Stephen Wolfram: Complexity and the Fabric of Reality

00:00:00.000 | The following is a conversation with Stephen Wolfram,

00:00:02.840 | his third time on the podcast.

00:00:04.920 | He's a computer scientist, mathematician,

00:00:07.600 | theoretical physicist, and the founder of Wolfram Research,

00:00:11.640 | a company behind Mathematica, Wolfram Alpha,

00:00:14.600 | Wolfram Language, and the new Wolfram Physics Project.

00:00:18.640 | This conversation is a wild, technical rollercoaster ride

00:00:22.840 | through topics of complexity, mathematics, physics,

00:00:26.000 | computing, and consciousness.

00:00:28.180 | I think this is what this podcast is becoming, a wild ride.

00:00:32.600 | Some episodes are about physics, some about robots,

00:00:36.040 | some are about war and power,

00:00:38.400 | some are about the human condition

00:00:40.480 | and our search for meaning,

00:00:41.900 | and some are just what the comedian Tim Dillon calls fun.

00:00:46.780 | This is the Lex Friedman Podcast.

00:00:49.820 | To support it, please check out the sponsors

00:00:51.680 | in the description.

00:00:52.920 | And now, here's my conversation with Stephen Wolfram.

00:00:57.680 | Almost 20 years ago, you published "A New Kind of Science,"

00:01:01.740 | where you presented a study of complexity

00:01:04.520 | and an approach for modeling of complex systems.

00:01:07.500 | So, let us return again to the core idea of complexity.

00:01:12.500 | What is complexity?

00:01:15.560 | - I don't know, I think that's not

00:01:16.840 | the most interesting question.

00:01:18.440 | It's like, you know, if you ask a biologist, what is life?

00:01:22.020 | - Yeah.

00:01:22.860 | - That's not the question they care the most about.

00:01:25.600 | What I was interested in is how does something

00:01:29.800 | that we would usually identify as complexity

00:01:32.240 | arise in nature?

00:01:33.080 | And I got interested in that question like 50 years ago,

00:01:35.740 | which is really embarrassingly a long time ago.

00:01:38.140 | And, you know, I was, you know,

00:01:40.760 | how does snowflakes get to have complicated forms?

00:01:43.240 | How do galaxies get to have complicated shapes?

00:01:45.440 | How does, you know, how do living systems get produced?

00:01:48.360 | Things like that.

00:01:49.440 | And the question is, what's the sort of underlying

00:01:52.040 | scientific basis for those kinds of things?

00:01:54.640 | And the thing that I was at first very surprised by,

00:01:57.840 | 'cause I've been doing physics and particle physics

00:02:00.200 | and fancy mathematical physics and so on.

00:02:02.360 | And it's like, I know all this fancy stuff.

00:02:04.280 | I should be able to solve this sort of basic

00:02:06.360 | science question.

00:02:07.640 | And I couldn't, this was like early,

00:02:10.440 | maybe 1980-ish timeframe.

00:02:13.520 | And it's like, okay, what can one do to understand

00:02:17.120 | the sort of basic secret that nature seems to have?

00:02:19.480 | 'Cause it seems like nature, you know,

00:02:20.880 | you look around in the natural world,

00:02:22.120 | it's full of incredibly complicated forms.

00:02:24.480 | You look at sort of most engineered kinds of things,

00:02:28.160 | for instance, they tend to be, you know,

00:02:29.920 | we got sort of circles and lines and things like this.

00:02:34.320 | The question is, what secret does nature have

00:02:36.760 | that lets it make all this complexity

00:02:38.820 | that we in doing engineering, for example,

00:02:41.120 | don't naturally seem to have?

00:02:43.120 | And so that was the kind of the thing

00:02:44.480 | that I got interested in.

00:02:45.920 | And then the question was, you know,

00:02:47.240 | could I understand that with things

00:02:49.360 | like mathematical physics?

00:02:50.600 | Well, it didn't work very well.

00:02:52.160 | So then I got to thinking about, okay,

00:02:54.160 | is there some other way to try to understand this?

00:02:56.840 | And then the question was,

00:02:57.920 | if you're going to look at some system in nature,

00:03:00.320 | how do you make a model for that system,

00:03:02.080 | for what that system does?

00:03:03.520 | So, you know, a model is some abstract representation

00:03:05.980 | of the system, some formal representation of the system.

00:03:08.960 | What is the raw material

00:03:10.760 | that you can make that model out of?

00:03:12.720 | And so what I realized was, well, actually,

00:03:15.880 | programs are really good source of raw material

00:03:19.000 | for making models of things.

00:03:20.640 | And, you know, in terms of my personal history,

00:03:23.480 | the, to me, that seemed really obvious.

00:03:26.200 | And the reason it seemed really obvious

00:03:27.480 | is because I just spent several years building

00:03:29.960 | this big piece of software that was sort of a predecessor

00:03:32.360 | to Mathematica and Morphine Language,

00:03:34.200 | thing called SMP, Symbolic Manipulation Program,

00:03:37.240 | which was something that had this idea

00:03:39.760 | of starting from just these computational primitives

00:03:43.200 | and building up everything one had to build up.

00:03:44.920 | And so kind of the notion of, well,

00:03:47.000 | let's just try and make models

00:03:48.320 | by starting from computational primitives

00:03:50.120 | and seeing what we can build up.

00:03:51.600 | That seemed like a totally obvious thing to do.

00:03:54.160 | In retrospect, it might not have been externally

00:03:57.400 | quite so obvious, but it was obvious to me at the time,

00:03:59.680 | given the path that I happened to have been on.

00:04:02.040 | So, you know, so that got me into this question

00:04:04.040 | of let's use programs to model what happens in nature.

00:04:08.300 | And the question then is, well, what kind of programs?

00:04:11.160 | And, you know, we're used to programs

00:04:13.200 | that you write for some particular purpose

00:04:15.080 | and it's a big, long piece of code

00:04:16.320 | and it does some specific thing.

00:04:18.080 | But what I got interested in was, okay,

00:04:20.600 | if you just go out into the sort of computational universe

00:04:23.480 | of possible programs, you say,

00:04:25.480 | take the simplest program you can imagine, what does it do?

00:04:28.740 | And so I started studying these things

00:04:30.880 | called cellular automata.

00:04:32.800 | Actually, I didn't know at first

00:04:33.720 | they were called cellular automata,

00:04:34.880 | but I found that out subsequently.

00:04:37.140 | But it's just a line of cells, you know,

00:04:38.960 | each one is black or white,

00:04:40.440 | and it's just some rule that says the color of the cell

00:04:43.400 | is determined by the color that it had on the previous step

00:04:45.720 | and its two neighbors on the previous step.

00:04:48.080 | And I had initially thought that, you know,

00:04:51.640 | sufficiently simple setup

00:04:53.680 | is not gonna do anything interesting.

00:04:55.080 | It's always gonna be simple, no complexity,

00:04:57.500 | simple rule, simple behavior.

00:04:59.560 | Okay, but then I actually ran the computer experiment,

00:05:02.000 | which is pretty easy to do.

00:05:04.080 | I mean, it probably took a few hours originally.

00:05:07.260 | And the results were not what I'd expected at all.

00:05:11.640 | Now, needless to say,

00:05:12.560 | in the way that science actually works,

00:05:14.960 | the results that I got had a lot of unexpected things

00:05:17.240 | which I thought were really interesting,

00:05:18.840 | but the really strongest result,

00:05:20.880 | which was already right there in the printouts I made,

00:05:23.000 | I didn't really understand for a couple more years.

00:05:25.680 | So it was not, you know,

00:05:27.560 | the compressed version of the story is

00:05:30.080 | you run the experiment

00:05:31.160 | and you immediately see what's going on,

00:05:33.080 | but I wasn't smart enough to do that, so to speak.

00:05:36.220 | But the big thing is,

00:05:38.500 | even with very simple rules of that type,

00:05:41.000 | sort of the minimal, tiniest program,

00:05:43.640 | sort of the one line program or something,

00:05:46.840 | it's possible to get very complicated behavior.

00:05:49.240 | My favorite example is this thing called rule 30,

00:05:52.280 | which is a particular cellular automaton rule.

00:05:54.120 | You just start it off from one black cell

00:05:56.200 | and it makes this really complicated pattern.

00:05:58.980 | And so that, for me, was sort of a critical discovery

00:06:03.680 | that then kind of said, playing back onto, you know,

00:06:07.740 | how does nature make complexity?

00:06:09.960 | I sort of realized that might be how it does it.

00:06:12.480 | That might be kind of the secret that it's using

00:06:14.980 | is that in this kind of computational universe

00:06:16.900 | of possible programs,

00:06:18.460 | it's actually pretty easy to get programs

00:06:20.620 | where even though the program is simple,

00:06:22.580 | the behavior when you run the program is not simple at all.

00:06:25.480 | And that was, so for me,

00:06:26.980 | that was the kind of the story of kind of how,

00:06:31.220 | that was sort of the indication that one had got an idea

00:06:34.260 | of what the sort of secret that nature uses

00:06:36.880 | to make complexity

00:06:38.020 | and how complexity can be made in other places.

00:06:41.640 | Now, if you say, what is complexity?

00:06:44.180 | You know, it's, complexity is,

00:06:47.860 | it's not easy to tell what's going on.

00:06:49.960 | That's the informal version of what is complexity.

00:06:53.420 | - But there is something going on.

00:06:55.180 | - But there's a rule. - But it's not easy

00:06:56.000 | to know what. - Right.

00:06:57.100 | - Well, no, the rules can generate just randomness, right?

00:07:01.680 | - Well, that's not obvious.

00:07:03.880 | In other words-- - That's not obvious,

00:07:04.960 | that's right. - It's not obvious at all.

00:07:06.440 | And it wasn't what I expected.

00:07:07.800 | It's not what people's intuition had been

00:07:10.180 | and has been for, you know, for a long time.

00:07:13.180 | That is, one might think you have a rule,

00:07:15.560 | you can tell there's a rule behind it.

00:07:18.020 | I mean, it's just like, you know,

00:07:19.340 | the early, you know, robots in science fiction movies,

00:07:23.220 | right, you can tell it's a robot

00:07:24.900 | 'cause it does simple things, right?

00:07:27.860 | Turns out that isn't actually the right story,

00:07:30.520 | but it's not obvious that isn't the right story

00:07:32.360 | 'cause people assume simple rules, simple behavior.

00:07:35.520 | And that, the sort of the key discovery

00:07:37.880 | about the computational universe is that isn't true.

00:07:40.340 | And that discovery goes very deep

00:07:42.980 | and relates to all kinds of things

00:07:45.100 | that I've spent years and years studying.

00:07:47.520 | But, you know, in the end,

00:07:49.920 | the sort of the what is complexity is,

00:07:52.340 | well, you can't easily tell what it's going to do.

00:07:55.060 | You could just run the rule and see what happens,

00:07:57.920 | but you can't just say, oh, you know, show me the rule.

00:08:01.300 | Great, now I know what's gonna happen.

00:08:03.420 | And, you know, the key phenomenon around that

00:08:05.740 | is this thing I call computational irreducibility.

00:08:08.740 | This fact that in something like rule 30,

00:08:12.340 | you might say, well, what's it gonna do

00:08:13.580 | after a million steps?

00:08:15.180 | Well, you can run it for a million steps

00:08:17.340 | and just do what it does to find out,

00:08:19.820 | but you can't compress that, you can't reduce that

00:08:22.740 | and say, I'm gonna be able to jump ahead and say,

00:08:25.140 | this is what it's gonna do after a million steps,

00:08:26.680 | but I don't have to go through anything

00:08:27.940 | like that computational effort.

00:08:29.520 | - By the way, has anybody succeeded at that?

00:08:31.340 | Do you had to challenge a competition

00:08:33.460 | for predicting the middle column of rule 30?

00:08:36.700 | - Indeed.

00:08:37.540 | - Anybody?

00:08:38.380 | - A number of people have sent things in

00:08:39.820 | and sort of people are picking away at it,

00:08:41.740 | but it's hard.

00:08:42.820 | I mean, I've been actually even proving

00:08:47.820 | that the center column of rule 30 doesn't repeat.

00:08:51.860 | That's something I think might be doable, okay?

00:08:54.620 | - Mathematically proving.

00:08:55.840 | - Yes, and so that's analogous to a similar kind of thing

00:08:59.620 | is like the digits of pi,

00:09:01.140 | which are also generated in this very deterministic way.

00:09:04.060 | And so a question is how random are the digits of pi?

00:09:06.780 | For example, does every, first of all,

00:09:09.140 | do the digits of pi ever repeat?

00:09:10.780 | Well, we know they don't.

00:09:11.980 | This was proved in the 1800s

00:09:13.840 | that pi is not a rational number.

00:09:15.740 | So that means only rational numbers

00:09:17.780 | have digit sequences that repeat.

00:09:19.460 | So we know the digits of pi don't repeat.

00:09:21.600 | So now the question is, does, you know,

00:09:23.500 | zero, one, two, three, or whatever,

00:09:25.140 | do all the digits base 10 or base two,

00:09:27.220 | or however you work it out,

00:09:28.480 | do they all occur with equal frequency?

00:09:30.720 | Nobody knows.

00:09:32.200 | That's far away from what can be understood mathematically

00:09:35.100 | at this point.

00:09:36.320 | And that's kind of, but I'm even looking for step one,

00:09:41.320 | which is prove that the center column doesn't repeat

00:09:45.460 | and then prove other things about it,

00:09:46.920 | like equidistribution of equal numbers of zeros and ones.

00:09:50.620 | And those are things which I, you know,

00:09:52.220 | I kind of set up this little prize thing

00:09:54.900 | because I thought those were not too out of range.

00:09:58.660 | Those are things which are within, you know,

00:10:02.220 | a modest amount of time,

00:10:04.020 | it's conceivable that those could be done.

00:10:05.540 | They're not far away from what current mathematics

00:10:09.300 | might allow.

00:10:10.140 | They'll require a bunch of cleverness

00:10:11.480 | and hopefully some interesting new ideas

00:10:14.060 | that, you know, will be useful other places.

00:10:16.500 | - But you started in 1980 with this idea

00:10:18.900 | before I think you realized, you know,

00:10:22.220 | this idea of programs.

00:10:24.460 | You thought that there might be some kind of

00:10:26.580 | thermodynamic like randomness,

00:10:28.780 | and then the complexity comes from a clever filter

00:10:32.780 | that you kind of, like, I don't know,

00:10:35.380 | spaghetti or something.

00:10:36.740 | You filter the randomness and outcomes complexity,

00:10:40.180 | which is an interesting intuition.

00:10:42.540 | How do we know that's not actually what's happening?

00:10:44.820 | So just because you were then able to develop,

00:10:49.060 | look, you don't need this like incredible randomness.

00:10:52.780 | You can just have very simple, predictable,

00:10:55.720 | initial conditions and predictable rules.

00:10:58.380 | And then from that emerged complexity.

00:11:00.820 | Still, there might be some systems

00:11:02.820 | where it's filtering randomness in the inputs.

00:11:07.660 | - Well, the point is, when you have quotes

00:11:10.780 | randomness in the input,

00:11:12.100 | that means there's all kinds of information in the input.

00:11:14.680 | And in a sense, what you get out

00:11:16.620 | will be maybe just something close to what you put in.

00:11:20.100 | Like people are very, in dynamical systems theory,

00:11:23.280 | sort of big area of mathematics that developed

00:11:25.940 | from the early 1900s and really got big in the 1980s.

00:11:29.720 | You know, an example of what people study there a lot,

00:11:32.140 | and it's popular version is chaos theory.

00:11:35.180 | And an example of what people study a lot

00:11:37.900 | is the shift map, which is basically taking 2X mod one,

00:11:42.900 | the fractional part of 2X,

00:11:44.340 | which is basically just taking digits in binary

00:11:47.260 | and shifting them to the left.

00:11:48.760 | So at every step, you get to see,

00:11:50.800 | if you say, how big is this number that I got out?

00:11:53.560 | Well, the most important digit in that number

00:11:55.480 | is whatever ended up at the left-hand end.

00:11:58.720 | But now if you start off from an arbitrary random number,

00:12:01.940 | which is quotes randomly chosen,

00:12:03.740 | so all its digits are random,

00:12:05.520 | then when you run that sort of chaos theory shift map,

00:12:09.000 | all that you get out is just whatever you put in.

00:12:12.080 | You just get to see what you,

00:12:14.220 | it's not obvious that you would excavate

00:12:16.400 | all of those digits.

00:12:17.800 | And if you're, for example, making a theory,

00:12:19.440 | I don't know, fluid mechanics, for example,

00:12:21.600 | if there was that phenomenon in fluid mechanics,

00:12:24.400 | then the equations of fluid mechanics can't be right.

00:12:27.160 | Because what that would be saying is,

00:12:29.120 | the equations of that it matters to the fluid,

00:12:32.060 | what happens in the fluid at the level of the,

00:12:34.740 | you know, millionth digit of the initial conditions,

00:12:38.020 | which is far below the point at which you're hitting

00:12:40.760 | kind of sizes of molecules and things like that.

00:12:42.980 | So it's kind of almost explaining,

00:12:45.100 | if that phenomenon is an important thing,

00:12:47.860 | it's kind of telling you that the, you know,

00:12:49.540 | fluid dynamics, which describes fluids as continuous media

00:12:52.540 | and so on, isn't really right.

00:12:54.540 | But so, you know, so this idea that, you know,

00:12:57.620 | there's a, it's a tricky thing,

00:12:59.360 | because as soon as you put randomness in,

00:13:01.540 | you have to know, you know, what,

00:13:03.660 | how much of what's coming out is what you put in,

00:13:06.160 | versus how much is actually something

00:13:07.760 | that's being generated.

00:13:08.800 | And what's really nice about these systems

00:13:10.940 | where you just have very simple initial conditions,

00:13:13.360 | and where you get random stuff out,

00:13:15.800 | or seemingly random stuff out,

00:13:17.760 | is you don't have that issue.

00:13:18.760 | You don't have to argue about,

00:13:20.420 | was there something complicated put in?

00:13:22.580 | Because it's plainly obvious there wasn't.

00:13:24.160 | Now, as a practical matter in doing experiments,

00:13:26.920 | the big thing is, if the thing you see

00:13:30.160 | is complex and reproducible,

00:13:32.740 | then it didn't come from just filtering some,

00:13:35.500 | quotes, "randomness from the outside world."

00:13:37.860 | It has to be something that is intrinsically made,

00:13:40.680 | because it wouldn't otherwise be, I mean, you know,

00:13:44.080 | it could be the case that you set things up,

00:13:45.940 | and it's always the same each time,

00:13:47.540 | and you say, well, it's kind of the same,

00:13:50.120 | but it's not random each time,

00:13:52.000 | because it's kind of the definition of it being random,

00:13:54.400 | is it was kind of picked at random each time, so to speak.

00:13:58.520 | - So is it possible to for sure know

00:14:01.360 | that our universe does not,

00:14:02.960 | at the fundamental level, have randomness?

00:14:06.360 | Is it possible to conclusively say,

00:14:08.920 | there's no randomness at the bottom?

00:14:11.720 | - Well, it's an interesting question.

00:14:13.040 | I mean, you know, science, natural science,

00:14:15.980 | is an inductive business, right?

00:14:17.720 | You observe a bunch of things, and you say,

00:14:20.240 | can we fit these together?

00:14:21.760 | What is our hypothesis for what's going on?

00:14:24.100 | The thing that I think I can say fairly definitively

00:14:27.780 | is at this point, we understand enough

00:14:29.900 | about fundamental physics that there is,

00:14:33.240 | if there was sort of an extra dice being thrown,

00:14:37.260 | it's something that doesn't need to be there.

00:14:39.540 | We can get what we see without that.

00:14:42.460 | Now, you know, could you add that in

00:14:45.220 | as an extra little featureoid, you know,

00:14:48.560 | without breaking the universe?

00:14:50.740 | Probably, but in fact, almost certainly yes.

00:14:54.260 | But is it necessary for understanding the universe?

00:14:56.460 | No, and I think actually from a more fundamental

00:14:59.420 | point of view, it's, I think I might be able to argue.

00:15:04.320 | So one of the things that I've been interested in,

00:15:06.380 | I've been pretty surprised that I've had anything

00:15:08.700 | sentient to say about, is the question of,

00:15:11.080 | why does the universe exist?

00:15:13.220 | I didn't think that was a question that I would,

00:15:15.120 | you know, I thought that was a far out there

00:15:17.540 | metaphysical kind of thing.

00:15:20.580 | Even the philosophers have stayed away

00:15:22.060 | from that question for the most part.

00:15:23.740 | It's so such a kind of, you know,

00:15:26.060 | difficult to address question.

00:15:28.480 | But I actually think to my great surprise

00:15:30.900 | that from our physics project and so on,

00:15:32.860 | that it is possible to actually address that question

00:15:36.260 | and explain why the universe exists.

00:15:38.100 | And I kind of have a suspicion, I've not thought it through.

00:15:41.140 | I kind of have a suspicion that that explanation

00:15:43.880 | will eventually show you that in no meaningful sense,

00:15:47.780 | can there be randomness underneath the universe?

00:15:50.180 | That is that if there is, it's something

00:15:52.960 | that is necessarily irrelevant

00:15:55.740 | to our perception of the universe.

00:15:57.860 | That is that it could be there, but it doesn't matter.

00:16:01.020 | Because in a sense, we've already, you know,

00:16:03.460 | whatever it would do, whatever extra thing it would add

00:16:06.940 | is not relevant to our perception of what's going on.

00:16:09.300 | - So why does the universe exist?

00:16:12.220 | How does the irrelevance of randomness

00:16:15.580 | connect to the big why question of the universe?

00:16:19.420 | - So, okay, so I mean, why does the universe exist?

00:16:22.140 | Well, let's see.

00:16:23.140 | - And is this the only universe we got?

00:16:25.700 | - It's the only one.

00:16:27.300 | About that, I'm pretty sure.

00:16:28.900 | - So you may be, which one,

00:16:30.740 | which of these topics is better to enter first?

00:16:33.780 | Why does the universe exist?

00:16:36.000 | And why you think it's the only one that exists?

00:16:39.660 | - Well, I think they're very closely related.

00:16:41.340 | - Okay. - Okay?

00:16:42.460 | So I mean, the first thing, let's see.

00:16:45.160 | I mean, this why does the universe exist question

00:16:47.740 | is built on top of all these things

00:16:50.020 | that we've been figuring out about fundamental physics.

00:16:53.300 | 'Cause if you wanna know why the universe exists,

00:16:55.220 | you kind of have to know what the universe is made of.

00:16:57.620 | And I think the, well, let me describe a little bit

00:17:02.620 | about the why does the universe exist question.

00:17:05.140 | So the main issue is,

00:17:06.620 | let's say you have a model for the universe.

00:17:08.980 | And you say, I've got this program or something,

00:17:11.780 | and you run it and you make the universe.

00:17:13.920 | Now you say, well, how do you actually,

00:17:15.500 | why is that program actually running?

00:17:17.700 | And people say, you've got this program

00:17:19.540 | that makes the universe, what computer is it running on?

00:17:22.140 | Right?

00:17:22.980 | What does it mean?

00:17:23.980 | What actualizes something?

00:17:25.580 | You know, two plus two equals four,

00:17:27.380 | but that's different from saying there's two,

00:17:29.260 | a pile of two rocks, another pile of two rocks,

00:17:31.300 | and somebody moves them together and makes four,

00:17:33.640 | so to speak.

00:17:34.660 | And so what is it that kind of turns it

00:17:37.220 | from being just this formal thing

00:17:39.500 | to being something that is actualized?

00:17:42.060 | Okay, so there we have to start thinking about,

00:17:44.900 | well, what do we actually know

00:17:47.100 | about what's going on in the universe?

00:17:48.500 | Well, we are observers of this universe,

00:17:51.540 | but confusingly enough, we're part of this universe.

00:17:54.540 | So in a sense, if we say,

00:17:57.820 | what do we know about what's going on in the universe?

00:18:00.420 | Well, what we know is what sort of our consciousness records

00:18:04.340 | about what's going on in the universe.

00:18:06.340 | - And consciousness is part of the fabric of the universe,

00:18:09.260 | so we're in it.

00:18:10.240 | - Yes, we're in it.

00:18:11.340 | And maybe I should start off

00:18:13.740 | by saying something about the consciousness story,

00:18:16.780 | because that's--

00:18:18.180 | - Yes, maybe we should begin even before that,

00:18:22.900 | at the very base layer of the Wolfram Physics Project.

00:18:26.800 | Maybe you can give a broad overview, once again,

00:18:30.580 | really quick about this hypergraph model.

00:18:33.380 | - Yes. - And also,

00:18:34.620 | what is it, a year and a half ago,

00:18:36.620 | since you've brought this project to the world,

00:18:39.240 | what is the status update?

00:18:41.220 | What are all the beautiful ideas you have come across?

00:18:45.620 | What are the interesting things you can sort of mention?

00:18:48.540 | - I mean, it's a frigging Cambrian explosion.

00:18:51.260 | I mean, it's crazy.

00:18:53.500 | I mean, there are all these things,

00:18:54.680 | which I've kind of wondered about for years,

00:18:57.020 | and suddenly, there's actually a way to think about them.

00:19:00.720 | And I really did not see,

00:19:02.820 | I mean, the real strength of what's happened,

00:19:04.780 | I absolutely did not see coming.

00:19:06.460 | And the real strength of it is,

00:19:08.300 | we've got this model for physics,

00:19:09.740 | but it turns out it's a foundational kind of model

00:19:12.420 | that's a different kind of computation-like model,

00:19:15.300 | that I'm kind of calling the sort of

00:19:16.700 | multi-computational model.

00:19:19.140 | And that that kind of model is applicable,

00:19:22.800 | not only to physics,

00:19:23.800 | but also to lots of other kinds of things.

00:19:26.200 | And one reason that's extremely powerful

00:19:28.700 | is because physics has been very successful.

00:19:30.820 | So we know a lot, based on what we figured out in physics.

00:19:33.780 | And if we know that the same model governs physics,

00:19:37.020 | and governs, I don't know, economics,

00:19:38.620 | linguistics, immunology, whatever,

00:19:41.100 | we know that the same kind of model governs those things,

00:19:44.060 | we can start using things

00:19:45.740 | that we've successfully discovered in physics,

00:19:47.980 | and applying those intuitions in all these other areas.

00:19:50.740 | And that's pretty exciting, and very surprising to me.

00:19:54.540 | And in fact, it's kind of like,

00:19:56.160 | in the original story of, sort of,

00:19:58.800 | you go and you explain why is there complexity

00:20:01.340 | in the natural world,

00:20:02.820 | then you realize, well, there's all this complexity,

00:20:04.820 | there's all this computational irreducibility,

00:20:07.140 | you know, there's a lot we can't know

00:20:08.740 | about what's going to happen.

00:20:09.820 | It's kind of a very confusing thing for people who say,

00:20:12.740 | you know, science has nailed everything down,

00:20:14.760 | we're gonna, you know,

00:20:15.600 | based on science, we can know everything.

00:20:17.360 | Well, actually, there's this computational irreducibility

00:20:19.580 | thing right in the middle of that,

00:20:21.820 | thrown up by science, so to speak.

00:20:24.180 | And then the question is,

00:20:25.020 | well, given computational irreducibility,

00:20:27.220 | how can we actually figure out anything

00:20:28.880 | about what happens in the world?

00:20:30.060 | Why aren't we, why are we able to predict anything?

00:20:32.740 | Why are we able to sort of operate in the world?

00:20:34.900 | And the answer is that we sort of live

00:20:36.340 | in these slices of computational reusability

00:20:39.380 | that exist in this kind of ocean

00:20:41.220 | of computational irreducibility.

00:20:43.220 | And it turns out that it seems

00:20:45.140 | that it's a very fundamental feature

00:20:46.940 | of the kind of model that seems to operate in physics

00:20:50.940 | and perhaps in a lot of these other areas,

00:20:53.940 | that there are these particular slices

00:20:55.820 | of computational reducibility that are relevant to us.

00:20:59.580 | And those are the things that both allow us

00:21:02.220 | to operate in the world

00:21:03.740 | and not just have everything be completely unpredictable,

00:21:06.460 | but they're also things that potentially give us

00:21:09.040 | what amount to sort of physics-like laws

00:21:11.740 | in all these other areas.

00:21:13.120 | So that's been sort of an exciting thing,

00:21:15.580 | but I would say that in general for our project,

00:21:18.540 | it's been going spectacularly well.

00:21:20.240 | I mean, you know, it's very, honestly,

00:21:22.940 | it wasn't something I expected to happen in my lifetime.

00:21:26.420 | I mean, it's, you know, it's something where it's,

00:21:29.940 | and in fact, one of the things about it,

00:21:32.220 | some of the things that we've discovered

00:21:34.220 | are things where I was pretty sure

00:21:36.140 | that wasn't how things worked and turns out I'm wrong.

00:21:40.020 | And, you know, in a major area in meta-mathematics,

00:21:43.180 | I'd be realizing that something I've long believed,

00:21:46.100 | we can talk about it later,

00:21:47.700 | that just really isn't right.

00:21:50.860 | But I think that the thing that,

00:21:55.100 | so what's happened with the physics project,

00:21:56.860 | I mean, you know, it's a,

00:21:59.420 | it can explain a little bit about how the model works,

00:22:01.940 | but basically--

00:22:02.780 | - We can maybe ask you the following question.

00:22:05.620 | So it's easy through words

00:22:07.900 | to describe how cellular automata works.

00:22:09.780 | You've explained this.

00:22:11.840 | And it's the fundamental mechanism

00:22:15.400 | by which you, in your book,

00:22:17.260 | a new kind of science,

00:22:18.300 | explored the idea of complexity

00:22:20.020 | and how to do science in this world

00:22:22.580 | of reducible islands and irreducible,

00:22:26.660 | generally irreducibility.

00:22:28.380 | Okay, so how does the model of hypergraphs

00:22:32.300 | differ from cellular automata?

00:22:33.860 | And how does the idea of multi-computation differ?

00:22:36.960 | Like maybe that's a way to describe it.

00:22:39.100 | - Right, we're, yeah, right.

00:22:40.900 | This is a, you know, my life is,

00:22:43.260 | like all of our lives,

00:22:44.300 | something of a story of computational irreducibility.

00:22:47.180 | And, you know, it's been going for a few years now.

00:22:49.580 | So it's always a challenge

00:22:51.220 | to kind of find these appropriate pockets of reducibility.

00:22:54.580 | But let me see what I can do.

00:22:56.180 | So, I mean, first of all,

00:22:58.260 | let's talk about physics, first of all.

00:23:01.100 | And, you know, a key observation,

00:23:04.540 | the starting point of our physics project

00:23:06.860 | is things about what is space?

00:23:10.140 | What is the universe made of?

00:23:11.960 | And, you know, ever since Euclid,

00:23:13.980 | people just sort of say space is just this thing

00:23:16.100 | where you can put things at any position you want.

00:23:18.740 | And they're just points,

00:23:19.860 | and they're just geometrical things

00:23:21.540 | that you can just arbitrarily put

00:23:23.220 | at different coordinate positions.

00:23:25.660 | Sort of the first thing in our physics project

00:23:28.100 | is the idea that space is made of something.

00:23:30.580 | Just like water is made of molecules,

00:23:32.420 | space is made of kind of atoms of space.

00:23:35.260 | And the only thing we can say about these atoms of space

00:23:37.940 | is they have some identity.

00:23:39.260 | It's this atom as opposed to this atom.

00:23:43.220 | And, you know, you could give them,

00:23:44.200 | if you were a computer person,

00:23:45.180 | you'd give them UUIDs or something.

00:23:46.940 | (Luke laughs)

00:23:48.660 | - Yes.

00:23:49.500 | - And that's all there is to say about them, so to speak.

00:23:53.300 | And then all we know about these atoms of space

00:23:58.140 | is how they relate to each other.

00:24:00.020 | So we say these three atoms of space

00:24:03.700 | are associated with each other in some relation.

00:24:06.160 | So you can think about that as, you know,

00:24:08.540 | what atom of space is friends

00:24:10.220 | with what other atom of space?

00:24:12.100 | You can build this essentially friend network

00:24:14.140 | of the atoms of space.

00:24:15.860 | And the sort of starting point of our physics project

00:24:18.540 | is that's what our universe is.

00:24:20.380 | It's a giant friend network of the atoms of space.

00:24:23.420 | And so how can that possibly represent our universe?

00:24:27.140 | Well, it's like in something like water,

00:24:30.780 | you know, there are molecules bouncing around,

00:24:32.540 | but on a large scale, that produces fluid flow

00:24:36.500 | and we have fluid vortices

00:24:37.900 | and we have all of these phenomena

00:24:39.560 | that are sort of the emergent phenomena

00:24:41.820 | from that underlying kind of collection of molecules

00:24:45.120 | bouncing around.

00:24:46.220 | And by the way, it's important

00:24:47.300 | that that collection of molecules bouncing around

00:24:49.440 | have this phenomenon of computational irreducibility.

00:24:51.860 | That's actually what leads

00:24:53.100 | to the second law of thermodynamics among other things.

00:24:55.660 | And that leads to the sort of randomness

00:24:58.300 | of the underlying behavior,

00:24:59.860 | which is what gives you something,

00:25:01.520 | which on a large scale

00:25:03.020 | seems like it's a smooth, continuous type of thing.

00:25:07.060 | And so, okay, so first thing is space is made of something.

00:25:11.060 | It's made of all these atoms of space

00:25:13.380 | connected together in this network.

00:25:15.260 | And then everything that we experience

00:25:18.700 | is sort of features of that structure of space.

00:25:21.660 | So, you know, when we have an electron or something

00:25:23.460 | or a photon, it's some kind of tangle

00:25:26.280 | in the structure of space,

00:25:27.380 | much like kind of a vortex in a fluid

00:25:29.540 | would be just this thing that is, you know,

00:25:31.780 | it can actually, the vortex can move around,

00:25:34.300 | it can involve different molecules in the fluid,

00:25:37.020 | but the vortex still stays there.

00:25:38.900 | - And if you zoom out enough,

00:25:40.060 | the vortex looks like an atom itself,

00:25:42.300 | like a basic element.

00:25:43.300 | - Yes.

00:25:44.140 | - So there's the levels of abstraction.

00:25:46.100 | If you squint and kind of blur things out,

00:25:49.780 | it looks like at every level of abstraction,

00:25:52.460 | you can define what is a basic individual entity.

00:25:55.820 | - Yes, but, you know, in this model,

00:25:58.780 | there's a bottom level.

00:26:00.020 | - Yeah.

00:26:00.860 | - You know, there's an elementary length,

00:26:01.680 | maybe 10 to the minus 100 meters, let's say,

00:26:04.740 | which is really small, you know,

00:26:05.780 | a proton is 10 to the minus 15 meters.

00:26:08.140 | The smallest we've ever been able to sort of see

00:26:11.580 | with a particle accelerator

00:26:12.660 | is around 10 to the minus 21 meters.

00:26:14.780 | So, you know, if we don't know precisely

00:26:17.740 | what the correct scale is,

00:26:18.860 | but it's perhaps over the order of 10 to the minus 100 meters

00:26:21.380 | so it's pretty small.

00:26:22.440 | And, but that's the end, that's what things are made of.

00:26:27.020 | - What's your intuition

00:26:28.100 | where the 10 to the minus 100 comes from?

00:26:31.180 | What's your intuition about this scale?

00:26:33.300 | - Well, okay, so there's a calculation

00:26:35.220 | which I consider to be somewhat rickety, okay?

00:26:37.980 | Which has to do with comparing,

00:26:40.460 | so there are various fundamental constants.

00:26:42.940 | There's the speed of light,

00:26:44.220 | the speed of light, once you know the elementary time,

00:26:47.080 | the speed of light tells you the conversion

00:26:49.660 | from the elementary time to the elementary length.

00:26:52.360 | Then there's the question of how do you convert

00:26:54.140 | to the elementary energy?

00:26:55.940 | And how do you convert to, between other things?

00:26:58.700 | And the various constants we know,

00:27:00.220 | we know the speed of light,

00:27:01.140 | we know the gravitational constant,

00:27:03.460 | we know Planck's constant in quantum mechanics,

00:27:05.860 | those are the three important ones.

00:27:07.700 | And we actually know some other things,

00:27:09.620 | we know things like the size of the universe,

00:27:11.820 | the Hubble constant, things like that.

00:27:14.080 | And essentially this calculation of the elementary length

00:27:17.860 | comes from looking at the sort of combination of those,

00:27:21.340 | okay, so the most obvious thing,

00:27:23.080 | people have sort of assumed that quantum gravity

00:27:25.540 | happens at this thing, the Planck scale,

00:27:27.260 | 10 to the minus 34 meters,

00:27:28.980 | which is the sort of the combination of Planck's constant

00:27:32.660 | and the gravitational constant, the speed of light,

00:27:34.700 | that gives you that kind of length.

00:27:36.480 | Turns out in our model, there is an additional parameter,

00:27:41.520 | which is essentially the number of simultaneous threads

00:27:44.260 | of execution of the universe,

00:27:46.140 | which is essentially the number of sort of

00:27:47.640 | independent quantum processes that are going on.

00:27:51.220 | And that number, let's see if I remember that number,

00:27:53.420 | that number is 10 to the 170, I think,

00:27:55.660 | and so it's a big number,

00:27:57.900 | but that number then connects,

00:28:01.960 | sort of modifies what you might think

00:28:04.180 | from all these Planck units

00:28:07.360 | to give you the things we're giving.

00:28:08.540 | And there's been sort of a mystery actually,

00:28:10.060 | and there's a more technical physics thing,

00:28:12.720 | that the Planck mass, the Planck energy,

00:28:16.740 | Planck energy is actually surprisingly big.

00:28:19.100 | The Planck length is tiny, 10 to the minus 34 meters,

00:28:21.540 | the Planck time, 10 to the minus 43 meters, I think,

00:28:24.500 | that seconds, I think,

00:28:26.420 | but the Planck energy is like the energy

00:28:30.180 | of a lightning strike, okay, which is pretty weird.

00:28:33.940 | In our models, the actual elementary energy

00:28:36.760 | is that divided by the number of sort of

00:28:38.940 | simultaneous quantum threads,

00:28:40.880 | and it ends up being really small too.

00:28:42.860 | And that sort of explains that mystery

00:28:44.680 | that's been around for a while

00:28:46.220 | about how Planck units work.

00:28:49.000 | But whether that precise estimate is right,

00:28:52.540 | we don't know yet.

00:28:53.380 | I mean, that's one of the things

00:28:54.780 | that's sort of been a thing we've been pretty interested in

00:28:57.660 | is how do you see through,

00:28:59.740 | how do you make a gravitational microscope

00:29:02.520 | that can kind of see through to the atoms of space?

00:29:05.860 | You know, how do you get, in fluid flow, for example,

00:29:08.580 | if you go to hypersonic flow or something,

00:29:10.420 | you know, you've got a Mark 20,

00:29:12.260 | you know, space plane or something,

00:29:13.980 | it really matters that there are individual molecules

00:29:16.860 | hitting the space plane, not a continuous fluid.

00:29:19.800 | The question is, what is the analogous kind of,

00:29:22.420 | what is the analog of hypersonic flow

00:29:24.620 | for things about the structure of space-time?

00:29:28.780 | And it looks like a rapidly rotating black hole, right,

00:29:33.260 | at the sort of critical rotation rate,

00:29:38.020 | it looks as if that's a case where essentially

00:29:40.820 | the structure of space-time is just about to fall apart.

00:29:44.900 | And you may be able to kind of see the evidence

00:29:48.780 | of sort of discrete elements, you know,

00:29:52.080 | you may be able to kind of see there

00:29:54.220 | the sort of gravitational microscope

00:29:55.920 | of actually seeing these discrete elements of space.

00:29:58.840 | And there may be some effect in, for example,

00:30:01.380 | gravitational waves produced by rapidly rotating black hole

00:30:05.620 | that in which one could actually see some phenomenon

00:30:08.300 | where one can say, yes,

00:30:09.860 | these don't come out the way one would expect

00:30:12.340 | based on having a continuous structure of space-time,

00:30:15.900 | that is it something where you can kind of see through

00:30:18.140 | to the discrete structure?

00:30:20.020 | We don't know that yet.

00:30:20.980 | - So can you maybe elaborate a little bit deeper

00:30:23.740 | how a microscope that can see to 10 to the minus 100,

00:30:28.740 | how rotating black holes and presumably

00:30:32.980 | the detailed accurate detection of gravitational waves

00:30:37.980 | from such black holes can reveal the discreteness of space?

00:30:42.900 | - Okay, first thing is what is a black hole?

00:30:44.980 | Actually, we need to go a little bit further

00:30:47.140 | in the story of what space-time is

00:30:48.700 | 'cause I explained a little bit about what space is,

00:30:50.780 | but I didn't talk about what time is.

00:30:52.700 | And that's sort of important

00:30:53.940 | in understanding space-time, so to speak.

00:30:56.580 | - And your sense is both space and time

00:30:58.620 | in the story are discrete.

00:31:00.020 | - Absolutely, absolutely.

00:31:01.860 | But it's a complicated story.

00:31:03.740 | And needless to say.

00:31:05.540 | - Well, it's simple at the bottom.

00:31:07.260 | - It's very simple at the bottom.

00:31:09.220 | It's very, in the end, it's simple but deeply abstract.

00:31:13.860 | And something that is simple in conception,

00:31:18.460 | but kind of wrapping one's head around what's going on

00:31:21.060 | is pretty hard.

00:31:22.280 | But so first of all, we have this,

00:31:25.460 | so I've described these kind of atoms of space

00:31:27.940 | and their connections.

00:31:29.180 | You can think about these things as a hypergraph,

00:31:31.660 | a graph is just, you connect nodes to nodes,

00:31:34.140 | but a hypergraph, you can have sort of not just friends,

00:31:38.980 | individual friends to friends,

00:31:40.180 | but you can have these triplets of friends or whatever else.

00:31:43.580 | And so we're just saying,

00:31:45.980 | and that's just the relations between atoms of space

00:31:48.940 | are the hyper edges of the hypergraph.

00:31:50.940 | And so we got some big collection of these atoms of space,

00:31:54.000 | maybe 10 to the 400 or something in our universe.

00:31:57.820 | And that's the structure of space.

00:32:00.180 | That's an every feature of what we experience in the world

00:32:04.740 | is a feature of that hypergraph, that spatial hypergraph.

00:32:09.100 | So then the question is,

00:32:09.980 | well, what does that spatial hypergraph do?

00:32:13.020 | Well, the idea is that there are rules

00:32:15.780 | that update that spatial hypergraph.

00:32:18.540 | And in a cellular automaton,

00:32:19.940 | you've just got this line of cells

00:32:21.780 | and you just say at every step, at every time step,

00:32:24.460 | you've got fixed time steps, fixed array of cells.

00:32:27.220 | At every step, every cell gets updated

00:32:29.940 | according to a certain rule.

00:32:31.500 | And that's kind of the, that's the way it works.

00:32:34.360 | Now in this hypergraph,

00:32:35.780 | it's sort of vaguely the same kind of thing.

00:32:38.660 | We say, every time you see a little piece of hypergraph

00:32:41.140 | that looks like this, update it to one that looks like this.

00:32:45.060 | So it's just keep rewriting this hypergraph.

00:32:47.460 | Every time you see something that looks like that,

00:32:49.320 | anywhere in the universe, it gets rewritten.

00:32:52.020 | Now, one thing that's tricky about that,

00:32:53.880 | which we'll come to is this multi-computational idea,

00:32:56.700 | which has to do with, you're not saying

00:32:59.220 | in some kind of lockstep way,

00:33:01.220 | do this one, then this one, then this one.

00:33:03.380 | It's just whenever you see one you can do,

00:33:05.760 | you can go ahead and do it.

00:33:07.260 | And that leads one not to have a single thread of time

00:33:10.020 | in the universe.

00:33:11.260 | Because if you knew which one to do,

00:33:13.760 | you just say, okay, we do this one,

00:33:15.140 | then we do this one, then we do this one.

00:33:16.860 | But if you say, just do whichever one you feel like,

00:33:19.260 | you end up with these multiple threads of time,

00:33:21.180 | these kind of multiple histories of the universe,

00:33:23.180 | depending on which order you happen to do

00:33:24.980 | the things you could do in.

00:33:27.300 | - So it's fundamentally asynchronous and parallel.

00:33:29.900 | - Yes, yes.

00:33:31.100 | - Which is very uncomfortable for the human brain

00:33:33.520 | that seeks for things to be sequential and synchronous.

00:33:37.740 | - Right, well, I think that this is part

00:33:40.500 | of the story of consciousness,

00:33:42.620 | is I think the key aspect of consciousness

00:33:45.620 | that is important for parsing the universe

00:33:48.620 | is this point that we have a single thread of experience.

00:33:52.380 | We have a memory of what happened in the past,

00:33:54.420 | we can say something, predict something about the future,

00:33:57.160 | but there's a single thread of experience.

00:33:58.500 | And it's not obvious it should work that way.

00:34:00.300 | I mean, we've got 100 billion neurons in our brains

00:34:02.500 | and they're all firing at all kinds of different ways,

00:34:04.660 | but yet our experience is that there is the single thread

00:34:09.140 | of time that goes along.

00:34:12.740 | And I think that one of the things I've kind of realized

00:34:15.380 | with a lot more clarity in the last year

00:34:17.440 | is the fact that we conclude that the universe

00:34:21.820 | has the laws it has as a consequence of the fact

00:34:24.940 | that we have consciousness the way we have consciousness.

00:34:28.500 | And so the fact, so I mean, just to go on

00:34:31.100 | with kind of the basic setup,

00:34:33.180 | it's so we've got this spatial hypergraph,

00:34:35.500 | it's got all these atoms of space,

00:34:37.500 | they're getting these little clumps of atoms of space

00:34:40.220 | are getting turned into other clumps of atoms of space,

00:34:41.980 | and that's happening everywhere in the universe all the time.

00:34:44.620 | And so one thing that's a little bit weird

00:34:46.060 | is there's nothing permanent in the universe.

00:34:48.620 | The universe is getting rewritten everywhere all the time.

00:34:51.260 | And if it wasn't getting rewritten,

00:34:52.860 | space wouldn't be knitted together.

00:34:54.780 | That is space would just fall apart.

00:34:56.540 | There wouldn't be any way in which we could say

00:34:58.740 | this part of space is next to this part of space.

00:35:01.380 | You know, one of the things that I was,

00:35:03.720 | people were confused about back in antiquity,

00:35:06.700 | the ancient Greek philosophers and so on,

00:35:08.500 | is how does motion work?

00:35:10.660 | You know, how can it be the case that you can take a thing

00:35:13.120 | that we can walk around and it's still us

00:35:15.500 | when we walked a foot forward, so to speak.

00:35:18.620 | And in a sense with our models, that's again a question

00:35:22.380 | because it's a different set of atoms of space.

00:35:24.800 | When I move my hand,

00:35:27.180 | it's moving into a different set of atoms of space.

00:35:30.220 | It's having to be recreated.

00:35:31.660 | It's not the thing itself is not there.

00:35:34.180 | It's being continuously recreated all the time.

00:35:37.020 | Now it's a little bit like waves in an ocean,

00:35:39.020 | you know, vortices in a fluid,

00:35:40.740 | which again, the actual molecules that exist in those

00:35:44.060 | are not what define the identity of the thing.

00:35:47.380 | But it's a little bit, you know,

00:35:49.980 | this idea that there can be pure motion,

00:35:52.460 | that it is even possible for an object

00:35:55.460 | to just move around in the universe and not change.

00:35:58.940 | It's not self-evident that such a thing should be possible.

00:36:01.940 | And that is part of our perception of the universe

00:36:04.700 | is that we parse those aspects of the universe

00:36:07.980 | where things like pure motion are possible.

00:36:10.220 | Now, pure motion, even in general relativity,

00:36:12.500 | the theory of gravity,

00:36:14.620 | pure motion is a little bit of a complicated thing.

00:36:16.820 | I mean, if you imagine your average, you know,

00:36:19.620 | teacup or something approaching a black hole,

00:36:21.900 | it is deformed and distorted by the structure of space time.

00:36:25.180 | And to say, you know, is it really pure motion?

00:36:27.700 | Is it that same teacup that's the same shape?

00:36:29.780 | Well, it's a bit of a complicated story.

00:36:32.020 | And this is a more extreme version of that.

00:36:34.820 | So anyway, the thing that's happening is we've got space,

00:36:38.980 | we've got this notion of time.

00:36:41.100 | So time is this kind of this rewriting of the hypergraph.

00:36:45.100 | And one of the things that's important about that,

00:36:46.780 | time is this sort of computational irreducible process.

00:36:50.140 | There's something, you know, time is not something where,

00:36:53.300 | in kind of the mathematical view of time,

00:36:56.180 | tends to be time is just a coordinate.

00:36:57.980 | We can, you know, slide a slider, turn a knob,

00:37:01.620 | and we'll change the time that we've got in this equation.

00:37:04.740 | But in this picture of time, that's not how it works at all.

00:37:08.020 | Time is this inexorable, irreducible

00:37:11.620 | kind of set of computations that go on,

00:37:13.740 | that go from where we are now to the future.

00:37:16.860 | But so the thing, and one of the things that is, again,

00:37:20.340 | something one sort of has to break out of

00:37:22.460 | is your average trained physicist like me says,

00:37:25.380 | you know, space and time are the same kind of thing.

00:37:27.180 | They're related by, you know, the Poincaré group

00:37:30.380 | and Lorentz transformations and relativity

00:37:32.820 | and all these kinds of things.

00:37:34.300 | And, you know, space and time, you know,

00:37:37.180 | there are all these kind of sort of folk stories

00:37:38.940 | you can tell about why space and time

00:37:40.620 | are the same kind of thing.

00:37:42.100 | In this model, they're fundamentally

00:37:43.500 | not the same kind of thing.

00:37:44.940 | Space is this kind of sort of connections

00:37:47.740 | between these atoms of space.

00:37:49.420 | Time is this computational process.

00:37:51.620 | So the thing that the first sort of surprising thing

00:37:54.820 | is, well, it turns out you get relativity anyway.

00:37:57.460 | And the reason that happens,

00:37:58.900 | there are a few bits and pieces here,

00:38:00.820 | which one has to understand,

00:38:01.980 | but the fundamental point is,

00:38:04.700 | if you are an observer embedded in the system

00:38:08.460 | that are part of this whole story

00:38:10.580 | of things getting updated in this way and that,

00:38:13.580 | there's sort of a limit to what you can tell

00:38:15.980 | about what's going on.

00:38:17.420 | And really in the end, the only thing you can tell

00:38:19.340 | is what are the causal relationships between events.

00:38:23.020 | So an event in this sort of,

00:38:25.740 | an elementary event is a little piece of hypergraph

00:38:29.060 | got rewritten.

00:38:30.100 | And that means a few hyper edges of the hypergraph

00:38:32.780 | were consumed by the event

00:38:34.860 | and you produce some other hyper edges.

00:38:36.860 | And that's an elementary event.

00:38:38.780 | And so then the question is what we can tell

00:38:42.140 | is kind of what the network of causal relationships

00:38:45.300 | between elementary events is.

00:38:47.300 | That's the ultimate thing, the causal graph of the universe.

00:38:50.580 | And it turns out that,

00:38:52.500 | well, there's this property of causal invariance

00:38:55.220 | that is true of a bunch of these models.

00:38:57.580 | And I think is inevitably true for a variety of reasons

00:39:01.420 | that makes it be the case that it doesn't matter

00:39:05.580 | kind of if you are sort of saying,

00:39:07.980 | well, I've got this hypergraph

00:39:09.300 | and I can rewrite this piece here and this piece here

00:39:11.740 | and I do them all in different orders.

00:39:13.540 | When you construct the causal graph

00:39:15.100 | for each of those orders that you choose to do things in,

00:39:19.140 | you'll end up with the same causal graph.

00:39:21.420 | And so that's essentially why,

00:39:24.460 | well, that's in the end why relativity works.

00:39:27.020 | It's why our perception of space and time

00:39:29.900 | is as having this kind of connection

00:39:32.940 | that relativity says they should have.

00:39:35.060 | And that's kind of how that works.

00:39:37.940 | - I think I'm missing a little piece.

00:39:39.580 | If we can go there again,

00:39:41.020 | you said the fact that the observer is embedded

00:39:44.100 | in this hypergraph, what's missing?

00:39:47.300 | What is the observer not able to state

00:39:50.540 | about this universe of space and time?

00:39:52.780 | - So if you look from the outside,

00:39:54.460 | you can say, oh, I see this particular place was updated

00:39:59.460 | and then this one was updated

00:40:04.100 | and I'm seeing which order things were updated in.

00:40:07.100 | But the observer embedded in the universe

00:40:08.940 | doesn't know which order things were updated in

00:40:10.860 | because until they've been updated,

00:40:13.020 | they have no idea what else happened.

00:40:14.900 | So the only thing they know

00:40:16.380 | is the set of causal relationships.

00:40:18.660 | Let me give an extreme example.

00:40:20.340 | Let's imagine that the universe is a Turing machine.

00:40:23.060 | Turing machines have just this one update head,

00:40:26.380 | which does something

00:40:27.700 | and otherwise the Turing machine just does nothing.

00:40:30.420 | And the Turing machine works by having this head

00:40:32.620 | move around and do its updating,

00:40:35.260 | just where the head happens to be.

00:40:37.260 | The question is, could the universe be a Turing machine?

00:40:39.820 | Could the universe just have a single updating head

00:40:42.300 | that's just zipping around all over the place?

00:40:44.220 | You say, that's crazy because I'm talking to you,

00:40:47.300 | you seem to be updating, I'm updating, et cetera.

00:40:50.460 | But the thing is, there's no way to know that

00:40:52.460 | because if there was just this head moving around,

00:40:54.780 | it's like, okay, it updates me,

00:40:56.820 | but you're completely frozen at that point.

00:40:59.100 | Until the head has come over and updated you,

00:41:01.380 | you have no idea what happened to me.

00:41:03.420 | And so if you sort of unravel that argument,

00:41:05.700 | you realize the only thing we actually can tell

00:41:08.380 | is what the network of causal relationships

00:41:11.540 | between the things that happened were.

00:41:13.460 | We don't get to know from some sort of outside

00:41:16.820 | sort of God's eye view of the thing.

00:41:18.940 | We don't get to know what sort of

00:41:21.580 | from the outside what happened.

00:41:23.660 | We only get to know sort of what the set of relationships

00:41:27.580 | between the things that happened actually were.

00:41:29.780 | - Yeah, but if I somehow record like a trace

00:41:33.020 | of this, I guess would be called multi-computation,

00:41:37.020 | can't I then look back in the-

00:41:40.740 | - Where do you record the trace?

00:41:42.820 | - Some, you place throughout the universe,

00:41:45.020 | like throughout like a log that records

00:41:49.580 | in my own pocket in this hypergraph,

00:41:52.060 | can't I like realizing that I'm getting an outdated picture,

00:41:57.060 | can't I record-

00:41:59.700 | - See, the problem is,

00:42:00.540 | and this is where things start getting very entangled

00:42:04.100 | in terms of what one understands.

00:42:06.220 | The problem is that any such recording device

00:42:09.460 | is itself part of the universe.

00:42:11.820 | So you don't get to say, you never get to say,

00:42:14.980 | let's go outside the universe and go do this.

00:42:17.660 | And that's why, I mean, lots of the features of this model

00:42:21.740 | and the way things work end up being a result of that.

00:42:24.740 | - So, but what, I guess from on a human level,

00:42:27.940 | what is the cost you're paying?

00:42:30.100 | What are you missing from not getting

00:42:32.180 | an updated picture all the time?

00:42:34.300 | Okay, I understand what you're just saying.

00:42:36.020 | - Yeah, yeah, right.

00:42:36.860 | - But like what, like how does consciousness

00:42:38.700 | emerge from that?

00:42:40.020 | Like how, like what are the limitations of that observer?

00:42:44.420 | I understand you're getting a delayed picture.

00:42:46.220 | - Well, there's a, okay,

00:42:47.540 | so there's a bunch of limitations of the observer, I think.

00:42:51.540 | Maybe just explain something about quantum mechanics,

00:42:53.620 | 'cause that maybe is an extreme version

00:42:55.860 | of some of these issues,

00:42:57.060 | which helps to kind of motivate

00:42:59.020 | why one should sort of think things through

00:43:00.740 | a little bit more carefully.

00:43:02.220 | So one feature of this, okay,

00:43:05.340 | so in standard physics, like high school physics,

00:43:09.260 | you learn the equations of motion for a ball.

00:43:12.020 | And it says, you throw the ball this angle, this velocity,

00:43:16.940 | things will move in this way,

00:43:18.140 | and there's a definite answer, right?

00:43:20.380 | The story, the key story of quantum mechanics

00:43:22.860 | is there aren't definite answers to where does the ball go?

00:43:25.580 | There's kind of this whole sort of bundle of possible paths.

00:43:29.140 | And all we say we know from quantum mechanics

00:43:32.180 | is certain probabilities for where the ball will end up.

00:43:35.740 | Okay, so that's kind of the core idea of quantum mechanics.

00:43:38.420 | So in our models, you, quantum mechanics

00:43:41.260 | is not some kind of plugin add-on type thing.

00:43:44.500 | You absolutely cannot get away from quantum mechanics,

00:43:46.660 | because as you think about updating this hypergraph,

00:43:49.580 | there isn't just one sequence of things,

00:43:51.900 | one definite sequence of things that can happen.

00:43:53.980 | There are all these different possible update sequences

00:43:56.300 | that can occur.

00:43:57.260 | You could do this piece of the hypergraph now,

00:43:59.500 | and then this one later, and et cetera, et cetera, et cetera.

00:44:02.420 | All those different paths of history

00:44:04.540 | correspond to these quantum paths in quantum mechanics,

00:44:08.460 | these different possible quantum histories.

00:44:10.860 | And one of the things that's kind of surprising about it

00:44:12.860 | is they branch, you know,

00:44:15.500 | there can be a certain state of the universe,

00:44:17.740 | and it could do this, or it could do that,

00:44:20.020 | but they can also merge.

00:44:21.540 | There can be two states of the universe,

00:44:23.020 | which their next state,

00:44:25.100 | the next state they produce is the same for both of them.

00:44:27.980 | And that process of branching and merging

00:44:30.060 | is kind of critical,

00:44:30.900 | and the idea that they can be merging is critical,

00:44:33.220 | and somewhat non-trivial for these hypergraphs,

00:44:35.140 | because there's a whole graph isomorphism story,

00:44:37.740 | and there's a whole very elaborate set of mathematics.

00:44:40.300 | - And that's where the causal invariance comes in?

00:44:42.180 | - Yes, among other things, right, yes.

00:44:44.700 | But so then what happens is that what one's seeing,

00:44:49.700 | okay, so we've got this thing,

00:44:51.900 | it's branching, it's merging, et cetera, et cetera, et cetera.

00:44:54.180 | Okay, so now the question is, how do we perceive that?

00:44:57.540 | Why don't we notice that the universe

00:45:01.820 | is branching and merging?

00:45:03.420 | Why is it the case that we just think

00:45:05.500 | a definite set of things happen?

00:45:07.360 | Well, the answer is we are embedded in that universe,

00:45:10.660 | and our brains are branching and merging too.

00:45:13.580 | And so what quantum mechanics becomes a story of

00:45:16.300 | is how does a branching brain perceive a branching universe?

00:45:20.460 | And the key thing is, as soon as you say,

00:45:23.820 | "I think definite things happen in the universe,"

00:45:26.360 | that means you are essentially conflating

00:45:28.820 | lots of different parts of history.

00:45:30.700 | You're saying, "Actually, as far as I'm concerned,

00:45:33.540 | "because I'm convinced that definite things happen

00:45:36.040 | "in the universe, all these parts of history

00:45:38.040 | "must be equivalent."

00:45:39.380 | Now, it's not obvious that that would be

00:45:40.940 | a consistent thing to do.

00:45:42.420 | It might be you say, "All these parts of history

00:45:43.980 | "are equivalent, but by golly, moments later,

00:45:47.320 | "that would be a completely inconsistent point of view.

00:45:49.140 | "Everything would have gone to hell in different ways."

00:45:52.500 | The fact that that doesn't happen is,

00:45:54.700 | well, that's a consequence of this causal invariance thing,

00:45:57.260 | but that's, and the fact that that does happen a little bit

00:46:00.340 | is what causes little quantum effects.

00:46:02.700 | And that, if that didn't happen at all,

00:46:05.220 | there wouldn't be anything that sort of

00:46:07.860 | is like quantum mechanics.

00:46:09.460 | It would be, quantum mechanics is kind of like in this,

00:46:13.300 | in this kind of this bundle of paths,

00:46:15.840 | it's a little bit like what happens

00:46:17.100 | in statistical mechanics and fluid mechanics, whatever,

00:46:19.700 | that most of the time, you just see this continuous fluid.

00:46:22.380 | You just see the world just progressing

00:46:24.540 | in this kind of way that's like this continuous fluid.

00:46:26.620 | But every so often, if you look at the exact right

00:46:28.560 | experiment, you can start seeing,

00:46:30.500 | well, actually, it's made of these molecules

00:46:32.360 | where they might go that way or they might go this way,

00:46:34.700 | and that's kind of quantum effects.

00:46:36.600 | And so, that's, so this kind of idea of

00:46:40.980 | where we're sort of embedded in the universe,

00:46:43.060 | this branching brain is perceiving this branching universe,

00:46:46.700 | and that ends up being sort of a story of quantum mechanics.

00:46:49.420 | That's part of the whole picture of what's going on.

00:46:52.780 | But I think, I mean, to come back to sort of

00:46:55.180 | where does conscious, what is the story of consciousness?

00:46:58.020 | So, in the universe, we've got, you know,

00:47:01.260 | whatever it is, 10 to the 400 atoms of space,

00:47:03.360 | they're all doing these complicated things.

00:47:05.420 | It's all a big, complicated, irreducible computation.

00:47:08.500 | The question is, what do we perceive from all of that?

00:47:11.800 | And the answer is that we are parsing the universe

00:47:16.800 | in a particular way.

00:47:18.460 | Let me again go back to the gas molecules analogy.

00:47:21.700 | You know, in the gas in this room,

00:47:24.200 | there are molecules bouncing around

00:47:25.400 | in all kinds of complicated patterns, but we don't care.

00:47:28.440 | All we notice is there's, you know,

00:47:31.120 | the gas laws are satisfied,

00:47:33.120 | maybe there's some fluid dynamics.

00:47:35.080 | These are kind of features of that assembly of molecules

00:47:38.500 | that we notice, and there are lots of details

00:47:40.640 | we don't notice.

00:47:41.680 | - When you say we, do you mean the tools of physics,

00:47:43.840 | or do you mean literally the human brain

00:47:45.880 | and its perception system?

00:47:47.720 | - Well, okay, so the human brain is where it starts,

00:47:50.440 | but we've built a bunch of instruments

00:47:51.760 | to do a bit better than the human brain,

00:47:53.520 | but they still have many of the same kinds of ideas.

00:47:55.800 | You know, they're cameras, and they're pressure sensors,

00:47:58.420 | and they're these kinds of things.

00:48:00.060 | They're not, you know, at this point,

00:48:02.200 | we don't know how to make fundamentally, qualitatively

00:48:05.760 | different sensory devices.

00:48:07.440 | - Right, so it's always just an extension

00:48:09.640 | of the conscious experience.

00:48:11.720 | - Or our sensory experience.

00:48:13.640 | - Sensory experience, but sensory experience

00:48:17.440 | is somehow intricately tied to consciousness.

00:48:20.440 | - Right, well, so one question is,

00:48:22.240 | when we are looking at all these molecules in the gas,

00:48:24.800 | and there might be 10th to 20th molecules

00:48:26.480 | in some little box or something,

00:48:28.780 | it's like, what do we notice about those molecules?

00:48:32.160 | So one thing that we can say is,

00:48:33.760 | we don't notice that much.

00:48:35.640 | We are, you know, we are computationally bounded observers.

00:48:39.980 | We can't go in and say, okay,

00:48:42.520 | I'm the 10th to 20th molecules,

00:48:44.360 | and I know that I can sort of decrypt their motions,

00:48:47.200 | and I can figure out this and that.

00:48:48.840 | It's like, I'm just going to say,

00:48:49.960 | what's the average density of molecules?

00:48:51.960 | And so one key feature of us

00:48:54.360 | is that we are computationally bounded,

00:48:56.520 | and that when you are looking at a universe,

00:48:59.080 | which is full of computation,

00:49:00.920 | and doing huge amounts of computation,

00:49:03.200 | but we are computationally bounded,

00:49:05.480 | there's only certain things about that universe

00:49:07.400 | that we're going to be sensitive to.

00:49:08.920 | We're not going to be figuring out

00:49:11.220 | what all the atoms of space are doing,

00:49:13.200 | because we're just computationally bounded observers,

00:49:15.960 | and we are only sampling these small set of features.

00:49:20.960 | So I think the two defining features of consciousness,

00:49:23.800 | and I would say that the sort of the preamble to this is,

00:49:28.800 | for years, as I've talked about sort of computation

00:49:31.760 | and fundamental features of physics and science,

00:49:34.480 | people ask me, so what about consciousness?

00:49:37.040 | And I, for years, I've said,

00:49:38.680 | I have nothing to say about consciousness.

00:49:40.800 | And I've kind of told this story,

00:49:43.080 | you talk about intelligence, you talk about life.

00:49:46.400 | These are both features where you say,

00:49:48.520 | what's the abstract definition of life?

00:49:50.200 | We don't really know the abstract definition.

00:49:51.760 | We know the one for life on Earth,

00:49:53.440 | it's got RNA, it's got cell membranes,

00:49:55.400 | it's got all this kind of stuff.

00:49:57.080 | Similarly for intelligence,

00:49:58.200 | we know the human definition of intelligence,

00:50:00.760 | but what is intelligence abstractly?

00:50:02.640 | We don't really know.

00:50:03.840 | And so what I've long believed is that

00:50:06.400 | sort of the abstract definition of intelligence

00:50:08.720 | is just computational sophistication.

00:50:11.280 | That is, that as soon as you can be

00:50:13.200 | computationally sophisticated,

00:50:14.940 | that's kind of the abstract version,

00:50:17.400 | the generalized version of intelligence.

00:50:19.840 | So then the question is, what about consciousness?

00:50:22.040 | And what I sort of realized is that consciousness

00:50:24.440 | is actually a step down from intelligence.

00:50:27.520 | That is, that you might think,

00:50:29.880 | oh, consciousness is the top of the pile,

00:50:34.320 | but actually I don't think it is.

00:50:35.740 | I think that there's this notion

00:50:37.240 | of kind of computational sophistication,

00:50:38.960 | which is the generalized intelligence,

00:50:41.440 | but consciousness has two limitations, I think.

00:50:44.840 | One of them is computational boundedness.

00:50:47.160 | That is, that we're only perceiving

00:50:49.020 | a sort of computationally bounded view of the universe.

00:50:52.680 | And the other is this idea of a single thread of time.

00:50:55.560 | That is, that we, and in fact, we know,

00:50:58.240 | neurophysiologically, our brains go to some trouble

00:51:01.240 | to give us this one thread of attention, so to speak.

00:51:04.480 | And it isn't the case that in all the neurons in our brains,

00:51:07.720 | that at least in our conscious,

00:51:10.720 | note the correspondence of language,

00:51:12.800 | in our conscious experience,

00:51:14.680 | we just have this single thread of attention,

00:51:16.660 | single thread of perception.

00:51:19.120 | And maybe there's something unconscious

00:51:21.540 | that's bubbling around that's the kind of

00:51:23.840 | almost the quantum version of what's happening

00:51:25.600 | in our brain, so to speak.

00:51:26.760 | We've got the classical flow

00:51:29.080 | of what we are mostly thinking about, so to speak.

00:51:32.200 | But there's this kind of bubbling around of other paths

00:51:34.960 | that is all those other neurons that didn't make it

00:51:37.280 | to be part of our sort of conscious stream of experience.

00:51:40.780 | - So in that sense, intelligence

00:51:42.940 | as computational sophistication is much broader

00:51:46.280 | than the computational constraints

00:51:51.280 | which consciousness operates under,

00:51:53.760 | and also the sequential thing.

00:51:56.520 | - Yes, right. - Like the notion of time.

00:51:59.120 | That's kind of interesting,

00:51:59.960 | but then the follow-up question is like,

00:52:02.280 | okay, starting to get a sense of what is intelligence,

00:52:05.200 | and how does that connect to our human brain?

00:52:07.240 | 'Cause you're saying intelligence is almost like a fabric,

00:52:12.240 | like what, we like plug into it or something?

00:52:15.000 | Like our consciousness plugs into it?

00:52:18.320 | - Yeah, I mean, the intelligence, I think, the core,

00:52:22.060 | I mean, intelligence at some level is just a word,

00:52:24.540 | but we are asking what is the notion of intelligence

00:52:28.640 | as we generalize it beyond the bounds of humans,

00:52:30.920 | beyond the bounds of even the AIs

00:52:33.080 | that we humans have built and so on, what is intelligence?

00:52:38.000 | Is the weather, people say the weather

00:52:39.960 | has a mind of its own, what does that mean?

00:52:41.920 | Can the weather be intelligent?

00:52:43.920 | - Yeah, what does agency have to do with intelligence here?

00:52:47.000 | So is intelligence just like your conception of computation?

00:52:50.440 | Is just intelligence, is the capacity

00:52:54.260 | to perform computation in a sea of?

00:52:56.980 | - Yeah, I think so.

00:52:57.820 | I mean, I think that's right,

00:52:58.900 | and I think that this question of is it for a purpose,

00:53:03.900 | that quickly degenerates into a horrible philosophical mess

00:53:08.220 | because whenever you say,

00:53:10.540 | did the weather do that for a purpose?

00:53:12.900 | - Yeah. - Right?

00:53:13.860 | Well, yes, it did, it was trying to move a bunch of hot air

00:53:16.260 | from the equator to the poles or something,

00:53:18.580 | that's its purpose.

00:53:19.820 | But why, 'cause I seem to be equally as dumb today

00:53:23.700 | as I was yesterday, so there's some persistence,

00:53:26.620 | like a consistency over time

00:53:29.840 | that the intelligence I plugged into.

00:53:32.540 | So it seems like there's a hard constraint

00:53:35.620 | between the amount of computation

00:53:38.620 | I can perform in my consciousness.

00:53:40.980 | Like they seem to be really closely connected somehow.

00:53:43.380 | - Well, I think the point is that the thing

00:53:45.740 | that gives you kind of the ability

00:53:47.840 | to have kind of conscious intelligence,

00:53:52.840 | you can have kind of this, okay,

00:53:54.660 | so one thing is we don't know intelligences

00:53:58.180 | other than the ones that are very much like us, right?

00:54:01.900 | And the ones that are very much like us,

00:54:04.020 | I think have this feature of single thread of time,

00:54:06.900 | bounded, computationally bounded.

00:54:09.400 | Now, that, but you also need computational sophistication.

00:54:13.460 | Having a single thread of time

00:54:15.020 | and being computationally bounded,

00:54:16.720 | you could just be a clock going tick-tock, you know,

00:54:19.920 | that would satisfy those conditions.

00:54:21.900 | But the fact that we have this sort of irreducible,

00:54:26.900 | you know, computational ability,

00:54:29.040 | that's an important feature.

00:54:31.340 | That's the sort of the bedrock

00:54:33.540 | on which we can construct the things we construct.

00:54:35.860 | Now, the fact that we have this experience of the world

00:54:40.500 | that has a single thread of time

00:54:41.960 | and computational boundedness,

00:54:43.680 | the thing that I sort of realized is

00:54:46.020 | it's that that causes us to deduce

00:54:49.620 | from this irreducible mess of what's going on

00:54:52.060 | in the physical world,

00:54:53.600 | the laws of physics that we think exist.

00:54:56.820 | So in other words, if we say,

00:54:59.180 | why do we believe that there is, you know,

00:55:02.500 | continuous space, let's say,

00:55:04.060 | why do we believe that gravity works the way it does?

00:55:07.440 | Well, in principle,

00:55:09.120 | we could be kind of parsing details of the universe

00:55:12.740 | that were, you know, that,

00:55:15.740 | okay, the analogy is, again,

00:55:18.300 | with the statistical mechanics and molecules in a box,

00:55:22.640 | we could be sensitive to every little detail

00:55:25.500 | of the swirling around of those molecules.

00:55:27.020 | And we could say, what really matters is the,

00:55:30.180 | you know, the wiggle effect.

00:55:31.740 | - Yes. - That is, you know,

00:55:33.020 | that is something that we humans just never noticed

00:55:35.260 | because it's some weird thing that happens

00:55:37.420 | when there are 15 collisions of air molecules

00:55:40.400 | and this happens and that happens.

00:55:41.860 | - We just see the pure motion of a ball moving about.

00:55:45.260 | - Right. - Why do we see that?

00:55:47.180 | - Right, and the point is that what seems to be the case

00:55:50.780 | is that the things that,

00:55:52.700 | if we say, given this sort of hypergraph that's updating

00:55:55.860 | and all the details about all the sort of,

00:55:58.700 | sort of atoms of space and what they do,

00:56:00.300 | and we say, how do we slice that

00:56:02.180 | to what we can be sensitive to?

00:56:04.200 | What seems to be the case is that as soon as we assume,

00:56:07.380 | you know, computational boundedness,

00:56:09.540 | single thread of time, that leads us to general relativity.

00:56:13.100 | In other words, we can't avoid that.

00:56:14.460 | That's the way that we will parse the universe.

00:56:18.060 | Given those constraints, we parse the universe

00:56:20.700 | according to those particular,

00:56:23.220 | in such a way that we say the aggregate reducible,

00:56:27.860 | sort of pocket of computational reducibility

00:56:31.620 | that we slice out of this kind of whole

00:56:34.380 | computationally irreducible ocean of behavior

00:56:37.580 | is just this one that corresponds to general relativity.

00:56:39.900 | - Yeah, but we don't perceive general relativity.

00:56:42.860 | - Well, we do if we do fancy experiments.

00:56:45.180 | - So you're saying, so perceive really does mean the full.

00:56:48.020 | - We drop something.

00:56:49.060 | That's a great example of general relativity in action.

00:56:51.700 | The gravity force. - No, but like,

00:56:52.740 | what's the difference in that and Newtonian mechanics?

00:56:55.380 | I mean, what? - Oh, it doesn't,

00:56:56.580 | this is, when I say general relativity,

00:56:58.660 | that's just the-- - You mean gravity.

00:57:00.140 | - The Uber theory, so to speak.

00:57:01.940 | I mean, Newtonian gravity is just the approximation

00:57:05.340 | that we can make, you know,

00:57:06.940 | on the earth and things like that.

00:57:08.620 | So this is, you know, the phenomenon of gravity

00:57:11.680 | is one that is a consequence of, you know,

00:57:15.020 | we would perceive something very different from gravity.

00:57:17.540 | So the way to understand that is when we think about,

00:57:22.100 | okay, so we make up reference frames

00:57:26.300 | with which we parse what's happening in space and time.

00:57:29.420 | So in other words, one of the things that we do

00:57:32.660 | is we say as time progresses,

00:57:36.880 | everywhere in space, something happens at a particular time

00:57:41.300 | and then we go to the next time

00:57:42.900 | and we say this is what space is like at the next time,

00:57:44.980 | this is what space is like at the next time.

00:57:47.140 | That's, it's, the reason we are used to doing that

00:57:51.380 | is because, you know, when we look around,

00:57:53.800 | we might see, you know, 10, 100 meters away.

00:57:56.460 | The time it takes light to travel that distance

00:57:59.900 | is really short compared to the time it takes our brains

00:58:03.000 | to know what happened.

00:58:04.180 | So as far as our brains are concerned,

00:58:06.340 | we are parsing the universe in this,

00:58:09.160 | there is a moment in time, it's all of space.

00:58:11.560 | There's a moment in time, it's all of space.

00:58:13.560 | You know, if we were the size of planets or something,

00:58:16.140 | we would have a different perception

00:58:17.340 | 'cause the speed of light

00:58:18.180 | would be much more important to us.

00:58:19.760 | We wouldn't have this perception

00:58:21.680 | that things happen progressively in time,

00:58:25.000 | everywhere in space.

00:58:26.680 | And so that's an important kind of constraint.

00:58:29.160 | And the reason that we kind of parse the universe

00:58:31.840 | in the way that causes us to say gravity works

00:58:34.600 | the way it does is because we're doing things

00:58:36.960 | like deciding that we can say the universe exists,

00:58:41.040 | space has a definite structure.

00:58:43.560 | There is a moment in time,

00:58:44.800 | space has this definite structure.

00:58:46.520 | We move to the next moment in time,

00:58:47.880 | space has another structure.

00:58:49.240 | That kind of setup is what lets us kind of deduce,

00:58:53.620 | kind of parse the universe in such a way that we say

00:58:57.740 | gravity works the way it does.

00:58:59.240 | - So that kind of reference frame,

00:59:01.400 | is that the illusion of that,

00:59:04.000 | is that you're saying that's somehow useful

00:59:06.740 | for consciousness?

00:59:08.720 | - That's what consciousness does.

00:59:10.560 | Because in a sense, what consciousness is doing is,

00:59:13.620 | it's insisting that the universe is kind of sequentialized.

00:59:19.840 | And it is not allowing the possibility that,

00:59:23.580 | oh, there are these multiple threads of time

00:59:25.680 | and they're all flowing differently.

00:59:27.320 | It's like saying, no, everything is happening

00:59:30.560 | in this one thread of experience that we have.

00:59:33.600 | - And that illusion of that one thread of experience

00:59:36.280 | cannot happen at the planetary scale.

00:59:38.440 | So are you saying typical human,

00:59:40.360 | are you saying we are at a human level is special

00:59:43.960 | here for consciousness?

00:59:45.440 | - Well, for our kind of consciousness,

00:59:47.560 | if we existed at a scale close to the elementary length,

00:59:51.360 | for example, then our perception of the universe

00:59:53.720 | will be absurdly different.

00:59:55.160 | - Okay, so, but this makes consciousness seem like

00:59:57.520 | a weird side effect to this particular scale.

01:00:00.680 | And so who cares?

01:00:01.880 | I mean, so consciousness is not that special.

01:00:04.760 | - I think, look, I think that a very interesting question is

01:00:08.200 | which I've certainly thought a little bit about,

01:00:10.220 | is what can you imagine?

01:00:11.820 | What is the sort of factoring of something,

01:00:15.320 | what are some other possible ways

01:00:17.000 | you could exist, so to speak?

01:00:19.000 | And if you were a photon, if you were sort of,

01:00:23.080 | some kind of thing that was some kind of intelligence

01:00:27.880 | represented in terms of photons.

01:00:30.600 | For example, the photons we receive

01:00:32.720 | in the cosmic microwave background,

01:00:34.400 | those photons, as far as they're concerned,

01:00:36.400 | the universe just started.

01:00:37.760 | They were emitted 100,000 years

01:00:40.520 | after the beginning of the universe.

01:00:41.600 | They've been traveling at the speed of light.

01:00:43.280 | Time stayed still for them, and then they just arrived

01:00:46.760 | and we just detected them.

01:00:48.140 | So for them, the universe just started.

01:00:50.960 | And that's a different perception of,

01:00:53.240 | that has implications for a very different

01:00:55.320 | perception of time.

01:00:56.160 | - They don't have that single thread

01:00:57.920 | that seems to be really important

01:01:00.040 | for being able to tell a heck of a good story.

01:01:02.000 | So we humans-- - Yes.

01:01:03.240 | - Tell a story. - We can tell a story.

01:01:05.160 | Right, we can tell a story.

01:01:06.000 | - What other kind of stories can you tell?

01:01:08.320 | So a photon is a really boring story.

01:01:10.920 | - Yeah, I mean, so that's a,

01:01:12.520 | I don't know if they're a boring story,

01:01:13.720 | but I think it's, you know,

01:01:15.360 | I've been wondering about this

01:01:16.760 | and I've been asking friends of mine

01:01:18.680 | who are science fiction writers and things,

01:01:20.000 | have you written stuff about this?

01:01:21.320 | And I've got one example,

01:01:22.720 | the great collection of books from my friend,

01:01:25.200 | Rudy Rooker, which were, which I have to say,

01:01:29.280 | they're books about, that are very informed

01:01:32.520 | by a bunch of science that I've done.

01:01:34.320 | And the thing that I really loved about them is,

01:01:36.480 | you know, in the first chapter of the book,

01:01:39.920 | the Earth is consumed by these things he called Nantes,

01:01:42.960 | which are nano, nanobot type things.

01:01:45.720 | - Nice.

01:01:46.560 | - And it's, so, you know, so the Earth is gone

01:01:48.440 | in the first, but then it comes back.

01:01:49.720 | But then-- - Spoiler alert.

01:01:52.120 | - Yeah, right, that was only a micro spoiler.

01:01:54.200 | It's only chapter one.

01:01:55.240 | - Okay, good.

01:01:56.080 | - It's, but the thing that is not a real spoiler alert

01:02:01.240 | because it's such a complicated concept,

01:02:03.200 | but in the end, the Earth is saved by this thing

01:02:07.840 | called the principle of computational equivalence,

01:02:09.520 | which is a kind of a core scientific idea of mine.

01:02:12.760 | And I was just like, like thrilled.

01:02:14.680 | I don't read fiction books very often.

01:02:17.080 | And I was just thrilled I get to the end of this.

01:02:18.840 | And it's like, oh my gosh, you know,

01:02:21.160 | everything is saved by this sort of

01:02:22.760 | deep scientific principle.

01:02:24.200 | - Can you maybe elaborate how the principle

01:02:26.640 | of computational equivalence can save a planet?

01:02:31.640 | - That would be a terrible spoiler for real.

01:02:35.840 | - That would be a spoiler, okay.

01:02:36.680 | - Yeah, yeah, but no, but let me say what

01:02:38.760 | the principle of computational equivalence is.

01:02:41.120 | So the question is, you have a system, you have some rule.

01:02:46.920 | You can think of its behavior

01:02:48.320 | as corresponding to a computation.

01:02:50.360 | The question is, how sophisticated is that computation?

01:02:53.580 | The statement of the principle of computational equivalence

01:02:55.800 | is as soon as it's not obviously simple,

01:02:59.440 | it will be as sophisticated as anything.

01:03:01.840 | And so that has the implication that, you know, rule 30,

01:03:05.720 | you know, our brains, other things in physics,

01:03:08.920 | they're all ultimately equivalent

01:03:10.520 | in the computations they can do.

01:03:12.240 | And that's what leads to this

01:03:13.360 | computational irreducibility idea,

01:03:15.000 | because the reason we don't get to jump ahead,

01:03:18.000 | you know, and out think rule 30,

01:03:20.320 | is because we're just computationally equivalent to rule 30.

01:03:23.240 | So we're kind of just both just running computations

01:03:26.520 | that are the same sort of raw,

01:03:28.880 | the same level of computation, so to speak.

01:03:31.000 | So that's kind of the idea there.

01:03:33.360 | And the question, I mean, it's like,

01:03:35.720 | you know, in the science fiction version would be,

01:03:40.240 | okay, somebody says, we just need more servers,

01:03:42.800 | get us more servers.

01:03:43.960 | The way to get even more servers is turn the whole planet

01:03:47.400 | into a bunch of micro servers.

01:03:49.920 | And that's where it starts.

01:03:52.320 | And so the question of, you know,

01:03:54.160 | computational equivalence,

01:03:55.320 | principle of computational equivalence is,

01:03:56.720 | well, actually, you don't need to build those custom servers.

01:04:00.360 | Actually, you can just use natural computation

01:04:05.360 | to compute things, so to speak.

01:04:08.200 | You can use nature to compute.

01:04:10.120 | You don't need to have done all that engineering.

01:04:12.040 | And it's kind of feels a little disappointing

01:04:15.840 | that you say, we're going to build all these servers.

01:04:17.880 | We're going to do all these things.

01:04:18.960 | We're going to make, you know,

01:04:20.000 | maybe we're going to have human consciousness

01:04:22.520 | uploaded into, you know, some elaborate digital environment.

01:04:26.160 | And then you look at that thing and you say,

01:04:27.920 | it's got electrons moving around, just like in a rock.

01:04:31.040 | And then you say, well, what's the difference?

01:04:33.240 | And the principle of computational equivalence says,

01:04:35.560 | there isn't at some level a fundamental, you know,

01:04:38.720 | you can't say mathematically,

01:04:41.280 | there's a fundamental difference between the rock

01:04:44.560 | that is the future of human consciousness

01:04:46.680 | and the rock that's just a rock.

01:04:48.640 | Now, what I've sort of realized

01:04:50.800 | with this kind of consciousness thing is

01:04:52.760 | there is an aspect of this that seems to be more special

01:04:57.760 | that isn't, and for example,

01:04:59.720 | something I haven't really teased apart properly

01:05:02.480 | is when it comes to something like the weather

01:05:04.480 | and the weather having a mind of its own or whatever,

01:05:06.640 | or your average, you know, pulsar magnetosphere

01:05:09.440 | acting like a sort of intelligent thing,

01:05:11.680 | how does that relate to, you know,

01:05:14.320 | how is that entity related to the kind of consciousness

01:05:19.320 | that we have and sort of what would the world look like,

01:05:22.920 | you know, to the weather?

01:05:24.160 | If we think about the weather as a mind,

01:05:26.600 | what will it perceive?

01:05:27.680 | What will its laws of physics be?

01:05:30.240 | I don't really know.

01:05:31.720 | - 'Cause it's very parallel.

01:05:33.440 | - It's very parallel among other things.

01:05:35.160 | And it's not obvious.

01:05:37.400 | I mean, this is a really kind of mind bending thing

01:05:40.480 | 'cause we've got to try and imagine where, you know,

01:05:43.840 | we've got to try and imagine a parsing of the universe

01:05:46.160 | different from the one we have.

01:05:47.800 | And by the way, when we think about

01:05:49.480 | extraterrestrial intelligence and so on,

01:05:51.920 | I think that's kind of the key thing is, you know,

01:05:54.880 | we have always assumed, I've always assumed,

01:05:57.120 | okay, the extraterrestrials,

01:05:58.840 | at least they have the same physics.

01:06:00.200 | We all live in the same universe.

01:06:01.840 | They've got the same physics.

01:06:03.440 | But actually that's not really right

01:06:05.040 | because the extraterrestrials

01:06:07.320 | could have a completely different way of parsing

01:06:10.400 | that the universe.

01:06:11.280 | So it's as if, you know, there could be for all we know,

01:06:14.400 | right here in this room, you know,

01:06:15.680 | in the details of the motion of these gas molecules,

01:06:18.760 | there could be an amazing intelligence that we were like,

01:06:22.600 | but we have no way of,

01:06:24.800 | we're not parsing the universe in the same way.

01:06:26.640 | If only we could parse the universe in the right way,

01:06:29.560 | you know, immediately this amazing thing that's going on

01:06:32.880 | and this, you know, huge culture that's developed

01:06:35.000 | and all that kind of thing would be obvious to us.

01:06:37.000 | But it's not because we have our particular way

01:06:38.920 | of parsing the universe.

01:06:39.760 | - Would that thing also have an agency?

01:06:42.960 | I don't know the right word to use,

01:06:44.240 | but something like consciousness,

01:06:45.840 | but a different kind of consciousness?

01:06:48.120 | - I think it's a question of just what you mean by the word,

01:06:50.280 | because I think that the, you know,

01:06:51.720 | this notion of consciousness and the, okay,

01:06:54.560 | so some people think of consciousness

01:06:56.520 | as sort of a key aspect of it is that we feel that,

01:07:00.840 | the sort of a feeling of that we exist in some way,

01:07:04.360 | that we have this intrinsic feeling about ourselves.

01:07:08.120 | You know, I suspect that any of these things

01:07:11.920 | would also have an intrinsic feeling about themselves.

01:07:14.320 | I've been sort of trying to think recently

01:07:16.160 | about constructing an experiment

01:07:18.080 | about what if you were just a piece of a cellular automaton,

01:07:20.840 | let's say, you know,

01:07:22.320 | what would your feeling about yourself actually be?

01:07:25.200 | And, you know, can we put ourselves in the shoes,

01:07:28.640 | in the cells of the cellular automaton, so to speak?

01:07:31.520 | Can we get ourselves close enough to that,

01:07:34.600 | that we could have a sense of what the world would be like

01:07:38.200 | if you were operating in that way?

01:07:40.720 | And it's a little difficult because, you know,

01:07:42.680 | you have to not only think about what are you perceiving,

01:07:46.080 | but also what's actually going on in your brain,

01:07:48.560 | and our brains do what they actually do.

01:07:51.000 | And they don't, it's, you know,

01:07:52.720 | I think there might be some experiments that are possible

01:07:55.000 | with, you know, neural nets and so on,

01:07:58.000 | where you can have something where you can at least see

01:08:00.520 | in detail what's happening inside the system.

01:08:03.040 | And I've been sort of one of my projects to think about is,

01:08:06.560 | is there a way of kind of getting a sense

01:08:10.440 | kind of from inside the system

01:08:11.960 | about what its view of the world is and how it, you know,

01:08:16.680 | can we make a bridge?

01:08:18.320 | See, the main issue is this, where, you know,

01:08:21.320 | it's a sort of philosophically difficult thing,

01:08:23.480 | because it's like, we do what we do.

01:08:25.920 | We understand ourselves, at least to some extent.

01:08:29.440 | - We humans understand ourselves.

01:08:30.880 | - That's correct.

01:08:31.760 | And, but yet, okay, so what are we trying to do,

01:08:34.720 | for example, when we are trying to make a model of physics,

01:08:37.280 | what are we actually trying to do?

01:08:39.000 | Because, you know, you say, well,

01:08:40.320 | can we work out what the universe does?

01:08:42.440 | Well, of course we can, we just watch the universe.

01:08:44.360 | The universe does what it does.

01:08:46.080 | But what we're trying to do when we make a model of physics

01:08:48.720 | is we're trying to get to the point

01:08:50.120 | where we can tell a story to ourselves

01:08:52.680 | that we understand that is also a representation

01:08:55.840 | of what the universe does.

01:08:57.480 | So it's this kind of, you know,

01:08:58.680 | can we make a bridge between what we humans

01:09:00.960 | can understand in our minds and what the universe does?

01:09:04.480 | And in a sense, you know, a large part of my kind of life

01:09:09.240 | efforts have been devoted to making computational language,

01:09:12.160 | which kind of is a bridge between what is possible

01:09:15.120 | in the computational universe

01:09:16.840 | and what we humans can conceptualize and think about.

01:09:20.120 | In a sense, what, you know, when I built Wolfram Language

01:09:22.760 | and our whole sort of computational language story,

01:09:25.520 | it's all about how do you take sort of raw computation

01:09:29.400 | and this ocean of computational possibility

01:09:31.720 | and how do we sort of represent pieces of it

01:09:34.880 | in a way that we humans can understand

01:09:37.080 | and that map onto things that we care about doing.

01:09:39.720 | And in a sense, when you add physics,

01:09:42.080 | you're adding this other piece where we can,

01:09:44.360 | you know, mediated by a computer,

01:09:46.360 | can we get physics to the point where we humans

01:09:49.560 | can understand something about what's happening in it?

01:09:52.360 | And when we talk about an alien intelligence,

01:09:54.800 | it's kind of the same story.

01:09:56.040 | It's like, is there a way of mapping what's happening there

01:10:00.280 | onto something that we humans can understand?

01:10:02.760 | And, you know, physics in some sense is like our exhibit one

01:10:07.760 | of the story of alien intelligence.

01:10:10.600 | It's a, you know, it's an alien intelligence in some sense.

01:10:14.240 | And what we're doing in making a model of physics

01:10:17.000 | is mapping that onto something that we understand.

01:10:20.080 | And I think, you know, a lot of these other things

01:10:22.160 | that I've recently been kind of studying,

01:10:25.080 | whether it's molecular biology, other kinds of things,

01:10:28.240 | which we can talk about a bit,

01:10:29.800 | those are other cases where we're in a sense

01:10:33.920 | trying to again, make that bridge

01:10:35.600 | between what we humans understand

01:10:37.840 | and sort of the natural language

01:10:39.840 | of that sort of alien intelligence in some sense.

01:10:42.280 | - When you're talking about,

01:10:44.240 | just to backtrack a little bit,

01:10:46.240 | about cellular automata being able to,

01:10:50.280 | what's it like to be a cellular automata

01:10:53.960 | in the way that's equivalent

01:10:55.880 | to what is it like to be a conscious human being?

01:10:58.860 | How do you approach that?

01:11:02.320 | So is it looking at some subset of the cellular automata,

01:11:06.040 | asking questions of that subset,

01:11:08.520 | like how the world is perceived,

01:11:11.680 | how you as that subset,

01:11:15.200 | like for that local pocket of computation,

01:11:17.640 | what are you able to say about the broader cellular automata?

01:11:21.640 | And that somehow then can give you a sense

01:11:24.720 | of how to step outside of that cellular automata.

01:11:26.480 | - Right, but the tricky part is that that little subset,

01:11:31.480 | it's what it's doing is it has a view of itself.

01:11:35.520 | And the question is, how do you get inside it?

01:11:38.280 | It's like, when we with humans, right?

01:11:40.840 | It's like, we can't get inside each other's consciousness.

01:11:44.840 | That doesn't really even make sense.

01:11:48.780 | It's like, there is an experience

01:11:50.480 | that somebody is having,

01:11:51.800 | but you can perceive things from the outside,

01:11:54.440 | but sort of getting inside it,

01:11:56.560 | it doesn't quite make sense.

01:11:58.400 | And for me, these sort of philosophical issues

01:12:00.840 | and this one I have not untangled.

01:12:02.200 | So let's be, for me,

01:12:06.080 | the thing that has been really interesting

01:12:07.600 | in thinking through some of these things is,

01:12:09.760 | when it comes to questions about consciousness

01:12:12.120 | or whatever else, it's like, when I can run a program

01:12:15.360 | and actually see pictures and make things concrete,

01:12:19.360 | I have a much better chance to understand what's going on

01:12:21.840 | than when I'm just trying to reason about things

01:12:23.720 | in a very abstract way.

01:12:24.760 | - Yeah, but there may be a way to map the program

01:12:29.760 | to your conscious experience.

01:12:32.280 | So for example, when you play a video game,

01:12:34.060 | you do a first person shooter,

01:12:35.640 | you walk around inside this entity,

01:12:39.880 | it's a very different thing than watching this entity.

01:12:42.020 | So if you can somehow connect more and more,

01:12:45.560 | connect this full conscious experience

01:12:48.960 | to the subset of the cellular automata.

01:12:51.280 | - Yeah, it's something like that.

01:12:52.440 | But the difference in the first person shooter thing

01:12:54.280 | is there's still your brain and your memory

01:12:57.580 | is still remembering, you still have, it's hard to,

01:13:02.420 | I mean, again, what one's gonna get,

01:13:04.960 | one is not going to actually be able

01:13:06.480 | to be the cellular automaton.

01:13:08.200 | One's gonna be able to watch

01:13:09.280 | what the cellular automaton does.

01:13:11.000 | But this is the frustrating thing

01:13:12.280 | that I'm trying to understand,

01:13:13.780 | you know, how to think about being it, so to speak.

01:13:18.240 | - Okay, so like in virtual reality,

01:13:19.800 | there's a concept of immersion,

01:13:21.320 | like with anything, with video game, with books,

01:13:23.440 | there's a concept of immersion.

01:13:24.940 | It feels like over time,

01:13:26.720 | if the virtual reality experience is well done,

01:13:31.000 | and maybe in the future it'll be extremely well done,

01:13:33.880 | the immersion leads you to feel like,

01:13:37.680 | you mentioned memories,

01:13:39.000 | you forget that you even ever existed

01:13:41.960 | outside that experience.

01:13:43.720 | - Yeah. - It's so immersive.

01:13:45.500 | I mean, you could argue sort of mathematically

01:13:47.400 | that you can never truly become immersed,

01:13:49.960 | but maybe you can.

01:13:51.560 | I mean, why can't you merge with the cellular automaton?

01:13:54.760 | - Yeah, right.

01:13:55.600 | - I mean, aren't you just part of the same fabric?

01:13:57.920 | Why can't you just like--

01:13:59.520 | - Well, that's a good question.

01:14:00.640 | I mean, so let's imagine the following scenario.

01:14:02.920 | Let's imagine-- - Then can you return?

01:14:04.280 | (laughing)

01:14:05.120 | - What's that?

01:14:05.940 | - But then can you return back?

01:14:07.240 | - Well, yeah, right.

01:14:08.080 | I mean, it's like, let's imagine you've uploaded,

01:14:10.000 | you know, your brain is scanned,

01:14:11.520 | you've got every synapse, you know, mapped out.

01:14:14.560 | You upload everything about you,

01:14:16.760 | the brain simulator, you upload the brain simulator,

01:14:19.080 | and the brain simulator is basically, you know,

01:14:21.900 | some glorified cellular automaton.

01:14:24.200 | And then you say, well, now we've got an answer

01:14:26.400 | to what does it feel like to be a cellular automaton?

01:14:28.720 | It feels just like it felt to be ordinary you,

01:14:32.320 | because they're both computational systems,

01:14:34.680 | and they're both, you know, operating in the same way.

01:14:36.720 | So in a sense, but I think there's somehow more to it,

01:14:39.880 | because in that sense,

01:14:41.200 | when you're just making a brain simulator,

01:14:43.280 | it's just, you know, we're just saying

01:14:45.980 | there's another version of our consciousness.

01:14:47.680 | The question that we're asking is,

01:14:49.400 | if we tease away from our consciousness

01:14:52.160 | and get to something that is different,

01:14:54.100 | how do we make a bridge

01:14:55.340 | to understanding what's going on there?

01:14:57.240 | And, you know, there's a way of thinking about this.

01:14:59.560 | Okay, so this is coming on to sort of questions

01:15:02.020 | about the existence of the universe and so on.

01:15:04.040 | But one of the things is there's this notion

01:15:06.600 | that we have of ruleal space.

01:15:09.220 | So we have this idea of this physical space,

01:15:11.760 | which is, you know, something you can move around in

01:15:14.160 | that's associated with the actual,

01:15:16.660 | the extent of the spatial hypergraph.

01:15:18.820 | Then there's what we call branchial space,

01:15:21.080 | the space of quantum branches.

01:15:22.640 | So in this thing we call the multi-way graph

01:15:25.600 | of all of this sort of branching histories,

01:15:27.980 | there's this idea of a kind of space

01:15:30.340 | where instead of moving around in physical space,

01:15:32.760 | you're moving from history to history, so to speak,

01:15:35.280 | from one possible history to another possible history.

01:15:37.700 | And that's kind of a different kind of space

01:15:40.300 | that is the space in which quantum mechanics plays out.

01:15:43.660 | Quantum mechanics, like for example,

01:15:46.060 | or something like, I think we're slowly understanding

01:15:49.060 | things like destructive interference in quantum mechanics.

01:15:51.780 | That what's happening is branchial space

01:15:54.340 | is associated with phase in quantum mechanics.

01:15:56.960 | And what's happening is the two photons

01:15:58.700 | that are supposed to be interfering

01:15:59.780 | and destructively interfering

01:16:01.940 | are winding up at different ends of branchial space.

01:16:04.420 | And so us, as these poor observers that are trying to,

01:16:07.700 | that have branching brains,

01:16:09.380 | that are trying to conflate together

01:16:11.100 | these different threads of history,

01:16:13.040 | and say, we've really got a consistent story

01:16:15.040 | that we're telling here.

01:16:16.120 | We're really knitting together these threads of history.

01:16:18.460 | By the time the two photons

01:16:20.300 | wound up at opposite ends of branchial space,

01:16:22.820 | we just can't knit them together to tell a consistent story.

01:16:25.860 | So for us, that's sort of the analog

01:16:28.180 | of destructive interference.

01:16:30.060 | - Got it, and then there's rule-ial space too,

01:16:32.040 | which is the space of rules.

01:16:33.900 | - Yes, well, that's another level up.

01:16:36.060 | So there's the question,

01:16:38.980 | actually, I do want to mention one thing,

01:16:41.140 | 'cause it's something I've realized in recent times,

01:16:43.080 | and I think it's really, really kind of cool,

01:16:45.560 | which is about time dilation in relativity.

01:16:47.280 | And it kind of helps to understand,

01:16:49.240 | it's something that kind of helps

01:16:51.080 | in understanding what's going on.

01:16:52.300 | So according to relativity,

01:16:55.060 | if you have a clock, it's ticking at a certain rate,

01:16:59.000 | you send it in a spacecraft

01:17:00.480 | that's going at some significant fraction

01:17:02.520 | of the speed of light,

01:17:03.800 | to you as an observer at rest,

01:17:06.440 | that clock that's in the spacecraft

01:17:08.720 | will seem to be ticking much more slowly.

01:17:11.240 | And so in other words, it's kind of like

01:17:13.480 | the twin who goes off to Alpha Centauri

01:17:16.760 | and goes very fast will age much less

01:17:19.260 | than the twin who's on Earth

01:17:20.360 | that is just hanging out where they're hanging out.

01:17:23.800 | Okay, why does that happen?

01:17:25.440 | Okay, so it has to do with what motion is.

01:17:28.800 | So in our models of physics, what is motion?

01:17:32.660 | Well, when you move from somewhere to somewhere,

01:17:34.980 | it's you having to sort of recreate yourself

01:17:38.440 | at a different place in space.

01:17:40.640 | When you exist at a particular place

01:17:42.720 | and you just evolve with time,

01:17:44.440 | you're again, you're updating yourself,

01:17:46.240 | you're following these rules to update what happens.

01:17:49.360 | Well, so the question is,

01:17:51.000 | when you have a certain amount of computation in you,

01:17:53.560 | so to speak, when there's a certain amount,

01:17:55.600 | you know, you're computing,

01:17:56.760 | the universe is computing at a certain rate,

01:17:58.920 | you can either use that computation

01:18:01.120 | to work out sitting still where you are,

01:18:03.960 | what's going to happen successively in time,

01:18:06.440 | or you can use that computation

01:18:08.180 | to recreate yourself as you move around the universe.

01:18:11.200 | And so time dilation ends up being,

01:18:13.560 | it's really cool actually that this is explainable

01:18:15.680 | in a way that isn't just,

01:18:17.480 | imagine the mathematics of relativity.

01:18:19.600 | But that time dilation is a story of the fact that

01:18:23.200 | as you kind of are recreating yourself as you move,

01:18:26.980 | you are using up some of your computation.

01:18:29.240 | And so you don't have as much computation left over

01:18:32.100 | to actually work out what happens progressively with time.

01:18:35.120 | So that means that time is running more slowly for you

01:18:38.300 | because it is, you're using up your computation,

01:18:41.900 | your clock can't tick as quickly

01:18:44.560 | because every tick of the clock

01:18:46.180 | is using up some computation,

01:18:47.420 | but you already use that computation up

01:18:49.380 | on moving at half the speed of light or something.

01:18:52.420 | And so that's why time dilation happens.

01:18:55.660 | And so you can start,

01:18:57.620 | so it's kind of interesting

01:18:58.900 | that one can sort of get an intuition

01:19:00.380 | about something like that,

01:19:01.660 | because it has seemed like just a mathematical fact

01:19:04.320 | about the mathematics of special relativity and so on.

01:19:07.300 | - Well, for me, it's a little bit confusing

01:19:09.220 | what the U in that picture is,

01:19:11.420 | 'cause you're using up computation.

01:19:15.020 | - Okay, so we're simply saying the entity

01:19:18.940 | is updating itself according to

01:19:21.740 | the way that the universe updates itself.

01:19:24.220 | And the question is, those updates,

01:19:27.580 | let's imagine the U is a clock, okay?

01:19:30.300 | And the clock is, there's all these little updates,

01:19:32.820 | the hypergraph and a sequence of updates

01:19:35.560 | cause the pendulum to swing back the other way

01:19:37.900 | and then swing back and forth, okay?

01:19:41.280 | And all of those updates are contributing

01:19:45.200 | to the motion of the pendulum going back and forth

01:19:47.800 | or the little oscillator moving, whatever it is, okay?

01:19:51.280 | But then the alternative is that sort of situation one,

01:19:54.640 | where the thing is at rest,

01:19:56.200 | situation two, where it's kind of moving,

01:19:58.400 | what's happening is it is having to recreate itself

01:20:02.440 | at every moment.

01:20:04.320 | The thing is going to have to do the computations

01:20:07.640 | to be able to sort of recreate itself

01:20:10.240 | at a different position in space.

01:20:12.000 | And that's kind of the intuition behind,

01:20:14.040 | so it's either going to spend its computation

01:20:16.780 | recreating itself at a different position in space,

01:20:19.400 | or it's gonna spend its computation

01:20:21.160 | sort of doing the updating of the ticking of the clock,

01:20:27.940 | so to speak.

01:20:28.780 | - So the more updating it's doing,

01:20:30.360 | the less the ticking of the clock update is doing.

01:20:33.480 | - That's right.

01:20:34.320 | The more it's having to update because of motion,

01:20:36.480 | the less it can update the clock.

01:20:38.980 | So that's, I mean, obviously there's a sort

01:20:42.160 | of mathematical version of it that relates

01:20:43.880 | to how it actually works in relativity,

01:20:45.800 | but that's kind of, to me, that was sort of exciting to me

01:20:48.840 | that it's possible to have a really mechanically

01:20:51.640 | explainable story there that isn't,

01:20:54.560 | and similarly in quantum mechanics,

01:20:56.120 | this notion of branching brains,

01:20:57.680 | perceiving branching universes,

01:20:59.360 | to me, that's getting towards a sort

01:21:00.920 | of mechanically explainable version

01:21:02.880 | of what happens in quantum mechanics,

01:21:04.200 | even though it's a little bit mind bending

01:21:06.600 | to see these things about under what circumstances

01:21:09.960 | can you successfully knit together

01:21:12.240 | those different threads of history,

01:21:14.000 | and when do things sort of escape,

01:21:15.800 | and those kinds of things.

01:21:17.400 | But the thing about this physical space,

01:21:21.200 | in physical space, the main sort of big theory

01:21:25.040 | is general relativity, the theory of gravity,

01:21:27.140 | and that tells you how things move in physical space.

01:21:30.400 | In branchial space, the big theory

01:21:32.180 | is the Feynman path integral, which it turns out,

01:21:35.480 | tells you essentially how things move

01:21:37.320 | in the space of quantum phases.

01:21:40.040 | So it's kind of like motion in branchial space.

01:21:42.900 | And it's kind of a fun thing to start thinking about

01:21:45.620 | what, oh, you know, all these things

01:21:48.340 | that we know in physical space,

01:21:49.960 | like event horizons and black holes and so on,

01:21:52.480 | what are the analogous things in branchial space?

01:21:54.860 | For example, the speed of light,

01:21:55.940 | what's the analog of the speed of light in branchial space?

01:21:58.700 | It's the maximum speed of quantum entanglement.

01:22:01.540 | So the speed of light is a flashbulb goes off here,

01:22:05.580 | what's the maximum rate at which the effect

01:22:08.180 | of that flashbulb is detectable moving away in space?

01:22:12.700 | So similarly, in branchial space, something happens,

01:22:15.840 | and the question is, how far in this branchial space,

01:22:18.500 | in the space of quantum states,

01:22:20.420 | how far away can that get within a certain period of time?

01:22:23.920 | And so there's this notion of a maximum entanglement speed,

01:22:27.100 | and that might be observable.

01:22:28.900 | That's the thing we've been sort of poking at,

01:22:31.200 | is might there be a way to observe it

01:22:32.880 | even in some atomic physics kind of situation?

01:22:35.660 | 'Cause one of the things that's weird in quantum mechanics

01:22:39.260 | is when we study quantum mechanics,

01:22:42.000 | we mostly study it in terms of small numbers of particles.

01:22:45.140 | You know, this electron does this,

01:22:46.580 | this thing on an ion trap does that, and so on.

01:22:49.420 | But when we deal with large numbers of particles,

01:22:51.460 | kind of all bets are off.

01:22:52.440 | It's kind of too complicated to deal with quantum mechanics.

01:22:55.140 | And so what ends up happening is,

01:22:57.300 | so this question about maximum entanglement speed

01:23:00.320 | and things like that may actually play in one of these,

01:23:03.300 | in the sort of story of many-body quantum mechanics,

01:23:06.180 | and even have some suspicions about things

01:23:08.860 | that might happen even in,

01:23:10.860 | one of the things I realized I'd never understood,

01:23:13.620 | and it's kind of embarrassing,

01:23:14.740 | but I think I now understand a little better,

01:23:17.180 | is when you have chemistry and you have quantum mechanics,

01:23:20.660 | it's like, well, there's two carbon atoms.

01:23:22.260 | There's this molecule, and we do a reaction,

01:23:24.560 | and we draw a diagram, and we say,

01:23:25.920 | this carbon atom ends up in this place.

01:23:28.160 | And it's like, but wait a minute.

01:23:29.480 | In quantum mechanics, nothing ends up in a definite place.

01:23:31.920 | There's always just some wave function for this to happen.

01:23:34.380 | How can it be the case that we can draw these reasonable,

01:23:37.400 | it just ended up in this place?

01:23:39.080 | And you have to kind of say,

01:23:40.000 | well, the environment of the molecule

01:23:42.120 | effectively made a bunch of measurements on the molecule

01:23:44.960 | to keep it kind of classical.

01:23:46.800 | And that's a story that has to do with this whole thing

01:23:49.800 | about measurements have to do with this idea of,

01:23:54.600 | can we conclude that something definite happened?

01:23:57.080 | Because in quantum mechanics,

01:23:58.520 | the intrinsic quantum mechanics,

01:24:00.380 | the mathematics of quantum mechanics is all about,

01:24:02.640 | they're just these amplitudes

01:24:03.640 | for different things to happen.

01:24:05.160 | Then there's this thing of, and then we make a measurement,

01:24:08.200 | and we conclude that something definite happened.

01:24:10.680 | And that has to do with this thing, I think,

01:24:12.960 | about sort of moving, about knitting together

01:24:15.560 | these different threads of history and saying,

01:24:18.200 | this is now something where we can definitively say

01:24:20.220 | something definite happened.

01:24:21.360 | In the traditional theory of quantum mechanics,

01:24:23.620 | it's just like,

01:24:25.440 | after you've done all this amplitude computation,

01:24:27.680 | then this big hammer comes down and you do a measurement,

01:24:30.720 | and it's all over.

01:24:31.800 | And that's been very confusing,

01:24:33.080 | for example, in quantum computing,

01:24:34.800 | it's been a very confusing thing because when you say,

01:24:38.160 | in quantum computing, the basic idea is you're gonna use

01:24:40.360 | all these separate threads of computation, so to speak,

01:24:43.360 | to do all the different parts of,

01:24:45.180 | try these different factors for an integer

01:24:46.880 | or something like this.

01:24:48.100 | And it looks like you can do a lot

01:24:50.080 | because you've got all these different threads going on.

01:24:52.880 | But then you have to say, well, at the end of it,

01:24:55.180 | you've got all these threads,

01:24:56.240 | and every thread came up with a definite answer,

01:24:58.640 | but we got to conflate those together

01:25:00.600 | to figure out a definite thing that we humans

01:25:03.120 | can take away from it, a definite,

01:25:04.880 | so the computer actually produced this output.

01:25:07.340 | - So having this branchial space

01:25:10.660 | and this hypergraph model of physics,

01:25:13.520 | do you think it's possible to then make predictions

01:25:16.660 | that are definite about many body

01:25:19.640 | quantum mechanical systems?

01:25:21.400 | Is that the hope?

01:25:22.240 | - I think it's likely, yes.

01:25:23.740 | But I don't, you know, this is,

01:25:25.580 | every one of these things,

01:25:26.680 | when you go from the underlying theory,

01:25:28.980 | which is complicated enough, and it's,

01:25:30.760 | I mean, the theory at some level is beautifully simple,

01:25:33.600 | but as soon as you start actually trying to,

01:25:35.280 | it's this whole question about how do you bridge it

01:25:37.640 | to things that we humans can talk about,

01:25:40.160 | it gets really complicated.

01:25:41.700 | And this thing about actually getting it

01:25:44.200 | to a definite prediction about, you know,

01:25:48.300 | definite thing you can say about chemistry

01:25:50.100 | or something like this, you know,

01:25:51.900 | that's just a lot of work.

01:25:52.740 | So I'll give you an example.

01:25:54.020 | There's a thing called the quantum Zeno effect.

01:25:56.280 | So the idea is, you know, quantum stuff happens,

01:26:00.120 | but then if you make a measurement,

01:26:01.860 | you're kind of freezing time in quantum mechanics.

01:26:04.820 | And so it looks like there's a possibility

01:26:07.780 | that with sort of the relationship

01:26:09.460 | between the quantum Zeno effect

01:26:11.180 | and the way that many body quantum mechanics works

01:26:13.140 | and so on, maybe just conceivably,

01:26:16.200 | it may be possible to actually figure out a way

01:26:18.360 | to measure the maximum entanglement speed.

01:26:21.720 | And the reason we can potentially do that

01:26:24.060 | is because the systems we deal with

01:26:26.520 | in terms of atoms and things, they're pretty big.

01:26:28.720 | You know, a mole of atoms is, you know,

01:26:30.760 | it's a lot of atoms and, you know,

01:26:32.640 | but it isn't a very, you know,

01:26:33.880 | it's something where to get, you know,

01:26:36.160 | when we're dealing with how can you see 10

01:26:37.880 | to the minus 100, so to speak?

01:26:39.760 | Well, by the time you've got, you know,

01:26:41.700 | 10 to the 30th atoms, you're not, you know,

01:26:44.380 | you're within a little bit closer striking distance of that.

01:26:47.900 | It's not like, oh, we've just got, you know,

01:26:50.620 | two atoms and we're trying to see down

01:26:52.980 | to 10 to the minus 100 meters or whatever.

01:26:55.400 | So I don't know how it will work,

01:26:57.180 | but this is a potential direction.

01:27:00.020 | And if you can tell, by the way,

01:27:02.020 | if we could measure the maximum entanglement speed,

01:27:04.540 | we would know the elementary length.

01:27:06.300 | These are all related.

01:27:07.740 | So if we got that one number, we just need one number.

01:27:11.440 | If we can get that one number, we can, you know,

01:27:13.640 | the theory has no parameters anymore.

01:27:16.120 | And, you know, there are other places.

01:27:18.640 | Well, there's another hope for doing that is in cosmology.

01:27:22.920 | In this model, one of the features is

01:27:24.760 | the universe is not fixed dimensional.

01:27:26.400 | I mean, we think we live in three-dimensional space,

01:27:28.640 | but this hypergraph doesn't have any particular dimension.

01:27:31.480 | It can emerge as something which on an approximation,

01:27:35.080 | it's as if, you know, you say,

01:27:36.440 | what's the volume of a sphere in the hypergraph

01:27:38.780 | where a sphere is defined as how many nodes do you get to

01:27:42.180 | when you go a distance R away from a given point?

01:27:45.200 | And you can say, well, if I get to about R cubed nodes,

01:27:49.380 | when I go a distance R away in the hypergraph,

01:27:51.900 | then I'm living roughly in three-dimensional space.

01:27:54.500 | But you might also get to R to the point, you know, 2.92,

01:27:59.080 | you know, for some value of R in, you know,

01:28:02.180 | as R increases, that might be the sort of fit

01:28:05.080 | to what happens.

01:28:06.300 | And so one of the things we suspect is that

01:28:08.200 | the very early universe was essentially

01:28:10.180 | infinite dimensional, and that as the universe expanded,

01:28:14.360 | it became lower dimensional.

01:28:16.600 | And so one of the things that is another little sort of point

01:28:19.880 | where we think there might be a way

01:28:21.460 | to actually measure some things is dimension fluctuations

01:28:24.400 | in the early universe.

01:28:25.640 | That is, is there a leftover dimension fluctuation of,

01:28:29.760 | at the time of the cosmic microwave background,

01:28:31.960 | 100,000 years or something after the beginning

01:28:33.440 | of the universe, is it still the case that there were pieces

01:28:37.060 | of the universe that didn't have dimension three,

01:28:39.700 | that had dimension 3.01 or something?

01:28:42.180 | And can we tell that?

01:28:43.500 | - Is that possible to observe the fluctuations

01:28:47.940 | in dimensions?

01:28:49.200 | I don't even know what that entails.

01:28:51.180 | - Okay, so the question, which should be an elementary

01:28:54.820 | exercise in electrodynamics, except it isn't,

01:28:57.860 | is understanding what happens to a photon

01:29:00.440 | when it propagates through 3.01 dimensional space.

01:29:03.660 | So for example, the inverse square law is a consequence

01:29:06.780 | of the surface area of a sphere is proportional

01:29:11.300 | to R squared.

01:29:12.580 | But if you're not in three dimensional space,

01:29:15.680 | the surface area of a sphere is not proportional

01:29:18.260 | to R squared, it's R to the whatever, 2.01 or something.

01:29:22.460 | And so that means that I think when you try and do optics,

01:29:28.660 | a common principle in optics is Huygens principle,

01:29:31.380 | which basically says that every piece of a wave front

01:29:34.280 | of light is a source of new spherical waves.

01:29:39.280 | And those spherical waves, if they're different dimensional

01:29:41.780 | spherical waves, will have other characteristics.

01:29:45.320 | And so there will be bizarre optical phenomena,

01:29:48.360 | which we haven't figured out yet.

01:29:50.000 | - So you're looking for some weird photon trajectories

01:29:55.880 | that designate that it's 3.01 dimensional space?

01:29:59.860 | - Yeah, yeah, that would be an example of, I mean,

01:30:02.620 | you know, there are only a certain number of things

01:30:04.540 | we can measure about photons.

01:30:06.180 | You know, we can measure their polarization,

01:30:07.900 | we can measure their frequency,

01:30:09.540 | we can measure their direction, those kinds of things.

01:30:12.660 | And you know, how that all works out,

01:30:15.540 | and you know, in the current models of physics,

01:30:19.300 | you know, it's been hard to explain how the universe

01:30:21.800 | manages to be as uniform as it is.

01:30:23.980 | And that's led to this inflation idea that,

01:30:27.040 | to the great annoyance of my then collaborator,

01:30:29.680 | we figured out in like 1979, we had this realization

01:30:33.360 | that you could get something like this,

01:30:35.320 | but it seemed implausible that that's the way

01:30:37.180 | the universe worked, so we put in a footnote.

01:30:39.460 | And that was, so that's a, but in any case,

01:30:42.480 | I've never really completely believed it,

01:30:44.740 | but that's an idea for how to sort of puff out the universe

01:30:48.520 | faster than the speed of light,

01:30:50.000 | early moments of the universe,

01:30:51.600 | that that's the sort of the inflation idea.

01:30:53.760 | And that you can somehow explain how the universe manages

01:30:57.820 | to be as uniform as it is.

01:30:59.640 | In our model, this turns out to be much more natural,

01:31:03.320 | because the universe just starts very connected.

01:31:05.520 | The hypergraph is not such that the ball that you grow

01:31:09.300 | starting from a single point has volume R cubed,

01:31:11.960 | it might have volume R to the 500 or R to the infinity.

01:31:16.700 | And so that means that you sort of naturally get

01:31:19.540 | this much higher degree of connectivity and uniformity

01:31:21.700 | in the universe.

01:31:22.760 | And then the question is,

01:31:24.560 | this is sort of the mathematical physics challenge,

01:31:27.400 | is in the standard theory of the universe,

01:31:29.200 | there's the Friedman-Robertson-Walker universe,

01:31:31.640 | which is the kind of standard model where the universe

01:31:33.840 | is isotropic and homogeneous,

01:31:35.980 | and you can then work out the equations of general relativity

01:31:38.720 | and you can figure out how the universe expands.

01:31:41.260 | We would like to do the same kind of thing,

01:31:42.700 | including dimension change.

01:31:44.720 | This is just difficult mathematical physics.

01:31:47.140 | I mean, the reason it's difficult

01:31:48.880 | is the sort of fundamental reason it's difficult.

01:31:50.880 | When people invented calculus 300 years ago,

01:31:53.960 | calculus was a story of understanding change

01:31:57.560 | and change as a function of a variable.

01:32:00.040 | And so people study univariate calculus,

01:32:02.220 | they study multivariate calculus,

01:32:03.760 | it's one variable, it's two variables, three variables,

01:32:06.440 | but whoever studied 2.5 variable calculus,

01:32:10.880 | turns out nobody.

01:32:12.360 | Turns out that, but what we need to have

01:32:15.060 | to understand these fractional dimensional spaces,

01:32:18.360 | which don't work like,

01:32:19.960 | well, they're spaces where the effective dimension

01:32:24.080 | is not an integer.

01:32:25.840 | - So you can't apply the tools of calculus

01:32:28.160 | and naturally and easily to fractional dimensions.

01:32:31.440 | - No.

01:32:32.280 | - So somebody has to figure out how to do that.

01:32:34.040 | - Yeah, yeah, we're trying to figure this out.

01:32:35.720 | I mean, it's very interesting.

01:32:37.560 | I mean, it's very connected to very frontier issues

01:32:40.280 | in mathematics.

01:32:41.120 | It's very beautiful, but-

01:32:42.240 | - So is it possible, is it possible,

01:32:44.720 | we're dealing with a scale that's so, so much smaller

01:32:48.200 | than our human scale.

01:32:50.480 | Is it possible to make predictions versus explanations?

01:32:53.720 | Do you have a hope that with this hypergraph model,

01:32:57.440 | you'd be able to make predictions?

01:32:59.080 | - Yeah.

01:32:59.920 | - That then could be validated with a physics experiment,

01:33:04.360 | predictions that couldn't have been done

01:33:06.360 | or weren't done otherwise?

01:33:07.680 | - Yeah, yeah, yeah.

01:33:08.520 | I mean, you know, I think-

01:33:09.360 | - In which domain do you think that prediction will-

01:33:11.000 | - Okay, so there are gonna be cosmology ones

01:33:12.960 | to do with dimension fluctuations in the universe.

01:33:14.800 | That's a very bizarre effect.

01:33:16.240 | Nobody, you know, dimension fluctuation is just something,

01:33:18.760 | nobody ever looked for that.

01:33:19.640 | If anybody sees dimension fluctuation, that's a huge flag,

01:33:23.240 | that's something like our model is going on.

01:33:26.120 | If, and how one detects that, you know,

01:33:28.880 | that's a problem of kind of, you know,

01:33:30.720 | that's a problem of traditional physics in a sense

01:33:32.760 | of what's the best way to actually figure that out.

01:33:35.840 | And for example, that's one,

01:33:37.760 | there are all kinds of things one can imagine.

01:33:40.360 | I mean, there are things that in black hole mergers,

01:33:44.560 | it's possible that there will be effects

01:33:47.240 | of maximum entanglement speed in large black hole mergers.

01:33:50.840 | That's another possible thing.

01:33:53.080 | - And all of that is detected through like what?

01:33:55.440 | Do you have a hope for LIGO type of situation?

01:33:57.840 | Like that's gravitational waves?

01:33:59.520 | - Yeah, or alternatively, I mean, I think it's, you know,

01:34:03.480 | look, figuring out experiments

01:34:05.840 | is like figuring out technology inventions.

01:34:08.760 | That is, you know, you've got a set of raw materials,

01:34:11.160 | you've got an underlying model,

01:34:12.800 | and now you've got to be very clever

01:34:14.500 | to figure out, you know, what is that thing I can measure

01:34:16.960 | that just somehow, you know,

01:34:18.800 | leverages into the right place.

01:34:21.040 | And we've spent less effort on that than I would have liked,

01:34:24.700 | because one of the reasons is that I think that the,

01:34:28.280 | you know, the physicists who've been working on our models,

01:34:32.360 | and we've now, lots of physicists actually,

01:34:34.480 | it's very, very nice.

01:34:35.320 | It's kind of, you know, it's one of these cases

01:34:37.640 | where I'm almost, I'm really kind of pleasantly surprised

01:34:41.500 | that the sort of absorption of the things we've done

01:34:43.720 | has been quite rapid and quite sort of,

01:34:47.640 | you know, very positive.

01:34:48.880 | - So it's a Cambrian explosion of physicists too,

01:34:51.000 | not just ideas.

01:34:52.400 | - Yes, I mean, you know, a lot of what's happened

01:34:55.340 | that's really interesting, and again,

01:34:56.960 | not what I expected is, there are a lot of areas

01:34:59.680 | of sort of very elaborate,

01:35:02.240 | sophisticated mathematical physics,

01:35:04.320 | whether that's causal set theory,

01:35:05.920 | whether it's higher category theory,

01:35:07.520 | whether it's categorical quantum mechanics,

01:35:09.820 | all sorts of elaborate names for these things,

01:35:12.080 | spin networks, perhaps, you know,

01:35:15.760 | causal dynamical triangulations,

01:35:17.340 | all kinds of names of these fields.

01:35:19.600 | And these fields have a bunch

01:35:21.320 | of good mathematical physicists in them

01:35:23.120 | who've been working for decades in these particular areas.

01:35:26.240 | And the question is,

01:35:27.880 | but they've been building these mathematical structures,

01:35:30.840 | and the mathematical structures are interesting,

01:35:32.600 | but they don't typically sit on anything.

01:35:35.100 | They're just mathematical structures.

01:35:37.040 | And I think what's happened is our models provide

01:35:39.440 | kind of a machine code that lives underneath those models.

01:35:43.400 | So a typical example, this is due to Jonathan Gorod,

01:35:47.720 | who's one of the key people

01:35:49.080 | who's been working on our project.

01:35:51.400 | This is in, okay, so I'll give you an example,

01:35:54.680 | just to give a sense of how these things connect.

01:35:56.320 | This is in causal set theory.

01:35:58.040 | So the idea of causal set theory is there are,

01:36:02.080 | in space-time, we imagine that there's space and time,

01:36:05.080 | it's a three plus one dimensional, you know, setup.

01:36:08.360 | We imagine that there are just events that happen

01:36:12.320 | at different times and places in space and time.

01:36:15.440 | And the idea of causal set theory is the only thing

01:36:17.800 | you say about the universe is there are a bunch of events

01:36:20.520 | that happen sort of randomly

01:36:22.400 | at different places in space and time.

01:36:24.360 | And then the whole sort of theory of physics

01:36:26.480 | has to be to do with this graph of causal relationships

01:36:30.680 | between these randomly thrown down events.

01:36:34.040 | So they've always been confused by the fact that

01:36:37.080 | to get even Lorentz invariance,

01:36:38.500 | even relativistic invariance,

01:36:40.080 | you need a very special way to throw down those events.

01:36:43.040 | And they've had no natural way

01:36:44.560 | to understand how that would happen.

01:36:46.400 | So what Jonathan figured out is that,

01:36:48.800 | in fact, from our models,

01:36:50.480 | they, instead of just generating events at random,

01:36:55.200 | our models necessarily generate events in some pattern

01:36:58.880 | in space-time effectively,

01:37:01.080 | that then leads to Lorentz invariance

01:37:02.880 | and relativistic invariance and all those kinds of things.

01:37:05.200 | So it's a place where all the mathematics

01:37:07.200 | that's been done on,

01:37:08.040 | well, we just have a random collection of events.

01:37:10.400 | Now, what consequences does that have

01:37:12.800 | in terms of causal set theory and so on?

01:37:15.300 | That can all be kind of wheeled in

01:37:17.360 | now that we have some different underlying foundational idea

01:37:20.760 | for what the particular distribution of events is

01:37:23.880 | as opposed to just where we throw down random events.

01:37:26.560 | And so that's a typical sort of example

01:37:28.920 | of what we're seeing in all these different areas

01:37:31.640 | of kind of how you can take really interesting things

01:37:34.880 | that have been done in mathematical physics

01:37:36.640 | and connect them.

01:37:37.480 | And it's really kind of beautiful

01:37:39.160 | because the sort of the abstract models we have

01:37:43.600 | just seem to plug into all these different,

01:37:45.920 | very interesting, very elegant, abstract ideas,

01:37:48.760 | but we're now giving sort of a reason

01:37:51.120 | for that to be the way,

01:37:53.160 | for a reason for one to care.

01:37:54.820 | I mean, it's like saying,

01:37:56.920 | you can think about computation abstractly.

01:38:00.720 | You can think about, I don't know,

01:38:01.800 | combinators or something as abstract computational things.

01:38:04.760 | And you can sort of do all kinds of study of them,

01:38:07.480 | but it's like, why do we care?

01:38:09.260 | Well, okay, Turing machines are a good start

01:38:11.080 | 'cause you can kind of see

01:38:11.920 | they're sort of mechanically doing things.

01:38:13.620 | But when we actually start thinking about computers

01:38:16.160 | computing things, we have a really good reason to care.

01:38:19.360 | And this is sort of what we're providing, I think,

01:38:21.920 | is a reason to care about a lot of these areas

01:38:24.360 | of mathematical physics.

01:38:25.200 | So that's been very nice.

01:38:27.200 | - So I'm not sure we've ever got to the question

01:38:31.440 | of why does the universe exist at all.

01:38:33.480 | Let's talk about that.

01:38:35.240 | So it's not the simplest question in the world.

01:38:38.200 | So it takes a few steps to get to it.

01:38:41.640 | - And it's nevertheless even surprising

01:38:43.920 | that you can even begin to answer this question,

01:38:46.040 | as you were saying.

01:38:47.220 | - I'm very surprised.

01:38:49.680 | So the next thing to perhaps understand

01:38:52.880 | is this idea of ruleal space.

01:38:55.180 | So we've got kind of physical space,

01:38:57.540 | we've got branchial space,

01:38:58.920 | the space of possible quantum histories.

01:39:01.360 | And now we've got another level of kind of abstraction,

01:39:04.560 | which is ruleal space.

01:39:05.880 | And here's where that comes from.

01:39:08.180 | So you say, okay, you say,

01:39:10.400 | we've got this model for the universe,

01:39:12.480 | we've got a particular rule,

01:39:15.080 | and we run this rule and we get the universe.

01:39:17.420 | Okay, so that's interesting.

01:39:19.640 | Why that rule?

01:39:20.520 | Why not another rule?

01:39:22.160 | And so that confused me for a long time.

01:39:24.600 | And I realized, well, actually,

01:39:26.600 | what if the thing could be using all possible rules?

01:39:30.000 | What if at every step,

01:39:31.660 | in addition to saying apply a particular rule

01:39:34.800 | at all places in this hypergraph,

01:39:36.720 | one could say, just take all possible rules

01:39:39.320 | and apply all possible rules

01:39:40.640 | at all possible places in this hypergraph.

01:39:43.160 | Okay, and then you make this ruleal multi-way graph,

01:39:46.380 | which both is all possible histories

01:39:48.840 | for a particular rule and all possible rules.

01:39:51.480 | So the next thing you'd say is,

01:39:52.860 | how can you get anything reasonable out of it?

01:39:54.560 | How can anything real come out of

01:39:57.360 | the set of all possible rules applied

01:39:59.560 | in all possible ways?

01:40:00.980 | Okay, this is a subtle thing,

01:40:02.760 | so which I haven't fully untangled.

01:40:05.060 | There is this object,

01:40:07.320 | which is the result of running all possible rules

01:40:10.220 | in all possible ways.

01:40:11.640 | And you might say, if you're running all possible rules,

01:40:13.340 | why can't everything possible happen?

01:40:15.840 | Well, the answer is because when you,

01:40:19.520 | there's sort of this entanglement that occurs.

01:40:21.940 | So let's say that you have

01:40:24.560 | a lot of different possible initial conditions,

01:40:26.840 | a lot of different possible states.

01:40:28.760 | Then you're applying these different rules.

01:40:30.800 | Well, some of those rules can end up with the same state.

01:40:34.600 | So it isn't the case that you can just get

01:40:36.100 | from anywhere to anywhere.

01:40:37.360 | There's this whole entangled structure

01:40:39.580 | of what can lead to what,

01:40:41.120 | and there's a definite structure that's produced.

01:40:43.560 | I think I'm gonna call that definite structure

01:40:45.200 | the Rulliad,

01:40:46.400 | the limit of kind of all possible rules

01:40:50.680 | being applied in all possible ways.

01:40:52.280 | - And you're saying that structure is finite,

01:40:54.580 | so that somehow connects to maybe a similar kind of thing

01:40:57.580 | as like causal invariance.

01:40:59.560 | - Well, it happens that the Rulliad

01:41:00.960 | necessarily has causal invariance.

01:41:02.760 | That's a feature of,

01:41:03.820 | that's just a mathematical consequence

01:41:05.560 | of essentially using all possible rules

01:41:08.240 | plus universal computation gives you the fact

01:41:11.300 | that for many diverging paths,

01:41:13.180 | you can always, the paths will always converge.

01:41:15.440 | - But does that say that the Rulli,

01:41:16.760 | does that necessarily infer that the Rulliad is a finite?

01:41:21.760 | - In the end, it's not necessarily finite.

01:41:23.960 | I mean, it's a,

01:41:26.320 | just like the history of the universe may not be finite.

01:41:28.940 | The history of the universe, time may keep going forever.

01:41:31.520 | You can keep running the computations of the Rulliad

01:41:34.120 | and you'll keep spewing out more and more and more structure.

01:41:37.320 | It's like time doesn't have to end.

01:41:39.720 | It's that, but the issue is there are three limits

01:41:44.440 | that happen in this Rulliad object.

01:41:46.520 | One is how long you run the computation for.

01:41:49.280 | Another is how many different rules you're applying.

01:41:52.240 | And another is how many different states you start from.

01:41:55.440 | And the mixture of those three limits,

01:41:57.400 | I mean, this is just mathematically a horrendous object.

01:42:01.160 | And what's interesting about this object is

01:42:04.080 | the one thing that does seem to be the case

01:42:05.740 | about this object is it connects with ideas

01:42:07.960 | in higher category theory.

01:42:09.520 | And in particular, it connects to some of the 20th century's

01:42:12.600 | most abstract mathematics done by this chap Grothendieck.

01:42:17.000 | Grothendieck had a thing called the infinity groupoid,

01:42:19.560 | which is closely related to this Rulliad object.

01:42:23.060 | Although the details of the relationship,

01:42:25.320 | I don't fully understand yet.

01:42:29.320 | But I think that what's interesting is this thing

01:42:32.120 | that is sort of this very limiting object.

01:42:33.840 | So, okay, so a way to think about this,

01:42:36.520 | that again, will take us into another direction,

01:42:40.080 | which is the equivalence between physics and mathematics.

01:42:43.400 | The way that, well, let's see, maybe this is,

01:42:48.400 | just to give a sense of this kind of groupoid

01:42:51.240 | and things like that.

01:42:52.080 | You can think about, in mathematics,

01:42:53.780 | you can think you have certain axioms,

01:42:55.700 | they're kind of like atoms, and you,

01:42:58.860 | well, actually, let's say,

01:43:00.860 | let's talk about mathematics for a second.

01:43:02.340 | So what is mathematics?

01:43:03.500 | What is it made of, so to speak?

01:43:06.340 | Mathematics, there's a bunch of statements,

01:43:08.280 | like for addition, X plus Y is equal to Y plus X.

01:43:12.220 | That's a statement of mathematics.

01:43:14.260 | Another statement would be, you know,

01:43:15.740 | X squared minus one is equal to X plus one X minus one.

01:43:18.900 | There are infinite number of these possible statements

01:43:21.260 | of mathematics.

01:43:22.100 | - So it's not, I mean, it's not just, I guess, a statement,

01:43:24.500 | but with X plus Y, it's a rule that you can,

01:43:28.020 | it's a, I mean, you think of it as a rule.

01:43:29.980 | - It's a, it is a rule.

01:43:32.480 | It's also just a thing that is true in mathematics.

01:43:35.860 | - Right, it's a statement of truth, okay.

01:43:37.740 | - Right, and what you can imagine is,

01:43:39.940 | you imagine just laying out this giant kind of ocean

01:43:44.140 | of all statements, well, actually, you first start,

01:43:47.460 | okay, this is where,

01:43:48.820 | this, we're segueing into a different thing.

01:43:50.480 | Let me not go in this direction for a second.

01:43:52.340 | - Let's not go to meta-mathematics just yet.

01:43:54.420 | - Yeah, we'll maybe get to meta-mathematics,

01:43:56.500 | but it's, so let me not,

01:43:59.500 | let me explain the groupoid and things later.

01:44:01.380 | - Yes.

01:44:02.220 | - But, so let's come back to the universe,

01:44:05.440 | always a good place to be in, so to speak.

01:44:07.540 | - Yeah, so what does the universe have to do

01:44:09.420 | with the Rulliad, the Rullio space,

01:44:11.340 | and how that's possibly connected

01:44:15.180 | to why the thing exists at all,

01:44:17.060 | and why there's just one of them?

01:44:18.800 | - Yes, okay, so here's the point.

01:44:20.940 | So the thing that had confused me for a long time was,

01:44:24.260 | let's say we get the rule for the universe.

01:44:26.780 | We hold it in our hand.

01:44:27.660 | We say, "This is our universe."

01:44:29.420 | Then the immediate question is,

01:44:30.580 | "Well, why isn't it another one?"

01:44:32.420 | And that's kind of the,

01:44:34.180 | the sort of the lesson of Copernicus is,

01:44:37.100 | we're not very special.

01:44:38.300 | So how come we got universe number 312

01:44:42.440 | and not universe quadrillion, quadrillion, quadrillion?

01:44:46.060 | And I think the resolution of that is the realization

01:44:48.640 | that the universe is running all possible rules.

01:44:53.640 | So then you say, "Well, how on earth do we perceive

01:44:58.040 | "the universe to be running according to a particular rule?

01:45:00.560 | "How do we perceive definite things

01:45:02.260 | "happening in the universe?"

01:45:03.140 | Well, it's the same story.

01:45:05.620 | It's the observer.

01:45:07.100 | There is a reference frame that we are picking

01:45:09.480 | in this Rullio space,

01:45:11.280 | and that that is what determines

01:45:13.340 | our perception of the universe.

01:45:15.000 | With our particular sensory information and so on,

01:45:18.120 | we are parsing the universe in this particular way.

01:45:21.520 | So here's the way to think about it.

01:45:23.080 | In physical space,

01:45:24.880 | we live in a particular place in the universe.

01:45:27.300 | And we could live on Alpha Centauri,

01:45:29.240 | but we don't, we live here.

01:45:30.600 | And similarly, in Rullio space,

01:45:34.480 | we could live in many different places in Rullio space,

01:45:37.520 | but we happen to live here.

01:45:39.240 | And what does it mean to live here?

01:45:40.360 | It means we have certain sensory input.

01:45:43.160 | We have certain ways to parse the universe.

01:45:45.760 | Those are our interpretation of the universe.

01:45:48.840 | What would it mean to travel in Rullio space?

01:45:51.560 | What it basically means is that we are successively

01:45:53.920 | interpreting the universe in different ways.

01:45:56.240 | So in other words,

01:45:57.160 | to be at a different point in Rullio space

01:45:59.680 | is to have a different, in a sense,

01:46:01.680 | a different interpretation of what's going on

01:46:03.520 | in the universe.

01:46:04.680 | And we can imagine even things like an analog

01:46:07.280 | of the speed of light as the maximum speed

01:46:09.800 | of translation in Rullio space and so on.

01:46:12.560 | - So wait, what's the interpretation?

01:46:15.840 | So Rullio space, and we, I'm confused by the we

01:46:19.680 | and the interpretation and the universe.

01:46:22.400 | I thought moving about in Rullio space

01:46:25.040 | changes the way the universe is.

01:46:29.040 | - The way we would perceive it.

01:46:32.280 | The way that--

01:46:33.120 | - So it ultimately has to do with the perception.

01:46:35.400 | So it doesn't, Rullio space is not somehow changing,

01:46:41.720 | like branching into another universe or something like that.

01:46:45.720 | - No, I mean, the point is, the whole point of this

01:46:48.560 | is the Rulliard is sort of the encapsulated version

01:46:53.280 | of everything that is the universe

01:46:55.400 | running according to all possible rules.

01:46:56.880 | - We think of our universe,

01:46:59.240 | the observable universe as its thing.

01:47:03.320 | So we're a little bit loose with the word universe then

01:47:05.960 | because wouldn't the Rulliard potentially encapsulate

01:47:10.760 | a very large number, like combinatorially large,

01:47:14.040 | maybe infinite set of what we human physicists

01:47:18.440 | think of as universes?

01:47:20.280 | - That's an interesting parsing of the word universe, right?

01:47:23.880 | Because what we're saying is,

01:47:25.800 | just as we're at a particular place in physical space,

01:47:27.960 | we're at a particular place in Rullio space,

01:47:30.640 | at that particular place in Rullio space,

01:47:32.760 | our experience of the universe is this.

01:47:34.960 | Just as if we lived at the center of the galaxy,

01:47:36.960 | our universe, our experience of the universe

01:47:38.520 | will be different from the one it is

01:47:40.320 | given where we actually live.

01:47:42.000 | And so what we're saying is,

01:47:44.280 | what you might say,

01:47:47.160 | I mean, in a sense,

01:47:48.000 | this Rulliard is sort of a super universe, so to speak,

01:47:51.880 | but it's all entangled together.

01:47:53.560 | It's not like you can separate out.

01:47:55.120 | You can say, let me,

01:47:57.080 | it's like when we take a reference, okay.

01:47:59.480 | It's like our experience of the universe

01:48:01.000 | is based on where we are in the universe.

01:48:03.400 | We could imagine moving to somewhere else in the universe,

01:48:05.800 | but it's still the same universe.

01:48:07.120 | - So there's not like universes

01:48:09.960 | existing in parallel.

01:48:12.280 | - No, no, because,

01:48:14.200 | because, and the whole point is that

01:48:16.320 | if we were able to change our interpretation

01:48:19.240 | of what's going on,

01:48:20.620 | we could perceive a different reference frame

01:48:24.280 | in this Rulliard.

01:48:25.280 | - Yeah, but that's not,

01:48:26.600 | that's not, that's just, yeah,

01:48:28.680 | that's the same Rulliard,

01:48:30.600 | that's the same universe.

01:48:32.480 | You're just moving about.

01:48:34.000 | These are just coordinates in the universe.

01:48:35.840 | - So the way that's,

01:48:36.920 | the reason that's interesting is,

01:48:38.840 | imagine the extraterrestrial intelligence,

01:48:40.920 | so the alien intelligence, we should say.

01:48:43.460 | The alien intelligence might live on Alpha Centauri,

01:48:47.400 | but it might also live at a different place in Rullio space.

01:48:50.240 | - It can live right here on earth.

01:48:51.680 | It just has a different reference frame

01:48:53.400 | that includes a very different perception of the universe.

01:48:57.680 | And then because that Rullio space is very large,

01:49:02.100 | I mean,

01:49:02.940 | - Do we get to communicate with them?

01:49:05.620 | Right, that's.

01:49:06.460 | - Yeah, but it's also,

01:49:07.880 | well, one thing is how different

01:49:11.840 | the perception of the universe could be.

01:49:14.840 | - I think it could be bizarrely,

01:49:17.560 | unimaginably, completely different.

01:49:19.920 | And I mean, one thing to realize is,

01:49:21.880 | even in kind of things I don't understand well,

01:49:25.280 | you know, I know about the kind of Western tradition

01:49:28.280 | of understanding, you know, science

01:49:30.080 | and all that kind of thing.

01:49:31.320 | And, you know, you talk to people who say,

01:49:33.040 | well, I, you know, I'm really into some, you know,

01:49:37.160 | Eastern tradition of this, that, and the other.

01:49:39.560 | And it's really obvious to me how things work.

01:49:42.440 | I don't understand it at all, but, you know,

01:49:45.120 | it is not obvious, I think, with this kind of realization

01:49:48.280 | that there's these very different ways

01:49:50.440 | to interpret what's going on in the universe.

01:49:52.760 | That kind of gives me at least,

01:49:54.160 | it doesn't help me to understand

01:49:55.600 | that different interpretation,

01:49:57.120 | but it gives me at least more respect for the possibility

01:50:00.120 | that there will be other interpretations.

01:50:01.520 | - Yeah, it humbles you to the possibility that like,

01:50:04.840 | what is it, reincarnation,

01:50:06.120 | or all these like eternal recurrence,

01:50:09.320 | when you share like just these ideas, yeah.

01:50:12.800 | - Well, you know, the thing that I've realized

01:50:14.160 | about a bunch of those things is that, you know,

01:50:15.960 | I've been sort of doing my little survey

01:50:17.840 | of the history of philosophy, just trying to understand,

01:50:20.360 | you know, what can I actually say now

01:50:22.200 | about some of these things?

01:50:23.600 | And you realize that some of these concepts,

01:50:25.440 | like the immortal soul concept, which, you know,

01:50:28.720 | I remember when I was a kid and, you know,

01:50:31.080 | it was kind of a lots of religion bashing type stuff

01:50:34.240 | of people saying, you know, well, we know about physics,

01:50:37.240 | tell us how much does a soul weigh?

01:50:39.920 | And people are like, well, how can it be a thing

01:50:42.920 | if it doesn't weigh anything?

01:50:44.800 | Well, now we understand, you know,

01:50:46.560 | there is this notion of what's in brains

01:50:48.600 | that isn't the matter of brains

01:50:50.240 | and it's something computational.

01:50:52.040 | And there is a sense, and in fact, it is correct,

01:50:54.840 | that it is in some sense immortal

01:50:56.400 | because this pattern of computation is something abstract

01:50:59.600 | that is not specific to the particular material of a brain.

01:51:03.680 | Now, we don't know how to extract it, you know,

01:51:05.960 | in our traditional scientific approach,

01:51:08.400 | but it's still something where it isn't a crazy thing

01:51:11.840 | to say there is something, it doesn't weigh anything.

01:51:14.520 | That's a kind of a silly question.

01:51:16.240 | How much does it weigh?

01:51:18.160 | Well, actually, maybe it isn't such a silly question

01:51:20.360 | in our model of physics

01:51:21.360 | because the actual computational activity

01:51:24.240 | has a consequence for gravity and things,

01:51:26.520 | but that's a very subtle--

01:51:27.880 | - You can start talking about mass and energy and so on.

01:51:30.600 | There could be a, what would you call it, a solitron.

01:51:34.080 | - Yes, yes, yes.

01:51:36.360 | - A particle that somehow contains soleness.

01:51:39.680 | - Yeah, right.

01:51:40.520 | Well, that's what, by the way, that's what Leibniz said.

01:51:43.280 | And, you know, one thing, I've never understood this.

01:51:45.680 | You know, Leibniz had this idea of monads and monodology

01:51:48.480 | and he had this idea that what exists in the universe

01:51:51.200 | is this big collection of monads

01:51:53.200 | and that the only thing that one knows about the monads

01:51:56.560 | is sort of how they relate to each other,

01:51:58.320 | which sounds awfully like hypergraphs, right?

01:52:00.640 | But Leibniz had really lost me at the following thing.

01:52:04.120 | He said, "Each of these monads has a soul

01:52:06.880 | "and each of them has a consciousness."

01:52:09.240 | And it's like, okay, I'm out of here.

01:52:10.640 | I don't understand this at all.

01:52:12.160 | I don't know what's going on.

01:52:13.000 | But I realized recently that in his day,

01:52:16.240 | the concept that a thing could do something,

01:52:19.520 | could spontaneously do something,

01:52:21.640 | that was his only way of describing that.

01:52:23.920 | And so what I would now say is,

01:52:25.600 | well, there's this abstract rule that runs

01:52:28.160 | to Leibniz that would have been, you know,

01:52:30.680 | in 1690 or whatever, that would have been kind of,

01:52:33.600 | well, it has a soul, it has a consciousness.

01:52:36.440 | And so, you know, in a sense, it's like one of these,

01:52:39.100 | there's no new idea under the sun, so to speak.

01:52:41.440 | That's a sort of a version of the same kinds of ideas,

01:52:44.580 | but couched in terms that are sort of bizarrely different

01:52:48.480 | from the ones that we would use today.

01:52:50.380 | - Would you be able to maybe play devil's advocate

01:52:52.900 | on your conception of consciousness,

01:52:55.120 | that like the two characteristics of it,

01:52:58.040 | that it's constrained and there's a single thread of time,

01:53:01.640 | is it possible that Leibniz was onto something

01:53:04.200 | that the basic atom, the screwed atom of space

01:53:09.200 | has a consciousness?

01:53:10.760 | So these are just words, right?

01:53:14.240 | But like, is there some sense where consciousness

01:53:18.160 | is much more fundamental than you're making it seem?

01:53:21.760 | - I don't know.

01:53:22.600 | I mean, you know, I think--

01:53:24.200 | - Can you construct a world

01:53:25.360 | in which it is much more fundamental?

01:53:27.440 | - I think that, okay, so the question would be,

01:53:31.000 | is there a way to think about kind of,

01:53:33.640 | if we sort of parse the universe down

01:53:36.240 | at the level of atoms of space or something,

01:53:38.720 | could we say, well, so that's really a question

01:53:41.340 | of a different point of view,

01:53:42.240 | a different place in real space.

01:53:43.560 | We're asking, you're asking the question,

01:53:45.560 | could there be a civilization that exists?

01:53:48.520 | Could there be sort of conscious entities

01:53:52.600 | that exist at the level of atoms of space?

01:53:54.920 | And what would that be like?

01:53:56.240 | And I think that comes back to this question of,

01:53:58.000 | can we, you know, what's it like

01:53:59.080 | to be a cellular automaton type thing?

01:54:01.160 | I mean, it's, you know, I'm not yet there.

01:54:04.880 | I don't know.

01:54:06.160 | I mean, I think that this is a,

01:54:08.460 | and I don't even know yet quite how to think about this

01:54:12.960 | in the sense that I was considering, you know,

01:54:15.720 | I never write fiction, but I haven't written it

01:54:17.680 | since I was like 10 years old.

01:54:18.800 | And my fiction, I made one attempt,

01:54:20.840 | which I sent to some science fiction writer friends of mine,

01:54:23.320 | and they told me it was terrible.

01:54:24.240 | So, but--

01:54:25.720 | - This is a long time ago?

01:54:26.880 | - No, it was recently.

01:54:28.000 | - Recently, and they said it was terrible.

01:54:29.480 | That'd be interesting to see you write a short story

01:54:32.000 | based on what sounds like it's already inspiring

01:54:34.760 | short stories by, or stories--

01:54:37.080 | - Yeah, right. - By science fiction writers.

01:54:38.800 | - But I think the interesting thing for me is,

01:54:42.400 | you know, in the what does it,

01:54:43.520 | what is it like to be a whatever?

01:54:45.480 | - Yeah. - How do you describe that?

01:54:46.920 | I mean, it's like, that's not a thing

01:54:48.240 | that you describe in mathematics,

01:54:49.640 | that what is it like to be such and such?

01:54:51.920 | - Well, see, to me, when you say,

01:54:53.760 | what is it like to be something,

01:54:56.360 | presumes that you're talking about a singular entity.

01:55:01.160 | So-- - Yeah.

01:55:02.760 | - Like, there's some kind of feeling of the entity,

01:55:07.760 | the stuff that's inside of it,

01:55:10.840 | and the stuff that's outside of it.

01:55:12.800 | And then that's when consciousness starts making sense.

01:55:17.000 | But then, it seems like that could be generalizable.

01:55:21.440 | If you take some subset of a cellular automata,

01:55:25.960 | you could start talking about what does that subset--

01:55:29.640 | - Maybe. - Feel.

01:55:30.800 | But then you can, I think you could just take

01:55:32.720 | arbitrary numbers of subsets.

01:55:35.280 | Like, to me, like, you and I,

01:55:38.840 | individually are consciousnesses,

01:55:41.880 | but you could also say the two of us together

01:55:44.600 | is a singular consciousness.

01:55:45.720 | - Maybe, maybe.

01:55:47.040 | I'm not so sure about that.

01:55:48.120 | I think that the single thread of time thing

01:55:50.000 | may be pretty important.

01:55:51.480 | And that as soon as you start saying,

01:55:53.480 | there are two different threads of time,

01:55:55.440 | there are two different experiences,

01:55:57.800 | and then we have to say, how do they relate?

01:55:59.400 | How are they sort of entangled with each other?

01:56:01.600 | I mean, that may be a different story

01:56:03.200 | of a thing that isn't much like, you know,

01:56:06.360 | what are the ants?

01:56:07.480 | You know, what's it like to be an ant?

01:56:08.960 | You know, where there's a sort of more collective view

01:56:11.360 | of the world, so to speak.

01:56:13.040 | I don't know.

01:56:13.960 | I think that, I mean, this is, you know,

01:56:19.120 | I don't really have a good, I mean,

01:56:21.000 | you know, my best thought is, you know,

01:56:23.360 | can we turn it into a human story?

01:56:25.000 | It's like the question of, you know,

01:56:27.440 | when we try and understand physics,

01:56:28.920 | can we turn that into something

01:56:30.080 | which is sort of a human understandable narrative?

01:56:32.360 | And now what's it like to be a such and such?

01:56:35.320 | You know, maybe the only medium in which we can describe

01:56:37.920 | that is something like fiction,

01:56:39.920 | where it's kind of like you're telling, you know,

01:56:42.280 | the life story in that setting.

01:56:45.440 | But this is beyond what I've yet understood how to do.

01:56:49.640 | - Yeah, but it does seem so, like with human consciousness,

01:56:53.160 | you know, we're made up of cells,

01:56:55.000 | and like there's a bunch of systems that are networked

01:56:59.600 | that work together that at the human level

01:57:04.520 | feel like a singular consciousness when you take.

01:57:06.760 | - Yes.

01:57:07.600 | - And so maybe like an ant colony is just too low level.

01:57:11.400 | Sorry, an ant is too low level.

01:57:13.960 | Maybe you have to look at the ant colony.

01:57:16.000 | - Yeah, I agree.

01:57:16.840 | - There's some level at which it's a conscious being.

01:57:20.160 | And then if you go to the planetary scale,

01:57:22.600 | then maybe that's going too far.

01:57:23.960 | So there's a nice sweet spot for consciousness.

01:57:26.840 | - No, I agree.

01:57:28.160 | I think the difficulty is that, you know, okay,

01:57:32.360 | so in sort of people who talk about consciousness,

01:57:35.600 | one of the terrible things I've realized,

01:57:37.560 | 'cause I've now interacted with some of this community,

01:57:40.120 | so to speak, some interesting people

01:57:42.280 | who do that kind of thinking,

01:57:44.360 | but one of the things I was saying

01:57:46.120 | to one of the leading people in that area,

01:57:48.160 | I was saying that it must be kind of frustrating

01:57:53.160 | because it's kind of like a poetry story.

01:57:55.640 | That is, many people are writing poems,

01:57:57.320 | but few people are reading them.

01:57:58.800 | - Yes.

01:57:59.640 | - So there are always these different,

01:58:01.000 | everybody has their own theory of consciousness,

01:58:03.360 | and they are very non-interdiscussable.

01:58:08.200 | And by the way, I mean, my own approach

01:58:11.440 | to sort of the question of consciousness,

01:58:13.720 | as far as I'm concerned,

01:58:14.600 | I'm an applied consciousness operative, so to speak,

01:58:17.200 | because I don't really, in a sense,

01:58:19.640 | the thing I'm trying to get out of it

01:58:21.360 | is how does it help me to understand

01:58:23.400 | what's a possible theory of physics?

01:58:25.520 | And how does it help me to say,

01:58:27.720 | how do I go from this incoherent collection

01:58:30.880 | of things happening in the universe

01:58:32.720 | to our definite perception and definite laws and so on,

01:58:35.760 | and sort of an applied version of consciousness?

01:58:38.320 | And I think the reason it sort of segues

01:58:40.840 | to a different kind of topic,

01:58:41.840 | but the reason that one of the things

01:58:44.360 | I'm particularly interested in

01:58:45.480 | is kind of what's the analog of consciousness

01:58:48.040 | in systems very different from brains?

01:58:50.600 | And so why does that matter?

01:58:52.600 | Well, this whole description of this kind of,

01:58:55.720 | well, actually, you know what?

01:58:57.640 | We haven't talked about why the universe exists,

01:58:59.440 | so let's get to why the universe exists,

01:59:01.360 | and then we can talk about, perhaps a little bit about

01:59:05.440 | what these models of physics kind of show you

01:59:09.040 | about other kinds of things

01:59:10.320 | like molecular computing and so on.

01:59:12.120 | - Yes, that's good. - Okay,

01:59:13.280 | why does the universe exist?

01:59:14.840 | Okay, so we finally sort of more or less set the stage.

01:59:17.240 | We've got this idea of this Rouliad,

01:59:19.400 | of this object that is made

01:59:21.040 | from following all possible rules,

01:59:22.960 | the fact that it's sort of not just this incoherent mess,

01:59:26.400 | it's got all this entangled structure in it, and so on.

01:59:29.520 | Okay, so what is this Rouliad?

01:59:32.600 | Well, it is the working out of all possible formal systems.

01:59:37.520 | So the sort of the question of why does the universe exist,

01:59:41.080 | its core question, which we kind of started with,

01:59:43.360 | is you've got two plus two equals four,

01:59:45.680 | you've got some other abstract result,

01:59:48.760 | but that's not actualized, it's just an abstract thing.

01:59:52.680 | And when we say we've got a model for the universe,

01:59:54.400 | okay, it's this rule, you run it,

01:59:56.280 | and it'll make the universe, but it's like,

01:59:58.200 | but where's it actually running?

02:00:01.400 | What is it actually doing, right?

02:00:04.560 | What, is it actual,

02:00:06.720 | or is it merely a formal description of something?

02:00:09.720 | Okay, so the thing to realize with this,

02:00:13.240 | the thing about the Rouliad is it's an inevitable,

02:00:16.520 | it is the entangled running of all possible rules.

02:00:21.240 | So you don't get to say, it's not like you're saying,

02:00:24.280 | which Rouliad are you picking?

02:00:26.160 | Because it's all possible formal rules.

02:00:28.640 | It's not like it's just, you know,

02:00:31.520 | well, actually it's only footnote,

02:00:33.760 | the only footnote, it's an important footnote,

02:00:35.560 | is it's all possible computational rules,

02:00:38.960 | not hyper computational rules.

02:00:41.160 | That is, it's running all the rules

02:00:44.640 | that would be accessible to a Turing machine,

02:00:48.600 | but it is not running all the rules

02:00:50.640 | that will be accessible to a thing

02:00:52.160 | that can solve problems in finite time

02:00:54.720 | that would take a Turing machine infinite time to solve.

02:00:57.280 | So you can, even Alan Turing knew this,

02:00:59.280 | that you could make oracles for Turing machines,

02:01:01.640 | where you say a Turing machine can't solve

02:01:03.640 | a halting problem for Turing machines.

02:01:05.200 | It can't know what will happen in any Turing machine

02:01:07.680 | after an infinite time, in any finite time,

02:01:10.120 | but you could invent a box, just make a black box.

02:01:13.240 | You say, I'm gonna sell you an oracle

02:01:15.760 | that will just tell you, you know, press this button,

02:01:18.120 | it'll tell you what the Turing machine

02:01:19.400 | will do after an infinite time.

02:01:20.800 | You can imagine such a box.

02:01:22.880 | You can't necessarily build one in the physical universe,

02:01:24.860 | but you can imagine such a box.

02:01:26.800 | And so we could say, well, in addition to,

02:01:29.160 | so in this Rouliad, we're imagining

02:01:32.080 | that there is a computational, that at the end,

02:01:35.600 | it's running rules that are computational.

02:01:37.920 | It doesn't have a bunch of oracle black boxes in it.

02:01:42.240 | You say, well, why not?

02:01:44.020 | Well, it turns out if there are oracle black boxes,

02:01:47.240 | the Rouliad that is, you can make a sort of super Rouliad

02:01:50.680 | that contains those oracle black boxes,

02:01:53.220 | but it has a cosmological event horizon

02:01:55.440 | relative to the first one, they can't communicate.

02:01:58.160 | In other words, you can end up with,

02:02:00.720 | what you end up happening, what ends up happening

02:02:03.320 | is it's like in the physical universe,

02:02:06.000 | we in this causal graph that represents

02:02:07.960 | the causal relationships of different things,

02:02:10.080 | you can have an event horizon,

02:02:11.720 | where the causal graph is disconnected,

02:02:14.760 | where the effect here, an event happening here

02:02:17.640 | does not affect an event happening here

02:02:19.800 | because there's a disconnection in the causal graph.

02:02:22.000 | And that's what happens in an event horizon.

02:02:24.200 | And so what will happen between this kind of

02:02:27.120 | the ordinary Rouliad and the hyper Rouliad

02:02:30.320 | is there is an event horizon and we in our Rouliad

02:02:35.320 | will just never know that there is,

02:02:39.480 | that they're just separate things, they're not connected.

02:02:43.080 | - Maybe I'm not understanding,

02:02:44.400 | but just because we can't observe it,

02:02:46.300 | why does that mean it doesn't exist?

02:02:49.620 | - It might exist, but it's not clear what it,

02:02:54.400 | so what, so to speak, whether it exists.

02:02:57.160 | What we're trying to understand

02:02:58.280 | is why does our universe exist?

02:03:00.760 | We're not trying to ask the question,

02:03:02.600 | what, you know, it's, let me say another thing,

02:03:06.480 | let me make a meta comment, okay?

02:03:08.960 | Which is that I have not thought through

02:03:11.280 | this hyper Rouliad business properly.

02:03:13.200 | So I can't, the--

02:03:15.440 | - The hyper Rouliad is referring to a Rouliad

02:03:20.720 | in which hyper computation is possible.

02:03:22.760 | - That's correct, yes.

02:03:24.320 | - So like what, that footnote,

02:03:27.120 | the footnote to the footnote is,

02:03:29.640 | we're not sure why this is important.

02:03:33.340 | - Yeah, that's right.

02:03:34.260 | So let's ignore that, okay?

02:03:36.660 | It's already abstract enough, okay?

02:03:38.960 | So, okay, so the one question is,

02:03:42.120 | we have to say, if we're saying,

02:03:45.080 | why does the universe exist?

02:03:46.880 | One question is, why is it this universe

02:03:48.800 | and not another universe, okay?

02:03:51.000 | So the important point about this Rouliad idea

02:03:54.240 | is that it's, in the Rouliad are all possible formal systems.

02:03:59.160 | So there's no choice being made.

02:04:01.120 | There's no like, oh, we pick this particular universe

02:04:04.240 | and not that one.

02:04:05.280 | That's the first thing.

02:04:06.280 | The second thing is that we have to ask the question.

02:04:10.000 | So you say, why does two plus two equals four exist?

02:04:15.000 | That's not really a, that is a thing

02:04:17.200 | that necessarily is that way,

02:04:19.840 | just on the basis of the meaning of the terms,

02:04:21.880 | two and plus and equals and so on, right?

02:04:24.980 | So the thing is that this Rouliad object

02:04:28.340 | is in a sense a necessary object.

02:04:30.920 | It is just a thing that is the consequence

02:04:33.400 | of working out the consequence

02:04:35.900 | of the formal definition of things.

02:04:38.120 | You don't, it is not a thing where you're saying,

02:04:40.560 | and this is picked as the particular thing.

02:04:43.680 | This is just something which necessarily is that thing

02:04:47.840 | because of the definition

02:04:49.160 | of what it means to have computation.

02:04:50.920 | - So the Rouliad, it's a formal system.

02:04:54.560 | - Yes.

02:04:55.400 | - But does it exist?

02:04:58.800 | - Ah, well, where are we in this whole thing?

02:05:03.480 | We are part of this Rouliad.

02:05:05.680 | And so our, so there is no sense to say,

02:05:09.960 | does two plus two equals four exist?

02:05:13.240 | Well, that's, in some sense, it necessarily exists.

02:05:18.120 | It's a necessary object.

02:05:19.520 | It's not a thing that where you can ask.

02:05:21.840 | Usually in philosophy, there's a sort of distinction made

02:05:26.080 | between necessary truths, contingent truths,

02:05:29.920 | analytic propositions, synthetic propositions,

02:05:32.160 | there are a variety of different versions of this.

02:05:34.320 | There are things which are necessarily true

02:05:36.960 | just based on the definition of terms.

02:05:39.600 | And there are things which happen to be true in our universe.

02:05:42.880 | - But we don't exist in Roulial space.

02:05:46.800 | That's one of the coordinates that define our existence.

02:05:50.280 | - Well, okay, so yes, yes.

02:05:53.440 | But this Rouliad is the set

02:05:56.120 | of all possible Roulial coordinates.

02:05:58.400 | So what we're saying is it contains that.

02:06:01.120 | So what we're saying is we exist as, okay,

02:06:04.520 | so our perception of what's going on

02:06:06.760 | is we're at a particular place in this Rouliad,

02:06:09.400 | and we are concluding certain things

02:06:11.060 | about how the universe works based on that.

02:06:13.700 | But the question is, do we understand,

02:06:17.760 | is there something where we say,

02:06:20.640 | so why does it work that way?

02:06:23.520 | Well, the answer is, I think it has to work that way

02:06:27.480 | because this Rouliad is a necessary object

02:06:32.480 | in the sense that it is a purely formal object,

02:06:35.520 | just like two plus two equals four.

02:06:37.500 | It's not an object that was made of something.

02:06:40.740 | It's an object that is just an expression

02:06:43.040 | of the necessary collection of formal relations that exist.

02:06:47.280 | And so then the issue is, can we, in our experience of that,

02:06:52.280 | is it, can we have tables and chairs, so to speak,

02:06:56.200 | in that just by virtue of our experience

02:06:59.540 | of that necessary thing?

02:07:01.560 | And what people have generally thought,

02:07:03.640 | and honestly, I don't know of a lot of discussion of this

02:07:07.800 | why does the universe exist question.

02:07:09.720 | It's been a very, I've been surprised, actually,

02:07:12.920 | at how little, I mean, I think it's one of these things

02:07:15.520 | that's really kind of far out there.

02:07:18.440 | But the thing that is, the surprise here

02:07:22.800 | is that all possible formal rules,

02:07:26.080 | when you run them together, and that's the critical thing,

02:07:29.120 | when you run them together,

02:07:30.080 | they produce this kind of entangled structure

02:07:32.880 | that has a definite structure.

02:07:34.920 | It's not just a random arbitrary thing.

02:07:38.040 | It's a thing with definite structure.

02:07:40.040 | And that structure is the thing,

02:07:42.360 | when we are embedded in that structure,

02:07:44.440 | when an entity embedded in that structure

02:07:48.800 | perceives something which is,

02:07:51.400 | then we can interpret as physics and things like this.

02:07:54.600 | So in other words, we don't have to ask the question,

02:07:57.200 | why does it exist?

02:07:59.740 | It necessarily exists.

02:08:01.320 | - I'm missing this part.

02:08:02.320 | Why does it necessarily exist?

02:08:04.240 | - Okay, let me try.

02:08:05.080 | - So like you need to have it if you want to formalize

02:08:09.220 | the relation between entities,

02:08:11.540 | but why do you need to have relations?

02:08:15.880 | - Okay, okay.

02:08:16.720 | So let's say you say, well-

02:08:20.960 | - It's like, why does math have to exist?

02:08:25.800 | - Okay, fair question.

02:08:27.520 | Yeah, okay, fair question.

02:08:29.000 | Let's see.

02:08:31.180 | I think the thing to think about is

02:08:33.680 | the existence of mathematics is something where,

02:08:36.880 | given a definition of terms,

02:08:40.160 | what follows from that definition inevitably follows.

02:08:44.480 | So now you can say, why define any terms?

02:08:48.480 | But in a sense, the, well, that's okay.

02:08:53.120 | So the definition of terms, I mean,

02:08:55.880 | I think the way to think about this, let me see.

02:08:58.960 | - So like concrete terms.

02:09:02.320 | - Well, not very concrete.

02:09:04.400 | I mean, they're just things like, you know,

02:09:09.080 | logical or.

02:09:10.480 | - Right, but that's a thing.

02:09:12.800 | That's a powerful thing.

02:09:14.080 | - Well, it's a, yes, okay.

02:09:15.720 | But it's a, the point is that it is not a thing of a,

02:09:19.200 | you know, people imagine there is, I don't know,

02:09:22.760 | the, you know, an elephant or something,

02:09:25.800 | or the, you know, elephants are presumably

02:09:29.100 | not necessary objects.

02:09:31.280 | They are, they happen to exist as a result of

02:09:34.240 | kind of biological evolution and whatever else.

02:09:37.080 | But the thing is that in some sense,

02:09:41.360 | that there is, it is a different kind of thing

02:09:44.320 | to say does plus exist.

02:09:46.760 | It is not like an elephant.

02:09:49.640 | - So a plus is, seems more fundamental,

02:09:51.880 | more basic than an elephant, yes.

02:09:54.200 | But you can imagine a world without plus

02:09:58.800 | or anything like it.

02:10:00.880 | Like why do formal things that are discrete,

02:10:04.800 | that can be used to reason have to exist?

02:10:09.480 | - Well, okay, so why, okay, so then the question is,

02:10:12.880 | but the whole point is computation,

02:10:15.560 | we can certainly imagine computation.

02:10:18.500 | That is, we can certainly say there is a formal system

02:10:21.560 | that we can construct abstractly in our minds

02:10:24.880 | that is computation.

02:10:26.820 | And that's the, you know, we can imagine it, right?

02:10:32.120 | Now the question is, is it is that formal system,

02:10:37.120 | once we exist as observers embedded in that formal system,

02:10:41.720 | that's enough to have something which is like our universe.

02:10:45.560 | And so then what you're kind of asking is perhaps,

02:10:49.720 | is why, I mean, the point is we definitely can imagine it.

02:10:54.360 | There's nothing that says that,

02:10:56.120 | we're not saying that there's,

02:10:59.000 | it's sort of inevitable that that is a thing

02:11:03.400 | that we can imagine.

02:11:04.240 | We don't have to ask, does it exist?

02:11:06.600 | We're just, it is definitely something we can imagine.

02:11:09.400 | Now that's, then we have this thing

02:11:12.520 | that is a formally constructible thing that we can imagine.

02:11:16.940 | And now we have to ask the question,

02:11:18.840 | what, you know, given that formally constructible thing,

02:11:22.880 | what is, what consequences does that,

02:11:25.920 | if we were to perceive that formally,

02:11:28.640 | if we were embedded in that formally constructible thing,

02:11:31.840 | what would we perceive about the world?

02:11:33.840 | And we would say, we perceive that the world exists

02:11:38.480 | because we are seeing all of this mechanism

02:11:41.080 | of all these things happening.

02:11:42.600 | And, but that's something that is just a feature of,

02:11:46.080 | it's something where we are--

02:11:48.600 | - See another way of asking this,

02:11:50.800 | that I'm trying to get at,

02:11:52.800 | I understand why it feels like this Rouliad

02:11:57.280 | is necessary,

02:11:59.480 | but maybe it's just me being human,

02:12:03.740 | but it feels like then you should be able to,

02:12:07.560 | not us, but somehow step outside of the Rouliad.

02:12:11.640 | Like what's outside the Rouliad?

02:12:14.200 | - Well, the Rouliad is all formal systems.

02:12:16.920 | So there's nothing because--

02:12:18.600 | - But that's what a human would say.

02:12:20.480 | - I know that's what a human would say

02:12:21.760 | 'cause we're used to the idea that there's,

02:12:24.660 | but the whole point is that

02:12:26.040 | by the time it's all possible formal systems,

02:12:28.860 | it's like, it is all things you can imagine, but--

02:12:34.520 | - Not all computations you can imagine,

02:12:37.160 | but like we don't--

02:12:39.140 | - Well, so the issue is can we encode?

02:12:41.480 | Okay, so that's a fair question.

02:12:44.240 | Is it possible to encode all,

02:12:47.960 | I mean, once we,

02:12:50.000 | is there something that isn't

02:12:51.760 | what we can represent formally?

02:12:53.480 | - Right.

02:12:54.320 | - That is, is there something that,

02:12:56.320 | and that's I think related to the hyper-Rouliad footnote,

02:12:59.520 | so to speak, of which I'm afraid that the,

02:13:04.360 | one of the things sort of interesting about this is,

02:13:07.440 | there has been some discussion of this in theology

02:13:09.880 | and things like that,

02:13:11.680 | but which I don't necessarily understand all of,

02:13:15.480 | but the key sort of new input is this idea

02:13:20.480 | that all possible formal systems,

02:13:23.080 | it's like, if you make a world,

02:13:25.920 | people say, well, you make a world

02:13:27.880 | with a particular, in a particular way,

02:13:30.040 | with particular rules, but no, you don't do that.

02:13:32.560 | You can make a world that deals with all possible rules

02:13:35.840 | and then merely by virtue of living in a particular place

02:13:40.760 | in that world, so to speak,

02:13:42.440 | we have the perception we have of what the world is like.

02:13:45.620 | Now, I have to say,

02:13:46.880 | it's sort of interesting 'cause I've,

02:13:50.520 | I wrote this piece about this

02:13:51.840 | and I, this philosophy stuff is not super easy

02:13:56.120 | and I've, as I'm talking to you about it

02:13:59.720 | and I actually haven't,

02:14:01.280 | people have been interested in lots of different things

02:14:02.840 | we've been doing, but this, why does the universe exist,

02:14:05.240 | has been, I would say, one of the ones

02:14:08.080 | that you would think people would be most interested in,

02:14:11.040 | but actually, I think they're just like,

02:14:13.400 | oh, that's just something complicated that,

02:14:16.560 | so I haven't explained it as much

02:14:19.880 | as I've explained a bunch of other things

02:14:21.240 | and I have to say, I think I may be missing

02:14:23.640 | a couple of pieces of that argument that would be,

02:14:27.800 | so it's kind of like--

02:14:29.520 | - Well, you're conscious being is computationally bounded,

02:14:33.840 | so you're missing-- - Indeed.

02:14:34.960 | - Having written quite a few articles yourself,

02:14:38.160 | you're now missing some of the pieces.

02:14:40.520 | - Yes, well, it's always-- - That's the limitation

02:14:41.840 | of being human.

02:14:42.680 | - Right, one of the consequences of this,

02:14:44.900 | why the universe exists thing and this kind of concept

02:14:48.520 | of Rouillades and places in there representing

02:14:53.320 | our perception of the universe and so on,

02:14:55.360 | one of the weird consequences is,

02:14:57.760 | if the universe exists, mathematics must also exist.

02:15:01.380 | And that's a weird thing because mathematics,

02:15:05.140 | people have been very confused, including me,

02:15:07.360 | have been very confused about the question

02:15:11.640 | of kind of what is the foundation of mathematics?

02:15:15.480 | What is, what kind of a thing is mathematics?

02:15:17.600 | Is mathematics something where we just write down axioms

02:15:21.680 | like Euclid did for geometry and we just build the structure

02:15:24.920 | and we could have written down different axioms

02:15:26.520 | and we'd have a different structure?

02:15:28.200 | Or is it something that has a more fundamental

02:15:30.600 | sort of truth to it?

02:15:32.000 | And I have to say, it's one of these cases where

02:15:34.040 | I've long believed that mathematics has a great deal

02:15:37.000 | of arbitrariness to it, that there are particular axioms

02:15:39.840 | that kind of got written down by the Babylonians

02:15:42.420 | and that's what we've ended up with the mathematics

02:15:45.080 | that we have.

02:15:46.000 | And I have to say, actually, my wife has been telling me

02:15:48.400 | for 25 years, she's a mathematician,

02:15:50.480 | she's been telling me, "You're wrong about the foundations

02:15:52.680 | "of mathematics."

02:15:53.520 | And I'm like, "No, no, no, I know what I'm talking about."

02:15:57.740 | And finally, she's much more right than I've been.

02:16:02.120 | So it's one of the--

02:16:03.880 | - So I mean, her sense and your sense, are we just,

02:16:08.560 | so this is to the question of mathematics,

02:16:11.280 | are we just kind of on a trajectory through

02:16:14.920 | ruleal space except in mathematics,

02:16:17.000 | is there a trajectory, a certain kind of--

02:16:19.320 | - I think that's partly the idea.

02:16:21.080 | So I think that the notion is this.

02:16:22.800 | So 100 years ago, a little bit more than 100 years ago,

02:16:26.200 | well, people have been doing mathematics for ages,

02:16:28.200 | but then in the late 1800s, people decided to try

02:16:31.160 | and formalize mathematics and say,

02:16:33.800 | mathematics is, we're gonna break it down,

02:16:37.320 | we're gonna make it like logic, we're gonna make it

02:16:39.200 | out of sort of fundamental primitives.

02:16:42.020 | And that was people like Frege and Piano and Hilbert

02:16:44.120 | and so on, and they kind of got this idea of,

02:16:47.680 | let's do kind of Euclid, but even better,

02:16:50.280 | let's just make everything just in terms of this sort of

02:16:52.600 | symbolic axioms, and then build up mathematics from that.

02:16:56.300 | And that, they thought at the time,

02:16:59.420 | as soon as they get these symbolic axioms,

02:17:02.320 | that they made the same mistake,

02:17:03.800 | the kind of computational irreducibility mistake.

02:17:06.240 | They thought as soon as we've written down the axioms,

02:17:09.440 | then it'll just, we'll just have a machine,

02:17:11.640 | kind of a super Mathematica, so to speak,

02:17:13.960 | that can just grind out all true theorems of mathematics.

02:17:17.760 | That got exploded by Godel's theorem,

02:17:20.000 | which is basically the story

02:17:21.280 | of computational irreducibility.

02:17:23.120 | It's that even though you know those underlying rules,

02:17:25.880 | you can't deduce all the consequences in any finite way.

02:17:29.680 | And so that was, but now the question is,

02:17:32.040 | okay, so they broke mathematics down into these axioms,

02:17:35.600 | and they say, now you build up from that.

02:17:37.800 | So what I'm increasingly coming to realize is,

02:17:41.460 | that's similar to saying, let's take a gas

02:17:44.260 | and break it down into molecules.

02:17:46.340 | There's gas laws that are the large scale structure

02:17:49.500 | and so on that we humans are familiar with,

02:17:52.060 | and then there's the underlying molecular dynamics.

02:17:54.740 | And I think that the axiomatic level of mathematics,

02:17:57.640 | which we can access with automated theorem proving

02:18:00.180 | and proof assistance and these kinds of things,

02:18:02.820 | that's the molecular dynamics of mathematics.

02:18:05.340 | And occasionally we see through to that molecular dynamics.

02:18:08.700 | We see undecidability, we see other things like this.

02:18:11.300 | One of the things I've always found very mysterious

02:18:13.820 | is that Godel's theorem shows that there are sort of things

02:18:18.220 | which cannot be finitely proved in mathematics.

02:18:20.420 | There are proofs of arbitrary length,

02:18:22.200 | infinite length proofs that you might need.

02:18:24.500 | But in practical mathematics,

02:18:26.060 | mathematicians don't typically run into this.

02:18:28.300 | They just happily go along doing their mathematics.

02:18:31.420 | And I think what's actually happening is that

02:18:33.580 | what they're doing is they're looking at this,

02:18:36.600 | they are essentially observers in meta-mathematical space,

02:18:41.600 | and they are picking a reference frame

02:18:43.900 | in meta-mathematical space,

02:18:45.600 | and they are computationally bounded observers

02:18:47.720 | of meta-mathematical space,

02:18:49.340 | which is causing them to deduce

02:18:52.000 | that the laws of meta-mathematics

02:18:54.120 | and the laws of mathematics,

02:18:55.680 | like the laws of fluid mechanics,

02:18:57.380 | are much more understandable

02:18:59.240 | than this underlying molecular dynamics.

02:19:01.840 | And so what gets really bizarre is thinking about

02:19:05.240 | kind of the analogy between meta-mathematics,

02:19:08.660 | this idea of you exist in this kind of,

02:19:11.780 | in this sort of space of possible,

02:19:16.040 | in this kind of mathematical space

02:19:17.920 | where the individual kind of points

02:19:20.960 | in the mathematical space are statements in mathematics,

02:19:24.160 | and they're connected by proofs,

02:19:26.200 | where one statement, you know,

02:19:27.440 | you take a couple of different statements,

02:19:29.040 | you can use those to prove some other statement,

02:19:31.160 | and you've got this whole network of proofs.

02:19:33.600 | That's the kind of causal network of mathematics,

02:19:35.920 | of what can prove what, and so on.

02:19:38.120 | And you can say at any moment

02:19:40.320 | in the history of a mathematician,

02:19:42.940 | of a single mathematical consciousness,

02:19:45.280 | you are in a single kind of slice

02:19:48.520 | of this kind of meta-mathematical space.

02:19:51.280 | You know a certain set of mathematical statements.

02:19:54.160 | You can then deduce with proofs,

02:19:55.920 | you can deduce other ones, and so on.

02:19:57.820 | You're kind of gradually moving

02:19:59.180 | through meta-mathematical space.

02:20:01.160 | And so it's kind of the view is

02:20:03.520 | that the reason that mathematicians perceive mathematics

02:20:07.000 | to have the sort of integrity

02:20:08.680 | and lack of kind of undecidability and so on that they do,

02:20:11.580 | is because they, like we as observers

02:20:14.200 | of the physical universe,

02:20:15.520 | we have these limitations associated

02:20:17.320 | with computational boundedness, single thread of time,

02:20:20.040 | consciousness limitations, basically,

02:20:22.240 | that the same thing is true of mathematicians

02:20:24.600 | perceiving sort of meta-mathematical space.

02:20:26.440 | And so what's happening is that when you look at,

02:20:29.160 | if you look at one of these formalized mathematics systems,

02:20:32.080 | something like Pythagoras' theorem,

02:20:34.400 | it'll be, it'll take, oh, I don't know, what is it?

02:20:38.320 | Maybe 10,000 individual little steps

02:20:41.400 | to prove Pythagoras' theorem.

02:20:43.240 | And one of the bizarre things,

02:20:45.200 | that's sort of an empirical fact

02:20:46.920 | that I'm trying to understand a little bit better,

02:20:48.640 | if you look at different proof,

02:20:50.240 | if you look at different formalized mathematics systems,

02:20:52.800 | they actually have different axioms underneath,

02:20:55.120 | but they can all prove Pythagoras' theorem.

02:20:57.360 | And so, in other words,

02:20:58.680 | it's a little bit like what happens with gases.

02:21:01.080 | We can have air molecules, we can have water molecules,

02:21:03.440 | but they still have fluid dynamics.

02:21:05.080 | Both of them have fluid dynamics.

02:21:06.800 | And so similarly, at the level that mathematics,

02:21:09.440 | that mathematicians care about mathematics,

02:21:11.760 | it's way above the molecular dynamics, so to speak.

02:21:14.680 | And there are all kinds of weird things,

02:21:16.280 | like for example, one thing I was realizing recently

02:21:18.280 | is that the quantum theory of mathematics,

02:21:20.480 | that's a very bizarre idea.

02:21:22.200 | But basically, when you prove what is, you know,

02:21:25.720 | a proof is you've got one statement in mathematics,

02:21:29.120 | you go through other statements,

02:21:30.200 | you eventually get to a statement

02:21:31.560 | you're trying to prove, for example,

02:21:33.080 | that's a path in metamathematical space.

02:21:36.620 | And that's a single path, a single proof is a single path.

02:21:39.900 | But you can imagine there are other proofs

02:21:41.960 | of the same result.

02:21:43.520 | There are a bundle of proofs.

02:21:45.160 | There's this whole set of possible proofs.

02:21:47.480 | - You could think of it as branching,

02:21:48.720 | similar to the quantum mechanics model

02:21:50.320 | that you were talking about.

02:21:51.160 | - Exactly, and so-

02:21:52.000 | - And then there's some invariance that you can formalize

02:21:54.600 | in the same way that you can for the quantum mechanical.

02:21:56.880 | - Right, so the question is in proof space,

02:21:59.240 | you know, as you start thinking about multiple proofs,

02:22:01.720 | are there analogs of, for example,

02:22:03.000 | destructive interference of multiple proofs?

02:22:05.440 | So here's a bizarre idea, it's just a couple of days old,

02:22:08.360 | so not yet fully formed.

02:22:10.640 | But as you try and do that,

02:22:12.640 | when you have two different proofs,

02:22:14.480 | it's like two photons going in different directions.

02:22:16.360 | You have two proofs which at an intermediate stage

02:22:19.040 | are incompatible.

02:22:20.400 | And that's kind of like destructive interference.

02:22:22.160 | - Is it possible for this to instruct the engineering

02:22:25.720 | of automated proof systems?

02:22:28.080 | - Absolutely, I mean, as a practical matter,

02:22:29.840 | I mean, you know, this whole question,

02:22:32.040 | in fact, Jonathan Gorad has a nice heuristic

02:22:34.440 | for automated theorem provers

02:22:35.960 | that's based on our physics project

02:22:37.880 | that is looking for essentially using kind of,

02:22:42.280 | using energy, in our models,

02:22:44.920 | energy is kind of level of activity in this hypergraph.

02:22:49.400 | And so there's sort of a heuristic

02:22:51.200 | for automated theorem proving

02:22:52.800 | about how do you pick which path to go down

02:22:56.120 | that is based on essentially physics.

02:22:59.800 | And I mean, the thing that gets interesting about this

02:23:02.440 | is the way that one can sort of have the interplay

02:23:04.920 | between like, for example, a black hole.

02:23:06.720 | What is a black hole in mathematics?

02:23:09.160 | So the answer is, what is a black hole in physics?

02:23:11.800 | A black hole in physics is where,

02:23:14.160 | in the simplest form of black hole, time ends.

02:23:16.960 | That is all, you know, everything is crunched down

02:23:20.000 | to the space-time singularity

02:23:21.720 | and everything just ends up at that singularity.

02:23:24.600 | So in our models, and that's a little hard to understand

02:23:27.440 | in general relativity with continuous mathematics

02:23:29.640 | and what does singularity look like.

02:23:31.400 | In our models, it's something very pragmatic.

02:23:33.280 | It's just, you're applying these rules,

02:23:35.080 | time is moving forward,

02:23:36.520 | and then there comes a moment where the rules,

02:23:38.320 | no rules apply, so time stops.

02:23:41.000 | It's kind of like the universe dies.

02:23:42.800 | There's, you know, nothing happens in the universe anymore.

02:23:45.880 | Well, in mathematics, that's a decidable theory.

02:23:49.360 | That's a theory, so theories which have undecidability,

02:23:52.800 | which are things like arithmetic, set theory,

02:23:54.720 | all the serious models, theories in mathematics,

02:23:57.560 | they all have the feature that there are proofs

02:23:59.360 | of arbitrary long length.

02:24:01.440 | In something like Boolean algebra,

02:24:03.200 | which is a decidable theory,

02:24:04.880 | there are, you know, any question in Boolean algebra,

02:24:07.320 | you can just go crunch, crunch, crunch,

02:24:08.880 | and in a known number of steps, you can answer it.

02:24:11.880 | You know, satisfiability, you know, might be hard,

02:24:14.800 | but it's still a bounded number of steps

02:24:16.560 | to answer any satisfiability problem.

02:24:18.600 | And so that's the notion of a black hole in physics

02:24:22.320 | where time stops.

02:24:24.000 | That's analogous to in mathematics

02:24:27.400 | where there aren't infinite length proofs.

02:24:29.720 | Where when in physics, you know,

02:24:32.240 | you can wander around the universe forever

02:24:34.280 | if you don't run into a black hole.

02:24:35.440 | If you run into a black hole and time stops, you're done.

02:24:38.680 | And it's the same thing in mathematics

02:24:40.360 | between decidable theories and undecidable theories.

02:24:43.120 | So it's an example, and I think we're sort of,

02:24:46.520 | the attempt to understand, so another question is kind of,

02:24:49.600 | what is the generativity of metamathematics?

02:24:54.560 | What is the bulk theory of metamathematics?

02:24:57.400 | So in the literature of mathematics,

02:24:59.240 | there are about 3 million theorems

02:25:00.480 | that people have published.

02:25:02.520 | And those represent, it's kind of on this,

02:25:04.960 | it's like on the earth, we would be, you know,

02:25:09.240 | we've put cities in particular places on the earth,

02:25:11.960 | but yet there is ultimately, you know,

02:25:13.480 | we know the earth is roughly spherical

02:25:15.640 | and there's an underlying space.

02:25:17.160 | And we could just talk about, you know,

02:25:19.440 | the world of space in terms of where our cities

02:25:21.880 | happen to be, but there's actually an underlying space.

02:25:24.480 | And so the question is, what's that for metamathematics?

02:25:27.000 | And as we kind of explore what is, for example,

02:25:29.520 | for mathematics, which is always likes taking

02:25:32.040 | sort of abstract limits.

02:25:33.680 | So an obvious abstract limit for mathematics to take

02:25:36.360 | is the limit of the future of mathematics.

02:25:38.960 | That is, what will be, you know,

02:25:40.920 | the ultimate structure of mathematics?

02:25:43.280 | And one of the things that's an empirical observation

02:25:45.200 | about mathematics that's quite interesting

02:25:47.640 | is that a lot of theories in one area of mathematics,

02:25:50.600 | algebraic geometry or something, might have,

02:25:53.200 | they play into another area of mathematics.

02:25:55.840 | That same kind of a fundamental construct

02:25:59.160 | seem to occur in very different areas of mathematics.

02:26:02.320 | And that's structurally captured a bit

02:26:03.880 | with category theory and things like that.

02:26:05.900 | But I think that there's probably an understanding

02:26:08.240 | of this metamathematical space that will explain

02:26:11.080 | why different areas of mathematics

02:26:12.600 | ultimately sort of map into the same thing.

02:26:15.360 | And I mean, you know, my little challenge to myself

02:26:17.840 | is what's time dilation in metamathematics?

02:26:22.120 | In other words, as you basically,

02:26:24.320 | as you move around in this mathematical space

02:26:26.560 | of possible statements, you know,

02:26:29.360 | what's, how does that moving around?

02:26:31.480 | It's basically what's happening is that

02:26:34.040 | as you move around in the space of mathematical statements,

02:26:36.400 | it's like you're changing from algebra to geometry

02:26:38.400 | to whatever else.

02:26:39.640 | And you're trying to prove the same theorem.

02:26:42.220 | But as you try, if you keep on moving

02:26:44.440 | to these different places,

02:26:45.960 | it's slower to prove that theorem

02:26:47.400 | 'cause you keep on having to translate what you're doing

02:26:49.660 | back to where you started from.

02:26:50.640 | And that's kind of the beginnings of the analog

02:26:52.320 | of time dilation in metamathematics.

02:26:54.800 | - Plus there's probably fractional dimensions

02:26:56.680 | in this space as well.

02:26:58.160 | - Oh, this space is a very messy space.

02:27:00.600 | This space is much messier than physical space.

02:27:02.840 | I mean, even in the models of physics,

02:27:05.640 | physical space is very tame

02:27:08.000 | compared to branchial space and ruleal space.

02:27:10.920 | I mean, the mathematical structure, you know,

02:27:13.000 | branchial space is probably more like Hilbert space,

02:27:15.040 | but it's a rather complicated Hilbert space.

02:27:17.320 | And ruleal space is more like this weird

02:27:21.880 | infinity groupoid story of growth and decay.

02:27:24.240 | And I can explain that a little bit

02:27:25.600 | because in metamathematical space,

02:27:29.840 | a path in metamathematical space

02:27:32.600 | is a path between two statements

02:27:35.120 | is a way to get by proofs,

02:27:37.280 | is a way to find a proof

02:27:38.900 | that goes from one statement to another.

02:27:41.000 | And so one of the things you can do,

02:27:42.760 | you can think about is you've got,

02:27:44.160 | between statements, you've got proofs.

02:27:46.400 | They are paths between statements.

02:27:48.280 | Okay, so now you can go to the next level

02:27:50.440 | and you can ask,

02:27:51.480 | what about a mapping from one proof to another?

02:27:54.400 | And so that's in category theory,

02:27:56.560 | that's kind of a higher category,

02:27:58.560 | a notion of higher categories

02:28:00.080 | where you're mapping not just between objects,

02:28:04.240 | but you're mapping between the mappings

02:28:05.680 | between objects and so on.

02:28:07.480 | And so you can keep doing that.

02:28:09.160 | You can keep saying higher order proofs.

02:28:10.960 | I want mappings between proofs between proofs and so on.

02:28:14.160 | And that limiting structure,

02:28:15.400 | oh, by the way,

02:28:16.280 | one thing that's very interesting is

02:28:18.640 | imagine in proof space,

02:28:19.720 | you've got these two proofs.

02:28:21.360 | And the question is,

02:28:22.320 | what is the topology of proof space?

02:28:24.600 | In other words, if you take these two paths,

02:28:26.640 | can you continuously deform them into each other?

02:28:29.220 | Or is there some big hole in the middle

02:28:31.000 | that prevents you from continuously deforming them

02:28:33.300 | one into the other?

02:28:34.280 | It's kind of like,

02:28:35.120 | when you think about some,

02:28:36.760 | I don't know, some puzzle, for example,

02:28:38.440 | you're moving pieces around on some puzzle,

02:28:40.960 | and you can think about the space

02:28:42.320 | of possible states of the puzzle,

02:28:44.160 | and you can make this graph that shows

02:28:46.040 | from one state of the puzzle

02:28:47.180 | to another state of the puzzle and so on.

02:28:49.040 | And sometimes you can easily get

02:28:51.160 | from one state to any other state,

02:28:52.520 | but sometimes there'll be a hole in that space.

02:28:55.480 | And there'll be,

02:28:56.320 | you always have to go around the circuitous route

02:28:58.920 | to get from here to there.

02:29:00.000 | There won't be any direct way.

02:29:01.840 | That's kind of a question

02:29:03.360 | of whether there's sort of an obstruction in the space.

02:29:06.760 | And so the question is, in proof space,

02:29:09.180 | what is the, what are,

02:29:11.920 | what does it mean if there's an obstruction in proof space?

02:29:14.760 | - Yeah, I don't even know what an obstruction means

02:29:17.360 | in proof space,

02:29:18.200 | 'cause for it to be an obstruction,

02:29:20.240 | it should be reachable some other way

02:29:22.040 | from some other place, right?

02:29:24.320 | So this is like an unreachable part of the graph.

02:29:27.720 | - No, it's not just an unreachable part.

02:29:29.320 | It's a part where there are paths that go one way,

02:29:32.080 | there are paths that go the other way.

02:29:33.720 | And this question of homotopy and mathematics

02:29:35.600 | is this question, can you continuously deform,

02:29:38.400 | from one path to another path,

02:29:40.400 | or do you have to go in a jump, so to speak?

02:29:42.600 | So if you're going around a sphere, for example,

02:29:45.120 | if you're going around, I don't know,

02:29:47.200 | a cylinder or something, you can wind around one way

02:29:50.200 | and you can, there's no,

02:29:51.840 | there are paths where you can easily deform one path

02:29:55.080 | into another, because it's just sort of sitting

02:29:56.560 | on the same side of the cylinder.

02:29:58.120 | But when you've got something

02:29:59.120 | that winds all the way around a cylinder,

02:30:00.560 | you can't continuously deform that down to a point

02:30:03.400 | because it's stuck, wrapped around a cylinder.

02:30:05.520 | - My intuition about proof spaces,

02:30:07.080 | you should be able to deform it.

02:30:08.320 | I mean that, 'cause then otherwise

02:30:09.840 | it doesn't even make sense.

02:30:10.840 | 'Cause if the topology matters

02:30:13.560 | of the way you move about the space,

02:30:15.760 | then I don't even know what that means.

02:30:17.360 | - Well, what it would mean is that you would have

02:30:19.760 | one way of doing a proof of something over here in algebra

02:30:23.560 | and another way of doing a proof of something

02:30:25.120 | over here in geometry,

02:30:26.720 | and there would not be an intermediate way

02:30:29.440 | to map between those proofs.

02:30:30.960 | - But how would that be possible

02:30:32.240 | if they start at the same place and end at the same place?

02:30:35.280 | - Well, it's the same thing as we've got points on a,

02:30:39.040 | if we've got paths on a cylinder.

02:30:41.000 | - Now I understand how it works in physical space,

02:30:43.240 | but it just doesn't,

02:30:44.440 | it feels like proof space shouldn't have that.

02:30:47.160 | Okay, I mean--

02:30:48.000 | - I'm not sure, I don't know.

02:30:49.560 | We'll know very soon,

02:30:50.760 | 'cause we get to do some experiments.

02:30:52.080 | This is the great thing about this stuff,

02:30:53.840 | is that in fact, in the next few days,

02:30:57.120 | I hope to do a bunch of experiments on this.

02:30:58.760 | - So you're playing with like proofs in this kind of space?

02:31:02.040 | - Yes, yes.

02:31:03.040 | I mean, so this is toy theories,

02:31:06.640 | and we've got good,

02:31:08.320 | so this kind of segues to perhaps another thing,

02:31:10.560 | which is this whole idea of multi-computation.

02:31:13.320 | So this is another kind of bigger idea that,

02:31:18.320 | so, okay, this has to do with

02:31:20.800 | how do you make models of things?

02:31:22.760 | And it's going to, it's some,

02:31:25.040 | so I've sort of claimed that there've been sort of four epochs

02:31:28.960 | in the history of making models of things.

02:31:31.720 | And this multi-computation thing is the fourth,

02:31:35.600 | is a new epoch.

02:31:36.520 | - What are the first three?

02:31:38.080 | - The first one is back in antiquity,

02:31:40.680 | ancient Greek times,

02:31:42.600 | people were like, what's the universe made of?

02:31:44.560 | Oh, it's made of, you know, everything is water, Thales,

02:31:47.800 | you know, or everything is made of atoms.

02:31:50.880 | It's sort of what are things made of?

02:31:53.000 | Or, you know, there are these crystal spheres

02:31:55.400 | that represent where the planets are, and so on.

02:31:58.240 | It's like a structural idea

02:31:59.680 | of how the universe is constructed.

02:32:01.560 | There's no real notion of dynamics,

02:32:03.280 | it's just what is the universe, how is the universe made?

02:32:06.520 | Then we get to the 1600s,

02:32:08.640 | and we get to the sort of revolution of mathematics

02:32:11.080 | being introduced into physics.

02:32:12.920 | And then we have this kind of idea

02:32:15.920 | of you write down some equation,

02:32:18.680 | the what happens in the universe

02:32:20.560 | is the solving of that equation,

02:32:22.360 | time enters, but it's usually just a parameter.

02:32:25.120 | We just can, you know, sort of slide it back and forth

02:32:28.080 | and say, here's where it is.

02:32:30.320 | Okay, then we come to this kind of computational idea

02:32:33.480 | that I kind of started really pushing in the early 1980s.

02:32:38.160 | As a result, you know, the things we were talking about

02:32:40.200 | before about complexity, that was my motivation,

02:32:43.280 | but the bigger story was the story

02:32:45.200 | of kind of computational models of things.

02:32:47.760 | And the big difference there from the mathematical models

02:32:50.480 | is in mathematical models, there's an equation,

02:32:52.880 | you solve it, you got kind of slide time

02:32:55.360 | to the place where you want it.

02:32:57.000 | In computational models, you give the rule

02:33:00.320 | and then you just say, go run the rule.

02:33:02.680 | And time is not something you get to slide,

02:33:05.720 | time is something where it just, you run the rule,

02:33:07.960 | time goes in steps, and that's how you work out

02:33:12.160 | how the system behaves.

02:33:13.240 | You don't, time is not just a parameter,

02:33:15.560 | time is something that is about the running of these rules.

02:33:19.240 | And so there's this computational irreducibility,

02:33:21.360 | you can't jump ahead in time,

02:33:23.160 | but there's still, important thing is

02:33:25.000 | there's still one thread of time.

02:33:27.040 | It's still the case, you know, the cellular automaton state,

02:33:29.760 | then it has the next state and the next state and so on.

02:33:32.160 | The thing that is kind of, we've sort of tipped off

02:33:35.040 | by quantum mechanics in a sense,

02:33:36.480 | although it actually feeds back even into relativity

02:33:39.720 | and things like that,

02:33:41.000 | that there are these multiple threads of time.

02:33:43.840 | And so in this multi-computation paradigm,

02:33:46.360 | the kind of idea is, instead of there being

02:33:48.800 | this single thread of time,

02:33:50.280 | there are these kind of distributed asynchronous threads

02:33:52.720 | of time that are happening.

02:33:54.640 | And the thing that's sort of different there

02:33:56.960 | is if you want to know what happened,

02:33:58.800 | if you say what happened in the system,

02:34:01.240 | in the case of the computational paradigm,

02:34:03.480 | you just say, well, after a thousand steps,

02:34:06.640 | we got this result, right?

02:34:08.600 | But in the multi-computational paradigm,

02:34:10.840 | after a thousand steps,

02:34:11.840 | not even clear what a thousand steps means,

02:34:13.400 | because you've got all these different threads of time,

02:34:15.400 | but there is no state.

02:34:17.160 | There's all these different possible,

02:34:19.040 | you know, there's all these different parts.

02:34:21.000 | And so the only way you can know what happened

02:34:22.960 | is to have some kind of observer who is saying,

02:34:25.360 | here's how to parse the results of what was going on.

02:34:28.800 | - Right, but that observer is embedded

02:34:30.240 | and they don't have a complete picture, so.

02:34:32.360 | - In the case of physics, that's right, yes.

02:34:34.560 | And then, but that's, but so the idea is

02:34:37.320 | that in this multi-computation setup,

02:34:39.560 | that it's this idea of these multiple threads of time

02:34:42.440 | and models that are based on that.

02:34:44.520 | And this is similar to what people think about

02:34:47.880 | in non-deterministic computation.

02:34:49.840 | So you have a Turing machine,

02:34:50.960 | usually it has a definite state,

02:34:52.480 | it follows another state, it follows another state.

02:34:54.560 | But typically what people have done

02:34:55.960 | when they've thought about these kinds of things

02:34:57.920 | is they've said, well, there are all these possible paths,

02:35:00.000 | a non-deterministic Turing machine

02:35:01.600 | can follow all these possible paths,

02:35:03.400 | but we just want one of them.

02:35:04.480 | We just want the one that's the winner,

02:35:06.400 | that factors the number or whatever else.

02:35:08.600 | And similarly, you know, it's the same story

02:35:10.280 | in logic programming and so on,

02:35:11.920 | where we say, we've got this goal,

02:35:13.640 | find us a path to that goal.

02:35:15.360 | I just want one path, then I'm happy.

02:35:17.600 | Or theorem proving, same story.

02:35:19.280 | I just want one proof and then I'm happy.

02:35:21.480 | What's happening in multi-computation in physics

02:35:24.480 | is we actually care about many paths.

02:35:27.040 | And well, there is a case, for example,

02:35:29.000 | probabilistic programming is a version of multi-computation

02:35:31.880 | in which you're looking at all the paths,

02:35:33.760 | you're just asking for probabilities of things.

02:35:36.560 | But in a sense in physics,

02:35:38.080 | we're taking different kinds of samplings.

02:35:40.480 | For example, in quantum mechanics,

02:35:41.680 | we're taking a different kind of sampling

02:35:43.880 | of all these multiple paths.

02:35:46.080 | But the thing that is notable

02:35:48.560 | is that when you're an observer embedded in this thing,

02:35:51.920 | et cetera, et cetera, et cetera,

02:35:53.760 | with various other sort of footnotes and so on,

02:35:56.280 | it is inevitable that the thing that you parse

02:35:59.880 | out of the system looks like general relativity

02:36:02.560 | and quantum mechanics.

02:36:04.320 | In other words, that just by the very structure

02:36:06.760 | of this multi-computational setup,

02:36:08.920 | it inevitably is the case

02:36:11.280 | that you have certain emergent laws.

02:36:14.800 | Now, why is this perhaps not surprising?

02:36:18.280 | In thermodynamics and statistical mechanics,

02:36:20.400 | there are sort of inevitable emergent laws

02:36:22.840 | of sort of gas dynamics that are independent

02:36:25.720 | of the details of the molecular dynamics,

02:36:28.440 | sort of the same kind of thing.

02:36:30.120 | But I think what happens is,

02:36:31.520 | what's a sort of a funny thing

02:36:32.920 | that I've just been understanding very recently

02:36:35.760 | is when I kind of introduced this whole

02:36:39.160 | sort of computational paradigm complexity-ish thing

02:36:42.480 | back in the '80s, it was kind of like a big downer

02:36:45.000 | because it's like there's a lot of stuff you can't say

02:36:47.120 | about what systems will do.

02:36:49.040 | And then what I realized is,

02:36:50.080 | and then you might say, now we've got multi-computation,

02:36:52.520 | it's even worse.

02:36:53.760 | You know, it isn't just one thread of time

02:36:55.400 | that we can't explain, it's all these threads of time

02:36:57.280 | we can't explain anything.

02:36:58.840 | But the following thing happens.

02:37:01.160 | Because there is all this irreducibility

02:37:04.240 | and any detailed thing you might want to answer,

02:37:06.760 | it's very hard to answer.

02:37:08.240 | But when you have an observer

02:37:10.360 | who has certain characteristics

02:37:12.040 | like computational boundedness,

02:37:13.800 | sequentiality of time and so on,

02:37:15.960 | that observer only samples certain aspects

02:37:19.280 | of this incredible complexity going on

02:37:21.000 | in this multi-computational system.

02:37:22.960 | And that observer is sensitive only to

02:37:26.360 | some underlying core structure

02:37:28.240 | of this multi-computational system.

02:37:30.040 | There is all this irreducible computation going on,

02:37:32.480 | all these details, but to that kind of observer,

02:37:35.760 | what's important is only the core structure

02:37:38.760 | of multi-computation, which means that observer

02:37:41.600 | observes comparatively simple laws.

02:37:44.720 | And I think it is inevitable that that observer

02:37:47.360 | observes laws which are mathematically structured

02:37:50.580 | like general relativity and quantum mechanics,

02:37:52.660 | which by the way are the same law in our model of physics.

02:37:56.000 | - So that's an explanation why there's simple laws

02:37:58.920 | that explain a lot for this observer.

02:38:01.740 | - Potentially, yes.

02:38:02.580 | But the place where this gets really interesting

02:38:06.160 | is there are all these fields of science

02:38:09.120 | where people have kind of gotten stuck,

02:38:10.800 | where they say we'd really love to have

02:38:12.520 | a physics-like theory of economics.

02:38:14.680 | We'd really love to have a physics-like law in linguistics.

02:38:18.040 | - We gotta talk about molecular biology here.

02:38:20.600 | - Okay.

02:38:21.440 | - So where does multi-computation come in for biology?

02:38:24.480 | Economics is super interesting too, but biology--

02:38:26.680 | - Okay, let's talk about that.

02:38:27.600 | So let's talk about chemistry for a second, okay?

02:38:30.260 | So I mean, I have to say, you know,

02:38:32.280 | this is, it's such a weird business for me

02:38:34.000 | because, you know, there are these kind of

02:38:35.840 | paradigmatic ideas and then the actual applications.

02:38:38.920 | And it's like I've always said,

02:38:39.920 | I know nothing about chemistry.

02:38:41.240 | I learned all the chemistry I know, you know,

02:38:42.920 | the night before some exam when I was 14 years old.

02:38:45.080 | But I've actually learned a bunch more chemistry.

02:38:47.360 | And in Wolfram language these days,

02:38:49.120 | we have really pretty nice symbolic

02:38:50.640 | representation of chemistry.

02:38:52.200 | And in understanding the design of that,

02:38:54.180 | I've actually, I think, learned a certain amount of chemistry

02:38:56.660 | that if you quizzed me on sort of basic high school

02:38:58.680 | chemistry, I would probably totally fail.

02:39:01.120 | But, okay, so what is chemistry?

02:39:04.520 | I mean, chemistry is sort of a story of, you know,

02:39:07.320 | chemical reactions are like you've got

02:39:09.840 | this particular chemical, it's represented

02:39:11.600 | as some graph of, you know, these are,

02:39:14.000 | these are this configuration of molecules

02:39:15.760 | with these bonds and so on.

02:39:17.440 | And a chemical reaction happens,

02:39:19.620 | you've got these sort of two graphs,

02:39:21.580 | they interact in some way, you've got another graph

02:39:23.520 | or multiple other graphs out.

02:39:24.840 | So that's kind of the, the sort of the abstract view

02:39:28.840 | of what's happening in chemistry.

02:39:30.480 | And so when you do a chemical synthesis, for example,

02:39:33.640 | you are given certain sort of these are possible reactions

02:39:36.940 | that can happen, and you're asked, can you piece together

02:39:40.220 | this sequence of such reactions, a sequence of such sort of

02:39:43.400 | axiomatic reactions, usually called name reactions

02:39:45.720 | in chemistry, can you piece together a sequence

02:39:48.060 | of these reactions so that you get out at the end

02:39:51.620 | this great molecule you were trying to synthesize?

02:39:53.980 | And so that's a story very much like theorem proving.

02:39:56.340 | And people have done, actually, they started in the 1960s,

02:39:59.680 | looking at kind of the theorem proving approach to that,

02:40:02.600 | although it didn't really, it didn't, it didn't,

02:40:05.100 | was sort of done too early, I think.

02:40:07.480 | But anyway, so that's kind of the view is that chemistry,

02:40:10.060 | chemical reactions are the story of all these different

02:40:12.940 | sort of paths of possible things that go on.

02:40:16.180 | Okay, let's go to an even lower level.

02:40:18.420 | Let's say, instead of asking about which species

02:40:22.820 | of molecules we're talking about,

02:40:24.220 | let's look at individual molecules.

02:40:26.180 | And let's say we're looking at individual molecules,

02:40:28.500 | and they are having chemical reactions,

02:40:30.420 | and we're building up this big graph

02:40:32.000 | of all these reactions that are happening, okay?

02:40:34.540 | So then we've got this big graph, and by the way,

02:40:37.100 | that big graph is incredibly similar

02:40:40.260 | to these hypergraph rewriting things.

02:40:42.540 | In fact, in the underlying theory of multi-computation,

02:40:45.860 | there are these things we call token event graphs,

02:40:48.240 | which are basically, you've broken your state into tokens,

02:40:52.160 | like in the case of a hypergraph,

02:40:53.300 | you've broken it into hyperedges,

02:40:55.100 | and each event is just consuming some number of tokens

02:40:58.380 | and producing some number of tokens.

02:41:00.100 | - Yeah, but then you have to,

02:41:01.260 | there's a lot of work to be done on update rules.

02:41:04.420 | - In terms of what they actually are for chemistry?

02:41:06.700 | - Yeah, what they are for our observed chemistry.

02:41:09.740 | - Yes, indeed, yes, indeed.

02:41:11.180 | We've been working on that, actually,

02:41:12.660 | because we have this beautiful system in Wolfram language

02:41:15.580 | for representing chemistry symbolically.

02:41:17.220 | So we actually have, this is an ongoing thing

02:41:20.180 | to actually figure out what they are

02:41:21.420 | for some practical cases.

02:41:22.780 | - Does that require human injection,

02:41:24.720 | or can it be automatically discovered, these update rules?

02:41:28.600 | - Well, if we could do quantum chemistry better,

02:41:30.300 | we could probably discover them automatically,

02:41:31.620 | but I think in reality right now,

02:41:34.460 | it's like there are these particular reactions.

02:41:36.380 | And really, to understand what's going on,

02:41:38.560 | we're probably gonna pick a particular subtype of chemistry,

02:41:41.860 | and just, because let me explain where this is going.

02:41:44.700 | The place that, here's where this is going.

02:41:47.480 | So, you've got this whole network of all these molecules

02:41:51.060 | having all these reactions and so on.

02:41:53.180 | And this is some whole multi-computational story,

02:41:55.780 | because each sort of chemical reaction event

02:42:00.960 | is its own separate event.

02:42:02.300 | We're saying they all happen asynchronously.

02:42:03.980 | We're not describing in what order they happen.

02:42:06.820 | Maybe that order is governed

02:42:08.020 | by some quantum mechanics thing, doesn't really matter.

02:42:10.740 | We're just saying they happen in some order.

02:42:12.840 | And then we ask, what is the,

02:42:14.980 | how do we think about the system?

02:42:17.540 | Well, this thing is some kind

02:42:20.020 | of big multi-computational system.

02:42:21.600 | The question is, what is the chemical observer?

02:42:24.140 | And one possible chemical observer is,

02:42:26.420 | all you care about is,

02:42:27.300 | did you make that particular drug molecule?

02:42:29.520 | You're just asking for the one path.

02:42:31.880 | Another thing you might care about is,

02:42:33.500 | I want to know the concentration of each species.

02:42:36.760 | I want to know, at every stage,

02:42:39.400 | I'm going to solve the differential equations

02:42:40.980 | that represent the concentrations,

02:42:42.500 | and I want to know what those all are.

02:42:44.200 | But there's more, because when,

02:42:46.320 | and it's kind of like,

02:42:47.520 | you're going below in statistical mechanics,

02:42:50.380 | there's kind of all these molecules bouncing around,

02:42:52.920 | and you might say, we're just going to ignore,

02:42:56.100 | we're just going to look at the aggregate densities

02:42:59.000 | of certain kinds of molecules,

02:43:00.160 | but you can look at a lower level.

02:43:01.560 | You can look at this whole graph of possible interactions.

02:43:04.960 | And so, the kind of the idea would be,

02:43:07.400 | what, is the only chemical observer,

02:43:10.640 | one who just cares about overall concentrations,

02:43:13.320 | or can there be a chemical observer

02:43:15.280 | who cares about this network of what happened?

02:43:17.840 | And so, that, the question then is,

02:43:20.760 | so let me give an analogy.

02:43:22.240 | So this is where I think this is potentially

02:43:23.960 | very relevant to molecular biology and molecular computing.

02:43:27.920 | When we think about a computation,

02:43:29.720 | usually we say it's input, it's output.

02:43:32.480 | We, you know, or chemistry, we say, there's this input,

02:43:35.440 | we're going to make this molecule as the output.

02:43:38.000 | But what if what we actually encode,

02:43:41.120 | what if our computation,

02:43:42.600 | what if the thing we care about

02:43:44.240 | is some part of this dynamic network?

02:43:46.600 | What if it isn't just the input and the output

02:43:48.560 | that we care about?

02:43:49.400 | What if there's some dynamics of the network

02:43:51.200 | that we care about?

02:43:52.040 | Now, imagine you're a chemical observer.

02:43:54.540 | What is a chemical observer?

02:43:56.020 | Well, in molecular biology,

02:43:57.860 | there are all kinds of weird sorts of observers.

02:44:00.880 | There are membranes that exist

02:44:02.760 | that have, you know, different kinds of molecules

02:44:04.720 | that can bind to them, things like this.

02:44:06.880 | It's not obvious that the, from a human scale,

02:44:10.320 | we just measure the concentration of something,

02:44:12.480 | is the relevant story.

02:44:13.880 | We can imagine that, for example,

02:44:15.960 | when we look at this whole network of possible reactions,

02:44:18.600 | we can imagine, you know, at a physical level,

02:44:20.480 | we can imagine, well, what was the actual

02:44:22.200 | momentum direction of that molecule?

02:44:24.800 | What was it, which we don't pay any attention to

02:44:26.740 | when we're just talking about chemical concentrations.

02:44:29.020 | What was the orientation of that molecule?

02:44:31.180 | These kinds of things.

02:44:32.540 | And so here's the place where I have a little suspicion.

02:44:36.180 | Okay?

02:44:37.020 | So one of the questions in biology

02:44:38.540 | is what matters in biology?

02:44:40.660 | And that is, you know, we have all these chemical reactions.

02:44:42.780 | We have all these molecular processes going on

02:44:45.860 | in biological systems.

02:44:48.220 | What matters?

02:44:49.740 | And, you know, one of the things is

02:44:51.920 | to be able to tell what matters,

02:44:53.540 | well, so a big story of the what matters question

02:44:56.480 | was what happened in genetics in 1953,

02:44:58.640 | when DNA, when it was figured out how DNA worked.

02:45:01.820 | Because before that time, you know,

02:45:03.160 | genetics had been all these different effects

02:45:04.960 | and complicated things.

02:45:06.360 | And then it was realized, ah, there's something new.

02:45:09.120 | A molecule can store information,

02:45:11.240 | which wasn't obvious before that time.

02:45:13.160 | A single molecule can store information.

02:45:14.880 | So there's a place where there can be something important

02:45:18.080 | that's happening in molecular biology,

02:45:19.600 | and it's just in the sequence

02:45:21.400 | that's storing information in a molecule.

02:45:23.420 | So the possibility now is, imagine this dynamic network,

02:45:27.760 | this, you know, causal graphs and multi-way causal graphs

02:45:31.200 | and so on, that represent all of these different reactions

02:45:34.080 | between molecules.

02:45:35.160 | What if there is some aspect of that

02:45:37.400 | that is storing information

02:45:39.000 | that's relevant for molecular biology?

02:45:41.120 | - And the dynamic aspect of that.

02:45:42.920 | - Yes, that's right.

02:45:43.760 | - So it's similar to how the structure

02:45:46.120 | of a DNA molecule stores information.

02:45:49.280 | It could be the dynamics of the system

02:45:51.160 | somehow stores information.

02:45:52.680 | And this kind of process might allow you

02:45:55.180 | to give predictions of what that would be.

02:45:58.540 | - Well, yes, but also imagine that you're trying to do,

02:46:02.180 | for example, imagine you're trying

02:46:03.860 | to do molecular computation, okay?

02:46:06.340 | You might think the way we're gonna do

02:46:07.940 | molecular computation is, we're just gonna run the thing,

02:46:10.460 | we're gonna see what came out,

02:46:11.460 | we're gonna see what molecule came out.

02:46:13.500 | This is saying, that's not the only thing you can do.

02:46:16.260 | There is a different kind of chemical observer

02:46:18.300 | that you can imagine constructing,

02:46:20.120 | which is somehow sensitive to this dynamic network.

02:46:23.680 | Exactly how that works, how we make that measurement,

02:46:25.620 | I don't know, but I have a few ideas,

02:46:27.960 | but that's what's important, so to speak.

02:46:31.580 | And that means, and by the way,

02:46:32.940 | you can do the same thing even for Turing machines.

02:46:35.200 | You can say, if you have a multi-way Turing machine,

02:46:38.260 | you can say, how do you compute

02:46:40.100 | with a multi-way Turing machine?

02:46:41.640 | You can't say, well, we've got this input and this output,

02:46:44.500 | because the thing has all these threads of time,

02:46:46.620 | and it's got lots of outputs.

02:46:48.220 | And so then you say, well, what does it even mean

02:46:50.160 | to be a universal multi-way Turing machine?

02:46:52.400 | I don't fully know the answer to that.

02:46:54.360 | - That's an interesting idea, it would freak Turing out,

02:46:57.040 | for sure, 'cause then the dynamics,

02:47:00.040 | the trajectory of the computation matters.

02:47:02.920 | - Yes, yes, but the thing is,

02:47:06.480 | so this is, again, a story of what's the observer,

02:47:08.960 | so to speak, in chemistry, what's the observer there?

02:47:11.760 | Now, to give an example of where that might matter,

02:47:14.760 | a very sort of present-day example is in immunology,

02:47:18.720 | where we have whatever it is,

02:47:22.860 | 10 billion different kinds of antibodies

02:47:25.060 | that are all these different shapes and so on.

02:47:27.660 | We have a trillion different kinds of T-cell receptors

02:47:31.080 | that we produce, and the traditional theory of immunology

02:47:36.080 | is this clonal selection theory

02:47:38.060 | where we are constantly producing,

02:47:39.980 | randomly producing all these different antibodies,

02:47:42.540 | and as soon as one of them binds to an antigen,

02:47:45.000 | then that one gets amplified,

02:47:46.360 | and we produce more of that antibody and so on.

02:47:49.440 | Back in the 1960s, an immunologist called Nils Joerner,

02:47:53.640 | who was the guy who invented monoclonal antibodies,

02:47:56.120 | various other things, kind of had this network theory

02:47:59.440 | of the immune system, where it would be like,

02:48:01.000 | well, we produce antibodies,

02:48:02.520 | but then we produce antibodies to the antibodies,

02:48:05.120 | anti-antibodies, and we produce anti-anti-antibodies,

02:48:07.960 | and we get this whole dynamic network of interactions

02:48:10.800 | between different immune system cells,

02:48:13.180 | and that was kind of a qualitative theory at that time,

02:48:18.080 | and I've been a little disappointed

02:48:20.260 | 'cause I've been studying immunology a bit recently,

02:48:22.540 | and I knew something about this 35 years ago or something,

02:48:25.440 | and I knew, I'd read a bunch of the books,

02:48:27.460 | and I'd talked to a bunch of the people and so on,

02:48:29.420 | and it was like an emerging theoretical immunology world,

02:48:33.660 | and then I look at the books now,

02:48:35.420 | and they're very thick because they've got,

02:48:37.540 | there's just a ton known about immunology,

02:48:39.900 | and all these different pathways,

02:48:41.640 | all these different details and so on,

02:48:43.800 | but the theoretical sections seem to have shrunk,

02:48:46.240 | and so it's, so the question is, what,

02:48:51.600 | for example, immune memory,

02:48:53.200 | where does the immune memory reside?

02:48:55.040 | Is it actually some cell sitting in our bone marrow

02:48:57.800 | that is living for the whole of our lives

02:48:59.840 | that's gonna spring into action

02:49:01.560 | as soon as we're shown the same antigen,

02:49:04.000 | or is it something different from that?

02:49:05.560 | Is it something more dynamic?

02:49:07.260 | Is it something more like some network of interactions

02:49:09.640 | between these different kinds of immune system cells

02:49:12.420 | and so on, and it's known

02:49:13.660 | that there are plenty of interactions between T cells,

02:49:15.880 | and there's plenty of dynamics,

02:49:18.280 | but what the consequence of that dynamics is is not clear,

02:49:21.740 | and to have a qualitative theory for that

02:49:24.640 | doesn't seem to exist.

02:49:26.480 | In fact, I was just been trying to study this,

02:49:28.520 | so I'm quite incomplete in my study of these things,

02:49:30.840 | but I was a little bit taken aback

02:49:32.520 | 'cause I've been looking at these things,

02:49:34.460 | and it's like, and then they get to the end

02:49:35.920 | where they have the most advanced theory that they've got,

02:49:38.360 | and it turns out it's the cellular automaton theory.

02:49:41.560 | It's like, okay, well, at least I understand that theory,

02:49:44.720 | but I think that the possibility is that

02:49:49.280 | this is a place where if you want to know,

02:49:53.600 | explain roughly how the immune system works,

02:49:56.140 | it ends up being this dynamic network,

02:49:58.440 | and then the immune consciousness, so to speak,

02:50:02.360 | the observer, ends up being something that in the end,

02:50:06.120 | it's kind of like does the human get sick or whatever,

02:50:08.720 | but it's something which is a complicated story

02:50:12.040 | that relates to this whole sort of dynamic network

02:50:14.560 | and so on, and I think that's another place

02:50:16.560 | where this kind of notion of,

02:50:18.440 | where I think multi-computation has the possibility.

02:50:21.700 | See, one of the things, okay,

02:50:23.240 | you can end up with something where,

02:50:24.440 | yes, there is a general relativity in there,

02:50:27.000 | but it turns out, but it may turn out

02:50:28.560 | that the observer who sees general relativity

02:50:31.860 | in the immune system is an observer that's irrelevant

02:50:34.640 | to what we care about about the immune system.

02:50:36.880 | I mean, it could be, yes, there is some effect

02:50:38.640 | where there's some time dilation of T cells

02:50:42.840 | interacting with whatever, but it's like,

02:50:44.780 | that's an effect that's just irrelevant,

02:50:46.800 | and the thing we actually care about is things about

02:50:49.880 | what happens when you have a vaccine

02:50:51.920 | that goes into some place in shape space,

02:50:53.840 | and how does that affect other places in shape space,

02:50:56.560 | and how does that spread?

02:50:58.160 | What's the analog of the speed of light in shape space,

02:51:01.080 | for example?

02:51:02.000 | That's an important issue

02:51:03.280 | if you have one of these dynamic theories.

02:51:04.800 | It's like you poke into shape space by having,

02:51:08.480 | let's say, a vaccine or something

02:51:10.160 | that has a particular configuration in shape space.

02:51:13.160 | How quickly, as this dynamic network spreads out,

02:51:16.880 | how quickly do you get sort of other antibodies

02:51:20.360 | in different places in shape space, things like that.

02:51:22.360 | - When you say shape space,

02:51:23.320 | you mean the shape of the molecules?

02:51:25.240 | And then, so this is like,

02:51:27.680 | could be deeply connected to the protein

02:51:29.480 | and multi-protein folding, all of that kind of stuff.

02:51:32.240 | - To be able to say something interesting

02:51:33.960 | about the dance of proteins.

02:51:36.400 | - Right, exactly.

02:51:37.240 | - That actually has an impact on

02:51:39.440 | helping develop drugs, for example,

02:51:42.920 | or has an impact on virology, immunology,

02:51:46.600 | helping to deal with viruses.

02:51:47.440 | - Well, I think the big thing is,

02:51:49.880 | when we think about molecular biology,

02:51:52.060 | what is the qualitative way to think about it?

02:51:57.320 | In other words, is it chemical reaction networks?

02:52:00.280 | Is it genetics, DNA, big news,

02:52:05.280 | it's kind of, there's a digital aspect to the whole thing.

02:52:08.640 | What is the qualitative way to think about

02:52:10.940 | how things work in biology?

02:52:13.240 | When we think about, I don't know,

02:52:14.460 | some phenomenon like aging or something,

02:52:16.440 | which is a big, complicated phenomenon,

02:52:17.960 | which just seems to have all these different tentacles,

02:52:20.360 | is it really the case that that can be thought about

02:52:22.920 | in some, without DNA,

02:52:25.240 | when people were describing genetic phenomena,

02:52:28.480 | there were dominant, recessive, this, that, and the other,

02:52:31.080 | it got very, very complicated,

02:52:32.840 | and then people realized, oh, it's just,

02:52:35.200 | and what is a gene, and so on, and so on, and so on,

02:52:37.880 | then people realize it's just base pairs,

02:52:39.800 | and there's this digital representation.

02:52:41.440 | And so the question is,

02:52:42.280 | what is the overarching representation

02:52:44.640 | that we can now start to think about using in microbiology?

02:52:47.360 | I don't know how this will work out,

02:52:48.560 | and this is, again, one of these things where,

02:52:51.000 | and the place where that gets important is,

02:52:54.280 | maybe molecular biology is doing molecular computing

02:52:58.100 | by using some dynamic process

02:53:00.520 | that is something where it is very happily saying,

02:53:03.360 | oh, I just got a result.

02:53:04.720 | It's in the dynamic structure of this network.

02:53:06.440 | Now I'm gonna go and do some other thing

02:53:08.400 | based on that result, for example,

02:53:10.320 | but we're like, oh, I don't know what's going on.

02:53:12.440 | It's just, we just measured the levels of these chemicals,

02:53:15.780 | and we couldn't conclude anything,

02:53:17.640 | but it just, we're looking at the wrong thing.

02:53:19.760 | And so that's kind of the potential there,

02:53:23.600 | and it's, I mean, these things are,

02:53:26.000 | I don't know, it's, for me, it's like,

02:53:28.740 | I've not really, that was not a view.

02:53:31.500 | I mean, I've thought about molecular computing

02:53:33.060 | for ages and ages and ages,

02:53:34.540 | and I've always imagined that the big story

02:53:37.100 | is kind of the original promise of nanotechnology

02:53:40.540 | of like, can we make a molecular scale constructor

02:53:43.020 | that will just build a molecule in any shape?

02:53:45.940 | But I don't think, I'm now increasingly concluding

02:53:48.780 | that's not the big point.

02:53:50.240 | The big point is something more dynamic.

02:53:52.360 | That will be an interesting end point

02:53:54.180 | for any of these things,

02:53:55.220 | but that's perhaps not the thing,

02:53:57.940 | 'cause the one example we have in molecular computing

02:54:00.340 | that's really working is us biological organisms.

02:54:03.380 | And maybe the thing that's important there

02:54:06.340 | is not this, what chemicals do you make, so to speak,

02:54:10.060 | but more this kind of dynamic process.

02:54:11.980 | - Dynamic process, and then you can have a good model

02:54:14.100 | like the hypergraph to then explore,

02:54:16.360 | what, like simulate, again, make predictions,

02:54:20.660 | and if they-- - I think just have a way

02:54:22.220 | to reason about biology.

02:54:24.020 | I mean, it's hard.

02:54:25.740 | First of all, biology doesn't have theories like physics.

02:54:29.420 | Physics is a much more successful

02:54:31.540 | sort of global theory kind of area.

02:54:34.500 | Biology, what are the global theories of biology?

02:54:37.340 | Pretty much Darwinian evolution.

02:54:39.040 | That's the only global theory of biology.

02:54:41.700 | Any other theory is just a, well, the kidneys work this way,

02:54:44.820 | this thing works this way, and so on.

02:54:46.760 | There isn't, I suppose another global theory

02:54:48.860 | is digital information in DNA.

02:54:50.980 | That's another sort of global fact about biology.

02:54:53.260 | - But the difficult thing to do is to match

02:54:56.340 | something you have a model of in the hypergraph

02:55:00.540 | to the actual, like how do you discover the theory?

02:55:03.460 | How do you discover the theory?

02:55:04.980 | Okay, you have something that looks nice and makes sense,

02:55:07.220 | but like you have to match it to validation.

02:55:10.420 | - Oh, sure, right. - And that's tricky

02:55:12.340 | because you're walking around in the dark.

02:55:15.220 | - Not entirely.

02:55:16.140 | I mean, so, you know, for example,

02:55:18.180 | in what we've been trying to think about

02:55:19.980 | is take actual chemical reactions, okay?

02:55:23.060 | So, you know, one of my goals is

02:55:25.900 | can I compute the primes with molecules?

02:55:28.340 | Okay, that's, if I can do that,

02:55:30.020 | then I kind of, maybe I can compute things.

02:55:32.860 | And, you know, there's this nice automated lab,

02:55:34.900 | these guys, these Emerald Cloud Lab people

02:55:37.220 | have built with Wolfram Language and so on.

02:55:38.980 | That's an actual physical lab,

02:55:40.860 | and you send it a piece of Wolfram Language code,

02:55:42.700 | and it goes and, you know,

02:55:44.140 | actually does physical experiments.

02:55:45.980 | And so one of my goals,

02:55:47.900 | because I'm not a test tube kind of guy,

02:55:50.020 | I'm more of a software kind of person,

02:55:52.060 | is can I make something where, you know,

02:55:54.380 | in this automated lab, we can actually get it

02:55:56.900 | so that there's some gel that we made,

02:55:58.820 | and, you know, the positions of the stripes are the primes.

02:56:00.900 | - Is the primes, I love it, yeah.

02:56:02.900 | - I mean, that would be an example of where,

02:56:06.020 | and that would be with a particular, you know,

02:56:08.740 | framework for actually doing the molecular computing,

02:56:12.100 | you know, with particular kinds of molecules.

02:56:13.900 | And there's a lot of kind of ambient technological mess,

02:56:17.580 | so to speak, associated with, oh, is it carbon?

02:56:19.700 | Is it this, is it that?

02:56:21.180 | You know, is it important that there's a bromine atom here?

02:56:24.020 | Et cetera, et cetera, et cetera.

02:56:24.940 | This is all chemistry that I don't know much about.

02:56:27.940 | And, you know, that's a sort of, you know,

02:56:30.300 | unfortunately, that's down at the level, you know,

02:56:32.500 | I would like to be at the software level,

02:56:34.700 | not at the level of the transistors, so to speak.

02:56:37.180 | But in chemistry, you know, there's a certain amount

02:56:39.700 | we have to do, I think, at the level of transistors

02:56:41.680 | before we get up to being able to do it,

02:56:44.100 | although, you know, automated labs

02:56:45.740 | certainly help in setting that up.

02:56:48.620 | - I talked to a guy named Charles Hoskinson.

02:56:53.100 | He mentioned that he's collaborating with you.

02:56:55.820 | He's an interesting guy.

02:56:56.940 | He sends me papers on, speaking of automated theorem

02:57:00.500 | proving a lot.

02:57:01.420 | He's exceptionally well read on that area as well.

02:57:04.180 | So what's the nature of your collaboration with him?

02:57:06.780 | He's the creator of Cardano.

02:57:08.420 | What's the nature of the collaboration between Cardano

02:57:12.300 | and the whole space of blockchain and Wolfram,

02:57:14.340 | Wolfram Alpha, Wolfram Blockchain, all that kind of stuff?

02:57:17.420 | - Well, okay, we're segueing to a slightly different world.

02:57:21.220 | But so, although not completely unconnected.

02:57:25.300 | - Right, the whole thing is somehow connected.

02:57:27.860 | - I know, I mean, you know, the strange thing in my life

02:57:31.060 | is I've sort of alternated between doing basic science

02:57:33.580 | and doing technology about five times in my life so far.

02:57:37.140 | And the thing that's just crazy about it is, you know,

02:57:40.140 | every time I do one of these alternations,

02:57:42.300 | I think there's not gonna be a way back to the other thing.

02:57:45.420 | And like I thought for this physics project,

02:57:47.060 | I thought, you know,

02:57:48.020 | we're doing fundamental theory of physics,

02:57:50.300 | maybe it'll have an application in 200 years.

02:57:53.300 | But now I've realized,

02:57:55.460 | actually this multi-computation idea

02:57:57.500 | is applicable here and now.

02:57:59.580 | It's, and in fact, it's also giving us this way.

02:58:02.380 | I'll just mention one other thing

02:58:03.780 | and then we can talk about blockchain.

02:58:05.740 | The question of,

02:58:09.620 | actually that relates to several different things,

02:58:11.780 | but one of the things about, okay,

02:58:15.060 | so our Wolfram Language,

02:58:17.900 | which is our attempt to kind of represent everything

02:58:20.740 | in the world computationally.

02:58:22.460 | And it's the thing I kind of started building 40 years ago

02:58:25.300 | in the form of actual Wolfram Language 35 years ago.

02:58:29.500 | It's kind of this idea of,

02:58:30.900 | can we express things about the world

02:58:35.140 | in computational terms?

02:58:36.860 | And, you know, we've come a long way

02:58:38.500 | in being able to do that.

02:58:39.940 | Wolfram Alpha is kind of the consumer version of that

02:58:42.300 | where you're just using natural languages as input.

02:58:44.580 | And it turns it into our symbolic language.

02:58:47.900 | And that's, you know, the symbolic language,

02:58:49.860 | Wolfram Language is what people use

02:58:51.660 | and have been using for the last 33 years.

02:58:54.020 | Actually, Mathematica, which is its first instantiation,

02:58:57.500 | will be one third of a century old in October.

02:59:01.860 | And that, it's kind of interesting.

02:59:06.140 | - What do you mean one third of a century?

02:59:07.500 | Does that mean 33 or 30?

02:59:08.860 | What are we--

02:59:09.700 | - 33 and a third.

02:59:10.900 | - 33 and a third.

02:59:12.860 | (laughing)

02:59:14.860 | - I've never heard of anyone celebrating that anniversary,

02:59:17.060 | but I like it.

02:59:17.900 | - I know, a third of a century though.

02:59:19.220 | It's like, you don't get many slices of a century

02:59:22.180 | that are interesting.

02:59:23.260 | But, you know, I think that the thing

02:59:25.260 | that's really striking about that is that means,

02:59:28.100 | you know, including the whole sort of technology stack

02:59:29.980 | I built around that's about 40 years old,

02:59:32.060 | and that means it's a significant fraction

02:59:33.820 | of the total age of the computer industry.

02:59:36.340 | And it's, I mean, I think it's cool

02:59:38.140 | that we can still run, you know,

02:59:39.500 | Mathematica version one programs today and so on,

02:59:42.700 | and we've sort of maintained compatibility.

02:59:45.100 | And we've been just building this big tower

02:59:47.300 | all those years of just more and more

02:59:49.620 | and more computational capabilities.

02:59:51.060 | It's sort of interesting.

02:59:51.900 | We just made this picture of kind of the different

02:59:55.260 | kind of threads of computational content,

02:59:59.020 | of, you know, mathematical content,

03:00:00.660 | and, you know, all sorts of things with, you know,

03:00:04.220 | data and graphs and whatever else.

03:00:06.580 | And what you see in this picture

03:00:07.780 | is about the first 10 years,

03:00:09.620 | it's kind of like it's just a few threads.

03:00:11.980 | And then about maybe 15, 20 years ago,

03:00:15.260 | it kind of explodes in this whole collection

03:00:17.180 | of different threads of all these different capabilities

03:00:19.980 | that are now part of Wolfram Language

03:00:21.460 | and representing different things in the world.

03:00:23.500 | But the thing that was super lucky in some sense

03:00:27.260 | is it's all based on one idea.

03:00:29.340 | It's all based on the idea of symbolic expressions

03:00:31.980 | and transformation rules for symbolic expressions,

03:00:34.580 | which was kind of what I originally

03:00:36.300 | put into this SMP system back in 1979

03:00:39.940 | that was a predecessor of the whole Wolfram Language stack.

03:00:42.980 | So that idea was an idea that I got

03:00:46.220 | from sort of trying to understand

03:00:47.500 | mathematical logic and so on.

03:00:48.980 | It was my attempt to kind of make a general

03:00:52.180 | human comprehensible model of computation

03:00:54.980 | of just everything is a symbolic expression

03:00:57.260 | and all you do is transform symbolic expressions.

03:01:00.100 | And, you know, in retrospect,

03:01:02.860 | I was very lucky that I understood

03:01:05.180 | as little as I understood then,

03:01:07.020 | because had I understood more,

03:01:08.700 | I would have been completely freaked out

03:01:10.700 | about all the different ways

03:01:11.940 | that that kind of model can fail.

03:01:14.660 | Because what do you do when you have a symbolic expression,

03:01:18.180 | you make transformations for symbolic expressions?

03:01:20.620 | Well, for example, one question is there may be

03:01:22.780 | many transformations that could be made

03:01:24.620 | in a very multi-computational kind of way.

03:01:26.940 | But what we're doing is picking,

03:01:28.700 | we're using the first transformation that applies.

03:01:31.860 | And we keep doing that until we reach a fixed point.

03:01:34.420 | And that's the result.

03:01:35.820 | And that's kind of a very,

03:01:37.300 | it's kind of a way of sort of sliding around

03:01:40.380 | the edge of multi-computation.

03:01:42.220 | And back when I was working on SMP and things,

03:01:44.620 | I actually thought about these questions

03:01:46.300 | about how, you know, how,

03:01:48.740 | what determines this kind of evaluation path.

03:01:52.140 | So for example, you know, you work out Fibonacci,

03:01:54.340 | you know, Fibonacci is a recursive thing.

03:01:56.020 | F of N is F of N minus one plus F of N minus two.

03:01:59.100 | And you get this whole tree of recursion, right?

03:02:01.780 | And there's the question of how do you evaluate

03:02:03.500 | that tree of recursion?

03:02:04.460 | Do you do it sort of depth first,

03:02:06.500 | where you go all the way down one side?

03:02:07.980 | Do you do it breadth first,

03:02:09.580 | where you're kind of collecting the terms together,

03:02:12.180 | where you know that, you know,

03:02:13.020 | F of eight plus F of seven,

03:02:14.260 | F of seven plus F of six,

03:02:15.780 | you can collect the F of sevens and so on.

03:02:18.020 | These are, you know, I didn't realize it at the time.

03:02:20.780 | It's kind of funny.

03:02:21.620 | I was working on gauge field theories back in 1979.

03:02:25.220 | And I was also working on the evaluation model in SMP

03:02:29.220 | and they're the same problem.

03:02:30.740 | But it took me 40 more years to realize that.

03:02:33.420 | And this question about how you do

03:02:35.460 | this sort of evaluation front,

03:02:37.220 | that's a question of reference frames.

03:02:39.220 | It's a question of kind of the story of,

03:02:42.540 | I mean, that is basically this question of

03:02:45.580 | in what order is the universe evaluated?

03:02:48.300 | And that, and so what you realize is

03:02:50.620 | there's this whole sort of world

03:02:52.220 | of different kinds of computation that you can do

03:02:54.620 | sort of multi computationally.

03:02:56.140 | And that's an interesting thing.

03:02:58.140 | It has a lot of implications

03:02:59.140 | for distributed computing and so on.

03:03:01.180 | It also has a potential implication for blockchain,

03:03:03.620 | which we haven't fully worked out,

03:03:05.380 | which is, and this is not what we're doing with Cardano,

03:03:07.940 | but this is a different thing.

03:03:09.940 | This is something where one of the questions is

03:03:15.940 | when you have, in a sense,

03:03:17.900 | blockchain is a deeply sequentialized story of time.

03:03:21.420 | Because in blockchain,

03:03:22.660 | there's just one copy of the ledger.

03:03:25.220 | And you're saying, this is what happened.

03:03:27.620 | You know, time has progressed in this way.

03:03:29.300 | And there are little things around the edge

03:03:30.780 | as you try and reach consensus and so on.

03:03:33.180 | And, you know, actually we just recently,

03:03:36.660 | we've had this little conference we organized

03:03:38.460 | about the theory of distributed consensus.

03:03:40.580 | 'Cause I realized that a bunch of interesting things

03:03:42.900 | that some of our science can tell one about that.

03:03:45.380 | But that's a different, let's not go down that path.

03:03:47.860 | - Yeah, but distributed consensus,

03:03:49.220 | that still has a sequential, there's like one-

03:03:51.140 | - There's still sequentiality.

03:03:52.380 | So distributed consensus-

03:03:53.220 | - Don't tell me you're thinking through like

03:03:55.460 | how to apply multi computation to blockchain.

03:03:59.020 | - Yes, and so that becomes a story of, you know,

03:04:03.060 | instead of transactions all having to settle in one ledger,

03:04:06.660 | it's like a story of all these different ledgers

03:04:09.580 | and they all have to have some ultimate consistency,

03:04:12.220 | which is what causal invariance would give one,

03:04:14.460 | but it can take a while.

03:04:15.940 | And the, it can take a while

03:04:17.420 | is kind of like quantum mechanics.

03:04:19.180 | So it's kind of what's happening is

03:04:20.860 | there are these different paths of history

03:04:23.140 | that correspond to, you know,

03:04:24.740 | in one path of history, you got paid this amount.

03:04:27.100 | In another path of history, you got paid this amount.

03:04:29.500 | In the end, the universe will always become consistent.

03:04:32.460 | Now, the way it works is,

03:04:35.980 | okay, it's a little bit more complicated than that.

03:04:37.580 | What happens is the way space is knitted together

03:04:40.500 | in our theory of physics is through all these events.

03:04:43.700 | And the idea is that the way that economic space

03:04:48.060 | is knitted together is there these autonomous events

03:04:52.340 | that essentially knit together economic space.

03:04:54.900 | So there are all these threads of transactions

03:04:56.580 | that are happening.

03:04:57.580 | And the question is, can they be made consistent?

03:04:59.500 | Are there, is there something forcing them

03:05:01.580 | to be sort of a consistent fabric of economic reality?

03:05:05.540 | And sort of what this has led me to

03:05:07.740 | is trying to realize how does economics fundamentally work?

03:05:11.380 | And, you know, what is economics?

03:05:13.660 | And, you know, what are the atoms of economics,

03:05:16.860 | so to speak?

03:05:17.780 | And so what I've kind of realized is that,

03:05:20.220 | that sort of the, perhaps,

03:05:22.620 | I don't even know if this is right yet.

03:05:24.380 | There's sort of events in economics of transactions.

03:05:27.420 | There are states of agents

03:05:28.980 | that are kind of the atoms of economics.

03:05:31.620 | And then transactions are kind of agents

03:05:34.740 | transact in some,

03:05:36.540 | transact in some way, and that's an event.

03:05:38.700 | And then the question is,

03:05:39.860 | how do you knit together sort of economic space from that?

03:05:43.420 | What is there in economic space?

03:05:44.780 | Well, all these transactions,

03:05:46.340 | there's a whole complicated collection

03:05:47.820 | of possible transactions.

03:05:48.820 | But one thing that's true about economics

03:05:50.820 | is we tend to have the notion

03:05:52.660 | of a definite value for things.

03:05:54.300 | We could imagine that, you know,

03:05:57.580 | you buy a cookie from somebody

03:06:01.700 | and they want to get a movie ticket.

03:06:05.380 | And there is some way that AI bots could make some path

03:06:09.740 | from the cookie to the movie ticket

03:06:12.380 | by all these different intermediate transactions.

03:06:15.340 | But in fact, we have an approximation to that,

03:06:18.820 | which is we say they each have a dollar value.

03:06:21.620 | And we have this kind of numeraire concept

03:06:24.180 | of there's just a way of kind of,

03:06:26.660 | of taking this whole complicated space of transactions

03:06:29.940 | and parsing it in something

03:06:31.980 | which is a kind of a simplified thing

03:06:34.300 | that is kind of like a parsing of physical space.

03:06:37.700 | And so my guess is that the, yet again, I mean, it's crazy

03:06:42.220 | that all these things are so connected.

03:06:44.180 | This is another multi-computation story,

03:06:46.620 | another story of where what's happening

03:06:48.900 | is that the economic consciousness,

03:06:51.220 | the economic observer is not going to deal

03:06:54.260 | with all of those different microscopic transactions.

03:06:56.780 | They're just going to parse the whole thing by saying,

03:06:59.020 | there's this value, it's a number.

03:07:00.900 | And that's their understanding of their summary

03:07:03.940 | of this economic network.

03:07:05.460 | And there will be all kinds of things,

03:07:06.900 | like there are all kinds of arbitrage opportunities,

03:07:08.980 | which are kind of like the quantum effects

03:07:10.940 | in this whole thing.

03:07:12.300 | And that's, you know, and places where there's sort

03:07:15.940 | of different paths that can be followed and so on.

03:07:18.940 | And so the question is,

03:07:21.820 | can one make a sort of global theory of economics?

03:07:24.820 | And then my test case is, again,

03:07:27.180 | what is time dilation in economics?

03:07:29.580 | And I know for, you know,

03:07:31.500 | if you imagine a very agricultural economics

03:07:33.500 | where people are growing lettuces in fields

03:07:35.620 | and things like this, and you ask questions about,

03:07:38.020 | well, if you're transporting lettuces to different places,

03:07:41.020 | you know, what is the value of the lettuces

03:07:43.100 | after you have to transport them

03:07:44.940 | versus if you're just sitting in one place and selling them?

03:07:47.660 | And you can kind of get a little bit of an analogy there,

03:07:49.460 | but I think there's a better and more complete analogy.

03:07:52.580 | And that's the question of,

03:07:53.620 | is there a theory like general relativity

03:07:55.900 | that is a global theory of economics?

03:07:58.060 | And is it about something we care about?

03:08:00.100 | It could be that there is a global theory,

03:08:01.540 | but it's about a feature of economic reality

03:08:04.220 | that isn't important to us.

03:08:05.780 | Now, another part of the story is,

03:08:07.860 | can one use those ideas to make essentially

03:08:10.580 | a distributed blockchain,

03:08:12.180 | a distributed generalization of blockchain,

03:08:14.820 | kind of the quantum analog of money, so to speak,

03:08:17.100 | where you have, for example,

03:08:19.460 | you can have uncertainty relations where you're saying,

03:08:22.100 | you know, well, if I insist on knowing my bank account

03:08:25.100 | right now, there'll be some uncertainty.

03:08:27.740 | If I'm prepared to wait a while,

03:08:29.660 | then it'll be much more certain.

03:08:31.620 | And so there's, you know, is there a way of using,

03:08:34.300 | and so we've made a bunch of prototypes of this,

03:08:37.740 | which I'm not yet happy with,

03:08:39.660 | because what I realized is

03:08:41.180 | to really understand these prototypes,

03:08:42.620 | I actually have to have a foundational theory of economics.

03:08:45.260 | And so that's kind of a, you know,

03:08:47.100 | it may be that we could deploy one of these prototypes

03:08:49.820 | as a practical system,

03:08:51.180 | but I think it's really gonna be much better

03:08:52.620 | if we actually have an understanding

03:08:54.460 | of how this plugs into kind of the economic system.

03:08:56.420 | - And that means like a fundamental theory

03:08:58.500 | of transactions between entities.

03:09:01.500 | - Well, and how- - That's what you mean

03:09:02.740 | by economics.

03:09:03.900 | - Yes, I think so.

03:09:04.780 | But I mean, you know, how there emerge

03:09:07.500 | sort of laws of economics,

03:09:08.620 | I don't even know, and I've been asking friends of mine

03:09:10.620 | who are economists and things, what is economics?

03:09:14.300 | You know, is it an axiomatic theory?

03:09:16.140 | Is it a theory that is a kind of

03:09:18.140 | a qualitative description theory?

03:09:20.580 | Is it, you know, what kind of a theory is it?

03:09:22.540 | Is it a theory, you know, what kind of thinking?

03:09:24.660 | It's like in biology, in evolutionary biology, for example,

03:09:28.140 | there's a certain pattern of thinking

03:09:30.380 | that goes on in evolutionary biology,

03:09:31.920 | where if you're a good evolutionary biologist,

03:09:35.100 | somebody says, "That creature has a weird horn."

03:09:37.980 | And they'll say, "Well, that's because this and this

03:09:40.100 | "and this and this selection of this kind and that kind,

03:09:42.800 | "and that's the story."

03:09:44.680 | And it's not a mathematical story,

03:09:46.340 | it's a story of a different type of thinking

03:09:48.580 | about these things.

03:09:49.420 | By the way, evolutionary biology is yet another place

03:09:52.960 | where it looks like this multi-computational idea

03:09:55.280 | can be applied.

03:09:56.420 | And that's where maybe speciation is related

03:09:59.620 | to things like event horizons,

03:10:01.500 | and there's a whole other kind of world of that.

03:10:04.200 | But- - It seems like this kind of model

03:10:06.260 | can be applicable to so many aspects,

03:10:09.180 | like at the different levels of understanding of our reality.

03:10:14.180 | So it could be the biology, the chemistry,

03:10:16.720 | at the physics level, the economics,

03:10:19.600 | and you could potentially...

03:10:21.480 | The thing is, it's like, okay, sure,

03:10:25.080 | at all these levels, it might rhyme,

03:10:26.560 | it might make sense as a model.

03:10:28.200 | The question is, can you make useful predictions

03:10:30.640 | at one of these levels? - That's right.

03:10:32.040 | That's right, and that's really a question of...

03:10:35.600 | It's a weird situation, because it's a situation

03:10:37.620 | where the model probably has definite consequences.

03:10:41.800 | The question is, are they consequences we care about?

03:10:44.560 | And that's some...

03:10:45.840 | In the case of, in the economic case,

03:10:50.300 | so one thing is this idea of using physics-like notions

03:10:59.720 | to construct a distributed analog of blockchain.

03:11:03.160 | Okay, the much more pragmatic thing

03:11:05.520 | is a different direction,

03:11:07.320 | and it has to do with this computational language

03:11:09.360 | that we built to describe the world

03:11:11.280 | that knows about different kinds of cookies

03:11:14.160 | and knows about different cities

03:11:15.760 | and knows about how to compute all these kinds of things.

03:11:18.960 | One of the things that is of interest is,

03:11:21.220 | if you want to run the world,

03:11:23.220 | you need, with contracts and laws and rules and so on,

03:11:27.720 | there are rules at a human level,

03:11:29.520 | and there are kind of things like...

03:11:31.960 | And so this gets one into the idea

03:11:34.000 | of computational contracts.

03:11:36.000 | Right now, when we write a contract,

03:11:38.080 | it's a piece of legalese, it's just written in English,

03:11:41.960 | and it's not something that's automatically

03:11:43.880 | analyzable, executable, whatever else.

03:11:45.760 | It's just English.

03:11:47.960 | Back in Gottfried Leibniz, back in 1680 or whatever,

03:11:52.960 | was like, "I'm gonna figure out how to use logic

03:11:57.560 | "to decide legal cases," and so on,

03:11:59.600 | and he had kind of this idea of,

03:12:01.160 | "Let's make a computational language for human law.

03:12:05.480 | "Forget about modeling nature,

03:12:07.320 | "forgot about natural laws, what about human law?

03:12:09.960 | "Can we make kind of a computational

03:12:11.440 | "representation of that?"

03:12:13.160 | Well, I think finally we're close to being able to do that,

03:12:16.400 | and one of the projects that I hope to get to

03:12:18.720 | as soon as there's a little bit of slowing down

03:12:21.260 | of some of this Cambrian explosion that's happening

03:12:23.800 | is a project I've been meaning to really do for a long time,

03:12:26.360 | which is what I'm calling a symbolic discourse language.

03:12:29.240 | It's just finishing the job of being able

03:12:31.900 | to represent everything, like the conversation we're having

03:12:35.400 | in computational terms, and one of the use cases for that

03:12:38.800 | is computational contracts.

03:12:40.400 | Another use case is something like the Constitution

03:12:43.400 | that says what the AIs, what we want the AIs to do.

03:12:46.200 | - But this is useful, so you're saying,

03:12:48.400 | so these are like, you're saying computational contracts,

03:12:50.980 | but smart contracts, this is what's in the domain

03:12:53.880 | of cryptocurrencies known as smart contracts,

03:12:56.080 | and so the language you've developed,

03:12:58.000 | this symbolic or seek to further develop

03:13:01.480 | symbolic discourse language enables you

03:13:04.200 | to write a contract.

03:13:06.680 | - Write a contract that richly represents

03:13:10.760 | some aspect of the world, yeah.

03:13:12.160 | - But so, I mean, smart contracts tend to be right now

03:13:15.500 | mostly about things happening on the blockchain.

03:13:18.360 | Sometimes they have oracles, and in fact,

03:13:20.280 | Wolfram Alpha API is the main thing people use

03:13:23.580 | to get information about the real world, so to speak,

03:13:26.360 | within smart contracts.

03:13:27.560 | - So Wolfram Alpha, as it stands, is a really good oracle

03:13:31.000 | for whoever wants to use it.

03:13:32.440 | That's perhaps where the relationship with Cardano is.

03:13:34.800 | - Yeah, well, that's how we started getting involved

03:13:36.600 | with blockchains is we realized people were using,

03:13:38.960 | you know, Wolfram Alpha as the oracle

03:13:41.200 | for smart contracts, so to speak,

03:13:42.720 | and so that got us interested in blockchains in general,

03:13:45.840 | and what was ended up happening is Wolfram Language is,

03:13:49.480 | with its symbolic representation of things,

03:13:51.240 | is really very good at representing things like blockchains,

03:13:54.980 | and so I think we now have,

03:13:56.720 | and we don't really know all the comparisons,

03:13:58.360 | but we now have a really nice environment

03:14:00.240 | within Wolfram Language for dealing with the sort of,

03:14:03.900 | you know, for representing what happens in blockchains,

03:14:06.280 | for analyzing what happens in blockchains.

03:14:08.400 | We have a whole effort in blockchain analytics,

03:14:12.040 | and, you know, we've sort of published some samples

03:14:15.040 | of how that works, but it's, you know,

03:14:17.000 | because our technology stack, Wolfram Language

03:14:19.600 | and Mathematica, are very widely used

03:14:21.480 | in the quant finance world, there's a sort of immediate

03:14:25.980 | sort of co-evolution there of sort of

03:14:29.360 | the quant finance kind of thing, and blockchain analytics,

03:14:32.840 | and that's, so it's kind of the representation

03:14:35.360 | of blockchain in computational language,

03:14:37.640 | then ultimately, it's kind of like,

03:14:39.800 | how do you run the world with code?

03:14:41.760 | That is, how do you write sort of all these things

03:14:44.460 | which are right now regulations, and laws,

03:14:46.560 | and contracts, and things in computational language,

03:14:49.360 | and kind of the ultimate vision is that sort of

03:14:52.520 | something happens in the world,

03:14:53.940 | and then there's this giant domino effect

03:14:55.840 | of all these computational contracts

03:14:57.580 | that trigger based on the thing that happened,

03:14:59.640 | and there's a whole story to that,

03:15:01.720 | and of course, you know, I like to always pay attention

03:15:05.080 | to the latest things that are going on,

03:15:07.040 | and I really, I kind of like blockchain

03:15:08.920 | because it's another rethinking of kind of computation.

03:15:13.400 | It's kind of like, you know, cloud computing

03:15:14.960 | was a little bit of that, of sort of persistent

03:15:18.000 | kind of computational resources and so on,

03:15:21.200 | and, you know, this multi-computation

03:15:23.120 | is a big rethinking of kind of what it means to compute.

03:15:26.560 | Blockchain is another bit of rethinking

03:15:28.320 | of what it means to compute.

03:15:29.960 | The idea that you lodge kind of these autonomous lumps

03:15:32.480 | of computation out there in the blockchain world,

03:15:35.600 | and one of the things that just sort of,

03:15:38.760 | for fun, so to speak, is we've been doing a bit of stuff

03:15:41.160 | with NFTs, and we just did some NFTs on Cardano,

03:15:44.320 | and we'll be doing some more,

03:15:45.680 | and, you know, we did some cellular automaton NFTs

03:15:48.520 | on Cardano, which people seem to like quite a bit,

03:15:51.920 | and, you know, one of the things I've realized about NFTs

03:15:55.280 | is that there's kind of this notion,

03:15:57.240 | and we're really working on this, you know,

03:15:59.840 | I like recording stuff, you know,

03:16:02.400 | one of the things that's come out of kind of my science,

03:16:05.200 | I suppose, is this history matters type story

03:16:09.120 | of, you know, it's not just the current stage,

03:16:10.680 | it's the history that matters,

03:16:12.080 | and I've kind of, I don't think this is,

03:16:14.280 | I should be realizing, maybe it's not coincidental

03:16:16.840 | that I'm sort of the human who's recorded

03:16:18.640 | more about themselves than anybody else,

03:16:20.480 | and then I end up with these science results

03:16:22.720 | that say history matters, which was not,

03:16:24.960 | those things, I didn't think those were connected, but--

03:16:27.760 | - They're at least correlated, yes.

03:16:29.400 | - Yeah, right, so, you know, this question

03:16:31.720 | about sort of recording what has happened,

03:16:34.040 | and having sort of a permanent record of things,

03:16:36.980 | one of the things that's kind of interesting there

03:16:39.080 | is, you know, you put up a website,

03:16:40.440 | and it's got a bunch of stuff on it,

03:16:41.960 | but, you know, you have to keep paying the hosting fees,

03:16:43.800 | or the thing's gonna go away,

03:16:45.520 | but one of the things about blockchain

03:16:47.200 | that's kind of interesting is,

03:16:48.960 | if you put something on a blockchain,

03:16:50.400 | and you pay, you know, your commission to get that thing,

03:16:53.280 | you know, put on, you know, mine, put on the blockchain,

03:16:56.880 | then, in a sense, everybody who comes after you is,

03:17:01.120 | you know, they are motivated to keep your thing alive,

03:17:03.800 | 'cause that's what keeps the consistency of the blockchain.

03:17:06.340 | So, in a sense, with sort of the NFT world,

03:17:08.700 | it's kind of like, if you want to have something permanent,

03:17:11.300 | well, at least for the life of the blockchain,

03:17:13.440 | but even if the blockchain goes out of circulation,

03:17:16.520 | so to speak, there's gonna be enough value

03:17:18.580 | in that whole collection of transactions

03:17:20.800 | that people are gonna archive the thing,

03:17:22.520 | but that means that, you know, pay once,

03:17:25.000 | and you're kind of, you're lodged in the blockchain forever,

03:17:28.120 | and so we've been kind of playing around

03:17:29.600 | with sort of a hobby thing of mine,

03:17:32.520 | of thinking about sort of the NFTs,

03:17:35.400 | and how you, and sort of the consumer idea

03:17:39.100 | of kind of the, it's the anti, you know,

03:17:41.880 | it's the opposite of the Snapchat view of the world.

03:17:44.600 | - Sure, there's a permanence to it

03:17:45.960 | that's heavily incentivized,

03:17:48.120 | and thereby you can have a permanence of history.

03:17:52.880 | - Right, and that's kind of the, now, you know,

03:17:56.280 | so that's one of the things we've been doing with Cardano,

03:17:58.720 | and it's kind of fun.

03:17:59.960 | I think that, I mean, this whole question about,

03:18:02.480 | you know, you mentioned automated theorem proving,

03:18:04.280 | and blockchains, and so on,

03:18:06.160 | and as I've thought about this kind of physics-inspired

03:18:08.480 | distributed blockchain,

03:18:09.880 | obviously there, the sort of the proof that it works,

03:18:14.180 | that there are no double spends, there's no whatever else,

03:18:16.920 | that proof becomes a very formal kind of,

03:18:20.160 | almost a matter of physics, so to speak.

03:18:22.760 | And, you know, it's been an interesting thing

03:18:25.120 | for the practical blockchains

03:18:27.360 | to do kind of actual automated theorem proving,

03:18:29.880 | and I don't think anybody's really managed it

03:18:31.640 | in an interesting case yet.

03:18:33.240 | It's a thing that people, you know, aspire to,

03:18:35.760 | but I think it's a challenging thing,

03:18:37.580 | 'cause basically the point is,

03:18:39.200 | one of the things about proving correctness of something

03:18:42.980 | is, well, you know, people say, "I've got this program,

03:18:44.960 | "and I'm going to prove it's correct."

03:18:46.600 | And it's like, what does that mean?

03:18:47.880 | You have to say what correct means.

03:18:49.620 | I mean, it's kind of like,

03:18:50.980 | then you have to have another language,

03:18:52.340 | and people were very confused back in past decades of,

03:18:55.400 | you know, "Oh, we're going to prove the correctness

03:18:57.560 | "by representing the program in another language,

03:19:00.220 | "which we also don't know whether it's correct."

03:19:02.480 | And, you know, often by correctness,

03:19:04.120 | we just mean it can't crash, or it can't scribble on memory,

03:19:07.520 | but the thing is that there's this complicated trade-off,

03:19:10.760 | because as soon as you're really using computation,

03:19:14.460 | you have computational irreducibility,

03:19:16.480 | you have undecidability.

03:19:18.000 | If you want to use computation seriously,

03:19:20.620 | you have to kind of let go of the idea

03:19:23.620 | that you're going to be able to box it in,

03:19:25.560 | and say, "We're going to have just this happen,

03:19:27.820 | "and not anything else."

03:19:28.880 | I mean, this is an old fact.

03:19:30.800 | I mean, Godel's theorem tries to say, you know,

03:19:33.440 | Peano arithmetic, the axioms of arithmetic,

03:19:35.800 | can you box in the integers,

03:19:37.800 | and say these axioms give just the integers,

03:19:39.880 | and nothing but the integers.

03:19:41.320 | Godel's theorem showed that wasn't the case.

03:19:43.280 | There's a, you know, you can have all these wild,

03:19:45.560 | weird things that obey the Peano axioms,

03:19:48.160 | but aren't integers.

03:19:49.400 | And there's this kind of infinite hierarchy

03:19:51.520 | of additional axioms you would have to add,

03:19:53.680 | and it's kind of the same thing.

03:19:54.720 | You don't get to, you know, if you want to say,

03:19:57.680 | "I want to know what happens," you're boxing yourself in,

03:20:00.440 | and there's a limit to what can happen, so to speak.

03:20:02.640 | So it's a complicated trade-off,

03:20:04.120 | and it's a big trade-off for AI, so to speak.

03:20:06.960 | It's kind of like, do you want to let computation

03:20:09.260 | actually do what it can do, or do you want to say,

03:20:12.120 | "No, it's very, very boxed in to the point

03:20:14.000 | "where we can understand every step?"

03:20:16.160 | And that's kind of a thing that becomes difficult to do.

03:20:20.040 | But that's some, I mean, in general,

03:20:22.720 | I would say one of the things that's kind of complicated

03:20:25.580 | in my sort of life and the whole sort of story

03:20:29.040 | of computational language and all this technology

03:20:31.680 | and science and so on, I mean, I kind of,

03:20:34.400 | in the flow of one's life, it's sort of interesting

03:20:36.900 | to see how these things play out,

03:20:38.880 | because I, you know, I've kind of concluded

03:20:41.180 | that I'm in the business of making kind of artifacts

03:20:43.720 | from the future, which means, you know,

03:20:46.440 | there are things that I've done, I don't know,

03:20:48.320 | this physics project, I don't know whether anybody

03:20:49.800 | would have gotten to it for 50 years.

03:20:52.280 | You know, the fact that Mathematica

03:20:53.680 | is a third of a century old, and I know

03:20:56.240 | that a bunch of the core ideas are not well-absorbed.

03:20:59.440 | I mean, that is, people finally got this idea

03:21:01.480 | that I thought was a triviality of notebooks.

03:21:03.800 | That was 25 years.

03:21:05.420 | And, you know, some of these core ideas

03:21:07.560 | about symbolic computation and so on are not absorbed.

03:21:11.240 | I mean, people use them every day in Wolfram Language

03:21:15.300 | and, you know, do all kinds of cool things with them,

03:21:17.120 | but if you say, what is the fundamental

03:21:19.100 | intellectual point here, it's not well-absorbed.

03:21:22.560 | And it's something where you kind of realize

03:21:24.600 | that you're sort of building things,

03:21:26.400 | and I kind of made this thing about, you know,

03:21:29.340 | we're building artifacts from the future, so to speak,

03:21:31.080 | and I mentioned that at our, we have a conference,

03:21:34.480 | it's coming up actually in a couple of weeks,

03:21:36.080 | our annual technology conference,

03:21:38.740 | where we talk about all the things we're doing.

03:21:41.660 | And, you know, so I was talking about it last year

03:21:44.600 | about, you know, we're making artifacts from the future,

03:21:46.680 | and I was kind of like, I had some version of that

03:21:49.620 | that was kind of a dark and frustrated thing of like,

03:21:52.540 | you know, I'm building things which nobody's gonna care

03:21:54.740 | about until long after I'm dead, so to speak.

03:21:57.040 | But then I realized, you know, people were sort of telling

03:22:01.780 | me afterwards, you know, that's exactly how, you know,

03:22:05.180 | we're using Wolfram Language in some particular setting

03:22:07.560 | in some computational X field or some organization

03:22:10.620 | or whatever, and it's like people are saying,

03:22:13.020 | oh, you know, what did you manage to do?

03:22:15.280 | You know, well, we know that in principle

03:22:16.940 | it will be possible to do that,

03:22:18.020 | but we didn't know that was possible now,

03:22:20.220 | and it's kind of like that's sort of the business we're in,

03:22:22.820 | and in a sense, with some of these ideas in science,

03:22:25.740 | you know, I feel a little bit the same way,

03:22:27.440 | that there are some of these things where, you know,

03:22:29.740 | some things, like for example, this whole idea,

03:22:33.380 | well, so to relate to another sort of piece of history

03:22:36.740 | and the future, one of, you know, I mentioned,

03:22:38.980 | we mentioned at the beginning kind of complexity

03:22:41.460 | as this thing that I was interested in back 40 years ago

03:22:44.060 | and so on, where does complexity come from?

03:22:46.540 | Well, I think we kind of nailed that.

03:22:48.860 | The answer is in the computational universe,

03:22:51.260 | even simple programs make it, and that's kind of the secret

03:22:54.300 | that nature has that allows you to make it.

03:22:56.460 | So that's kind of the, that's that part,

03:22:59.860 | but the bigger picture there was this idea

03:23:02.220 | of this kind of computational paradigm,

03:23:04.220 | the idea that you could go beyond mathematical equations,

03:23:06.820 | which have been sort of the primary modeling medium

03:23:09.860 | for 300 years, and so it was like, look,

03:23:13.160 | it is inexorably the case that people will use programs

03:23:16.380 | rather than just equations, and you know,

03:23:18.460 | I was saying that in the 1980s, and people were,

03:23:21.260 | you know, I published my big book, "New Kind of Science,"

03:23:23.540 | that'll be 20 years ago next year, so in 2002,

03:23:27.580 | and people were saying, oh no, this can't possibly be true,

03:23:30.260 | you know, we know for 300 years,

03:23:31.940 | we've been doing all this stuff, right?

03:23:33.860 | To be fair, I now realize, on a little bit more analysis

03:23:37.160 | of what people actually said, in pretty much every field

03:23:40.620 | other than physics, people said, oh, these are new models,

03:23:44.120 | that's pretty interesting, and physics, people were like,

03:23:47.400 | we've got our physics models, we're very happy with them.

03:23:49.900 | - Yeah, in physics, there's more resistance

03:23:51.740 | because of the attachment and the power of the equations.

03:23:54.820 | The idea that programs might be the right way

03:23:57.540 | to approach this field was, there's some resistance,

03:24:01.620 | and like you're saying, it takes time.

03:24:04.300 | For somebody who likes the idea of time dilation

03:24:06.860 | and all these applications,

03:24:08.100 | I thought you would understand this.

03:24:09.700 | - Yeah, right, but you know,

03:24:10.980 | and computational irreducibility as well.

03:24:12.700 | - Yes, exactly.

03:24:13.900 | - But I mean, it is really interesting that just 20 years,

03:24:17.380 | the span of 20 years, it's gone from, you know,

03:24:20.300 | pitchforks and horror to, yeah, we get it,

03:24:24.380 | and you know, it's helped that we've, you know,

03:24:27.540 | in our current effort in fundamental physics,

03:24:30.880 | we've gotten a lot further,

03:24:32.020 | and we've managed to put a lot of puzzle pieces together

03:24:35.260 | that make sense.

03:24:36.580 | But the thing that I've been thinking about recently

03:24:38.540 | is this field of complexity.

03:24:39.980 | So I've kind of was a sort of a field builder

03:24:43.740 | back in the 1980s.

03:24:44.860 | I was kind of like, okay, you know, can we, you know,

03:24:49.100 | I'd understood this point

03:24:50.540 | that there was this sort of fundamental phenomenon

03:24:52.180 | of complexity, and it showed up in lots of places.

03:24:54.540 | And I was like,

03:24:55.380 | this is an interesting sort of field of science.

03:24:58.020 | And I was recently was reminded,

03:25:01.560 | I was at this, the very first sort of get together

03:25:04.800 | of what became the Santa Fe Institute.

03:25:07.280 | I was like, in fact, there's even an audio recording

03:25:09.200 | of me sort of saying, people have been talking about,

03:25:11.640 | oh, what should this, you know, outfit do?

03:25:13.520 | And I was saying, well, there is this thing

03:25:15.920 | that I've been thinking about.

03:25:16.840 | It's this kind of idea of complexity.

03:25:18.880 | And it's kind of like, and that's what that ended up.

03:25:22.640 | - And you planted the seed of complexity at Santa Fe.

03:25:25.080 | That's beautiful.

03:25:25.920 | That's a beautiful vision.

03:25:26.760 | - But, I mean, so that, but what's happened then

03:25:29.460 | is this idea of complexity and, you know,

03:25:32.180 | and I started the first research center

03:25:34.660 | at University of Illinois for doing that

03:25:36.100 | in the first journal, complex systems and so on.

03:25:39.080 | And it's kind of an interesting thing in my life,

03:25:42.820 | at least that it's kind of like you plant the seed,

03:25:45.460 | you have this idea, it's a kind of a science idea.

03:25:48.660 | You have this idea of sort of focusing

03:25:50.220 | on the phenomenon of complexity.

03:25:52.020 | The deeper idea was this computational paradigm.

03:25:54.820 | But the nominal idea is this kind of idea of complexity.

03:25:58.040 | Okay, then you roll time forward 30 years or whatever,

03:26:01.280 | 35 years, whatever it is, and you say, what happened?

03:26:05.460 | Okay, well, now there are a thousand

03:26:06.680 | complexity institutes around the world.

03:26:09.280 | I think more or less, we've been trying to count them.

03:26:12.120 | And, you know, there are 40 complexity journals, I think.

03:26:16.340 | And so it's kind of like what actually happened

03:26:19.360 | in this field, right?

03:26:20.920 | And I look at a lot of what happened

03:26:22.820 | and I'm like, you know, I have to admit

03:26:25.680 | to some eye rolling, so to speak,

03:26:27.940 | because it's kind of like, what's actually going on?

03:26:31.880 | Well, what people definitely got

03:26:34.100 | was this idea of computational models.

03:26:36.640 | And then they got, but they thought,

03:26:38.440 | one of the kind of cognitive mistakes I think is,

03:26:41.520 | they say, we've got a computational model

03:26:43.960 | and we're looking at a system that's complex

03:26:48.480 | and our computational model gives complexity.

03:26:51.280 | By golly, that must mean it's right.

03:26:53.580 | And unfortunately, because complexity

03:26:55.960 | is a generic phenomenon and computational irreducibility

03:26:58.840 | is a generic phenomenon that actually tells you nothing.

03:27:01.960 | And so then the question is, well, what can you do?

03:27:04.680 | You know, there's a lot of things

03:27:06.180 | that have been sort of done under this banner of complexity.

03:27:08.440 | I think it's been very successful

03:27:10.080 | in providing sort of an interdisciplinary way

03:27:12.800 | of connecting different fields together.

03:27:14.600 | - Which is powerful in itself.

03:27:16.000 | - Right, I mean, it's a very useful--

03:27:16.840 | - Biology and economics and yeah, it is.

03:27:18.920 | - Right, it's a good organizing principle.

03:27:20.640 | But in the end, a lot of that is around

03:27:22.880 | this sort of computational paradigm, computational modeling.

03:27:25.560 | That's the raw material that powers

03:27:27.760 | that kind of correspondence, I think.

03:27:30.520 | But the question is sort of what is the,

03:27:32.560 | you know, I was just thinking recently,

03:27:34.520 | you know, we've been, I mean, the other,

03:27:36.600 | we've been, for years people have told me,

03:27:39.400 | you should start some Wolfram Institute

03:27:41.200 | that does basic science.

03:27:42.880 | You know, all I have is a company that builds software

03:27:45.600 | and we, you know, we have a little piece

03:27:47.400 | that does basic science as kind of a hobby.

03:27:49.400 | People are saying, you should start

03:27:50.840 | this Wolfram Institute thing.

03:27:52.640 | And I've been, you know, 'cause I've known

03:27:54.320 | about lots of institutes and I've seen kind of

03:27:56.000 | that flow of money and kind of, you know,

03:27:58.160 | what happens in different situations and so on.

03:28:00.200 | So I've been kind of reluctant, but I have realized

03:28:03.920 | that, you know, what we've done with our company

03:28:05.840 | over the last 35 years, you know,

03:28:07.480 | we built a very good machine for doing R&D

03:28:10.600 | and, you know, innovating and creating things.

03:28:12.920 | And I just applied that machine to the physics project.

03:28:16.120 | That's how we did the physics project

03:28:17.680 | in a fairly short amount of time with a, you know,

03:28:20.560 | efficient machine with, you know,

03:28:22.640 | various people involved and so on.

03:28:25.040 | And so, you know, it works for basic science

03:28:28.000 | and it's like, we can do more of this.

03:28:30.360 | And so now-- - In biology and chemistry,

03:28:32.200 | so it's become an institute.

03:28:34.600 | - Yes, well, it needs to become an institute.

03:28:36.280 | - An official institute. - Right, right.

03:28:37.840 | But the thing that, so I was thinking about,

03:28:40.120 | okay, so what do we do with complexity?

03:28:42.800 | You know, what, there are all these people who've,

03:28:45.440 | you know, what should happen to that field?

03:28:47.640 | And what I realized is there's kind of this area

03:28:50.040 | of foundations of complexity that's about these questions

03:28:53.560 | about simple programs, what they do,

03:28:55.560 | that's far away from a bunch of the detailed applications

03:28:58.000 | that people, well, it's not far away.

03:28:59.520 | It's the under, you know,

03:29:01.560 | the bedrock underneath those applications.

03:29:04.480 | And so I realized recently,

03:29:05.640 | this is my recent kind of little innovation of a sort,

03:29:10.400 | a post that I'll do very soon,

03:29:13.920 | about kind of, you know, the foundations of complexity,

03:29:18.920 | what really are they?

03:29:20.320 | I think they're really two ideas, two conceptual ideas

03:29:23.880 | that I hadn't really enunciated, I think, before.

03:29:26.680 | One is what I call metamodeling, the other is ruleology.

03:29:30.200 | So what is metamodeling?

03:29:31.400 | So metamodeling is, you've got this complicated model,

03:29:34.160 | and it's a model of, you know, hedgehogs interacting

03:29:36.680 | with this, interacting with that.

03:29:38.640 | And the question is, what's really underneath that?

03:29:40.840 | What is it?

03:29:41.880 | You know, is it a Turing machine?

03:29:43.600 | Is it a cellular automaton?

03:29:45.240 | You know, what is the underlying stuff

03:29:47.800 | underneath that model?

03:29:49.120 | And so there's this kind of meta-science question

03:29:52.120 | of, given these models, what is the core model?

03:29:55.440 | And I realized, I mean, to me,

03:29:56.760 | that's sort of an obvious question,

03:29:58.440 | but then I realized I've been doing language design

03:30:00.520 | for 40 years, and language design is exactly that question.

03:30:03.960 | You know, underneath all of this detailed stuff people do,

03:30:06.840 | what are the underlying primitives?

03:30:08.800 | And that's a question people haven't tended to ask

03:30:11.040 | about models.

03:30:12.000 | They say, "Well, we've got this nice model

03:30:13.280 | for this and that and the other.

03:30:14.520 | What's really underneath it?

03:30:16.120 | And what, you know, because once you have the thing

03:30:18.520 | that's underneath it, well, for example,

03:30:20.840 | this multi-computation idea

03:30:22.600 | is an ultimate metamodeling idea,

03:30:24.760 | because it's saying underneath all these fields

03:30:27.240 | is one kind of paradigmatic structure.

03:30:29.720 | And, you know, you can imagine the same kind of thing

03:30:32.080 | in much more sort of, much sort of shallower levels

03:30:36.840 | in different kinds of modeling.

03:30:38.960 | So the first activity is this kind of metamodeling,

03:30:41.880 | the kind of the models about models, so to speak.

03:30:45.920 | You know, what is the, what's, you know,

03:30:48.000 | drilling down into models?

03:30:49.920 | That's one thing.

03:30:50.840 | The other thing is this thing that I think

03:30:53.240 | we're going to call ruleology,

03:30:54.920 | which is kind of the, okay, you've got these simple rules.

03:30:57.760 | You've got cellular automata, you've got Turing machines,

03:30:59.800 | you've got substitution systems,

03:31:01.160 | you've got register machines,

03:31:02.400 | you've got all these different things.

03:31:03.440 | What do they actually do in the wild?

03:31:05.960 | And this is an area that I've spent a lot of time,

03:31:08.920 | you know, working on.

03:31:09.840 | It's a lot of stuff in my new kind of science book

03:31:11.800 | is about this.

03:31:13.440 | You know, this new book I wrote about combinators

03:31:15.360 | is full of stuff like this.

03:31:17.560 | And this journal, "Complex Systems,"

03:31:19.720 | has lots of papers about these kinds of things.

03:31:21.960 | But there isn't really a home

03:31:23.920 | for people who do ruleology or whatever.

03:31:26.360 | - As you call the basic science of rules.

03:31:29.640 | - Yes, yes, right.

03:31:31.000 | So it's like you've got some, what is it?

03:31:34.120 | Is it mathematics?

03:31:35.100 | No, it isn't really like mathematics.

03:31:36.440 | In fact, from my now understanding of metamathematics,

03:31:39.120 | I understand that it's the molecular dynamics level.

03:31:41.840 | It's not the level that mathematicians

03:31:43.920 | have traditionally cared about.

03:31:45.480 | It's not computer science,

03:31:47.040 | because computer science is about writing programs

03:31:48.960 | that do things, you know, that were for a purpose,

03:31:51.560 | not programs in the wild, so to speak.

03:31:53.920 | It's not physics.

03:31:54.760 | It doesn't have anything to do with, you know,

03:31:56.320 | it may be underneath some physics,

03:31:57.760 | but it's not physics as such.

03:31:59.520 | So it just hasn't had a home.

03:32:01.280 | And if you look at, you know,

03:32:02.880 | but what's great about it is it's a surviving field,

03:32:07.040 | so to speak.

03:32:07.880 | It's something where, you know,

03:32:08.920 | one of the things I find sort of inspiring

03:32:11.640 | about mathematics, for example,

03:32:13.520 | is you look at mathematics that was done,

03:32:15.480 | you know, in ancient Greece, ancient, you know,

03:32:17.480 | Babylon, Egypt, and so on.

03:32:19.480 | It's still here today.

03:32:20.800 | You know, you find an icosahedron

03:32:22.320 | that somebody made in ancient Egypt.

03:32:24.720 | You look at it, oh, that's a very modern thing.

03:32:27.080 | It's an icosahedron.

03:32:28.480 | You know, it's a timeless kind of activity.

03:32:31.680 | And this idea of studying simple rules and what they do,

03:32:34.680 | it's a timeless activity.

03:32:36.240 | And I can see that over the last 40 years or so,

03:32:38.800 | as, you know, even with cellular automata,

03:32:41.600 | it's kind of like, you know,

03:32:43.040 | you can sort of catalog what are the different

03:32:45.200 | cellular automata used for,

03:32:47.080 | and, you know, like the simplest rules,

03:32:49.160 | like one, you might even know this one, rule 184.

03:32:52.600 | It's rule 184 is a minimal model for road traffic flow.

03:32:56.200 | And, you know, it's also a minimal model

03:32:57.720 | for various other things.

03:32:58.960 | But it's kind of fun that you can literally say,

03:33:01.280 | you know, rule 90 is a minimal model

03:33:03.840 | for this and this and this.

03:33:05.320 | Rule four is a minimal model for this.

03:33:07.800 | And it's kind of remarkable that you can just,

03:33:10.000 | by in this raw level of this kind of study of rules,

03:33:13.360 | they then branch, they're the raw material

03:33:16.160 | that you can use to make models of different things.

03:33:18.000 | So it's a very pure basic science,

03:33:20.920 | but it's one that, you know, people have explored it,

03:33:23.320 | but they've been kind of a little bit in the wilderness.

03:33:26.000 | And I think, you know, one of the things

03:33:27.440 | that I would like to do finally is, you know,

03:33:30.920 | I always thought that sort of this notion of pure

03:33:33.560 | and chaos pure and chaos being the acronym for my book,

03:33:36.800 | "New Kind of Science" was something

03:33:40.800 | that people should be doing.

03:33:41.920 | And, you know, we tried to figure out

03:33:43.600 | what's the right institutional structure to do this stuff.

03:33:45.960 | You know, we dealt with a bunch of universities.

03:33:48.360 | Oh, you know, can we do this here?

03:33:50.000 | Well, what department would it be in?

03:33:51.320 | Well, it isn't in a department.

03:33:52.560 | It's its own new kind of thing.

03:33:54.480 | That's why the book was called "A New Kind of Science."

03:33:58.360 | It's kind of the, because that's an increasingly

03:34:01.080 | good description of what it is, so to speak.

03:34:03.240 | We're actually, we were thinking about kind

03:34:05.160 | of the ruleological society, because we're realizing

03:34:08.640 | that it's kind of, it's, you know,

03:34:11.080 | there's a, it's very interesting.

03:34:13.320 | I mean, I've never really done something like this before,

03:34:15.080 | because there's this whole group of researchers

03:34:17.680 | who've been doing things that are really,

03:34:20.720 | in some cases, very elegant, very surviving, very solid.

03:34:24.240 | You know, here's this thing that happens

03:34:26.240 | in this very abstract system.

03:34:28.120 | But it's like, what is that part of?

03:34:31.240 | You know, it doesn't have a home.

03:34:33.960 | And I think that's something, you know,

03:34:35.560 | I kind of fault myself for not having been more,

03:34:38.040 | you know, when complexity was developing in the '80s,

03:34:40.440 | I didn't understand the danger of applications.

03:34:45.440 | That is, it's really cool that you can apply this

03:34:47.640 | to economics, and you can apply it to evolutionary biology,

03:34:50.200 | and this and that and the other.

03:34:51.600 | But what happens with applications is everything

03:34:53.920 | gets sucked into the applications.

03:34:55.920 | And the pure stuff, it's like the pure mathematics,

03:34:58.760 | there isn't any pure mathematics, so to speak.

03:35:01.000 | It's all just applications of mathematics.

03:35:03.320 | And I failed to kind of make sure

03:35:05.800 | that this kind of pure area

03:35:07.800 | was kind of maintained and developed.

03:35:11.440 | And I think now, you know,

03:35:12.840 | one of the things I want to try to do,

03:35:14.760 | and you know, it's a funny thing,

03:35:16.240 | because I'm used to, look, I've been a tech CEO

03:35:19.360 | for more than half my life now.

03:35:20.640 | So, you know, this is what I know how to do.

03:35:23.120 | And, you know, I can make stuff happen

03:35:26.480 | and get projects to happen,

03:35:27.760 | even as it turns out basic science projects

03:35:30.200 | in that kind of setting,

03:35:31.520 | and how that translates into kind of, you know,

03:35:35.040 | there are a lot of people working on, for example,

03:35:36.600 | our physics project sort of distributed

03:35:38.160 | through the academic world, and that's working just great.

03:35:40.560 | But the question is, you know,

03:35:41.480 | can we have a sort of accelerator mechanism

03:35:44.640 | that makes use of kind of what we've learned

03:35:46.600 | in sort of R&D innovation?

03:35:49.320 | And, you know, but on the other hand,

03:35:50.880 | it's a funny thing because, you know,

03:35:53.040 | in a company, in the end, the thing is, you know,

03:35:56.680 | it's a company, it makes products,

03:35:57.960 | it sells things to people.

03:36:00.680 | And, you know, when you're doing basic research,

03:36:02.440 | one of the challenges is there isn't that same kind

03:36:04.840 | of sort of mechanism.

03:36:06.960 | And so it's, you know, how do you drive the thing

03:36:10.040 | in a kind of, in a lead kind of way

03:36:12.920 | so that it really can make forward progress

03:36:15.160 | rather than, you know, what can often happen in,

03:36:17.840 | you know, in academic settings where it's like,

03:36:20.240 | well, there are all these flowers blooming,

03:36:21.640 | but it's not clear that they're, you know, that it's-

03:36:24.520 | - You have to have a central mission and a drive,

03:36:27.320 | just like you do with a company

03:36:28.920 | that's delivering a big overarching product.

03:36:31.360 | And that's- - Right.

03:36:32.840 | But the challenge is, you know, when you have a,

03:36:34.960 | the economics of the world are such that, you know,

03:36:39.000 | when you're delivering a product and people say,

03:36:40.600 | "Wow, that's useful, we'll buy it."

03:36:42.800 | And then that kind of feeds back and, okay,

03:36:44.480 | then you can pay the people who build it to eat,

03:36:48.080 | you know, so they can eat and so on.

03:36:50.120 | And with basic science, the payoff is very much less visible

03:36:55.760 | and, you know, with this physics project, as I say,

03:36:57.520 | the big surprise has been that, I mean, you know,

03:37:00.680 | for example, well, the big surprise with the physics project

03:37:03.400 | is that it looks like it has near-term applications.

03:37:07.120 | And I was like, I'm guessing this is 200 years away.

03:37:10.160 | It's, I was kind of using the analogy of, you know,

03:37:13.520 | Newton starting a satellite launch company,

03:37:16.920 | which would have been kind of wrong time.

03:37:19.440 | And, you know, but it turns out that's not the case,

03:37:22.360 | but we can't guarantee that.

03:37:23.960 | And if you say we're signing up to do basic research,

03:37:27.160 | basic rheology, let's say, and, you know,

03:37:30.560 | and we can't, we don't know the horizon, you know,

03:37:33.120 | it's an unknown horizon.

03:37:34.560 | It's kind of like an undecidable kind of proposition

03:37:37.120 | of when is this proof going to end, so to speak?

03:37:39.540 | When is it going to be something that gets applied?

03:37:43.280 | - Well, I hope this is,

03:37:45.660 | this becomes a vibrant new field of rheology.

03:37:48.520 | I love it.

03:37:49.360 | Like I told you many, many times,

03:37:50.720 | it's one of the most amazing ideas

03:37:54.280 | that has been brought to this world.

03:37:55.720 | So I hope you get a bunch of people to explore this world.

03:37:59.980 | Thank you once again

03:38:02.920 | for spending your really valuable time with me today.

03:38:05.880 | - Fun stuff.

03:38:06.840 | Thank you.

03:38:07.680 | - Thanks for listening to this conversation

03:38:10.120 | with Stephen Wolfram.

03:38:11.400 | To support this podcast,

03:38:12.600 | please check out our sponsors in the description.

03:38:15.360 | And now let me leave you with some words

03:38:17.540 | from Richard Feynman.

03:38:19.400 | "Nature uses only the longest threads

03:38:22.680 | "to weave her patterns.

03:38:24.360 | "So each small piece of her fabric

03:38:27.080 | "reveals the organization of the entire tapestry."

03:38:30.260 | Thank you for listening and hope to see you next time.

03:38:34.000 | (upbeat music)

03:38:36.580 | (upbeat music)

03:38:39.160 | [BLANK_AUDIO]

Stephen Wolfram: Complexity and the Fabric of Reality | Lex Fridman Podcast #234

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