The following is a conversation with Stephen Wolfram, his third time on the podcast.

He's a computer scientist, mathematician, theoretical physicist, and the founder of

Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the new

Wolfram Physics Project. This conversation is a wild technical roller coaster ride

through topics of complexity, mathematics, physics, computing, and consciousness.

I think this is what this podcast is becoming, a wild ride. Some episodes are about physics,

some about robots, some are about war and power, some are about the human condition

and our search for meaning, and some are just what the comedian Tim Dillon calls fun.

This is the Lex Friedman Podcast, to support it please check out the sponsors in the description,

and now here's my conversation with Stephen Wolfram.

Stephen.

Almost 20 years ago, you published A New Kind of Science, where you presented a study of

complexity and an approach for modeling of complex systems. So, let us return again to

the core idea of complexity. What is complexity?

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

you know, if you ask a biologist what is life, that's not the question they care the most about.

But what I was interested in is, how does something that we would usually identify as

complexity arise in nature? And I got interested in that question like 50 years ago, which is

really embarrassingly long time ago. And, you know, I was, you know, how does snowflakes get

to have complicated forms? How do galaxies get to have complicated shapes? How do living systems

get produced? Things like that. And the question is, what's the sort of underlying scientific

basis for those kinds of things? And the thing that I was at first very surprised by, because

I've been doing physics and particle physics, some fancy mathematical physics and so on.

And it's like, I know all this fancy stuff, I should be able to solve this sort of basic

science question. And I couldn't, this was like early, maybe 1980 ish timeframe. And it's like,

okay, what can one do to understand the sort of basic secret that nature seems to have?

Because it seems like nature, you look around in the natural world, it's full of incredibly

complicated forms. You look at sort of most engineered kinds of things, for instance,

they tend to be, you know, we've got sort of circles and lines and things like this.

And the question is, what secret does nature have that lets it make all this complexity

that we in doing engineering, for example, don't naturally seem to have?

And so that was the kind of the thing that I got interested in. And then the question was,

you know, could I understand that with things like mathematical physics? Well, it didn't work

very well. So then I got to thinking about, okay, is there some other way to try to understand this?

And then the question was, if you're going to look at some system in nature,

how do you make a model for that system, for what that system does? So, you know,

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

What is the raw material that you can make that model out of? And so what I realized was,

well, actually, programs are a really good source of raw material for making models of things.

And, you know, in terms of my personal history, to me, that seemed really obvious. And the reason

it seemed really obvious is because I just spent several years building this big piece of software

that was sort of a predecessor to Mathematica and Morphan Language, then called SMP, Symbolic

Manipulation Program, which was something that had this idea of starting from just these

computational primitives and building up everything one had to build up. And so kind of the notion of,

well, let's just try and make models by starting from computational primitives and seeing what we

can build up, that seemed like a totally obvious thing to do. In retrospect, it might not have been

externally quite so obvious, but it was obvious to me at the time, given the path that I happened

to have been on. So, you know, so that got me into this question of, let's use programs

to model what happens in nature. And the question then is, well, what kind of programs?

And, you know, we're used to programs that you write for some particular purpose, and it's a

big, long piece of code, and it does some specific thing. But what I got interested in was, okay,

if you just go out into the sort of computational universe of possible programs, you say,

take the simplest program you can imagine, what does it do? And so I started studying these things

called cellular automata. Actually, I didn't know at first they were called cellular automata,

but I found that out subsequently. But it's just a line of cells, you know, each one is black or

white, and it's just some rule that says the color of the cell is determined by the color that it had

on the previous step and its two neighbors on the previous step. And I had initially thought,

that's, you know, sufficiently simple setup is not going to do anything interesting. It's always

going to be simple, no complexity, simple rule, simple behavior. Okay, but then I actually ran

the computer experiment, which was pretty easy to do. I mean, it probably took a few hours

originally. And the results were not what I'd expected at all. Now, needless to say,

in the way that science actually works, the results that I got had a lot of unexpected

things which I thought were really interesting, but the really strongest results, which was

already right there in the printouts I made, I didn't really understand for a couple more years.

So it was not, you know, the compressed version of the story is you run the experiment and you

immediately see what's going on, but I wasn't smart enough to do that, so to speak. But the

big thing is, even with very simple rules of that type, sort of the minimal, tiniest program,

sort of the one line program or something, it's possible to get very complicated behavior. My

favorite example is this thing called Rule 30, which is a particular cellular automaton rule.

You just started off from one black cell and it makes this really complicated pattern. And so that

for me was sort of a critical discovery that then kind of said, playing back onto, you know,

how does nature make complexity, I sort of realized that might be how it does it.

That might be kind of the secret that it's using is that in this kind of computational

universe of possible programs, it's actually pretty easy to get programs where even though

the program is simple, the behavior when you run the program is not simple at all.

And so for me, that was the kind of the story of kind of how that was sort of the indication that

one had got an idea of what the sort of secret that nature uses to make complexity and how

complexity can be made in other places. Now, if you say, what is complexity? You know,

complexity is it's not easy to tell what's going on. That's the informal version of what is

complexity, but there is something going on, but there's a rule to know what, right? Well, no,

the rules can generate just randomness, right? Well, that's not obvious. In other words,

it's not obvious at all. And it wasn't what I expected. It's not what people's intuition

had been and has been for, you know, for a long time. That is one might think you have a rule.

You can tell there's a rule behind it. I mean, it's just like, you know, the early, you know,

robots in science fiction movies, right? You can tell it's a robot cause it does simple things,

right? It turns out that isn't actually the right story, but it's not obvious that isn't the right

story because people assume simple rules, simple behavior. And that the sort of the key discovery

about the computational universe is that isn't true. And that discovery goes very deep and

relates to all kinds of things that I've spent years and years studying. But, you know, that in

the end, the sort of the, the what is complexity is, well, you can't easily tell what it's going

to do. You could just run the rule and see what happens, but you can't just say, oh, you know,

show me the rule. Great. And now I know what's going to happen. And, you know, the key phenomenon

around that is this thing I call computational irreducibility. This fact that in something like

rule 30, you might say, well, what's it going to do after a million steps? Well, you can run it

for a million steps and just do what it does to find out, but you can't compress that. You can't

reduce that and say, I'm going to be able to jump ahead and say, this is what it's going to do after

a million steps, but I don't have to go through anything like that computational effort.

CB. By the way, has anybody succeeded at that? Do you have to challenge a competition

for predicting the middle column of rule 30? Anybody?

MG. A number of people have sent things in and sort of people are picking away at it,

but it's hard. I mean, I've been actually even proving that the center column of rule 30 doesn't

repeat. That's something I think might be doable. Okay?

CB. Mathematically proving.

MG. Yes. And so that's analogous to a similar kind of thing as like the digits of pi,

which are also generated in this very deterministic way. And so a question is how random are the

digits of pi? For example, first of all, do the digits of pi ever repeat? We know they don't,

because it was proved in the 1800s that pi is not a rational number. So that means only rational

numbers have digit sequences that repeat. So we know the digits of pi don't repeat.

So now the question is, does 0, 1, 2, 3 or whatever, do all the digits base 10 or base 2 or

however you work it out, do they all occur with equal frequency? Nobody knows. That's far away

from what can be understood mathematically at this point. But I'm even looking for step one,

which is prove that the center column doesn't repeat and then prove other things about it,

like equidistribution of equal numbers of zeros and ones. And those are things which I kind of

set up this little prize thing because I thought those were not too out of range. Those are things

which are within a modest amount of time, it's conceivable that those could be done. They're not

far away from what current mathematics might allow. They'll require a bunch of cleverness

and hopefully some interesting new ideas that will be useful other places.

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

You thought that there might be some kind of a thermodynamic randomness and then complexity

comes from a clever filter that you kind of like, I don't know, spaghetti or something. You filter

the randomness and outcomes complexity, which is an interesting intuition. How do we know that's

not actually what's happening? So just because you were then able to develop, look, you don't need

this like incredible randomness. You can just have very simple, predictable initial conditions

and predictable rules. And then from that emerged complexity, still there might be some systems

where it's filtering randomness on the inputs. Well, the point is when you have quotes randomness

in the input, that means there's all kinds of information in the input. And in a sense,

what you get out will be maybe just something close to what you put in. Like people are very

in dynamical systems theory, sort of big area mathematics that developed

from the early 1900s and really got big in the 1980s. An example of what people study

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

is the shift map, which is basically taking 2x mod one to the fractional part of 2x,

which is basically just taking digits in binary and shifting them to the left. So at every step,

you get to see if you say, how big is this number that I got out? Well, the most important digit in

that number is whatever ended up at the left hand end. But now if you start off from an arbitrary

random number, which is quotes randomly chosen, so all its digits are random, then when you run

that sort of chaos theory shift map, all that you get out is just whatever you put in. You just get

to see what you... It's not obvious that you would excavate all of those digits. And if you're,

for example, making a theory, I don't know, fluid mechanics, for example, if there was that

phenomenon in fluid mechanics, then the equations of fluid mechanics can't be right. Because what

that would be saying is the equations that it matters to the fluid, what happens in the fluid

at the level of the millionth digit of the initial conditions, which is far below the point at which

you're hitting sizes of molecules and things like that. So it's kind of almost explaining

if that phenomenon is an important thing, it's kind of telling you that fluid dynamics,

which describes fluids as continuous media and so on, isn't really right.

But so this idea that... It's a tricky thing because as soon as you put randomness in,

you have to know how much of what's coming out is what you put in versus how much is actually

something that's being generated. And what's really nice about these systems where you just

have very simple initial conditions and where you get random stuff out or seemingly random stuff out

is you don't have that issue. You don't have to argue about, was there something complicated put

in? Because it's plainly obvious there wasn't. Now, as a practical matter in doing experiments,

the big thing is if the thing you see is complex and reproducible, then it didn't come from just

filtering some, quotes, randomness from the outside world. It has to be something that is

intrinsically made because it wouldn't otherwise be... It could be the case that you set things up

and it's always the same each time and you say, well, it's kind of the same, but it's not random

each time because it's kind of the definition of it being random is it was kind of picked at random

each time, so to speak. So is it possible to for sure know that our universe does not at the

fundamental level have randomness? Is it possible to conclusively say there's no randomness at the

bottom? Well, it's an interesting question. I mean, you know, science, natural science is an

inductive business, right? You observe a bunch of things and you say, can we fit these together?

What is our hypothesis for what's going on? The thing that I think I can say fairly definitively

is at this point, we understand enough about fundamental physics that if there was sort of

an extra dice being thrown, it's something that doesn't need to be there. We can get what we see

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

universe? Probably, but in fact, almost certainly yes. But is it necessary for understanding the

universe? No. And I think actually from a more fundamental point of view, I think I might be

able to argue. So one of the things that I've been interested in and been pretty surprised that I've

had anything sentient to say about is the question of why does the universe exist? I didn't think

that was a question that I would, you know, I thought that was a far out there metaphysical

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

It's such a kind of difficult to address question. But I actually think to my great surprise that

from our physics project and so on, that it is possible to actually address that question and

explain why the universe exists. And I kind of have a suspicion. I've not thought it through.

I kind of have a suspicion that that explanation will eventually show you that in no meaningful

sense can there be randomness underneath the universe. That is that if there is, it's something

that is necessarily irrelevant to our perception of the universe. That is that it could be there,

but doesn't matter because in a sense, we've already, you know, whatever it would do,

whatever extra thing it would add is not relevant to our perception of what's going on.

So why does the universe exist? How does the relevance of randomness connect to the big

why question of the universe? So, OK, so I mean, why does the universe exist? Well, let's see.

And is this the only universe we got? It's the only one that about that I'm pretty sure.

So now maybe which one which of these topics is better to enter first? Why does the universe exist

and why you think it's the only one that exists? Well, I think they're very closely related. OK.

OK. So, I mean, the first thing, let's see, I mean, this why does the universe exist question

is built on top of all these things that we've been figuring out about fundamental physics,

because if you want to know why the universe exists, you kind of have to know what the

universe is made of. And I think the well, let me let me describe a little bit about

the why does the universe exist question. So the main issue is let's say you have a model

for the universe and you say I've got this this program or something and you run it and you make

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

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

Right. What what does it mean? What actualizes something? You know, two plus two equals four.

But that's different from saying this to a pile of two rocks, another pile of two rocks, and so

many moves them together and makes four, so to speak. And so what is it that kind of turns it

from being just this formal thing to being something that is actualized? OK, so there we

have to start thinking about, well, well, what do we actually know about what's going on in the

universe? Well, we are observers of this universe. But confusingly enough, we're part of this

universe. So in a sense, we what what what if we say what do we what do we know about what's

going on in the universe? Well, what we know is what sort of our consciousness records about

what's going on in the universe. And consciousness is part of the fabric of the universe. So we're

in it. Yes, we're in it. And maybe I should maybe I should start off by saying something about

the consciousness story, because that's some. Maybe we should begin even before that at the

very base layer of the Wolfram physics project. Maybe you can give a broad overview once again

really quick about this hypergraph model. Yes. And also, what is it a year and a half ago since

you've brought this project to the world? What is the status update where what are all the beautiful

ideas you have come across? What are the interesting things you can mention? It's I mean,

it's a it's a frigging Cambrian explosion. I mean, it's it's crazy. I mean, there are all these

things which I've kind of wondered about for years. And suddenly, there's actually a way to

think about them. And I really did not see. I mean, the real strength of what's happened,

I absolutely did not see coming. And the real strength of it is we've got this model for physics,

but it turns out it's a foundational kind of model. That's a different kind of computation

like model that I'm kind of calling the sort of multi computational model. And that that kind of

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

that's extremely powerful is because physics has been very successful. So we know a lot based on

what we figured out in physics. And if we know that the same model governs physics and governs,

I don't know, economics, linguistics, immunology, whatever, we know that the same kind of model

governs those things. We can start using things that we've successfully discovered in physics

and applying those intuitions in all these other areas. And that's that's pretty exciting and very

and very surprising to me. And in fact, it's kind of like in the original story of sort of you go

and you explain why is there complexity in the natural world, then you realize, well, there's all

this complexity, there's all this computational irreducibility. You know, there's a lot we can't

know about what's going to happen. It's kind of kind of very confusing thing for people who say,

you know, science has nailed everything down. We're going to, you know, based on science,

we can know everything. Well, actually, there's this computational irreducibility thing

right in the middle of that, thrown up by science, so to speak. And then the question is, well,

given computational irreducibility, how can we actually figure out anything about what happens

in the world? Why aren't we why are we able to predict anything? Why are we able to operate in

the world? And the answer is that we sort of live in these slices of computational reusability

that exist in this kind of ocean of computational irreducibility. And it turns out that seems that

it's a very fundamental feature of the kind of model that seems to operate in physics,

and perhaps in a lot of these other areas, that there are these particular slices of

computational reusability that are relevant to us. And those are the things that both allow us to

operate in the world, and not just have everything be completely unpredictable. But there are also

things that potentially give us what amount to sort of physics like laws in all these other areas.

So that's, that's been sort of an exciting thing. But, but I would say that in general, for our

project, it's been going spectacularly well. I mean, you know, I, it's very, honestly, it wasn't

something I expected to happen in my lifetime. I mean, it's, you know, it's something where,

where it's, it's an in fact, one of the things about it, some of the things that we've discovered,

are things where I was pretty sure that wasn't how things worked. And turns out I'm wrong. And,

you know, in a major area in metamathematics, I've been realizing that I something I've long

believed we can talk about it later that that that just just really isn't right. But But I think that

the the thing that so so what's happened with the physics project? I mean, you know, it's a

can explain a little bit about how the how the model works. But basically,

we can maybe ask you the following question. So it's easy through words describe how cellular

automata works, you've you've explained this. And it's the fundamental mechanism by which you in

your book, and you kind of science explored the idea of complexity and how to do science in this

world of island reducible islands and irreducible general irreducibility. Okay, so how does the model

of hypergraphs differ from cellular automata? And how does the idea of multi computation

differ? Like, maybe that's a way to describe it. We're we're, you know, right. This is a, you know,

my life is like all of our lives, something of a story of computational irreducibility. Yes.

And, you know, it's been going for a few years now. So it's always a challenge to kind of find

these appropriate pockets of reducibility. But let me see what I can do. So, so I mean,

first of all, let's let's talk about physics, first of all. And, you know, a key observation,

that one of the starting point of our physics project is things about what is space? What is

the universe made of? And, you know, ever since Euclid, people just sort of say space is just this

thing where you can put things at any position you want. And they're just points. And they're just

geometrical things that you can just arbitrarily put at different different coordinate positions.

So the first thing in our physics project is the idea that space is made of something, just like

just like water is made of molecules, space is made of kind of atoms of space. And the only thing we

can say about these atoms of space is they have some identity. There's a there's a there is it's

this atom as opposed to this atom. And, you know, you could give them a few a computer person, you

give them UUIDs or something. And that's all there is to say about them, so to speak. And then all we

know about these atoms of space is how they relate to each other. So we say, these three atoms of

space are associated with each other in some relation. So you can think about that as you know,

what atom of space is friends with what other atom of space, you can build this essentially friend

network of the atoms of space. And the sort of starting point of our physics project is that's

what our universe is, it's a giant friend network of the atoms of space. And so how can that

possibly represent our universe? Well, it's like in something like water, you know, their molecules

bouncing around, but on a large scale that, you know, that produces fluid flow, and we have fluid

vortices, and we have all of these phenomena that are sort of the emergent phenomena from that

underlying kind of collection of molecules bouncing around. And by the way, it's important that that

collection of molecules bouncing around have this phenomenon of computational irreducibility,

that's actually what leads to the second law of thermodynamics among other things.

And that leads to the sort of randomness of the underlying behavior, which is what gives you

something which on a large scale seems like it's a smooth continuous type of thing. And so okay,

so first thing is space is made of something, it's made of all these atoms of space connected

together in this network. And then everything that we experience is sort of features of that

structure of space. So, you know, when we have an electron or something or a photon,

it's some kind of tangle in the structure of space, much like kind of a vortex in a fluid

would be just this thing that is, you know, it can actually, the vortex can move around,

it can involve different molecules in the fluid, but the vortex still stays there.

And if you zoom out enough, the vortex looks like an atom itself, like a basic

element. So there's the levels of abstraction. If you squint and kind of blur things out,

it looks like at every level of abstraction, you can define what is a basic individual entity.

Yes. But, you know, in this model, there's a bottom level, you know, there's an elementary

length, maybe 10 to the minus 100 meters, let's say, which is really small, you know,

proton is 10 to the minus 15 meters, the smallest we've ever been able to sort of see with a particle

accelerator is around 10 to the minus 21 meters. So, you know, if we don't know precisely what

the correct scale is, but it's perhaps over the order of 10 to the minus 100 meters, so it's

pretty small. But that's the end, that's what things are made of.

What's your intuition where the 10 to the minus 100 comes from? What's your intuition about this

scale?

Well, okay, so there's a calculation, which I consider to be somewhat rickety,

okay, which has to do with comparing, so there are various fundamental constants,

there's a speed of light, the speed of light, once you know the elementary time,

the speed of light tells you the conversion from the elementary time to the elementary length.

Then there's the question of how do you convert to the elementary energy? And how do you convert

to between other things? And the various constants we know, we know the speed of light,

we know the gravitational constant, we know Planck's constant and quantum mechanics,

those are the three important ones. And we actually know some other things, we know things

like the size of the universe, the Hubble constant, things like that. And essentially,

this calculation of the elementary length comes from looking at the combination of those.

Okay, so the most obvious thing, people have assumed that quantum gravity happens at this

thing, the Planck scale, 10 to the minus 34 meters, which is the combination of Planck's

constant and the gravitational constant, the speed of light, that gives you that kind of length.

Turns out in our model, there is an additional parameter, which is essentially the number of

simultaneous threads of execution of the universe, which is essentially the number of sort of

independent quantum processes that are going on. And that number, let's see if I remember that

number, that number is 10 to the 170, I think, and so it's a big number. But that number then

connects, sort of modifies what you might think from all these Planck units to give you the things

we're giving. And there's been sort of a mystery actually in the more technical physics thing,

that the Planck mass, the Planck energy, Planck energy is actually surprisingly big. The Planck

length is tiny, 10 to the minus 34 meters, you know, Planck time, 10 to the minus 43 meters,

I think, seconds, I think. But the Planck energy is like the energy of a lightning strike,

okay, which is pretty weird. In our models, the actual elementary energy is that divided by the

number of sort of simultaneous quantum threads, and it ends up being really small too. And that

sort of explains that mystery that's been around for a while about how Planck units work. But

whether that precise estimate is right, we don't know yet. I mean, that's one of the things that's

sort of been a thing we've been pretty interested in is how do you see through, you know, how do you

make a gravitational microscope that can kind of see through to the atoms of space? You know,

how do you get in fluid flow, for example, if you go to hypersonic flow or something, you know,

you've got a Mach 20, you know, space plane or something, it really matters that there are

individual molecules hitting the space plane, not a continuous fluid. The question is, what is the

analog of hypersonic flow for things about the structure of spacetime? And it looks like a

rapidly rotating black hole, right, at the sort of critical rotation rate, it looks as if that's

a case where essentially the structure of spacetime is just about to fall apart, and you

may be able to kind of see the evidence of sort of discrete elements, you know, you may be able

to kind of see there the sort of gravitational microscope of actually seeing these discrete

elements of space. And there may be some effect in, for example, gravitational waves produced by

rapidly rotating black hole that in which one could actually see some phenomenon where one

can say, yes, these don't come out the way one would expect based on having a continuous structure

of spacetime, that is something where you can kind of see through to the discrete structure.

We don't know that yet. So can you maybe elaborate a little bit deeper how a microscope that can see

the 10 to the minus 100, how rotating black holes and presumably the detailed accurate

detection of gravitational waves from such black holes can reveal the discreteness of space?

Okay, first thing is, what is a black hole? Actually, we need to go a little bit further in

the story of what spacetime is, because I explained a little bit about what space is,

but I didn't talk about what time is. And that's sort of important in understanding spacetime,

so to speak. And your sense is both space and time in the story are discrete.

Absolutely. Absolutely. But it's a complicated story. And needless to say.

Well, it's simple at the bottom. It's very simple at the bottom. In the end,

it's simple but deeply abstract. And something that is simple in conception,

but kind of wrapping one's head around what's going on is pretty hard. So first of all,

we have this. So I've described these kind of atoms of space and their connections.

You can think about these things as a hypergraph. A graph is just you connect nodes to nodes,

but a hypergraph you can have not just individual friends to friends, but you can have these

triplets of friends or whatever else. And so we're just saying that's just the relations

between atoms of space are the hyperedges of the hypergraph. And so we got some big collection of

these atoms of space, maybe 10 to the 400 or something in our universe. And that's the structure

of space. And every feature of what we experience in the world is a feature of that hypergraph,

that spatial hypergraph. So then the question is, well, what does that spatial hypergraph do?

Well, the idea is that there are rules that update that spatial hypergraph. And in a cellular

automaton, you've just got this line of cells and you just say at every step, at every time step,

you've got fixed time steps, fixed array of cells. At every step, every cell gets updated

according to a certain rule. And that's the way it works. Now in this hypergraph, it's sort of

vaguely the same kind of thing. We say every time you see a little piece of hypergraph that looks

like this, update it to one that looks like this. So just keep rewriting this hypergraph. Every time

you see something that looks like that, anywhere in the universe, it gets rewritten. Now, one thing

that's tricky about that, which we'll come to, is this multi computational idea, which has to do

with you're not saying in some kind of lockstep way, do this one, then this one, then this one.

It's just whenever you see one you can do, you can go ahead and do it. And that leads one not to

have a single thread of time in the universe. Because if you knew which one to do, you just say,

okay, we do this one, then we do this one, then we do this one. But if you say, just do whichever

one you feel like, you end up with these multiple threads of time, these kind of multiple histories

of the universe, depending on which order you happen to do the things you could do in.

So it's fundamentally asynchronous and parallel.

Yes. Yes.

Which is very uncomfortable for the human brain that seeks for things to be sequential.

Yes.

And synchronous.

Right. Well, I think that this is part of the story of consciousness,

is I think the key aspect of consciousness that is important for sort of parsing the universe,

is this point that we have a single thread of experience. We have a memory of what happened

in the past. We can say something, predict something about the future, but there's a single

thread of experience. And it's not obvious it should work that way. I mean, we've got 100

billion neurons in our brains and they're all firing at all kinds of different ways.

But yet, our experience is that there is the single thread of time that goes along. And I

think that one of the things I've kind of realized with a lot more clarity in the last year is the

fact that the fact that we conclude that the universe has the laws it has is a consequence

of the fact that we have consciousness the way we have consciousness. And so, just to go on with

kind of the basic setup, so we've got this spatial hypergraph, it's got all these atoms of space,

they're getting these little clumps of atoms of space, they're getting turned into other clumps

of atoms of space, and that's happening everywhere in the universe all the time. And so, one thing

that's a little bit weird is there's nothing permanent in the universe. The universe is getting

rewritten everywhere all the time. And if it wasn't getting rewritten, space wouldn't be knitted

together. That is, space would just fall apart. There wouldn't be any way in which we could say

this part of space is next to this part of space. One of the things that people were confused about

back in antiquity, the ancient Greek philosophers and so on, is how does motion work? How can it be

the case that you can take a thing that we can walk around and it's still us when we walked a

foot forward, so to speak? And in a sense, with our models, that's again a question because it's

a different set of atoms of space. When I move my hand, it's moving into a different set of atoms

of space. It's having to be recreated. The thing itself is not there. It's being continuously

recreated all the time. Now, it's a little bit like waves in an ocean, vortices in a fluid,

which again, the actual molecules that exist in those are not what define the identity of the

thing. But this idea that there can be pure motion, that it is even possible for an object

to just move around in the universe and not change, it's not self evident that such a thing

should be possible. And that is part of our perception of the universe is that we parse

those aspects of the universe where things like pure motion are possible. Now, pure motion,

even in general relativity, the theory of gravity, pure motion is a little bit of a complicated

thing. I mean, if you imagine your average teacup or something approaching a black hole,

it is deformed and distorted by the structure of space time. And to say, is it really pure motion?

Is it that same teacup that's the same shape? Well, it's a bit of a complicated story. And this

is a more extreme version of that. So anyway, the thing that's happening is we've got space,

we've got this notion of time. So time is this kind of this rewriting of the hypergraph. And one

of the things that's important about that time is this sort of computational irreducible process.

There's something, you know, time is not something where it's kind of the mathematical view of time

tends to be time is just to coordinate. We can, you know, slide a slider, turn a knob,

and we'll change the time that we've got in this equation. But in this picture of time,

that's not how it works at all. Time is this inexorable, irreducible kind of set of computations

that go on, that go from where we are now to the future. And one of the things that is, again,

something one sort of has to break out of is your average trained physicist like me says,

you know, space and time are the same kind of thing. They're related by, you know,

the Poincare group and Lorentz transformations and relativity and all these kinds of things.

And, you know, space and time, you know, there are all these kind of sort of folk stories you

can tell about why space and time are the same kind of thing. In this model, they're fundamentally

not the same kind of thing. Space is this kind of sort of connections between these atoms of space.

Time is this computational process. So the thing that the first sort of surprising thing is, well,

it turns out you get relativity anyway. And the reason that happens, there are a few bits and

pieces here which one has to understand. But the fundamental point is if you are an observer

embedded in the system that are part of this whole story of things getting updated in this way and

that, there's sort of a limit to what you can tell about what's going on. And really, in the end,

the only thing you can tell is what are the causal relationships between events. So an event in this

sort of an elementary event is a little piece of hypergraph got rewritten. And that means a few

hyper edges of the hypergraph were consumed by the event and you produce some other hyper edges.

And that's an elementary event. And so then the question is what we can tell is kind of what the

network of causal relationships between elementary events is. That's the ultimate thing,

the causal graph of the universe. And it turns out that, well, there's this property of causal

invariance that is true of a bunch of these models and I think is inevitably true for a variety of

reasons that makes it be the case that it doesn't matter kind of if you are sort of saying, well,

I've got this hypergraph and I can rewrite this piece here and this piece here and I do them all

in different orders. When you construct the causal graph for each of those orders that you choose to

do things in, you'll end up with the same causal graph. And so that's essentially why, well,

that's in the end why relativity works. It's why our perception of space and time is as having

this kind of connection that relativity says they should have. And that's kind of how that works.

I think I'm missing a little piece. If we can go there again, you said the fact that the

observer is embedded in this hypergraph, what's missing? What is the observer not able to state

about this universe of space and time? If you look from the outside, you can say,

oh, I see this particular place was updated and then this one was updated and I'm seeing which

order things were updated in. But the observer embedded in the universe doesn't know which order

things were updated in because until they've been updated, they have no idea what else happened.

So the only thing they know is the set of causal relationships. Let me give an extreme example.

Let's imagine that the universe is a Turing machine. Turing machines have just this one

update head which does something and otherwise the Turing machine just does nothing.

And the Turing machine works by having this head move around and do its updating just where the

head happens to be. The question is, could the universe be a Turing machine? Could the universe

just have a single updating head that's just zipping around all over the place? You say,

that's crazy because I'm talking to you, you seem to be updating, I'm updating,

et cetera. But the thing is, there's no way to know that because if there was just this head

moving around, it's like, okay, it updates me, but you're completely frozen at that point.

Until the head has come over and updated you, you have no idea what happened to me.

And so if you sort of unravel that argument, you realize the only thing we actually can tell

is what the network of causal relationships between the things that happened were. We don't

get to know from some sort of outside, sort of God's eye view of the thing. We don't get to know

what sort of from the outside, what happened. We only get to know sort of what the set of

relationships between the things that happened actually were.

Yeah. But if I somehow record like a trace of this, I guess it would be called multi computation.

Can't I then look back in the causal tree?

Where do you record the trace?

Some, you place throughout the universe, like throughout like a log that records in my own

pocket of, in this hypergraph. Can't I, like realizing that I'm getting an outdated picture,

can't I record?

See, the problem is, and this is where things start getting very entangled in terms of what

one understands. The problem is that any such recording device is itself part of the universe.

Yeah.

So you don't get to say, you never get to say, let's go outside the universe and go do this.

And that's why, I mean, lots of the features of this model and the way things work end up being

a result of that.

So, but what, I guess from on a human level, what is the cost you're paying? What are you missing

from not getting an updated picture all the time? Okay. I got, I understand what you're saying.

Yeah, yeah, right.

But like what, like, how does consciousness emerge from that? Like how, like, what are

the limitations of that observer? I understand you're getting a delayed picture.

Well, there's, there's a, okay. So there's, there's a bunch of limitations of the observer, I think.

Yeah. Maybe just explain something about quantum mechanics, because that maybe is a,

is an extreme version of some of these issues, which helps to kind of motivate why one should

sort of think things through a little bit more carefully. So one feature of the, of this, okay.

So in standard physics, like high school physics, you learn, you know, the equations of motion for

a ball and the, the, you know, it says you throw the ball this angle, this velocity,

things will move in this way. And there's a definite answer, right? The story, the key story

of quantum mechanics is there aren't definite answers to where does the ball go? There's kind

of this whole sort of bundle of possible paths. And all we say we know from quantum mechanics

is certain probabilities for where the ball will end up. Okay. So that's kind of the,

the core idea of quantum mechanics. So in our models, you, quantum mechanics is not some kind

of plugin add on type thing. You absolutely cannot get away from quantum mechanics because

as you think about updating this hypergraph, there isn't just one sequence of things,

one definite sequence of things that can happen. There are all these different possible update

sequences that can occur. You could do this, you know, piece of the hypergraph now, and then this

one later and et cetera, et cetera, et cetera. All those different paths of history correspond to

these quantum, quantum paths and quantum mechanics, these different possible quantum histories.

And one of the things that's kind of surprising about it is they, they branch, you know, there can

be a certain state of the universe and it could do this or it could do that, but they can also

merge. There can be two states of the universe, which their next state, the next state they

produce is the same for both of them. And that process of branching and merging is kind of

critical. And the idea that there can be merging is critical and somewhat non trivial for these

hypergraphs because there's a whole graph isomorphism story and there's a whole very

elaborate set of mathematics. Yes. Among other things. Right. Yes. But so then what happens is

that what one's seeing, okay, so we've got this thing, it's branching, it's merging, et cetera,

et cetera, et cetera. Okay. So now the question is how do we perceive that? Why don't we notice

that the universe is branching and merging? Why is it the case that we just think a definite set

of things happen? Well, the answer is we are embedded in that universe and our brains are

branching and merging too. And so what quantum mechanics becomes a story of is how does a

branching brain perceive a branching universe? And the key thing is as soon as you say,

I think definite things happen in the universe, that means you are essentially conflating

lots of different parts of history. You're saying, actually, as far as I'm concerned,

because I'm convinced that definite things happen in the universe, all these parts of history must

be equivalent. Now, it's not obvious that that would be a consistent thing to do. It might be,

you say, all these parts of history are equivalent, but by golly, moments later,

that would be a completely inconsistent point of view. Everything would have gone to hell in

different ways. The fact that that doesn't happen is, well, that's a consequence of this causal

invariance thing. And the fact that that does happen a little bit is what causes little quantum

effects. And if that didn't happen at all, there wouldn't be anything that sort of is like quantum

mechanics. Quantum mechanics is kind of like in this bundle of paths. It's a little bit like what

happens in statistical mechanics and fluid mechanics, whatever, that most of the time,

you just see this continuous fluid. You just see the world just progressing in this kind of way

that's like this continuous fluid. But every so often, if you look at the exact right experiment,

you can start seeing, well, actually, it's made of these molecules where they might go that way,

or they might go this way, and that's kind of quantum effects. And so, this kind of idea of

where we're sort of embedded in the universe, this branching brain is perceiving this branching

universe, and that ends up being sort of a story of quantum mechanics. That's part of the whole

picture of what's going on. But I think, I mean, to come back to sort of what is the story of

consciousness. So, in the universe, we've got whatever it is, 10 to the 400 atoms of space,

they're all doing these complicated things. It's all a big, complicated, irreducible computation.

The question is, what do we perceive from all of that? And the answer is that we are parsing the

universe in a particular way. Let me again go back to the gas molecules analogy. In the gas in this

room, there are molecules bouncing around all kinds of complicated patterns, but we don't care.

All we notice is there's, you know, the gas laws are satisfied. Maybe there's some fluid dynamics.

These are kind of features of that assembly of molecules that we notice, and then lots of details

we don't notice. When you say we, do you mean the tools of physics, or do you mean literally

the human brain and its perception system? Well, okay. So, the human brain is where it starts,

but we've built a bunch of instruments to do a bit better than the human brain, but they still

have many of the same kinds of ideas, you know, their cameras and their pressure sensors and

these kinds of things. They're not, you know, at this point, we don't know how to make

fundamentally qualitatively different sensory devices. Right. So, it's always just an extension

of the consciousness experience. Or our sensory experience. Sensory experience, but

sensory experience is somehow intricately tied to consciousness. Right. Well, so one question is,

when we are looking at all these molecules in the gas, and there might be 10 to the 20th molecules

in some little box or something, it's like, what do we notice about those molecules? So,

one thing that we can say is, we don't notice that much. We are, you know, we are computationally

bounded observers. We can't go in and say, okay, I'm the 10 to the 20th molecules, and I know

that I can sort of decrypt their motions, and I can figure out this and that. It's like, I'm just

going to say, what's the average density of molecules? And so, one key feature of us is that

we are computationally bounded. And that when you are looking at a universe which is full of

computation and doing huge amounts of computation, but we are computationally bounded, there's only

certain things about that universe that we're going to be sensitive to. We're not going to be,

you know, figuring out what all the atoms of space are doing, because we're just computationally

bounded observers, and we are only sampling these small set of features. So, I think the

two defining features of consciousness that, and I, you know, I would say that the sort of the

preamble to this is, for years, you know, as I've talked about sort of computation and fundamental

features of physics and science, people ask me, so what about consciousness? And I, for years,

I've said, I have nothing to say about consciousness. And, you know, I've kind of

told this story, you know, you talk about intelligence, you talk about life. These are

both features where you say, what's the abstract definition of life? We don't really know the

abstract definition. We know the one for life on Earth, it's got RNA, it's got cell membranes,

it's got all this kind of stuff. Similarly for intelligence, we know the human definition of

intelligence, but what is intelligence abstractly? We don't really know. And so, what I've long

believed is that sort of the abstract definition of intelligence is just computational sophistication.

That is, that as soon as you can be computationally sophisticated, that's kind of the abstract

version, the generalized version of intelligence. So, then the question is, what about consciousness?

And what I sort of realized is that consciousness is actually a step down from intelligence. That

is, that you might think, oh, you know, consciousness is the top of the pie, but it's

the top of the pile. But actually, I don't think it is. I think that there's this notion of kind

of computational sophistication, which is the generalized intelligence. But consciousness

has two limitations, I think. One of them is computational boundedness. That is, that we're

only perceiving a sort of computationally bounded view of the universe. And the other is this idea

of a single thread of time. That is, that we, and in fact, we know neurophysiologically our brains

go to some trouble to give us this one thread of attention, so to speak. And it isn't the case that

in all the neurons in our brains that, at least in our conscious, the correspondence of language,

in our conscious experience, we just have the single thread of attention, single thread of

perception. And maybe there's something unconscious that's bubbling around that's the kind of

almost the quantum version of what's happening in our brain, so to speak. We've got the classical

flow of what we are mostly thinking about, so to speak. But there's this kind of bubbling around

of other paths that is all those other neurons that didn't make it to be part of our sort of

conscious stream of experience. So in that sense, intelligence as computational sophistication is

much broader than the computational constraints which consciousness operates under, and also the

sequential, like the sequential thing, like the notion of time. That's kind of interesting. But

then the follow up question is like, okay, starting to get a sense of what is intelligence, and how

does that connect to our human brain? Because you're saying intelligence is almost like a fabric,

like what we like plug into it or something, like our consciousness plugs into it.

Yeah, I mean, the intelligence, I think the core, I mean, you know, intelligence at some

level is just a word, but we are asking, you know, what is the notion of intelligence as we

generalize it beyond the bounds of humans, beyond the bounds of even the AIs that we humans have

built and so on? You know, what is intelligence? You know, is the weather, you know, people say the

weather has a mind of its own. What does that mean? You know, can the weather be intelligent?

Yeah. What does agency have to do with intelligence here? So is intelligence just

like your conception of computation, just intelligence is the capacity to perform

computation and the sea of? Yeah, I think so. I mean, I think that's right. And I think that,

you know, this question of, is it for a purpose? Okay, that quickly degenerates into a horrible

philosophical mess. Because, you know, whenever you say, did the weather do that for a purpose?

Yeah. Right? Well, yes, it did. It was trying to move a bunch of hot air from the equator to the

poles or something. That's its purpose. But why? Because I seem to be equally as dumb today as I

was yesterday. So there's some persistence, like a consistency over time that the intelligence

I plugged into. So like, what's, it seems like there's a hard constraint between the amount of

computation I can perform in my consciousness. Like they seem to be really closely connected

somehow. Well, I think the point is that the thing that gives you kind of the ability to have

kind of conscious intelligence, you can have kind of this, okay, so one thing is we don't know

intelligences other than the ones that are very much like us. Yes. Right. And the ones that are

very much like us, I think have this feature of single thread of time, bounded, you know,

computationally bounded. But you also need computational sophistication. Having a single

thread of time and being computationally bounded, you could just be a clock going tick tock. That

would satisfy those conditions. But the fact that we have this sort of irreducible computational

ability, that's an important feature. That's sort of the bedrock on which we can construct

the things we construct. Now, the fact that we have this experience of the world that has the

single thread of time and computational boundedness, the thing that I sort of realized is it's that

that causes us to deduce from this irreducible mess of what's going on in the physical world,

the laws of physics that we think exist. So in other words, if we say, why do we believe that

there is, you know, continuous space, let's say, why do we believe that gravity works the way it

does? Well, in principle, we could be kind of parsing details of the universe that were, you

know, that OK, the analogy is, again, with the statistical mechanics and molecules in a box,

we could be sensitive to every little detail of the swirling around of those molecules. And we

could say what really matters is the, you know, the wiggle effect that is, you know, that is

something that we humans just never noticed because it's some weird thing that happens when

there are 15 collisions of air molecules and this happens and that happens. We just see the pure

motion of a ball moving about. Right. Why do we see that? Right. And the point is that that what

seems to be the case is that the things that if we say, given this sort of hypergraph that's

updating and all the details about all the sort of atoms of space and what they do, and we say,

how do we slice that to what we can be sensitive to? What seems to be the case is that as soon as

we assume, you know, computational boundedness, single thread of time, that leads us to general

relativity. In other words, we can't avoid that. That's the way that we will parse the universe.

Given those constraints, we parse the universe according to those particular in such a way that

we say the aggregate reducible sort of pocket of computational reducibility that we slice out of

this kind of whole computational irreducible ocean of behavior is just this one that corresponds to

general relativity. Yeah, but we don't perceive general relativity. Well, we do if we do fancy

experiments. So you're saying so perceive really does mean the full. We drop something. That's a

great example of general relativity in action. No, but like what's the difference in that and

Newtonian mechanics? I mean, oh, it doesn't. This is when I say general relativity, that's

the uber theory, so to speak. I mean, Newtonian gravity is just the approximation that we can make,

you know, on the earth and things like that. So this is, you know, the phenomenon of gravity

is one that is a consequence of, you know, we would perceive something very different from

gravity. So so the way to understand that is when we think about OK, so we make up reference frames

with which we parse what's happening in space and time. So in other words, one of the one of

the things that we do is we say as time progresses everywhere in space is something happens at a

particular time and then we go to the next time and we say this is what space is like at the next

time is what space is like at the next time. That's it's the reason we are used to doing that

is because, you know, when we look around, we might see, you know, ten hundred meters away.

The time it takes light to travel that distance is really short compared to the time it takes our

brains to know what happened. So as far as our brains are concerned, we are parsing the universe

in this. There is a moment in time, it's all of space. There's a moment in time, it's all of

space. If we were the size of planets or something, we would have a different perception because the

speed of light would be much more important to us. We wouldn't have this perception that

things happen progressively in time everywhere in space. And so that's an important kind of

constraint. And the reason that we kind of parse the universe in the way that causes us to say

gravity works the way it does is because we're doing things like deciding that we can say the

universe exists, space has a definite structure. There is a moment in time, space has this definite

structure. We move to the next moment in time, space has another structure. That kind of setup

is what lets us kind of deduce kind of what parse the universe in such a way that we say gravity

works the way it does. So that kind of reference frame is that the illusion of that is that you're

saying that's somehow useful for consciousness. That's what consciousness does. Because in a

sense, what consciousness is doing is it's insisting that the universe is kind of sequentialized.

And it is not allowing the possibility that, oh, there are these multiple threads of time

and they're all flowing differently. It's like saying, no, everything is happening in this one

thread of experience that we have. And that illusion of that one thread of experience

cannot happen at the planetary scale. Are you saying typical human, are you saying we are at a

human level is special here for consciousness? Well, for our kind of consciousness, if we existed

at a scale close to the elementary length, for example, then our perception of the universe

will be absurdly different. Okay. But this makes consciousness seem like a weird side effect to

this particular scale. And so who cares? I mean, consciousness is not that special.

Look, I think that a very interesting question is, which I've certainly thought a little bit about,

is what can you imagine? What is a sort of factoring of something? What are some other

possible ways you could exist, so to speak? And if you were a photon, if you were some kind of thing

that was kind of, you know, intelligence represented in terms of photons, you know,

for example, the photons we receive in the cosmic microwave background, those photons,

as far as they're concerned, the universe just started. They were emitted, you know,

100,000 years after the beginning of the universe, they've been traveling at the speed of light,

time stayed still for them, and then they just arrived and we just detected them. So for them,

the universe just started. And that's a different perception of, you know, that has

implications for a very different perception of time. They don't have that single thread

that seems to be really important for being able to tell a heck of a good story.

So we humans, we can tell a story. Right. We can tell a story. What other kind of stories can you

tell? So photon is a really boring story. Yeah. I mean, so that's a, I don't know if they're a

boring story, but I think it's, you know, I've been wondering about this and I've been asking,

you know, friends of mine who are science fiction writers and things, have you written stuff about

this? And I've got one example, a great collection of books from my friend Rudy Rooker, which I have

to say, they're books that are very informed by a bunch of science that I've done. And the thing

that I really loved about them is, you know, in the first chapter of the book, the Earth is consumed

by these things called nants, which are nano, nanobot type things. So, you know, so the Earth

is gone in the first, but then it comes back. But then, yeah, right. That was only a micro

spoiler. It's only chapter one. But the thing that is not a real spoiler alert because it's

such a complicated concept, but in the end, the Earth is saved by this thing called the

principle of computational equivalence, which is a kind of a core scientific idea of mine.

And I was just like, like thrilled. I don't read fiction books very often. And I was just thrilled.

I get to the end of this and it's like, oh, my gosh, you know, everything is saved by this sort

of deep scientific principle. Can you maybe elaborate how the principle of computational

equivalence can save a planet? That would, that would be a terrible spoiler. That would be a

spoiler. But no, but let me say what the principle of computational equivalence is. So the question

is, you are, you have a system, you have some rule, you can think of its behavior as corresponding

to a computation. The question is, how sophisticated is that computation? The statement of the principle

of computational equivalence is, as soon as it's not obviously simple, it will be as sophisticated

as anything. And so that has the implication that, you know, rule 30, you know, our brains,

other things in physics, they're all ultimately equivalent in the computations they can do.

And that's what leads to this computational irreducibility idea because the reason we don't

get to jump ahead, you know, and out think rule 30 is because we're just computationally equivalent

to rule 30. So we're kind of just both just running computations that are the same sort of

raw, the same level of computation, so to speak. So that's kind of the idea there. And the question,

I mean, it's like the, you know, in the science fiction version would be, okay, somebody says,

we just need more servers, get us more servers. The way to get even more servers is turn the

whole planet into a bunch of microservers. And that's where it starts. And so the question of,

you know, computational equivalence, principle of computational equivalence is, well, actually,

you don't need to build those custom servers. Actually, you can just use natural computation

to compute things, so to speak. You can use nature to compute. You don't need to have done

all that engineering. I mean, it kind of feels a little disappointing that you say, we're going to

build all these servers. We're going to do all these things. We're going to make, you know,

maybe we're going to have human consciousness uploaded into, you know, some elaborate digital

environment. And then you look at that thing and you say, it's got electrons moving around,

just like in a rock. And then you say, well, what's the difference? And the principle of

computational equivalence says there isn't, at some level, a fundamental, you know, you can't say,

mathematically, there's a fundamental difference between the rock that is the future of human

consciousness and the rock that's just a rock. Now, what I've sort of realized with this kind

of consciousness thing is there is an aspect of this that seems to be more special. And for

example, something I haven't really teased apart properly is when it comes to something like the

weather and the weather having a mind of its own or whatever, or your average, you know,

pulsar magnetosphere acting like a sort of intelligent thing, how does that relate to,

you know, how is that entity related to the kind of consciousness that we have? And sort of,

what would the world look like, you know, to the weather? If we think about the weather as a mind,

what will it perceive? What will its laws of physics be? I don't really know.

Because it's very parallel.

It's very parallel, among other things. And it's not obvious. I mean, this is a really kind of

mindbending thing because we've got to try and imagine a parsing of the universe different from

the one we have. And by the way, when we think about extraterrestrial intelligence and so on,

I think that's kind of the key thing is, you know, we've always assumed, I've always assumed,

okay, the extraterrestrials, at least they have the same physics. We all live in the same universe.

They've got the same physics. But actually, that's not really right because the extraterrestrials

could have a completely different way of parsing the universe. So it's as if, you know, there could

be for all we know, right here in this room, you know, in the details of the motion of these gas

molecules, there could be an amazing intelligence that we were like, but we have no way of, we're

not parsing the universe in the same way. If only we could parse the universe in the right way,

you know, immediately this amazing thing that's going on and this, you know, huge culture that's

developed and all that kind of thing would be obvious to us, but it's not because we have our

particular way of parsing the universe. Would that thing also have an agency? I don't know the right

word to use, but something like consciousness, but a different kind of consciousness?

I think it's a question of just what you mean by the word, because I think that the,

you know, this notion of consciousness and the, okay, so some people think of consciousness as

sort of a key aspect of it is that we feel that there's sort of a feeling of that we exist in

some way, that we have this intrinsic feeling about ourselves. You know, I suspect that any

of these things would also have an intrinsic feeling about themselves. I've been sort of

trying to think recently about constructing an experiment about what if you were just a piece

of a cellular automaton, let's say, you know, what would your feeling about yourself actually be?

And, you know, can we put ourselves in the shoes, in the cells of the cellular automaton,

so to speak? Can we get ourselves close enough to that, that we could have a sense of what the

world would be like if you were operating in that way? And it's a little difficult because,

you know, you have to not only think about what are you perceiving, but also what's actually

going on in your brain. And our brains do what they actually do. And they don't, it's, you know,

I think there might be some experiments that are possible with neural nets and so on,

where you can have something where you can at least see in detail what's happening inside the

system. And one of my projects to think about is, is there a way of kind of getting a sense

kind of from inside the system about what its view of the world is and how it, you know,

can we make a bridge? See, the main issue is this. It's a sort of philosophically difficult thing

because it's like we do what we do. We understand ourselves, at least to some extent.

We humans understand ourselves.

That's correct. But yet, okay, so what are we trying to do, for example, when we are trying to

make a model of physics? What are we actually trying to do? Because, you know, you say, well,

can we work out what the universe does? Well, of course we can. We just watch the universe. The

universe does what it does. But what we're trying to do when we make a model of physics is we're

trying to get to the point where we can tell a story to ourselves that we understand that is also

a representation of what the universe does. So it's this kind of, you know, can we make a bridge

between what we humans can understand in our minds and what the universe does? And in a sense,

you know, a large part of my kind of life efforts have been devoted to making computational

language, which kind of is a bridge between what is possible in the computational universe

and what we humans can conceptualize and think about. In a sense, when I built Wolfram Language

and our whole sort of computational language story, it's all about how do you take sort of raw

computation and this ocean of computational possibility and how do we sort of represent

pieces of it in a way that we humans can understand and that map onto things that we care about doing.

And in a sense, when you add physics, you're adding this other piece where we can, you know,

mediated by computer, can we get physics to the point where we humans can understand something

about what's happening in it? And when we talk about an alien intelligence, it's kind of the

same story. It's like, is there a way of mapping what's happening there onto something that we

humans can understand? And, you know, physics in some sense is like our exhibit one of the story

of alien intelligence. It's an alien intelligence in some sense. And what we're doing in making a

model of physics is mapping that onto something that we understand. And I think, you know, a lot

of these other things that I've recently been kind of studying, whether it's molecular biology,

other kinds of things, which we can talk about a bit, those are other cases where we're in a sense

trying to, again, make that bridge between what we humans understand and sort of the natural

language of that sort of alien intelligence in some sense. When you're talking about,

just to backtrack a little bit about cellular automata, being able to, what's it like to be

a cellular automata in the way that's equivalent to what is it like to be a conscious human being?

How do you approach that? So is it looking at some subset of the cellular automata, asking questions

of that subset, like how the world is perceived, how you as that subset, like for that local pocket

of computation, what are you able to say about the broader cellular time? And that somehow then

can give you a sense of how to step outside of that cellular time. Right, but the tricky part is

that that little subset, what it's doing is it has a view of itself. And the question is,

how do you get inside it? It's like when we, with humans, it's like we can't get inside each other's

consciousness. That doesn't really even make sense. It's like there is an experience that

somebody is having, but you can perceive things from the outside, but sort of getting inside

it, it doesn't quite make sense. And for me, these sort of philosophical issues, and this one I have

not untangled, so let's be... For me, the thing that has been really interesting in thinking

through some of these things is when it comes to questions about consciousness or whatever else,

it's like when I can run a program and actually see pictures and make things concrete, I have a

much better chance to understand what's going on than when I'm just trying to figure out what's

going on. I have a much better chance to understand what's going on than when I'm just trying to

reason about things in a very abstract way. Yeah, but there may be a way to map the program to your

conscious experience. So for example, when you play a video game, you do a first person shooter,

you walk around inside this entity. It's a very different thing than watching this entity. So

connect more and more, connect this full conscious experience to the subset of the cellular automata.

Yeah, it's something like that. But the difference in the first person shooter thing is there's still

your brain and your memory is still remembering. You still have... It's hard to... I mean, again,

what one's going to get, one is not going to actually be able to be the cellular automaton.

One's going to be able to watch what the cellular automaton does. But this is the frustrating thing

that I'm trying to understand how to think about being it, so to speak.

Okay. So like in virtual reality, there's a concept of immersion, like with anything,

with video games, with books, there's a concept of immersion. It feels like over time, if the

virtual reality experience is well done, and maybe in the future it'll be extremely well done,

the immersion leads you to feel like... You mentioned memories. You forget that you even

ever existed outside that experience. It's so immersive. I mean, you could argue sort of

mathematically that you can never truly become immersed, but maybe you can. I mean, why can't you

merge with the cellular automata? I mean, aren't you just part of the same fabric? Why can't you

just like... Well, that's a good question. I mean, so let's imagine the following scenario. Let's

imagine... Can you return? But then can you return back? Well, yeah, right. I mean, it's like,

let's imagine you've uploaded, your brain is scanned, you've got every synapse mapped out,

you upload everything about you, the brain simulator, you upload the brain simulator,

and the brain simulator is basically some glorified cellular automaton. And then you say,

well, now we've got an answer to what does it feel like to be a cellular automaton?

It feels just like it felt to be ordinary you, because they're both computational systems,

and they're both operating in the same way. But I think there's somehow more to it,

because in that sense, when you're just making a brain simulator, we're just saying there's

another version of our consciousness. The question that we're asking is, if we tease away from our

consciousness and get to something that is different, how do we make a bridge to understanding

what's going on there? And there's a way of thinking about this. Okay, so this is coming

on to questions about the existence of the universe and so on. But one of the things is

there's this notion that we have of ruleal space. So we have this idea of this physical space,

which is something you can move around in that's associated with the extent of the

spatial hypergraph. Then there's what we call branchial space, the space of quantum branches.

So in this thing we call the multiway graph of all of this branching histories,

there's this idea of a kind of space where instead of moving around in physical space,

you're moving from history to history, so to speak, from one possible history to another

possible history. And that's kind of a different kind of space that is the space in which quantum

mechanics plays out. Quantum mechanics, for example, I think we're slowly understanding

things like destructive interference in quantum mechanics, that what's happening is branchial

space is associated with phase in quantum mechanics. And what's happening is the two

photons that are supposed to be interfering and destructively interfering are winding up at

different ends of branchial space. And so us as these poor observers that have branching brains

that are trying to conflate together these different threads of history and say,

we've really got a consistent story that we're telling here. We're really knitting together

these threads of history. By the time the two photons wound up at opposite ends of branchial

space, we just can't knit them together to tell a consistent story. So for us,

that's sort of the analog of destructive interference. Got it. And then there's

rule space too, which is the space of rules. Yes. Well, that's another level up. So there's

the question. Actually, I do want to mention one thing because it's something I've realized in

recent times and I think it's really, really kind of cool, which is about time dilation and

relativity. And it kind of helps to understand it's something that kind of helps in understanding

what's going on. So according to relativity, if you have a clock, it's ticking at a certain rate,

you send it in a spacecraft that's going at some significant fraction of the speed of light,

to you as an observer at rest, that clock that's in the spacecraft will seem to be ticking much

more slowly. And so in other words, it's kind of like the twin who goes off to Alpha Centauri and

goes very fast will age much less than the twin who's on Earth that is just hanging out where

they're hanging out. Okay, why does that happen? Okay, so it has to do with what motion is.

So in our models of physics, what is motion? Well, when you move from somewhere to somewhere,

you're having to sort of recreate yourself at a different place in space.

When you exist at a particular place and you just evolve with time, again, you're updating yourself,

you're following these rules to update what happens. Well, so the question is, when you

have a certain amount of computation in you, so to speak, when there's a certain amount,

you know, you're computing, the universe is computing at a certain rate, you can either

use that computation to work out sitting still where you are, what's going to happen successively

in time, or you can use that computation to recreate yourself as you move around the universe.

Mm hmm. And so time dilation ends up being, it's really cool, actually, that this is explainable

in a way that isn't just imagine the mathematics of relativity. But time dilation is a story of

the fact that as you kind of are recreating yourself as you move, you are using up some

of your computation. And so you don't have as much computation left over to actually work out what

happens progressively with time. So that means that time is running more slowly for you because

it is, you're using up your computation, your clock can't tick as quickly, because every tick

of the clock is using up some computation, but you already use that computation up on moving at,

you know, half the speed of light or something. And so that's why time dilation happens.

And so you can start, so it's kind of interesting that one can sort of get an intuition about

something like that, because it has seemed like just a mathematical fact about the mathematics of

special relativity and so on. Well, for me, it's a little bit confusing what the you in that picture

is, because you're using up computation. Okay, so we're simply saying the entity is updating

itself according to the way that the universe updates itself. And the question is, you know,

those updates, let's imagine the you as a clock. Okay. And the clock is, you know, there's all

these little updates, the hypergraph and a sequence of updates cause the pendulum to swing back the

other way, and then swing back, swinging back and forth. Okay. And all of those updates are

contributing to the motion of, you know, the pendulum going back and forth or the little

oscillator moving, whatever it is. Okay. But then the alternative is that sort of situation one,

where the thing is at rest, situation two, where it's kind of moving, what's happening is it is

having to recreate itself at every moment, the thing is going to have to do the computations

to be able to sort of recreate itself at a different position in space. And that's kind of

the intuition behind, so it's either going to spend its computation recreating itself at a

different position in space, or it's going to spend its computation doing the sort of doing the

updating of the, you know, of the ticking of the clock, so to speak. So the more updating is doing,

the less the ticking of the clock update is doing. That's right. The more it's having to update

because of motion, the less it can update the clock. Obviously, there's a sort of mathematical

version of it that relates to how it actually works in relativity, but that's kind of, to me,

that was sort of exciting to me that it's possible to have a really mechanically explainable story

there. And similarly in quantum mechanics, this notion of branching brains perceiving branching

universes, to me, that's getting towards a sort of mechanically explainable version of what happens

in quantum mechanics, even though it's a little bit mind bending to see, you know, these things

about under what circumstances can you successfully knit together those different threads of history,

and when do things sort of escape, and those kinds of things. But the thing about this physical space

and physical space, the main sort of big theory is general relativity, the theory of gravity,

and that tells you how things move in physical space. In branchial space, the big theory is the

Feynman path integral, which it turns out tells you essentially how things move in quantum in the

space of quantum phases. So it's kind of like motion in branchial space. And it's kind of a

fun thing to start thinking about all these things that we know in physical space, like event horizons

and black holes and so on. What are the analogous things in branchial space? For example, the speed

of light, what's the analog of the speed of light in branchial space? It's the maximum speed of

quantum entanglement. So the speed of light is a flash bulb goes off here. What's the maximum rate

at which the effect of that flash bulb is detectable moving away in space? So similarly,

in branchial space, something happens. And the question is, how far in this branchial space,

in the space of quantum states, how far away can that get within a certain period of time?

And so there's this notion of a maximum entanglement speed. And that might be observable.

That's the thing we've been sort of poking at, is might there be a way to observe it,

even in some atomic physics kind of situation? Because one of the things that's weird in

quantum mechanics is when we study quantum mechanics, we mostly study it in terms of small

numbers of particles. This electron does this, this thing on an ion trap does that and so on.

But when we deal with large numbers of particles, kind of all bets are off. It's kind of too

complicated to deal with quantum mechanics. And so what ends up happening is, so this question

about maximum entanglement speed and things like that may actually play in the sort of story of

many body quantum mechanics and even have some suspicions about things that might happen even in

one of the things I realized I'd never understood and it's kind of embarrassing, but I think I now

understand a little better, is when you have chemistry and you have quantum mechanics,

it's like, well, there's two carbon atoms in this molecule and we do a reaction and we draw a

diagram and we say this carbon atom ends up in this place. And it's like, but wait a minute,

in quantum mechanics, nothing ends up in a definite place. There's always just some wave

function for this to happen. How can it be the case that we can draw these reasonable, it just

ended up in this place? And you have to kind of say, well, the environment of the molecule

effectively made a bunch of measurements on the molecule to keep it kind of classical.

And that's a story that has to do with this whole thing about measurements have to do with this

idea of, can we conclude that something definite happened? Because in quantum mechanics,

the intrinsic quantum mechanics, the mathematics of quantum mechanics is all about,

they're just these amplitudes for different things to happen. Then there's this thing of,

and then we make a measurement and we conclude that something definite happened. And that has

to do with this thing, I think, about sort of moving about knitting together these different

threads of history and saying, this is now something where we can definitively say something

definite happened. In the traditional theory of quantum mechanics, it's just like, after you've

done all this amplitude computation, then this big hammer comes down and you do a measurement

and it's all over. And that's been very confusing. For example, in quantum computing,

it's been a very confusing thing because when you say, in quantum computing, the basic idea is

you're going to use all these separate threads of computation, so to speak, to do all the different

parts of, try these different factors for an integer or something like this. And it looks

like you can do a lot because you've got all these different threads going on. But then you have to

say, well, at the end of it, you've got all these threads and every thread came up with a definite

answer, but we got to conflate those together to figure out a definite thing that we humans

can take away from it, a definite, so the computer actually produced this output.

So having this branchial space and this hypergraph model of physics, do you think it's possible to

then make predictions that are definite about many body quantum mechanical systems?

I think it's likely, yes. Every one of these things, when you go from the underlying theory,

which is complicated enough and it's, I mean, the theory at some level is beautifully simple,

but as soon as you start actually trying to, it's this whole question about how do you bridge it to

things that we humans can talk about, it gets really complicated. And this thing about actually

getting it to a definite prediction about definite thing you can say about chemistry or something

like this, that's just a lot of work. So I'll give you an example. There's a thing called the

quantum Zeno effect. So the idea is quantum stuff happens, but then if you make a measurement,

you're kind of freezing time in quantum mechanics. So it looks like there's a possibility that with

sort of the relationship between the quantum Zeno effect and the way that many body quantum

mechanics works and so on, maybe just conceivably, it may be possible to actually figure out a way

to measure the maximum entanglement speed. And the reason we can potentially do that

is because the systems we deal with in terms of atoms and things, they're pretty big. A mole of

atoms is a lot of atoms, but it's something where to get, when we're dealing with how can you see

10 to the minus 100, so to speak? Well, by the time you've got 10 to the 30th atoms, you're within

a little bit closer striking distance of that. It's not like, oh, we've just got two atoms and

we're trying to see down to 10 to the minus 100 meters or whatever. So I don't know how it will

work, but this is a potential direction. And if you can tell, by the way, if we could measure

the maximum entanglement speed, we would know the elementary length. These are all related.

So if we get that one number, we just need one number. If we can get that one number,

the theory has no parameters anymore. And there are other places, well, there's another hope for

doing that is in cosmology. In this model, one of the features is the universe is not fixed

dimensional. We think we live in three dimensional space, but this hypergraph doesn't have any

particular dimension. It can emerge as something which on an approximation, it's as if you say,

what's the volume of a sphere in the hypergraph where a sphere is defined as how many nodes do

you get to when you go a distance R away from a given point? And you can say, well, if I get to

about R cubed nodes, when I go a distance R away in the hypergraph, then I'm living roughly in

three dimensional space. But you might also get to R to the point 2.92 for some value of R. As R

increases, that might be the sort of fit to what happens. And so one of the things we suspect is

that the very early universe was essentially infinite dimensional, and that as the universe

expanded, it became lower dimensional. And so one of the things that is another little sort of point

where we think there might be a way to actually measure some things is dimension fluctuations in

the early universe. That is, is there leftover dimension fluctuation of at the time of the cosmic

microwave background, 100,000 years or something after the beginning of the universe? Is it still

the case that there were pieces of the universe that didn't have dimension three, that had

dimension 3.01 or something? And can we tell that? Is that possible to observe fluctuations in

dimensions? I don't even know what that entails. Okay. So the question, which should be an

elementary exercise in electrodynamics, except it isn't, is understanding what happens to a

photon when it propagates through 3.01 dimensional space. So for example, the inverse square law

is a consequence of the surface area of a sphere is proportional to R squared. But if you're not

in three dimensional space, the surface area of sphere is not proportional to R squared. It's R

to the whatever 2.01 or something. And so that means that I think when you kind of try and do

optics, you know, a common principle in optics is Huygens principle, which basically says that every

piece of a wave front of light is a source of new spherical waves. And those spherical waves,

if they're different dimensional spherical waves, will have other characteristics. And so there will

be bizarre optical phenomena which we haven't figured out yet. So you're looking for some weird

photon trajectories that designate that it's 3.01 dimensional space? Yeah. Yeah. That would be an

example of, I mean, you know, there are only a certain number of things we can measure about

photons. You know, we can measure their polarization, we can measure their frequency,

we can measure their direction, those kinds of things. And, you know, how that all works out.

And, you know, in the current models of physics, you know, it's been hard to explain how the

universe manages to be as uniform as it is. And that's led to this inflation idea that,

to the great annoyance of my then collaborator, we figured out in like 1979, we had this

realization that you could get something like this. But it seemed implausible that that's the

way the universe worked. So we put it in a footnote. But in any case, I've never really

completely believed it. But that's an idea for how to sort of puff out the universe faster than the

speed of light, early moments of the universe. That's the sort of the inflation idea and that

you can somehow explain how the universe manages to be as uniform as it is. In our model, this turns

out to be much more natural because the universe just starts very connected. The hypergraph is not

such that the ball that you grow starting from a single point has volume R cubed, it might have

volume R to the 500 or R to the infinity. And so that means that you sort of naturally get this

much higher degree of connectivity and uniformity in the universe. And then the question is,

this is sort of the mathematical physics challenge, is in the standard theory of the universe,

there's the Friedman Robertson Walker universe, which is the kind of standard model where the

universe is isotropic and homogeneous. And you can then work out the equations of general relativity,

and you can figure out how the universe expands. We would like to do the same kind of thing,

including dimension change. This is just difficult mathematical physics. I mean,

the reason it's difficult is the sort of fundamental reason it's difficult. When

people invented calculus 300 years ago, calculus was a story of understanding change and change

as a function of a variable. So people study univariate calculus, they study multivariate

calculus, it's one variable, it's two variables, three variables. But whoever studied, you know,

2.5 variable calculus, turns out nobody. Turns out that what we need to have to understand these

fractional dimensional spaces, which don't work like well, they're spaces where the effective

dimension is not an integer. So you can't apply the tools of calculus naturally and easily to

fractional dimensions? No. So somebody has to figure out how to do that. Yeah,

we're trying to figure this out. I mean, it's very interesting. I mean, it's very connected to

very frontier issues in mathematics. It's very beautiful. So is it possible? Is it possible?

We're dealing with a scale that's so, so much smaller than our human scale. Is it possible

to make predictions versus explanations? Do you have a hope that with this hypergraph model,

you'd be able to make predictions that then could be validated with a physics experiment,

predictions that couldn't have been done or weren't done otherwise? Yeah, yeah, yeah. I mean,

you know, I think which, in which domain do you think? Okay, so they're going to be cosmology ones

to do with dimension fluctuations in the universe. That's a very bizarre effect. Nobody, you know,

dimension fluctuations is just something nobody ever looked for that. If anybody sees dimension

fluctuation, that's a huge flag that something like our model is going on. And how one detects

that, you know, that's a problem of kind of, you know, that's a problem of traditional physics in

a sense of what's the best way to actually figure that out. And for example, that's one,

there are all kinds of things one could imagine. I mean, there are things that in black hole mergers,

it's possible that there will be effects of maximum entanglement speed in large black hole mergers.

That's another possible thing. And all of that is detected through like what? Do you have a

hope for LIGO type of situation? Like that's gravitational waves? Yeah. Or alternatively,

I mean, I think it's, you know, look, figuring out experiments is like figuring out technology

inventions. That is, you know, you've got a set of raw materials, you've got an underlying model,

and now you've got to be very clever to figure out, you know, what is that thing I can measure

that just somehow, you know, leverages into the right place. And we've spent less effort on that

than I would have liked. Because one of the reasons is that I think that the physicists

who've been working on our models, with now lots of physicists actually, it's very, very nice. It's

kind of, it's one of these cases where I'm almost, I'm really kind of pleasantly surprised that the

sort of absorption of the things we've done has been quite rapid and quite sort of, you know,

very positive. So it's a Cambrian explosion of physicists too, not just ideas. Yes. I mean,

you know, a lot of what's happened that's really interesting, and again, not what I expected,

is there are a lot of areas of sort of very elaborate, sophisticated mathematical physics,

whether that's causal set theory, whether it's higher category theory, whether it's categorical

quantum mechanics, all sorts of elaborate names for these things, spin networks, perhaps,

you know, causal dynamical triangulations, all kinds of names of these fields. And these fields

have a bunch of good mathematical physicists in them who've been working for decades in these

particular areas. And the question is, but they've been building these mathematical structures.

And the mathematical structures are interesting, but they don't typically sit on anything.

They're just mathematical structures. And I think what's happened is our models provide kind of

a machine code that lives underneath those models. So a typical example, this is due to

Jonathan Gorod, who's one of the key people who's been working on our project. This is in,

okay, so I'll give you an example just to give a sense of how these things connect. This is in

causal set theory. So the idea of causal set theory is there are, in spacetime, we imagine

that there's space and time. It's a three plus one dimensional, you know, setup. We imagine that

there are just events that happen at different times and places in space and time. And the idea

of causal set theory is the only thing you say about the universe is there are a bunch of events

that happen sort of randomly at different places in space and time. And then the whole sort of

theory of physics has to be to do with this graph of causal relationships between these randomly

thrown down events. So they've always been confused by the fact that to get even Lorentz

invariants, even relativistic invariants, you need a very special way to throw down those events.

And they've had no natural way to understand how that would happen. So what Jonathan figured out

is that, in fact, from our models, instead of just generating events at random, our models

necessarily generate events in some pattern in spacetime effectively that then leads to Lorentz

invariants and relativistic invariants and all those kinds of things. So it's a place where

all the mathematics that's been done on, well, we just have a random collection of events.

Now what consequences does that have in terms of causal set theory and so on? That can all be kind

of wheeled in now that we have some different underlying foundational idea for what the

particular distribution of events is as opposed to just what we throw down random events.

And so that's a typical sort of example of what we're seeing in all these different areas of kind

of how you can take really interesting things that have been done in mathematical physics

and connect them. And it's really kind of beautiful because the abstract models we have

just seem to plug into all these different very interesting, very elegant abstract ideas.

But we're now giving sort of a reason for that to be the way, a reason for one to care. I mean,

it's like saying you can think about computation abstractly. You can think about, I don't know,

combinators or something as abstract computational things. And you can sort of do all kinds of study

of them. But it's like, why do we care? Well, okay, Turing machines are a good start because

you can kind of see they're sort of mechanically doing things. But when we actually start thinking

about computers, computing things, we have a really good reason to care. And this is sort of

what we're providing, I think, is a reason to care about a lot of these areas of mathematical

physics. So that's been very nice. So I'm not sure we've ever got to the

question of why does the universe exist at all? No, no, let's talk about that. So it's not the

simplest question in the world. So it takes a few steps to get to it. And it's nevertheless even

surprising that you can even begin to answer this question, as you were saying.

Indeed. I'm very surprised. So the next thing to perhaps understand is this idea of ruleal space.

So we've got kind of physical space. We've got branchial space, the space of possible quantum

histories. And now we've got another level of kind of abstraction, which is ruleal space. And

here's where that comes from. So you say, okay, you say we've got this model for the universe.

We've got a particular rule. And we run this rule and we get the universe. So that's interesting.

Why that rule? Why not another rule? And so that confused me for a long time. And I realized,

well, actually, what if the thing could be using all possible rules? What if at every step,

in addition to saying apply a particular rule at all places in this hypergraph, one could say,

just take all possible rules and apply all possible rules at all possible places in this

hypergraph. And then you make this ruleal multiway graph, which both is all possible

histories for a particular rule and all possible rules. So the next thing you'd say is, how can you

get anything reasonable out of it? How can anything real come out of the set of all possible

rules applied in all possible ways? This is a subtle thing, which I haven't fully untangled.

There is this object, which is the result of running all possible rules in all possible ways.

And you might say, if you're running all possible rules, why can't everything possible happen?

Well, the answer is because when you, there's sort of this entanglement that occurs.

So let's say that you have a lot of different possible initial conditions, a lot of different

possible states. Then you're applying these different rules. Well, some of those rules can

end up with the same state. So it isn't the case that you can just get from anywhere to anywhere.

There's this whole entangled structure of what can lead to what, and there's a definite structure

that's produced. I think I'm going to call that definite structure the rulead, the limit of kind

of all possible rules being applied in all possible ways. And you're saying that structure is finite,

so that somehow connects to maybe a similar kind of thing as like causal invariance.

Well, it happens that the rulead necessarily has causal invariance. That's a feature of,

that's just a mathematical consequence of essentially using all possible rules

plus universal computation gives you the fact that from any diverging paths, the paths will

always converge. But does that necessarily infer that the rulead is finite?

In the end, it's not necessarily finite. I mean, just like the history of the universe may not be

finite. The history of the universe, time may keep going forever. You can keep running the

computations of the rulead and you'll keep spewing out more and more and more structure. It's like

time doesn't have to end. But the issue is there are three limits that happen in this rulead

object. One is how long you run the computation for. Another is how many different rules you're

applying. And another is how many different states you start from. And the mixture of those

three limits. I mean, this is just mathematically a horrendous object. And what's interesting about

this object is the one thing that does seem to be the case about this object is it connects with

ideas in higher category theory. And in particular, it connects to some of the 20th century's most

abstract mathematics done by this chap Grothendieck. Grothendieck had a thing called the infinity

groupoid, which is closely related to this rulead object. Although the details of the relationship,

you know, I don't fully understand yet. But I think that what's interesting is this thing that

is sort of this very limiting object. So, okay, so a way to think about this that, again, will

take us into another direction, which is the equivalence between physics and mathematics.

The way that, well, let's see, maybe this is just to give a sense of this kind of groupoid and

things like that. You can think about, in mathematics, you can think you have certain axioms,

they're kind of like atoms, and you, well, actually, let's say, let's talk about mathematics

for a second. So what is mathematics? What is it made of, so to speak? Mathematics, there's a bunch

of statements, like, for addition, x plus y is equal to y plus x, that's a statement in mathematics.

Another statement would be, you know, x squared minus one is equal to x plus one, x minus one.

There are an infinite number of these possible statements of mathematics.

Well, it's not, I mean, it's not just, I guess, a statement, but with x plus y,

it's a rule that you can, I mean, you think of it as a rule.

It is a rule. It's also just a thing that is true in mathematics.

Right. The statement of truth, okay.

Right. And what you can imagine is, you imagine just laying out this giant kind of ocean

of all statements. Well, actually, you first start, okay, this is where this was segueing

into a different thing. Let me not go in this direction for a second.

Let's not go to metamathematics just yet.

Yeah, we'll maybe get to metamathematics, but it's, so let me not, let me explain the groupoid

and things later. But, so let's come back to the universe, always a good place to be in,

so to speak.

Yeah, so what does the universe have to do with the rule add, the rule of L space,

and how that's possibly connected to why the thing exists at all, and why there's just

one of them?

Yes. Okay. So here's the point. So the thing that had confused me for a long time was,

let's say we get the rule for the universe. We hold it in our hand. We say, this is our

universe. Then the immediate question is, well, why isn't it another one? And that's

kind of the sort of the lesson of Copernicus is, we're not very special. So how come we

got universe number 312 and not universe quadrillion, quadrillion, quadrillion? And

I think the resolution of that is the realization that the universe is running all possible

rules. So then you say, well, how on earth do we perceive the universe to be running

according to a particular rule? How do we perceive definite things happening in the

universe? Well, it's the same story. It's the observer, there is a reference frame that

we are picking in this ruleal space, and that that is what determines our perception of

the universe. With our particular sensory information and so on, we are parsing the

universe in this particular way. So here's the way to think about it. In physical space,

we live in a particular place in the universe. And we could live on Alpha Centauri, but we

don't. We live here. And similarly, in ruleal space, we could live in many different places

in ruleal space, but we happen to live here. And what does it mean to live here? It means

we have certain sensory input. We have certain ways to parse the universe. Those are our

interpretation of the universe. What would it mean to travel in ruleal space? What it

basically means is that we are successively interpreting the universe in different ways.

So in other words, to be at a different point in ruleal space is to have a different, in a sense,

a different interpretation of what's going on in the universe. And we can imagine even

things like an analog of the speed of light as the maximum speed of translation in ruleal

space and so on. So wait, what's the interpretation? So ruleal space and we,

I'm confused by the we and the interpretation and the universe. I thought moving about in

ruleal space changes the way the universe is. The way we would perceive it. So it ultimately

has to do with the perception. So it doesn't real, ruleal space is not somehow changing,

like branching into another universe or something like that. No, I mean, the point is that the whole

point of this is the rule yard is sort of the encapsulated version of everything that is the

universe running according to all possible rules. We think of our universe, the observable universe,

as a thing. So we're a little bit loose with the word universe then, because wouldn't the rule yard

potentially encapsulate a very large number, like combinatorially large, maybe infinite

set of what we human physicists think of as universes? That's an interesting, interesting

parsing of the word universe, right? Because what we're saying is, just as we're at a particular

place in physical space, we're at a particular place in ruleal space, at that particular place

in ruleal space, our experience of the universe is this. Just as if we lived at the center of the

galaxy, our universe, our experience of the universe will be different from the one it is,

given where we actually live. And so what we're saying is, you might say, I mean, in a sense,

this rule yard is sort of a super universe, so to speak. But it's all entangled together. It's not

like you can separate out. You can say, let me, it's like when we take a reference, okay, it's like

our experience of the universe is based on where we are in the universe. We could imagine moving

to somewhere else in the universe, but it's still the same universe.

So there's not like universes existing in parallel?

No. Because, and the whole point is that if we were able to change our interpretation of what's

going on, we could perceive a different reference frame in this rule yard.

Yeah, but that's not, that's just, yeah, that's the same rule yard. That's the same universe.

You're just moving about. These are just coordinates in the universe.

Right. So the reason that's interesting is, imagine the extraterrestrial intelligence,

so the alien intelligence, we should say. The alien intelligence might live on Alpha Centauri,

but it might also live at a different place in real space.

It can live right here on Earth. It just has a different reference frame that

includes a very different perception of the universe. And then because that

real space is very large, I mean,

Do we get to communicate with them? Right.

Yeah, but it's also, well, one thing is how different the perception of the universe could be.

I think it could be bizarrely, unimaginably completely different. And I mean, one thing to

realize is, even in kind of things I don't understand well, you know, I know about the kind

of Western tradition of understanding, you know, science and all that kind of thing. And, you know,

you talk to people who say, well, I, you know, I'm really into some, you know, Eastern tradition of

this, that and the other. And it's really obvious to me how things work. I don't understand it

at all. But, you know, it is not obvious, I think, with this kind of realization that there's these

very different ways to interpret what's going on in the universe. That kind of gives me at least,

it doesn't help me to understand that different interpretation. But it gives me at least more

respect for the possibility that there will be other interpretations.

Yeah, it humbles you to the possibility that like, what is it, reincarnation or all these like

eternal recurrence with Nietzsche, like just these ideas? Yeah.

Well, you know, the thing that I realized about a bunch of those things is that, you know,

I've been sort of doing my little survey of the history of philosophy, just trying to understand,

you know, what can I actually say now about some of these things? And you realize that some of

these concepts like the immortal soul concept, which, you know, I remember when I was a kid,

and, you know, it was kind of a lots of religion bashing type stuff of people saying, you know,

well, we know about physics, tell us how much does a soul weigh? And people are like, well,

how can it be a thing if it doesn't weigh anything? Well, now we understand, you know,

there is this notion of what's in brains that isn't the matter of brains, and it's something

computational. And there is a sense and in fact, it is correct, that it is in some sense, immortal,

because this pattern of computation is something abstract that is not specific to the particular

material of a brain. Now, we don't know how to extract it, you know, in our traditional scientific

approach. But it's still something where it isn't a crazy thing to say there is something doesn't

weigh anything. That's a kind of a silly question. How much does it weigh? Well, actually, maybe it

isn't such a silly question in our model of physics, because the actual computational activity

has has a consequence for gravity and things, but that's a very subtle.

You can talk about mass and energy and so on. That could be a, what would you call it, a solitron.

Yes, yes, yes.

A particle that somehow contains soulness.

Yeah, right. Well, that's what, by the way, that's what Leibniz said. And, you know,

one thing I've never understood this, you know, Leibniz had this idea of monads and monadology,

and he had this idea that what exists in the universe is this big collection of monads.

And that they that the only thing that one knows about the monads is sort of how they relate to

each other. It sounds awfully like hypergraphs, right? But Leibniz had really lost me at the

following thing. He said, each of these monads has a soul, and each of them has a consciousness.

And it's like, okay, I'm out of here. I don't understand this at all. I don't know what's

going on. But I realized recently that in his day, the concept that a thing could do something

could spontaneously do something. That was his only way of describing that.

And so what I would now say is, well, there's this abstract rule that runs. To Leibniz,

that would have been, you know, in 1690 or whatever, that would have been kind of,

well, it has a soul, it has a consciousness. And so, you know, in a sense, it's like one

of these, there's no new idea under the sun, so to speak. That's a sort of a version of the same

kinds of ideas, but couched in terms that are sort of bizarrely different from the ones that

we would use today. Would you be able to maybe play devil's advocate on your conception of

consciousness that, like the two characteristics of it that is constrained, and there's a

single thread of time? Is it possible that Leibniz was onto something that the basic atom,

the discrete atom of space has a consciousness? Is that, so these are just words, right? But like,

what is there? Is there some sense where consciousness is much more fundamental

than you're making it seem? I don't know. I mean, you know, I think...

Can you construct a world in which it is much more fundamental?

I think that, okay, so the question would be, is there a way to think about kind of,

if we sort of parse the universe down at the level of atoms of space or something,

could we say, well, so that's really a question of a different point of view,

a different place in real space. We're asking the question, could there be a civilization

that exists? Could there be sort of conscious entities that exist at the level of atoms of

space? And what would that be like? And I think that comes back to this question of,

what's it like to be a cellular automaton type thing? I mean, I'm not yet there. I don't know.

I mean, I think that this is a... And I know I don't even know yet quite how to think about this

in the sense that I was considering, you know, I never write fiction, but I haven't written it

since I was like 10 years old. And my fiction, I made one attempt, which I sent to some science

fiction writer friends of mine, and they told me it was terrible. So, but...

This is a long time ago?

No, this is recently.

Recently. They said it was terrible. That'd be interesting to see you write a short story

based on what sounds like it's already inspiring short stories or stories by science fiction

writers.

But I think the interesting thing for me is, you know, what is it like to be a whatever?

How do you describe that? I mean, that's not a thing that you describe in mathematics,

the what is it like to be such and such.

Well, see, to me, when you say what is it like to be something,

it presumes that you're talking about a singular entity. So, like, there's some kind of feeling of

the entity, the stuff that's inside of it and the stuff that's outside of it.

And then that's when consciousness starts making sense. But then it seems like that could be

generalizable. If you take some subset of a cellular automata, you could start talking

about what does that subset feel. But then you can, I think you could just take arbitrary

numbers of subsets. Like, to me, like, you and I individually are consciousnesses,

but you could also say the two of us together is a singular consciousness.

Maybe, maybe. I'm not so sure about that. I think that the single thread of time thing

may be pretty important. And that as soon as you start saying, there are two different threads

of time, there are two different experiences, and then we have to say, how do they relate?

How are they sort of entangled with each other? I mean, that may be a different story of a thing

that isn't much like, you know, what do the ants, you know, what's it like to be an ant,

you know, where there's a sort of more collective view of the world, so to speak?

I don't know. I think that, I mean, this is, you know, I don't really have a good, I mean,

you know, my best thought is, you know, can we turn it into a human story? It's like the question

of, you know, when we try and understand physics, can we turn that into something which is sort of

a human understandable narrative? And now what's it like to be a such and such? You know, maybe the

only medium in which we can describe that is something like fiction, where it's kind of like

you're telling, you know, the life story in that setting. But I'm, this is beyond what I've yet

understood how to do. Yeah, but it does seem so, like with human consciousness, you know,

we're made up of cells and like, there's a bunch of systems that are networked that work together

that at this, at the human level, feel like a singular consciousness when you take, and so

maybe like an ant colony is just too low level. Sorry, an ant is too low level. Maybe you have to

look at the ant colony. Yeah, I agree. There's some level at which it's a conscious being. And then

if you go to the planetary scale, then maybe that's going too far. So there's a nice sweet spot for

consciousness. No, I agree. I think the difficulty is that, you know, okay, so in sort of people who

talk about consciousness, one of the terrible things I've realized, because I've now interacted

with some of this community, so to speak, some interesting people who do that kind of thinking.

But, you know, one of the things I was saying to one of the leading people in that area, I was

saying, you know, that, you know, it must be kind of frustrating because it's kind of like a poetry

story. That is many people are writing poems, but few people are reading them. So there are always

these different, you know, everybody has their own theory of consciousness, and they are very

non inter sort of inter discussable. And by the way, I mean, you know, my own approach to sort of

the question of consciousness, as far as I'm concerned, I'm an applied consciousness operative,

so to speak, because I don't really, in a sense, the thing I'm trying to get out of it is how does

it help me to understand what's a possible theory of physics? And how does it help me to say,

how do I go from this incoherent collection of things happening in the universe to our definite

perception and definite laws and so on, and sort of an applied version of consciousness? And I

think the reason it sort of segues to a different kind of topic, but the reason that one of the

things I'm particularly interested in is kind of what's the analog of consciousness in systems

very different from brains? And so why is that matter? Well, you know, this whole description

of this kind of, you know what, we haven't talked about why the universe exists. So let's get to why

the universe exists. And then we can talk about perhaps a little bit about what these models of

physics kind of show you about other kinds of things like molecular computing and so on.

Yes, that's good.

Why does the universe exist? Okay, so we finally sort of more or less set the stage,

we've got this idea of this rule yard of this object that is made from following all possible

rules, the fact that it's sort of not just this incoherent mess, it's got all this entangled

structure in it, and so on. Okay, so what is this rule yard? Well, it is the working out of all

possible formal systems. So the sort of the question of why does the universe exist? Its

core question, which we kind of started with is, you've got two plus two equals four, you've got

some other abstract result, but that's not actualized. It's just an abstract thing.

And when we say we've got a model for the universe, okay, it's this rule, you run it,

and it'll make the universe, but it's like, but where's it actually running? What is it actually

doing? Is it actual, or is it merely a formal description of something? So the thing to realize

with this, the thing about the rule yard is it's an inevitable, it is the entangled running of all

possible rules. So you don't get to say, it's not like you're saying, which rule yard are you

picking? Because it's all possible formal rules. It's not like it's just, well, actually, it's

only footnote. The only footnote, it's an important footnote, is it's all possible

computational rules, not hyper computational rules. That is, it's running all the rules that would be

accessible to a Turing machine, but it is not running all the rules that will be accessible

to a thing that can solve problems in finite time that would take a Turing machine infinite time to

solve. So you can, even Alan Turing knew this, that you could make oracles for Turing machines,

where you say a Turing machine can't solve the whole thing problem for Turing machines. It can't

know what will happen in any Turing machine after an infinite time, in any finite time,

but you could invent a box, just make a black box. You say, I'm going to sell you an oracle

that will just tell you, you know, press this button. It'll tell you what the Turing machine

will do after an infinite time. You can imagine such a box. You can't necessarily build one in

the physical universe, but you can imagine such a box. And so we could say, well, in addition to,

so in this Rulliad, we're imagining that there is a computational, that at the end, it's running

rules that are computational. It doesn't have a bunch of oracle black boxes in it. You say, well,

why not? Well, it turns out if there are oracle black boxes, the Rulliad that is,

you can make a sort of super Rulliad that contains those oracle black boxes,

but it has a cosmological event horizon relative to the first one. They can't communicate.

In other words, you can end up with, what ends up happening is it's like in the physical universe,

in this causal graph that represents the causal relationships of different things,

you can have an event horizon where the causal graph is disconnected, where the effect here,

an event happening here does not affect an event happening here because there's a disconnection

in the causal graph. And that's what happens in an event horizon. And so what will happen between

this kind of the ordinary Rulliad and the hyper Rulliad is there is an event horizon and we,

in our Rulliad, will just never know that they're just separate things. They're not connected.

And maybe I'm not understanding, but just because we can't observe it,

why does that mean it doesn't exist?

So it might exist, but it's not clear what it... So what, so to speak, whether it exists. What

we're trying to understand is why does our universe exist? We're not trying to ask the

question what... Let me say another thing. Let me make a meta comment, which is that I have not

thought through this hyper Rulliad business properly. So I can't... The hyper Rulliad is

referring to a Rulliad in which hyper computation is possible.

That's correct. Yes.

Okay. So the footnote to the footnote is we're not sure why this is important.

Yeah, that's right. So let's ignore that. Okay. It's already abstract enough. Okay. So,

okay. So the one question is we have to say, if we're saying, why does the universe exist?

One question is why is it this universe and not another universe? Okay. So the important point

about this Rulliad idea is that in the Rulliad are all possible formal systems. So there's no

choice being made. There's no like, oh, we pick this particular universe and not that one. That's

the first thing. The second thing is that we have to ask the question. So you say, why does two plus

two equals four exist? That is a thing that necessarily is that way just on the basis of

the meaning of the terms, two and plus and equals and so on. So the thing is that this Rulliad

object is in a sense a necessary object. It is just the thing that is the consequence of working

out the consequence of the formal definition of things. It is not a thing where you're saying,

and this is picked as the particular thing. This is just something which necessarily is that thing

because of the definition of what it means to have computation. So the Rulliad, it's a formal system.

Yes. But does it exist? Ah, well, where are we in this whole thing?

Yes. We are part of this Rulliad. So there is no sense to say, does two plus

two equals four exist? Well, in some sense, it necessarily exists. It's a necessary object. It's

not a thing that way you can ask. Usually in philosophy, there's a sort of distinction made

between necessary truths, contingent truths, analytic propositions, synthetic propositions

that are a variety of different versions of this. They're things which are necessarily true just

based on the definition of terms. And there are things which happen to be true in our universe.

But we don't exist in Rullial space. That's one of the coordinates that define our existence.

Well, okay. So yes, yes. But this Rulliad is the set of all possible Rullial coordinates.

So what we're saying is it contains that. So what we're saying is we exist as, okay, so

our perception of what's going on is we're at a particular place in this Rulliad,

and we are concluding certain things about how the universe works based on that.

But the question is, do we understand, you know, is there something where we say,

okay, so why does it work that way? Well, the answer is, I think it has to work that way,

because this Rulliad is a necessary object in the sense that it is a purely formal object,

just like 2 plus 2 equals 4. It's not an object that was made of something. It's an object that

is just an expression of the necessary collection of formal relations that exist.

And so then the issue is, can we, in our experience of that, is it, you know, can we have

tables and chairs, so to speak, in that just by virtue of our experience of that necessary thing?

And, you know, what people have generally thought, and I don't know of a lot of discussion of this,

why does the universe exist question? It's been a very, you know, I've been surprised actually at

how little, I mean, I think it's one of these things that's really kind of far out there. But

the thing that is, you know, the surprise here is that all possible formal rules, when you run them

together, and that's the critical thing, when you run them together, they produce this kind of

entangled structure that has a definite structure. It's not just, you know, a random arbitrary thing,

it's a thing with definite structure. And that structure is the thing when we are embedded in

that structure, when anything, you know, an entity embedded in that structure perceives something,

which is then we can interpret as physics and things like this. So in other words, we don't

have to ask the question, the why does it exist? It necessarily exists.

I'm missing this part. Why does it necessarily exist?

Okay, okay.

So like, you need to have it if you want to formalize the relation between entities, but

why do you need to have relations?

Okay, okay. So let's say you say, well...

It's like, why does math have to exist?

Fair question. Okay, fair question. Let's see. I think the thing to think about is

the existence of mathematics is something where given a definition of terms,

what follows from that definition inevitably follows. So now you can say, why define any terms?

But in a sense, the, well, that's okay. So the definition of terms, I mean, I think the way to

think about this, let me see.

So like concrete terms.

Well, they're not very concrete. I mean, they're just things like, you know, logical or.

Right, but that's a thing. That's a powerful thing.

Well, yes, okay. But the point is that it is not a thing of a, you know, people imagine there is,

I don't know, the, you know, an elephant or something or the, you know, elephants are presumably

not necessary objects. They happen to exist as a result of kind of biological evolution and

whatever else. But the thing is that in some sense that there is, it is a different kind of thing

to say, does plus exist? It's not like an elephant.

So a plus seems more fundamental, more basic than an elephant. Yes. But you can imagine a world

without plus or anything like it. Like, why do formal things that are discrete, that can be used

to reason have to exist?

Well, okay. So why? Okay. So then the question is, but the whole point is computation.

We can certainly imagine computation. That is, we can certainly say there is a formal system that

we can construct abstractly in our minds that is computation. And that's the, you know, we can

imagine it. Now the question is, is it that formal system, once we exist as observers embedded in

that formal system, that's enough to have something which is like our universe. And so then what

you're kind of asking is perhaps is why, I mean, the point is we definitely can imagine it.

There's nothing that says that we're not saying that it's sort of inevitable that that is a thing

that we can imagine. We don't have to ask, does it exist? We're just, it is definitely something

we can imagine. Now that's, then we have this thing that is a formally constructible thing

that we can imagine. And now we have to ask the question, what, you know, given that formally

constructible thing, what is, what consequences does that, if we were to perceive that formally,

if we were embedded in that formally constructible thing, what would we perceive about the world?

And we would say, we perceive that the world exists because we are seeing all of this mechanism

of all these things happening. And, but that's something that is just a feature of, it's something

where we are... See, another way of asking this that I'm trying to get at, I understand why it

feels like this ruley ad is necessary, but maybe it's just me being human, but it feels like then

you should be able to, not us, but somehow step outside of the ruley ad. Like what's outside the

ruley ad? Well, the ruley ad is all formal systems. So there's nothing because... But that's what a

human would say. I know that's what a human would say, because we're used to the idea that there are,

there's, but the whole point is that by the time it's all possible formal systems, it's, it's like,

it is all things you can imagine, but... All computations you can imagine, but like we don't...

Well, so the issue is, can we encode? Okay. So that's a fair question. Is it possible to encode

all, I mean, once we, is there something that isn't what we can represent formally?

Right. That is, is there something that, and that's, I think, related to the hyper ruley ad

footnote, so to speak, which I'm afraid that the, you know, one of the things sort of interesting

about this is, you know, there has been some discussion of this in theology and things like

that, but, which I don't necessarily understand all of, but the key sort of new input is this idea

that all possible formal systems, it's like, you know, if you make a world, people say, well, you

make a world with a particular, in a particular way with particular rules, but no, you don't do

that. You can make a world that deals with all possible rules, and then merely by virtue of

living in a particular place in that world, so to speak, we have the perception we have of what the

world is like. Now, I have to say the, it's sort of interesting because I've, you know, I wrote this

piece about this, and I, you know, this philosophy stuff is not super easy, and I've, as I'm talking

to you about it, and I actually haven't, you know, people have been interested in lots of different

things we've been doing, but this, why does the universe exist, has been, I would say, one of the,

one of the ones that you would think people will be most interested in, but actually, I think

they're just like, oh, that's just something complicated that, so I haven't, I haven't explained

it as much as I've explained a bunch of other things, and I have to say, I think I, I think I

may be missing a couple of pieces of that argument that would be, so it's kind of a like…

Well, you are, your conscious being is computationally bounded, so you're missing…

Indeed.

Having written quite a few articles yourself, you're now missing some of the pieces.

Yes, right.

That's the limitation of being human.

Right. One of the consequences of this, why the universe exists thing, is that you're missing

something, and this kind of concept of rule adds and, you know, places in there representing our

perception of the universe and so on. One of the weird consequences is, if the universe exists,

mathematics must also exist. And that's a weird thing, because mathematics, people have been very

confused, including me, have been very confused about the question of kind of what, what is the

definition of mathematics? What is, what kind of a thing is mathematics? Is mathematics something

where we just write down axioms like Euclid did for geometry, and we just build the structure,

and we could have written down different axioms, and we'd have a different structure? Or is it

something that has a more fundamental sort of truth to it? And I have to say, this is one of

these cases where I've long believed that mathematics has a great deal of arbitrariness to

it, that there are particular axioms that kind of got written down by the Babylonians, and, you

know, that's what we've ended up with the mathematics that we have. And I have to say,

actually, my wife has been telling me for 25 years, she was a mathematician, she's been telling me,

you're wrong about the foundations of mathematics. And, you know, I'm like, no, no, no, I know what

I'm talking about. And finally, she's much more right than I've been. So it's one of the...

So, I mean, her sense and your sense, are we just, so this is to the question of metamathematics,

just kind of on a trajectory through ruleal space, except in mathematics, through a trajectory of

a certain kind of... I think that's partly the idea. So I think that the notion is this. So 100

years ago, a little bit more than 100 years ago, people have been doing mathematics for ages,

but then in the late 1800s, people decided to try and formalize mathematics and say, you know,

it is mathematics is, you know, we're going to break it down, we're going to make it like logic,

make it out of sort of fundamental primitives. And that was people like Frager and Piano and

Hilbert and so on. And they kind of got this idea of let's do kind of Euclid, but even better,

let's just make everything just in terms of this sort of symbolic axioms, and then build

up mathematics from that. And that, you know, they thought at the time, as soon as they get

these symbolic axioms, that they made the same mistake, the kind of computational irreducibility

mistake. They thought as soon as we've written down the axioms, then we'll just have a machine,

kind of a super mathematical, so to speak, that can just grind out all true theorems of mathematics.

That got exploited by Gödel's theorem, which is basically the story of computational

irreducibility. It's that even though you know those underlying rules, you can't deduce all

the consequences in any finite way. But now the question is, okay, so they broke mathematics down

into these axioms, and they say now you build up from that. So what I'm increasingly coming to

realize is that's similar to saying let's take a gas and break it down into molecules. There's gas

laws that are the large scale structure and so on that we humans are familiar with, and then there's

the underlying molecular dynamics. And I think that the axiomatic level of mathematics, which

we can access with automated theorem proving and proof assistance and these kinds of things,

that's the molecular dynamics of mathematics. And occasionally we see through to that molecular

dynamics. We see undecidability, we see other things like this. One of the things I've always

found very mysterious is that Gödel's theorem shows that there are sort of things which cannot

be finitely proved in mathematics. There are proofs of arbitrary length, infinite length proofs that

you might need. But in practical mathematics, mathematicians don't typically run into this.

They just happily go along doing their mathematics. And I think what's actually

happening is that what they're doing is they're looking at this. They are essentially observers

in metamathematical space, and they are picking a reference frame in metamathematical space,

and they are computationally bounded observers in metamathematical space,

which is causing them to deduce that the laws of metamathematics and the laws of mathematics,

like the laws of fluid mechanics, are much more understandable than this underlying

molecular dynamics. And so what gets really bizarre is thinking about kind of the analogy

between metamathematics, this idea of you exist in this sort of space of possible,

in this kind of mathematical space where the individual kind of points in the mathematical

space are statements in mathematics, and they're connected by proofs where one statement, you know,

you take a couple of different statements, you can use those to prove some other statement,

and you've got this whole network of proofs. That's the kind of causal network of mathematics,

of what can prove what and so on. And you can say at any moment in the history of a mathematician,

of a single mathematical consciousness, you are in a single kind of slice of this

kind of metamathematical space. You know a certain set of mathematical statements.

You can then deduce with proofs, you can deduce other ones, and so on. You're kind of gradually

moving through metamathematical space. And so it's kind of the view is that the reason that

mathematicians perceive mathematics to have the sort of integrity and lack of kind of undecidability

and so on that they do is because they, like we as observers of the physical universe,

we have these limitations associated with computational boundedness, single thread of time,

consciousness limitations, basically, that the same thing is true of mathematicians perceiving

sort of metamathematical space. And so what's happening is that if you look at one of these

formalized mathematics systems, something like Pythagoras's theorem, it'll take, oh, I don't know,

what is it, maybe 10,000 individual little steps to prove Pythagoras's theorem. And one of the

bizarre things that's sort of an empirical fact that I'm trying to understand a little bit better,

if you look at different formalized mathematics systems, they actually have different axioms

underneath that they can all prove Pythagoras's theorem. And so in other words, it's a little bit

like what happens with gases. We can have air molecules, we can have water molecules, but they

still have fluid dynamics. Both of them have fluid dynamics. And so similarly, at the level that

mathematicians care about mathematics, it's way above the molecular dynamics, so to speak.

And there are all kinds of weird things. Like, for example, one thing I was realizing recently

is that the quantum theory of mathematics, that's a very bizarre idea. But basically,

when you prove what is a proof is you've got one statement in mathematics, you go through

other statements, you eventually get to a statement you're trying to prove, for example,

that's a path in metamathematical space. And that's a single path, a single proof is a single

path. But you can imagine there are other proofs of the same result. There are a bundle of proofs.

There's this whole set of possible proofs. Yeah, you could think of it as branching,

similar to the quantum mechanics model that you were talking about. Exactly. And then there's

some invariance that you can formalize in the same way that you can for the quantum mechanical.

Right. So the question is, in proof space, as you start thinking about multiple proofs,

are there analogs of, for example, destructive interference of multiple proofs? So here's a

bizarre idea that's just a couple of days old, so not yet fully formed. But as you try and do that,

when you have two different proofs, it's like two photons going in different directions,

you have two proofs, which at an intermediate stage are incompatible. And that's kind of like

destructive interference. Is it possible for this to instruct the engineering of automated proof

systems? Absolutely. I mean, as a practical matter, I mean, you know, this whole question,

in fact, Jonathan Gorod has a nice heuristic for automated theorem provers that's based on

our physics project that is looking for essentially using kind of using energy in our

models. Energy is kind of level of activity in this hypergraph. And so it's sort of a heuristic

for automated theorem proving about how do you pick which path to go down that is based on

essentially physics. And I mean, the thing that gets interesting about this is the way that one

can sort of have the interplay between, like, for example, a black hole. What is a black hole

in metamathematics? So the answer is, what is black hole in physics? A black hole in physics

is where in the simplest form of black hole time ends. That is all, you know, everything is crunched

down to the space time singularity, and everything just ends up at that singularity. So in our

models, and that's a little hard to understand in general relativity with continuous mathematics,

and what does singularity look like? In our models, it's something very pragmatic. It's just,

you're applying these rules, time is moving forward. And then there comes a moment where

the rules, no rules apply. So time stops. It's kind of like the universe dies, that, you know,

that nothing happens in the universe anymore. Well, in mathematics, that's a decidable theory.

That's a theory. So theories which have undecidability, which are things like

arithmetic, set theory, all the serious models, theories in mathematics, they all have the feature

that there are proofs of arbitrarily long length. In something like Boolean algebra,

which is a decidable theory, there are, you know, any question in Boolean algebra, you can just go

crunch, crunch, crunch, and in a known number of steps, you can answer it. You know, satisfiability,

you know, might be hard, but it's still a bounded number of steps to answer any satisfiability

problem. And so that's the notion of a black hole in physics where time stops. That's analogous to

in mathematics where there aren't infinite length proofs, where when in physics, you know, you can

wander around the universe forever if you don't run into a black hole. If you run into a black

hole and time stops, you're done. And it's the same thing in mathematics between decidable

theories and undecidable theories. That's an example. And I think where sort of the attempt

to understand, so another question is kind of what is the general activity of metamathematics?

What is the bulk theory of metamathematics? So in the literature of mathematics, there are about

three million theorems that people have published. And those represent, it's kind of on this, it's

like on the earth, we would be, you know, we've put cities in particular places on the earth,

but yet there is ultimately, you know, we know the earth is roughly spherical,

and there's an underlying space. And we could just talk about, you know, the world of space

in terms of where our cities happen to be, but there's actually an underlying space. And so the

question is, what's that for metamathematics? And as we kind of explore what is, for example,

for mathematics, which is always likes taking sort of abstract limits. So an obvious abstract

limit for mathematics to take is the limit of the future of mathematics. That is, what will be,

you know, the ultimate structure of mathematics. And one of the things that's an empirical

observation about mathematics that's quite interesting is that a lot of theories in one

area of mathematics, algebraic geometry or something, might have, they play into another area

of mathematics. That same kind of fundamental construct seemed to occur in very different

areas of mathematics. And that's structurally captured a bit with category theory and things

like that. But I think that there's probably an understanding of this metamathematical space that

will explain why different areas of mathematics ultimately sort of map into the same thing.

And I mean, you know, my little challenge to myself is what's time dilation in metamathematics?

In other words, as you basically, as you move around in this mathematical space of possible

statements, you know, how does that moving around? It's basically what's happening is

that as you move around in the space of mathematical statements, it's like you're

changing from algebra to geometry to whatever else. And you're trying to prove the same theorem.

But as you try, if you keep on moving to these different places, it's slower to prove that

theorem because you keep on having to translate what you're doing back to where you started from.

And that's kind of the beginnings of the analog of time dilation in metamathematics.

Plus, there's probably fractional dimensions in this space as well.

Oh, this space is a very messy space. This space is much messier than physical space. I mean,

even in the models of physics, physical space is very tame compared to branchial space and

ruleal space. I mean, the mathematical structure, you know, branchial space is probably more like

Hilbert space, but it's a rather complicated Hilbert space. And ruleal space is more like