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.
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Anyway, go to masterclass.com slash 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 importance as breakthroughs where a 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 Schoedinger, 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
mechanics 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?
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 Gelman, 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 1940s.
Yeah.
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?
Yeah. There's a couple of different stages to this.
I mean, one is, 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 it took me a few years to really say,
wow, there's a big important phenomenon here that lets sort of complex things arise from very simple programs.
That kind of happened back in 1984 or so.
Then, you know, a bunch of other years go by, then I start actually doing a lot of much more systematic computer experiments and things
and find out that 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 happened 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, 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 sort of 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 of Steve Jobs of Albert Einstein.
He also wrote a book, I think it's called the innovators, where he discusses how a lot of the innovations in the history of computing has been done by groups.
There's a complicated group dynamic going on.
But there's also a romanticized notion that the individual is at the core of the revolution.
Like, where does your sense fall?
Is ultimately like one person responsible for these revolutions that creates the spark, or one or two, whatever.
Or is it just the big mush and mess and chaos of people interacting, of personalities interacting?
I think it ends up being like many things.
There's leadership and there ends up being, it's a lot easier for 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.
But 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 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, was that sort of going to happen anyway? Was that a consequence of 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, 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?
Was there a chain of 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 I think that people think of it as probably more conceptual inspiration than kind of a, this is a line from here to here to here in our particular field.
I think that the thing which I am disappointed by and which will eventually happen is this kind of study of the sort of pure computationalism, this kind of study of the abstract behavior of the computational universe.
That should be a big thing that lots of people do.
You mean in mathematics purely, almost like for itself?
It's like pure mathematics, but it isn't mathematics.
But it isn't.
It's a new kind of mathematics and titles of books.
Yeah, right.
That's why the book is called that.
That's not coincidental.
It's interesting that I haven't seen really rigorous investigation by thousands of people of this idea.
I mean, you look at your competition around Rule 30.
I mean, that's fascinating.
If you can say something, is there some aspect of this thing that could be predicted?
That's the fundamental question of science.
That's the core.
That's the question of science.
I think that is some people's view of what science is about, and it's not clear that's the right view.
In fact, as we live through this pandemic full of predictions and so on, it's an interesting moment to be pondering what science's actual role in those kinds of things is.
Oh, you think it's possible that in science, clean, beautiful, simple prediction may not even be possible in real systems?
That's the open question.
Right.
That's the open. I think that question is answered, and the answer is no.
The answer could be just humans are not smart enough yet.
We don't have the tools yet.
No, that's the whole point.
I mean, that's sort of the big discovery of this principle of computational equivalence of mine.
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, 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 sort of 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 are much harder to predict.
And it's, 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 essential concept underlying all the things we're talking about.
Do you think there's pockets of reducibility inside rule 30?
Yes, that is 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's 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.
Yeah, 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, 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.
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, 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 really 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 could happen 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, 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.
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, 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 the seasons change, people will show symptoms and people don't even understand, you know, seasonal variation of flu, for example.
It's something where, you know, there could be a big story or it could be just a zillion little details that mount up.
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 use cellular 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 dynamic of you have a graph, it probably is closer to the hypergraph model.
It is, yes.
It's exactly.
That's another funny thing.
Yes.
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.
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 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 as like, as long as they are cliques or whatever, like, 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 the many situations where you would like to get away from computational irreducibility.
The 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 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 is 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 clearly measurable mortality
curves and so on for the Northern Hemisphere have gone down.
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 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 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 knowing that you know nothing about the world.
Well, I think 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've got to make some decision about what to do.
And it's some...
Tell some narrative that while amidst the mystery and knowing not much about 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, 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 would 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 it'll be interesting to see, for example, with this pandemic.
To me, when you look at organizations, for example, having some kind of perturbation, some kick to the system, usually the end result of that is actually quite good.
Unless it kills the system, it's actually quite good usually.
And I think in this case, people, I mean, my impression, it's a little weird for me because I've been a remote tech CEO for 30 years.
This is bizarrely...
And the fact that this coming to see you here is the first time in six months that I've been in a building other than my house.
So I'm a kind of ridiculous outlier in these kinds of things.
Overall, your sense is when you shake up the system and throw in chaos, you challenge the system, we humans emerge better.
It seems to be that way.
Who's to know?
But I think that people...
My vague impression is that people are sort of, oh, what's actually important?
What is worth caring about and so on?
And that seems to be something that perhaps is more 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.
We're trying to figure out little puzzles.
And then that somehow creates this graph of collective intelligence where we figure out...
And then you throw in these viruses of which there's millions different, you know, this entire taxonomy.
And the viruses are thrown into the system of collective human intelligence.
And when 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 fee...
Just you said the computation of reducibility.
There's always a fear of the darkness of the uncertainty before us.
It's scary.
I mean, the thing is, if you knew everything, it would be boring.
And worse than boring, so to speak.
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 happens in our lives.
That's funny.
And so the computation of reducibility is kind of like, it gives the meaning to life.
It is the meaning of life.
Computational reducibility is the meaning of life.
There you go.
It gives it meaning, yes.
I mean, 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, orphan alpha sunburn computation thing
as long as I can get network here.
Actually, you know what?
It says sunburn unlikely.
This is a QA moment.
This is a good moment.
Okay.
Let me just check what it thinks.
I will 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 trust the science
or do we use common sense?
The UV thing is cool.
Yeah, yeah.
Well, we'll see.
It's a QA moment, as I say.
Do 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,
if you think about 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 question is, how do these computations compare?
Are there dumb computations and smart computations?
Or are they somehow all equivalent?
And the thing that I 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 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.
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 is 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,
basically, we got that.
Who's going to win or lose the battle?
No, we didn't crack that one.
That one.
Game theorists are trying.
And then the weather...
It's kind of halfway on that one.
Halfway?
Yeah, I think we're doing OK on that one.
Long term climate, different story.
But the weather, we're much closer on that.
But do you think eventually we'll figure out the weather?
Do you think eventually most will 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 there is an infinite collection of these local pockets.
We'll never run out of local pockets.
And by the way, those local pockets are where we build engineering, for example.
That's how we...
If we want to have a predictable life, so to speak,
then we have to build in these sort of pockets of reducibility.
Otherwise, if we were sort of existing in this kind of irreducible world,
we'd never be able to have definite things to know what's going to happen.
I have to say, I think one of the features when we look at 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.
If we describe, oh, I don't know, something like heat, for instance,
we say, oh, the air in here, 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.
Actually, I realized there's a thing I realized last week, actually,
was a thing that people say 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.
So those little molecules interacting in complex ways,
there could be intelligence in that, there could be...
Absolutely. I mean, this is what you learn from this principle.
Wow, 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.
I mean, because, you know, we imagine that with sort of all the things we do
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 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 they're special
because kind of they're connected to our purposes,
our ways of thinking about things and so on.
And that's some...
That's very human-centric.
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?
So I mean, the question is, can we kind of reduce what has been physics
as 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 because of computational irreducibility,
that's not something where you say,
okay, you've got the fundamental theory of everything,
then tell me whether lions are going to eat tigers or something.
No, you have to run this thing for 10 to the 500 steps or something
to know something like that.
So at some moment, potentially, you say, this is a rule
and run this rule enough times and you will get the whole universe.
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 as if you generate the digits of pi.
There's a definite procedure, you just generate them.
And it'll be the same thing if you have a fundamental theory of physics
of the kind that I'm imagining.
You get 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
in a unified way.
It's not there's a bunch of disparate modules.
Does it feel like if you create a rule,
and we'll talk about the Wolfram physics model,
which is fascinating, but if you have a simple set of rules
with a data structure, like a hypergraph,
does that feel like a satisfying theory of everything?
Because then you really run up against the irreducibility,
computation irreducibility.
Right, so that's a really interesting question.
What I thought was going to happen is I thought we had a pretty good idea
for what the structure of this sort of theory that's underneath space and time
and so on might be like.
And I thought, gosh, 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 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 all these simple rules run into,
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 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 20th century physics is essentially pockets of reducibility.
And then it is incredibly surprising that any kind of model that's generative
from simple rules 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 thing that is sort of remarkable.
And that's the thing to me that's just, it's really beautiful.
And the thing that's even more beautiful is that it turns out that people have been struggling for a long time.
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 it's just great as far as I'm concerned.
So 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 I mean, the, you know, okay, very, very quick history of this, right?
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 they 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, prekepia matematica,
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 hundred years
for people to actually be able to do the math to the level that was needed.
But so that had been the 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 that 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.
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 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?
Usually you think of what's the shortest distance between two points,
like ordinarily on a plane in space, it's a straight line.
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 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 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 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 Altsverte.
And that 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 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, like the universe is expanding.
But then it took until the 1940s, probably even really until the 1960s,
until people understood that black holes were a consequence of general relativity and so on.
But the big surprise has been that so far this theory of gravity has perfectly agreed
with these collisions of black holes seen by their gravitational waves, 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 relativity,
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 relativity
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
and not specific to the reference frames you're operating in and so on and so on and so on.
But fundamentally, general relativity 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, not at the Big Bang actually, right?
Well, features of the expansion of the universe, yes.
And there are lots of details where we don't quite know how it's working.
Where's the dark matter? Is there dark energy, et cetera, et cetera, et cetera.
But fundamentally, the testable features of general relativity, it all works very beautifully.
And in a sense, it is mathematically sophisticated,
but it is not conceptually hard to understand in some sense.
Okay, so that's general relativity.
And once it's friendly neighbor, like you said, there's two theories, quantum mechanics.
Right. So quantum mechanics, the way that that originated was,
one question was, is the world continuous or is it discrete?
In ancient Greek times, people have been debating this.
People debated it throughout history, as light made of waves, as it continues,
as it discreet, as it made of particles, corpuscles, whatever.
What had become clear in the 1800s is that atoms, 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.
Does it have mass, those kinds of questions?
Yeah, yeah, right.
Well, there's a 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,
particularly in features of atoms and so on.
And, you know, what developed was this mathematical theory
that was a theory, 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, 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 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 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 a dozen decimal places, certain things.
You can measure them.
It all works.
It's all beautiful.
The underlying fabric is the model of that particular theory's 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.
The quantum field.
That's a classical field.
The quantum field is a much more mathematically elaborate kind of thing.
I should explain that one of the pictures of quantum mechanics that's really important
is in classical physics, one believes that 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 or whatever else.
In quantum mechanics, the picture is definite things don't happen.
Instead what happens is this whole structure of all many different paths being followed.
We can calculate certain aspects of what happens.
Certain probabilities of different outcomes and so on.
You say what really happened?
What's really going on?
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?
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 whole career out of calculating things about quantum mechanics.
Nevertheless, it's what the quantum field theory is very accurate at predicting a lot
of the physical phenomena.
It works.
Yes.
But there are things about it, it has certain, when we apply it, the standard model of particle
physics, for example, which we apply to calculate all kinds of things, it works really well.
You say, well, it has certain parameters.
It has a whole bunch of parameters, actually.
You say, 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
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, and then in the context
of a theory of everything, what's traditionally the task of the unification of these theories?
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 particles of gravity, the kind of mathematical
tricks that get used in working things out in quantum field theory don't work.
So that's been a sort of fundamental issue.
And when you think about black holes, which are a place where sort of the structure of
space 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 been a bunch of mathematical developments 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.
But it hasn't been, you know, and the other thing to realize is, as far as physics is
concerned, it's just like, here's general relativity, here's quantum field theory, you know, be happy.
Yeah, so do you think there's a quantization of gravity, the 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,
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, 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 various features of domain-specific languages,
so to speak, that talk about various aspects of this machine code. And I think 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 all the work that's been
done in those areas 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. That is, 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 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. I mean, the best analogy that I can see is what happened with the early days
of computerability 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, I mean, one of the things that's really interesting is
one of the most abstract things that's come out 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 the Wolfram physics model view 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?
Yeah, right. I mean, 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 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 put us 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 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. 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.
And 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 turn out not to be right.
And, you know, the most important assumption is that space is a continuous thing.
The point 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, you know, Euclid who kind of wrote down the original kind of axiomatization of
geometry back in 300 BC or so, you know, his very first definition, he says, a point is
that which has no part.
A point is this, you know, this indivisible, you know, infinitesimal thing.
Okay, 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, you know, 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 this is 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 in what we experience in the universe.
So you think this 3D aspect of it is fundamental?
No, I don't think it's 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 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.
And so...
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
discreet 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.
The underlying nature of reality is kind of like a Facebook.
We don't know their location, but we have the friends.
Yeah, 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, 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 we don't know exactly the size, but maybe around 10 to the minus 100 meters.
So 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.
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.
So you're a domino or beautiful.
We'll talk about it.
Right.
So the thing about continuity arising from discrete systems is in today's world is actually
not so surprising.
I mean, your average computer screen, right?
Every computer screen is made of discrete pixels, yet we have the idea that we're seeing
these continuous pictures.
I mean, it's 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, wait, wait, 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, OK.
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, like the relationship creates a constraint, which then in an emergent sense creates a spike.
Yeah. Like a, uh, basically a spatial coordinate for that thing, even though the individual point doesn't have a space, even though the individual point doesn't know anything, it just knows what it's, you know, what its neighbors are, they 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 isn't just a square grid or something. It's something much more dynamic and complicated, which we'll talk about. But, um, uh, so, you know, the 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, uh, every atom of space, uh, where, 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, uh, outside of computer science.
Let's call it a network. I think that's called a network is better. So, 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 the nodes represent some abstract entity and then the edges represent relationships between those entities.
Right. Exactly.
So that's what a graph says. 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.
Right. That's correct. That's correct. But so then, so, okay, so 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.
Right. 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 a property of the space.
It's just features of space. Mind-blowing, first of all. 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 a transformation.
Let's talk about time in a second. On the subject of space, there's this question 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 and 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 in 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 you can't say intended.
There's no intention here that just maintains the structure of space.
Let me let me load that in. It's, it just makes me feel so good as a human being.
Well, to be the froth on the one in the 10 to the 120 or something of well, and also just humbling how in this mathematical framework, how much work needs to be done on the infrastructure.
Right. Yes, that's right.
To maintain the infrastructure of our universe is a lot of work. We are, we are merely writing a little tiny things on top of that infrastructure.
But, but, you know, you were just starting to talk a little bit about what, you know, we talked about, you know, 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, 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 hypergrass?
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, 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 then 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.
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.
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.
So that's like the prerequisite for the event as it exists.
So that defines a kind of this sort of set of causal relationships between events.
It says this event has to have happened before this event.
But that is...
But that's not a very limited constraint.
No, it's not.
You still get the zillion, that's the technical term, options.
That's correct.
So this is where things get a little bit more elaborate.
But they're mind-blowing.
So what happens is, so the first thing you might say is, you know, let's...
So this question about the freedom of which event you do when.
Well, 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 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 beautiful thing.
So there's this idea of what I call causal invariance.
Causal invariance, exactly.
Really, really powerful idea.
It's a 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 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 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 multiply them out in any order, you'll always get the same answer.
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 some random order, you know, BAA, BBBAA, whatever.
And you have a little rule that says every time you see BAA, flip it around to AB.
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, there are many different orders in which you can do 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 with sorting a string, it sounds obvious.
That's to me surprising 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.
It is not obvious and it was something that, you know,
I sort of discovered that idea for these kinds of systems
and back in the 1990s and for various reasons,
I was not satisfied by how sort of fragile finding that particular property was.
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 let's ignore that for a second.
We can come to that later.
Is it useful to talk about observation?
Not yet.
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?
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 are 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 of 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 elaborate, but the basic point is that
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 a way to think about this, you know,
in terms of 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 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 it might be 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, how do you go from the lowest source code of space and time
to the more traditional terminology of space and time?
The key thing is this thing we call the causal graph.
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 has a causal relationship to other events
in the sense that if another event needs as its input,
the output from the first event,
there will be a causal relationship of the future event
will depend on the past event.
So you can say 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, let's say we were sorting a string, for example,
I did that particular transposition of characters at this time.
Then I did that one.
Then I did this one.
Turns out if you look at the network of connections
between those updating events,
that network is the same.
It's the structure.
So in other words, if you were to draw 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 nodes of the network will be different,
but the way the nodes are connected will always be the same.
But the causal graph is kind of an observation.
It's not enforced.
It's just emergent from a set of events.
It's a feature of...
The characteristic, I guess, is the way events happen.
Right.
An event can't happen until its input is ready.
Right. And so that creates this network of causal relationships.
That's the causal graph.
The next thing to realize is,
when you're going to observe what happens in the universe,
you have to make sense of this causal graph.
You are an observer who yourself is part of this causal graph.
That means...
Let me give you an example of how that works.
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 update at every moment in time,
and it's just going to be like a Turing machine.
It has a little head that runs around
and is always just updating one thing at a time.
So you say, 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 it's plainly obvious that things are being updated
at the same time.
But the fact is that the thing is that if I'm talking to you
and you seem to be being updated as I'm being updated,
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 clear or is that a hypothesis?
Is that clear that there's a unique causal graph?
If there's causal invariance, there's a unique causal graph.
So it's okay to think of what we're talking about
as a hypergraph and the operations on it
as a kind of a Turing 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 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 around.
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.
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.
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.
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 hypergraph that are communicating with each other
and experiencing this whole thing as a real-time simultaneous update
with, I'm taking in photons for you right now,
but there's something much, much deeper going on here.
Right, it does have a...
It's paralyzing sometimes just to remember that.
Right, no, I mean, you know...
Sorry.
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, you know,
how do we set our clocks?
You know, if we've got a spacecraft landing on Mars,
you know, do we say that it, you know,
what time is it landing at?
Was it, you know, even though there's a 20-minute
speed of light delay or something,
you know, 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 the,
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, you know, one way to think about it
is given that you have a basic structure
that just involves updating things
in these, you know, 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, not a big deal
because it's kind of, it's kind of a,
you know, it was completely unobvious.
When you started off with saying,
we've got this graph, it's being updated in time, etc, etc, etc,
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,
you know, water seems continuous on a large scale.
So this hypergraph seems continuous on a large scale.
One question is, you know, how many dimensions of space
does it correspond to?
So one question you can ask is,
if you 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, that's pretty easy to explain.
So basically if you say, you got a point
and you look at how many neighbors does that point have?
Okay, 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, you know, the number of,
the area of a circle is pi r squared.
So the, it's 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, 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?
There's a, I mean, obviously the visual aspect
of these hypergraphs,
they're often visualized in three dimensions.
Right.
And then there's a certain kind of structure.
Like you said, there's the, I mean, a circle,
a sphere, there's a planar aspect to it.
Right.
To this graph to where it kind of,
it almost starts creating a surface,
like a complicated surface, but a surface.
So how does that connect to effective dimension?
Okay.
So I mean, if you can lay out the graph in such a way
that the points in the graph that,
you know, the points that are neighbors on the graph
on 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.
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?
Right. So, I mean, what, you know,
one of the features of computational irreducibility 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.
That's, 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,
that any one of those features,
we can get a rule that has that feature.
Yes.
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.
Yes.
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, yeah, 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,
appear within the graphs that emerge from that rule.
That's what I thought it was going to be.
Uh-oh, okay.
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, you know, it wasn't at all obvious to me
that even if we were completely correct,
and even if we had, you know, this is the rule,
you know, 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?
Okay, 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,
the Einstein equations are about curvature of space.
Curvature 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.
General relativity is about curvature
in this space represented by this hypergraph.
So, what is the general relativity
of the hypergraph?
So, the general relativity of the hypergraph
of the hypergraph of the hypergraph
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, but...
Right, that's what this is about.
What this is about is,
if 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,
this 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
in a 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 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 1 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 it the way they say it should work?
And the answer is,
yes.
And so, how does that work?
I mean,
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,
non-infinite dimensional space.
Non-infinite dimensional.
It can grow infinitely,
but it can't be infinite dimensional.
What does an infinitely dimensional hypergraph look like?
For example,
you start from one root of the tree,
it 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 with a 2 there.
On a tree,
you get to, for example, 2 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.
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 it only,
as 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 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,
then 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.
The, okay,
so Einstein's equations
in their 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 GDSIC,
that's a term that means shortest path
comes from measuring shortest paths on the earth.
So you look at a bunch of,
a bundle of GDSICs,
a bunch of shortest paths.
It's like the paths that photons
would take between two points.
Then the statement of Einstein's equations,
it's basically a statement about
a certain the,
that as you look at a bundle of GDSICs,
the structure of space has to be such that
although the
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 a,
the most simple-minded version of
army nu minus a half hour,
g mu nu equals zero,
which is the more mathematical version
of Einstein's equations.
It's a statement,
it's a statement of the thing called
the Richie tensor is equal to zero.
That's Einstein's equations for the vacuum.
So we get that
and as a result of this model,
but footnote,
big footnote,
because all the matter in the universe
is 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,
you know,
last late 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.
The notion of space-like hypersurfaces.
So this is,
it's not as scary as it sounds.
It's a common notion in general, so to speak.
The notion is
you are defining
what is a possibly,
what is,
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
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
and 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.
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'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...
But this hypersurface
gives some more formalism to that.
It gives a way to connect that.
But intuitively we should think about
as 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.
So the 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 and 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...
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 so there's some concept of energy
that's
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...
Mass 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 this, of the
way this model works.
It's an intrinsic consequence of the
way this model works.
And so what we have to do with
that, 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, like, that's, hence
the general relativity,
you have a sense that
it appears to be baked in
to the fundamental properties of
the general relativity.
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
spacetime and matter.
And that's some...
So is that, have you,
that last piece with curvature
have, is 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, you know, we have the
mathematical derivation, it's all
okay. So one thing that's sort of
a, you know, 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, there's a, there's a
tower of many, many of these
mathematical limits that have to
be taken. So if you're a pure
scientist, you can, you know, we
can try each one of them
computationally and we could say
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, so they can't do
the limits. Yeah, because you
can't do the limits.
And very, 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 the hard derivation.
Yeah, it's just, it's just the
mathematical structure kind of
in, you know, ends up running
right into computational
reducibility and you end up with
a bunch of, a bunch of difficulty
there. But here's the way that
researchers, using Einstein's
equations, what do they actually
do? Well, they actually use
Mathematica 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
on a computer and it 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 on the computer.
That 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 hole
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.
As 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?
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.
And one of my realizations
is that, you know, so it's
very hard to get in your brain
how you deal with parallel
computation, and you're always
worrying about, you know, if
multiple things can happen on
different computers at different
times, oh, what happens if this
thing happens before that thing
and we've really got, you know,
we have these race conditions
where something can race to get
to the answer before another
session to lock things down to
the point where you've had locks
and mutexes and God knows what
else, where you've
arranged it so that there can
only be one sequence of things
that can happen. So you don't
have to think about all the
different kinds of things that
can happen. Well, in these models,
physics is throwing us into
forcing us to think about all
these possible things that can
happen. But these models, together
with all the possible things
happening about all these
different things happening in
parallel. And so I'm guessing
they have built-in protection for
some of the parallelism. Well,
causal invariance is the built-in
protection. Causal invariance is
what means that even though
things happen in different orders,
it doesn't matter in the end.
As a person who struggled with
concurrent programming in
Java with all the basic concepts
that could be built up a strong
mathematical framework for
causal invariance, that's
so liberating. And that could
be not just liberating, but
really powerful for
massively distributed computation.
Absolutely. No, I mean, you know,
what's eventual consistency in
distributed databases is essentially
the causal invariance idea.
So that's-
But have you thought about,
you know, we're like really
large simulations?
Yeah. I mean, I'm also thinking
about, look, the fact is,
you know, I've spent much of my life
as a language designer, right?
So I can't possibly not
think about, you know, what does
this mean for designing languages
for parallel computation? In fact,
another thing that's one of these,
you know, I'm always embarrassed
at how long it's taken me to figure
stuff out. But, you know, back
in the 1980s, I worked on
trying to make up languages for
parallel computation.
I thought about doing graph
rewriting. I thought about doing
these kinds of things, but I
couldn't see how to actually make
the connections to actually do
something useful. I think now
physics is kind of showing us
how to make those things useful.
And so my guess is that in time,
we'll be talking about, you know,
we do parallel programming.
We'll be talking about programming
in a certain reference frame,
just as we think about thinking
about physics in a certain
reference frame. It's a certain
coordination of what's going on.
We say, we're going to program in
this reference frame.
Oh, let's change the reference
frame to this reference frame.
And then our program will seem
different and we'll have a
different way to think about it.
But it's still the same program
underneath.
So let me ask on this topic,
because I put out that I'm talking
to you. I got way more questions
than I can deal with. But what pops
the minds, a question somebody
asked on Reddit, I think, is,
please ask Dr. Wolfram,
what are the specs of the computer
running the universe?
So we're talking about specs of
hardware and software for
simulations of a large scale
thing. What about a scale that
is comparative to something that
eventually leads to the two of us
talking and about?
Right, right, right.
So actually, I did try to
estimate that. And we actually
go a couple more stages before
we can really get to that answer
because we're talking about
this thing.
This is what happens when you
build these abstract systems and
you're trying to explain the
universe that quite a number of
levels deep, so to speak.
But the
you mean conceptually or like
literally because you're talking
about small objects and there's
10 to the 120 something
number.
It is conceptually deep.
And one of the things that's
happening sort of structurally in
this project is, you know, there
were ideas, there's another layer
of ideas, another layer of ideas
to get to the different things
that correspond to physics.
They're just different layers
of ideas.
And they are, you know, it's
actually probably, if anything,
getting harder to explain this
project, because I'm realizing
that the fraction of way through
that I am so far in explaining
this to you is less than, you
know, it might be because there's
be no more now, you know, every
every week, basically, we know a
little bit more.
And like those are just layers
on the initial fundamental
Yes, the layers are, you know,
you might be asking me, you know,
how do we get, you know, the
difference between fermions and
bosons, the difference between
particles that can be all in the
same state and particles that
exclude each other.
Okay.
Last three days, we've kind of
figured that out.
Okay.
But and it's very interesting.
It's very cool.
And it's very
And those are some kind of
properties at a certain level,
layer of abstraction on the
graph.
Yes.
Yes.
And there's, but the layers of
abstraction are kind of, they're
compounding.
Stacking up.
It's difficult, but
But the specs nevertheless remain
the same.
Okay.
The specs underneath.
So I have an estimate.
So the question is, what are the
units?
So we've got these different
fundamental constants about the
world.
So one of them is the speed of
light, which is the so the thing
that's always the same and all
these different ways of thinking
about the universe is the notion
of time because time is
computation.
And so there's an elementary
time, which is sort of the
the amount of time that we
ascribe to elapsing
in a single computational
step.
Yeah.
Okay.
So that's the elementary time.
So then there's an element or
whatever.
It's a constant.
It's whatever we define it to
be.
Because I mean, we, we don't,
you know, it's all relative.
Right.
It doesn't matter.
It doesn't matter what it is
because we could be, it could be
slower.
It's just a number which, which
we use to convert that to
second, so to speak, because we
are experiencing things and we
say this amount of time has
elapsed.
So we're within this thing.
Absolutely.
It doesn't, yeah.
It doesn't matter.
Right.
But what does matter is the
ratio, what we can, the ratio
of the spatial distance and this
hypergraph to this, to this
moment of time.
Again, that's an arbitrary thing,
but we measure that in meters
per second, for example.
And that ratio is the speed of
light.
So the ratio of the elementary
distance to the elementary time
is the speed of light.
Okay.
Perfect.
And so there's another, there
are two other levels of this.
Okay.
So there is a thing which we can
talk about, which is the
maximum entanglement speed, which
is a thing that happens at another
level in this whole sort of story
of how these things get constructed.
That's a sort of maximum speed in
quantum, in the space of quantum
states, just as the speed of
light is a maximum speed in
physical space.
This is a maximum speed in the
space of quantum states.
There's another level which is
associated with what we call
rural space, which is a, another
level which is associated with
these maximum speeds.
We'll get to this.
So these are limitations on the
system that are able to capture
the kind of physical universe
which we live in, the quantum
mechanical.
There are inevitable features of
having a rule that has only a
finite amount of information in
the rule.
So long as you have a rule that
only involves a bounded amount,
a limited amount of, only
involving a limited number of
elements, limited number of
relations, it is inevitable that
there will be a limit to the
speed constraints.
We knew about the one for speed
of light.
We didn't know about the one for
maximum entanglement speed, which
is actually something that is
possibly measurable, particularly
in black hole systems and things
like this.
But anyway, this is long, long
story short.
You're asking what the processing
specs of the universe, of the
sort of computation of the
universe.
There's a question of even what
are the units of some of these
measurements?
Okay.
So the units I'm using are
Wolfram language instructions
per second.
Okay.
Because you got to have some,
what, what computation are you
doing?
There got to be some kind of
frame of reference.
Right, right.
So because it turns out in the
end, there will be, there's sort
of an arbitrariness in the
language that you use to
describe the universe.
So in those terms, I think it's
like 10 to the 500 Wolfram
language operations per second,
I think, is the, I think it's
of that order.
You know, so that's the scale
of the computation.
What about memory?
If there's an interesting thing
to say about storage and memory?
Well, there's a question of how
many sort of atoms of space
might there be?
You know, maybe 10 to the 400.
We don't know exactly how to
estimate these numbers.
I mean, this is, this is based
on some, some, I would say
somewhat rickety way of estimating
things.
You know, when they start to be
able to be experiments done, if
we're lucky, there will be
experiments that can actually
nail down some of these numbers.
And because of computation
reducibility, there's not much
hope for very efficient
compression, like very efficient
representation of this.
Question.
Good question.
I mean, there's probably certain
things, you know, the fact that
we can deduce anything.
Okay.
The question is how deep does
the reducibility go?
Right.
Okay.
And I keep on being surprised
that it's a lot deeper than I
thought.
Okay.
And so one of the things is that
that there's a question of sort
of how much of the whole of
physics do we have to be able to
get in order to explain certain
kinds of phenomena?
Like, for example, if we want to
study quantum interference, do we
have to know what an electron is?
Turns out, I thought we did.
Turns out we don't.
I thought to know what energy is,
we would have to know what
electrons were.
We don't.
So you can get a lot of really
powerful shortcuts.
Right.
There's a bunch of sort of bulk
information about the world.
The thing that I'm excited about
last few days, okay, is the idea
of fermions versus bosons,
fundamental idea that, I mean,
it's the reason we have matter
that doesn't just self-destruct
is because of the exclusion principle
that means that two electrons
can never be in the same quantum
state.
Is it useful for us to maybe
first talk about how quantum
mechanics fits into the Wolfram
physics model?
Yes.
Let's go there.
So we talked about general
relativity.
Now, what have you found?
What's the story of quantum
mechanics?
Right.
Outside of the Wolfram physics.
Right.
So I mean, the key idea of quantum
mechanics, sort of the typical
interpretation is classical physics
says a definite thing happens.
Quantum physics says there's this
whole set of paths of things that
might happen and we are just
observing some overall probability
of how those paths work.
Okay.
So when you think about our
hypergraphs and all these little
updates that are going on, there's
a very remarkable thing to realize
which is if you say, well, which
particular sequence of updates
should you do?
Say, well, it's not really defined.
You can do any of a whole collection
of possible sequences of updates.
Okay.
That set of possible sequences of
updates defines yet another kind
of graph that we call a multi-way
graph.
And a multi-way graph just is a
graph where at every node there
is a choice of several different
possible things that could happen.
So for example, you go this way, you
go that way.
Those are two different edges in the
multi-way graph and you're building
up the set of possibilities.
So actually, like for example, I just
made the one, the multi-way graph
for tic-tac-toe.
Okay.
So tic-tac-toe, you start off with
some board that is everything is
blank and then somebody can put down
an X somewhere, an O somewhere, and
then there are different possibilities.
At each stage, there are different
possibilities.
And so you build up this multi-way
graph and you notice that even in
tic-tac-toe, you have the feature
that there can be something where
you have two different things that
happen and then those branches merge
because you end up with the same
configuration of the board, even
though you got there in two different
ways.
So the thing that's sort of an
inevitable feature of our models is
that just like quantum mechanics
suggests, definite things don't
happen.
Instead, you get this whole multi-way
graph.
Okay.
So that's sort of a picture of
what's going on.
Now you say, okay, well, quantum
mechanics has all these features of
all this mathematical structure and
so on.
How do you get that mathematical
structure?
Okay.
A couple of things to say.
So quantum mechanics is actually, in
a sense, two different theories glued
together.
Quantum mechanics is the theory of
how quantum amplitudes work that
more or less give you the probabilities
of things happening and it's the
theory of quantum measurement, which
is the theory of how we actually
conclude definite things because
the mathematics just gives you these
quantum amplitudes which are more or
less probabilities of things happening
but yet we actually observe definite
things in the world.
Quantum measurement has always been a
bit mysterious.
It's always been something where people
just say, well, the mathematics says
this but then you do a measurement and
there are philosophical arguments about
the measurement.
Somebody on Reddit also asked,
please ask Steven to
tell his story of
this, the double
solid experiment.
Okay.
Yeah, I can.
Does that make sense?
Oh yeah, it makes sense.
Absolutely makes sense.
Why, is this like a good way to discuss
a little bit?
Let me go, let me explain a couple
of things first.
So the structure of quantum
mechanics is mathematically quite
complicated.
One of the features,
let's see, how to describe this.
Okay, so first point is there's
this multi-way graph of all these
different paths of
things that can happen in the world
and the important point is that
these, you can have
branchings and you can have
mergings.
Okay, so this property
turns out causal invariance
is the statement that
the number of
mergings is equal to the number of
branchings.
Yeah.
So in other words, every time there's
a branch, eventually there will also
be a merge.
In other words, every time there were
two possibilities for what might
have happened, eventually those will
merge.
Beautiful concept, by the way.
Yeah.
So that idea, okay.
So then, so that's
one thing and that's
closely related to the
sort of objectivity in quantum
mechanics.
The fact that we believe definite
things happen, it's because although
there are all these different paths,
in some sense, because of causal
invariance, they all imply the same
thing.
I'm cheating a little bit in saying
that, but that's roughly the essence
of what's going on.
Okay.
Next thing to think about is
you have this multi-way graph.
It has all these different possible
things that are happening.
Now, we ask, this multi-way
graph is sort of evolving with time.
Over time, it's branching,
it's merging, it's doing all these
things, okay?
The question we can ask is
if we slice it at a particular
time, what do we see?
And that slice represents, in a
sense, something to do with the
state of the universe at a particular
time.
So in other words, we've got this
multi-way graph of all these
possibilities and then we're asking
and, okay, we take this slice,
this slice represents, okay,
each of these different paths
corresponds to a different quantum
possibility for what's happening.
When we take this slice, we're saying
what are the set of quantum possibilities
that exist at a particular time?
And when you say slice, are these,
you slice the graph and then there's a
bunch of leaves.
A bunch of leaves.
And those represent the state of
things.
Right.
But then, okay, so the important
thing that you are quickly picking up
on is that what matters is kind
of how these leaves are related to
each other.
So a good way to tell how leaves
are related is just to say, on the
map before, did they have a common
ancestor?
So two leaves might be, they might
have just branched from one thing
or they might be far away, you know,
way far apart in this graph where
to get to a common ancestor, maybe you
have to go all the way back to the
beginning of the graph, all the way
back to the beginning.
There's some kind of measure of
distance.
Right.
But what you get is by making this
slice, what you call it,
branchial space, the space of
branches.
And in this branchial space,
you have a graph that represents
the relationships between these
quantum states in branchial space.
You have this notion of distance
in branchial space.
Okay.
Is this connected to quantum
entanglement?
Yes.
Yes.
It's basically, the distance in
branchial space is kind of an
entanglement distance.
So this...
That's a very nice model.
Right.
It is very nice.
It's very beautiful.
I mean, it's so clean.
I mean, it's really, you know,
and it tells one...
Okay.
So anyway, so then this
branchial space has this sort of
map of the entanglements
between quantum states.
So in physical space, we have...
So, you know, you can say...
Let's say the causal graph,
and we can slice that at a
particular time, and then we get
this map of how things are laid out
in physical space.
When we do the same kind of thing,
there's a thing called the
multi-way causal graph, which is
the analog of a causal graph for
the multi-way system.
We slice that, we get essentially
the relationships between things,
not in physical space, but in the
space of quantum states.
It's like which quantum state is
similar to which other quantum
state?
Okay.
So now, the next thing to say is
just to mention how quantum
measurement works.
So quantum measurement has to do
with reference frames in
branchial space.
So, okay.
So measurement in physical space,
it matters whether how we
assign spatial position and how
we define coordinates in space
and time.
And that's how we make measurements
in ordinary space.
Are we making a measurement based
on us sitting still here?
Are we traveling at half the speed
of light and making measurements
that way?
These are reference frames in
which we're making our measurements.
And the relationship between
different events and different
points in space and time will be
different depending on what reference
frame we're in.
Okay.
So then we have this idea of
quantum observation frames, which
are the analog of reference frames
but in branchial space.
And so what happens is what we
realize is that a quantum
measurement is the observer is
sort of arbitrarily determining
this reference frame.
The observer is saying,
I'm going to understand the world
by saying that space and time
are coordinated this way.
I'm going to understand the world
by saying that quantum states
and time are coordinated in this
way.
And essentially what happens is
that the process of quantum
measurement is a process of
deciding how you slice up this
multi-way system in these quantum
observation frames.
So in a sense, the observer, the
way the observer enters is by
their choice of these quantum
observation frames.
And what happens is that the
observer because, okay, this is
again another stack of other
concepts.
But anyway, because the observer
is computationally bounded, there
is a limit to the type of quantum
observation frames that they can
construct.
Interesting.
Okay.
So there's some constraints, some
limit on the choice of
observation frames.
Right.
And by the way, I just want to
mention that there's a, I mean,
it's bizarre, but there's a hierarchy
of these things.
So in thermodynamics, the fact
that we believe entropy increases,
we believe things get more
disordered is a consequence of the
fact that we can't track each
individual molecule.
If we could track every single
molecule, we could run every
movie in reverse, so to speak, and
we would, you know, we would not
see that things are getting more
disordered.
But it's because we are
computationally bounded, we can
only look at these big blobs of
what all these molecules
collectively do, that we think
that things are, that we
describe it in terms of entropy
increasing and so on.
And it's the same phenomenon,
basically.
Also, the consequence of
computational irreducibility
that causes us to basically be
forced to conclude that definite
things happen in the world, even
though there's this quantum, you
know, this set of all these
different quantum processes that
are going on.
So, I mean, I'm, I'm, I'm
skipping a little bit and the,
but that's a, that's a rough
picture.
And in the evolution of the
Wolfram Physics Project, where
do you feel stand on some of the
puzzles that are along the way?
See, you're skipping along a
bunch of, you're skipping a
bunch of stuff.
Oh, it's amazing how much these
things are unraveling.
I mean, you know, these things,
look, it used to be the case
that I would agree with Dick
Feynman, nobody understands
quantum mechanics, including me.
Yeah.
Okay.
I'm getting to the point where I
think I actually understand
quantum mechanics.
My, my exercise, okay, is can I
explain quantum mechanics for real
at the level of kind of middle
school type explanation?
Right.
And I'm getting closer.
It's getting, it's getting there.
I'm not quite there.
I've tried it a few times and I
realized that there are things
that, where I have to start
talking about elaborate
mathematical concepts and so on.
But I think, and you've got to
realize that it's not self-evident
that we can explain, you know, at
an intuitively graspable level,
something which, you know, about
the way the universe works.
The universe wasn't built for our
understanding, so to speak.
But, but I think then, then, okay,
so another important, important
idea is this idea of branch
shield space, which I mentioned,
this sort of space of quantum
states.
It is, okay, so I mentioned
Einstein's equations describing,
you know, the effect of, the
effect of mass and energy on
trajectories of particles, on
GD6.
The curvature of physical space
is associated with the presence
of energy according to Einstein's
equations, okay?
So it turns out that rather
amazingly the same thing is true
in branch shield space, so it
turns out the presence of energy
or more accurately Lagrangian
density, which is a kind of
relativistic, invariant version
of energy, the presence of that
causes essentially deflection of
GD6 in this branch shield space,
okay?
So you might say, so what?
Well, it turns out that the sort
of the best formulation we have
of quantum mechanics, this, the
Feynman-Parth integral, is a
thing that describes quantum
processes in terms of mathematics
that can be interpreted as, well,
in quantum mechanics, the big
thing is you get these quantum
amplitudes, which are complex
numbers that represent, when you
combine them together, represent
probabilities of things happening.
And so the big story has been how
do you derive these quantum
amplitudes?
And people think these quantum
amplitudes, they have a complex
number, has, you know, real part
and imaginary part, you can also
think of it as having a magnitude
and a phase, and it, people have
sort of thought these quantum
amplitudes have magnitude and
phase, and you compute those
together.
Turns out that magnitude, the
magnitude and the phase come
from completely different places.
The magnitude comes, okay, so
what do you, how do you compute
things in quantum mechanics?
Roughly, I'm telling you, I'm
getting there to be able to do
this at a middle school level,
but I'm not there yet.
The, the, roughly what happens is
you're asking, does this
state in quantum mechanics
evolve to this other state in
quantum mechanics?
And you can think about that like
a particle traveling, or something
traveling through physical space,
but instead it's traveling through
branchial space.
And so what's happening is, does
this quantum state evolve to this
other quantum state?
It's like saying, does this object
move from this place in space to
this other place in space?
Okay, now the way that you, these
quantum amplitudes characterize
kind of to what extent the thing
will successfully reach some
particular point in branchial
space.
Just like in physical space you
could say, oh it had a certain
velocity and it went in this
direction.
In branchial space there's a
similar kind of concept.
Is there a nice way to visualize
for me now mentally branchial
space?
It's just, you have this
hypergraph, sorry, you have this
multi-way graph, it's this big
branching thing, branching and
merging thing.
But I mean like moving through
that space, I'm just trying to
understand what that looks like.
You know, that space is probably
exponential dimensional, which
makes it, again, another kind of
worms in understanding what's
going on.
That space has an ordinary
space, this hypergraph, the
spatial hypergraph, limits to
something which is like a
manifold, like something like
three-dimensional space.
Almost certainly the multi-way
graph limits to a Hilbert space
which is something that, I mean
it's just a weirder exponential
dimensional space.
And by the way, you can ask, I
mean there are much weirder things
that go on.
For example, one of the things I've
been interested in is the
expansion of the universe in
branchial space.
So we know the universe is
expanding in physical space, but
the universe is probably also
expanding in branchial space.
So that means the number of
quantum states of the universe is
increasing with time.
The diameter of the thing is
growing.
Right.
So that means that the, and by
the way, this is related to
whether quantum computing can
ever work.
Why?
Okay.
So let me explain why.
So let's talk about, okay.
So first of all, just to finish
the thought about quantum
amplitudes, the incredibly
beautiful thing.
I'm just very excited about
this.
The final path integral is
this formula that says that the
amplitude, the quantum amplitude
is e to the is over h bar, where
s is the thing called the action
and it, okay, so that can be
thought of as representing a
deflection of the angle of this
path in the multi-way graph.
So it's a deflection of a
geodesic in the multi-way path
that is caused by this thing
called the action, which is
essentially associated with
energy, okay?
And so this is a deflection of a
path in branchial space that is
described by this path integral,
which is the thing that is the
mathematical essence of quantum
mechanics.
It turns out that deflection is
the deflection of geodesics in
branchial space follows the exact
same mathematical setup as the
deflection of geodesics in physical
space, except the deflection of
geodesics in physical space is
described with Einstein's equations,
the deflection of geodesics in
branchial space is defined by the
deflection path integral and they
are the same.
In other words, they are
mathematically the same.
So that means that general
utility is a story of essentially
motion in physical space.
Quantum mechanics is a story of
essentially motion in branchial
space.
And the underlying equation for
those two things, although it's
presented differently because one's
interested in different things in
branchial space and physical space,
but the underlying equation is the
same.
So in other words, it's just these
two theories, which are the two
pillars of 20th century physics,
which have seemed to be often
different directions, are actually
facets of the exact same theory.
That's exciting to see where that
evolves and exciting that that just
is there.
Right.
I mean, to me, having spent some
part of my early life working in
the context of these theories of
20th century physics, they seem
so different and the fact that
they're really the same is just
really amazing.
Actually, you mentioned double
slit experiment.
So the double slit experiment is
an interference phenomenon where
you can have a photon or an
electron and you say there are
these two slits that could have gone
through either one, but there is
this interference pattern where it's
there's destructive interference
where you might have said in classical
physics, oh, well, if there are two
slits, then there's a better chance
that it gets through one or the other
of them.
But in quantum mechanics, there's this
phenomenon of destructive interference
that means that even though there are
two slits, two can lead to nothing,
as opposed to two leading to more
than, for example, one slit.
And in what happens in this model,
and we've just been understanding this
essentially, is that what
essentially happens is that
the double slit experiment is a
story of the interface between
branched space and physical space.
And what's essentially happening is
that the destructive interference is
the result of the two possible paths
associated with photons going through
those two slits winding up at
opposite ends of branched space.
And so they don't, and so that's why
there's sort of nothing there when you
look at it, is because these
two different sort of branches
couldn't get merged together
to produce something that you can
measure in physical space.
Is there a lot to be understood
about branched space?
Yes, there's a lot.
It's a very beautiful mathematical
thing, and it's very, I mean,
by the way, this whole theory
is just amazingly rich
in terms of the mathematics that
it says should exist.
Calculus is a
story of infinitesimal change
in integer-dimensional space,
one-dimensional, two-dimensional, three-dimensional space.
We need a theory
of infinitesimal change
in fractional-dimensional and dynamic-dimensional
space. No such
theory exists. So there's tools of mathematics
that are needed here, and this is a motivation
for that, actually. Right, and it's
there are indications
and we can do computer experiments and we
can see how it's going to come out, but we need
to, you know, the actual mathematics
doesn't exist,
and in branched space it's actually even worse.
There's even more
layers of mathematics that are
we can see how it works
roughly by doing computer experiments,
but to really understand it
we need more sort of mathematical
sophistication. Quantum computers.
Okay, so the basic
idea of quantum computers, the
promise of quantum computers
is quantum mechanics does
things in parallel,
and so you can sort of intrinsically
do computations in parallel,
and somehow that can be much more efficient
than just doing them
one after another.
You know, I actually worked on quantum computing
a bit with Dick Feynman back in
1980, one, two, three,
that kind of timeframe, and we
The fascinating image.
You and Feynman work on quantum computers.
Well, we tried to work, the big thing
we tried to do was invent a randomness chip
that would generate randomness
at a high speed using quantum
mechanics, and the discovery
that that wasn't really possible
was part of the
the story of, we never really wrote
anything about it. I think maybe he wrote some stuff,
but we didn't write stuff about
what we figured out about sort of
the fact that it really seemed like
the measurement process in quantum mechanics
was a serious damper on what was
possible to do in sort of,
you know, the possible advantages
of quantum mechanics for computing.
But anyway, so
the sort of the promise of quantum computing
is, let's say
you're trying to factor an integer.
Well, you can instead of,
when you factor an integer, you might say, well, does this
factor work? Does this factor work? Does this factor
work? In
ordinary computing, it seems like we pretty much
just have to try all these different factors,
you know, kind of one
after another, but in quantum mechanics
you might have the idea, oh, you can just
sort of have the physics
try all of them in parallel.
Okay. And
the, you know, and there's
this algorithm, Schor's algorithm
which allows
you, according to the formalism of quantum
mechanics, to do everything in parallel
and to do it much faster than you can on a classical
computer. Okay.
The only little footnote is
you have to figure out what the answer is. You have
to measure the result.
So the quantum mechanics internally has figured out all
these different branches, but then you have to
pull all these branches together
to say, and the classical answer is this.
Okay. The standard theory
of quantum mechanics does not tell you how to do that.
It tells you how the branching works,
but doesn't tell you the process
of corralling all these things together.
And that process, which intuitively
you can see is going to be kind of tricky,
but our model
actually does tell you how that process
of pulling things together works.
And the answer seems to be,
we're not absolutely sure. We've only got to
two times three so far
which is kind of
in this
factorization in quantum computers, but we can
what seems to be the case is that
the advantage you get from the parallelization
from quantum mechanics
is lost from the
amount that you have to spend pulling together
all those parallel threads to get to a classical
answer at the end.
Now, that phenomenon is not unrelated
to various decoherence phenomena
that have seen in practical quantum computers and so on.
I mean, I should say, as a very practical
point, I mean, it's like, should
people stop bothering to do quantum computing research?
No.
Because what they're really doing is they're trying to use
physics
to get to a new level of what's possible
in computing, and that's a completely valid
activity. Whether
you can really put, you know, whether you can
say, oh, you can solve an NP-complete problem,
you can reduce exponential time to polynomial
time, you know, we're not sure.
And I'm suspecting the answer
is no, but that's
not relevant to the practical speed-ups you can
get by using different kinds of technologies,
different kinds of physics
to do basic computing.
So you're saying, I mean, some
of the models you're playing with, the indication
is that
to get all the
sheet back together
and, you know,
to corral everything together to get
the actual solution to the algorithm
is
you lose all the
by the way, I mean, so again, this
question, do we actually know what we're
talking about about quantum computing and so on?
So again,
we're doing proof by compilation.
So we have a quantum computing framework
and Wolfram Language,
which is, you know, standard quantum computing
framework that represents things in terms of the
standard, you know, formalism of quantum
mechanics, and
we have a compiler that simply compiles
the representation
of quantum gates into
multi-way systems.
So, and in fact, the message that I got
was from somebody who's working on the project
who has managed to compile
one of the sort of
a core formalism based on category
theory
of core quantum formalism
into multi-way systems.
When you say multi-way systems, these multi-way graphs?
Yes.
Yeah, okay, that's awesome. And then you can do
all kinds of experiments on that multi-way graph.
Right, but the point is that what we're saying
is the thing, we've got this representation
of, let's say, Shaw's algorithm
in terms of standard quantum gates,
and it's just a pure matter
of sort of computation to just say
that is equivalent. We will get the same
result as
running this multi-way system. Can you do
complexity analysis on that multi-way system?
Well, that's what we're being trying to do.
Yes, we're getting there. We haven't done that yet.
I mean, there's a pretty good indication
of how that's going to work out. We've done
as I say, our computer experiments
we've unimpressively gotten
to about two times three in terms of
factorization, which is kind of about
how far people have got with physical
quantum computers as well. But
yes, we will be able to
we definitely will be able to do complexity analysis
and we will be able to know. So
the one remaining hope
for quantum computing really, really working
at this formal level
of quantum brand
exponential stuff being done in polynomial time
and so on, the one hope
which is very bizarre is that you can
kind of
piggyback on the expansion of branch
shield space. So here's
how that might work. So
you think, you know,
energy conservation, standard thing in high
school physics, energy is conserved, right?
But now you imagine
you think about energy in the context
of cosmology and the context of the whole
universe. It's a much more complicated
story. The expansion of the universe kind
of violates energy conservation.
And so, for example, if you imagine you've got
two galaxies, they're receding from each other
very quickly, they've got two big central
black holes, you connect
a spring between these two central
black holes. Not easy to do in
practice, but let's imagine you could do it.
Now, that spring
is being pulled apart. It's getting
more potential energy in the spring
as a result of the expansion of the universe.
So, in a sense,
you are piggybacking
on the expansion that exists in the universe
and the sort of violation of energy
conservation that's associated with that
cosmological expansion to
essentially get energy. You're essentially building
a perpetual motion machine by
using the expansion of the universe.
And that is a physical
version of that. It is conceivable
that the same thing can be done in branch
shield space to essentially
mine
the expansion of the universe in branch
shield space as a way to get
sort of
quantum computing for
free, so to speak, just from the
expansion of the universe in branch shield space.
Now, the physical space version is kind
of absurd and involves, you know, springs between
black holes and so on.
It's conceivable that the branch shield
space version is not as absurd
and that it's actually something you can reach
with physical things you can build
in labs and so on. We don't know yet.
Okay, so you were saying
the branch shield space might be
expanding and there might be
something that could be exploited.
Right. In the same kind of way
that you can exploit
that expansion of the universe
in principle, in physical
space. You just have
like a glimmer of hope. Right. I think that
the real answer is going to be
that for practical purposes
the official brand
that says you can do
exponential things in polynomial time is probably not going to work.
For people curious
to kind of learn more, so this is more like
it's not middle school. We're going to go to
elementary school for a second.
Maybe middle school. Let's go to middle school.
So
if I were to try to maybe
write a
pamphlet
of like
Wolfram Physics project for dummies
a.k.a. for me
or maybe make a video on the basics
but not just
the basics of
the physics project but
the basics
plus the most
beautiful central ideas.
How would you go
about doing that? Could you help me out
a little bit? Yeah, I mean
as a really practical matter we have
this kind of visual summary
picture that we made.
Which I think is a pretty good
when I've tried to explain this to people
and it's a pretty good place
to start. As you got this rule
you apply the rule, you're
building up this big hypergraph
you've got all these possibilities
you're kind of thinking about that
in terms of quantum mechanics. I mean
that's a decent place
to start. So basically
the things we've talked about which is
space represented as a hypergraph
transformation
of that space is kind of time
and then
structure of that space
into the curvature of that
space as gravity. That
can be explained without going anywhere near quantum mechanics.
I would say that's
actually easier to explain than special relativity.
Also going into general
so going into curvature
yeah I mean special relativity
I think is it's a little bit
elaborate to explain and honestly
you only care about it if you know
about special relativity. If you know how special relativity
is ordinarily derived and so on.
So general relativity is easier.
It's easier, yes. And then what about quantum
what's the easiest way to reveal
I think the basic point is
just this fact
that there are all these different branches
that there's this kind of map of how the
branches work and
that I mean
I think actually the
recent things that we have about the double slit experiment
are pretty good because you can actually
see this you can see how
the double slit phenomenon
arises from just features
of these graphs. Now
having said that
there is a little bit of sleight of
hand there because
the true story of the way that
double slit thing works
depends on the coordination of branch
shield space that
for example in our internal team
there is still a vigorous battle going on
about how that works and
what's becoming clear
is I mean what's becoming clear
is that it's mathematically really quite
interesting. I mean that is that there's a
you know it involves essentially
putting space-filling curves you basically
have a thing which is naturally two-dimensional
and you're sort of mapping it into one dimension
with a space-filling curve
and it's like why is it this space-filling curve
and another space-filling curve and that becomes
a story about reamon surfaces
and things and it's quite elaborate
and but
there's a little bit sleight
of hand way of doing it where
it's you know it's surprisingly
direct.
So a question
that might be difficult to answer
but
for several levels of people
could you give me advice
on how we can learn more
specifically.
There is people that are completely
outside and just curious and
are captivated by
the beauty of hypergraphs actually
so people there just want
to explore play around with this.
Second level
is people from
say people like me
who somehow got a PhD
in computer science
but are not physicists and but
fundamentally the work you're doing
is of computational nature
so it feels very accessible.
So what
can a person like that
do to learn enough physics
or not
to one, explore the beauty
of it and two
that's the final level
of contribute something
of a level of even
publishable.
Strong, interesting ideas
at all those layers. Complete
beginner,
a CS person and the CS person
that wants to publish. I think that
I've written a bunch of stuff
doesn't go Jonathan Gorod
who's been a key person working on this project
and a bunch of stuff
and some other people started writing things too.
He's a physicist.
Well, he's I would say a mathematical
physicist. He's pretty mathematically
sophisticated. He regularly
out-mathematosizes me.
Strong mathematical
physics. I looked at some of the papers.
Right, but so
I mean, you know, I wrote
this kind of original announcement
blog post about this project which people
seem to have found. I've been really
happy actually that people
who
people seem to have
rocked key points from that
much deeper key points
people seem to have rocked than I thought
they would rock.
That's a kind of a long blog post. They explain
some of the things we talked about like the
hypergraph and the basic rules and
I don't, does it, I forget
it doesn't have any quantum mechanics.
Oh yeah, it goes through quantum mechanics.
But we know a little bit more since that
blog post that probably
clarifies, but that blog post is a pretty
decent job.
Talking about things like, again
something we didn't mention, the fact that the uncertainty
principle is a consequence of curvature
in branchial space. How much
physics should a person know
to be able to understand
the beauty of this
framework and to
contribute something novel? Okay, so I think
that those are different questions.
So, I mean, I think that
the, why does this work? Why does this
make any sense?
To really
know that, you have to know a fair amount of physics.
Okay?
And for example, have a... When you say
why does this work, you're referring to
the connection between this model
and... General activity, for example.
You have to understand something about general
activity. There's also
a side of this where just as a pure mathematical
framework is fascinating. Yes.
If you throw the physics out.
Then it's quite accessible to...
I mean, I wrote this sort of
long technical introduction to the project
which seems to have been very
accessible to people who are
who understand computation and
formal abstract ideas, but are not
specialists in physics or
other kinds of things. I mean, the thing with
the physics part of it is
it's... There's both a way
of thinking and a... Literally
a mathematical formalism. I mean, it's like
to know that we get the Einstein equations.
To know we get the energy and momentum tensor.
You kind of have to know what the energy and momentum tensor
is. And that's physics.
I mean, that's kind of graduate level physics, basically.
And
so that, you know, making that
final connection is... Requires
some depth of physics
knowledge. I mean, that's the unfortunate
thing. The difference in machine learning
and physics in the 21st century.
Is it really out
of reach of a year
or two worth of study? No.
You could get it in a year or two.
But you can't get it in a month. Right.
I mean, so... But it doesn't require
necessarily like 15 years.
No, it does not. And in fact, a lot of
what has happened with this project
makes a lot of this stuff much more
accessible. There are things where it has
been quite difficult to explain what's going on
and it requires much more,
you know, having the concreteness
of being able to do simulations, knowing
knowing that
this thing that you might have thought was just
an analogy is really actually what's
going on makes one
feel much more secure about just sort of saying
this is how this works.
And I think it will be, you know,
the... I'm hoping the textbooks
of the future, the physics textbooks of the future,
there will be a certain compression.
There will be things that used to be very much more elaborate.
Because, for example, even doing continuous mathematics
versus this discrete mathematics,
that, you know, to know
how things work in continuous mathematics, you have
to be talking about stuff and waving your hands about
things. Whereas with the
discrete version, it's just like, here is
a picture. This is how it works.
And there's no, oh,
do we get the limit right to this, you know,
to this thing that is of, you know,
zero, you know, measure
zero object, you know, interact
with this thing in the right way. You don't
have to have that whole discussion. It's just like, here's
a picture, you know, this is
what it does. And, you know, you can,
then it takes more effort to say, what does it do
in the limit when the picture gets very big.
But you can do experiments to build up an intuition
actually. Yes, right. And you can get sort
of core intuition for what's going on. Now, in terms
of contributing to this, the, you know,
I would say that the study of
the computational universe and how all these programs
work in the computational universe,
there's just an unbelievable amount to do
there. And it is very
close to the surface. That is,
you know, high school kids,
you can do experiments.
It's not, you know, and
you can discover things. I mean, you know, we
you can discover stuff about
I don't know, like this thing about expansion
of partial space. That's an absolutely accessible
thing to look at. Now,
you know, the main issue with doing
these things is not, there isn't
a lot of technical depth
difficulty there.
The actual doing of the experiments, you know,
all the code is all on our website to do
all these things. The real thing
is sort of the judgment of
what's the right experiment to do? How do you
interpret what you see?
That's the part that, you know,
people will do amazing things with.
And that's the part that, but it isn't
like you have to have done 10 years
of study to get to the point where
you can do the experiments. That's the
cool thing. You can do experiments day one
basically. That's the
amazing thing about, and you've actually put
the tools out there as beautiful
and mysterious.
There's still, I would say, maybe
you can correct me. It feels like there's a huge
number of low-hanging fruit
on the mathematical side, at least,
not the physics side, perhaps.
No, look, on the
okay, on the physics side
we are definitely
in harvesting mode.
Of which fruit?
The low-hanging ones? The low-hanging ones.
I mean, basically, here's the thing.
There's a certain list of, you know,
here are the effects in quantum mechanics,
here are the effects in general relativity.
It's just like industrial harvesting.
It's like, can we get this one, this one,
this one, this one, this one, and the
thing that's really, you know, interesting
and satisfying, and it's like, you know,
is one climbing the right mountain, does one have
the right model? The thing that's just
amazing is, you know,
we keep on like, are we going to get this one?
How hard is this one?
It's like, oh, you know,
it looks really hard, it looks really hard.
Oh, actually, we can get it.
And you're
continually surprised. I mean, it seems like
you've been following your progress.
It's kind of exciting, all the in-harvesting
mode, all the things you're picking up along the way.
Right, right. No, I mean, it's the thing that is,
I keep on thinking it's going to be more
difficult than it is. Now, that's a, you know,
who knows what, I mean, the one
thing, so the
thing that's been a, was a
big thing that I think we're pretty close
to, I mean, I can give you a little bit
of the roadmap, it's sort of interesting to see
it's like, what are particles?
What are things like electrons? How do they really work?
Are you close to get, like, what,
what's a, are you close
to trying to understand, like, the atom,
the electrons, the protons?
Okay, so this is the stack.
So the first thing we want to understand
is the quantization
of spin. So particles,
they kind of spin, they
have a certain angular momentum.
That angular momentum, even though
the masses of particles are all over the
place, you know, the electron has a mass of
0.511 MeV, but
you know, the proton is 938 MeV,
etc., etc., etc., they're all kind of random numbers.
The, the spins
of all these particles are either integers or half integers.
And that's the fact that was discovered
in the 1920s, I guess.
The,
I think that
we are close to understanding
why spin is quantized.
And that's a, and it appears
to be a quite elaborate mathematical
story about homotopy groups in
twister space and all kinds of things.
But bottom line is
that seems within reach.
And that's, that's a big deal because that's a
very core feature of understanding how
particles work in quantum mechanics.
Another core feature is
this difference between particles that obey the
exclusion principle and sort of stay
apart that leads to the stability
of matter and things like that.
And particles that love to get together and be in the same
state, things like photons
that, and that's what leads to
phenomena like lasers
where you can get sort of coherently everything
in the same state.
That difference is
the particles of integer spin or bosons
like to get together in the same state.
The particles of half integer spin of fermions
like electrons that they
tend to stay apart.
And so the question is, can we,
can we get that in our models?
And well, just the last few days,
I think we made, I mean,
I think the story of,
I mean, it's, it's, it's one of these things
that we're really close.
It's just connected fermions and bosons.
Yeah, yeah, yeah. So this was what happens is
what seems to happen, okay?
It's, you know, subject to revision
next, even in the next few days.
But what seems to be the case is that
bosons are associated with
essentially merging in multi-way graphs
and fermions are associated
with branching in multi-way graphs
and that essentially the
exclusion principle is the fact
that in branchial space
things have a certain extent
in branchial space that
in which things are being sort of forced
to part in branchial space, whereas
the case of bosons, they get, they, they
come together in branchial space.
And the real question is, can we explain
the relationship between that and these things
called spinners, which are the representation
of half integer spin particles
that have this weird feature that usually
when you go around 360 degree rotation,
you get back to where you started from.
But for a spinner, you don't get back to
it takes 720 degrees of rotation
to get back to where you started from
and we are just, it feels
like we are, we're just incredibly
close to actually having that understanding
how that works. And it turns out
it looks like, my current speculation
is, that it's as simple as
the directed
hypergraphs versus undirected
hypergraphs of the
relationship between spinners and vectors.
So which is just...
Yeah, that would be interesting if these are all these kind of
nice properties
of this multi-way graphs of
branching and rejoining.
Spinners have been very mysterious.
And if that's what they turn out to be
there's going to be an easy explanation of what's going on.
It's directed versus undirected.
It's just, and that's why there's only two different cases.
It's...
Why are spinners important in quantum mechanics?
Can you just give a...
Yeah, so spinners are important because they are
they're the representation
of electrons which have
half an inch of spin.
They are the wave functions
of electrons are spinners.
Just like the wave functions of photons
are vectors, the wave functions
of electrons are spinners.
And they have this property
that when you rotate
by 360 degrees
they come back to minus one
of themselves and take 720
degrees to get back to the original
value. And they are a consequence
of...
We usually think of
rotation in space
as being, you know, when you have
this notion of rotational invariance
and rotational invariance
as we ordinarily experience it
doesn't have the feature. You know, if you go
360 degrees you go back to where you started from
but that's not true for electrons.
And so that's
why understanding how that works is important.
Yeah, I've been playing with Mobius
strip quite a bit lately just for fun.
Yes.
It adds some funk. It has the same
kind of funky properties. Yes, right, exactly.
You can have this so-called belt trick
which is this way of taking an extended object
and you can see properties like spinners
with that kind of extended object.
Yeah, it would be very cool if there's
somehow connects the directive or some directive.
I think that's what it's going to be. I think it's going to be as simple
as that. But we'll see.
I mean, this is the thing that, you know,
this is the big sort of bizarre surprise
is that, you know, because, you know,
I learnt physics is probably
let's say, let's say
a fifth generation in the sense that, you know,
if you go back to the 1920s and so on,
there were the people who were originating
quantum mechanics and so on. Maybe it's a little less
than that. Maybe I was like a
third generation or something. I don't know.
But, you know, the people from whom
I learnt physics were the people
who were, you know, have been students
of the students of the people
who originated the current understanding
of physics. And we're now at, you know,
probably the seventh generation of physicists
or something from the early days
of 20th century physics.
And, you know, whenever a field
gets that many generations
deep, it seems
the foundations seem quite inaccessible
and they seem, you know, it seems
like you can't possibly understand that. We've
gone through, you know, seven academic
generations and that's been,
you know, that's been this thing that's been
difficult to understand for that long.
It just can't be that simple.
But in a sense,
maybe that journey takes you
to a simple explanation
that was there all along as the whole.
Right, right, right. I mean, you know, and the thing,
for me personally, the thing that's been quite
interesting is, you know, I didn't expect
this project to work in this way.
And I, you know, but I had
this sort of weird piece of personal history
that I used to be a physicist. And I
used to do all this stuff and I know,
you know, the standard canon
of physics, I knew it very
well. And, you know,
but then I'd been working on this kind of
computational paradigm for basically 40
years. And
the fact that, you know, I'm sort of now
coming back to, you know,
trying to apply that in physics,
it kind of felt like that journey was
necessary. Was this,
when did you first try to play with a
hypograph?
Yeah, so what I had was,
okay, so this is again, you know,
one always feels dumb after the fact.
It's obvious
after the fact. But so
back in the early 1990s,
I realized that using
graphs as a sort of
underlying thing underneath space and time
was going to be a useful thing to do.
I figured out about multi-way systems.
I figured out
the things about general relativity I had figured out by the end
of the 1990s.
But I always felt there was a certain
inelegance because I was using these graphs
and there were certain constraints on these graphs
that seemed like they were kind of awkward.
It was kind of like, you can pick,
it's like you couldn't pick any rule.
It was like pick any number, but the number
has to be prime. It was kind of like,
it was kind of an awkward special constraint.
I had these trivalent graphs,
graphs with just three connections
from every node. Okay, so
but I discovered a bunch of stuff with that.
I thought it was kind of inelegant.
And, you know, the other piece of sort of
personal history is obviously I spent my life
as a computational language designer.
And so the story of
computational language design is a story of
how do you take all these random ideas
in the world and kind of grind them down
into something that is
computationally as simple as possible.
And so, you know, I've been very
interested in kind of simple
computational frameworks for representing
things and have,
you know, ridiculous amounts of experience
in trying to do that.
And actually all of those trajectories of your
life kind of came together. So
you make it sound like you could have come up with
everything you're working on now
decades ago, but in reality
Look, two things slowed me down.
I mean, one thing that slowed me down was
I couldn't figure out how to make it elegant.
And that turns out
hypergraphs were the key to that. And that I
figured out about less than
two years ago now.
And the other
I mean, I think so that was
that was sort of a key thing.
Well, okay, so the real embarrassment of this project
is that
the final structure that we have
that is the foundation
for this project is
basically a
kind of an idealized version
of formalized version of the
exact same structure that I've used
to build computational languages for more than
40 years. But it took me
but I didn't realize that.
And you know, and there yet
may be other, so we're focused on physics now,
but I mean
that's what the new kind of science is about, same
kind of stuff. And this in terms
of mathematically,
the beauty of it. So there could be entire
other kind of objects
that are useful for like
we're not talking about, you know, machine
learning, for example,
maybe there's other variants of the hypergraph that
are very useful for
see whether the multi-way graph or machine
learning system is interesting.
Okay, let's leave it at
that. That's conversation number three.
That's that's that's we're not going to go there right now.
But one of the things
you've mentioned is
the space of all possible
rules that we kind of discussed a little bit
that
you know, there could be, I guess, the
set of possible rules as infinite.
Right. Well, so here's
the big sort of one of the conundrums
that that I'm kind of
trying to deal with is let's
say we think we found the rule
for the universe. And we say
here it is, you know, write it down.
It's a little tiny thing. And then
we say, gosh, that's really weird.
Why did we get that one?
Right. And then we're in this whole
situation because let's say
it's fairly simple. How did we
come up the winners getting one of the
simple possible universe rules?
Why didn't we get some incredibly
complicated rule? Why did we get
one of the simpler ones? And and that's a thing
which, you know, in the history of science,
you know, the whole sort of story of
Copernicus and so on
was, you know, we used to think the Earth
was the center of the universe, but now we find out
it's not. And we're actually just in some, you know,
random corner of some random galaxy
out in this big universe. There's nothing
special about us.
So if we get, you know,
universe number 317
out of all the infinite number of possibilities,
how do we get something that small and
simple? Right. So I was very confused
by this. And it's like, what are we going to
say about this? How are we going to explain
this? And I thought it was might be one of
these things where you just, you know, you can get
it to the threshold and then you find
out its rule number such and such and you just
have no idea why it's like that. Yeah.
Okay. So then I realized
it's actually more bizarre than that.
Okay. So we talked about
multi-way graphs. We talked about this
idea that you take these underlying
transformation rules on these hypergraphs
and you apply them
wherever the rule can apply,
you apply it. And that makes this whole
multi-way graph of possibilities.
So let's go a little bit weirder.
Let's say that at
every place, not only do you apply a particular
rule in all possible ways
it can apply, but you apply
all possible rules in all possible
ways they can apply.
As you say, that's just crazy. That's
way too complicated. You're never going to be able to conclude
anything. Okay.
However, turns out
that
some kind of invariance. Yeah.
Yeah.
And that would be amazing.
Right. So
this thing that you get is this kind of
rural multi-way graph. This multi-way
graph that is a branching of rules
as well as a branching of possible
applications of rules.
This thing has causal invariance.
It's an inevitable feature
that it shows causal invariance. And that means
that you can take different
reference frames, different ways of slicing this
thing and
they will all in some sense be equivalent.
If you make the right translation, they
will be equivalent.
Okay. So the basic point here is
if that's true, that would be
beautiful. It is true.
So it's not
just an intuition. There is some
mathematical hints. No, no, no. There's real mathematics
behind this.
Okay.
Yeah.
That's amazing.
So by the way, the mathematics it's connected
to is the mathematics of higher category
theory and group voids and things like
this, which I've always been afraid of.
But now I'm finally
wrapping my arms around it.
But it's also related to
it also relates to
computational complexity theory.
It's also deeply related to the
P versus NP problem and other things like
this. Again, seems completely bizarre
that these things are connected. But here's why it's connected.
This
space of all possible
okay, so a Turing machine.
Very simple model of computation.
You just got this tape
where you write down, you know, ones and
zeros or something on the tape and you have
this rule that says, you know,
you change the number, you move the head
on the tape, etc.
You have a definite rule for doing that.
A deterministic Turing machine
just does that deterministically.
Given the configuration of the tape,
it will always do the same thing.
A non-deterministic Turing machine
can have different choices that it makes
every step.
And so, you know,
this stuff, you probably teach this stuff.
It
you know, so a non-deterministic
Turing machine has this set
of branching possibilities, which is
in fact one of these multi-way graphs.
And in fact, if you say
imagine the extremely
non-deterministic Turing machine, the Turing
machine that can just do
that takes any possible
rule at each step. That is
this RULEAL multi-way graph.
The set of
possible histories of that
extreme non-deterministic Turing machine
is a RULEAL multi-way graph.
What term are you using? RULEAL?
RULEAL.
Weird word. Yeah, it's a weird word.
RULEAL multi-way graph.
Okay, so this, so that
I'm trying to think of
I'm trying to think of the space
of rules.
These are basic transformations.
So in a Turing machine, it's
like it says move left, move
you know, if it's a one, if it's
a black square under the head
move left and right a green
square. That's a RULEAL.
That's a very basic rule, but I'm trying to see
the rules on the hypergraphs
how rich of the programs can they be
or do they all ultimately just map
into something simple?
Yeah, they're all, I mean, hypergraphs
that's another layer of complexity on this whole
thing. You can think about these in
terms of hypergraphs, but Turing
machines are a little bit similar.
They're a lot simpler.
So if you look at these extreme
non-deterministic Turing machines, you're
mapping out all the possible
non-deterministic paths that the Turing
machine can follow.
And if you ask the question
can you reach, okay, so
a deterministic Turing machine follows
a single path. The non-deterministic
Turing machine fills out this whole
sort of ball of possibilities.
And so then the P versus
NP problem ends up being
questions about, and we haven't
completely figured out all the details of this, but
it basically has to do with questions
about the growth of that
ball relative to what happens
with individual paths and so on.
So essentially there's a geometrization
of the P versus NP problem that comes out of this.
That's a sideshow, okay?
The main event here
is the statement that
you can look at this
multi-way graph
where the branches correspond
not just to different applications of a single rule
but to different applications, to applications
of different rules, okay?
And that then, that
when you say
I'm going to be an observer
embedded in that system, and I'm going
to try and make sense of what's going on in the system.
And to do that
I essentially am picking a reference
frame. And that turns out
to be
well, okay, so the way this comes out essentially
is the reference frame you pick
is the rule that you infer
is what's going on in the universe.
Even though
all possible rules are being run
although all those
possible rules are in a sense giving
the same answer because of causal invariance.
But what you see
could be completely
different. If you pick different reference frames
you essentially have a different
description language for describing the universe.
Okay, so how does
what does this really mean in practice? So
imagine there's us.
We think about the universe in terms of space
and time and we have various kinds of description models
and so on. Now let's imagine
the friendly aliens for example,
right? How do they describe
their universe? Well
our description of the universe probably
is affected by the fact that
we are about the size we are
a meter-ish tall, so to speak.
We have brain processing speeds
about the speeds we have.
We're not the size of planets, for example
where the speed of light really would matter.
You know, in our everyday life
the speed of light doesn't really matter.
Everything can be, you know, the fact that
speed of light is finite is irrelevant. It could as well be infinite.
We wouldn't make any difference.
You know, it affects the
ping-times on the internet. That's about
the level of
how we notice the speed of light
in our sort of everyday existence. We don't really notice it.
And so
we have a way of describing the universe
that's based on our
sensory, you know, our senses
these days
also on the mathematics we've constructed and so on.
But the realization
is it's not the only way to do it.
There will be completely
utterly incoherent descriptions of the universe
which
correspond to different reference frames
in this sort of rural space.
In the rural space. That's fascinating.
So we have some kind of reference
frame in this rural space. Right.
And from that
that's why we are attributing
this rule to the universe.
So in other words, when we say
why is it this rule and not another,
the answer is just,
you know, shine the light back on us,
so to speak. It's because of the reference
frame that we've picked in our way
of understanding what's happening in this sort of
space of all possible rules and so on.
But also in the space
from this reference frame
because of the rule,
the
invariance
that's simple
that the rule on which the
universe, with which
you can run the universe might
as well be simple. Yes.
Yes. Okay. So here's another point.
So this is again, these are a little bit
mind twisting in some ways, but
another thing that's sort of we know
from computation
is this idea of computation universality.
The fact that
given that we have a program that runs on one kind of
computer, we can as well,
you know, we can convert it
to run on any other kind of computer. We can
emulate one kind of computer with another.
So that might lead you to say,
well, you think you have the rule for the
universe, but you might as well be running it
on a Turing machine because we know we can
emulate any computational
rule on any kind of
machine. And that's essentially the same
thing that's being said here.
That is that what we're doing is we're
saying these
different interpretations of physics
correspond to essentially
running physics on
different underlying, you know,
thinking about the physics as running
with different underlying rules as if
different underlying computers were running
them. But
because of computation universality
or more accurately because of this principle
of computational equivalence thing of mine,
there's that they are
these things
are ultimately equivalent. So the
only thing that is the ultimate fact
about the universe, the ultimate fact
that doesn't depend on any of these, you know,
we don't have to talk about specific rules, etc,
etc, etc. The ultimate fact is
the universe is computational
and it is
the things that happen in the universe
are the kinds of computations
that the principle of computational equivalence
says should happen. Now
that might sound like you're not
really saying anything there, but you are
because
you could in principle have a hypercomputer
that
things that take an ordinary computer
an infinite time to do, the hypercomputer can just
say, oh, I know the answer. It's this
immediately.
What this is saying is the universe is not
a hypercomputer. It's
not simpler than
an ordinary Turing machine type computer.
It's exactly like
an ordinary Turing machine type computer.
And so that's the, that's in the end
the sort of net, net
conclusion is that's the thing
that is the sort of the hard
immovable fact about the universe.
That's sort of the fundamental
principle of the universe is that
it is computational and not
hypercomputational and not sort
of inferocomputational. It is
this level of computational ability
and it's
it kind of has and that's sort of the
the core fact.
But now, you know, this
idea that you can have these different kind
of rural reference frames,
these different description languages for
the universe, it makes
me, you know, I used to think, okay,
you know, imagine the aliens, imagine
the extraterrestrial intelligence thing,
you know, at least they experience
the same physics. Right. And now I've
realized, isn't true. They have
a different rural frame. That's fascinating.
They can end up with
a description
of the universe that is utterly, utterly
incoherent with ours.
And that's also interesting in terms of
how we think about, well, intelligence,
the nature of intelligence and so on, you know,
I'm fond of the quote, you know, the
weather has a mind of its own because
these are, you know, these are sort of
computationally that that system
is computationally equivalent to
the system that is our brains and so
on. And what's different is
we don't have a way to understand,
you know, what the weather is trying to do,
so to speak. We have a story about what's happening
in our brains. We don't have a sort of connection
to what's happening there.
So we actually, it's funny, last
time we talked, maybe
over a year ago,
we talked about how
it was more based on your work
with Arrival,
we talked about how would we communicate with
alien intelligence is
can you maybe comment on
how we might
how the Wolfram Physics Project
changed your view of how we might be able to communicate
with alien intelligence. Like if they showed
up, is it possible
that because of our
comprehension
of the physics of the world might
be completely different? We would
just not be able to communicate
at all. Here's the thing,
you know, intelligence
is everywhere. The fact, this
idea that there's this notion of, oh,
there's going to be this amazing extra-restral intelligence,
and it's going to be this unique
thing, it's just not true.
It's the same thing. You know, I think
people will realize this about the time
when people decide that artificial intelligences
are kind of just
natural things that are like human intelligences.
They'll realize
that extra-restral intelligences
or intelligences
associated with physical systems and so on,
it's all the same kind of thing.
It's ultimately computation. It's all the same.
It's all just computation. And the issue is
can you
are you sort of inside it? Are you
thinking about it? Do you have
sort of a story you're telling yourself
about it? And, you know,
the weather could have a story it's telling itself
about what it's doing. We just
it's utterly incoherent
with the stories that we tell ourselves
based on how our brains work. I mean,
ultimately it must be
a question whether we can
align
with the kind of intelligence
in the systematic way of doing it.
Right. So the question is in the space of all possible
intelligences, what's the
how do you think about the distance
between description languages
for one intelligence versus another?
And needless to say, I have thought about this.
And, you know,
I don't have a great
answer yet, but I think that's
a thing where there will be things that can be said.
And there'll be things that where you can sort of
start to characterize, you know,
what is the translation distance
between
this, you know,
version of the universe or this,
you know, kind of set of computational rules
and this other one. In fact, okay,
so this is a, you know, there's this
idea of algorithmic information theory. There's this
question of sort of what is the
when you have some
something, what is the sort of shortest
description you can make of it, where that
description could be saying, run this
program to get the thing.
Right. So I'm pretty sure
that
that the
that
there will be a physicalization of the idea
of algorithmic information
and that
okay, this is again a little bit bizarre, but
so I mentioned that there's the
speed of light, maximum speed of information
transmission in physical space.
There's a maximum speed of information transmission
in branchial space, which is a maximum entanglement
speed. There's a maximum
speed of information transmission in rural
space, which has to do with
a maximum speed of translation
between different
description languages.
And again, I'm not fully
wrapped my brain around this one.
Yeah, that one just blows my mind to think about
that, but that starts getting closer to the
yeah, the
the intelligence. It's kind of a physicalization.
Right. It's a, and it's also a physicalization
of algorithmic information
and I think there's probably a connection between
I mean, there's probably a connection between
the notion of energy and some of these
things, which again, I
hadn't seen all this coming. I've
always been a little bit resistant to the idea of connecting
physical energy to things
in computation theory, but I think that's
probably coming. And that's essentially
at the core with the physics project
is that you're connecting
information theory
with physics. Yeah, it's
computation and computation
with our physical universe. Yeah, right.
I mean, the fact that our physical universe
is right, that we
can think of it as a computation and that
we can have discussions like
you know, the theory of the physical universe
is the same
kind of a theory as the p versus mp
problem and so on is
really, you know, I think that's really
interesting. And the fact that
well, okay, so this
kind of brings me to one more
thing that I have to in terms of this sort of unification
of different ideas, which
is metamathematics. Yeah, let's talk
about that. You mentioned that earlier. What the heck
is metamathematics
and so here's what
here's okay. So what is mathematics?
Mathematics
sort of
at a lowest level, one
thinks of mathematics as you have certain
axioms, you say
you know, you say things like X
plus Y is the same as Y plus X. That's
an axiom
about addition. And then you say we got
these axioms and we
derive all these theorems that fill
up the literature of mathematics. The
activity of mathematicians
is to derive all these theorems.
Actually, the axioms of mathematics
are very small.
You can fit, you know, when I did my
new kind of science book, I fit
all of the standard axioms of mathematics on
basically a page and a half.
It's not much stuff. It's like
a very simple rule from which
all of mathematics arises.
The way it works though is a little
different from the way things work
in sort of
a computation, because
in mathematics what you're interested in is a proof.
And the proof says
from here, you can use
from this expression, for example,
you can use these axioms to get
to this other expression. So that proves these two
things are equal. Okay, so
we can begin to see
how this is going to work. What's going to happen
is there are paths in metamathematical
space. So what
happens is each
two different ways to look at it, you can
just look at it as mathematical expressions
or you can look at it as mathematical
statements, postulates or something.
But either way, you think of these things
and they are connected
by
these axioms. So in other words,
you have some fact
or you have some expression,
you apply this axiom, you get some other expression.
And in general,
given some expression, there may be
many possible different expressions
you can get. You basically build up a
multi-way graph. And a
proof is a path
through the multi-way graph that goes from
one thing to another thing.
The path tells you
how did you get from one thing to the other thing.
It's the story of how you got from this
to that. The theorem is
the thing at one end is equal to the thing at the other
end. The proof is
the path you go down to get from one thing
to the other. You mentioned that Gato's
incompleteness theorem is the natural
it fits naturally there.
So what happens there is that
the Gato's theorem is basically
saying that there are paths of infinite
length. That is
there's no upper bound. If you know these two
things, you say, I'm trying to get from here to here,
how long do I have to go?
You say, well, I've looked at all the paths
of length 10. Somebody says, that's not good
enough. That path might be of length
a billion. And there's no
upper bound on how long that path is. And that's
what leads to the incompleteness theorem.
The thing that
is kind of an emerging
idea is, you can start
asking, what's the analog of Einstein's equations
in metamathematical space?
What's the analog of a black hole in metamathematical
space?
It's fascinating to model all the mathematics
in this way.
This is mathematics in bulk.
So human mathematicians
have made a few million theorems.
They published a few million theorems.
But imagine the infinite future of mathematics.
Apply something to mathematics
that mathematics likes to apply to other
things. Take a limit. What is the
limit of the infinite future of mathematics?
What does it look like? What is
the continuum limit of mathematics?
As you just fill in more and more
and more theorems, what does it look like?
What does it do? How does what kinds
of conclusions can you make? So, for
example, one thing I've just been doing
is taking Euclid. So Euclid, very
impressive. He had 10 axioms.
He derived 465
theorems. Okay? His
book, you know, that was
the sort of defining book of mathematics
for 2,000 years.
So you can actually map out.
I actually did this
20 years ago, but I've done it more seriously
now. You can map out the theorem
dependency of those 465
theorems. So from the axioms
you grow this graph, it's actually a
multi-way graph, of how all these
theorems get proved from other theorems.
And so you can ask questions about,
you know, you can ask things like
what's the hardest theorem in Euclid? The answer
is the hardest theorem is that there are 5
platonic solids. That turns out to be the
hardest theorem in Euclid. That's actually
his last theorem in all his books.
What's the hardness? The distance you have to
travel? Yeah, let's say it's 33
steps from the longest
path in the graph is 33 steps. So that's
the, there's a 33
step path you have to follow to go from
the axioms according to Euclid's
proofs to the statement there are 5
platonic solids. So
okay, so then the
question is in
what does it mean
if you have this map
okay, so in a
sense this metamathematical space
is the infrastructural space of
all possible theorems that you could prove
in mathematics. That's the
geometry of metamathematics.
There's also the geography
of mathematics. That is where did people
choose to live in space?
And that's what, for example,
exploring the sort of empirical
mathematics as Euclid is doing that.
You could put each individual, like human
mathematician, you could embed them into
that space. I mean, they kind of live.
They represent a path. The little path.
Maybe a set of paths. Right.
A set of axioms that are chosen.
Right, so for example, here's an example
of a thing that I realized.
So one of the surprising things about,
well, the two surprising facts about math.
One is that it's hard, and the other
is that it's doable.
So first question is, why is math hard?
You know, you've got these axioms, they're
very small. Why can't you just
solve every problem in math easily?
Yeah, it's just logic. Right.
Well, logic happens to be a particular
special case that does have certain simplicity
to it. But general mathematics,
even arithmetic, already
doesn't have the simplicity that logic has.
So why is it hard? Because
of computational irreducibility.
Right.
Because what happens is, to know
what's true, and this is this whole
story about the path you have to follow
and how long is the path, and Goethe
theorem is the statement, there could be
an infinite, that the path is not a bounded
length, but the fact that the path
is not always compressible to something
tiny is the story of computational
irreducibility. So that's
why math is hard. Now, the next question
is, why is math doable?
Because it might be the case that most
things you care about don't have finite length
paths. Most things you care about
might be things where you get lost
in the sea of computational irreducibility
and worse, undecidability.
That is, there's just no finite
length path that gets you there.
You know, why is mathematics doable?
You know, Goethe
proved his incompleteness theorem in 1931.
Most working mathematicians
don't really care about it. They just go ahead
and do mathematics, even though
it could be that the questions they're asking
are undecidable. It could have been that
Fermat's last theorem is undecidable.
It turned out it had a proof. It's a long
complicated proof. The twin prime
conjecture might be undecidable.
The Riemann hypothesis might be undecidable.
These things might be
the axioms of mathematics might not
be strong enough to
reach those statements. It might be the case
that depending on what axioms you choose
you can either say that's true or that's not
true. And by the way
Fermat's last theorem, it could be
a shorter path.
Absolutely. Yeah, so the notion of
geodesics in mathematical space
is a notion of shortest proofs
in mathematical space.
And that's a, you know, human mathematicians
do not find shortest paths,
nor do automated theorem provers.
But the fact, and by the way
this stuff is so
bizarrely connected. I mean, if you're
into automated theorem proving
there are the so-called critical pair lemmas
in automated theorem proving, those are
branch pairs in our
that in multi-way graphs.
Let me just finish on the why mathematics
is doable. Yes, the second part.
You know why it's hard. Why is it doable?
Right. Why do we not just get lost
in undecidability all the time?
So, and here's another
fact is in doing computer
experiments and doing experimental
mathematics you do get lost
in that way. When you just say
I'm picking a random
integer equation, how do I
does it have a solution or not?
And you just pick it at random without
any human sort of path getting
there. Often
it's really, really hard. It's really hard
to answer those questions. We just pick them at random
from the space of possibilities.
But what's, what I think is happening
is, and that's a case where you just
fell off into this ocean of sort of
irreducibility and so on. What's happening
is human mathematics
is a story of building a path.
You started off, you're always
building out on this path
where you are proving things.
You've got this proof trajectory
and you're basically, human mathematics
is the sort of the exploration
of the world
along this proof trajectory
so to speak. You're not just
parachuting in
from anywhere
you're following Lewis and Clark
or whatever. You're actually
doing the path
and the fact that you are
constrained to go along that path
is the reason you don't end up with a lot.
Every so often you'll see a little piece of undecidability
and you'll avoid that part of the path
but that's basically the story of why
human mathematics has seemed to be doable.
It's a story of exploring
these paths that
are, by their nature, they have been constructed
to be paths that can be
followed and so you can follow them further.
Now, you know, why is this relevant
to anything? So, okay, so here's
the, my
my belief.
The fact that human mathematics works that way
is
I think there's some sort of connections
between the way that
observers work in physics
and the way that the axiom systems of mathematics
are set up to make mathematics
be doable in that kind of way.
And so, in other words
in particular, I think there is an analog
of causal invariance
which I think is, and this is again
in sort of the upper reaches of mathematics
and stuff that
are, it's a thing
there's this thing called homotopy type theory
which is an abstract
it's came out of category theory
and it's sort of an abstraction of mathematics.
Mathematics itself is an abstraction
but it's an abstraction
of the abstraction of mathematics
and there is a thing called the univalence axiom
which is a sort of a
a key axiom
in that set of ideas
and I'm pretty sure the univalence axiom
is equivalent to causal invariance.
What was the term used again?
Univalence. Is that something
for somebody like me accessible?
There's a statement of it
that's fairly accessible.
I mean, the statement of it is
basically
it says things which are equivalent
can be considered to be
identical.
In which space?
Yeah, it's in higher category.
In category.
So it's a
the thing just to give a sketch of how that works
so category theory is an attempt
to idealize
it's an attempt to sort of have a formal theory
of mathematics that is at a sort of higher
level than mathematics.
It's where you just think about these
mathematical objects
and these categories of objects
and these morphisms
these connections between categories.
So it turns out the morphisms and categories
at least weak categories
are very much like
the paths in our hypergraphs and things.
And it turns out
again, this is where it all gets
crazy. I mean, it's the fact that these
things are connected is just bizarre.
So category theory
our causal
graphs are like second
order category theory
and it turns out you can take
the limits of infinite order category theory
so just give roughly
the idea. This is a
roughly explainable idea. So
a mathematical proof
will be a path that says
you can get from this thing to this other thing
and here's the path that you get from this thing to this other thing.
But in general, there may be many paths
many proofs
that get you many different paths
that all successfully go from this thing to this other thing.
Now
you can define a higher order proof
which is a proof of the equivalence
of those proofs.
So you're saying there's a path between
those proofs essentially? Yes, a path between
the paths.
And so you do that, that's the sort of second order
thing. That path between the paths
is essentially related
to our causal graphs.
Then you take the limit
path between path
between path, the infinite limit
that infinite limit turns out
to be our Rulial Multi-Way System.
Yeah, the Rulial
the Rulial Multi-Way System, that's a fascinating
thing both in the physics world and
as you're saying, that's
fascinating. I'm not sure I've loaded it
in completely. Well, I'm not sure I have
either and it may be one of these things
where in another five
years or something, it's like, this was obvious
but I didn't see it. Now, but the thing
which is sort of interesting to me is that
there's sort of an upper reach of
mathematics, of the abstraction of mathematics.
This
thing, there's this mathematician
called Grothendieke who's generally viewed
as being sort of one of the most abstract
sort of creator of the most abstract mathematics
of 1970s-ish
time frame.
And one of the things that
he constructed with this thing, he called the
Infinity Groupoid
and he has this sort of hypothesis about
the inevitable appearance of geometry
from essentially logic
in the structure of this thing.
Well, it turns out this Rulial Multi-Way System
is the Infinity Groupoid.
So it's this
limiting object and this
is an instance
of that limiting object.
So what to me is, I mean, again, I've
been always afraid of this kind of mathematics
because it seemed incomprehensibly
abstract to me.
But what's
what I'm sort of excited about with this is that
that we've sort of
concretified the way that you can reach
this kind of mathematics
which makes it
both seem more relevant and also
the fact that that, you know, I don't yet
know exactly what mileage we're going to get
from using the sort of
apparatus that's been built in those areas
of mathematics to analyze what we're doing.
But the thing that's- So both ways
using the mathematics and understanding what you're doing
and using what you're doing computationally
to understand that- Right. So for example
the understanding of
metamathematical space, one
of the reasons I really want to do that
is because I want to understand quantum mechanics better.
And that
what you see, you know,
we live that
kind of the multi-way graph of mathematics
because we actually know this is a theorem
we've heard of. This is another one we've heard of.
We can actually say these are actual
things in the world that we relate to
which we can't really do as
readily for the
physics case. And so it's kind of a way
to help my intuition. It's also,
you know, there are bizarre things like
what's the analog of Einstein's equations
in metamathematical space?
What's the analog of a black hole?
It turns out it looks like
not completely sure yet,
but there's this notion of non-constructive
proofs in mathematics.
And I think those relate to
well, actually
they relate to things
related to event horizons.
So the fact that you can take
ideas from physics
like event horizons- And map them into the same kind of
space metamathematical space.
Do you think there will be-
do you think you might stumble
on some breakthrough ideas
in theorem-proving
like for- from the
other direction? Yeah, yeah, yeah. No, I mean
what's really nice is that we are using
so this
absolutely directly maps to theorem-proving.
So paths and multi-way graphs, that's what a theorem-prover
is trying to do. But I also mean like
automated theorem-prover. Yeah, yeah, yeah.
That's what- Right, so the finding of paths,
the finding of shortest paths, or finding of paths
at all is what automated theorem-provers
do. And actually
what we've been doing. So we've, you know, we've
actually been using automated theorem-proving both
in the physics project to prove things
and using that
as a way to understand multi-way graphs
and because
what an automated theorem-prover is doing
is it's trying to find a path through a
multi-way graph. And its critical
pair lemmas are precisely
little stubs of
branch pairs going off into branched
space. And that's- I mean it's
really weird. You know, we have these visualizations
in wealth and language of
proof graphs
from our automated theorem-proving system.
And they look reminiscent of- Well,
it's just bizarre because we made these up a few years
ago and they have these little triangle
things and they are, we
didn't quite get it right. We didn't quite get the
analogy perfectly right, but it's very close.
You know, just to say in terms of
how these things are connected.
So there's another bizarre connection that I
have to mention because
which is
which again, we don't fully know,
but it's a connection to
something else you might not have thought was in
the slightest bit connected, which
is distributed blockchain-like things.
Now you might figure out that that's-
you would figure out that that's connected
because it's a story of distributed computing.
And the issue, you know, with a blockchain
you're saying there's going to be this one
ledger that
globally says this is what
happened in the world. But
that's a bad deal
if you've got all these different transactions that are
happening and, you know, this
transaction in country A
doesn't have to be
reconciled with the transaction in country B
at least not for a while.
And that story
is just like what happens with our causal
graphs. That whole
reconciliation thing is just like what happens with
light cones and all this kind of thing.
Yes, because that's where the causal invariance comes into play.
That's, you know, most of your
conversations are about physics, but
it's kind of funny that
this probably
and possibly might have even bigger
impact
and revolutionary ideas
and totally other disciplines.
Right, so the question is
why is that happening, right? And the
reason it's happening, I've thought about this
obviously because I like to think about these
meta-questions of, you know, what's
happening is this model that we have
is an incredibly minimal model.
And once you have an incredibly
minimal model, and this happened
with cellular automator as well, cellular automator
are an incredibly minimal model.
And so it's inevitable
that it gets you, it's sort of an upstream
thing that gets used in lots of different places.
And it's like, you know,
the fact that it gets used, you know, cellular automator
is sort of a minimal model of like, say,
road traffic flow or something. And they're also a minimal model
of something in, you know, chemistry
and they're also a minimal model of something in
epidemiology, right?
It's because they're such a simple model that they can
apply to all these different things.
Similarly, this model that we have of the physics
project is another
cellular automator
are a minimal model of
basically of parallel computation
where you've defined space and time.
These models are
minimal models where you have not defined space
and time. And they have been very
hard to understand in the past.
But I think the
perhaps the most important breakthrough there
is the realization that these are models
of physics and therefore
that you can use everything that's been developed in
physics to get intuition
about how things like that work.
And that's why you can potentially use
ideas from physics to get intuition
about how to do parallel computing
and because the underlying
model is the same.
And but we have all of this
achievement in physics. I mean, you know, you might
say, oh, you've come up with the fundamental theory of physics
that throws out what people have done in physics
before. Well, it doesn't. But also
the real power is to use
what's been done before in physics
to apply it in these other places. Yes.
And this kind of brings up.
I know you probably don't
particularly
love commenting on the work of others.
But let me let me bring up
a couple of personalities just because it's fun
and people are curious about it. So there's
a
Sabine Hassenfelder.
I don't know if you're familiar with her.
She she wrote
this book that I need to
read. But I
forget what the title is, but it's
beauty leads us astray in physics
is a subtitle or something like that,
which so much about what we're
talking about now, like this simplification
is a
humans seems to be beautiful.
Like there's a certain intuition
with physicists, with people
that a simple
theory like this reducibility
pockets of reducibility is the ultimate goal.
And I think what she tries to
argue is
no, we just need to come up
with theories that are
just really good at predicting physical phenomena.
It's okay to have a bunch of
disparate theories
as opposed to trying to chase this
beautiful
theory of everything is the ultimate beautiful
theory, a simple one.
You know, what's your response
to that? Well, so what you're quoting
is I don't know the Sabine
Hassanfelder's, you know, exactly
what she said, but I mean,
I'm quoting the title of a book.
Let me
respond to what you were describing, which
may or may not have anything to do with
what Sabine Hassanfelder
says or thinks.
Sorry Sabine.
Sorry for misquoting.
The question is,
is beauty
a guide to whether something is correct?
Which is kind of also the story of Occam's
razor. You know, if you've got a bunch of
different explanations of things, you know,
is the thing that is the simplest
explanation likely to be the correct explanation?
And there are situations where that's true
and there are situations where it isn't true.
Sometimes in human systems, it is true
because people have kind of, you know, an evolutionary
system, sometimes it's true because
it's sort of been kicked to the point where it's minimized.
But, you know,
in physics, does Occam's
razor work? You know, is there
a simple, quotes, beautiful
explanation for things, or is it a big
mess? You know, we don't
intrinsically know. You know, I think
that the, I wouldn't, before
I worked on the project in recent
times, I would have said
we do not know how complicated the rule
for the universe will be.
And I would have said, you know,
the one thing we know,
which is a fundamental fact about science, that's
the thing that makes science possible, is that
there is order in the universe.
I mean, you know, early theologians
would have used that as an argument for the existence
of God, because it's like
why is there order in the universe? Why doesn't
every single particle in the universe just do
its own thing? You know,
something must be making there be order in
the universe. We,
you know, in the sort of
early theology point of view,
that's, you know, the role of God is to do
that, so to speak. In our,
you know, we might say it's
the role of a formal theory to do that.
And then the question is, but how simple
should that theory be? And should that
theory be one that, that,
you know, where
I think the point is, if it's simple,
it's almost inevitably
somewhat beautiful in the sense that
because all the stuff
that we see has to fit into this little tiny
theory. And the way it does that
has to be, you know, it
depends on your notion of beauty, but I mean,
and for me, the
sort of the surprising
connectivity of it is at least
in my aesthetic,
that's something that, you know,
responds to my aesthetic. But the question is,
I mean, you're
a fascinating person in the
sense that you're
at once talking about
computational, the fundamental
computational reducibility of the universe.
And on the other hand,
trying to come up with a theory
of everything, which simply
describes the
the simple
origins of that
computational reducibility. Right. I mean, both
of those things are kind of, it's
paralyzing to think that we can't make any
sense of the universe in the general case.
But it's
hopeful to think like, one, we can think
of a rule and
that generates this whole complexity.
And two, we can find
pockets of
reducibility that are
powerful for our everyday life to do
different kinds of predictions. I suppose
Sabine wants
to find, focus on the finding
of small pockets
of reducibility versus
the theory of
everything. You know, it's a funny
thing because, because, you know, a bunch
of people have started working on this, this,
you know, physics project, people who are,
you know, physicists, basically.
And it is
really a fascinating sociological phenomenon
because what, you know,
when I was working on this before
in the 1990s, you know,
wrote it up, put
it, it's 100 pages of this 1200 page
book that I wrote, New Kind of Science, it's, you know, 100
pages of that is about physics.
Right. I, I saw it in that,
at that time, not
as a pinnacle achievement, but
rather as a use case, so to speak.
I mean, my main point was this new kind of science
and it's like, you can apply it to biology,
you can apply it to, you know, other kinds
of physics, you can apply it to fundamental physics.
It's just, it's just an application,
so to speak. It's not the core
thing. But, but
then, you know, one of the things that was
interesting with that, with that book
was, you know, book comes out,
lots of people think it's
pretty interesting and lots of people start
using what it has in different kinds of fields.
The one field where
there was sort of a heavy pitchforking
was from my friends,
the fundamental physics people.
Yeah. Which was, it's like, no, this
can't possibly be right. And, you know, it's like,
you know, if what you're doing is right,
it'll overturn 50 years of what we've been doing.
And it's like, no, it won't
was what I was saying. And it's like,
but, you know,
for a while when I started, you know,
I was going to go on back in
2002, well, 2004, actually,
I was going to go on working on this project
and I actually stopped
partly because it's like, why
am I, you know, this is like,
I've been in business a long time, right? I'm
building a product for a target
market that doesn't want the product.
And it's like, why work, yeah,
why work against the swim against
the current or whatever. Right. But you see what's
happened, which is sort of interesting is
that a couple of things happened and
it was, it was like,
you know, it was like, I,
I don't want to do this project because
I can do so many other
things which I'm really interested in
where, you know,
people say, great, thanks for those tools,
thanks for those ideas, etc.
Whereas, you know, if you're dealing with
kind of a, a,
you know, a sort of a structure
where people are saying, no, no, we don't want this
new stuff, we don't need any new stuff, we're really fine
with what we're doing. Yeah, there's like, literally, like,
I don't know, millions of people who are thankful
for Wolfram Alpha, a bunch of people
wrote to me how thankful they are,
they are a different crowd than
the theoretical physics community, perhaps.
Yeah, well, right. But, you know, the theoretical
physics community pretty much uniformly uses
Wolfram language and Mathematica, right?
And so, it's, it's kind of like,
like, you know, and that's,
but the thing is, what happens,
you know, this is what happens,
mature fields do not,
you know, it's like, we're doing what we're doing,
we have the methods that we have,
and we're, we're just fine here.
Now, what's happened in the last
18 years or so, I think
there's a couple of things that have happened.
First of all, the, the hope
that, you know, string theory or whatever
would, would deliver the fundamental
theory of physics, that hope has disappeared.
That the, another thing
that's happened is the, the sort of
the interest in computation around
physics has been greatly
enhanced by the whole quantum information,
quantum computing story.
People, you know, the idea there might be
something sort of computational
related to physics has somehow,
somehow grown. And I think,
you know, it's, it's sort of interesting.
I mean, right now, if we say, you know,
it's like, if you're like, who else
is trying to come up with the fundamental theory of physics?
It's like, there aren't professional
for, no professional. No professional.
No professional. What are your,
I mean, you've talked
with him, but just as a matter
of personalities, because it's a beautiful story,
what are your thoughts about Eric Weinstein's work?
You know, I think
his, his, I mean,
he did a PhD thesis in
mathematical physics at Harvard.
Mathematical physics. And, and, you know, it's
it seems like it's kind of,
you know, it's in that
framework and it's kind of like,
I'm not sure how much further
it's got than this PhD thesis,
which was 20 years ago or something.
And I think that, you know, the,
the, you know, it's a fairly specific
piece of mathematical physics
that's quite nice and
What trajectory do you hope it takes?
I mean, well, I think in his particular
case, I mean, from what I understand, which is
not everything at all, but, you know, I think
I know the rough tradition at least
is operating in his sort of
theory of gauge theories, gauge theories,
local gauge invariance and so on. Okay.
We are very close to
understanding how local gauge invariance works in
our models and it's very beautiful
and it's very, and,
you know, does some of the mathematical
structure that he's enthusiastic about
fit quite possibly, yes.
So there might be a possibility of trying to understand
how those things fit, how gauge theory fits.
Might very well. I mean, the question is,
you know, so there are a couple of things one might try to get
in the world. So for example, it's like,
can we get three dimensions of space? We haven't
managed to get that yet. Gauge theory,
the standard model of particle physics
says that it's SU3
cross SU2 cross U1.
Those are the designations of these
Lee groups.
It doesn't, but anyway, so
those are, those are sort of representations
of symmetries of the
theory. And so,
you know, it is conceivable
that it is generically true.
Okay, so all those are
subgroups of a group called E8, which is a
weird,
exceptional Lee group. Okay.
It is conceivable. I don't know whether it's the case
that, that will be generic
in these models, that it will be generic
that the gauge
invariance of
the model has this property,
just as things like general
relativity, which
corresponds to think of
general covariance,
which is another gauge-like
invariance.
It could conceivably be the case
that the kind of local gauge invariance
that we see in particle physics
is somehow generic. And, and that would
be a, you know, the thing that's, that's
really cool, I think, you know,
sociologically, although this hasn't really hit yet,
is that all of these
different things, all these different things people have been working on in these,
in some cases
quite obstruous areas of mathematical
physics. An awful lot of them
seem to tie in to what we're doing.
And, you know, it might not be that way.
Yeah, absolutely. That's the beautiful thing about
here. I mean, but the reason I,
the reason our quinestine is important
is to the point that you mentioned
before, which is, is strange
that the theory of everything
is not
at the core of
the passion, the dream,
the focus, the funding
of the physics community.
It's too hard.
It's too hard and people gave
up. I mean, basically
what happened is, ancient
Greece, people thought we're nearly there.
You know, the world is made of platonic solids.
It's, you know, water is a tetrahedron
or something. Yes. We're almost there.
Okay. Long period of time
where people were like, no, we don't
know how it works. You know, time of Newton.
You know, we're almost
there. Everything is gravitation.
You know, time of Faraday
and Maxwell. We're almost there. Everything is
fields. Everything is the ether.
You know, then the whole time
we're making big progress though.
Oh, yes. Absolutely. But the fundamental
theory of physics is almost a footnote
because it's like,
it's the machine code. It's like
we're operating in the high level languages.
Yeah. You know, that's what we really
care about. That's what's relevant for our everyday
physics. We talked about different centuries
in the 21st century will be
everything's computation. Yes.
If that takes us all the way, we don't
know, but it might take us pretty far.
Yes. Right. That's right. But I think
the point is that it's like, you know, if you're
doing biology, you might say, how can you not
be really interested in the origin of life
and the definition of life? Well, it's irrelevant.
You know, you're studying the properties of some
virus. It doesn't matter, you know,
where, you know, you're operating
at some much higher level. And it's the same
what's happened with physics
is I was sort of surprised
actually, I was sort of mapping out this history
of people's efforts to understand
the fundamental theory of physics.
And it's remarkable how little has been done
on this question.
And it's, you know, because, you know, there
have been times when there's been bursts of enthusiasm.
Oh, we're almost there. And
then it decays and people
just say, oh, it's too
hard, but it's not relevant anyway.
And I think that the thing that
you know, so
the question of, you know,
one question is, why does anybody,
why should anybody care, right?
Why should anybody care what the fundamental theory of
physics is? I think it's intellectually
interesting, but what will be
the sort of, what will be the impact of
this? What, I mean, this is the key question.
What do you think will happen
if we
figure out the fundamental
theory of physics? Right.
Outside of the intellectual curiosity
of us. Okay, so here's what, here's my best guess.
Okay.
So if you look at the history of science,
I think a very interesting
analogy is Copernicus.
Okay, so what did Copernicus do?
There had been this Ptolemaic system
for working out the motion of planets.
It did pretty well.
It used epicycles, et cetera, et cetera, et cetera.
It had all this computational
ways of working out where planets will be.
When we work out where planets are today,
we're basically using epicycles.
But Copernicus had this different way of
formulating things in which
he said, you know, and
and that had a consequence.
The consequence was you can use
this mathematical theory
to conclude something which is
absolutely not what we can tell from
common sense.
Right, so it's like trust the mathematics,
trust the science.
Okay, now fast forward
400 years and
you know, and now we're in this pandemic
and it's kind of like everybody thinks
the science will figure out everything.
It's like from the science
we can just figure out what to do.
We can figure out everything.
That was before Copernicus, nobody would have
thought if the science says something
that doesn't agree with our everyday
experience where we just have to,
you know, compute the science and then figure out
what to do, people say that's completely crazy.
And so your sense is once
we figure out the framework of computation
that can basically do any
understand the fabric of reality
we'll be able to
derive totally counterintuitive
things. No, the point
I think is the following, that
right now, you know, I talk about
computational irreducibility.
People, you know, I was very proud
that I managed to get the term computational irreducibility
into the congressional record last year.
That's right, by the way.
That's a whole nother topic we could talk about.
Different topic.
Different topic.
In any case, you know, so computational irreducibility
is one of these sort of concepts
that I think is important in understanding lots of things
in the world, but the question is
it's only important if you believe
the world is fundamentally computational, right?
But if you
know the fundamental theory of physics
and it's fundamentally computational
then you've rooted the whole thing.
That is, you know
the world is computational and while
you can discuss whether
you know, it's not
the case that people would say, well, you have this whole computational
irreducibility, all these features of computation
we don't care about those
because after all the world isn't computational,
you might say.
But if you know, you know, base, base, base thing
physics is
computational, then you know
that that stuff is, you know,
that's kind of the grounding for that stuff.
Just as, in a sense, Copernicus
was the grounding for the idea that
you could figure out something with math and science
that was not
what you would
intuitively think from your senses.
So now we've got to this point
where, for example, we say
once we have the idea that computation
is the foundational thing
that explains our whole universe
then we have to say, well, what does it mean
for other things? Like, it means there's
computational irreducibility. That means science
is limited in certain ways.
That means this, that means that.
But the fact that we have that grounding
means that, you know,
and I think, for example, for Copernicus, for instance,
the implications
of his work on the sort of mathematics
of astronomy were cool,
but they involved a very small number of people.
The implications of his work for sort
of the philosophy of how you think about things
were vast and
involved, you know, everybody more or less.
But do you think so that's actually
the way scientists and people
see the world around
us? So it has a huge impact in that sense.
Do you think it might have an impact
more directly
to engineering
derivations from physics
like propulsion systems, our ability
to colonize the world?
For example, okay, this is like sci-fi,
but if you
understand
the computational nature, say,
of
the different forces of physics,
you know, there's a notion
of being able to, you know, warp gravity,
things like this. Yeah, can we make warp
drive? Warp drive, yeah.
So, like, would we be able to,
will, you know,
Elon Musk start paying attention like,
it's awfully costly to launch these
rockets. Do you think we'll be able to, yeah,
create warp drive? Right, you know,
I set myself some homework. I agreed to give
a talk at some NASA workshop in a few weeks
about faster than light travel.
So I haven't figured it out yet.
You got two weeks. Yeah, right.
But do you think that kind of understanding
of fundamental theory of physics can lead
to those engineering breakthroughs? Okay, I think
it's far away, but I'm not certain.
I mean, you know, this is the thing that
I set myself an exercise
when gravity waves, gravitational waves were
discovered, right? I set myself
the exercise of what would black hole
technology look like? In other words,
right now, you know, black holes are far
away. You know, how on earth can we do things
with them? But just imagine that we could get,
you know, pet black holes right in our backyard.
You know, what kind of technology could
we build with them? I got a certain distance, not that
far. But I think in,
you know, so there are ideas, you know,
I have this one of the weirder ideas
is things I'm calling space tunnels,
which are higher dimensional pieces
of space time, where
basically you can, you know,
in our three-dimensional space,
there might be a five-dimensional, you know,
region, which actually
will appear as a white hole on one end and a black hole
at the other end. You know, who knows whether
they exist. And then the questions are
another one. Okay, this is another crazy one.
It's the thing that I'm calling a vacuum
cleaner. Okay, so
so, so I mentioned
that, you know, there's all this activity in the
universe, which is maintaining the structure of
space. Yes. And that leads
to a certain energy density
effectively in space.
And so the question, in fact,
dark energy is a story
of essentially negative mass
produced by
the absence of
energy you thought would be there,
so to speak. And we don't know exactly
how it works in our model
of the physical universe, but
this notion of a vacuum cleaner
is a thing where,
you know, you have all these things that are maintaining the structure
of space, but what if
you could clean out some of that stuff that's
maintaining the structure of space and make
a simpler vacuum somewhere? Yeah.
You know, what would that do? A totally different kind of vacuum.
Right. And that would lead to
negative energy density, which would need
so gravity is usually a purely
attractive force, but negative
mass would lead to
repulsive gravity
and lead to all kinds of weird things.
Now, can it be done in our universe?
You know,
my immediate thought is no,
but, you know,
the fact is that, okay, so
I want to understand the fact, because you're saying
like, at this level of abstraction, can we reach
to the lower levels and
mess with it? Yes.
Once you understand the levels, I think
you can start. I know, and I'm,
you know, I have to say that this reminds
me of people telling one
years ago that, you know, you'll never transmit
data over a copper wire at more than
a thousand, you know, a thousand
board or something, right? And this
is, why did that not happen?
You know, why do we have these much, much faster
data transmission? Because we've understood many
more of the details of what's actually going on.
Yeah. And it's the same exact
story here. And it's the same, you know,
I think that this, as I say, I think one
of the features of, sort
of, one of the things about our time
that will seem incredibly naive in the
future is the belief that,
you know, things like heat
is just random motion of molecules.
That it's just
throw up your hands. It's just random.
We can't say anything about it.
That will seem naive.
Yeah, at the heat death of the universe
those particles would be laughing at us humans
thinking... Yes, right.
That life is not beautiful. Life is not
beautiful. You know, humans used to think
they're special with their little
brains. Well, right, but also
they used to think that this would just
be random and interesting.
But that's... So this question
about whether you can, you know,
mess with the underlying structure
and how you find a way to mess with the underlying
structure, that's a, you know,
I have to say, you know, my
immediate thing is, boy, that seems really hard.
But then
and, you know, possibly
computational irreducibility will bite you
but then there's always some path of
computational reducibility and that path
of computational reducibility is the
engineering invention that has to be
made. Those little pockets can have huge
engineering impact.
Right. And I think that that's right.
I mean, we live in, you know, we make use
of so many of those pockets. And the fact is,
you know, I
you know, this is
yes, it's a
you know, it's one of these things where
where, you know,
I'm a person who likes to
figure out ideas and so on and the sort of
tests of my level of imagination,
so to speak. And so
a couple of places where there's sort of
serious humility in
terms of my level of imagination. One is
this thing about different reference frames
for understanding the universe
where like, imagine the physics of the
aliens. What will it be like? And I'm
like, that's really hard.
I don't know, you know, and
I mean, once you have the framework in place,
you can at least reason about
the things you don't know. Yes,
maybe can't know or like, it's too hard
for you to know, but then
the mathematics can,
that's exactly it. Allow
you to reach beyond where you can
reason. Right. So
I'm, you know, I'm, I'm trying
to not have, you know, if you think back
to Alan Turing, for example, and, you
know, when he invented Turing machines,
you know, and imagining what computers
would end up doing, so to speak. Yeah.
You know, and it's very difficult.
It's difficult, right. And it's
a few reasonable predictions, but most
of it he couldn't predict possibly. By the time
by 1950, he was making reasonable predictions
about some things. But not in the 30s.
Right. Not, not, not in the,
not when he first, you know, conceptualized,
you know, and he conceptualized
universal computing for a very specific
mathematical reason that wasn't,
wasn't as general. But, but yes,
it's a, it's a good sort of exercise in humility
to realize that, that it's kind of like,
it's, it's really hard
to figure these things out. The engineering
of, of the universe,
if we know how the universe works,
how can we engineer it?
That's such a beautiful vision. That's such a beautiful vision.
By the way, I have to mention one more thing, which is
the ultimate question of, of
from physics is, okay,
so we have this abstract model of the
universe. Why does the universe
exist at all?
Right. So, you know,
we might say there is a formal
model that if you run
this model, you get the universe.
The model gives you,
you know, a model of the universe, right?
You, you, you run this mathematical
thing and the mathematics
unfolds in the way that corresponds
to the universe. But the question is,
why was that actualized?
Why does the actual universe
actually exist?
And so this is, this is another one
of these humility and, and
it's like, can you figure this out? I have a
guess, okay, about the answer to that.
And my guess is
somewhat unsatisfying,
but my guess is that it's a little bit
similar to Goethe's second incompleteness
theorem, which is the statement that
from within, as an axiomatic
theory like Piano Arithmetic,
you cannot from within that theory prove
the consistency of the theory.
So my guess is
that for entities
within the universe,
there is no finite determination
that can be made of
the, the statement the universe
exists is essentially undecidable
to any entity
that is embedded in the universe.
Within that universe, how does that make you feel?
Is that, is that
does that put you at peace
that it's impossible
or is it really ultimately
frustrating? Well, I think it just says
that it's not a kind
of question that,
you know, it's, there are things
that it is reasonable.
I mean, there's kinds of
you know, you can talk about hyper
computation as well. You can say, imagine
there was a hyper computer, here's what it would do.
So great, it would be lovely to have a hyper
computer, but unfortunately we can't make it in the
universe. Like, it would be lovely to answer
this, but unfortunately we can't do it in the universe.
And, you know, this is all
we have, so to speak. And I think
it's really just a
statement. It's sort of, in the end
it'll be a kind of a logical
logically inevitable statement, I think.
I think it will be something where
it is, as you understand what
it means to have, what it means
to have a sort of predicate of existence
and what it means to have these kinds of things, it will
sort of be inevitable that this has
to be the case, that from within that universe
you can't establish the reason
for its existence, so to speak. You can't prove that it
exists and so on. And nevertheless
because of computation or
reusability, the future
is ultimately not predictable, full
of mystery, and that's what makes life worth
living. Right. I mean, right.
You know, it's funny for me because
as a pure sort of human being
doing what I do, it's, you know,
I'm, you know, I like
I'm interested in people, I like sort of,
you know, the whole human experience,
so to speak. And yet
it's a little bit weird when I'm thinking,
you know, it's all hypergraphs down
there, and it's all just
hypergraphs all the way down. Right.
It's like turtles all the way down. Yeah, yeah, right.
And it's kind of, you know, it's,
to me, it is
a funny thing because every so often I get this,
you know, as I'm thinking about, I think we've really gotten,
you know, we've really figured out kind
of the essence of how physics works and I'm
thinking to myself, you know, here's this physical
thing and I'm like, you know, this
feels like a very definite thing.
How can it be the case that this is just some
rural reference frame of, you know,
this infinite creature that
is so abstract and so on.
And I kind of, it is a
it's a funny
sort of feeling that, you know,
we are, we're sort of
it's like it's, in the
end, it's just sort of, we're just
happy we're just humans type thing.
And it's kind of like, but we're
making, we make things
as it's not like
we're just a tiny spec.
We are, in a sense
the, we are more important
by virtue of the fact that
in a sense
it's not like there's
there is no ultimate,
you know, it's like, we're important
because
because, you know, we're
here, so to speak, and we're not, it's not
like there's a thing where we're saying
you know, we are
just but one sort of
intelligence out of all these other intelligences
and so, you know,
ultimately there'll be the super intelligence
which is all of these put together
and it'll be very different from us. No, it's actually
going to be equivalent to us. And the thing
that makes us a sort
of special is just
the details of
us, so to speak. It's not something where we can
say, oh, there's this other
thing, you know, just you think humans
are cool, just wait until you've
seen this, you know, it's going to be
much more impressive. Well, no,
it's all going to be kind of computationally
equivalent. And the thing that
you know, it's not going to be, oh, this thing
is amazingly much more impressive
and amazingly much more meaningful, let's say.
No,
we're it. I mean, that's
that's the
symbolism of this particular moment.
So this has been one of
the one of the
favorite conversations I've ever had, Stephen.
It's a huge honor to talk
to you to talk about a topic
like this for four plus hours
on the fundamental theory of physics
and yet we're just two
finite descendants of apes
that have to end this
conversation because darkness
have come upon us.
Right. And we're going to get bitten by mosquitoes
and all kinds of terrible things. The symbolism of that
we're talking about the most
basic fabric of reality
and having to end
because of the fact that things end.
It's tragic and beautiful, Stephen.
Thank you so much, huge honor.
I can't wait to see what you do in the next
couple of days and next week, a month.
We're all watching
with excitement. Thank you so much. Thanks.
Thanks for listening to this
conversation with Stephen Wolfram and thank you
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And now, let me leave you
with some words from Richard Feynman.
Physics
isn't the most important thing.
Love is.
Thank you for listening.
See you next time.