Stephen Wolfram: Complexity and the Fabric of Reality
物理与宇宙学技术与编程生物与进化数学太空与探索
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AI 智能总结
沃尔弗拉姆谈复杂性、物理现实与计算宇宙
这是 Stephen Wolfram 第三次登上 Lex Fridman 播客，对话是一场关于复杂性、数学、物理和意识的「狂野技术过山车」。Wolfram 分享了他的 Wolfram Physics Project 的最新进展，以及他对宇宙本质是计算的深刻信念。
复杂性理论物理学计算宇宙数学Wolfram Physics
Stephen Wolfram 是计算机科学家、数学家和理论物理学家，Wolfram Research 创始人，开发了 Mathematica、Wolfram Alpha 和 Wolfram Language，著有《一种新科学》（A New Kind of Science），现主导 Wolfram Physics Project。
📌 核心观点
- Wolfram 的核心主张是「计算等价原则」（Principle of Computational Equivalence）：几乎所有足够复杂的系统都具有相同的计算能力，这意味着简单规则可以产生无限复杂的行为，宇宙本身可能就是一个简单规则运行的计算过程。
- 他的 Wolfram Physics Project 试图用超图（hypergraph）重写规则来推导出物理学的基本定律，包括广义相对论和量子力学，认为时空本身是从离散的计算结构中涌现出来的。
- 关于复杂性，Wolfram 认为复杂性不是神秘的，而是简单规则迭代的必然结果——就像元胞自动机 Rule 110 这样极简的规则，也能产生图灵完备的复杂行为。
- 他对 AI 和 LLM 的看法：ChatGPT 等模型的成功证明了语言中存在深层的数学结构，这与他长期以来关于计算和规律性的研究一脉相承。
- Wolfram 分享了他极度高产的工作方式：每天工作超过12小时，使用 Wolfram Language 作为思考工具，将计算作为探索想法的主要媒介。
✨ 金句摘录
Wolfram：几乎所有足够复杂的系统都具有相同的计算能力——这就是计算等价原则。
Wolfram：宇宙可能就是一个简单规则运行的计算过程，时空从离散的计算结构中涌现。
Wolfram：复杂性不是神秘的，它是简单规则迭代的必然结果。
📋 章节目录
暂无章节信息
🔑 关键词
universespacegotgoingphysicsdoncomputationalpossiblemathematicsstorycomputationquantumconsciousnesstheorymodelsayinginterestingwholerulemechanics
💬 精彩语录
"human would say. I know that's what a human would say, because we're used to the idea that there are,"
— Stephen Wolfram （2:12:17.600）
"pieces of it in a way that we humans can understand and that map onto things that we care about doing."
— Stephen Wolfram （1:09:33.760）
"believed we can talk about it later that that that just just really isn't right. But But I think that"
— Stephen Wolfram （21:45.520）
"fun thing to start thinking about all these things that we know in physical space, like event horizons"
— Stephen Wolfram （1:21:43.840）
"because of the definition of what it means to have computation. So the Rulliad, it's a formal system."
— Stephen Wolfram （2:04:47.760）
🎙️ 完整对话（2415 条）
Lex Fridman (00:00.000)
The following is a conversation with Stephen Wolfram, his third time on the podcast.
Lex Fridman (00:04.880)
He's a computer scientist, mathematician, theoretical physicist, and the founder of
Lex Fridman (00:10.240)
Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the new
Lex Fridman (00:16.560)
Wolfram Physics Project. This conversation is a wild technical roller coaster ride
Lex Fridman (00:22.800)
through topics of complexity, mathematics, physics, computing, and consciousness.
Stephen Wolfram (00:28.160)
I think this is what this podcast is becoming, a wild ride. Some episodes are about physics,
Stephen Wolfram (00:34.400)
some about robots, some are about war and power, some are about the human condition
Lex Fridman (00:40.400)
and our search for meaning, and some are just what the comedian Tim Dillon calls fun.
Stephen Wolfram (00:47.680)
This is the Lex Friedman Podcast, to support it please check out the sponsors in the description,
Lex Fridman (00:52.800)
and now here's my conversation with Stephen Wolfram.
Lex Fridman (00:56.480)
Stephen.
Stephen Wolfram (00:57.680)
Almost 20 years ago, you published A New Kind of Science, where you presented a study of
Stephen Wolfram (01:03.120)
complexity and an approach for modeling of complex systems. So, let us return again to
Lex Fridman (01:10.160)
the core idea of complexity. What is complexity?
Lex Fridman (01:15.360)
I don't know, I think that's not the most interesting question. It's like,
Stephen Wolfram (01:19.200)
you know, if you ask a biologist what is life, that's not the question they care the most about.
Lex Fridman (01:24.560)
But what I was interested in is, how does something that we would usually identify as
Stephen Wolfram (01:31.440)
complexity arise in nature? And I got interested in that question like 50 years ago, which is
Stephen Wolfram (01:35.920)
really embarrassingly long time ago. And, you know, I was, you know, how does snowflakes get
Stephen Wolfram (01:41.920)
to have complicated forms? How do galaxies get to have complicated shapes? How do living systems
Stephen Wolfram (01:47.680)
get produced? Things like that. And the question is, what's the sort of underlying scientific
Stephen Wolfram (01:52.560)
basis for those kinds of things? And the thing that I was at first very surprised by, because
Stephen Wolfram (01:57.840)
I've been doing physics and particle physics, some fancy mathematical physics and so on.
Lex Fridman (02:02.160)
And it's like, I know all this fancy stuff, I should be able to solve this sort of basic
Stephen Wolfram (02:06.320)
science question. And I couldn't, this was like early, maybe 1980 ish timeframe. And it's like,
Lex Fridman (02:13.920)
okay, what can one do to understand the sort of basic secret that nature seems to have?
Stephen Wolfram (02:19.280)
Because it seems like nature, you look around in the natural world, it's full of incredibly
Stephen Wolfram (02:22.960)
complicated forms. You look at sort of most engineered kinds of things, for instance,
Stephen Wolfram (02:28.640)
they tend to be, you know, we've got sort of circles and lines and things like this.
Lex Fridman (02:34.080)
And the question is, what secret does nature have that lets it make all this complexity
Lex Fridman (02:38.640)
that we in doing engineering, for example, don't naturally seem to have?
Lex Fridman (02:42.960)
And so that was the kind of the thing that I got interested in. And then the question was,
Stephen Wolfram (02:46.800)
you know, could I understand that with things like mathematical physics? Well, it didn't work
Lex Fridman (02:51.120)
very well. So then I got to thinking about, okay, is there some other way to try to understand this?
Lex Fridman (02:56.640)
And then the question was, if you're going to look at some system in nature,
Lex Fridman (03:00.160)
how do you make a model for that system, for what that system does? So, you know,
Stephen Wolfram (03:03.760)
a model is some abstract representation of the system, some formal representation system.
Lex Fridman (03:08.800)
What is the raw material that you can make that model out of? And so what I realized was,
Stephen Wolfram (03:15.120)
well, actually, programs are a really good source of raw material for making models of things.
Stephen Wolfram (03:20.480)
And, you know, in terms of my personal history, to me, that seemed really obvious. And the reason
Stephen Wolfram (03:26.480)
it seemed really obvious is because I just spent several years building this big piece of software
Stephen Wolfram (03:30.960)
that was sort of a predecessor to Mathematica and Morphan Language, then called SMP, Symbolic
Stephen Wolfram (03:35.600)
Manipulation Program, which was something that had this idea of starting from just these
Stephen Wolfram (03:41.600)
computational primitives and building up everything one had to build up. And so kind of the notion of,
Stephen Wolfram (03:46.560)
well, let's just try and make models by starting from computational primitives and seeing what we
Stephen Wolfram (03:50.480)
can build up, that seemed like a totally obvious thing to do. In retrospect, it might not have been
Stephen Wolfram (03:56.800)
externally quite so obvious, but it was obvious to me at the time, given the path that I happened
Stephen Wolfram (04:00.880)
to have been on. So, you know, so that got me into this question of, let's use programs
Lex Fridman (04:06.000)
to model what happens in nature. And the question then is, well, what kind of programs?
Stephen Wolfram (04:11.040)
And, you know, we're used to programs that you write for some particular purpose, and it's a
Stephen Wolfram (04:15.120)
big, long piece of code, and it does some specific thing. But what I got interested in was, okay,
Stephen Wolfram (04:20.400)
if you just go out into the sort of computational universe of possible programs, you say,
Stephen Wolfram (04:25.280)
take the simplest program you can imagine, what does it do? And so I started studying these things
Stephen Wolfram (04:30.720)
called cellular automata. Actually, I didn't know at first they were called cellular automata,
Lex Fridman (04:34.720)
but I found that out subsequently. But it's just a line of cells, you know, each one is black or
Stephen Wolfram (04:39.600)
white, and it's just some rule that says the color of the cell is determined by the color that it had
Stephen Wolfram (04:44.800)
on the previous step and its two neighbors on the previous step. And I had initially thought,
Stephen Wolfram (04:50.480)
that's, you know, sufficiently simple setup is not going to do anything interesting. It's always
Stephen Wolfram (04:55.280)
going to be simple, no complexity, simple rule, simple behavior. Okay, but then I actually ran
Stephen Wolfram (05:00.720)
the computer experiment, which was pretty easy to do. I mean, it probably took a few hours
Stephen Wolfram (05:05.280)
originally. And the results were not what I'd expected at all. Now, needless to say,
Stephen Wolfram (05:12.400)
in the way that science actually works, the results that I got had a lot of unexpected
Stephen Wolfram (05:16.800)
things which I thought were really interesting, but the really strongest results, which was
Stephen Wolfram (05:21.040)
already right there in the printouts I made, I didn't really understand for a couple more years.
Lex Fridman (05:25.520)
So it was not, you know, the compressed version of the story is you run the experiment and you
Stephen Wolfram (05:31.200)
immediately see what's going on, but I wasn't smart enough to do that, so to speak. But the
Stephen Wolfram (05:36.640)
big thing is, even with very simple rules of that type, sort of the minimal, tiniest program,
Stephen Wolfram (05:43.520)
sort of the one line program or something, it's possible to get very complicated behavior. My
Stephen Wolfram (05:49.520)
favorite example is this thing called Rule 30, which is a particular cellular automaton rule.
Stephen Wolfram (05:54.000)
You just started off from one black cell and it makes this really complicated pattern. And so that
Stephen Wolfram (06:00.240)
for me was sort of a critical discovery that then kind of said, playing back onto, you know,
Lex Fridman (06:07.600)
how does nature make complexity, I sort of realized that might be how it does it.
Stephen Wolfram (06:12.320)
That might be kind of the secret that it's using is that in this kind of computational
Stephen Wolfram (06:16.400)
universe of possible programs, it's actually pretty easy to get programs where even though
Stephen Wolfram (06:20.960)
the program is simple, the behavior when you run the program is not simple at all.
Lex Fridman (06:24.720)
And so for me, that was the kind of the story of kind of how that was sort of the indication that
Stephen Wolfram (06:33.120)
one had got an idea of what the sort of secret that nature uses to make complexity and how
Stephen Wolfram (06:38.960)
complexity can be made in other places. Now, if you say, what is complexity? You know,
Stephen Wolfram (06:46.080)
complexity is it's not easy to tell what's going on. That's the informal version of what is
Stephen Wolfram (06:52.560)
complexity, but there is something going on, but there's a rule to know what, right? Well, no,
Stephen Wolfram (06:57.360)
the rules can generate just randomness, right? Well, that's not obvious. In other words,
Stephen Wolfram (07:04.880)
it's not obvious at all. And it wasn't what I expected. It's not what people's intuition
Stephen Wolfram (07:09.520)
had been and has been for, you know, for a long time. That is one might think you have a rule.
Stephen Wolfram (07:15.440)
You can tell there's a rule behind it. I mean, it's just like, you know, the early, you know,
Stephen Wolfram (07:20.960)
robots in science fiction movies, right? You can tell it's a robot cause it does simple things,
Stephen Wolfram (07:27.280)
right? It turns out that isn't actually the right story, but it's not obvious that isn't the right
Stephen Wolfram (07:31.840)
story because people assume simple rules, simple behavior. And that the sort of the key discovery
Stephen Wolfram (07:37.680)
about the computational universe is that isn't true. And that discovery goes very deep and
Stephen Wolfram (07:43.360)
relates to all kinds of things that I've spent years and years studying. But, you know, that in
Stephen Wolfram (07:48.960)
the end, the sort of the, the what is complexity is, well, you can't easily tell what it's going
Stephen Wolfram (07:54.240)
to do. You could just run the rule and see what happens, but you can't just say, oh, you know,
Stephen Wolfram (08:00.080)
show me the rule. Great. And now I know what's going to happen. And, you know, the key phenomenon
Stephen Wolfram (08:04.960)
around that is this thing I call computational irreducibility. This fact that in something like
Stephen Wolfram (08:11.120)
rule 30, you might say, well, what's it going to do after a million steps? Well, you can run it
Stephen Wolfram (08:16.240)
for a million steps and just do what it does to find out, but you can't compress that. You can't
Stephen Wolfram (08:21.520)
reduce that and say, I'm going to be able to jump ahead and say, this is what it's going to do after
Stephen Wolfram (08:25.920)
a million steps, but I don't have to go through anything like that computational effort.
Stephen Wolfram (08:29.040)
CB. By the way, has anybody succeeded at that? Do you have to challenge a competition
Lex Fridman (08:34.080)
for predicting the middle column of rule 30? Anybody?
Stephen Wolfram (08:37.040)
MG. A number of people have sent things in and sort of people are picking away at it,
Lex Fridman (08:41.600)
but it's hard. I mean, I've been actually even proving that the center column of rule 30 doesn't
Lex Fridman (08:50.400)
repeat. That's something I think might be doable. Okay?
Lex Fridman (08:54.240)
CB. Mathematically proving.
Stephen Wolfram (08:55.520)
MG. Yes. And so that's analogous to a similar kind of thing as like the digits of pi,
Stephen Wolfram (09:00.880)
which are also generated in this very deterministic way. And so a question is how random are the
Stephen Wolfram (09:06.000)
digits of pi? For example, first of all, do the digits of pi ever repeat? We know they don't,
Stephen Wolfram (09:11.760)
because it was proved in the 1800s that pi is not a rational number. So that means only rational
Stephen Wolfram (09:17.280)
numbers have digit sequences that repeat. So we know the digits of pi don't repeat.
Lex Fridman (09:21.360)
So now the question is, does 0, 1, 2, 3 or whatever, do all the digits base 10 or base 2 or
Stephen Wolfram (09:27.200)
however you work it out, do they all occur with equal frequency? Nobody knows. That's far away
Stephen Wolfram (09:33.040)
from what can be understood mathematically at this point. But I'm even looking for step one,
Stephen Wolfram (09:41.280)
which is prove that the center column doesn't repeat and then prove other things about it,
Stephen Wolfram (09:46.800)
like equidistribution of equal numbers of zeros and ones. And those are things which I kind of
Stephen Wolfram (09:52.480)
set up this little prize thing because I thought those were not too out of range. Those are things
Stephen Wolfram (09:59.120)
which are within a modest amount of time, it's conceivable that those could be done. They're not
Stephen Wolfram (10:06.560)
far away from what current mathematics might allow. They'll require a bunch of cleverness
Lex Fridman (10:11.440)
and hopefully some interesting new ideas that will be useful other places.
Lex Fridman (10:16.400)
But you started in 1980 with this idea before I think you realized this idea of programs.
Stephen Wolfram (10:23.360)
You thought that there might be some kind of a thermodynamic randomness and then complexity
Stephen Wolfram (10:29.680)
comes from a clever filter that you kind of like, I don't know, spaghetti or something. You filter
Stephen Wolfram (10:37.840)
the randomness and outcomes complexity, which is an interesting intuition. How do we know that's
Stephen Wolfram (10:43.200)
not actually what's happening? So just because you were then able to develop, look, you don't need
Stephen Wolfram (10:50.560)
this like incredible randomness. You can just have very simple, predictable initial conditions
Lex Fridman (10:56.640)
and predictable rules. And then from that emerged complexity, still there might be some systems
Stephen Wolfram (11:02.720)
where it's filtering randomness on the inputs. Well, the point is when you have quotes randomness
Stephen Wolfram (11:11.120)
in the input, that means there's all kinds of information in the input. And in a sense,
Lex Fridman (11:15.120)
what you get out will be maybe just something close to what you put in. Like people are very
Stephen Wolfram (11:21.280)
in dynamical systems theory, sort of big area mathematics that developed
Stephen Wolfram (11:25.840)
from the early 1900s and really got big in the 1980s. An example of what people study
Stephen Wolfram (11:31.520)
there a lot and it's popular version is chaos theory. An example of what people study a lot
Stephen Wolfram (11:37.760)
is the shift map, which is basically taking 2x mod one to the fractional part of 2x,
Stephen Wolfram (11:44.160)
which is basically just taking digits in binary and shifting them to the left. So at every step,
Stephen Wolfram (11:49.840)
you get to see if you say, how big is this number that I got out? Well, the most important digit in
Stephen Wolfram (11:54.880)
that number is whatever ended up at the left hand end. But now if you start off from an arbitrary
Stephen Wolfram (12:00.560)
random number, which is quotes randomly chosen, so all its digits are random, then when you run
Stephen Wolfram (12:06.400)
that sort of chaos theory shift map, all that you get out is just whatever you put in. You just get
Stephen Wolfram (12:12.480)
to see what you... It's not obvious that you would excavate all of those digits. And if you're,
Stephen Wolfram (12:18.080)
for example, making a theory, I don't know, fluid mechanics, for example, if there was that
Stephen Wolfram (12:22.400)
phenomenon in fluid mechanics, then the equations of fluid mechanics can't be right. Because what
Stephen Wolfram (12:27.600)
that would be saying is the equations that it matters to the fluid, what happens in the fluid
Stephen Wolfram (12:33.600)
at the level of the millionth digit of the initial conditions, which is far below the point at which
Stephen Wolfram (12:40.080)
you're hitting sizes of molecules and things like that. So it's kind of almost explaining
Stephen Wolfram (12:45.280)
if that phenomenon is an important thing, it's kind of telling you that fluid dynamics,
Stephen Wolfram (12:50.080)
which describes fluids as continuous media and so on, isn't really right.
Lex Fridman (12:54.400)
But so this idea that... It's a tricky thing because as soon as you put randomness in,
Stephen Wolfram (13:01.440)
you have to know how much of what's coming out is what you put in versus how much is actually
Stephen Wolfram (13:07.360)
something that's being generated. And what's really nice about these systems where you just
Stephen Wolfram (13:11.280)
have very simple initial conditions and where you get random stuff out or seemingly random stuff out
Stephen Wolfram (13:17.600)
is you don't have that issue. You don't have to argue about, was there something complicated put
Stephen Wolfram (13:21.920)
in? Because it's plainly obvious there wasn't. Now, as a practical matter in doing experiments,
Stephen Wolfram (13:26.800)
the big thing is if the thing you see is complex and reproducible, then it didn't come from just
Stephen Wolfram (13:34.320)
filtering some, quotes, randomness from the outside world. It has to be something that is
Stephen Wolfram (13:39.120)
intrinsically made because it wouldn't otherwise be... It could be the case that you set things up
Lex Fridman (13:45.760)
and it's always the same each time and you say, well, it's kind of the same, but it's not random
Stephen Wolfram (13:51.440)
each time because it's kind of the definition of it being random is it was kind of picked at random
Stephen Wolfram (13:57.040)
each time, so to speak. So is it possible to for sure know that our universe does not at the
Stephen Wolfram (14:03.040)
fundamental level have randomness? Is it possible to conclusively say there's no randomness at the
Stephen Wolfram (14:10.400)
bottom? Well, it's an interesting question. I mean, you know, science, natural science is an
Lex Fridman (14:16.240)
inductive business, right? You observe a bunch of things and you say, can we fit these together?
Lex Fridman (14:21.520)
What is our hypothesis for what's going on? The thing that I think I can say fairly definitively
Stephen Wolfram (14:27.680)
is at this point, we understand enough about fundamental physics that if there was sort of
Stephen Wolfram (14:34.480)
an extra dice being thrown, it's something that doesn't need to be there. We can get what we see
Stephen Wolfram (14:41.120)
without that. Now, could you add that in as an extra little featureoid without breaking the
Stephen Wolfram (14:49.360)
universe? Probably, but in fact, almost certainly yes. But is it necessary for understanding the
Stephen Wolfram (14:56.000)
universe? No. And I think actually from a more fundamental point of view, I think I might be
Stephen Wolfram (15:03.360)
able to argue. So one of the things that I've been interested in and been pretty surprised that I've
Stephen Wolfram (15:07.680)
had anything sentient to say about is the question of why does the universe exist? I didn't think
Stephen Wolfram (15:13.520)
that was a question that I would, you know, I thought that was a far out there metaphysical
Stephen Wolfram (15:18.400)
kind of thing. Even the philosophers have stayed away from that question for the most part.
Stephen Wolfram (15:23.600)
It's such a kind of difficult to address question. But I actually think to my great surprise that
Stephen Wolfram (15:30.880)
from our physics project and so on, that it is possible to actually address that question and
Stephen Wolfram (15:36.320)
explain why the universe exists. And I kind of have a suspicion. I've not thought it through.
Stephen Wolfram (15:40.960)
I kind of have a suspicion that that explanation will eventually show you that in no meaningful
Stephen Wolfram (15:46.800)
sense can there be randomness underneath the universe. That is that if there is, it's something
Stephen Wolfram (15:52.880)
that is necessarily irrelevant to our perception of the universe. That is that it could be there,
Lex Fridman (15:59.600)
but doesn't matter because in a sense, we've already, you know, whatever it would do,
Stephen Wolfram (16:04.400)
whatever extra thing it would add is not relevant to our perception of what's going on.
Lex Fridman (16:09.200)
So why does the universe exist? How does the relevance of randomness connect to the big
Lex Fridman (16:17.680)
why question of the universe? So, OK, so I mean, why does the universe exist? Well, let's see.
Lex Fridman (16:23.040)
And is this the only universe we got? It's the only one that about that I'm pretty sure.
Lex Fridman (16:28.800)
So now maybe which one which of these topics is better to enter first? Why does the universe exist
Lex Fridman (16:35.920)
and why you think it's the only one that exists? Well, I think they're very closely related. OK.
Stephen Wolfram (16:41.600)
OK. So, I mean, the first thing, let's see, I mean, this why does the universe exist question
Stephen Wolfram (16:47.040)
is built on top of all these things that we've been figuring out about fundamental physics,
Stephen Wolfram (16:52.640)
because if you want to know why the universe exists, you kind of have to know what the
Stephen Wolfram (16:55.520)
universe is made of. And I think the well, let me let me describe a little bit about
Stephen Wolfram (17:02.880)
the why does the universe exist question. So the main issue is let's say you have a model
Stephen Wolfram (17:07.040)
for the universe and you say I've got this this program or something and you run it and you make
Lex Fridman (17:12.160)
the universe. Now you say, well, how do you actually why is that program actually running?
Lex Fridman (17:17.440)
And people say you've got this program that makes the universe. What computer is it running on?
Stephen Wolfram (17:21.920)
Right. What what does it mean? What actualizes something? You know, two plus two equals four.
Lex Fridman (17:27.120)
But that's different from saying this to a pile of two rocks, another pile of two rocks, and so
Stephen Wolfram (17:31.280)
many moves them together and makes four, so to speak. And so what is it that kind of turns it
Stephen Wolfram (17:37.040)
from being just this formal thing to being something that is actualized? OK, so there we
Stephen Wolfram (17:43.440)
have to start thinking about, well, well, what do we actually know about what's going on in the
Stephen Wolfram (17:47.920)
universe? Well, we are observers of this universe. But confusingly enough, we're part of this
Stephen Wolfram (17:53.360)
universe. So in a sense, we what what what if we say what do we what do we know about what's
Stephen Wolfram (17:59.440)
going on in the universe? Well, what we know is what sort of our consciousness records about
Stephen Wolfram (18:04.400)
what's going on in the universe. And consciousness is part of the fabric of the universe. So we're
Stephen Wolfram (18:09.520)
in it. Yes, we're in it. And maybe I should maybe I should start off by saying something about
Stephen Wolfram (18:15.120)
the consciousness story, because that's some. Maybe we should begin even before that at the
Stephen Wolfram (18:23.040)
very base layer of the Wolfram physics project. Maybe you can give a broad overview once again
Stephen Wolfram (18:29.760)
really quick about this hypergraph model. Yes. And also, what is it a year and a half ago since
Stephen Wolfram (18:36.160)
you've brought this project to the world? What is the status update where what are all the beautiful
Stephen Wolfram (18:42.240)
ideas you have come across? What are the interesting things you can mention? It's I mean,
Stephen Wolfram (18:48.240)
it's a it's a frigging Cambrian explosion. I mean, it's it's crazy. I mean, there are all these
Stephen Wolfram (18:53.680)
things which I've kind of wondered about for years. And suddenly, there's actually a way to
Stephen Wolfram (18:58.960)
think about them. And I really did not see. I mean, the real strength of what's happened,
Stephen Wolfram (19:04.240)
I absolutely did not see coming. And the real strength of it is we've got this model for physics,
Lex Fridman (19:09.120)
but it turns out it's a foundational kind of model. That's a different kind of computation
Stephen Wolfram (19:13.680)
like model that I'm kind of calling the sort of multi computational model. And that that kind of
Stephen Wolfram (19:20.720)
model is applicable not only to physics, but also to lots of other kinds of things. And one reason
Stephen Wolfram (19:26.640)
that's extremely powerful is because physics has been very successful. So we know a lot based on
Lex Fridman (19:31.920)
what we figured out in physics. And if we know that the same model governs physics and governs,
Stephen Wolfram (19:37.040)
I don't know, economics, linguistics, immunology, whatever, we know that the same kind of model
Stephen Wolfram (19:42.080)
governs those things. We can start using things that we've successfully discovered in physics
Lex Fridman (19:47.360)
and applying those intuitions in all these other areas. And that's that's pretty exciting and very
Lex Fridman (19:52.640)
and very surprising to me. And in fact, it's kind of like in the original story of sort of you go
Lex Fridman (19:59.040)
and you explain why is there complexity in the natural world, then you realize, well, there's all
Stephen Wolfram (1:00:05.680)
Look, I think that a very interesting question is, which I've certainly thought a little bit about,
Stephen Wolfram (1:00:10.160)
is what can you imagine? What is a sort of factoring of something? What are some other
Stephen Wolfram (1:00:16.000)
possible ways you could exist, so to speak? And if you were a photon, if you were some kind of thing
Stephen Wolfram (1:00:23.840)
that was kind of, you know, intelligence represented in terms of photons, you know,
Stephen Wolfram (1:00:30.480)
for example, the photons we receive in the cosmic microwave background, those photons,
Stephen Wolfram (1:00:35.280)
as far as they're concerned, the universe just started. They were emitted, you know,
Stephen Wolfram (1:00:39.520)
100,000 years after the beginning of the universe, they've been traveling at the speed of light,
Stephen Wolfram (1:00:43.200)
time stayed still for them, and then they just arrived and we just detected them. So for them,
Stephen Wolfram (1:00:49.280)
the universe just started. And that's a different perception of, you know, that has
Stephen Wolfram (1:00:53.920)
implications for a very different perception of time. They don't have that single thread
Stephen Wolfram (1:00:57.760)
that seems to be really important for being able to tell a heck of a good story.
Lex Fridman (1:01:01.840)
So we humans, we can tell a story. Right. We can tell a story. What other kind of stories can you
Stephen Wolfram (1:01:07.920)
tell? So photon is a really boring story. Yeah. I mean, so that's a, I don't know if they're a
Stephen Wolfram (1:01:13.040)
boring story, but I think it's, you know, I've been wondering about this and I've been asking,
Stephen Wolfram (1:01:17.760)
you know, friends of mine who are science fiction writers and things, have you written stuff about
Stephen Wolfram (1:01:20.960)
this? And I've got one example, a great collection of books from my friend Rudy Rooker, which I have
Stephen Wolfram (1:01:28.240)
to say, they're books that are very informed by a bunch of science that I've done. And the thing
Stephen Wolfram (1:01:34.640)
that I really loved about them is, you know, in the first chapter of the book, the Earth is consumed
Stephen Wolfram (1:01:41.360)
by these things called nants, which are nano, nanobot type things. So, you know, so the Earth
Stephen Wolfram (1:01:47.920)
is gone in the first, but then it comes back. But then, yeah, right. That was only a micro
Stephen Wolfram (1:01:53.760)
spoiler. It's only chapter one. But the thing that is not a real spoiler alert because it's
Stephen Wolfram (1:02:01.600)
such a complicated concept, but in the end, the Earth is saved by this thing called the
Stephen Wolfram (1:02:07.920)
principle of computational equivalence, which is a kind of a core scientific idea of mine.
Lex Fridman (1:02:12.640)
And I was just like, like thrilled. I don't read fiction books very often. And I was just thrilled.
Stephen Wolfram (1:02:17.760)
I get to the end of this and it's like, oh, my gosh, you know, everything is saved by this sort
Stephen Wolfram (1:02:22.480)
of deep scientific principle. Can you maybe elaborate how the principle of computational
Stephen Wolfram (1:02:27.920)
equivalence can save a planet? That would, that would be a terrible spoiler. That would be a
Stephen Wolfram (1:02:36.240)
spoiler. But no, but let me say what the principle of computational equivalence is. So the question
Stephen Wolfram (1:02:42.720)
is, you are, you have a system, you have some rule, you can think of its behavior as corresponding
Stephen Wolfram (1:02:48.800)
to a computation. The question is, how sophisticated is that computation? The statement of the principle
Stephen Wolfram (1:02:54.560)
of computational equivalence is, as soon as it's not obviously simple, it will be as sophisticated
Stephen Wolfram (1:03:00.640)
as anything. And so that has the implication that, you know, rule 30, you know, our brains,
Stephen Wolfram (1:03:07.280)
other things in physics, they're all ultimately equivalent in the computations they can do.
Lex Fridman (1:03:12.080)
And that's what leads to this computational irreducibility idea because the reason we don't
Stephen Wolfram (1:03:16.480)
get to jump ahead, you know, and out think rule 30 is because we're just computationally equivalent
Stephen Wolfram (1:03:22.080)
to rule 30. So we're kind of just both just running computations that are the same sort of
Stephen Wolfram (1:03:28.160)
raw, the same level of computation, so to speak. So that's kind of the idea there. And the question,
Stephen Wolfram (1:03:34.320)
I mean, it's like the, you know, in the science fiction version would be, okay, somebody says,
Stephen Wolfram (1:03:41.200)
we just need more servers, get us more servers. The way to get even more servers is turn the
Stephen Wolfram (1:03:46.640)
whole planet into a bunch of microservers. And that's where it starts. And so the question of,
Stephen Wolfram (1:03:53.520)
you know, computational equivalence, principle of computational equivalence is, well, actually,
Stephen Wolfram (1:03:57.600)
you don't need to build those custom servers. Actually, you can just use natural computation
Stephen Wolfram (1:04:06.640)
to compute things, so to speak. You can use nature to compute. You don't need to have done
Stephen Wolfram (1:04:11.120)
all that engineering. I mean, it kind of feels a little disappointing that you say, we're going to
Stephen Wolfram (1:04:16.480)
build all these servers. We're going to do all these things. We're going to make, you know,
Stephen Wolfram (1:04:19.920)
maybe we're going to have human consciousness uploaded into, you know, some elaborate digital
Stephen Wolfram (1:04:25.120)
environment. And then you look at that thing and you say, it's got electrons moving around,
Stephen Wolfram (1:04:29.520)
just like in a rock. And then you say, well, what's the difference? And the principle of
Stephen Wolfram (1:04:33.760)
computational equivalence says there isn't, at some level, a fundamental, you know, you can't say,
Stephen Wolfram (1:04:39.920)
mathematically, there's a fundamental difference between the rock that is the future of human
Stephen Wolfram (1:04:45.440)
consciousness and the rock that's just a rock. Now, what I've sort of realized with this kind
Stephen Wolfram (1:04:51.120)
of consciousness thing is there is an aspect of this that seems to be more special. And for
Stephen Wolfram (1:04:59.200)
example, something I haven't really teased apart properly is when it comes to something like the
Stephen Wolfram (1:05:03.920)
weather and the weather having a mind of its own or whatever, or your average, you know,
Stephen Wolfram (1:05:07.600)
pulsar magnetosphere acting like a sort of intelligent thing, how does that relate to,
Stephen Wolfram (1:05:13.520)
you know, how is that entity related to the kind of consciousness that we have? And sort of,
Lex Fridman (1:05:21.360)
what would the world look like, you know, to the weather? If we think about the weather as a mind,
Lex Fridman (1:05:26.480)
what will it perceive? What will its laws of physics be? I don't really know.
Stephen Wolfram (1:05:31.520)
Because it's very parallel.
Stephen Wolfram (1:05:33.280)
It's very parallel, among other things. And it's not obvious. I mean, this is a really kind of
Stephen Wolfram (1:05:39.360)
mindbending thing because we've got to try and imagine a parsing of the universe different from
Stephen Wolfram (1:05:46.480)
the one we have. And by the way, when we think about extraterrestrial intelligence and so on,
Stephen Wolfram (1:05:51.760)
I think that's kind of the key thing is, you know, we've always assumed, I've always assumed,
Stephen Wolfram (1:05:57.040)
okay, the extraterrestrials, at least they have the same physics. We all live in the same universe.
Stephen Wolfram (1:06:01.680)
They've got the same physics. But actually, that's not really right because the extraterrestrials
Stephen Wolfram (1:06:07.200)
could have a completely different way of parsing the universe. So it's as if, you know, there could
Stephen Wolfram (1:06:12.960)
be for all we know, right here in this room, you know, in the details of the motion of these gas
Stephen Wolfram (1:06:17.680)
molecules, there could be an amazing intelligence that we were like, but we have no way of, we're
Stephen Wolfram (1:06:24.800)
not parsing the universe in the same way. If only we could parse the universe in the right way,
Stephen Wolfram (1:06:29.360)
you know, immediately this amazing thing that's going on and this, you know, huge culture that's
Stephen Wolfram (1:06:34.400)
developed and all that kind of thing would be obvious to us, but it's not because we have our
Stephen Wolfram (1:06:38.240)
particular way of parsing the universe. Would that thing also have an agency? I don't know the right
Lex Fridman (1:06:43.440)
word to use, but something like consciousness, but a different kind of consciousness?
Stephen Wolfram (1:06:47.920)
I think it's a question of just what you mean by the word, because I think that the,
Stephen Wolfram (1:06:51.360)
you know, this notion of consciousness and the, okay, so some people think of consciousness as
Stephen Wolfram (1:06:56.480)
sort of a key aspect of it is that we feel that there's sort of a feeling of that we exist in
Stephen Wolfram (1:07:03.840)
some way, that we have this intrinsic feeling about ourselves. You know, I suspect that any
Stephen Wolfram (1:07:11.040)
of these things would also have an intrinsic feeling about themselves. I've been sort of
Stephen Wolfram (1:07:14.720)
trying to think recently about constructing an experiment about what if you were just a piece
Lex Fridman (1:07:19.680)
of a cellular automaton, let's say, you know, what would your feeling about yourself actually be?
Stephen Wolfram (1:07:25.120)
And, you know, can we put ourselves in the shoes, in the cells of the cellular automaton,
Lex Fridman (1:07:30.480)
so to speak? Can we get ourselves close enough to that, that we could have a sense of what the
Stephen Wolfram (1:07:36.640)
world would be like if you were operating in that way? And it's a little difficult because,
Stephen Wolfram (1:07:42.240)
you know, you have to not only think about what are you perceiving, but also what's actually
Stephen Wolfram (1:07:46.880)
going on in your brain. And our brains do what they actually do. And they don't, it's, you know,
Stephen Wolfram (1:07:52.560)
I think there might be some experiments that are possible with neural nets and so on,
Stephen Wolfram (1:07:57.840)
where you can have something where you can at least see in detail what's happening inside the
Stephen Wolfram (1:08:02.080)
system. And one of my projects to think about is, is there a way of kind of getting a sense
Stephen Wolfram (1:08:10.320)
kind of from inside the system about what its view of the world is and how it, you know,
Stephen Wolfram (1:08:16.960)
can we make a bridge? See, the main issue is this. It's a sort of philosophically difficult thing
Stephen Wolfram (1:08:23.360)
because it's like we do what we do. We understand ourselves, at least to some extent.
Lex Fridman (1:08:29.360)
We humans understand ourselves.
Stephen Wolfram (1:08:30.800)
That's correct. But yet, okay, so what are we trying to do, for example, when we are trying to
Stephen Wolfram (1:08:35.920)
make a model of physics? What are we actually trying to do? Because, you know, you say, well,
Stephen Wolfram (1:08:40.160)
can we work out what the universe does? Well, of course we can. We just watch the universe. The
Stephen Wolfram (1:08:44.320)
universe does what it does. But what we're trying to do when we make a model of physics is we're
Stephen Wolfram (1:08:49.040)
trying to get to the point where we can tell a story to ourselves that we understand that is also
Stephen Wolfram (1:08:54.880)
a representation of what the universe does. So it's this kind of, you know, can we make a bridge
Stephen Wolfram (1:08:59.680)
between what we humans can understand in our minds and what the universe does? And in a sense,
Stephen Wolfram (1:09:05.360)
you know, a large part of my kind of life efforts have been devoted to making computational
Stephen Wolfram (1:09:11.600)
language, which kind of is a bridge between what is possible in the computational universe
Lex Fridman (1:09:16.720)
and what we humans can conceptualize and think about. In a sense, when I built Wolfram Language
Lex Fridman (1:09:22.640)
and our whole sort of computational language story, it's all about how do you take sort of raw
Stephen Wolfram (1:09:28.560)
computation and this ocean of computational possibility and how do we sort of represent
Stephen Wolfram (1:09:33.760)
pieces of it in a way that we humans can understand and that map onto things that we care about doing.
Lex Fridman (1:09:39.520)
And in a sense, when you add physics, you're adding this other piece where we can, you know,
Stephen Wolfram (1:09:44.480)
mediated by computer, can we get physics to the point where we humans can understand something
Stephen Wolfram (1:09:50.560)
about what's happening in it? And when we talk about an alien intelligence, it's kind of the
Stephen Wolfram (1:09:55.200)
same story. It's like, is there a way of mapping what's happening there onto something that we
Stephen Wolfram (1:10:00.960)
humans can understand? And, you know, physics in some sense is like our exhibit one of the story
Stephen Wolfram (1:10:08.800)
of alien intelligence. It's an alien intelligence in some sense. And what we're doing in making a
Stephen Wolfram (1:10:15.600)
model of physics is mapping that onto something that we understand. And I think, you know, a lot
Stephen Wolfram (1:10:21.200)
of these other things that I've recently been kind of studying, whether it's molecular biology,
Stephen Wolfram (1:10:26.320)
other kinds of things, which we can talk about a bit, those are other cases where we're in a sense
Stephen Wolfram (1:10:33.760)
trying to, again, make that bridge between what we humans understand and sort of the natural
Stephen Wolfram (1:10:39.280)
language of that sort of alien intelligence in some sense. When you're talking about,
Stephen Wolfram (1:10:44.240)
just to backtrack a little bit about cellular automata, being able to, what's it like to be
Lex Fridman (1:10:51.840)
a cellular automata in the way that's equivalent to what is it like to be a conscious human being?
Lex Fridman (1:10:58.560)
How do you approach that? So is it looking at some subset of the cellular automata, asking questions
Stephen Wolfram (1:11:04.240)
of that subset, like how the world is perceived, how you as that subset, like for that local pocket
Stephen Wolfram (1:11:13.920)
of computation, what are you able to say about the broader cellular time? And that somehow then
Stephen Wolfram (1:11:21.120)
can give you a sense of how to step outside of that cellular time. Right, but the tricky part is
Stephen Wolfram (1:11:25.760)
that that little subset, what it's doing is it has a view of itself. And the question is,
Lex Fridman (1:11:33.440)
how do you get inside it? It's like when we, with humans, it's like we can't get inside each other's
Stephen Wolfram (1:11:40.320)
consciousness. That doesn't really even make sense. It's like there is an experience that
Stephen Wolfram (1:11:47.360)
somebody is having, but you can perceive things from the outside, but sort of getting inside
Stephen Wolfram (1:11:52.640)
it, it doesn't quite make sense. And for me, these sort of philosophical issues, and this one I have
Stephen Wolfram (1:11:58.160)
not untangled, so let's be... For me, the thing that has been really interesting in thinking
Stephen Wolfram (1:12:04.640)
through some of these things is when it comes to questions about consciousness or whatever else,
Stephen Wolfram (1:12:09.760)
it's like when I can run a program and actually see pictures and make things concrete, I have a
Stephen Wolfram (1:12:16.400)
much better chance to understand what's going on than when I'm just trying to figure out what's
Stephen Wolfram (1:12:20.160)
going on. I have a much better chance to understand what's going on than when I'm just trying to
Stephen Wolfram (1:12:24.240)
reason about things in a very abstract way. Yeah, but there may be a way to map the program to your
Stephen Wolfram (1:12:32.800)
conscious experience. So for example, when you play a video game, you do a first person shooter,
Stephen Wolfram (1:12:37.120)
you walk around inside this entity. It's a very different thing than watching this entity. So
Stephen Wolfram (1:12:43.920)
connect more and more, connect this full conscious experience to the subset of the cellular automata.
Stephen Wolfram (1:12:51.120)
Yeah, it's something like that. But the difference in the first person shooter thing is there's still
Stephen Wolfram (1:12:55.280)
your brain and your memory is still remembering. You still have... It's hard to... I mean, again,
Lex Fridman (1:13:02.960)
what one's going to get, one is not going to actually be able to be the cellular automaton.
Stephen Wolfram (1:13:08.000)
One's going to be able to watch what the cellular automaton does. But this is the frustrating thing
Stephen Wolfram (1:13:12.080)
that I'm trying to understand how to think about being it, so to speak.
Stephen Wolfram (1:13:18.080)
Okay. So like in virtual reality, there's a concept of immersion, like with anything,
Stephen Wolfram (1:13:21.920)
with video games, with books, there's a concept of immersion. It feels like over time, if the
Stephen Wolfram (1:13:26.880)
virtual reality experience is well done, and maybe in the future it'll be extremely well done,
Stephen Wolfram (1:13:33.680)
the immersion leads you to feel like... You mentioned memories. You forget that you even
Stephen Wolfram (1:13:40.960)
ever existed outside that experience. It's so immersive. I mean, you could argue sort of
Stephen Wolfram (1:13:46.480)
mathematically that you can never truly become immersed, but maybe you can. I mean, why can't you
Stephen Wolfram (1:13:52.880)
merge with the cellular automata? I mean, aren't you just part of the same fabric? Why can't you
Stephen Wolfram (1:13:58.400)
just like... Well, that's a good question. I mean, so let's imagine the following scenario. Let's
Stephen Wolfram (1:14:02.960)
imagine... Can you return? But then can you return back? Well, yeah, right. I mean, it's like,
Stephen Wolfram (1:14:08.400)
let's imagine you've uploaded, your brain is scanned, you've got every synapse mapped out,
Stephen Wolfram (1:14:14.320)
you upload everything about you, the brain simulator, you upload the brain simulator,
Lex Fridman (1:14:18.960)
and the brain simulator is basically some glorified cellular automaton. And then you say,
Lex Fridman (1:14:25.040)
well, now we've got an answer to what does it feel like to be a cellular automaton?
Stephen Wolfram (1:14:28.560)
It feels just like it felt to be ordinary you, because they're both computational systems,
Lex Fridman (1:14:34.480)
and they're both operating in the same way. But I think there's somehow more to it,
Stephen Wolfram (1:14:39.760)
because in that sense, when you're just making a brain simulator, we're just saying there's
Stephen Wolfram (1:14:46.000)
another version of our consciousness. The question that we're asking is, if we tease away from our
Stephen Wolfram (1:14:50.960)
consciousness and get to something that is different, how do we make a bridge to understanding
Stephen Wolfram (1:14:55.840)
what's going on there? And there's a way of thinking about this. Okay, so this is coming
Stephen Wolfram (1:15:00.880)
on to questions about the existence of the universe and so on. But one of the things is
Stephen Wolfram (1:15:05.440)
there's this notion that we have of ruleal space. So we have this idea of this physical space,
Stephen Wolfram (1:15:11.600)
which is something you can move around in that's associated with the extent of the
Stephen Wolfram (1:15:17.200)
spatial hypergraph. Then there's what we call branchial space, the space of quantum branches.
Lex Fridman (1:15:22.480)
So in this thing we call the multiway graph of all of this branching histories,
Stephen Wolfram (1:15:28.000)
there's this idea of a kind of space where instead of moving around in physical space,
Stephen Wolfram (1:15:32.560)
you're moving from history to history, so to speak, from one possible history to another
Stephen Wolfram (1:15:36.560)
possible history. And that's kind of a different kind of space that is the space in which quantum
Stephen Wolfram (1:15:42.160)
mechanics plays out. Quantum mechanics, for example, I think we're slowly understanding
Stephen Wolfram (1:15:48.960)
things like destructive interference in quantum mechanics, that what's happening is branchial
Stephen Wolfram (1:15:53.600)
space is associated with phase in quantum mechanics. And what's happening is the two
Stephen Wolfram (1:15:58.080)
photons that are supposed to be interfering and destructively interfering are winding up at
Stephen Wolfram (1:16:02.480)
different ends of branchial space. And so us as these poor observers that have branching brains
Stephen Wolfram (1:16:09.200)
that are trying to conflate together these different threads of history and say,
Stephen Wolfram (1:16:13.440)
we've really got a consistent story that we're telling here. We're really knitting together
Stephen Wolfram (1:16:17.040)
these threads of history. By the time the two photons wound up at opposite ends of branchial
Stephen Wolfram (1:16:22.000)
space, we just can't knit them together to tell a consistent story. So for us,
Lex Fridman (1:16:26.880)
that's sort of the analog of destructive interference. Got it. And then there's
Stephen Wolfram (1:16:30.800)
rule space too, which is the space of rules. Yes. Well, that's another level up. So there's
Stephen Wolfram (1:16:37.520)
the question. Actually, I do want to mention one thing because it's something I've realized in
Stephen Wolfram (1:16:42.240)
recent times and I think it's really, really kind of cool, which is about time dilation and
Stephen Wolfram (1:16:46.640)
relativity. And it kind of helps to understand it's something that kind of helps in understanding
Stephen Wolfram (1:16:51.520)
what's going on. So according to relativity, if you have a clock, it's ticking at a certain rate,
Stephen Wolfram (1:16:58.800)
you send it in a spacecraft that's going at some significant fraction of the speed of light,
Stephen Wolfram (1:17:03.600)
to you as an observer at rest, that clock that's in the spacecraft will seem to be ticking much
Stephen Wolfram (1:17:09.920)
more slowly. And so in other words, it's kind of like the twin who goes off to Alpha Centauri and
Stephen Wolfram (1:17:16.720)
goes very fast will age much less than the twin who's on Earth that is just hanging out where
Stephen Wolfram (1:17:22.640)
they're hanging out. Okay, why does that happen? Okay, so it has to do with what motion is.
Lex Fridman (1:17:28.720)
So in our models of physics, what is motion? Well, when you move from somewhere to somewhere,
Lex Fridman (1:17:35.360)
you're having to sort of recreate yourself at a different place in space.
Stephen Wolfram (1:17:40.480)
When you exist at a particular place and you just evolve with time, again, you're updating yourself,
Stephen Wolfram (1:17:46.080)
you're following these rules to update what happens. Well, so the question is, when you
Stephen Wolfram (1:17:51.200)
have a certain amount of computation in you, so to speak, when there's a certain amount,
Stephen Wolfram (1:17:55.440)
you know, you're computing, the universe is computing at a certain rate, you can either
Stephen Wolfram (1:17:59.520)
use that computation to work out sitting still where you are, what's going to happen successively
Stephen Wolfram (1:18:05.360)
in time, or you can use that computation to recreate yourself as you move around the universe.
Stephen Wolfram (1:18:10.480)
Mm hmm. And so time dilation ends up being, it's really cool, actually, that this is explainable
Stephen Wolfram (1:18:16.000)
in a way that isn't just imagine the mathematics of relativity. But time dilation is a story of
Stephen Wolfram (1:18:21.920)
the fact that as you kind of are recreating yourself as you move, you are using up some
Stephen Wolfram (1:18:27.840)
of your computation. And so you don't have as much computation left over to actually work out what
Stephen Wolfram (1:18:33.120)
happens progressively with time. So that means that time is running more slowly for you because
Stephen Wolfram (1:18:38.880)
it is, you're using up your computation, your clock can't tick as quickly, because every tick
Stephen Wolfram (1:18:45.600)
of the clock is using up some computation, but you already use that computation up on moving at,
Stephen Wolfram (1:18:50.160)
you know, half the speed of light or something. And so that's why time dilation happens.
Lex Fridman (1:18:55.520)
And so you can start, so it's kind of interesting that one can sort of get an intuition about
Stephen Wolfram (1:19:00.560)
something like that, because it has seemed like just a mathematical fact about the mathematics of
Stephen Wolfram (1:19:05.520)
special relativity and so on. Well, for me, it's a little bit confusing what the you in that picture
Stephen Wolfram (1:19:10.560)
is, because you're using up computation. Okay, so we're simply saying the entity is updating
Stephen Wolfram (1:19:19.840)
itself according to the way that the universe updates itself. And the question is, you know,
Stephen Wolfram (1:19:26.800)
those updates, let's imagine the you as a clock. Okay. And the clock is, you know, there's all
Stephen Wolfram (1:19:31.680)
these little updates, the hypergraph and a sequence of updates cause the pendulum to swing back the
Stephen Wolfram (1:19:37.120)
other way, and then swing back, swinging back and forth. Okay. And all of those updates are
Stephen Wolfram (1:19:44.240)
contributing to the motion of, you know, the pendulum going back and forth or the little
Stephen Wolfram (1:19:48.240)
oscillator moving, whatever it is. Okay. But then the alternative is that sort of situation one,
Stephen Wolfram (1:19:54.480)
where the thing is at rest, situation two, where it's kind of moving, what's happening is it is
Stephen Wolfram (1:20:00.880)
having to recreate itself at every moment, the thing is going to have to do the computations
Stephen Wolfram (1:20:07.520)
to be able to sort of recreate itself at a different position in space. And that's kind of
Stephen Wolfram (1:20:12.480)
the intuition behind, so it's either going to spend its computation recreating itself at a
Stephen Wolfram (1:20:17.760)
different position in space, or it's going to spend its computation doing the sort of doing the
Stephen Wolfram (1:20:24.240)
updating of the, you know, of the ticking of the clock, so to speak. So the more updating is doing,
Stephen Wolfram (1:20:30.240)
the less the ticking of the clock update is doing. That's right. The more it's having to update
Stephen Wolfram (1:20:35.120)
because of motion, the less it can update the clock. Obviously, there's a sort of mathematical
Stephen Wolfram (1:20:42.640)
version of it that relates to how it actually works in relativity, but that's kind of, to me,
Stephen Wolfram (1:20:47.200)
that was sort of exciting to me that it's possible to have a really mechanically explainable story
Stephen Wolfram (1:20:52.560)
there. And similarly in quantum mechanics, this notion of branching brains perceiving branching
Stephen Wolfram (1:20:58.320)
universes, to me, that's getting towards a sort of mechanically explainable version of what happens
Stephen Wolfram (1:21:03.200)
in quantum mechanics, even though it's a little bit mind bending to see, you know, these things
Stephen Wolfram (1:21:07.920)
about under what circumstances can you successfully knit together those different threads of history,
Lex Fridman (1:21:13.840)
and when do things sort of escape, and those kinds of things. But the thing about this physical space
Lex Fridman (1:21:21.040)
and physical space, the main sort of big theory is general relativity, the theory of gravity,
Lex Fridman (1:21:26.960)
and that tells you how things move in physical space. In branchial space, the big theory is the
Stephen Wolfram (1:21:32.240)
Feynman path integral, which it turns out tells you essentially how things move in quantum in the
Stephen Wolfram (1:21:38.320)
space of quantum phases. So it's kind of like motion in branchial space. And it's kind of a
Stephen Wolfram (1:21:43.840)
fun thing to start thinking about all these things that we know in physical space, like event horizons
Lex Fridman (1:21:51.280)
and black holes and so on. What are the analogous things in branchial space? For example, the speed
Stephen Wolfram (1:21:55.440)
of light, what's the analog of the speed of light in branchial space? It's the maximum speed of
Stephen Wolfram (1:21:59.840)
quantum entanglement. So the speed of light is a flash bulb goes off here. What's the maximum rate
Stephen Wolfram (1:22:06.720)
at which the effect of that flash bulb is detectable moving away in space? So similarly,
Stephen Wolfram (1:22:13.280)
in branchial space, something happens. And the question is, how far in this branchial space,
Lex Fridman (1:22:18.400)
in the space of quantum states, how far away can that get within a certain period of time?
Lex Fridman (1:22:23.760)
And so there's this notion of a maximum entanglement speed. And that might be observable.
Stephen Wolfram (1:22:28.720)
That's the thing we've been sort of poking at, is might there be a way to observe it,
Stephen Wolfram (1:22:32.800)
even in some atomic physics kind of situation? Because one of the things that's weird in
Stephen Wolfram (1:22:37.920)
quantum mechanics is when we study quantum mechanics, we mostly study it in terms of small
Stephen Wolfram (1:22:44.160)
numbers of particles. This electron does this, this thing on an ion trap does that and so on.
Lex Fridman (1:22:49.200)
But when we deal with large numbers of particles, kind of all bets are off. It's kind of too
Stephen Wolfram (1:22:52.880)
complicated to deal with quantum mechanics. And so what ends up happening is, so this question
Stephen Wolfram (1:22:58.480)
about maximum entanglement speed and things like that may actually play in the sort of story of
Stephen Wolfram (1:23:04.320)
many body quantum mechanics and even have some suspicions about things that might happen even in
Stephen Wolfram (1:23:10.880)
one of the things I realized I'd never understood and it's kind of embarrassing, but I think I now
Stephen Wolfram (1:23:15.840)
understand a little better, is when you have chemistry and you have quantum mechanics,
Stephen Wolfram (1:23:20.480)
it's like, well, there's two carbon atoms in this molecule and we do a reaction and we draw a
Stephen Wolfram (1:23:25.040)
diagram and we say this carbon atom ends up in this place. And it's like, but wait a minute,
Stephen Wolfram (1:23:29.280)
in quantum mechanics, nothing ends up in a definite place. There's always just some wave
Stephen Wolfram (1:23:32.800)
function for this to happen. How can it be the case that we can draw these reasonable, it just
Stephen Wolfram (1:23:37.600)
ended up in this place? And you have to kind of say, well, the environment of the molecule
Stephen Wolfram (1:23:42.000)
effectively made a bunch of measurements on the molecule to keep it kind of classical.
Lex Fridman (1:23:46.640)
And that's a story that has to do with this whole thing about measurements have to do with this
Stephen Wolfram (1:23:52.960)
idea of, can we conclude that something definite happened? Because in quantum mechanics,
Stephen Wolfram (1:23:58.400)
the intrinsic quantum mechanics, the mathematics of quantum mechanics is all about,
Stephen Wolfram (1:24:02.400)
they're just these amplitudes for different things to happen. Then there's this thing of,
Lex Fridman (1:24:06.320)
and then we make a measurement and we conclude that something definite happened. And that has
Stephen Wolfram (1:24:11.040)
to do with this thing, I think, about sort of moving about knitting together these different
Stephen Wolfram (1:24:16.000)
threads of history and saying, this is now something where we can definitively say something
Stephen Wolfram (1:24:20.320)
definite happened. In the traditional theory of quantum mechanics, it's just like, after you've
Stephen Wolfram (1:24:25.680)
done all this amplitude computation, then this big hammer comes down and you do a measurement
Lex Fridman (1:24:30.560)
and it's all over. And that's been very confusing. For example, in quantum computing,
Stephen Wolfram (1:24:34.640)
it's been a very confusing thing because when you say, in quantum computing, the basic idea is
Stephen Wolfram (1:24:39.680)
you're going to use all these separate threads of computation, so to speak, to do all the different
Stephen Wolfram (1:24:44.080)
parts of, try these different factors for an integer or something like this. And it looks
Stephen Wolfram (1:24:48.560)
like you can do a lot because you've got all these different threads going on. But then you have to
Stephen Wolfram (1:24:53.680)
say, well, at the end of it, you've got all these threads and every thread came up with a definite
Stephen Wolfram (1:24:57.760)
answer, but we got to conflate those together to figure out a definite thing that we humans
Stephen Wolfram (1:25:02.960)
can take away from it, a definite, so the computer actually produced this output.
Lex Fridman (1:25:06.720)
So having this branchial space and this hypergraph model of physics, do you think it's possible to
Lex Fridman (1:25:14.640)
then make predictions that are definite about many body quantum mechanical systems?
Stephen Wolfram (1:25:21.840)
I think it's likely, yes. Every one of these things, when you go from the underlying theory,
Stephen Wolfram (1:25:28.800)
which is complicated enough and it's, I mean, the theory at some level is beautifully simple,
Lex Fridman (1:25:33.520)
but as soon as you start actually trying to, it's this whole question about how do you bridge it to
Stephen Wolfram (1:25:37.680)
things that we humans can talk about, it gets really complicated. And this thing about actually
Stephen Wolfram (1:25:43.440)
getting it to a definite prediction about definite thing you can say about chemistry or something
Stephen Wolfram (1:25:50.320)
like this, that's just a lot of work. So I'll give you an example. There's a thing called the
Stephen Wolfram (1:25:54.560)
quantum Zeno effect. So the idea is quantum stuff happens, but then if you make a measurement,
Stephen Wolfram (1:26:01.680)
you're kind of freezing time in quantum mechanics. So it looks like there's a possibility that with
Stephen Wolfram (1:26:08.000)
sort of the relationship between the quantum Zeno effect and the way that many body quantum
Stephen Wolfram (1:26:12.240)
mechanics works and so on, maybe just conceivably, it may be possible to actually figure out a way
Stephen Wolfram (1:26:18.240)
to measure the maximum entanglement speed. And the reason we can potentially do that
Stephen Wolfram (1:26:23.920)
is because the systems we deal with in terms of atoms and things, they're pretty big. A mole of
Stephen Wolfram (1:26:29.360)
atoms is a lot of atoms, but it's something where to get, when we're dealing with how can you see
Stephen Wolfram (1:26:37.520)
10 to the minus 100, so to speak? Well, by the time you've got 10 to the 30th atoms, you're within
Stephen Wolfram (1:26:45.120)
a little bit closer striking distance of that. It's not like, oh, we've just got two atoms and
Stephen Wolfram (1:26:51.760)
we're trying to see down to 10 to the minus 100 meters or whatever. So I don't know how it will
Stephen Wolfram (1:26:56.800)
work, but this is a potential direction. And if you can tell, by the way, if we could measure
Stephen Wolfram (1:27:02.640)
the maximum entanglement speed, we would know the elementary length. These are all related.
Lex Fridman (1:27:07.680)
So if we get that one number, we just need one number. If we can get that one number,
Stephen Wolfram (1:27:13.440)
the theory has no parameters anymore. And there are other places, well, there's another hope for
Stephen Wolfram (1:27:20.240)
doing that is in cosmology. In this model, one of the features is the universe is not fixed
Stephen Wolfram (1:27:25.680)
dimensional. We think we live in three dimensional space, but this hypergraph doesn't have any
Stephen Wolfram (1:27:29.920)
particular dimension. It can emerge as something which on an approximation, it's as if you say,
Stephen Wolfram (1:27:36.320)
what's the volume of a sphere in the hypergraph where a sphere is defined as how many nodes do
Stephen Wolfram (1:27:41.600)
you get to when you go a distance R away from a given point? And you can say, well, if I get to
Stephen Wolfram (1:27:47.040)
about R cubed nodes, when I go a distance R away in the hypergraph, then I'm living roughly in
Stephen Wolfram (1:27:52.960)
three dimensional space. But you might also get to R to the point 2.92 for some value of R. As R
Stephen Wolfram (1:28:02.800)
increases, that might be the sort of fit to what happens. And so one of the things we suspect is
Stephen Wolfram (1:28:07.920)
that the very early universe was essentially infinite dimensional, and that as the universe
Stephen Wolfram (1:28:13.120)
expanded, it became lower dimensional. And so one of the things that is another little sort of point
Stephen Wolfram (1:28:19.680)
where we think there might be a way to actually measure some things is dimension fluctuations in
Stephen Wolfram (1:28:24.320)
the early universe. That is, is there leftover dimension fluctuation of at the time of the cosmic
Stephen Wolfram (1:28:30.720)
microwave background, 100,000 years or something after the beginning of the universe? Is it still
Stephen Wolfram (1:28:34.880)
the case that there were pieces of the universe that didn't have dimension three, that had
Stephen Wolfram (1:28:39.840)
dimension 3.01 or something? And can we tell that? Is that possible to observe fluctuations in
Stephen Wolfram (1:28:47.920)
dimensions? I don't even know what that entails. Okay. So the question, which should be an
Stephen Wolfram (1:28:54.240)
elementary exercise in electrodynamics, except it isn't, is understanding what happens to a
Stephen Wolfram (1:28:59.920)
photon when it propagates through 3.01 dimensional space. So for example, the inverse square law
Stephen Wolfram (1:29:05.680)
is a consequence of the surface area of a sphere is proportional to R squared. But if you're not
Stephen Wolfram (1:29:13.920)
in three dimensional space, the surface area of sphere is not proportional to R squared. It's R
Stephen Wolfram (1:29:19.280)
to the whatever 2.01 or something. And so that means that I think when you kind of try and do
Stephen Wolfram (1:29:27.040)
optics, you know, a common principle in optics is Huygens principle, which basically says that every
Stephen Wolfram (1:29:32.960)
piece of a wave front of light is a source of new spherical waves. And those spherical waves,
Stephen Wolfram (1:29:40.560)
if they're different dimensional spherical waves, will have other characteristics. And so there will
Stephen Wolfram (1:29:46.080)
be bizarre optical phenomena which we haven't figured out yet. So you're looking for some weird
Stephen Wolfram (1:29:53.680)
photon trajectories that designate that it's 3.01 dimensional space? Yeah. Yeah. That would be an
Stephen Wolfram (1:30:01.360)
example of, I mean, you know, there are only a certain number of things we can measure about
Stephen Wolfram (1:30:05.200)
photons. You know, we can measure their polarization, we can measure their frequency,
Stephen Wolfram (1:30:09.360)
we can measure their direction, those kinds of things. And, you know, how that all works out.
Stephen Wolfram (1:30:15.360)
And, you know, in the current models of physics, you know, it's been hard to explain how the
Stephen Wolfram (1:30:21.360)
universe manages to be as uniform as it is. And that's led to this inflation idea that,
Stephen Wolfram (1:30:26.880)
to the great annoyance of my then collaborator, we figured out in like 1979, we had this
Stephen Wolfram (1:30:32.560)
realization that you could get something like this. But it seemed implausible that that's the
Stephen Wolfram (1:30:36.880)
way the universe worked. So we put it in a footnote. But in any case, I've never really
Stephen Wolfram (1:30:43.280)
completely believed it. But that's an idea for how to sort of puff out the universe faster than the
Stephen Wolfram (1:30:48.880)
speed of light, early moments of the universe. That's the sort of the inflation idea and that
Stephen Wolfram (1:30:54.480)
you can somehow explain how the universe manages to be as uniform as it is. In our model, this turns
Stephen Wolfram (1:31:01.600)
out to be much more natural because the universe just starts very connected. The hypergraph is not
Stephen Wolfram (1:31:07.040)
such that the ball that you grow starting from a single point has volume R cubed, it might have
Stephen Wolfram (1:31:12.320)
volume R to the 500 or R to the infinity. And so that means that you sort of naturally get this
Stephen Wolfram (1:31:19.600)
much higher degree of connectivity and uniformity in the universe. And then the question is,
Stephen Wolfram (1:31:24.400)
this is sort of the mathematical physics challenge, is in the standard theory of the universe,
Stephen Wolfram (1:31:29.040)
there's the Friedman Robertson Walker universe, which is the kind of standard model where the
Stephen Wolfram (1:31:33.360)
universe is isotropic and homogeneous. And you can then work out the equations of general relativity,
Lex Fridman (1:31:38.560)
and you can figure out how the universe expands. We would like to do the same kind of thing,
Stephen Wolfram (1:31:42.640)
including dimension change. This is just difficult mathematical physics. I mean,
Stephen Wolfram (1:31:47.280)
the reason it's difficult is the sort of fundamental reason it's difficult. When
Stephen Wolfram (1:31:51.360)
people invented calculus 300 years ago, calculus was a story of understanding change and change
Stephen Wolfram (1:31:58.240)
as a function of a variable. So people study univariate calculus, they study multivariate
Stephen Wolfram (1:32:03.120)
calculus, it's one variable, it's two variables, three variables. But whoever studied, you know,
Stephen Wolfram (1:32:08.320)
2.5 variable calculus, turns out nobody. Turns out that what we need to have to understand these
Stephen Wolfram (1:32:16.320)
fractional dimensional spaces, which don't work like well, they're spaces where the effective
Stephen Wolfram (1:32:23.280)
dimension is not an integer. So you can't apply the tools of calculus naturally and easily to
Lex Fridman (1:32:30.080)
fractional dimensions? No. So somebody has to figure out how to do that. Yeah,
Stephen Wolfram (1:32:34.480)
we're trying to figure this out. I mean, it's very interesting. I mean, it's very connected to
Lex Fridman (1:32:39.120)
very frontier issues in mathematics. It's very beautiful. So is it possible? Is it possible?
Stephen Wolfram (1:32:44.560)
We're dealing with a scale that's so, so much smaller than our human scale. Is it possible
Stephen Wolfram (1:32:51.040)
to make predictions versus explanations? Do you have a hope that with this hypergraph model,
Stephen Wolfram (1:32:57.280)
you'd be able to make predictions that then could be validated with a physics experiment,
Stephen Wolfram (1:33:04.160)
predictions that couldn't have been done or weren't done otherwise? Yeah, yeah, yeah. I mean,
Stephen Wolfram (1:33:08.480)
you know, I think which, in which domain do you think? Okay, so they're going to be cosmology ones
Stephen Wolfram (1:33:12.800)
to do with dimension fluctuations in the universe. That's a very bizarre effect. Nobody, you know,
Stephen Wolfram (1:33:16.720)
dimension fluctuations is just something nobody ever looked for that. If anybody sees dimension
Stephen Wolfram (1:33:20.560)
fluctuation, that's a huge flag that something like our model is going on. And how one detects
Stephen Wolfram (1:33:27.760)
that, you know, that's a problem of kind of, you know, that's a problem of traditional physics in
Stephen Wolfram (1:33:32.240)
a sense of what's the best way to actually figure that out. And for example, that's one,
Stephen Wolfram (1:33:37.600)
there are all kinds of things one could imagine. I mean, there are things that in black hole mergers,
Stephen Wolfram (1:33:44.400)
it's possible that there will be effects of maximum entanglement speed in large black hole mergers.
Stephen Wolfram (1:33:50.720)
That's another possible thing. And all of that is detected through like what? Do you have a
Stephen Wolfram (1:33:55.680)
hope for LIGO type of situation? Like that's gravitational waves? Yeah. Or alternatively,
Stephen Wolfram (1:34:01.040)
I mean, I think it's, you know, look, figuring out experiments is like figuring out technology
Stephen Wolfram (1:34:07.600)
inventions. That is, you know, you've got a set of raw materials, you've got an underlying model,
Lex Fridman (1:34:12.640)
and now you've got to be very clever to figure out, you know, what is that thing I can measure
Stephen Wolfram (1:34:16.800)
that just somehow, you know, leverages into the right place. And we've spent less effort on that
Stephen Wolfram (1:34:23.280)
than I would have liked. Because one of the reasons is that I think that the physicists
Stephen Wolfram (1:34:30.320)
who've been working on our models, with now lots of physicists actually, it's very, very nice. It's
Stephen Wolfram (1:34:35.360)
kind of, it's one of these cases where I'm almost, I'm really kind of pleasantly surprised that the
Stephen Wolfram (1:34:41.600)
sort of absorption of the things we've done has been quite rapid and quite sort of, you know,
Stephen Wolfram (1:34:47.760)
very positive. So it's a Cambrian explosion of physicists too, not just ideas. Yes. I mean,
Stephen Wolfram (1:34:53.200)
you know, a lot of what's happened that's really interesting, and again, not what I expected,
Stephen Wolfram (1:34:57.920)
is there are a lot of areas of sort of very elaborate, sophisticated mathematical physics,
Stephen Wolfram (1:35:04.160)
whether that's causal set theory, whether it's higher category theory, whether it's categorical
Stephen Wolfram (1:35:08.880)
quantum mechanics, all sorts of elaborate names for these things, spin networks, perhaps,
Stephen Wolfram (1:35:14.880)
you know, causal dynamical triangulations, all kinds of names of these fields. And these fields
Stephen Wolfram (1:35:20.160)
have a bunch of good mathematical physicists in them who've been working for decades in these
Stephen Wolfram (1:35:24.640)
particular areas. And the question is, but they've been building these mathematical structures.
Lex Fridman (1:35:30.640)
And the mathematical structures are interesting, but they don't typically sit on anything.
Stephen Wolfram (1:35:34.960)
They're just mathematical structures. And I think what's happened is our models provide kind of
Stephen Wolfram (1:35:39.920)
a machine code that lives underneath those models. So a typical example, this is due to
Stephen Wolfram (1:35:46.800)
Jonathan Gorod, who's one of the key people who's been working on our project. This is in,
Stephen Wolfram (1:35:52.960)
okay, so I'll give you an example just to give a sense of how these things connect. This is in
Stephen Wolfram (1:35:56.480)
causal set theory. So the idea of causal set theory is there are, in spacetime, we imagine
Stephen Wolfram (1:36:03.520)
that there's space and time. It's a three plus one dimensional, you know, setup. We imagine that
Stephen Wolfram (1:36:09.040)
there are just events that happen at different times and places in space and time. And the idea
Stephen Wolfram (1:36:16.160)
of causal set theory is the only thing you say about the universe is there are a bunch of events
Stephen Wolfram (1:36:20.400)
that happen sort of randomly at different places in space and time. And then the whole sort of
Stephen Wolfram (1:36:25.520)
theory of physics has to be to do with this graph of causal relationships between these randomly
Stephen Wolfram (1:36:32.080)
thrown down events. So they've always been confused by the fact that to get even Lorentz
Stephen Wolfram (1:36:37.920)
invariants, even relativistic invariants, you need a very special way to throw down those events.
Lex Fridman (1:36:42.880)
And they've had no natural way to understand how that would happen. So what Jonathan figured out
Stephen Wolfram (1:36:48.080)
is that, in fact, from our models, instead of just generating events at random, our models
Stephen Wolfram (1:36:56.000)
necessarily generate events in some pattern in spacetime effectively that then leads to Lorentz
Stephen Wolfram (1:37:02.160)
invariants and relativistic invariants and all those kinds of things. So it's a place where
Stephen Wolfram (1:37:06.080)
all the mathematics that's been done on, well, we just have a random collection of events.
Stephen Wolfram (1:37:10.240)
Now what consequences does that have in terms of causal set theory and so on? That can all be kind
Stephen Wolfram (1:37:16.000)
of wheeled in now that we have some different underlying foundational idea for what the
Stephen Wolfram (1:37:22.000)
particular distribution of events is as opposed to just what we throw down random events.
Lex Fridman (1:37:26.400)
And so that's a typical sort of example of what we're seeing in all these different areas of kind
Stephen Wolfram (1:37:32.160)
of how you can take really interesting things that have been done in mathematical physics
Lex Fridman (1:37:36.480)
and connect them. And it's really kind of beautiful because the abstract models we have
Stephen Wolfram (1:37:43.440)
just seem to plug into all these different very interesting, very elegant abstract ideas.
Lex Fridman (1:37:48.560)
But we're now giving sort of a reason for that to be the way, a reason for one to care. I mean,
Stephen Wolfram (1:37:54.960)
it's like saying you can think about computation abstractly. You can think about, I don't know,
Stephen Wolfram (1:38:01.680)
combinators or something as abstract computational things. And you can sort of do all kinds of study
Stephen Wolfram (1:38:06.640)
of them. But it's like, why do we care? Well, okay, Turing machines are a good start because
Stephen Wolfram (1:38:11.040)
you can kind of see they're sort of mechanically doing things. But when we actually start thinking
Stephen Wolfram (1:38:14.880)
about computers, computing things, we have a really good reason to care. And this is sort of
Lex Fridman (1:38:19.920)
what we're providing, I think, is a reason to care about a lot of these areas of mathematical
Stephen Wolfram (1:38:24.640)
physics. So that's been very nice. So I'm not sure we've ever got to the
Stephen Wolfram (1:38:30.880)
question of why does the universe exist at all? No, no, let's talk about that. So it's not the
Stephen Wolfram (1:38:36.640)
simplest question in the world. So it takes a few steps to get to it. And it's nevertheless even
Lex Fridman (1:38:42.960)
surprising that you can even begin to answer this question, as you were saying.
Stephen Wolfram (1:38:46.800)
Indeed. I'm very surprised. So the next thing to perhaps understand is this idea of ruleal space.
Lex Fridman (1:38:55.040)
So we've got kind of physical space. We've got branchial space, the space of possible quantum
Stephen Wolfram (1:39:00.240)
histories. And now we've got another level of kind of abstraction, which is ruleal space. And
Stephen Wolfram (1:39:05.840)
here's where that comes from. So you say, okay, you say we've got this model for the universe.
Stephen Wolfram (1:39:12.400)
We've got a particular rule. And we run this rule and we get the universe. So that's interesting.
Lex Fridman (1:39:19.600)
Why that rule? Why not another rule? And so that confused me for a long time. And I realized,
Stephen Wolfram (1:39:25.200)
well, actually, what if the thing could be using all possible rules? What if at every step,
Stephen Wolfram (1:39:31.520)
in addition to saying apply a particular rule at all places in this hypergraph, one could say,
Stephen Wolfram (1:39:37.600)
just take all possible rules and apply all possible rules at all possible places in this
Stephen Wolfram (1:39:41.840)
hypergraph. And then you make this ruleal multiway graph, which both is all possible
Stephen Wolfram (1:39:48.240)
histories for a particular rule and all possible rules. So the next thing you'd say is, how can you
Stephen Wolfram (1:39:53.120)
get anything reasonable out of it? How can anything real come out of the set of all possible
Stephen Wolfram (1:39:58.720)
rules applied in all possible ways? This is a subtle thing, which I haven't fully untangled.
Stephen Wolfram (1:40:05.520)
There is this object, which is the result of running all possible rules in all possible ways.
Lex Fridman (1:40:11.440)
And you might say, if you're running all possible rules, why can't everything possible happen?
Stephen Wolfram (1:40:15.680)
Well, the answer is because when you, there's sort of this entanglement that occurs.
Lex Fridman (1:40:21.840)
So let's say that you have a lot of different possible initial conditions, a lot of different
Stephen Wolfram (1:40:27.280)
possible states. Then you're applying these different rules. Well, some of those rules can
Stephen Wolfram (1:40:32.800)
end up with the same state. So it isn't the case that you can just get from anywhere to anywhere.
Stephen Wolfram (1:40:37.200)
There's this whole entangled structure of what can lead to what, and there's a definite structure
Stephen Wolfram (1:40:42.080)
that's produced. I think I'm going to call that definite structure the rulead, the limit of kind
Stephen Wolfram (1:40:48.880)
of all possible rules being applied in all possible ways. And you're saying that structure is finite,
Lex Fridman (1:40:54.480)
so that somehow connects to maybe a similar kind of thing as like causal invariance.
Stephen Wolfram (1:40:59.440)
Well, it happens that the rulead necessarily has causal invariance. That's a feature of,
Stephen Wolfram (1:41:03.600)
that's just a mathematical consequence of essentially using all possible rules
Stephen Wolfram (1:41:08.080)
plus universal computation gives you the fact that from any diverging paths, the paths will
Lex Fridman (1:41:14.720)
always converge. But does that necessarily infer that the rulead is finite?
Stephen Wolfram (1:41:21.760)
In the end, it's not necessarily finite. I mean, just like the history of the universe may not be
Stephen Wolfram (1:41:28.240)
finite. The history of the universe, time may keep going forever. You can keep running the
Stephen Wolfram (1:41:32.240)
computations of the rulead and you'll keep spewing out more and more and more structure. It's like
Stephen Wolfram (1:41:37.600)
time doesn't have to end. But the issue is there are three limits that happen in this rulead
Stephen Wolfram (1:41:45.520)
object. One is how long you run the computation for. Another is how many different rules you're
Stephen Wolfram (1:41:51.280)
applying. And another is how many different states you start from. And the mixture of those
Stephen Wolfram (1:41:56.800)
three limits. I mean, this is just mathematically a horrendous object. And what's interesting about
Stephen Wolfram (1:42:02.720)
this object is the one thing that does seem to be the case about this object is it connects with
Stephen Wolfram (1:42:07.440)
ideas in higher category theory. And in particular, it connects to some of the 20th century's most
Stephen Wolfram (1:42:12.800)
abstract mathematics done by this chap Grothendieck. Grothendieck had a thing called the infinity
Stephen Wolfram (1:42:18.480)
groupoid, which is closely related to this rulead object. Although the details of the relationship,
Stephen Wolfram (1:42:24.960)
you know, I don't fully understand yet. But I think that what's interesting is this thing that
Stephen Wolfram (1:42:31.120)
is sort of this very limiting object. So, okay, so a way to think about this that, again, will
Stephen Wolfram (1:42:37.360)
take us into another direction, which is the equivalence between physics and mathematics.
Stephen Wolfram (1:42:42.400)
The way that, well, let's see, maybe this is just to give a sense of this kind of groupoid and
Stephen Wolfram (1:42:50.320)
things like that. You can think about, in mathematics, you can think you have certain axioms,
Stephen Wolfram (1:42:55.120)
they're kind of like atoms, and you, well, actually, let's say, let's talk about mathematics
Stephen Wolfram (1:43:01.280)
for a second. So what is mathematics? What is it made of, so to speak? Mathematics, there's a bunch
Stephen Wolfram (1:43:06.960)
of statements, like, for addition, x plus y is equal to y plus x, that's a statement in mathematics.
Stephen Wolfram (1:43:13.680)
Another statement would be, you know, x squared minus one is equal to x plus one, x minus one.
Lex Fridman (1:43:18.240)
There are an infinite number of these possible statements of mathematics.
Stephen Wolfram (1:43:21.840)
Well, it's not, I mean, it's not just, I guess, a statement, but with x plus y,
Lex Fridman (1:43:25.520)
it's a rule that you can, I mean, you think of it as a rule.
Stephen Wolfram (1:43:29.920)
It is a rule. It's also just a thing that is true in mathematics.
Lex Fridman (1:43:35.760)
Right. The statement of truth, okay.
Stephen Wolfram (1:43:37.680)
Right. And what you can imagine is, you imagine just laying out this giant kind of ocean
Stephen Wolfram (1:43:44.000)
of all statements. Well, actually, you first start, okay, this is where this was segueing
Stephen Wolfram (1:43:49.680)
into a different thing. Let me not go in this direction for a second.
Lex Fridman (1:43:52.240)
Let's not go to metamathematics just yet.
Stephen Wolfram (1:43:54.320)
Yeah, we'll maybe get to metamathematics, but it's, so let me not, let me explain the groupoid
Lex Fridman (1:44:00.640)
and things later. But, so let's come back to the universe, always a good place to be in,
Lex Fridman (1:44:07.040)
so to speak.
Stephen Wolfram (1:44:07.440)
Yeah, so what does the universe have to do with the rule add, the rule of L space,
Lex Fridman (1:44:11.200)
and how that's possibly connected to why the thing exists at all, and why there's just
Lex Fridman (1:44:17.920)
one of them?
Stephen Wolfram (1:44:18.720)
Yes. Okay. So here's the point. So the thing that had confused me for a long time was,
Stephen Wolfram (1:44:24.160)
let's say we get the rule for the universe. We hold it in our hand. We say, this is our
Stephen Wolfram (1:44:28.320)
universe. Then the immediate question is, well, why isn't it another one? And that's
Stephen Wolfram (1:44:33.200)
kind of the sort of the lesson of Copernicus is, we're not very special. So how come we
Stephen Wolfram (1:44:39.920)
got universe number 312 and not universe quadrillion, quadrillion, quadrillion? And
Stephen Wolfram (1:44:46.000)
I think the resolution of that is the realization that the universe is running all possible
Stephen Wolfram (1:44:52.720)
rules. So then you say, well, how on earth do we perceive the universe to be running
Stephen Wolfram (1:44:58.880)
according to a particular rule? How do we perceive definite things happening in the
Stephen Wolfram (1:45:02.640)
universe? Well, it's the same story. It's the observer, there is a reference frame that
Stephen Wolfram (1:45:08.560)
we are picking in this ruleal space, and that that is what determines our perception of
Stephen Wolfram (1:45:14.000)
the universe. With our particular sensory information and so on, we are parsing the
Stephen Wolfram (1:45:18.960)
universe in this particular way. So here's the way to think about it. In physical space,
Stephen Wolfram (1:45:24.800)
we live in a particular place in the universe. And we could live on Alpha Centauri, but we
Stephen Wolfram (1:45:29.360)
don't. We live here. And similarly, in ruleal space, we could live in many different places
Stephen Wolfram (1:45:36.560)
in ruleal space, but we happen to live here. And what does it mean to live here? It means
Stephen Wolfram (1:45:41.040)
we have certain sensory input. We have certain ways to parse the universe. Those are our
Stephen Wolfram (1:45:47.040)
interpretation of the universe. What would it mean to travel in ruleal space? What it
Stephen Wolfram (1:45:51.680)
basically means is that we are successively interpreting the universe in different ways.
Lex Fridman (1:45:56.080)
So in other words, to be at a different point in ruleal space is to have a different, in a sense,
Stephen Wolfram (1:46:01.520)
a different interpretation of what's going on in the universe. And we can imagine even
Stephen Wolfram (1:46:06.240)
things like an analog of the speed of light as the maximum speed of translation in ruleal
Lex Fridman (1:46:10.880)
space and so on. So wait, what's the interpretation? So ruleal space and we,
Stephen Wolfram (1:46:18.320)
I'm confused by the we and the interpretation and the universe. I thought moving about in
Stephen Wolfram (1:46:23.920)
ruleal space changes the way the universe is. The way we would perceive it. So it ultimately
Stephen Wolfram (1:46:33.680)
has to do with the perception. So it doesn't real, ruleal space is not somehow changing,
Stephen Wolfram (1:46:41.600)
like branching into another universe or something like that. No, I mean, the point is that the whole
Stephen Wolfram (1:46:47.840)
point of this is the rule yard is sort of the encapsulated version of everything that is the
Stephen Wolfram (1:46:54.800)
universe running according to all possible rules. We think of our universe, the observable universe,
Stephen Wolfram (1:47:00.320)
as a thing. So we're a little bit loose with the word universe then, because wouldn't the rule yard
Stephen Wolfram (1:47:07.600)
potentially encapsulate a very large number, like combinatorially large, maybe infinite
Stephen Wolfram (1:47:14.720)
set of what we human physicists think of as universes? That's an interesting, interesting
Stephen Wolfram (1:47:20.960)
parsing of the word universe, right? Because what we're saying is, just as we're at a particular
Stephen Wolfram (1:47:25.920)
place in physical space, we're at a particular place in ruleal space, at that particular place
Stephen Wolfram (1:47:30.720)
in ruleal space, our experience of the universe is this. Just as if we lived at the center of the
Stephen Wolfram (1:47:35.280)
galaxy, our universe, our experience of the universe will be different from the one it is,
Stephen Wolfram (1:47:39.120)
given where we actually live. And so what we're saying is, you might say, I mean, in a sense,
Stephen Wolfram (1:47:47.120)
this rule yard is sort of a super universe, so to speak. But it's all entangled together. It's not
Stephen Wolfram (1:47:52.800)
like you can separate out. You can say, let me, it's like when we take a reference, okay, it's like
Stephen Wolfram (1:47:58.720)
our experience of the universe is based on where we are in the universe. We could imagine moving
Lex Fridman (1:48:03.520)
to somewhere else in the universe, but it's still the same universe.
Lex Fridman (1:48:05.840)
So there's not like universes existing in parallel?
Stephen Wolfram (1:48:10.800)
No. Because, and the whole point is that if we were able to change our interpretation of what's
Stephen Wolfram (1:48:18.240)
going on, we could perceive a different reference frame in this rule yard.
Stephen Wolfram (1:48:24.000)
Yeah, but that's not, that's just, yeah, that's the same rule yard. That's the same universe.
Stephen Wolfram (1:48:31.040)
You're just moving about. These are just coordinates in the universe.
Stephen Wolfram (1:48:34.480)
Right. So the reason that's interesting is, imagine the extraterrestrial intelligence,
Lex Fridman (1:48:39.680)
so the alien intelligence, we should say. The alien intelligence might live on Alpha Centauri,
Lex Fridman (1:48:46.080)
but it might also live at a different place in real space.
Stephen Wolfram (1:48:48.880)
It can live right here on Earth. It just has a different reference frame that
Lex Fridman (1:48:52.560)
includes a very different perception of the universe. And then because that
Stephen Wolfram (1:48:57.840)
real space is very large, I mean,
Lex Fridman (1:49:01.760)
Do we get to communicate with them? Right.
Stephen Wolfram (1:49:04.640)
Yeah, but it's also, well, one thing is how different the perception of the universe could be.
Stephen Wolfram (1:49:13.360)
I think it could be bizarrely, unimaginably completely different. And I mean, one thing to
Stephen Wolfram (1:49:19.360)
realize is, even in kind of things I don't understand well, you know, I know about the kind
Stephen Wolfram (1:49:25.600)
of Western tradition of understanding, you know, science and all that kind of thing. And, you know,
Stephen Wolfram (1:49:30.240)
you talk to people who say, well, I, you know, I'm really into some, you know, Eastern tradition of
Stephen Wolfram (1:49:36.880)
this, that and the other. And it's really obvious to me how things work. I don't understand it
Stephen Wolfram (1:49:41.760)
at all. But, you know, it is not obvious, I think, with this kind of realization that there's these
Stephen Wolfram (1:49:47.280)
very different ways to interpret what's going on in the universe. That kind of gives me at least,
Stephen Wolfram (1:49:52.560)
it doesn't help me to understand that different interpretation. But it gives me at least more
Lex Fridman (1:49:57.120)
respect for the possibility that there will be other interpretations.
Stephen Wolfram (1:49:59.920)
Yeah, it humbles you to the possibility that like, what is it, reincarnation or all these like
Lex Fridman (1:50:06.000)
eternal recurrence with Nietzsche, like just these ideas? Yeah.
Stephen Wolfram (1:50:12.640)
Well, you know, the thing that I realized about a bunch of those things is that, you know,
Stephen Wolfram (1:50:15.840)
I've been sort of doing my little survey of the history of philosophy, just trying to understand,
Stephen Wolfram (1:50:20.160)
you know, what can I actually say now about some of these things? And you realize that some of
Stephen Wolfram (1:50:24.480)
these concepts like the immortal soul concept, which, you know, I remember when I was a kid,
Stephen Wolfram (1:50:29.920)
and, you know, it was kind of a lots of religion bashing type stuff of people saying, you know,
Stephen Wolfram (1:50:35.360)
well, we know about physics, tell us how much does a soul weigh? And people are like, well,
Lex Fridman (1:50:41.760)
how can it be a thing if it doesn't weigh anything? Well, now we understand, you know,
Stephen Wolfram (1:50:46.400)
there is this notion of what's in brains that isn't the matter of brains, and it's something
Stephen Wolfram (1:50:50.800)
computational. And there is a sense and in fact, it is correct, that it is in some sense, immortal,
Stephen Wolfram (1:50:56.320)
because this pattern of computation is something abstract that is not specific to the particular
Stephen Wolfram (1:51:01.440)
material of a brain. Now, we don't know how to extract it, you know, in our traditional scientific
Stephen Wolfram (1:51:07.360)
approach. But it's still something where it isn't a crazy thing to say there is something doesn't
Stephen Wolfram (1:51:13.440)
weigh anything. That's a kind of a silly question. How much does it weigh? Well, actually, maybe it
Stephen Wolfram (1:51:19.120)
isn't such a silly question in our model of physics, because the actual computational activity
Stephen Wolfram (1:51:24.160)
has has a consequence for gravity and things, but that's a very subtle.
Stephen Wolfram (1:51:27.520)
You can talk about mass and energy and so on. That could be a, what would you call it, a solitron.
Stephen Wolfram (1:51:35.040)
Yes, yes, yes.
Lex Fridman (1:51:36.160)
A particle that somehow contains soulness.
Stephen Wolfram (1:51:39.520)
Yeah, right. Well, that's what, by the way, that's what Leibniz said. And, you know,
Stephen Wolfram (1:51:43.680)
one thing I've never understood this, you know, Leibniz had this idea of monads and monadology,
Lex Fridman (1:51:48.320)
and he had this idea that what exists in the universe is this big collection of monads.
Lex Fridman (1:51:53.040)
And that they that the only thing that one knows about the monads is sort of how they relate to
Stephen Wolfram (1:51:57.520)
each other. It sounds awfully like hypergraphs, right? But Leibniz had really lost me at the
Stephen Wolfram (1:52:02.880)
following thing. He said, each of these monads has a soul, and each of them has a consciousness.
Lex Fridman (1:52:09.040)
And it's like, okay, I'm out of here. I don't understand this at all. I don't know what's
Stephen Wolfram (1:52:12.480)
going on. But I realized recently that in his day, the concept that a thing could do something
Stephen Wolfram (1:52:19.360)
could spontaneously do something. That was his only way of describing that.
Lex Fridman (1:52:23.760)
And so what I would now say is, well, there's this abstract rule that runs. To Leibniz,
Stephen Wolfram (1:52:29.120)
that would have been, you know, in 1690 or whatever, that would have been kind of,
Stephen Wolfram (1:52:33.440)
well, it has a soul, it has a consciousness. And so, you know, in a sense, it's like one
Stephen Wolfram (1:52:38.640)
of these, there's no new idea under the sun, so to speak. That's a sort of a version of the same
Stephen Wolfram (1:52:43.760)
kinds of ideas, but couched in terms that are sort of bizarrely different from the ones that
Stephen Wolfram (1:52:48.880)
we would use today. Would you be able to maybe play devil's advocate on your conception of
Stephen Wolfram (1:52:54.320)
consciousness that, like the two characteristics of it that is constrained, and there's a
Stephen Wolfram (1:52:59.920)
single thread of time? Is it possible that Leibniz was onto something that the basic atom,
Stephen Wolfram (1:53:07.600)
the discrete atom of space has a consciousness? Is that, so these are just words, right? But like,
Lex Fridman (1:53:14.960)
what is there? Is there some sense where consciousness is much more fundamental
Lex Fridman (1:53:20.000)
than you're making it seem? I don't know. I mean, you know, I think...
Lex Fridman (1:53:24.000)
Can you construct a world in which it is much more fundamental?
Stephen Wolfram (1:53:27.280)
I think that, okay, so the question would be, is there a way to think about kind of,
Stephen Wolfram (1:53:33.440)
if we sort of parse the universe down at the level of atoms of space or something,
Lex Fridman (1:53:38.560)
could we say, well, so that's really a question of a different point of view,
Stephen Wolfram (1:53:42.080)
a different place in real space. We're asking the question, could there be a civilization
Stephen Wolfram (1:53:47.200)
that exists? Could there be sort of conscious entities that exist at the level of atoms of
Stephen Wolfram (1:53:54.080)
space? And what would that be like? And I think that comes back to this question of,
Stephen Wolfram (1:53:58.400)
what's it like to be a cellular automaton type thing? I mean, I'm not yet there. I don't know.
Stephen Wolfram (1:54:05.920)
I mean, I think that this is a... And I know I don't even know yet quite how to think about this
Stephen Wolfram (1:54:12.800)
in the sense that I was considering, you know, I never write fiction, but I haven't written it
Stephen Wolfram (1:54:17.520)
since I was like 10 years old. And my fiction, I made one attempt, which I sent to some science
Lex Fridman (1:54:22.160)
fiction writer friends of mine, and they told me it was terrible. So, but...
Lex Fridman (1:54:25.280)
This is a long time ago?
Lex Fridman (1:54:26.720)
No, this is recently.
Stephen Wolfram (1:54:27.920)
Recently. They said it was terrible. That'd be interesting to see you write a short story
Stephen Wolfram (1:54:31.920)
based on what sounds like it's already inspiring short stories or stories by science fiction
Stephen Wolfram (1:54:38.080)
writers.
Lex Fridman (1:54:38.800)
But I think the interesting thing for me is, you know, what is it like to be a whatever?
Lex Fridman (1:54:45.680)
How do you describe that? I mean, that's not a thing that you describe in mathematics,
Lex Fridman (1:54:49.520)
the what is it like to be such and such.
Stephen Wolfram (1:54:51.760)
Well, see, to me, when you say what is it like to be something,
Stephen Wolfram (1:54:55.600)
it presumes that you're talking about a singular entity. So, like, there's some kind of feeling of
Stephen Wolfram (1:55:07.520)
the entity, the stuff that's inside of it and the stuff that's outside of it.
Lex Fridman (1:55:12.800)
And then that's when consciousness starts making sense. But then it seems like that could be
Stephen Wolfram (1:55:20.080)
generalizable. If you take some subset of a cellular automata, you could start talking
Stephen Wolfram (1:55:26.880)
about what does that subset feel. But then you can, I think you could just take arbitrary
Stephen Wolfram (1:55:34.000)
numbers of subsets. Like, to me, like, you and I individually are consciousnesses,
Lex Fridman (1:55:41.760)
but you could also say the two of us together is a singular consciousness.
Stephen Wolfram (1:55:45.680)
Maybe, maybe. I'm not so sure about that. I think that the single thread of time thing
Stephen Wolfram (1:55:49.840)
may be pretty important. And that as soon as you start saying, there are two different threads
Lex Fridman (1:55:54.800)
of time, there are two different experiences, and then we have to say, how do they relate?
Lex Fridman (1:55:59.280)
How are they sort of entangled with each other? I mean, that may be a different story of a thing
Stephen Wolfram (1:56:03.520)
that isn't much like, you know, what do the ants, you know, what's it like to be an ant,
Lex Fridman (1:56:08.960)
you know, where there's a sort of more collective view of the world, so to speak?
Stephen Wolfram (1:56:12.880)
I don't know. I think that, I mean, this is, you know, I don't really have a good, I mean,
Stephen Wolfram (1:56:20.800)
you know, my best thought is, you know, can we turn it into a human story? It's like the question
Stephen Wolfram (1:56:26.240)
of, you know, when we try and understand physics, can we turn that into something which is sort of
Stephen Wolfram (1:56:30.480)
a human understandable narrative? And now what's it like to be a such and such? You know, maybe the
Stephen Wolfram (1:56:36.160)
only medium in which we can describe that is something like fiction, where it's kind of like
Stephen Wolfram (1:56:41.040)
you're telling, you know, the life story in that setting. But I'm, this is beyond what I've yet
Stephen Wolfram (1:56:48.720)
understood how to do. Yeah, but it does seem so, like with human consciousness, you know,
Stephen Wolfram (1:56:53.280)
we're made up of cells and like, there's a bunch of systems that are networked that work together
Stephen Wolfram (1:57:01.120)
that at this, at the human level, feel like a singular consciousness when you take, and so
Stephen Wolfram (1:57:07.920)
maybe like an ant colony is just too low level. Sorry, an ant is too low level. Maybe you have to
Stephen Wolfram (1:57:14.400)
look at the ant colony. Yeah, I agree. There's some level at which it's a conscious being. And then
Stephen Wolfram (1:57:20.320)
if you go to the planetary scale, then maybe that's going too far. So there's a nice sweet spot for
Stephen Wolfram (1:57:26.080)
consciousness. No, I agree. I think the difficulty is that, you know, okay, so in sort of people who
Stephen Wolfram (1:57:33.920)
talk about consciousness, one of the terrible things I've realized, because I've now interacted
Stephen Wolfram (1:57:38.400)
with some of this community, so to speak, some interesting people who do that kind of thinking.
Stephen Wolfram (1:57:44.240)
But, you know, one of the things I was saying to one of the leading people in that area, I was
Stephen Wolfram (1:57:48.400)
saying, you know, that, you know, it must be kind of frustrating because it's kind of like a poetry
Stephen Wolfram (1:57:55.200)
story. That is many people are writing poems, but few people are reading them. So there are always
Stephen Wolfram (1:57:59.840)
these different, you know, everybody has their own theory of consciousness, and they are very
Stephen Wolfram (1:58:04.720)
non inter sort of inter discussable. And by the way, I mean, you know, my own approach to sort of
Stephen Wolfram (1:58:11.760)
the question of consciousness, as far as I'm concerned, I'm an applied consciousness operative,
Lex Fridman (1:58:16.560)
so to speak, because I don't really, in a sense, the thing I'm trying to get out of it is how does
Stephen Wolfram (1:58:21.760)
it help me to understand what's a possible theory of physics? And how does it help me to say,
Lex Fridman (1:58:27.600)
how do I go from this incoherent collection of things happening in the universe to our definite
Stephen Wolfram (1:58:34.000)
perception and definite laws and so on, and sort of an applied version of consciousness? And I
Stephen Wolfram (1:58:38.880)
think the reason it sort of segues to a different kind of topic, but the reason that one of the
Stephen Wolfram (1:58:44.000)
things I'm particularly interested in is kind of what's the analog of consciousness in systems
Stephen Wolfram (1:58:48.480)
very different from brains? And so why is that matter? Well, you know, this whole description
Stephen Wolfram (1:58:54.640)
of this kind of, you know what, we haven't talked about why the universe exists. So let's get to why
Stephen Wolfram (1:59:00.400)
the universe exists. And then we can talk about perhaps a little bit about what these models of
Stephen Wolfram (1:59:06.800)
physics kind of show you about other kinds of things like molecular computing and so on.
Lex Fridman (1:59:12.000)
Yes, that's good.
Lex Fridman (1:59:13.200)
Why does the universe exist? Okay, so we finally sort of more or less set the stage,
Stephen Wolfram (1:59:17.120)
we've got this idea of this rule yard of this object that is made from following all possible
Stephen Wolfram (1:59:22.080)
rules, the fact that it's sort of not just this incoherent mess, it's got all this entangled
Stephen Wolfram (1:59:27.600)
structure in it, and so on. Okay, so what is this rule yard? Well, it is the working out of all
Stephen Wolfram (1:59:35.600)
possible formal systems. So the sort of the question of why does the universe exist? Its
Stephen Wolfram (1:59:41.200)
core question, which we kind of started with is, you've got two plus two equals four, you've got
Stephen Wolfram (1:59:46.240)
some other abstract result, but that's not actualized. It's just an abstract thing.
Lex Fridman (1:59:52.560)
And when we say we've got a model for the universe, okay, it's this rule, you run it,
Lex Fridman (1:59:56.160)
and it'll make the universe, but it's like, but where's it actually running? What is it actually
Stephen Wolfram (20:03.920)
this complexity, there's all this computational irreducibility. You know, there's a lot we can't
Stephen Wolfram (20:08.320)
know about what's going to happen. It's kind of kind of very confusing thing for people who say,
Stephen Wolfram (20:12.560)
you know, science has nailed everything down. We're going to, you know, based on science,
Stephen Wolfram (20:16.080)
we can know everything. Well, actually, there's this computational irreducibility thing
Stephen Wolfram (20:20.080)
right in the middle of that, thrown up by science, so to speak. And then the question is, well,
Stephen Wolfram (20:25.040)
given computational irreducibility, how can we actually figure out anything about what happens
Stephen Wolfram (20:29.440)
in the world? Why aren't we why are we able to predict anything? Why are we able to operate in
Stephen Wolfram (20:33.920)
the world? And the answer is that we sort of live in these slices of computational reusability
Stephen Wolfram (20:39.200)
that exist in this kind of ocean of computational irreducibility. And it turns out that seems that
Stephen Wolfram (20:45.440)
it's a very fundamental feature of the kind of model that seems to operate in physics,
Lex Fridman (20:50.800)
and perhaps in a lot of these other areas, that there are these particular slices of
Stephen Wolfram (20:55.760)
computational reusability that are relevant to us. And those are the things that both allow us to
Stephen Wolfram (21:02.240)
operate in the world, and not just have everything be completely unpredictable. But there are also
Stephen Wolfram (21:06.880)
things that potentially give us what amount to sort of physics like laws in all these other areas.
Lex Fridman (21:12.960)
So that's, that's been sort of an exciting thing. But, but I would say that in general, for our
Stephen Wolfram (21:17.440)
project, it's been going spectacularly well. I mean, you know, I, it's very, honestly, it wasn't
Stephen Wolfram (21:23.360)
something I expected to happen in my lifetime. I mean, it's, you know, it's something where,
Stephen Wolfram (21:28.400)
where it's, it's an in fact, one of the things about it, some of the things that we've discovered,
Stephen Wolfram (21:34.080)
are things where I was pretty sure that wasn't how things worked. And turns out I'm wrong. And,
Stephen Wolfram (21:40.240)
you know, in a major area in metamathematics, I've been realizing that I something I've long
Stephen Wolfram (21:45.520)
believed we can talk about it later that that that just just really isn't right. But But I think that
Stephen Wolfram (21:53.040)
the the thing that so so what's happened with the physics project? I mean, you know, it's a
Lex Fridman (21:59.440)
can explain a little bit about how the how the model works. But basically,
Stephen Wolfram (22:02.640)
we can maybe ask you the following question. So it's easy through words describe how cellular
Stephen Wolfram (22:08.880)
automata works, you've you've explained this. And it's the fundamental mechanism by which you in
Stephen Wolfram (22:16.480)
your book, and you kind of science explored the idea of complexity and how to do science in this
Stephen Wolfram (22:21.920)
world of island reducible islands and irreducible general irreducibility. Okay, so how does the model
Stephen Wolfram (22:30.640)
of hypergraphs differ from cellular automata? And how does the idea of multi computation
Stephen Wolfram (22:35.840)
differ? Like, maybe that's a way to describe it. We're we're, you know, right. This is a, you know,
Stephen Wolfram (22:42.160)
my life is like all of our lives, something of a story of computational irreducibility. Yes.
Stephen Wolfram (22:47.040)
And, you know, it's been going for a few years now. So it's always a challenge to kind of find
Stephen Wolfram (22:52.240)
these appropriate pockets of reducibility. But let me see what I can do. So, so I mean,
Stephen Wolfram (22:57.200)
first of all, let's let's talk about physics, first of all. And, you know, a key observation,
Stephen Wolfram (23:03.760)
that one of the starting point of our physics project is things about what is space? What is
Stephen Wolfram (23:09.680)
the universe made of? And, you know, ever since Euclid, people just sort of say space is just this
Stephen Wolfram (23:15.120)
thing where you can put things at any position you want. And they're just points. And they're just
Stephen Wolfram (23:19.600)
geometrical things that you can just arbitrarily put at different different coordinate positions.
Lex Fridman (23:25.040)
So the first thing in our physics project is the idea that space is made of something, just like
Stephen Wolfram (23:30.400)
just like water is made of molecules, space is made of kind of atoms of space. And the only thing we
Stephen Wolfram (23:36.240)
can say about these atoms of space is they have some identity. There's a there's a there is it's
Stephen Wolfram (23:40.640)
this atom as opposed to this atom. And, you know, you could give them a few a computer person, you
Stephen Wolfram (23:45.120)
give them UUIDs or something. And that's all there is to say about them, so to speak. And then all we
Stephen Wolfram (23:54.960)
know about these atoms of space is how they relate to each other. So we say, these three atoms of
Stephen Wolfram (24:02.480)
space are associated with each other in some relation. So you can think about that as you know,
Lex Fridman (24:08.400)
what atom of space is friends with what other atom of space, you can build this essentially friend
Stephen Wolfram (24:13.520)
network of the atoms of space. And the sort of starting point of our physics project is that's
Lex Fridman (24:18.800)
what our universe is, it's a giant friend network of the atoms of space. And so how can that
Stephen Wolfram (24:24.800)
possibly represent our universe? Well, it's like in something like water, you know, their molecules
Stephen Wolfram (24:31.360)
bouncing around, but on a large scale that, you know, that produces fluid flow, and we have fluid
Stephen Wolfram (24:37.120)
vortices, and we have all of these phenomena that are sort of the emergent phenomena from that
Stephen Wolfram (24:42.160)
underlying kind of collection of molecules bouncing around. And by the way, it's important that that
Stephen Wolfram (24:47.360)
collection of molecules bouncing around have this phenomenon of computational irreducibility,
Stephen Wolfram (24:51.760)
that's actually what leads to the second law of thermodynamics among other things.
Lex Fridman (24:55.520)
And that leads to the sort of randomness of the underlying behavior, which is what gives you
Stephen Wolfram (25:00.960)
something which on a large scale seems like it's a smooth continuous type of thing. And so okay,
Lex Fridman (25:07.840)
so first thing is space is made of something, it's made of all these atoms of space connected
Stephen Wolfram (25:13.680)
together in this network. And then everything that we experience is sort of features of that
Stephen Wolfram (25:20.640)
structure of space. So, you know, when we have an electron or something or a photon,
Stephen Wolfram (25:24.400)
it's some kind of tangle in the structure of space, much like kind of a vortex in a fluid
Stephen Wolfram (25:29.360)
would be just this thing that is, you know, it can actually, the vortex can move around,
Stephen Wolfram (25:34.160)
it can involve different molecules in the fluid, but the vortex still stays there.
Lex Fridman (25:38.480)
And if you zoom out enough, the vortex looks like an atom itself, like a basic
Stephen Wolfram (25:42.880)
element. So there's the levels of abstraction. If you squint and kind of blur things out,
Stephen Wolfram (25:49.680)
it looks like at every level of abstraction, you can define what is a basic individual entity.
Stephen Wolfram (25:55.760)
Yes. But, you know, in this model, there's a bottom level, you know, there's an elementary
Stephen Wolfram (26:01.040)
length, maybe 10 to the minus 100 meters, let's say, which is really small, you know,
Stephen Wolfram (26:05.680)
proton is 10 to the minus 15 meters, the smallest we've ever been able to sort of see with a particle
Stephen Wolfram (26:12.000)
accelerator is around 10 to the minus 21 meters. So, you know, if we don't know precisely what
Stephen Wolfram (26:17.760)
the correct scale is, but it's perhaps over the order of 10 to the minus 100 meters, so it's
Stephen Wolfram (26:21.520)
pretty small. But that's the end, that's what things are made of.
Stephen Wolfram (26:26.880)
What's your intuition where the 10 to the minus 100 comes from? What's your intuition about this
Lex Fridman (26:32.400)
scale?
Lex Fridman (26:33.360)
Well, okay, so there's a calculation, which I consider to be somewhat rickety,
Stephen Wolfram (26:37.280)
okay, which has to do with comparing, so there are various fundamental constants,
Stephen Wolfram (26:42.800)
there's a speed of light, the speed of light, once you know the elementary time,
Stephen Wolfram (26:46.880)
the speed of light tells you the conversion from the elementary time to the elementary length.
Stephen Wolfram (26:52.160)
Then there's the question of how do you convert to the elementary energy? And how do you convert
Stephen Wolfram (26:56.960)
to between other things? And the various constants we know, we know the speed of light,
Stephen Wolfram (27:00.960)
we know the gravitational constant, we know Planck's constant and quantum mechanics,
Stephen Wolfram (27:05.600)
those are the three important ones. And we actually know some other things, we know things
Stephen Wolfram (27:09.920)
like the size of the universe, the Hubble constant, things like that. And essentially,
Stephen Wolfram (27:15.120)
this calculation of the elementary length comes from looking at the combination of those.
Stephen Wolfram (27:21.280)
Okay, so the most obvious thing, people have assumed that quantum gravity happens at this
Stephen Wolfram (27:26.160)
thing, the Planck scale, 10 to the minus 34 meters, which is the combination of Planck's
Stephen Wolfram (27:32.080)
constant and the gravitational constant, the speed of light, that gives you that kind of length.
Stephen Wolfram (27:37.280)
Turns out in our model, there is an additional parameter, which is essentially the number of
Stephen Wolfram (27:42.960)
simultaneous threads of execution of the universe, which is essentially the number of sort of
Stephen Wolfram (27:47.520)
independent quantum processes that are going on. And that number, let's see if I remember that
Stephen Wolfram (27:52.960)
number, that number is 10 to the 170, I think, and so it's a big number. But that number then
Stephen Wolfram (28:00.560)
connects, sort of modifies what you might think from all these Planck units to give you the things
Stephen Wolfram (28:07.920)
we're giving. And there's been sort of a mystery actually in the more technical physics thing,
Stephen Wolfram (28:12.560)
that the Planck mass, the Planck energy, Planck energy is actually surprisingly big. The Planck
Stephen Wolfram (28:19.440)
length is tiny, 10 to the minus 34 meters, you know, Planck time, 10 to the minus 43 meters,
Stephen Wolfram (28:24.000)
I think, seconds, I think. But the Planck energy is like the energy of a lightning strike,
Stephen Wolfram (28:32.080)
okay, which is pretty weird. In our models, the actual elementary energy is that divided by the
Stephen Wolfram (28:38.240)
number of sort of simultaneous quantum threads, and it ends up being really small too. And that
Stephen Wolfram (28:43.040)
sort of explains that mystery that's been around for a while about how Planck units work. But
Stephen Wolfram (28:50.000)
whether that precise estimate is right, we don't know yet. I mean, that's one of the things that's
Stephen Wolfram (28:54.800)
sort of been a thing we've been pretty interested in is how do you see through, you know, how do you
Stephen Wolfram (29:00.400)
make a gravitational microscope that can kind of see through to the atoms of space? You know,
Lex Fridman (29:05.920)
how do you get in fluid flow, for example, if you go to hypersonic flow or something, you know,
Stephen Wolfram (29:10.480)
you've got a Mach 20, you know, space plane or something, it really matters that there are
Stephen Wolfram (29:15.040)
individual molecules hitting the space plane, not a continuous fluid. The question is, what is the
Stephen Wolfram (29:22.640)
analog of hypersonic flow for things about the structure of spacetime? And it looks like a
Stephen Wolfram (29:30.480)
rapidly rotating black hole, right, at the sort of critical rotation rate, it looks as if that's
Stephen Wolfram (29:38.880)
a case where essentially the structure of spacetime is just about to fall apart, and you
Stephen Wolfram (29:45.920)
may be able to kind of see the evidence of sort of discrete elements, you know, you may be able
Stephen Wolfram (29:52.640)
to kind of see there the sort of gravitational microscope of actually seeing these discrete
Stephen Wolfram (29:57.280)
elements of space. And there may be some effect in, for example, gravitational waves produced by
Stephen Wolfram (2:00:03.440)
doing? Is it actual, or is it merely a formal description of something? So the thing to realize
Stephen Wolfram (2:00:11.760)
with this, the thing about the rule yard is it's an inevitable, it is the entangled running of all
Stephen Wolfram (2:00:19.760)
possible rules. So you don't get to say, it's not like you're saying, which rule yard are you
Stephen Wolfram (2:00:25.280)
picking? Because it's all possible formal rules. It's not like it's just, well, actually, it's
Stephen Wolfram (2:00:32.560)
only footnote. The only footnote, it's an important footnote, is it's all possible
Stephen Wolfram (2:00:37.120)
computational rules, not hyper computational rules. That is, it's running all the rules that would be
Stephen Wolfram (2:00:46.400)
accessible to a Turing machine, but it is not running all the rules that will be accessible
Stephen Wolfram (2:00:51.520)
to a thing that can solve problems in finite time that would take a Turing machine infinite time to
Stephen Wolfram (2:00:56.400)
solve. So you can, even Alan Turing knew this, that you could make oracles for Turing machines,
Stephen Wolfram (2:01:01.520)
where you say a Turing machine can't solve the whole thing problem for Turing machines. It can't
Stephen Wolfram (2:01:05.520)
know what will happen in any Turing machine after an infinite time, in any finite time,
Lex Fridman (2:01:10.000)
but you could invent a box, just make a black box. You say, I'm going to sell you an oracle
Stephen Wolfram (2:01:15.600)
that will just tell you, you know, press this button. It'll tell you what the Turing machine
Stephen Wolfram (2:01:19.280)
will do after an infinite time. You can imagine such a box. You can't necessarily build one in
Stephen Wolfram (2:01:23.920)
the physical universe, but you can imagine such a box. And so we could say, well, in addition to,
Lex Fridman (2:01:29.120)
so in this Rulliad, we're imagining that there is a computational, that at the end, it's running
Stephen Wolfram (2:01:36.400)
rules that are computational. It doesn't have a bunch of oracle black boxes in it. You say, well,
Lex Fridman (2:01:42.880)
why not? Well, it turns out if there are oracle black boxes, the Rulliad that is,
Stephen Wolfram (2:01:48.800)
you can make a sort of super Rulliad that contains those oracle black boxes,
Lex Fridman (2:01:53.040)
but it has a cosmological event horizon relative to the first one. They can't communicate.
Stephen Wolfram (2:01:57.360)
In other words, you can end up with, what ends up happening is it's like in the physical universe,
Stephen Wolfram (2:02:06.160)
in this causal graph that represents the causal relationships of different things,
Stephen Wolfram (2:02:09.920)
you can have an event horizon where the causal graph is disconnected, where the effect here,
Stephen Wolfram (2:02:16.400)
an event happening here does not affect an event happening here because there's a disconnection
Stephen Wolfram (2:02:20.720)
in the causal graph. And that's what happens in an event horizon. And so what will happen between
Stephen Wolfram (2:02:26.400)
this kind of the ordinary Rulliad and the hyper Rulliad is there is an event horizon and we,
Stephen Wolfram (2:02:34.480)
in our Rulliad, will just never know that they're just separate things. They're not connected.
Lex Fridman (2:02:42.880)
And maybe I'm not understanding, but just because we can't observe it,
Lex Fridman (2:02:47.760)
why does that mean it doesn't exist?
Lex Fridman (2:02:49.200)
So it might exist, but it's not clear what it... So what, so to speak, whether it exists. What
Stephen Wolfram (2:02:57.200)
we're trying to understand is why does our universe exist? We're not trying to ask the
Stephen Wolfram (2:03:01.600)
question what... Let me say another thing. Let me make a meta comment, which is that I have not
Stephen Wolfram (2:03:10.640)
thought through this hyper Rulliad business properly. So I can't... The hyper Rulliad is
Lex Fridman (2:03:18.320)
referring to a Rulliad in which hyper computation is possible.
Stephen Wolfram (2:03:22.640)
That's correct. Yes.
Lex Fridman (2:03:23.680)
Okay. So the footnote to the footnote is we're not sure why this is important.
Stephen Wolfram (2:03:33.280)
Yeah, that's right. So let's ignore that. Okay. It's already abstract enough. Okay. So,
Lex Fridman (2:03:39.920)
okay. So the one question is we have to say, if we're saying, why does the universe exist?
Stephen Wolfram (2:03:46.800)
One question is why is it this universe and not another universe? Okay. So the important point
Stephen Wolfram (2:03:52.480)
about this Rulliad idea is that in the Rulliad are all possible formal systems. So there's no
Stephen Wolfram (2:03:59.840)
choice being made. There's no like, oh, we pick this particular universe and not that one. That's
Stephen Wolfram (2:04:05.360)
the first thing. The second thing is that we have to ask the question. So you say, why does two plus
Stephen Wolfram (2:04:12.640)
two equals four exist? That is a thing that necessarily is that way just on the basis of
Stephen Wolfram (2:04:20.720)
the meaning of the terms, two and plus and equals and so on. So the thing is that this Rulliad
Stephen Wolfram (2:04:27.520)
object is in a sense a necessary object. It is just the thing that is the consequence of working
Stephen Wolfram (2:04:34.560)
out the consequence of the formal definition of things. It is not a thing where you're saying,
Lex Fridman (2:04:40.480)
and this is picked as the particular thing. This is just something which necessarily is that thing
Stephen Wolfram (2:04:47.760)
because of the definition of what it means to have computation. So the Rulliad, it's a formal system.
Lex Fridman (2:04:54.480)
Yes. But does it exist? Ah, well, where are we in this whole thing?
Lex Fridman (2:05:02.560)
Yes. We are part of this Rulliad. So there is no sense to say, does two plus
Stephen Wolfram (2:05:10.560)
two equals four exist? Well, in some sense, it necessarily exists. It's a necessary object. It's
Stephen Wolfram (2:05:19.600)
not a thing that way you can ask. Usually in philosophy, there's a sort of distinction made
Stephen Wolfram (2:05:25.920)
between necessary truths, contingent truths, analytic propositions, synthetic propositions
Stephen Wolfram (2:05:32.000)
that are a variety of different versions of this. They're things which are necessarily true just
Stephen Wolfram (2:05:37.200)
based on the definition of terms. And there are things which happen to be true in our universe.
Lex Fridman (2:05:42.800)
But we don't exist in Rullial space. That's one of the coordinates that define our existence.
Stephen Wolfram (2:05:51.200)
Well, okay. So yes, yes. But this Rulliad is the set of all possible Rullial coordinates.
Lex Fridman (2:05:58.240)
So what we're saying is it contains that. So what we're saying is we exist as, okay, so
Stephen Wolfram (2:06:04.880)
our perception of what's going on is we're at a particular place in this Rulliad,
Lex Fridman (2:06:09.280)
and we are concluding certain things about how the universe works based on that.
Lex Fridman (2:06:13.520)
But the question is, do we understand, you know, is there something where we say,
Stephen Wolfram (2:06:19.760)
okay, so why does it work that way? Well, the answer is, I think it has to work that way,
Stephen Wolfram (2:06:27.360)
because this Rulliad is a necessary object in the sense that it is a purely formal object,
Stephen Wolfram (2:06:35.360)
just like 2 plus 2 equals 4. It's not an object that was made of something. It's an object that
Stephen Wolfram (2:06:41.600)
is just an expression of the necessary collection of formal relations that exist.
Lex Fridman (2:06:46.480)
And so then the issue is, can we, in our experience of that, is it, you know, can we have
Lex Fridman (2:06:53.280)
tables and chairs, so to speak, in that just by virtue of our experience of that necessary thing?
Stephen Wolfram (2:07:00.720)
And, you know, what people have generally thought, and I don't know of a lot of discussion of this,
Lex Fridman (2:07:06.960)
why does the universe exist question? It's been a very, you know, I've been surprised actually at
Lex Fridman (2:07:12.240)
how little, I mean, I think it's one of these things that's really kind of far out there. But
Stephen Wolfram (2:07:17.520)
the thing that is, you know, the surprise here is that all possible formal rules, when you run them
Stephen Wolfram (2:07:25.840)
together, and that's the critical thing, when you run them together, they produce this kind of
Stephen Wolfram (2:07:30.080)
entangled structure that has a definite structure. It's not just, you know, a random arbitrary thing,
Stephen Wolfram (2:07:37.040)
it's a thing with definite structure. And that structure is the thing when we are embedded in
Stephen Wolfram (2:07:42.640)
that structure, when anything, you know, an entity embedded in that structure perceives something,
Stephen Wolfram (2:07:48.960)
which is then we can interpret as physics and things like this. So in other words, we don't
Stephen Wolfram (2:07:54.240)
have to ask the question, the why does it exist? It necessarily exists.
Lex Fridman (2:08:00.080)
I'm missing this part. Why does it necessarily exist?
Stephen Wolfram (2:08:02.880)
Okay, okay.
Lex Fridman (2:08:03.520)
So like, you need to have it if you want to formalize the relation between entities, but
Lex Fridman (2:08:14.160)
why do you need to have relations?
Lex Fridman (2:08:15.760)
Okay, okay. So let's say you say, well...
Lex Fridman (2:08:22.480)
It's like, why does math have to exist?
Stephen Wolfram (2:08:24.800)
Fair question. Okay, fair question. Let's see. I think the thing to think about is
Stephen Wolfram (2:08:33.520)
the existence of mathematics is something where given a definition of terms,
Lex Fridman (2:08:40.080)
what follows from that definition inevitably follows. So now you can say, why define any terms?
Lex Fridman (2:08:47.520)
But in a sense, the, well, that's okay. So the definition of terms, I mean, I think the way to
Lex Fridman (2:08:56.240)
think about this, let me see.
Lex Fridman (2:08:58.080)
So like concrete terms.
Stephen Wolfram (2:09:01.360)
Well, they're not very concrete. I mean, they're just things like, you know, logical or.
Stephen Wolfram (2:09:09.280)
Right, but that's a thing. That's a powerful thing.
Stephen Wolfram (2:09:13.280)
Well, yes, okay. But the point is that it is not a thing of a, you know, people imagine there is,
Stephen Wolfram (2:09:20.720)
I don't know, the, you know, an elephant or something or the, you know, elephants are presumably
Stephen Wolfram (2:09:28.080)
not necessary objects. They happen to exist as a result of kind of biological evolution and
Stephen Wolfram (2:09:34.720)
whatever else. But the thing is that in some sense that there is, it is a different kind of thing
Lex Fridman (2:09:43.360)
to say, does plus exist? It's not like an elephant.
Lex Fridman (2:09:48.640)
So a plus seems more fundamental, more basic than an elephant. Yes. But you can imagine a world
Stephen Wolfram (2:09:56.800)
without plus or anything like it. Like, why do formal things that are discrete, that can be used
Lex Fridman (2:10:05.920)
to reason have to exist?
Stephen Wolfram (2:10:08.400)
Well, okay. So why? Okay. So then the question is, but the whole point is computation.
Stephen Wolfram (2:10:14.960)
We can certainly imagine computation. That is, we can certainly say there is a formal system that
Stephen Wolfram (2:10:21.120)
we can construct abstractly in our minds that is computation. And that's the, you know, we can
Stephen Wolfram (2:10:30.240)
imagine it. Now the question is, is it that formal system, once we exist as observers embedded in
Stephen Wolfram (2:10:39.840)
that formal system, that's enough to have something which is like our universe. And so then what
Stephen Wolfram (2:10:46.720)
you're kind of asking is perhaps is why, I mean, the point is we definitely can imagine it.
Stephen Wolfram (2:10:53.760)
There's nothing that says that we're not saying that it's sort of inevitable that that is a thing
Stephen Wolfram (2:11:02.800)
that we can imagine. We don't have to ask, does it exist? We're just, it is definitely something
Stephen Wolfram (2:11:07.760)
we can imagine. Now that's, then we have this thing that is a formally constructible thing
Stephen Wolfram (2:11:15.200)
that we can imagine. And now we have to ask the question, what, you know, given that formally
Stephen Wolfram (2:11:20.640)
constructible thing, what is, what consequences does that, if we were to perceive that formally,
Lex Fridman (2:11:28.080)
if we were embedded in that formally constructible thing, what would we perceive about the world?
Lex Fridman (2:11:33.280)
And we would say, we perceive that the world exists because we are seeing all of this mechanism
Stephen Wolfram (2:11:40.480)
of all these things happening. And, but that's something that is just a feature of, it's something
Stephen Wolfram (2:11:46.720)
where we are... See, another way of asking this that I'm trying to get at, I understand why it
Stephen Wolfram (2:11:53.120)
feels like this ruley ad is necessary, but maybe it's just me being human, but it feels like then
Stephen Wolfram (2:12:04.560)
you should be able to, not us, but somehow step outside of the ruley ad. Like what's outside the
Stephen Wolfram (2:12:11.280)
ruley ad? Well, the ruley ad is all formal systems. So there's nothing because... But that's what a
Stephen Wolfram (2:12:17.600)
human would say. I know that's what a human would say, because we're used to the idea that there are,
Stephen Wolfram (2:12:22.240)
there's, but the whole point is that by the time it's all possible formal systems, it's, it's like,
Stephen Wolfram (2:12:29.200)
it is all things you can imagine, but... All computations you can imagine, but like we don't...
Stephen Wolfram (2:12:36.960)
Well, so the issue is, can we encode? Okay. So that's a fair question. Is it possible to encode
Lex Fridman (2:12:45.200)
all, I mean, once we, is there something that isn't what we can represent formally?
Stephen Wolfram (2:12:52.000)
Right. That is, is there something that, and that's, I think, related to the hyper ruley ad
Stephen Wolfram (2:12:57.600)
footnote, so to speak, which I'm afraid that the, you know, one of the things sort of interesting
Stephen Wolfram (2:13:04.000)
about this is, you know, there has been some discussion of this in theology and things like
Stephen Wolfram (2:13:08.880)
that, but, which I don't necessarily understand all of, but the key sort of new input is this idea
Stephen Wolfram (2:13:19.440)
that all possible formal systems, it's like, you know, if you make a world, people say, well, you
Stephen Wolfram (2:13:25.280)
make a world with a particular, in a particular way with particular rules, but no, you don't do
Stephen Wolfram (2:13:30.400)
that. You can make a world that deals with all possible rules, and then merely by virtue of
Stephen Wolfram (2:13:37.520)
living in a particular place in that world, so to speak, we have the perception we have of what the
Stephen Wolfram (2:13:42.800)
world is like. Now, I have to say the, it's sort of interesting because I've, you know, I wrote this
Stephen Wolfram (2:13:49.360)
piece about this, and I, you know, this philosophy stuff is not super easy, and I've, as I'm talking
Stephen Wolfram (2:13:57.520)
to you about it, and I actually haven't, you know, people have been interested in lots of different
Stephen Wolfram (2:14:00.880)
things we've been doing, but this, why does the universe exist, has been, I would say, one of the,
Stephen Wolfram (2:14:05.360)
one of the ones that you would think people will be most interested in, but actually, I think
Stephen Wolfram (2:14:10.720)
they're just like, oh, that's just something complicated that, so I haven't, I haven't explained
Stephen Wolfram (2:14:17.200)
it as much as I've explained a bunch of other things, and I have to say, I think I, I think I
Stephen Wolfram (2:14:21.120)
may be missing a couple of pieces of that argument that would be, so it's kind of a like…
Stephen Wolfram (2:14:27.520)
Well, you are, your conscious being is computationally bounded, so you're missing…
Lex Fridman (2:14:32.720)
Indeed.
Stephen Wolfram (2:14:33.200)
Having written quite a few articles yourself, you're now missing some of the pieces.
Lex Fridman (2:14:38.560)
Yes, right.
Stephen Wolfram (2:14:39.120)
That's the limitation of being human.
Stephen Wolfram (2:14:40.880)
Right. One of the consequences of this, why the universe exists thing, is that you're missing
Stephen Wolfram (2:14:46.960)
something, and this kind of concept of rule adds and, you know, places in there representing our
Stephen Wolfram (2:14:53.840)
perception of the universe and so on. One of the weird consequences is, if the universe exists,
Stephen Wolfram (2:14:59.680)
mathematics must also exist. And that's a weird thing, because mathematics, people have been very
Stephen Wolfram (2:15:06.320)
confused, including me, have been very confused about the question of kind of what, what is the
Stephen Wolfram (2:15:14.640)
definition of mathematics? What is, what kind of a thing is mathematics? Is mathematics something
Stephen Wolfram (2:15:20.080)
where we just write down axioms like Euclid did for geometry, and we just build the structure,
Lex Fridman (2:15:25.200)
and we could have written down different axioms, and we'd have a different structure? Or is it
Stephen Wolfram (2:15:28.960)
something that has a more fundamental sort of truth to it? And I have to say, this is one of
Stephen Wolfram (2:15:33.280)
these cases where I've long believed that mathematics has a great deal of arbitrariness to
Stephen Wolfram (2:15:38.320)
it, that there are particular axioms that kind of got written down by the Babylonians, and, you
Stephen Wolfram (2:15:43.360)
know, that's what we've ended up with the mathematics that we have. And I have to say,
Stephen Wolfram (2:15:47.120)
actually, my wife has been telling me for 25 years, she was a mathematician, she's been telling me,
Stephen Wolfram (2:15:51.600)
you're wrong about the foundations of mathematics. And, you know, I'm like, no, no, no, I know what
Stephen Wolfram (2:15:57.120)
I'm talking about. And finally, she's much more right than I've been. So it's one of the...
Stephen Wolfram (2:16:04.160)
So, I mean, her sense and your sense, are we just, so this is to the question of metamathematics,
Stephen Wolfram (2:16:11.600)
just kind of on a trajectory through ruleal space, except in mathematics, through a trajectory of
Stephen Wolfram (2:16:18.080)
a certain kind of... I think that's partly the idea. So I think that the notion is this. So 100
Stephen Wolfram (2:16:23.920)
years ago, a little bit more than 100 years ago, people have been doing mathematics for ages,
Lex Fridman (2:16:28.320)
but then in the late 1800s, people decided to try and formalize mathematics and say, you know,
Stephen Wolfram (2:16:34.640)
it is mathematics is, you know, we're going to break it down, we're going to make it like logic,
Stephen Wolfram (2:16:38.720)
make it out of sort of fundamental primitives. And that was people like Frager and Piano and
Stephen Wolfram (2:16:43.600)
Hilbert and so on. And they kind of got this idea of let's do kind of Euclid, but even better,
Stephen Wolfram (2:16:50.160)
let's just make everything just in terms of this sort of symbolic axioms, and then build
Stephen Wolfram (2:16:54.480)
up mathematics from that. And that, you know, they thought at the time, as soon as they get
Stephen Wolfram (2:17:00.880)
these symbolic axioms, that they made the same mistake, the kind of computational irreducibility
Stephen Wolfram (2:17:05.280)
mistake. They thought as soon as we've written down the axioms, then we'll just have a machine,
Stephen Wolfram (2:17:11.520)
kind of a super mathematical, so to speak, that can just grind out all true theorems of mathematics.
Stephen Wolfram (2:17:17.600)
That got exploited by Gödel's theorem, which is basically the story of computational
Stephen Wolfram (2:17:21.680)
irreducibility. It's that even though you know those underlying rules, you can't deduce all
Stephen Wolfram (2:17:26.720)
the consequences in any finite way. But now the question is, okay, so they broke mathematics down
Stephen Wolfram (2:17:34.000)
into these axioms, and they say now you build up from that. So what I'm increasingly coming to
Stephen Wolfram (2:17:40.160)
realize is that's similar to saying let's take a gas and break it down into molecules. There's gas
Stephen Wolfram (2:17:46.960)
laws that are the large scale structure and so on that we humans are familiar with, and then there's
Stephen Wolfram (2:17:52.480)
the underlying molecular dynamics. And I think that the axiomatic level of mathematics, which
Stephen Wolfram (2:17:57.680)
we can access with automated theorem proving and proof assistance and these kinds of things,
Stephen Wolfram (2:18:02.640)
that's the molecular dynamics of mathematics. And occasionally we see through to that molecular
Stephen Wolfram (2:18:07.440)
dynamics. We see undecidability, we see other things like this. One of the things I've always
Stephen Wolfram (2:18:12.160)
found very mysterious is that Gödel's theorem shows that there are sort of things which cannot
Stephen Wolfram (2:18:18.560)
be finitely proved in mathematics. There are proofs of arbitrary length, infinite length proofs that
Stephen Wolfram (2:18:23.280)
you might need. But in practical mathematics, mathematicians don't typically run into this.
Stephen Wolfram (2:18:28.080)
They just happily go along doing their mathematics. And I think what's actually
Stephen Wolfram (2:18:32.640)
happening is that what they're doing is they're looking at this. They are essentially observers
Stephen Wolfram (2:18:38.720)
in metamathematical space, and they are picking a reference frame in metamathematical space,
Lex Fridman (2:18:45.440)
and they are computationally bounded observers in metamathematical space,
Stephen Wolfram (2:18:49.120)
which is causing them to deduce that the laws of metamathematics and the laws of mathematics,
Stephen Wolfram (2:18:55.520)
like the laws of fluid mechanics, are much more understandable than this underlying
Stephen Wolfram (2:19:00.080)
molecular dynamics. And so what gets really bizarre is thinking about kind of the analogy
Stephen Wolfram (2:19:06.320)
between metamathematics, this idea of you exist in this sort of space of possible,
Stephen Wolfram (2:19:16.000)
in this kind of mathematical space where the individual kind of points in the mathematical
Stephen Wolfram (2:19:21.760)
space are statements in mathematics, and they're connected by proofs where one statement, you know,
Stephen Wolfram (2:19:27.280)
you take a couple of different statements, you can use those to prove some other statement,
Lex Fridman (2:19:30.960)
and you've got this whole network of proofs. That's the kind of causal network of mathematics,
Stephen Wolfram (2:19:35.760)
of what can prove what and so on. And you can say at any moment in the history of a mathematician,
Stephen Wolfram (2:19:42.720)
of a single mathematical consciousness, you are in a single kind of slice of this
Stephen Wolfram (2:19:49.280)
kind of metamathematical space. You know a certain set of mathematical statements.
Stephen Wolfram (2:19:54.000)
You can then deduce with proofs, you can deduce other ones, and so on. You're kind of gradually
Stephen Wolfram (2:19:58.640)
moving through metamathematical space. And so it's kind of the view is that the reason that
Stephen Wolfram (2:20:04.400)
mathematicians perceive mathematics to have the sort of integrity and lack of kind of undecidability
Lex Fridman (2:20:10.160)
and so on that they do is because they, like we as observers of the physical universe,
Stephen Wolfram (2:20:15.360)
we have these limitations associated with computational boundedness, single thread of time,
Stephen Wolfram (2:20:19.920)
consciousness limitations, basically, that the same thing is true of mathematicians perceiving
Stephen Wolfram (2:20:24.960)
sort of metamathematical space. And so what's happening is that if you look at one of these
Stephen Wolfram (2:20:30.080)
formalized mathematics systems, something like Pythagoras's theorem, it'll take, oh, I don't know,
Lex Fridman (2:20:37.680)
what is it, maybe 10,000 individual little steps to prove Pythagoras's theorem. And one of the
Stephen Wolfram (2:20:43.600)
bizarre things that's sort of an empirical fact that I'm trying to understand a little bit better,
Stephen Wolfram (2:20:48.400)
if you look at different formalized mathematics systems, they actually have different axioms
Stephen Wolfram (2:20:54.160)
underneath that they can all prove Pythagoras's theorem. And so in other words, it's a little bit
Stephen Wolfram (2:20:59.200)
like what happens with gases. We can have air molecules, we can have water molecules, but they
Stephen Wolfram (2:21:03.840)
still have fluid dynamics. Both of them have fluid dynamics. And so similarly, at the level that
Stephen Wolfram (2:21:09.440)
mathematicians care about mathematics, it's way above the molecular dynamics, so to speak.
Lex Fridman (2:21:14.560)
And there are all kinds of weird things. Like, for example, one thing I was realizing recently
Stephen Wolfram (2:21:18.160)
is that the quantum theory of mathematics, that's a very bizarre idea. But basically,
Stephen Wolfram (2:21:23.280)
when you prove what is a proof is you've got one statement in mathematics, you go through
Stephen Wolfram (2:21:29.520)
other statements, you eventually get to a statement you're trying to prove, for example,
Stephen Wolfram (2:21:32.960)
that's a path in metamathematical space. And that's a single path, a single proof is a single
Stephen Wolfram (2:21:38.880)
path. But you can imagine there are other proofs of the same result. There are a bundle of proofs.
Stephen Wolfram (2:21:44.960)
There's this whole set of possible proofs. Yeah, you could think of it as branching,
Stephen Wolfram (2:21:48.560)
similar to the quantum mechanics model that you were talking about. Exactly. And then there's
Stephen Wolfram (2:21:52.320)
some invariance that you can formalize in the same way that you can for the quantum mechanical.
Stephen Wolfram (2:21:56.720)
Right. So the question is, in proof space, as you start thinking about multiple proofs,
Stephen Wolfram (2:22:01.520)
are there analogs of, for example, destructive interference of multiple proofs? So here's a
Stephen Wolfram (2:22:05.680)
bizarre idea that's just a couple of days old, so not yet fully formed. But as you try and do that,
Stephen Wolfram (2:22:12.480)
when you have two different proofs, it's like two photons going in different directions,
Stephen Wolfram (2:22:16.240)
you have two proofs, which at an intermediate stage are incompatible. And that's kind of like
Stephen Wolfram (2:22:20.960)
destructive interference. Is it possible for this to instruct the engineering of automated proof
Stephen Wolfram (2:22:26.960)
systems? Absolutely. I mean, as a practical matter, I mean, you know, this whole question,
Stephen Wolfram (2:22:31.920)
in fact, Jonathan Gorod has a nice heuristic for automated theorem provers that's based on
Stephen Wolfram (2:22:36.560)
our physics project that is looking for essentially using kind of using energy in our
Stephen Wolfram (2:22:44.400)
models. Energy is kind of level of activity in this hypergraph. And so it's sort of a heuristic
Stephen Wolfram (2:22:51.040)
for automated theorem proving about how do you pick which path to go down that is based on
Stephen Wolfram (2:22:57.440)
essentially physics. And I mean, the thing that gets interesting about this is the way that one
Stephen Wolfram (2:23:03.600)
can sort of have the interplay between, like, for example, a black hole. What is a black hole
Stephen Wolfram (2:23:07.360)
in metamathematics? So the answer is, what is black hole in physics? A black hole in physics
Stephen Wolfram (2:23:12.960)
is where in the simplest form of black hole time ends. That is all, you know, everything is crunched
Stephen Wolfram (2:23:19.600)
down to the space time singularity, and everything just ends up at that singularity. So in our
Stephen Wolfram (2:23:24.960)
models, and that's a little hard to understand in general relativity with continuous mathematics,
Lex Fridman (2:23:29.520)
and what does singularity look like? In our models, it's something very pragmatic. It's just,
Stephen Wolfram (2:23:33.840)
you're applying these rules, time is moving forward. And then there comes a moment where
Stephen Wolfram (2:23:37.760)
the rules, no rules apply. So time stops. It's kind of like the universe dies, that, you know,
Stephen Wolfram (2:23:43.280)
that nothing happens in the universe anymore. Well, in mathematics, that's a decidable theory.
Stephen Wolfram (2:23:49.200)
That's a theory. So theories which have undecidability, which are things like
Stephen Wolfram (2:23:53.280)
arithmetic, set theory, all the serious models, theories in mathematics, they all have the feature
Stephen Wolfram (2:23:58.400)
that there are proofs of arbitrarily long length. In something like Boolean algebra,
Stephen Wolfram (2:24:02.960)
which is a decidable theory, there are, you know, any question in Boolean algebra, you can just go
Stephen Wolfram (2:24:07.680)
crunch, crunch, crunch, and in a known number of steps, you can answer it. You know, satisfiability,
Stephen Wolfram (2:24:13.360)
you know, might be hard, but it's still a bounded number of steps to answer any satisfiability
Stephen Wolfram (2:24:17.840)
problem. And so that's the notion of a black hole in physics where time stops. That's analogous to
Stephen Wolfram (2:24:26.000)
in mathematics where there aren't infinite length proofs, where when in physics, you know, you can
Stephen Wolfram (2:24:32.640)
wander around the universe forever if you don't run into a black hole. If you run into a black
Stephen Wolfram (2:24:36.080)
hole and time stops, you're done. And it's the same thing in mathematics between decidable
Stephen Wolfram (2:24:41.760)
theories and undecidable theories. That's an example. And I think where sort of the attempt
Lex Fridman (2:24:47.360)
to understand, so another question is kind of what is the general activity of metamathematics?
Lex Fridman (2:24:54.400)
What is the bulk theory of metamathematics? So in the literature of mathematics, there are about
Stephen Wolfram (2:24:59.440)
three million theorems that people have published. And those represent, it's kind of on this, it's
Stephen Wolfram (2:25:05.040)
like on the earth, we would be, you know, we've put cities in particular places on the earth,
Lex Fridman (2:25:11.760)
but yet there is ultimately, you know, we know the earth is roughly spherical,
Lex Fridman (2:25:15.440)
and there's an underlying space. And we could just talk about, you know, the world of space
Stephen Wolfram (2:25:20.640)
in terms of where our cities happen to be, but there's actually an underlying space. And so the
Stephen Wolfram (2:25:24.720)
question is, what's that for metamathematics? And as we kind of explore what is, for example,
Stephen Wolfram (2:25:29.360)
for mathematics, which is always likes taking sort of abstract limits. So an obvious abstract
Stephen Wolfram (2:25:34.640)
limit for mathematics to take is the limit of the future of mathematics. That is, what will be,
Stephen Wolfram (2:25:40.480)
you know, the ultimate structure of mathematics. And one of the things that's an empirical
Stephen Wolfram (2:25:44.640)
observation about mathematics that's quite interesting is that a lot of theories in one
Stephen Wolfram (2:25:49.520)
area of mathematics, algebraic geometry or something, might have, they play into another area
Stephen Wolfram (2:25:54.560)
of mathematics. That same kind of fundamental construct seemed to occur in very different
Stephen Wolfram (2:26:00.880)
areas of mathematics. And that's structurally captured a bit with category theory and things
Stephen Wolfram (2:26:04.880)
like that. But I think that there's probably an understanding of this metamathematical space that
Stephen Wolfram (2:26:09.760)
will explain why different areas of mathematics ultimately sort of map into the same thing.
Lex Fridman (2:26:15.200)
And I mean, you know, my little challenge to myself is what's time dilation in metamathematics?
Stephen Wolfram (2:26:21.840)
In other words, as you basically, as you move around in this mathematical space of possible
Stephen Wolfram (2:26:27.440)
statements, you know, how does that moving around? It's basically what's happening is
Stephen Wolfram (2:26:33.280)
that as you move around in the space of mathematical statements, it's like you're
Stephen Wolfram (2:26:36.720)
changing from algebra to geometry to whatever else. And you're trying to prove the same theorem.
Lex Fridman (2:26:42.080)
But as you try, if you keep on moving to these different places, it's slower to prove that
Stephen Wolfram (2:26:46.960)
theorem because you keep on having to translate what you're doing back to where you started from.
Lex Fridman (2:26:50.480)
And that's kind of the beginnings of the analog of time dilation in metamathematics.
Stephen Wolfram (2:26:54.640)
Plus, there's probably fractional dimensions in this space as well.
Stephen Wolfram (2:26:58.000)
Oh, this space is a very messy space. This space is much messier than physical space. I mean,
Stephen Wolfram (2:27:02.960)
even in the models of physics, physical space is very tame compared to branchial space and
Stephen Wolfram (2:27:09.280)
ruleal space. I mean, the mathematical structure, you know, branchial space is probably more like
Stephen Wolfram (2:27:14.160)
Hilbert space, but it's a rather complicated Hilbert space. And ruleal space is more like
Stephen Wolfram (2:27:20.480)
this weird infinity groupoid story of Grothendieck. And, you know, I can explain that a little bit
Stephen Wolfram (2:27:25.520)
because in metamathematical space, a path in metamathematical space is a path between two
Stephen Wolfram (2:27:34.400)
statements is a way to get by proofs, is a way to find a proof that goes from one statement to
Stephen Wolfram (2:27:39.920)
another. And so one of the things you can do, you can think about is between statements, you've got
Stephen Wolfram (2:27:45.360)
proofs and they are paths between statements. Okay, so now you can go to the next level and you
Stephen Wolfram (2:27:50.560)
can ask, what about a mapping from one proof to another? And so that's in category theory,
Stephen Wolfram (2:27:56.480)
that's kind of a higher category, the notion of higher categories where you're mapping not just
Stephen Wolfram (2:28:03.280)
between objects, but you're mapping between the mappings between objects and so on.
Lex Fridman (2:28:07.360)
And so you can keep doing that. You keep saying higher order proofs. I want mappings between
Stephen Wolfram (2:28:12.160)
proofs between proofs and so on. And that limiting structure, oh, by the way, one thing that's very
Stephen Wolfram (2:28:17.360)
interesting is imagine in proof space, you've got these two proofs. And the question is,
Lex Fridman (2:28:22.160)
what is the topology of proof space? In other words, if you take these two paths,
Lex Fridman (2:28:26.480)
can you continuously deform them into each other? Or is there some big hole in the middle that
Stephen Wolfram (2:28:31.040)
prevents you from continuously deforming them one into the other? It's kind of like, you know,
Stephen Wolfram (2:28:35.040)
when you think about some, I don't know, some puzzle, for example, you're moving pieces around
Stephen Wolfram (2:28:39.760)
on some puzzle, and you can think about the space of possible states of the puzzle.
Lex Fridman (2:28:44.000)
And you can make this graph that shows from one state of the puzzle to another state of
Stephen Wolfram (2:28:47.680)
the puzzle and so on. And sometimes you can easily get from one state to any other state,
Lex Fridman (2:28:52.400)
but sometimes there'll be a hole in that space. And there'll be, you know, you always have to
Stephen Wolfram (2:28:56.720)
go around the circuitous route to get from here to there. There won't be any direct way.
Stephen Wolfram (2:29:01.680)
That's kind of a question of whether there's sort of an obstruction in the space. And so the question
Stephen Wolfram (2:29:07.440)
is in proof space, what is the, what are, you know, what does it mean if there's an obstruction in proof
Stephen Wolfram (2:29:14.080)
space? Yeah, I don't even know what an obstruction means in proof space because for it to be an
Stephen Wolfram (2:29:19.600)
obstruction, it should be reachable some other way from some other place, right? So this is like
Stephen Wolfram (2:29:25.040)
an unreachable part of the graph. No, it's not just an unreachable part. It's a part where
Stephen Wolfram (2:29:30.240)
there are paths that go one way, there are paths that go the other way. And this question of
Stephen Wolfram (2:29:34.240)
homotopy in mathematics is this question, can you continuously deform, you know, from one path to
Stephen Wolfram (2:29:39.200)
another path or do you have to go in a jump, so to speak? So it's like if you're going around a
Stephen Wolfram (2:29:44.160)
sphere, for example, if you're going around, I don't know, a cylinder or something, you can
Stephen Wolfram (2:29:48.480)
wind around one way and you can, there's no paths where you can easily deform one path into another
Stephen Wolfram (2:29:55.360)
because it's just sort of sitting on the same side of the cylinder. But when you've got something
Stephen Wolfram (2:29:58.960)
that winds all the way around a cylinder, you can't continuously deform that down to a point
Stephen Wolfram (2:30:03.280)
because it's, it's stuck wrapped around. My intuition about proof spaces, you should be
Stephen Wolfram (2:30:07.360)
able to deform it. I mean that because then otherwise it doesn't even make sense because
Stephen Wolfram (2:30:11.600)
if the topology matters of the way you move about the space that I don't even know what that means.
Stephen Wolfram (2:30:17.200)
Well, what it would mean is that you would have one way of doing a proof of something over here
Stephen Wolfram (2:30:22.320)
in algebra and another way of doing a proof of something over here in geometry. And there would
Stephen Wolfram (2:30:27.120)
not be an intermediate way to map between those proofs. How would that be possible if they started
Stephen Wolfram (2:30:32.800)
the same place and ended the same place? Well, it's the same thing as, you know,
Stephen Wolfram (2:30:37.120)
we've got points on a, you know, if we've got paths on a cylinder.
Lex Fridman (2:30:40.800)
Now I understand how it works in physical space, but it just doesn't,
Stephen Wolfram (2:30:44.320)
it feels like proof space shouldn't have that. Okay. I mean,
Stephen Wolfram (2:30:47.840)
I'm not sure. I don't know. We'll know very soon because we get to do some experiments. This is
Stephen Wolfram (2:30:52.160)
the great thing about this stuff is that in fact, you know, in the next few days,
Stephen Wolfram (2:30:56.960)
I hope to do a bunch of experiments on this. So you're playing like proofs in this kind of space.
Stephen Wolfram (2:31:01.920)
Yes. Yes. I mean, so, you know, this is toy, you know, theories and, you know, we've got
Stephen Wolfram (2:31:07.680)
good. So this kind of segues to perhaps another thing, which is this whole idea of multi computation.
Lex Fridman (2:31:13.200)
So this is another kind of bigger idea that, so, okay, this has to do with how do you make models
Stephen Wolfram (2:31:21.680)
of things? And it's going to, so I've sort of claimed that there've been sort of four epochs
Stephen Wolfram (2:31:28.880)
in the history of making models of things. And this multi computation thing is the fourth,
Stephen Wolfram (2:31:35.440)
is a new epoch. What are the first three? The first one is back in antiquity, ancient Greek
Stephen Wolfram (2:31:41.520)
times. People were like, what's the universe made of? Oh, it's made of, you know, everything is
Lex Fridman (2:31:46.480)
water, Thales, you know, or everything is made of atoms. It's sort of, what are things made of?
Stephen Wolfram (2:31:52.800)
Or the, you know, there are these crystal spheres that represent where the planets are and so on.
Stephen Wolfram (2:31:58.080)
It's like a structural idea of how the universe is constructed. There's no real notion of dynamics.
Stephen Wolfram (2:32:03.120)
It's just, what is the universe? How is the universe made? Then we get to the 1600s and we
Stephen Wolfram (2:32:08.720)
get to the sort of revolution of mathematics being introduced into physics. And then we have this
Stephen Wolfram (2:32:14.720)
kind of idea of you write down some equation. The, what happens in the universe is the solving of
Stephen Wolfram (2:32:21.120)
that equation. Time enters, but it's usually just a parameter. We just can, you know, sort of slide
Stephen Wolfram (2:32:26.720)
it back and forth and say, here's where it is. Okay. Then we come to this kind of computational
Stephen Wolfram (2:32:32.400)
idea that I kind of started really pushing in the early 1980s as a result, you know,
Stephen Wolfram (2:32:39.120)
the things that we were talking about before about complexity, that was my motivation. But
Stephen Wolfram (2:32:43.280)
the bigger story was the story of kind of computational models of things. And the big
Stephen Wolfram (2:32:48.160)
difference there from the mathematical models is, in mathematical models, there's an equation,
Stephen Wolfram (2:32:52.720)
you solve it, you kind of slide time to the place where you want it. In computational models,
Stephen Wolfram (2:32:58.720)
you give the rule and then you just say, go run the rule. And time is not something you get to
Stephen Wolfram (2:33:04.800)
slide. Time is something where it just, you run the rule, time goes in steps. And that's how you
Stephen Wolfram (2:33:11.440)
work out how the system behaves. You don't, time is not just a parameter. Time is something that
Stephen Wolfram (2:33:16.560)
is about the running of these rules. And so there's this computational irreducibility. You can't jump
Stephen Wolfram (2:33:21.920)
ahead in time. But there's still, important thing is there's still one thread of time. It's still
Stephen Wolfram (2:33:27.360)
the case, you know, the cellular automaton state, then it has the next state and the next state and
Lex Fridman (2:33:31.360)
so on. The thing that is kind of, we've sort of tipped off by quantum mechanics in a sense,
Stephen Wolfram (2:33:36.400)
although it actually feeds back even into relativity and things like that, that there's
Stephen Wolfram (2:33:41.760)
these multiple threads of time. And so in this multi computation paradigm, the kind of idea is,
Stephen Wolfram (2:33:47.760)
instead of there being the single thread of time, there are these kind of distributed asynchronous
Stephen Wolfram (2:33:52.240)
threads of time that are happening. And the thing that's sort of different there is if you want to
Stephen Wolfram (2:33:57.920)
know what happened, if you say what happened in the system, in the case of the computational
Stephen Wolfram (2:34:02.480)
paradigm, you just say, well, after a thousand steps, we got this result, right? But in the
Stephen Wolfram (2:34:08.880)
multi computational paradigm, after a thousand steps, not even clear what a thousand steps means,
Stephen Wolfram (2:34:13.200)
because you've got all these different threads of time, but there is no state. There's all these
Stephen Wolfram (2:34:17.600)
different possible, you know, there's all these different paths. And so the only way you can know
Lex Fridman (2:34:22.240)
what happened is to have some kind of observer who is saying, here's how to parse the results
Stephen Wolfram (2:34:27.280)
of what was going on. Right. But that observer is embedded and they don't have a complete picture.
Lex Fridman (2:34:31.600)
So in the case of physics, that's right. Yes. And then in the, but that's, but so the idea is
Stephen Wolfram (2:34:37.120)
that in this multi computation setup, that it's this idea of these multiple threads of time
Lex Fridman (2:34:42.320)
and models that are based on that. And this is similar to what people think about in
Stephen Wolfram (2:34:47.760)
non deterministic computation. So you have a Turing machine. Usually it has a definite state. It
Stephen Wolfram (2:34:52.400)
follows another state, follows another state. But typically what people have done when they
Stephen Wolfram (2:34:56.080)
thought about these kinds of things is they've said, well, there are all these possible paths,
Lex Fridman (2:34:59.760)
and non deterministic Turing machine can follow all these possible paths, but we just want one
Stephen Wolfram (2:35:04.080)
of them. We just want the one that's the winner that factors the number or whatever else. And
Stephen Wolfram (2:35:08.880)
similarly, it's the same story in logic programming and so on, but we say, we've got this goal,
Stephen Wolfram (2:35:13.520)
find us a path to that goal. I just want one path, then I'm happy. Or theorem proving,
Stephen Wolfram (2:35:18.320)
same story. I just want one proof and then I'm happy. What's happening in multi computation
Stephen Wolfram (2:35:23.200)
in physics is we actually care about many paths. And well, there is a case, for example, probabilistic
Stephen Wolfram (2:35:29.440)
programming is a version of multi computation in which you're looking at all the paths. You're just
Stephen Wolfram (2:35:33.920)
asking for probabilities of things. But in a sense in physics, we're taking different kinds of
Stephen Wolfram (2:35:39.280)
samplings. For example, in quantum mechanics, we're taking a different kind of sampling
Stephen Wolfram (2:35:43.680)
of all these multiple paths. But the thing that is notable is that when you're an observer embedded
Stephen Wolfram (2:35:51.280)
in this thing, et cetera, et cetera, et cetera, with various other sort of footnotes and so on,
Stephen Wolfram (2:35:56.080)
it is inevitable that the thing that you parse out of the system looks like general relativity
Lex Fridman (2:36:02.400)
and quantum mechanics. In other words, that just by the very structure of this multi computational
Stephen Wolfram (2:36:07.760)
setup, it inevitably is the case that you have certain emergent laws. Now, why is this perhaps
Stephen Wolfram (2:36:16.720)
not surprising? In thermodynamics and statistical mechanics, there are sort of inevitable emergent
Stephen Wolfram (2:36:21.840)
laws of sort of gas dynamics that are independent of the details of the molecular dynamics,
Stephen Wolfram (2:36:28.320)
sort of the same kind of thing. But I think what happens is what's a sort of a funny thing that I
Stephen Wolfram (2:36:33.440)
just been understanding very recently is when when I kind of introduced this whole sort of
Stephen Wolfram (2:36:39.200)
computational paradigm complexity ish thing back in the 80s, it was kind of like a big downer
Stephen Wolfram (2:36:44.880)
because it's like there's a lot of stuff you can't say about what systems will do.
Lex Fridman (2:36:48.880)
And then what I realized is and then you might say, now we've got multi computation, it's even
Stephen Wolfram (2:36:52.800)
worse. You know, it isn't just one thread of time that we can't explain. It's all these threads of
Stephen Wolfram (2:36:56.960)
time. It can't explain anything. But the following thing happens because there is all this
Stephen Wolfram (2:37:03.120)
irreducibility and any detailed thing you might want to answer, it's very hard to answer. But
Stephen Wolfram (2:37:08.720)
when you have an observer who has certain characteristics like computational boundedness,
Stephen Wolfram (2:37:13.760)
sequentiality of time and so on, that observer only samples certain aspects of this incredible
Stephen Wolfram (2:37:19.920)
complexity going on in this multi computational system. And that observer is sensitive only to
Stephen Wolfram (2:37:25.760)
to some underlying core structure of this multi computational system. There is all this
Stephen Wolfram (2:37:30.960)
irreducible computation going on, all these details. But to that kind of observer, what's
Stephen Wolfram (2:37:36.160)
important is only the core structure of multi computation, which means that observer
Stephen Wolfram (2:37:41.760)
observes comparatively simple laws. And I think it is inevitable that that observer
Stephen Wolfram (2:37:47.520)
observes laws which are mathematically structured like general relativity and quantum
Stephen Wolfram (2:37:51.920)
mechanics, which, by the way, are the same law in our in our model of physics.
Lex Fridman (2:37:56.240)
So that's an explanation why there are simple laws that explain a lot for this observer.
Stephen Wolfram (2:38:01.920)
Potentially, yes. But what the place where this gets really interesting is there are all these
Stephen Wolfram (2:38:07.760)
fields of science where people have kind of gotten stuck, where they say we'd really love to
Stephen Wolfram (2:38:12.480)
have a physics like theory of economics. We'd really love to have a physics like law and
Stephen Wolfram (2:38:16.800)
linguistics. You got to talk about molecular biology here. OK, so where where where does
Stephen Wolfram (2:38:22.560)
multi computation come in for biology? Economics is super interesting, too, but biology. OK,
Stephen Wolfram (2:38:27.040)
let's talk about that. So let's talk about chemistry for a second. OK, so I mean, I have
Stephen Wolfram (2:38:31.760)
to say, you know, this is it's such a weird business for me because, you know, there are
Stephen Wolfram (2:38:35.520)
these kind of paradigmatic ideas and then the actual applications. And it's like I've always
Stephen Wolfram (2:38:39.840)
said, I know nothing about chemistry. I learned all the chemistry I know, you know, the night
Stephen Wolfram (2:38:43.360)
before some exam when I was 14 years old. But I've actually learned a bunch more chemistry.
Lex Fridman (2:38:47.520)
And in Wolfram language these days, we have really pretty nice symbolic representation
Stephen Wolfram (2:38:51.360)
of chemistry. And in understanding the design of that, I've actually, I think, learned a certain
Stephen Wolfram (2:38:55.760)
amount of chemistry. So if you quizzed me on sort of basic high school chemistry, I would
Stephen Wolfram (2:38:59.840)
probably totally fail. But but but OK, so what is chemistry? I mean, chemistry is sort of a
Stephen Wolfram (2:39:06.000)
story of, you know, chemical reactions are like you've got this particular chemical that's
Stephen Wolfram (2:39:11.200)
represented as some graph of, you know, these are these are this configuration of molecules
Stephen Wolfram (2:39:15.840)
with these bonds and so on. And a chemical reaction happens. You've got these sort of
Stephen Wolfram (2:39:20.480)
two graphs. They interact in some way. You've got another graph or multiple other graphs
Stephen Wolfram (2:39:24.720)
out. So that's kind of the sort of the the abstract view of what's happening in chemistry.
Lex Fridman (2:39:30.560)
And so when you do a chemical synthesis, for example, you are given certain sort of these
Stephen Wolfram (2:39:36.000)
are possible reactions that can happen. And you're asked, can you piece together this
Stephen Wolfram (2:39:40.640)
sequence of such reactions, a sequence of such sort of axiomatic reactions usually called name
Stephen Wolfram (2:39:45.120)
reactions in chemistry? Can you piece together a sequence of these reactions so that you get out
Stephen Wolfram (2:39:50.640)
at the end this great molecule you were trying to synthesize? And so that's a story very much
Stephen Wolfram (2:39:55.040)
like theorem proving. And people have done actually they start in the 1960s looking at
Stephen Wolfram (2:40:00.720)
kind of the theorem proving approach to that, although it didn't really it didn't it didn't
Stephen Wolfram (2:40:04.960)
was sort of done too early, I think. But anyway, so that's kind of the view is that that chemistry,
Stephen Wolfram (2:40:09.920)
chemical reactions are the story of of all these different sort of paths of possible things that
Stephen Wolfram (2:40:15.520)
go on. OK, let's let's go to an even lower level. Let's say instead of asking about which species
Stephen Wolfram (2:40:22.640)
of molecules we're talking about, let's look at individual molecules and let's say we're looking
Stephen Wolfram (2:40:26.880)
at individual molecules and they are having chemical reactions and we're building up this
Stephen Wolfram (2:40:31.120)
big graph of all these reactions that are happening. OK, so so then we've got this big
Stephen Wolfram (2:40:36.000)
graph. And by the way, that big graph is incredibly similar to this hypergraph rewriting things.
Stephen Wolfram (2:40:42.400)
In fact, in the underlying theory of multi computation there, these things we call token
Stephen Wolfram (2:40:46.880)
event graphs, which are basically you've broken your state into tokens. Like in the case of a
Stephen Wolfram (2:40:52.640)
hypergraph, you've broken it into hyper edges and each event is just consuming some number of tokens
Lex Fridman (2:40:58.160)
and producing some number of tokens. But then you have to there's a lot of work to be done
Stephen Wolfram (2:41:02.320)
on update rules in terms of what they actually are for chemistry. Yeah, what they offer are
Stephen Wolfram (2:41:08.400)
observed chemistry. Yes, indeed. Yes, indeed. And we've been working on that actually because we
Stephen Wolfram (2:41:12.880)
have this beautiful system and Wolfram language for representing chemistry symbolically. So we
Stephen Wolfram (2:41:17.360)
actually have you know, this is this is an ongoing thing to actually figure out what they are for
Stephen Wolfram (2:41:21.440)
some practical cases. Does that require human injection or can it be automatically discovered
Stephen Wolfram (2:41:27.040)
these update rules? Well, if we can do chemistry better, we could probably discover them
Stephen Wolfram (2:41:30.960)
automatically. But I think in, in reality, right now, it's like there are these particular
Stephen Wolfram (2:41:35.600)
reactions. And really, to understand what's going on, we're probably going to pick a particular
Stephen Wolfram (2:41:39.840)
subtype of chemistry. And just because because let me explain where this is going to the place
Stephen Wolfram (2:41:45.440)
that his his where this is going. So got this whole network of all these molecules,
Stephen Wolfram (2:41:50.880)
having all these reactions and so on. And this is some whole multi computational story because each
Stephen Wolfram (2:41:56.560)
each sort of chemical reaction event is its own separate event. We're saying they will happen
Stephen Wolfram (2:42:02.560)
asynchronously. We're not describing in what order they happen. You know, maybe that order is governed
Stephen Wolfram (2:42:07.120)
by some quantum mechanics thing doesn't really matter. We're just saying they happen in some
Lex Fridman (2:42:11.280)
order. And then we ask, what is the what what's the you know, how do we think about the system?
Stephen Wolfram (2:42:16.720)
Well, this thing is some kind of big multi computational system. The question is what is
Stephen Wolfram (2:42:21.600)
the chemical observer? And one possible chemical observer is all you care about is did you make
Stephen Wolfram (2:42:27.120)
that particular drug molecule? You're just asking, you know, the for the one path. Another thing you
Stephen Wolfram (2:42:31.600)
might care about is I want to know the concentration of each species. I want to know,
Stephen Wolfram (2:42:36.960)
you know, at every stage, I'm going to solve the differential equations that represent the
Stephen Wolfram (2:42:40.960)
concentrations. And I want to know what those all are. But there's more. Because when and it's kind
Stephen Wolfram (2:42:46.240)
of like you're going below and statistical mechanics, there's kind of all these molecules
Stephen Wolfram (2:42:51.760)
bouncing around. And you might say, we're just going to ignore we're just going to look at the
Stephen Wolfram (2:42:57.120)
aggregate densities of certain kinds of molecules. But you can look at a lower level, you can look
Stephen Wolfram (2:43:02.080)
at this whole graph of possible interactions. And so the kind of the idea would be what, you know,
Stephen Wolfram (2:43:08.480)
is the only chemical observer, one who just cares about overall concentrations? Or can there be a
Stephen Wolfram (2:43:14.240)
chemical observer who cares about this network of what happened? And so that the question then is,
Lex Fridman (2:43:20.880)
so let me give an analogy. So this is where I think this is potentially very relevant to molecular
Stephen Wolfram (2:43:25.440)
biology and molecular computing. When we think about a computation, usually, we say it's input,
Stephen Wolfram (2:43:32.000)
it's output, we, you know, or chemistry, we say there's this input, we're going to make this
Stephen Wolfram (2:43:36.320)
molecule as the output. But what if what we actually encode, what if our computation, what
Stephen Wolfram (2:43:42.960)
thing we care about is some part of this dynamic network? What if it isn't just the input and the
Stephen Wolfram (2:43:48.160)
output that we care about? What if there's some dynamics of the network that we care about? Now,
Stephen Wolfram (2:43:52.320)
imagine you're a chemical observer, what is a chemical observer? Well, in molecular biology,
Stephen Wolfram (2:43:57.840)
there are all kinds of weird sorts of observers, there are membranes that exist, that have, you
Stephen Wolfram (2:44:03.280)
know, different kinds of molecules that can bind to them, things like this, it's not obvious that
Stephen Wolfram (2:44:08.080)
the from a human scale, we just measure the concentration of something is the relevant story.
Stephen Wolfram (2:44:13.760)
We can imagine that, for example, when we look at this whole network of possible reactions,
Stephen Wolfram (2:44:18.480)
we can imagine, you know, at a physical level, we can imagine, well, what was the actual momentum
Stephen Wolfram (2:44:22.640)
direction of that of that molecule? What was it which we don't pay any attention to when we're
Stephen Wolfram (2:44:26.880)
just talking about chemical concentrations? What was the orientation of that molecule,
Stephen Wolfram (2:44:31.040)
these kinds of things? And so here's the place where I'm, I have a little suspicion, okay? So
Stephen Wolfram (2:44:36.800)
one of the questions in biology is what matters in biology? And that is, you know, we have all
Stephen Wolfram (2:44:41.600)
these chemical reactions, we have all these, all these molecular processes going on in, you know,
Stephen Wolfram (2:44:46.640)
in biological systems, what matters? And, you know, one of the things is to be able to tell
Lex Fridman (2:44:52.720)
what matters, well, so a big story of the what matters question was what happened in genetics
Stephen Wolfram (2:44:57.600)
in 1953, when DNA, when it was figured out how DNA worked. Because before that time, you know,
Stephen Wolfram (2:45:03.040)
genetics have been all these different effects and complicated things. And then it was realized,
Stephen Wolfram (2:45:07.440)
ah, there's something new, a molecule can store information, which wasn't obvious before that
Stephen Wolfram (2:45:12.480)
time, a single molecule can store information. So there's a place where there can be something
Stephen Wolfram (2:45:17.040)
important that's happening in molecular biology, and it's just in the sequence that's storing
Stephen Wolfram (2:45:21.760)
information in a molecule. So the possibility now is imagine this dynamic network, this, you know,
Stephen Wolfram (2:45:28.720)
causal graphs and multiway causal graphs and so on, that represent all of these different reactions
Stephen Wolfram (2:45:33.920)
between molecules. What if there is some aspect of that, that is storing information that's relevant
Stephen Wolfram (2:45:39.360)
for molecular biology? And the dynamic aspect of that. Yes, that's right. So that it's similar to
Lex Fridman (2:45:45.120)
how the structure of a DNA molecule stores information, it could be the dynamics of the
Stephen Wolfram (2:45:50.480)
system somehow stores information. And this kind of process might allow you to give predictions
Stephen Wolfram (2:45:56.800)
of what that would be. Well, yes, but also imagine that you're trying to do, for example, imagine
Stephen Wolfram (2:46:03.360)
you're trying to do molecular computation. Okay. You might think the way we're going to do molecular
Stephen Wolfram (2:46:08.240)
computation is we're just going to run the thing. We're going to see what came out. We're going to
Stephen Wolfram (2:46:11.600)
see what molecule came out. This is saying that's not the only thing you can do. There is a different
Stephen Wolfram (2:46:16.960)
kind of chemical observer that you can imagine constructing, which is somehow sensitive to this
Stephen Wolfram (2:46:22.240)
dynamic network. Exactly how that works, how we make that measurement, I don't know, but a few
Stephen Wolfram (2:46:27.360)
ideas, but that's what's important, so to speak. And that means, and by the way, you can do the
Stephen Wolfram (2:46:33.200)
same thing even for Turing machines. You can say, if you have a multiway Turing machine, you can say,
Lex Fridman (2:46:39.040)
how do you compute with a multiway Turing machine? You can't say, well, we've got this input and this
Stephen Wolfram (2:46:43.600)
output because the thing has all these threads of time and it's got lots of outputs. And so then you
Stephen Wolfram (2:46:48.640)
say, well, what does it even mean to be a universal multiway Turing machine? I don't fully know the
Stephen Wolfram (2:46:53.200)
answer to that. It's an interesting idea. It would freak Turing out for sure, because then the
Stephen Wolfram (2:46:59.200)
dynamics of the trajectory of the computation matters. Yes. Yes. I mean, but the thing is
Stephen Wolfram (2:47:05.840)
that that, so this is again, a story of what's the observer, so to speak. In chemistry, what's
Stephen Wolfram (2:47:10.560)
the observer there? Now to give an example of where that might matter, a very sort of present
Stephen Wolfram (2:47:16.480)
day example is in immunology, where we have whatever it is, 10 billion different kinds of
Stephen Wolfram (2:47:23.840)
antibodies that are all these different shapes and so on. We have a trillion different kinds of T
Stephen Wolfram (2:47:29.680)
cell receptors that we produce. And the traditional theory of immunology is this clonal
Stephen Wolfram (2:47:37.120)
selection theory where we are constantly producing, randomly producing all these different antibodies.
Lex Fridman (2:47:42.320)
And as soon as one of them binds to an antigen, then that one gets amplified and we produce more
Stephen Wolfram (2:47:46.880)
of that antibody and so on. Back in the 1960s, an immunologist called Nils Joerner, who was the guy
Stephen Wolfram (2:47:53.920)
who invented monoclonal antibodies, various other things, kind of had this network theory of the
Stephen Wolfram (2:47:59.520)
immune system where it would be like, well, we produce antibodies, but then we produce antibodies
Stephen Wolfram (2:48:04.240)
to the antibodies, anti antibodies, and we produce anti anti antibodies. And we get this whole dynamic
Stephen Wolfram (2:48:09.120)
network of interactions between different immune system cells. And that was kind of a qualitative
Stephen Wolfram (2:48:16.400)
theory at that time. And I've been a little disappointed because I've been studying immunology
Stephen Wolfram (2:48:21.360)
a bit recently. And I knew something about this like 35 years ago or something. And I knew,
Stephen Wolfram (2:48:26.080)
you know, I'd read a bunch of the books and I talked to a bunch of the people and so on.
Lex Fridman (2:48:29.280)
And it was like an emerging theoretical immunology world. And then I look at the books now,
Lex Fridman (2:48:35.280)
and they're very thick because they've got, you know, there's just a ton known about immunology
Stephen Wolfram (2:48:39.760)
and, you know, all these different pathways, all these different details and so on.
Lex Fridman (2:48:43.680)
But the theoretical sections seem to have shrunk. And so it's so the question is, what, you know,
Stephen Wolfram (2:48:51.440)
for example, immune memory, where is the where does the immune memory reside? Is it actually
Stephen Wolfram (2:48:55.680)
some cells sitting in our bone marrow that is, you know, living for the whole of our lives that's
Stephen Wolfram (2:48:59.920)
going to spring into action as soon as we're shown the same antigen? Or is it something different
Stephen Wolfram (2:49:05.120)
from that? Is it something more dynamic? Is it something more like some network of interactions
Stephen Wolfram (2:49:09.520)
between these different kinds of immune system cells and so on? And it's known that there are
Stephen Wolfram (2:49:14.000)
plenty of interactions between T cells and, you know, there's plenty of dynamics. But what the
Stephen Wolfram (2:49:19.040)
consequence of that dynamics is, is not clear. And to have a qualitative theory for that doesn't
Stephen Wolfram (2:49:25.840)
seem to exist. In fact, I was just been trying to study this. So I'm quite incomplete in my study
Stephen Wolfram (2:49:30.240)
of these things. But I was a little bit taken aback because I've been looking at these things
Lex Fridman (2:49:34.320)
and it's like, and then they get to the end where they have the most advanced theory that they've
Stephen Wolfram (2:49:37.680)
got. And it turns out it's a cellular automaton theory. It's like, okay, well, at least I understand
Stephen Wolfram (2:49:43.920)
that theory. But but, you know, I think that the possibility is that in that this is a place where
Stephen Wolfram (2:49:52.160)
if you want to know, you know, explain roughly how the immune system works, it ends up being
Stephen Wolfram (2:49:56.720)
this sort of dynamic network. And then the the, you know, the immune consciousness, so to speak,
Stephen Wolfram (2:50:02.240)
the observer ends up being something that, you know, in the end, it's kind of like, does the
Stephen Wolfram (2:50:06.960)
human get sick or whatever? But it's a it's something which is a complicated story that
Stephen Wolfram (2:50:12.080)
relates to this whole sort of dynamic network and so on. And I think that's another place where this
Stephen Wolfram (2:50:16.800)
kind of notion of where I think multi computation has the possibility. See, one of the things, okay,
Stephen Wolfram (2:50:23.040)
you can end up with something where yes, there is a general relativity in there. But it turns up,
Lex Fridman (2:50:27.520)
but it may turn out that the observer who sees general relativity in the immune system is an
Stephen Wolfram (2:50:33.360)
observer that's irrelevant to what we care about about the immune system. I mean, it could be yes,
Stephen Wolfram (2:50:37.600)
there is some effect where, you know, there's some, you know, time dilation of T cells interacting
Stephen Wolfram (2:50:43.280)
with whatever. But it's like, that's an effect that's just irrelevant. And the thing we actually
Stephen Wolfram (2:50:47.600)
care about is things about, you know, what happens when you have a vaccine that goes into some place
Lex Fridman (2:50:52.880)
in shapespace? And, you know, how does that affect other places in shapespace? And how does that spread?
Stephen Wolfram (2:50:57.760)
You know, what's the what's the analog of the speed of light in shapespace, for example, that's an
Stephen Wolfram (2:51:01.840)
that's an important issue. If you have one of these dynamic theories, it's like, you know, you
Stephen Wolfram (2:51:06.160)
you're poking to shapespace by having, you know, let's say, a vaccine or something that has a
Stephen Wolfram (2:51:10.400)
particular configuration in shapespace. How, how quickly as this dynamic network spreads out, how
Lex Fridman (2:51:16.960)
quickly do you get sort of other antibodies in different places in shapespace, things like that?
Stephen Wolfram (2:51:22.160)
When you say shapespace, you mean the shape of the molecules? And then, so this is like,
Stephen Wolfram (2:51:27.520)
could be deeply connected to the protein and multi protein folding, all of that kind of stuff.
Stephen Wolfram (2:51:32.080)
To be able to say something interesting about the the dance of proteins that
Lex Fridman (2:51:36.240)
Right, exactly.
Stephen Wolfram (2:51:36.960)
then actually has an impact on helping develop drugs, for example, or has an impact on
Lex Fridman (2:51:44.800)
virology, immunology, helping.
Stephen Wolfram (2:51:46.800)
Well, I think the big thing is, you know, when we think about molecular biology, the you know,
Stephen Wolfram (2:51:54.080)
what, what is the qualitative way to think about it? You know, in other words, is it chemical
Stephen Wolfram (2:51:58.640)
reaction networks? Is it, you know, genetics, you know, DNA, big, you know, big news, it's kind of
Stephen Wolfram (2:52:05.920)
there's a digital aspect to the whole thing. You know, what is the qualitative way to think about
Lex Fridman (2:52:10.800)
how things work in biology? You know, when we think about, I don't know, some phenomenon like
Stephen Wolfram (2:52:15.200)
aging or something, which is a big, complicated phenomenon, which just seems to have all these
Stephen Wolfram (2:52:18.880)
different tentacles. Is it really the case that that can be thought about in some, you know,
Stephen Wolfram (2:52:23.600)
without DNA, when people were describing, you know, genetic phenomena, there were, you know,
Stephen Wolfram (2:52:29.040)
dominant recessive, this, that and the other got very, very complicated. And then people realize,
Stephen Wolfram (2:52:33.680)
oh, it's just, you know, and what is a gene and so on and so on and so on. Then people realize
Stephen Wolfram (2:52:38.400)
it's just base pairs. And there's this digital representation. And so the question is, what is
Lex Fridman (2:52:42.480)
the overarching representation that we can now start to think about using a molecular biology?
Stephen Wolfram (2:52:47.200)
I don't know how this will work out. And this is again, one of these things where, and the place
Stephen Wolfram (2:52:51.920)
where that gets important is, you know, maybe molecular biology is doing molecular computing
Stephen Wolfram (2:52:58.000)
by using some dynamic process that is something where it is very happily saying, oh, I just got
Stephen Wolfram (2:53:03.760)
a result. It's in the dynamic structure of this network. Now I'm going to go and do some other
Stephen Wolfram (2:53:07.680)
thing based on that result, for example. But we're like, oh, I don't know what's going on. You know,
Stephen Wolfram (2:53:12.320)
it's just, we just measured the levels of these chemicals and we couldn't conclude anything.
Lex Fridman (2:53:17.520)
But it just, we're looking at the wrong thing. And so that's the, that's kind of the potential
Stephen Wolfram (2:53:22.880)
there. And it's, I mean, these things are, I don't know, it's for me, it's like, I've not really,
Stephen Wolfram (2:53:30.080)
that was not a view. I mean, I've thought about molecular computing for ages and ages and ages.
Lex Fridman (2:53:34.400)
And I've always imagined that the big story is kind of the original promise of nanotechnology
Lex Fridman (2:53:40.400)
of like, can we make a molecular scale constructor that will just build a molecule in any shape?
Stephen Wolfram (2:53:45.920)
I don't think I'm now increasingly concluding that's not the big point. The big point is
Stephen Wolfram (2:53:50.880)
something more dynamic. That will be an interesting endpoint for any of these things. But that's
Stephen Wolfram (2:53:56.000)
perhaps not the thing, you know, because the one example we have in molecular computing
Stephen Wolfram (2:54:00.160)
that's really working is us biological organisms. And, you know, maybe the thing that's important
Stephen Wolfram (2:54:05.840)
there is not this, you know, what chemicals do you make, so to speak, but more this kind of
Stephen Wolfram (2:54:10.880)
dynamic process. The dynamic process. And then you can have a good model like the hypergraph to then
Stephen Wolfram (2:54:15.440)
explore what, like simulate again, make predictions. And if they, I think just have a way to reason
Stephen Wolfram (2:54:22.640)
about biology. I mean, it's hard, you know, but first of all, biology doesn't have theories like
Stephen Wolfram (2:54:28.160)
physics. You know, physics is a much more successful sort of global theory kind of area.
Stephen Wolfram (2:54:34.080)
You know, biology, what are the global theories of biology? Pretty much Darwinian evolution. That's
Stephen Wolfram (2:54:39.120)
the only global theory of biology. You know, are there any other theories just say, well,
Stephen Wolfram (2:54:43.440)
the kidneys work this way, this thing works this way and so on. There isn't, I suppose,
Stephen Wolfram (2:54:47.840)
another global theory is digital information in DNA. That's another sort of global fact about
Stephen Wolfram (2:54:52.640)
biology. But the difficult thing to do is to match something you have a model of in the hypergraph
Stephen Wolfram (2:55:00.400)
to the actual, like how do you discover the theory? How do you discover the theory? Okay,
Stephen Wolfram (2:55:05.120)
you have something that looks nice and makes sense, but like you have to match it to validation.
Lex Fridman (2:55:10.080)
Oh, sure. Right. And that's tricky because you're walking around in the dark.
Stephen Wolfram (2:55:15.280)
Not entirely. I mean, so, you know, for example, in what we've been trying to think about is
Stephen Wolfram (2:55:20.320)
take actual chemical reactions. Okay. So, you know, one of my goals is can I compute the primes
Stephen Wolfram (2:55:26.960)
with molecules? Okay. If I can do that, then I kind of, maybe I can compute things. And, you know,
Stephen Wolfram (2:55:33.200)
there's this nice automated lab, these guys, these Emerald Cloud Lab people have built with
Stephen Wolfram (2:55:37.520)
Wolfram language and so on. That's an actual physical lab and you send it a piece of Wolfram
Stephen Wolfram (2:55:42.000)
language code and it goes and, you know, actually does physical experiments. And so one of my goals,
Stephen Wolfram (2:55:47.760)
because I'm not a test tube kind of guy, I'm more of a software kind of person, is can I make
Stephen Wolfram (2:55:52.880)
something where, you know, in this automated lab, we can actually get it so that there's some gel
Stephen Wolfram (2:55:57.840)
that we made and, you know, the positions of the stripes are the primes. I love it. Yeah.
Stephen Wolfram (2:56:02.720)
I mean, that would be an example of where, and that would be with a particular, you know,
Stephen Wolfram (2:56:08.720)
framework for actually doing the molecular computing, you know, with particular kinds
Stephen Wolfram (2:56:13.120)
of molecules. And there's a lot of kind of ambient technological mess, so to speak,
Stephen Wolfram (2:56:18.000)
associated with, oh, is it carbon? Is it this? Is it that? You know, is it important that there's
Stephen Wolfram (2:56:22.240)
a bromine atom here, et cetera, et cetera, et cetera. This is all chemistry that I don't know
Stephen Wolfram (2:56:26.240)
much about. And, you know, that's a sort of, you know, unfortunately that's down at the level,
Stephen Wolfram (2:56:32.000)
you know, I would like to be at the software level, not at the level of the transistors,
Lex Fridman (2:56:36.080)
so to speak. But in chemistry, you know, there's a certain amount we have to do, I think, at the
Stephen Wolfram (2:56:40.560)
level of transistors before we get up to being able to do it. Although, you know, the automated
Stephen Wolfram (2:56:45.280)
labs certainly help in setting that up. I talked to a guy named Charles Hoskinson.
Stephen Wolfram (2:56:52.960)
He mentioned that he's collaborating with you. He's an interesting guy. He sends me papers on
Stephen Wolfram (2:56:58.640)
speaking of automated theorem proving a lot. He's exceptionally well read on that area as well.
Lex Fridman (2:57:04.160)
So what's the nature of your collaboration with him? He's the creator of Cardano.
Stephen Wolfram (2:57:08.240)
What's the nature of the collaboration between Cardano and the whole space of blockchain and
Stephen Wolfram (2:57:13.680)
Wolfram, Wolfram Alpha, Wolfram blockchain, all that kind of stuff? Well, OK, we're segueing to a
Stephen Wolfram (2:57:20.000)
slightly different world. But so although not completely unconnected. Right. The whole thing
Stephen Wolfram (2:57:26.240)
is somehow connected. I know. I mean, you know, the strange thing in my life is I've sort of
Stephen Wolfram (2:57:31.520)
alternated between doing basic science and doing technology about five times in my life so far.
Lex Fridman (2:57:36.960)
And the thing that's just crazy about it is, you know, every time I do one of these alternations,
Stephen Wolfram (2:57:42.160)
I think there's not going to be a way back to the other thing. And like I thought for this
Stephen Wolfram (2:57:46.160)
physics project, I thought, you know, we're doing fundamental theory of physics. Maybe it'll have
Stephen Wolfram (2:57:50.640)
an application in 200 years. But now I've realized actually this multi computation idea is is
Stephen Wolfram (2:57:57.840)
applicable here now. It's and in fact, it's also giving us this way. I'll just mention one other
Stephen Wolfram (2:58:03.440)
thing and then talk about blockchain. The the question of actually that relates to several
Stephen Wolfram (2:58:11.040)
different things. But but one of the things about about OK, so our Wolfram language, which is our
Stephen Wolfram (2:58:18.960)
attempt to kind of represent everything in the world computationally. And it's the thing I kind
Stephen Wolfram (2:58:23.200)
of started building 40 years ago in the form of actual Wolfram language 35 years ago. It's kind
Stephen Wolfram (2:58:29.760)
of this idea of can we can we express things about the world in computational terms? And, you know,
Stephen Wolfram (2:58:37.520)
we've come a long way in being able to do that. Wolfram Alpha is kind of the consumer version of
Stephen Wolfram (2:58:42.000)
that where you're just using natural language as input. The and it turns it into our symbolic
Stephen Wolfram (2:58:46.800)
language. And that's, you know, the symbolic language Wolfram language is what people use
Lex Fridman (2:58:51.520)
and have been using for the last 33 years. Actually, Mathematica, which is its first
Stephen Wolfram (2:58:56.160)
instantiation, will be one third of a century old in in October. And that it's it's kind of
Stephen Wolfram (2:59:05.360)
interesting. What do you mean one third of a century? I mean, 33 or 30? What are we? 33 and a
Stephen Wolfram (2:59:09.920)
third. 33 and a third. So I've never heard of anyone celebrating that anniversary, but I like
Stephen Wolfram (2:59:17.440)
it. I know. A third of a century, though, it's it's kind of get many, many slices of a century
Stephen Wolfram (2:59:22.000)
that are interesting. But but, you know, I think that the the thing that's really striking about
Stephen Wolfram (2:59:26.240)
that is that means, you know, including the whole sort of technology stack I built around that's
Stephen Wolfram (2:59:30.640)
about 40 years old. And that means it's a significant fraction of the total age of the
Stephen Wolfram (2:59:34.480)
computer industry. And it's I mean, I think it's cool that we can still run, you know,
Stephen Wolfram (2:59:39.360)
Mathematica version one programs today and so on. And we've sort of maintained compatibility.
Lex Fridman (2:59:44.960)
And we've been just building this big tower all those years of just more and more and more
Stephen Wolfram (2:59:49.760)
computational capabilities. It's sort of interesting. We just made this this picture
Stephen Wolfram (2:59:54.160)
of kind of the different kind of threads of of of computational content, of, you know,
Stephen Wolfram (2:59:59.280)
mathematical content and and, you know, all sorts of things with, you know, data and graphs and
Stephen Wolfram (30:03.520)
rapidly rotating black hole that in which one could actually see some phenomenon where one
Stephen Wolfram (30:08.480)
can say, yes, these don't come out the way one would expect based on having a continuous structure
Stephen Wolfram (30:14.640)
of spacetime, that is something where you can kind of see through to the discrete structure.
Stephen Wolfram (30:19.840)
We don't know that yet. So can you maybe elaborate a little bit deeper how a microscope that can see
Stephen Wolfram (30:25.280)
the 10 to the minus 100, how rotating black holes and presumably the detailed accurate
Lex Fridman (30:36.320)
detection of gravitational waves from such black holes can reveal the discreteness of space?
Stephen Wolfram (30:42.800)
Okay, first thing is, what is a black hole? Actually, we need to go a little bit further in
Stephen Wolfram (30:47.360)
the story of what spacetime is, because I explained a little bit about what space is,
Lex Fridman (30:50.560)
but I didn't talk about what time is. And that's sort of important in understanding spacetime,
Lex Fridman (30:55.600)
so to speak. And your sense is both space and time in the story are discrete.
Stephen Wolfram (30:59.920)
Absolutely. Absolutely. But it's a complicated story. And needless to say.
Lex Fridman (31:05.360)
Well, it's simple at the bottom. It's very simple at the bottom. In the end,
Stephen Wolfram (31:11.520)
it's simple but deeply abstract. And something that is simple in conception,
Lex Fridman (31:18.320)
but kind of wrapping one's head around what's going on is pretty hard. So first of all,
Stephen Wolfram (31:24.480)
we have this. So I've described these kind of atoms of space and their connections.
Stephen Wolfram (31:29.040)
You can think about these things as a hypergraph. A graph is just you connect nodes to nodes,
Lex Fridman (31:34.000)
but a hypergraph you can have not just individual friends to friends, but you can have these
Stephen Wolfram (31:40.800)
triplets of friends or whatever else. And so we're just saying that's just the relations
Stephen Wolfram (31:47.200)
between atoms of space are the hyperedges of the hypergraph. And so we got some big collection of
Stephen Wolfram (31:52.960)
these atoms of space, maybe 10 to the 400 or something in our universe. And that's the structure
Stephen Wolfram (31:59.440)
of space. And every feature of what we experience in the world is a feature of that hypergraph,
Lex Fridman (32:07.120)
that spatial hypergraph. So then the question is, well, what does that spatial hypergraph do?
Stephen Wolfram (32:12.240)
Well, the idea is that there are rules that update that spatial hypergraph. And in a cellular
Stephen Wolfram (32:18.800)
automaton, you've just got this line of cells and you just say at every step, at every time step,
Stephen Wolfram (32:23.760)
you've got fixed time steps, fixed array of cells. At every step, every cell gets updated
Stephen Wolfram (32:29.120)
according to a certain rule. And that's the way it works. Now in this hypergraph, it's sort of
Stephen Wolfram (32:36.240)
vaguely the same kind of thing. We say every time you see a little piece of hypergraph that looks
Stephen Wolfram (32:40.800)
like this, update it to one that looks like this. So just keep rewriting this hypergraph. Every time
Stephen Wolfram (32:47.120)
you see something that looks like that, anywhere in the universe, it gets rewritten. Now, one thing
Stephen Wolfram (32:51.920)
that's tricky about that, which we'll come to, is this multi computational idea, which has to do
Stephen Wolfram (32:56.640)
with you're not saying in some kind of lockstep way, do this one, then this one, then this one.
Stephen Wolfram (33:02.560)
It's just whenever you see one you can do, you can go ahead and do it. And that leads one not to
Stephen Wolfram (33:07.920)
have a single thread of time in the universe. Because if you knew which one to do, you just say,
Stephen Wolfram (33:13.440)
okay, we do this one, then we do this one, then we do this one. But if you say, just do whichever
Stephen Wolfram (33:17.360)
one you feel like, you end up with these multiple threads of time, these kind of multiple histories
Stephen Wolfram (33:21.520)
of the universe, depending on which order you happen to do the things you could do in.
Lex Fridman (33:26.000)
So it's fundamentally asynchronous and parallel.
Lex Fridman (33:28.880)
Yes. Yes.
Stephen Wolfram (33:30.240)
Which is very uncomfortable for the human brain that seeks for things to be sequential.
Lex Fridman (33:35.200)
Yes.
Lex Fridman (33:35.680)
And synchronous.
Lex Fridman (33:36.880)
Right. Well, I think that this is part of the story of consciousness,
Stephen Wolfram (33:42.480)
is I think the key aspect of consciousness that is important for sort of parsing the universe,
Stephen Wolfram (33:48.400)
is this point that we have a single thread of experience. We have a memory of what happened
Stephen Wolfram (33:53.600)
in the past. We can say something, predict something about the future, but there's a single
Stephen Wolfram (33:57.600)
thread of experience. And it's not obvious it should work that way. I mean, we've got 100
Stephen Wolfram (34:00.880)
billion neurons in our brains and they're all firing at all kinds of different ways.
Lex Fridman (34:04.480)
But yet, our experience is that there is the single thread of time that goes along. And I
Stephen Wolfram (34:12.880)
think that one of the things I've kind of realized with a lot more clarity in the last year is the
Stephen Wolfram (34:18.000)
fact that the fact that we conclude that the universe has the laws it has is a consequence
Stephen Wolfram (34:24.240)
of the fact that we have consciousness the way we have consciousness. And so, just to go on with
Stephen Wolfram (34:31.120)
kind of the basic setup, so we've got this spatial hypergraph, it's got all these atoms of space,
Stephen Wolfram (34:38.160)
they're getting these little clumps of atoms of space, they're getting turned into other clumps
Stephen Wolfram (34:41.200)
of atoms of space, and that's happening everywhere in the universe all the time. And so, one thing
Stephen Wolfram (34:45.040)
that's a little bit weird is there's nothing permanent in the universe. The universe is getting
Stephen Wolfram (34:49.280)
rewritten everywhere all the time. And if it wasn't getting rewritten, space wouldn't be knitted
Stephen Wolfram (34:53.840)
together. That is, space would just fall apart. There wouldn't be any way in which we could say
Stephen Wolfram (34:58.560)
this part of space is next to this part of space. One of the things that people were confused about
Stephen Wolfram (35:04.880)
back in antiquity, the ancient Greek philosophers and so on, is how does motion work? How can it be
Stephen Wolfram (35:11.440)
the case that you can take a thing that we can walk around and it's still us when we walked a
Stephen Wolfram (35:16.800)
foot forward, so to speak? And in a sense, with our models, that's again a question because it's
Stephen Wolfram (35:23.040)
a different set of atoms of space. When I move my hand, it's moving into a different set of atoms
Stephen Wolfram (35:29.200)
of space. It's having to be recreated. The thing itself is not there. It's being continuously
Stephen Wolfram (35:35.360)
recreated all the time. Now, it's a little bit like waves in an ocean, vortices in a fluid,
Stephen Wolfram (35:40.560)
which again, the actual molecules that exist in those are not what define the identity of the
Stephen Wolfram (35:46.080)
thing. But this idea that there can be pure motion, that it is even possible for an object
Stephen Wolfram (35:55.280)
to just move around in the universe and not change, it's not self evident that such a thing
Stephen Wolfram (36:00.480)
should be possible. And that is part of our perception of the universe is that we parse
Stephen Wolfram (36:06.560)
those aspects of the universe where things like pure motion are possible. Now, pure motion,
Stephen Wolfram (36:11.360)
even in general relativity, the theory of gravity, pure motion is a little bit of a complicated
Stephen Wolfram (36:16.400)
thing. I mean, if you imagine your average teacup or something approaching a black hole,
Lex Fridman (36:21.760)
it is deformed and distorted by the structure of space time. And to say, is it really pure motion?
Stephen Wolfram (36:27.600)
Is it that same teacup that's the same shape? Well, it's a bit of a complicated story. And this
Stephen Wolfram (36:32.320)
is a more extreme version of that. So anyway, the thing that's happening is we've got space,
Stephen Wolfram (36:38.880)
we've got this notion of time. So time is this kind of this rewriting of the hypergraph. And one
Stephen Wolfram (36:45.360)
of the things that's important about that time is this sort of computational irreducible process.
Stephen Wolfram (36:50.000)
There's something, you know, time is not something where it's kind of the mathematical view of time
Stephen Wolfram (36:56.080)
tends to be time is just to coordinate. We can, you know, slide a slider, turn a knob,
Lex Fridman (37:01.440)
and we'll change the time that we've got in this equation. But in this picture of time,
Stephen Wolfram (37:06.800)
that's not how it works at all. Time is this inexorable, irreducible kind of set of computations
Stephen Wolfram (37:12.960)
that go on, that go from where we are now to the future. And one of the things that is, again,
Stephen Wolfram (37:20.240)
something one sort of has to break out of is your average trained physicist like me says,
Stephen Wolfram (37:25.200)
you know, space and time are the same kind of thing. They're related by, you know,
Stephen Wolfram (37:29.200)
the Poincare group and Lorentz transformations and relativity and all these kinds of things.
Stephen Wolfram (37:34.160)
And, you know, space and time, you know, there are all these kind of sort of folk stories you
Stephen Wolfram (37:38.880)
can tell about why space and time are the same kind of thing. In this model, they're fundamentally
Stephen Wolfram (37:43.440)
not the same kind of thing. Space is this kind of sort of connections between these atoms of space.
Stephen Wolfram (37:49.360)
Time is this computational process. So the thing that the first sort of surprising thing is, well,
Stephen Wolfram (37:55.040)
it turns out you get relativity anyway. And the reason that happens, there are a few bits and
Stephen Wolfram (38:00.160)
pieces here which one has to understand. But the fundamental point is if you are an observer
Stephen Wolfram (38:06.560)
embedded in the system that are part of this whole story of things getting updated in this way and
Stephen Wolfram (38:12.720)
that, there's sort of a limit to what you can tell about what's going on. And really, in the end,
Stephen Wolfram (38:18.160)
the only thing you can tell is what are the causal relationships between events. So an event in this
Stephen Wolfram (38:24.720)
sort of an elementary event is a little piece of hypergraph got rewritten. And that means a few
Stephen Wolfram (38:31.200)
hyper edges of the hypergraph were consumed by the event and you produce some other hyper edges.
Lex Fridman (38:36.720)
And that's an elementary event. And so then the question is what we can tell is kind of what the
Stephen Wolfram (38:43.520)
network of causal relationships between elementary events is. That's the ultimate thing,
Stephen Wolfram (38:48.080)
the causal graph of the universe. And it turns out that, well, there's this property of causal
Stephen Wolfram (38:53.920)
invariance that is true of a bunch of these models and I think is inevitably true for a variety of
Stephen Wolfram (38:59.840)
reasons that makes it be the case that it doesn't matter kind of if you are sort of saying, well,
Stephen Wolfram (39:08.160)
I've got this hypergraph and I can rewrite this piece here and this piece here and I do them all
Stephen Wolfram (39:12.160)
in different orders. When you construct the causal graph for each of those orders that you choose to
Stephen Wolfram (39:17.760)
do things in, you'll end up with the same causal graph. And so that's essentially why, well,
Stephen Wolfram (39:24.480)
that's in the end why relativity works. It's why our perception of space and time is as having
Stephen Wolfram (39:31.920)
this kind of connection that relativity says they should have. And that's kind of how that works.
Stephen Wolfram (39:37.760)
I think I'm missing a little piece. If we can go there again, you said the fact that the
Stephen Wolfram (39:42.480)
observer is embedded in this hypergraph, what's missing? What is the observer not able to state
Stephen Wolfram (39:50.400)
about this universe of space and time? If you look from the outside, you can say,
Stephen Wolfram (39:55.440)
oh, I see this particular place was updated and then this one was updated and I'm seeing which
Stephen Wolfram (3:00:05.360)
whatever else. And what you see in this picture is about the first 10 years. It's kind of like
Stephen Wolfram (3:00:10.160)
it's just a few threads. And then then about maybe 15, 20 years ago, it kind of explodes
Stephen Wolfram (3:00:16.160)
in this whole collection, different threads of all these different capabilities that are now
Stephen Wolfram (3:00:20.400)
part of open language and representing different things in the world. But the thing that was super
Stephen Wolfram (3:00:25.760)
lucky in some sense is it's all based on one idea. It's all based on the idea of symbolic expressions
Lex Fridman (3:00:31.840)
and transformation rules for symbolic expressions, which was kind of what I originally
Stephen Wolfram (3:00:36.240)
put into this SMP system back in 1979 that was a predecessor of the whole open language stack.
Lex Fridman (3:00:42.880)
So that idea was an idea that I got from sort of trying to understand mathematical logic and so on.
Stephen Wolfram (3:00:48.880)
It was my attempt to kind of make a general human comprehensible model of computation
Stephen Wolfram (3:00:54.880)
of just everything is a symbolic expression. And all you do is transform symbolic expressions.
Stephen Wolfram (3:01:00.000)
And, you know, in in retrospect, I was very lucky that I understood as little as I understood then,
Stephen Wolfram (3:01:06.960)
because had I understood more, I would have been completely freaked out about all the different
Stephen Wolfram (3:01:11.520)
ways that that kind of model can can fail. Because what do you do when you have a symbolic
Stephen Wolfram (3:01:17.680)
expression, you make transformations for symbolic expressions? Well, for example, one question is,
Stephen Wolfram (3:01:22.320)
there may be many transformations that could be made in a very multi computational kind of way.
Lex Fridman (3:01:26.800)
But what we're doing is picking, we're using the first transformation
Stephen Wolfram (3:01:30.400)
that applies. And we keep doing that until we reach a fixed point. And that's the result. And
Stephen Wolfram (3:01:35.840)
that's kind of a very, it's kind of a way of sort of sliding around the edge of multi computation.
Lex Fridman (3:01:42.080)
And back when I was working on SMP and things, I actually thought about these questions about
Stephen Wolfram (3:01:46.800)
about how, you know, how, what determines the this kind of evaluation path. So for example,
Stephen Wolfram (3:01:52.560)
you know, you work out Fibonacci, you know, Fibonacci is a recursive thing, f of n is f of
Stephen Wolfram (3:01:57.040)
n minus one plus f of n minus two, and you get this whole tree of recursion, right? And there's
Stephen Wolfram (3:02:02.000)
the question of how do you evaluate that tree of recursion? Do you do it sort of depth first,
Stephen Wolfram (3:02:06.400)
where you go all the way down one side? Do you do it breadth first, where you're kind of collecting
Stephen Wolfram (3:02:10.640)
the terms together, where you know that, you know, f of eight plus f of seven, f of seven,
Stephen Wolfram (3:02:14.640)
plus f of six, you can collect the f of sevens, and so on. These are, you know, I didn't realize
Stephen Wolfram (3:02:20.160)
that at the time, it's kind of funny, I was working on on gauge field theories back in 1979.
Lex Fridman (3:02:25.040)
And I was also working on the evaluation model in SMP. And they're the same problem. But it took me
Stephen Wolfram (3:02:31.280)
40 more years to realize that. And this question about how you do this sort of evaluation front,
Stephen Wolfram (3:02:37.120)
that's a question of reference frames. It's a question of kind of the story of I mean,
Lex Fridman (3:02:42.640)
that that's, that is basically this question of, in what order is the universe evaluated?
Lex Fridman (3:02:48.240)
And that's, and so what you realize is, there's this whole sort of world of different kinds of
Stephen Wolfram (3:02:52.960)
computation that you can do, sort of multi computationally. And that's a, that's an
Stephen Wolfram (3:02:57.440)
interesting thing. It has a lot of implications for distributed computing, and so on. It also has
Stephen Wolfram (3:03:01.680)
a potential implication for blockchain, which we haven't fully worked out, which is, and this is
Stephen Wolfram (3:03:06.400)
not what we're doing with Cardano, but but this is a different thing. The this is something where
Stephen Wolfram (3:03:13.760)
one of the questions is, when you have, in a sense, blockchain is a deeply sequentialized
Stephen Wolfram (3:03:19.840)
story of time. Because in blockchain, there's just one copy of the ledger. And you're saying,
Stephen Wolfram (3:03:26.000)
this is what happened, you know, time has progressed in this way. And there are little
Stephen Wolfram (3:03:29.760)
things around the edges, as you try and reach consensus and so on. And, and, you know, actually,
Stephen Wolfram (3:03:34.880)
we just recently, we've had this little conference we organized about the theory of distributed
Stephen Wolfram (3:03:39.920)
consensus, because I realized that a bunch of interesting things that some of our science can
Stephen Wolfram (3:03:44.160)
tell one about that. But that's a different let's let's not go down that that part. Yeah,
Lex Fridman (3:03:48.000)
but distributed consensus that still has a sequential there's like, there's still
Stephen Wolfram (3:03:51.520)
sequentiality. So don't tell me you're thinking through like how to apply multi computation to
Stephen Wolfram (3:03:57.360)
blockchain. Yes. And so so that becomes a story of, you know, instead of transactions all having
Stephen Wolfram (3:04:04.960)
to settle in one ledger, it's like a story of all these different ledgers. And they all have to have
Stephen Wolfram (3:04:10.320)
some ultimate consistency, which is what causal invariance would give one, but it can take a
Stephen Wolfram (3:04:15.120)
while. And the it can take a while is kind of like quantum mechanics. So it's kind of what's
Stephen Wolfram (3:04:19.920)
happening is there these different paths of history that correspond to, you know, in one path
Stephen Wolfram (3:04:25.280)
of history, you got paid this amount in another path of history, you got paid this amount. In the
Stephen Wolfram (3:04:29.760)
end, the universe will always become consistent. Now, now the way it will it works is, okay, it's
Stephen Wolfram (3:04:36.240)
a little bit more complicated than that. What happens is, the way space is knitted together
Stephen Wolfram (3:04:40.400)
in our theory of physics is through all these events. And the the idea is that the way that
Stephen Wolfram (3:04:47.040)
economic space is knitted together is between is there these autonomous events that essentially
Stephen Wolfram (3:04:52.880)
knit together economic space. So there are all these threads of transactions that are happening.
Lex Fridman (3:04:57.520)
And the question is, can they be made consistent? Are there is there something forcing them to be
Stephen Wolfram (3:05:01.760)
sort of a consistent fabric of economic reality? And sort of what this has led me to is trying to
Stephen Wolfram (3:05:08.240)
realize how does economics fundamentally work? And, you know, what is economics? And, you know,
Lex Fridman (3:05:14.640)
what what are the atoms of economics, so to speak? And so what I've kind of realized is that, that
Stephen Wolfram (3:05:20.720)
sort of the perhaps I don't even know if this is right yet, there's sort of events in economics,
Stephen Wolfram (3:05:25.920)
the transactions, there are states of agents that are kind of the atoms of economics. And then
Stephen Wolfram (3:05:32.240)
transactions are kind of agents transact in some transact in some way, and that's an event. And
Stephen Wolfram (3:05:38.720)
then the question is, how do you knit together sort of economic space from that? What is there
Stephen Wolfram (3:05:43.920)
in economic space? Well, all these transactions, there's a whole complicated collection of possible
Stephen Wolfram (3:05:48.160)
transactions. But one thing that's true about economics is we tend to have the notion of a
Stephen Wolfram (3:05:52.720)
definite value for things. We could imagine that, you know, you buy a cookie from somebody, and
Stephen Wolfram (3:06:02.480)
they want to get a movie ticket. And there is some way that AI bots could make some path
Stephen Wolfram (3:06:09.680)
from the cookie to the movie ticket by all these different intermediate transactions. But in fact,
Stephen Wolfram (3:06:16.000)
we have an approximation to that, which is we say they each have a dollar value. And we have this
Stephen Wolfram (3:06:21.600)
kind of numeraire concept of there's just a way of kind of taking this whole complicated space of
Stephen Wolfram (3:06:28.240)
transactions and parsing it in something which is a kind of a simplified thing that is kind of like
Stephen Wolfram (3:06:34.560)
our parsing of physical space. And so my guess is that the yet again, I mean, it's crazy that all
Stephen Wolfram (3:06:41.920)
these things are so connected. This is another multi computation story. Another story of where
Stephen Wolfram (3:06:48.160)
what's happening is that the economic consciousness, the economic observer is not going to deal with
Stephen Wolfram (3:06:54.320)
all of those are different microscopic transactions. They're just going to parse the
Stephen Wolfram (3:06:57.680)
whole thing by saying, there's this value, it's a number. And that's their understanding of their
Stephen Wolfram (3:07:03.040)
summary of this economic network. And there will be all kinds of things like there are all kinds of
Stephen Wolfram (3:07:07.680)
arbitrage opportunities, which are kind of like the quantum effects in this whole thing. And that's
Stephen Wolfram (3:07:14.000)
in places where there's sort of different paths that can be followed and so on. So the question
Stephen Wolfram (3:07:21.520)
is, can one make a sort of global theory of economics? And then my test case is again,
Lex Fridman (3:07:27.040)
what is time dilation in economics? And I know if you imagine a very agricultural economics where
Stephen Wolfram (3:07:33.520)
people are growing lettuces and fields and things like this, and you ask questions about, well,
Stephen Wolfram (3:07:38.000)
if you're transporting lettuces to different places, what is the value of the lettuces after
Stephen Wolfram (3:07:43.280)
you have to transport them versus if you're just sitting in one place and selling them,
Stephen Wolfram (3:07:47.440)
you can kind of get a little bit of an analogy there. But I think there's a better and more
Stephen Wolfram (3:07:51.120)
complete analogy. And that's the question of, is there a theory like general relativity that is a
Stephen Wolfram (3:07:56.080)
global theory of economics? And is it about something we care about? It could be that there
Stephen Wolfram (3:08:00.560)
is a global theory, but it's about a feature of economic reality that isn't important to us.
Stephen Wolfram (3:08:05.520)
Now, another part of the story is, can one use those ideas to make essentially a distributed
Stephen Wolfram (3:08:11.040)
blockchain, a distributed generalization of blockchain, kind of the quantum analog of money,
Lex Fridman (3:08:16.240)
so to speak, where you have, for example, you can have uncertainty relations where you're saying,
Stephen Wolfram (3:08:21.920)
you know, well, if I insist on knowing my bank account right now, there'll be some uncertainty.
Stephen Wolfram (3:08:27.600)
If I'm prepared to wait a while, then it'll be much more certain. And so there's, you know,
Stephen Wolfram (3:08:32.960)
is there a way of using and so we've made a bunch of prototypes of this, which I'm not yet happy
Stephen Wolfram (3:08:39.040)
with. But what I realized is, to really understand these prototypes, I actually have to have a
Stephen Wolfram (3:08:43.280)
foundational theory of economics. And so that's kind of a, you know, it may be that we could
Stephen Wolfram (3:08:48.080)
deploy one of these prototypes as a practical system. But I think it's really going to be much
Stephen Wolfram (3:08:52.240)
better if we actually have an understanding of how this plugs into kind of the economics.
Lex Fridman (3:08:56.160)
And that means like a fundamental theory of transactions between
Lex Fridman (3:09:00.320)
entities. That's what you mean by economics.
Stephen Wolfram (3:09:03.760)
Yes, I think so. But I mean, you know, how there emerge sort of laws of economics,
Stephen Wolfram (3:09:08.480)
I don't even know. And I've been asking friends of mine who are economists and things,
Lex Fridman (3:09:12.560)
what is economics? You know, is it an axiomatic theory? Is it a theory
Stephen Wolfram (3:09:17.120)
that is kind of a qualitative description theory? Is it, you know, what kind of a theory is it? Is
Stephen Wolfram (3:09:22.480)
it a theory, you know, what kind of thinking? It's like in biology, in evolutionary biology,
Stephen Wolfram (3:09:27.520)
for example, there's a certain pattern of thinking that goes on in evolutionary biology where
Stephen Wolfram (3:09:32.240)
if you're a, you know, a good evolutionary biologist, somebody says, that creature has a
Stephen Wolfram (3:09:36.720)
weird horn. And they'll say, well, that's because this and this and this and the selection of this
Stephen Wolfram (3:09:41.440)
kind and that kind. And that's the story. And it's not a mathematical story. It's a story of
Stephen Wolfram (3:09:46.960)
a different type of thinking about these things. By the way, evolutionary biology is yet another
Stephen Wolfram (3:09:52.080)
place where it looks like this multi computational idea can be applied. And that's where maybe
Stephen Wolfram (3:09:58.080)
speciation is related to things like event horizons. And there's a whole other kind of
Stephen Wolfram (3:10:03.360)
world of that. But it seems like this kind of model can be applicable to so many aspects,
Stephen Wolfram (3:10:09.120)
like the different levels of understanding of our reality. So it could be the biology,
Stephen Wolfram (3:10:15.840)
the chemistry, at the physics level, the economics. And you could potentially, the thing is, it's like,
Stephen Wolfram (3:10:24.240)
okay, sure, at all these levels, it might rhyme. It might make sense as a model. The question is,
Lex Fridman (3:10:28.800)
can you make useful predictions as one of these levels? That's right. And that's really a question
Stephen Wolfram (3:10:34.080)
of, you know, it's a weird situation because the situation where the model probably has definite
Stephen Wolfram (3:10:40.480)
consequences. The question is, are they consequences we care about? Yeah. And that's
Stephen Wolfram (3:10:45.040)
some, you know, and so in the case of, in the economic case, the, where, so, you know,
Stephen Wolfram (3:10:55.600)
one thing is this idea of using kind of physics like notions to construct a kind of distributed
Stephen Wolfram (3:11:02.000)
analog of blockchain. Okay. The much more pragmatic thing is a different direction.
Lex Fridman (3:11:07.120)
And it has to do with this computational language that we built to describe the world
Stephen Wolfram (3:11:11.120)
that knows about, you know, different kinds of cookies and knows about different cities and
Stephen Wolfram (3:11:15.760)
knows about how to compute all these kinds of things. One of the things that is of interest is
Stephen Wolfram (3:11:21.120)
if you want to run the world, you need, you know, with contracts and laws and rules and so on,
Stephen Wolfram (3:11:27.520)
there are rules at a human level and there are kind of things like, and so this gets one into
Stephen Wolfram (3:11:33.520)
the idea of computational contracts. You know, right now when we write a contract, it's a piece
Stephen Wolfram (3:11:38.320)
of legalese. It's, you know, it's just written in English and it's not something that's automatically
Stephen Wolfram (3:11:43.760)
analyzable, executable, whatever else. It's just English. You know, back in Gottfried Leibniz,
Stephen Wolfram (3:11:50.080)
back in, you know, 1680 or whatever was like, I'm going to, you know, figure out how to use logic
Stephen Wolfram (3:11:57.520)
to decide legal cases and so on. And he had kind of this idea of let's make a computational language
Lex Fridman (3:12:02.720)
for the human law. Forget about modeling nature, forgot about natural laws. What about human law?
Stephen Wolfram (3:12:09.920)
Can we make kind of a computational representation of that? Well, I think finally we're close to
Stephen Wolfram (3:12:14.880)
being able to do that. And one of the projects that I hope to get to as soon as there's a little
Stephen Wolfram (3:12:20.000)
bit of slowing down of some of this Cambrian explosion that's happening is a project I've
Stephen Wolfram (3:12:24.400)
been meaning to really do for a long time, which is what I'm calling a symbolic discourse language.
Stephen Wolfram (3:12:29.040)
It's just finishing the job of being able to represent everything like the conversation we're
Stephen Wolfram (3:12:34.400)
having in computational terms. And one of the use cases for that is computational contracts.
Stephen Wolfram (3:12:40.240)
Another use case is something like the constitution that says what the AIs, what we want the AIs to do.
Stephen Wolfram (3:12:45.920)
So, but this is useful. So you're saying, so these are like, you're saying computational contracts,
Lex Fridman (3:12:50.880)
but smart contracts. This is what's in the domain of cryptocurrency is known as smart contracts.
Lex Fridman (3:12:55.920)
And so the language you've developed, this symbolic or seek to further develop symbolic discourse
Stephen Wolfram (3:13:02.240)
language enables you to write a contract and write a contract that richly represents
Stephen Wolfram (3:13:10.640)
some aspect of the world. So, I mean, smart contracts tend to be right now mostly about
Stephen Wolfram (3:13:16.320)
things happening on the blockchain. And sometimes they have oracles. And in fact, our Wolfman Alpha
Stephen Wolfram (3:13:20.800)
API is the main thing people use to get information about the real world, so to speak,
Stephen Wolfram (3:13:26.160)
within smart contracts. So Wolfram Alpha, as it stands, is a really good oracle for
Stephen Wolfram (3:13:31.360)
whoever wants to use it. That's perhaps where the relationship with Cardano is.
Stephen Wolfram (3:13:34.640)
Yeah, well, that's how we started getting involved with blockchains. As we realized,
Stephen Wolfram (3:13:37.680)
people were using Wolfram Alpha as the oracle for smart contracts, so to speak. And so that
Stephen Wolfram (3:13:43.200)
got us interested in blockchains in general. And what was ended up happening is Wolfram Language
Stephen Wolfram (3:13:49.040)
is, with its symbolic representation of things, is really very good at representing things like
Stephen Wolfram (3:13:53.760)
blockchains. And so I think we now have, and we don't really know all the comparisons, but we now
Stephen Wolfram (3:13:58.640)
have a really nice environment within Wolfram Language for dealing with the sort of, for
Stephen Wolfram (3:14:04.320)
representing what happens in blockchains, for analyzing what happens in blockchains.
Stephen Wolfram (3:14:08.240)
We have a whole effort in blockchain analytics. And we've sort of published some samples of how
Stephen Wolfram (3:14:15.120)
that works. But it's because our technology stack, Wolfram Language and Mathematica,
Stephen Wolfram (3:14:20.400)
are very widely used in the quant finance world. There's a sort of immediate coevolution there of
Stephen Wolfram (3:14:29.200)
the quant finance kind of thing and blockchain analytics. So it's kind of the representation
Stephen Wolfram (3:14:35.200)
of blockchain in computational language. Then ultimately, it's kind of like, how do you run
Stephen Wolfram (3:14:40.240)
the world with code? That is, how do you write sort of all these things which are right now,
Stephen Wolfram (3:14:45.040)
regulations and laws and contracts and things in computational language? And kind of the ultimate
Stephen Wolfram (3:14:50.720)
vision is that sort of something happens in the world, and then there's this giant domino effect
Stephen Wolfram (3:14:55.680)
of all these computational contracts that trigger based on the thing that happened. And there's a
Stephen Wolfram (3:15:00.400)
whole story to that. And of course, I like to always pay attention to the latest things that
Stephen Wolfram (3:15:06.480)
are going on. And I really, I kind of like blockchain because it's another rethinking
Stephen Wolfram (3:15:11.680)
of kind of computation. It's kind of like cloud computing was a little bit of that, of sort of
Stephen Wolfram (3:15:16.240)
persistent kind of computational resources and so on. And this multi computation is a big
Stephen Wolfram (3:15:23.600)
rethinking of kind of what it means to compute. Blockchain is another bit of rethinking of what
Stephen Wolfram (3:15:28.400)
it means to compute. The idea that you lodge kind of these autonomous lumps of computation
Stephen Wolfram (3:15:33.520)
out there in the blockchain world. And one of the things that just sort of for fun,
Lex Fridman (3:15:39.200)
so to speak, is we've been doing a bit of stuff with NFTs, and we just did some NFTs on Cardano,
Lex Fridman (3:15:44.080)
and we'll be doing some more. And we did some cellular automaton NFTs on Cardano,
Stephen Wolfram (3:15:48.880)
which people seem to like quite a bit. And one of the things I've realized about NFTs
Stephen Wolfram (3:15:55.120)
is that there's kind of this notion, and we're really working on this, I like recording stuff.
Stephen Wolfram (3:16:01.520)
You know, one of the things that's come out of kind of my science, I suppose, is this history
Stephen Wolfram (3:16:06.640)
matters type story of, you know, it's not just the current state, it's the history that matters.
Lex Fridman (3:16:11.840)
And I've kind of, I don't think this is actually realizing, maybe it's not coincidental that I'm
Stephen Wolfram (3:16:17.120)
sort of the human who's recorded more about themselves than anybody else. And then I end up
Stephen Wolfram (3:16:20.960)
with these science results that say history matters, which was not those things. I didn't
Stephen Wolfram (3:16:26.160)
think those were connected, but they're at least correlated, yes. Yeah, right. So, you know,
Stephen Wolfram (3:16:30.880)
this question about sort of recording what has happened and having sort of a permanent record
Stephen Wolfram (3:16:36.000)
of things, one of the things that's kind of interesting there is, you know, you put up a
Stephen Wolfram (3:16:39.840)
website and it's got a bunch of stuff on it, but you know, you have to keep paying the hosting
Stephen Wolfram (3:16:43.360)
fees or the thing's going to go away. But one of the things about blockchain is quite interesting
Stephen Wolfram (3:16:48.160)
is if you put something on a blockchain and you pay, you know, your commission to get that thing,
Stephen Wolfram (3:16:53.120)
you know, put on, you know, mine, put on the blockchain, then in a sense, everybody who comes
Stephen Wolfram (3:16:59.120)
after you is, you know, they are motivated to keep your thing alive because that's what keeps
Stephen Wolfram (3:17:04.480)
the consistency of the blockchain. So in a sense with sort of the NFT world, it's kind of like if
Stephen Wolfram (3:17:09.200)
you want to have something permanent, well, at least for the life of the blockchain, but even if
Stephen Wolfram (3:17:14.400)
the blockchain goes out of circulation, so to speak, there's going to be enough value in that
Stephen Wolfram (3:17:18.800)
whole collection of transactions that people are going to archive the thing. But that means that,
Stephen Wolfram (3:17:23.200)
you know, pay once and you're kind of, you're lodged in the blockchain forever. And so we've
Stephen Wolfram (3:17:28.400)
been kind of playing around with sort of a hobby thing of mine of thinking about sort of the NFTs
Lex Fridman (3:17:35.280)
and how you and sort of the consumer idea of kind of the it's the it's the anti, you know,
Stephen Wolfram (3:17:41.760)
it's the opposite of the Snapchat view of the world. There's a permanence to it that's heavily
Stephen Wolfram (3:17:46.720)
incentivized and thereby you can have a permanence of history. Right. And that's that's that's kind of
Stephen Wolfram (3:17:54.640)
the now, you know, so that's so that's one of the things we've been doing with Cardano. And it's
Stephen Wolfram (3:17:59.040)
kind of fun. I think that I mean, this whole question about, you know, you mentioned automated
Stephen Wolfram (3:18:03.360)
theorem proving and blockchains and so on. And as I've thought about this kind of physics inspired
Stephen Wolfram (3:18:08.320)
distributed blockchain, obviously, there, the sort of the proof that it works, that there are no
Stephen Wolfram (3:18:14.560)
double spends, there's no whatever else, that proof becomes a very formal kind of almost a
Stephen Wolfram (3:18:20.400)
matter of physics, so to speak. And, you know, it's been it's been an interesting thing for the
Stephen Wolfram (3:18:25.440)
for the practical blockchains to do kind of actual automated theorem proving. And I don't think
Stephen Wolfram (3:18:30.400)
anybody's really managed it in an interesting case yet. It's a thing that people, you know,
Stephen Wolfram (3:18:34.880)
aspire to. But I think it's a challenging thing because basically, the point is one of the one
Stephen Wolfram (3:18:39.600)
of the things about proving correctness of something as well. You know, people say I've
Stephen Wolfram (3:18:44.080)
got this program and I'm going to prove it's correct. It's like, what does that mean? You
Stephen Wolfram (3:18:47.840)
have to say what correct means. I mean, it's it's kind of like then you have to have another
Stephen Wolfram (3:18:51.760)
language. And people are very confused back in past decades of, you know, oh, we're going to
Stephen Wolfram (3:18:56.240)
prove the correctness by representing the program in another language, which we also don't know
Stephen Wolfram (3:19:00.960)
whether it's correct. And, you know, often by correctness, we just mean it can't crash or it
Stephen Wolfram (3:19:06.240)
can't scribble on memory. But but the thing is that there's this complicated trade off,
Stephen Wolfram (3:19:10.640)
because as soon as there's as soon as you're really using computation, you have computational
Stephen Wolfram (3:19:15.200)
irreducibility, you have undecidability. If you want to use computation seriously,
Stephen Wolfram (3:19:20.480)
you have to kind of let go of the idea that you're going to be able to box it in and say,
Stephen Wolfram (3:19:26.160)
we're going to have just this happen and not anything else. I mean, this is a this is an old
Stephen Wolfram (3:19:30.240)
fact. I mean, Gödel's theorem tries to say, you know, piano arithmetic, the axioms of arithmetic,
Lex Fridman (3:19:35.680)
can you box in the integers and say these axioms give just the integers and nothing about the
Stephen Wolfram (3:19:40.400)
integers. Gödel's theorem showed that wasn't the case. You can have all these wild, weird things
Stephen Wolfram (3:19:46.160)
that are obey the piano axioms, but aren't integers. And there's this kind of infinite
Stephen Wolfram (3:19:50.480)
hierarchy of additional axioms you would have to add. And it's kind of the same thing. You don't
Stephen Wolfram (3:19:55.280)
get to, you know, if you want to say, I want to know what happens, you're boxing yourself in and
Stephen Wolfram (3:20:00.400)
there's a limit to what can happen, so to speak. So it's a complicated trade off. And it's a big
Stephen Wolfram (3:20:05.360)
trade off for AI, so to speak. It's kind of like, do you want to let computation actually do what
Stephen Wolfram (3:20:09.920)
it can do? Or do you want to say, no, it's very, very boxed in to the point where we can understand
Stephen Wolfram (3:20:14.960)
every step. And that's kind of a thing that becomes difficult to do. But that's, I mean,
Stephen Wolfram (3:20:21.680)
in general, I would say one of the things that's kind of complicated in my sort of life and the
Stephen Wolfram (3:20:28.000)
whole sort of story of computational language and all this technology and science and so on.
Stephen Wolfram (3:20:32.960)
I mean, I kind of in the flow of one's life, it's sort of interesting to see how these things play
Stephen Wolfram (3:20:38.480)
out because I've kind of concluded that I'm in the business of making kind of artifacts from the
Stephen Wolfram (3:20:43.920)
future, which means, you know, there are things that I've done, I don't know, this physics project,
Stephen Wolfram (3:20:48.960)
I don't know whether anybody would have gotten to it for 50 years. You know, the fact that
Stephen Wolfram (3:20:52.960)
Mathematica is a third of a century old, and I know that a bunch of the core ideas are not
Stephen Wolfram (3:20:58.160)
well absorbed. I mean, that is people finally got this idea that I thought was a triviality
Stephen Wolfram (3:21:02.960)
of notebooks, that was 25 years. And, you know, some of these core ideas about symbolic computation
Lex Fridman (3:21:08.800)
and so on are not absorbed. I mean, people use them every day in Wolfram language and, you know,
Stephen Wolfram (3:21:15.680)
do all kinds of cool things with them. But if you say, what is the fundamental intellectual point
Stephen Wolfram (3:21:19.920)
here? It's not well absorbed. And it's something where you kind of realize that you're sort of
Stephen Wolfram (3:21:25.440)
building things. And I kind of made this thing about, you know, we're building artifacts from
Stephen Wolfram (3:21:30.160)
the future, so to speak. And I mentioned that we have a conference coming up actually in a couple
Stephen Wolfram (3:21:35.600)
of weeks, our annual technology conference, where we talk about all the things we're doing.
Stephen Wolfram (3:21:41.520)
And, you know, so I was talking about it last year, about, you know, we're making artifacts
Stephen Wolfram (3:21:46.080)
from the future. And I was kind of like, I had some version of that, that was kind of a dark
Lex Fridman (3:21:50.800)
and frustrated thing of like, you know, I'm building things which nobody's going to care
Stephen Wolfram (3:21:54.560)
about until long after I'm dead, so to speak. But then I realized, you know, people were sort of
Stephen Wolfram (3:22:01.360)
telling me afterwards, you know, that's exactly how, you know, we're using Wolfram language in
Stephen Wolfram (3:22:06.320)
some particular setting and, you know, some computational X field or some organization or
Stephen Wolfram (3:22:10.560)
whatever. And it's like, people are saying, oh, you know, what did you manage to do? You know,
Stephen Wolfram (3:22:15.440)
well, we know that in principle, it will be possible to do that. But we didn't know that
Stephen Wolfram (3:22:18.480)
was possible now. And it's kind of like, that's sort of the business we're in. And in a sense,
Stephen Wolfram (3:22:23.280)
with some of these ideas in science, you know, I feel a little bit the same way that there are
Stephen Wolfram (3:22:27.760)
some of these things where, you know, some things like, for example, this whole idea, well, so to
Stephen Wolfram (3:22:35.040)
relate to another sort of piece of history and the future, one of, you know, I mentioned at the
Stephen Wolfram (3:22:39.440)
beginning kind of complexity as this thing that I was interested in back 40 years ago and so on.
Stephen Wolfram (3:22:44.560)
Where does complexity come from? Well, I think we kind of nailed that. The answer is in the
Stephen Wolfram (3:22:50.080)
computational universe, even simple programs make it. And that's kind of the secret that nature has
Stephen Wolfram (3:22:54.880)
that allows you to make it. So that's that part. But the bigger picture there was this idea of
Stephen Wolfram (3:23:02.160)
this kind of computational paradigm, the idea that you could go beyond mathematical equations,
Stephen Wolfram (3:23:06.640)
which have been sort of the primary modeling medium for 300 years. And so it was like, look,
Stephen Wolfram (3:23:13.040)
it is inexorably the case that people will use programs rather than just equations. And, you
Stephen Wolfram (3:23:18.160)
know, I was saying that in the 1980s and people were, you know, I published my big book, New Kind
Stephen Wolfram (3:23:22.720)
of Science, that'll be 20 years ago next year. So in 2002, and people were saying, oh, no,
Stephen Wolfram (3:23:28.880)
this can't possibly be true. You know, we know for 300 years we've been doing all this stuff.
Stephen Wolfram (3:23:32.960)
Right. To be fair, I now realize I'm a little bit more analysis of what people actually
Stephen Wolfram (3:23:38.480)
said in pretty much every field other than physics. People said, oh, these are new models.
Stephen Wolfram (3:23:44.000)
That's pretty interesting. In physics, people were like, we've got our physics models. We're
Stephen Wolfram (3:23:48.640)
very happy with them. Yeah, in physics, there's more resistance because of the attachment and
Stephen Wolfram (3:23:53.040)
the power of the equations. The idea that programs might be the right way to approach
Stephen Wolfram (3:23:59.200)
this field. Was there some resistance? And like you're saying, it takes time. For somebody who
Stephen Wolfram (3:24:05.120)
likes the idea of time dilation and all these applications, I thought you would understand this.
Stephen Wolfram (3:24:09.520)
Yeah, right. But, you know, and computational irreducibility. Yes, exactly. But I mean,
Stephen Wolfram (3:24:14.480)
it is really interesting that just 20 years, a span of 20 years, it's gone from, you know,
Stephen Wolfram (3:24:20.160)
pitchforks and horror to, yeah, we get it. And, you know, it's helped that we've, you know, in our
Stephen Wolfram (3:24:28.240)
current effort in fundamental physics, we've gotten a lot further and we've managed to
Stephen Wolfram (3:24:33.200)
put a lot of puzzle pieces together that make sense. But the thing that I've been thinking
Stephen Wolfram (3:24:37.680)
about recently is this field of complexity. So I've kind of was a sort of a field builder.
Stephen Wolfram (3:24:43.600)
Back in the 1980s, I was kind of like, okay, you know, can we, you know, I'd understood this point
Stephen Wolfram (3:24:50.320)
that there was this sort of fundamental phenomenon of complexity that showed up in lots of places.
Lex Fridman (3:24:54.320)
And I was like, this is an interesting sort of field of science. And I was recently was reminded,
Stephen Wolfram (3:25:01.360)
I was at this, the very first sort of get together of what became the Santa Fe Institute. And I was
Stephen Wolfram (3:25:07.360)
like, in fact, there's even an audio recording of me sort of saying, people have been talking about,
Stephen Wolfram (3:25:11.440)
oh, what should this, you know, outfit do? And I was saying, well, there is this thing that I've
Stephen Wolfram (3:25:16.000)
been thinking about. It's this kind of idea of complexity. And it's kind of like, and that's
Lex Fridman (3:25:21.520)
what that ended up. And you planted the seed of complexity at Santa Fe. That's beautiful.
Stephen Wolfram (3:25:25.520)
It's a beautiful vision. But I mean, so that, but what's happened then is this idea of complexity
Stephen Wolfram (3:25:31.120)
and, you know, and I started the first research center at University of Illinois for doing that
Stephen Wolfram (3:25:35.920)
in the first journal, complex systems and so on. And it's kind of an interesting thing in my life,
Stephen Wolfram (3:25:42.640)
at least that it's kind of like you plant the seed, you have this idea. It's a kind of a science
Stephen Wolfram (3:25:47.680)
idea. You have this idea of sort of focusing on the phenomenon of complexity. The deeper idea was
Stephen Wolfram (3:25:52.960)
this computational paradigm. But the nominal idea is this kind of idea of complexity. Okay. Then you
Stephen Wolfram (3:25:58.480)
roll time forward 30 years or whatever, 35 years, whatever it is. And you say, what happened? Okay.
Stephen Wolfram (3:26:05.520)
Well now there are a thousand complexity institutes around the world. I think more or less,
Stephen Wolfram (3:26:10.080)
we've been trying to count them. And, you know, there are 40 complexity journals, I think.
Lex Fridman (3:26:16.160)
And so it's kind of like what actually happened in this field, right? And I look at a lot of what
Stephen Wolfram (3:26:22.160)
happened and I'm like, you know, I have to admit to some eye rolling, so to speak, because it's
Stephen Wolfram (3:26:28.160)
kind of like, like, what is, what's actually going on? Well, what people definitely got
Stephen Wolfram (3:26:33.360)
was this idea of computational models. And then they got, but they thought one of the,
Stephen Wolfram (3:26:38.240)
one of the kind of cognitive mistakes, I think is they say, we've got a computational model
Lex Fridman (3:26:43.200)
and it, and we're looking at a system that's complex and our computational model gives
Stephen Wolfram (3:26:49.600)
complexity. By golly, that must mean it's right. And unfortunately, because complexity is a generic
Stephen Wolfram (3:26:55.920)
phenomenon and computational irreducibility is a generic phenomenon that actually tells you nothing.
Lex Fridman (3:27:01.120)
And so then the question is, well, what can you do? You know, there's a lot of things that have
Stephen Wolfram (3:27:06.240)
been sort of done under this banner of complexity. And I think it's been very successful in providing
Stephen Wolfram (3:27:10.560)
sort of an interdisciplinary way of connecting different fields together. Which is powerful
Stephen Wolfram (3:27:15.200)
in itself. Right. I mean, that's a very useful. Biology and economics and physics. Right. It's a
Stephen Wolfram (3:27:19.440)
good organizing principle, but in the end, a lot of that is around this sort of computational
Stephen Wolfram (3:27:23.760)
paradigm, computational modeling. That's the raw material that powers that kind of, that kind of
Stephen Wolfram (3:27:28.960)
correspondence, I think. But the question is sort of, what is the, you know, I was just thinking
Stephen Wolfram (3:27:33.360)
recently, you know, we've been, I mean, the other we've been, we've been for years, people have
Stephen Wolfram (3:27:38.960)
told me you should start some Wolfram Institute that does basic science. You know, all I have
Stephen Wolfram (3:27:43.440)
is a company that, that builds software and we, you know, we have a little piece that does basic
Stephen Wolfram (3:27:47.920)
science as kind of a hobby. People are saying you should start this Wolfram Institute thing.
Lex Fridman (3:27:52.480)
And I've been, you know, cause I've known about lots of institutes and I've seen kind of their
Stephen Wolfram (3:27:56.000)
flow of money and, and kind of, you know, what happens in different situations and so on. So I've
Stephen Wolfram (3:28:00.240)
been kind of reluctant, but, but I've, I've, I have realized that, you know, what we've done with
Stephen Wolfram (3:28:05.120)
our company over the last 35 years, you know, we built a very good machine for doing R and D and,
Stephen Wolfram (3:28:10.720)
you know, innovating and creating things. And I just applied that machine to the physics project.
Stephen Wolfram (3:28:16.000)
That's how we did the physics project in a fairly short amount of time with a, you know,
Stephen Wolfram (3:28:20.080)
a efficient machine with, you know, various people involved and so on. And so, you know,
Stephen Wolfram (3:28:25.840)
it, it works for basic science and it's like, we can do more of this. And so now.
Stephen Wolfram (3:28:31.040)
In biology and chemistry, so it's, it's become an institute.
Lex Fridman (3:28:34.480)
Yes. Well, it needs to become an institute.
Stephen Wolfram (3:28:36.160)
An official institute.
Stephen Wolfram (3:28:37.280)
Right. Right. But the, the thing that, so I was thinking about, okay, so what do we do with
Stephen Wolfram (3:28:41.600)
complexity? You know, what, what, there are all these people who've, you know, what, what should
Stephen Wolfram (3:28:46.240)
happen to that field? And what I realized is there's kind of this area of foundations of
Stephen Wolfram (3:28:50.800)
complexity. That's about these questions about simple programs, what they do that's far away
Stephen Wolfram (3:28:56.160)
from a bunch of the detailed applications that people, it's not far away. It's, it's the,
Stephen Wolfram (3:29:00.000)
it's the under, you know, the, the bedrock underneath those applications. And so I realized
Stephen Wolfram (3:29:05.040)
recently, this is my recent kind of little innovation of a sort, a post that I'll do very
Stephen Wolfram (3:29:12.160)
soon about kind of, you know, the foundations of complexity. What really are they? I think
Stephen Wolfram (3:29:20.400)
there are really two ideas, two conceptual ideas that I hadn't really enunciated, I think before.
Stephen Wolfram (3:29:26.480)
One is what I call meta modeling. The other is ruleology. So what is meta modeling? So
Stephen Wolfram (3:29:31.440)
meta modeling is you've got this complicated model and it's a model of, you know, hedgehogs
Lex Fridman (3:29:36.000)
interacting with this, interacting with that. And the question is what's really underneath that?
Lex Fridman (3:29:40.720)
What is it? You know, is it a Turing machine? Is it a cellular automaton? You know,
Lex Fridman (3:29:45.600)
what is the underlying stuff underneath that model? And so there's this kind of meta science
Stephen Wolfram (3:29:51.120)
question of given these models, what is the core model? And I realized, I mean, to me,
Stephen Wolfram (3:29:56.560)
that's sort of an obvious question, but then I realized I've been doing language design for 40
Stephen Wolfram (3:30:00.880)
years and language design is exactly that question. You know, underneath all of this
Stephen Wolfram (3:30:05.120)
detailed stuff people do, what are the underlying primitives? And that's a question people haven't
Stephen Wolfram (3:30:10.080)
tended to ask about models. They say, well, we've got this nice model for this and that and the
Stephen Wolfram (3:30:13.920)
other, what's really underneath it? And what, you know, because once you have the thing that's
Stephen Wolfram (3:30:18.640)
underneath it, well, for example, this multi computation idea is an ultimate meta modeling
Stephen Wolfram (3:30:24.000)
idea because it's saying underneath all these fields is one kind of paradigmatic structure.
Stephen Wolfram (3:30:29.680)
And, you know, you can imagine the same kind of thing in much more sort of much sort of shallower
Stephen Wolfram (3:30:36.240)
levels in different kinds of modeling. So the first activity is this kind of meta modeling,
Stephen Wolfram (3:30:41.760)
the kind of the models about models, so to speak. You know, what is the, what's, you know,
Stephen Wolfram (3:30:47.920)
drilling down into models? That's one thing. The other thing is this thing that I think we're
Stephen Wolfram (3:30:53.200)
going to call ruleology, which is kind of the, okay, you've got these simple rules. You've got
Stephen Wolfram (3:30:57.840)
cellular automata, you've got turing machines, you've got substitution systems, you've got
Stephen Wolfram (3:31:01.600)
register machines, you've got all these different things. What do they actually do in the wild? And
Stephen Wolfram (3:31:06.160)
this is an area that I've spent a lot of time, you know, working on. It's a lot of stuff in my new
Stephen Wolfram (3:31:10.880)
kind of science book is about this. You know, this new book I wrote about combinators is full of
Stephen Wolfram (3:31:16.160)
stuff like this. And this journal Complex Systems has lots of papers about these kinds of things.
Lex Fridman (3:31:21.840)
But there isn't really a home for people who do ruleology or what I'm now...
Stephen Wolfram (3:31:26.240)
As you call the basic science of rules.
Stephen Wolfram (3:31:29.520)
Yes. Yes. Right. So it's like, you've got some, what is it? Is it mathematics? No,
Stephen Wolfram (3:31:35.120)
it isn't really like mathematics. In fact, from my now understanding of metamathematics,
Stephen Wolfram (3:31:38.960)
I understand that it's the molecular dynamics level. It's not the level that mathematicians
Stephen Wolfram (3:31:43.760)
have traditionally cared about. It's not computer science because computer science is about writing
Stephen Wolfram (3:31:48.400)
programs that do things, you know, that were for a purpose, not programs in the wild, so to speak.
Stephen Wolfram (3:31:53.760)
It's not physics. It doesn't have anything to do with, you know, maybe underneath some physics,
Lex Fridman (3:31:57.600)
but it's not physics as such. So it just hasn't had a home. And if you look at, you know,
Lex Fridman (3:32:02.720)
but what's great about it is it's a surviving field, so to speak. It's something where,
Stephen Wolfram (3:32:08.480)
you know, one of the things I find sort of inspiring about mathematics, for example,
Stephen Wolfram (3:32:13.360)
is you look at mathematics that was done, you know, in ancient Greece, ancient, you know, Babylon,
Stephen Wolfram (3:32:18.240)
Egypt, and so on. It's still here today. You know, you find an icosahedron that somebody made
Stephen Wolfram (3:32:23.360)
in ancient Egypt. You look at it. Oh, that's a very modern thing. It's an icosahedron. You know,
Stephen Wolfram (3:32:28.640)
it's a timeless kind of activity. And this idea of studying simple rules and what they do,
Stephen Wolfram (3:32:34.560)
it's a timeless activity. And I can see that over the last 40 years or so as, you know,
Stephen Wolfram (3:32:39.920)
even with cellular automata, it's kind of like, you know, you can sort of catalog what are the
Stephen Wolfram (3:32:44.800)
different cellular automata used for and, you know, like the simplest rules like one, you might
Stephen Wolfram (3:32:50.400)
even know this one, Rule 184. Rule 184 is a minimal model for road traffic flow. And, you know, it's
Stephen Wolfram (3:32:56.640)
also a minimal model for various other things. But it's kind of fun that you can literally say,
Stephen Wolfram (3:33:01.120)
you know, Rule 90 is a minimal model for this and this and this. Rule 4 is a minimal model for this.
Lex Fridman (3:33:07.600)
And it's kind of remarkable that you can just by in this raw level of this kind of study of rules,
Stephen Wolfram (3:33:13.200)
they then branch, they're the raw material that you can use to make models of different things.
Lex Fridman (3:33:17.840)
So it's a very pure basic science, but it's one that, you know, people have explored it,
Lex Fridman (3:33:23.200)
but they've been kind of a little bit in the wilderness. And I think, you know, one of the
Stephen Wolfram (3:33:27.040)
things that I would like to do finally is, you know, I always thought that sort of this notion
Stephen Wolfram (3:33:32.720)
of pure NKS, pure NKS being the acronym for my book, New Kind of Science, was something that
Stephen Wolfram (3:33:40.800)
people should be doing. And, you know, we tried to figure out what's the right institutional
Stephen Wolfram (3:33:44.640)
structure to do this stuff. You know, we dealt with a bunch of universities. Oh, you know,
Stephen Wolfram (3:33:48.720)
can we do this here? Well, what department would be in it? Well, it isn't in a department. It's
Stephen Wolfram (3:33:53.040)
its own new kind of thing. That's why the book was called The New Kind of Science.
Stephen Wolfram (3:33:58.240)
It's kind of the, because that's an increasingly good description of what it is, so to speak.
Stephen Wolfram (3:34:03.040)
We're actually, we were thinking about kind of the ruleological society because we're realizing
Stephen Wolfram (3:34:08.480)
that it's kind of, it's, you know, it's very interesting. I mean, I've never really done
Stephen Wolfram (3:34:14.080)
something like this before because there's this whole group of researchers who are,
Stephen Wolfram (3:34:18.080)
who've been doing things that are really, in some cases, very elegant, very surviving, very solid,
Stephen Wolfram (3:34:24.080)
you know, here's this thing that happens in this very abstract system. But it's like,
Stephen Wolfram (3:34:29.280)
it's like, what is that part of, you know, it doesn't have a home. And I think that's something
Stephen Wolfram (3:34:34.880)
I, you know, I kind of fault myself for not having been more, you know, when complexity
Stephen Wolfram (3:34:38.800)
was developing in the 80s, I didn't understand the danger of applications. That is, it's really
Stephen Wolfram (3:34:46.400)
cool that you can apply this to economics and you can apply it to evolutionary biology and this and
Stephen Wolfram (3:34:50.480)
that and the other. But what happens with applications is everything gets sucked into
Stephen Wolfram (3:34:54.560)
the applications. And the pure stuff, it's like the pure mathematics, there isn't any pure
Stephen Wolfram (3:34:59.520)
mathematics, so to speak. It's all just applications of mathematics. And I failed to kind of make sure
Stephen Wolfram (3:35:05.600)
that this kind of pure area was kind of maintained and developed. And I think now, you know, one of
Stephen Wolfram (3:35:12.880)
the things I want to try to do and, you know, it's a funny thing because I'm used to, look,
Stephen Wolfram (3:35:17.280)
I've been a tech CEO for more than half my life now. So, you know, this is what I know how to do.
Stephen Wolfram (3:35:22.960)
And, you know, I can make stuff happen and get projects to happen, even as it turns out,
Stephen Wolfram (3:35:28.400)
basic science projects in that kind of setting and how that translates into kind of, you know,
Stephen Wolfram (3:35:34.880)
there are a lot of people working on, for example, our physics project sort of distributed through
Stephen Wolfram (3:35:38.160)
the academic world and that's working just great. But the question is, you know, can we have a sort
Lex Fridman (3:35:42.800)
of accelerator mechanism that makes use of kind of what we've learned in sort of R&D innovation?
Stephen Wolfram (3:35:49.200)
And, you know, but on the other hand, it's a funny thing because, you know, in a company,
Stephen Wolfram (3:35:54.080)
in the end, the thing is, you know, it's a company, it makes products, it sells things,
Stephen Wolfram (3:35:58.480)
sells things to people. And, you know, when you're doing basic research, one of the challenges is
Stephen Wolfram (3:36:03.360)
there isn't that same kind of sort of mechanism. And so it's, you know, how do you drive the thing
Stephen Wolfram (3:36:09.840)
in a kind of, in a led kind of way so that it really can make forward progress rather than,
Stephen Wolfram (3:36:16.000)
you know, what can often happen in, you know, in academic settings where it's like,
Stephen Wolfram (3:36:20.000)
well, there are all these flowers blooming, but it's not clear that, you know, that it's...
Stephen Wolfram (3:36:24.160)
You have to have a central mission and a drive, just like you do with a company that's delivering
Stephen Wolfram (3:36:29.520)
a big overarching product. And that's... But the challenge is, you know, when you have
Stephen Wolfram (3:36:35.600)
the economics of the world are such that, you know, when you're delivering a product and people
Stephen Wolfram (3:36:40.320)
say, wow, that's useful, we'll buy it. And then that kind of feeds back and, okay, then you can
Stephen Wolfram (3:36:45.680)
pay the people who build it to eat, you know, so they can eat and so on. And with basic science,
Stephen Wolfram (3:36:52.400)
the payoff is very much less visible. And, you know, with this physics project, as I say,
Stephen Wolfram (3:36:57.440)
the big surprise has been that, I mean, you know, for example, well, the big surprise with
Stephen Wolfram (3:37:02.320)
the physics project is that it looks like it has near term applications. And I was like,
Stephen Wolfram (3:37:07.920)
I'm guessing this is 200 years away. I was kind of using the analogy of, you know, Newton
Lex Fridman (3:37:14.720)
starting a satellite launch company, which would have been kind of wrong time.
Stephen Wolfram (3:37:19.360)
And, you know, but it turns out that's not the case, but we can't guarantee that. And if you say
Stephen Wolfram (3:37:24.880)
we're signing up to do basic research, basic rheology, let's say, and, you know, and we can't,
Stephen Wolfram (3:37:31.600)
we don't know the horizon, you know, it's an unknown horizon. It's kind of like an undecidable
Stephen Wolfram (3:37:36.000)
kind of proposition of when is this proof going to end, so to speak? When is it going to be
Stephen Wolfram (3:37:40.160)
something that gets applied? Well, I hope this becomes a vibrant new field of rheology. I love
Stephen Wolfram (3:37:48.720)
it. Like I told you many, many times, it's one of the most amazing ideas that has been brought to
Stephen Wolfram (3:37:55.120)
this world. So I hope you get a bunch of people to explore this world. Thank you once again for
Stephen Wolfram (3:38:03.040)
spending your really valuable time with me today. Fun stuff. Thank you. Thanks for listening to this
Stephen Wolfram (3:38:09.440)
conversation with Stephen Wolfram. To support this podcast, please check out our sponsors in the
Stephen Wolfram (3:38:14.080)
description. And now, let me leave you with some words from Richard Feynman. Nature uses only the
Stephen Wolfram (3:38:21.280)
longest threads to weave her patterns, so each small piece of her fabric reveals the organization
Lex Fridman (3:38:28.400)
of the entire tapestry. Thank you for listening and hope to see you next time.
Stephen Wolfram (40:05.120)
order things were updated in. But the observer embedded in the universe doesn't know which order
Stephen Wolfram (40:09.760)
things were updated in because until they've been updated, they have no idea what else happened.
Lex Fridman (40:14.720)
So the only thing they know is the set of causal relationships. Let me give an extreme example.
Stephen Wolfram (40:20.240)
Let's imagine that the universe is a Turing machine. Turing machines have just this one
Stephen Wolfram (40:25.040)
update head which does something and otherwise the Turing machine just does nothing.
Lex Fridman (40:30.560)
And the Turing machine works by having this head move around and do its updating just where the
Stephen Wolfram (40:35.680)
head happens to be. The question is, could the universe be a Turing machine? Could the universe
Stephen Wolfram (40:40.400)
just have a single updating head that's just zipping around all over the place? You say,
Stephen Wolfram (40:44.320)
that's crazy because I'm talking to you, you seem to be updating, I'm updating,
Stephen Wolfram (40:49.520)
et cetera. But the thing is, there's no way to know that because if there was just this head
Stephen Wolfram (40:53.600)
moving around, it's like, okay, it updates me, but you're completely frozen at that point.
Stephen Wolfram (40:58.960)
Until the head has come over and updated you, you have no idea what happened to me.
Lex Fridman (41:02.720)
And so if you sort of unravel that argument, you realize the only thing we actually can tell
Stephen Wolfram (41:07.680)
is what the network of causal relationships between the things that happened were. We don't
Stephen Wolfram (41:13.040)
get to know from some sort of outside, sort of God's eye view of the thing. We don't get to know
Lex Fridman (41:19.840)
what sort of from the outside, what happened. We only get to know sort of what the set of
Stephen Wolfram (41:26.080)
relationships between the things that happened actually were.
Stephen Wolfram (41:28.880)
Yeah. But if I somehow record like a trace of this, I guess it would be called multi computation.
Lex Fridman (41:36.880)
Can't I then look back in the causal tree?
Lex Fridman (41:40.560)
Where do you record the trace?
Stephen Wolfram (41:42.720)
Some, you place throughout the universe, like throughout like a log that records in my own
Stephen Wolfram (41:50.080)
pocket of, in this hypergraph. Can't I, like realizing that I'm getting an outdated picture,
Lex Fridman (41:56.880)
can't I record?
Stephen Wolfram (41:58.560)
See, the problem is, and this is where things start getting very entangled in terms of what
Stephen Wolfram (42:03.760)
one understands. The problem is that any such recording device is itself part of the universe.
Lex Fridman (42:10.080)
Yeah.
Lex Fridman (42:10.580)
So you don't get to say, you never get to say, let's go outside the universe and go do this.
Lex Fridman (42:16.560)
And that's why, I mean, lots of the features of this model and the way things work end up being
Stephen Wolfram (42:22.560)
a result of that.
Stephen Wolfram (42:23.600)
So, but what, I guess from on a human level, what is the cost you're paying? What are you missing
Stephen Wolfram (42:30.240)
from not getting an updated picture all the time? Okay. I got, I understand what you're saying.
Lex Fridman (42:34.960)
Yeah, yeah, right.
Lex Fridman (42:35.520)
But like what, like, how does consciousness emerge from that? Like how, like, what are
Stephen Wolfram (42:41.760)
the limitations of that observer? I understand you're getting a delayed picture.
Stephen Wolfram (42:45.200)
Well, there's, there's a, okay. So there's, there's a bunch of limitations of the observer, I think.
Stephen Wolfram (42:50.320)
Yeah. Maybe just explain something about quantum mechanics, because that maybe is a,
Stephen Wolfram (42:54.480)
is an extreme version of some of these issues, which helps to kind of motivate why one should
Stephen Wolfram (42:59.680)
sort of think things through a little bit more carefully. So one feature of the, of this, okay.
Lex Fridman (43:05.280)
So in standard physics, like high school physics, you learn, you know, the equations of motion for
Stephen Wolfram (43:10.960)
a ball and the, the, you know, it says you throw the ball this angle, this velocity,
Stephen Wolfram (43:16.800)
things will move in this way. And there's a definite answer, right? The story, the key story
Stephen Wolfram (43:21.920)
of quantum mechanics is there aren't definite answers to where does the ball go? There's kind
Stephen Wolfram (43:25.840)
of this whole sort of bundle of possible paths. And all we say we know from quantum mechanics
Stephen Wolfram (43:32.080)
is certain probabilities for where the ball will end up. Okay. So that's kind of the,
Stephen Wolfram (43:36.720)
the core idea of quantum mechanics. So in our models, you, quantum mechanics is not some kind
Stephen Wolfram (43:42.080)
of plugin add on type thing. You absolutely cannot get away from quantum mechanics because
Stephen Wolfram (43:47.280)
as you think about updating this hypergraph, there isn't just one sequence of things,
Stephen Wolfram (43:51.760)
one definite sequence of things that can happen. There are all these different possible update
Stephen Wolfram (43:55.600)
sequences that can occur. You could do this, you know, piece of the hypergraph now, and then this
Stephen Wolfram (43:59.760)
one later and et cetera, et cetera, et cetera. All those different paths of history correspond to
Stephen Wolfram (44:05.200)
these quantum, quantum paths and quantum mechanics, these different possible quantum histories.
Lex Fridman (44:10.720)
And one of the things that's kind of surprising about it is they, they branch, you know, there can
Stephen Wolfram (44:15.760)
be a certain state of the universe and it could do this or it could do that, but they can also
Stephen Wolfram (44:20.640)
merge. There can be two states of the universe, which their next state, the next state they
Stephen Wolfram (44:25.680)
produce is the same for both of them. And that process of branching and merging is kind of
Stephen Wolfram (44:30.400)
critical. And the idea that there can be merging is critical and somewhat non trivial for these
Stephen Wolfram (44:34.400)
hypergraphs because there's a whole graph isomorphism story and there's a whole very
Stephen Wolfram (44:39.040)
elaborate set of mathematics. Yes. Among other things. Right. Yes. But so then what happens is
Stephen Wolfram (44:47.680)
that what one's seeing, okay, so we've got this thing, it's branching, it's merging, et cetera,
Stephen Wolfram (44:53.360)
et cetera, et cetera. Okay. So now the question is how do we perceive that? Why don't we notice
Stephen Wolfram (45:01.120)
that the universe is branching and merging? Why is it the case that we just think a definite set
Stephen Wolfram (45:06.000)
of things happen? Well, the answer is we are embedded in that universe and our brains are
Stephen Wolfram (45:11.520)
branching and merging too. And so what quantum mechanics becomes a story of is how does a
Stephen Wolfram (45:16.720)
branching brain perceive a branching universe? And the key thing is as soon as you say,
Stephen Wolfram (45:23.760)
I think definite things happen in the universe, that means you are essentially conflating
Stephen Wolfram (45:28.720)
lots of different parts of history. You're saying, actually, as far as I'm concerned,
Stephen Wolfram (45:33.440)
because I'm convinced that definite things happen in the universe, all these parts of history must
Stephen Wolfram (45:38.160)
be equivalent. Now, it's not obvious that that would be a consistent thing to do. It might be,
Stephen Wolfram (45:42.720)
you say, all these parts of history are equivalent, but by golly, moments later,
Stephen Wolfram (45:47.200)
that would be a completely inconsistent point of view. Everything would have gone to hell in
Stephen Wolfram (45:51.280)
different ways. The fact that that doesn't happen is, well, that's a consequence of this causal
Stephen Wolfram (45:56.000)
invariance thing. And the fact that that does happen a little bit is what causes little quantum
Stephen Wolfram (46:01.520)
effects. And if that didn't happen at all, there wouldn't be anything that sort of is like quantum
Stephen Wolfram (46:08.400)
mechanics. Quantum mechanics is kind of like in this bundle of paths. It's a little bit like what
Stephen Wolfram (46:16.640)
happens in statistical mechanics and fluid mechanics, whatever, that most of the time,
Stephen Wolfram (46:20.880)
you just see this continuous fluid. You just see the world just progressing in this kind of way
Stephen Wolfram (46:25.120)
that's like this continuous fluid. But every so often, if you look at the exact right experiment,
Stephen Wolfram (46:29.440)
you can start seeing, well, actually, it's made of these molecules where they might go that way,
Stephen Wolfram (46:33.280)
or they might go this way, and that's kind of quantum effects. And so, this kind of idea of
Stephen Wolfram (46:41.040)
where we're sort of embedded in the universe, this branching brain is perceiving this branching
Stephen Wolfram (46:45.760)
universe, and that ends up being sort of a story of quantum mechanics. That's part of the whole
Stephen Wolfram (46:51.600)
picture of what's going on. But I think, I mean, to come back to sort of what is the story of
Stephen Wolfram (46:56.880)
consciousness. So, in the universe, we've got whatever it is, 10 to the 400 atoms of space,
Stephen Wolfram (47:03.200)
they're all doing these complicated things. It's all a big, complicated, irreducible computation.
Stephen Wolfram (47:08.320)
The question is, what do we perceive from all of that? And the answer is that we are parsing the
Stephen Wolfram (47:15.600)
universe in a particular way. Let me again go back to the gas molecules analogy. In the gas in this
Stephen Wolfram (47:23.520)
room, there are molecules bouncing around all kinds of complicated patterns, but we don't care.
Stephen Wolfram (47:28.320)
All we notice is there's, you know, the gas laws are satisfied. Maybe there's some fluid dynamics.
Stephen Wolfram (47:34.960)
These are kind of features of that assembly of molecules that we notice, and then lots of details
Stephen Wolfram (47:40.480)
we don't notice. When you say we, do you mean the tools of physics, or do you mean literally
Stephen Wolfram (47:44.960)
the human brain and its perception system? Well, okay. So, the human brain is where it starts,
Lex Fridman (47:50.240)
but we've built a bunch of instruments to do a bit better than the human brain, but they still
Stephen Wolfram (47:53.840)
have many of the same kinds of ideas, you know, their cameras and their pressure sensors and
Stephen Wolfram (47:58.640)
these kinds of things. They're not, you know, at this point, we don't know how to make
Stephen Wolfram (48:04.160)
fundamentally qualitatively different sensory devices. Right. So, it's always just an extension
Stephen Wolfram (48:09.440)
of the consciousness experience. Or our sensory experience. Sensory experience, but
Stephen Wolfram (48:14.720)
sensory experience is somehow intricately tied to consciousness. Right. Well, so one question is,
Stephen Wolfram (48:20.240)
when we are looking at all these molecules in the gas, and there might be 10 to the 20th molecules
Stephen Wolfram (48:24.480)
in some little box or something, it's like, what do we notice about those molecules? So,
Stephen Wolfram (48:30.240)
one thing that we can say is, we don't notice that much. We are, you know, we are computationally
Stephen Wolfram (48:36.640)
bounded observers. We can't go in and say, okay, I'm the 10 to the 20th molecules, and I know
Stephen Wolfram (48:43.120)
that I can sort of decrypt their motions, and I can figure out this and that. It's like, I'm just
Stephen Wolfram (48:47.440)
going to say, what's the average density of molecules? And so, one key feature of us is that
Stephen Wolfram (48:52.640)
we are computationally bounded. And that when you are looking at a universe which is full of
Stephen Wolfram (48:57.920)
computation and doing huge amounts of computation, but we are computationally bounded, there's only
Stephen Wolfram (49:03.920)
certain things about that universe that we're going to be sensitive to. We're not going to be,
Stephen Wolfram (49:08.240)
you know, figuring out what all the atoms of space are doing, because we're just computationally
Stephen Wolfram (49:13.040)
bounded observers, and we are only sampling these small set of features. So, I think the
Stephen Wolfram (49:19.920)
two defining features of consciousness that, and I, you know, I would say that the sort of the
Stephen Wolfram (49:25.040)
preamble to this is, for years, you know, as I've talked about sort of computation and fundamental
Stephen Wolfram (49:30.480)
features of physics and science, people ask me, so what about consciousness? And I, for years,
Stephen Wolfram (49:36.800)
I've said, I have nothing to say about consciousness. And, you know, I've kind of
Stephen Wolfram (49:40.480)
told this story, you know, you talk about intelligence, you talk about life. These are
Stephen Wolfram (49:45.040)
both features where you say, what's the abstract definition of life? We don't really know the
Stephen Wolfram (49:49.200)
abstract definition. We know the one for life on Earth, it's got RNA, it's got cell membranes,
Stephen Wolfram (49:53.680)
it's got all this kind of stuff. Similarly for intelligence, we know the human definition of
Stephen Wolfram (49:58.480)
intelligence, but what is intelligence abstractly? We don't really know. And so, what I've long
Stephen Wolfram (50:03.600)
believed is that sort of the abstract definition of intelligence is just computational sophistication.
Stephen Wolfram (50:09.440)
That is, that as soon as you can be computationally sophisticated, that's kind of the abstract
Lex Fridman (50:14.880)
version, the generalized version of intelligence. So, then the question is, what about consciousness?
Lex Fridman (50:20.080)
And what I sort of realized is that consciousness is actually a step down from intelligence. That
Stephen Wolfram (50:26.000)
is, that you might think, oh, you know, consciousness is the top of the pie, but it's
Stephen Wolfram (50:32.800)
the top of the pile. But actually, I don't think it is. I think that there's this notion of kind
Stephen Wolfram (50:37.440)
of computational sophistication, which is the generalized intelligence. But consciousness
Stephen Wolfram (50:42.560)
has two limitations, I think. One of them is computational boundedness. That is, that we're
Stephen Wolfram (50:47.760)
only perceiving a sort of computationally bounded view of the universe. And the other is this idea
Stephen Wolfram (50:53.760)
of a single thread of time. That is, that we, and in fact, we know neurophysiologically our brains
Stephen Wolfram (50:59.920)
go to some trouble to give us this one thread of attention, so to speak. And it isn't the case that
Stephen Wolfram (51:05.760)
in all the neurons in our brains that, at least in our conscious, the correspondence of language,
Stephen Wolfram (51:12.640)
in our conscious experience, we just have the single thread of attention, single thread of
Stephen Wolfram (51:17.920)
perception. And maybe there's something unconscious that's bubbling around that's the kind of
Stephen Wolfram (51:23.680)
almost the quantum version of what's happening in our brain, so to speak. We've got the classical
Stephen Wolfram (51:28.160)
flow of what we are mostly thinking about, so to speak. But there's this kind of bubbling around
Stephen Wolfram (51:33.600)
of other paths that is all those other neurons that didn't make it to be part of our sort of
Stephen Wolfram (51:38.800)
conscious stream of experience. So in that sense, intelligence as computational sophistication is
Stephen Wolfram (51:44.560)
much broader than the computational constraints which consciousness operates under, and also the
Stephen Wolfram (51:54.240)
sequential, like the sequential thing, like the notion of time. That's kind of interesting. But
Stephen Wolfram (51:59.920)
then the follow up question is like, okay, starting to get a sense of what is intelligence, and how
Stephen Wolfram (52:05.360)
does that connect to our human brain? Because you're saying intelligence is almost like a fabric,
Stephen Wolfram (52:12.720)
like what we like plug into it or something, like our consciousness plugs into it.
Stephen Wolfram (52:18.240)
Yeah, I mean, the intelligence, I think the core, I mean, you know, intelligence at some
Stephen Wolfram (52:23.520)
level is just a word, but we are asking, you know, what is the notion of intelligence as we
Stephen Wolfram (52:28.880)
generalize it beyond the bounds of humans, beyond the bounds of even the AIs that we humans have
Stephen Wolfram (52:33.760)
built and so on? You know, what is intelligence? You know, is the weather, you know, people say the
Lex Fridman (52:39.600)
weather has a mind of its own. What does that mean? You know, can the weather be intelligent?
Stephen Wolfram (52:43.840)
Yeah. What does agency have to do with intelligence here? So is intelligence just
Stephen Wolfram (52:48.320)
like your conception of computation, just intelligence is the capacity to perform
Stephen Wolfram (52:54.640)
computation and the sea of? Yeah, I think so. I mean, I think that's right. And I think that,
Stephen Wolfram (52:59.840)
you know, this question of, is it for a purpose? Okay, that quickly degenerates into a horrible
Lex Fridman (53:07.120)
philosophical mess. Because, you know, whenever you say, did the weather do that for a purpose?
Stephen Wolfram (53:12.800)
Yeah. Right? Well, yes, it did. It was trying to move a bunch of hot air from the equator to the
Stephen Wolfram (53:17.440)
poles or something. That's its purpose. But why? Because I seem to be equally as dumb today as I
Stephen Wolfram (53:23.760)
was yesterday. So there's some persistence, like a consistency over time that the intelligence
Stephen Wolfram (53:30.880)
I plugged into. So like, what's, it seems like there's a hard constraint between the amount of
Stephen Wolfram (53:37.280)
computation I can perform in my consciousness. Like they seem to be really closely connected
Stephen Wolfram (53:42.720)
somehow. Well, I think the point is that the thing that gives you kind of the ability to have
Stephen Wolfram (53:48.720)
kind of conscious intelligence, you can have kind of this, okay, so one thing is we don't know
Stephen Wolfram (53:57.040)
intelligences other than the ones that are very much like us. Yes. Right. And the ones that are
Stephen Wolfram (54:02.880)
very much like us, I think have this feature of single thread of time, bounded, you know,
Stephen Wolfram (54:07.680)
computationally bounded. But you also need computational sophistication. Having a single
Stephen Wolfram (54:14.000)
thread of time and being computationally bounded, you could just be a clock going tick tock. That
Stephen Wolfram (54:19.920)
would satisfy those conditions. But the fact that we have this sort of irreducible computational
Stephen Wolfram (54:27.840)
ability, that's an important feature. That's sort of the bedrock on which we can construct
Stephen Wolfram (54:34.640)
the things we construct. Now, the fact that we have this experience of the world that has the
Stephen Wolfram (54:40.800)
single thread of time and computational boundedness, the thing that I sort of realized is it's that
Stephen Wolfram (54:47.120)
that causes us to deduce from this irreducible mess of what's going on in the physical world,
Stephen Wolfram (54:53.440)
the laws of physics that we think exist. So in other words, if we say, why do we believe that
Stephen Wolfram (55:00.720)
there is, you know, continuous space, let's say, why do we believe that gravity works the way it
Stephen Wolfram (55:06.480)
does? Well, in principle, we could be kind of parsing details of the universe that were, you
Stephen Wolfram (55:14.560)
know, that OK, the analogy is, again, with the statistical mechanics and molecules in a box,
Stephen Wolfram (55:22.560)
we could be sensitive to every little detail of the swirling around of those molecules. And we
Stephen Wolfram (55:27.120)
could say what really matters is the, you know, the wiggle effect that is, you know, that is
Stephen Wolfram (55:33.200)
something that we humans just never noticed because it's some weird thing that happens when
Stephen Wolfram (55:37.440)
there are 15 collisions of air molecules and this happens and that happens. We just see the pure
Stephen Wolfram (55:42.720)
motion of a ball moving about. Right. Why do we see that? Right. And the point is that that what
Stephen Wolfram (55:49.600)
seems to be the case is that the things that if we say, given this sort of hypergraph that's
Stephen Wolfram (55:55.280)
updating and all the details about all the sort of atoms of space and what they do, and we say,
Lex Fridman (56:00.640)
how do we slice that to what we can be sensitive to? What seems to be the case is that as soon as
Stephen Wolfram (56:06.080)
we assume, you know, computational boundedness, single thread of time, that leads us to general
Stephen Wolfram (56:12.080)
relativity. In other words, we can't avoid that. That's the way that we will parse the universe.
Stephen Wolfram (56:17.920)
Given those constraints, we parse the universe according to those particular in such a way that
Stephen Wolfram (56:24.720)
we say the aggregate reducible sort of pocket of computational reducibility that we slice out of
Stephen Wolfram (56:33.200)
this kind of whole computational irreducible ocean of behavior is just this one that corresponds to
Stephen Wolfram (56:38.880)
general relativity. Yeah, but we don't perceive general relativity. Well, we do if we do fancy
Stephen Wolfram (56:44.160)
experiments. So you're saying so perceive really does mean the full. We drop something. That's a
Stephen Wolfram (56:49.600)
great example of general relativity in action. No, but like what's the difference in that and
Stephen Wolfram (56:54.080)
Newtonian mechanics? I mean, oh, it doesn't. This is when I say general relativity, that's
Stephen Wolfram (57:00.000)
the uber theory, so to speak. I mean, Newtonian gravity is just the approximation that we can make,
Stephen Wolfram (57:05.920)
you know, on the earth and things like that. So this is, you know, the phenomenon of gravity
Stephen Wolfram (57:11.600)
is one that is a consequence of, you know, we would perceive something very different from
Stephen Wolfram (57:17.040)
gravity. So so the way to understand that is when we think about OK, so we make up reference frames
Stephen Wolfram (57:26.160)
with which we parse what's happening in space and time. So in other words, one of the one of
Stephen Wolfram (57:31.120)
the things that we do is we say as time progresses everywhere in space is something happens at a
Stephen Wolfram (57:40.240)
particular time and then we go to the next time and we say this is what space is like at the next
Stephen Wolfram (57:44.560)
time is what space is like at the next time. That's it's the reason we are used to doing that
Stephen Wolfram (57:51.280)
is because, you know, when we look around, we might see, you know, ten hundred meters away.
Stephen Wolfram (57:57.200)
The time it takes light to travel that distance is really short compared to the time it takes our
Stephen Wolfram (58:02.320)
brains to know what happened. So as far as our brains are concerned, we are parsing the universe
Stephen Wolfram (58:08.320)
in this. There is a moment in time, it's all of space. There's a moment in time, it's all of
Stephen Wolfram (58:12.640)
space. If we were the size of planets or something, we would have a different perception because the
Stephen Wolfram (58:17.440)
speed of light would be much more important to us. We wouldn't have this perception that
Stephen Wolfram (58:22.720)
things happen progressively in time everywhere in space. And so that's an important kind of
Stephen Wolfram (58:28.160)
constraint. And the reason that we kind of parse the universe in the way that causes us to say
Stephen Wolfram (58:33.760)
gravity works the way it does is because we're doing things like deciding that we can say the
Stephen Wolfram (58:39.520)
universe exists, space has a definite structure. There is a moment in time, space has this definite
Stephen Wolfram (58:45.680)
structure. We move to the next moment in time, space has another structure. That kind of setup
Stephen Wolfram (58:50.640)
is what lets us kind of deduce kind of what parse the universe in such a way that we say gravity
Stephen Wolfram (58:58.000)
works the way it does. So that kind of reference frame is that the illusion of that is that you're
Stephen Wolfram (59:05.280)
saying that's somehow useful for consciousness. That's what consciousness does. Because in a
Stephen Wolfram (59:11.040)
sense, what consciousness is doing is it's insisting that the universe is kind of sequentialized.
Lex Fridman (59:21.040)
And it is not allowing the possibility that, oh, there are these multiple threads of time
Lex Fridman (59:25.520)
and they're all flowing differently. It's like saying, no, everything is happening in this one
Stephen Wolfram (59:31.760)
thread of experience that we have. And that illusion of that one thread of experience
Stephen Wolfram (59:36.160)
cannot happen at the planetary scale. Are you saying typical human, are you saying we are at a
Stephen Wolfram (59:41.760)
human level is special here for consciousness? Well, for our kind of consciousness, if we existed
Stephen Wolfram (59:49.280)
at a scale close to the elementary length, for example, then our perception of the universe
Stephen Wolfram (59:53.600)
will be absurdly different. Okay. But this makes consciousness seem like a weird side effect to
Stephen Wolfram (59:58.720)
this particular scale. And so who cares? I mean, consciousness is not that special.
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