula pi r squared as a little correction term that

depends on the ratio of the size of the circle to the radius of the earth.

Okay, so it's the same basic thing, allows you to measure from one of these hypergraphs

what is its effective curvature.

So the little piece of mathematics that explains special general relativity is, can map nicely

to describe fundamental property of the hypergraphs, the curvature of the hypergraphs.

Okay, so special relativity is about the relationship of time to space.

Modern relativity is about curvature in this space represented by this hypergraph.

So what is the curvature of a hypergraph?

Okay, so first I have to explain, what we're explaining is, first thing you have to have

is a notion of dimension.

You don't get to talk about curvature of things.

If you say, oh, it's a curved line, but I don't know what a line is yet.

So yeah, what is the dimension of a hypergraph then, from where we've talked about effective

dimension.

Right, that's what this is about.

That's what this is about is, you have your hypergraph, it's got a trillion nodes in it.

What is it roughly like?

Is it roughly like a grid, a two dimensional grid?

Is it roughly like all those nodes are arranged online?

What's it roughly like?

And there's a pretty simple mathematical way to estimate that by just looking at the,

this thing I was describing, the sort of the size of a ball that you construct in the hypergraph.

You just measure that, you can just compute it on a computer for a given hypergraph, and

you can say, oh, this thing is wiggling around, but it's roughly corresponds to two or something

like that, roughly corresponds to 2.6 or whatever.

So that's how you have a notion of dimension in these hypergraphs.

Curvature is something a little bit beyond that.

If you look at how the size of this ball increases as you increase its radius, curvature is a

correction to the size increases associated with dimension.

It's a sort of a second order term in determining the size.

Just like the area of a circle is roughly pi r squared, so it goes up like r squared.

The two is because it's in two dimensions.

But when that circle is drawn on a big sphere, the actual formula is pi r squared times one

minus r squared over a squared and some coefficient.

So in other words, there's a correction, and that correction term, that gives you curvature.

And that correction term is what makes this hypergraph have the potential to correspond

to curved space.

Now the next question is, is that curvature, is the way that curvature works, the way that

Einstein's equations for general relativity, is that the way they say it should work?

And the answer is yes.

And so how does that work?

The calculation of the curvature of this hypergraph for some set of rules?

No.

It doesn't matter what the rules are.

It doesn't.

So long as they have causal invariance and computational irreducibility and they lead

to finite dimensional space, noninfinite dimensional space, noninfinite dimensional.

It can grow infinitely, but it can't be infinite dimensional.

What does an infinitely dimensional hypergraph look like?

So that means?

For example.

On a tree, you start from one root of the tree, it doubles, doubles again, doubles

again, doubles again.

And that means if you ask the question, starting from a given point, how many points do you

get to?

Remember, in like a circle, you get to r squared, the two there.

On a tree, you get to, for example, two to the r.

It's exponential dimensional, so to speak, or infinite dimensional.

Do you have a sense of, in the space of all possible rules, how many lead to infinitely

dimensional hypergraphs?

Is that?

No.

Okay.

Is that an important thing to know?

Yes, it's an important thing to know.

I would love to know the answer to that.

But it gets a little bit more complicated because, for example, it's very possible in the case

that in our physical universe, that the universe started infinite dimensional.

And only at the Big Bang, it was very likely infinite dimensional.

And as the universe sort of expanded and cooled, its dimension gradually went down.

And so one of the bizarre possibilities, which actually there are experiments you can do

to try and look at this, the universe can have dimension fluctuations.

So in other words, we think we live in a three dimensional universe, but actually there may

be places where it's actually 3.01 dimensional, or where it's 2.99 dimensional, and it may

be that in the very early universe, it was actually infinite dimensional, and it's only

a late stage phenomenon that we end up getting three dimensional space.

But from your perspective of the hypergraph, one of the underlying assumptions kind of

implied, but do you have a sense, a hope, set of assumptions that the rules that underlie

our universe or the rule that underlies our universe is static?

Is that one of the assumptions you're currently operating under?

Yes, but there's a footnote to that, which we should get to because it requires a few

more steps.

Well, actually then let's backtrack to the curvature because we're talking about as

long as it's finite dimensional, finite dimensional computational irreducibility and causal invariance,

and it follows that the large scale structure will follow Einstein's equations.

And now let me again qualify that a little bit more, there's a little bit more complexity

to it.

So Einstein's equations in the simplest form apply to the vacuum, no matter just the vacuum.

And they say, in particular what they say is if you have, so there's this term JDSIC,

that's a term that means shortest path, comes from measuring shortest paths on the earth.

So you look at a bundle of JDSICs, a bunch of shortest paths, it's like the paths that

photons would take between two points.

Then the statement of Einstein's equations is basically a statement about a certain,

as you look at a bundle of JDSICs, the structure of space has to be such that although the

cross sectional area of this bundle may, although the actual shape of the cross section may

change, the cross sectional area does not.

That's a version, that's the most simple minded version of R mu nu minus a half R g mu nu

equals zero, which is the more mathematical version of Einstein's equations.

It's a statement of the thing called the Ritchie tensor is equal to zero.

That's Einstein's equations for the vacuum.

So we get that as a result of this model, but footnote, big footnote, because all the

matter in the universe is the stuff we actually care about.

The vacuum is not stuff we care about.

So the question is, how does matter come into this?

And for that, you have to understand what energy is in these models.

And one of the things that we realized last year was that there's a very simple interpretation

of energy in these models.

And energy is basically, well, intuitively, it's the amount of activity in these hypergraphs

and the way that that remains over time.

So a little bit more formally, you can think about this causal graph as having these edges

that represent causal relationships, you can think about, oh boy, there's one more concept

that we didn't get to.

It's the notion of space like hypersurfaces.

So this is not as scary as it sounds.

It's a common notion in general activity.

The notion is you are defining what is a possibly, what is, what, where in space time might be

a particular moment in time.

So in other words, what is a consistent set of places where you can say, this is happening

now, so to speak.

And you make this series of sort of slices through the space time, through this causal

graph to represent sort of what we consider to be successive moments in time.

It's somewhat arbitrary because you can deform that if you're going at a different speed

in special activity, you tip those things, there are different kinds of deformations,

but only certain deformations are allowed by the structure of the causal graph.

Anyway, be that as it may.

The basic point is there is a way of figuring out, you say, what is the energy associated

with what's going on in this hypergraph?

And the answer is there is a precise definition of that, and it is the formal way to say it

is, it's the flux of causal edges through space like hypersurfaces.

The slightly less formal way to say it, it's basically the amount of activity.

See, the reason it gets tricky is you might say, it's the amount of activity per unit

volume in this hypergraph, but you haven't defined what volume is.

So it's a little bit, you have to be a little bit more careful.

But this hypersurface gives some more formalism to that, that doesn't exist.

Yeah, it gives a way to connect that.

What intuitive we should think about is the amount of activity.

So the amount of activity that kind of remains in one place in the hypergraph corresponds

to energy.

The amount of activity that is kind of where an activity here affects an activity somewhere

else corresponds to momentum.

And so one of the things that's kind of cool is that I'm trying to think about how to say

this intuitively.

The mathematics is easy, but the intuitive version, I'm not sure.

But basically the way that things sort of stay in the same place and have activity is

associated with rest mass.

And so one of the things that you get to derive is E equals MC squared.

That is a consequence of this interpretation of energy in terms of the way the causal graph

works, which is the whole thing is sort of a consequence of this whole story about updates

in hypergraphs and so on.

So can you linger on that a little bit?

How do we get E equals MC squared?

So where does the mass come from?

So I mean, is there an intuitive?

So okay, first of all, you're pretty deep in the mathematical explorations of this thing

right now.

We're in a very, we're in flux currently.

So maybe you haven't even had time to think about intuitive explanations.

But yeah, I mean, this one is, look, roughly what's happening.

That derivation is actually rather easy.

And everybody, and I've been saying we should pay more attention to this derivation because

it's such, you know, because people care about this point, but everybody says, it's just

easy.

It's easy.

So there's some concept of energy that can be intuitively thought of as the activity,

the flux, the level, the level of changes that are occurring based on the transformations

within a certain volume, however, the heck do you find the volume?

Okay.

So and then mass.

Well, mass is what?

This is associated with kind of the energy that does not cause you to that does not somehow

propagate through time.

Yeah.

I mean, one of the things that was not obvious in the usual formulation of special relativity

is that space and time are connected in a certain way.

Energy and momentum are also connected in a certain way.

The fact that the connection of energy to momentum is analogous to the connection to

space between space and time is not self evident in ordinary relativity.

It is a consequence of the way this model works.

It's an intrinsic consequence of the way this model works.

And it's all to do with unraveling that connection that ends up giving you this relationship

between energy and, well, it's energy, momentum, mass, they're all connected.

And so that's hence the general relativity, you have a sense that it appears to be baked

in to the fundamental properties of the way these hypergraphs are evolved.

Well, I didn't yet get to it.

So I got as far as special relativity and equals mc squared.

The one last step is in general relativity, the final connection is energy and mass cause

curvature in space.

And that's something that when you understand this interpretation of energy and you kind

of understand the correspondence to curvature and hypergraphs, then you can finally sort

of the big final answer is you derive the full version of Einstein's equations for

space, time and matter.

And that's some...

Is that...

Have you...

That last piece with curvature, has that...

Have you arrived there yet?

Oh, yeah.

We're with...

Yes.

And here's the way that we...

Here's how we're really, really going to know we've arrived, okay?

So we have the mathematical derivation, it's all fine, but mathematical derivations, okay.

So one thing that's sort of a...

We're taking this limit of what happens when...

The limit, you have to look at things which are large compared to the size of an elementary

length, small compared to the whole size of the universe, large compared to certain kinds

of fluctuations, blah, blah, blah, there's a tower of many, many of these mathematical

limits that have to be taken.

So if you're a pure mathematician saying, where's the precise proof?

It's like, well, there are all these limits, we can try each one of them computationally

and we can say, yeah, it really works, but the formal mathematics is really hard to do.

I mean, for example, in the case of deriving the equations of fluid dynamics from molecular

dynamics, that derivation has never been done.

There is no rigorous version of that derivation.

So...

Because you can't do the limits?

Yeah, because you can't do the limits.

But so the limits allow you to try to describe something general about the system and very

particular kinds of limits that you need to take with these very...

Right.

And the limits will definitely work the way we think they work and we can do all kinds

of computer experiments.

It's just some hard derivation.

Yeah, it's just the mathematical structure kind of ends up running right into computational

or reducibility and you end up with a bunch of difficulty there.

But here's the way that we're getting really confident that we know completely what we're

talking about, which is when people study things like black hole mergers using Einstein's

equations, what do they actually do?

Well, they actually use mathematics or a whole bunch to analyze the equations and so on.

But in the end, they do numerical relativity, which means they take these nice mathematical

equations and they break them down so that they can run them on a computer and they break

them down into something which is actually a discrete approximation to these equations.

Then they run them on a computer, they get results, then you look at the gravitational

waves and you see if they match.

Turns out that our model gives you a direct way to do numerical relativity.

So in other words, instead of saying you start from these continuum equations from Einstein,

you break them down into these discrete things, you run them on a computer, you say, we're

doing it the other way around.

We're starting from these discrete things that come from our model and we're just running

big versions of them on a computer and what we're saying is this is how things will work.

So the way I'm calling this is proof by compilation, so to speak.

That is, in other words, you're taking something where we've got this description of a black

whole system and what we're doing is we're showing that what we get by just running our

model agrees with what you would get by doing the computation from the Einstein equations.

There's a small tangent or actually a very big tangent, but proof by compilation is

a beautiful concept.

In a sense, the way of doing physics with this model is by running it or compiling it.

Have you thought about, and these things can be very large, is there a totally new possibilities

of computing hardware and computing software, which allows you to perform this kind of compilation?

Well, algorithms, software, hardware.

So first comment is, these models seem to give one a lot of intuition about distributed

computing, a lot of different intuition about how to think about parallel computation.

And that particularly comes from the quantum mechanics side of things, which we didn't

talk about much yet.

But the question of what, given our current computer hardware, how can we most efficiently

simulate things, that's actually partly a story of the model itself, because the model

itself has deep parallelism in it.

The ways that we're simulating it, we're just starting to be able to use that deep parallelism

to be able to be more efficient in the way that we simulate things.

But in fact, the structure of the model itself allows us to think about parallel computation

in different ways, and one of my realizations is that, so it's very hard to get in your