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. 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,

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

What I was interested in is how does something that we would usually identify as complexity

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

a long time ago. 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 underlying scientific basis for those kinds of things? And the thing that I was at first

very surprised by, because I've been doing physics and particle physics and fancy mathematical

physics and so on, and it's like, I know all this fancy stuff. I should be able to solve this basic

science question. And I couldn't. This was like early maybe 1980ish time frame. 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, 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 a model is some abstract

representation of the system, some formal representation of the system. What is the

raw material that you can make that model out of? And so what I realized was, well, actually,

programs are 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 mathematical and morphine 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 it's 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 is pretty easy to do. I mean, it probably took a few hours

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

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

which I thought were really interesting, but the really strongest result, which was already right

there in the printouts I made, I didn't really understand for a couple more years. So it was,

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,

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

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

My, my favorite example is the single rule 30, which is a particular cellular automaton rule,

you just started off in 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 that was,

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

the indication that one had got an idea of what the sort of secret that nature uses

to make complexity and the complexity, how complexity can be made in other places.

Now, if you say, what is complexity, you know, it's, it's 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, that'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? 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.

By the way, has anybody succeeded at that? You had a challenge, a competition.

Right.

For predicting the middle column of rule 30.

Indeed.

Anybody.

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

I mean, it's, I've been, 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.

Mathematically proving.

Yes. And so that's analogous to a similar kind of things like the digits of Pi,

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

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

Well, 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,

you know, zero, one, two, three or whatever do all the digits base 10 or base two, 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. And that's, that's kind of, 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 equally distribution of equal numbers of zeros and ones. And those are

things which I, you know, I kind of set up this little prize thing, because I thought those were

not too out of range. Those are things which are within, you know, a modest amount of time,

it's conceivable that those could be done. They're not, 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, you know, will be useful other places.

But you started in 1980 with this idea, before I think you realized, you know, this idea of

programs, you thought that there might be some kind of thermodynamic like randomness, and then

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

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

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 of

mathematics that developed from the early 1900s and really got big in the 1980s. You know,

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

An example of what people study a lot is the shift map, which is basically taking

2x mod 1 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 what 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 and fluid mechanics,

then the equations of fluid mechanics can't be right. Because what that would be saying is

the equations of that, that it matters to the fluid, what happens in the fluid at the level of

the, you know, millionth digit of the initial conditions, which is far below the points at

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

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

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

you know, so this idea that, you know, there's a, it's a tricky thing, because as soon as you put

randomness in, you have to know, you know, what, 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 plainly obvious there wasn't. Now,

as a practical matter in doing experiments, the big thing is, if the thing you see is complex

and reproducible, then it didn't come from just filtering some quotes randomness from the outside

world. It has to be something that is intrinsically made, because it wouldn't otherwise be, I mean,

you know, the, the, the, 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 then it's not random each time,

because kind of the definition of it being random is it was kind of picked, 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 there is 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, you know, could you add that in as an extra little featureoid?

You know, 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, it's, 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 so such a kind of, you know, difficult

to address question. But I actually think to my great surprise that from our physics project and

so on, that it is possible to actually address that question and explain why the universe exists.

And I kind of have a suspicion. I've not thought it through. I kind of have a suspicion that that

explanation will eventually show you that in no meaningful sense, can there be randomness

underneath the universe? That is that if there is, it's something that is necessarily irrelevant

to our perception of the universe. That is that it could be there, but it doesn't matter. Because

in a sense, we've already, you know, whatever it would do, whatever extra thing it would add,

is not relevant to our perception of what's going on.

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

the big why question of the universe? So, okay. 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. About that, I'm pretty sure.

So you may be, 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. Okay. 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 act? 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 there's two,

a pile of two rocks and 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? Okay, 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 that's, 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, and, 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

it's kind of a 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 sort of operate in the world? And the answer is that we sort of live

in these slices of computational reusability that exists in this kind of ocean of computational

irreducibility. And it turns out that seems that it's a very fundamental feature of the kind of

model that seems to operate in physics, and perhaps in the bottom 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

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 been sort of an exciting thing. But I would say that in general, for our project,

it's been going spectacularly well. I mean, it's very, honestly, it wasn't something I expected

to happen in my lifetime. I mean, it's something where it's, and 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 mathematics, I'd be

realizing that I've something I've long believed, we can talk about it later, that just really

isn't right. But I think that the thing that, so what's happened with the physics project,

I mean, you know, it's a 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 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 generally 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. Right. 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 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, if you were a

computer person, you give them UUIDs or something. But 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, there are 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 the 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 and 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 the particle accelerators 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. And 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, so there are various fundamental constants, there's the speed

of light, the speed of light, once you know the elementary time, the speed of light is 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 these sort of combination of those, okay, so the most obvious

thing, people have sort of assumed that quantum gravity happens at this thing, the Planck scale,

10 to the minus 34 meters, which is the sort of the combination of Planck's constant and the

gravitational constant and 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,

you know, 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, that 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, 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 analogous kind of, what is the analog of hypersonic flow for our, for things about

the structure of spacetime? And it looks like a rapidly rotating black hole right at the sort of

critical rotation rate is, 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 it 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 to 10 to the minus 100, how rotating black holes and

presumably the detailed accurate detection of gravitational waves from black holes can

reveal the discreetness 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. It's very, 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.

But 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 sort of not just friends,

individual friends to friends, but you can have these triplets of friends or whatever else.

And so we're just saying, and that's just the relations between atoms of space

are the hyper edges 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.

That's an 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 kind of 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 it's 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 lock step 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 would 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

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 in 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 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 the fact, so I mean,

just to go on with kind of the basic setup, it's, so we got this spatial hypergraph,

it's got all these atoms of space, they're getting these little clumps of atoms of space

are 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 we, you know,

when I move my hand, it's moving into a different set of atoms of space. It's having to be recreated,

it's not 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, you know, vortices and fluid, which again, the actual

molecules that exist in those are not what define the identity of the thing. And but it's a little

bit, you know, this idea that there can be pure motion, that it can, 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, you know, teacup or something approaching a black hole,

it is deformed and distorted by the structure of space time. And to say, you know, 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, so anyway, the thing that that's happening is

we 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 a 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. But so so the thing, 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 prank

array group and Lawrence 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 that a few bits and

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

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

that, there are 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, etc. 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 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 we'll be called multi computation.

Can't I then look back? When 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.

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 just 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 delay. Well, there's a, okay,

there's, there's, there's a bunch of limitations of the observer, I think. 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 plug in 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 they can

be merging is critical and somewhat nontrivial for these hypergraphs, because there's a whole

graph isomorphism story, and there's a whole very elaborate set of mathematics.

That's where the causal invariance comes in.

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? What, you know, how do we,

do we, why don't we notice that the universe is branching and merging? Why, you know, 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, you know, gone to hell in different

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

invariance thing. But that's, and the fact that that does happen a little bit is what causes little

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

is like quantum mechanics. It would be quantum mechanics is kind of like in this,

in this kind of 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 that's so the 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, that's part of the whole picture of

what's going on. But I think, I mean, to come back to sort of where does conscious, what is,

what is the story of consciousness? So in the universe, we've got, you know, 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, we are parsing the universe in a particular way. Let me again, go back to the gas molecules

analogy. You know, 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 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 conscious experience or our sensory experience.

Sensory experience, but sensory experience that's somehow intricately tied to consciousness.

Right. Well, so, so one question is when we are looking at all these molecules in the gas,

and there might be 10 to 20 molecules in some little, little box or something, it's like,

what, 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 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, 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,

because 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 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, you know, in all the neurons in our brains, that, that in at least in our conscious,

note the, you know, the correspondence of language in our conscious experience,

we just have the single thread of attention, single thread of, of perception. And, you know,

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

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

But then the, 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,

yeah, I think, you know, people, 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're asking, you know, what is the, 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, 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 a, is the capacity to perform

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

you know, this question of, 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.

Well, that's not. 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, so one thing is we don't know intelligence is 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.

Now, that, 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, you know,

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

you know, computational ability, that's, that's an important feature. That's, that's the 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, a 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, okay,

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. Yes. That is, you know, that is something

that we humans just never notice 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, 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 that's the way that we, 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 computationally 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 fault. We drop something. That's a great example of general relativity in action. No,

but like, what's the difference between that and Newtonian mechanics? I mean,

Oh, it doesn't. This is, when I say general relativity, that's even gravity, 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, 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, okay, 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, this 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, 10, 100 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. You know, 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 to 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 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. That is, 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 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. But this makes consciousness seem like a weird side effect

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

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 intelligence represented in terms of photons. For example, the photons we

receive in the cosmic microwave background, those photons, as far as their concern, the universe

just started. They were emitted 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

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 tell a story. We can tell a story. Right. We can tell a story. What other kinds of

stories can you tell? So a 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, I've been wondering about this and I've been

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

this? And I've got one example, great, great collection of books from my friend Rudy Rucker,

which were, which I have to say, the, their books about, 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. Nice. So, you know, so the earth is gone in the first, but then it comes back.

But, but, but then spoiler alert. Yeah, right. That was a, that was only a micro spoiler. It's

only chapter one. Okay. It's, it's the, but, but the thing that is, is not a real spoiler alert

because it's such a complicated concept. But, but in the end, in the end, the, 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, can you maybe elaborate how the principle

of computational equivalence can save a planet? That would, that would be a terrible spoiler for

me. That would be a spoiler. Okay. But, but, 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, 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 outthink 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, the idea there. And the question, I mean, it's,

it's like, the, you know, in, 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 that's, 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, 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. And it's kind of the, it's 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, there is an aspect of this that seems to be more special,

that isn't, 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, how does, how is that, 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 it laws, its laws of physics be? I don't really know.

Because it's very parallel. It's very parallel, among other things. And it, it, it's not obvious.

I mean, this is a really kind of mind bending thing, because we've got to try and imagine

where, you know, 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 that 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, 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 us 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 the 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, in the shoes, in the cells of the cellular automaton, so to speak?

Can we, 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, with, you know, 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 I've been sort of one of the, one of my projects to think about is, is there a way of

kind of, kind of getting a sense, kind of from inside the system about what its view of the world

is and how it, how it, you know, can, can we make a bridge? See, the main issue is this,

what, where, you know, it's a, 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. And, 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 what,

you know, when I built Wolfman 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 on to 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 a, you know, 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 have 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 type? And that somehow then can give you a sense of how to step outside

of that cellular automata. Right. But the tricky part is that that little subset, it's what it's

doing is it has a view of itself. And the question is, how do you get inside it? It's like, you know,

when we, with humans, right, it's like, we can't get inside each other's consciousness.

That doesn't really, you know, 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, you know, when it comes to questions

about consciousness or whatever else, it's like, when I can run a program and actually

see pictures and, you know, make things concrete, 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 if you can somehow connect,

more and more connect this, 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 know, you, 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, you know, how to,

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 game, 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 automaton? 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...

Then can you return?

But then can you return back?

Well, yeah, right. I mean, it's like, let's imagine you've uploaded, you know, your brain

is scanned, you've got every synapse, you know, mapped out, you upload everything about you,

the brain simulator, you upload the brain simulator, and the brain simulator is basically,

you know, 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, you know, operating in the same way.

So in a sense, but I think there's somehow more to it, because in that sense, when you're just

making a brain simulator, it's just, you know, 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, you know, there's a way of thinking about this. Okay, so this is coming on to sort

of questions about the existence of the universe and so on. But one of the things is there's this

notion that we have of rural space. So we have this idea of this physical space, which is, you

know, something you can move around in that's associated with the actual, 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 sort of 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, like for example, oh, something like, I think we're slowly

understanding things like destructive interference in quantum mechanics, that what's happening is

branchial space is associated with phase and 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 are trying to,

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 rural 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 it's, 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 taking 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 in our models of physics, what is motion? Well, when you move from somewhere to somewhere,

it's 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, you're again, you're updating yourself,

you're 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 successfully in

time, or you can use that computation to recreate yourself as you move around the universe. And so

time dilation ends up being, it's really cool, actually, that this is explainable in a in a way

that isn't just imagine the mathematics of relativity. But that 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 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 that's why time dilation happens.

And so you can 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 so we're simply saying the entity is

updating itself according to the way that the universe updates itself. And the question is,

you're, 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 the 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 but then the alternative

is that sort of situation one, where the thing is at rest, situation two, where it's kind of moving

the the what's happening is, it is having to recreate itself at every, 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 updates doing.

That's right. The more it has having to update because of motion, yeah, the less it can update

the clock. So that that's, I mean, obviously, there's a 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

that that isn't, and it's 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, you know, the thing about this physical space and physical space, the the main sort of

big theory is general relativity, the theory of gravity. And that tells you how things move in

physical space. In branching 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 branching space. And it's kind of a fun thing to start thinking

about what, oh, you know, all these things that we know in physical space, like event horizons

and black holes and so on, what are the analogous things in branching space, for example, the speed

of light, what's the analog of the speed of light in branching 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 branching space, something happens. And the question is, how far in this branching 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 we're, you know, when we study quantum mechanics, we mostly study it in terms

of small numbers of particles, you know, 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 one of these, 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 as 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, you know, measurements have to do with this idea of, you know, 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, you know, 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, you know, 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, you know, 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? Is that the hope? I think it's likely, yes. But I don't, you know,

this is every one of these things, when you, 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, you know, definite thing you can say about chemistry

or something like this, you know, 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, you know, quantum stuff happens,

but then if you make a measurement, you're kind of freezing time in quantum mechanics. And 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, you know, a mole of atoms is, you know, is a lot of atoms. And, you know, but it isn't a

very, you know, it's something where to get, you know, when we're dealing with how can you see 10

to the minus 100, so to speak, well, by the time you've got, you know, 10 to the 30th atoms, you're

not, you know, you're within a little bit closer striking distance of that. It's not like, oh,

we've just got, you know, 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, 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 got that one number, we just need one

number, if we can get that one number, we can, you know, the theory has no parameters anymore.

And, you know, 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.

I mean, 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 know,

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 cube 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, you know, 2.92, you know, for some value of r in, you know, 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 a, 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 are, 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, you know,

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 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, I we had, 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 in a footnote. And that was, so that's a, but in any case, I've

never really completely believed it. But this, 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 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, Roberts and 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 fundamental reason it's difficult, when people invented calculus 300 years ago,

calculus was the story of understanding change and change as a function of a variable.

And so people study univariate calculus, they study multivariate calculus, it's one variable,

it's two variables, three variables, but whoever studied 2.5 variable calculus turns out nobody.

It turns out that, but 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 and natural 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, 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 that could be validated with a physics experiment, predictions that couldn't have

been done or weren't done otherwise. 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. Dimension fluctuation is just something nobody ever looked for that.

If anybody sees dimension fluctuation, that's a huge flag, that's something like our model

is going on. And how one detects that, 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 can 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 a LIGO type of situation, like that's gravitational waves?

Yeah, or alternatively, I mean, I think it's, look, figuring out experiments is like

figuring out technology inventions. That is, 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,

what is that thing I can measure that just somehow 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, we've 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 very positive.

So it's a camber and explosion of physicists too, and 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

a due to Jonathan Gorod, who's one of the key people who's been working on a 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 space time,

we imagine that there's space and time, it's a three plus one dimensional, you know, set up,

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 invariance, even relativistic invariance, 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, they instead of just generating events at

random, our models necessarily generate events in some pattern in space time effectively, that

then leads to Lorentz invariance and relativistic invariance 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 that 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 what we're providing, I think, is a reason to care about a lot of these

areas of mathematical physics. So that's been, 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, let's talk about that. Yes.

So we're, 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. I'm very surprised. So the next thing to perhaps understand is this idea

of rural space. So we've got kind of physical space, we've got bronchial space, the space of

possible quantum histories. And now we've got another level of kind of abstraction, which is

rural space. And here's the, 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. Okay, so that's, 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. Okay. And then you make this

rural 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? How can anything,

you know, real come out of the set of all possible rules applied in all possible ways?

Okay, this is a subtle thing. So which I haven't fully untangled. The 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 RULIAD, the limit of the limits 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, RULIAD 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 you can always, the paths will always convert.

But does that necessarily infer that the RULIAD is a finite?

In the end, it's not necessarily finite. I mean, it's 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 RULIAD 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 RULIAD object.

One is how long you run the computation for. Another is how many different rules you're

applying. 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, growth and deke. Growth and deke had a thing

called the infinity group void, which is closely related to this RULIAD 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

group void 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 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

of mathematics. Another statement would be, you know, x squared minus one is equal to x plus

one x minus one. There are infinite number of these possible statements of mathematics.

So 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's a, it is a rule. It's also just a thing that is

true in mathematics. The statement is true. 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 segwaying into a different thing. Let me not go in this direction

for a second. Let's not go to meta mathematics just yet. Yeah, we'll maybe get to meta mathematics,

but it's, so let me not, let me explain the groupoid and things later. Yes. But so let's

come back to the universe, always a good place to be in. So what does the universe have to do

with the rule of the all 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, you know, that's kind of the, you know, the, the sort of the lesson of Copernicus is,

we're not very special. So how come we got universe number 312 and not universe quadriline,

quadriline, quadriline. And I think the resolution of that is the realization that

there, 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 rural 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, in, in physical space,

we live in a particular place in the universe. And, you know, we could live on Alpha Centauri,

but we don't, we live here. And similarly, in rural space, we could live in many different

places in rural 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 rural 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 rural 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 rural space and so on.

So wait, what's the interpretation? So rural space, we, I'm confused by the we and the

interpretation and the universe. I thought moving about in rural space changes the way the universe

is, is the way we would perceive it. The way that that ultimately has to do with the perception.

So it doesn't real, rural space is not somehow changing, like,

branching into another universe, something like that. No, I mean, the point is that the whole

point of this is the Rouliat is sort of the encapsulated version of everything that is the

universe running according to all possible rules. Yeah, we think of our universe, the observable

universe as its thing. So we're a little bit loose with the word universe then, because wouldn't the

Rouliat 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

rural space. At that particular place in rural 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 in what we're saying is

when you might say, I mean, in a sense, this Rouliat 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 Rouliat.

Yeah, but that's not, that's just, yeah, that's the same Rouliat. That's the same universe.

You're just moving about. These are just coordinates in the universe.

So the way that's, 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 rural 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 rural space is

very large, I mean... Do we get to communicate with them? Right, that's...

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, I know about the kind of

Western tradition of understanding science and all that kind of thing. And you talk to people

who say, well, I'm really into some 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 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,

it 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. There could be a what would you call a solitron.

Yes, yes. A particle that somehow contains soleness.

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 monodology, and he had

this idea that what exists in the universe is this big collection of monads, and 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 as well is this

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, you

know, 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 screwy atom of space has a consciousness?

Is that, so these are just words, right? But 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, that, 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, you'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, can we, you know, what's it like to be a cellular

automaton type thing? I mean, it's, you know, I'm not yet there. I don't know.

I mean, I think that this is a, and I don't even know yet quite how to think about this

in the sense that I was considering, you know, I'm, 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 the bedtime... This is a long time ago?

No, it was 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 by, or stories by science fiction writers.

But, but I think the interesting thing for me is, you know, in the, what does it,

what is it like to be a whatever? How do you describe that? I mean, it's like,

that's not a thing that you describe in mathematics, that what is it like to be such and such?

Well, see, to me, when you say, what is it like to be something presumes that you're talking about

a singular entity? So, yeah, 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, 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

may 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, what are the ants? What's it like to be an ant,

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, I don't really have a good, I mean, my best thought is, can we turn it

into a human story? It's like the question of, 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? Maybe the only medium in which we can describe that is something like

fiction, where it's kind of like you're telling the life story in that setting. But this is

beyond what I've yet understood how to do. Yeah, but it does seem so like with human consciousness,

we're made up of cells. And 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,

yes. 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 one of the things I was saying

to one of the leading people in that area, I was saying that 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 they're always these different, you know,

everybody has their own theory of consciousness, and they are very non inter sort of interdiscussable.

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

that 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 does that matter? Well, you know, this whole description of this kind of

well, actually, you know what, we haven't talked about why the universe exists. So let's let's

get to why the universe exists. And then we then we can 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 really add 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 really add? Well, it is the working out

of all possible formal systems. So the sort of a question of why does the universe exist? It's

core question, you kind of started with is, you've got two plus two equals four, you've got some other

abstract results. 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, but, you know, where's it actually running? What, what, what is what is it actually

doing? Right? What is is it actual? Or is it merely a formal description of something? Okay.

So the thing to realize with this, 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,

you know, 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 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 Ruliad, we're imagining that there is a computational that at the end,

it's, 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, turns out if there are oracle black boxes,

the Ruliad that is, you can make a sort of super Ruliad 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, you can end up with what you end up happening, what ends up happening is

it's, it's, it's like in the physical universe, we, in this causal graph that represents the causal

relationships of different things, you can have an event horizon, where there's, 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 Ruliad and the hyper Ruliad

is there is an event horizon, and you, you know, we in our Ruliad will just never know that there

is, that they're just separate things. They're not, they're not connected.

Maybe I'm not understanding, but just because we can't observe it,

why does that mean it doesn't exist? It might exist, but it does, it's not clear what it,

it's so what, so to speak, whether it exists. You know, what we're trying to understand is why

does our universe exist? We're not trying to ask the question what, you know, it's,

let me say another thing, let me make a meta comment, okay, which is that, that I have not

thought through this hyper Ruliad business properly. So I can't, the hyper Ruliad is referring to

a Ruliad in which hyper computation is possible. That's correct. Okay. So like what the, that foot

note, the footnote to the footnote is we're not sure why this is important. Yeah, that's right.

So let's, let's ignore that. Okay. It's already abstract enough. Okay. So, 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? Yeah. Okay. So the important point about this

Ruliad idea is that it's in the Ruliad are all possible formal systems. So there's no choice

being made. There's no, there's no like, oh, we picked this particular universe and not that one.

That's the first thing. The second thing is the that we have to ask the question. So, so you say,

why does two plus two equals four exist? That's not really a 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.

Right. So the thing is that this, this Ruliad 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. You don't, 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 it's a Ruliad. It's a formal system. Yes.

But does it exist? Ah, well, where are we in this whole thing? We are part of this Ruliad.

And so our, so there is no sense to say, does two plus two equals four exist? Well, that's,

that's in some sense, it necessarily exists. It's a necessary object. It's not a thing that

where you can ask, you know, it's, it's usually in philosophy, there's a sort of distinction

made between, you know, necessary truths, contingent truths, analytic propositions,

synthetic propositions, there 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're weird, we don't exist in Rulial space. We, that's one of the

coordinates that define our existence, right? Well, okay, so, so yes, yes, but this Ruliad

is the set of all possible Rulial 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 Ruliad. 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,

so, so why does it work that way? Well, the answer is, I think it has to work that way,

because this, there isn't, this Ruliad is a necessary object in the sense that it is a purely

formal object, just like two plus two equals four. 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 also that 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 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, the 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? Okay, that's the question. Yeah, 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, that's 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, it's a, yes, okay. But it's a, the point is that it is not a thing about,

people imagine there is, I don't know, the, an elephant or something or the,

elephants are presumably not necessary objects. They happen to exist as a result of kind of

biological evolution and whatever else. But the, the thing is that in some sense, that there is,

it is a different kind of thing to say, does plus exist? The, it is not, it's not, not like an

elephant. So a plus is, 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 discreet, 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, that's the, and you know, we can, we can imagine it, right? Now,

the question is, is it is 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 the,

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 there's, 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 be perceived about the world? And we would say, we perceive that the world exists,

because we are, 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, it's, 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

rulliad 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 rulliad. Like what's

outside the rulliad? Well, the rulliad 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 no, all computations you can

imagine. But like, we don't, well, so that could be a code. Okay. So, so that's a, that's a fair

question. Is it possible to encode all, I mean, once we, is, is there something that isn't what

we can represent formally? Right. That is, that is, there's something that, and that's, I think,

related to the hyper rulliad 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, 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, of what the world is like. Now, I have to say,

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, 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. So, so I haven't, I haven't explained it as,

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, so it's kind of a

like, well, you're, you're conscious being is computationally bounded. So you're missing,

having written quite a few articles yourself, you, you're now missing some of the pieces.

Yes, right. The limitation of being human. Right. One of the consequences of this,

why the, why the universe exists thing and this kind of concept of Rulee ads and, 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, the, the question of, of kind of what, what is the foundation 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 it's one of these cases where I've, I've long

believed that mathematics has a great deal of arbitraryness 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, 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, and, you know, I'm like, no, no, no, I know what I'm talking about. And

finally, she's, she's much more right than, than I've been. So it's, it's one of the.

So I mean, her sense, in your sense, are we just, so this is to the question of metamath,

mathematics, are we just kind of on a trajectory through

through rural space, except in mathematics, through a trajectory of 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, what people have been doing mathematics for ages,

but then in the, 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, we're going to make it out of, 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 it'll just

we'll just have a machine, kind of a supermathematica, so to speak, that can just grind out all true

theorems of mathematics. That got exploited by Goedl'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. And so, so that was, 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 Goedl'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 kind of, 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 a 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 when you look at, if you look at one of these formalized

mathematics systems, something like, you know, Pythagoras's theorem, it'll be, 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 proof, 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 mathematics,

that mathematicians care about mathematics, it's way above the molecular dynamics, so to speak.

And they're 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, you know, 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,

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 results. They're a bundle of proofs.

There's this whole set of possible proofs.

You could think of as branching, similar to the quantum mechanics model that you were talking

about. Exactly. And so 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,

you know, as you start thinking about multiple proofs, are there analogs of, for example,

destructive interference of multiple proofs? So here's a bizarre idea. It'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, it's a practical matter. I mean, this whole question, in fact, Jonathan

Gorat 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 and in our models, energy is kind of

level of activity in this hypergraph. And so there'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, is the way that one can sort of have

the interplay between like, for example, a black hole, what is a black hole in mathematics?

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 spacetime 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. The, you know, the,

the 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 arbitrary long length. And 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 the,

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, decidable theories and undecidable theories. That's a,

that's an example. And I think we're sort of the, the, the attempt to understand. So, so another

question is kind of what is the, what is the generativity of, of metamathematics? What is the

bulk theory of metamathematics? So in the literature of mathematics, there are about 3 million

theorems that people have, have published. And those represent, it's kind of on this, it's like,

like on the earth, we would be, you know, 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 is the limit of

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