Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe

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

00:00:02.800 | his second time on the podcast.

00:00:05.080 | He's a computer scientist, mathematician,

00:00:07.200 | theoretical physicist, and the founder and CEO

00:00:10.660 | of Wolfram Research, a company behind Mathematica,

00:00:14.400 | Wolfram Alpha, Wolfram Language,

00:00:16.680 | and the new Wolfram Physics Project.

00:00:19.240 | He's the author of several books,

00:00:21.240 | including A New Kind of Science,

00:00:23.400 | and the new book, A Project to Find

00:00:25.880 | the Fundamental Theory of Physics.

00:00:28.280 | This second round of our conversation

00:00:30.000 | is primarily focused on this latter endeavor

00:00:32.400 | of searching for the physics of our universe

00:00:34.920 | in simple rules that do their work on hypergraphs,

00:00:38.520 | and eventually generate the infrastructure

00:00:40.920 | from which space, time, and all of modern physics can emerge.

00:00:45.400 | Quick summary of the sponsors.

00:00:47.200 | SimplySafe, SunBasket, and Masterclass.

00:00:50.240 | Please check out these sponsors in the description

00:00:52.860 | to get a discount and to support this podcast.

00:00:55.960 | As a side note, let me say that to me,

00:00:58.680 | the idea that seemingly infinite complexity can arise

00:01:02.040 | from very simple rules and initial conditions

00:01:05.080 | is one of the most beautiful and important

00:01:07.720 | mathematical and philosophical mysteries in science.

00:01:10.460 | I find that both cellular automata

00:01:12.400 | and the hypergraph data structure

00:01:14.920 | that Stephen and team are currently working on

00:01:17.360 | to be the kind of simple, clear mathematical playground

00:01:21.080 | within which fundamental ideas about intelligence,

00:01:24.560 | consciousness, and the fundamental laws of physics

00:01:28.400 | can be further developed in totally new ways.

00:01:31.680 | In fact, I think I'll try to make a video or two

00:01:34.320 | about the most beautiful aspects of these models

00:01:37.500 | in the coming weeks.

00:01:38.800 | Especially, I think, trying to describe

00:01:41.240 | how fellow curious minds like myself

00:01:43.320 | can jump in and explore them, either just for fun,

00:01:47.440 | or potentially for publication of new, innovative research

00:01:51.700 | in math, computer science, and physics.

00:01:54.080 | But honestly, I think the emerging complexity

00:01:56.320 | in these hypergraphs can capture the imagination of everyone,

00:01:59.960 | even if you're someone who never really connected

00:02:02.300 | with mathematics.

00:02:04.020 | That's my hope, at least, to have these conversations

00:02:06.760 | that inspire everyone to look up to the skies

00:02:09.840 | and into our own minds in awe of our amazing universe.

00:02:14.840 | Let me also mention that this is the first time

00:02:17.820 | I ever recorded a podcast outdoors,

00:02:20.360 | as a kind of experiment to see if this is an option

00:02:23.520 | in times of COVID.

00:02:25.360 | I'm sorry if the audio is not great.

00:02:27.840 | I did my best, and promise to keep improving

00:02:30.560 | and learning, as always.

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00:02:39.880 | or connect with me on Twitter @LexFriedman.

00:02:42.880 | As usual, I'll do a few minutes of ads now,

00:02:44.960 | and no ads in the middle.

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00:03:48.800 | In fact, when I was younger, the idea of being a hit man

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00:03:56.440 | which is how I thought about it, really appealed to me.

00:03:59.640 | The skill of it, the planning, the craftsmanship.

00:04:02.860 | In another life, perhaps, if I didn't love engineering

00:04:06.680 | and science so much, I could see myself being

00:04:09.040 | something like a Navy SEAL.

00:04:10.740 | And in general, I love the idea of serving my country,

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00:05:01.920 | is watch people cook, especially people who love cooking,

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00:05:09.040 | I still tend to be strict in my diet, no matter what,

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00:05:22.600 | My mom, in fact, for much of my life,

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00:07:09.340 | And now, finally, here's my conversation

00:07:12.180 | with Stephen Wolfram.

00:07:13.740 | You said that there are moments in history of physics,

00:07:17.380 | and maybe mathematical physics or even mathematics,

00:07:20.140 | where breakthroughs happen

00:07:22.420 | and then a flurry of progress follows.

00:07:24.740 | So if you look back through the history of physics,

00:07:28.280 | what moments stand out to you as important

00:07:31.140 | such breakthroughs where a flurry of progress follows?

00:07:34.500 | - So the big famous one was 1920s,

00:07:36.820 | the invention of quantum mechanics,

00:07:38.900 | where in about five or 10 years,

00:07:41.900 | lots of stuff got figured out.

00:07:43.700 | That's now quantum mechanics.

00:07:44.980 | - Can you mention the people involved?

00:07:46.580 | - Yeah, it was kind of the Schrodinger, Heisenberg,

00:07:50.580 | Einstein had been a key figure,

00:07:52.420 | originally Planck, then Dirac was a little bit later.

00:07:56.520 | That was something that happened at that time,

00:07:58.140 | that's sort of before my time, right?

00:08:00.420 | In my time was in the 1970s,

00:08:03.980 | there was this sort of realization

00:08:06.260 | that quantum field theory was actually going to be useful

00:08:09.060 | in physics and QCD, quantum carbon dynamics theory

00:08:13.000 | of quarks and gluons and so on was really getting started.

00:08:16.060 | And there was again,

00:08:17.900 | sort of big flurry of things happened then.

00:08:20.340 | I happened to be a teenager at that time

00:08:22.380 | and happened to be really involved in physics.

00:08:26.500 | And so I got to be part of that, which was really cool.

00:08:29.700 | - Who were the key figures

00:08:31.060 | aside from your young selves at that time?

00:08:33.860 | - You know, who won the Nobel prize for QCD, okay?

00:08:37.020 | People, David Gross, Frank Wilczek, David Politzer,

00:08:41.420 | the people who are the sort of the slightly older generation,

00:08:43.980 | Dick Feynman, Murray Gell-Mann, people like that,

00:08:47.080 | who were Steve Weinberg, Gerhard Hoft,

00:08:51.700 | he's younger, he's in the younger group actually,

00:08:54.780 | but these are all characters who were involved.

00:08:59.220 | I mean, it's funny because those are all people

00:09:02.500 | who are kind of in my time and I know them

00:09:05.020 | and they don't seem like sort of

00:09:06.940 | these historical, iconic figures.

00:09:10.140 | They seem more like everyday characters, so to speak.

00:09:13.740 | So it's always, when you look at history

00:09:18.060 | from long afterwards,

00:09:20.380 | it always seems like everything happened instantly.

00:09:23.120 | And that's usually not the case.

00:09:25.680 | There was usually a long buildup,

00:09:27.380 | but usually there's some methodological thing happens

00:09:30.900 | and then there's a whole bunch of low-hanging fruit

00:09:32.540 | to be picked and that usually lasts five or 10 years.

00:09:36.700 | We see it today with machine learning

00:09:38.700 | and deep learning neural nets and so on,

00:09:43.200 | methodological advance, things actually started working

00:09:45.780 | in 2011, 2012 and so on.

00:09:48.380 | And there's been this sort of rapid picking

00:09:52.060 | of low-hanging fruit, which is probably

00:09:54.820 | some significant fraction of the way done, so to speak.

00:10:00.060 | - Do you think there's a key moment?

00:10:01.580 | Like if I had to really introspect,

00:10:03.100 | like what was the key moment for the deep learning

00:10:05.700 | quote unquote revolution?

00:10:08.020 | I mean-- - It's probably

00:10:08.940 | the AlexNet business. - AlexNet with ImageNet.

00:10:11.460 | So is there something like that with physics where,

00:10:14.440 | so deep learning neural networks have been around

00:10:18.540 | for a long time.

00:10:19.860 | - Absolutely, since the 1940s, yeah.

00:10:21.980 | - There's a bunch of little pieces that came together

00:10:23.900 | and then all of a sudden everybody's eyes lit up.

00:10:27.440 | Like, wow, there's something here.

00:10:29.780 | Like even just looking at your own work,

00:10:32.460 | just your thinking about the universe,

00:10:34.300 | that there's simple rules can create complexity.

00:10:38.860 | At which point was there a thing where your eyes light up?

00:10:45.060 | It's like, wait a minute, there's something here.

00:10:46.500 | Is it the very first idea or is it some moment

00:10:51.500 | along the line of implementations and experiments

00:10:54.060 | and so on? - Yeah, there's a couple

00:10:55.340 | of different stages to this.

00:10:56.580 | One is the think about the world computationally.

00:11:01.060 | Can we use programs instead of equations

00:11:03.900 | to make models of the world?

00:11:05.900 | That's something that I got interested in

00:11:07.740 | in the beginning of the 1980s.

00:11:10.380 | I did a bunch of computer experiments.

00:11:13.020 | When I first did them, I didn't really,

00:11:15.820 | I could see some significance to them,

00:11:17.500 | but it took me a few years to really say,

00:11:19.980 | wow, there's a big important phenomenon here

00:11:22.900 | that lets sort of complex things arise

00:11:25.380 | from very simple programs.

00:11:27.340 | That kind of happened back in 1984 or so.

00:11:30.540 | Then a bunch of other years go by,

00:11:32.980 | then I start actually doing a lot

00:11:35.500 | of much more systematic computer experiments and things

00:11:37.700 | and find out that this phenomenon

00:11:39.900 | that I could only have said occurs in one particular case

00:11:43.020 | is actually something incredibly general.

00:11:45.100 | And then that led me to this thing

00:11:46.380 | called principle of computational equivalence.

00:11:48.660 | And that was a long story.

00:11:51.100 | And then as part of that process, I was like,

00:11:54.420 | okay, you can make simple programs,

00:11:56.860 | can make models of complicated things.

00:11:59.220 | What about the whole universe?

00:12:00.700 | That's our sort of ultimate example of a complicated thing.

00:12:03.740 | And so I got to thinking,

00:12:05.100 | could we use these ideas to study fundamental physics?

00:12:09.540 | I happen to know a lot

00:12:11.420 | about traditional fundamental physics.

00:12:13.940 | My first, I had a bunch of ideas

00:12:17.300 | about how to do this in the early 1990s.

00:12:19.380 | I made a bunch of technical progress.

00:12:21.060 | I figured out a bunch of things

00:12:22.140 | I thought were pretty interesting.

00:12:24.220 | I wrote about them back in 2002.

00:12:26.620 | - With the new kind of science

00:12:27.820 | in the cellular automata world.

00:12:29.220 | - Right.

00:12:30.060 | - There's echoes in the cellular automata world

00:12:32.220 | with your new Wolfram physics project.

00:12:36.700 | We'll get to all that.

00:12:37.660 | Allow me to sort of romanticize a little more

00:12:40.300 | on the philosophy of science.

00:12:41.980 | So Thomas Kuhn, a philosopher of science,

00:12:45.620 | describes that the progress in science

00:12:49.460 | is made with these paradigm shifts.

00:12:53.140 | And so to linger on the sort of original line of discussion,

00:12:56.940 | do you agree with this view

00:12:58.140 | that there is revolutions in science

00:13:01.540 | that just kind of flip the table?

00:13:03.420 | - What happens is it's a different way

00:13:05.900 | of thinking about things.

00:13:07.020 | It's a different methodology for studying things.

00:13:09.940 | And that opens stuff up.

00:13:11.740 | - There's this idea of,

00:13:13.220 | he's a famous biographer,

00:13:16.820 | but I think it's called the Innovators.

00:13:19.620 | The biographer of Steve Jobs, of Albert Einstein.

00:13:22.660 | He also wrote a book,

00:13:23.620 | I think it's called The Innovators,

00:13:24.780 | where he discusses how a lot of the innovations

00:13:29.780 | in the history of computing has been done by groups.

00:13:33.860 | There's a complicated group dynamic going on.

00:13:37.380 | But there's also a romanticized notion

00:13:39.340 | that the individual is at the core of the revolution.

00:13:42.780 | Like where does your sense fall?

00:13:45.300 | Is ultimately like one person responsible

00:13:49.940 | for these revolutions that creates the spark?

00:13:52.700 | Or one or two, whatever.

00:13:54.620 | Or is it just the big mush and mess and chaos

00:13:58.820 | of people interacting, of personalities interacting?

00:14:01.380 | - I think it ends up being like many things,

00:14:03.180 | there's leadership and there ends up being,

00:14:05.420 | it's a lot easier for one person to have a crisp new idea

00:14:08.100 | than it is for a big committee to have a crisp new idea.

00:14:10.900 | And I think, but I think it can happen

00:14:13.740 | that you have a great idea,

00:14:16.500 | but the world isn't ready for it.

00:14:19.180 | And you can, I mean, this has happened to me plenty, right?

00:14:24.180 | You have an idea, it's actually a pretty good idea,

00:14:27.220 | but things aren't ready.

00:14:29.300 | Either you're not really ready for it,

00:14:31.700 | or the ambient world isn't ready for it.

00:14:34.540 | And it's hard to get the thing to get traction.

00:14:37.900 | - It's kind of interesting.

00:14:38.740 | I mean, when I look at a new kind of science,

00:14:41.740 | you're now living inside the history,

00:14:43.660 | so you can't tell the story of these decades.

00:14:46.700 | But it seems like the new kind of science

00:14:49.660 | has not had the revolutionary impact

00:14:54.660 | I would think it might.

00:14:59.140 | Like, it feels like at some point, of course it might be,

00:15:02.620 | but it feels at some point people will return to that book

00:15:06.260 | and say there was something special here.

00:15:09.580 | This was incredible.

00:15:10.420 | - Well, look, what happened--

00:15:11.860 | - Or do you think that's already happened?

00:15:13.580 | - Oh yeah, it's happened, except that people aren't,

00:15:16.020 | you know, the sort of the heroism of it may not be there.

00:15:19.500 | But what's happened is for 300 years,

00:15:22.780 | people basically said,

00:15:24.540 | if you want to make a model of things in the world,

00:15:27.060 | mathematical equations are the best place to go.

00:15:29.780 | Last 15 years, doesn't happen.

00:15:32.220 | You know, new models that get made of things

00:15:34.620 | most often are made with programs, not with equations.

00:15:38.620 | Now, you know, was that sort of going to happen anyway?

00:15:42.300 | Was that a consequence of, you know,

00:15:44.620 | my particular work and my particular book?

00:15:47.260 | It's hard to know for sure.

00:15:48.820 | I mean, I am always amazed at the amounts of feedback

00:15:51.580 | that I get from people where they say,

00:15:52.980 | oh, by the way, you know,

00:15:54.340 | I started doing this whole line of research

00:15:56.100 | because I read your book, blah, blah, blah, blah, blah.

00:15:58.580 | It's like, well, can you tell that

00:15:59.940 | from the academic literature?

00:16:01.060 | You know, was there a chain of, you know,

00:16:03.100 | academic references?

00:16:04.540 | Probably not.

00:16:05.860 | - One of the interesting side effects of publishing

00:16:09.100 | in the way you did this tome

00:16:11.980 | is it serves as an education tool and an inspiration

00:16:15.340 | to hundreds of thousands, millions of people,

00:16:19.260 | but because it's not a single,

00:16:21.700 | it's not a chain of papers with 50 titles,

00:16:25.220 | it doesn't create a splash of citations.

00:16:28.780 | - It's had plenty of citations,

00:16:30.620 | but it's, you know, I think that the,

00:16:32.900 | people think of it as probably more, you know,

00:16:36.900 | conceptual inspiration than kind of a, you know,

00:16:42.020 | this is a line from here to here to here

00:16:43.860 | in our particular field.

00:16:45.420 | I think that the, you know,

00:16:46.700 | the thing which I am disappointed by

00:16:49.500 | and which will eventually happen

00:16:51.420 | is this kind of study of the,

00:16:53.900 | this sort of pure computationalism,

00:16:55.820 | this kind of study of the abstract behavior

00:16:58.580 | of the computational universe.

00:17:00.500 | That should be a big thing that lots of people do.

00:17:03.980 | - You mean in mathematics purely, almost like-

00:17:06.340 | - It's like pure mathematics, but it isn't mathematics.

00:17:08.860 | - But it isn't.

00:17:09.700 | - It's a new kind of mathematics.

00:17:12.340 | Is it a title of a book?

00:17:14.380 | - Yeah, right.

00:17:15.220 | - Good title.

00:17:16.060 | - That's why the book is called that, right?

00:17:17.900 | That's not coincidental.

00:17:19.180 | - Yeah.

00:17:20.180 | It's interesting that I haven't seen

00:17:22.860 | really rigorous investigation

00:17:24.980 | by thousands of people of this idea.

00:17:26.900 | I mean, you look at your competition around rule 30.

00:17:30.100 | I mean, that's fascinating.

00:17:31.340 | If you can say something,

00:17:33.540 | is there some aspect of this thing that could be predicted?

00:17:38.820 | That's the fundamental question of science.

00:17:40.940 | That's the core.

00:17:41.780 | - Well, that has been a question of science.

00:17:42.860 | I think that is some people's view of what science is about,

00:17:47.460 | and it's not clear that's the right view.

00:17:48.940 | In fact, as we live through this pandemic

00:17:51.500 | full of predictions and so on,

00:17:53.300 | it's an interesting moment to be pondering

00:17:55.340 | what science's actual role in those kinds of things is.

00:17:58.420 | - Oh, you think it's possible that in science,

00:18:02.060 | clean, beautiful, simple prediction

00:18:04.900 | may not even be possible in real systems.

00:18:07.220 | That's the open question.

00:18:08.260 | - Right, I don't think it's open.

00:18:09.540 | I think that question is answered, and the answer is no.

00:18:12.180 | - Well, no, no.

00:18:13.100 | The answer could be just humans are not smart enough yet.

00:18:16.700 | We don't have the tools yet.

00:18:17.540 | - No, no, that's the whole point.

00:18:18.660 | I mean, that's sort of the big discovery

00:18:20.660 | of this principle of computational equivalence of mind.

00:18:23.300 | And this is something which is kind of a follow-on

00:18:26.820 | to Godel's theorem, to Turing's work on the halting problem,

00:18:30.180 | all these kinds of things,

00:18:31.620 | that there is this fundamental limitation

00:18:34.660 | built into science,

00:18:36.300 | this idea of computational irreducibility,

00:18:39.060 | that says that even though you may know the rules

00:18:42.420 | by which something operates,

00:18:44.100 | that does not mean that you can readily

00:18:47.100 | sort of be smarter than it and jump ahead

00:18:49.700 | and figure out what it's going to do.

00:18:51.580 | - Yes, but do you think there's a hope

00:18:53.700 | for pockets of computational reducibility?

00:18:56.700 | - Yes, yes.

00:19:02.060 | - So, and then a set of tools and mathematics

00:19:04.780 | that help you discover such pockets.

00:19:07.020 | - That's where we live, is in the pockets of reducibility.

00:19:10.140 | That's why, and this is one of the things

00:19:12.500 | that sort of come out of this physics project

00:19:14.020 | and actually something that, again,

00:19:15.460 | I should have realized many years ago, but didn't,

00:19:17.900 | it could very well be that everything about the world

00:19:23.380 | is computationally irreducible and completely unpredictable.

00:19:26.540 | But in our experience of the world,

00:19:29.700 | there is at least some amount of prediction we can make.

00:19:32.500 | And that's because we have sort of chosen a slice of,

00:19:36.540 | probably talk about this in much more detail,

00:19:38.300 | but I mean, we've kind of chosen a slice

00:19:39.900 | of how to think about the universe

00:19:41.740 | in which we can kind of sample a certain amount

00:19:44.500 | of computational reducibility.

00:19:46.620 | And that's sort of where we exist.

00:19:51.620 | And it may not be the whole story of how the universe is,

00:19:55.900 | but it is the part of the universe that we care about

00:19:59.220 | and we sort of operate in.

00:20:00.980 | And that's, in science,

00:20:03.580 | that's been sort of a very special case of that.

00:20:05.700 | That is science has chosen to talk a lot about places

00:20:09.340 | where there is this computational reducibility

00:20:12.100 | that it can find, the motion of the planets

00:20:14.740 | can be more or less predicted.

00:20:16.260 | Something about the weather is much harder to predict.

00:20:20.660 | Something about other kinds of things

00:20:22.820 | are much harder to predict.

00:20:25.180 | And it's, these are, but science has tended to

00:20:29.380 | concentrate itself on places where its methods

00:20:32.500 | have allowed successful prediction.

00:20:35.100 | - So you think rule 30, if we could linger on it,

00:20:38.220 | because it's just such a beautiful, simple formulation

00:20:41.580 | of the essential concept underlying

00:20:43.500 | all the things we're talking about.

00:20:45.020 | Do you think there's pockets of reducibility

00:20:47.260 | inside rule 30?

00:20:48.500 | - Yes.

00:20:49.380 | That is the question of how big are they?

00:20:51.620 | What will they allow you to say?

00:20:53.140 | And so on.

00:20:53.980 | And that's, and figuring out where those pockets are,

00:20:56.980 | I mean, in a sense, that's the,

00:20:58.740 | that's sort of a, you know,

00:21:00.900 | that is an essential thing that one

00:21:03.260 | would like to do in science.

00:21:05.820 | But it's also, the important thing to realize

00:21:08.820 | that has not been, you know, is that science,

00:21:13.820 | if you just pick an arbitrary thing,

00:21:15.420 | you say, what's the answer to this question?

00:21:18.140 | That question may not be one

00:21:20.220 | that has a computationally reducible answer.

00:21:22.900 | That question, if you choose, you know,

00:21:26.220 | if you walk along the series of questions

00:21:28.860 | and you've got one that's reducible

00:21:30.260 | and you get to another one that's nearby

00:21:31.660 | and it's reducible too,

00:21:32.980 | if you stick to that kind of,

00:21:35.020 | stick to the land, so to speak,

00:21:37.220 | then you can go down this chain

00:21:39.620 | of sort of reducible, answerable things.

00:21:41.940 | But if you just say,

00:21:42.980 | I'm just pick a question at random,

00:21:44.460 | I'm going to have my computer pick a question at random.

00:21:46.980 | - Yeah, most likely it's going to be reducible.

00:21:49.260 | - Most likely it will be irreducible.

00:21:50.940 | And what we're throwing in the world, so to speak,

00:21:54.700 | we, you know, when we engineer things,

00:21:56.420 | we tend to engineer things to sort of keep

00:21:58.300 | in the zone of reducibility.

00:22:00.260 | When we're throwing things by the natural world,

00:22:02.260 | for example, not at all certain

00:22:05.500 | that we will be kept in this kind of zone of reducibility.

00:22:08.660 | - Can we talk about this pandemic then?

00:22:11.260 | - Sure.

00:22:12.100 | (laughing)

00:22:12.940 | - For a second.

00:22:13.780 | Is this, so how do we,

00:22:15.980 | there's obviously huge amount of economic pain

00:22:18.900 | that people are feeling.

00:22:19.780 | There's a huge incentive and medical pain,

00:22:23.940 | health, just all kinds of psychological.

00:22:26.740 | There's a huge incentive to figure this out,

00:22:28.740 | to walk along the trajectory of reducibility.

00:22:33.300 | There's a lot of disparate data.

00:22:38.060 | You know, people understand generally how virus is spread,

00:22:40.500 | but it's very complicated

00:22:43.220 | because there's a lot of uncertainty.

00:22:45.060 | There could be a lot of variability,

00:22:49.340 | like so many, obviously,

00:22:51.740 | a nearly infinite number of variables

00:22:53.620 | that represent human interaction.

00:22:57.940 | And so you have to figure out,

00:22:59.940 | from the perspective of reducibility,

00:23:02.700 | figure out which variables are really important

00:23:06.620 | in this kind of, from an epidemiological perspective.

00:23:10.620 | So why aren't we,

00:23:13.140 | you kind of said that we're clearly failing.

00:23:15.980 | - Well, I think it's a complicated thing.

00:23:17.380 | So, I mean, you know, when this pandemic started up,

00:23:20.220 | you know, I happened to be in the middle

00:23:21.860 | of being about to release this whole physics project thing.

00:23:24.780 | But I thought, you know-

00:23:25.620 | - The timing is just cosmically absurd.

00:23:28.260 | - A little bit bizarre.

00:23:29.100 | But, you know, but I thought, you know,

00:23:31.340 | I should do the public service thing of, you know,

00:23:33.980 | trying to understand what I could about the pandemic.

00:23:36.020 | And, you know, we've been curating data about it

00:23:38.140 | and all that kind of thing.

00:23:39.300 | But, you know, so I started looking at the data

00:23:41.660 | and started looking at modeling,

00:23:43.620 | and I decided it's just really hard.

00:23:46.020 | You need to know a lot of stuff

00:23:47.260 | that we don't know about human interactions.

00:23:49.860 | It's actually clear now that there's a lot of stuff

00:23:51.620 | we didn't know about viruses

00:23:53.500 | and about the way immunity works and so on.

00:23:56.020 | And it's, you know, I think what will come out in the end

00:23:58.860 | is there's a certain amount of what happens

00:24:02.020 | that we just kind of have to trace each step

00:24:04.380 | and see what happens.

00:24:05.820 | There's a certain amount of stuff

00:24:06.980 | where there's gonna be a big narrative

00:24:08.340 | about this happened because, you know, of T cell immunity.

00:24:12.260 | This happened because there's this whole giant

00:24:14.380 | sort of field of asymptomatic viral stuff out there.

00:24:18.700 | You know, there will be a narrative,

00:24:20.180 | and that narrative, whenever there's a narrative,

00:24:22.380 | that's kind of a sign of reducibility.

00:24:24.620 | But when you just say, "Let's from first principles

00:24:27.180 | figure out what's going on,"

00:24:28.860 | then you can potentially be stuck

00:24:30.860 | in this kind of mess of irreducibility

00:24:33.700 | where you just have to simulate each step,

00:24:35.660 | and you can't do that unless you know details

00:24:37.820 | about, you know, human interaction networks

00:24:40.100 | and so on and so on and so on.

00:24:41.340 | The thing that has been very sort of frustrating to see

00:24:46.340 | is the mismatch between people's expectations

00:24:48.900 | about what science can deliver

00:24:50.740 | and what science can actually deliver, so to speak,

00:24:53.700 | because people have this idea that, you know, it's science,

00:24:56.780 | so there must be a definite answer,

00:24:58.460 | and we must be able to know that answer.

00:25:00.500 | And, you know, this is, it is both, you know,

00:25:05.100 | when you've, after you've played around

00:25:07.580 | with sort of little programs in the computational universe,

00:25:10.100 | you don't have that intuition anymore.

00:25:11.820 | You know, it's, I always, I'm always fond of saying,

00:25:14.500 | you know, the computational animals

00:25:17.020 | are always smarter than you are.

00:25:18.260 | That is, you know, you look at one of these things,

00:25:20.260 | and it's like, it can't possibly do such and such a thing.

00:25:23.260 | Then you run it, and it's like, wait a minute,

00:25:25.260 | it's doing that thing.

00:25:26.180 | How does that work?

00:25:27.500 | Okay, now I can go back and understand it.

00:25:29.340 | - But that's the brave thing about science,

00:25:31.520 | is that in the chaos of the irreducible universe,

00:25:35.900 | we nevertheless persist to find those pockets.

00:25:38.620 | That's kind of the whole point.

00:25:40.260 | That's, like you say that the limits of science,

00:25:43.060 | but that, you know, yes, it's highly limited,

00:25:46.820 | but there's a hope there.

00:25:48.860 | And like, there's so many questions I wanna ask here.

00:25:52.020 | So one, you said narrative, which is really interesting.

00:25:54.220 | So obviously from a, at every level of society,

00:25:58.100 | you look at Twitter, everybody's constructing narratives

00:26:00.460 | about the pandemic, about not just the pandemic,

00:26:03.200 | but all the cultural tension that we're going through.

00:26:06.100 | So there's narratives, but they're not necessarily

00:26:08.860 | connected to the underlying reality of these systems.

00:26:14.700 | So our human narratives, I don't even know if they're,

00:26:18.300 | I don't like those pockets of reducibility,

00:26:22.500 | 'cause we're, it's like constructing things

00:26:26.900 | that are not actually representative of reality,

00:26:29.180 | and thereby not giving us like good solutions

00:26:33.660 | to how to predict the system.

00:26:36.820 | - Look, it gets complicated because, you know,

00:26:38.420 | people want to say, explain the pandemic to me.

00:26:41.220 | Explain what's gonna happen.

00:26:42.500 | - In the future, like predict.

00:26:43.620 | - Yes, but also, can you explain it?

00:26:45.300 | Is there a story to tell?

00:26:46.580 | - What already happened in the past.

00:26:48.580 | - Yeah, or what's going to happen, but I mean,

00:26:50.700 | it's similar to sort of explaining things in AI

00:26:54.100 | or in any computational system.

00:26:55.420 | It's like, you know, explain what happened.

00:26:57.820 | Well, it could just be this happened

00:26:59.860 | because of this detail and this detail and this detail

00:27:02.100 | and a million details, and there isn't a big story to tell.

00:27:05.460 | There's no kind of big arc of the story

00:27:07.900 | that's going to happen.

00:27:08.740 | There's no kind of big arc of the story that says,

00:27:12.020 | oh, it's because, you know, there's a viral field

00:27:14.500 | that has these properties and people start showing symptoms.

00:27:17.700 | You know, when the seasons change,

00:27:20.060 | people will show symptoms and people don't even understand,

00:27:22.300 | you know, seasonal variation of flu, for example.

00:27:24.700 | It's something where, you know,

00:27:28.500 | there could be a big story

00:27:29.980 | or it could be just a zillion little details that mount up.

00:27:33.860 | - See, but, okay, let's pretend that this pandemic,

00:27:38.260 | like the coronavirus, resembles something

00:27:41.100 | like the 1D Rule 30 cellular automata, okay?

00:27:45.860 | So, I mean, that's how epidemiologists model virus spread.

00:27:50.860 | - Indeed, yes.

00:27:52.740 | They sometimes use cellular automata, yes.

00:27:55.380 | - And, okay, so you could say it's simplistic,

00:27:57.300 | but, okay, let's say it's representative

00:28:00.540 | of actually what happens.

00:28:02.340 | You know, the dynamic of, you have a graph.

00:28:07.500 | It probably is closer to the hypergraph model.

00:28:09.740 | - It is, yes.

00:28:10.580 | It's actually, that's another funny thing.

00:28:13.300 | As we were getting ready to release this physics project,

00:28:15.340 | we realized that a bunch of things we'd worked out

00:28:17.220 | about foliations of causal graphs and things

00:28:20.700 | were directly relevant to thinking about contact tracing

00:28:24.220 | and interactions with cell phones and so on,

00:28:25.940 | which is really weird.

00:28:27.220 | - But, like, it just feels like we should be able

00:28:30.620 | to get some beautiful core insight

00:28:32.980 | about the spread of this particular virus

00:28:36.740 | on the hypergraph of human civilization, right?

00:28:40.100 | - I tried.

00:28:40.940 | I didn't manage to figure it out.

00:28:42.380 | - But you're one person.

00:28:43.580 | - Yeah, but, I mean, I think, actually,

00:28:45.380 | it's a funny thing 'cause it turns out the main model,

00:28:48.420 | you know, this SIR model, I only realized recently,

00:28:51.340 | was invented by the grandfather of a good friend of mine

00:28:54.340 | from high school, so that was just a,

00:28:56.740 | you know, it's a weird thing, right?

00:28:58.860 | The question is, you know, okay, so you know,

00:29:02.060 | you know, on this graph of how humans are connected,

00:29:04.460 | you know something about what happens

00:29:05.940 | if this happens and that happens.

00:29:07.580 | That graph is made in complicated ways

00:29:09.740 | that depends on all sorts of issues that,

00:29:12.060 | where we don't have the data about how human society works

00:29:14.780 | well enough to be able to make that graph.

00:29:17.220 | There's actually, one of my kids did a study

00:29:20.580 | of sort of what happens on different kinds of graphs

00:29:23.420 | and how robust are the results.

00:29:25.580 | Okay, his basic answer is there are few general results

00:29:28.820 | that you can get that are quite robust,

00:29:30.820 | like, you know, a small number of big gatherings

00:29:33.180 | is worse than a large number of small gatherings, okay?

00:29:36.380 | That's quite robust, but when you ask

00:29:38.660 | more detailed questions, it seemed like it just depends.

00:29:43.060 | It depends on details, in other words,

00:29:44.740 | it's kind of telling you, in that case, you know,

00:29:47.780 | the irreducibility matters, so to speak.

00:29:49.860 | It's not, there's not gonna be this kind of one

00:29:53.140 | sort of master theorem that says,

00:29:55.140 | and therefore this is how things are gonna work.

00:29:57.580 | - Yeah, but there's a certain kind of,

00:29:59.060 | from a graph perspective, the certain kind of dynamic

00:30:02.780 | to human interaction, so like large groups and small groups,

00:30:07.780 | I think it matters who the groups are.

00:30:10.580 | For example, you could imagine,

00:30:12.660 | depends how you define large,

00:30:13.780 | but you can imagine groups of 30 people,

00:30:16.400 | as long as they are cliques or whatever,

00:30:22.140 | as long as the outgoing degree of that graph is small

00:30:27.620 | or something like that, like you can imagine

00:30:29.340 | some beautiful underlying rule

00:30:31.340 | of human dynamic interaction where I can still be happy,

00:30:34.620 | where I can have a conversation with you

00:30:36.500 | and a bunch of other people that mean a lot to me

00:30:38.940 | in my life and then stay away from the bigger,

00:30:41.700 | I don't know, not going to a Miley Cyrus concert

00:30:44.300 | or something like that, and figuring out mathematically

00:30:48.640 | some nice rule of behavior. - See, this is

00:30:50.300 | an interesting thing, so I mean,

00:30:52.380 | this is the question of what you're describing

00:30:54.760 | is kind of the problem of the many situations

00:30:59.320 | where you would like to get away

00:31:00.580 | from computational irreducibility.

00:31:01.980 | A classic one in physics is thermodynamics.

00:31:05.620 | The second law of thermodynamics,

00:31:06.820 | the law that says entropy tends to increase,

00:31:09.500 | things that start orderly tend to get more disordered,

00:31:13.220 | or which is also the thing that says,

00:31:15.040 | given that you have a bunch of heat,

00:31:16.620 | it's hard, heat is the microscopic motion of molecules,

00:31:19.780 | it's hard to turn that heat

00:31:21.580 | into systematic mechanical work.

00:31:23.580 | It's hard to just take something being hot

00:31:26.260 | and turn that into, oh, all the atoms are gonna line up

00:31:29.820 | in the bar of metal and the piece of metal

00:31:31.500 | is gonna shoot in some direction.

00:31:33.620 | That's essentially the same problem

00:31:35.780 | as how do you go from this computationally irreducible

00:31:40.060 | mess of things happening

00:31:41.700 | and get something you want out of it?

00:31:43.580 | It's kind of mining, you're kind of,

00:31:45.740 | now, actually, I've understood in recent years

00:31:48.340 | that the story of thermodynamics

00:31:50.900 | is actually precisely a story

00:31:52.540 | of computational irreducibility,

00:31:54.380 | but it is already an analogy. - It's interesting.

00:31:58.620 | You can kind of see that, is can you take the,

00:32:02.100 | what you're asking to do there

00:32:03.580 | is you're asking to go from the kind of,

00:32:07.820 | the mess of all these complicated human interactions

00:32:10.100 | and all this kind of computational processes going on,

00:32:12.380 | and you say, I want to achieve

00:32:14.100 | this particular thing out of it.

00:32:15.260 | I want to kind of extract

00:32:16.900 | from the heat of what's happening,

00:32:18.700 | I want to kind of extract this useful piece

00:32:22.180 | of sort of mechanical work that I find helpful.

00:32:25.220 | I mean-- - Do you have a hope

00:32:26.380 | for the pandemic?

00:32:27.340 | So we'll talk about physics,

00:32:28.620 | but for the pandemic, can that be extracted?

00:32:31.340 | Do you think? - Well, I think--

00:32:32.180 | - What's your intuition? - The good news is

00:32:34.380 | the curves basically, for reasons we don't understand,

00:32:38.500 | the curves, the clearly measurable mortality curves

00:32:42.580 | and so on for the Northern Hemisphere have gone down.

00:32:46.420 | - Yeah, but the bad news is that

00:32:49.140 | it could be a lot worse for future viruses,

00:32:51.700 | and what this pandemic revealed

00:32:53.260 | is we're highly unprepared

00:32:55.220 | for the discovery of the pockets of reducibility

00:32:59.860 | within a pandemic that's much more dangerous.

00:33:02.580 | - Well, my guess is the specific risk of viral pandemics,

00:33:07.580 | that the pure virology and immunology of the thing,

00:33:12.800 | this will cause that to advance to the point

00:33:14.740 | where this particular risk is probably

00:33:17.420 | considerably mitigated.

00:33:19.060 | But it's, does, is the structure of modern society

00:33:24.500 | robust to all kinds of risks?

00:33:26.980 | Well, the answer is clearly no.

00:33:29.220 | And it's surprising to me the extent to which people,

00:33:34.140 | as I say, it's kind of scary actually

00:33:37.380 | how much people believe in science.

00:33:39.380 | That is people say, oh, because the science says this,

00:33:42.780 | that and the other, we'll do this and this and this,

00:33:44.340 | even though from a sort of common sense point of view,

00:33:46.780 | it's a little bit crazy.

00:33:48.500 | And people are not prepared,

00:33:50.460 | and it doesn't really work in society as it is

00:33:53.020 | for people to say, well, actually,

00:33:54.420 | we don't really know how the science works.

00:33:56.580 | People say, well, tell us what to do.

00:33:58.620 | - Yeah, because then, yeah, what's the alternative?

00:34:01.620 | For the masses, it's difficult to sit,

00:34:05.020 | it's difficult to meditate on computational reducibility.

00:34:08.600 | It's difficult to sit,

00:34:10.300 | it's difficult to enjoy a good dinner meal

00:34:13.140 | while knowing that you know nothing about the world.

00:34:15.740 | - Well, I think this is a place where,

00:34:17.860 | this is what politicians and political leaders do

00:34:21.220 | for a living, so to speak,

00:34:22.140 | is you gotta make some decision about what to do.

00:34:24.940 | And it's--

00:34:25.900 | - Tell some narrative.

00:34:26.980 | - Right.

00:34:28.260 | - While amidst the mystery and knowing not much

00:34:30.980 | about the past or the future,

00:34:33.820 | still telling a narrative that somehow gives people hope

00:34:37.300 | that we know what the heck we're doing.

00:34:39.060 | - Yeah, and get society through the issue.

00:34:41.900 | Even though the idea that we're just gonna

00:34:44.820 | be able to get the definitive answer from science,

00:34:48.660 | and it's gonna tell us exactly what to do,

00:34:50.660 | unfortunately, it's interesting,

00:34:54.380 | because let me point out that if that was possible,

00:34:56.900 | if science could always tell us what to do,

00:34:59.240 | then in a sense, that would be a big downer for our lives.

00:35:03.980 | If science could always tell us

00:35:05.100 | what the answer was gonna be,

00:35:06.820 | it's like, well, it's kind of fun to live one's life

00:35:10.180 | and just sort of see what happens.

00:35:11.760 | If one could always just say, let me check my science,

00:35:15.140 | oh, I know the result of everything is gonna be 42,

00:35:18.380 | I don't need to live my life and do what I do,

00:35:21.060 | it's just we already know the answer.

00:35:23.040 | It's actually good news in a sense

00:35:24.900 | that there is this phenomenon

00:35:26.020 | of computational irreducibility

00:35:27.700 | that doesn't allow you to just sort of jump through time

00:35:30.780 | and say this is the answer, so to speak.

00:35:33.740 | And so that's a good thing.

00:35:35.200 | The bad thing is it doesn't allow you

00:35:37.220 | to jump through time and know what the answer is.

00:35:39.700 | - It's scary.

00:35:41.020 | Do you think we're gonna be okay as a human civilization?

00:35:44.220 | You said we don't know. - Absolutely.

00:35:46.180 | Absolutely.

00:35:47.980 | - Do you think we'll prosper or destroy ourselves?

00:35:52.980 | - In general?

00:35:54.820 | - In general.

00:35:55.780 | - I'm an optimist.

00:35:57.060 | No, I think that it'll be interesting to see,

00:36:00.480 | for example, with this pandemic.

00:36:02.700 | To me, when you look at organizations, for example,

00:36:08.140 | having some kind of perturbation, some kick to the system,

00:36:12.900 | usually the end result of that is actually quite good

00:36:16.380 | unless it kills the system.

00:36:17.780 | It's actually quite good usually.

00:36:19.580 | And I think in this case, people, I mean, my impression,

00:36:23.860 | it's a little weird for me

00:36:24.900 | because I've been a remote tech CEO for 30 years.

00:36:28.140 | This is bizarrely, and the fact that

00:36:31.660 | this coming to see you here is--

00:36:34.620 | - One of the rare moments

00:36:35.700 | that human interaction-- - Is the first time

00:36:36.740 | in six months that I've been in a building

00:36:40.220 | other than my house.

00:36:41.220 | - Yeah, that's amazing.

00:36:42.460 | - So I'm a kind of ridiculous outlier

00:36:46.220 | in these kinds of things.

00:36:47.140 | - But overall, your sense is when you shake up the system

00:36:50.980 | and throw in chaos, that you challenge the system,

00:36:55.260 | we humans emerge better.

00:36:57.820 | - Seems to be that way.

00:36:58.900 | Who's to know?

00:36:59.740 | But I think that people,

00:37:02.060 | my sort of vague impression is that people are sort of,

00:37:05.540 | oh, what's actually important?

00:37:07.140 | What is worth caring about and so on?

00:37:10.460 | And that seems to be something that perhaps

00:37:13.060 | is more emergent in this kind of situation.

00:37:16.860 | - It's so fascinating that on the individual level,

00:37:19.860 | we have our own complex cognition.

00:37:22.340 | We have consciousness, we have intelligence.

00:37:24.140 | We're trying to figure out little puzzles.

00:37:25.980 | And then that somehow creates this graph

00:37:28.300 | of collective intelligence, where we figure out,

00:37:31.700 | and then you throw in these viruses

00:37:33.940 | of which there's millions different,

00:37:35.740 | there's entire taxonomy,

00:37:37.900 | and the viruses are thrown into the system

00:37:40.140 | of collective human intelligence.

00:37:42.660 | And the little humans figure out what to do about it.

00:37:45.740 | We get like, we tweet stuff about information.

00:37:48.700 | There's doctors as conspiracy theorists.

00:37:50.820 | And then we play with different information.

00:37:53.180 | I mean, the whole of it is fascinating.

00:37:55.740 | I am, like you, also very optimistic,

00:37:58.100 | but there's a, just you said the computational reducibility.

00:38:02.700 | There's always a fear of the darkness

00:38:06.480 | of the uncertainty before us.

00:38:09.820 | - Yeah, I know. - And it's scary.

00:38:11.140 | - I mean, the thing is, if you knew everything,

00:38:13.420 | it will be boring.

00:38:14.380 | (Dave laughs)

00:38:15.300 | And it would be, and then,

00:38:17.660 | and worse than boring, so to speak.

00:38:20.340 | It would be, it would reveal the pointlessness, so to speak.

00:38:24.140 | And in a sense, the fact that there is

00:38:26.580 | this computational reducibility,

00:38:28.020 | it's like as we live our lives, so to speak,

00:38:30.340 | something is being achieved.

00:38:31.660 | We're computing what our lives,

00:38:33.820 | what happens in our lives.

00:38:36.900 | - That's funny.

00:38:37.740 | So the computational reducibility

00:38:39.260 | is kind of like, it gives the meaning to life.

00:38:41.940 | It is the meaning of life.

00:38:43.300 | Computational reducibility is the meaning of life.

00:38:45.700 | There you go.

00:38:46.540 | - It gives it meaning, yes.

00:38:47.420 | I mean, it's what causes it to not be something

00:38:51.540 | where you can just say, you know,

00:38:53.500 | you went through all those steps to live your life,

00:38:55.740 | but we already knew what the answer was.

00:38:58.060 | - Right.

00:38:58.880 | - Hold on one second.

00:38:59.720 | I'm going to use my handy Wolfram Alpha

00:39:02.540 | sunburn computation thing,

00:39:04.140 | so long as I can get network here.

00:39:06.140 | There we go.

00:39:08.220 | Oh, actually, you know what?

00:39:09.460 | It says sunburn unlikely.

00:39:11.460 | This is a QA moment.

00:39:12.660 | (laughing)

00:39:15.460 | - This is a good moment.

00:39:16.700 | - Okay, well, let me just check what it thinks.

00:39:20.220 | I can see why it thinks that.

00:39:22.020 | It doesn't seem like my intuition.

00:39:23.540 | This is one of these cases where we can,

00:39:25.340 | the question is, do we trust the science

00:39:27.820 | or do we use common sense?

00:39:30.340 | - The UV thing is cool.

00:39:31.980 | - Yeah, yeah, well, we'll see.

00:39:32.860 | This is a QA moment, as I say.

00:39:35.100 | (laughing)

00:39:36.940 | Do we trust the product?

00:39:37.940 | Yes, we trust the product.

00:39:39.580 | - And then there'll be a data point either way.

00:39:41.940 | - If I'm desperately sunburned,

00:39:43.540 | I will send in an angry feedback.

00:39:46.820 | - Because we mentioned the concept so much,

00:39:50.780 | and a lot of people know it,

00:39:51.940 | but can you say what computation reducibility is?

00:39:54.460 | - Yeah, right.

00:39:55.300 | So the question is, if you think about things

00:39:58.780 | that happen as being computations,

00:40:01.180 | you think about some process in physics,

00:40:06.100 | something that you compute in mathematics, whatever else,

00:40:09.140 | it's a computation in the sense it has definite rules.

00:40:11.940 | You follow those rules, you follow them many steps,

00:40:16.540 | and you get some result.

00:40:18.380 | So then the issue is, if you look at all these different

00:40:21.100 | kinds of computations that can happen,

00:40:22.740 | whether they're computations that are happening

00:40:24.220 | in the natural world,

00:40:25.060 | whether they're happening in our brains,

00:40:26.540 | whether they're happening in our mathematics,

00:40:28.060 | whatever else, the big question is,

00:40:29.860 | how do these computations compare?

00:40:32.100 | Is, are there dumb computations and smart computations?

00:40:35.540 | Or are they somehow all equivalent?

00:40:37.540 | And the thing that I kind of was sort of surprised to realize

00:40:41.700 | from a bunch of experiments that I did in the early '90s,

00:40:43.940 | and now we have tons more evidence for it,

00:40:46.060 | this thing I call

00:40:46.900 | the principle of computational equivalence,

00:40:48.860 | which basically says, when one of these computations,

00:40:51.940 | one of these processes that follows rules,

00:40:54.300 | doesn't seem like it's doing something obviously simple,

00:40:57.640 | then it has reached the sort of equivalent level

00:41:00.100 | of computational sophistication of everything.

00:41:03.700 | So what does that mean?

00:41:04.540 | That means that, you know, you might say,

00:41:07.220 | gosh, I'm studying this little tiny, you know,

00:41:10.140 | tiny program on my computer,

00:41:11.580 | I'm studying this little thing in nature,

00:41:14.260 | but I have my brain,

00:41:15.320 | and my brain is surely much smarter than that thing.

00:41:18.380 | I'm gonna be able to systematically outrun

00:41:20.480 | the computation that it does,

00:41:22.060 | because I have a more sophisticated computation

00:41:23.980 | that I can do.

00:41:25.160 | But what the principle of computational equivalence says

00:41:27.420 | is that doesn't work.

00:41:28.980 | Our brains are doing computations

00:41:31.780 | that are exactly equivalent

00:41:33.480 | to the kinds of computations that are being done

00:41:35.120 | in all these other sorts of systems.

00:41:36.900 | And so what consequences does that have?

00:41:38.300 | Well, it means that we can't systematically

00:41:40.660 | outrun these systems.

00:41:42.240 | These systems are computationally irreducible,

00:41:45.820 | in the sense that there's no sort of shortcut

00:41:47.780 | that we can make that jumps to the answer.

00:41:50.420 | - In a general case.

00:41:51.860 | - Right, right.

00:41:52.700 | But the, so what has happened, you know,

00:41:55.280 | what science has become used to doing

00:41:58.740 | is using the little sort of pockets

00:42:00.740 | of computational reducibility,

00:42:02.820 | which by the way are an inevitable consequence

00:42:04.780 | of computational irreducibility,

00:42:06.700 | that there have to be these pockets scattered around

00:42:09.500 | of computational reducibility

00:42:11.480 | to be able to find those particular cases

00:42:14.420 | where you can jump ahead.

00:42:15.260 | I mean, one thing, sort of a little bit

00:42:17.300 | of a parable type thing that I think is fun to tell,

00:42:20.260 | you know, if you look at ancient Babylon,

00:42:22.420 | they were trying to predict three kinds of things.

00:42:25.120 | They tried to predict, you know,

00:42:26.460 | where the planets would be,

00:42:27.940 | what the weather would be like,

00:42:29.440 | and who would win or lose a certain battle.

00:42:32.140 | And they had no idea which of these things

00:42:34.620 | would be more predictable than the other.

00:42:36.500 | - That's funny.

00:42:37.340 | - And, you know, it turns out, you know,

00:42:39.640 | where the planets are is a piece

00:42:41.860 | of computational reducibility that, you know,

00:42:44.380 | 300 years ago or so, we pretty much cracked.

00:42:46.700 | I mean, it's been technically difficult

00:42:48.040 | to get all the details right,

00:42:49.080 | but it's basically, we got that.

00:42:51.740 | You know, who's gonna win or lose the battle?

00:42:54.200 | No, we didn't crack that one.

00:42:55.420 | That one, that one.

00:42:56.260 | - I can't.

00:42:57.080 | - Right.

00:42:57.920 | - Game theorists are trying.

00:42:58.980 | - Yes.

00:42:59.820 | - And then the weather.

00:43:00.820 | - It's kind of halfway on that one.

00:43:02.620 | - Halfway?

00:43:03.460 | - Yeah, I think we're doing okay on that one.

00:43:04.980 | You know, long-term climate, different story.

00:43:07.420 | But the weather, you know, we're much closer on that.

00:43:10.100 | - But do you think eventually we'll figure out the weather?

00:43:11.940 | So do you think eventually most think

00:43:15.160 | we'll figure out the local pockets in everything,

00:43:17.660 | essentially, the local pockets of reducibility?

00:43:19.820 | - No, I think that it's an interesting question,

00:43:22.700 | but I think that the, you know,

00:43:24.060 | there is an infinite collection of these local pockets.

00:43:26.700 | We'll never run out of local pockets.

00:43:28.580 | And by the way, those local pockets

00:43:30.620 | are where we build engineering, for example.

00:43:33.180 | That's how we, you know, when we,

00:43:34.900 | if we want to have a predictable life, so to speak,

00:43:38.060 | then, you know, we have to build

00:43:40.540 | in these sort of pockets of reducibility.

00:43:43.060 | Otherwise, you know, if we were,

00:43:44.900 | if we were sort of existing

00:43:46.560 | in this kind of irreducible world,

00:43:48.760 | we'd never be able to, you know,

00:43:50.700 | have definite things to know what's gonna happen.

00:43:53.080 | You know, I have to say, I think one of the features,

00:43:55.260 | you know, when we look at sort of today

00:43:58.060 | from the future, so to speak,

00:43:59.940 | I suspect one of the things where people will say,

00:44:02.060 | "I can't believe they didn't see that,"

00:44:04.460 | is stuff to do with the following kind of thing.

00:44:07.020 | So, you know, if we describe, oh, I don't know,

00:44:10.180 | something like heat, for instance,

00:44:12.900 | we say, "Oh, you know, the air in here,

00:44:16.900 | "it's, you know, it's this temperature, this pressure."

00:44:19.540 | That's as much as we can say.

00:44:20.820 | Otherwise, just a bunch of random molecules bouncing around.

00:44:23.740 | People will say, "I just can't believe

00:44:25.700 | "they didn't realize that there was all this detail

00:44:27.640 | "and how all these molecules were bouncing around

00:44:29.740 | "and they could make use of that."

00:44:32.300 | And actually, I realized,

00:44:33.140 | there's a thing I realized last week, actually,

00:44:35.220 | was a thing that people say, you know,

00:44:37.180 | one of the scenarios for the very long-term history

00:44:39.460 | of our universe is a so-called heat death of the universe,

00:44:43.060 | where basically everything just becomes

00:44:45.340 | thermodynamically boring.

00:44:47.660 | Everything's just this big kind of gas

00:44:49.340 | in thermal equilibrium.

00:44:50.580 | People say, "That's a really bad outcome."

00:44:53.140 | But actually, it's not a really bad outcome.

00:44:55.460 | It's an outcome where there's all this computation

00:44:57.460 | going on and all those individual gas molecules

00:44:59.440 | are all bouncing around in very complicated ways,

00:45:01.920 | doing this very elaborate computation.

00:45:04.020 | It just happens to be a computation that right now,

00:45:06.880 | we haven't found ways to understand.

00:45:10.080 | We haven't found ways, you know, our brains haven't,

00:45:12.800 | you know, and our mathematics and our science and so on,

00:45:15.440 | haven't found ways to tell an interesting story about that.

00:45:18.440 | It just looks boring to us.

00:45:20.080 | - You're saying there's a hopeful view of the heat death,

00:45:25.080 | quote-unquote, of the universe,

00:45:26.760 | where there's actual beautiful complexity going on,

00:45:30.840 | similar to the kind of complexity we think of

00:45:34.900 | that creates rich experience in human life

00:45:37.320 | and life on Earth? - Yes.

00:45:38.580 | - So those little molecules interact in complex ways.

00:45:41.120 | There could be intelligence in that.

00:45:43.160 | There could be-- - Absolutely.

00:45:44.440 | I mean, this is what you learn from this principle.

00:45:46.440 | - Wow, that's a hopeful message.

00:45:48.280 | - Right, I mean, this is what you kind of learn

00:45:49.840 | from this principle of computational equivalence.

00:45:52.000 | You learn it's both a message of sort of hope

00:45:56.480 | and a message of kind of, you know,

00:45:59.320 | you're not as special as you think you are, so to speak.

00:46:01.400 | I mean, because, you know, we imagine that

00:46:03.800 | with sort of all the things we do with human intelligence

00:46:06.640 | and all that kind of thing,

00:46:07.920 | and all of the stuff we've constructed in science,

00:46:10.180 | it's like, we're very special,

00:46:12.280 | but actually it turns out, well, no, we're not.

00:46:15.480 | We're just doing computations

00:46:17.280 | like things in nature do computations,

00:46:19.760 | like those gas molecules do computations,

00:46:21.600 | like the weather does computations.

00:46:23.560 | The only thing about the computations that we do

00:46:26.400 | that's really special is that we understand

00:46:30.320 | what they are, so to speak.

00:46:31.460 | In other words, we have a, you know,

00:46:33.400 | to us, they're special because kind of,

00:46:35.600 | they're connected to our purposes,

00:46:37.320 | our ways of thinking about things and so on.

00:46:39.460 | And that's some, but so--

00:46:41.200 | - That's very human-centric.

00:46:42.600 | That's, we're just attached to this kind of thing.

00:46:45.560 | So let's talk a little bit of physics.

00:46:48.320 | Maybe let's ask the biggest question.

00:46:51.020 | What is a theory of everything in general?

00:46:55.360 | What does that mean?

00:46:56.200 | - Yeah, so I mean, the question is,

00:46:58.040 | can we kind of reduce what has been physics

00:47:01.760 | as a something where we have to sort of pick away and say,

00:47:05.720 | do we roughly know how the world works

00:47:08.320 | to something where we have a complete formal theory

00:47:11.080 | where we say, if we were to run this program

00:47:14.260 | for long enough, we would reproduce everything,

00:47:17.720 | you know, down to the fact that we're having

00:47:19.640 | this conversation at this moment, et cetera, et cetera,

00:47:21.880 | et cetera.

00:47:22.840 | - Any physical phenomena, any phenomena in this world?

00:47:25.520 | - Phenomena in the universe.

00:47:27.080 | But the, you know, because of computational irreducibility,

00:47:30.360 | it's not, you know, that's not something where you say,

00:47:33.760 | okay, you've got the fundamental theory of everything.

00:47:36.200 | Then, you know, tell me whether, you know,

00:47:39.960 | lions are going to eat tigers or something.

00:47:42.520 | You know, that's a, no, you have to run this thing

00:47:45.480 | for, you know, 10 to the 500 steps or something

00:47:48.580 | to know something like that, okay?

00:47:50.840 | So at some moment, potentially, you say,

00:47:54.240 | this is a rule and run this rule enough times

00:47:57.600 | and you will get the whole universe, right?

00:47:59.760 | That's what it means to kind of have

00:48:02.400 | a fundamental theory of physics, as far as I'm concerned,

00:48:04.720 | is you've got this rule, it's potentially quite simple.

00:48:07.760 | We don't know for sure it's simple,

00:48:09.400 | but we have various reasons to believe it might be simple.

00:48:12.600 | And then you say, okay, I'm showing you this rule.

00:48:15.840 | You just run it only 10 to the 500 times

00:48:18.760 | and you'll get everything.

00:48:20.120 | In other words, you've kind of reduced

00:48:22.260 | the problem of physics to a problem of mathematics,

00:48:24.600 | so to speak.

00:48:25.640 | It's like, it's as if, you know,

00:48:27.360 | you'd like you'd generate the digits of pi.

00:48:29.800 | There's a definite procedure, you just generate them.

00:48:32.600 | And it'd be the same thing if you have

00:48:34.240 | a fundamental theory of physics of the kind

00:48:36.400 | that I'm imagining, you know, you get this rule

00:48:41.240 | and you just run it out and you get everything

00:48:43.760 | that happens in the universe.

00:48:45.900 | - So a theory of everything is a mathematical framework

00:48:52.160 | within which you can explain everything that happens

00:48:55.360 | in the universe kind of in a unified way.

00:48:58.640 | It's not there's a bunch of disparate modules of...

00:49:01.760 | Does it feel like if you create a rule,

00:49:07.080 | and we'll talk about the Wolfram physics model,

00:49:11.160 | which is fascinating, but if you have a simple set of rules

00:49:16.160 | with a data structure like a hypergraph,

00:49:21.820 | does that feel like a satisfying theory of everything?

00:49:25.120 | Because then you really run up against the irreducibility,

00:49:30.120 | computational reducibility.

00:49:32.360 | - Right, so that's a really interesting question.

00:49:34.240 | So I, you know, what I thought was gonna happen

00:49:38.180 | is I thought we, you know, I thought we had a pretty good,

00:49:42.260 | I had a pretty good idea for what the structure

00:49:45.480 | of this sort of theory that's sort of underneath space

00:49:47.940 | and time and so on might be like.

00:49:50.200 | And I thought, gosh, you know, in my lifetime, so to speak,

00:49:53.440 | we might be able to figure out what happens

00:49:55.080 | in the first 10 to the minus 100 seconds of the universe.

00:49:58.180 | And that would be cool, but it's pretty far away

00:50:01.520 | from anything that we can see today.

00:50:03.880 | And it will be hard to test whether that's right

00:50:05.780 | and so on and so on and so on.

00:50:07.560 | To my huge surprise, although it should have been obvious,

00:50:10.500 | and it's embarrassing that it wasn't obvious to me,

00:50:12.600 | but to my huge surprise,

00:50:15.620 | we managed to get unbelievably much further than that.

00:50:18.420 | And basically what happened is that it turns out

00:50:21.540 | that even though there's this kind of bed

00:50:23.180 | of computational irreducibility

00:50:25.300 | that sort of all these simple rules run into,

00:50:30.100 | there are certain pieces of computational reducibility

00:50:34.300 | that quite generically occur

00:50:36.260 | for large classes of these rules.

00:50:38.460 | And, and this is the really exciting thing

00:50:41.020 | as far as I'm concerned,

00:50:42.460 | the big pieces of computational reducibility

00:50:46.060 | are basically the pillars of 20th century physics.

00:50:49.340 | That's the amazing thing,

00:50:50.300 | that general relativity and quantum field theory,

00:50:52.740 | the sort of the pillars of 20th century physics

00:50:55.540 | turn out to be precisely the stuff you can say.

00:50:59.760 | There's a lot you can't say.

00:51:00.900 | There's a lot that's kind of at this irreducible level

00:51:03.420 | where you kind of don't know what's going to happen.

00:51:05.180 | You have to run it.

00:51:06.100 | You know, you can't run it within our universe,

00:51:07.860 | et cetera, et cetera, et cetera, et cetera, et cetera.

00:51:10.300 | But the thing is there are things you can say

00:51:13.620 | and the things you can say turn out to be very beautifully,

00:51:17.900 | exactly the structure that was found

00:51:19.820 | in 20th century physics,

00:51:21.580 | namely general relativity and quantum mechanics.

00:51:24.100 | - And general relativity and quantum mechanics

00:51:27.040 | are these pockets of reducibility that we think of as,

00:51:30.560 | that 20th century physics

00:51:34.180 | is essentially pockets of reducibility.

00:51:36.940 | And then it is incredibly surprising

00:51:39.460 | that any kind of model that's generative

00:51:43.500 | from simple rules would have such pockets.

00:51:48.020 | - Yeah, well, I think what's surprising

00:51:49.980 | is we didn't know where those things came from.

00:51:53.300 | It's like general relativity,

00:51:54.500 | it's a very nice mathematically elegant theory.

00:51:57.420 | Why is it true?

00:51:58.980 | You know, quantum mechanics, why is it true?

00:52:01.540 | What we realized is that from this,

00:52:04.720 | that these theories are generic

00:52:07.620 | to a huge class of systems

00:52:09.820 | that have these particular,

00:52:10.960 | very unstructured underlying rules.

00:52:14.020 | And that's the thing that is sort of remarkable.

00:52:17.500 | And that's the thing to me that's just,

00:52:19.980 | it's really beautiful.

00:52:20.820 | I mean, it's, and the thing that's even more beautiful

00:52:23.300 | is that it turns out that, you know,

00:52:24.900 | people have been struggling for a long time.

00:52:26.620 | You know, how does general relativity,

00:52:28.180 | theory of gravity relate to quantum mechanics?

00:52:30.580 | They seem to have all kinds of incompatibilities.

00:52:32.900 | It turns out what we realized is at some level,

00:52:35.580 | they are the same theory.

00:52:37.520 | And that's just, it's just great as far as I'm concerned.

00:52:41.340 | - So maybe like taking a little step back

00:52:43.660 | from your perspective, not from the low,

00:52:47.600 | not from the beautiful hypergraph,

00:52:50.700 | well, from physics model perspective,

00:52:52.500 | but from the perspective of 20th century physics,

00:52:55.460 | what is general relativity?

00:52:57.220 | What is quantum mechanics?

00:52:58.340 | How do you think about these two theories

00:53:00.900 | from the context of the theory of everything?

00:53:04.020 | Like, just even definitions.

00:53:05.740 | - Yeah, yeah, yeah, right.

00:53:06.580 | So I mean, you know, a little bit of history of physics.

00:53:08.780 | Right, so I mean the, you know, okay,

00:53:12.020 | very, very quick history of physics, right?

00:53:14.180 | So, I mean, you know, physics, you know,

00:53:16.240 | in ancient Greek times, people basically said,

00:53:18.980 | we can just figure out how the world works.

00:53:21.200 | As, you know, we're philosophers,

00:53:22.540 | we're gonna figure out how the world works.

00:53:24.540 | You know, some philosophers thought there were atoms.

00:53:26.580 | Some philosophers thought there were, you know,

00:53:28.940 | continuous flows of things.

00:53:30.580 | People had different ideas about how the world works.

00:53:32.980 | And they tried to just say,

00:53:33.820 | we're gonna construct this idea of how the world works.

00:53:36.820 | They didn't really have sort of notions

00:53:38.180 | of doing experiments and so on quite the same way

00:53:40.620 | as developed later.

00:53:41.460 | So that was sort of an early tradition

00:53:43.300 | for thinking about sort of models of the world.

00:53:46.620 | Then by the time of 1600s, time of Galileo and then Newton,

00:53:51.180 | sort of the big idea there was, you know,

00:53:55.260 | title of Newton's book, you know,

00:53:56.540 | Principia Mathematica,

00:53:57.620 | Mathematical Principles of Natural Philosophy.

00:54:00.420 | We can use mathematics to understand natural philosophy,

00:54:04.220 | to understand things about the way the world works.

00:54:07.100 | And so that then led to this kind of idea that, you know,

00:54:10.460 | we can write down a mathematical equation

00:54:12.760 | and have that represent how the world works.

00:54:14.960 | So Newton's, one of his most famous ones

00:54:16.800 | is his universal law of gravity,

00:54:19.240 | inverse square law of gravity

00:54:21.140 | that allowed him to compute all sorts of features

00:54:23.340 | of the planets and so on.

00:54:24.940 | Although some of them he got wrong

00:54:26.260 | and it took another hundred years

00:54:27.980 | for people to actually be able to do the math

00:54:30.220 | to the level that was needed.

00:54:31.420 | But so that had been,

00:54:33.740 | this sort of tradition was we write down

00:54:35.260 | these mathematical equations.

00:54:36.300 | We don't really know where these equations come from.

00:54:38.620 | We write them down, then we figure out,

00:54:40.960 | we work out the consequences and we say, yes,

00:54:43.220 | that agrees with what we actually observe

00:54:45.300 | in astronomy or something like this.

00:54:47.320 | So that tradition continued.

00:54:49.500 | And then the first of these two sort of great

00:54:51.940 | 20th century innovations was,

00:54:55.460 | well, the history is actually a little bit more complicated,

00:54:57.340 | but let's say that there were two,

00:55:01.620 | quantum mechanics and general relativity.

00:55:03.420 | Quantum mechanics, the kind of 1900

00:55:05.420 | was kind of the very early stuff done by Planck

00:55:08.380 | that led to the idea of photons, particles of light.

00:55:12.340 | But let's take general relativity first.

00:55:14.900 | One feature of the story is that special relativity,

00:55:19.260 | thing Einstein invented in 1905,

00:55:21.800 | was something which surprisingly

00:55:24.260 | was a kind of logically invented theory.

00:55:27.040 | It was not a theory where,

00:55:28.820 | it was something where given these ideas

00:55:31.460 | that were sort of axiomatically thought to be true

00:55:33.620 | about the world, it followed that

00:55:36.180 | such and such a thing would be the case.

00:55:38.380 | It was a little bit different

00:55:39.380 | from the kind of methodological structure

00:55:42.020 | of some existing theories in the more recent times,

00:55:45.900 | where it had just been, we write down an equation

00:55:47.620 | and we find out that it works.

00:55:49.940 | So what happened there--

00:55:51.540 | - So there's some reasoning about the light.

00:55:53.700 | The basic idea was the speed of light

00:55:57.160 | appears to be constant.

00:55:59.960 | Even if you're traveling very fast,

00:56:01.920 | you shine a flashlight, the light will come out.

00:56:05.080 | Even if you're going at half the speed of light,

00:56:07.140 | the light doesn't come out of your flashlight

00:56:08.920 | at one and a half times the speed of light.

00:56:11.160 | It's still just the speed of light.

00:56:13.080 | And to make that work, you have to change your view

00:56:15.780 | of how space and time work to be able to account

00:56:19.640 | for the fact that when you're going faster,

00:56:21.480 | it appears that length is foreshortened

00:56:24.440 | and time is dilated and things like this.

00:56:26.240 | - And that's special relativity.

00:56:27.200 | - That's special relativity.

00:56:28.560 | So then Einstein went on with sort of

00:56:32.120 | vaguely similar kinds of thinking.

00:56:34.760 | In 1915, invented general relativity,

00:56:37.960 | which is a theory of gravity.

00:56:39.920 | And the basic point of general relativity

00:56:42.480 | is it's a theory that says when there is mass in space,

00:56:47.480 | space is curved.

00:56:49.680 | And what does that mean?

00:56:51.720 | You usually you think of what's the shortest distance

00:56:55.140 | between two points, like ordinarily on a plane in space,

00:56:58.880 | it's a straight line.

00:56:59.920 | Photons, light goes in straight lines.

00:57:04.620 | Well, then the question is,

00:57:06.480 | if you have a curved surface,

00:57:10.300 | a straight line is no longer straight.

00:57:12.160 | On the surface of the earth,

00:57:13.560 | the shortest distance between two points is a great circle.

00:57:16.200 | It's a circle.

00:57:18.600 | So Einstein's observation was maybe the physical

00:57:23.000 | structure of space is such that space is curved.

00:57:26.800 | So the shortest distance between two points,

00:57:29.640 | the path, the straight line in quotes,

00:57:32.900 | won't be straight anymore.

00:57:34.160 | And in particular, if a photon is traveling near the sun

00:57:38.920 | or something or if a particle is going,

00:57:40.580 | something is traveling near the sun,

00:57:42.400 | maybe the shortest path will be one that is

00:57:47.360 | something which looks curved to us because it seems curved

00:57:49.800 | to us because space has been deformed by the presence

00:57:52.800 | of mass associated with that massive object.

00:57:55.480 | So the kind of the idea there is think of the structure

00:58:00.480 | of space as being a dynamical changing kind of thing.

00:58:03.680 | But then what Einstein did was he wrote down

00:58:05.520 | these differential equations that basically represented

00:58:09.240 | the curvature of space and its response to the presence

00:58:11.600 | of mass and energy.

00:58:13.040 | - And that ultimately is connected to the force

00:58:16.740 | of gravity, which is one of the forces that seems to,

00:58:20.600 | based on its strength, operate on a different scale

00:58:23.600 | than some of the other forces.

00:58:24.800 | So it operates at a scale that's very large.

00:58:27.760 | - What happens there is just this curvature of space

00:58:32.160 | which causes the paths of objects to be deflected.

00:58:35.960 | That's what gravity does.

00:58:37.200 | It causes the paths of objects to be deflected.

00:58:39.720 | And this is an explanation for gravity, so to speak.

00:58:43.160 | And the surprise is that from 1915 until today,

00:58:47.280 | everything that we've measured about gravity

00:58:49.680 | precisely agrees with general relativity.

00:58:52.160 | And that it wasn't clear black holes were sort of a,

00:58:56.440 | well, actually the expansion of the universe

00:58:57.700 | was an early potential prediction,

00:58:59.560 | although Einstein tried to sort of patch up his equations

00:59:02.720 | to make it not cause the universe to expand

00:59:05.100 | 'cause it was kind of so obvious

00:59:06.320 | the universe wasn't expanding.

00:59:08.140 | And it turns out it was expanding

00:59:10.480 | and he should have just trusted the equations.

00:59:11.960 | And that's a lesson for those of us

00:59:14.480 | interested in making fundamental theories of physics

00:59:16.680 | is you should trust your theory

00:59:18.640 | and not try and patch it because of something

00:59:20.580 | that you think might be the case,

00:59:22.000 | that might turn out not to be the case.

00:59:25.320 | - Even if the theory says something crazy is happening.

00:59:28.360 | - Yeah, right. - Like the universe

00:59:29.400 | is expanding. - Like the universe

00:59:30.240 | is expanding, right.

00:59:31.280 | But then it took until the 1940s,

00:59:35.120 | probably even really until the 1960s,

00:59:36.800 | until people understood that black holes

00:59:38.560 | were a consequence of general relativity and so on.

00:59:42.140 | But that's some, the big surprise has been that so far,

00:59:46.840 | this theory of gravity has perfectly agreed

00:59:49.960 | with these collisions of black holes

00:59:51.840 | seen by the gravitational waves, it all just works.

00:59:55.840 | So that's been kind of one pillar of the story of physics.

00:59:59.120 | It's mathematically complicated

01:00:00.560 | to work out the consequences of general relativity,

01:00:03.040 | but it's not, there's no, I mean,

01:00:05.680 | and some things are kind of squiggly and complicated,

01:00:09.320 | like people believe energy is conserved.

01:00:12.040 | Okay, well, energy conservation doesn't really work

01:00:14.400 | in general relativity in the same way

01:00:15.720 | as it ordinarily does.

01:00:16.760 | And it's all a big mathematical story

01:00:19.220 | of how you actually nail down something

01:00:21.880 | that is definitive that you can talk about

01:00:23.600 | and not specific to the reference frames

01:00:26.320 | you're operating in and so on and so on and so on.

01:00:28.320 | But fundamentally, general relativity is a straight shot

01:00:31.280 | in the sense that you have this theory,

01:00:32.840 | you work out its consequences.

01:00:34.880 | - And that theory is useful in terms of basic science

01:00:39.280 | and trying to understand the way black holes work,

01:00:41.200 | the way the creation of galaxies work,

01:00:43.560 | sort of all of these kind of cosmological thing,

01:00:45.840 | understanding what happened, like you said, at the Big Bang.

01:00:49.200 | - Yeah. - Like all those kinds of,

01:00:50.560 | well, no, not at the Big Bang, actually, right?

01:00:52.880 | - Well, features of the expansion of the universe, yes.

01:00:55.880 | I mean, and there are lots of details

01:00:58.200 | where we don't quite know how it's working.

01:00:59.680 | You know, where's the dark matter?

01:01:02.080 | Is there dark energy?

01:01:03.240 | You know, et cetera, et cetera, et cetera.

01:01:04.440 | But fundamentally, the testable features

01:01:07.640 | of general relativity, it all works very beautifully.

01:01:10.080 | And it's, in a sense, it is mathematically sophisticated,

01:01:13.720 | but it is not conceptually hard to understand in some sense.

01:01:17.160 | - Okay, so that's general relativity.

01:01:18.720 | And what's its friendly neighbor?

01:01:20.760 | Like you said, there's two theories.

01:01:22.080 | Quantum mechanics. - Quantum mechanics, right.

01:01:23.360 | So quantum mechanics, the sort of,

01:01:26.200 | the way that that originated was,

01:01:28.280 | one question was, is the world continuous

01:01:30.280 | or is it discrete?

01:01:31.400 | You know, in ancient Greek times,

01:01:32.500 | people have been debating this.

01:01:34.020 | People debated it throughout history.

01:01:36.400 | Is light made of waves?

01:01:38.360 | Is it continuous?

01:01:39.200 | Is it discrete?

01:01:40.020 | Is it made of particles, corpuscles, whatever?

01:01:42.600 | What had become clear in the 1800s is that atoms,

01:01:47.800 | that materials are made of discrete atoms.

01:01:51.360 | You know, when you take some water,

01:01:53.940 | the water is not a continuous fluid,

01:01:55.560 | even though it seems like a continuous fluid

01:01:57.360 | to us at our scale.

01:01:58.880 | But if you say, let's look at it,

01:02:00.760 | smaller and smaller and smaller and smaller scale,

01:02:02.480 | eventually you get down to these molecules and then atoms.

01:02:06.320 | It's made of discrete things.

01:02:07.940 | So the question is sort of how important

01:02:10.060 | is this discreteness?

01:02:10.940 | Just what's discrete, what's not discrete?

01:02:12.900 | Is energy discrete?

01:02:14.060 | Is, you know, what's discrete, what's not?

01:02:17.380 | And so-- - Does it have mass?

01:02:19.580 | Those kinds of questions.

01:02:20.900 | - Yeah, yeah, right.

01:02:21.720 | Well, there's a question, I mean, for example,

01:02:23.620 | is mass discrete is an interesting question,

01:02:26.020 | which is now something we can address.

01:02:28.100 | But, you know, what happened in

01:02:31.940 | the, coming up to the 1920s,

01:02:35.680 | there was this kind of mathematical theory developed

01:02:37.680 | that could explain certain kinds of discreteness

01:02:40.440 | in particularly in features of atoms and so on.

01:02:44.280 | And, you know, what developed was this mathematical theory

01:02:47.740 | that was the theory of quantum mechanics,

01:02:50.160 | theory of wave functions, Schrodinger's equation,

01:02:52.480 | things like this.

01:02:53.640 | That's a mathematical theory that allows you to calculate

01:02:57.280 | lots of features of the microscopic world,

01:02:59.240 | lots of things about how atoms work,

01:03:01.440 | et cetera, et cetera, et cetera.

01:03:02.960 | Now, the calculations all work just great.

01:03:05.720 | The question of what does it really mean

01:03:09.360 | is a complicated question.

01:03:11.260 | Now, I mean, to just explain a little bit historically,

01:03:14.240 | the, you know, the early calculations of things like atoms

01:03:17.000 | worked great in 1920s, 1930s, and so on.

01:03:20.280 | There was always a problem there were

01:03:22.660 | in quantum field theory, which is a theory of,

01:03:26.400 | in quantum mechanics, you're dealing with a certain number

01:03:28.400 | of atoms, a certain number of electrons,

01:03:30.480 | and you fix the number of electrons.

01:03:31.940 | You say, I'm dealing with a two electron thing.

01:03:34.900 | In quantum field theory, you allow for particles

01:03:37.180 | being created and destroyed.

01:03:38.880 | So you can emit a photon that didn't exist before.

01:03:41.200 | You can absorb a photon, things like that.

01:03:43.440 | That's a more complicated,

01:03:44.560 | mathematically complicated theory.

01:03:46.280 | And it had all kinds of mathematical issues

01:03:47.960 | and all kinds of infinities that cropped up.

01:03:49.960 | And it was finally figured out more or less

01:03:51.400 | how to get rid of those.

01:03:52.920 | But there were only certain ways of doing the calculations.

01:03:55.920 | And those didn't work for atomic nuclei,

01:03:57.920 | among other things.

01:03:59.640 | And that led to a lot of development up until the 1960s

01:04:03.800 | of alternative ideas for how one could understand

01:04:07.160 | what was happening in atomic nuclei, et cetera, et cetera,

01:04:09.360 | et cetera, end result.

01:04:11.240 | In the end, the kind of most quotes,

01:04:13.960 | obvious mathematical structure of quantum field theory

01:04:17.220 | seems to work, although it's mathematically difficult

01:04:19.780 | to deal with, but you can calculate all kinds of things.

01:04:22.980 | You can calculate to, you know, a dozen decimal places,

01:04:26.120 | certain things, you can measure them.

01:04:27.800 | It all works.

01:04:28.640 | It's all beautiful.

01:04:29.600 | Now you say- - By the way,

01:04:30.440 | the underlying fabric is the model

01:04:32.520 | of that particular theory is fields.

01:04:34.800 | Like you keep saying fields.

01:04:36.680 | - Those are quantum fields.

01:04:37.960 | Those are different from classical fields.

01:04:40.400 | A field is something like you say,

01:04:44.120 | there's like you say, the temperature field in this room.

01:04:46.920 | It's like there is a value of temperature

01:04:49.560 | at every point around the room.

01:04:51.400 | That's, or you can say the wind field

01:04:54.000 | would be the vector direction of the wind at every point.

01:04:56.920 | - It's continuous.

01:04:57.880 | - Yes, and that's a classical field.

01:05:00.200 | The quantum field is a much more mathematically

01:05:02.000 | elaborate kind of thing.

01:05:04.320 | And I should explain that one of the pictures

01:05:06.400 | of quantum mechanics that's really important

01:05:08.400 | is, you know, in classical physics,

01:05:11.060 | one believes that sort of definite things

01:05:12.840 | happen in the world.

01:05:13.800 | You pick up a ball, you throw it.

01:05:16.180 | The ball goes in a definite trajectory

01:05:18.000 | that has certain equations of motion.

01:05:20.200 | It goes in a parabola, whatever else.

01:05:22.240 | In quantum mechanics, the picture is

01:05:25.320 | definite things don't happen.

01:05:26.880 | Instead, sort of what happens is this whole

01:05:29.720 | sort of structure of all, you know,

01:05:32.560 | many different paths being followed.

01:05:34.840 | And we can calculate certain aspects of what happens,

01:05:37.840 | certain probabilities of different outcomes and so on.

01:05:40.560 | And you say, well, what really happened?

01:05:42.440 | What's really going on?

01:05:43.440 | What's the sort of, what's the underlying, you know,

01:05:45.680 | what's the underlying story?

01:05:46.880 | What, how do we, how do we turn this mathematical theory

01:05:50.680 | that we can calculate things with into something

01:05:53.040 | that we can really understand and have a narrative about?

01:05:56.400 | And that's been really, really hard for quantum mechanics.

01:05:59.480 | My friend Dick Feynman always used to say,

01:06:01.560 | nobody understands quantum mechanics,

01:06:03.680 | even though he'd made his whole career

01:06:06.440 | out of calculating things about quantum mechanics.

01:06:10.200 | And, you know, so it's a little--

01:06:11.760 | - But nevertheless, it's what the quantum field theory

01:06:15.160 | is very, very accurate at predicting

01:06:18.680 | a lot of the physical phenomena.

01:06:20.680 | So it works.

01:06:21.720 | - Yeah, but there are things about it, you know,

01:06:24.240 | it has certain, when we apply it,

01:06:26.160 | the standard model of particle physics, for example,

01:06:28.840 | we, you know, which we apply to calculate

01:06:31.520 | all kinds of things, it works really well.

01:06:33.440 | And you say, well, it has certain parameters.

01:06:34.880 | It has a whole bunch of parameters, actually.

01:06:36.920 | You say, why is the, you know,

01:06:38.800 | why does the muon particle exist?

01:06:41.560 | Why is it 206 times the mass of the electron?

01:06:44.920 | We don't know, no idea.

01:06:46.680 | - But so the standard model of physics

01:06:48.960 | is one of the models that's very accurate

01:06:50.880 | for describing three of the fundamental forces of physics.

01:06:55.200 | And it's looking at the world of the very small.

01:06:58.240 | - Right.

01:06:59.080 | - And then there's back to the neighbor

01:07:01.160 | of gravity, of general relativity.

01:07:04.760 | So, and in the context of a theory of everything,

01:07:07.640 | what's traditionally the task of the unification

01:07:13.560 | of these theories?

01:07:15.160 | And why is it hard?

01:07:16.000 | - Well, the issue is, you try to use the methods

01:07:18.160 | of quantum field theory to talk about gravity,

01:07:20.840 | and it doesn't work.

01:07:22.000 | Just like there are photons of light.

01:07:24.000 | So there are gravitons, which are sort of

01:07:26.320 | the particles of gravity.

01:07:27.960 | And when you try and compute sort of the properties

01:07:30.280 | of the particles of gravity,

01:07:32.680 | the kind of mathematical tricks that get used

01:07:36.040 | in working things out in quantum field theory don't work.

01:07:39.240 | And that's, so that's been a sort of fundamental issue.

01:07:43.000 | And when you think about black holes,

01:07:44.800 | which are a place where sort of the structure of space

01:07:48.920 | is, you know, has sort of rapid variation,

01:07:52.760 | and you get kind of quantum effects mixed in

01:07:55.320 | with effects from general relativity,

01:07:57.520 | things get very complicated,

01:07:58.720 | and there are apparent paradoxes and things like that.

01:08:01.320 | And people have, you know, there have been a bunch

01:08:03.720 | of mathematical developments in physics over the last,

01:08:07.080 | I don't know, 30 years or so,

01:08:08.600 | which have kind of picked away at those kinds of issues

01:08:11.560 | and got hints about how things might work.

01:08:14.960 | And, but it hasn't been, you know,

01:08:17.280 | and the other thing to realize is,

01:08:19.040 | as far as physics is concerned,

01:08:20.720 | it's just like, here's general relativity,

01:08:22.840 | here's quantum field theory, you know, be happy.

01:08:25.800 | - Yeah, so do you think there's a quantization of gravity,

01:08:28.840 | so quantum gravity, what do you think of efforts

01:08:31.120 | that people have tried to, yeah,

01:08:33.760 | what do you think in general of the efforts

01:08:36.360 | of the physics community to try to unify these laws?

01:08:39.600 | - So I think what's, it's interesting.

01:08:41.320 | I mean, I would have said something very different

01:08:43.360 | before what's happened with our physics project.

01:08:46.400 | I mean, you know, the remarkable thing is,

01:08:48.880 | what we've been able to do is to make

01:08:51.720 | from this very simple, structurally simple,

01:08:55.560 | underlying set of ideas, we've been able to build this,

01:08:59.440 | this, you know, very elaborate structure

01:09:02.400 | that's both very abstract

01:09:04.480 | and very sort of mathematically rich.

01:09:06.880 | And the big surprise, as far as I'm concerned,

01:09:09.240 | is that it touches many of the ideas that people have had.

01:09:12.960 | So in other words, things like string theory and so on,

01:09:15.520 | twister theory, it's like, you know, we might've thought,

01:09:18.880 | I had thought we're out on a prong,

01:09:21.000 | we're building something that's computational,

01:09:22.640 | it's completely different from what other people have done.

01:09:25.040 | But actually, it seems like what we've done

01:09:27.320 | is to provide essentially the machine code that,

01:09:30.440 | you know, these things are various features

01:09:33.080 | of domain-specific languages, so to speak,

01:09:35.440 | that talk about various aspects of this machine code.

01:09:37.920 | And I think there's a, this is something that to me

01:09:40.320 | is very exciting because it allows one both for us

01:09:44.600 | to provide sort of a new foundation

01:09:46.720 | for what's been thought about there

01:09:48.440 | and for all the work that's been done in those areas

01:09:52.000 | to, you know, to give us, you know, more momentum

01:09:55.760 | to be able to figure out what's going on.

01:09:57.160 | Now, you know, people have sort of hoped,

01:09:58.840 | oh, we're just gonna be able to get, you know,

01:10:01.200 | string theory to just answer everything.

01:10:03.400 | That hasn't worked out.

01:10:04.920 | And I think we now kind of can see a little bit

01:10:07.640 | about just sort of how far away certain kinds of things are

01:10:10.400 | from being able to explain things.

01:10:12.520 | Some things, one of the big surprises to me,

01:10:14.760 | actually, I literally just got a message

01:10:16.640 | about one aspect of this is the, you know,

01:10:20.840 | it's turning out to be easier.

01:10:22.680 | I mean, this project has been so much easier

01:10:24.920 | than I could ever imagine it would be.

01:10:26.720 | That is, I thought we would be, you know,

01:10:29.760 | just about able to understand

01:10:31.400 | the first 10 to the minus 100 seconds of the universe.

01:10:34.160 | And, you know, it would be 100 years

01:10:35.840 | before we get much further than that.

01:10:37.680 | It's just turned out it actually wasn't that hard.

01:10:40.480 | I mean, we're not finished, but, you know--

01:10:42.520 | - So you're seeing echoes of all the disparate theories

01:10:45.880 | of physics in this framework?

01:10:47.440 | - Yes, yes.

01:10:48.480 | I mean, it's a very interesting, you know,

01:10:50.880 | sort of history of science-like phenomenon.

01:10:53.360 | I mean, the best analogy that I can see

01:10:55.960 | is what happened with the early days

01:10:58.000 | of computability and computation theory.

01:11:00.600 | You know, Turing machines were invented in 1936.

01:11:03.520 | People sort of understand computation

01:11:06.040 | in terms of Turing machines,

01:11:07.240 | but actually there had been preexisting theories

01:11:09.920 | of computation, combinators, general recursive functions,

01:11:12.880 | lambda calculus, things like this.

01:11:14.880 | But people hadn't, those hadn't been concrete enough

01:11:18.240 | that people could really wrap their arms around them

01:11:20.320 | and understand what was going on.

01:11:21.760 | And I think what we're gonna see in this case

01:11:23.440 | is that a bunch of these mathematical theories,

01:11:25.960 | including some very,

01:11:28.000 | I mean, one of the things that's really interesting

01:11:29.680 | is one of the most abstract things

01:11:31.800 | that's come out of sort of mathematics,

01:11:36.200 | higher category theory,

01:11:37.480 | things about infinity groupoids, things like this,

01:11:40.280 | which to me always just seemed like

01:11:41.720 | they were floating off into the stratosphere,

01:11:44.320 | ionosphere of mathematics,

01:11:46.760 | turn out to be things which our sort of theory

01:11:51.080 | anchors down to something fairly definite

01:11:53.760 | and says are super relevant to the way

01:11:56.640 | that we can understand how physics works.

01:11:59.200 | - Give me a sec.

01:12:00.040 | By the way, I just threw a hat on.

01:12:01.520 | You've said that,

01:12:02.800 | this metaphor analogy that

01:12:06.880 | theory of everything is a big mountain.

01:12:09.360 | And you have a sense that

01:12:11.720 | however far we are up the mountain,

01:12:15.520 | that the Wolfram physics model,

01:12:21.400 | a view of the universe is at least the right mountain.

01:12:25.640 | - We're the right mountain, yes, without question.

01:12:28.360 | - So which aspect of it is the right mountain?

01:12:30.960 | So for example, I mean,

01:12:32.520 | so there's so many aspects to just the way

01:12:35.640 | of the Wolfram physics project,

01:12:37.520 | the way it approaches the world,

01:12:39.280 | that's clean, crisp,

01:12:42.360 | and unique and powerful.

01:12:46.040 | So there's a discrete nature to it.

01:12:49.280 | There's a hypergraph.

01:12:51.320 | There's a computational nature.

01:12:53.040 | There's a generative aspect.

01:12:54.480 | You start from nothing, you generate everything.

01:12:56.880 | Do you think the actual model

01:13:00.760 | is actually a really good one?

01:13:02.120 | Or do you think this general principle

01:13:04.120 | from simplicity generating complexity is the right?

01:13:06.600 | Like what aspect of the mountain is the correct?

01:13:09.040 | - I think that the kind of the meta idea

01:13:12.760 | about using simple computational systems to do things,

01:13:17.160 | that's the ultimate big paradigm

01:13:21.080 | that is sort of super important.

01:13:24.560 | The details of the particular model

01:13:26.720 | are very nice and clean

01:13:28.560 | and allow one to actually understand what's going on.

01:13:30.880 | They are not unique.

01:13:32.200 | And in fact, we know that.

01:13:33.600 | We know that there's a large number of different ways

01:13:37.120 | to describe essentially the same thing.

01:13:38.600 | I mean, I can describe things in terms of hypergraphs.

01:13:41.120 | I can describe them in terms of higher category theory.

01:13:43.480 | I can describe them in a bunch of different ways.

01:13:45.240 | They are in some sense all the same thing,

01:13:47.480 | but our sort of story about what's going on

01:13:50.240 | and the kind of cultural mathematical resonances

01:13:53.600 | are a bit different.

01:13:54.720 | I mean, I think it's perhaps worth

01:13:56.760 | sort of saying a little bit about kind of the,

01:13:58.840 | the foundational ideas of these models and things.

01:14:03.840 | - Great.

01:14:05.640 | So can you maybe, can we like rewind?

01:14:09.920 | We've talked about it a little bit,

01:14:11.120 | but can you say like what the central idea is

01:14:14.080 | of the Wolfram Physics Project?

01:14:16.680 | - Right.

01:14:17.520 | So the question is we're interested in finding

01:14:20.160 | sort of simple computational rule

01:14:21.920 | that describes our whole universe.

01:14:24.080 | - Can we just pause on that?

01:14:25.480 | It's just so beautiful.

01:14:26.320 | That's such a beautiful, that's such a beautiful idea

01:14:30.920 | that we can generate our universe from a data structure,

01:14:35.920 | simple structure, simple set of rules,

01:14:40.760 | and we can generate our entire universe.

01:14:42.680 | - Yes.

01:14:43.520 | - That's awe-inspiring.

01:14:44.840 | - Right.

01:14:45.680 | But so, so, you know, the question is

01:14:49.080 | how do you actualize that?

01:14:50.480 | What might this rule be like?

01:14:52.560 | And so one thing you quickly realize is

01:14:55.160 | if you're going to pack everything about a universe

01:14:57.160 | into this tiny rule,

01:14:59.040 | not much that we are familiar with in our universe

01:15:02.440 | will be obvious in that rule.

01:15:04.000 | So you don't get to fit all these parameters of the universe,

01:15:07.920 | all these features of, you know, this is how space works,

01:15:10.120 | this is how time works, et cetera, et cetera, et cetera.

01:15:12.000 | You don't get to fit that all in.

01:15:13.080 | It all has to be sort of packed in to this, this thing,

01:15:16.640 | something much smaller, much more basic,

01:15:18.640 | much lower level machine code, so to speak, than that.

01:15:22.000 | And all the stuff that we're familiar with

01:15:23.520 | has to kind of emerge from the operation of-

01:15:26.200 | - So the rule in itself,

01:15:27.840 | because of the computational reducibility,

01:15:30.400 | is not going to tell you the story.

01:15:32.320 | It's not going to give you the answer to,

01:15:35.660 | it's not going to let you predict

01:15:38.360 | what you're going to have for lunch tomorrow.

01:15:40.400 | - Right.

01:15:41.240 | - And it's not going to let you predict

01:15:42.200 | basically anything about your life, about the universe.

01:15:44.800 | - Right, but, and you're not going to be able to see

01:15:46.760 | in that rule, oh, there's the three

01:15:49.160 | for the number of dimensions of space and so on.

01:15:50.960 | - Right.

01:15:51.800 | - That's not going to be just-

01:15:52.640 | - The problem is not going to be obviously-

01:15:54.600 | - Right, so the question is then,

01:15:55.720 | what is the universe made of?

01:15:57.800 | That's a basic question.

01:16:00.240 | And we've had some assumptions

01:16:01.680 | about what the universe is made of

01:16:03.000 | for the last few thousand years,

01:16:04.880 | that I think in some cases just turn out not to be right.

01:16:08.720 | And the most important assumption

01:16:11.080 | is that space is a continuous thing.

01:16:14.000 | That is, that you can, if you say,

01:16:17.080 | let's pick a point in space.

01:16:19.240 | We're going to do geometry.

01:16:20.180 | We're going to pick a point.

01:16:21.520 | We can pick a point absolutely anywhere in space.

01:16:24.320 | Precise numbers, we can specify of where that point is.

01:16:28.080 | In fact, Euclid, who kind of wrote down

01:16:30.320 | the original kind of axiomatization of geometry

01:16:32.960 | back in 300 BC or so, his very first definition, he says,

01:16:37.960 | "A point is that which has no part."

01:16:40.680 | A point is this indivisible, infinitesimal thing.

01:16:45.680 | Okay, so we might've said that about material objects.

01:16:50.440 | We might've said that about water, for example.

01:16:52.880 | We might've said water is a continuous thing

01:16:54.820 | that we can just pick any point we want in some water.

01:16:59.160 | But actually we know it isn't true.

01:17:00.780 | We know that water is made of molecules that are discrete.

01:17:04.140 | And so the question, one fundamental question

01:17:06.600 | is what is space made of?

01:17:08.360 | And so one of the things that's sort of a starting point

01:17:10.880 | for what I've done is to think of space as a discrete thing,

01:17:15.640 | to think of there being sort of atoms of space

01:17:18.560 | just as there are atoms of material things,

01:17:20.600 | although very different kinds of atoms.

01:17:23.120 | And by the way, I mean, this idea,

01:17:25.600 | there were ancient Greek philosophers who had this idea.

01:17:28.360 | There were, Einstein actually thought

01:17:30.260 | this is probably how things would work out.

01:17:31.840 | I mean, he said repeatedly,

01:17:33.840 | he thought that's the way it would work out.

01:17:35.520 | We don't have the mathematical tools in our time,

01:17:38.680 | which was 1940s, 1950s, and so on, to explore this.

01:17:42.520 | - Like the way he thought, you mean that there is something

01:17:45.820 | very, very small and discrete that's underlying space?

01:17:50.820 | - Yes, and that means that, so the mathematical theory,

01:17:56.580 | mathematical theories in physics assume that space

01:17:59.940 | can be described just as a continuous thing.

01:18:02.380 | You can just pick coordinates

01:18:03.980 | and the coordinates can have any values,

01:18:05.980 | and that's how you define space.

01:18:07.820 | Space is this just sort of background sort of theater

01:18:11.660 | on which the universe operates.

01:18:13.580 | - But can we draw a distinction between space

01:18:17.220 | as a thing that could be described

01:18:19.100 | by three values, coordinates,

01:18:23.620 | and how you're, are you using the word space

01:18:26.980 | more generally when you say?

01:18:29.300 | - No, I'm just talking about space

01:18:30.940 | as in what we experience in the universe.

01:18:34.340 | - So you think this 3D aspect of it is fundamental?

01:18:38.460 | - No, I don't think that 3D is fundamental at all, actually.

01:18:40.820 | I think that the thing that has been assumed

01:18:45.140 | is that space is this continuous thing

01:18:48.180 | where you can just describe it by,

01:18:49.460 | let's say, three numbers, for instance.

01:18:51.300 | But the most important thing about that

01:18:53.140 | is that you can describe it by precise numbers,

01:18:56.060 | because you can pick any point in space,

01:18:58.180 | and you can talk about motions,

01:18:59.620 | any infinitesimal motion in space.

01:19:01.740 | - And that's what continuous means?

01:19:03.300 | - That's what continuous means.

01:19:04.260 | That's what, you know, Newton invented calculus

01:19:06.140 | to describe these kind of continuous,

01:19:07.620 | small variations and so on.

01:19:09.420 | That's kind of a fundamental idea.

01:19:11.380 | From Euclid on, that's been a fundamental idea about space.

01:19:15.340 | And so-- - Is that right or wrong?

01:19:17.540 | - It's not right.

01:19:19.980 | It's not right.

01:19:20.940 | It's right at the level of our experience most of the time.

01:19:25.700 | It's not right at the level of the machine code,

01:19:27.740 | so to speak.

01:19:28.900 | And so-- - Machine code.

01:19:31.020 | Yeah, of the simulation, that's right, that's right.

01:19:33.660 | The very lowest level of the fabric of the universe,

01:19:36.980 | at least under the Wolfram physics model,

01:19:41.980 | is your sense is discrete.

01:19:44.220 | - Right, so now, what does that mean?

01:19:46.300 | So it means, what is space then?

01:19:49.140 | So in models, the basic idea is you say,

01:19:54.140 | there are these sort of atoms of space,

01:19:56.420 | there are these points that represent,

01:19:59.060 | you know, represent places in space,

01:20:02.060 | but they're just discrete points.

01:20:03.940 | And the only thing we know about them

01:20:06.100 | is how they're connected to each other.

01:20:07.980 | We don't know where they are.

01:20:09.460 | They don't have coordinates.

01:20:10.500 | We don't get to say, this is a position such and such.

01:20:12.900 | It's just, here's a big bag of points.

01:20:15.260 | Like in our universe,

01:20:16.100 | there might be 10 to the 100 of these points.

01:20:18.420 | And all we know is this point

01:20:20.860 | is connected to this other point.

01:20:22.460 | So it's like, you know,

01:20:23.460 | all we have is the friend network, so to speak.

01:20:25.540 | We don't have, you know, people's physical addresses.

01:20:29.100 | All we have is the friend network of these points.

01:20:31.540 | - Yeah, the underlying nature of reality

01:20:33.500 | is kind of like a Facebook.

01:20:35.180 | We don't know their location, but we have the friends.

01:20:37.180 | - Yeah, yeah, right.

01:20:38.020 | We know which point is connected to which other points.

01:20:41.900 | And that's all we know.

01:20:43.420 | And so you might say, well, how on earth

01:20:44.820 | can you get something which is like our experience

01:20:48.260 | of, you know, what seems like continuous space?

01:20:50.500 | Well, the answer is,

01:20:51.580 | by the time you have 10 to the 100 of these things,

01:20:54.220 | those connections can work in such a way

01:20:57.780 | that on a large scale,

01:20:59.660 | it will seem to be like continuous space

01:21:02.260 | in, let's say, three dimensions

01:21:03.740 | or some other number of dimensions

01:21:05.220 | or 2.6 dimensions or whatever else.

01:21:07.740 | - Because they're much, much, much, much larger.

01:21:10.380 | So like the number of relationships here

01:21:14.460 | we're talking about is just a humongous amount.

01:21:16.460 | So the kind of thing you're talking about

01:21:18.860 | is very, very, very small

01:21:20.220 | relative to our experience of daily life.

01:21:22.700 | - Right, so it's, I mean, you know,

01:21:23.740 | we don't know exactly the size,

01:21:25.060 | but maybe 10 to the minus,

01:21:30.060 | maybe around 10 to the minus 100 meters.

01:21:32.740 | So, you know, the size of, to give a comparison,

01:21:34.860 | you know, the size of a proton is 10 to the minus 15 meters.

01:21:38.460 | And so this is something incredibly tiny compared to that.

01:21:42.460 | - And the idea that from that would emerge

01:21:45.940 | the experience of continuous space is mind-blowing.

01:21:50.940 | What's your intuition why that's possible?

01:21:53.500 | Like, first of all, I mean, we'll get into it,

01:21:57.460 | but I don't know if we will

01:21:59.340 | through the medium of conversation,

01:22:01.860 | but the construct of hypergraphs is just beautiful.

01:22:06.420 | - Right.

01:22:07.260 | - Cellular automata are beautiful.

01:22:08.220 | We'll talk about it, but okay.

01:22:09.060 | - Right, but this thing about, you know,

01:22:11.140 | continuity arising from discrete systems

01:22:14.220 | is in today's world is actually not so surprising.

01:22:17.260 | I mean, you know, your average computer screen, right?

01:22:19.500 | Every computer screen is made of discrete pixels,

01:22:21.980 | yet we have the, you know,

01:22:23.740 | we have the idea that we're seeing these continuous pictures.

01:22:27.060 | I mean, it's, you know, the fact that on a large scale,

01:22:29.540 | continuity can arise from lots of discrete elements.

01:22:33.180 | This is at some level unsurprising now.

01:22:35.700 | - But, wait, wait, wait, wait, wait,

01:22:37.060 | but the pixels have a very definitive structure

01:22:42.060 | of neighbors on a computer screen.

01:22:46.020 | - Right.

01:22:46.860 | - There's no concept of spatial, of space,

01:22:51.860 | inherent in the underlying fabric of reality.

01:22:55.780 | - Right, right, right.

01:22:56.740 | So the point is, but there are cases where there are.

01:22:59.940 | So for example, let's just imagine

01:23:01.740 | you have a square grid, okay?

01:23:03.580 | And at every point on the grid,

01:23:05.380 | you have one of these atoms of space,

01:23:07.700 | and it's connected to four other atoms of space

01:23:10.860 | on the, you know, northeast, southwest corners, right?

01:23:14.500 | There you have something where if you zoom out from that,

01:23:17.620 | it's like a computer screen.

01:23:19.060 | - Yeah, so the relationship creates the spatial,

01:23:23.260 | like the relationship creates a constraint,

01:23:26.740 | which then in an emergent sense creates a,

01:23:31.740 | like, yeah, like a, basically a spatial coordinate

01:23:37.060 | for that thing. - Yes, yeah, right.

01:23:38.140 | - Even though the individual point doesn't have a spatial.

01:23:40.580 | - Even though the individual point doesn't know anything,

01:23:42.340 | it just knows what its, you know, what its neighbors are.

01:23:44.820 | The, on a large scale, it can be described by saying,

01:23:48.860 | oh, it looks like it's a, you know,

01:23:50.980 | this grid, this zoomed out grid.

01:23:52.820 | You can say, well, you can describe these different points

01:23:54.940 | by saying they have certain positions, coordinates,

01:23:57.020 | et cetera.

01:23:57.900 | Now, in the sort of real setup,

01:23:59.940 | it's more complicated than that.

01:24:00.780 | It isn't just a square grid or something.

01:24:03.100 | It's something much more dynamic and complicated,

01:24:05.780 | which we'll talk about.

01:24:07.260 | But so, you know, the first idea,

01:24:10.860 | the first key idea is, you know,

01:24:12.780 | what's the universe made of?

01:24:13.860 | It's made of atoms of space, basically,

01:24:15.740 | with these connections between them.

01:24:17.820 | What kind of connections do they have?

01:24:19.380 | Well, so the simplest kind of thing you might say

01:24:22.500 | is we've got something like a graph

01:24:25.260 | where every atom of space,

01:24:28.500 | where we have these edges that go between,

01:24:30.940 | out of these connections that go between atoms of space.

01:24:33.180 | We're not saying how long these edges are.

01:24:35.020 | We're just saying there is a connection

01:24:36.420 | from this place to the, from this atom to this atom.

01:24:39.140 | - Just a quick pause,

01:24:40.660 | 'cause there's a lot of very people that listen to this.

01:24:44.540 | Just to clarify, 'cause I did a poll, actually.

01:24:46.980 | What do you think a graph is a long time ago?

01:24:49.660 | And it's kind of funny how few people

01:24:52.100 | know the term graph outside of computer science.

01:24:55.900 | - Let's call it a network.

01:24:57.300 | I think that's-- - Let's call it a network

01:24:58.340 | is better.

01:24:59.180 | So, but every time, I like the word graph, though.

01:25:00.900 | So let's define, let's just say that a graph

01:25:03.860 | will use terms nodes and edges, maybe.

01:25:06.660 | And it's just nodes represent some abstract entity,

01:25:11.580 | and then the edges represent relationships

01:25:13.940 | between those entities.

01:25:14.860 | - Right, exactly.

01:25:15.860 | - So that's what a graph, sorry, so.

01:25:18.060 | So there you go.

01:25:18.900 | So that's the basic structure.

01:25:20.660 | - That is the simplest case of a basic structure.

01:25:23.420 | Actually, it tends to be better to think about hypergraphs.

01:25:27.900 | So a hypergraph is just, instead of saying

01:25:31.620 | there are connections between pairs of things,

01:25:34.660 | we say there are connections between any number of things.

01:25:37.220 | So there might be ternary edges.

01:25:39.260 | So instead of just having two points

01:25:42.980 | are connected by an edge, you say three points

01:25:45.900 | are all associated with a hyperedge,

01:25:48.380 | are all connected by a hyperedge.

01:25:50.260 | That's just, at some level, that's a detail.

01:25:54.180 | It's a detail that happens to make the, for me,

01:25:57.660 | you know, sort of in the history of this project,

01:26:00.060 | the realization that you could do things that way

01:26:02.380 | broke out of certain kinds of arbitrariness

01:26:04.420 | that I felt that there was in the model

01:26:06.140 | before I had seen how this worked.

01:26:07.940 | - I mean, a hypergraph can be mapped to a graph.

01:26:12.500 | It's just a convenient representation,

01:26:14.420 | mathematically speaking. - Right, that's correct.

01:26:16.180 | That's correct.

01:26:17.020 | But so then, so, okay, so the first question,

01:26:19.740 | the first idea of these models of ours is

01:26:22.780 | space is made of these, you know,

01:26:24.420 | connected sort of atoms of space.

01:26:26.580 | The next idea is space is all there is.

01:26:29.860 | There's nothing except for this space.

01:26:31.900 | So in traditional ideas in physics,

01:26:33.940 | people have said there's space, it's kind of a background,

01:26:37.020 | and then there's matter, all these particles,

01:26:38.780 | electrons, all these other things,

01:26:40.340 | which exist in space, right?

01:26:43.420 | But in this model, one of the key ideas is

01:26:46.220 | there's nothing except space.

01:26:48.420 | So in other words, everything that exists in the universe

01:26:52.180 | is a feature of this hypergraph.

01:26:54.660 | So how can that possibly be?

01:26:55.940 | Well, the way that works is that

01:26:58.660 | there are certain structures in this hypergraph

01:27:01.660 | where you say that little twisty, knotted thing,

01:27:05.780 | we don't know exactly how this works yet,

01:27:07.260 | but we have sort of idea about how it works mathematically.

01:27:10.980 | This sort of twisted, knotted thing,

01:27:13.020 | that's the core of an electron.

01:27:14.860 | This thing over there that has this different form,

01:27:17.380 | that's something else.

01:27:18.540 | - So the different peculiarities of the structure

01:27:21.060 | of this graph are the very things that

01:27:25.300 | we think of as the particles inside the space,

01:27:29.020 | but in fact, it's just the property of the space.

01:27:31.780 | Mind-blowing, first of all.

01:27:33.900 | It's mind-blowing, and we'll probably talk,

01:27:35.900 | in its simplicity and beauty.

01:27:38.540 | - Yes, I think it's very beautiful.

01:27:40.340 | - But that's space, and then there's another concept

01:27:44.300 | we didn't really kind of mention,

01:27:45.860 | but you think of computation as a transformation.

01:27:50.500 | - Let's talk about time in a second.

01:27:51.660 | Let's just, I mean, on the subject of space,

01:27:55.340 | there's this question of kind of what,

01:27:57.660 | there's this idea, there is this hypergraph,

01:27:59.900 | it represents space, and it represents

01:28:02.380 | everything that's in space.

01:28:03.620 | The features of that hypergraph, you can say,

01:28:06.260 | certain features in this part we do know,

01:28:08.300 | certain features of the hypergraph

01:28:09.660 | represent the presence of energy, for example,

01:28:11.780 | or the presence of mass or momentum,

01:28:13.980 | and we know what the features of the hypergraph

01:28:16.060 | that represent those things are,

01:28:17.900 | but it's all just the same hypergraph.

01:28:20.300 | So one thing you might ask is,

01:28:22.220 | if you just look at this hypergraph and you say,

01:28:24.260 | and we're gonna talk about sort of what the hypergraph does,

01:28:27.140 | but if you say, how much of what's going on

01:28:30.020 | in this hypergraph is things we know and care about,

01:28:34.020 | like particles and atoms and electrons

01:28:36.500 | and all this kind of thing,

01:28:37.540 | and how much is just the background of space?

01:28:40.900 | So it turns out, so far as in one rough estimate of this,

01:28:45.260 | or everything that we care about in the universe

01:28:47.900 | is only one part in 10 to the 120

01:28:50.820 | of what's actually going on.

01:28:52.060 | The vast majority of what's happening

01:28:54.060 | is purely things that maintain the structure of space.

01:28:57.380 | That, in other words, the things that are

01:28:59.780 | the features of space that are the things

01:29:03.300 | that we consider notable,

01:29:04.660 | like the presence of particles and so on,

01:29:06.500 | that's a tiny little piece of froth

01:29:08.780 | on the top of all this activity

01:29:10.700 | that mostly is just intended to,

01:29:13.860 | mostly, I can't say intended, there's no intention here,

01:29:16.500 | that just maintains the structure of space.

01:29:19.020 | - Let me load that in.

01:29:21.980 | It just makes me feel so good as a human being.

01:29:26.700 | To be the froth on the one in the 10 to the--

01:29:31.060 | - 120 or something of, well--

01:29:33.180 | - And also just humbling how,

01:29:37.980 | in this mathematical framework,

01:29:39.900 | how much work needs to be done on the infrastructure

01:29:43.060 | of our universe. - Right, yes.

01:29:44.860 | Right, to maintain the infrastructure of our universe

01:29:46.860 | is a lot of work.

01:29:47.940 | We are merely writing little tiny things

01:29:51.540 | on top of that infrastructure.

01:29:53.380 | But you were just starting to talk a little bit about,

01:29:57.500 | we talked about space,

01:29:59.780 | that represents all the stuff that's in the universe.

01:30:03.260 | The question is, what does that stuff do?

01:30:06.060 | And for that, we have to start talking about time

01:30:09.180 | and what is time and so on.

01:30:11.420 | And one of the basic idea of this model

01:30:15.220 | is time is the progression of computation.

01:30:17.980 | So in other words, we have a structure of space

01:30:21.020 | and there is a rule that says how that structure of space

01:30:24.020 | will change, and it's the application,

01:30:26.180 | the repeated application of that rule

01:30:28.500 | that defines the progress of time.

01:30:31.340 | - And what does the rule look like

01:30:34.100 | in the space of hypergraphs?

01:30:35.980 | - Right, so what the rule says is something like,

01:30:38.660 | if you have a little tiny piece of hypergraph

01:30:40.460 | that looks like this,

01:30:42.220 | then it will be transformed into a piece of hypergraph

01:30:44.700 | that looks like this.

01:30:46.660 | So that's all it says.

01:30:47.900 | It says you pick up these elements of space

01:30:51.260 | and you can think of these edges, these hyper edges

01:30:55.180 | as being relations between elements in space.

01:30:57.700 | You might pick up these two relations

01:31:01.220 | between elements in space.

01:31:03.260 | And we're not saying where those elements are

01:31:04.820 | or what they are, but every time there's a certain

01:31:06.940 | arrangement of elements in space,

01:31:09.220 | then arrangement in the sense of the way they're connected,

01:31:12.220 | then we transform it into some other arrangement.

01:31:14.660 | - So there's a little tiny pattern

01:31:16.300 | and you transform it into another little pattern.

01:31:18.500 | - That's right.

01:31:19.340 | - And then because of this, I mean, again,

01:31:21.500 | it's kind of similar to cellular automata in that like,

01:31:24.500 | on paper, the rule looks like super simple.

01:31:26.820 | It's like, yeah, okay.

01:31:29.100 | Yeah, like, yeah, right, from this,

01:31:32.260 | the universe can be born.

01:31:33.620 | But like, once you start applying it,

01:31:36.660 | beautiful structure starts being,

01:31:39.020 | potentially can be created.

01:31:40.980 | And what you're doing is you're applying that rule

01:31:43.540 | to different parts, like anytime you match it

01:31:47.260 | within the hypergraph.

01:31:48.660 | - Exactly.

01:31:49.500 | - And then one of the like incredibly beautiful

01:31:53.100 | and interesting things to think about is the order

01:31:57.140 | in which you apply that rule.

01:31:59.260 | Because that pattern appears all over the place.

01:32:01.980 | - Right, so this is a big, complicated thing,

01:32:04.340 | very hard to wrap one's brain around.

01:32:05.940 | Okay, so you say the rule is,

01:32:09.020 | every time you see this little pattern,

01:32:10.660 | transform it in this way.

01:32:12.500 | But yet, as you look around the space

01:32:15.780 | that represents the universe,

01:32:17.340 | there may be zillions of places

01:32:18.740 | where that little pattern occurs.

01:32:20.580 | So what it says is, just do this,

01:32:24.380 | apply this rule wherever you feel like.

01:32:26.900 | And what is extremely non-trivial is,

01:32:31.340 | well, okay, so this is happening sort of

01:32:33.500 | in computer science terms sort of asynchronously.

01:32:35.860 | You're just doing it wherever you feel like doing it.

01:32:38.980 | And the only constraint is that if you're going

01:32:41.780 | to apply the rule somewhere,

01:32:43.820 | the things to which you apply the rule,

01:32:46.700 | the little elements to which you apply the rule,

01:32:50.020 | if they have to be, okay,

01:32:54.940 | you can think of each application of the rule

01:32:56.500 | as being kind of an event that happens in the universe.

01:32:59.780 | And the input to an event has to be ready

01:33:04.740 | for the event to occur.

01:33:06.220 | That is, if one event occurred,

01:33:08.220 | if one transformation occurred,

01:33:09.940 | and it produced a particular atom of space,

01:33:12.700 | then that atom of space has to already exist

01:33:17.180 | before another transformation that's going to apply

01:33:20.860 | to that atom of space can occur.

01:33:23.220 | - Yeah, so that's like the prerequisite for the event.

01:33:25.820 | - That's right, that's right.

01:33:26.900 | So that defines a kind of this sort of set

01:33:31.820 | of causal relationships between events.

01:33:33.860 | It says this event has to have happened before this event.

01:33:37.980 | But that is--

01:33:40.220 | - But that's not a very limited constraint.

01:33:42.940 | - No, it's not.

01:33:44.100 | And what's interesting--

01:33:44.940 | - You still get the zillion,

01:33:47.180 | that's the technical term, options.

01:33:49.740 | - That's correct.

01:33:50.660 | But, okay, so this is where things get

01:33:52.820 | a little bit more elaborate, but--

01:33:54.460 | - But they're mind-blowing, so.

01:33:56.620 | - Right, but so what happens is,

01:33:59.100 | so the first thing you might say is,

01:34:01.020 | well, okay, so this question about the freedom

01:34:04.780 | of which event you do when,

01:34:07.220 | well, let me sort of state an answer and then explain it.

01:34:10.220 | Okay?

01:34:11.060 | The validity of special relativity is a consequence

01:34:15.500 | of the fact that in some sense it doesn't matter

01:34:18.260 | in what order you do these underlying things

01:34:20.700 | so long as they respect this kind of set

01:34:22.980 | of causal relationships.

01:34:25.380 | - So that's, the part that's in a certain sense

01:34:30.380 | is a really important one,

01:34:31.820 | but the fact that it sometimes doesn't matter,

01:34:35.660 | that's a, I don't know, that's another beautiful thing.

01:34:39.180 | - So there's this idea of what I call causal invariance.

01:34:42.540 | - Causal invariance, exactly.

01:34:44.060 | So that's a really, really powerful, powerful idea.

01:34:46.980 | - Powerful idea which has actually arisen

01:34:49.180 | in different forms many times in the history

01:34:51.340 | of mathematics, mathematical logic, even computer science,

01:34:54.860 | has many different names.

01:34:56.780 | I mean, our particular version of it is a little bit tighter

01:34:59.260 | than other versions, but it's basically the same idea.

01:35:01.460 | Here's how to think about that idea.

01:35:03.660 | So imagine that, well, let's talk about it

01:35:06.340 | in terms of math for a second.

01:35:08.100 | Let's say you're doing algebra and you're told,

01:35:11.220 | multiply out this series of polynomials

01:35:14.260 | that are multiplied together, okay?

01:35:16.780 | You say, well, which order should I do that in?

01:35:19.140 | Say, well, do I multiply the third one by the fourth one

01:35:21.500 | and then do it by the first one?

01:35:22.620 | Or do I do the fifth one by the sixth one

01:35:24.580 | and then do that?

01:35:25.940 | Well, it turns out it doesn't matter.

01:35:27.820 | You can multiply them out in any order,

01:35:29.740 | you'll always get the same answer.

01:35:31.580 | That's a property, if you think about kind of making

01:35:35.460 | a kind of network that represents

01:35:37.100 | in what order you do things, you'll get different orders

01:35:40.700 | for different ways of multiplying things out,

01:35:42.780 | but you'll always get the same answer.

01:35:44.900 | Same thing if you, let's say you're sorting,

01:35:46.700 | you've got a bunch of A's and B's,

01:35:48.900 | they're in some random order, you know, BAA, BBBAA,

01:35:52.500 | whatever, and you have a little rule

01:35:54.380 | that says every time you see BA, flip it around to AB, okay?

01:35:59.380 | Eventually you apply that rule enough times,

01:36:02.300 | you'll have sorted the string so that it's all the A's first

01:36:05.420 | and then all the B's.

01:36:06.500 | Again, there are many different orders

01:36:10.060 | in which you can do that, many different sort of places

01:36:13.220 | where you can apply that update.

01:36:15.300 | In the end, you'll always get the string sorted

01:36:17.140 | the same way.

01:36:18.500 | - I know with sorting a string, it sounds obvious.

01:36:22.300 | That's to me, surprising.

01:36:24.660 | That there is, in complicated systems,

01:36:28.300 | obviously with a string, but in a hypergraph,

01:36:31.020 | that the application of the rule,

01:36:33.340 | a synchronous rule can lead to the same results sometimes.

01:36:36.700 | - Yes, yes, that is not obvious,

01:36:39.060 | and it was something that, you know,

01:36:40.700 | I sort of discovered that idea for these kinds of systems

01:36:44.060 | and back in the 1990s, and for various reasons,

01:36:46.620 | I was not satisfied by how sort of fragile

01:36:52.020 | finding that particular property was.

01:36:54.260 | And let me just make another point,

01:36:56.300 | which is that it turns out that even if the underlying rule

01:37:01.060 | does not have this property of causal invariance,

01:37:03.860 | it can turn out that every observation made by observers

01:37:07.260 | of the rule, they can impose what amounts

01:37:11.180 | to causal invariance on the rule.

01:37:13.820 | We can explain that, it's a little bit more complicated.

01:37:15.460 | I mean, technically that has to do with this idea

01:37:17.940 | of completions, which is something that comes up

01:37:20.100 | in term rewriting systems, automated theorem proving systems

01:37:23.100 | and so on, but let's ignore that for a second.

01:37:26.260 | We can come to that later.

01:37:27.660 | - Is it useful to talk about observation?

01:37:29.780 | - Not yet, not yet.

01:37:31.380 | - Okay, so great.

01:37:33.100 | So there's some concept of causal invariance

01:37:35.500 | as you apply these rules in an asynchronous way,

01:37:39.420 | you can think of those transformations as events.

01:37:42.140 | So there's this hypergraph that represents space

01:37:44.340 | and all of these events happening in the space,

01:37:46.980 | and the graph grows in interesting, complicated ways,

01:37:50.420 | and eventually the froth arises of what we experience

01:37:54.540 | as human existence.

01:37:56.180 | - That's some version of the picture,

01:37:58.900 | but let's explain a little bit more.

01:38:00.740 | - Exactly, a little more detail.

01:38:03.580 | - Right, so one thing that is sort of surprising

01:38:06.740 | in this theory is one of the sort of achievements

01:38:10.060 | of 20th century physics was kind of bringing space

01:38:12.340 | and time together.

01:38:13.860 | That was special relativity, people talk about

01:38:16.500 | space-time, this sort of unified thing where space

01:38:20.060 | and time kind of are mixed, and there's a nice

01:38:22.580 | mathematical formalism in which space and time

01:38:27.260 | sort of appear as part of the space-time continuum,

01:38:30.780 | the space-time four vectors and things like this.

01:38:34.700 | We talk about time as the fourth dimension

01:38:37.340 | and all these kinds of things.

01:38:38.820 | It's, you know, and it seems like the theory of relativity

01:38:42.180 | sort of says space and time are fundamentally

01:38:44.060 | the same kind of thing.

01:38:45.420 | So one of the things that took a while to understand

01:38:48.700 | in this approach of mine is that in my kind of approach,

01:38:53.700 | space and time are really not fundamentally

01:38:56.660 | the same kind of thing.

01:38:57.500 | Space is the extension of this hypergraph,

01:39:00.500 | time is the kind of progress of this inexorable computation

01:39:04.420 | of these rules getting applied to the hypergraph.

01:39:07.060 | So they seem like very different kinds of things.

01:39:10.020 | And so that, at first, seems like how can that

01:39:13.260 | possibly be right?

01:39:14.180 | How can that possibly be Lorentz invariant?

01:39:16.460 | That's the term for things being, you know,

01:39:18.860 | following the rules of special relativity.

01:39:21.620 | Well, it turns out that when you have causal invariance,

01:39:26.140 | that, and let's see, we can, it's worth explaining

01:39:30.140 | a little bit how this works.

01:39:31.020 | It's a little bit elaborate, but the basic point is

01:39:35.100 | that even though space and time sort of come

01:39:39.940 | from very different places, it turns out that the rules

01:39:43.660 | of sort of space time that special relativity talks about

01:39:47.260 | come out of this model when you're looking

01:39:51.740 | at large enough systems.

01:39:53.700 | So a way to think about this, you know,

01:39:56.100 | in terms of when you're looking at large enough systems,

01:39:59.500 | the part of that story is when you look at some fluid

01:40:03.820 | like water, for example, there are equations

01:40:06.300 | that govern the flow of water.

01:40:07.860 | Those equations are things that apply on a large scale.

01:40:12.740 | If you look at the individual molecules,

01:40:14.420 | they don't know anything about those equations.

01:40:16.280 | It's just the sort of the large scale effect

01:40:19.340 | of those molecules turns out to follow those equations.

01:40:22.820 | And it's the same kind of thing happening in our models.

01:40:25.860 | - I know this might be a small point,

01:40:27.980 | but it might be a very big one.

01:40:29.580 | We've been talking about space and time

01:40:32.540 | at the lowest level of the model, which is space.

01:40:35.980 | The hypergraph time is the evolution of this hypergraph.

01:40:39.860 | But there's also space time that we think about

01:40:43.160 | in general relativity for your special relativity.

01:40:46.400 | Like what, how do you go from the lowest source code

01:40:52.400 | of space and time we're talking about

01:40:55.940 | to the more traditional terminology of space and time?

01:40:58.180 | - Yeah, right.

01:40:59.020 | So the key thing is this thing we call the causal graph.

01:41:01.820 | So the causal graph is the graph of causal relationships

01:41:05.260 | between events.

01:41:06.660 | So every one of these little updating events,

01:41:08.980 | every one of these little transformations

01:41:10.300 | of the hypergraph happens somewhere in the hypergraph,

01:41:13.380 | happens at some stage in the computation.

01:41:16.820 | That's an event.

01:41:18.240 | That event has a causal relationship to other events

01:41:22.280 | in the sense that if another event needs as its input,

01:41:27.280 | the output from the first event,

01:41:29.420 | there will be a causal relationship of the future event

01:41:33.300 | will depend on the past event.

01:41:35.220 | So you can say it has a causal connection.

01:41:37.980 | So you can make this graph of causal relationships

01:41:40.980 | between events.

01:41:42.380 | That graph of causal relationships,

01:41:44.180 | causal invariance implies that that graph is unique.

01:41:47.620 | It doesn't matter, even though you think,

01:41:51.220 | oh, I'm, you know, let's say we were sorting a string.

01:41:53.520 | For example, I did that particular transposition

01:41:56.340 | of characters at this time.

01:41:58.100 | And then I did that one.

01:41:59.020 | Then I did this one.

01:42:00.140 | Turns out if you look at the network of connections

01:42:02.960 | between those updating events, that network is the same.

01:42:06.620 | It's the, if you were to--

01:42:08.940 | - I see.

01:42:09.780 | - The structure, so in other words,

01:42:11.460 | if you were to draw that,

01:42:13.300 | if you were to put that network on a picture

01:42:15.380 | of where you're doing all the updating,

01:42:17.060 | the places where you put the nodes of the network

01:42:20.020 | will be different, but the way the nodes are connected

01:42:22.420 | will always be the same.

01:42:23.820 | - But the causal graph is, I don't,

01:42:27.280 | it's kind of an observate, it's not enforced.

01:42:31.060 | It's just emergent from a set of events.

01:42:33.740 | - It's a feature of, okay, so what it is--

01:42:36.380 | - It's characteristic, I guess, of the way events happen.

01:42:38.860 | - Right, it's an event can't happen

01:42:40.780 | until its input is ready.

01:42:42.540 | And so that creates this network of causal relationships.

01:42:46.380 | And that's the causal graph.

01:42:48.300 | And the thing, the next thing to realize is,

01:42:51.580 | okay, we, when you're going to observe

01:42:54.480 | what happens in the universe,

01:42:56.400 | you have to sort of make sense of this causal graph.

01:42:59.580 | So, and you are an observer

01:43:01.980 | who yourself is part of this causal graph.

01:43:05.040 | And so that means, so let me give you an example

01:43:07.540 | of how that works.

01:43:08.380 | So imagine we have a really weird theory of physics

01:43:11.140 | of the world where it says this updating process,

01:43:15.100 | there's only going to be one update at every moment in time.

01:43:18.180 | And there's just going to be like a Turing machine

01:43:19.700 | that has a little head that runs around

01:43:21.540 | and just is always just updating one thing at a time.

01:43:23.660 | So you say, I have a theory of physics

01:43:26.040 | and the theory of physics says,

01:43:27.480 | there's just this one little place where things get updated.

01:43:30.460 | You say, that's completely crazy

01:43:31.820 | because it's plainly obvious

01:43:34.340 | that things are being updated sort of at the same time.

01:43:37.420 | - Asynchronously, yeah, or at the same time, yeah.

01:43:39.260 | - But the fact is that the thing is that

01:43:42.440 | if I'm talking to you and you seem to be being updated

01:43:45.580 | as I'm being updated,

01:43:47.180 | but if there's just this one little head

01:43:48.960 | that's running around updating things,

01:43:51.000 | I will not know whether you've been updated or not

01:43:53.440 | until I'm updated.

01:43:55.440 | So in other words, when you draw this causal graph

01:43:58.640 | of the causal relationship between the updatings in you

01:44:01.000 | and the update is in me,

01:44:02.440 | it'll still be the same causal graph,

01:44:04.400 | whether even though the underlying sort of story

01:44:07.120 | of what happens is, oh, there's just this one little thing

01:44:10.120 | and it goes and updates in different places in the universe.

01:44:13.320 | - Is that clear or is that a hypothesis?

01:44:18.040 | Is that clear that there's a unique causal graph?

01:44:21.440 | - If there's causal invariance,

01:44:22.720 | there's a unique causal graph.

01:44:24.240 | - So it's okay to think of what we're talking about

01:44:28.060 | as a hypergraph and the operations on it

01:44:30.600 | as a kind of Turing machine with a single head,

01:44:32.960 | like a single guy running around updating stuff.

01:44:35.740 | Is that safe to intuitively think of it this way?

01:44:39.640 | - Let me think about that for a second.

01:44:41.680 | Yes, I think so.

01:44:42.560 | I think there's nothing, it doesn't matter.

01:44:44.800 | I mean, you can say, okay, there is one,

01:44:47.960 | the reason I'm pausing for a second is that I'm wondering,

01:44:52.880 | well, when you say running around,

01:44:55.840 | depends how far it jumps every time it runs around.

01:44:58.000 | - Yeah, yeah, that's right.

01:44:59.160 | - But I mean like one operation at a time.

01:45:01.960 | - Yeah, you can think of it as one operation at a time.

01:45:03.760 | - It's easier for the human brain to think of it that way

01:45:06.680 | as opposed to simultaneous.

01:45:08.280 | - Well, maybe it's not, okay, but the thing is

01:45:10.720 | that's not how we experience the world.

01:45:12.720 | What we experience is we look around,

01:45:15.760 | everything seems to be happening at successive moments

01:45:19.280 | in time everywhere in space.

01:45:21.360 | That is the, and that's partly a feature

01:45:23.880 | of our particular construction.

01:45:25.580 | I mean, that is the speed of light is really fast

01:45:28.460 | compared to, we look around,

01:45:30.680 | I can see maybe a hundred feet away right now.

01:45:33.280 | My brain does not process very much

01:45:38.960 | in the time it takes light to go a hundred feet.

01:45:41.480 | - The brain operates at a scale of hundreds of milliseconds

01:45:44.200 | or something like that, I don't know.

01:45:45.480 | - Right.

01:45:46.320 | - And speed of light is much faster.

01:45:47.760 | - Right, light goes in a billionth of a second,

01:45:50.320 | light has gone a foot.

01:45:51.160 | So it goes a billion feet every second.

01:45:53.880 | - There's certain moments through this conversation

01:45:56.640 | where I imagine the absurdity of the fact

01:46:01.360 | that there's two descendants of apes

01:46:03.780 | modeled by a hypergraph that are communicating

01:46:06.020 | with each other and experiencing this whole thing

01:46:09.100 | as a real-time simultaneous update with,

01:46:13.400 | I'm taking in photons from you right now,

01:46:15.420 | but there's something much, much deeper going on here.

01:46:18.620 | - Right, it does have a--

01:46:19.900 | - It's paralyzing sometimes just to remember that.

01:46:24.140 | - Right, no, I mean, you know,

01:46:26.420 | as a small little tangent, I just remembered

01:46:30.780 | that we're talking about, I mean,

01:46:32.580 | this, about the fabric of reality.

01:46:37.100 | - Right, so we've got this causal graph

01:46:40.100 | that represents the sort of causal relationships

01:46:41.940 | between all these events in the universe.

01:46:43.800 | That causal graph kind of is a representation of space-time,

01:46:47.720 | but our experience of it requires

01:46:50.820 | that we pick reference frames.

01:46:53.000 | This is kind of a key idea, Einstein had this idea

01:46:55.940 | that what that means is we have to say

01:46:58.980 | what are we going to pick as being the,

01:47:03.380 | sort of what we define as simultaneous moments in time.

01:47:06.880 | So for example, we can say, you know,

01:47:11.420 | how do we set our clocks?

01:47:13.100 | You know, if we've got a spacecraft landing on Mars,

01:47:16.460 | you know, do we say that it, you know,

01:47:17.860 | what time is it landing at?

01:47:19.540 | Was it, you know, even though there's a 20-minute

01:47:21.700 | speed of light delay or something,

01:47:23.540 | you know, what time do we say it landed at?

01:47:25.380 | How do we set up sort of time coordinates for the world?

01:47:30.020 | And that turns out to be, there's kind of this arbitrariness

01:47:33.860 | to how we set these reference frames

01:47:35.960 | that define sort of what counts as simultaneous.

01:47:39.200 | And what is the essence of special relativity

01:47:42.020 | is to think about reference frames going

01:47:44.340 | at different speeds and to think about sort of

01:47:47.180 | how they assign what counts as space,

01:47:49.820 | what counts as time, and so on.

01:47:52.320 | That's all a bit technical, but the basic bottom line is

01:47:55.680 | that this causal invariance property,

01:47:58.920 | that means that it's always the same causal graph,

01:48:01.780 | independent of how you slice it with these reference frames,

01:48:04.760 | you'll always sort of see the same physical processes go on.

01:48:07.840 | And that's basically why special relativity works.

01:48:10.360 | - So there's something like special relativity,

01:48:14.600 | like everything around space and time

01:48:19.400 | that fits this idea of the causal graph.

01:48:22.920 | - Right, well, you know, one way to think about it is

01:48:24.920 | given that you have a basic structure

01:48:27.320 | that just involves updating things

01:48:29.920 | in these connected updates and looking

01:48:33.200 | at the causal relationships between connected updates,

01:48:35.680 | that's enough.

01:48:37.200 | When you unravel the consequences of that,

01:48:39.800 | that together with the fact that there are lots

01:48:41.540 | of these things and that you can take a continuum limit

01:48:43.920 | and so on, implies special relativity.

01:48:46.940 | And so that, it's kind of a, not a big deal,

01:48:51.000 | because it's kind of a, you know,

01:48:52.920 | it was completely unobvious when you started off

01:48:56.520 | with saying we've got this graph,

01:48:57.880 | it's being updated in time, et cetera, et cetera, et cetera,

01:49:00.200 | that just looks like nothing to do with special relativity.

01:49:03.280 | And yet you get that.

01:49:05.040 | And what, I mean, then the thing, I mean,

01:49:08.280 | this was stuff that I figured out back in the 1990s.

01:49:11.160 | The next big thing you get is general relativity.

01:49:16.200 | And so in this hypergraph,

01:49:18.920 | the sort of limiting structure,

01:49:20.700 | when you have a very big hypergraph,

01:49:22.440 | you can think of as being just like, you know,

01:49:24.480 | water seems continuous on a large scale.

01:49:27.040 | So this hypergraph seems continuous on a large scale.

01:49:30.120 | One question is, you know,

01:49:31.660 | how many dimensions of space does it correspond to?

01:49:35.200 | So one question you can ask is,

01:49:36.440 | if you've just got a bunch of points

01:49:38.000 | and they're connected together,

01:49:39.480 | how do you deduce what effective dimension of space

01:49:43.140 | that bundle of points corresponds to?

01:49:46.000 | And that's pretty easy to explain.

01:49:47.680 | So basically, if you say, you've got a point

01:49:50.520 | and you look at how many neighbors does that point have?

01:49:52.760 | Okay, imagine it's on a square grid.

01:49:54.640 | Then it'll have four neighbors.

01:49:56.220 | Go another level out.

01:49:58.240 | How many neighbors do you get then?

01:49:59.960 | What you realize is, as you go more and more levels out,

01:50:02.760 | as you go more and more distance on the graph out,

01:50:05.880 | you're capturing something which is essentially a circle

01:50:09.680 | in two dimensions so that, you know,

01:50:11.440 | the number of the area of a circle is pi r squared.

01:50:14.680 | So it's the number of points that you get to

01:50:18.360 | goes up like the distance you've gone squared.

01:50:21.480 | And in general, in d-dimensional space,

01:50:24.400 | it's r to the power d.

01:50:25.880 | It's the number of points you get to

01:50:28.640 | if you go r steps on the graph

01:50:31.520 | grows like the number of steps you go

01:50:33.680 | to the power of the dimension.

01:50:35.520 | And that's a way that you can estimate

01:50:37.720 | the effective dimension of one of these graphs.

01:50:39.920 | - So what does that grow to?

01:50:41.040 | So how does the dimension grow?

01:50:42.520 | 'Cause, I mean, obviously the visual aspect

01:50:45.880 | of these hypergraphs,

01:50:47.360 | they're often visualized in three dimensions.

01:50:50.080 | - Right.

01:50:50.920 | - And then there's a certain kind of structure.

01:50:53.040 | Like you said, there's, I mean, a circle, a sphere.

01:50:58.880 | There's a planar aspect to it, to this graph,

01:51:03.680 | to where it kinda, it almost starts creating a surface,

01:51:06.760 | like a complicated surface, but a surface.

01:51:09.120 | So how does that connect to effective dimension?

01:51:11.880 | - Okay, so I mean, if you can lay out the graph

01:51:14.400 | in such a way that the points in the graph,

01:51:17.640 | points that are neighbors on the graph

01:51:21.320 | are neighbors as you lay them out,

01:51:23.480 | and you can do that in two dimensions,

01:51:25.640 | then it's gonna approximate a two-dimensional thing.

01:51:28.320 | If you can't do that in two dimensions,

01:51:29.720 | if everything would have to fold over a lot

01:51:31.200 | in two dimensions, then it's not approximating

01:51:33.240 | a two-dimensional thing.

01:51:34.080 | Maybe you can lay it out in three dimensions.

01:51:36.160 | Maybe you have to lay it out in five dimensions

01:51:38.600 | to have it be the case that it sort of

01:51:40.040 | smoothly lays out like that.

01:51:42.000 | - Well, but, okay, so, and I apologize

01:51:44.680 | for the different tangent questions,

01:51:46.040 | but there's an infinity number of possible rules.

01:51:49.420 | So we have to look for rules that create

01:51:55.760 | the kind of structures that are reminiscent for,

01:52:00.600 | that have echoes of the different physics theories in them.

01:52:05.080 | So what kind of rules, is there something simple

01:52:07.760 | to be said about the kind of rules

01:52:09.940 | that you have found beautiful,

01:52:12.080 | that you have found powerful?

01:52:13.480 | - Right, so, I mean, what, you know,

01:52:15.400 | one of the features of computational irreducibility is

01:52:18.800 | it's very, you can't say in advance

01:52:22.000 | what's gonna happen with any particular,

01:52:23.960 | you can't say, I'm gonna pick these rules

01:52:26.000 | from this part of rule space, so to speak,

01:52:28.920 | 'cause they're gonna be the ones that are gonna work.

01:52:30.960 | That's, you can make some statements along those lines,

01:52:33.360 | but you can't generally say that.

01:52:35.220 | Now, you know, the state of what we've been able to do

01:52:38.280 | is, you know, different properties of the universe,

01:52:40.700 | like dimensionality, you know, integer dimensionality,

01:52:44.620 | features of other features of quantum mechanics,

01:52:47.960 | things like that.

01:52:48.980 | At this point, what we've got is we've got rules

01:52:52.020 | that any one of those features,

01:52:55.380 | we can get a rule that has that feature.

01:52:58.100 | - Yeah, so the-- - But we don't have

01:52:59.140 | the sort of, the final, here's a rule

01:53:01.340 | which has all of these features.

01:53:02.620 | We do not have that yet.

01:53:03.660 | - So if I were to try to summarize

01:53:06.980 | the Wolfram Physics Project, which is, you know,

01:53:11.380 | something that's been in your brain for a long time,

01:53:13.920 | but really has just exploded in activity,

01:53:17.300 | you know, only just months ago.

01:53:19.180 | - Yes.

01:53:20.020 | - So it's an evolving thing, and next week,

01:53:23.300 | I'll try to publish this conversation as quickly as possible

01:53:26.540 | because by the time it's published,

01:53:27.820 | already new things will probably have come out.

01:53:29.620 | So if I were to summarize it,

01:53:33.180 | we've talked about the basics of,

01:53:35.940 | there's a hypergraph that represents space,

01:53:38.380 | there is transformations in that hypergraph

01:53:42.380 | that represents time. - Progress of time.

01:53:45.180 | - That progress of time, there's a causal graph

01:53:47.860 | that's a characteristic of this,

01:53:49.660 | and the basic process of science,

01:53:53.720 | of, yeah, of science within the Wolfram Physics model

01:53:58.660 | is to try different rules and see which properties

01:54:02.540 | of physics that we know of, known physical theories,

01:54:06.120 | are, appear within the graphs that emerge from that rule.

01:54:10.700 | - That's what I thought it was going to be.

01:54:12.380 | - Uh-oh, okay.

01:54:13.660 | So what, so what is it?

01:54:16.060 | - It turns out we can do a lot better than that.

01:54:18.180 | It turns out that using kind of mathematical ideas,

01:54:21.420 | we can say, and computational ideas,

01:54:25.140 | we can make general statements,

01:54:28.380 | and those general statements turn out

01:54:30.340 | to correspond to things that we know

01:54:32.340 | from 20th century physics.

01:54:34.100 | In other words, the idea of you just try a bunch of rules

01:54:36.940 | and see what they do,

01:54:37.780 | that's what I thought we were going to have to do.

01:54:40.260 | But in fact, we can say, given causal invariance

01:54:43.780 | and computational irreducibility,

01:54:45.740 | we can derive, and this is where it gets

01:54:48.380 | really pretty interesting,

01:54:49.460 | we can derive special relativity,

01:54:51.140 | we can derive general relativity,

01:54:52.920 | we can derive quantum mechanics.

01:54:55.140 | And that's where things really start to get exciting,

01:54:58.300 | is it wasn't at all obvious to me

01:55:01.340 | that even if we were completely correct,

01:55:03.340 | and even if we had, this is the rule,

01:55:05.420 | even if we found the rule, to be able to say,

01:55:07.980 | yes, it corresponds to things we already know,

01:55:10.340 | I did not expect that to be the case.

01:55:12.660 | And--

01:55:13.500 | - So for somebody who is a simple mind

01:55:16.900 | and definitely not a physicist, not even close,

01:55:19.460 | what does derivation mean in this case?

01:55:22.780 | - Okay, so let me, this is an interesting question.

01:55:26.940 | Okay, so one thing--

01:55:29.180 | - In the context of computational irreducibility.

01:55:31.900 | - Yeah, yeah, right, right.

01:55:32.940 | So what you have to do, let me go back to, again,

01:55:36.860 | the mundane example of fluids and water

01:55:38.980 | and things like that, right?

01:55:40.420 | So you have a bunch of molecules bouncing around.

01:55:44.020 | You can say, just as a piece of mathematics,

01:55:47.340 | I happened to do this from cellular automata

01:55:49.260 | back in the mid-1980s, you can say,

01:55:52.180 | just as a matter of mathematics,

01:55:54.200 | you can say the continuum limit

01:55:57.240 | of these little molecules bouncing around

01:55:59.240 | is the Navier-Stokes equations.

01:56:01.640 | That's just a piece of mathematics.

01:56:03.260 | It's not, it doesn't rely on,

01:56:06.620 | you have to make certain assumptions

01:56:08.480 | that you have to say there's enough randomness

01:56:10.900 | in the way the molecules bounce around

01:56:12.420 | that certain statistical averages work,

01:56:14.220 | et cetera, et cetera, et cetera.

01:56:15.660 | Okay, it is a very similar derivation

01:56:18.320 | to derive, for example, the Einstein equations.

01:56:21.220 | Okay, so the way that works, roughly,

01:56:23.700 | the Einstein equations are about curvature of space.

01:56:26.740 | Curvature of space, I talked about

01:56:28.880 | sort of how you can figure out dimension of space.

01:56:31.860 | There's a similar kind of way of figuring out

01:56:34.260 | if you just sort of say, you know,

01:56:37.220 | you're making a larger and larger ball

01:56:39.060 | or larger and larger, if you draw a circle

01:56:40.900 | on the surface of the Earth, for example,

01:56:43.220 | you might think the area of a circle is pi r squared,

01:56:45.980 | but on the surface of the Earth,

01:56:47.940 | because it's a sphere, it's not flat,

01:56:50.540 | the area of a circle isn't precisely pi r squared,

01:56:53.360 | as the circle gets bigger,

01:56:55.060 | the area is slightly smaller than you would expect

01:56:57.020 | from the formula pi r squared as a little correction term

01:56:59.580 | that depends on the ratio of the size of the circle

01:57:02.060 | to the radius of the Earth.

01:57:03.700 | Okay, so it's the same basic thing,

01:57:05.660 | allows you to measure from one of these hypergraphs,

01:57:08.240 | what is its effective curvature?

01:57:10.100 | And that was- - So,

01:57:12.580 | the little piece of mathematics

01:57:15.440 | that explains special general relativity

01:57:20.980 | can map nicely to describe

01:57:23.600 | fundamental property of the hypergraphs,

01:57:26.640 | of the curvature of the hypergraphs.

01:57:27.480 | - Okay, so, special relativity

01:57:30.240 | is about the relationship of time to space.

01:57:32.720 | General relativity is about curvature

01:57:35.300 | and the space represented by this hypergraph.

01:57:38.600 | - So, what is the curvature of a hypergraph?

01:57:40.760 | - Okay, so, first I have to explain,

01:57:43.120 | what I'm explaining is,

01:57:44.680 | first thing you have to have is a notion of dimension.

01:57:47.120 | You don't get to talk about curvature of things.

01:57:49.280 | If you say, "Oh, it's a curved line,

01:57:51.740 | "but I don't know what a line is yet."

01:57:53.840 | So- - Yeah, what is the dimension

01:57:55.220 | of a hypergraph then?

01:57:56.460 | Where, from where,

01:57:57.980 | we've talked about effective dimension, but-

01:58:00.600 | - Right, that's what this is about.

01:58:03.100 | What this is about is, you have your hypergraph,

01:58:05.220 | it's got a trillion nodes in it.

01:58:07.420 | What is it roughly like?

01:58:08.780 | Is it roughly like a grid, a two-dimensional grid?

01:58:11.500 | Is it roughly like all those nodes are arranged on a line?

01:58:15.280 | What's it roughly like?

01:58:16.780 | And there's a pretty simple mathematical way

01:58:19.600 | to estimate that by just looking at the,

01:58:23.340 | this thing I was describing,

01:58:24.760 | this sort of the size of a ball

01:58:26.340 | that you construct in the hypergraph.

01:58:28.240 | That's a, you just measure that,

01:58:29.800 | you can just compute it on a computer

01:58:31.580 | for a given hypergraph,

01:58:32.980 | and you can say, "Oh, this thing is wiggling around,

01:58:35.060 | "but it's roughly corresponds to two,"

01:58:37.540 | or something like that,

01:58:38.380 | or roughly corresponds to 2.6, or whatever.

01:58:41.460 | So, that's how you have a notion of dimension

01:58:44.100 | in these hypergraphs.

01:58:45.620 | Curvature is something a little bit beyond that.

01:58:48.380 | It's, if you look at the,

01:58:49.760 | how the size of this ball increases

01:58:52.140 | as you increase its radius,

01:58:53.960 | curvature is a correction to the size increase

01:58:57.380 | associated with dimension.

01:58:58.900 | It's a sort of a second order term in determining size,

01:59:03.340 | just like the area of a circle is roughly pi r squared,

01:59:07.000 | so it goes up like r squared,

01:59:08.500 | the two is because it's in two dimensions.

01:59:11.080 | But when that circle is drawn on a big sphere,

01:59:14.420 | the actual formula is pi r squared

01:59:16.660 | times one minus r squared over a squared,

01:59:20.900 | and some coefficient.

01:59:22.660 | So, in other words, there's a correction to,

01:59:24.980 | and that correction term, that gives you curvature.

01:59:28.260 | And that correction term is what makes this hypergraph

01:59:32.100 | correspond, have the potential

01:59:33.700 | to correspond to curved space.

01:59:35.860 | Now, the next question is, is that curvature,

01:59:38.460 | is the way that curvature works,

01:59:40.400 | the way that Einstein's equations for general relativity,

01:59:43.420 | is it the way they say it should work?

01:59:46.060 | And the answer is yes.

01:59:49.180 | - Really?

01:59:50.540 | - And so, how does that work?

01:59:52.260 | - The calculation of the curvature of this hypergraph

01:59:57.220 | for some set of rules?

01:59:59.780 | - No, it doesn't matter what the rules are.

02:00:01.540 | It doesn't, so long as they have causal invariance

02:00:03.380 | and computational irreducibility,

02:00:05.460 | and they lead to finite dimensional space.

02:00:09.380 | Non-infinite dimensional space.

02:00:11.380 | - Oh, oh, dimensional. - Non-infinite dimensional.

02:00:13.620 | It can grow infinitely,

02:00:14.740 | but it can't be infinite dimensional.

02:00:16.540 | So-- - What does a infinitely

02:00:17.980 | dimensional hypergraph look like?

02:00:19.860 | So that means-- - For example,

02:00:21.420 | so in a tree, you start from one root of the tree,

02:00:25.420 | it doubles, doubles again, doubles again, doubles again,

02:00:28.380 | and that means if you ask the question,

02:00:30.740 | starting from a given point, how many points do you get to?

02:00:34.160 | Remember, like a circle, you get to r squared,

02:00:36.700 | the two there.

02:00:37.820 | On a tree, you get to, for example, two to the r.

02:00:41.220 | It's exponential dimensional, so to speak,

02:00:43.300 | or infinite dimensional.

02:00:44.340 | - Do you have a sense of, in the space of all possible rules,

02:00:48.460 | how many lead to infinitely dimensional hypergraphs?

02:00:53.460 | Is that-- - No.

02:00:55.260 | - Okay.

02:00:56.100 | Is that an important thing to know?

02:00:57.940 | - Yes, it's an important thing to know.

02:00:59.540 | I would love to know the answer to that.

02:01:01.300 | But it gets a little bit more complicated,

02:01:03.500 | because, for example, it's very possibly the case

02:01:05.700 | that in our physical universe,

02:01:07.420 | that the universe started infinite dimensional,

02:01:09.980 | and it only, as the big bang,

02:01:13.780 | it was very likely infinite dimensional.

02:01:16.100 | And as the universe sort of expanded and cooled,

02:01:21.100 | its dimension gradually went down.

02:01:23.700 | And so one of the bizarre possibilities,

02:01:25.380 | which actually there are experiments you can do

02:01:27.100 | to try and look at this,

02:01:28.520 | the universe can have dimension fluctuations.

02:01:31.000 | So in other words, we think we live

02:01:32.200 | in a three-dimensional universe,

02:01:33.380 | but actually there may be places

02:01:35.580 | where it's actually 3.01 dimensional,

02:01:37.940 | or where it's 2.99 dimensional.

02:01:40.540 | And it may be that in the very early universe,

02:01:43.300 | it was actually infinite dimensional,

02:01:45.180 | and it's only a late-stage phenomenon

02:01:47.180 | that we end up getting three-dimensional space.

02:01:49.220 | - But from your perspective of the hypergraph,

02:01:51.900 | one of the underlying assumptions you kind of implied,

02:01:55.220 | but you have a sense, a hope,

02:01:57.820 | set of assumptions that the rules that underlie our universe

02:02:03.100 | or the rule that underlies our universe is static.

02:02:08.200 | Is that one of the assumptions

02:02:10.160 | you're currently operating under?

02:02:11.820 | - Yes, but there's a footnote to that,

02:02:14.840 | which we should get to,

02:02:15.680 | 'cause it requires a few more steps.

02:02:17.560 | - Well, actually then, but let's backtrack to the curvature,

02:02:19.920 | because we're talking about

02:02:21.040 | as long as it's finite dimensional.

02:02:23.160 | - Finite dimensional computational irreducibility

02:02:28.040 | and causal invariance,

02:02:29.720 | then it follows that the large-scale structure

02:02:35.840 | will follow Einstein's equations.

02:02:37.920 | And now let me, again, qualify that a little bit more.

02:02:40.760 | There's a little bit more complexity to it.

02:02:42.960 | Okay, so Einstein's equations in their simplest form

02:02:48.640 | apply to the vacuum, no matter just the vacuum.

02:02:52.280 | And they say, in particular, what they say is if you have,

02:02:56.400 | so there's this term geodesic.

02:02:59.080 | That's a term that means shortest path,

02:03:01.440 | comes from measuring the shortest paths on the earth.

02:03:04.220 | So you look at a bunch of, a bundle of geodesics,

02:03:08.160 | a bunch of shortest paths.

02:03:10.080 | It's like the paths that photons would take

02:03:12.040 | between two points.

02:03:13.580 | Then the statement of Einstein's equations

02:03:15.540 | is basically a statement about a certain,

02:03:18.520 | that as you look at a bundle of geodesics,

02:03:20.880 | the structure of space has to be such that

02:03:23.440 | although the cross-sectional area of this bundle may,

02:03:28.280 | although the actual shape of the cross-section may change,

02:03:30.520 | the cross-sectional area does not.

02:03:32.300 | That's a version, that's the most simple-minded version

02:03:35.760 | of R mu nu minus a half R, g mu nu equals zero,

02:03:39.480 | which is the more mathematical version

02:03:41.520 | of Einstein's equations.

02:03:42.960 | It's a statement of the thing called

02:03:44.960 | the Ritchie tensor is equal to zero.

02:03:47.360 | That's Einstein's equations for the vacuum.

02:03:50.600 | Okay, so we get that as a result of this model,

02:03:54.880 | but footnote, big footnote,

02:03:58.360 | because all the matter in the universe

02:04:00.760 | is the stuff we actually care about,

02:04:02.180 | the vacuum is not stuff we care about.

02:04:04.080 | So the question is, how does matter come into this?

02:04:06.920 | And for that, you have to understand

02:04:08.840 | what energy is in these models.

02:04:11.640 | And one of the things that we realized, you know,

02:04:15.760 | last, late last year,

02:04:18.400 | was that there's a very simple interpretation

02:04:20.880 | of energy in these models, okay?

02:04:23.080 | And energy is basically, well,

02:04:27.240 | intuitively it's the amount of activity

02:04:31.480 | in these hypergraphs and the way that that remains over time.

02:04:36.480 | So a little bit more formally,

02:04:39.140 | you can think about this causal graph

02:04:41.580 | as having these edges that represent causal relationships.

02:04:44.900 | You can think about, oh boy,

02:04:46.160 | there's one more concept that we didn't get to.

02:04:47.940 | There's the notion of space-like hyper surfaces.

02:04:51.820 | So this is not as scary as it sounds.

02:04:55.700 | It's a common notion in general relativity.

02:04:59.780 | The notion is you're defining what is a possibly,

02:05:04.780 | what is, what, where in space-time

02:05:10.020 | might be a particular moment in time.

02:05:14.020 | So in other words, what is a consistent set of places

02:05:18.240 | where you can say this is happening now, so to speak,

02:05:21.780 | and you make this series of sort of slices

02:05:25.620 | through the space-time, through this causal graph,

02:05:29.220 | to represent sort of what we consider

02:05:32.000 | to be successive moments in time.

02:05:34.660 | It's somewhat arbitrary because you can deform that

02:05:37.700 | if you're going at a different speed in special activity,

02:05:39.940 | you tip those things.

02:05:41.460 | There are different kinds of deformations,

02:05:45.460 | but only certain deformations are allowed

02:05:47.300 | by the structure of the causal graph.

02:05:48.380 | Anyway, be as it may, the basic point is

02:05:52.340 | there is a way of figuring out,

02:05:54.900 | you say what is the energy associated

02:05:57.100 | with what's going on in this hypergraph?

02:06:00.380 | And the answer is there is a precise definition of that.

02:06:04.340 | And it is, the formal way to say it is

02:06:06.860 | it's the flux of causal edges

02:06:08.560 | through space-like hyper surfaces.

02:06:10.660 | The slightly less formal way to say it,

02:06:12.280 | it's basically the amount of activity.

02:06:14.620 | See, the reason it gets tricky is you might say

02:06:18.020 | it's the amount of activity per unit volume

02:06:20.980 | in this hypergraph, but you haven't defined what volume is.

02:06:25.260 | So it's a little bit, you have to be a little bit more--

02:06:27.140 | - But this hyper surface gives some more formalism to that.

02:06:30.620 | - Yeah, yeah, it gives a way to connect that.

02:06:32.860 | - But intuitively we should think about as the just--

02:06:34.940 | - The amount of activity.

02:06:36.420 | Right, so the amount of activity that kind of remains

02:06:39.620 | in one place in the hypergraph corresponds to energy.

02:06:42.780 | The amount of activity that is kind of where

02:06:44.660 | an activity here affects an activity somewhere else

02:06:47.700 | corresponds to momentum.

02:06:50.460 | And so one of the things that's kind of cool

02:06:53.820 | is that I'm trying to think about

02:06:55.620 | how to say this intuitively.

02:06:56.700 | The mathematics is easy, but the intuitive version,

02:06:58.960 | I'm not sure, but basically the way that things

02:07:01.060 | sort of stay in the same place and have activity

02:07:03.940 | is associated with rest mass.

02:07:05.920 | And so one of the things that you get to derive

02:07:08.060 | is E equals MC squared.

02:07:09.860 | That is a consequence of this interpretation of energy

02:07:14.860 | in terms of the way the causal graph works,

02:07:18.040 | which is the whole thing is sort of a consequence

02:07:20.160 | of this whole story about updates and hypergraphs and so on.

02:07:23.700 | - So can you linger on that a little bit?

02:07:26.300 | How do we get E equals MC squared?

02:07:28.820 | So where does the mass come from?

02:07:30.740 | - Okay, okay.

02:07:32.220 | - I mean, is there an intuitive, it's okay.

02:07:34.980 | First of all, you're pretty deep

02:07:37.720 | in the mathematical explorations of this thing right now.

02:07:41.580 | We're in a very, we're in a flux currently.

02:07:45.900 | So maybe you haven't even had time

02:07:47.980 | to think about intuitive explanations.

02:07:50.040 | But--

02:07:51.720 | - Yeah, I mean, this one is, look,

02:07:54.100 | roughly what's happening,

02:07:56.340 | that derivation is actually rather easy.

02:07:58.420 | And everybody, and I've been saying

02:07:59.820 | we should pay more attention to this derivation

02:08:01.620 | because it's such, you know,

02:08:02.500 | 'cause people care about this one.

02:08:04.340 | But everybody says, "It's just easy."

02:08:05.900 | - It's easy.

02:08:07.180 | So there's some concept of energy

02:08:09.300 | that can be intuitively thought of as the activity,

02:08:12.900 | the flux, the level of changes that are occurring

02:08:16.780 | based on the transformations within a certain volume,

02:08:19.380 | however the heck do you find the volume.

02:08:21.240 | - Okay, so, and then mass--

02:08:23.540 | - Well, mass is-- - What?

02:08:25.700 | - Mass is associated with kind of the energy

02:08:28.720 | that does not cause you to,

02:08:30.660 | that does not somehow propagate through time.

02:08:34.180 | Yeah, I mean, one of the things that was not obvious

02:08:36.140 | in the usual formulation of special relativity

02:08:38.580 | is that space and time are connected in a certain way,

02:08:43.020 | energy and momentum are also connected in a certain way.

02:08:46.460 | The fact that the connection of energy to momentum

02:08:49.300 | is analogous to the connection to space

02:08:51.000 | between space and time is not self-evident

02:08:53.820 | in ordinary relativity.

02:08:55.140 | It is a consequence of the way this model works.

02:08:58.540 | It's an intrinsic consequence of the way this model works.

02:09:01.180 | And it's all to do with that,

02:09:03.020 | with unraveling that connection

02:09:05.460 | that ends up giving you this relationship

02:09:07.940 | between energy and, well, it's energy, momentum, mass,

02:09:12.680 | they're all connected.

02:09:13.780 | - And so, like, hence the general relativity,

02:09:19.780 | you have a sense that it appears to be baked in

02:09:24.780 | to the fundamental properties

02:09:27.220 | of the way these hypergraphs are evolved.

02:09:29.580 | - Well, I didn't yet get to,

02:09:30.620 | so I got as far as special relativity and E equals MC squared.

02:09:33.920 | The one last step is, in general relativity,

02:09:37.540 | the final connection is energy and mass

02:09:42.060 | cause curvature in space.

02:09:44.660 | And that's something that,

02:09:46.860 | when you understand this interpretation of energy

02:09:49.980 | and you kind of understand the correspondence

02:09:52.340 | to curvature and hypergraphs,

02:09:54.260 | then you can finally sort of,

02:09:56.100 | the big final answer is you derive

02:09:58.500 | the full version of Einstein's equations

02:10:00.700 | for space, time, and matter.

02:10:03.500 | And that's--

02:10:04.700 | - Is that, have you, that last piece with curvature,

02:10:09.700 | have, is that, have you arrived there yet?

02:10:12.540 | - Oh yeah, we're there, yes.

02:10:13.980 | And here's the way that we,

02:10:15.660 | here's how we're really, really going to know

02:10:17.420 | we've arrived, okay?

02:10:18.720 | So, you know, we have the mathematical derivation,

02:10:20.980 | it's all fine, but, you know, mathematical derivations,

02:10:24.740 | okay, so one thing that's sort of a,

02:10:27.980 | you know, we're taking this limit

02:10:29.500 | of what happens when,

02:10:30.860 | the limit, you have to look at things

02:10:32.360 | which are large compared to the size of an elementary length,

02:10:35.500 | small compared to the whole size of the universe,

02:10:37.700 | large compared to certain kinds of fluctuations,

02:10:40.740 | blah, blah, blah.

02:10:41.860 | There's a tower of many, many of these mathematical limits

02:10:45.420 | that have to be taken.

02:10:46.660 | So if you're a pure mathematician saying,

02:10:48.980 | where's the precise proof?

02:10:50.740 | It's like, well, there are all these limits,

02:10:52.740 | we can, you know, we can try each one of them

02:10:54.820 | computationally and we could say, yeah, it really works,

02:10:57.500 | but the formal mathematics is really hard to do.

02:11:00.540 | I mean, for example, in the case of deriving

02:11:03.060 | the equations of fluid dynamics from molecular dynamics,

02:11:06.160 | that derivation has never been done.

02:11:07.980 | There is no rigorous version of that derivation.

02:11:11.340 | So, so--

02:11:12.180 | - Because you can't do the limits?

02:11:13.720 | - Yeah, 'cause you can't do the limits.

02:11:15.860 | - But so the limits allow you to try to describe

02:11:18.300 | something general about the system

02:11:20.220 | and very, very particular kinds of limits

02:11:22.100 | that you need to take with these very--

02:11:23.620 | - Right, and the limits will definitely work

02:11:25.980 | the way we think they work,

02:11:27.180 | and we can do all kinds of computer experiments--

02:11:28.620 | - It's just a hard derivation.

02:11:29.740 | - Yeah, it's just the mathematical structure

02:11:32.740 | kind of ends up running right into

02:11:35.220 | computational irreducibility,

02:11:37.020 | and you end up with a bunch of difficulty there.

02:11:39.500 | But here's the way that we're getting really confident

02:11:42.300 | that we know completely what we're talking about,

02:11:43.920 | which is when people study things like black hole mergers

02:11:47.840 | using Einstein's equations, what do they actually do?

02:11:50.920 | Well, they actually use Mathematica a whole bunch

02:11:52.720 | to analyze the equations and so on,

02:11:54.360 | but in the end, they do numerical relativity,

02:11:57.300 | which means they take these nice mathematical equations

02:12:01.360 | and they break them down

02:12:02.480 | so that they can run them on a computer,

02:12:04.280 | and they break them down into something

02:12:05.840 | which is actually a discrete approximation

02:12:07.620 | to these equations.

02:12:08.880 | Then they run them on a computer, they get results,

02:12:11.480 | then you look at the gravitational waves

02:12:12.800 | and you see if they match, okay?

02:12:14.760 | Turns out that our model gives you a direct way

02:12:18.120 | to do numerical relativity.

02:12:19.680 | So in other words, instead of saying

02:12:21.020 | you start from these continuum equations from Einstein,

02:12:23.880 | you break them down into these discrete things,

02:12:26.160 | you run them on a computer,

02:12:27.520 | you say, "We're doing it the other way around.

02:12:28.760 | "We're starting from these discrete things

02:12:30.500 | "that come from our model,

02:12:31.680 | "and we're just running big versions on a computer,

02:12:34.320 | "and what we're saying is,

02:12:36.880 | "and this is how things will work."

02:12:39.440 | So the way I'm calling this

02:12:41.920 | is proof by compilation, so to speak.

02:12:44.640 | - Proof by comp--

02:12:45.620 | - That is, in other words, you're taking something

02:12:48.420 | where we've got this description of a black hole system,

02:12:52.240 | and what we're doing is we're showing that

02:12:54.960 | what we get by just running our model

02:12:58.680 | agrees with what you would get

02:13:01.060 | by doing the computation from the Einstein equations.

02:13:04.240 | - As a small tangent, or actually a very big tangent,

02:13:08.280 | but proof by compilation is a beautiful concept.

02:13:13.280 | In a sense, the way of doing physics with this model

02:13:20.160 | is by running it or compiling it.

02:13:26.040 | - At some level, yes.

02:13:27.920 | - Have you thought about,

02:13:29.760 | and these things can be very large,

02:13:31.960 | is there totally new possibilities of computing hardware

02:13:38.060 | and computing software which allows you

02:13:40.680 | to perform this kind of compilation?

02:13:43.140 | - Well--

02:13:43.980 | - Algorithms, software, hardware?

02:13:45.780 | - So first comment is,

02:13:47.560 | these models seem to give one a lot of intuition

02:13:51.580 | about distributed computing,

02:13:53.420 | a lot of different intuition

02:13:54.660 | about how to think about parallel computation,

02:13:57.560 | and that particularly comes

02:13:58.980 | from the quantum mechanics side of things,

02:14:00.680 | which we didn't talk about much yet,

02:14:02.820 | but the question of what,

02:14:05.620 | given our current computer hardware,

02:14:07.740 | how can we most efficiently simulate things?

02:14:10.120 | That's actually partly a story of the model itself,

02:14:12.900 | because the model itself has deep parallelism in it.

02:14:16.140 | The ways that we are simulating it,

02:14:17.780 | we're just starting to be able to use that deep parallelism

02:14:21.100 | to be able to be more efficient

02:14:22.580 | in the way that we simulate things.

02:14:24.400 | But in fact, the structure of the model itself

02:14:27.860 | allows us to think about parallel computation

02:14:30.260 | in different ways,

02:14:31.500 | and one of my realizations is that,

02:14:34.600 | so it's very hard to get in your brain

02:14:36.980 | how you deal with parallel computation,

02:14:38.500 | and you're always worrying about,

02:14:40.220 | if multiple things can happen on different computers

02:14:42.700 | at different times,

02:14:43.820 | oh, what happens if this thing happens before that thing,

02:14:46.440 | and we have these race conditions

02:14:48.740 | where something can race to get to the answer

02:14:50.900 | before another thing,

02:14:51.800 | and you get all tangled up

02:14:53.120 | because you don't know which thing is gonna come in first.

02:14:55.960 | And usually when you do parallel computing,

02:14:58.300 | there's a big obsession to lock things down

02:15:00.500 | to the point where you've had locks and mutexes

02:15:03.900 | and God knows what else,

02:15:05.220 | where you've arranged it

02:15:08.500 | so that there can only be one sequence of things

02:15:10.780 | that can happen,

02:15:11.620 | so you don't have to think about

02:15:12.620 | all the different kinds of things that can happen.

02:15:14.780 | Well, in these models,

02:15:16.420 | physics is throwing us into,

02:15:18.220 | forcing us to think about all these possible things

02:15:20.220 | that can happen,

02:15:21.260 | but these models,

02:15:22.460 | together with what we know from physics,

02:15:24.620 | is giving us new ways to think about

02:15:26.540 | all possible things happening,

02:15:28.260 | about all these different things happening in parallel.

02:15:30.660 | And so I'm guessing--

02:15:31.500 | - They have built-in protection for some of the parallelism.

02:15:34.600 | - Well, causal invariance is the built-in protection.

02:15:37.260 | Causal invariance is what means that

02:15:39.700 | even though things happen in different orders,

02:15:41.660 | it doesn't matter in the end.

02:15:43.420 | - As a person who struggled with concurrent programming

02:15:46.460 | in like Java,

02:15:50.220 | with all the basic concepts of concurrent programming,

02:15:53.460 | if there could be built up

02:15:55.740 | a strong mathematical framework for causal invariance,

02:16:00.020 | that's so liberating.

02:16:01.700 | And that could be not just liberating,

02:16:03.660 | but really powerful for massively distributed computation.

02:16:08.280 | - Absolutely.

02:16:09.120 | No, I mean, what's eventual consistency

02:16:11.760 | in distributed databases

02:16:13.960 | is essentially the causal invariance idea.

02:16:16.120 | - Yeah.

02:16:16.960 | - Okay, so that's--

02:16:17.800 | - But have you thought about

02:16:19.640 | really large simulations?

02:16:26.000 | - Yeah, I mean, I'm also thinking about,

02:16:28.040 | look, the fact is,

02:16:29.280 | I've spent much of my life as a language designer, right?

02:16:31.600 | So I can't possibly not think about,

02:16:34.320 | what does this mean for designing languages

02:16:37.220 | for parallel computation?

02:16:38.300 | In fact, another thing that's one of these,

02:16:40.620 | I'm always embarrassed at

02:16:43.500 | how long it's taken me to figure stuff out.

02:16:45.620 | But back in the 1980s,

02:16:47.340 | I worked on trying to make up languages

02:16:49.540 | for parallel computation.

02:16:50.920 | I thought about doing graph rewriting.

02:16:53.060 | I thought about doing these kinds of things,

02:16:54.400 | but I couldn't see how to actually make the connections

02:16:57.100 | to actually do something useful.

02:16:59.300 | I think now physics is kind of showing us

02:17:02.480 | how to make those things useful.

02:17:04.160 | And so my guess is that in time,

02:17:06.260 | we'll be talking about,

02:17:07.480 | we do parallel programming,

02:17:08.960 | we'll be talking about programming

02:17:10.320 | in a certain reference frame,

02:17:12.040 | just as we think about thinking about physics

02:17:14.080 | in a certain reference frame.

02:17:15.040 | It's a certain co-ordinatization of what's going on.

02:17:17.600 | We say, we're gonna program in this reference frame.

02:17:19.920 | Oh, let's change the reference frame to this reference frame.

02:17:22.620 | And then our program will seem different

02:17:25.200 | and we'll have a different way to think about it,

02:17:27.100 | but it's still the same program underneath.

02:17:28.960 | - So let me ask on this topic,

02:17:30.760 | 'cause I put out that I'm talking to you.

02:17:32.360 | I got way more questions than I can deal with,

02:17:34.560 | but what pops to mind is a question somebody asked

02:17:37.520 | on Reddit, I think, is,

02:17:39.480 | please ask Dr. Wolfram,

02:17:42.560 | what are the specs of the computer running the universe?

02:17:46.200 | So we're talking about specs of hardware and software

02:17:51.200 | for simulations of a large scale thing.

02:17:54.100 | What about a scale that is comparative

02:17:57.560 | to something that eventually leads

02:17:59.760 | to the two of us talking about?

02:18:01.600 | - Right, right, right.

02:18:02.640 | So actually I did try to estimate that

02:18:05.080 | and we actually have to go a couple more stages

02:18:07.280 | before we can really get to that answer

02:18:08.720 | because we're talking about this thing.

02:18:13.720 | This is what happens when you build these abstract systems

02:18:16.940 | and you're trying to explain the universe.

02:18:19.600 | They're quite a number of levels deep, so to speak.

02:18:23.680 | But the--

02:18:25.560 | - You mean conceptually or like literally,

02:18:27.320 | 'cause you're talking about small objects

02:18:28.800 | and there's 10 to the 120 something.

02:18:31.640 | - Yeah, right.

02:18:32.480 | It is conceptually deep.

02:18:35.160 | And one of the things that's happening

02:18:36.800 | sort of structurally in this project is,

02:18:39.600 | you know, there were ideas,

02:18:40.640 | there's another layer of ideas,

02:18:41.800 | there's another layer of ideas

02:18:43.260 | to get to the different things that correspond to physics.

02:18:46.960 | They're just different layers of ideas.

02:18:49.280 | And they are, you know, it's actually probably,

02:18:52.380 | if anything, getting harder to explain this project

02:18:54.480 | 'cause I'm realizing that the fraction of way through

02:18:56.520 | that I am so far in explaining this to you

02:18:58.640 | is less than, you know, it might be because,

02:19:01.520 | 'cause we know more now, you know,

02:19:03.080 | and every week basically we know a little bit more.

02:19:06.160 | And like--

02:19:07.000 | - Those are just layers on the initial fundamental--

02:19:10.440 | - Yes, but the layers are, you know,

02:19:12.320 | you might be asking me, you know,

02:19:14.320 | how do we get, you know,

02:19:16.560 | the difference between fermions and bosons,

02:19:18.680 | the difference between particles that can be

02:19:20.780 | all in the same state

02:19:21.720 | and particles that exclude each other, okay?

02:19:24.060 | Last three days we've kind of figured that out, okay?

02:19:27.300 | But, and it's very interesting, it's very cool.

02:19:31.060 | And it's very--

02:19:32.060 | - And those are some kind of properties

02:19:34.420 | at a certain level, layer of abstraction on the hydrograph.

02:19:37.860 | - Yes, yes, and there's, but the layers of abstraction

02:19:40.620 | are kind of, they're compounding--

02:19:42.740 | - Stacking up, so it's difficult, but--

02:19:45.300 | - But okay, but this thing--

02:19:46.300 | - But the specs nevertheless remain the same.

02:19:48.460 | - The specs underneath, so I have an estimate.

02:19:50.940 | So the question is, what are the units?

02:19:52.460 | So we've got these different fundamental constants

02:19:54.860 | about the world.

02:19:56.160 | So one of them is the speed of light, which is the,

02:19:58.540 | so the thing that's always the same

02:20:00.180 | in all these different ways of thinking about the universe

02:20:02.700 | is the notion of time, because time is computation.

02:20:06.180 | And so there's an elementary time,

02:20:08.080 | which is sort of the amount of time that we ascribe

02:20:12.220 | to elapsing in a single computational step, okay?

02:20:17.100 | So that's the elementary time.

02:20:18.420 | So then there's an elementary--

02:20:19.260 | - That's a parameter or whatever, that's a constant.

02:20:21.900 | - It's whatever we define it to be,

02:20:23.380 | because I mean, we don't, you know--

02:20:25.380 | - I mean, it's all relative, right?

02:20:26.700 | It doesn't matter. - Yes, it doesn't matter

02:20:28.100 | what it is, because we could be, it could be slow,

02:20:30.380 | it's just a number which we use to convert that to seconds,

02:20:34.460 | so to speak, because we are experiencing things,

02:20:37.180 | and we say this amount of time has elapsed, so to speak.

02:20:39.900 | - But we're within this thing, so it doesn't--

02:20:42.420 | - It doesn't matter, right?

02:20:43.700 | But what does matter is the ratio, what we can,

02:20:47.360 | the ratio of the spatial distance in this hypergraph

02:20:51.020 | to this moment of time, again, that's an arbitrary thing,

02:20:55.860 | but we measure that in meters per second, for example,

02:20:58.780 | and that ratio is the speed of light.

02:21:00.940 | So the ratio of the elementary distance

02:21:03.220 | to the elementary time is the speed of light, okay?

02:21:06.700 | - Perfect. - And so there's another,

02:21:08.300 | there are two other levels of this, okay?

02:21:11.420 | So there is a thing which we can talk about,

02:21:13.940 | which is the maximum entanglement speed,

02:21:16.580 | which is a thing that happens at another level

02:21:19.380 | in this whole sort of story of how

02:21:20.980 | these things get constructed,

02:21:22.900 | that's a sort of maximum speed in quantum,

02:21:24.900 | in the space of quantum states,

02:21:26.980 | just as the speed of light is a maximum speed

02:21:28.900 | in physical space, this is a maximum speed

02:21:31.100 | in the space of quantum states,

02:21:32.740 | there's another level which is associated

02:21:35.040 | with what we call ruleal space,

02:21:36.620 | which is another one of these maximum speeds,

02:21:39.160 | we'll get to this.

02:21:40.380 | - So these are limitations on the system

02:21:42.140 | that are able to capture the kind of physical universe

02:21:45.300 | which we live in, the quantum mechanical--

02:21:47.060 | - They are inevitable features of having a rule

02:21:51.820 | that has only a finite amount of information in the rule.

02:21:54.620 | So long as you have a rule that only involves

02:21:57.300 | a bounded amount, a limited amount of,

02:22:01.580 | only involving a limited number of elements,

02:22:03.260 | limited number of relations, it is inevitable

02:22:05.660 | that there are these speed constraints.

02:22:07.300 | We knew about the one for speed of light,

02:22:08.820 | we didn't know about the one for maximum entanglement speed,

02:22:11.440 | which is actually something that is possibly measurable,

02:22:14.060 | particularly in black hole systems and things like this.

02:22:17.020 | But anyway, this is long story short,

02:22:19.660 | you're asking what the processing specs of the universe,

02:22:22.340 | of the sort of computation of the universe,

02:22:25.180 | there's a question of even what are the units

02:22:27.420 | of some of these measurements, okay?

02:22:29.060 | So the units I'm using are Wolfram language

02:22:31.460 | instructions per second, okay?

02:22:33.340 | Because you gotta have some, you know,

02:22:34.860 | what computation are you doing?

02:22:37.020 | - There gotta be some kind of frame of reference.

02:22:38.380 | - Right, right, so because it turns out in the end,

02:22:41.840 | there will be, there's sort of an arbitrariness

02:22:44.300 | in the language that you use to describe the universe.

02:22:47.020 | So in those terms, I think it's like 10 to the 500

02:22:51.660 | Wolfram language operations per second, I think,

02:22:54.380 | is the, I think it's of that order.

02:22:56.580 | You know, basically--

02:22:57.420 | - So that's the scale of the computation.

02:22:58.840 | What about memory, if there's an interesting thing

02:23:01.020 | to say about storage and memory?

02:23:02.780 | - Well, there's a question of how many sort of atoms

02:23:04.420 | of space might there be?

02:23:06.340 | You know, maybe 10 to the 400.

02:23:08.740 | We don't know exactly how to estimate these numbers.

02:23:11.380 | I mean, this is based on some, I would say,

02:23:14.740 | somewhat rickety way of estimating things.

02:23:17.260 | When there start to be able to be experiments done,

02:23:20.300 | if we're lucky, there will be experiments

02:23:21.900 | that can actually nail down some of these numbers.

02:23:24.220 | - And because of computation reducibility,

02:23:27.980 | there's not much hope for very efficient compression,

02:23:31.580 | like very efficient representation of this atom space?

02:23:34.580 | - Good question, good question.

02:23:35.740 | I mean, there's probably certain things, you know.

02:23:38.020 | The fact that we can deduce, okay,

02:23:41.140 | the question is how deep does the reducibility go?

02:23:44.540 | - Right. - Okay?

02:23:45.380 | And I keep on being surprised

02:23:46.620 | that it's a lot deeper than I thought, okay?

02:23:48.860 | And so one of the things is that there's a question

02:23:52.940 | of sort of how much of the whole of physics

02:23:55.020 | do we have to be able to get

02:23:57.520 | in order to explain certain kinds of phenomena?

02:23:59.340 | Like, for example, if we want to study quantum interference,

02:24:02.880 | do we have to know what an electron is?

02:24:05.860 | Turns out I thought we did, turns out we don't.

02:24:08.540 | I thought to know what energy is,

02:24:10.440 | we would have to know what electrons were.

02:24:12.360 | We don't.

02:24:13.200 | - So you can get a lot of really powerful shortcuts.

02:24:15.580 | - Right, there's a bunch of sort of bulk information

02:24:18.220 | about the world.

02:24:19.300 | The thing that I'm excited about last few days, okay,

02:24:22.980 | is the idea of fermions versus bosons,

02:24:26.660 | fundamental idea that, I mean,

02:24:28.060 | it's the reason we have matter

02:24:29.860 | that doesn't just self-destruct

02:24:31.980 | is because of the exclusion principle

02:24:33.860 | that means that two electrons

02:24:35.840 | can never be in the same quantum state.

02:24:38.300 | - Is it useful for us to maybe first talk about

02:24:41.920 | how quantum mechanics fits into the Wolfram physics model?

02:24:46.520 | - Yes. - Let's go there.

02:24:47.480 | So we talked about general relativity.

02:24:49.720 | Now, what have you found from quantum mechanics?

02:24:54.720 | - What's the story of quantum mechanics?

02:24:56.640 | Right.

02:24:57.480 | - Within and outside of the Wolfram physics.

02:24:59.960 | - Right, so I mean, the key idea of quantum mechanics,

02:25:04.220 | that sort of the typical interpretation is

02:25:06.880 | classical physics says a definite thing happens.

02:25:09.920 | Quantum physics says there's this whole set of paths

02:25:12.860 | of things that might happen,

02:25:14.560 | and we are just observing some overall probability

02:25:17.440 | of how those paths work.

02:25:19.640 | Okay, so when you think about our hypergraphs

02:25:22.440 | and all these little updates that are going on,

02:25:24.640 | there's a very remarkable thing to realize,

02:25:26.960 | which is if you say,

02:25:28.960 | well, which particular sequence of updates should you do?

02:25:32.320 | Say, well, it's not really defined.

02:25:33.720 | You can do any of a whole collection

02:25:35.360 | of possible sequences of updates.

02:25:37.400 | Okay, that set of possible sequences of updates

02:25:41.960 | defines yet another kind of graph

02:25:44.220 | that we call a multi-way graph.

02:25:46.080 | And a multi-way graph just is a graph

02:25:48.640 | where at every node,

02:25:50.840 | there is a choice of several different possible things

02:25:54.160 | that could happen.

02:25:55.280 | So for example, you go this way, you go that way,

02:25:57.680 | those are two different edges in the multi-way graph,

02:26:00.880 | and you're building up the set of possibilities.

02:26:02.600 | So actually, like for example, I just made the one,

02:26:04.840 | the multi-way graph for tic-tac-toe, okay?

02:26:07.360 | So tic-tac-toe, you start off with some board

02:26:10.960 | that, you know, everything is blank,

02:26:12.240 | and then somebody can put down an X somewhere,

02:26:15.200 | an O somewhere,

02:26:16.760 | and then there are different possibilities.

02:26:18.160 | At each stage, there are different possibilities.

02:26:20.280 | And so you build up this multi-way graph

02:26:22.720 | of all those possibilities.

02:26:23.720 | Now, notice that even in tic-tac-toe,

02:26:25.920 | you have the feature that there can be something

02:26:28.120 | where you have two different things that happen,

02:26:30.960 | and then those branches merge

02:26:33.360 | because you end up with the same shape,

02:26:35.200 | you know, the same configuration of the board,

02:26:37.360 | even though you got there in two different ways.

02:26:39.920 | So the thing that's sort of an inevitable feature

02:26:42.760 | of our models is that just like quantum mechanics suggests,

02:26:47.320 | definite things don't happen.

02:26:48.800 | Instead, you get this whole multi-way graph

02:26:50.800 | of all these possibilities.

02:26:52.720 | Okay, so then the question is,

02:26:54.600 | so, okay, so that's sort of a picture of what's going on.

02:26:58.280 | Now you say, okay, well, quantum mechanics

02:27:00.480 | has all these features of, you know,

02:27:02.680 | all this mathematical structure and so on.

02:27:04.840 | How do you get that mathematical structure?

02:27:07.120 | Okay, a couple of things to say.

02:27:08.800 | So quantum mechanics is actually, in a sense,

02:27:11.600 | two different theories glued together.

02:27:13.920 | Quantum mechanics is the theory

02:27:15.600 | of how quantum amplitudes work

02:27:18.080 | that more or less give you the probabilities

02:27:19.400 | of things happening.

02:27:20.680 | And it's the theory of quantum measurement,

02:27:22.760 | which is the theory of how we actually

02:27:25.160 | conclude definite things,

02:27:26.960 | because the mathematics just gives you

02:27:29.040 | these quantum amplitudes,

02:27:30.000 | which are more or less probabilities of things happening,

02:27:32.440 | but yet we actually observe definite things in the world.

02:27:35.840 | Quantum measurement has always been a bit mysterious.

02:27:39.080 | It's always been something where people just say,

02:27:41.120 | well, the mathematics says this,

02:27:42.360 | but then you do a measurement

02:27:43.440 | and there are philosophical arguments

02:27:45.080 | about what the measurement is.

02:27:46.600 | But it's not something where there's a theory

02:27:48.760 | of the measurement.

02:27:49.680 | - Somebody on Reddit also asked,

02:27:52.080 | please ask Stephen to tell his story

02:27:56.800 | of the double slit experiment.

02:27:59.800 | - Okay, yeah, I can.

02:28:01.160 | - Does that make sense?

02:28:02.880 | - Oh yeah, it makes sense.

02:28:03.960 | Absolutely makes sense.

02:28:05.000 | - Why, is this like a good way to discuss?

02:28:07.760 | - A little bit.

02:28:08.600 | Let me explain a couple of things first.

02:28:10.560 | So the structure of quantum mechanics

02:28:13.840 | is mathematically quite complicated.

02:28:16.240 | One of the features, let's see,

02:28:18.600 | well, how to describe this.

02:28:20.520 | Okay, so first point is there's this multi-way graph

02:28:23.800 | of all these different paths

02:28:25.840 | of things that can happen in the world.

02:28:28.760 | And the important point is that these,

02:28:32.640 | you can have branchings and you can have mergings.

02:28:35.600 | Okay, so this property turns out causal invariance

02:28:39.680 | is the statement that the number of mergings

02:28:43.360 | is equal to the number of branchings.

02:28:45.800 | So in other words, every time there's a branch,

02:28:48.720 | eventually there will also be a merge.

02:28:50.640 | In other words, every time there were two possibilities

02:28:52.600 | for what might've happened, eventually those will merge.

02:28:55.120 | - Beautiful concept, by the way.

02:28:56.240 | But yeah, yeah, yeah.

02:28:57.400 | - So that idea, okay.

02:29:00.080 | So then, so that's one thing,

02:29:03.880 | and that's closely related to the sort of objectivity

02:29:07.680 | in quantum mechanics.

02:29:08.520 | The fact that we believe definite things happen,

02:29:10.680 | it's because although there are all these different paths,

02:29:13.160 | in some sense, because of causal invariance,

02:29:15.560 | they all imply the same thing.

02:29:17.640 | I'm cheating a little bit in saying that,

02:29:19.360 | but that's roughly the essence of what's going on.

02:29:22.080 | Okay, next thing to think about is

02:29:26.080 | we have this multi-way graph.

02:29:27.400 | It has all these different possible things

02:29:28.840 | that are happening.

02:29:30.040 | Now we ask, this multi-way graph

02:29:32.440 | is sort of evolving with time.

02:29:34.120 | Over time, it's branching, it's merging,

02:29:36.680 | it's doing all these things, okay?

02:29:38.400 | Question we can ask is,

02:29:41.280 | if we slice it at a particular time, what do we see?

02:29:46.120 | And that slice represents, in a sense,

02:29:48.840 | something to do with the state of the universe

02:29:51.240 | at a particular time.

02:29:53.080 | So in other words, we've got this multi-way graph

02:29:55.120 | of all these possibilities,

02:29:56.680 | and then we're asking, okay, we take this slice.

02:30:01.320 | This slice represents, okay,

02:30:04.440 | each of these different paths corresponds

02:30:06.120 | to a different quantum possibility for what's happening.

02:30:09.360 | When we take the slice, we're saying,

02:30:11.440 | what are the set of quantum possibilities

02:30:13.120 | that exist at a particular time?

02:30:14.960 | - And when you say slice, you slice the graph,

02:30:17.680 | and then there's a bunch of leaves.

02:30:19.720 | - A bunch of leaves.

02:30:20.560 | - And those represent the state of things.

02:30:23.520 | - Right, but then, okay, so the important thing

02:30:26.320 | that you are quickly picking up on

02:30:29.120 | is that what matters is kind of how these leaves

02:30:32.880 | are related to each other.

02:30:34.680 | So a good way to tell how leaves are related

02:30:37.640 | is just to say, on the step before,

02:30:40.000 | did they have a common ancestor?

02:30:42.240 | So two leaves might be,

02:30:44.040 | they might have just branched from one thing,

02:30:45.880 | or they might be far away, way far apart in this graph,

02:30:50.800 | where to get to a common ancestor,

02:30:52.360 | maybe you have to go all the way back

02:30:53.480 | to the beginning of the graph,

02:30:54.320 | all the way back to the beginning of the--

02:30:55.160 | - So there's some kind of measure of distance.

02:30:57.240 | - Right, but what you get is by making the slice,

02:31:01.640 | we call it branchial space, the space of branches.

02:31:05.960 | And in this branchial space, you have a graph

02:31:09.760 | that represents the relationships

02:31:11.320 | between these quantum states in branchial space.

02:31:14.720 | You have this notion of distance in branchial space.

02:31:18.080 | Okay, so--

02:31:18.920 | - It's connected to quantum entanglement?

02:31:20.960 | - Yes, yes.

02:31:21.960 | It's basically, the distance in branchial space

02:31:25.640 | is kind of an entanglement distance.

02:31:27.880 | So this--

02:31:28.720 | - That's a very nice model.

02:31:29.920 | - Right, it is very nice.

02:31:31.280 | It's very beautiful.

02:31:32.400 | I mean, it's so clean.

02:31:35.560 | I mean, it's really, you know, and it tells one,

02:31:38.960 | okay, so anyway, so then this branchial space

02:31:42.840 | has this sort of map of the entanglements

02:31:46.120 | between quantum states.

02:31:47.760 | So in physical space, we have,

02:31:50.360 | so you know, you can say, take, let's say the causal graph,

02:31:54.720 | and we can slice that at a particular time,

02:31:57.840 | and then we get this map of how things are laid out

02:31:59.800 | in physical space.

02:32:01.440 | When we do the same kind of thing,

02:32:02.760 | there's a thing called the multi-way causal graph,

02:32:04.880 | which is the analog of a causal graph

02:32:06.400 | for the multi-way system.

02:32:07.800 | We slice that, we get essentially the relationships

02:32:11.400 | between things, not in physical space,

02:32:13.760 | but in the space of quantum states.

02:32:15.760 | It's like which quantum state is similar

02:32:17.480 | to which other quantum state.

02:32:19.400 | Okay, so now I think next thing to say

02:32:22.320 | is just to mention how quantum measurement works.

02:32:24.840 | So quantum measurement has to do with reference frames

02:32:27.600 | in branchial space.

02:32:29.760 | So, okay, so measurement in physical space,

02:32:33.760 | it matters whether how we assign spatial position

02:32:38.760 | and how we define coordinates in space and time.

02:32:42.680 | And that's how we make measurements in ordinary space.

02:32:45.520 | So we're making a measurement

02:32:46.560 | based on us sitting still here,

02:32:48.400 | are we traveling at half the speed of light

02:32:50.040 | and making measurements that way?

02:32:51.760 | These are different reference frames

02:32:53.240 | in which we're making our measurements.

02:32:54.920 | And the relationship between different events

02:32:57.960 | and different points in space and time

02:32:59.880 | will be different depending on what reference frame

02:33:03.640 | we're in.

02:33:04.480 | Okay, so then we have this idea

02:33:06.640 | of quantum observation frames,

02:33:09.000 | which are the analog of reference frames,

02:33:11.200 | but in branchial space.

02:33:13.160 | And so what happens is what we realize

02:33:16.040 | is that a quantum measurement is,

02:33:18.600 | the observer is sort of arbitrarily determining

02:33:21.760 | this reference frame.

02:33:23.160 | The observer is saying,

02:33:24.120 | I'm going to understand the world

02:33:27.000 | by saying that space and time are coordinatized this way.

02:33:30.720 | I'm gonna understand the world by saying

02:33:32.760 | that quantum states and time are coordinatized in this way.

02:33:36.680 | And essentially what happens is that,

02:33:39.080 | you know, the process of quantum measurement

02:33:41.080 | is a process of deciding how you slice up

02:33:45.080 | this multi-way system in these quantum observation frames.

02:33:48.760 | So in a sense, the observer,

02:33:50.320 | the way the observer enters

02:33:51.960 | is by their choice of these quantum observation frames.

02:33:55.800 | And what happens is that the observer,

02:33:59.080 | because, okay, this is again,

02:34:00.680 | another stack of other concepts,

02:34:02.600 | but anyway, because the observer is computationally bounded,

02:34:06.380 | there is a limit to the type of quantum observation frames

02:34:09.040 | that they can construct.

02:34:10.160 | - Interesting, okay.

02:34:11.000 | So there's, okay, so there's some constraints,

02:34:12.760 | some limit on-

02:34:14.720 | - On the choice of observation frames.

02:34:17.960 | - Right, and by the way,

02:34:18.800 | I just want to mention that there's a,

02:34:20.960 | I mean, it's bizarre,

02:34:22.040 | but there's a hierarchy of these things.

02:34:23.840 | So in thermodynamics,

02:34:27.600 | the fact that we believe entropy increases,

02:34:29.780 | we believe things get more disordered

02:34:31.680 | is a consequence of the fact

02:34:32.680 | that we can't track each individual molecule.

02:34:34.440 | If we could track every single molecule,

02:34:36.360 | we could run every movie in reverse, so to speak,

02:34:38.440 | and we would, you know,

02:34:39.560 | that we would not see that things are getting more disordered

02:34:42.400 | but it's because we are computationally bounded.

02:34:44.960 | We can only look at these big blobs

02:34:46.920 | of what all these molecules collectively do

02:34:49.720 | that we think that things are,

02:34:52.440 | that we describe it in terms of entropy increasing and so on.

02:34:55.960 | And it's the same phenomenon, basically,

02:34:58.720 | also a consequence of computational irreducibility

02:35:01.560 | that causes us to basically be forced to conclude

02:35:04.840 | that definite things happen in the world,

02:35:06.940 | even though there's this quantum, you know,

02:35:08.720 | this set of all these different quantum processes

02:35:10.700 | that are going on.

02:35:11.900 | So, I mean, I'm skipping a little bit,

02:35:15.440 | but that's a rough picture.

02:35:18.600 | - And in the evolution of the Wolfram Physics Project,

02:35:21.920 | where do you feel you stand on some of the puzzles

02:35:24.320 | that are along the way?

02:35:25.160 | See, you're skipping along a bunch of,

02:35:27.040 | you're skipping a bunch of stuff.

02:35:27.880 | - Oh, it's amazing how much these things are unraveling.

02:35:30.480 | I mean, you know, these things,

02:35:31.940 | look, it used to be the case

02:35:33.560 | that I would agree with Dick Feynman,

02:35:35.680 | nobody understands quantum mechanics, including me, okay?

02:35:38.860 | I'm getting to the point

02:35:39.760 | where I think I actually understand quantum mechanics.

02:35:41.580 | My exercise, okay, is can I explain quantum mechanics

02:35:45.760 | for real at the level of kind of middle school

02:35:48.800 | type explanation?

02:35:50.320 | And I'm getting closer, it's getting there.

02:35:52.620 | I'm not quite there, I've tried it a few times,

02:35:54.960 | and I realized that there are things

02:35:56.360 | that where I have to start talking

02:35:58.920 | about elaborate mathematical concepts and so on.

02:36:00.900 | But I think, and you've got to realize

02:36:03.000 | that it's not self-evident that we can explain,

02:36:05.840 | you know, at an intuitively graspable level,

02:36:09.240 | something which, you know,

02:36:11.140 | about the way the universe works.

02:36:12.380 | The universe wasn't built for our understanding,

02:36:14.760 | so to speak.

02:36:16.280 | But I think then, okay, so another important idea

02:36:21.280 | is this idea of branchial space, which I mentioned,

02:36:25.280 | this sort of space of quantum states.

02:36:27.420 | It is, okay, so I mentioned Einstein's equations

02:36:31.260 | describing, you know, the effect of mass and energy

02:36:37.400 | on trajectories of particles, on geodesics.

02:36:40.840 | The curvature of physical space is associated

02:36:44.900 | with the presence of energy,

02:36:47.040 | according to Einstein's equations, okay?

02:36:49.400 | So it turns out that, rather amazingly,

02:36:51.920 | the same thing is true in branchial space.

02:36:54.880 | So it turns out the presence of energy,

02:36:57.360 | or more accurately, Lagrangian density,

02:36:59.420 | which is a kind of relativistic,

02:37:00.920 | invariant version of energy,

02:37:03.200 | the presence of that causes, essentially,

02:37:06.320 | deflection of geodesics in this branchial space, okay?

02:37:11.160 | So you might say, so what?

02:37:12.560 | Well, it turns out that the sort of,

02:37:16.000 | the best formulation we have of quantum mechanics,

02:37:18.800 | this Feynman path integral,

02:37:21.360 | is a thing that describes quantum processes

02:37:26.200 | in terms of mathematics that can be interpreted as,

02:37:31.200 | well, in quantum mechanics, the big thing

02:37:33.880 | is you get these quantum amplitudes,

02:37:35.360 | which are complex numbers that represent,

02:37:38.320 | when you combine them together,

02:37:39.400 | represent probabilities of things happening.

02:37:41.560 | And so the big story has been,

02:37:42.840 | how do you derive these quantum amplitudes?

02:37:45.320 | And people think these quantum amplitudes,

02:37:47.500 | they have a complex number,

02:37:49.160 | has a real part and an imaginary part.

02:37:51.200 | You can also think of it as a magnitude and a phase.

02:37:53.920 | And people have sort of thought these quantum amplitudes

02:37:58.160 | have magnitude and phase, and you compute those together.

02:38:01.000 | Turns out that the magnitude and the phase

02:38:04.560 | come from completely different places.

02:38:07.000 | The magnitude comes, okay, so what do you,

02:38:10.240 | how do you compute things in quantum mechanics?

02:38:11.680 | Roughly, I'm telling you, I'm getting there

02:38:14.280 | to be able to do this at a middle school level,

02:38:15.960 | but I'm not there yet.

02:38:17.160 | Roughly what happens is you're asking,

02:38:21.400 | does this state in quantum mechanics

02:38:24.960 | evolve to this other state in quantum mechanics?

02:38:27.800 | And you can think about that like a particle traveling

02:38:31.340 | or something traveling through physical space,

02:38:33.960 | but instead it's traveling through branchial space.

02:38:36.860 | And so what's happening is,

02:38:37.940 | does this quantum state evolve to this other quantum state?

02:38:40.680 | It's like saying, does this object move

02:38:42.880 | from this place in space to this other place in space?

02:38:45.920 | Okay, now the way that you,

02:38:48.440 | these quantum amplitudes characterize kind of

02:38:52.740 | to what extent the thing will successfully reach

02:38:55.560 | some particular point in branchial space.

02:38:57.240 | Just like in physical space, you could say,

02:38:59.000 | oh, it had a certain velocity and it went in this direction.

02:39:02.440 | In branchial space, there's a similar kind of concept.

02:39:05.200 | - Is there a nice way to visualize,

02:39:07.760 | for me now, mentally branchial space?

02:39:10.600 | - It's just, you have this hypergraph,

02:39:13.760 | sorry, you have this multi-way graph.

02:39:15.760 | It's this big branching thing, branching and merging thing.

02:39:18.480 | - But I mean, like moving through that space.

02:39:21.840 | I'm just trying to understand what that looks like.

02:39:24.400 | (both laugh)

02:39:26.000 | - You know, that space is probably exponential dimensional,

02:39:29.360 | which makes it, again, another can of worms

02:39:32.360 | in understanding what's going on.

02:39:33.960 | That space, as in ordinary space, this hypergraph,

02:39:37.760 | the spatial hypergraph, limits to something

02:39:40.200 | which is like a manifold,

02:39:42.680 | like something like three-dimensional space.

02:39:45.080 | Almost certainly, the multi-way graph limits

02:39:48.760 | to a Hilbert space, which is something that,

02:39:52.400 | I mean, it's just a weird exponential dimensional space.

02:39:55.600 | And by the way, you can ask,

02:39:57.240 | I mean, there are much weirder things that go on.

02:39:58.920 | For example, one of the things I've been interested in

02:40:00.760 | is the expansion of the universe in branchial space.

02:40:03.960 | So we know the universe is expanding in physical space,

02:40:07.120 | but the universe is probably also expanding

02:40:09.240 | in branchial space. - Expanding in branchial space.

02:40:10.960 | - So that means the number of quantum states

02:40:13.320 | of the universe is increasing with time.

02:40:15.800 | - The diameter of the thing is growing.

02:40:17.920 | - Right, so that means that the, and by the way,

02:40:20.720 | this is related to whether quantum computing can ever work.

02:40:25.120 | And-- - Why?

02:40:28.960 | - Okay, so let me explain why.

02:40:30.000 | So let's talk about, okay, so first of all,

02:40:33.120 | just to finish the thought about quantum amplitudes,

02:40:35.360 | the incredibly beautiful thing,

02:40:37.360 | but I'm just very excited about this.

02:40:40.760 | The Feynman path integral is this formula.

02:40:44.720 | It says that the amplitude, the quantum amplitude

02:40:47.440 | is e to the i s over h bar,

02:40:49.560 | where s is this thing called the action.

02:40:51.640 | And it, okay, so that can be thought of

02:40:55.800 | as representing a deflection of the angle

02:40:59.320 | of this path in the multi-way graph.

02:41:02.240 | So it's a deflection of a geodesic in the multi-way path

02:41:05.080 | that is caused by this thing called the action,

02:41:07.000 | which is essentially associated with the energy, okay?

02:41:10.080 | And so this is a deflection of a path in branchial space

02:41:13.800 | that is described by this path integral,

02:41:15.560 | which is the thing that is the mathematical essence

02:41:17.800 | of quantum mechanics.

02:41:19.480 | Turns out that deflection is,

02:41:22.800 | the deflection of geodesics in branchial space

02:41:25.280 | follows the exact same mathematical setup

02:41:28.760 | as the deflection of geodesics in physical space,

02:41:31.920 | except the deflection of geodesics in physical space

02:41:34.280 | is described with Einstein's equations.

02:41:36.520 | The deflection of geodesics in branchial space

02:41:38.640 | is defined by the Feynman path integral,

02:41:40.920 | and they are the same.

02:41:42.840 | In other words, they are mathematically the same.

02:41:45.800 | So that means that general relativity

02:41:48.400 | is a story of essentially motion in physical space.

02:41:53.240 | Quantum mechanics is a story of essentially motion

02:41:55.560 | in branchial space.

02:41:57.360 | And the underlying equation for those two things,

02:42:01.360 | although it's presented differently

02:42:02.560 | because one's interested in different things

02:42:04.160 | in branchial space than physical space,

02:42:06.120 | but the underlying equation is the same.

02:42:08.720 | So in other words, it's just, you know,

02:42:12.480 | these two theories,

02:42:13.440 | which are those two sort of pillars of 20th century physics,

02:42:16.360 | which have seemed to be off in different directions

02:42:19.120 | are actually facets of the exact same theory.

02:42:21.780 | And this, I mean--

02:42:24.240 | - That's exciting to see where that evolves,

02:42:27.000 | and exciting that that just is there.

02:42:29.160 | - Right, I mean, to me, you know,

02:42:31.040 | look, having spent some part of my early life,

02:42:34.240 | you know, working in the context of these theories

02:42:36.800 | of, you know, 20th century physics,

02:42:39.400 | it's, they just, they seem so different.

02:42:41.960 | And the fact that they're really the same

02:42:44.080 | is just really amazing.

02:42:46.480 | Actually, you mentioned double-slit experiment, okay?

02:42:49.120 | So the double-slit experiment

02:42:50.280 | is an interference phenomenon where you say there are,

02:42:54.040 | you know, you can have a photon or an electron,

02:42:56.600 | and you say there are these two slits,

02:42:58.240 | it could have gone through either one,

02:43:00.320 | but there is this interference pattern

02:43:02.560 | where there's destructive interference,

02:43:05.080 | where you might've said in classical physics,

02:43:07.160 | oh, well, if there are two slits,

02:43:09.000 | then there's a better chance

02:43:10.440 | that it gets through one or the other of them.

02:43:12.120 | But in quantum mechanics,

02:43:13.240 | there's this phenomenon of destructive interference

02:43:15.720 | that means that even though there are two slits,

02:43:18.140 | two can lead to nothing,

02:43:20.240 | as opposed to two leading to more than,

02:43:23.640 | for example, one slit.

02:43:25.240 | And what happens in this model,

02:43:27.480 | and we've just been understanding this

02:43:29.040 | in the last few weeks, actually,

02:43:30.780 | is that the, what essentially happens

02:43:34.400 | is that the double-slit experiment

02:43:38.040 | is a story of the interface

02:43:39.400 | between branchial space and physical space.

02:43:41.960 | And what's essentially happening is

02:43:43.720 | that the destructive interference

02:43:45.520 | is the result of the two possible paths

02:43:48.520 | associated with photons going through those two slits,

02:43:51.200 | winding up at opposite ends of branchial space.

02:43:54.160 | And so they don't, and so that's why

02:43:56.000 | there's sort of nothing there when you look at it,

02:43:58.480 | is because these two different sort of branches

02:44:02.160 | couldn't get merged together to produce something

02:44:05.160 | that you can measure in physical space.

02:44:07.720 | - Is there a lot to be understood about branchial space?

02:44:10.720 | I guess, mathematically speaking.

02:44:13.960 | - Yes, it's a very beautiful mathematical thing,

02:44:16.440 | and it's very, I mean, by the way,

02:44:18.320 | this whole theory is just amazingly rich

02:44:22.060 | in terms of the mathematics

02:44:23.220 | that it says should exist, okay?

02:44:25.120 | So for example, calculus, you know,

02:44:27.700 | is the story of infinitesimal change

02:44:30.360 | in integer-dimensional space,

02:44:32.000 | one-dimensional, two-dimensional, three-dimensional space.

02:44:34.880 | We need a theory of infinitesimal change

02:44:37.960 | in fractional-dimensional and dynamic-dimensional space.

02:44:41.440 | No such theory exists.

02:44:42.640 | - So there's tools in mathematics that are needed here.

02:44:45.320 | - Right.

02:44:46.140 | - And this is the motivation for that, actually.

02:44:47.040 | - Right, and it's, you know, there are indications,

02:44:50.320 | and we can do computer experiments,

02:44:51.760 | and we can see how it's gonna come out,

02:44:53.560 | but we need to, you know,

02:44:54.920 | the actual mathematics doesn't exist.

02:44:58.040 | And in branchial space, it's actually even worse.

02:45:00.720 | There's even more sort of layers of mathematics that are,

02:45:04.560 | you know, we can see how it works, roughly,

02:45:06.260 | by doing computer experiments,

02:45:07.960 | but to really understand it,

02:45:10.100 | we need more sort of mathematical sophistication.

02:45:13.280 | - So quantum computers.

02:45:14.880 | - Okay, so the basic idea of quantum computers,

02:45:17.780 | the promise of quantum computers

02:45:19.960 | is quantum mechanics does things in parallel,

02:45:23.640 | and so you can sort of intrinsically

02:45:26.180 | do computations in parallel,

02:45:27.880 | and somehow that can be much more efficient

02:45:30.160 | than just doing them one after another.

02:45:33.280 | And, you know, I actually worked on quantum computing a bit

02:45:36.240 | with Dick Feynman back in 1980, one, two, three,

02:45:40.680 | that kind of timeframe, and we--

02:45:42.120 | - A fascinating image.

02:45:43.680 | You and Feynman work on quantum computers.

02:45:46.600 | - Well, we tried to work,

02:45:47.840 | the big thing we tried to do was invent a randomness chip

02:45:51.000 | that would generate randomness at a high speed

02:45:53.760 | using quantum mechanics.

02:45:55.440 | And the discovery that that wasn't really possible

02:45:58.880 | was part of the story of,

02:46:01.480 | we never really wrote anything about it.

02:46:02.980 | I think maybe he wrote some stuff,

02:46:04.200 | but we didn't write stuff about what we figured out

02:46:07.480 | about sort of the fact that it really seemed like

02:46:10.040 | the measurement process in quantum mechanics

02:46:12.280 | was a serious damper on what was possible to do

02:46:15.640 | in sort of, you know, the possible advantages

02:46:18.360 | of quantum mechanics for computing.

02:46:20.680 | But anyway, so the sort of the promise of quantum computing

02:46:24.680 | is let's say you're trying to, you know, factor an integer.

02:46:28.220 | Well, you can, instead of, you know,

02:46:30.040 | when you factor an integer, you might say,

02:46:31.440 | well, does this factor work?

02:46:32.640 | Does this factor work?

02:46:33.480 | Does this factor work?

02:46:34.580 | In ordinary computing, it seems like we pretty much

02:46:38.200 | just have to try all these different factors,

02:46:41.060 | you know, kind of one after another.

02:46:43.040 | But in quantum mechanics, you might have the idea,

02:46:45.120 | oh, you can just sort of have the physics,

02:46:48.320 | try all of them in parallel, okay?

02:46:51.280 | And the, you know, and there's this algorithm,

02:46:54.880 | Shor's algorithm, which allows you,

02:46:58.720 | according to the formalism of quantum mechanics,

02:47:01.040 | to do everything in parallel and to do it much faster

02:47:03.400 | than you can on a classical computer.

02:47:05.280 | Okay, the only little footnote is,

02:47:08.100 | you have to figure out what the answer is.

02:47:09.880 | You have to measure the results.

02:47:11.960 | So the quantum mechanics internally has figured out

02:47:13.920 | all these different branches,

02:47:15.480 | but then you have to pull all these branches together

02:47:17.840 | to say, and the classical answer is this, okay?

02:47:21.000 | The standard theory of quantum mechanics

02:47:22.560 | does not tell you how to do that.

02:47:24.180 | It tells you how the branching works,

02:47:26.140 | but it doesn't tell you the process

02:47:27.840 | of corralling all these things together.

02:47:30.200 | And that process, which intuitively you can see

02:47:32.780 | is going to be kind of tricky,

02:47:34.360 | but our model actually does tell you

02:47:37.040 | how that process of pulling things together works.

02:47:40.160 | And the answer seems to be, we're not absolutely sure.

02:47:42.840 | We've only got to two times three so far,

02:47:45.320 | which is kind of in this factorization

02:47:50.320 | in quantum computers, but we can,

02:47:52.120 | what seems to be the case is that the advantage you get

02:47:56.760 | from the parallelization from quantum mechanics

02:47:59.960 | is lost from the amount that you have to spend

02:48:03.520 | pulling together all those parallel threads

02:48:05.320 | to get to a classical answer at the end.

02:48:07.680 | Now, that phenomenon is not unrelated

02:48:10.280 | to various decoherence phenomena

02:48:11.880 | that are seen in practical quantum computers and so on.

02:48:14.280 | I mean, I should say as a very practical point,

02:48:16.760 | I mean, it's like, should people stop bothering

02:48:19.060 | to do quantum computing research?

02:48:20.760 | No, because what they're really doing

02:48:23.120 | is they're trying to use physics

02:48:25.240 | to get to a new level of what's possible in computing.

02:48:28.720 | And that's a completely valid activity.

02:48:30.920 | Whether you can really put,

02:48:33.400 | whether you can say,

02:48:34.240 | oh, you can solve an NP complete problem,

02:48:35.960 | you can reduce exponential time to polynomial time,

02:48:39.600 | we're not sure.

02:48:40.600 | And I'm suspecting the answer is no,

02:48:43.080 | but that's not relevant to the practical speed-ups

02:48:46.080 | you can get by using different kinds of technologies,

02:48:48.520 | different kinds of physics to do basic computing.

02:48:52.320 | - So you're saying, I mean,

02:48:53.640 | some of the models you're playing with,

02:48:55.280 | the indication is that to get all the sheep back together

02:49:00.280 | and to corral everything together

02:49:05.980 | to get the actual solution to the algorithm

02:49:08.920 | is-- - You lose all the--

02:49:10.840 | - You lose all the--

02:49:12.240 | - By the way, I mean, so again, this question,

02:49:14.400 | do we actually know what we're talking about

02:49:16.600 | about quantum computing and so on?

02:49:18.240 | So again, we're doing proof by compilation.

02:49:22.440 | So we have a quantum computing framework

02:49:24.880 | in Wolfram language,

02:49:26.080 | which is a standard quantum computing framework

02:49:28.360 | that represents things in terms of the standard

02:49:31.320 | formalism of quantum mechanics.

02:49:32.840 | And we have a compiler that simply compiles

02:49:36.920 | the representation of quantum gates into multi-way systems.

02:49:41.520 | So, and in fact, the message that I got

02:49:43.920 | was from somebody who's working on the project

02:49:46.000 | who has managed to compile one of the sort of

02:49:49.920 | a core formalism based on category theory

02:49:53.200 | and core quantum formalism into multi-way systems.

02:49:57.520 | So this-- - When you say multi-way system,

02:49:58.920 | these multi-way graphs?

02:50:00.160 | - Yes, yes. - So you're,

02:50:02.160 | okay, that's awesome.

02:50:03.160 | And then you can do all kinds of experiments

02:50:05.200 | on that multi-way graph.

02:50:06.280 | - Right, but the point is that what we're saying is

02:50:08.640 | the thing, we've got this representation

02:50:10.400 | of let's say Shor's algorithm

02:50:12.000 | in terms of standard quantum gates.

02:50:14.040 | And it's just a pure matter of sort of computation

02:50:17.480 | to just say that is equivalent.

02:50:19.240 | We will get the same result as running this multi-way system.

02:50:23.360 | - Can you do complexity analysis on that multi-way system?

02:50:26.640 | - Well, that's what we've been trying to do, yes.

02:50:28.600 | We're getting there.

02:50:29.440 | We haven't done that yet.

02:50:30.280 | I mean, there's a pretty good indication

02:50:32.480 | of how that's gonna work out.

02:50:33.480 | And we've done, as I say, our computer experiments,

02:50:36.240 | we've unimpressively gotten to about two times three

02:50:39.440 | in terms of factorization,

02:50:41.040 | which is kind of about how far people have got

02:50:43.120 | with physical quantum computers as well.

02:50:45.400 | But yes, we will be able to,

02:50:48.040 | we definitely will be able to do complexity analysis

02:50:50.440 | and we will be able to know.

02:50:51.800 | So the one remaining hope for quantum computing

02:50:55.240 | really, really working at this formal level

02:50:58.200 | of quantum brand exponential stuff being done

02:51:01.120 | in polynomial time and so on,

02:51:03.040 | the one hope, which is very bizarre,

02:51:05.240 | is that you can kind of piggyback

02:51:08.960 | on the expansion of Brownshield space.

02:51:11.200 | So here's how that might work.

02:51:13.440 | So you think, you know, energy conservation,

02:51:17.120 | standard thing in high school physics,

02:51:18.680 | energy is conserved, right?

02:51:20.560 | But now you imagine, you think about energy

02:51:23.600 | in the context of cosmology,

02:51:24.960 | in the context of the whole universe.

02:51:26.880 | It's a much more complicated story.

02:51:28.640 | The expansion of the universe

02:51:29.760 | kind of violates energy conservation.

02:51:32.440 | And so, for example, if you imagine

02:51:33.720 | you've got two galaxies,

02:51:34.920 | they're receding from each other very quickly.

02:51:37.000 | They've got two big central black holes.

02:51:39.320 | You connect a spring between these two central black holes.

02:51:42.960 | Not easy to do in practice,

02:51:44.560 | but let's imagine you could do it.

02:51:46.520 | Now that spring is being pulled apart.

02:51:49.120 | It's getting more potential energy in the spring

02:51:52.320 | as a result of the expansion of the universe.

02:51:55.040 | So in a sense, you are piggybacking

02:51:58.000 | on the expansion that exists in the universe

02:52:00.440 | and the sort of violation of energy conservation

02:52:03.040 | that's associated with that cosmological expansion

02:52:05.760 | to essentially get energy.

02:52:07.080 | You're essentially building a perpetual motion machine

02:52:09.600 | by using the expansion of the universe.

02:52:12.320 | And that is a physical version of that.

02:52:15.200 | It is conceivable that the same thing

02:52:17.120 | could be done in branchial space

02:52:19.120 | to essentially mine the expansion of the universe

02:52:23.080 | in branchial space as a way to get

02:52:26.720 | the sort of quantum computing for free, so to speak,

02:52:31.160 | just from the expansion of the universe in branchial space.

02:52:34.160 | Now, the physical space version is kind of absurd

02:52:36.520 | and involves springs between black holes and so on.

02:52:40.120 | It's conceivable that the branchial space version

02:52:42.680 | is not as absurd and that it's actually something

02:52:45.240 | you can reach with physical things

02:52:47.680 | you can build in labs and so on.

02:52:49.200 | We don't know yet.

02:52:50.280 | - Okay, so like you were saying,

02:52:51.920 | the branchial space might be expanding

02:52:54.640 | and there might be something that could be exploited.

02:52:57.720 | - Right, in the same kind of way

02:52:59.640 | that you can exploit that expansion of the universe

02:53:04.360 | in principle in physical space.

02:53:07.120 | - You just have like a glimmer of hope.

02:53:09.160 | - Right, I think that the, look,

02:53:10.480 | I think the real answer is going to be

02:53:12.400 | that for practical purposes,

02:53:14.520 | the official brand that says you can do exponential things

02:53:18.840 | in polynomial time is probably not gonna work.

02:53:21.120 | - For people curious to kind of learn more,

02:53:22.880 | so this is more like, this is not middle school.

02:53:25.240 | We're gonna go to elementary school for a second.

02:53:28.520 | Maybe middle school, let's go to middle school.

02:53:31.280 | So if I were to try to maybe write a pamphlet

02:53:36.280 | of like Wolfram Physics Project for dummies,

02:53:41.880 | aka for me, or maybe make a video on the basics,

02:53:47.240 | but not just the basics of the physics project,

02:53:51.200 | but the basics plus the most beautiful central ideas,

02:53:56.200 | how would you go about doing that?

02:54:01.160 | Could you help me out a little bit?

02:54:02.680 | - Yeah, yeah, I mean, as a really practical matter,

02:54:05.720 | we have this kind of visual summary picture that we made,

02:54:10.240 | which I think is a pretty good,

02:54:12.280 | when I've tried to explain this to people,

02:54:14.480 | and it's a pretty good place to start,

02:54:17.080 | is you got this rule, you apply the rule,

02:54:19.760 | you're building up this big hypergraph,

02:54:22.720 | you've got all these possibilities,

02:54:24.520 | you're kind of thinking about that

02:54:25.920 | in terms of quantum mechanics.

02:54:27.640 | I mean, that's a decent place to start.

02:54:30.640 | - So basically, the things we've talked about,

02:54:32.960 | which is space represented as a hypergraph,

02:54:36.200 | transformation of that space is kind of time.

02:54:40.740 | - Yes. - And then--

02:54:42.000 | - Structure of that space,

02:54:45.040 | the curvature of that space is gravity.

02:54:47.800 | That can be explained without going

02:54:49.120 | anywhere near quantum mechanics.

02:54:51.200 | I would say that's actually easier to explain

02:54:53.120 | than special relativity.

02:54:54.320 | - Oh, so going into general, so going to curvature?

02:54:58.400 | - Yeah, I mean, special relativity, I think,

02:55:00.640 | is it's a little bit elaborate to explain.

02:55:03.480 | And honestly, you only care about it

02:55:05.560 | if you know about special relativity,

02:55:06.800 | if you know how special relativity

02:55:07.960 | is ordinarily derived and so on.

02:55:09.880 | - So general relativity is easier?

02:55:11.760 | - Is easier, yes.

02:55:12.600 | - And then what about quantum,

02:55:13.760 | what's the easiest way to reveal--

02:55:16.320 | - I think the basic point is just this fact

02:55:20.160 | that there are all these different branches,

02:55:22.120 | that there's this kind of map of how the branches work,

02:55:25.280 | and that, I mean, I think actually the recent things

02:55:30.280 | that we have about the double slit experiment

02:55:32.280 | are pretty good, 'cause you can actually see this,

02:55:34.920 | you can see how the double slit phenomenon arises

02:55:39.080 | from just features of these graphs.

02:55:41.360 | Now, having said that, there is a little bit

02:55:44.760 | of sleight of hand there, because the true story

02:55:49.520 | of the way that double slit thing works

02:55:51.800 | depends on the co-ordinatization of branchial space

02:55:55.080 | that, for example, in our internal team,

02:55:57.800 | there is still a vigorous battle going on

02:56:00.200 | about how that works.

02:56:01.560 | And what's becoming clear is, I mean,

02:56:04.960 | what's becoming clear is that it's mathematically

02:56:07.440 | really quite interesting.

02:56:08.840 | I mean, that is that there's a, you know,

02:56:10.680 | it involves essentially putting space-filling curves,

02:56:13.160 | you basically have a thing which is naturally

02:56:14.800 | two-dimensional, and you're sort of mapping it

02:56:17.240 | into one dimension with a space-filling curve,

02:56:20.000 | and it's like, why is it this space-filling curve

02:56:21.640 | and not another space-filling curve?

02:56:23.360 | And that becomes a story about Riemann surfaces and things,

02:56:26.600 | and it's quite elaborate.

02:56:28.200 | But there's a more, a little bit sleight of hand way

02:56:32.680 | of doing it where it's, you know, it's surprisingly direct.

02:56:36.680 | - So a question that might be difficult to answer,

02:56:42.600 | but for several levels of people,

02:56:46.120 | could you give me advice on how we can learn more?

02:56:50.360 | Specifically, there is people that are completely outside

02:56:54.640 | and just curious and are captivated

02:56:57.080 | by the beauty of hypergraphs, actually.

02:57:00.880 | So people that just want to explore, play around with this.

02:57:04.000 | Second level is people from, say, people like me,

02:57:10.080 | who somehow got a PhD in computer science,

02:57:13.720 | but are not physicists, but fundamentally,

02:57:16.480 | the work you're doing is of computational nature,

02:57:19.680 | so it feels very accessible.

02:57:21.360 | - Yes.

02:57:22.200 | - So what can a person like that do to learn enough physics

02:57:27.200 | or not to be able to, one, explore the beauty of it,

02:57:32.640 | and two, the final level of contribute something

02:57:38.200 | of a level of even publishable, you know,

02:57:41.520 | like strong, interesting ideas.

02:57:44.320 | So at all those layers, complete beginner,

02:57:47.320 | kind of a CS person,

02:57:48.920 | and a CS person that wants to publish.

02:57:50.640 | - Right, I mean, I think that, you know,

02:57:52.440 | I've written a bunch of stuff.

02:57:54.560 | A person called Jonathan Gorod,

02:57:55.720 | who's been a key person working on this project,

02:57:57.480 | has also written a bunch of stuff.

02:57:59.920 | And some other people started writing things, too.

02:58:02.080 | - And he's a physicist.

02:58:03.400 | - Physicist, well, I would say a mathematical physicist.

02:58:06.440 | - Mathematical physicist.

02:58:07.280 | - Pretty mathematically sophisticated.

02:58:08.840 | He regularly out-mathematicizes me.

02:58:11.680 | - Yeah, strong mathematical physicist, yeah.

02:58:14.920 | I looked at some of the papers.

02:58:16.600 | - Right, but so, I mean, you know,

02:58:19.480 | I wrote this kind of original announcement blog post

02:58:22.480 | about this project, which people seem to have found.

02:58:25.520 | I've been really happy, actually, that people who,

02:58:29.040 | you know, people seem to have grokked key points from that.

02:58:34.800 | Much deeper key points people seem to have grokked

02:58:37.440 | than I thought they would grokk.

02:58:39.560 | - And that's a kind of a long blog post

02:58:41.600 | that explains some of the things we talked about,

02:58:43.160 | like the hypergraph and the basic rules.

02:58:45.200 | - Yes, yes.

02:58:46.040 | - And I don't, does it, I forget,

02:58:47.960 | it doesn't have any quantum mechanics in it.

02:58:49.280 | - Oh, yeah, yeah, it does.

02:58:50.120 | It does have quantum mechanics, yes, it does.

02:58:51.920 | But we know a little bit more since that blog post

02:58:54.760 | that probably clarifies, but that blog post

02:58:57.720 | does a pretty decent job.

02:58:59.600 | And, you know, talking about things like, again,

02:59:02.160 | something we didn't mention,

02:59:03.000 | the fact that the uncertainty principle

02:59:04.920 | is a consequence of curvature in Brown-Shield space.

02:59:07.760 | - How much physics should a person know

02:59:10.120 | to be able to understand the beauty of this framework

02:59:14.440 | and to contribute something novel?

02:59:16.880 | - Okay, so I think that those are different questions.

02:59:20.200 | So, I mean, I think that the why does this work,

02:59:23.820 | why does this make any sense,

02:59:25.560 | to really know that,

02:59:28.460 | you have to know a fair amount of physics, okay?

02:59:32.040 | And for example, have a decent--

02:59:33.520 | - When you say why does this work,

02:59:35.040 | you're referring to the connection between this model and--

02:59:39.120 | - General relativity, for example.

02:59:39.960 | - And general relativity.

02:59:40.780 | - Like you have to understand

02:59:41.620 | something about general relativity.

02:59:43.160 | - There's also a side of this where just,

02:59:45.240 | as the pure mathematical framework is fascinating.

02:59:47.880 | - Yes.

02:59:48.720 | - If you throw the physics out completely.

02:59:49.920 | - Right, then it's quite accessible to, I mean, you know,

02:59:52.520 | I wrote this sort of long technical introduction

02:59:55.280 | to the project, which seems to have been very accessible

02:59:58.480 | to people who are, you know, who understand computation

03:00:01.400 | and formal abstract ideas,

03:00:03.680 | but are not specialists in physics

03:00:05.720 | or other kinds of things.

03:00:07.240 | I mean, the thing with the physics part of it is,

03:00:10.320 | you know, there's both a way of thinking

03:00:14.600 | and a literally a mathematical formalism.

03:00:16.840 | I mean, it's like, you know,

03:00:18.080 | to know that we get the Einstein equations,

03:00:19.980 | to know we get the energy momentum tensor,

03:00:22.120 | you kind of have to know what the energy momentum tensor is,

03:00:24.820 | and that's physics.

03:00:25.920 | I mean, that's kind of graduate level physics, basically.

03:00:29.260 | And so that, you know, making that final connection

03:00:33.360 | is, requires some depth of physics knowledge.

03:00:37.440 | - I mean, that's the unfortunate thing,

03:00:38.880 | the difference in machine learning and physics

03:00:40.600 | in the 21st century.

03:00:42.880 | Is it really out of reach of a year or two worth of study?

03:00:47.440 | - No, you could get it in a year or two,

03:00:49.920 | but you can't get it in a month.

03:00:51.600 | - Right.

03:00:52.440 | - I mean, it--

03:00:53.260 | - But it doesn't require necessarily like 15 years.

03:00:56.160 | - No, it does not.

03:00:57.000 | And in fact, a lot of what has happened with this project

03:01:00.200 | makes a lot of this stuff much more accessible.

03:01:02.760 | There are things where it has been quite difficult

03:01:04.760 | to explain what's going on,

03:01:06.000 | and it requires much more, you know,

03:01:09.120 | having the concreteness of being able to do simulations,

03:01:11.800 | knowing that this thing that you might've thought

03:01:15.120 | was just an analogy is really actually what's going on,

03:01:18.960 | makes one feel much more secure

03:01:21.000 | about just sort of saying, this is how this works.

03:01:24.200 | And I think it will be, you know,

03:01:26.200 | I'm hoping the textbooks of the future,

03:01:28.480 | the physics textbooks of the future,

03:01:30.440 | there will be a certain compression.

03:01:32.080 | There will be things that used to be

03:01:33.320 | very much more elaborate, because for example,

03:01:35.200 | even doing continuous mathematics

03:01:36.720 | versus this discrete mathematics,

03:01:38.840 | that, you know, to know how things work

03:01:40.640 | in continuous mathematics,

03:01:41.760 | you have to be talking about stuff

03:01:43.080 | and waving your hands about things.

03:01:44.720 | Whereas with the discrete version,

03:01:47.080 | it's just like, here is a picture, this is how it works.

03:01:50.880 | And there's no, oh, did we get the limit right?

03:01:53.200 | Did this, you know, did this thing that is of,

03:01:55.520 | you know, zero, you know, measure zero object,

03:01:59.360 | you know, interact with this thing in the right way.

03:02:01.920 | You don't have to have that whole discussion.

03:02:03.360 | It's just like, here's a picture, you know,

03:02:05.480 | this is what it does.

03:02:07.120 | And, you know, you can, then it takes more effort

03:02:09.280 | to say, what does it do in the limit

03:02:10.560 | when the picture gets very big?

03:02:12.000 | - But you can do experiments

03:02:13.080 | to build up an intuition actually.

03:02:14.320 | - Yes, right.

03:02:15.160 | And you can get sort of core intuition for what's going on.

03:02:17.440 | Now, in terms of contributing to this,

03:02:19.680 | the, you know, I would say that the study

03:02:21.880 | of the computational universe

03:02:23.160 | and how all these programs work

03:02:24.480 | in the computational universe,

03:02:25.960 | there's just an unbelievable amount to do there.

03:02:28.720 | And it is very close to the surface.

03:02:31.280 | That is, you know, high school kids,

03:02:34.360 | you can do experiments.

03:02:36.040 | It's not, you know, and you can discover things.

03:02:38.920 | I mean, you know, we, you can discover stuff about,

03:02:42.560 | I don't know, like this thing about expansion

03:02:44.280 | of branchial space.

03:02:45.120 | That's an absolutely accessible thing to look at.

03:02:47.720 | Now, you know, the main issue with doing these things

03:02:50.680 | is not, there isn't a lot of technical depth

03:02:54.600 | difficulty there.

03:02:56.000 | The actual doing of the experiments, you know,

03:02:58.040 | all the code is all on our website to do all these things.

03:03:01.360 | The real thing is sort of the judgment

03:03:03.880 | of what's the right experiment to do.

03:03:05.600 | How do you interpret what you see?

03:03:07.760 | That's the part that, you know,

03:03:09.920 | people will do amazing things with,

03:03:11.840 | and that's the part that,

03:03:13.520 | but it isn't like you have to have done 10 years of study

03:03:17.040 | to get to the point where you can do the experiments.

03:03:18.840 | You don't.

03:03:19.680 | - That's the cool thing.

03:03:20.520 | You can do experiments day one, basically.

03:03:22.480 | It's that, that's the amazing thing about,

03:03:25.080 | and you've actually put the tools out there.

03:03:26.920 | It's beautiful, it's mysterious.

03:03:29.680 | There's still, I would say, maybe you can correct me.

03:03:32.760 | It feels like there's a huge number of low-hanging fruit

03:03:35.520 | on the mathematical side, at least,

03:03:37.840 | not the physics side, perhaps.

03:03:40.120 | - No, look, on the, okay, on the physics side,

03:03:44.440 | we are, we're definitely in harvesting mode, you know.

03:03:48.480 | - Of which fruit, the low-hanging ones or?

03:03:51.000 | - The low-hanging ones, yeah, right.

03:03:52.560 | I mean, basically, here's the thing.

03:03:54.200 | There's a certain list of, you know,

03:03:56.120 | here are the effects in quantum mechanics,

03:03:57.800 | here are the effects in general relativity.

03:03:59.760 | It's just like industrial harvesting.

03:04:02.200 | It's like, can we get this one, this one, this one,

03:04:04.480 | this one, this one?

03:04:05.560 | And the thing that's really, you know,

03:04:07.560 | interesting and satisfying, and it's like, you know,

03:04:10.120 | is one climbing the right mountain?

03:04:11.520 | Does one have the right model?

03:04:12.920 | The thing that's just amazing is, you know,

03:04:15.920 | we keep on like, are we gonna get this one?

03:04:18.280 | How hard is this one?

03:04:19.920 | It's like, oh, you know, it looks really hard,

03:04:22.920 | it looks really hard.

03:04:23.800 | Oh, actually, we can get it.

03:04:25.800 | And--

03:04:27.560 | - And you're continually surprised.

03:04:29.040 | I mean, it seems like, I've been following your progress.

03:04:31.520 | It's kind of exciting, all the, in harvesting mode,

03:04:34.320 | all the things you're picking up along the way.

03:04:35.880 | - Right, right, no, I mean, it's the thing that is,

03:04:38.320 | I keep on thinking it's gonna be more difficult than it is.

03:04:40.560 | Now, that's a, you know, that's a, who knows what,

03:04:43.360 | I mean, the one thing, so the thing that's been,

03:04:47.400 | was a big thing that I think we're pretty close to,

03:04:50.920 | I mean, I can give you a little bit of the roadmap,

03:04:52.480 | it's sort of interesting to see,

03:04:54.000 | is like, what are particles?

03:04:55.720 | What are things like electrons?

03:04:56.880 | How do they really work?

03:04:58.520 | - Are you close to get, like, what's,

03:05:01.400 | are you close to trying to understand, like,

03:05:03.160 | the atom, the electrons, neutrons, protons,

03:05:06.480 | like just particles? - Okay, so this is,

03:05:07.320 | this is the stack.

03:05:08.160 | So the first thing we want to understand is

03:05:10.600 | the quantization of spin.

03:05:13.360 | So particles, they kind of spin,

03:05:15.960 | they have a certain angular momentum.

03:05:18.080 | That angular momentum, even though the masses of particles

03:05:21.520 | are all over the place, you know,

03:05:22.400 | the electron has a mass of 0.511 MeV,

03:05:26.000 | but, you know, the proton is 938 MeV,

03:05:28.240 | et cetera, et cetera, et cetera,

03:05:29.080 | they're all kind of random numbers.

03:05:30.640 | The spins of all these particles

03:05:32.720 | are either integers or half integers.

03:05:34.840 | And that's a fact that was discovered in the 1920s,

03:05:37.720 | I guess.

03:05:38.560 | I think that we are close to understanding

03:05:44.160 | why spin is quantized.

03:05:46.160 | And that's a, and it appears to be

03:05:48.320 | a quite elaborate mathematical story

03:05:50.320 | about homotopy groups in crystal space

03:05:53.080 | and all kinds of things.

03:05:54.480 | But bottom line is that seems within reach.

03:05:58.040 | And that's a big deal because that's a very core feature

03:06:01.160 | of understanding how particles work in quantum mechanics.

03:06:04.240 | Another core feature is this difference

03:06:06.600 | between particles that obey the exclusion principle

03:06:09.240 | and sort of stay apart,

03:06:10.640 | that leads to the stability of matter and things like that,

03:06:13.720 | and particles that love to get together

03:06:15.400 | and be in the same state, things like photons,

03:06:18.120 | that, and that's what leads to phenomena like lasers,

03:06:22.200 | where you can get sort of coherently everything

03:06:24.200 | in the same state.

03:06:25.520 | That difference is the particles of integer spin

03:06:29.280 | or bosons like to get together in the same state,

03:06:31.760 | the particles of half integers spin, of fermions,

03:06:34.480 | like electrons, that they tend to stay apart.

03:06:37.560 | And so the question is, can we get that in our models?

03:06:41.840 | And just the last few days, I think we made,

03:06:45.440 | I mean, I think the story of,

03:06:47.960 | I mean, it's one of these things where we're really close.

03:06:51.440 | - Is this connected to fermions and bosons?

03:06:53.400 | You were talking about? - Yeah, yeah, yeah.

03:06:54.240 | So this was, what happens is what seems to happen, okay?

03:06:57.760 | It's subject to revision even the next few days.

03:07:01.480 | But what seems to be the case is that bosons

03:07:04.960 | are associated with essentially merging in multi-way graphs

03:07:08.400 | and fermions are associated

03:07:09.720 | with branching in multi-way graphs.

03:07:11.960 | And that essentially the exclusion principle

03:07:15.160 | is the fact that in branchial space,

03:07:18.320 | things have a certain extent in branchial space

03:07:21.400 | that in which things are being sort of forced apart

03:07:24.040 | in branchial space, whereas the case of bosons,

03:07:26.320 | they get, they come together in branchial space.

03:07:29.440 | And the real question is,

03:07:30.880 | can we explain the relationship between that

03:07:32.960 | and these things called spinners,

03:07:34.560 | which are the representation

03:07:35.640 | of half-integer spin particles

03:07:37.480 | that have this weird feature that usually

03:07:38.960 | when you go around 360 degree rotation,

03:07:41.600 | you get back to where you started from.

03:07:43.440 | But for a spinner,

03:07:44.280 | you don't get back to where you started from.

03:07:46.080 | It takes 720 degrees of rotation

03:07:48.440 | to get back to where you started from.

03:07:50.280 | And we are just, it feels like we are,

03:07:53.200 | we're just incredibly close to actually having that,

03:07:55.480 | understanding how that works.

03:07:57.200 | And it turns out, it looks like,

03:07:59.080 | my current speculation is,

03:08:00.680 | that it's as simple as the directed hypergraphs

03:08:05.000 | versus undirected hypergraphs.

03:08:06.560 | - Oh, interesting.

03:08:07.840 | - The relationship between spinners and vectors.

03:08:10.320 | So, which is just--

03:08:11.160 | - Nice, interesting.

03:08:12.000 | Yeah, that would be interesting

03:08:12.840 | if these are all these kind of nice properties

03:08:16.320 | of this multigraphs of branching and rejoining.

03:08:20.000 | - Spinners have been very mysterious.

03:08:21.800 | And if that's what they turn out to be,

03:08:23.960 | there's gonna be an easy explanation

03:08:25.360 | of what's going on.

03:08:26.200 | - Yeah, if it's directed versus undirected.

03:08:27.240 | - It's just, and that's why

03:08:28.800 | there's only two different cases.

03:08:30.440 | - Why are spinners important in quantum mechanics?

03:08:34.240 | Can you just give a--

03:08:35.720 | - Yeah, so spinners are important

03:08:37.040 | because they are the representation of electrons

03:08:41.520 | which have half an integer spin.

03:08:43.440 | They are the wave functions of electrons are spinners.

03:08:48.360 | Just like the wave functions of photons are vectors,

03:08:51.320 | the wave functions of electrons are spinners.

03:08:54.320 | And they have this property

03:08:56.200 | that when you rotate by 360 degrees,

03:09:00.120 | they come back to minus one of themselves

03:09:02.960 | and take 720 degrees to get back to the original value.

03:09:06.800 | And they are a consequence of,

03:09:08.520 | we usually think of rotation in space

03:09:14.280 | as being when you have this notion of rotational invariance

03:09:18.760 | and rotational invariance, as we ordinarily experience it,

03:09:22.200 | doesn't have the feature.

03:09:23.320 | If you go through 360 degrees,

03:09:24.800 | you go back to where you started from,

03:09:26.480 | but that's not true for electrons.

03:09:28.520 | And so that's why understanding how that works is important.

03:09:32.520 | - Yeah, I've been playing with Mobius strip

03:09:34.960 | quite a bit lately just for fun.

03:09:37.040 | - Yes, yes.

03:09:37.880 | - It has the same kind of funky properties.

03:09:41.040 | - Yes, right, exactly.

03:09:41.880 | You can have this, the so-called belt trick,

03:09:43.600 | which is this way of taking an extended object

03:09:46.000 | and you can see properties like spinners

03:09:47.640 | with that kind of extended object that--

03:09:50.280 | - Yeah, it would be very cool if it somehow connects

03:09:52.640 | the directive versus undirected.

03:09:53.840 | - I think that's what it's gonna be.

03:09:54.680 | I think it's gonna be as simple as that, but we'll see.

03:09:57.480 | I mean, this is the thing that,

03:09:59.680 | this is the big sort of bizarre surprise

03:10:02.040 | is that, because I learned physics as probably,

03:10:07.040 | let's say a fifth generation in the sense that,

03:10:10.080 | if you go back to the 1920s and so on,

03:10:11.960 | there were the people who were originating

03:10:13.720 | quantum mechanics and so on.

03:10:15.400 | Maybe it's a little less than that.

03:10:16.280 | Maybe I was like a third generation or something.

03:10:19.760 | I don't know, but the people from whom I learned physics

03:10:23.560 | were the people who have been students of the students

03:10:26.760 | of the people who originated

03:10:28.920 | the current understanding of physics.

03:10:31.240 | And we're now at probably the seventh generation

03:10:33.920 | of physicists or something from the early days

03:10:36.600 | of 20th century physics.

03:10:38.360 | And whenever a field gets that many generations deep,

03:10:43.360 | it seems the foundations seem quite inaccessible

03:10:46.520 | and it seems like you can't possibly understand that.

03:10:49.800 | We've gone through seven academic generations

03:10:52.720 | and that's been this thing that's been difficult

03:10:56.280 | to understand for that long.

03:10:58.600 | It just can't be that simple.

03:11:01.040 | - But in a sense, maybe that journey takes you

03:11:03.800 | to a simple explanation that was there all along.

03:11:07.640 | That's the whole-- - Right, right, right.

03:11:08.480 | I mean, and the thing for me personally,

03:11:10.640 | the thing that's been quite interesting is,

03:11:13.200 | I didn't expect this project to work in this way.

03:11:15.980 | But I had this sort of weird piece of personal history

03:11:19.880 | that I used to be a physicist

03:11:21.840 | and I used to do all this stuff.

03:11:23.040 | And I know the standard canon of physics.

03:11:26.880 | I knew it very well.

03:11:30.080 | But then I'd been working on this kind

03:11:31.680 | of computational paradigm for basically 40 years.

03:11:35.100 | And the fact that I'm sort of now coming back

03:11:38.800 | to trying to apply that in physics,

03:11:42.240 | it kind of felt like that journey was necessary.

03:11:44.880 | - When did you first try to play with a hypergraph?

03:11:49.040 | - So what happened is-- - Is this recent?

03:11:50.520 | - Yeah, so what I had was, okay, so this is again,

03:11:53.840 | one always feels dumb after the fact.

03:11:56.280 | It's obvious after the fact.

03:11:58.800 | But so back in the early 1990s,

03:12:02.240 | I realized that using graphs as a sort

03:12:05.720 | of underlying thing underneath space and time

03:12:07.780 | was going to be a useful thing to do.

03:12:09.720 | I figured out about multi-way systems.

03:12:11.920 | I figured out the things about general relativity.

03:12:14.960 | I'd figured out by the end of the 1990s.

03:12:17.400 | But I always felt there was a certain inelegance

03:12:20.040 | because I was using these graphs

03:12:21.880 | and there were certain constraints on these graphs

03:12:23.880 | that seemed like they were kind of awkward.

03:12:26.440 | It was kind of like you can pick,

03:12:28.320 | it's like you couldn't pick any rule.

03:12:30.200 | It was like pick any number, but the number has to be prime.

03:12:33.360 | It was kind of like you couldn't,

03:12:34.600 | it was kind of an awkward special constraint.

03:12:36.900 | I had these trivalent graphs,

03:12:38.400 | graphs with just three connections from every node.

03:12:41.440 | Okay, so, but I discovered a bunch of stuff with that.

03:12:44.280 | I thought it was kind of inelegant.

03:12:46.280 | And the other piece of sort of personal history

03:12:48.680 | is obviously I spent my life

03:12:50.200 | as a computational language designer.

03:12:52.960 | And so the story of computational language design

03:12:55.160 | is a story of how do you take all these random ideas

03:12:58.000 | in the world and kind of grind them down

03:13:00.740 | into something that is computationally

03:13:02.720 | as simple as possible.

03:13:04.760 | And so, I've been very interested

03:13:06.680 | in kind of simple computational frameworks

03:13:09.300 | for representing things and have ridiculous amounts

03:13:13.440 | of experience in trying to do that.

03:13:15.840 | - And actually all of those trajectories of your life

03:13:18.300 | kind of came together.

03:13:19.320 | So you make it sound like you could have come up

03:13:21.600 | with everything you're working on now decades ago,

03:13:24.640 | but in reality.

03:13:26.440 | - Look, two things slowed me down.

03:13:28.080 | I mean, one thing that slowed me down was

03:13:30.280 | I couldn't figure out how to make it elegant.

03:13:32.840 | And that turns out hypergraphs were the key to that.

03:13:35.600 | And that I figured out about less than two years ago now.

03:13:39.180 | And the other, I mean, I think,

03:13:43.360 | so that was sort of a key thing.

03:13:46.160 | Well, okay, so the real embarrassment of this project

03:13:49.760 | is that the final structure that we have

03:13:52.680 | that is the foundation for this project

03:13:55.800 | is basically a kind of an idealized version,

03:14:00.000 | a formalized version of the exact same structure

03:14:03.560 | that I've used to build computational languages

03:14:05.640 | for more than 40 years.

03:14:07.140 | But it took me, but I didn't realize that.

03:14:09.700 | - And there yet may be other,

03:14:12.800 | so we're focused on physics now,

03:14:14.360 | but I mean, that's what the new kind of science is about,

03:14:17.720 | same kind of stuff.

03:14:19.120 | And this, in terms of mathematically,

03:14:21.040 | the beauty of it, so there could be

03:14:23.760 | entire other kind of objects that are useful for,

03:14:27.600 | like we're not talking about machine learning, for example.

03:14:31.920 | Maybe there's other variants of the hypergraph

03:14:33.880 | that are very useful for reasoning about--

03:14:35.720 | - Well, we'll see whether the multi-way graph

03:14:37.440 | for a machine learning system is interesting, okay?

03:14:40.640 | (Luke laughs)

03:14:41.480 | - Let's leave it at that.

03:14:42.320 | That's conversation number three.

03:14:43.680 | - That's, we're not gonna go there right now.

03:14:46.240 | - One of the things you've mentioned

03:14:49.040 | is the space of all possible rules

03:14:52.640 | that we kind of discussed a little bit,

03:14:55.200 | that there could be, I guess,

03:14:58.000 | the set of possible rules is infinite.

03:14:59.900 | - Right, well, so here's the big,

03:15:02.720 | sort of one of the conundrums

03:15:04.200 | that I'm kind of trying to deal with,

03:15:07.080 | is let's say we think we found the rule for the universe.

03:15:11.720 | And we say, here it is, write it down.

03:15:14.200 | It's a little tiny thing.

03:15:15.780 | And then we say, gosh, that's really weird.

03:15:18.000 | Why did we get that one?

03:15:20.840 | And then we're in this whole situation

03:15:23.240 | because let's say it's fairly simple.

03:15:25.480 | How did we come up the winners,

03:15:27.680 | getting one of the simple possible universe rules?

03:15:30.400 | Why didn't we get some incredibly complicated rule?

03:15:33.600 | Why did we get one of the simpler ones?

03:15:35.280 | And that's the thing which, in the history of science,

03:15:38.800 | the whole sort of story of Copernicus and so on was,

03:15:42.840 | we used to think the Earth was the center of the universe,

03:15:44.960 | but now we find out it's not.

03:15:46.320 | And we're actually just in some random corner

03:15:48.760 | of some random galaxy out in this big universe.

03:15:51.580 | There's nothing special about us.

03:15:53.800 | So if we get universe number 317

03:15:58.120 | out of all the infinite number of possibilities,

03:16:00.400 | how do we get something that small and simple?

03:16:02.920 | So I was very confused by this.

03:16:05.040 | And it's like, what are we going to say about this?

03:16:06.740 | How are we going to explain this?

03:16:08.560 | And I thought it might be one of these things

03:16:10.320 | where you just, you can get it to the threshold,

03:16:13.300 | and then you find out its rule number such and such,

03:16:15.480 | and you just have no idea why it's like that.

03:16:17.760 | Okay, so then I realized

03:16:19.120 | it's actually more bizarre than that, okay?

03:16:22.560 | So we talked about multi-way graphs.

03:16:25.020 | We talked about this idea

03:16:26.200 | that you take these underlying transformation rules

03:16:29.020 | on these hypergraphs, and you apply them

03:16:31.840 | wherever the rule can apply, you apply it.

03:16:34.720 | And that makes this whole multi-way graph of possibilities.

03:16:37.680 | Okay, so let's go a little bit weirder.

03:16:39.960 | Let's say that at every place,

03:16:42.820 | not only do you apply a particular rule

03:16:45.260 | in all possible ways it can apply,

03:16:47.160 | but you apply all possible rules

03:16:49.520 | in all possible ways they can apply.

03:16:51.920 | As you say, that's just crazy.

03:16:53.760 | That's way too complicated.

03:16:54.920 | You're never going to be able to conclude anything.

03:16:57.240 | Okay, however, turns out that-

03:17:00.840 | - Don't tell me there's some kind of invariance.

03:17:02.880 | - Yeah, yeah.

03:17:03.880 | (laughing)

03:17:05.360 | So what happens is-

03:17:06.200 | - Oh man, that would be amazing.

03:17:08.080 | - Right, so this thing that you get,

03:17:11.280 | there's this kind of ruleal multi-way graph,

03:17:13.400 | this multi-way graph that is a branching of rules

03:17:15.920 | as well as a branching of possible applications of rules.

03:17:19.800 | This thing has causal invariance.

03:17:22.100 | It's an inevitable feature that it shows causal invariance.

03:17:25.360 | And that means that you can take different reference frames,

03:17:28.640 | different ways of slicing this thing,

03:17:30.960 | and they will all in some sense be equivalent.

03:17:33.960 | If you make the right translation, they will be equivalent.

03:17:37.380 | So, okay, so the basic point here is-

03:17:40.440 | - If that's true, that would be beautiful.

03:17:43.080 | - It is true, and it is beautiful.

03:17:44.400 | - So it's not just an intuition, there is some-

03:17:47.520 | - No, no, no, there's real mathematics behind this.

03:17:50.280 | And it is, okay, so here's how it comes out.

03:17:55.280 | - That's amazing.

03:17:57.360 | - Right, so by the way, I mean,

03:17:58.800 | the mathematics it's connected to is the mathematics

03:18:01.160 | of higher category theory and groupoids

03:18:03.640 | and things like this, which I've always been afraid of,

03:18:05.900 | but now I'm finally wrapping my arms around it.

03:18:09.960 | But it's also related to,

03:18:13.280 | it also relates to computational complexity theory.

03:18:16.160 | It's also deeply related to the P versus NP problem

03:18:19.200 | and other things like this.

03:18:20.480 | Again, it seems completely bizarre

03:18:21.880 | that these things are connected,

03:18:22.960 | but here's why it's connected.

03:18:25.160 | This space of all possible, okay, so a Turing machine,

03:18:30.160 | very simple model of computation.

03:18:32.080 | You just got this tape where you write down ones and zeros

03:18:36.480 | or something on the tape, and you have this rule

03:18:38.880 | that says, you change the number,

03:18:41.520 | you move the head on the tape, et cetera.

03:18:44.320 | You have a definite rule for doing that.

03:18:46.040 | A deterministic Turing machine

03:18:47.880 | just does that deterministically.

03:18:50.000 | Given the configuration of the tape,

03:18:51.800 | it will always do the same thing.

03:18:53.640 | A non-deterministic Turing machine

03:18:55.800 | can have different choices that it makes at every step.

03:18:59.000 | And so, you know this stuff, you probably teach this stuff.

03:19:07.120 | So a non-deterministic Turing machine

03:19:09.240 | has the set of branching possibilities,

03:19:11.720 | which is in fact one of these multi-way graphs.

03:19:14.400 | And in fact, if you say,

03:19:16.280 | imagine the extremely non-deterministic Turing machine,

03:19:19.560 | the Turing machine that can just do,

03:19:22.600 | that takes any possible rule at each step.

03:19:25.480 | That is this real multi-way graph.

03:19:27.560 | The set of possible histories

03:19:31.340 | of that extreme non-deterministic Turing machine

03:19:33.760 | is a really a multi-way graph.

03:19:36.820 | - What term are you using, Rulio?

03:19:38.520 | - Rulio.

03:19:39.360 | - Rulio, I like it. - It's a weird word.

03:19:40.760 | Yeah, it's a weird word.

03:19:41.600 | - Rulio. - Multi-way graph.

03:19:44.200 | Okay, so this, so that.

03:19:45.920 | - I'm trying to think of the space of rules.

03:19:50.920 | So these are basic transformations.

03:19:54.280 | - So in a Turing machine, it's like it says,

03:19:57.080 | move left, move, you know, if it's a one,

03:19:59.800 | if it's a black square under the head,

03:20:02.360 | move left and right a green square.

03:20:04.880 | That's a rule.

03:20:05.760 | That's a very basic rule,

03:20:06.780 | but I'm trying to see the rules on the hypergraphs,

03:20:09.900 | how rich of the programs can they be?

03:20:12.260 | Or do they all ultimately just map into something simple?

03:20:15.580 | - Yeah, they're all, I mean, hypergraphs,

03:20:18.060 | that's another layer of complexity on this whole thing.

03:20:20.220 | You can think about these in transformations of hypergraphs,

03:20:23.100 | but Turing machines are a little bit simpler.

03:20:23.940 | - You should stick up with Turing machines, okay.

03:20:25.620 | - Right, they're a little bit simpler.

03:20:27.320 | So if you look at these extreme

03:20:29.140 | non-deterministic Turing machines,

03:20:30.980 | you're mapping out all the possible non-deterministic paths

03:20:35.180 | that the Turing machine can follow.

03:20:37.220 | And if you ask the question, can you reach,

03:20:40.820 | okay, so a deterministic Turing machine

03:20:43.260 | follows a single path.

03:20:44.860 | The non-deterministic Turing machine

03:20:46.340 | fills out this whole sort of ball of possibilities.

03:20:50.740 | And so then the P versus NP problem

03:20:53.340 | ends up being questions about,

03:20:55.220 | and we haven't completely figured out

03:20:56.820 | all the details of this,

03:20:57.660 | but it's basically has to do with questions

03:20:59.980 | about the growth of that ball

03:21:02.840 | relative to what happens with individual paths.

03:21:05.060 | And so on.

03:21:05.900 | So essentially there's a geometrization

03:21:07.860 | of the P versus NP problem that comes out of this.

03:21:10.180 | That's a sideshow, okay.

03:21:12.060 | The main event here is the statement

03:21:15.020 | that you can look at this multi-way graph

03:21:20.020 | where the branches correspond,

03:21:21.860 | not just to different applications of a single rule,

03:21:24.260 | but to different applications,

03:21:25.460 | to applications of different rules, okay.

03:21:28.260 | And that then that when you say,

03:21:32.020 | I'm going to be an observer embedded in that system,

03:21:35.500 | and I'm going to try and make sense

03:21:37.020 | of what's going on in the system.

03:21:38.820 | And to do that,

03:21:40.200 | I essentially am picking a reference frame.

03:21:43.100 | And that turns out to be, well, okay.

03:21:46.620 | So the way this comes out essentially

03:21:48.660 | is the reference frame you pick

03:21:50.780 | is the rule that you infer

03:21:52.700 | is what's going on in the universe.

03:21:55.340 | Even though all possible rules are being run,

03:21:58.940 | although all those possible rules

03:22:01.260 | are in a sense giving the same answer

03:22:02.740 | because of causal invariance.

03:22:04.580 | But what you see could be completely different.

03:22:08.500 | If you pick different reference frames,

03:22:10.380 | you essentially have a different description language

03:22:12.940 | for describing the universe.

03:22:15.000 | Okay, so what does this really mean in practice?

03:22:17.340 | So imagine there's us.

03:22:19.660 | We think about the universe in terms of space and time,

03:22:22.340 | and we have various kinds of description models and so on.

03:22:25.060 | Now let's imagine the friendly aliens, for example, right?

03:22:29.080 | How do they describe their universe?

03:22:31.360 | Well, our description of the universe

03:22:33.480 | probably is affected by the fact that

03:22:36.200 | we are about the size we are,

03:22:37.920 | a meter-ish tall, so to speak.

03:22:40.280 | We have brain processing speeds

03:22:41.880 | of about the speeds we have.

03:22:43.720 | We're not the size of planets, for example,

03:22:46.360 | where the speed of light really would matter.

03:22:49.040 | In our everyday life,

03:22:50.060 | the speed of light doesn't really matter.

03:22:51.820 | Everything can be,

03:22:52.960 | the fact that the speed of light is finite is irrelevant.

03:22:55.240 | It could as well be infinite.

03:22:56.740 | We wouldn't make any difference.

03:22:58.760 | It affects the ping times on the internet.

03:23:01.280 | That's about the level of how we notice the speed of light.

03:23:06.080 | In our sort of everyday existence,

03:23:07.440 | we don't really notice it.

03:23:09.400 | And so we have a way of describing the universe

03:23:12.280 | that's based on our sensory,

03:23:14.920 | our senses, these days,

03:23:17.960 | also on the mathematics we've constructed and so on.

03:23:20.760 | But the realization is it's not the only way to do it.

03:23:24.200 | There will be completely, utterly incoherent descriptions

03:23:28.240 | of the universe which correspond

03:23:30.880 | to different reference frames in this sort of ruleal space.

03:23:34.280 | - In the ruleal space, that's fascinating.

03:23:36.120 | So we have some kind of reference frame

03:23:38.240 | in this ruleal space.

03:23:39.400 | - Right.

03:23:40.240 | - And from that--

03:23:41.720 | - That's why we are attributing this rule to the universe.

03:23:45.640 | So in other words, when we say,

03:23:47.240 | "Why is it this rule and not another?"

03:23:49.480 | The answer is just shine the light back on us, so to speak.

03:23:54.480 | It's because of the reference frame that we've picked

03:23:57.280 | in our way of understanding what's happening

03:23:59.000 | in this sort of space of all possible rules and so on.

03:24:02.360 | - But also in the space from this reference frame,

03:24:05.200 | because of the ruleal, the invariance,

03:24:11.160 | that simple, that the rule on which the universe,

03:24:17.360 | with which you can run the universe,

03:24:19.800 | might as well be simple.

03:24:21.320 | - Yes, yes.

03:24:22.240 | Okay, so here's another point.

03:24:23.680 | So this is, again,

03:24:25.040 | these are a little bit mind twisting in some ways,

03:24:27.320 | but the, okay, another thing that's sort of we know

03:24:31.880 | from computation is this idea of computation universality.

03:24:36.440 | The fact that given that we have a program

03:24:38.840 | that runs on one kind of computer,

03:24:40.680 | we can as well, you know,

03:24:42.800 | we can convert it to run on any other kind of computer.

03:24:45.360 | We can emulate one kind of computer with another.

03:24:47.880 | So that might lead you to say,

03:24:50.240 | "Well, you think you have the rule for the universe,

03:24:52.760 | but you might as well be running it on a Turing machine,

03:24:54.840 | because we know we can emulate any computational rule

03:24:59.000 | on any kind of machine."

03:25:00.920 | And that's essentially the same thing

03:25:02.320 | that's being said here.

03:25:03.680 | That is that what we're doing is we're saying

03:25:07.320 | these different interpretations of physics

03:25:10.440 | correspond to essentially running physics

03:25:13.400 | on different underlying, you know,

03:25:16.040 | thinking about the physics as running in different,

03:25:18.160 | with different underlying rules,

03:25:19.520 | as if different underlying computers were running them.

03:25:22.960 | And, but because of computation universality,

03:25:26.040 | or more accurately,

03:25:26.880 | because of this principle

03:25:27.720 | of computational equivalence thing of mine,

03:25:30.360 | there's, they are,

03:25:32.040 | these things are ultimately equivalent.

03:25:35.760 | So the only thing that is the ultimate fact

03:25:38.120 | about the universe,

03:25:39.440 | the ultimate fact that doesn't depend on any of these,

03:25:41.520 | you know, we don't have to talk about specific rules,

03:25:43.760 | et cetera, et cetera, et cetera.

03:25:44.640 | The ultimate fact is the universe is computational,

03:25:48.360 | and it is the things that happen in the universe

03:25:52.640 | are the kinds of computations

03:25:54.400 | that the principle of computational equivalence

03:25:56.000 | says should happen.

03:25:57.560 | Now, that might sound like,

03:25:59.480 | hey, you're not really saying anything there,

03:26:01.560 | but you are, because you can,

03:26:03.920 | you could in principle have a hypercomputer

03:26:06.640 | that things that take an ordinary computer

03:26:09.720 | an infinite time to do,

03:26:10.800 | the hypercomputer can just say,

03:26:11.920 | "Oh, I know the answer.

03:26:13.440 | It's this, immediately."

03:26:15.720 | What this is saying is the universe is not a hypercomputer.

03:26:19.600 | It's not simpler than an ordinary Turing machine

03:26:23.040 | type computer.

03:26:24.040 | It's exactly like an ordinary Turing machine type computer.

03:26:28.080 | And so that's in the end,

03:26:30.040 | the sort of net net conclusion is that's the thing

03:26:34.000 | that is the sort of the hard immovable fact

03:26:36.600 | about the universe.

03:26:38.000 | That's sort of the fundamental principle of the universe

03:26:41.600 | is that it is computational and not hypercomputational

03:26:45.440 | and not sort of infracomputational.

03:26:47.280 | It is this level of computational ability

03:26:50.360 | and it kind of has,

03:26:53.080 | and that's sort of the core fact.

03:26:56.120 | But now, this idea that you can have

03:26:59.200 | these different kind of ruleal reference frames,

03:27:02.280 | these different description languages for the universe,

03:27:05.280 | it makes me, I used to think, okay,

03:27:08.800 | imagine the aliens,

03:27:09.840 | imagine the extraterrestrial intelligence thing,

03:27:12.600 | at least they experienced the same physics.

03:27:15.560 | And now I've realized it isn't true.

03:27:17.440 | - They could have a different ruleal frame.

03:27:19.240 | That's fascinating.

03:27:21.120 | - They can end up with a description of the universe

03:27:25.160 | that is utterly, utterly incoherent with ours.

03:27:28.040 | And that's also interesting in terms of how we think about,

03:27:31.320 | well, intelligence, the nature of intelligence and so on.

03:27:34.240 | I'm fond of the quote,

03:27:35.360 | "The weather has a mind of its own,"

03:27:37.400 | because these are sort of computationally,

03:27:41.040 | that system is computationally equivalent

03:27:43.600 | to the system that is our brains and so on.

03:27:46.560 | And what's different is we don't have a way to understand

03:27:50.320 | what the weather is trying to do, so to speak.

03:27:52.480 | We have a story about what's happening in our brains.

03:27:54.880 | We don't have a sort of connection

03:27:56.680 | to what's happening there.

03:27:57.800 | - So we actually, it's funny,

03:27:59.680 | last time we talked, maybe over a year ago,

03:28:03.280 | we talked about how it was more

03:28:07.320 | based on your work with Arrival.

03:28:09.960 | We talked about how would we communicate

03:28:11.600 | with alien intelligences.

03:28:14.160 | Can you maybe comment on how we might,

03:28:18.000 | how the Wolfram Physics Project changed your view

03:28:20.680 | of how we might be able to communicate

03:28:22.200 | with alien intelligence?

03:28:23.280 | Like if they showed up, is it possible that

03:28:27.040 | because of our comprehension of the physics of the world

03:28:31.800 | might be completely different,

03:28:33.640 | we would just not be able to communicate at all?

03:28:36.640 | - Here's the thing.

03:28:38.040 | Intelligence is everywhere.

03:28:41.520 | The fact, this idea that there's this notion of,

03:28:43.800 | oh, there's gonna be this amazing

03:28:45.080 | extraterrestrial intelligence

03:28:46.400 | and it's gonna be this unique thing,

03:28:48.760 | it's just not true.

03:28:50.080 | It's the same thing.

03:28:51.360 | You know, I think people will realize this

03:28:53.240 | about the time when people decide

03:28:54.840 | that artificial intelligences are kind of

03:28:57.280 | just natural things that are like human intelligences.

03:29:01.160 | They'll realize that extraterrestrial intelligences

03:29:04.520 | or intelligences associated with physical systems and so on,

03:29:08.600 | it's all the same kind of thing.

03:29:09.440 | - It's ultimately computation.

03:29:11.120 | It's all the same.

03:29:12.080 | It's all just computation.

03:29:13.280 | And the issue is, are you sort of inside it?

03:29:17.160 | Are you thinking about it?

03:29:19.200 | Do you have sort of a story you're telling yourself about it?

03:29:23.160 | And, you know, the weather could have a story

03:29:25.160 | it's telling itself about what it's doing.

03:29:27.560 | We just, it's utterly incoherent with the stories

03:29:30.880 | that we tell ourselves based on how our brains work.

03:29:33.560 | - I mean, ultimately it must be a question

03:29:37.080 | whether we can align.

03:29:39.280 | - Exactly, exactly.

03:29:40.120 | - Align with the kind of intelligence.

03:29:41.960 | - Right, right, right.

03:29:42.800 | - There's a systematic way of doing it.

03:29:44.200 | - Right, so the question is in the space

03:29:45.520 | of all possible intelligences,

03:29:47.240 | what's the, how do you think about the distance

03:29:50.440 | between description languages

03:29:52.400 | for one intelligence versus another?

03:29:54.680 | And needless to say, I have thought about this.

03:29:57.120 | And, you know, I don't have a great answer yet,

03:30:00.880 | but I think that's a thing where there will be things

03:30:03.760 | that can be said and there'll be things

03:30:05.080 | that where you can sort of start to characterize,

03:30:07.800 | you know, what is the translation distance

03:30:10.880 | between this, you know, version of the universe

03:30:15.120 | or this, you know, kind of set of computational rules

03:30:17.840 | and this other one.

03:30:18.800 | In fact, okay, so this is a, you know,

03:30:21.480 | there's this idea of algorithmic information theory.

03:30:23.560 | There's this question of sort of what is the,

03:30:25.800 | when you have some something,

03:30:28.700 | what is the sort of shortest description you can make of it

03:30:31.520 | where that description could be saying,

03:30:33.320 | run this program to get the thing, right?

03:30:36.480 | So I'm pretty sure that there will be a physicalization

03:30:41.480 | of the idea of algorithmic information and that,

03:30:49.700 | okay, this is again, a little bit bizarre,

03:30:51.560 | but so I mentioned that there's the speed of light,

03:30:54.480 | maximum speed of information transmission

03:30:56.120 | in physical space.

03:30:57.560 | There's a maximum speed of information transmission

03:30:59.840 | in branchial space, which is a maximum entanglement speed.

03:31:02.920 | There's a maximum speed of information transmission

03:31:05.240 | in ruleal space, which has to do with a maximum speed

03:31:09.200 | of translation between different description languages.

03:31:14.200 | And again, I'm not fully wrapped my brain around this one.

03:31:17.480 | - Yeah, that one just blows my mind to think about that,

03:31:20.120 | but that starts getting closer to the, yeah, the--

03:31:23.600 | - It's kind of a physicalization, right.

03:31:26.360 | And it's also a physicalization of algorithmic information.

03:31:29.960 | And I think there's probably a connection between,

03:31:32.360 | I mean, there's probably a connection

03:31:33.640 | between the notion of energy and some of these things,

03:31:36.600 | which again, I hadn't seen all this coming.

03:31:39.400 | I've always been a little bit resistant

03:31:41.120 | to the idea of connecting physical energy

03:31:43.500 | to things in computation theory,

03:31:45.660 | but I think that's probably coming.

03:31:47.200 | - And that's what essentially at the core

03:31:48.560 | with the physics project is that you're connecting

03:31:52.000 | information theory with physics.

03:31:55.560 | - Yeah, it's computation.

03:31:56.920 | - Computation with our physical universe.

03:31:59.580 | - Yeah, right.

03:32:00.420 | I mean, the fact that our physical universe is,

03:32:03.520 | right, that we can think of it as a computation

03:32:05.760 | and that we can have discussions like,

03:32:08.760 | the theory of the physical universe

03:32:11.040 | is the same kind of a theory

03:32:13.080 | as the P versus NP problem and so on,

03:32:15.520 | is really, I think that's really interesting.

03:32:18.640 | And the fact that, well, okay,

03:32:21.520 | so this kind of brings me to one more thing

03:32:24.240 | that I have to in terms of this sort of unification

03:32:26.140 | of different ideas, which is metamathematics.

03:32:29.640 | - Yeah, let's talk about that.

03:32:30.520 | You mentioned that earlier.

03:32:31.680 | What the heck is mathematics and--

03:32:34.760 | - Okay, so here's what, here's, okay.

03:32:36.880 | So what is mathematics?

03:32:38.840 | Mathematics, sort of at a lowest level,

03:32:43.840 | one thinks of mathematics as you have certain axioms,

03:32:47.400 | you say, you know, you say things like X plus Y

03:32:50.560 | is the same as Y plus X.

03:32:51.840 | That's an axiom about addition.

03:32:55.320 | And then you say, we've got these axioms

03:32:57.360 | and from these axioms, we derive all these theorems

03:33:00.560 | that fill up the literature of mathematics.

03:33:02.400 | The activity of mathematicians

03:33:04.760 | is to derive all these theorems.

03:33:06.800 | Actually, the axioms of mathematics are very small.

03:33:10.360 | You can fit, you know, when I did my new kind

03:33:12.480 | of science book, I fit all of the standard axioms

03:33:15.400 | of mathematics on basically a page and a half.

03:33:17.760 | Not much stuff.

03:33:19.620 | It's like a very simple rule

03:33:21.400 | from which all of mathematics arises.

03:33:23.980 | The way it works, though, is a little different

03:33:26.680 | from the way things work in sort of a computation

03:33:31.680 | because in mathematics, what you're interested in

03:33:33.480 | is a proof and the proof says from here,

03:33:37.480 | you can use from this expression, for example,

03:33:40.360 | you can use these axioms to get to this other expression.

03:33:43.080 | So that proves these two things are equal.

03:33:45.480 | Okay, so we can begin to see how this is going to work.

03:33:49.080 | What's gonna happen is there are paths

03:33:51.380 | in metamathematical space.

03:33:53.420 | So what happens is each, two different ways to look at it.

03:33:57.680 | You can just look at it as mathematical expressions

03:33:59.920 | or you can look at it as mathematical statements,

03:34:02.680 | postulates or something, but either way,

03:34:05.200 | you think of these things and they are connected

03:34:07.880 | by these axioms.

03:34:11.500 | So in other words, you have some fact,

03:34:14.140 | you, or you have some expression,

03:34:15.960 | you apply this axiom, you get some other expression.

03:34:18.860 | And in general, given some expression,

03:34:21.640 | there may be many possible different expressions

03:34:23.920 | you can get.

03:34:24.880 | You basically build up a multi-way graph

03:34:27.360 | and a proof is a path through the multi-way graph

03:34:31.160 | that goes from one thing to another thing.

03:34:34.240 | The path tells you how did you get from one thing

03:34:36.960 | to the other thing?

03:34:37.800 | It's the story of how you got from this to that.

03:34:40.720 | The theorem is the thing at one end

03:34:42.880 | is equal to the thing at the other end.

03:34:44.680 | The proof is the path you go down

03:34:46.920 | to get from one thing to the other.

03:34:48.640 | - You mentioned that Gadel's incompleteness theorem

03:34:51.040 | is the natural, it fits naturally there.

03:34:53.560 | How does it fit?

03:34:54.400 | - Yeah, so what happens there is that

03:34:55.920 | the Gadel's theorem is basically saying

03:34:58.480 | that there are paths of infinite length.

03:35:01.240 | That is, that there's no upper bound.

03:35:03.120 | If you know these two things,

03:35:04.240 | you say, I'm trying to get from here to here,

03:35:06.200 | how long do I have to go?

03:35:07.940 | You say, well, I've looked at all the paths of length 10.

03:35:10.840 | Somebody says, that's not good enough.

03:35:12.620 | That path might be of length a billion.

03:35:14.720 | And there's no upper bound on how long that path is.

03:35:17.400 | And that's what leads to the incompleteness theorem.

03:35:19.760 | So, I mean, the thing that is kind of an emerging idea

03:35:24.520 | is you can start asking,

03:35:26.200 | what's the analog of Einstein's equations

03:35:27.840 | in metamathematical space?

03:35:29.760 | What's the analog of a black hole

03:35:31.160 | in metamathematical space?

03:35:33.160 | - What's the hope, so yeah,

03:35:34.940 | it's fascinating to model all the mathematics in this way.

03:35:37.040 | - Well, so here's what it is.

03:35:38.480 | This is mathematics in bulk.

03:35:40.360 | So human mathematicians have made a few million theorems.

03:35:44.040 | They published a few million theorems.

03:35:45.840 | But imagine the infinite future of mathematics.

03:35:48.440 | Apply something to mathematics

03:35:50.440 | that mathematics likes to apply to other things.

03:35:52.360 | Take a limit.

03:35:53.520 | What is the limit of the infinite future of mathematics?

03:35:56.320 | What does it look like?

03:35:57.560 | What is the continuum limit of mathematics?

03:35:59.560 | What is the, as you just fill in more and more

03:36:01.960 | and more theorems, what does it look like?

03:36:04.060 | What does it do?

03:36:05.040 | How does, what kinds of conclusions can you make?

03:36:07.380 | So for example, one thing I've just been doing

03:36:09.800 | is taking Euclid.

03:36:10.960 | So Euclid, very impressive.

03:36:12.760 | He had 10 axioms.

03:36:14.240 | He derived 465 theorems, okay?

03:36:17.400 | His book, you know, that was the sort of defining book

03:36:21.360 | of mathematics for 2000 years.

03:36:23.180 | So you can actually map out,

03:36:26.000 | I actually did this 20 years ago,

03:36:28.800 | but I've done it more seriously now.

03:36:30.740 | You can map out the theorem dependency

03:36:32.680 | of those 465 theorems.

03:36:34.760 | So from the axioms, you grow this graph,

03:36:37.520 | it's actually a multi-way graph,

03:36:39.220 | of how all these theorems get proved from other theorems.

03:36:42.420 | And so you can ask questions about, you know,

03:36:45.240 | well, you can ask things like,

03:36:46.080 | what's the hardest theorem in Euclid?

03:36:47.560 | The answer is, the hardest theorem is

03:36:49.000 | that there are five platonic solids.

03:36:50.980 | That turns out to be the hardest theorem in Euclid.

03:36:52.800 | That's actually his last theorem in all his books.

03:36:55.320 | That's the final-- - What's the hardness,

03:36:56.880 | the distance you have to travel?

03:36:58.480 | - Yeah, let's say it's 33 steps from the,

03:37:01.080 | the longest path in the graph is 33 steps.

03:37:03.740 | So that's the, there's a 33 step path you have to follow

03:37:07.400 | to go from the axioms, according to Euclid's proofs,

03:37:10.920 | to the statement there are five platonic solids.

03:37:13.560 | So, okay, so then-- - Great.

03:37:15.560 | - Then the question is, in, what does it mean,

03:37:20.060 | if you have this map, okay, so, in a sense,

03:37:24.520 | this meta-mathematical space is the infrastructural space

03:37:27.960 | of all possible theorems that you could prove in mathematics.

03:37:31.560 | That's the geometry of meta-mathematics.

03:37:34.340 | There's also the geography of mathematics.

03:37:37.120 | That is, where did people choose to live in space?

03:37:40.760 | And that's what, for example, exploring the sort

03:37:43.040 | of empirical meta-mathematics of Euclid is doing that.

03:37:45.480 | - Each individual, like, human mathematician,

03:37:48.360 | you can embed them into that space.

03:37:49.860 | I mean, they kind of live-- - Yeah, well,

03:37:51.200 | they represent a path in space.

03:37:52.040 | - The little path. - The things they do.

03:37:53.640 | - Maybe a set of paths. - Right.

03:37:55.140 | - So, like, a set of axioms that are chosen.

03:37:58.480 | - Right, so, for example, here's an example

03:38:00.300 | of a thing that I realized.

03:38:01.960 | So, one of the surprising things about,

03:38:03.920 | well, there are two surprising facts about math.

03:38:06.060 | One is that it's hard, and the other is that it's doable.

03:38:09.560 | Okay, so first question is, why is math hard?

03:38:12.640 | You know, you've got these axioms, they're very small.

03:38:15.000 | Why can't you just solve every problem in math easily?

03:38:17.640 | - Yeah, it's just logic.

03:38:19.120 | - Right, yeah, well, logic happens to be

03:38:21.280 | a particular special case that does have

03:38:23.120 | certain simplicity to it.

03:38:25.280 | But general mathematics, even arithmetic,

03:38:27.560 | already doesn't have the simplicity that logic has.

03:38:30.360 | - So, why is it hard?

03:38:31.720 | - Because of computational irreducibility.

03:38:33.840 | - Right.

03:38:34.680 | - Because what happens is, to know what's true,

03:38:38.900 | and this is this whole story about the path

03:38:40.720 | you have to follow, and how long is the path,

03:38:43.000 | and Gödel's theorem is the statement

03:38:44.520 | that the path is not a bounded length,

03:38:47.720 | but the fact that the path is not always compressible

03:38:50.480 | to something tiny is a story

03:38:52.480 | of computational irreducibility.

03:38:54.500 | So, that's why math is hard.

03:38:56.840 | Now, the next question is, why is math doable?

03:38:59.540 | Because it might be the case that most things

03:39:01.560 | you care about don't have finite length paths.

03:39:04.240 | Most things you care about might be things

03:39:06.760 | where you get lost in the sea of computational

03:39:09.000 | irreducibility and worse, undecidability.

03:39:12.580 | That is, there's just no finite length path

03:39:14.780 | that gets you there.

03:39:15.860 | Why is mathematics doable?

03:39:19.100 | Gödel proved his incompleteness theorem in 1931.

03:39:22.260 | Most working mathematicians don't really care about it.

03:39:25.260 | They just go ahead and do mathematics,

03:39:27.260 | even though it could be that the questions

03:39:29.220 | they're asking are undecidable.

03:39:31.060 | It could have been that Fermat's last theorem

03:39:32.920 | is undecidable.

03:39:33.760 | It turned out it had a proof.

03:39:35.160 | It's a long, complicated proof.

03:39:37.020 | The twin prime conjecture might be undecidable.

03:39:40.240 | The Riemann hypothesis might be undecidable.

03:39:43.060 | These things might be, the axioms of mathematics

03:39:45.960 | might not be strong enough to reach those statements.

03:39:49.060 | It might be the case that depending on what axioms

03:39:51.440 | you choose, you can either say that's true

03:39:53.460 | or that's not true.

03:39:54.820 | - And by the way, Fermat's last theorem,

03:39:57.700 | it could be a shorter path.

03:39:59.460 | - Absolutely.

03:40:00.420 | Yeah, so the notion of geodesics in metamathematical space

03:40:03.760 | is a notion of shortest proofs in metamathematical space.

03:40:07.300 | And that's a, you know, human mathematicians

03:40:09.440 | do not find shortest paths,

03:40:11.420 | nor do automated theorem provers.

03:40:13.980 | But the fact, and by the way,

03:40:16.140 | I mean, this stuff is so bizarrely connected.

03:40:18.820 | I mean, if you're into automated theorem proving,

03:40:21.700 | there are these so-called critical pair lemmas

03:40:23.540 | in automated theorem proving.

03:40:24.940 | Those are precisely the branch pairs in our,

03:40:28.620 | that in multi-way graphs.

03:40:30.620 | Let me just finish on the why mathematics is doable.

03:40:32.980 | - Oh yes, the second part.

03:40:34.140 | So we know why it's hard.

03:40:35.780 | Why is it doable?

03:40:36.700 | - Right, why do we not just get lost

03:40:38.180 | in undecidability all the time?

03:40:39.600 | - Yeah.

03:40:40.600 | - So, and here's another fact,

03:40:43.200 | is in doing computer experiments

03:40:45.440 | and doing experimental mathematics,

03:40:47.060 | you do get lost in that way.

03:40:49.060 | When you just say, I'm picking a random integer equation,

03:40:53.900 | how do I, does it have a solution or not?

03:40:56.220 | And you just pick it at random

03:40:57.440 | without any human sort of path getting there.

03:41:00.940 | Often, it's really, really hard.

03:41:03.320 | It's really hard to answer those questions.

03:41:04.780 | We just pick them at random from the space of possibilities.

03:41:07.880 | But what I think is happening is,

03:41:10.740 | and that's a case where you just fell off

03:41:12.500 | into this ocean of sort of irreducibility and so on.

03:41:15.580 | What's happening is,

03:41:16.620 | human mathematics is a story of building a path.

03:41:19.940 | You started off, you're always building out

03:41:23.260 | on this path where you are proving things.

03:41:25.740 | You've got this proof trajectory,

03:41:28.160 | and you're basically, human mathematics

03:41:30.340 | is the sort of the exploration of the world

03:41:34.200 | along this proof trajectory, so to speak.

03:41:36.780 | You're not just parachuting in from anywhere,

03:41:41.780 | you're following Lewis and Clark or whatever.

03:41:44.860 | You're actually going, doing the path.

03:41:48.180 | And the fact that you are constrained to go along that path

03:41:52.100 | is the reason you don't end up with,

03:41:53.780 | every so often, you'll see a little piece

03:41:55.100 | of undecidability and you'll avoid that part of the path.

03:41:58.020 | But that's basically the story

03:41:59.340 | of why human mathematics has seemed to be doable.

03:42:02.660 | It's a story of exploring these paths

03:42:05.220 | that are by their nature, they have been constructed

03:42:08.900 | to be paths that can be followed.

03:42:10.500 | And so you can follow them further.

03:42:12.260 | Now, why is this relevant to anything?

03:42:14.900 | So, okay, so here's my belief.

03:42:19.460 | The fact that human mathematics works that way is,

03:42:23.980 | I think there's some sort of connections

03:42:26.060 | between the way that observers work in physics

03:42:29.700 | and the way that the axiom systems of mathematics

03:42:32.060 | are set up to make mathematics be doable

03:42:34.900 | in that kind of way.

03:42:36.340 | And so, in other words, in particular,

03:42:38.860 | I think there is an analog of causal invariance,

03:42:41.700 | which I think is, and this is again,

03:42:44.820 | it's sort of the upper reaches of mathematics

03:42:46.620 | and stuff that it's a thing,

03:42:50.660 | there's this thing called homotopy type theory,

03:42:52.900 | which is an abstract, it's came out of category theory,

03:42:56.100 | and it's sort of an abstraction of mathematics.

03:42:58.380 | Mathematics itself is an abstraction,

03:43:00.340 | but it's an abstraction of the abstraction of mathematics.

03:43:03.980 | And there is the thing called the univalence axiom,

03:43:06.620 | which is a sort of a key axiom in that set of ideas.

03:43:11.620 | And I'm pretty sure the univalence axiom

03:43:14.180 | is equivalent to causal invariance.

03:43:16.220 | - What was the term used again?

03:43:18.100 | - Univalence.

03:43:18.980 | - Is that something for somebody like me accessible?

03:43:21.580 | Or is this?

03:43:23.260 | - There's a statement of it that's fairly accessible.

03:43:25.540 | I mean, the statement of it is,

03:43:27.100 | basically it says things which are equivalent

03:43:32.740 | can be considered to be identical.

03:43:34.620 | - In which space?

03:43:38.140 | - Yeah, it's in higher category.

03:43:40.420 | - Okay, in category theory.

03:43:41.660 | - Okay, so it's a, but I mean,

03:43:43.860 | the thing just to give a sketch of how that works,

03:43:46.140 | so category theory is an attempt to idealize,

03:43:49.660 | it's an attempt to sort of have a formal theory

03:43:52.020 | of mathematics that is at a sort of higher level

03:43:54.380 | than mathematics.

03:43:55.580 | It's where you just think about these mathematical objects

03:43:59.540 | and these categories of objects

03:44:01.820 | and these morphisms, these connections between categories.

03:44:05.540 | Okay, so it turns out the morphisms and categories,

03:44:08.580 | at least weak categories, are very much like the paths

03:44:12.780 | in our hypergraphs and things.

03:44:14.780 | And it turns out, again, this is where it all gets crazy.

03:44:18.420 | I mean, it's the fact that these things are connected

03:44:20.740 | is just bizarre.

03:44:21.940 | So category theory, our causal graphs

03:44:26.940 | are like second order category theory.

03:44:29.900 | And it turns out you can take the limits

03:44:32.620 | of infinite order category theory.

03:44:34.140 | So just give roughly the idea.

03:44:36.460 | This is a roughly explainable idea.

03:44:39.100 | So a mathematical proof will be a path

03:44:43.380 | that says you can get from this thing to this other thing.

03:44:45.900 | And here's the path that you get from this thing

03:44:47.460 | to this other thing.

03:44:48.700 | But in general, there may be many paths,

03:44:51.140 | many proofs that get you many different paths

03:44:53.940 | that all successfully go from this thing

03:44:55.780 | to this other thing, okay?

03:44:57.660 | Now you can define a higher order proof,

03:45:00.380 | which is a proof of the equivalence of those proofs.

03:45:03.820 | Okay, so you're saying there's a--

03:45:05.100 | - Path between those proofs, essentially.

03:45:07.100 | - Yes, a path between the paths, okay?

03:45:09.780 | And so you do that.

03:45:10.940 | That's the sort of second order thing.

03:45:12.260 | That path between the paths is essentially related

03:45:16.100 | to our causal graphs.

03:45:18.180 | Then you take the limit-- - Ah, wow, okay.

03:45:20.300 | - Path between path between path between path,

03:45:22.980 | the infinite limit, that infinite limit turns out

03:45:26.060 | to be our Rullio multiway system.

03:45:28.700 | - Yeah, the Rullio multiway system,

03:45:31.500 | that's a fascinating thing, both in the physics world

03:45:33.780 | and as you're saying now. - Yeah, yeah.

03:45:35.500 | - That's fascinating.

03:45:36.860 | I'm not sure I've loaded it in completely, but--

03:45:39.020 | - Well, I'm not sure I have either.

03:45:40.220 | And it may be one of these things

03:45:41.420 | where in another five years or something,

03:45:44.580 | it's like, this was obvious, but I didn't see it.

03:45:47.100 | No, but the thing which is sort of interesting to me

03:45:49.300 | is that there's sort of an upper reach of mathematics,

03:45:53.060 | of the abstraction of mathematics.

03:45:55.860 | This thing, there's this mathematician called Grothendieck

03:45:58.980 | who's generally viewed as being sort of

03:46:00.500 | one of the most abstract, sort of creator

03:46:03.020 | of the most abstract mathematics of 1970s-ish timeframe.

03:46:07.860 | And one of the things that he constructed was this thing

03:46:11.500 | he called the infinity groupoid.

03:46:13.220 | And he has this sort of hypothesis

03:46:15.780 | about the inevitable appearance of geometry

03:46:18.340 | from essentially logic in the structure of this thing.

03:46:22.380 | Well, it turns out this Rullio multiway system

03:46:24.620 | is the infinity groupoid.

03:46:26.540 | So it's this limiting object,

03:46:29.620 | and this is an instance of that limiting object.

03:46:33.500 | So what to me is, I mean, again,

03:46:35.420 | I've been always afraid of this kind of mathematics

03:46:37.940 | because it seemed incomprehensibly abstract to me.

03:46:42.220 | But what I'm sort of excited about with this

03:46:45.540 | is that we've sort of concretified

03:46:49.220 | the way that you can reach this kind of mathematics,

03:46:51.820 | which makes it, well, both seem more relevant

03:46:55.220 | and also the fact that that, you know,

03:46:57.380 | I don't yet know exactly what mileage we're gonna get

03:46:59.940 | from using the sort of the apparatus that's been built

03:47:03.300 | in those areas of mathematics to analyze what we're doing.

03:47:06.460 | But the thing that's--

03:47:07.300 | - So both ways, using the mathematics

03:47:09.100 | to understand what you're doing and using,

03:47:11.060 | what you're doing computationally

03:47:12.300 | to understand that mathematics.

03:47:13.140 | - Right, so for example,

03:47:14.180 | the understanding of metamathematical space,

03:47:17.820 | one of the reasons I really want to do that

03:47:19.820 | is because I want to understand quantum mechanics better.

03:47:22.580 | And that, what you see, you know,

03:47:25.940 | we live that kind of the multi-way graph of mathematics

03:47:30.220 | because we actually know this is a theorem we've heard of.

03:47:32.500 | This is another one we've heard of.

03:47:33.980 | We can actually say these are actual things in the world

03:47:36.860 | that we relate to, which we can't really do as readily

03:47:40.700 | for the physics case.

03:47:43.020 | And so it's kind of a way to help my intuition.

03:47:45.140 | It's also, you know, there are bizarre things

03:47:47.780 | like what's the analog of Einstein's equations

03:47:49.980 | in metamathematical space?

03:47:51.860 | What's the analog of a black hole?

03:47:53.740 | You know, it turns out it looks like,

03:47:55.740 | not completely sure yet,

03:47:57.620 | but there's this notion of non-constructive proofs

03:48:00.140 | in mathematics.

03:48:01.460 | And I think those relate to, well, actually,

03:48:04.420 | they relate to things related to event horizons.

03:48:10.380 | So the fact that you can take ideas from physics,

03:48:13.460 | like event horizons--

03:48:14.420 | - And map them into the same kind of space--

03:48:16.740 | - It's really--

03:48:17.980 | - Do you think you might stumble upon some breakthrough

03:48:22.980 | ideas in theorem proving, like from the other direction?

03:48:28.300 | - Yeah, yeah, yeah.

03:48:29.540 | No, I mean, what's really nice is that we are using,

03:48:32.140 | so this absolutely directly maps to theorem proving.

03:48:35.620 | So paths and multi-way graphs,

03:48:37.220 | that's what a theorem prover is trying to do.

03:48:38.500 | - But I also mean like automated theorem proving.

03:48:40.780 | - Yeah, yeah, yeah.

03:48:41.620 | That's what, right, so the finding of paths,

03:48:43.700 | the finding of shortest paths or finding of paths at all

03:48:46.820 | is what automated theorem provers do.

03:48:48.780 | And actually what we've been doing,

03:48:50.980 | so we've actually been using automated theorem proving

03:48:53.740 | both in the physics project to prove things

03:48:56.300 | and using that as a way to understand multi-way graphs.

03:49:00.500 | And because what an automated theorem prover is doing

03:49:04.060 | is it's trying to find a path through a multi-way graph.

03:49:07.380 | And it's critical pair lemmas are precisely little stubs

03:49:11.780 | of branch pairs going off into branchial space.

03:49:15.060 | And that's, I mean, it's really weird.

03:49:16.980 | We have these visualizations in Wolfram language

03:49:19.060 | of proof graphs from our automated theorem proving system.

03:49:24.060 | - And they look reminiscent of--

03:49:25.620 | - Well, it's just bizarre because we made these up

03:49:27.660 | a few years ago and they have these little triangle things.

03:49:30.700 | And they are, we didn't quite get it right.

03:49:32.980 | We didn't quite get the analogy perfectly right,

03:49:35.060 | but it's very close.

03:49:36.740 | Just to say in terms of how these things are connected.

03:49:39.900 | So there's another bizarre connection that I have

03:49:42.140 | to mention because, which again, we don't fully know,

03:49:47.140 | but it's a connection to something else

03:49:51.100 | you might not have thought was in the slightest

03:49:52.620 | bit connected, which is distributed blockchain like things.

03:49:56.780 | Now you might figure out that that's,

03:49:58.100 | you would figure out that that's connected

03:49:59.860 | because it's a story of distributed computing.

03:50:02.820 | And the issue, with a blockchain, you're saying

03:50:05.820 | there's gonna be this one ledger that globally says,

03:50:09.620 | this is what happened in the world.

03:50:11.660 | But that's a bad deal if you've got all these

03:50:14.740 | different transactions that are happening.

03:50:16.300 | And this transaction in country A doesn't have

03:50:21.220 | to be reconciled with the transaction in country B,

03:50:23.980 | at least not for a while.

03:50:25.340 | And that story is just like what happens

03:50:29.340 | with our causal graphs.

03:50:30.980 | That whole reconciliation thing is just like what happens

03:50:33.580 | with light cones and all this kind of thing.

03:50:35.660 | - Yeah, so that's where the causal invariance

03:50:36.780 | comes into play.

03:50:37.620 | I mean, that's, you know, most of your conversations

03:50:40.620 | are about physics, but it's kind of funny

03:50:43.060 | that this probably and possibly might have even bigger

03:50:48.060 | impact and revolutionary ideas

03:50:52.140 | in totally other disciplines.

03:50:53.980 | - Right, so the question is, why is that happening?

03:50:57.100 | Right, and the reason it's happening,

03:50:59.140 | I've thought about this, obviously,

03:51:00.700 | because I like to think about these meta questions

03:51:02.740 | of, you know, what's happening is this model

03:51:05.340 | that we have is an incredibly minimal model.

03:51:08.700 | And once you have an incredibly minimal model,

03:51:11.300 | and this happened with cellular automata as well,

03:51:13.580 | cellular automata are an incredibly minimal model.

03:51:15.980 | And so it's inevitable that it gets used,

03:51:19.140 | sort of an upstream thing that gets used

03:51:21.180 | in lots of different places.

03:51:22.660 | And it's like, you know, the fact that it gets used,

03:51:25.220 | you know, cellular automata are sort of a minimal model

03:51:27.340 | of like, say, road traffic flow or something.

03:51:29.100 | And they're also a minimal model of something

03:51:31.180 | in, you know, chemistry.

03:51:32.060 | And they're also a minimal model of something

03:51:33.540 | in epidemiology, right?

03:51:35.820 | It's because they're such a simple model

03:51:37.420 | that they can, that they apply

03:51:38.860 | to all these different things.

03:51:40.260 | Similarly, this model that we have of the physics project

03:51:43.020 | is another, cellular automata are a minimal model

03:51:47.260 | of parallel, of basically of parallel computation

03:51:50.540 | where you've defined space and time.

03:51:52.780 | These models are minimal models

03:51:54.780 | where you have not defined space and time.

03:51:57.140 | And they have been very hard to understand in the past.

03:52:00.300 | But the, I think the, perhaps the most important breakthrough

03:52:03.700 | there is the realization that these are models of physics.

03:52:07.380 | And therefore that you can use everything

03:52:09.140 | that's been developed in physics to get intuition

03:52:11.940 | about how things like that work.

03:52:13.820 | And that's why you can potentially use ideas from physics

03:52:17.420 | to get intuition about how to do parallel computing.

03:52:20.060 | And because the underlying model is the same.

03:52:24.380 | And, but we have all of this achievement in physics.

03:52:26.980 | I mean, you know, you might say,

03:52:28.380 | oh, you've come up with the fundamental theory of physics.

03:52:30.060 | That throws out what people have done in physics before.

03:52:32.420 | Well, it doesn't, but also the real power

03:52:35.460 | is to use what's been done before in physics

03:52:37.860 | to apply it in these other places.

03:52:39.540 | - Yes, absolutely.

03:52:41.420 | - This kind of brings up, I know you probably don't

03:52:44.060 | particularly love commenting on the work of others,

03:52:48.740 | but let me bring up a couple of personalities

03:52:51.180 | just 'cause it's fun and people are curious about it.

03:52:53.580 | So there's Sabine Hassenfelder.

03:52:58.620 | I don't know if you're familiar with her.

03:53:00.420 | She wrote this book that I need to read,

03:53:04.860 | but it based, I forget what the title is,

03:53:06.900 | but it's "Beauty Leads Us Astray in Physics"

03:53:10.420 | is a subtitle, something like that.

03:53:12.340 | Which so much about what we're talking about now,

03:53:15.060 | like this simplification is to us humans

03:53:19.340 | seems to be beautiful.

03:53:20.380 | Like there's a certain intuition with physicists,

03:53:23.460 | with people that a simple theory, like this reducibility,

03:53:27.980 | pockets of reducibility is the ultimate goal.

03:53:30.500 | And I think what she tries to argue is,

03:53:33.260 | no, we just need to come up with theories

03:53:37.660 | that are just really good at predicting physical phenomena.

03:53:40.540 | It's okay to have a bunch of disparate theories

03:53:44.300 | as opposed to trying to chase this beautiful theory

03:53:48.500 | of everything is the ultimate beautiful theory, a simple one.

03:53:52.140 | What's your response to that?

03:53:54.540 | - Well, so what you're quoting,

03:53:56.180 | so I don't know that Sabine Hossenfelder's,

03:53:59.780 | exactly what she said, but I mean-

03:54:00.620 | - You might be misquoting the title of her book.

03:54:03.740 | - Okay, well, let me respond to what you were describing,

03:54:07.740 | which may or may not have anything to do

03:54:09.340 | with what Sabine Hossenfelder says or thinks.

03:54:14.340 | - Sorry, Sabine.

03:54:15.500 | - The, right.

03:54:17.140 | - Sorry for misquoting.

03:54:18.260 | - But I mean, the question is,

03:54:23.340 | is beauty a guide to whether something is correct?

03:54:26.580 | Which is kind of also the story of Occam's razor.

03:54:29.260 | If you've got a bunch of different explanations of things,

03:54:32.180 | is the thing that is the simplest explanation

03:54:34.540 | likely to be the correct explanation?

03:54:36.620 | And there are situations where that's true

03:54:38.180 | and there are situations where it isn't true.

03:54:39.980 | Sometimes in human systems, it is true

03:54:41.940 | because people have kind of,

03:54:43.180 | in evolutionary systems, sometimes it's true

03:54:45.260 | because it's sort of been kicked

03:54:46.860 | to the point where it's minimized.

03:54:49.380 | But in physics, does Occam's razor work?

03:54:53.300 | Is there a simple, quote,

03:54:55.660 | "beautiful explanation for things," or is it a big mess?

03:54:58.740 | We don't intrinsically know.

03:55:01.900 | I think that the, I wouldn't,

03:55:03.660 | before I worked on the project in recent times,

03:55:07.180 | I would have said, "We do not know how complicated

03:55:09.860 | "the rule for the universe will be."

03:55:12.140 | And I would have said,

03:55:13.580 | the one thing we know,

03:55:15.940 | which is a fundamental fact about science,

03:55:17.780 | that's the thing that makes science possible,

03:55:19.740 | is that there is order in the universe.

03:55:21.860 | I mean, early theologians would have used that

03:55:24.860 | as an argument for the existence of God,

03:55:27.140 | because it's like, why is there order in the universe?

03:55:29.420 | Why doesn't every single particle in the universe

03:55:31.500 | just do its own thing?

03:55:32.660 | Something must be making there be order in the universe.

03:55:37.180 | We, in the sort of early theology point of view,

03:55:41.820 | that's, the role of God is to do that, so to speak.

03:55:45.180 | In our, we might say it's the role

03:55:48.180 | of a formal theory to do that.

03:55:50.140 | And then the question is, but how simple

03:55:51.820 | should that theory be?

03:55:53.260 | And should that theory be one that,

03:55:55.300 | where I think the point is, if it's simple,

03:56:00.620 | it's almost inevitably somewhat beautiful

03:56:03.180 | in the sense that, because all the stuff that we see

03:56:06.460 | has to fit into this little tiny theory.

03:56:08.740 | And the way it does that has to be,

03:56:10.860 | it depends on your notion of beauty,

03:56:13.300 | but I mean, for me, the sort of the surprising

03:56:17.940 | connectivity of it is, at least in my aesthetic,

03:56:21.980 | that's something that responds to my aesthetic.

03:56:25.100 | - But the question is, I mean, you're a fascinating person

03:56:29.660 | in the sense that you're at once talking about computational,

03:56:34.460 | the fundamental computational reducibility of the universe,

03:56:37.940 | and on the other hand, trying to come up

03:56:41.220 | with a theory of everything, which simply describes

03:56:44.340 | the simple origins of that computational reducibility.

03:56:49.340 | I mean, both of those things are kind of,

03:56:53.820 | it's paralyzing to think that we can't make any sense

03:56:56.340 | of the universe in the general case,

03:56:58.580 | but it's hopeful to think, like, one,

03:57:01.460 | we can think of a rule that generates this whole complexity,

03:57:05.980 | and two, we can find pockets of reducibility

03:57:10.980 | that are powerful for our everyday life

03:57:13.660 | to do different kinds of predictions.

03:57:15.780 | I suppose Sabine wants to find,

03:57:19.300 | focus on the finding of small pockets of reducibility

03:57:23.180 | versus the theory of everything.

03:57:26.980 | - You know, it's a funny thing because, you know,

03:57:29.700 | a bunch of people have started working on this,

03:57:32.180 | you know, physics project, people who are, you know,

03:57:34.620 | physicists, basically, and it is really

03:57:38.220 | a fascinating sociological phenomenon

03:57:40.060 | because what, you know, when I was working on this before

03:57:44.020 | in the 1990s, you know, wrote it up,

03:57:47.780 | put it, it's 100 pages of this 1200 page book

03:57:50.300 | that I wrote, "New Kind of Science,"

03:57:51.540 | it's, you know, 100 pages of that is about physics.

03:57:54.380 | But I saw it at that time, not as a pinnacle achievement,

03:57:59.380 | but rather as a use case, so to speak.

03:58:02.060 | I mean, my main point was this new kind of science,

03:58:04.340 | and it's like, you can apply it to biology,

03:58:06.180 | you can apply it to, you know, other kinds of physics,

03:58:08.660 | you can apply it to fundamental physics.

03:58:09.980 | It's just an application, so to speak.

03:58:12.620 | It's not the core thing.

03:58:14.940 | But then, you know, one of the things

03:58:17.740 | that was interesting with that book was, you know,

03:58:21.380 | book comes out, lots of people think it's pretty interesting

03:58:24.820 | and lots of people start using what it has

03:58:26.700 | in different kinds of fields.

03:58:28.300 | The one field where there was sort of a heavy pitchforking

03:58:32.700 | was from my friends, the fundamental physics people,

03:58:36.140 | which was, it's like, no, this can't possibly be right.

03:58:38.900 | And, you know, it's like, you know,

03:58:40.420 | if what you're doing is right,

03:58:41.740 | it'll overturn 50 years of what we've been doing.

03:58:44.420 | And it's like, no, it won't, was what I was saying.

03:58:47.180 | And it's like, but, you know, for a while,

03:58:51.020 | when I started, you know, I was going to go on

03:58:53.300 | back in 2002, well, 2004, actually,

03:58:55.980 | I was going to go on working on this project.

03:58:58.700 | And I actually stopped, partly because it's like,

03:59:01.620 | why am I, you know, this is like,

03:59:04.140 | I've been in business a long time, right?

03:59:05.580 | I'm building a product for a target market

03:59:08.300 | that doesn't want the product.

03:59:09.900 | And it's like--

03:59:10.860 | - Why work, yeah, yeah, why work against,

03:59:13.460 | swim against the current or whatever.

03:59:14.820 | - Right, but you see what's happened,

03:59:16.300 | which is sort of interesting,

03:59:17.380 | is that a couple of things happened.

03:59:19.700 | And it was like, you know, it was like,

03:59:23.660 | I don't want to do this project

03:59:25.900 | because I can do so many other things,

03:59:28.700 | which I'm really interested in,

03:59:30.580 | where, you know, people say, great, thanks for those tools,

03:59:34.260 | thanks for those ideas, et cetera.

03:59:36.540 | Whereas, you know, if you're dealing with kind of a,

03:59:39.140 | you know, sort of a structure where people are saying,

03:59:42.980 | no, no, we don't want this new stuff,

03:59:44.380 | we don't need any new stuff,

03:59:45.460 | we're really fine with what we're doing.

03:59:46.300 | - Yeah, there's like literally, like, I don't know,

03:59:48.460 | millions of people who are thankful for Wolfram Alpha,

03:59:51.300 | a bunch of people wrote to me how thankful,

03:59:53.420 | they are a different crowd

03:59:55.620 | than the theoretical physics community, perhaps.

03:59:57.980 | - Yeah, well, right, but you know,

03:59:59.100 | the theoretical physics community

04:00:00.420 | pretty much uniformly uses

04:00:01.940 | Wolfram language and Mathematica, right?

04:00:04.580 | And so it's kind of like, you know,

04:00:07.780 | and that's, but the thing is, what happens,

04:00:10.820 | you know, this is what happens,

04:00:12.300 | mature fields do not, you know,

04:00:15.140 | it's like, we're doing what we're doing,

04:00:16.580 | we have the methods that we have,

04:00:18.420 | and we're just fine here.

04:00:20.420 | Now, what's happened in the last 18 years or so,

04:00:23.580 | I think there's a couple of things have happened.

04:00:25.620 | First of all, the hope that, you know,

04:00:29.420 | string theory or whatever

04:00:30.460 | would deliver the fundamental theory of physics,

04:00:32.660 | that hope has disappeared.

04:00:34.740 | That the, another thing that's happened is the,

04:00:37.500 | the sort of the interest in computation around physics

04:00:41.220 | has been greatly enhanced by the whole quantum information,

04:00:44.180 | quantum computing story.

04:00:46.220 | People, you know, the idea

04:00:47.260 | there might be something sort of computational

04:00:50.140 | related to physics has somehow grown.

04:00:53.260 | And I think, you know, it's sort of interesting,

04:00:55.980 | I mean, right now, if we say, you know,

04:00:58.260 | it's like, if you're like,

04:00:59.860 | who else is trying to come up

04:01:00.980 | with the fundamental theory of physics?

04:01:02.620 | It's like, there aren't professional,

04:01:04.660 | no professional physicists. - Oh, no professional.

04:01:06.020 | - No professional physicists.

04:01:07.420 | - What are your, I mean, you've talked with him,

04:01:11.020 | but just as a matter of personalities,

04:01:13.020 | 'cause it's a beautiful story,

04:01:14.020 | what are your thoughts about Eric Weinstein's work?

04:01:17.340 | - You know, I think his, I mean,

04:01:20.780 | he did a PhD thesis in mathematical physics at Harvard.

04:01:23.660 | - He's a mathematical physicist.

04:01:24.740 | - And, you know, it's, it seems like it's kind of,

04:01:29.100 | you know, it's in that framework

04:01:31.100 | and it's kind of like, I'm not sure how much further

04:01:34.220 | it's got than his PhD thesis,

04:01:36.060 | which was 20 years ago or something.

04:01:37.740 | And I think that, you know,

04:01:39.540 | it's a fairly specific piece of mathematical physics

04:01:43.940 | that's quite nice.

04:01:45.100 | And- - What trajectory

04:01:46.660 | do you hope it takes?

04:01:47.700 | I mean- - Well, I think

04:01:49.220 | in his particular case, I mean, from what I understand,

04:01:51.540 | which is not everything at all,

04:01:53.100 | but, you know, I think I know the rough tradition,

04:01:55.020 | at least, that he's operating in

04:01:56.740 | is sort of theory of gauge theories.

04:01:59.180 | - Gauge theories, yeah.

04:02:00.020 | - Local gauge invariance and so on.

04:02:01.260 | Okay, we are very close to understanding

04:02:04.380 | how local gauge invariance works in our models

04:02:06.420 | and it's very beautiful and it's very,

04:02:09.580 | and, you know, does some of the mathematical structure

04:02:12.460 | that he's enthusiastic about fit?

04:02:14.540 | Quite possibly, yes.

04:02:15.980 | - So there might be a possibility of trying to understand

04:02:17.900 | how those things fit, how gauge theory fits.

04:02:19.940 | - Yeah, might very well.

04:02:20.780 | I mean, the question is, you know,

04:02:22.180 | so there are a couple of things

04:02:23.020 | one might try to get in the world.

04:02:24.260 | So for example, it's like,

04:02:25.820 | can we get three dimensions of space?

04:02:27.260 | We haven't managed to get that yet.

04:02:29.020 | Gauge theory, the standard model of particle physics says

04:02:32.540 | that it's SU3 cross SU2 cross U1.

04:02:35.780 | Those are the designations of these Lie groups.

04:02:40.140 | It doesn't, but anyway, so those are sort of

04:02:42.860 | representations of symmetries of the theory.

04:02:46.620 | And so, you know, it is conceivable

04:02:50.220 | that it is generically true.

04:02:52.780 | Okay, so all those are subgroups of a group called E8,

04:02:55.460 | which is a weird, exceptional Lie group.

04:02:59.100 | Okay, it is conceivable, I don't know whether it's the case,

04:03:02.220 | that that will be generic in these models,

04:03:05.220 | that it will be generic,

04:03:06.900 | that the gauge invariance of the model has this property,

04:03:11.900 | just as things like general relativity,

04:03:15.220 | which corresponds to a thing called general covariance,

04:03:20.220 | which is another gauge-like invariance.

04:03:23.780 | It could conceivably be the case

04:03:26.020 | that the kind of local gauge invariance

04:03:28.100 | that we see in particle physics is somehow generic.

04:03:31.260 | And that would be a, you know,

04:03:32.980 | the thing that's really cool, I think, you know,

04:03:36.020 | sociologically, although this hasn't really hit yet,

04:03:38.740 | is that all of these different things,

04:03:40.700 | all these different things people have been working on

04:03:42.300 | in these, in some cases, quite abstruse areas

04:03:45.740 | of mathematical physics, an awful lot of them

04:03:48.060 | seem to tie into what we're doing.

04:03:50.100 | And, you know, it might not be that way.

04:03:51.900 | - Yeah, absolutely.

04:03:52.740 | That's a beautiful thing of the theory.

04:03:54.220 | I mean, but the reason I,

04:03:56.140 | the reason Erick Weinstein is important

04:03:58.580 | is to the point that you mentioned before,

04:04:00.660 | which is it's strange that the theory of everything

04:04:04.860 | is not at the core of the passion, the dream,

04:04:09.860 | the focus, the funding of the physics community.

04:04:14.620 | - It's too hard.

04:04:15.580 | It's too hard, and people gave up.

04:04:19.340 | I mean, basically what happened is,

04:04:21.500 | ancient Greece, people thought we're nearly there.

04:04:24.340 | You know, the world is made of platonic solids.

04:04:26.340 | It's, you know, water is a tetrahedron or something.

04:04:29.100 | We're almost there, okay?

04:04:30.980 | Long period of time where people were like,

04:04:33.380 | no, we don't know how it works.

04:04:35.180 | You know, time of Newton, you know, we're almost there.

04:04:38.220 | Everything is gravitation.

04:04:39.900 | You know, time of Faraday and Maxwell, we're almost there.

04:04:43.500 | Everything is fields.

04:04:44.380 | Everything is the ether.

04:04:46.020 | You know, then--

04:04:47.100 | - And the whole time we're making big progress, though.

04:04:49.940 | - Oh, yes, absolutely.

04:04:51.140 | But the fundamental theory of physics is almost a footnote

04:04:54.820 | because it's like, it's the machine code.

04:04:57.820 | It's like, we're operating in the high-level languages.

04:05:00.260 | - Yeah.

04:05:01.140 | - You know, that's what we really care about.

04:05:02.580 | That's what's relevant for our everyday physics.

04:05:04.580 | - You talked about different centuries,

04:05:06.020 | and the 21st century will be everything is computation.

04:05:09.700 | - Yes.

04:05:10.540 | - If that takes us all the way, we don't know,

04:05:12.460 | but it might take us pretty far.

04:05:14.100 | - Yes, right, that's right.

04:05:15.540 | But I think the point is that it's like, you know,

04:05:17.620 | if you're doing biology, you might say,

04:05:19.300 | "How can you not be really interested

04:05:20.820 | "in the origin of life and the definition of life?"

04:05:23.420 | Well, it's irrelevant.

04:05:24.300 | You know, you're studying the properties of some virus.

04:05:26.700 | It doesn't matter, you know, where, you know,

04:05:28.700 | you're operating at some much higher level.

04:05:31.300 | And it's the same, what's happened with physics is,

04:05:34.820 | I was sort of surprised, actually.

04:05:36.100 | I was sort of mapping out this history of people's efforts

04:05:39.460 | to understand the fundamental theory of physics.

04:05:41.900 | And it's remarkable how little has been done

04:05:44.580 | on this question.

04:05:45.820 | And it's, you know, because, you know,

04:05:47.660 | there've been times when there's been bursts of enthusiasm.

04:05:49.940 | Oh, we're almost there.

04:05:51.500 | And then it decays, and people just say,

04:05:55.420 | "Oh, it's too hard, but it's not relevant anyway."

04:05:57.820 | And I think that the thing that, you know,

04:06:01.660 | so the question of, you know,

04:06:04.620 | one question is why does anybody,

04:06:06.020 | why should anybody care, right?

04:06:07.980 | Why should anybody care

04:06:09.060 | what the fundamental theory of physics is?

04:06:10.940 | I think it's intellectually interesting,

04:06:13.100 | but what will be the sort of,

04:06:14.820 | what will be the impact of this?

04:06:16.460 | - What, I mean, this is the key question.

04:06:18.900 | What do you think will happen

04:06:20.660 | if we figure out the fundamental theory of physics?

04:06:25.260 | - Right.

04:06:26.100 | - Outside of the intellectual curiosity of us.

04:06:28.140 | - Okay, so here's my best guess, okay?

04:06:31.340 | So if you look at the history of science,

04:06:33.540 | I think a very interesting analogy is Copernicus.

04:06:37.420 | Okay, so what did Copernicus do?

04:06:39.740 | There'd been this Ptolemaic system

04:06:41.340 | for working out the motion of planets.

04:06:43.260 | It did pretty well.

04:06:44.740 | It used epicycles, et cetera, et cetera, et cetera.

04:06:47.100 | It had all this computational ways

04:06:49.340 | of working out what planets will be.

04:06:51.180 | When we work out where planets are today,

04:06:52.740 | we're basically using epicycles.

04:06:54.860 | But Copernicus had this different way of formulating things

04:06:58.060 | in which he said, you know,

04:07:00.180 | "And the Earth is going around the sun."

04:07:02.980 | And that had a consequence.

04:07:04.180 | The consequence was you can use this mathematical theory

04:07:07.900 | to conclude something which is absolutely not

04:07:10.740 | what we can tell from common sense, right?

04:07:14.140 | So it's like, trust the mathematics, trust the science.

04:07:17.860 | Okay, now fast forward 400 years,

04:07:21.060 | and now we're in this pandemic,

04:07:23.900 | and it's kind of like everybody thinks

04:07:25.660 | the science will figure out everything.

04:07:28.260 | It's like, from the science,

04:07:30.020 | we can just figure out what to do.

04:07:31.340 | We can figure out everything.

04:07:32.940 | That was before Copernicus.

04:07:34.820 | Nobody would have thought if the science says something

04:07:37.700 | that doesn't agree with our everyday experience,

04:07:40.820 | where we just have to compute the science

04:07:43.220 | and then figure out what to do.

04:07:44.460 | People say that's completely crazy.

04:07:46.420 | - And so your sense is,

04:07:47.620 | once we figure out the framework of computation

04:07:49.860 | that can basically do any,

04:07:51.820 | understand the fabric of reality,

04:07:53.820 | we'll be able to derive totally counterintuitive things.

04:07:58.820 | - No, the point, I think, is the following,

04:08:01.140 | that right now, I talk about computational irreducibility.

04:08:05.780 | People, I was very proud that I managed

04:08:08.260 | to get the term computational irreducibility

04:08:10.180 | into the congressional record last year.

04:08:13.060 | - That's right, by the way.

04:08:13.900 | That's a whole 'nother topic we could talk about.

04:08:15.380 | Fascinating. - Different topic.

04:08:16.700 | - Different day. - Different topic.

04:08:18.260 | But in any case, so computational irreducibility

04:08:22.180 | is one of these sort of concepts

04:08:23.940 | that I think is important in understanding

04:08:25.460 | lots of things in the world.

04:08:27.020 | But the question is, it's only important

04:08:29.220 | if you believe the world is fundamentally computational.

04:08:33.180 | But if you know the fundamental theory of physics

04:08:36.020 | and it's fundamentally computational,

04:08:38.300 | then you've rooted the whole thing.

04:08:40.260 | That is, you know the world is computational.

04:08:43.180 | And while you can discuss whether,

04:08:46.060 | it's not the case that people would say,

04:08:48.860 | well, you have this whole computational irreducibility,

04:08:50.980 | all these features of computation,

04:08:52.620 | we don't care about those

04:08:54.140 | because after all, the world isn't computational,

04:08:56.220 | you might say.

04:08:57.340 | But if you know, base, base, base thing,

04:09:01.300 | physics is computational,

04:09:03.220 | then you know that that stuff is,

04:09:05.260 | you know, that that's kind of the grounding for that stuff.

04:09:07.700 | Just as in a sense, Copernicus was the grounding

04:09:10.540 | for the idea that you could figure out something

04:09:12.900 | with math and science that was not what you

04:09:17.380 | would intuitively think from your senses.

04:09:20.100 | So now we've got to this point where, for example,

04:09:22.820 | we say, you know, once we have the idea

04:09:25.260 | that computation is the foundational thing

04:09:27.980 | that explains our whole universe,

04:09:30.140 | then we have to say, well,

04:09:31.380 | what does it mean for other things?

04:09:32.820 | Like it means there's computational irreducibility.

04:09:35.260 | That means science is limited in certain ways.

04:09:37.900 | That means this, that means that.

04:09:39.780 | But the fact that we have that grounding means that,

04:09:43.300 | you know, and I think for example,

04:09:44.820 | for Copernicus, for instance,

04:09:47.220 | the implications of his work

04:09:49.180 | on the set of mathematics of astronomy were cool,

04:09:52.380 | but they involved a very small number of people.

04:09:54.580 | The implications of his work for sort of the philosophy

04:09:56.940 | of how you think about things were vast

04:09:59.860 | and involved, you know, everybody more or less.

04:10:02.860 | - But do you think, so that's actually the way scientists

04:10:05.780 | and people see the world around us.

04:10:08.580 | So it has a huge impact in that sense.

04:10:10.620 | Do you think it might have an impact more directly

04:10:14.260 | to engineering derivations from physics,

04:10:18.140 | like propulsion systems, our ability to colonize the world?

04:10:22.020 | Like for example, okay, this is like sci-fi,

04:10:24.640 | but if you understand the computational nature,

04:10:29.920 | say, of the different forces of physics,

04:10:34.000 | you know, there's a notion of being able to,

04:10:37.240 | you know, warp gravity, things like this.

04:10:39.040 | - Yeah, can we make warp drive?

04:10:40.520 | - Warp drive, yeah.

04:10:41.760 | So like, would we be able to, will it,

04:10:44.160 | will, you know, will like Elon Musk start paying attention?

04:10:47.640 | Like it's awfully costly to launch these rockets.

04:10:50.520 | Do you think we'll be able to, yeah, create warp drive?

04:10:52.880 | - Right, you know, I set myself some homework.

04:10:55.400 | I agreed to give a talk at some NASA workshop

04:10:57.640 | in a few weeks about faster than light travel.

04:10:59.920 | So I haven't figured it out yet, but no, but--

04:11:02.800 | - You got two weeks.

04:11:03.640 | - Yeah, right.

04:11:04.460 | - But do you think that kind of understanding

04:11:06.320 | of fundamental theory of physics

04:11:07.640 | can lead to those engineering breakthroughs?

04:11:09.640 | - Okay, I think it's far away, but I'm not certain.

04:11:12.120 | I mean, you know, this is the thing that,

04:11:14.760 | I set myself an exercise when gravity waves,

04:11:17.040 | gravitational waves were discovered, right?

04:11:19.300 | I set myself the exercise of

04:11:21.000 | what would black hole technology look like?

04:11:23.880 | In other words, right now, you know,

04:11:25.340 | black holes are far away.

04:11:26.480 | They're, you know, how on earth can we do things with them?

04:11:28.120 | But just imagine that we could get, you know,

04:11:30.120 | pet black holes right in our backyard.

04:11:32.480 | You know, what kind of technology could we build with them?

04:11:34.520 | I got a certain distance, not that far.

04:11:36.720 | But I think in, you know, so there are ideas.

04:11:39.840 | You know, I have this, one of the weirder ideas

04:11:42.000 | is things I'm calling space tunnels,

04:11:44.160 | which are higher dimensional pieces of space time,

04:11:47.840 | where basically you can, you know,

04:11:50.040 | in our three-dimensional space,

04:11:52.000 | there might be a five-dimensional, you know, region,

04:11:55.480 | which actually will appear as a white hole

04:11:57.040 | at one end and a black hole at the other end.

04:11:59.320 | You know, who knows whether they exist?

04:12:01.080 | And then the question's another one,

04:12:02.760 | okay, this is another crazy one,

04:12:04.480 | is the thing that I'm calling a vacuum cleaner, okay?

04:12:07.640 | So I mentioned that, you know,

04:12:10.660 | there's all this activity in the universe,

04:12:12.620 | which is maintaining the structure of space.

04:12:15.000 | And that leads to a certain energy density,

04:12:18.280 | effectively, in space.

04:12:20.120 | And so the question, in fact, dark energy

04:12:23.640 | is a story of essentially negative mass

04:12:26.840 | produced by the absence of energy

04:12:30.960 | you thought would be there, so to speak.

04:12:33.200 | And we don't know exactly how it works

04:12:34.840 | in either our model or the physical universe,

04:12:37.720 | but this notion of a vacuum cleaner

04:12:40.620 | is a thing where, you know, you have all these things

04:12:43.080 | that are maintaining the structure of space,

04:12:44.520 | but what if you could clean out some of that stuff

04:12:47.600 | that's maintaining the structure of space

04:12:49.480 | and make a simpler vacuum somewhere?

04:12:51.600 | - Yeah. - You know, what would that do?

04:12:52.880 | - Totally different kind of vacuum.

04:12:54.240 | - Right, and that would lead to negative energy density,

04:12:57.220 | which would need to, so gravity is usually

04:12:59.460 | a purely attractive force, but negative mass

04:13:02.480 | would lead to repulsive gravity

04:13:06.220 | and lead to all kinds of weird things.

04:13:08.560 | Now, can it be done in our universe?

04:13:11.280 | You know, my immediate thought is no,

04:13:14.840 | but, you know, the fact is that, okay, so--

04:13:18.440 | - Well, once you understand the fact,

04:13:19.640 | 'cause you're saying, like, at this level of abstraction,

04:13:21.600 | you can reach to the lower levels and mess with it.

04:13:25.480 | - Yes. - Once you understand

04:13:26.840 | the levels, I think you can start to--

04:13:29.000 | - I know, and I'm, you know, I have to say

04:13:30.760 | that this reminds me of people telling one years ago

04:13:34.720 | that, you know, you'll never transmit data

04:13:36.360 | over a copper wire at more than 1,000, you know,

04:13:39.680 | 1,000 baud or something, right?

04:13:41.520 | And this is, why did that not happen?

04:13:44.000 | You know, why do we have these much, much faster

04:13:46.240 | data transmission?

04:13:47.080 | Because we've understood many more of the details

04:13:48.920 | of what's actually going on.

04:13:50.480 | And it's the same exact story here.

04:13:52.600 | And it's the same, you know, I think that this,

04:13:54.800 | as I say, I think one of the features of sort of,

04:13:58.640 | one of the things about our time

04:14:00.600 | that will seem incredibly naive in the future

04:14:03.080 | is the belief that, you know, things like heat

04:14:06.280 | is just random motion of molecules,

04:14:08.440 | that it's just, just throw up your hands,

04:14:11.360 | it's just random, we can't say anything about it.

04:14:14.120 | That will seem naive.

04:14:15.680 | - Yeah, at the heat death of the universe,

04:14:18.160 | those particles would be laughing at us humans

04:14:20.400 | thinking that life is not beautiful.

04:14:23.640 | - Right, we'll have a whole civilization, you know.

04:14:25.960 | - Humans used to think they're special

04:14:27.600 | with their little brains.

04:14:29.000 | - Well, right, but also, and they used to think

04:14:31.280 | that this would just be random and uninteresting.

04:14:33.960 | But that's, but so this question about whether you can,

04:14:37.640 | you know, mess with the underlying structure

04:14:40.000 | and how you find a way to mess

04:14:41.320 | with the underlying structure, that's a, you know,

04:14:44.040 | I have to say, you know, my immediate thing is,

04:14:47.000 | boy, that seems really hard.

04:14:48.800 | But then, and, you know, possibly computational

04:14:52.240 | irreducibility will bite you,

04:14:54.000 | but then there's always some path

04:14:55.520 | of computational reducibility.

04:14:57.360 | And that path of computational reducibility

04:14:59.720 | is the engineering invention that has to be made.

04:15:02.520 | - Those little pockets can have huge engineering impact.

04:15:05.960 | - Right, and I think that that's right.

04:15:07.760 | And I mean, we live in, you know,

04:15:09.120 | we make use of so many of those pockets.

04:15:11.400 | And the fact is, you know, I, you know, this is, yes,

04:15:16.960 | it's a, you know, it's one of these things where,

04:15:20.360 | where, you know, I'm a person who likes to figure out ideas

04:15:24.720 | and so on, and there's sort of tests

04:15:26.400 | of my level of imagination, so to speak.

04:15:29.120 | And so a couple of places where there's sort

04:15:32.080 | of serious humility in terms of my level of imagination.

04:15:35.440 | One is this thing about different reference frames

04:15:38.160 | for understanding the universe, where like,

04:15:40.600 | imagine the physics of the aliens, what will it be like?

04:15:43.600 | And I'm like, that's really hard.

04:15:45.720 | I don't know, you know?

04:15:47.440 | And I mean, I think-

04:15:48.280 | - But once you have the framework in place,

04:15:49.920 | you can at least reason about the things you don't know.

04:15:53.600 | - Yes. - Or maybe can't know,

04:15:55.200 | or like it's too hard for you to know.

04:15:57.560 | But then the mathematics can, that's exactly it.

04:16:01.560 | Allow you to reach beyond what you can reason about.

04:16:05.400 | - Right, so I'm, you know, I'm trying to not have,

04:16:09.160 | you know, if you think back to Alan Turing, for example,

04:16:11.640 | and, you know, when he invented Turing machines,

04:16:13.880 | you know, and imagining what computers would end up doing,

04:16:16.960 | so to speak.

04:16:17.800 | - Yeah.

04:16:18.640 | - You know, and it's- - It's very difficult.

04:16:19.960 | - It's difficult, right.

04:16:21.000 | And it's, I mean, this thing-

04:16:21.840 | - He made a few reasonable predictions,

04:16:23.440 | but most of it he couldn't predict, possibly.

04:16:25.480 | - By the time, by 1950, he was making reasonable predictions

04:16:28.280 | about something.

04:16:29.120 | - But not the '30s, yeah.

04:16:30.080 | - Right, not when he first, you know, conceptualized,

04:16:34.600 | you know, and he conceptualized universal computing

04:16:37.320 | for a very specific mathematical reason

04:16:39.120 | that wasn't as general.

04:16:41.280 | But yes, it's a good sort of exercise in humility

04:16:44.160 | to realize that it's kind of like,

04:16:46.760 | it's really hard to figure these things out.

04:16:49.520 | The engineering of the universe,

04:16:52.200 | if we know how the universe works, how can we engineer it?

04:16:55.800 | - That's such a beautiful vision.

04:16:57.520 | That's such a beautiful-

04:16:58.360 | - By the way, I have to mention one more thing,

04:16:59.680 | which is the ultimate question from physics is,

04:17:04.200 | okay, so we have this abstract model of the universe.

04:17:07.280 | Why does the universe exist at all, right?

04:17:11.160 | So, you know, we might say there is a formal model

04:17:15.120 | that if you run this model, you get the universe,

04:17:18.000 | or the model gives you, you know,

04:17:20.440 | a model of the universe, right?

04:17:22.000 | You run this mathematical thing,

04:17:25.160 | and the mathematics unfolds in the way

04:17:27.720 | that corresponds to the universe.

04:17:29.320 | But the question is, why was that actualized?

04:17:32.320 | Why does the actual universe actually exist?

04:17:35.840 | And so this is another one of these humility,

04:17:39.080 | and it's like, can you figure this out?

04:17:41.560 | I have a guess, okay, about the answer to that.

04:17:44.600 | And my guess is somewhat unsatisfying,

04:17:47.640 | but my guess is that it's a little bit similar

04:17:50.200 | to Godel's second incompleteness theorem,

04:17:52.560 | which is the statement that from within

04:17:55.000 | as an axiomatic theory like Peano arithmetic,

04:17:57.880 | you cannot from within that theory

04:17:59.560 | prove the consistency of the theory.

04:18:02.240 | So my guess is that for entities within the universe,

04:18:07.920 | there is no finite determination that can be made

04:18:11.360 | of the statement the universe exists

04:18:15.080 | is essentially undecidable to any entity

04:18:18.400 | that is embedded in the universe.

04:18:19.680 | - Within that universe, how does that make you feel?

04:18:22.640 | Does that put you at peace that it's impossible,

04:18:27.640 | or is it really ultimately frustrating?

04:18:30.880 | - Well, I think it just says that it's not a kind

04:18:34.080 | of question that, you know, there are things

04:18:38.720 | that it is reasonable.

04:18:40.120 | I mean, there's kinds of, you know,

04:18:42.760 | you can talk about hypercomputation as well.

04:18:44.560 | You can say, imagine there was a hypercomputer,

04:18:46.480 | here's what it would do.

04:18:47.640 | So, okay, great, it would be lovely to have a hypercomputer,

04:18:49.920 | but unfortunately we can't make it in the universe.

04:18:52.240 | Like, it would be lovely to answer this,

04:18:53.520 | but unfortunately we can't do it in the universe.

04:18:56.280 | And, you know, this is all we have, so to speak.

04:18:59.040 | And I think it's really just a statement.

04:19:02.320 | It's sort of, in the end, it'll be a kind of a logical,

04:19:06.160 | logically inevitable statement, I think.

04:19:08.320 | I think it will be something where it is,

04:19:10.640 | as you understand what it means to have a sort of predicate

04:19:14.960 | of existence and what it means to have these kinds

04:19:17.440 | of things, it will sort of be inevitable

04:19:19.320 | that this has to be the case,

04:19:20.400 | that from within that universe,

04:19:21.680 | you can't establish the reason for its existence,

04:19:24.600 | so to speak.

04:19:25.440 | You can't prove that it exists and so on.

04:19:26.880 | - And nevertheless, because of computational reducibility,

04:19:29.880 | the future is ultimately not predictable, full of mystery,

04:19:34.080 | and that's what makes life worth living.

04:19:36.840 | - Right, I mean, right.

04:19:37.680 | And, you know, it's funny for me,

04:19:39.280 | because as a pure sort of human being doing what I do,

04:19:43.040 | it's, you know, I'm, you know,

04:19:45.320 | I like, I'm interested in people.

04:19:46.720 | I like sort of, you know, the whole human experience,

04:19:49.880 | so to speak.

04:19:50.960 | And yet, it's a little bit weird when I'm thinking,

04:19:53.920 | you know, it's all hypergraphs down there,

04:19:56.400 | and it's all just--

04:19:57.720 | - Hypergraphs all the way down.

04:19:59.560 | - Right.

04:20:00.400 | - It's like turtles all the way down.

04:20:01.360 | - Yeah, yeah, right.

04:20:03.040 | And it's kind of, you know, it's, to me,

04:20:05.720 | it is a funny thing, because every so often I get this,

04:20:08.000 | you know, as I'm thinking about,

04:20:09.120 | I think we've really gotten, you know,

04:20:10.800 | we've really figured out kind of the essence

04:20:12.480 | of how physics works, and I'm like thinking to myself,

04:20:14.760 | you know, here's this physical thing,

04:20:16.400 | and I'm like, you know,

04:20:17.760 | this feels like a very definite thing.

04:20:19.880 | How can it be the case that this is just

04:20:21.480 | some ruleal reference frame of, you know,

04:20:24.000 | this infinite creature that is so abstract and so on?

04:20:28.440 | And I kind of, it is a, it's a funny sort of feeling

04:20:32.960 | that, you know, we are, we're sort of,

04:20:35.720 | it's like, in the end, it's just sort of--

04:20:39.560 | - We're just like a little speck.

04:20:40.400 | - Be happy we're just humans type thing.

04:20:42.200 | And it's kind of like, but we're making,

04:20:44.960 | we make things as, it's not like we're just a tiny speck.

04:20:49.960 | We are, in a sense, we are more important

04:20:54.480 | by virtue of the fact that, in a sense,

04:20:58.280 | it's not like there's, there is no ultimate,

04:21:02.160 | you know, it's like we're important because,

04:21:05.000 | because, you know, we're here, so to speak,

04:21:08.880 | and we're not, it's not like there's a thing

04:21:10.880 | where we're saying, you know,

04:21:13.560 | we are just but one sort of intelligence

04:21:16.720 | out of all these other intelligences,

04:21:18.360 | and so, you know, ultimately,

04:21:20.560 | there'll be the super intelligence,

04:21:22.040 | which is all of these put together,

04:21:23.960 | and it'll be very different from us.

04:21:25.240 | No, it's actually gonna be equivalent to us.

04:21:27.520 | And the thing that makes us sort of special

04:21:31.360 | is just the details of us, so to speak.

04:21:34.720 | It's not something where we can say,

04:21:36.640 | oh, there's this other thing, you know,

04:21:38.960 | just you think humans are cool,

04:21:40.880 | just wait until you've seen this.

04:21:43.240 | You know, it's gonna be much more impressive.

04:21:45.080 | Well, no, it's all going to be

04:21:47.000 | kind of computationally equivalent.

04:21:48.880 | And the thing that, you know, it's not gonna be,

04:21:51.360 | oh, this thing is amazingly much more impressive

04:21:53.960 | and amazingly much more meaningful, let's say.

04:21:56.840 | No, we're it.

04:21:58.960 | I mean, that's the--

04:22:01.480 | - And the symbolism of this particular moment,

04:22:04.400 | so this has been one of the favorite conversations

04:22:09.000 | I've ever had, Stephen.

04:22:10.840 | It's a huge honor to talk to you,

04:22:12.720 | to talk about a topic like this for four plus hours

04:22:16.640 | on the fundamental theory of physics,

04:22:18.600 | and yet we're just two finite descendants of apes

04:22:22.880 | that have to end this conversation

04:22:24.920 | because darkness have come upon us.

04:22:28.040 | - Right, and we're gonna get bitten by mosquitoes

04:22:30.000 | and all kinds of terrible things.

04:22:30.840 | - The symbolism of that,

04:22:32.600 | we're talking about the most basic fabric of reality

04:22:36.320 | and having to end because of the fact that things end.

04:22:39.940 | It's tragic and beautiful, Stephen.

04:22:42.520 | Thank you so much, huge honor.

04:22:44.360 | I can't wait to see what you do in the next couple of days

04:22:47.080 | and next week, a month.

04:22:48.560 | We're all watching with excitement.

04:22:50.640 | Thank you so much.

04:22:51.520 | - Thanks.

04:22:53.000 | - Thanks for listening to this conversation

04:22:54.440 | with Stephen Wolfram, and thank you to our sponsors,

04:22:57.480 | Simply Safe, Sun Basket, and Masterclass.

04:23:00.880 | Please check out our sponsors in the description

04:23:03.160 | to get a discount and to support this podcast.

04:23:05.960 | If you enjoy this thing, subscribe on YouTube,

04:23:08.160 | review it with Five Stars on Apple Podcast,

04:23:10.360 | follow on Spotify, support on Patreon,

04:23:12.920 | or connect with me on Twitter @LexFriedman.

04:23:16.520 | And now, let me leave you with some words

04:23:19.040 | from Richard Feynman.

04:23:20.260 | Physics isn't the most important thing.

04:23:24.540 | Love is.

04:23:25.460 | Thank you for listening.

04:23:28.060 | I hope to see you next time.

04:23:29.940 | (upbeat music)

04:23:32.520 | (upbeat music)

04:23:35.100 | Thanks for watching.

Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe | Lex Fridman Podcast #124

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