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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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spatial hypergraph. Then there's what we call branchial space, the space of quantum branches.

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there's this idea of a kind of space where instead of moving around in physical space,

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you're moving from history to history, so to speak, from one possible history to another

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possible history. And that's kind of a different kind of space that is the space in which quantum

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mechanics plays out. Quantum mechanics, for example, I think we're slowly understanding

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

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space is associated with phase in quantum mechanics. And what's happening is the two

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photons that are supposed to be interfering and destructively interfering are winding up at

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different ends of branchial space. And so us as these poor observers that have branching brains

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that are trying to conflate together these different threads of history and say,

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we've really got a consistent story that we're telling here. We're really knitting together

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these threads of history. By the time the two photons wound up at opposite ends of branchial

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rule space too, which is the space of rules. Yes. Well, that's another level up. So there's

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the question. Actually, I do want to mention one thing because it's something I've realized in

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recent times and I think it's really, really kind of cool, which is about time dilation and

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relativity. And it kind of helps to understand it's something that kind of helps in understanding

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what's going on. So according to relativity, if you have a clock, it's ticking at a certain rate,

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you send it in a spacecraft that's going at some significant fraction of the speed of light,

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to you as an observer at rest, that clock that's in the spacecraft will seem to be ticking much

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more slowly. And so in other words, it's kind of like the twin who goes off to Alpha Centauri and

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goes very fast will age much less than the twin who's on Earth that is just hanging out where

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they're hanging out. Okay, why does that happen? Okay, so it has to do with what motion is.

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So in our models of physics, what is motion? Well, when you move from somewhere to somewhere,

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When you exist at a particular place and you just evolve with time, again, you're updating yourself,

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you're following these rules to update what happens. Well, so the question is, when you

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have a certain amount of computation in you, so to speak, when there's a certain amount,

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you know, you're computing, the universe is computing at a certain rate, you can either

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use that computation to work out sitting still where you are, what's going to happen successively

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

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Mm hmm. And so time dilation ends up being, it's really cool, actually, that this is explainable

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in a way that isn't just imagine the mathematics of relativity. But time dilation is a story of

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the fact that as you kind of are recreating yourself as you move, you are using up some

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of your computation. And so you don't have as much computation left over to actually work out what

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happens progressively with time. So that means that time is running more slowly for you because

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it is, you're using up your computation, your clock can't tick as quickly, because every tick

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of the clock is using up some computation, but you already use that computation up on moving at,

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you know, half the speed of light or something. And so that's why time dilation happens.

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And so you can start, so it's kind of interesting that one can sort of get an intuition about

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something like that, because it has seemed like just a mathematical fact about the mathematics of

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special relativity and so on. Well, for me, it's a little bit confusing what the you in that picture

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is, because you're using up computation. Okay, so we're simply saying the entity is updating

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

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those updates, let's imagine the you as a clock. Okay. And the clock is, you know, there's all

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these little updates, the hypergraph and a sequence of updates cause the pendulum to swing back the

link |

other way, and then swing back, swinging back and forth. Okay. And all of those updates are

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contributing to the motion of, you know, the pendulum going back and forth or the little

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oscillator moving, whatever it is. Okay. But then the alternative is that sort of situation one,

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where the thing is at rest, situation two, where it's kind of moving, what's happening is it is

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having to recreate itself at every moment, the thing is going to have to do the computations

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to be able to sort of recreate itself at a different position in space. And that's kind of

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the intuition behind, so it's either going to spend its computation recreating itself at a

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different position in space, or it's going to spend its computation doing the sort of doing the

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updating of the, you know, of the ticking of the clock, so to speak. So the more updating is doing,

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the less the ticking of the clock update is doing. That's right. The more it's having to update

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because of motion, the less it can update the clock. Obviously, there's a sort of mathematical

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version of it that relates to how it actually works in relativity, but that's kind of, to me,

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that was sort of exciting to me that it's possible to have a really mechanically explainable story

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there. And similarly in quantum mechanics, this notion of branching brains perceiving branching

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universes, to me, that's getting towards a sort of mechanically explainable version of what happens

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in quantum mechanics, even though it's a little bit mind bending to see, you know, these things

link |

about under what circumstances can you successfully knit together those different threads of history,

link |

and when do things sort of escape, and those kinds of things. But the thing about this physical space

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and physical space, the main sort of big theory is general relativity, the theory of gravity,

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and that tells you how things move in physical space. In branchial space, the big theory is the

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Feynman path integral, which it turns out tells you essentially how things move in quantum in the

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space of quantum phases. So it's kind of like motion in branchial space. And it's kind of a

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fun thing to start thinking about all these things that we know in physical space, like event horizons

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and black holes and so on. What are the analogous things in branchial space? For example, the speed

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of light, what's the analog of the speed of light in branchial space? It's the maximum speed of

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quantum entanglement. So the speed of light is a flash bulb goes off here. What's the maximum rate

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at which the effect of that flash bulb is detectable moving away in space? So similarly,

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in branchial space, something happens. And the question is, how far in this branchial space,

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in the space of quantum states, how far away can that get within a certain period of time?

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And so there's this notion of a maximum entanglement speed. And that might be observable.

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That's the thing we've been sort of poking at, is might there be a way to observe it,

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even in some atomic physics kind of situation? Because one of the things that's weird in

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quantum mechanics is when we study quantum mechanics, we mostly study it in terms of small

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numbers of particles. This electron does this, this thing on an ion trap does that and so on.

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But when we deal with large numbers of particles, kind of all bets are off. It's kind of too

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complicated to deal with quantum mechanics. And so what ends up happening is, so this question

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about maximum entanglement speed and things like that may actually play in the sort of story of

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many body quantum mechanics and even have some suspicions about things that might happen even in

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one of the things I realized I'd never understood and it's kind of embarrassing, but I think I now

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understand a little better, is when you have chemistry and you have quantum mechanics,

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it's like, well, there's two carbon atoms in this molecule and we do a reaction and we draw a

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diagram and we say this carbon atom ends up in this place. And it's like, but wait a minute,

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in quantum mechanics, nothing ends up in a definite place. There's always just some wave

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function for this to happen. How can it be the case that we can draw these reasonable, it just

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ended up in this place? And you have to kind of say, well, the environment of the molecule

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effectively made a bunch of measurements on the molecule to keep it kind of classical.

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And that's a story that has to do with this whole thing about measurements have to do with this

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idea of, can we conclude that something definite happened? Because in quantum mechanics,

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the intrinsic quantum mechanics, the mathematics of quantum mechanics is all about,

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they're just these amplitudes for different things to happen. Then there's this thing of,

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and then we make a measurement and we conclude that something definite happened. And that has

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to do with this thing, I think, about sort of moving about knitting together these different

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threads of history and saying, this is now something where we can definitively say something

link |

definite happened. In the traditional theory of quantum mechanics, it's just like, after you've

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done all this amplitude computation, then this big hammer comes down and you do a measurement

link |

and it's all over. And that's been very confusing. For example, in quantum computing,

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it's been a very confusing thing because when you say, in quantum computing, the basic idea is

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you're going to use all these separate threads of computation, so to speak, to do all the different

link |

parts of, try these different factors for an integer or something like this. And it looks

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like you can do a lot because you've got all these different threads going on. But then you have to

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say, well, at the end of it, you've got all these threads and every thread came up with a definite

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answer, but we got to conflate those together to figure out a definite thing that we humans

link |

can take away from it, a definite, so the computer actually produced this output.

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So having this branchial space and this hypergraph model of physics, do you think it's possible to

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then make predictions that are definite about many body quantum mechanical systems?

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I think it's likely, yes. Every one of these things, when you go from the underlying theory,

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which is complicated enough and it's, I mean, the theory at some level is beautifully simple,

link |

but as soon as you start actually trying to, it's this whole question about how do you bridge it to

link |

things that we humans can talk about, it gets really complicated. And this thing about actually

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getting it to a definite prediction about definite thing you can say about chemistry or something

link |

like this, that's just a lot of work. So I'll give you an example. There's a thing called the

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quantum Zeno effect. So the idea is quantum stuff happens, but then if you make a measurement,

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you're kind of freezing time in quantum mechanics. So it looks like there's a possibility that with

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sort of the relationship between the quantum Zeno effect and the way that many body quantum

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mechanics works and so on, maybe just conceivably, it may be possible to actually figure out a way

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to measure the maximum entanglement speed. And the reason we can potentially do that

link |

is because the systems we deal with in terms of atoms and things, they're pretty big. A mole of

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atoms is a lot of atoms, but it's something where to get, when we're dealing with how can you see

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10 to the minus 100, so to speak? Well, by the time you've got 10 to the 30th atoms, you're within

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a little bit closer striking distance of that. It's not like, oh, we've just got two atoms and

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we're trying to see down to 10 to the minus 100 meters or whatever. So I don't know how it will

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work, but this is a potential direction. And if you can tell, by the way, if we could measure

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the maximum entanglement speed, we would know the elementary length. These are all related.

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So if we get that one number, we just need one number. If we can get that one number,

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the theory has no parameters anymore. And there are other places, well, there's another hope for

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doing that is in cosmology. In this model, one of the features is the universe is not fixed

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dimensional. We think we live in three dimensional space, but this hypergraph doesn't have any

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particular dimension. It can emerge as something which on an approximation, it's as if you say,

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what's the volume of a sphere in the hypergraph where a sphere is defined as how many nodes do

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you get to when you go a distance R away from a given point? And you can say, well, if I get to

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about R cubed nodes, when I go a distance R away in the hypergraph, then I'm living roughly in

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three dimensional space. But you might also get to R to the point 2.92 for some value of R. As R

link |

increases, that might be the sort of fit to what happens. And so one of the things we suspect is

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that the very early universe was essentially infinite dimensional, and that as the universe

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expanded, it became lower dimensional. And so one of the things that is another little sort of point

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where we think there might be a way to actually measure some things is dimension fluctuations in

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the early universe. That is, is there leftover dimension fluctuation of at the time of the cosmic

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microwave background, 100,000 years or something after the beginning of the universe? Is it still

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the case that there were pieces of the universe that didn't have dimension three, that had

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dimension 3.01 or something? And can we tell that? Is that possible to observe fluctuations in

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dimensions? I don't even know what that entails. Okay. So the question, which should be an

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elementary exercise in electrodynamics, except it isn't, is understanding what happens to a

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photon when it propagates through 3.01 dimensional space. So for example, the inverse square law

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is a consequence of the surface area of a sphere is proportional to R squared. But if you're not

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in three dimensional space, the surface area of sphere is not proportional to R squared. It's R

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to the whatever 2.01 or something. And so that means that I think when you kind of try and do

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optics, you know, a common principle in optics is Huygens principle, which basically says that every

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piece of a wave front of light is a source of new spherical waves. And those spherical waves,

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if they're different dimensional spherical waves, will have other characteristics. And so there will

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be bizarre optical phenomena which we haven't figured out yet. So you're looking for some weird

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photon trajectories that designate that it's 3.01 dimensional space? Yeah. Yeah. That would be an

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example of, I mean, you know, there are only a certain number of things we can measure about

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photons. You know, we can measure their polarization, we can measure their frequency,

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we can measure their direction, those kinds of things. And, you know, how that all works out.

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And, you know, in the current models of physics, you know, it's been hard to explain how the

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universe manages to be as uniform as it is. And that's led to this inflation idea that,

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to the great annoyance of my then collaborator, we figured out in like 1979, we had this

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realization that you could get something like this. But it seemed implausible that that's the

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way the universe worked. So we put it in a footnote. But in any case, I've never really

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completely believed it. But that's an idea for how to sort of puff out the universe faster than the

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speed of light, early moments of the universe. That's the sort of the inflation idea and that

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you can somehow explain how the universe manages to be as uniform as it is. In our model, this turns

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out to be much more natural because the universe just starts very connected. The hypergraph is not

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such that the ball that you grow starting from a single point has volume R cubed, it might have

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volume R to the 500 or R to the infinity. And so that means that you sort of naturally get this

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much higher degree of connectivity and uniformity in the universe. And then the question is,

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this is sort of the mathematical physics challenge, is in the standard theory of the universe,

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there's the Friedman Robertson Walker universe, which is the kind of standard model where the

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universe is isotropic and homogeneous. And you can then work out the equations of general relativity,

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and you can figure out how the universe expands. We would like to do the same kind of thing,

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including dimension change. This is just difficult mathematical physics. I mean,

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the reason it's difficult is the sort of fundamental reason it's difficult. When

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people invented calculus 300 years ago, calculus was a story of understanding change and change

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as a function of a variable. So people study univariate calculus, they study multivariate

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calculus, it's one variable, it's two variables, three variables. But whoever studied, you know,

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2.5 variable calculus, turns out nobody. Turns out that what we need to have to understand these

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fractional dimensional spaces, which don't work like well, they're spaces where the effective

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dimension is not an integer. So you can't apply the tools of calculus naturally and easily to

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we're trying to figure this out. I mean, it's very interesting. I mean, it's very connected to

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very frontier issues in mathematics. It's very beautiful. So is it possible? Is it possible?

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We're dealing with a scale that's so, so much smaller than our human scale. Is it possible

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to make predictions versus explanations? Do you have a hope that with this hypergraph model,

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you'd be able to make predictions that then could be validated with a physics experiment,

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predictions that couldn't have been done or weren't done otherwise? Yeah, yeah, yeah. I mean,

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you know, I think which, in which domain do you think? Okay, so they're going to be cosmology ones

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to do with dimension fluctuations in the universe. That's a very bizarre effect. Nobody, you know,

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dimension fluctuations is just something nobody ever looked for that. If anybody sees dimension

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fluctuation, that's a huge flag that something like our model is going on. And how one detects

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that, you know, that's a problem of kind of, you know, that's a problem of traditional physics in

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a sense of what's the best way to actually figure that out. And for example, that's one,

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there are all kinds of things one could imagine. I mean, there are things that in black hole mergers,

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it's possible that there will be effects of maximum entanglement speed in large black hole mergers.

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That's another possible thing. And all of that is detected through like what? Do you have a

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hope for LIGO type of situation? Like that's gravitational waves? Yeah. Or alternatively,

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I mean, I think it's, you know, look, figuring out experiments is like figuring out technology

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inventions. That is, you know, you've got a set of raw materials, you've got an underlying model,

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and now you've got to be very clever to figure out, you know, what is that thing I can measure

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that just somehow, you know, leverages into the right place. And we've spent less effort on that

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than I would have liked. Because one of the reasons is that I think that the physicists

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who've been working on our models, with now lots of physicists actually, it's very, very nice. It's

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kind of, it's one of these cases where I'm almost, I'm really kind of pleasantly surprised that the

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sort of absorption of the things we've done has been quite rapid and quite sort of, you know,

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very positive. So it's a Cambrian explosion of physicists too, not just ideas. Yes. I mean,

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you know, a lot of what's happened that's really interesting, and again, not what I expected,

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is there are a lot of areas of sort of very elaborate, sophisticated mathematical physics,

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whether that's causal set theory, whether it's higher category theory, whether it's categorical

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quantum mechanics, all sorts of elaborate names for these things, spin networks, perhaps,

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you know, causal dynamical triangulations, all kinds of names of these fields. And these fields

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have a bunch of good mathematical physicists in them who've been working for decades in these

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particular areas. And the question is, but they've been building these mathematical structures.

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And the mathematical structures are interesting, but they don't typically sit on anything.

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They're just mathematical structures. And I think what's happened is our models provide kind of

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a machine code that lives underneath those models. So a typical example, this is due to

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Jonathan Gorod, who's one of the key people who's been working on our project. This is in,

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okay, so I'll give you an example just to give a sense of how these things connect. This is in

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causal set theory. So the idea of causal set theory is there are, in spacetime, we imagine

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that there's space and time. It's a three plus one dimensional, you know, setup. We imagine that

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there are just events that happen at different times and places in space and time. And the idea

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of causal set theory is the only thing you say about the universe is there are a bunch of events

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that happen sort of randomly at different places in space and time. And then the whole sort of

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theory of physics has to be to do with this graph of causal relationships between these randomly

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thrown down events. So they've always been confused by the fact that to get even Lorentz

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invariants, even relativistic invariants, you need a very special way to throw down those events.

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And they've had no natural way to understand how that would happen. So what Jonathan figured out

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is that, in fact, from our models, instead of just generating events at random, our models

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necessarily generate events in some pattern in spacetime effectively that then leads to Lorentz

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invariants and relativistic invariants and all those kinds of things. So it's a place where

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all the mathematics that's been done on, well, we just have a random collection of events.

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Now what consequences does that have in terms of causal set theory and so on? That can all be kind

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of wheeled in now that we have some different underlying foundational idea for what the

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particular distribution of events is as opposed to just what we throw down random events.

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And so that's a typical sort of example of what we're seeing in all these different areas of kind

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of how you can take really interesting things that have been done in mathematical physics

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and connect them. And it's really kind of beautiful because the abstract models we have

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just seem to plug into all these different very interesting, very elegant abstract ideas.

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But we're now giving sort of a reason for that to be the way, a reason for one to care. I mean,

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it's like saying you can think about computation abstractly. You can think about, I don't know,

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combinators or something as abstract computational things. And you can sort of do all kinds of study

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of them. But it's like, why do we care? Well, okay, Turing machines are a good start because

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you can kind of see they're sort of mechanically doing things. But when we actually start thinking

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about computers, computing things, we have a really good reason to care. And this is sort of

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what we're providing, I think, is a reason to care about a lot of these areas of mathematical

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question of why does the universe exist at all? No, no, let's talk about that. So it's not the

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simplest question in the world. So it takes a few steps to get to it. And it's nevertheless even

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Indeed. I'm very surprised. So the next thing to perhaps understand is this idea of ruleal space.

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So we've got kind of physical space. We've got branchial space, the space of possible quantum

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

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here's where that comes from. So you say, okay, you say we've got this model for the universe.

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We've got a particular rule. And we run this rule and we get the universe. So that's interesting.

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Why that rule? Why not another rule? And so that confused me for a long time. And I realized,

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well, actually, what if the thing could be using all possible rules? What if at every step,

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in addition to saying apply a particular rule at all places in this hypergraph, one could say,

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just take all possible rules and apply all possible rules at all possible places in this

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hypergraph. And then you make this ruleal multiway graph, which both is all possible

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histories for a particular rule and all possible rules. So the next thing you'd say is, how can you

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get anything reasonable out of it? How can anything real come out of the set of all possible

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rules applied in all possible ways? This is a subtle thing, which I haven't fully untangled.

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There is this object, which is the result of running all possible rules in all possible ways.

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And you might say, if you're running all possible rules, why can't everything possible happen?

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Well, the answer is because when you, there's sort of this entanglement that occurs.

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So let's say that you have a lot of different possible initial conditions, a lot of different

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possible states. Then you're applying these different rules. Well, some of those rules can

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end up with the same state. So it isn't the case that you can just get from anywhere to anywhere.

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There's this whole entangled structure of what can lead to what, and there's a definite structure

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that's produced. I think I'm going to call that definite structure the rulead, the limit of kind

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of all possible rules being applied in all possible ways. And you're saying that structure is finite,

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so that somehow connects to maybe a similar kind of thing as like causal invariance.

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Well, it happens that the rulead necessarily has causal invariance. That's a feature of,

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plus universal computation gives you the fact that from any diverging paths, the paths will

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In the end, it's not necessarily finite. I mean, just like the history of the universe may not be

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finite. The history of the universe, time may keep going forever. You can keep running the

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computations of the rulead and you'll keep spewing out more and more and more structure. It's like

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time doesn't have to end. But the issue is there are three limits that happen in this rulead

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

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applying. And another is how many different states you start from. And the mixture of those

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three limits. I mean, this is just mathematically a horrendous object. And what's interesting about

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this object is the one thing that does seem to be the case about this object is it connects with

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ideas in higher category theory. And in particular, it connects to some of the 20th century's most

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abstract mathematics done by this chap Grothendieck. Grothendieck had a thing called the infinity

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groupoid, which is closely related to this rulead object. Although the details of the relationship,

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you know, I don't fully understand yet. But I think that what's interesting is this thing that

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is sort of this very limiting object. So, okay, so a way to think about this that, again, will

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take us into another direction, which is the equivalence between physics and mathematics.

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The way that, well, let's see, maybe this is just to give a sense of this kind of groupoid and

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things like that. You can think about, in mathematics, you can think you have certain axioms,

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they're kind of like atoms, and you, well, actually, let's say, let's talk about mathematics

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for a second. So what is mathematics? What is it made of, so to speak? Mathematics, there's a bunch

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of statements, like, for addition, x plus y is equal to y plus x, that's a statement in mathematics.

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

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Right. And what you can imagine is, you imagine just laying out this giant kind of ocean

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of all statements. Well, actually, you first start, okay, this is where this was segueing

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Yeah, we'll maybe get to metamathematics, but it's, so let me not, let me explain the groupoid

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and things later. But, so let's come back to the universe, always a good place to be in,

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Yeah, so what does the universe have to do with the rule add, the rule of L space,

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and how that's possibly connected to why the thing exists at all, and why there's just

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Yes. Okay. So here's the point. So the thing that had confused me for a long time was,

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let's say we get the rule for the universe. We hold it in our hand. We say, this is our

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universe. Then the immediate question is, well, why isn't it another one? And that's

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kind of the sort of the lesson of Copernicus is, we're not very special. So how come we

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got universe number 312 and not universe quadrillion, quadrillion, quadrillion? And

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I think the resolution of that is the realization that the universe is running all possible

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rules. So then you say, well, how on earth do we perceive the universe to be running

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according to a particular rule? How do we perceive definite things happening in the

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universe? Well, it's the same story. It's the observer, there is a reference frame that

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we are picking in this ruleal space, and that that is what determines our perception of

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the universe. With our particular sensory information and so on, we are parsing the

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universe in this particular way. So here's the way to think about it. In physical space,

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

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don't. We live here. And similarly, in ruleal space, we could live in many different places

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in ruleal space, but we happen to live here. And what does it mean to live here? It means

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we have certain sensory input. We have certain ways to parse the universe. Those are our

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interpretation of the universe. What would it mean to travel in ruleal space? What it

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basically means is that we are successively interpreting the universe in different ways.

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So in other words, to be at a different point in ruleal space is to have a different, in a sense,

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a different interpretation of what's going on in the universe. And we can imagine even

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things like an analog of the speed of light as the maximum speed of translation in ruleal

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I'm confused by the we and the interpretation and the universe. I thought moving about in

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ruleal space changes the way the universe is. The way we would perceive it. So it ultimately

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has to do with the perception. So it doesn't real, ruleal space is not somehow changing,

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

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point of this is the rule yard is sort of the encapsulated version of everything that is the

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

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

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potentially encapsulate a very large number, like combinatorially large, maybe infinite

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set of what we human physicists think of as universes? That's an interesting, interesting

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parsing of the word universe, right? Because what we're saying is, just as we're at a particular

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place in physical space, we're at a particular place in ruleal space, at that particular place

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in ruleal space, our experience of the universe is this. Just as if we lived at the center of the

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galaxy, our universe, our experience of the universe will be different from the one it is,

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given where we actually live. And so what we're saying is, you might say, I mean, in a sense,

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this rule yard is sort of a super universe, so to speak. But it's all entangled together. It's not

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like you can separate out. You can say, let me, it's like when we take a reference, okay, it's like

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our experience of the universe is based on where we are in the universe. We could imagine moving

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No. Because, and the whole point is that if we were able to change our interpretation of what's

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

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Right. So the reason that's interesting is, imagine the extraterrestrial intelligence,

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so the alien intelligence, we should say. The alien intelligence might live on Alpha Centauri,

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Yeah, but it's also, well, one thing is how different the perception of the universe could be.

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I think it could be bizarrely, unimaginably completely different. And I mean, one thing to

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realize is, even in kind of things I don't understand well, you know, I know about the kind

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of Western tradition of understanding, you know, science and all that kind of thing. And, you know,

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you talk to people who say, well, I, you know, I'm really into some, you know, Eastern tradition of

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this, that and the other. And it's really obvious to me how things work. I don't understand it

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at all. But, you know, it is not obvious, I think, with this kind of realization that there's these

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very different ways to interpret what's going on in the universe. That kind of gives me at least,

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it doesn't help me to understand that different interpretation. But it gives me at least more

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Yeah, it humbles you to the possibility that like, what is it, reincarnation or all these like

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Well, you know, the thing that I realized about a bunch of those things is that, you know,

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I've been sort of doing my little survey of the history of philosophy, just trying to understand,

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you know, what can I actually say now about some of these things? And you realize that some of

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these concepts like the immortal soul concept, which, you know, I remember when I was a kid,

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and, you know, it was kind of a lots of religion bashing type stuff of people saying, you know,

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well, we know about physics, tell us how much does a soul weigh? And people are like, well,

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how can it be a thing if it doesn't weigh anything? Well, now we understand, you know,

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there is this notion of what's in brains that isn't the matter of brains, and it's something

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computational. And there is a sense and in fact, it is correct, that it is in some sense, immortal,

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because this pattern of computation is something abstract that is not specific to the particular

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material of a brain. Now, we don't know how to extract it, you know, in our traditional scientific

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approach. But it's still something where it isn't a crazy thing to say there is something doesn't

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weigh anything. That's a kind of a silly question. How much does it weigh? Well, actually, maybe it

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isn't such a silly question in our model of physics, because the actual computational activity

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You can talk about mass and energy and so on. That could be a, what would you call it, a solitron.

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Yeah, right. Well, that's what, by the way, that's what Leibniz said. And, you know,

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one thing I've never understood this, you know, Leibniz had this idea of monads and monadology,

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and he had this idea that what exists in the universe is this big collection of monads.

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And that they that the only thing that one knows about the monads is sort of how they relate to

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each other. It sounds awfully like hypergraphs, right? But Leibniz had really lost me at the

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following thing. He said, each of these monads has a soul, and each of them has a consciousness.

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And it's like, okay, I'm out of here. I don't understand this at all. I don't know what's

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going on. But I realized recently that in his day, the concept that a thing could do something

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And so what I would now say is, well, there's this abstract rule that runs. To Leibniz,

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that would have been, you know, in 1690 or whatever, that would have been kind of,

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well, it has a soul, it has a consciousness. And so, you know, in a sense, it's like one

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of these, there's no new idea under the sun, so to speak. That's a sort of a version of the same

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kinds of ideas, but couched in terms that are sort of bizarrely different from the ones that

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we would use today. Would you be able to maybe play devil's advocate on your conception of

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consciousness that, like the two characteristics of it that is constrained, and there's a

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single thread of time? Is it possible that Leibniz was onto something that the basic atom,

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the discrete atom of space has a consciousness? Is that, so these are just words, right? But like,

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I think that, okay, so the question would be, is there a way to think about kind of,

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if we sort of parse the universe down at the level of atoms of space or something,

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a different place in real space. We're asking the question, could there be a civilization

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that exists? Could there be sort of conscious entities that exist at the level of atoms of

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space? And what would that be like? And I think that comes back to this question of,

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what's it like to be a cellular automaton type thing? I mean, I'm not yet there. I don't know.

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

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in the sense that I was considering, you know, I never write fiction, but I haven't written it

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since I was like 10 years old. And my fiction, I made one attempt, which I sent to some science

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Recently. They said it was terrible. That'd be interesting to see you write a short story

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based on what sounds like it's already inspiring short stories or stories by science fiction

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But I think the interesting thing for me is, you know, what is it like to be a whatever?

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How do you describe that? I mean, that's not a thing that you describe in mathematics,

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it presumes that you're talking about a singular entity. So, like, there's some kind of feeling of

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And then that's when consciousness starts making sense. But then it seems like that could be

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generalizable. If you take some subset of a cellular automata, you could start talking

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about what does that subset feel. But then you can, I think you could just take arbitrary

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numbers of subsets. Like, to me, like, you and I individually are consciousnesses,

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Maybe, maybe. I'm not so sure about that. I think that the single thread of time thing

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may be pretty important. And that as soon as you start saying, there are two different threads

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of time, there are two different experiences, and then we have to say, how do they relate?

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How are they sort of entangled with each other? I mean, that may be a different story of a thing

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that isn't much like, you know, what do the ants, you know, what's it like to be an ant,

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you know, where there's a sort of more collective view of the world, so to speak?

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I don't know. I think that, I mean, this is, you know, I don't really have a good, I mean,

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you know, my best thought is, you know, can we turn it into a human story? It's like the question

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of, you know, when we try and understand physics, can we turn that into something which is sort of

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a human understandable narrative? And now what's it like to be a such and such? You know, maybe the

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only medium in which we can describe that is something like fiction, where it's kind of like

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you're telling, you know, the life story in that setting. But I'm, this is beyond what I've yet

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understood how to do. Yeah, but it does seem so, like with human consciousness, you know,

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we're made up of cells and like, there's a bunch of systems that are networked that work together

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that at this, at the human level, feel like a singular consciousness when you take, and so

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maybe like an ant colony is just too low level. Sorry, an ant is too low level. Maybe you have to

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look at the ant colony. Yeah, I agree. There's some level at which it's a conscious being. And then

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if you go to the planetary scale, then maybe that's going too far. So there's a nice sweet spot for

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consciousness. No, I agree. I think the difficulty is that, you know, okay, so in sort of people who

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talk about consciousness, one of the terrible things I've realized, because I've now interacted

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with some of this community, so to speak, some interesting people who do that kind of thinking.

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But, you know, one of the things I was saying to one of the leading people in that area, I was

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saying, you know, that, you know, it must be kind of frustrating because it's kind of like a poetry

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story. That is many people are writing poems, but few people are reading them. So there are always

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these different, you know, everybody has their own theory of consciousness, and they are very

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non inter sort of inter discussable. And by the way, I mean, you know, my own approach to sort of

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the question of consciousness, as far as I'm concerned, I'm an applied consciousness operative,

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so to speak, because I don't really, in a sense, the thing I'm trying to get out of it is how does

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it help me to understand what's a possible theory of physics? And how does it help me to say,

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how do I go from this incoherent collection of things happening in the universe to our definite

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perception and definite laws and so on, and sort of an applied version of consciousness? And I

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think the reason it sort of segues to a different kind of topic, but the reason that one of the

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things I'm particularly interested in is kind of what's the analog of consciousness in systems

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very different from brains? And so why is that matter? Well, you know, this whole description

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of this kind of, you know what, we haven't talked about why the universe exists. So let's get to why

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the universe exists. And then we can talk about perhaps a little bit about what these models of

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physics kind of show you about other kinds of things like molecular computing and so on.

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Why does the universe exist? Okay, so we finally sort of more or less set the stage,

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we've got this idea of this rule yard of this object that is made from following all possible

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rules, the fact that it's sort of not just this incoherent mess, it's got all this entangled

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structure in it, and so on. Okay, so what is this rule yard? Well, it is the working out of all

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possible formal systems. So the sort of the question of why does the universe exist? Its

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

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some other abstract result, but that's not actualized. It's just an abstract thing.

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And when we say we've got a model for the universe, okay, it's this rule, you run it,

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and it'll make the universe, but it's like, but where's it actually running? What is it actually

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doing? Is it actual, or is it merely a formal description of something? So the thing to realize

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with this, the thing about the rule yard is it's an inevitable, it is the entangled running of all

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possible rules. So you don't get to say, it's not like you're saying, which rule yard are you

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picking? Because it's all possible formal rules. It's not like it's just, well, actually, it's

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only footnote. The only footnote, it's an important footnote, is it's all possible

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computational rules, not hyper computational rules. That is, it's running all the rules that would be

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accessible to a Turing machine, but it is not running all the rules that will be accessible

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to a thing that can solve problems in finite time that would take a Turing machine infinite time to

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solve. So you can, even Alan Turing knew this, that you could make oracles for Turing machines,

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where you say a Turing machine can't solve the whole thing problem for Turing machines. It can't

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know what will happen in any Turing machine after an infinite time, in any finite time,

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but you could invent a box, just make a black box. You say, I'm going to sell you an oracle

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that will just tell you, you know, press this button. It'll tell you what the Turing machine

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will do after an infinite time. You can imagine such a box. You can't necessarily build one in

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the physical universe, but you can imagine such a box. And so we could say, well, in addition to,

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so in this Rulliad, we're imagining that there is a computational, that at the end, it's running

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rules that are computational. It doesn't have a bunch of oracle black boxes in it. You say, well,

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why not? Well, it turns out if there are oracle black boxes, the Rulliad that is,

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but it has a cosmological event horizon relative to the first one. They can't communicate.

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In other words, you can end up with, what ends up happening is it's like in the physical universe,

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in this causal graph that represents the causal relationships of different things,

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you can have an event horizon where the causal graph is disconnected, where the effect here,

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an event happening here does not affect an event happening here because there's a disconnection

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in the causal graph. And that's what happens in an event horizon. And so what will happen between

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this kind of the ordinary Rulliad and the hyper Rulliad is there is an event horizon and we,

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in our Rulliad, will just never know that they're just separate things. They're not connected.

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So it might exist, but it's not clear what it... So what, so to speak, whether it exists. What

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we're trying to understand is why does our universe exist? We're not trying to ask the

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question what... Let me say another thing. Let me make a meta comment, which is that I have not

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thought through this hyper Rulliad business properly. So I can't... The hyper Rulliad is

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Yeah, that's right. So let's ignore that. Okay. It's already abstract enough. Okay. So,

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okay. So the one question is we have to say, if we're saying, why does the universe exist?

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One question is why is it this universe and not another universe? Okay. So the important point

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about this Rulliad idea is that in the Rulliad are all possible formal systems. So there's no

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choice being made. There's no like, oh, we pick this particular universe and not that one. That's

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the first thing. The second thing is that we have to ask the question. So you say, why does two plus

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two equals four exist? That is a thing that necessarily is that way just on the basis of

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the meaning of the terms, two and plus and equals and so on. So the thing is that this Rulliad

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object is in a sense a necessary object. It is just the thing that is the consequence of working

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out the consequence of the formal definition of things. It is not a thing where you're saying,

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and this is picked as the particular thing. This is just something which necessarily is that thing

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because of the definition of what it means to have computation. So the Rulliad, it's a formal system.

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two equals four exist? Well, in some sense, it necessarily exists. It's a necessary object. It's

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not a thing that way you can ask. Usually in philosophy, there's a sort of distinction made

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between necessary truths, contingent truths, analytic propositions, synthetic propositions

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that are a variety of different versions of this. They're things which are necessarily true just

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based on the definition of terms. And there are things which happen to be true in our universe.

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But we don't exist in Rullial space. That's one of the coordinates that define our existence.

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Well, okay. So yes, yes. But this Rulliad is the set of all possible Rullial coordinates.

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So what we're saying is it contains that. So what we're saying is we exist as, okay, so

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our perception of what's going on is we're at a particular place in this Rulliad,

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and we are concluding certain things about how the universe works based on that.

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But the question is, do we understand, you know, is there something where we say,

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

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because this Rulliad is a necessary object in the sense that it is a purely formal object,

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just like 2 plus 2 equals 4. It's not an object that was made of something. It's an object that

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is just an expression of the necessary collection of formal relations that exist.

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And so then the issue is, can we, in our experience of that, is it, you know, can we have

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tables and chairs, so to speak, in that just by virtue of our experience of that necessary thing?

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And, you know, what people have generally thought, and I don't know of a lot of discussion of this,

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why does the universe exist question? It's been a very, you know, I've been surprised actually at

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how little, I mean, I think it's one of these things that's really kind of far out there. But

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the thing that is, you know, the surprise here is that all possible formal rules, when you run them

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together, and that's the critical thing, when you run them together, they produce this kind of

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entangled structure that has a definite structure. It's not just, you know, a random arbitrary thing,

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it's a thing with definite structure. And that structure is the thing when we are embedded in

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that structure, when anything, you know, an entity embedded in that structure perceives something,

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which is then we can interpret as physics and things like this. So in other words, we don't

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So like, you need to have it if you want to formalize the relation between entities, but

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Fair question. Okay, fair question. Let's see. I think the thing to think about is

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what follows from that definition inevitably follows. So now you can say, why define any terms?

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But in a sense, the, well, that's okay. So the definition of terms, I mean, I think the way to

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Well, they're not very concrete. I mean, they're just things like, you know, logical or.

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Well, yes, okay. But the point is that it is not a thing of a, you know, people imagine there is,

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I don't know, the, you know, an elephant or something or the, you know, elephants are presumably

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not necessary objects. They happen to exist as a result of kind of biological evolution and

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whatever else. But the thing is that in some sense that there is, it is a different kind of thing

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So a plus seems more fundamental, more basic than an elephant. Yes. But you can imagine a world

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without plus or anything like it. Like, why do formal things that are discrete, that can be used

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Well, okay. So why? Okay. So then the question is, but the whole point is computation.

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We can certainly imagine computation. That is, we can certainly say there is a formal system that

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we can construct abstractly in our minds that is computation. And that's the, you know, we can

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imagine it. Now the question is, is it that formal system, once we exist as observers embedded in

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that formal system, that's enough to have something which is like our universe. And so then what

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you're kind of asking is perhaps is why, I mean, the point is we definitely can imagine it.

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There's nothing that says that we're not saying that it's sort of inevitable that that is a thing

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that we can imagine. We don't have to ask, does it exist? We're just, it is definitely something

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we can imagine. Now that's, then we have this thing that is a formally constructible thing

link |

that we can imagine. And now we have to ask the question, what, you know, given that formally

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constructible thing, what is, what consequences does that, if we were to perceive that formally,

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if we were embedded in that formally constructible thing, what would we perceive about the world?

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And we would say, we perceive that the world exists because we are seeing all of this mechanism

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of all these things happening. And, but that's something that is just a feature of, it's something

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where we are... See, another way of asking this that I'm trying to get at, I understand why it

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feels like this ruley ad is necessary, but maybe it's just me being human, but it feels like then

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you should be able to, not us, but somehow step outside of the ruley ad. Like what's outside the

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ruley ad? Well, the ruley ad is all formal systems. So there's nothing because... But that's what a

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human would say. I know that's what a human would say, because we're used to the idea that there are,

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there's, but the whole point is that by the time it's all possible formal systems, it's, it's like,

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it is all things you can imagine, but... All computations you can imagine, but like we don't...

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Well, so the issue is, can we encode? Okay. So that's a fair question. Is it possible to encode

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all, I mean, once we, is there something that isn't what we can represent formally?

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Right. That is, is there something that, and that's, I think, related to the hyper ruley ad

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footnote, so to speak, which I'm afraid that the, you know, one of the things sort of interesting

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about this is, you know, there has been some discussion of this in theology and things like

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that, but, which I don't necessarily understand all of, but the key sort of new input is this idea

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that all possible formal systems, it's like, you know, if you make a world, people say, well, you

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make a world with a particular, in a particular way with particular rules, but no, you don't do

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that. You can make a world that deals with all possible rules, and then merely by virtue of

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living in a particular place in that world, so to speak, we have the perception we have of what the

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world is like. Now, I have to say the, it's sort of interesting because I've, you know, I wrote this

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piece about this, and I, you know, this philosophy stuff is not super easy, and I've, as I'm talking

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to you about it, and I actually haven't, you know, people have been interested in lots of different

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things we've been doing, but this, why does the universe exist, has been, I would say, one of the,

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one of the ones that you would think people will be most interested in, but actually, I think

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they're just like, oh, that's just something complicated that, so I haven't, I haven't explained

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it as much as I've explained a bunch of other things, and I have to say, I think I, I think I

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may be missing a couple of pieces of that argument that would be, so it's kind of a likeâ€¦

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Well, you are, your conscious being is computationally bounded, so you're missingâ€¦

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

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Right. One of the consequences of this, why the universe exists thing, is that you're missing

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something, and this kind of concept of rule adds and, you know, places in there representing our

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perception of the universe and so on. One of the weird consequences is, if the universe exists,

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mathematics must also exist. And that's a weird thing, because mathematics, people have been very

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confused, including me, have been very confused about the question of kind of what, what is the

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definition of mathematics? What is, what kind of a thing is mathematics? Is mathematics something

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where we just write down axioms like Euclid did for geometry, and we just build the structure,

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and we could have written down different axioms, and we'd have a different structure? Or is it

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something that has a more fundamental sort of truth to it? And I have to say, this is one of

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these cases where I've long believed that mathematics has a great deal of arbitrariness to

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it, that there are particular axioms that kind of got written down by the Babylonians, and, you

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know, that's what we've ended up with the mathematics that we have. And I have to say,

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actually, my wife has been telling me for 25 years, she was a mathematician, she's been telling me,

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you're wrong about the foundations of mathematics. And, you know, I'm like, no, no, no, I know what

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

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

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just kind of on a trajectory through ruleal space, except in mathematics, through a trajectory of

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a certain kind of... I think that's partly the idea. So I think that the notion is this. So 100

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years ago, a little bit more than 100 years ago, people have been doing mathematics for ages,

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but then in the late 1800s, people decided to try and formalize mathematics and say, you know,

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it is mathematics is, you know, we're going to break it down, we're going to make it like logic,

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make it out of sort of fundamental primitives. And that was people like Frager and Piano and

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Hilbert and so on. And they kind of got this idea of let's do kind of Euclid, but even better,

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let's just make everything just in terms of this sort of symbolic axioms, and then build

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up mathematics from that. And that, you know, they thought at the time, as soon as they get

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these symbolic axioms, that they made the same mistake, the kind of computational irreducibility

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mistake. They thought as soon as we've written down the axioms, then we'll just have a machine,

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kind of a super mathematical, so to speak, that can just grind out all true theorems of mathematics.

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That got exploited by GÃ¶del's theorem, which is basically the story of computational

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irreducibility. It's that even though you know those underlying rules, you can't deduce all

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the consequences in any finite way. But now the question is, okay, so they broke mathematics down

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into these axioms, and they say now you build up from that. So what I'm increasingly coming to

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realize is that's similar to saying let's take a gas and break it down into molecules. There's gas

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laws that are the large scale structure and so on that we humans are familiar with, and then there's

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the underlying molecular dynamics. And I think that the axiomatic level of mathematics, which

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we can access with automated theorem proving and proof assistance and these kinds of things,

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that's the molecular dynamics of mathematics. And occasionally we see through to that molecular

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dynamics. We see undecidability, we see other things like this. One of the things I've always

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found very mysterious is that GÃ¶del's theorem shows that there are sort of things which cannot

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be finitely proved in mathematics. There are proofs of arbitrary length, infinite length proofs that

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you might need. But in practical mathematics, mathematicians don't typically run into this.

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happening is that what they're doing is they're looking at this. They are essentially observers

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in metamathematical space, and they are picking a reference frame in metamathematical space,

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which is causing them to deduce that the laws of metamathematics and the laws of mathematics,

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like the laws of fluid mechanics, are much more understandable than this underlying

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molecular dynamics. And so what gets really bizarre is thinking about kind of the analogy

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between metamathematics, this idea of you exist in this sort of space of possible,

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in this kind of mathematical space where the individual kind of points in the mathematical

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space are statements in mathematics, and they're connected by proofs where one statement, you know,

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you take a couple of different statements, you can use those to prove some other statement,

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and you've got this whole network of proofs. That's the kind of causal network of mathematics,

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of what can prove what and so on. And you can say at any moment in the history of a mathematician,

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of a single mathematical consciousness, you are in a single kind of slice of this

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kind of metamathematical space. You know a certain set of mathematical statements.

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You can then deduce with proofs, you can deduce other ones, and so on. You're kind of gradually

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moving through metamathematical space. And so it's kind of the view is that the reason that

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mathematicians perceive mathematics to have the sort of integrity and lack of kind of undecidability

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and so on that they do is because they, like we as observers of the physical universe,

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we have these limitations associated with computational boundedness, single thread of time,

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consciousness limitations, basically, that the same thing is true of mathematicians perceiving

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sort of metamathematical space. And so what's happening is that if you look at one of these

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formalized mathematics systems, something like Pythagoras's theorem, it'll take, oh, I don't know,

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what is it, maybe 10,000 individual little steps to prove Pythagoras's theorem. And one of the

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bizarre things that's sort of an empirical fact that I'm trying to understand a little bit better,

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if you look at different formalized mathematics systems, they actually have different axioms

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underneath that they can all prove Pythagoras's theorem. And so in other words, it's a little bit

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like what happens with gases. We can have air molecules, we can have water molecules, but they

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still have fluid dynamics. Both of them have fluid dynamics. And so similarly, at the level that

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

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And there are all kinds of weird things. Like, for example, one thing I was realizing recently

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is that the quantum theory of mathematics, that's a very bizarre idea. But basically,

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when you prove what is a proof is you've got one statement in mathematics, you go through

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other statements, you eventually get to a statement you're trying to prove, for example,

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that's a path in metamathematical space. And that's a single path, a single proof is a single

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path. But you can imagine there are other proofs of the same result. There are a bundle of proofs.

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There's this whole set of possible proofs. Yeah, you could think of it as branching,

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similar to the quantum mechanics model that you were talking about. Exactly. And then there's

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some invariance that you can formalize in the same way that you can for the quantum mechanical.

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Right. So the question is, in proof space, as you start thinking about multiple proofs,

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are there analogs of, for example, destructive interference of multiple proofs? So here's a

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bizarre idea that's just a couple of days old, so not yet fully formed. But as you try and do that,

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when you have two different proofs, it's like two photons going in different directions,

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you have two proofs, which at an intermediate stage are incompatible. And that's kind of like

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destructive interference. Is it possible for this to instruct the engineering of automated proof

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systems? Absolutely. I mean, as a practical matter, I mean, you know, this whole question,

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in fact, Jonathan Gorod has a nice heuristic for automated theorem provers that's based on

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our physics project that is looking for essentially using kind of using energy in our

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models. Energy is kind of level of activity in this hypergraph. And so it's sort of a heuristic

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for automated theorem proving about how do you pick which path to go down that is based on

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essentially physics. And I mean, the thing that gets interesting about this is the way that one

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can sort of have the interplay between, like, for example, a black hole. What is a black hole

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in metamathematics? So the answer is, what is black hole in physics? A black hole in physics

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is where in the simplest form of black hole time ends. That is all, you know, everything is crunched

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down to the space time singularity, and everything just ends up at that singularity. So in our

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models, and that's a little hard to understand in general relativity with continuous mathematics,

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and what does singularity look like? In our models, it's something very pragmatic. It's just,

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you're applying these rules, time is moving forward. And then there comes a moment where

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the rules, no rules apply. So time stops. It's kind of like the universe dies, that, you know,

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that nothing happens in the universe anymore. Well, in mathematics, that's a decidable theory.

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arithmetic, set theory, all the serious models, theories in mathematics, they all have the feature

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that there are proofs of arbitrarily long length. In something like Boolean algebra,

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which is a decidable theory, there are, you know, any question in Boolean algebra, you can just go

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crunch, crunch, crunch, and in a known number of steps, you can answer it. You know, satisfiability,

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you know, might be hard, but it's still a bounded number of steps to answer any satisfiability

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problem. And so that's the notion of a black hole in physics where time stops. That's analogous to

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in mathematics where there aren't infinite length proofs, where when in physics, you know, you can

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wander around the universe forever if you don't run into a black hole. If you run into a black

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hole and time stops, you're done. And it's the same thing in mathematics between decidable

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theories and undecidable theories. That's an example. And I think where sort of the attempt

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to understand, so another question is kind of what is the general activity of metamathematics?

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What is the bulk theory of metamathematics? So in the literature of mathematics, there are about

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

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like on the earth, we would be, you know, we've put cities in particular places on the earth,

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and there's an underlying space. And we could just talk about, you know, the world of space

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in terms of where our cities happen to be, but there's actually an underlying space. And so the

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question is, what's that for metamathematics? And as we kind of explore what is, for example,

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for mathematics, which is always likes taking sort of abstract limits. So an obvious abstract

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limit for mathematics to take is the limit of the future of mathematics. That is, what will be,

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you know, the ultimate structure of mathematics. And one of the things that's an empirical

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observation about mathematics that's quite interesting is that a lot of theories in one

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area of mathematics, algebraic geometry or something, might have, they play into another area

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of mathematics. That same kind of fundamental construct seemed to occur in very different

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areas of mathematics. And that's structurally captured a bit with category theory and things

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like that. But I think that there's probably an understanding of this metamathematical space that

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will explain why different areas of mathematics ultimately sort of map into the same thing.

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And I mean, you know, my little challenge to myself is what's time dilation in metamathematics?

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In other words, as you basically, as you move around in this mathematical space of possible

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statements, you know, how does that moving around? It's basically what's happening is

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that as you move around in the space of mathematical statements, it's like you're

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changing from algebra to geometry to whatever else. And you're trying to prove the same theorem.

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But as you try, if you keep on moving to these different places, it's slower to prove that

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theorem because you keep on having to translate what you're doing back to where you started from.

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And that's kind of the beginnings of the analog of time dilation in metamathematics.

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Oh, this space is a very messy space. This space is much messier than physical space. I mean,

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even in the models of physics, physical space is very tame compared to branchial space and

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ruleal space. I mean, the mathematical structure, you know, branchial space is probably more like

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Hilbert space, but it's a rather complicated Hilbert space. And ruleal space is more like

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this weird infinity groupoid story of Grothendieck. And, you know, I can explain that a little bit

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because in metamathematical space, a path in metamathematical space is a path between two

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statements is a way to get by proofs, is a way to find a proof that goes from one statement to

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another. And so one of the things you can do, you can think about is between statements, you've got

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proofs and they are paths between statements. Okay, so now you can go to the next level and you

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can ask, what about a mapping from one proof to another? And so that's in category theory,

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that's kind of a higher category, the notion of higher categories where you're mapping not just

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between objects, but you're mapping between the mappings between objects and so on.

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And so you can keep doing that. You keep saying higher order proofs. I want mappings between

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proofs between proofs and so on. And that limiting structure, oh, by the way, one thing that's very

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interesting is imagine in proof space, you've got these two proofs. And the question is,

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what is the topology of proof space? In other words, if you take these two paths,

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can you continuously deform them into each other? Or is there some big hole in the middle that

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prevents you from continuously deforming them one into the other? It's kind of like, you know,

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when you think about some, I don't know, some puzzle, for example, you're moving pieces around

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on some puzzle, and you can think about the space of possible states of the puzzle.

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And you can make this graph that shows from one state of the puzzle to another state of

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the puzzle and so on. And sometimes you can easily get from one state to any other state,

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but sometimes there'll be a hole in that space. And there'll be, you know, you always have to

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go around the circuitous route to get from here to there. There won't be any direct way.

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That's kind of a question of whether there's sort of an obstruction in the space. And so the question

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is in proof space, what is the, what are, you know, what does it mean if there's an obstruction in proof

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space? Yeah, I don't even know what an obstruction means in proof space because for it to be an

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obstruction, it should be reachable some other way from some other place, right? So this is like

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an unreachable part of the graph. No, it's not just an unreachable part. It's a part where

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there are paths that go one way, there are paths that go the other way. And this question of

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homotopy in mathematics is this question, can you continuously deform, you know, from one path to

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another path or do you have to go in a jump, so to speak? So it's like if you're going around a

link |

sphere, for example, if you're going around, I don't know, a cylinder or something, you can

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wind around one way and you can, there's no paths where you can easily deform one path into another

link |

because it's just sort of sitting on the same side of the cylinder. But when you've got something

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that winds all the way around a cylinder, you can't continuously deform that down to a point

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because it's, it's stuck wrapped around. My intuition about proof spaces, you should be

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able to deform it. I mean that because then otherwise it doesn't even make sense because

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if the topology matters of the way you move about the space that I don't even know what that means.

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Well, what it would mean is that you would have one way of doing a proof of something over here

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in algebra and another way of doing a proof of something over here in geometry. And there would

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not be an intermediate way to map between those proofs. How would that be possible if they started

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the same place and ended the same place? Well, it's the same thing as, you know,

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I'm not sure. I don't know. We'll know very soon because we get to do some experiments. This is

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the great thing about this stuff is that in fact, you know, in the next few days,

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I hope to do a bunch of experiments on this. So you're playing like proofs in this kind of space.

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Yes. Yes. I mean, so, you know, this is toy, you know, theories and, you know, we've got

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good. So this kind of segues to perhaps another thing, which is this whole idea of multi computation.

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So this is another kind of bigger idea that, so, okay, this has to do with how do you make models

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of things? And it's going to, so I've sort of claimed that there've been sort of four epochs

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in the history of making models of things. And this multi computation thing is the fourth,

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is a new epoch. What are the first three? The first one is back in antiquity, ancient Greek

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times. People were like, what's the universe made of? Oh, it's made of, you know, everything is

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water, Thales, you know, or everything is made of atoms. It's sort of, what are things made of?

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Or the, you know, there are these crystal spheres that represent where the planets are and so on.

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It's like a structural idea of how the universe is constructed. There's no real notion of dynamics.

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It's just, what is the universe? How is the universe made? Then we get to the 1600s and we

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get to the sort of revolution of mathematics being introduced into physics. And then we have this

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kind of idea of you write down some equation. The, what happens in the universe is the solving of

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that equation. Time enters, but it's usually just a parameter. We just can, you know, sort of slide

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it back and forth and say, here's where it is. Okay. Then we come to this kind of computational

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idea that I kind of started really pushing in the early 1980s as a result, you know,

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the things that we were talking about before about complexity, that was my motivation. But

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the bigger story was the story of kind of computational models of things. And the big

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difference there from the mathematical models is, in mathematical models, there's an equation,

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you solve it, you kind of slide time to the place where you want it. In computational models,

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you give the rule and then you just say, go run the rule. And time is not something you get to

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slide. Time is something where it just, you run the rule, time goes in steps. And that's how you

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work out how the system behaves. You don't, time is not just a parameter. Time is something that

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is about the running of these rules. And so there's this computational irreducibility. You can't jump

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ahead in time. But there's still, important thing is there's still one thread of time. It's still

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the case, you know, the cellular automaton state, then it has the next state and the next state and

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so on. The thing that is kind of, we've sort of tipped off by quantum mechanics in a sense,

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although it actually feeds back even into relativity and things like that, that there's

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these multiple threads of time. And so in this multi computation paradigm, the kind of idea is,

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instead of there being the single thread of time, there are these kind of distributed asynchronous

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threads of time that are happening. And the thing that's sort of different there is if you want to

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know what happened, if you say what happened in the system, in the case of the computational

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paradigm, you just say, well, after a thousand steps, we got this result, right? But in the

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multi computational paradigm, after a thousand steps, not even clear what a thousand steps means,

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because you've got all these different threads of time, but there is no state. There's all these

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different possible, you know, there's all these different paths. And so the only way you can know

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what happened is to have some kind of observer who is saying, here's how to parse the results

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of what was going on. Right. But that observer is embedded and they don't have a complete picture.

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So in the case of physics, that's right. Yes. And then in the, but that's, but so the idea is

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that in this multi computation setup, that it's this idea of these multiple threads of time

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and models that are based on that. And this is similar to what people think about in

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non deterministic computation. So you have a Turing machine. Usually it has a definite state. It

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follows another state, follows another state. But typically what people have done when they

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thought about these kinds of things is they've said, well, there are all these possible paths,

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and non deterministic Turing machine can follow all these possible paths, but we just want one

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of them. We just want the one that's the winner that factors the number or whatever else. And

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similarly, it's the same story in logic programming and so on, but we say, we've got this goal,

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find us a path to that goal. I just want one path, then I'm happy. Or theorem proving,

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same story. I just want one proof and then I'm happy. What's happening in multi computation

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in physics is we actually care about many paths. And well, there is a case, for example, probabilistic

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programming is a version of multi computation in which you're looking at all the paths. You're just

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asking for probabilities of things. But in a sense in physics, we're taking different kinds of

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samplings. For example, in quantum mechanics, we're taking a different kind of sampling

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of all these multiple paths. But the thing that is notable is that when you're an observer embedded

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in this thing, et cetera, et cetera, et cetera, with various other sort of footnotes and so on,

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it is inevitable that the thing that you parse out of the system looks like general relativity

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and quantum mechanics. In other words, that just by the very structure of this multi computational

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setup, it inevitably is the case that you have certain emergent laws. Now, why is this perhaps

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not surprising? In thermodynamics and statistical mechanics, there are sort of inevitable emergent

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laws of sort of gas dynamics that are independent of the details of the molecular dynamics,

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sort of the same kind of thing. But I think what happens is what's a sort of a funny thing that I

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just been understanding very recently is when when I kind of introduced this whole sort of

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computational paradigm complexity ish thing back in the 80s, it was kind of like a big downer

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because it's like there's a lot of stuff you can't say about what systems will do.

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And then what I realized is and then you might say, now we've got multi computation, it's even

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worse. You know, it isn't just one thread of time that we can't explain. It's all these threads of

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time. It can't explain anything. But the following thing happens because there is all this

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irreducibility and any detailed thing you might want to answer, it's very hard to answer. But

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when you have an observer who has certain characteristics like computational boundedness,

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sequentiality of time and so on, that observer only samples certain aspects of this incredible

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complexity going on in this multi computational system. And that observer is sensitive only to

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to some underlying core structure of this multi computational system. There is all this

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irreducible computation going on, all these details. But to that kind of observer, what's

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important is only the core structure of multi computation, which means that observer

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observes comparatively simple laws. And I think it is inevitable that that observer

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observes laws which are mathematically structured like general relativity and quantum

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So that's an explanation why there are simple laws that explain a lot for this observer.

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Potentially, yes. But what the place where this gets really interesting is there are all these

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fields of science where people have kind of gotten stuck, where they say we'd really love to

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have a physics like theory of economics. We'd really love to have a physics like law and

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linguistics. You got to talk about molecular biology here. OK, so where where where does

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multi computation come in for biology? Economics is super interesting, too, but biology. OK,

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let's talk about that. So let's talk about chemistry for a second. OK, so I mean, I have

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to say, you know, this is it's such a weird business for me because, you know, there are

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these kind of paradigmatic ideas and then the actual applications. And it's like I've always

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said, I know nothing about chemistry. I learned all the chemistry I know, you know, the night

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before some exam when I was 14 years old. But I've actually learned a bunch more chemistry.

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And in Wolfram language these days, we have really pretty nice symbolic representation

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of chemistry. And in understanding the design of that, I've actually, I think, learned a certain

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amount of chemistry. So if you quizzed me on sort of basic high school chemistry, I would

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probably totally fail. But but but OK, so what is chemistry? I mean, chemistry is sort of a

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story of, you know, chemical reactions are like you've got this particular chemical that's

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represented as some graph of, you know, these are these are this configuration of molecules

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with these bonds and so on. And a chemical reaction happens. You've got these sort of

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two graphs. They interact in some way. You've got another graph or multiple other graphs

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out. So that's kind of the sort of the the abstract view of what's happening in chemistry.

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And so when you do a chemical synthesis, for example, you are given certain sort of these

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are possible reactions that can happen. And you're asked, can you piece together this

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sequence of such reactions, a sequence of such sort of axiomatic reactions usually called name

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reactions in chemistry? Can you piece together a sequence of these reactions so that you get out

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at the end this great molecule you were trying to synthesize? And so that's a story very much

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like theorem proving. And people have done actually they start in the 1960s looking at

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kind of the theorem proving approach to that, although it didn't really it didn't it didn't

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was sort of done too early, I think. But anyway, so that's kind of the view is that that chemistry,

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chemical reactions are the story of of all these different sort of paths of possible things that

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go on. OK, let's let's go to an even lower level. Let's say instead of asking about which species

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of molecules we're talking about, let's look at individual molecules and let's say we're looking

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at individual molecules and they are having chemical reactions and we're building up this

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big graph of all these reactions that are happening. OK, so so then we've got this big

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graph. And by the way, that big graph is incredibly similar to this hypergraph rewriting things.

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In fact, in the underlying theory of multi computation there, these things we call token

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event graphs, which are basically you've broken your state into tokens. Like in the case of a

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hypergraph, you've broken it into hyper edges and each event is just consuming some number of tokens

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and producing some number of tokens. But then you have to there's a lot of work to be done

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on update rules in terms of what they actually are for chemistry. Yeah, what they offer are

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observed chemistry. Yes, indeed. Yes, indeed. And we've been working on that actually because we

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have this beautiful system and Wolfram language for representing chemistry symbolically. So we

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actually have you know, this is this is an ongoing thing to actually figure out what they are for

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some practical cases. Does that require human injection or can it be automatically discovered

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these update rules? Well, if we can do chemistry better, we could probably discover them

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automatically. But I think in, in reality, right now, it's like there are these particular

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reactions. And really, to understand what's going on, we're probably going to pick a particular

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subtype of chemistry. And just because because let me explain where this is going to the place

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that his his where this is going. So got this whole network of all these molecules,

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having all these reactions and so on. And this is some whole multi computational story because each

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each sort of chemical reaction event is its own separate event. We're saying they will happen

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asynchronously. We're not describing in what order they happen. You know, maybe that order is governed

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by some quantum mechanics thing doesn't really matter. We're just saying they happen in some

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order. And then we ask, what is the what what's the you know, how do we think about the system?

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Well, this thing is some kind of big multi computational system. The question is what is

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the chemical observer? And one possible chemical observer is all you care about is did you make

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that particular drug molecule? You're just asking, you know, the for the one path. Another thing you

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might care about is I want to know the concentration of each species. I want to know,

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you know, at every stage, I'm going to solve the differential equations that represent the

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concentrations. And I want to know what those all are. But there's more. Because when and it's kind

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of like you're going below and statistical mechanics, there's kind of all these molecules

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bouncing around. And you might say, we're just going to ignore we're just going to look at the

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aggregate densities of certain kinds of molecules. But you can look at a lower level, you can look

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at this whole graph of possible interactions. And so the kind of the idea would be what, you know,

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is the only chemical observer, one who just cares about overall concentrations? Or can there be a

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chemical observer who cares about this network of what happened? And so that the question then is,

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so let me give an analogy. So this is where I think this is potentially very relevant to molecular

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biology and molecular computing. When we think about a computation, usually, we say it's input,

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it's output, we, you know, or chemistry, we say there's this input, we're going to make this

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molecule as the output. But what if what we actually encode, what if our computation, what

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thing we care about is some part of this dynamic network? What if it isn't just the input and the

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output that we care about? What if there's some dynamics of the network that we care about? Now,

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imagine you're a chemical observer, what is a chemical observer? Well, in molecular biology,

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there are all kinds of weird sorts of observers, there are membranes that exist, that have, you

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know, different kinds of molecules that can bind to them, things like this, it's not obvious that

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the from a human scale, we just measure the concentration of something is the relevant story.

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We can imagine that, for example, when we look at this whole network of possible reactions,

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we can imagine, you know, at a physical level, we can imagine, well, what was the actual momentum

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direction of that of that molecule? What was it which we don't pay any attention to when we're

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just talking about chemical concentrations? What was the orientation of that molecule,

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these kinds of things? And so here's the place where I'm, I have a little suspicion, okay? So

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one of the questions in biology is what matters in biology? And that is, you know, we have all

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these chemical reactions, we have all these, all these molecular processes going on in, you know,

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in biological systems, what matters? And, you know, one of the things is to be able to tell

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what matters, well, so a big story of the what matters question was what happened in genetics

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in 1953, when DNA, when it was figured out how DNA worked. Because before that time, you know,

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genetics have been all these different effects and complicated things. And then it was realized,

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ah, there's something new, a molecule can store information, which wasn't obvious before that

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time, a single molecule can store information. So there's a place where there can be something

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important that's happening in molecular biology, and it's just in the sequence that's storing

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information in a molecule. So the possibility now is imagine this dynamic network, this, you know,

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causal graphs and multiway causal graphs and so on, that represent all of these different reactions

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between molecules. What if there is some aspect of that, that is storing information that's relevant

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for molecular biology? And the dynamic aspect of that. Yes, that's right. So that it's similar to

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how the structure of a DNA molecule stores information, it could be the dynamics of the

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system somehow stores information. And this kind of process might allow you to give predictions

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of what that would be. Well, yes, but also imagine that you're trying to do, for example, imagine

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you're trying to do molecular computation. Okay. You might think the way we're going to do molecular

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computation is we're just going to run the thing. We're going to see what came out. We're going to

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see what molecule came out. This is saying that's not the only thing you can do. There is a different

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kind of chemical observer that you can imagine constructing, which is somehow sensitive to this

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dynamic network. Exactly how that works, how we make that measurement, I don't know, but a few

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ideas, but that's what's important, so to speak. And that means, and by the way, you can do the

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same thing even for Turing machines. You can say, if you have a multiway Turing machine, you can say,

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how do you compute with a multiway Turing machine? You can't say, well, we've got this input and this

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output because the thing has all these threads of time and it's got lots of outputs. And so then you

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say, well, what does it even mean to be a universal multiway Turing machine? I don't fully know the

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answer to that. It's an interesting idea. It would freak Turing out for sure, because then the

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dynamics of the trajectory of the computation matters. Yes. Yes. I mean, but the thing is

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that that, so this is again, a story of what's the observer, so to speak. In chemistry, what's

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the observer there? Now to give an example of where that might matter, a very sort of present

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day example is in immunology, where we have whatever it is, 10 billion different kinds of

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antibodies that are all these different shapes and so on. We have a trillion different kinds of T

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cell receptors that we produce. And the traditional theory of immunology is this clonal

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selection theory where we are constantly producing, randomly producing all these different antibodies.

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And as soon as one of them binds to an antigen, then that one gets amplified and we produce more

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of that antibody and so on. Back in the 1960s, an immunologist called Nils Joerner, who was the guy

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who invented monoclonal antibodies, various other things, kind of had this network theory of the

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immune system where it would be like, well, we produce antibodies, but then we produce antibodies

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to the antibodies, anti antibodies, and we produce anti anti antibodies. And we get this whole dynamic

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network of interactions between different immune system cells. And that was kind of a qualitative

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theory at that time. And I've been a little disappointed because I've been studying immunology

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a bit recently. And I knew something about this like 35 years ago or something. And I knew,

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you know, I'd read a bunch of the books and I talked to a bunch of the people and so on.

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And it was like an emerging theoretical immunology world. And then I look at the books now,

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and they're very thick because they've got, you know, there's just a ton known about immunology

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and, you know, all these different pathways, all these different details and so on.

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But the theoretical sections seem to have shrunk. And so it's so the question is, what, you know,

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for example, immune memory, where is the where does the immune memory reside? Is it actually

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some cells sitting in our bone marrow that is, you know, living for the whole of our lives that's

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going to spring into action as soon as we're shown the same antigen? Or is it something different

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from that? Is it something more dynamic? Is it something more like some network of interactions

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between these different kinds of immune system cells and so on? And it's known that there are

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plenty of interactions between T cells and, you know, there's plenty of dynamics. But what the

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consequence of that dynamics is, is not clear. And to have a qualitative theory for that doesn't

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seem to exist. In fact, I was just been trying to study this. So I'm quite incomplete in my study

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of these things. But I was a little bit taken aback because I've been looking at these things

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and it's like, and then they get to the end where they have the most advanced theory that they've

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got. And it turns out it's a cellular automaton theory. It's like, okay, well, at least I understand

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that theory. But but, you know, I think that the possibility is that in that this is a place where

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if you want to know, you know, explain roughly how the immune system works, it ends up being

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this sort of dynamic network. And then the the, you know, the immune consciousness, so to speak,

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the observer ends up being something that, you know, in the end, it's kind of like, does the

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human get sick or whatever? But it's a it's something which is a complicated story that

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relates to this whole sort of dynamic network and so on. And I think that's another place where this

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kind of notion of where I think multi computation has the possibility. See, one of the things, okay,

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you can end up with something where yes, there is a general relativity in there. But it turns up,

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but it may turn out that the observer who sees general relativity in the immune system is an

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observer that's irrelevant to what we care about about the immune system. I mean, it could be yes,

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there is some effect where, you know, there's some, you know, time dilation of T cells interacting

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with whatever. But it's like, that's an effect that's just irrelevant. And the thing we actually

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care about is things about, you know, what happens when you have a vaccine that goes into some place

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in shapespace? And, you know, how does that affect other places in shapespace? And how does that spread?

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You know, what's the what's the analog of the speed of light in shapespace, for example, that's an

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that's an important issue. If you have one of these dynamic theories, it's like, you know, you

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you're poking to shapespace by having, you know, let's say, a vaccine or something that has a

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particular configuration in shapespace. How, how quickly as this dynamic network spreads out, how

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quickly do you get sort of other antibodies in different places in shapespace, things like that?

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When you say shapespace, you mean the shape of the molecules? And then, so this is like,

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could be deeply connected to the protein and multi protein folding, all of that kind of stuff.

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then actually has an impact on helping develop drugs, for example, or has an impact on

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Well, I think the big thing is, you know, when we think about molecular biology, the you know,

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what, what is the qualitative way to think about it? You know, in other words, is it chemical

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reaction networks? Is it, you know, genetics, you know, DNA, big, you know, big news, it's kind of

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there's a digital aspect to the whole thing. You know, what is the qualitative way to think about

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how things work in biology? You know, when we think about, I don't know, some phenomenon like

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aging or something, which is a big, complicated phenomenon, which just seems to have all these

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different tentacles. Is it really the case that that can be thought about in some, you know,

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without DNA, when people were describing, you know, genetic phenomena, there were, you know,

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dominant recessive, this, that and the other got very, very complicated. And then people realize,

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oh, it's just, you know, and what is a gene and so on and so on and so on. Then people realize

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it's just base pairs. And there's this digital representation. And so the question is, what is

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the overarching representation that we can now start to think about using a molecular biology?

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I don't know how this will work out. And this is again, one of these things where, and the place

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where that gets important is, you know, maybe molecular biology is doing molecular computing

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by using some dynamic process that is something where it is very happily saying, oh, I just got

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a result. It's in the dynamic structure of this network. Now I'm going to go and do some other

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thing based on that result, for example. But we're like, oh, I don't know what's going on. You know,

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it's just, we just measured the levels of these chemicals and we couldn't conclude anything.

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But it just, we're looking at the wrong thing. And so that's the, that's kind of the potential

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there. And it's, I mean, these things are, I don't know, it's for me, it's like, I've not really,

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that was not a view. I mean, I've thought about molecular computing for ages and ages and ages.

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And I've always imagined that the big story is kind of the original promise of nanotechnology

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of like, can we make a molecular scale constructor that will just build a molecule in any shape?

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I don't think I'm now increasingly concluding that's not the big point. The big point is

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something more dynamic. That will be an interesting endpoint for any of these things. But that's

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perhaps not the thing, you know, because the one example we have in molecular computing

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that's really working is us biological organisms. And, you know, maybe the thing that's important

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there is not this, you know, what chemicals do you make, so to speak, but more this kind of

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dynamic process. The dynamic process. And then you can have a good model like the hypergraph to then

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explore what, like simulate again, make predictions. And if they, I think just have a way to reason

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about biology. I mean, it's hard, you know, but first of all, biology doesn't have theories like

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physics. You know, physics is a much more successful sort of global theory kind of area.

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You know, biology, what are the global theories of biology? Pretty much Darwinian evolution. That's

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the only global theory of biology. You know, are there any other theories just say, well,

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the kidneys work this way, this thing works this way and so on. There isn't, I suppose,

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another global theory is digital information in DNA. That's another sort of global fact about

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biology. But the difficult thing to do is to match something you have a model of in the hypergraph

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to the actual, like how do you discover the theory? How do you discover the theory? Okay,

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you have something that looks nice and makes sense, but like you have to match it to validation.

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Not entirely. I mean, so, you know, for example, in what we've been trying to think about is

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take actual chemical reactions. Okay. So, you know, one of my goals is can I compute the primes

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with molecules? Okay. If I can do that, then I kind of, maybe I can compute things. And, you know,

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there's this nice automated lab, these guys, these Emerald Cloud Lab people have built with

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Wolfram language and so on. That's an actual physical lab and you send it a piece of Wolfram

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language code and it goes and, you know, actually does physical experiments. And so one of my goals,

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because I'm not a test tube kind of guy, I'm more of a software kind of person, is can I make

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something where, you know, in this automated lab, we can actually get it so that there's some gel

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that we made and, you know, the positions of the stripes are the primes. I love it. Yeah.

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I mean, that would be an example of where, and that would be with a particular, you know,

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framework for actually doing the molecular computing, you know, with particular kinds

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of molecules. And there's a lot of kind of ambient technological mess, so to speak,

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associated with, oh, is it carbon? Is it this? Is it that? You know, is it important that there's

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a bromine atom here, et cetera, et cetera, et cetera. This is all chemistry that I don't know

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much about. And, you know, that's a sort of, you know, unfortunately that's down at the level,

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you know, I would like to be at the software level, not at the level of the transistors,

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so to speak. But in chemistry, you know, there's a certain amount we have to do, I think, at the

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level of transistors before we get up to being able to do it. Although, you know, the automated

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labs certainly help in setting that up. I talked to a guy named Charles Hoskinson.

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He mentioned that he's collaborating with you. He's an interesting guy. He sends me papers on

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speaking of automated theorem proving a lot. He's exceptionally well read on that area as well.

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So what's the nature of your collaboration with him? He's the creator of Cardano.

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What's the nature of the collaboration between Cardano and the whole space of blockchain and

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Wolfram, Wolfram Alpha, Wolfram blockchain, all that kind of stuff? Well, OK, we're segueing to a

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slightly different world. But so although not completely unconnected. Right. The whole thing

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is somehow connected. I know. I mean, you know, the strange thing in my life is I've sort of

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alternated between doing basic science and doing technology about five times in my life so far.

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And the thing that's just crazy about it is, you know, every time I do one of these alternations,

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I think there's not going to be a way back to the other thing. And like I thought for this

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physics project, I thought, you know, we're doing fundamental theory of physics. Maybe it'll have

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an application in 200 years. But now I've realized actually this multi computation idea is is

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applicable here now. It's and in fact, it's also giving us this way. I'll just mention one other

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thing and then talk about blockchain. The the question of actually that relates to several

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different things. But but one of the things about about OK, so our Wolfram language, which is our

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attempt to kind of represent everything in the world computationally. And it's the thing I kind

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of started building 40 years ago in the form of actual Wolfram language 35 years ago. It's kind

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of this idea of can we can we express things about the world in computational terms? And, you know,

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we've come a long way in being able to do that. Wolfram Alpha is kind of the consumer version of

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that where you're just using natural language as input. The and it turns it into our symbolic

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language. And that's, you know, the symbolic language Wolfram language is what people use

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and have been using for the last 33 years. Actually, Mathematica, which is its first

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instantiation, will be one third of a century old in in October. And that it's it's kind of

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interesting. What do you mean one third of a century? I mean, 33 or 30? What are we? 33 and a

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third. 33 and a third. So I've never heard of anyone celebrating that anniversary, but I like

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it. I know. A third of a century, though, it's it's kind of get many, many slices of a century

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that are interesting. But but, you know, I think that the the thing that's really striking about

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that is that means, you know, including the whole sort of technology stack I built around that's

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about 40 years old. And that means it's a significant fraction of the total age of the

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computer industry. And it's I mean, I think it's cool that we can still run, you know,

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Mathematica version one programs today and so on. And we've sort of maintained compatibility.

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And we've been just building this big tower all those years of just more and more and more

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computational capabilities. It's sort of interesting. We just made this this picture

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of kind of the different kind of threads of of of computational content, of, you know,

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mathematical content and and, you know, all sorts of things with, you know, data and graphs and

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whatever else. And what you see in this picture is about the first 10 years. It's kind of like

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it's just a few threads. And then then about maybe 15, 20 years ago, it kind of explodes

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in this whole collection, different threads of all these different capabilities that are now

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part of open language and representing different things in the world. But the thing that was super

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lucky in some sense is it's all based on one idea. It's all based on the idea of symbolic expressions

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and transformation rules for symbolic expressions, which was kind of what I originally

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put into this SMP system back in 1979 that was a predecessor of the whole open language stack.

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So that idea was an idea that I got from sort of trying to understand mathematical logic and so on.

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It was my attempt to kind of make a general human comprehensible model of computation

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of just everything is a symbolic expression. And all you do is transform symbolic expressions.

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And, you know, in in retrospect, I was very lucky that I understood as little as I understood then,

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because had I understood more, I would have been completely freaked out about all the different

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ways that that kind of model can can fail. Because what do you do when you have a symbolic

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expression, you make transformations for symbolic expressions? Well, for example, one question is,

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there may be many transformations that could be made in a very multi computational kind of way.

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that applies. And we keep doing that until we reach a fixed point. And that's the result. And

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that's kind of a very, it's kind of a way of sort of sliding around the edge of multi computation.

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And back when I was working on SMP and things, I actually thought about these questions about

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about how, you know, how, what determines the this kind of evaluation path. So for example,

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you know, you work out Fibonacci, you know, Fibonacci is a recursive thing, f of n is f of

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n minus one plus f of n minus two, and you get this whole tree of recursion, right? And there's

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the question of how do you evaluate that tree of recursion? Do you do it sort of depth first,

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where you go all the way down one side? Do you do it breadth first, where you're kind of collecting

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the terms together, where you know that, you know, f of eight plus f of seven, f of seven,

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plus f of six, you can collect the f of sevens, and so on. These are, you know, I didn't realize

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that at the time, it's kind of funny, I was working on on gauge field theories back in 1979.

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And I was also working on the evaluation model in SMP. And they're the same problem. But it took me

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40 more years to realize that. And this question about how you do this sort of evaluation front,

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that's a question of reference frames. It's a question of kind of the story of I mean,

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that that's, that is basically this question of, in what order is the universe evaluated?

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And that's, and so what you realize is, there's this whole sort of world of different kinds of

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computation that you can do, sort of multi computationally. And that's a, that's an

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interesting thing. It has a lot of implications for distributed computing, and so on. It also has

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a potential implication for blockchain, which we haven't fully worked out, which is, and this is

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not what we're doing with Cardano, but but this is a different thing. The this is something where

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one of the questions is, when you have, in a sense, blockchain is a deeply sequentialized

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story of time. Because in blockchain, there's just one copy of the ledger. And you're saying,

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this is what happened, you know, time has progressed in this way. And there are little

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things around the edges, as you try and reach consensus and so on. And, and, you know, actually,

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we just recently, we've had this little conference we organized about the theory of distributed

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consensus, because I realized that a bunch of interesting things that some of our science can

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tell one about that. But that's a different let's let's not go down that that part. Yeah,

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but distributed consensus that still has a sequential there's like, there's still

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sequentiality. So don't tell me you're thinking through like how to apply multi computation to

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blockchain. Yes. And so so that becomes a story of, you know, instead of transactions all having

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to settle in one ledger, it's like a story of all these different ledgers. And they all have to have

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some ultimate consistency, which is what causal invariance would give one, but it can take a

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while. And the it can take a while is kind of like quantum mechanics. So it's kind of what's

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happening is there these different paths of history that correspond to, you know, in one path

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of history, you got paid this amount in another path of history, you got paid this amount. In the

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end, the universe will always become consistent. Now, now the way it will it works is, okay, it's

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a little bit more complicated than that. What happens is, the way space is knitted together

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in our theory of physics is through all these events. And the the idea is that the way that

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economic space is knitted together is between is there these autonomous events that essentially

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knit together economic space. So there are all these threads of transactions that are happening.

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And the question is, can they be made consistent? Are there is there something forcing them to be

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sort of a consistent fabric of economic reality? And sort of what this has led me to is trying to

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realize how does economics fundamentally work? And, you know, what is economics? And, you know,

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what what are the atoms of economics, so to speak? And so what I've kind of realized is that, that

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sort of the perhaps I don't even know if this is right yet, there's sort of events in economics,

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the transactions, there are states of agents that are kind of the atoms of economics. And then

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transactions are kind of agents transact in some transact in some way, and that's an event. And

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then the question is, how do you knit together sort of economic space from that? What is there

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in economic space? Well, all these transactions, there's a whole complicated collection of possible

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transactions. But one thing that's true about economics is we tend to have the notion of a

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definite value for things. We could imagine that, you know, you buy a cookie from somebody, and

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they want to get a movie ticket. And there is some way that AI bots could make some path

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from the cookie to the movie ticket by all these different intermediate transactions. But in fact,

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we have an approximation to that, which is we say they each have a dollar value. And we have this

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kind of numeraire concept of there's just a way of kind of taking this whole complicated space of

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transactions and parsing it in something which is a kind of a simplified thing that is kind of like

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our parsing of physical space. And so my guess is that the yet again, I mean, it's crazy that all

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these things are so connected. This is another multi computation story. Another story of where

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what's happening is that the economic consciousness, the economic observer is not going to deal with

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all of those are different microscopic transactions. They're just going to parse the

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whole thing by saying, there's this value, it's a number. And that's their understanding of their

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summary of this economic network. And there will be all kinds of things like there are all kinds of

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arbitrage opportunities, which are kind of like the quantum effects in this whole thing. And that's

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in places where there's sort of different paths that can be followed and so on. So the question

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is, can one make a sort of global theory of economics? And then my test case is again,

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what is time dilation in economics? And I know if you imagine a very agricultural economics where

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people are growing lettuces and fields and things like this, and you ask questions about, well,

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if you're transporting lettuces to different places, what is the value of the lettuces after

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you have to transport them versus if you're just sitting in one place and selling them,

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you can kind of get a little bit of an analogy there. But I think there's a better and more

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complete analogy. And that's the question of, is there a theory like general relativity that is a

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global theory of economics? And is it about something we care about? It could be that there

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is a global theory, but it's about a feature of economic reality that isn't important to us.

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Now, another part of the story is, can one use those ideas to make essentially a distributed

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blockchain, a distributed generalization of blockchain, kind of the quantum analog of money,

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so to speak, where you have, for example, you can have uncertainty relations where you're saying,

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you know, well, if I insist on knowing my bank account right now, there'll be some uncertainty.

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If I'm prepared to wait a while, then it'll be much more certain. And so there's, you know,

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is there a way of using and so we've made a bunch of prototypes of this, which I'm not yet happy

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with. But what I realized is, to really understand these prototypes, I actually have to have a

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foundational theory of economics. And so that's kind of a, you know, it may be that we could

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deploy one of these prototypes as a practical system. But I think it's really going to be much

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better if we actually have an understanding of how this plugs into kind of the economics.

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Yes, I think so. But I mean, you know, how there emerge sort of laws of economics,

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I don't even know. And I've been asking friends of mine who are economists and things,

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that is kind of a qualitative description theory? Is it, you know, what kind of a theory is it? Is

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it a theory, you know, what kind of thinking? It's like in biology, in evolutionary biology,

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for example, there's a certain pattern of thinking that goes on in evolutionary biology where

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if you're a, you know, a good evolutionary biologist, somebody says, that creature has a

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weird horn. And they'll say, well, that's because this and this and this and the selection of this

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kind and that kind. And that's the story. And it's not a mathematical story. It's a story of

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a different type of thinking about these things. By the way, evolutionary biology is yet another

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place where it looks like this multi computational idea can be applied. And that's where maybe

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speciation is related to things like event horizons. And there's a whole other kind of

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world of that. But it seems like this kind of model can be applicable to so many aspects,

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like the different levels of understanding of our reality. So it could be the biology,

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the chemistry, at the physics level, the economics. And you could potentially, the thing is, it's like,

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okay, sure, at all these levels, it might rhyme. It might make sense as a model. The question is,

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can you make useful predictions as one of these levels? That's right. And that's really a question

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of, you know, it's a weird situation because the situation where the model probably has definite

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consequences. The question is, are they consequences we care about? Yeah. And that's

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some, you know, and so in the case of, in the economic case, the, where, so, you know,

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one thing is this idea of using kind of physics like notions to construct a kind of distributed

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analog of blockchain. Okay. The much more pragmatic thing is a different direction.

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And it has to do with this computational language that we built to describe the world

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that knows about, you know, different kinds of cookies and knows about different cities and

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knows about how to compute all these kinds of things. One of the things that is of interest is

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if you want to run the world, you need, you know, with contracts and laws and rules and so on,

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there are rules at a human level and there are kind of things like, and so this gets one into

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the idea of computational contracts. You know, right now when we write a contract, it's a piece

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of legalese. It's, you know, it's just written in English and it's not something that's automatically

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analyzable, executable, whatever else. It's just English. You know, back in Gottfried Leibniz,

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back in, you know, 1680 or whatever was like, I'm going to, you know, figure out how to use logic

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to decide legal cases and so on. And he had kind of this idea of let's make a computational language

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for the human law. Forget about modeling nature, forgot about natural laws. What about human law?

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Can we make kind of a computational representation of that? Well, I think finally we're close to

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being able to do that. And one of the projects that I hope to get to as soon as there's a little

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bit of slowing down of some of this Cambrian explosion that's happening is a project I've

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been meaning to really do for a long time, which is what I'm calling a symbolic discourse language.

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It's just finishing the job of being able to represent everything like the conversation we're

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having in computational terms. And one of the use cases for that is computational contracts.

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Another use case is something like the constitution that says what the AIs, what we want the AIs to do.

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So, but this is useful. So you're saying, so these are like, you're saying computational contracts,

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but smart contracts. This is what's in the domain of cryptocurrency is known as smart contracts.

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And so the language you've developed, this symbolic or seek to further develop symbolic discourse

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language enables you to write a contract and write a contract that richly represents

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some aspect of the world. So, I mean, smart contracts tend to be right now mostly about

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things happening on the blockchain. And sometimes they have oracles. And in fact, our Wolfman Alpha

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API is the main thing people use to get information about the real world, so to speak,

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within smart contracts. So Wolfram Alpha, as it stands, is a really good oracle for

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Yeah, well, that's how we started getting involved with blockchains. As we realized,

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people were using Wolfram Alpha as the oracle for smart contracts, so to speak. And so that

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got us interested in blockchains in general. And what was ended up happening is Wolfram Language

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is, with its symbolic representation of things, is really very good at representing things like

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blockchains. And so I think we now have, and we don't really know all the comparisons, but we now

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have a really nice environment within Wolfram Language for dealing with the sort of, for

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representing what happens in blockchains, for analyzing what happens in blockchains.

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We have a whole effort in blockchain analytics. And we've sort of published some samples of how

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that works. But it's because our technology stack, Wolfram Language and Mathematica,

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are very widely used in the quant finance world. There's a sort of immediate coevolution there of

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the quant finance kind of thing and blockchain analytics. So it's kind of the representation

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of blockchain in computational language. Then ultimately, it's kind of like, how do you run

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the world with code? That is, how do you write sort of all these things which are right now,

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regulations and laws and contracts and things in computational language? And kind of the ultimate

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vision is that sort of something happens in the world, and then there's this giant domino effect

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of all these computational contracts that trigger based on the thing that happened. And there's a

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whole story to that. And of course, I like to always pay attention to the latest things that

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are going on. And I really, I kind of like blockchain because it's another rethinking

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of kind of computation. It's kind of like cloud computing was a little bit of that, of sort of

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persistent kind of computational resources and so on. And this multi computation is a big

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rethinking of kind of what it means to compute. Blockchain is another bit of rethinking of what

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it means to compute. The idea that you lodge kind of these autonomous lumps of computation

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out there in the blockchain world. And one of the things that just sort of for fun,

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so to speak, is we've been doing a bit of stuff with NFTs, and we just did some NFTs on Cardano,

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and we'll be doing some more. And we did some cellular automaton NFTs on Cardano,

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which people seem to like quite a bit. And one of the things I've realized about NFTs

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is that there's kind of this notion, and we're really working on this, I like recording stuff.

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You know, one of the things that's come out of kind of my science, I suppose, is this history

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matters type story of, you know, it's not just the current state, it's the history that matters.

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And I've kind of, I don't think this is actually realizing, maybe it's not coincidental that I'm

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sort of the human who's recorded more about themselves than anybody else. And then I end up

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with these science results that say history matters, which was not those things. I didn't

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think those were connected, but they're at least correlated, yes. Yeah, right. So, you know,

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this question about sort of recording what has happened and having sort of a permanent record

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of things, one of the things that's kind of interesting there is, you know, you put up a

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website and it's got a bunch of stuff on it, but you know, you have to keep paying the hosting

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fees or the thing's going to go away. But one of the things about blockchain is quite interesting

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is if you put something on a blockchain and you pay, you know, your commission to get that thing,

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you know, put on, you know, mine, put on the blockchain, then in a sense, everybody who comes

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after you is, you know, they are motivated to keep your thing alive because that's what keeps

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the consistency of the blockchain. So in a sense with sort of the NFT world, it's kind of like if

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you want to have something permanent, well, at least for the life of the blockchain, but even if

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the blockchain goes out of circulation, so to speak, there's going to be enough value in that

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whole collection of transactions that people are going to archive the thing. But that means that,

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you know, pay once and you're kind of, you're lodged in the blockchain forever. And so we've

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been kind of playing around with sort of a hobby thing of mine of thinking about sort of the NFTs

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and how you and sort of the consumer idea of kind of the it's the it's the anti, you know,

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it's the opposite of the Snapchat view of the world. There's a permanence to it that's heavily

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incentivized and thereby you can have a permanence of history. Right. And that's that's that's kind of

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the now, you know, so that's so that's one of the things we've been doing with Cardano. And it's

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kind of fun. I think that I mean, this whole question about, you know, you mentioned automated

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theorem proving and blockchains and so on. And as I've thought about this kind of physics inspired

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distributed blockchain, obviously, there, the sort of the proof that it works, that there are no

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double spends, there's no whatever else, that proof becomes a very formal kind of almost a

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matter of physics, so to speak. And, you know, it's been it's been an interesting thing for the

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for the practical blockchains to do kind of actual automated theorem proving. And I don't think

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anybody's really managed it in an interesting case yet. It's a thing that people, you know,

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aspire to. But I think it's a challenging thing because basically, the point is one of the one

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of the things about proving correctness of something as well. You know, people say I've

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got this program and I'm going to prove it's correct. It's like, what does that mean? You

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have to say what correct means. I mean, it's it's kind of like then you have to have another

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language. And people are very confused back in past decades of, you know, oh, we're going to

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prove the correctness by representing the program in another language, which we also don't know

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whether it's correct. And, you know, often by correctness, we just mean it can't crash or it

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can't scribble on memory. But but the thing is that there's this complicated trade off,

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because as soon as there's as soon as you're really using computation, you have computational

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irreducibility, you have undecidability. If you want to use computation seriously,

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you have to kind of let go of the idea that you're going to be able to box it in and say,

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we're going to have just this happen and not anything else. I mean, this is a this is an old

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fact. I mean, GÃ¶del's theorem tries to say, you know, piano arithmetic, the axioms of arithmetic,

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can you box in the integers and say these axioms give just the integers and nothing about the

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integers. GÃ¶del's theorem showed that wasn't the case. You can have all these wild, weird things

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that are obey the piano axioms, but aren't integers. And there's this kind of infinite

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hierarchy of additional axioms you would have to add. And it's kind of the same thing. You don't

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get to, you know, if you want to say, I want to know what happens, you're boxing yourself in and

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there's a limit to what can happen, so to speak. So it's a complicated trade off. And it's a big

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trade off for AI, so to speak. It's kind of like, do you want to let computation actually do what

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it can do? Or do you want to say, no, it's very, very boxed in to the point where we can understand

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every step. And that's kind of a thing that becomes difficult to do. But that's, I mean,

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in general, I would say one of the things that's kind of complicated in my sort of life and the

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whole sort of story of computational language and all this technology and science and so on.

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I mean, I kind of in the flow of one's life, it's sort of interesting to see how these things play

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out because I've kind of concluded that I'm in the business of making kind of artifacts from the

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future, which means, you know, there are things that I've done, I don't know, this physics project,

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I don't know whether anybody would have gotten to it for 50 years. You know, the fact that

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Mathematica is a third of a century old, and I know that a bunch of the core ideas are not

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well absorbed. I mean, that is people finally got this idea that I thought was a triviality

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of notebooks, that was 25 years. And, you know, some of these core ideas about symbolic computation

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and so on are not absorbed. I mean, people use them every day in Wolfram language and, you know,

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do all kinds of cool things with them. But if you say, what is the fundamental intellectual point

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here? It's not well absorbed. And it's something where you kind of realize that you're sort of

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building things. And I kind of made this thing about, you know, we're building artifacts from

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the future, so to speak. And I mentioned that we have a conference coming up actually in a couple

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of weeks, our annual technology conference, where we talk about all the things we're doing.

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And, you know, so I was talking about it last year, about, you know, we're making artifacts

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from the future. And I was kind of like, I had some version of that, that was kind of a dark

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and frustrated thing of like, you know, I'm building things which nobody's going to care

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about until long after I'm dead, so to speak. But then I realized, you know, people were sort of

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telling me afterwards, you know, that's exactly how, you know, we're using Wolfram language in

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some particular setting and, you know, some computational X field or some organization or

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whatever. And it's like, people are saying, oh, you know, what did you manage to do? You know,

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well, we know that in principle, it will be possible to do that. But we didn't know that

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was possible now. And it's kind of like, that's sort of the business we're in. And in a sense,

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with some of these ideas in science, you know, I feel a little bit the same way that there are

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some of these things where, you know, some things like, for example, this whole idea, well, so to

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relate to another sort of piece of history and the future, one of, you know, I mentioned at the

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beginning kind of complexity as this thing that I was interested in back 40 years ago and so on.

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Where does complexity come from? Well, I think we kind of nailed that. The answer is in the

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computational universe, even simple programs make it. And that's kind of the secret that nature has

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that allows you to make it. So that's that part. But the bigger picture there was this idea of

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this kind of computational paradigm, the idea that you could go beyond mathematical equations,

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which have been sort of the primary modeling medium for 300 years. And so it was like, look,

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it is inexorably the case that people will use programs rather than just equations. And, you

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know, I was saying that in the 1980s and people were, you know, I published my big book, New Kind

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of Science, that'll be 20 years ago next year. So in 2002, and people were saying, oh, no,

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this can't possibly be true. You know, we know for 300 years we've been doing all this stuff.

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Right. To be fair, I now realize I'm a little bit more analysis of what people actually

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said in pretty much every field other than physics. People said, oh, these are new models.

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That's pretty interesting. In physics, people were like, we've got our physics models. We're

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very happy with them. Yeah, in physics, there's more resistance because of the attachment and

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the power of the equations. The idea that programs might be the right way to approach

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this field. Was there some resistance? And like you're saying, it takes time. For somebody who

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likes the idea of time dilation and all these applications, I thought you would understand this.

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Yeah, right. But, you know, and computational irreducibility. Yes, exactly. But I mean,

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it is really interesting that just 20 years, a span of 20 years, it's gone from, you know,

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pitchforks and horror to, yeah, we get it. And, you know, it's helped that we've, you know, in our

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current effort in fundamental physics, we've gotten a lot further and we've managed to

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put a lot of puzzle pieces together that make sense. But the thing that I've been thinking

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about recently is this field of complexity. So I've kind of was a sort of a field builder.

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Back in the 1980s, I was kind of like, okay, you know, can we, you know, I'd understood this point

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that there was this sort of fundamental phenomenon of complexity that showed up in lots of places.

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And I was like, this is an interesting sort of field of science. And I was recently was reminded,

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I was at this, the very first sort of get together of what became the Santa Fe Institute. And I was

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like, in fact, there's even an audio recording of me sort of saying, people have been talking about,

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oh, what should this, you know, outfit do? And I was saying, well, there is this thing that I've

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been thinking about. It's this kind of idea of complexity. And it's kind of like, and that's

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what that ended up. And you planted the seed of complexity at Santa Fe. That's beautiful.

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It's a beautiful vision. But I mean, so that, but what's happened then is this idea of complexity

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and, you know, and I started the first research center at University of Illinois for doing that

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in the first journal, complex systems and so on. And it's kind of an interesting thing in my life,

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at least that it's kind of like you plant the seed, you have this idea. It's a kind of a science

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idea. You have this idea of sort of focusing on the phenomenon of complexity. The deeper idea was

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this computational paradigm. But the nominal idea is this kind of idea of complexity. Okay. Then you

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roll time forward 30 years or whatever, 35 years, whatever it is. And you say, what happened? Okay.

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Well now there are a thousand complexity institutes around the world. I think more or less,

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we've been trying to count them. And, you know, there are 40 complexity journals, I think.

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And so it's kind of like what actually happened in this field, right? And I look at a lot of what

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happened and I'm like, you know, I have to admit to some eye rolling, so to speak, because it's

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kind of like, like, what is, what's actually going on? Well, what people definitely got

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was this idea of computational models. And then they got, but they thought one of the,

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one of the kind of cognitive mistakes, I think is they say, we've got a computational model

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and it, and we're looking at a system that's complex and our computational model gives

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complexity. By golly, that must mean it's right. And unfortunately, because complexity is a generic

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phenomenon and computational irreducibility is a generic phenomenon that actually tells you nothing.

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And so then the question is, well, what can you do? You know, there's a lot of things that have

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been sort of done under this banner of complexity. And I think it's been very successful in providing

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sort of an interdisciplinary way of connecting different fields together. Which is powerful

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in itself. Right. I mean, that's a very useful. Biology and economics and physics. Right. It's a

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good organizing principle, but in the end, a lot of that is around this sort of computational

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paradigm, computational modeling. That's the raw material that powers that kind of, that kind of

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correspondence, I think. But the question is sort of, what is the, you know, I was just thinking

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recently, you know, we've been, I mean, the other we've been, we've been for years, people have

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told me you should start some Wolfram Institute that does basic science. You know, all I have

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is a company that, that builds software and we, you know, we have a little piece that does basic

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science as kind of a hobby. People are saying you should start this Wolfram Institute thing.

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And I've been, you know, cause I've known about lots of institutes and I've seen kind of their

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flow of money and, and kind of, you know, what happens in different situations and so on. So I've

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been kind of reluctant, but, but I've, I've, I have realized that, you know, what we've done with

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our company over the last 35 years, you know, we built a very good machine for doing R and D and,

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you know, innovating and creating things. And I just applied that machine to the physics project.

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That's how we did the physics project in a fairly short amount of time with a, you know,

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a efficient machine with, you know, various people involved and so on. And so, you know,

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it, it works for basic science and it's like, we can do more of this. And so now.

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Right. Right. But the, the thing that, so I was thinking about, okay, so what do we do with

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complexity? You know, what, what, there are all these people who've, you know, what, what should

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happen to that field? And what I realized is there's kind of this area of foundations of

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complexity. That's about these questions about simple programs, what they do that's far away

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from a bunch of the detailed applications that people, it's not far away. It's, it's the,

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it's the under, you know, the, the bedrock underneath those applications. And so I realized

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recently, this is my recent kind of little innovation of a sort, a post that I'll do very

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soon about kind of, you know, the foundations of complexity. What really are they? I think

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there are really two ideas, two conceptual ideas that I hadn't really enunciated, I think before.

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One is what I call meta modeling. The other is ruleology. So what is meta modeling? So

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meta modeling is you've got this complicated model and it's a model of, you know, hedgehogs

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interacting with this, interacting with that. And the question is what's really underneath that?

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What is it? You know, is it a Turing machine? Is it a cellular automaton? You know,

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what is the underlying stuff underneath that model? And so there's this kind of meta science

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question of given these models, what is the core model? And I realized, I mean, to me,

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that's sort of an obvious question, but then I realized I've been doing language design for 40

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years and language design is exactly that question. You know, underneath all of this

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detailed stuff people do, what are the underlying primitives? And that's a question people haven't

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tended to ask about models. They say, well, we've got this nice model for this and that and the

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other, what's really underneath it? And what, you know, because once you have the thing that's

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underneath it, well, for example, this multi computation idea is an ultimate meta modeling

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idea because it's saying underneath all these fields is one kind of paradigmatic structure.

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And, you know, you can imagine the same kind of thing in much more sort of much sort of shallower

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levels in different kinds of modeling. So the first activity is this kind of meta modeling,

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the kind of the models about models, so to speak. You know, what is the, what's, you know,

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drilling down into models? That's one thing. The other thing is this thing that I think we're

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going to call ruleology, which is kind of the, okay, you've got these simple rules. You've got

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cellular automata, you've got turing machines, you've got substitution systems, you've got

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register machines, you've got all these different things. What do they actually do in the wild? And

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this is an area that I've spent a lot of time, you know, working on. It's a lot of stuff in my new

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kind of science book is about this. You know, this new book I wrote about combinators is full of

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stuff like this. And this journal Complex Systems has lots of papers about these kinds of things.

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Yes. Yes. Right. So it's like, you've got some, what is it? Is it mathematics? No,

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it isn't really like mathematics. In fact, from my now understanding of metamathematics,

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I understand that it's the molecular dynamics level. It's not the level that mathematicians

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have traditionally cared about. It's not computer science because computer science is about writing

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programs that do things, you know, that were for a purpose, not programs in the wild, so to speak.

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It's not physics. It doesn't have anything to do with, you know, maybe underneath some physics,

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but it's not physics as such. So it just hasn't had a home. And if you look at, you know,

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but what's great about it is it's a surviving field, so to speak. It's something where,

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you know, one of the things I find sort of inspiring about mathematics, for example,

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is you look at mathematics that was done, you know, in ancient Greece, ancient, you know, Babylon,

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Egypt, and so on. It's still here today. You know, you find an icosahedron that somebody made

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in ancient Egypt. You look at it. Oh, that's a very modern thing. It's an icosahedron. You know,

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it's a timeless kind of activity. And this idea of studying simple rules and what they do,

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it's a timeless activity. And I can see that over the last 40 years or so as, you know,

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even with cellular automata, it's kind of like, you know, you can sort of catalog what are the

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different cellular automata used for and, you know, like the simplest rules like one, you might

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even know this one, Rule 184. Rule 184 is a minimal model for road traffic flow. And, you know, it's

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also a minimal model for various other things. But it's kind of fun that you can literally say,

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you know, Rule 90 is a minimal model for this and this and this. Rule 4 is a minimal model for this.

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And it's kind of remarkable that you can just by in this raw level of this kind of study of rules,

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they then branch, they're the raw material that you can use to make models of different things.

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So it's a very pure basic science, but it's one that, you know, people have explored it,

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but they've been kind of a little bit in the wilderness. And I think, you know, one of the

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things that I would like to do finally is, you know, I always thought that sort of this notion

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of pure NKS, pure NKS being the acronym for my book, New Kind of Science, was something that

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people should be doing. And, you know, we tried to figure out what's the right institutional

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structure to do this stuff. You know, we dealt with a bunch of universities. Oh, you know,

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can we do this here? Well, what department would be in it? Well, it isn't in a department. It's

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its own new kind of thing. That's why the book was called The New Kind of Science.

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It's kind of the, because that's an increasingly good description of what it is, so to speak.

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We're actually, we were thinking about kind of the ruleological society because we're realizing

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that it's kind of, it's, you know, it's very interesting. I mean, I've never really done

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something like this before because there's this whole group of researchers who are,

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who've been doing things that are really, in some cases, very elegant, very surviving, very solid,

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you know, here's this thing that happens in this very abstract system. But it's like,

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it's like, what is that part of, you know, it doesn't have a home. And I think that's something

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I, you know, I kind of fault myself for not having been more, you know, when complexity

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was developing in the 80s, I didn't understand the danger of applications. That is, it's really

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cool that you can apply this to economics and you can apply it to evolutionary biology and this and

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that and the other. But what happens with applications is everything gets sucked into

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the applications. And the pure stuff, it's like the pure mathematics, there isn't any pure

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mathematics, so to speak. It's all just applications of mathematics. And I failed to kind of make sure

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that this kind of pure area was kind of maintained and developed. And I think now, you know, one of

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the things I want to try to do and, you know, it's a funny thing because I'm used to, look,

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I've been a tech CEO for more than half my life now. So, you know, this is what I know how to do.

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And, you know, I can make stuff happen and get projects to happen, even as it turns out,

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basic science projects in that kind of setting and how that translates into kind of, you know,

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there are a lot of people working on, for example, our physics project sort of distributed through

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the academic world and that's working just great. But the question is, you know, can we have a sort

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of accelerator mechanism that makes use of kind of what we've learned in sort of R&D innovation?

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And, you know, but on the other hand, it's a funny thing because, you know, in a company,

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in the end, the thing is, you know, it's a company, it makes products, it sells things,

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sells things to people. And, you know, when you're doing basic research, one of the challenges is

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there isn't that same kind of sort of mechanism. And so it's, you know, how do you drive the thing

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in a kind of, in a led kind of way so that it really can make forward progress rather than,

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you know, what can often happen in, you know, in academic settings where it's like,

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well, there are all these flowers blooming, but it's not clear that, you know, that it's...

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You have to have a central mission and a drive, just like you do with a company that's delivering

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a big overarching product. And that's... But the challenge is, you know, when you have

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the economics of the world are such that, you know, when you're delivering a product and people

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say, wow, that's useful, we'll buy it. And then that kind of feeds back and, okay, then you can

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pay the people who build it to eat, you know, so they can eat and so on. And with basic science,

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the payoff is very much less visible. And, you know, with this physics project, as I say,

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the big surprise has been that, I mean, you know, for example, well, the big surprise with

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the physics project is that it looks like it has near term applications. And I was like,

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I'm guessing this is 200 years away. I was kind of using the analogy of, you know, Newton

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And, you know, but it turns out that's not the case, but we can't guarantee that. And if you say

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we're signing up to do basic research, basic rheology, let's say, and, you know, and we can't,

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we don't know the horizon, you know, it's an unknown horizon. It's kind of like an undecidable

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kind of proposition of when is this proof going to end, so to speak? When is it going to be

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something that gets applied? Well, I hope this becomes a vibrant new field of rheology. I love

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it. Like I told you many, many times, it's one of the most amazing ideas that has been brought to

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this world. So I hope you get a bunch of people to explore this world. Thank you once again for

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spending your really valuable time with me today. Fun stuff. Thank you. Thanks for listening to this

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conversation with Stephen Wolfram. To support this podcast, please check out our sponsors in the

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description. And now, let me leave you with some words from Richard Feynman. Nature uses only the

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longest threads to weave her patterns, so each small piece of her fabric reveals the organization