Transcript
00:00:00 The following is a conversation with Stephen Wolfram,
00:00:02 his second time on the podcast.
00:00:05 He’s a computer scientist, mathematician,
00:00:07 theoretical physicist, and the founder and CEO
00:00:10 of Wolfram Research, a company behind Mathematica,
00:00:14 Wolfram Alpha, Wolfram Language,
00:00:16 and the new Wolfram Physics Project.
00:00:19 He’s the author of several books,
00:00:21 including A New Kind of Science, and the new book,
00:00:24 A Project to Find the Fundamental Theory of Physics.
00:00:28 This second round of our conversation is primarily focused
00:00:30 on this latter endeavor of searching for the physics
00:00:33 of our universe in simple rules that do their work
00:00:37 on hypergraphs and eventually generate the infrastructure
00:00:40 from which space, time, and all of modern physics can emerge.
00:00:45 Quick summary of the sponsors,
00:00:47 SimpliSafe, Sunbasket, and Masterclass.
00:00:50 Please check out these sponsors in the description
00:00:52 to get a discount and to support this podcast.
00:00:55 As a side note, let me say that to me,
00:00:58 the idea that seemingly infinite complexity can arise
00:01:02 from very simple rules and initial conditions
00:01:05 is one of the most beautiful and important
00:01:07 mathematical and philosophical mysteries in science.
00:01:10 I find that both cellular automata
00:01:12 and the hypergraph data structure
00:01:14 that Stephen and team are currently working on
00:01:17 to be the kind of simple, clear mathematical playground
00:01:21 within which fundamental ideas about intelligence,
00:01:24 consciousness, and the fundamental laws of physics
00:01:28 can be further developed in totally new ways.
00:01:31 In fact, I think I’ll try to make a video or two
00:01:34 about the most beautiful aspects of these models
00:01:37 in the coming weeks, especially, I think,
00:01:40 trying to describe how fellow curious minds like myself
00:01:43 can jump in and explore them either just for fun
00:01:47 or potentially for publication of new innovative research
00:01:51 in math, computer science, and physics.
00:01:54 But honestly, I think the emerging complexity
00:01:56 in these hypergraphs can capture the imagination
00:01:58 of everyone, even if you’re someone
00:02:00 who never really connected with mathematics.
00:02:04 That’s my hope, at least, to have these conversations
00:02:06 that inspire everyone to look up to the skies
00:02:09 and into our own minds in awe of our amazing universe.
00:02:15 Let me also mention that this is the first time
00:02:17 I ever recorded a podcast outdoors
00:02:20 as a kind of experiment to see if this is an option
00:02:23 in times of COVID.
00:02:25 I’m sorry if the audio is not great.
00:02:27 I did my best and promise to keep improving
00:02:30 and learning as always.
00:02:32 If you enjoy this thing, subscribe on YouTube,
00:02:35 review it with Five Stars and Apple Podcast,
00:02:37 follow on Spotify, support on Patreon,
00:02:39 or connect with me on Twitter at Lex Friedman.
00:02:42 As usual, I’ll do a few minutes of ads now
00:02:44 and no ads in the middle.
00:02:46 I tried to make these interesting,
00:02:48 but I do give you timestamps, so you’re welcome to skip,
00:02:52 but still, please do check out the sponsors
00:02:54 by clicking the links in the description.
00:02:56 It’s the best way to support this podcast.
00:02:59 Also, let me say, even though I’m talking way too much,
00:03:02 that I did a survey and it seems like over 90% of people
00:03:06 either enjoy these ad reads somehow magically
00:03:09 or don’t mind them, at least.
00:03:11 That honestly just warms my heart
00:03:14 that people are that supportive.
00:03:16 This show is sponsored by SimpliSafe,
00:03:18 a home security company.
00:03:20 Go to SimpliSafe.com to get a free HD camera.
00:03:23 It’s simple, no contracts, 15 bucks a month, easy setup.
00:03:28 Even I figured it out.
00:03:29 I have it set up in my apartment.
00:03:31 Of course, I also welcome intruders.
00:03:34 One of my favorite movies is Leon or The Professional
00:03:38 with Jean Reno, Gary Oldman,
00:03:40 and the brilliant young Natalie Portman.
00:03:43 If you haven’t seen the movie,
00:03:44 he’s a hit man with a minimalist life that resembles my own.
00:03:48 In fact, when I was younger, the idea of being a hit man
00:03:52 or targeting evil in a skilled way,
00:03:56 which is how I thought about it, really appealed to me.
00:03:59 The skill of it, the planning, the craftsmanship.
00:04:03 In another life, perhaps,
00:04:05 if I didn’t love engineering and science so much,
00:04:07 I could see myself being something like a Navy SEAL.
00:04:10 And in general, I love the idea of serving my country,
00:04:14 of serving society by contributing my skill
00:04:16 in some small way.
00:04:18 Anyway, go to Simplisafe.com slash Lex
00:04:21 to get a free HD camera and to support this podcast.
00:04:24 They’re a new sponsor, and this is a trial run,
00:04:27 so you know what to do.
00:04:28 This show is also sponsored by Sun Basket,
00:04:31 a meal delivery service.
00:04:33 Visit SunBasket.com slash Lex
00:04:35 and use code LEX to get $30 off your order
00:04:38 and to support this podcast.
00:04:40 This is the last read of the trial they’re doing,
00:04:43 so this is the time to get them if you’re considering it.
00:04:46 And if you do, it’ll help ensure
00:04:48 that they decide to support this podcast long term.
00:04:51 Their meals are healthy and delicious,
00:04:54 a nice break from the minimalist meals of meat
00:04:56 and vegetables that I usually eat.
00:04:59 Maybe on a personal note,
00:05:00 one of my favorite things to do is watch people cook,
00:05:03 especially people who love cooking,
00:05:05 and hang out with people over amazing meals.
00:05:09 I still tend to be strict in my diet no matter what,
00:05:11 even in fancy restaurants,
00:05:12 but it brings me joy to see friends and family indulge
00:05:17 something like a cake that has way too many calories
00:05:20 or ice cream or whatever.
00:05:22 My mom, in fact, for much of my life,
00:05:24 made this cake called an anthill on my birthday
00:05:27 that brings me a lot of joy and way too many calories.
00:05:32 I was thinking of doing a video with my mom as she makes it.
00:05:36 I thought it’d be a fun thing to do together.
00:05:39 Anyway, go to SunBasket.com slash Lex and use code LEX.
00:05:44 Do it now.
00:05:45 So they signed a longterm contract for this podcast.
00:05:48 This show is also sponsored by Masterclass.
00:05:50 Sign up at masterclass.com slash LEX.
00:05:53 180 bucks a year, you get an all access pass
00:05:57 to watch lessons from Chris Hadfield,
00:05:59 Neil deGrasse Tyson, Tony Hawk, Carlos Santana,
00:06:02 Garrett Casparov, Daniel Nagano,
00:06:03 and many more brilliant world experts.
00:06:07 Masterclass has been a really special sponsor.
00:06:10 They believe in this podcast in a way that gives me strength
00:06:13 and motivation to take intellectual risks.
00:06:16 I’m thinking of doing a few solo podcast episodes
00:06:18 on difficult topics, especially in history,
00:06:22 like the rise and fall of the Third Reich or Stalin, Putin,
00:06:26 and many other difficult topics that I’m fascinated by.
00:06:29 I have a worldview that seeks inspiring positive insights,
00:06:33 even and perhaps especially from periods of tragedy and evil
00:06:38 that perhaps some folks may find value in.
00:06:40 If I can only learn to convey the ideas in my mind
00:06:43 as clearly as I think them.
00:06:45 I think deeply and rigorously and precisely,
00:06:50 but to be honest, have trouble speaking in a way
00:06:53 that reflects that rigor of thought.
00:06:56 So it really does mean a lot, the love and support I get
00:07:00 as I try to get better at this thing,
00:07:02 at this talking thing.
00:07:03 Anyway, go to masterclass.com slash LEX to get a discount
00:07:07 and to support this podcast.
00:07:09 And now finally, here’s my conversation with Stephen Wolfram.
00:07:14 You said that there are moments in history of physics
00:07:17 and maybe mathematical physics or even mathematics
00:07:20 where breakthroughs happen
00:07:22 and then a flurry of progress follows.
00:07:24 So if you look back through the history of physics,
00:07:28 what moments stand out to you as important such breakthroughs
00:07:32 where a flurry of progress follows?
00:07:34 So the big famous one was 1920s,
00:07:36 the invention of quantum mechanics,
00:07:38 where in about five or 10 years,
00:07:41 lots of stuff got figured out.
00:07:43 That’s now quantum mechanics.
00:07:45 Can you mention the people involved?
00:07:46 Yeah, it was kind of the Schrodinger, Heisenberg,
00:07:50 Einstein had been a key figure, originally Planck,
00:07:53 then Dirac was a little bit later.
00:07:56 That was something that happened at that time,
00:07:58 that’s sort of before my time, right?
00:08:00 In my time was in the 1970s,
00:08:04 there was this sort of realization
00:08:06 that quantum field theory was actually going to be useful
00:08:09 in physics and QCD, quantum thermodynamics theory
00:08:13 of quarks and gluons and so on was really getting started.
00:08:16 And there was again, sort of big flurry of things
00:08:19 happened then, I happened to be a teenager at that time
00:08:22 and happened to be really involved in physics.
00:08:26 And so I got to be part of that, which was really cool.
00:08:29 Who were the key figures
00:08:31 aside from your young selves at that time?
00:08:33 You know, who won the Nobel Prize for QCD, okay?
00:08:37 People, David Gross, Frank Wilczek, you know, David Politzer.
00:08:41 The people who are the sort of the slightly older generation,
00:08:44 Dick Feynman, Murray Gellman, people like that,
00:08:48 who were Steve Weinberg, Gerhard Hoft, he’s younger,
00:08:52 he’s in the younger group actually.
00:08:54 But these are all, you know, characters who were involved.
00:08:59 I mean, it’s funny because those are all people
00:09:02 who are kind of in my time and I know them
00:09:05 and they don’t seem like sort of historical,
00:09:08 you know, iconic figures.
00:09:10 They seem more like everyday characters, so to speak.
00:09:14 And so it’s always, you know, when you look at history
00:09:18 from long afterwards, it always seems like
00:09:21 everything happened instantly.
00:09:24 And that’s usually not the case.
00:09:25 There was usually a long buildup,
00:09:27 but usually there’s, you know,
00:09:28 there’s some methodological thing happens
00:09:30 and then there’s a whole bunch of low hanging fruit
00:09:32 to be picked.
00:09:33 And that usually lasts five or 10 years.
00:09:36 You know, we see it today with machine learning
00:09:38 and, you know, deep learning neural nets and so on.
00:09:42 You know, methodological advance,
00:09:44 things actually started working in, you know, 2011, 2012
00:09:47 and so on.
00:09:48 And, you know, there’s been this sort of rapid
00:09:51 picking of low hanging fruit, which is probably, you know,
00:09:56 some significant fraction of the way done, so to speak.
00:10:00 Do you think there’s a key moment?
00:10:01 Like if I had to really introspect,
00:10:03 like what was the key moment
00:10:04 for the deep learning, quote unquote, revolution?
00:10:08 I mean.
00:10:08 It’s probably the AlexNet business.
00:10:10 AlexNet with ImageNet.
00:10:11 So is there something like that with physics
00:10:13 where, so deep learning neural networks
00:10:18 have been around for a long time.
00:10:19 Absolutely, since the 1940s, yeah.
00:10:22 There’s a bunch of little pieces that came together
00:10:23 and then all of a sudden everybody’s eyes lit up.
00:10:27 Like, wow, there’s something here.
00:10:29 Like even just looking at your own work,
00:10:32 just your thinking about the universe,
00:10:34 that there’s simple rules can create complexity.
00:10:40 You know, at which point was there a thing
00:10:42 where your eyes light up?
00:10:45 It’s like, wait a minute, there’s something here.
00:10:46 Is it the very first idea
00:10:49 or is it some moment along the line of implementations
00:10:53 and experiments and so on?
00:10:54 There’s a couple of different stages to this.
00:10:56 I mean, one is the think about the world computationally.
00:11:01 Can we use programs instead of equations
00:11:03 to make models of the world?
00:11:05 That’s something that I got interested in
00:11:07 in the beginning of the 1980s.
00:11:10 I did a bunch of computer experiments.
00:11:13 When I first did them, I didn’t really,
00:11:15 I could see some significance to them,
00:11:17 but it took me a few years to really say,
00:11:20 wow, there’s a big important phenomenon here
00:11:22 that lets sort of complex things arise
00:11:25 from very simple programs.
00:11:27 That kind of happened back in 1984 or so.
00:11:30 Then, you know, a bunch of other years go by,
00:11:33 then I start actually doing a lot
00:11:35 of much more systematic computer experiments and things
00:11:37 and find out that the, you know,
00:11:39 this phenomenon that I could only have said occurs
00:11:41 in one particular case
00:11:43 is actually something incredibly general.
00:11:45 And then that led me to this thing called
00:11:46 principle of computational equivalence.
00:11:48 And that was a long story.
00:11:51 And then, you know, as part of that process,
00:11:53 I was like, okay, you can make simple programs,
00:11:56 can make models of complicated things.
00:11:59 What about the whole universe?
00:12:00 That’s our sort of ultimate example of a complicated thing.
00:12:03 And so I got to thinking, you know,
00:12:05 could we use these ideas to study fundamental physics?
00:12:10 You know, I happen to know a lot about,
00:12:11 you know, traditional fundamental physics.
00:12:14 My first, you know, I had a bunch of ideas
00:12:17 about how to do this in the early 1990s.
00:12:19 I made a bunch of technical progress.
00:12:21 I figured out a bunch of things
00:12:22 I thought were pretty interesting.
00:12:23 You know, I wrote about them back in 2002.
00:12:26 With the new kind of science
00:12:27 in the cellular automata world.
00:12:29 And there’s echoes in the cellular automata world
00:12:32 with your new Wolfram physics project.
00:12:36 We’ll get to all that.
00:12:37 Allow me to sort of romanticize a little more
00:12:40 on the philosophy of science.
00:12:43 So Thomas Kuhn, philosopher of science,
00:12:45 describes that, you know, the progress in science
00:12:49 is made with these paradigm shifts.
00:12:52 And so to link on the sort of original line of discussion,
00:12:56 do you agree with this view
00:12:58 that there is revolutions in science
00:13:01 that just kind of flip the table?
00:13:03 What happens is it’s a different way
00:13:05 of thinking about things.
00:13:07 It’s a different methodology for studying things.
00:13:09 And that opens stuff up.
00:13:11 There’s this idea of,
00:13:15 he’s a famous biographer,
00:13:16 but I think it’s called the innovators.
00:13:19 There’s a biographer of Steve Jobs, of Albert Einstein.
00:13:22 He also wrote a book,
00:13:23 I think it’s called the innovators,
00:13:24 where he discusses how a lot of the innovations
00:13:30 in the history of computing has been done by groups.
00:13:33 There’s a complicated group dynamic going on,
00:13:37 but there’s also a romanticized notion
00:13:39 that the individual is at the core of the revolution.
00:13:42 Like where does your sense fall?
00:13:45 Is ultimately like one person responsible
00:13:49 for these revolutions that creates the spark
00:13:52 or one or two, whatever,
00:13:54 or is it just the big mush and mess and chaos
00:13:58 of people interacting, of personalities interacting?
00:14:01 I think it ends up being like many things,
00:14:03 there’s leadership and there ends up being,
00:14:05 it’s a lot easier for one person to have a crisp new idea
00:14:08 than it is for a big committee to have a crisp new idea.
00:14:10 And I think, but I think it can happen
00:14:13 that you have a great idea,
00:14:16 but the world isn’t ready for it.
00:14:19 And you can, I mean, this has happened to me plenty, right?
00:14:24 It’s, you have an idea, it’s actually a pretty good idea,
00:14:27 but things aren’t ready,
00:14:29 either you’re not really ready for it,
00:14:31 or the ambient world isn’t ready for it.
00:14:34 And it’s hard to get the thing to get traction.
00:14:37 It’s kind of interesting.
00:14:38 I mean, when I look at a new kind of science,
00:14:41 you’re now living inside the history,
00:14:43 so you can’t tell the story of these decades,
00:14:46 but it seems like the new kind of science
00:14:49 has not had the revolutionary impact
00:14:55 I would think it might.
00:14:59 Like, it feels like at some point, of course it might be,
00:15:02 but it feels at some point people will return to that book
00:15:07 and say, that was something special here.
00:15:09 This was incredible.
00:15:10 What happened?
00:15:11 Or do you think that’s already happened?
00:15:13 Oh, yeah, it’s happened, except that people aren’t,
00:15:16 the sort of the heroism of it may not be there,
00:15:19 but what’s happened is for 300 years,
00:15:22 people basically said,
00:15:24 if you want to make a model of things in the world,
00:15:27 mathematical equations are the best place to go.
00:15:29 Last 15 years, doesn’t happen.
00:15:32 New models that get made of things
00:15:34 most often are made with programs, not with equations.
00:15:38 Now, was that sort of going to happen anyway?
00:15:42 Was that a consequence of my particular work
00:15:45 and my particular book?
00:15:47 It’s hard to know for sure.
00:15:48 I mean, I am always amazed at the amounts of feedback
00:15:51 that I get from people where they say,
00:15:52 oh, by the way, I started doing this whole line of research
00:15:56 because I read your book, blah, blah, blah, blah, blah.
00:15:58 It’s like, well, can you tell that
00:15:59 from the academic literature?
00:16:01 Was there a chain of academic references?
00:16:04 Probably not.
00:16:05 One of the interesting side effects of publishing
00:16:09 in the way you did this tome
00:16:11 is it serves as an education tool and an inspiration
00:16:15 to hundreds of thousands, millions of people,
00:16:19 but because it’s not a single,
00:16:21 it’s not a chain of papers with spiffy titles,
00:16:25 it doesn’t create a splash of citations.
00:16:29 It’s had plenty of citations, but it’s, you know,
00:16:31 I think that people think of it as probably more,
00:16:36 you know, conceptual inspiration than kind of a,
00:16:41 you know, this is a line from here to here to here
00:16:43 in our particular field.
00:16:45 I think that the thing which I am disappointed by
00:16:49 and which will eventually happen
00:16:51 is this kind of study of the sort of pure computationalism,
00:16:55 this kind of study of the abstract behavior
00:16:58 of the computational universe.
00:17:00 That should be a big thing that lots of people do.
00:17:03 You mean in mathematics purely, almost like.
00:17:06 It’s like pure mathematics, but it isn’t mathematics.
00:17:08 But it isn’t, it isn’t.
00:17:10 It’s a new kind of mathematics.
00:17:12 Is it a new title of the book?
00:17:14 Yeah, right.
00:17:15 That’s why the book is called that.
00:17:17 Right, that’s not coincidental.
00:17:19 Yeah.
00:17:20 It’s interesting that I haven’t seen
00:17:22 really rigorous investigation
00:17:24 by thousands of people of this idea.
00:17:26 I mean, you look at your competition around rule 30.
00:17:30 I mean, that’s fascinating.
00:17:31 If you can say something.
00:17:34 Right.
00:17:35 Is there some aspect of this thing that could be predicted?
00:17:38 That’s the fundamental question of science.
00:17:40 That’s the core.
00:17:41 Well, that has been a question of science.
00:17:42 I think that is some people’s view of what science is about
00:17:47 and it’s not clear that’s the right view.
00:17:48 In fact, as we live through this pandemic
00:17:51 full of predictions and so on,
00:17:53 it’s an interesting moment to be pondering
00:17:55 what science’s actual role in those kinds of things is.
00:17:58 Or you think it’s possible that in science,
00:18:02 clean, beautiful, simple prediction
00:18:04 may not even be possible in real systems.
00:18:07 That’s the open question.
00:18:08 I don’t think it’s open.
00:18:09 I think that question is answered and the answer is no.
00:18:12 Well, no, no.
00:18:13 The answer could be just humans are not smart enough yet.
00:18:16 Like we don’t have the tools yet.
00:18:17 No, that’s the whole point.
00:18:18 I mean, that’s sort of the big discovery
00:18:20 of this principle of computational equivalence of mine.
00:18:23 And this is something which is kind of a follow on
00:18:26 to Gödel’s theorem, to Turing’s work
00:18:28 on the halting problem, all these kinds of things.
00:18:31 That there is this fundamental limitation
00:18:34 built into science,
00:18:36 this idea of computational irreducibility
00:18:39 that says that even though you may know the rules
00:18:42 by which something operates,
00:18:44 that does not mean that you can readily sort of
00:18:47 be smarter than it and jump ahead
00:18:49 and figure out what it’s going to do.
00:18:51 Yes, but do you think there’s a hope
00:18:53 for pockets of computational reducibility?
00:18:56 Computational reducibility.
00:19:02 And then a set of tools and mathematics
00:19:04 that help you discover such pockets.
00:19:07 That’s where we live is in the pockets of reducibility.
00:19:10 That’s why, and this is one of the things
00:19:12 that sort of come out of this physics project
00:19:14 and actually something that, again,
00:19:15 I should have realized many years ago, but didn’t,
00:19:18 is it could very well be that everything about the world
00:19:23 is computationally reducible and completely unpredictable.
00:19:26 But in our experience of the world,
00:19:29 there is at least some amount of prediction we can make.
00:19:32 And that’s because we have sort of chosen a slice of,
00:19:36 probably talk about this in much more detail,
00:19:38 but I mean, we’ve kind of chosen a slice
00:19:39 of how to think about the universe
00:19:41 in which we can kind of sample
00:19:43 a certain amount of computational reducibility.
00:19:46 And that’s sort of where we exist.
00:19:51 And it may not be the whole story of how the universe is,
00:19:55 but it is the part of the universe that we care about
00:19:59 and we sort of operate in.
00:20:01 And that’s, you know, in science,
00:20:03 that’s been sort of a very special case of that.
00:20:05 That is science has chosen to talk a lot about places
00:20:09 where there is this computational reducibility
00:20:12 that it can find, you know,
00:20:13 the motion of the planets can be more or less predicted.
00:20:16 You know, something about the weather
00:20:19 is much harder to predict.
00:20:20 Something about, you know, other kinds of things
00:20:22 that are much harder to predict.
00:20:25 And it’s, these are, but science has tended to,
00:20:29 you know, concentrate itself on places
00:20:31 where its methods have allowed successful prediction.
00:20:35 So you think rule 30, if we could linger on it,
00:20:39 because it’s just such a beautiful, simple formulation
00:20:41 of the essential concept underlying
00:20:43 all the things we’re talking about.
00:20:45 Do you think there’s pockets of reducibility
00:20:47 inside rule 30?
00:20:48 Yes, that is the question of how big are they?
00:20:51 What will they allow you to say?
00:20:53 And so on.
00:20:53 And that’s, and figuring out where those pockets are,
00:20:56 I mean, in a sense, that’s the, that’s sort of a,
00:21:00 you know, that is an essential thing
00:21:02 that one would like to do in science.
00:21:05 But it’s also, the important thing to realize
00:21:08 that has not been, you know, is that science,
00:21:13 if you just pick an arbitrary thing,
00:21:15 you say, what’s the answer to this question?
00:21:18 That question may not be one
00:21:20 that has a computationally reducible answer.
00:21:22 That question, if you choose, you know,
00:21:26 if you walk along the series of questions
00:21:28 and you’ve got one that’s reducible
00:21:30 and you get to another one that’s nearby
00:21:31 and it’s reducible too,
00:21:33 if you stick to that kind of stick to the land,
00:21:36 so to speak, then you can go down this chain
00:21:39 of sort of reducible, answerable things.
00:21:41 But if you just say, I’m just pick a question at random,
00:21:44 I’m gonna have my computer pick a question at random.
00:21:47 Most likely it’s gonna be reducible.
00:21:49 Most likely it will be reducible.
00:21:50 And what we’re thrown in the world, so to speak,
00:21:54 we, you know, when we engineer things,
00:21:56 we tend to engineer things to sort of keep
00:21:58 in the zone of reducibility.
00:22:00 When we’re throwing things by the natural world,
00:22:02 for example, not at all certain
00:22:05 that we will be kept in this kind of zone of reducibility.
00:22:08 Can we talk about this pandemic then?
00:22:11 Sure.
00:22:12 For a second, is a, so how do we,
00:22:16 there’s obviously huge amount of economic pain
00:22:18 that people are feeling.
00:22:19 There’s a huge incentive and medical pain,
00:22:23 health, just all kind of psychological.
00:22:26 There’s a huge incentive to figure this out,
00:22:28 to walk along the trajectory of reducible, of reducibility.
00:22:34 There’s a lot of disparate data.
00:22:38 You know, people understand generally how viruses spread,
00:22:40 but it’s very complicated
00:22:43 because there’s a lot of uncertainty.
00:22:45 There’s a, there could be a lot of variability also,
00:22:49 like so many, obviously a nearly infinite number
00:22:52 of variables that represent human interaction.
00:22:57 And so you have to figure out,
00:22:59 from the perspective of reducibility,
00:23:02 figure out which variables are really important
00:23:06 in this kind of, from an epidemiological perspective.
00:23:10 So why aren’t we, you kind of said
00:23:13 that we’re clearly failing.
00:23:15 Well, I think it’s a complicated thing.
00:23:17 So, I mean, you know, when this pandemic started up,
00:23:20 you know, I happened to be in the middle
00:23:21 of being about to release this whole physics project thing,
00:23:24 but I thought, you know.
00:23:25 The timing is just cosmically absurd.
00:23:28 A little bit bizarre, but you know,
00:23:30 but I thought, you know,
00:23:31 I should do the public service thing of, you know,
00:23:33 trying to understand what I could about the pandemic.
00:23:36 And, you know, we’d been curating data about it
00:23:38 and all that kind of thing.
00:23:39 But, you know, so I started looking at the data
00:23:41 and started looking at modeling
00:23:43 and I decided it’s just really hard.
00:23:46 You need to know a lot of stuff that we don’t know
00:23:48 about human interactions.
00:23:49 It’s actually clear now that there’s a lot of stuff
00:23:51 we didn’t know about viruses
00:23:53 and about the way immunity works and so on.
00:23:56 And it’s, you know, I think what will come out in the end
00:23:58 is there’s a certain amount of what happens
00:24:02 that we just kind of have to trace each step
00:24:04 and see what happens.
00:24:05 There’s a certain amount of stuff
00:24:06 where there’s going to be a big narrative
00:24:08 about this happened because, you know, of T cell immunity.
00:24:12 This could happen because there’s this whole giant
00:24:14 sort of field of asymptomatic viral stuff out there.
00:24:18 You know, there will be a narrative
00:24:20 and that narrative, whenever there’s a narrative,
00:24:22 that’s kind of a sign of reducibility.
00:24:24 But when you just say,
00:24:26 let’s from first principles figure out what’s going on,
00:24:28 then you can potentially be stuck
00:24:30 in this kind of a mess of irreducibility
00:24:33 where you just have to simulate each step
00:24:35 and you can’t do that unless you know details about,
00:24:38 you know, human interaction networks
00:24:40 and so on and so on and so on.
00:24:41 The thing that has been very sort of frustrating to see
00:24:46 is the mismatch between people’s expectations
00:24:48 about what science can deliver
00:24:50 and what science can actually deliver, so to speak.
00:24:53 Because people have this idea that, you know, it’s science.
00:24:56 So there must be a definite answer
00:24:58 and we must be able to know that answer.
00:25:00 And, you know, this is, it is both, you know,
00:25:05 when you’ve, after you’ve played around
00:25:07 with sort of little programs in the computational universe,
00:25:10 you don’t have that intuition anymore.
00:25:11 You know, it’s, I always, I’m always fond of saying,
00:25:14 you know, the computational animals
00:25:17 are always smarter than you are.
00:25:18 That is, you know, you look at one of these things
00:25:20 and it’s like, it can’t possibly do such and such a thing.
00:25:23 Then you run it and it’s like, wait a minute,
00:25:25 it’s doing that thing.
00:25:26 How does that work?
00:25:27 Okay, now I can go back and understand it.
00:25:29 But that’s the brave thing about science
00:25:31 is that in the chaos of the irreducible universe,
00:25:35 we nevertheless persist to find those pockets.
00:25:38 That’s kind of the whole point.
00:25:40 That’s like, you say that the limits of science,
00:25:43 but that, you know, yes, it’s highly limited,
00:25:46 but there’s a hope there.
00:25:48 And like, there’s so many questions I want to ask here.
00:25:51 So one, you said narrative, which is really interesting.
00:25:54 So obviously from a, at every level of society,
00:25:58 you look at Twitter, everybody’s constructing narratives
00:26:00 about the pandemic, about not just the pandemic,
00:26:03 but all the cultural tension that we’re going through.
00:26:06 So there’s narratives,
00:26:07 but they’re not necessarily connected
00:26:10 to the underlying reality of these systems.
00:26:17 So our human narratives, I don’t even know if they’re,
00:26:22 I don’t like those pockets of reducibility
00:26:25 because we’re, it’s like constructing things
00:26:29 that are not actually representative of reality,
00:26:33 and thereby not giving us like good solutions
00:26:36 to how to predict the system.
00:26:39 Look, it gets complicated because, you know,
00:26:41 people want to say, explain the pandemic to me,
00:26:43 explain what’s going to happen.
00:26:45 In the future.
00:26:46 Yes, but also, can you explain it?
00:26:48 Is there a story to tell?
00:26:49 What already happened in the past?
00:26:51 Yeah, or what’s going to happen,
00:26:53 but I mean, you know, it’s similar to sort of
00:26:55 explaining things in AI or in any computational system.
00:26:58 It’s like, you know, explain what happened.
00:27:00 Well, it could just be this happened
00:27:03 because of this detail and this detail and this detail,
00:27:05 and a million details,
00:27:06 and there isn’t a big story to tell.
00:27:08 There’s no kind of big arc of the story that says,
00:27:12 oh, it’s because, you know, there’s a viral field
00:27:14 that has these properties
00:27:15 and people start showing symptoms.
00:27:17 You know, when the seasons change,
00:27:20 people will show symptoms
00:27:21 and people don’t even understand, you know,
00:27:22 seasonal variation of flu, for example.
00:27:24 It’s something where, you know,
00:27:28 there could be a big story,
00:27:29 or it could be just a zillion little details that mount up.
00:27:33 See, but, okay, let’s pretend that this pandemic,
00:27:38 like the coronavirus, resembles something
00:27:41 like the 1D rule 30 cellular automata, okay?
00:27:45 So, I mean, that’s how epidemiologists model virus spread.
00:27:51 Indeed, yes.
00:27:52 They sometimes use cellular automata, yes.
00:27:54 Yeah, and okay, so you could say it’s simplistic,
00:27:57 but okay, let’s say it’s representative
00:28:00 of actually what happens.
00:28:02 You know, the dynamic of,
00:28:06 you have a graph,
00:28:07 it probably is closer to the hypergraph model.
00:28:09 It is, yes.
00:28:10 It’s actually, that’s another funny thing.
00:28:13 As we were getting ready to release this physics project,
00:28:15 we realized that a bunch of things we’d worked out
00:28:17 about foliations of causal graphs and things
00:28:20 were directly relevant to thinking about contact tracing.
00:28:23 Yeah, exactly.
00:28:24 And interactions with cell phones and so on,
00:28:25 which is really weird.
00:28:27 But like, it just feels like,
00:28:29 it feels like we should be able to get
00:28:31 some beautiful core insight about the spread
00:28:34 of this particular virus
00:28:36 on the hypergraph of human civilization, right?
00:28:40 I tried, I didn’t manage to figure it out.
00:28:42 But you’re one person.
00:28:43 Yeah, but I mean, I think actually it’s a funny thing
00:28:46 because it turns out the main model,
00:28:48 you know, this SIR model,
00:28:49 I only realized recently was invented by the grandfather
00:28:53 of a good friend of mine from high school.
00:28:55 So that was just a, you know, it’s a weird thing, right?
00:28:58 The question is, you know, okay, so you know,
00:29:02 on this graph of how humans are connected,
00:29:04 you know something about what happens
00:29:05 if this happens and that happens.
00:29:07 That graph is made in complicated ways
00:29:09 that depends on all sorts of issues
00:29:11 that where we don’t have the data
00:29:13 about how human society works well enough
00:29:15 to be able to make that graph.
00:29:17 There’s actually, one of my kids did a study
00:29:20 of sort of what happens on different kinds of graphs
00:29:23 and how robust are the results, okay?
00:29:25 His basic answer is there are a few general results
00:29:28 that you can get that are quite robust.
00:29:30 Like, you know, a small number of big gatherings
00:29:33 is worse than a large number of small gatherings, okay?
00:29:36 That’s quite robust.
00:29:37 But when you ask more detailed questions,
00:29:40 it seemed like it just depends.
00:29:42 It depends on details.
00:29:44 In other words, it’s kind of telling you in that case,
00:29:47 you know, the irreducibility matters, so to speak.
00:29:49 It’s not, there’s not gonna be this kind of one
00:29:53 sort of master theorem that says,
00:29:55 and therefore this is how things are gonna work.
00:29:57 Yeah, but there’s a certain kind of,
00:29:59 from a graph perspective,
00:30:01 the certain kind of dynamic to human interaction.
00:30:04 So like large groups and small groups,
00:30:08 I think it matters who the groups are.
00:30:10 For example, you could imagine large,
00:30:12 depends how you define large,
00:30:13 but you can imagine groups of 30 people,
00:30:17 as long as they are cliques or whatever.
00:30:22 Right.
00:30:23 As long as the outgoing degree of that graph is small
00:30:27 or something like that,
00:30:28 like you can imagine some beautiful underlying rule
00:30:31 of human dynamic interaction where I can still be happy,
00:30:34 where I can have a conversation with you
00:30:36 and a bunch of other people that mean a lot to me in my life
00:30:39 and then stay away from the bigger, I don’t know,
00:30:42 not going to a Miley Cyrus concert or something like that
00:30:45 and figuring out mathematically some nice.
00:30:49 See, this is an interesting thing.
00:30:51 So I mean, this is the question of what you’re describing
00:30:54 is kind of the problem of the many situations
00:30:59 where you would like to get away
00:31:00 from computational irreducibility.
00:31:02 A classic one in physics is thermodynamics.
00:31:05 The second law of thermodynamics,
00:31:06 the law that says entropy tends to increase things
00:31:09 that start orderly tend to get more disordered,
00:31:13 or which is also the thing that says,
00:31:15 given that you have a bunch of heat,
00:31:16 it’s hard, heat is the microscopic motion of molecules,
00:31:19 it’s hard to turn that heat into systematic mechanical work.
00:31:23 It’s hard to just take something being hot
00:31:26 and turn that into, oh, all the atoms are gonna line up
00:31:29 in the bar of metal and the piece of metal
00:31:31 is gonna shoot in some direction.
00:31:33 That’s essentially the same problem
00:31:35 as how do you go from this computationally irreducible
00:31:40 mess of things happening
00:31:41 and get something you want out of it.
00:31:43 It’s kind of mining, you’re kind of,
00:31:45 now, actually I’ve understood in recent years
00:31:48 that the story of thermodynamics
00:31:50 is actually precisely a story of computational irreducibility,
00:31:54 but it is a, it is already an analogy.
00:31:58 You can kind of see that as can you take the,
00:32:02 what you’re asking to do there
00:32:03 is you’re asking to go from the kind of,
00:32:07 the mess of all these complicated human interactions
00:32:10 and all this kind of computational processes going on
00:32:12 and you say, I want to achieve
00:32:14 this particular thing out of it.
00:32:15 I want to kind of extract from the heat of what’s happening.
00:32:18 I want to kind of extract this useful piece
00:32:22 of sort of mechanical work that I find helpful.
00:32:25 I mean.
00:32:26 Do you have a hope for the pandemic?
00:32:27 So we’ll talk about physics,
00:32:28 but for the pandemic, can that be extracted?
00:32:31 Do you think?
00:32:32 What’s your intuition?
00:32:33 The good news is the curves basically,
00:32:36 for reasons we don’t understand,
00:32:38 the curves, the clearly measurable mortality curves
00:32:42 and so on for the Northern Hemisphere have gone down.
00:32:46 Yeah, but the bad news is that it could be a lot worse
00:32:50 for future viruses.
00:32:51 And what this pandemic revealed is we’re highly unprepared
00:32:55 for the discovery of the pockets of reducibility
00:32:59 within a pandemic that’s much more dangerous.
00:33:02 Well, my guess is the specific risk of viral pandemics,
00:33:07 you know, that the pure virology
00:33:10 and immunology of the thing,
00:33:12 this will cause that to advance to the point
00:33:14 where this particular risk
00:33:16 is probably considerably mitigated.
00:33:19 But is the structure of modern society robust
00:33:25 to all kinds of risks?
00:33:26 Well, the answer is clearly no.
00:33:29 And it’s surprising to me the extent to which people,
00:33:34 as I say, it’s kind of scary actually
00:33:37 how much people believe in science.
00:33:39 That is people say, oh, you know,
00:33:41 because the science says this, that and the other,
00:33:43 we’ll do this and this and this,
00:33:44 even though from a sort of common sense point of view,
00:33:46 it’s a little bit crazy and people are not prepared
00:33:50 and it doesn’t really work in society
00:33:52 as it is for people to say,
00:33:53 well, actually we don’t really know how the science works.
00:33:56 People say, well, tell us what to do.
00:33:58 Yeah, because then, yeah, what’s the alternative?
00:34:01 For the masses, it’s difficult to sit,
00:34:04 it’s difficult to meditate on computational reducibility.
00:34:08 It’s difficult to sit,
00:34:10 it’s difficult to enjoy a good dinner meal
00:34:13 while knowing that you know nothing about the world.
00:34:15 Well, I think this is a place where, you know,
00:34:17 this is what politicians and political leaders do
00:34:21 for a living, so to speak,
00:34:22 is you’ve got to make some decision about what to do.
00:34:24 And it’s…
00:34:25 Tell some narrative that while amidst the mystery
00:34:29 and knowing not much about the past or the future,
00:34:33 still telling a narrative that somehow gives people hope
00:34:37 that we know what the heck we’re doing.
00:34:39 Yeah, and get society through the issue.
00:34:41 You know, even though, you know,
00:34:43 the idea that we’re just gonna, you know,
00:34:45 sort of be able to get the definitive answer from science
00:34:48 and it’s gonna tell us exactly what to do.
00:34:50 Unfortunately, you know, it’s interesting
00:34:54 because let me point out that if that was possible,
00:34:56 if science could always tell us what to do,
00:34:59 then in a sense, our, you know,
00:35:01 that would be a big downer for our lives.
00:35:03 If science could always tell us
00:35:05 what the answer is gonna be,
00:35:06 it’s like, well, you know,
00:35:08 it’s kind of fun to live one’s life
00:35:10 and just sort of see what happens.
00:35:11 If one could always just say,
00:35:12 let me check my science.
00:35:15 Oh, I know, you know,
00:35:16 the result of everything is gonna be 42.
00:35:18 I don’t need to live my life and do what I do.
00:35:21 It’s just, we already know the answer.
00:35:23 It’s actually good news in a sense
00:35:24 that there is this phenomenon
00:35:25 of computational irreducibility
00:35:27 that doesn’t allow you to just sort of jump through time
00:35:30 and say, this is the answer, so to speak.
00:35:33 And that’s, so that’s a good thing.
00:35:35 The bad thing is it doesn’t allow you to jump through time
00:35:38 and know what the answer is.
00:35:39 It’s scary.
00:35:40 Do you think we’re gonna be okay as a human civilization?
00:35:44 You said, we don’t know.
00:35:46 Absolutely.
00:35:47 Do you think we’ll prosper or destroy ourselves?
00:35:53 In general?
00:35:54 In general.
00:35:55 I’m an optimist.
00:35:57 No, I think that, you know,
00:35:59 it’ll be interesting to see, for example,
00:36:01 with this, you know, pandemic,
00:36:02 I, you know, to me, you know,
00:36:05 when you look at like organizations, for example,
00:36:08 you know, having some kind of perturbation,
00:36:10 some kick to the system,
00:36:12 usually the end result of that is actually quite good.
00:36:16 You know, unless it kills the system,
00:36:17 it’s actually quite good usually.
00:36:19 And I think in this case, you know, people,
00:36:22 I mean, my impression, you know,
00:36:23 it’s a little weird for me because, you know,
00:36:25 I’ve been a remote tech CEO for 30 years.
00:36:28 It doesn’t, you know, this is bizarrely, you know,
00:36:30 and the fact that, you know, like this coming to see you here
00:36:33 is the first time in six months that I’ve been like,
00:36:39 you know, in a building other than my house, okay?
00:36:41 So, you know, I’m a kind of ridiculous outlier
00:36:46 in these kinds of things.
00:36:47 But overall, your sense is when you shake up the system
00:36:50 and throw in chaos that you challenge the system,
00:36:55 we humans emerge better.
00:36:57 Seems to be that way.
00:36:58 Who’s to know?
00:36:59 I think that, you know, people, you know,
00:37:01 my sort of vague impression is that people are sort of,
00:37:05 you know, oh, what’s actually important?
00:37:07 You know, what is worth caring about and so on?
00:37:10 And that seems to be something that perhaps is more,
00:37:14 you know, emergent in this kind of situation.
00:37:16 It’s so fascinating that on the individual level,
00:37:19 we have our own complex cognition.
00:37:22 We have consciousness, we have intelligence,
00:37:24 we’re trying to figure out little puzzles.
00:37:25 And then that somehow creates this graph
00:37:28 of collective intelligence.
00:37:30 Well, we figure out, and then you throw in these viruses
00:37:33 of which there’s millions different, you know,
00:37:36 there’s entire taxonomy and the viruses are thrown
00:37:39 into the system of collective human intelligence.
00:37:42 And when little humans figure out what to do about it,
00:37:45 we get like, we tweet stuff about information.
00:37:48 There’s doctors as conspiracy theorists.
00:37:50 And then we play with different information.
00:37:53 I mean, the whole of it is fascinating.
00:37:55 I am like you also very optimistic,
00:37:58 but you said the computational reducibility.
00:38:04 There’s always a fear of the darkness
00:38:06 of the uncertainty before us.
00:38:09 Yeah, I know. And it’s scary.
00:38:11 I mean, the thing is, if you knew everything,
00:38:13 it will be boring.
00:38:15 And it would be, and then, and worse than boring,
00:38:19 so to speak.
00:38:20 It would reveal the pointlessness, so to speak.
00:38:24 And in a sense, the fact that there is
00:38:26 this computational irreducibility,
00:38:28 it’s like as we live our lives, so to speak,
00:38:30 something is being achieved.
00:38:31 We’re computing what our lives, you know,
00:38:35 what happens in our lives.
00:38:36 That’s funny.
00:38:37 So the computational reducibility is kind of like,
00:38:40 it gives the meaning to life.
00:38:41 It is the meaning of life.
00:38:43 Computational reducibility is the meaning of life.
00:38:45 There you go.
00:38:46 It gives it meaning, yes.
00:38:47 I mean, it’s what causes it to not be something
00:38:51 where you can just say, you know,
00:38:53 you went through all those steps to live your life,
00:38:55 but we already knew what the answer was.
00:38:58 Hold on one second.
00:38:59 I’m going to use my handy Wolfram Alpha sunburn
00:39:03 computation thing, so long as I can get network here.
00:39:06 There we go.
00:39:08 Oh, actually, you know what?
00:39:09 It says sunburn unlikely.
00:39:11 This is a QA moment.
00:39:12 This is a good moment.
00:39:16 Okay, well, let me just check what it thinks.
00:39:20 See why it thinks that.
00:39:22 It doesn’t seem like my intuition.
00:39:23 This is one of these cases where we can,
00:39:25 the question is, do we trust the science
00:39:27 or do we use common sense?
00:39:30 The UV thing is cool.
00:39:32 Yeah, yeah, well, we’ll see.
00:39:32 This is a QA moment, as I say.
00:39:35 It’s, do we trust the product?
00:39:37 Yes, we trust the product, so.
00:39:39 And then there’ll be a data point either way.
00:39:42 If I’m desperately sunburned,
00:39:43 I will send in an angry feedback.
00:39:46 Because we mentioned the concept so much
00:39:50 and a lot of people know it,
00:39:51 but can you say what computational reducibility is?
00:39:54 Yeah, right.
00:39:55 The question is, if you think about things
00:39:58 that happen as being computations,
00:40:01 you think about some process in physics,
00:40:06 something that you compute in mathematics, whatever else,
00:40:09 it’s a computation in the sense it has definite rules.
00:40:11 You follow those rules.
00:40:13 You follow them many steps and you get some result.
00:40:18 So then the issue is,
00:40:20 if you look at all these different kinds of computations
00:40:21 that can happen,
00:40:22 whether they’re computations
00:40:23 that are happening in the natural world,
00:40:24 whether they’re happening in our brains,
00:40:26 whether they’re happening in our mathematics,
00:40:28 whatever else,
00:40:29 the big question is, how do these computations compare?
00:40:32 Is, are there dumb computations and smart computations
00:40:35 or are they somehow all equivalent?
00:40:37 And the thing that I kind of was sort of surprised to realize
00:40:41 from a bunch of experiments that I did in the early nineties
00:40:43 and now we have tons more evidence for it,
00:40:46 this thing I call the principle of computational equivalence,
00:40:48 which basically says, when one of these computations,
00:40:51 one of these processes that follows rules,
00:40:54 doesn’t seem like it’s doing something obviously simple,
00:40:57 then it has reached the sort of equivalent level
00:41:00 of computational sophistication of everything.
00:41:03 So what does that mean?
00:41:04 That means that, you might say, gosh,
00:41:07 I’m studying this little tiny program on my computer.
00:41:11 I’m studying this little thing in nature,
00:41:14 but I have my brain
00:41:15 and my brain is surely much smarter than that thing.
00:41:18 I’m gonna be able to systematically outrun
00:41:20 the computation that it does
00:41:22 because I have a more sophisticated computation
00:41:24 that I can do.
00:41:25 But what the principle of computational equivalence says
00:41:27 is that doesn’t work.
00:41:29 Our brains are doing computations
00:41:31 that are exactly equivalent to the kinds of computations
00:41:34 that are being done in all these other sorts of systems.
00:41:36 And so what consequences does that have?
00:41:38 Well, it means that we can’t systematically
00:41:40 outrun these systems.
00:41:42 These systems are computationally irreducible
00:41:45 in the sense that there’s no sort of shortcut
00:41:47 that we can make that jumps to the answer.
00:41:50 Now the general case.
00:41:51 Right, right.
00:41:52 But the, so what has happened,
00:41:55 what science has become used to doing
00:41:58 is using the little sort of pockets
00:42:00 of computational reducibility,
00:42:02 which by the way are an inevitable consequence
00:42:04 of computational irreducibility,
00:42:06 that there have to be these pockets
00:42:08 scattered around of computational reducibility
00:42:11 to be able to find those particular cases
00:42:14 where you can jump ahead.
00:42:15 I mean, one thing sort of a little bit
00:42:17 of a parable type thing that I think is fun to tell.
00:42:20 If you look at ancient Babylon,
00:42:22 they were trying to predict three kinds of things.
00:42:25 They tried to predict where the planets would be,
00:42:27 what the weather would be like,
00:42:29 and who would win or lose a certain battle.
00:42:32 And they had no idea which of these things
00:42:34 would be more predictable than the other.
00:42:36 That’s funny.
00:42:37 And it turns out where the planets are
00:42:40 is a piece of computational reducibility
00:42:43 that 300 years ago or so we pretty much cracked.
00:42:46 I mean, it’s been technically difficult
00:42:48 to get all the details right,
00:42:49 but it’s basically, we got that.
00:42:52 Who’s gonna win or lose the battle?
00:42:54 No, we didn’t crack that one.
00:42:55 That one, that one, right.
00:42:57 Game theorists are trying.
00:42:58 Yes. And then the weather.
00:43:00 It’s kind of halfway on that one.
00:43:02 Halfway?
00:43:03 Yeah, I think we’re doing okay on that one.
00:43:05 Long term climate, different story.
00:43:07 But the weather, we’re much closer on that.
00:43:10 But do you think eventually we’ll figure out the weather?
00:43:11 So do you think eventually most think
00:43:15 we’ll figure out the local pockets in everything,
00:43:17 essentially the local pockets of reducibility?
00:43:19 No, I think that it’s an interesting question,
00:43:22 but I think that there is an infinite collection
00:43:25 of these local pockets.
00:43:26 We’ll never run out of local pockets.
00:43:28 And by the way, those local pockets
00:43:30 are where we build engineering, for example.
00:43:33 That’s how we, if we want to have a predictable life,
00:43:36 so to speak, then we have to build
00:43:40 in these sort of pockets of reducibility.
00:43:43 Otherwise, if we were sort of existing
00:43:46 in this kind of irreducible world,
00:43:48 we’d never be able to have definite things
00:43:51 to know what’s gonna happen.
00:43:53 I have to say, I think one of the features,
00:43:55 when we look at sort of today from the future, so to speak,
00:43:59 I suspect one of the things where people will say
00:44:02 I can’t believe they didn’t see that
00:44:04 is stuff to do with the following kind of thing.
00:44:07 So if we describe, oh, I don’t know,
00:44:10 something like heat, for instance,
00:44:12 we say, oh, the air in here, it’s this temperature,
00:44:17 this pressure, that’s as much as we can say.
00:44:20 Otherwise, just a bunch of random molecules bouncing around.
00:44:23 People will say, I just can’t believe they didn’t realize
00:44:26 that there was all this detail
00:44:27 and how all these molecules were bouncing around
00:44:29 and they could make use of that.
00:44:31 And actually, I realized there’s a thing
00:44:32 I realized last week, actually,
00:44:34 was a thing that people say, one of the scenarios
00:44:37 for the very long term history of our universe
00:44:40 is a so called heat death of the universe,
00:44:42 where basically everything just becomes
00:44:44 thermodynamically boring.
00:44:47 Everything’s just this big kind of gas
00:44:48 and thermal equilibrium.
00:44:50 People say, that’s a really bad outcome.
00:44:52 But actually, it’s not a really bad outcome.
00:44:54 It’s an outcome where there’s all this computation going on
00:44:57 and all those individual gas molecules
00:44:58 are all bouncing around in very complicated ways
00:45:01 doing this very elaborate computation.
00:45:03 It just happens to be a computation that right now,
00:45:06 we haven’t found ways to understand.
00:45:09 We haven’t found ways, our brains haven’t,
00:45:12 and our mathematics and our science and so on,
00:45:14 haven’t found ways to tell an interesting story about that.
00:45:17 It just looks boring to us.
00:45:19 So you’re saying there’s a hopeful view
00:45:23 of the heat death, quote unquote, of the universe
00:45:26 where there’s actual beautiful complexity going on.
00:45:30 Similar to the kind of complexity we think of
00:45:34 that creates rich experience in human life and life on Earth.
00:45:38 So those little molecules interacting complex ways,
00:45:40 that could be intelligence in that, there could be.
00:45:43 Absolutely.
00:45:44 I mean, this is what you learn from this principle.
00:45:46 Wow, that’s a hopeful message.
00:45:48 Right.
00:45:48 I mean, this is what you kind of learn
00:45:49 from this principle of computational equivalence.
00:45:51 You learn it’s both a message of sort of hope
00:45:56 and a message of kind of, you know,
00:45:59 you’re not as special as you think you are, so to speak.
00:46:01 I mean, because, you know, we imagine that
00:46:03 with sort of all the things we do with human intelligence
00:46:06 and all that kind of thing,
00:46:07 and all of the stuff we’ve constructed in science,
00:46:09 it’s like, we’re very special.
00:46:12 But actually it turns out, well, no, we’re not.
00:46:15 We’re just doing computations
00:46:17 like things in nature do computations,
00:46:19 like those gas molecules do computations,
00:46:21 like the weather does computations.
00:46:23 The only thing about the computations that we do
00:46:26 that’s really special is that we understand
00:46:30 what they are, so to speak.
00:46:31 In other words, we have a, you know,
00:46:33 to us they’re special because kind of,
00:46:35 they’re connected to our purposes,
00:46:37 our ways of thinking about things and so on.
00:46:39 And that’s some, but so.
00:46:41 That’s very human centric.
00:46:42 That’s, we’re just attached to this kind of thing.
00:46:45 So let’s talk a little bit of physics.
00:46:48 Maybe let’s ask the biggest question.
00:46:50 What is a theory of everything in general?
00:46:55 What does that mean?
00:46:56 Yeah, so I mean, the question is,
00:46:58 can we kind of reduce what has been physics
00:47:01 as a something where we have to sort of pick away and say,
00:47:05 do we roughly know how the world works
00:47:08 to something where we have a complete formal theory
00:47:11 where we say, if we were to run this program
00:47:14 for long enough, we would reproduce everything,
00:47:17 you know, down to the fact that we’re having
00:47:19 this conversation at this moment,
00:47:21 et cetera, et cetera, et cetera.
00:47:22 Any physical phenomena, any phenomena in this world?
00:47:25 Any phenomenon in the universe.
00:47:27 But the, you know, because of computational irreducibility,
00:47:30 it’s not, you know, that’s not something where you say,
00:47:33 okay, you’ve got the fundamental theory of everything.
00:47:36 Then, you know, tell me whether, you know,
00:47:39 lions are gonna eat tigers or something.
00:47:42 You know, that’s a, no, you have to run this thing
00:47:45 for, you know, 10 to the 500 steps or something
00:47:48 to know something like that, okay?
00:47:50 So at some moment, potentially, you say,
00:47:54 this is a rule and run this rule enough times
00:47:57 and you will get the whole universe, right?
00:47:59 That’s what it means to kind of have
00:48:02 a fundamental theory of physics as far as I’m concerned
00:48:04 is you’ve got this rule.
00:48:06 It’s potentially quite simple.
00:48:07 We don’t know for sure it’s simple,
00:48:09 but we have various reasons to believe it might be simple.
00:48:12 And then you say, okay, I’m showing you this rule.
00:48:15 You just run it only 10 to the 500 times
00:48:18 and you’ll get everything.
00:48:20 In other words, you’ve kind of reduced the problem
00:48:22 of physics to a problem of mathematics, so to speak.
00:48:25 It’s like, it’s as if, you know, you’d like,
00:48:27 you generate the digits of pi.
00:48:29 There’s a definite procedure.
00:48:30 You just generate them and it’d be the same thing
00:48:33 if you have a fundamental theory of physics
00:48:35 of the kind that I’m imagining, you know,
00:48:38 you get this rule and you just run it out
00:48:42 and you get everything that happens in the universe.
00:48:45 So a theory of everything is a mathematical framework
00:48:52 within which you can explain everything that happens
00:48:55 in the universe, it’s kind of in a unified way.
00:48:58 It’s not, there’s a bunch of disparate modules of,
00:49:01 does it feel like if you create a rule
00:49:07 and we’ll talk about the Wolfram physics model,
00:49:11 which is fascinating, but if you have a simple set
00:49:16 of rules with a data structure, like a hypergraph,
00:49:21 does that feel like a satisfying theory of everything?
00:49:25 Because then you really run up against the irreducibility,
00:49:29 computational irreducibility.
00:49:32 Right, so that’s a really interesting question.
00:49:34 So I, you know, what I thought was gonna happen
00:49:38 is I thought we, you know, I thought we had a pretty good,
00:49:42 I had a pretty good idea for what the structure
00:49:45 of this sort of theory that sort of underneath space
00:49:47 and time and so on might be like.
00:49:50 And I thought, gosh, you know, in my lifetime,
00:49:52 so to speak, we might be able to figure out what happens
00:49:55 in the first 10 to the minus 100 seconds of the universe.
00:49:58 And that would be cool, but it’s pretty far away
00:50:01 from anything that we can see today.
00:50:03 And it will be hard to test whether that’s right
00:50:05 and so on and so on and so on.
00:50:07 To my huge surprise, although it should have been obvious
00:50:10 and it’s embarrassing that it wasn’t obvious to me,
00:50:12 but to my huge surprise,
00:50:15 we managed to get unbelievably much further than that.
00:50:18 And basically what happened is that it turns out
00:50:21 that even though there’s this kind of bed
00:50:23 of computational irreducibility,
00:50:25 that sort of these, all these simple rules run into,
00:50:30 there are certain pieces of computational reducibility
00:50:34 that quite generically occur
00:50:36 for large classes of these rules.
00:50:38 And, and this is the really exciting thing
00:50:40 as far as I’m concerned,
00:50:42 the big pieces of computational reducibility
00:50:46 are basically the pillars of 20th century physics.
00:50:49 That’s the amazing thing,
00:50:50 that general relativity and quantum field theory
00:50:52 is sort of the pillars of 20th century physics
00:50:55 turn out to be precisely the stuff you can say.
00:50:59 There’s a lot you can’t say,
00:51:00 there’s a lot that’s kind of at this irreducible level
00:51:03 where you kind of don’t know what’s going to happen,
00:51:05 you have to run it, you know,
00:51:06 you can’t run it within our universe,
00:51:07 et cetera, et cetera, et cetera, et cetera.
00:51:10 But the thing is there are things you can say
00:51:13 and the things you can say turn out to be very beautifully
00:51:17 exactly the structure that was found
00:51:19 in 20th century physics,
00:51:21 namely general relativity and quantum mechanics.
00:51:24 And general relativity and quantum mechanics
00:51:26 are these pockets of reducibility that we think of as,
00:51:32 that 20th century physics
00:51:34 is essentially pockets of reducibility.
00:51:36 And then it is incredibly surprising
00:51:39 that any kind of model that’s generative
00:51:43 from simple rules would have such pockets.
00:51:47 Yeah, well, I think what’s surprising
00:51:49 is we didn’t know where those things came from.
00:51:52 It’s like general relativity,
00:51:53 it’s a very nice mathematically elegant theory.
00:51:56 Why is it true?
00:51:58 You know, quantum mechanics, why is it true?
00:52:00 What we realized is that from this,
00:52:04 that these theories are generic
00:52:07 to a huge class of systems
00:52:09 that have these particular
00:52:10 very unstructured underlying rules.
00:52:13 And that’s the thing that is sort of remarkable
00:52:16 and that’s the thing to me
00:52:18 that’s just, it’s really beautiful.
00:52:20 I mean, it’s, and the thing that’s even more beautiful
00:52:22 is that it turns out that, you know,
00:52:24 people have been struggling for a long time.
00:52:26 You know, how does general relativity theory of gravity
00:52:29 relate to quantum mechanics?
00:52:30 They seem to have all kinds of incompatibilities.
00:52:32 It turns out what we realized is
00:52:34 at some level they are the same theory.
00:52:37 And that’s just, it’s just great as far as I’m concerned.
00:52:40 So maybe like taking a little step back
00:52:43 from your perspective, not from the low,
00:52:47 not from the beautiful hypergraph,
00:52:50 well, from physics model perspective,
00:52:52 but from the perspective of 20th century physics,
00:52:55 what is general relativity?
00:52:57 What is quantum mechanics?
00:52:58 How do you think about these two theories
00:53:00 from the context of the theory of everything?
00:53:04 Like just even definition.
00:53:05 Yeah, yeah, yeah, right.
00:53:06 So I mean, you know, a little bit of history of physics,
00:53:08 right?
00:53:09 So, I mean the, you know, okay,
00:53:12 very, very quick history of this, right?
00:53:14 So, I mean, you know, physics, you know,
00:53:16 in ancient Greek times, people basically said,
00:53:19 we can just figure out how the world works.
00:53:21 As you know, we’re philosophers,
00:53:22 we’re gonna figure out how the world works.
00:53:24 You know, some philosophers thought there were atoms.
00:53:26 Some philosophers thought there were,
00:53:28 you know, continuous flows of things.
00:53:30 People had different ideas about how the world works.
00:53:33 And they tried to just say,
00:53:33 we’re gonna construct this idea of how the world works.
00:53:36 They didn’t really have sort of notions
00:53:38 of doing experiments and so on quite the same way
00:53:40 as developed later.
00:53:41 So that was sort of an early tradition
00:53:43 for thinking about sort of models of the world.
00:53:46 Then by the time of 1600s, time of Galileo and then Newton,
00:53:51 sort of the big idea there was, you know,
00:53:55 title of Newton’s book, you know, Principia Mathematica,
00:53:57 mathematical principles of natural philosophy.
00:54:00 We can use mathematics to understand natural philosophy,
00:54:04 to understand things about the way the world works.
00:54:07 And so that then led to this kind of idea that, you know,
00:54:10 we can write down a mathematical equation
00:54:12 and have that represent how the world works.
00:54:14 So Newton’s one of his most famous ones
00:54:16 is his universal law of gravity,
00:54:19 inverse square law of gravity
00:54:21 that allowed him to compute all sorts of features
00:54:23 of the planets and so on.
00:54:24 Although some of them he got wrong
00:54:26 and it took another hundred years
00:54:28 for people to actually be able to do the math
00:54:30 to the level that was needed.
00:54:31 But so that had been this sort of tradition
00:54:34 was we write down these mathematical equations.
00:54:36 We don’t really know where these equations come from.
00:54:38 We write them down.
00:54:39 Then we figure out, we work out the consequences
00:54:42 and we say, yes, that agrees with what we actually observe
00:54:45 in astronomy or something like this.
00:54:47 So that tradition continued.
00:54:49 And then the first of these two
00:54:51 sort of great 20th century innovations was,
00:54:55 well, the history is actually a little bit more complicated,
00:54:57 but let’s say that there were two,
00:55:01 quantum mechanics and general relativity.
00:55:03 Quantum mechanics kind of 1900
00:55:05 was kind of the very early stuff done by Planck
00:55:08 that led to the idea of photons, particles of light.
00:55:12 But let’s take general relativity first.
00:55:14 One feature of the story is that special relativity
00:55:19 thing Einstein invented in 1905
00:55:21 was something which surprisingly
00:55:24 was a kind of logically invented theory.
00:55:27 It was not a theory where it was something where
00:55:29 given these ideas that were sort of axiomatically
00:55:32 thought to be true about the world,
00:55:34 it followed that such and such a thing would be the case.
00:55:38 It was a little bit different
00:55:39 from the kind of methodological structure
00:55:42 of some existing theories in the more recent times,
00:55:45 where it’s just been, we write down an equation
00:55:47 and we find out that it works.
00:55:49 So what happened there.
00:55:51 So there’s some reasoning about the light.
00:55:53 The basic idea was the speed of light
00:55:57 appears to be constant.
00:55:59 Even if you’re traveling very fast,
00:56:01 you shine a flashlight, the light will come out.
00:56:05 Even if you’re going at half the speed of light,
00:56:07 the light doesn’t come out of your flashlight
00:56:08 at one and a half times the speed of light.
00:56:11 It’s still just the speed of light.
00:56:13 And to make that work,
00:56:14 you have to change your view of how space and time work
00:56:18 to be able to account for the fact
00:56:20 that when you’re going faster,
00:56:21 it appears that length is foreshortened
00:56:24 and time is dilated and things like this.
00:56:26 And that’s special relativity.
00:56:27 That’s special relativity.
00:56:28 So then Einstein went on with sort of
00:56:33 vaguely similar kinds of thinking.
00:56:34 In 1915, invented general relativity,
00:56:37 which is the theory of gravity.
00:56:39 And the basic point of general relativity
00:56:42 is it’s a theory that says,
00:56:44 when there is mass in space, space is curved.
00:56:49 And what does that mean?
00:56:52 Usually you think of what’s the shortest distance
00:56:55 between two points.
00:56:56 Like ordinarily on a plane in space, it’s a straight line.
00:57:00 Photons, light goes in straight lines.
00:57:04 Well, then the question is,
00:57:06 is if you have a curved surface,
00:57:10 a straight line is no longer straight.
00:57:12 On the surface of the earth,
00:57:13 the shortest distance between two points is a great circle.
00:57:16 It’s a circle.
00:57:18 So, you know, Einstein’s observation was
00:57:21 maybe the physical structure of space
00:57:24 is such that space is curved.
00:57:26 So the shortest distance between two points,
00:57:29 the path, the straight line in quotes,
00:57:32 won’t be straight anymore.
00:57:34 And in particular, if a photon is, you know,
00:57:37 traveling near the sun or something,
00:57:39 or if a particle is going,
00:57:40 something is traveling near the sun,
00:57:42 maybe the shortest path will be one
00:57:45 that is something which looks curved to us
00:57:48 because it seems curved to us
00:57:50 because space has been deformed by the presence of mass
00:57:53 associated with that massive object.
00:57:55 So the kind of the idea there is,
00:57:59 think of the structure of space
00:58:01 as being a dynamical changing kind of thing.
00:58:03 But then what Einstein did
00:58:04 was he wrote down these differential equations
00:58:07 that basically represented the curvature of space
00:58:10 and its response to the presence of mass and energy.
00:58:13 And that ultimately is connected to the force of gravity,
00:58:18 which is one of the forces that seems to,
00:58:20 based on its strength,
00:58:21 operate on a different scale than some of the other forces.
00:58:24 So it operates in a scale that’s very large.
00:58:27 What happens there is just this curvature of space,
00:58:32 which causes, you know, the paths of objects to be deflected.
00:58:35 That’s what gravity does.
00:58:37 It causes the paths of objects to be deflected.
00:58:39 And this is an explanation for gravity, so to speak.
00:58:43 And the surprise is that from 1915 until today,
00:58:47 everything that we’ve measured about gravity
00:58:49 precisely agrees with general relativity.
00:58:52 And that, you know, it wasn’t clear black holes
00:58:55 were sort of a predict,
00:58:56 well, actually the expansion of the universe
00:58:57 was an early potential prediction,
00:58:59 although Einstein tried to sort of patch up his equations
00:59:02 to make it not cause the universe to expand,
00:59:05 because it was kind of so obvious
00:59:06 the universe wasn’t expanding.
00:59:08 And, you know, it turns out it was expanding
00:59:10 and he should have just trusted the equations.
00:59:11 And that’s a lesson for those of us
00:59:14 interested in making fundamental theories of physics
00:59:16 is you should trust your theory and not try and patch it
00:59:19 because of something that you think might be the case
00:59:22 that might turn out not to be the case.
00:59:25 Even if the theory says something crazy is happening.
00:59:28 Yeah, right.
00:59:29 Like the universe is expanding.
00:59:30 Like the universe is expanding, right, which is,
00:59:31 but, you know, then it took until the 1940s,
00:59:35 probably even really until the 1960s,
00:59:36 until people understood that black holes
00:59:38 were a consequence of general relativity and so on.
00:59:42 But that’s, you know, the big surprise has been
00:59:45 that so far this theory of gravity has perfectly agreed
00:59:50 with, you know, these collisions of black holes
00:59:51 seen by their gravitational waves, you know,
00:59:54 it all just works.
00:59:55 So that’s been kind of one pillar of the story of physics
00:59:59 it’s mathematically complicated to work out
01:00:01 the consequences of general relativity,
01:00:03 but it’s not, there’s no, I mean,
01:00:05 and some things are kind of squiggly and complicated.
01:00:09 Like people believe, you know, energy is conserved.
01:00:12 Okay, well, energy conservation doesn’t really work
01:00:14 in general activity in the same way as it ordinarily does.
01:00:16 And it’s all a big mathematical story
01:00:19 of how you actually nail down something that is definitive
01:00:22 that you can talk about it and not specific to the,
01:00:25 you know, reference frames you’re operating in
01:00:27 and so on and so on and so on.
01:00:28 But fundamentally, general relativity is a straight shot
01:00:31 in the sense that you have this theory,
01:00:32 you work out its consequences.
01:00:34 And that theory is useful in terms of basic science
01:00:39 and trying to understand the way black holes work,
01:00:41 the way the creation of galaxies work,
01:00:43 sort of all of these kinds of cosmological things,
01:00:45 understanding what happened, like you said, at the Big Bang.
01:00:49 Yeah. Like all those kinds of,
01:00:50 well, no, not at the Big Bang actually, right?
01:00:52 But the…
01:00:53 Well, features of the expansion of the universe, yes.
01:00:55 I mean, and there are lots of details
01:00:58 where we don’t quite know how it’s working, you know,
01:00:59 is there, you know, where’s the dark matter,
01:01:02 is there dark energy, you know, et cetera, et cetera, et cetera.
01:01:04 But fundamentally, the, you know,
01:01:06 the testable features of general relativity,
01:01:08 it all works very beautifully.
01:01:10 And it’s in a sense, it is mathematically sophisticated,
01:01:13 but it is not conceptually hard to understand in some sense.
01:01:17 Okay. So that’s general relativity.
01:01:18 And what’s its friendly neighbor, like you said,
01:01:21 there’s two theories, quantum mechanics.
01:01:22 Right. So quantum mechanics,
01:01:24 the sort of the way that that originated was,
01:01:28 one question was, is the world continuous or is it discrete?
01:01:31 You know, in ancient Greek times,
01:01:32 people have been debating this.
01:01:34 People debated it, you know, throughout history.
01:01:36 Is light made of waves?
01:01:38 Is it continuous? Is it discrete?
01:01:39 Is it made of particles, corpuscles, whatever.
01:01:43 You know, what had become clear in the 1800s is that atoms,
01:01:47 that, you know, materials are made of discrete atoms.
01:01:51 You know, when you take some water,
01:01:53 the water is not a continuous fluid,
01:01:55 even though it seems like a continuous fluid
01:01:57 to us at our scale.
01:01:58 But if you say, let’s look at it,
01:02:00 smaller and smaller and smaller and smaller scale,
01:02:02 eventually you get down to these, you know,
01:02:04 these molecules and then atoms.
01:02:06 It’s made of discrete things.
01:02:07 The question is sort of how important is this discreteness?
01:02:10 Just what’s discrete, what’s not discrete?
01:02:12 Is energy discrete?
01:02:14 Is, you know, what’s discrete, what’s not?
01:02:17 And so.
01:02:18 Does it have mass?
01:02:19 Those kinds of questions.
01:02:20 Yeah, yeah, right.
01:02:21 Well, there’s a question, I mean, for example,
01:02:23 is mass discrete is an interesting question,
01:02:26 which is now something we can address.
01:02:28 But, you know, what happened in the coming up to the 1920s,
01:02:35 there was this kind of mathematical theory developed
01:02:37 that could explain certain kinds of discreteness
01:02:40 in particularly in features of atoms and so on.
01:02:44 And, you know, what developed was this mathematical theory
01:02:47 that was the theory of quantum mechanics,
01:02:50 theory of wave functions, Schrodinger’s equation,
01:02:52 things like this.
01:02:53 That’s a mathematical theory that allows you to calculate
01:02:57 lots of features of the microscopic world,
01:02:59 lots of things about how atoms work,
01:03:01 et cetera, et cetera, et cetera.
01:03:03 Now, the calculations all work just great.
01:03:05 The question of what does it really mean
01:03:09 is a complicated question.
01:03:11 Now, I mean, to just explain a little bit historically,
01:03:14 the, you know, the early calculations of things like atoms
01:03:17 worked great in 1920s, 1930s and so on.
01:03:20 There was always a problem.
01:03:21 There were, in quantum field theory,
01:03:24 which is a theory of, in quantum mechanics,
01:03:27 you’re dealing with a certain number of electrons
01:03:30 and you fix the number of electrons.
01:03:31 You say, I’m dealing with a two electron thing.
01:03:34 In quantum field theory,
01:03:35 you allow for particles being created and destroyed.
01:03:38 So you can emit a photon that didn’t exist before.
01:03:41 You can absorb a photon, things like that.
01:03:43 That’s a more complicated,
01:03:44 mathematically complicated theory.
01:03:46 And it had all kinds of mathematical issues
01:03:47 and all kinds of infinities that cropped up.
01:03:49 And it was finally figured out more or less
01:03:51 how to get rid of those.
01:03:52 But there were only certain ways of doing the calculations
01:03:55 and those didn’t work for atomic nuclei among other things.
01:03:59 And that led to a lot of development up until the 1960s
01:04:03 of alternative ideas for how one could understand
01:04:07 what was happening in atomic nuclei, et cetera,
01:04:09 et cetera, et cetera.
01:04:10 End result, in the end,
01:04:12 the kind of most quotes obvious mathematical structure
01:04:16 of quantum field theory seems to work.
01:04:18 Although it’s mathematically difficult to deal with,
01:04:20 but you can calculate all kinds of things.
01:04:22 You can calculate to a dozen decimal places,
01:04:26 certain things, you can measure them.
01:04:27 It all works.
01:04:28 It’s all beautiful.
01:04:29 Now you say…
01:04:30 The underlying fabric is the model
01:04:32 of that particular theory is fields.
01:04:34 Like you keep saying fields.
01:04:37 Those are quantum fields.
01:04:37 Those are different from classical fields.
01:04:40 A field is something like you say,
01:04:44 like you say the temperature field in this room.
01:04:46 It’s like there is a value of temperature
01:04:49 at every point around the room.
01:04:51 That’s some, or you can say the wind field
01:04:53 would be the vector direction of the wind at every point.
01:04:56 It’s continuous.
01:04:57 Yes, and that’s a classical field.
01:05:00 The quantum field is a much more
01:05:01 mathematically elaborate kind of thing.
01:05:04 And I should explain that one of the pictures
01:05:06 of quantum mechanics that’s really important is,
01:05:09 in classical physics, one believes
01:05:11 that sort of definite things happen in the world.
01:05:13 You pick up a ball, you throw it,
01:05:16 the ball goes in a definite trajectory
01:05:17 that has certain equations of motion.
01:05:20 It goes in a parabola, whatever else.
01:05:22 In quantum mechanics, the picture is
01:05:25 definite things don’t happen.
01:05:26 Instead, sort of what happens is this whole
01:05:29 sort of structure of all many different paths being followed
01:05:34 and we can calculate certain aspects of what happens,
01:05:37 certain probabilities of different outcomes and so on.
01:05:40 And you say, well, what really happened?
01:05:42 What’s really going on?
01:05:43 What’s the sort of, what’s the underlying,
01:05:45 what’s the underlying story?
01:05:47 How do we turn this mathematical theory
01:05:50 that we can calculate things with
01:05:52 into something that we can really understand
01:05:54 and have a narrative about?
01:05:56 And that’s been really, really hard for quantum mechanics.
01:05:58 My friend, Dick Feynman, always used to say,
01:06:01 nobody understands quantum mechanics,
01:06:03 even though he’d made his whole career
01:06:06 out of calculating things about quantum mechanics.
01:06:10 And so it’s a little bit.
01:06:11 Nevertheless, it’s what the quantum field theory is very,
01:06:16 very accurate at predicting a lot of the physical phenomena.
01:06:20 So it works.
01:06:21 Yeah.
01:06:22 But there are things about it, it has certain,
01:06:25 when we apply it, the standard model of particle physics,
01:06:27 for example, we, which we apply to calculate
01:06:31 all kinds of things that works really well.
01:06:33 And you say, well, it has certain parameters.
01:06:34 It has a whole bunch of parameters actually.
01:06:36 You say, why is the, why does the muon particle exist?
01:06:41 Why is it 206 times the mass of the electron?
01:06:44 We don’t know, no idea.
01:06:46 But so the standard model of physics is one of the models
01:06:50 that’s very accurate for describing
01:06:51 three of the fundamental forces of physics.
01:06:55 And it’s looking at the world of the very small.
01:06:58 Right.
01:06:59 And then there’s back to the neighbor of gravity,
01:07:03 of general relativity.
01:07:04 So, and then in the context of a theory of everything,
01:07:07 what’s traditionally the task of the unification
01:07:13 of these theories?
01:07:15 And why is it hard?
01:07:16 The issue is you try to use the methods
01:07:18 of quantum field theory to talk about gravity
01:07:20 and it doesn’t work.
01:07:22 Just like there are photons of light.
01:07:24 So there are gravitons,
01:07:25 which are sort of the particles of gravity.
01:07:27 And when you try and compute sort of the properties
01:07:30 of the particles of gravity,
01:07:32 the kind of mathematical tricks that get used
01:07:36 in working things out in quantum field theory don’t work.
01:07:39 And that’s, so that’s been a sort of fundamental issue.
01:07:43 And when you think about black holes,
01:07:44 which are a place where sort of the structure of space
01:07:48 is, you know, has sort of rapid variation
01:07:52 and you get kind of quantum effects mixed in
01:07:55 with effects from general relativity,
01:07:57 things get very complicated
01:07:58 and there are apparent paradoxes and things like that.
01:08:01 And people have, you know,
01:08:02 there’ve been a bunch of mathematical developments
01:08:05 in physics over the last, I don’t know, 30 years or so,
01:08:08 which have kind of picked away at those kinds of issues
01:08:11 and got hints about how things might work.
01:08:15 But it hasn’t been, you know,
01:08:17 and the other thing to realize is,
01:08:19 as far as physics is concerned,
01:08:20 it’s just like here’s general relativity,
01:08:22 here’s quantum field theory, you know, be happy.
01:08:25 Yeah, so do you think there’s a quantization of gravity,
01:08:28 so quantum gravity, what do you think of efforts
01:08:31 that people have tried to, yeah,
01:08:33 what do you think in general of the efforts
01:08:36 of the physics community to try to unify these laws?
01:08:39 So I think what’s, it’s interesting.
01:08:41 I mean, I would have said something very different
01:08:43 before what’s happened with our physics project.
01:08:46 I mean, you know, the remarkable thing is
01:08:48 what we’ve been able to do is to make
01:08:51 from this very simple, structurally simple,
01:08:55 underlying set of ideas,
01:08:57 we’ve been able to build this, you know,
01:09:00 very elaborate structure that’s both very abstract
01:09:04 and very sort of mathematically rich.
01:09:06 And the big surprise, as far as I’m concerned,
01:09:09 is that it touches many of the ideas that people have had.
01:09:12 So in other words, things like string theory and so on,
01:09:15 twister theory, it’s like the, you know,
01:09:18 we might’ve thought, I had thought we’re out on a prong,
01:09:21 we’re building something that’s computational,
01:09:22 it’s completely different from what other people have done.
01:09:25 But actually it seems like what we’ve done
01:09:27 is to provide essentially the machine code that, you know,
01:09:30 these things are various features
01:09:33 of domain specific languages, so to speak,
01:09:35 that talk about various aspects of this machine code.
01:09:37 And I think this is something that to me is very exciting
01:09:41 because it allows one both for us to provide
01:09:45 sort of a new foundation for what’s been thought about there
01:09:48 and for all the work that’s been done in those areas
01:09:52 to give us, you know, more momentum
01:09:55 to be able to figure out what’s going on.
01:09:57 Now, you know, people have sort of hoped,
01:09:58 oh, we’re just gonna be able to get, you know,
01:10:01 string theory to just answer everything.
01:10:03 That hasn’t worked out.
01:10:04 And I think we now kind of can see a little bit about
01:10:07 just sort of how far away certain kinds of things are
01:10:10 from being able to explain things.
01:10:12 Some things, one of the big surprises to me,
01:10:14 actually I literally just got a message
01:10:16 about one aspect of this is the, you know,
01:10:20 it’s turning out to be easier.
01:10:22 I mean, this project has been so much easier
01:10:24 than I could ever imagine it would be.
01:10:26 That is, I thought we would be, you know,
01:10:29 just about able to understand
01:10:31 the first 10 to the minus 100 seconds of the universe.
01:10:34 And, you know, it would be a hundred years
01:10:35 before we get much further than that.
01:10:37 It’s just turned out, it actually wasn’t that hard.
01:10:40 I mean, we’re not finished, but, you know.
01:10:42 So you’re seeing echoes of all the disparate theories
01:10:45 of physics in this framework.
01:10:47 Yes, yes.
01:10:48 I mean, it’s a very interesting, you know,
01:10:50 sort of history of science like phenomenon.
01:10:53 I mean, the best analogy that I can see
01:10:55 is what happened with the early days
01:10:58 of computability and computation theory.
01:11:00 You know, Turing machines were invented in 1936.
01:11:03 People sort of understand computation
01:11:06 in terms of Turing machines,
01:11:07 but actually there had been preexisting theories
01:11:09 of computation, combinators, general recursive functions,
01:11:12 Lambda calculus, things like this.
01:11:14 But people hadn’t, those hadn’t been concrete enough
01:11:18 that people could really wrap their arms around them
01:11:20 and understand what was going on.
01:11:21 And I think what we’re gonna see in this case
01:11:23 is that a bunch of these mathematical theories,
01:11:26 including some very,
01:11:28 I mean, one of the things that’s really interesting
01:11:29 is one of the most abstract things
01:11:31 that’s come out of sort of mathematics,
01:11:36 higher category theory, things about infinity group voids,
01:11:39 things like this, which to me always just seemed
01:11:41 like they were floating off into the stratosphere,
01:11:44 ionosphere of mathematics, turn out to be things
01:11:48 which our sort of theory anchors down
01:11:52 to something fairly definite and says are super relevant
01:11:56 to the way that we can understand how physics works.
01:11:59 Give me a sec.
01:12:00 By the way, I just threw a hat on.
01:12:01 You’ve said that with this metaphor analogy
01:12:06 that the theory of everything is a big mountain
01:12:09 and you have a sense that however far we are up the mountain,
01:12:14 that the Wolfram physics model view of the universe
01:12:21 is at least the right mountain.
01:12:22 We’re the right mountain, yes, without question.
01:12:25 Which aspect of it is the right mountain?
01:12:27 So for example, I mean, so there’s so many aspects
01:12:31 to just the way of the Wolfram physics project,
01:12:34 the way it approaches the world that’s clean, crisp,
01:12:39 and unique and powerful, so there’s a discreet nature to it,
01:12:45 there’s a hypergraph, there’s a computational nature,
01:12:48 there’s a generative aspect, you start from nothing,
01:12:51 you generate everything, do you think the actual model
01:12:56 is actually a really good one,
01:12:58 or do you think this general principle
01:13:00 from simplicity generating complexity is the right,
01:13:02 like what aspect of the mountain is the correct?
01:13:05 Yeah, right, I think that the kind of the meta idea
01:13:10 about using simple computational systems to do things,
01:13:14 that’s the ultimate big paradigm
01:13:18 that is sort of super important.
01:13:21 The details of the particular model are very nice and clean
01:13:25 and allow one to actually understand what’s going on.
01:13:27 They are not unique, and in fact, we know that.
01:13:30 We know that there’s a very, very, very, very,
01:13:34 there’s a large number of different ways
01:13:37 to describe essentially the same thing.
01:13:38 I mean, I can describe things in terms of hypergraphs,
01:13:41 I can describe them in terms of higher category theory,
01:13:43 I can describe them in a bunch of different ways.
01:13:45 They are in some sense all the same thing,
01:13:47 but our sort of story about what’s going on
01:13:50 and the kind of cultural mathematical resonances
01:13:53 are a bit different.
01:13:54 And I think it’s perhaps worth sort of saying a little bit
01:13:57 about kind of the foundational ideas
01:14:00 of these models and things.
01:14:04 Great, so can you maybe, can we like rewind?
01:14:09 We’ve talked about it a little bit,
01:14:11 but can you say like what the central idea is
01:14:14 of the Wolfram Physics Project?
01:14:16 Right, so the question is we’re interested
01:14:19 in finding sort of simple computational rule
01:14:21 that describes our whole universe.
01:14:24 Can we just pause on that?
01:14:25 It’s just so beautiful, that’s such a beautiful idea
01:14:30 that we can generate our universe
01:14:32 from a data structure, a simple structure,
01:14:39 simple set of rules, and we can generate our entire universe.
01:14:42 Yes, that’s the idea. That’s awe inspiring.
01:14:44 Right, but so the question is how do you actualize that?
01:14:50 What might this rule be like?
01:14:52 And so one thing you quickly realize is
01:14:55 if you’re gonna pack everything about our universe
01:14:57 into this tiny rule, not much that we are familiar with
01:15:01 in our universe will be obvious in that rule.
01:15:05 So you don’t get to fit all these parameters of the universe,
01:15:07 all these features of, you know, this is how space works,
01:15:10 this is how time works, et cetera, et cetera, et cetera.
01:15:12 You don’t get to fit that all in.
01:15:13 It all has to be sort of packed in to this thing,
01:15:16 something much smaller, much more basic,
01:15:18 much lower level machine code, so to speak, than that.
01:15:22 And all the stuff that we’re familiar with
01:15:23 has to kind of emerge from the operation.
01:15:26 So the rule in itself,
01:15:27 because of the computational reducibility,
01:15:30 is not gonna tell you the story.
01:15:32 It’s not gonna give you the answer to,
01:15:36 it’s not gonna let you predict
01:15:38 what you’re gonna have for lunch tomorrow,
01:15:40 and it’s not going to let you predict
01:15:42 basically anything about your life, about the universe.
01:15:44 Right, and you’re not going to be able to see in that rule,
01:15:47 oh, there’s the three
01:15:49 for the number of dimensions of space and so on.
01:15:51 That’s not gonna be there.
01:15:52 Spacetime is not going to be obviously.
01:15:54 Right, so the question is then,
01:15:55 what is the universe made of?
01:15:57 That’s a basic question.
01:16:00 And we’ve had some assumptions
01:16:01 about what the universe is made of
01:16:02 for the last few thousand years
01:16:04 that I think in some cases just turn out not to be right.
01:16:08 And the most important assumption
01:16:11 is that space is a continuous thing.
01:16:13 That is that you can, if you say,
01:16:17 let’s pick a point in space.
01:16:19 We’re gonna do geometry.
01:16:20 We’re gonna pick a point.
01:16:21 We can pick a point absolutely anywhere in space.
01:16:24 Precise numbers we can specify of where that point is.
01:16:28 In fact, Euclid who kind of wrote down
01:16:30 the original kind of axiomatization of geometry
01:16:32 back in 300 BC or so,
01:16:36 his very first definition, he says,
01:16:38 a point is that which has no part.
01:16:40 A point is this indivisible infinitesimal thing.
01:16:47 Okay, so we might’ve said that about material objects.
01:16:50 We might’ve said that about water, for example.
01:16:52 We might’ve said water is a continuous thing
01:16:54 that we can just pick any point we want in some water,
01:16:59 but actually we know it isn’t true.
01:17:00 We know that water is made of molecules that are discrete.
01:17:04 And so the question, one fundamental question
01:17:06 is what is space made of?
01:17:08 And so one of the things that’s sort of a starting point
01:17:10 for what I’ve done is to think of space as a discrete thing,
01:17:15 to think of there being sort of atoms of space
01:17:18 just as there are atoms of material things,
01:17:20 although very different kinds of atoms.
01:17:23 And by the way, I mean, this idea,
01:17:25 you know, there were ancient Greek philosophers
01:17:27 who had this idea.
01:17:28 There were, you know, Einstein actually thought
01:17:30 this is probably how things would work out.
01:17:31 I mean, he said, you know, repeatedly he thought
01:17:34 that’s the way it would work out.
01:17:35 We don’t have the mathematical tools in our time,
01:17:38 which was 1940s, 1950s and so on to explore this.
01:17:42 Like the way he thought,
01:17:44 you mean that there is something very, very small
01:17:48 and discrete that’s underlying space.
01:17:52 Yes.
01:17:53 And that means that, so, you know, the mathematical theory,
01:17:56 mathematical theories in physics assume that space
01:17:59 can be described just as a continuous thing.
01:18:02 You can just pick coordinates
01:18:04 and the coordinates can have any values.
01:18:06 And that’s how you define space.
01:18:07 Space is this just sort of background sort of theater
01:18:11 on which the universe operates.
01:18:13 But can we draw a distinction between space
01:18:17 as a thing that could be described by three values,
01:18:22 coordinates, and how you’re,
01:18:25 are you using the word space more generally when you say?
01:18:29 No, I’m just talking about space
01:18:30 as in what we experience in the universe.
01:18:34 So that you think this 3D aspect of it is fundamental.
01:18:38 No, I don’t think that 3D is fundamental at all, actually.
01:18:40 I think that the thing that has been assumed
01:18:45 is that space is this continuous thing
01:18:48 where you can just describe it by,
01:18:49 let’s say three numbers, for instance.
01:18:51 But most important thing about that
01:18:53 is that you can describe it by precise numbers
01:18:56 because you can pick any point in space
01:18:58 and you can talk about motions,
01:18:59 any infinitesimal motion in space.
01:19:01 And that’s what continuous means.
01:19:03 That’s what continuous means.
01:19:04 That’s what, you know, Newton invented calculus
01:19:06 to describe these kind of continuous small variations
01:19:08 and so on.
01:19:09 That was, that’s kind of a fundamental idea
01:19:11 from Euclid on that’s been a fundamental idea about space.
01:19:15 And so.
01:19:16 Is that right or wrong?
01:19:18 It’s not right.
01:19:20 It’s not right.
01:19:20 It’s right at the level of our experience most of the time.
01:19:25 It’s not right at the level of the machine code,
01:19:27 so to speak.
01:19:28 And so.
01:19:29 Machine code.
01:19:31 Yeah, of the simulation.
01:19:32 That’s right.
01:19:33 That’s right.
01:19:33 They’re the very lowest level of the fabric of the universe,
01:19:36 at least under the Wolfram physics model
01:19:41 is your senses is discrete.
01:19:44 Right.
01:19:45 So now what does that mean?
01:19:46 So it means what is space then?
01:19:49 So in models, the basic idea is you say
01:19:54 there are these sort of atoms of space.
01:19:56 They’re these points that represent,
01:19:59 you know, represent places in space,
01:20:02 but they’re just discrete points.
01:20:03 And the only thing we know about them
01:20:06 is how they’re connected to each other.
01:20:08 We don’t know where they are.
01:20:09 They don’t have coordinates.
01:20:10 We don’t get to say this is a position, such and such.
01:20:12 It’s just, here’s a big bag of points.
01:20:15 Like in our universe,
01:20:16 there might be 10 to the 100 of these points.
01:20:18 And all we know is this point is connected
01:20:21 to this other point.
01:20:22 So it’s like, you know,
01:20:23 all we have is the friend network, so to speak.
01:20:25 We don’t have, you know, people’s, you know,
01:20:27 physical addresses.
01:20:29 All we have is the friend network of these points.
01:20:31 Yeah.
01:20:32 The underlying nature of reality is kind of like a Facebook.
01:20:35 We don’t know their location, but we have the friends.
01:20:37 Yeah, yeah, right.
01:20:38 We know which point is connected to which other points.
01:20:41 And that’s all we know.
01:20:43 And so you might say, well,
01:20:44 how on earth can you get something
01:20:46 which is like our experience of, you know,
01:20:49 what seems like continuous space?
01:20:50 Well, the answer is,
01:20:51 by the time you have 10 to the 100 of these things,
01:20:54 those connections can work in such a way
01:20:57 that on a large scale,
01:20:59 it will seem to be like continuous space
01:21:02 in let’s say three dimensions
01:21:03 or some other number of dimensions
01:21:05 or 2.6 dimensions or whatever else.
01:21:07 Because they’re much, much, much, much larger.
01:21:10 So like the number of relationships here we’re talking about
01:21:15 is just a humongous amount.
01:21:16 So the kind of thing you’re talking about
01:21:18 is very, very, very small relative
01:21:20 to our experience of daily life.
01:21:22 Right, so I mean, you know,
01:21:23 we don’t know exactly the size,
01:21:25 but maybe 10 to the minus,
01:21:30 maybe around 10 to the minus 100 meters.
01:21:32 So, you know, the size of, to give a comparison,
01:21:34 the size of a proton is 10 to the minus 15 meters.
01:21:38 And so this is something incredibly tiny compared to that.
01:21:42 And the idea that from that would emerge
01:21:45 the experience of continuous space is mind blowing.
01:21:51 Well, what’s your intuition why that’s possible?
01:21:53 Like, first of all, I mean, we’ll get into it,
01:21:57 but I don’t know if we will
01:21:59 through the medium of conversation,
01:22:01 but the construct of hypergraphs is just beautiful.
01:22:06 Right.
01:22:07 Cellular automata are beautiful.
01:22:08 We’ll talk about it.
01:22:09 But this thing about, you know,
01:22:11 continuity arising from discrete systems
01:22:14 is in today’s world is actually not so surprising.
01:22:17 I mean, you know, your average computer screen, right?
01:22:19 Every computer screen is made of discrete pixels.
01:22:21 Yet we have the, you know,
01:22:23 we have the idea that we’re seeing
01:22:25 these continuous pictures.
01:22:27 I mean, it’s, you know,
01:22:27 the fact that on a large scale,
01:22:29 continuity can arise from lots of discrete elements.
01:22:33 This is at some level unsurprising now.
01:22:35 Wait, wait, wait, wait, wait, wait.
01:22:37 But the pixels have a very definitive structure
01:22:42 of neighbors on a computer screen.
01:22:46 Right.
01:22:46 There’s no concept of spatial,
01:22:50 of space inherent in the underlying fabric of reality.
01:22:55 Right, right, right.
01:22:56 So the point is that, but there are cases where there are.
01:22:59 So for example, let’s just imagine you have a square grid.
01:23:03 Okay, and at every point on the grid,
01:23:05 you have one of these atoms of space
01:23:07 and it’s connected to four other,
01:23:09 four other atoms of space on the, you know,
01:23:11 Northeast, Southwest corners, right?
01:23:14 There you have something where if you zoom out from that,
01:23:17 it’s like a computer screen.
01:23:19 Yeah, so the relationship creates the spatial,
01:23:23 like the relationship creates a constraint,
01:23:26 which then in an emergent sense creates a like,
01:23:33 yeah, like basically a spatial coordinate for that thing.
01:23:37 Yeah, right.
01:23:38 Even though the individual point doesn’t have a space.
01:23:40 Even though the individual point doesn’t know anything,
01:23:42 it just knows what its neighbors are.
01:23:45 On a large scale, it can be described by saying,
01:23:48 oh, it looks like it’s a, you know,
01:23:50 this grid is zoomed out grid.
01:23:52 You can say, well, you can describe these different points
01:23:54 by saying they have certain positions,
01:23:56 coordinates, et cetera.
01:23:57 Now, in the sort of real setup,
01:23:59 it’s more complicated than that.
01:24:00 It isn’t just a square grid or something.
01:24:03 It’s something much more dynamic and complicated,
01:24:05 which we’ll talk about.
01:24:07 But so, you know, the first idea,
01:24:10 the first key idea is, you know,
01:24:12 what’s the universe made of?
01:24:13 It’s made of atoms of space basically
01:24:15 with these connections between them.
01:24:17 What kind of connections do they have?
01:24:19 Well, so the simplest kind of thing you might say is,
01:24:23 we’ve got something like a graph
01:24:25 where every atom of space,
01:24:28 where we have these edges that go between,
01:24:31 these connections that go between atoms of space.
01:24:33 We’re not saying how long these edges are.
01:24:34 We’re just saying there is a connection
01:24:36 from this place, from this atom to this atom.
01:24:39 Just a quick pause,
01:24:40 because there’s a lot of very people that listen to this.
01:24:44 Just to clarify, because I did a poll actually,
01:24:46 what do you think a graph is a long time ago?
01:24:49 And it’s kind of funny how few people
01:24:52 know the term graph outside of computer science.
01:24:55 It’s good.
01:24:56 Let’s call it a network.
01:24:57 I think that’s it.
01:24:58 Let’s call it a network is better.
01:24:59 So, but every time, I like the word graph though.
01:25:00 So let’s define, let’s just say that a graph
01:25:03 will use terms nodes and edges maybe.
01:25:06 And it’s just the nodes represent some abstract entity
01:25:11 and then the edges represent relationships
01:25:13 between those entities.
01:25:14 Right, exactly.
01:25:15 So that’s what a graph says.
01:25:16 Sorry, so there you go.
01:25:18 So that’s the basic structure.
01:25:20 That is the simplest case of a basic structure.
01:25:23 Actually, it tends to be better to think about hypergraphs.
01:25:27 So a hypergraph is just, instead of saying
01:25:31 there are connections between pairs of things,
01:25:34 we say there are connections between any number of things.
01:25:37 So there might be ternary edges.
01:25:39 So instead of just having two points
01:25:42 are connected by an edge,
01:25:44 you say three points are all associated with a hyperedge,
01:25:48 are all connected by a hyperedge.
01:25:50 That’s just, at some level, that’s a detail.
01:25:54 It’s a detail that happens to make the, for me,
01:25:57 sort of in the history of this project,
01:26:00 the realization that you could do things that way
01:26:02 broke out of certain kinds of arbitrariness
01:26:04 that I felt that there was in the model
01:26:06 before I had seen how this worked.
01:26:07 I mean, a hypergraph can be mapped to a graph.
01:26:12 It’s just a convenient representation.
01:26:14 Mathematical speaking.
01:26:15 That’s correct. That’s correct.
01:26:16 But so then, so, okay, so the first question,
01:26:19 the first idea of these models of ours is
01:26:22 space is made of these connected sort of atoms of space.
01:26:26 The next idea is space is all there is.
01:26:29 There’s nothing except for this space.
01:26:31 So in traditional ideas in physics,
01:26:33 people have said there’s space, it’s kind of a background.
01:26:36 And then there’s matter, all these particles, electrons,
01:26:39 all these other things, which exist in space, right?
01:26:43 But in this model, one of the key ideas is
01:26:46 there’s nothing except space.
01:26:48 So in other words, everything that exists in the universe
01:26:52 is a feature of this hypergraph.
01:26:54 So how can that possibly be?
01:26:55 Well, the way that works is
01:26:58 that there are certain structures in this hypergraph
01:27:01 where you say that little twisty knotted thing,
01:27:05 we don’t know exactly how this works yet,
01:27:07 but we have sort of idea about how it works mathematically.
01:27:10 This sort of twisted knotted thing,
01:27:13 that’s the core of an electron.
01:27:14 This thing over there that has this different form,
01:27:17 that’s something else.
01:27:18 So the different peculiarities of the structure
01:27:21 of this graph are the very things
01:27:24 that we think of as the particles inside the space,
01:27:29 but in fact, it’s just a property of the space.
01:27:31 Mind blowing, first of all, that it’s mind blowing,
01:27:34 and we’ll probably talk in its simplicity and beauty.
01:27:38 Yes, I think it’s very beautiful.
01:27:40 I mean, this is, I’m…
01:27:41 But okay, but that’s space,
01:27:43 and then there’s another concept
01:27:44 we didn’t really kind of mention,
01:27:45 but you think it of computation as a transformation.
01:27:50 Let’s talk about time in a second.
01:27:51 Let’s just, I mean, on the subject of space,
01:27:55 there’s this question of kind of what,
01:27:57 there’s this idea, there is this hypergraph,
01:27:59 it represents space,
01:28:01 and it represents everything that’s in space.
01:28:03 The features of that hypergraph,
01:28:05 you can say certain features in this part we do know,
01:28:08 certain features of the hypergraph
01:28:09 represent the presence of energy, for example,
01:28:11 or the presence of mass or momentum,
01:28:13 and we know what the features of the hypergraph
01:28:16 that represent those things are,
01:28:17 but it’s all just the same hypergraph.
01:28:20 So one thing you might ask is,
01:28:22 you know, if you just look at this hypergraph and you say,
01:28:24 and we’re gonna talk about sort of what the hypergraph does,
01:28:27 but if you say, you know,
01:28:28 how much of what’s going on in this hypergraph
01:28:31 is things we know and care about,
01:28:34 like particles and atoms and electrons
01:28:36 and all this kind of thing,
01:28:37 and how much is just the background of space?
01:28:40 So it turns out, so far as in one rough estimate of this,
01:28:45 everything that we care about in the universe
01:28:47 is only one part in 10 to the 120
01:28:50 of what’s actually going on.
01:28:52 The vast majority of what’s happening
01:28:54 is purely things that maintain the structure of space.
01:28:57 That, in other words, that the things that are
01:28:59 the features of space that are the things
01:29:03 that we consider notable,
01:29:04 like the presence of particles and so on,
01:29:06 that’s a tiny little piece of froth
01:29:08 on the top of all this activity
01:29:10 that mostly is just intended to,
01:29:13 you know, mostly, I can’t say intended,
01:29:15 there’s no intention here,
01:29:16 that just maintains the structure of space.
01:29:20 Let me load that in.
01:29:24 It just makes me feel so good as a human being.
01:29:27 To be the froth on the one in a 10 to the 120
01:29:31 or something of, well.
01:29:33 And also just humbling how,
01:29:37 in this mathematical framework,
01:29:39 how much work needs to be done
01:29:41 on the infrastructure of our universe.
01:29:44 Right, to maintain the infrastructure of our universe
01:29:46 is a lot of work.
01:29:47 We are merely writing a little tiny things
01:29:51 on top of that infrastructure.
01:29:53 But you were just starting to talk a little bit about,
01:29:57 we talked about space,
01:29:59 that represents all the stuff that’s in the universe.
01:30:03 The question is, what does that stuff do?
01:30:06 And for that, we have to start talking about time
01:30:09 and what is time and so on.
01:30:11 And, you know, one of the basic idea of this model
01:30:15 is time is the progression of computation.
01:30:18 So in other words, we have a structure of space
01:30:21 and there is a rule that says
01:30:23 how that structure of space will change.
01:30:25 And it’s the application,
01:30:26 the repeated application of that rule
01:30:28 that defines the progress of time.
01:30:32 And what does the rule look like
01:30:34 in the space of hypergraphs?
01:30:36 Right, so what the rule says is something like,
01:30:38 if you have a little tiny piece of hypergraph
01:30:40 that looks like this,
01:30:42 then it will be transformed into a piece of hypergraph
01:30:44 that looks like this.
01:30:46 So that’s all it says.
01:30:47 It says you pick up these elements of space
01:30:51 and you can think of these edges,
01:30:54 these hyper edges as being relations
01:30:56 between elements in space.
01:30:57 You might pick up these two relations
01:31:01 between elements in space.
01:31:03 And we’re not saying where those elements are
01:31:04 or what they are,
01:31:05 but every time there’s a certain arrangement
01:31:07 of elements in space,
01:31:09 then arrangement in the sense of the way they’re connected,
01:31:12 then we transform it into some other arrangement.
01:31:14 So there’s a little tiny pattern
01:31:16 and you transform it into another little pattern.
01:31:18 That’s right.
01:31:19 And then because of this,
01:31:20 I mean, again, it’s kind of similar to cellular automata
01:31:23 in that like on paper, the rule looks like super simple.
01:31:26 It’s like, yeah, okay.
01:31:30 Yeah, right, from this, the universe can be born.
01:31:33 But like once you start applying it,
01:31:36 beautiful structure starts being,
01:31:39 potentially can be created.
01:31:41 And what you’re doing is you’re applying that rule
01:31:43 to different parts,
01:31:45 like anytime you match it within the hypergraph.
01:31:49 And then one of the like incredibly beautiful
01:31:53 and interesting things to think about
01:31:55 is the order in which you apply that rule,
01:31:59 because that pattern appears all over the place.
01:32:02 Right, so this is a big complicated thing,
01:32:04 very hard to wrap one’s brain around, okay?
01:32:06 So you say the rule is every time you see this little pattern
01:32:10 transform it in this way.
01:32:12 But yet, as you look around the space
01:32:15 that represents the universe,
01:32:17 there may be zillions of places
01:32:18 where that little pattern occurs.
01:32:20 So what it says is just do this,
01:32:24 apply this rule wherever you feel like.
01:32:26 And what is extremely non trivial is,
01:32:31 well, okay, so this is happening sort of
01:32:33 in computer science terms, sort of asynchronously,
01:32:35 you’re just doing it wherever you feel like doing it.
01:32:39 And the only constraint is
01:32:41 that if you’re going to apply the rule somewhere,
01:32:43 the things to which you apply the rule,
01:32:46 the little elements to which you apply the rule,
01:32:50 if they have to be,
01:32:54 okay, well, you can think of each application of the rule
01:32:56 as being kind of an event that happens in the universe.
01:32:59 And the input to an event has to be ready
01:33:04 for the event to occur.
01:33:06 That is, if one event occurred,
01:33:08 if one transformation occurred,
01:33:10 and it produced a particular atom of space,
01:33:12 then that atom of space has to already exist
01:33:17 before another transformation that’s going to apply
01:33:20 to that atom of space can occur.
01:33:23 So that’s like the prerequisite for the event.
01:33:25 That’s right, that’s right.
01:33:26 So that defines a kind of,
01:33:30 this sort of set of causal relationships between events.
01:33:33 It says, this event has to have happened before this event.
01:33:38 But that is…
01:33:40 But that’s not a very limiting constraint.
01:33:42 No, it’s not.
01:33:44 And what’s interesting…
01:33:44 You still get the zillion,
01:33:47 that’s a technical term, options.
01:33:49 That’s correct.
01:33:50 But, okay, so this is where things get a little bit more
01:33:53 elaborate, but…
01:33:54 But they’re mind blowing, so…
01:33:56 Right, but so what happens is,
01:33:59 so the first thing you might say is,
01:34:01 you know, let’s…
01:34:02 Well, okay, so this question about the freedom
01:34:04 of which event you do when.
01:34:07 Well, let me sort of state an answer and then explain it.
01:34:10 Okay, the validity of special relativity
01:34:14 is a consequence of the fact that in some sense,
01:34:17 it doesn’t matter in what order you do
01:34:19 these underlying things, so long as they respect
01:34:22 this kind of set of causal relationships.
01:34:25 So…
01:34:26 And that’s the part that’s in a certain sense
01:34:30 is a really important one,
01:34:31 but the fact that it sometimes doesn’t matter,
01:34:35 that’s a…
01:34:37 I don’t know what to…
01:34:37 That’s another, like, beautiful thing.
01:34:38 Well, okay, so there’s this idea
01:34:40 of what I call causal invariance.
01:34:42 Causal invariance, exactly.
01:34:44 So that’s a…
01:34:44 Really, really powerful idea.
01:34:46 Right, it’s a powerful idea,
01:34:47 which has actually arisen in different forms
01:34:50 many times in the history of mathematics,
01:34:52 mathematical logic, even computer science,
01:34:54 has many different names.
01:34:56 I mean, our particular version of it
01:34:58 is a little bit tighter than other versions,
01:35:00 but it’s basically the same idea.
01:35:01 Here’s how to think about that idea.
01:35:03 So imagine that…
01:35:05 Well, let’s talk about it in terms of math for a second.
01:35:08 Let’s say you’re doing algebra and you’re told,
01:35:10 you know, multiply out this series of polynomials
01:35:14 that are multiplied together, okay?
01:35:16 You say, well, which order should I do that in?
01:35:19 Say, well, do I multiply the third one by the fourth one
01:35:21 and then do it by the first one?
01:35:22 Or do I do the fifth one by the sixth one and then do that?
01:35:25 Well, it turns out it doesn’t matter.
01:35:27 You can multiply them out in any order,
01:35:29 you’ll always get the same answer.
01:35:31 That’s a property…
01:35:33 If you think about kind of making a kind of network
01:35:36 that represents in what order you do things,
01:35:38 you’ll get different orders
01:35:40 for different ways of multiplying things out,
01:35:42 but you’ll always get the same answer.
01:35:44 Same thing if you…
01:35:45 Let’s say you’re sorting.
01:35:46 You’ve got a bunch of A’s and B’s.
01:35:48 They’re in random, some random order,
01:35:50 you know, BAA, BBBAA, whatever.
01:35:53 And you have a little rule that says,
01:35:55 every time you see BA, flip it around to AB, okay?
01:36:00 Eventually you apply that rule enough times,
01:36:02 you’ll have sorted the string
01:36:03 so that it’s all the A’s first and then all the B’s.
01:36:07 Again, there are many different orders
01:36:10 in which you can do that to many different sort of places
01:36:13 where you can apply that update.
01:36:15 In the end, you’ll always get the string sorted the same way.
01:36:18 I know with sorting the string, it sounds obvious.
01:36:22 That’s to me surprising
01:36:24 that there is in complicated systems,
01:36:28 obviously with a string,
01:36:29 but in a hypergraph that the application of the rule,
01:36:33 asynchronous rule can lead to the same results sometimes.
01:36:36 Yes, yes, that is not obvious.
01:36:39 And it was something that, you know,
01:36:40 I sort of discovered that idea for these kinds of systems
01:36:44 and back in the 1990s.
01:36:45 And for various reasons, I was not satisfied
01:36:50 by how sort of fragile finding that particular property was.
01:36:54 And let me just make another point,
01:36:56 which is that it turns out that even if the underlying rule
01:37:01 does not have this property of causal invariance,
01:37:03 it can turn out that every observation
01:37:06 made by observers of the rule can,
01:37:09 they can impose what amounts to causal invariance
01:37:12 on the rule.
01:37:13 We can explain that.
01:37:14 It’s a little bit more complicated.
01:37:15 I mean, technically that has to do with this idea
01:37:18 of completions, which is something that comes up
01:37:20 in term rewriting systems,
01:37:21 automated theorem proving systems and so on.
01:37:24 But let’s ignore that for a second.
01:37:26 We can come to that later.
01:37:27 But is it useful to talk about observation?
01:37:29 Not yet.
01:37:30 Not yet.
01:37:31 It’s so great.
01:37:33 So there’s some concept of causal invariance
01:37:35 as you apply these rules in an asynchronous way,
01:37:39 you can think of those transformations as events.
01:37:42 So there’s this hypergraph that represents space
01:37:44 and all of these events happening in the space
01:37:47 and the graph grows in interesting complicated ways.
01:37:50 And eventually the froth arises of what we experience
01:37:54 as human existence.
01:37:56 So that’s it.
01:37:57 That’s some version of the picture,
01:37:58 but let’s explain a little bit more.
01:38:00 Exactly.
01:38:01 What’s a little more detail like?
01:38:03 Right.
01:38:04 Well, so one thing that is sort of surprising
01:38:06 in this theory is one of the sort of achievements
01:38:10 of 20th century physics was kind of bringing
01:38:12 space and time together.
01:38:13 That was, you know, special relativity.
01:38:15 People talk about space time, this sort of unified thing
01:38:19 where space and time kind of a mixed
01:38:21 and there’s a nice mathematical formalism
01:38:24 that in which, you know, space and time sort of appear
01:38:28 as part of the space time continuum,
01:38:30 the space time, you know, four vectors and things like this.
01:38:34 You know, we talk about time as the fourth dimension
01:38:37 and all these kinds of things.
01:38:38 It’s, you know, and it seems like the theory of relativity
01:38:42 sort of says space and time are fundamentally
01:38:44 the same kind of thing.
01:38:45 So one of the things that took a while to understand
01:38:48 in this approach of mine is that in my kind of approach,
01:38:54 space and time are really not fundamentally
01:38:56 the same kind of thing.
01:38:57 Space is the extension of this hypergraph.
01:39:00 Time is the kind of progress of this inexorable computation
01:39:04 of these rules getting applied to the hypergraph.
01:39:07 So it’s, they seem like very different kinds of things.
01:39:10 And so that at first seems like
01:39:12 how can that possibly be right?
01:39:14 How can that possibly be Lorentz invariant?
01:39:16 That’s the term for things being, you know,
01:39:18 following the rules of special relativity.
01:39:21 Well, it turns out that when you have causal invariants
01:39:26 that, and let’s see, we can, it’s worth explaining
01:39:30 a little bit how this works.
01:39:31 It’s a little bit elaborate,
01:39:32 but the basic point is that even though space and time
01:39:38 sort of come from very different places,
01:39:41 it turns out that the rules of sort of space time
01:39:45 that special relativity talks about come out of this model
01:39:51 when you’re looking at large enough systems.
01:39:53 So a way to think about this, you know,
01:39:56 in terms of when you’re looking at large enough systems,
01:39:59 the part of that story is when you look at some fluid
01:40:03 like water, for example, there are equations
01:40:06 that govern the flow of water.
01:40:08 Those equations are things that apply on a large scale.
01:40:12 If you look at the individual molecules,
01:40:14 they don’t know anything about those equations.
01:40:16 It’s just the sort of the large scale effect
01:40:19 of those molecules turns out to follow those equations.
01:40:22 And it’s the same kind of thing happening in our models.
01:40:25 I know this might be a small point,
01:40:27 but it might be a very big one.
01:40:29 We’ve been talking about space and time
01:40:32 at the lowest level of the model, which is space.
01:40:35 The hypergraph time is the evolution of this hypergraph.
01:40:39 But there’s also space time that we think about
01:40:43 and general relativity for your special relativity.
01:40:47 Like how do you go from the lowest source code
01:40:54 of space and time as we’re talking about
01:40:55 to the more traditional terminology of space and time?
01:40:58 So the key thing is this thing we call the causal graph.
01:41:01 So the causal graph is the graph
01:41:03 of causal relationships between events.
01:41:06 So every one of these little updating events,
01:41:08 every one of these little transformations
01:41:10 of the hypergraph happens somewhere in the hypergraph,
01:41:13 happens at some stage in the computation.
01:41:16 That’s an event.
01:41:18 That event has a causal relationship to other events
01:41:22 in the sense that if another event needs as its input,
01:41:27 the output from the first event,
01:41:29 there will be a causal relationship
01:41:31 of the future event will depend on the past event.
01:41:35 So you can say it has a causal connection.
01:41:37 And so you can make this graph
01:41:39 of causal relationships between events.
01:41:42 That graph of causal relationships,
01:41:44 causal invariance implies that that graph is unique.
01:41:47 It doesn’t matter even though you think,
01:41:51 oh, I’m, let’s say we were sorting a string, for example,
01:41:54 I did that particular transposition of characters
01:41:57 at this time, then I did that one, then I did this one.
01:42:00 Turns out if you look at the network of connections
01:42:03 between those updating events, that network is the same.
01:42:06 It’s the, if you were to, the structure.
01:42:11 So in other words, if you were to draw that,
01:42:13 if you were to put that network on a picture
01:42:15 of where you’re doing all the updating,
01:42:17 the places where you put the nodes of the network
01:42:20 will be different, but the way the nodes are connected
01:42:22 will always be the same.
01:42:23 So, but the causal graph is, I don’t know,
01:42:27 it’s kind of an observation, it’s not enforced,
01:42:31 it’s just emergent from a set of events.
01:42:33 It’s a feature of, okay, so what it is is.
01:42:36 The characteristic, I guess, of the way events happen.
01:42:38 Right, it’s an event can’t happen
01:42:40 until its input is ready.
01:42:42 And so that creates this network of causal relationships.
01:42:46 And that’s the causal graph.
01:42:48 And the thing that the next thing to realize is,
01:42:51 okay, we, when you’re going to observe
01:42:54 what happens in the universe,
01:42:56 you have to sort of make sense of this causal graph.
01:42:59 So, and you are an observer who yourself
01:43:02 is part of this causal graph.
01:43:05 And so that means, so let me give you an example
01:43:07 of how that works.
01:43:08 So imagine we have a really weird theory of physics
01:43:11 of the world where it says this updating process,
01:43:15 there’s only gonna be one update at every moment in time.
01:43:18 And there’s just gonna be like a Turing machine.
01:43:19 It has a little head that runs around
01:43:21 and just is always just updating one thing at a time.
01:43:23 So you say, I have a theory of physics
01:43:26 and the theory of physics says,
01:43:27 there’s just this one little place where things get updated.
01:43:30 You say, that’s completely crazy because,
01:43:32 it’s plainly obvious that things are being updated
01:43:35 sort of at the same time.
01:43:37 Async obviously, yeah, at the same time, yeah.
01:43:39 But the fact is that the thing is that if I’m talking to you
01:43:44 and you seem to be being updated as I’m being updated,
01:43:47 but if there’s just this one little head
01:43:48 that’s running around updating things,
01:43:51 I will not know whether you’ve been updated or not
01:43:53 until I’m updated.
01:43:55 So in other words, draw this causal graph
01:43:58 of the causal relationship between the updatings in you
01:44:01 and the updatings in me,
01:44:02 it’ll still be the same causal graph,
01:44:04 whether even though the underlying sort of story
01:44:07 of what happens is, oh, there’s just this one little thing
01:44:10 and it goes and updates in different places in the universe.
01:44:12 So is that clear or is that a hypothesis?
01:44:18 Is that clear that there’s a unique causal graph?
01:44:21 If there’s causal invariance, there’s unique causal graph.
01:44:24 So it’s okay to think of what we’re talking about
01:44:28 as a hypergraph and the operations on it
01:44:30 as a kind of touring machine with a single head,
01:44:32 like a single guy running around updating stuff.
01:44:37 Is that safe to intuitively think of it this way?
01:44:40 Let me think about that for a second.
01:44:41 Yes, I think so.
01:44:42 I think there’s nothing, it doesn’t matter.
01:44:44 I mean, you can say, okay, there is one,
01:44:47 the reason I’m pausing for a second is that I’m wondering,
01:44:52 well, when you say running around,
01:44:55 depends how far it jumps every time it runs.
01:44:57 Yeah, yeah, that’s right.
01:44:59 But I mean like one operation at a time.
01:45:02 Yeah, you can think of it as one operation at a time.
01:45:03 It’s easier for the human brain to think of it that way
01:45:06 as opposed to simultaneous.
01:45:08 Well, maybe it’s not, okay, but the thing is
01:45:10 that’s not how we experience the world.
01:45:12 What we experience is we look around,
01:45:15 everything seems to be happening
01:45:17 at successive moments in time everywhere in space.
01:45:21 Yes.
01:45:21 That is the, and that’s partly a feature
01:45:23 of our particular construction.
01:45:25 I mean, that is the speed of light is really fast
01:45:28 compared to, you know, we look around, you know,
01:45:30 I can see maybe a hundred feet away right now.
01:45:33 You know, it’s the, my brain does not process very much
01:45:38 in the time it takes light to go a hundred feet.
01:45:41 The brain operates at a scale of hundreds of milliseconds
01:45:44 or something like that, I don’t know.
01:45:45 Right.
01:45:46 And speed of light is much faster.
01:45:47 Right, you know, light goes,
01:45:49 in a billionth of a second light has gone afoot.
01:45:51 So it goes a billion feet every second.
01:45:53 There’s certain moments through this conversation
01:45:56 where I imagine the absurdity of the fact
01:46:01 that there’s two descendants of apes modeled by a hypergraph
01:46:05 that are communicating with each other
01:46:06 and experiencing this whole thing
01:46:09 as a real time simultaneous update with,
01:46:13 I’m taking in photons from you right now,
01:46:15 but there’s something much, much deeper going on here.
01:46:19 Right, it does have a.
01:46:20 It’s paralyzing sometimes to just.
01:46:22 Yes.
01:46:23 To remember that.
01:46:24 Right, no, I mean, you know, it’s a, you know.
01:46:26 Sorry.
01:46:27 Yes, yes, no.
01:46:28 As a small little tangent, I just remembered
01:46:30 that we’re talking about,
01:46:32 I mean, about the fabric of reality.
01:46:37 Right, so we’ve got this causal graph
01:46:40 that represents the sort of causal relationships
01:46:41 between all these events in the universe.
01:46:43 That causal graph kind of is a representation of space time,
01:46:47 but our experience of it requires
01:46:50 that we pick reference frames.
01:46:52 This is kind of a key idea.
01:46:54 Einstein had this idea that what that means is
01:46:57 we have to say, what are we going to pick
01:47:01 as being the sort of what we define
01:47:04 as simultaneous moments in time?
01:47:07 So for example, we can say, you know,
01:47:11 how do we set our clocks?
01:47:13 You know, if we’ve got a spacecraft landing on Mars,
01:47:16 you know, do we say that, you know,
01:47:17 what time is it landing at?
01:47:19 Was it, you know, even though there’s a 20 minute
01:47:21 speed of light delay or something, you know,
01:47:23 what time do we say it landed at?
01:47:25 How do we set up sort of time coordinates for the world?
01:47:30 And that turns out to be that there’s kind of
01:47:32 this arbitrariness to how we set these reference frames
01:47:35 that defines sort of what counts as simultaneous.
01:47:39 And what is the essence of special relativity
01:47:42 is to think about reference frames going at different speeds
01:47:45 and to think about sort of how they assign,
01:47:48 what counts as space, what counts as time and so on.
01:47:52 That’s all a bit technical, but the basic bottom line is
01:47:55 that this causal invariance property,
01:47:58 that means that it’s always the same causal graph,
01:48:01 independent of how you slice it with these reference frames,
01:48:04 you’ll always sort of see the same physical processes go on.
01:48:07 And that’s basically why special relativity works.
01:48:10 So there’s something like special relativity,
01:48:14 like everything around space and time
01:48:17 that fits this idea of the causal graph.
01:48:22 Right, well, you know, one way to think about it is
01:48:24 given that you have a basic structure
01:48:27 that just involves updating things in these,
01:48:31 you know, connected updates and looking at
01:48:33 the causal relationships between connected updates,
01:48:35 that’s enough when you unravel the consequences of that,
01:48:39 that together with the fact that there are lots
01:48:41 of these things and that you can take a continuum limit
01:48:43 and so on implies special relativity.
01:48:46 And so that, it’s kind of not a big deal
01:48:51 because it’s kind of a, you know,
01:48:52 it was completely unobvious when you started off
01:48:56 with saying, we’ve got this graph,
01:48:57 it’s being updated in time, et cetera, et cetera, et cetera,
01:49:00 that just looks like nothing to do with special relativity.
01:49:03 And yet you get that.
01:49:05 And what, I mean, then the thing,
01:49:08 I mean, this was stuff that I figured out back in the 1990s.
01:49:11 The next big thing you get is general relativity.
01:49:16 And so in this hypergraph,
01:49:18 the sort of limiting structure,
01:49:20 when you have a very big hypergraph,
01:49:22 you can think of as being just like, you know,
01:49:24 water seems continuous on a large scale.
01:49:27 So this hypergraph seems continuous on a large scale.
01:49:30 One question is, you know,
01:49:31 how many dimensions of space does it correspond to?
01:49:35 So one question you can ask is,
01:49:36 if you’ve just got a bunch of points
01:49:38 and they’re connected together,
01:49:39 how do you deduce what effective dimension of space
01:49:43 that bundle of points corresponds to?
01:49:46 And that’s pretty easy to explain.
01:49:47 So basically if you say you’ve got a point
01:49:50 and you look at how many neighbors does that point have?
01:49:52 Okay, imagine it’s on a square grid.
01:49:54 Then it’ll have four neighbors.
01:49:56 Go another level out.
01:49:58 How many neighbors do you get then?
01:50:00 What you realize is as you go more and more levels out,
01:50:02 as you go more and more distance on the graph out,
01:50:05 you’re capturing something which is essentially a circle
01:50:09 in two dimensions so that, you know,
01:50:11 the number of the area of a circle is pi R squared.
01:50:14 So it’s the number of points that you get to
01:50:18 goes up like the distance you’ve gone squared.
01:50:21 And in general, in D dimensional space,
01:50:24 it’s R to the power D.
01:50:25 It’s the number of points you get to
01:50:28 if you go R steps on the graph grows like
01:50:32 the number of steps you go to the power of the dimension.
01:50:35 And that’s a way that you can estimate
01:50:37 the effective dimension of one of these graphs.
01:50:39 So what does that grow to?
01:50:41 So how does the dimension grow?
01:50:42 There’s a, I mean, obviously the visual aspect
01:50:45 of these hypergraphs,
01:50:47 they’re often visualized in three dimensions.
01:50:50 Right.
01:50:50 So there’s a certain kind of structure,
01:50:54 like you said, there’s, I mean, a circle, a sphere,
01:50:58 there’s a planar aspect to it,
01:51:02 to this graph to where it kind of,
01:51:04 it almost starts creating a surface,
01:51:06 like a complicated surface, but a surface.
01:51:09 So how does that connect to effective dimension?
01:51:11 Okay, so if you can lay out the graph
01:51:14 in such a way that the points in the graph that,
01:51:18 you know, the points that are neighbors on the graph
01:51:21 are neighbors as you lay them out,
01:51:23 and you can do that in two dimensions,
01:51:25 then it’s gonna approximate a two dimensional thing.
01:51:28 If you can’t do that in two dimensions,
01:51:29 if everything would have to fold over a lot
01:51:31 in two dimensions,
01:51:32 then it’s not approximating a two dimensional thing.
01:51:34 Maybe you can lay it out in three dimensions.
01:51:36 Maybe you have to lay it out in five dimensions
01:51:38 to have it be the case
01:51:39 that it sort of smoothly lays out like that.
01:51:42 Well, but okay, so I apologize
01:51:44 for the different tangent questions,
01:51:46 but you know, there’s an infinity number of possible rules.
01:51:51 So we have to look for rules
01:51:54 that create the kind of structures
01:51:58 that are reminiscent for,
01:52:01 that have echoes of the different physics theories in them.
01:52:05 So what kind of rules,
01:52:06 is there something simple to be said
01:52:08 about the kind of rules that you have found beautiful,
01:52:12 that you have found powerful?
01:52:13 Right, so I mean, what, you know,
01:52:15 one of the features of computational irreducibility is,
01:52:18 it’s very, you can’t say in advance,
01:52:21 what’s gonna happen with any particular,
01:52:23 you can’t say, I’m gonna pick these rules
01:52:26 from this part of rule space, so to speak,
01:52:28 because they’re gonna be the ones that are gonna work.
01:52:30 That’s, you can make some statements along those lines,
01:52:33 but you can’t generally say that.
01:52:35 Now, you know, the state of what we’ve been able to do
01:52:38 is, you know, different properties of the universe,
01:52:40 like dimensionality, you know, integer dimensionality,
01:52:44 features of other features of quantum mechanics,
01:52:47 things like that.
01:52:48 At this point, what we’ve got is,
01:52:50 we’ve got rules that any one of those features,
01:52:55 we can get a rule that has that feature.
01:52:58 Yeah, so the.
01:52:58 We don’t have the sort of, the final,
01:53:00 here’s a rule which has all of these features,
01:53:02 we do not have that yet.
01:53:03 So if I were to try to summarize
01:53:06 the Wolfram physics project, which is, you know,
01:53:11 something that’s been in your brain for a long time,
01:53:13 but really has just exploded in activity,
01:53:17 you know, only just months ago.
01:53:19 Yes.
01:53:20 So it’s an evolving thing, and next week,
01:53:23 I’ll try to publish this conversation
01:53:24 as quickly as possible, because by the time it’s published,
01:53:27 already new things will probably have come out.
01:53:29 So if I were to summarize it,
01:53:33 we’ve talked about the basics of,
01:53:35 there’s a hypergraph that represents space,
01:53:38 there is transformations in that hypergraph
01:53:42 that represents time.
01:53:44 The progress of time.
01:53:45 The progress of time, there’s a causal graph
01:53:47 that’s a characteristic of this,
01:53:49 and the basic process of science,
01:53:53 of, yeah, of science within the Wolfram physics model
01:53:58 is to try different rules and see which properties
01:54:02 of physics that we know of, known physical theories,
01:54:06 are, appear within the graphs that emerge from that rule.
01:54:10 That’s what I thought it was going to be.
01:54:12 Uh oh, okay.
01:54:13 So what is it?
01:54:16 It turns out we can do a lot better than that.
01:54:18 It turns out that using kind of mathematical ideas,
01:54:21 we can say, and computational ideas,
01:54:25 we can make general statements,
01:54:28 and those general statements turn out to correspond
01:54:31 to things that we know from 20th century physics.
01:54:34 In other words, the idea of you just try a bunch of rules
01:54:36 and see what they do,
01:54:37 that’s what I thought we were gonna have to do.
01:54:40 But in fact, we can say, given causal invariance
01:54:43 and computational irreducibility, we can derive,
01:54:47 and this is where it gets really pretty interesting,
01:54:49 we can derive special relativity,
01:54:51 we can derive general relativity,
01:54:52 we can derive quantum mechanics.
01:54:55 And that’s where things really start to get exciting,
01:54:58 is, you know, it wasn’t at all obvious to me
01:55:01 that even if we were completely correct,
01:55:03 and even if we had, you know, this is the rule,
01:55:05 you know, even if we found the rule,
01:55:06 to be able to say, yes, it corresponds
01:55:08 to things we already know,
01:55:10 I did not expect that to be the case.
01:55:12 And…
01:55:13 So for somebody who is a simple mind
01:55:16 and definitely not a physicist, not even close,
01:55:19 what does derivation mean in this case?
01:55:22 Okay, so let me, this is an interesting question.
01:55:26 Okay, so there’s, so one thing…
01:55:29 In the context of computational irreducibility.
01:55:31 Yeah, yeah, right, right.
01:55:32 So what you have to do, let me go back to, again,
01:55:36 the mundane example of fluids and water
01:55:39 and things like that, right?
01:55:40 So you have a bunch of molecules bouncing around.
01:55:44 You can say, just as a piece of mathematics,
01:55:47 I happen to do this from cellular automata
01:55:49 back in the mid 1980s, you can say,
01:55:52 just as a matter of mathematics,
01:55:54 you can say the continuum limit
01:55:57 of these little molecules bouncing around
01:55:59 is the Navier Stokes equations.
01:56:01 That’s just a piece of mathematics.
01:56:03 It’s not, it doesn’t rely on…
01:56:06 You have to make certain assumptions
01:56:08 that you have to say there’s enough randomness
01:56:10 in the way the molecules bounce around
01:56:12 that certain statistical averages work,
01:56:14 et cetera, et cetera, et cetera.
01:56:15 Okay, it is a very similar derivation
01:56:18 to derive, for example, the Einstein equations.
01:56:21 Okay, so the way that works, roughly,
01:56:23 the Einstein equations are about curvature of space.
01:56:26 Curvature of space, I talked about sort of
01:56:29 how you can figure out dimension of space.
01:56:31 There’s a similar kind of way of figuring out
01:56:34 if you just sort of say, you know,
01:56:37 you’re making a larger and larger ball
01:56:39 or larger and larger, if you draw a circle
01:56:40 on the surface of the earth, for example,
01:56:42 you might think the area of a circle is pi r squared,
01:56:45 but on the surface of the earth,
01:56:47 because it’s a sphere, it’s not flat,
01:56:50 the area of a circle isn’t precisely pi r squared.
01:56:53 As the circle gets bigger, the area is slightly smaller
01:56:56 than you would expect from the formula pi r squared
01:56:58 as a little correction term that depends on the ratio
01:57:01 of the size of the circle to the radius of the earth.
01:57:03 Okay, so it’s the same basic thing,
01:57:05 allows you to measure from one of these hypergraphs
01:57:08 what is its effective curvature.
01:57:11 And that’s…
01:57:12 So the little piece of mathematics
01:57:15 that explains special general relativity
01:57:20 can map nicely to describe fundamental property
01:57:25 of the hypergraphs, the curvature of the hypergraphs.
01:57:27 So special relativity is about the relationship
01:57:31 of time to space.
01:57:32 General relativity is about curvature
01:57:35 and this space represented by this hypergraph.
01:57:38 So what is the curvature of a hypergraph?
01:57:40 Okay, so first I have to explain,
01:57:43 what we’re explaining is,
01:57:44 first thing you have to have is a notion of dimension.
01:57:47 You don’t get to talk about curvature of things.
01:57:49 If you say, oh, it’s a curved line,
01:57:51 but I don’t know what a line is yet.
01:57:53 So…
01:57:54 Yeah, what is the dimension of a hypergraph then?
01:57:56 From where, we’ve talked about effective dimension, but…
01:58:00 Right, that’s what this is about.
01:58:03 What this is about is, you have your hypergraph,
01:58:05 it’s got a trillion nodes in it.
01:58:07 What is it roughly like?
01:58:08 Is it roughly like a grid, a two dimensional grid?
01:58:11 Is it roughly like all those nodes are arranged online?
01:58:15 What’s it roughly like?
01:58:16 And there’s a pretty simple mathematical way
01:58:19 to estimate that by just looking at this thing
01:58:23 I was describing, this sort of the size of a ball
01:58:26 that you construct in the hypergraph.
01:58:28 That’s a, you just measure that,
01:58:29 you can just compute it on a computer for a given hypergraph
01:58:33 and you can say, oh, this thing is wiggling around,
01:58:35 but it’s roughly corresponds to two or something like that,
01:58:38 or roughly corresponds to 2.6 or whatever.
01:58:41 So that’s how you have a notion of dimension
01:58:44 in these hypergraphs.
01:58:45 Curvature is something a little bit beyond that.
01:58:48 If you look at how the size of this ball increases
01:58:52 as you increase its radius,
01:58:53 curvature is a correction
01:58:55 to the size increase associated with dimension.
01:58:58 It’s a sort of a second order term
01:59:01 in determining the size.
01:59:03 Just like the area of a circle is roughly pi R squared.
01:59:07 So it goes up like R squared.
01:59:08 The two is because it’s in two dimensions,
01:59:11 but when that circle is drawn on a big sphere,
01:59:14 the actual formula is pi R squared times one minus
01:59:19 R squared over A squared and some coefficient.
01:59:22 So in other words, there’s a correction to,
01:59:25 and that correction term, that gives you curvature.
01:59:28 And that correction term
01:59:29 is what makes this hypergraph correspond,
01:59:32 have the potential to correspond to curved space.
01:59:35 Now, the next question is, is that curvature,
01:59:38 is the way that curvature works
01:59:40 the way that Einstein’s equations for general relativity,
01:59:43 is it the way they say it should work?
01:59:46 And the answer is yes.
01:59:49 And so how does that work?
01:59:54 The calculation of the curvature of this hypergraph
01:59:57 for some set of rules?
01:59:59 No, it doesn’t matter what the rules are.
02:00:01 So long as they have causal invariance
02:00:03 and computational irreducibility,
02:00:05 and they lead to finite dimensional space,
02:00:09 noninfinite dimensional space.
02:00:11 Noninfinite dimensional.
02:00:13 It can grow infinitely,
02:00:14 but it can’t be infinite dimensional.
02:00:16 So what is a infinitely dimensional hypergraph look like?
02:00:19 So that means, for example, so in a tree,
02:00:22 you start from one root of the tree,
02:00:25 it doubles, doubles again, doubles again, doubles again.
02:00:28 And that means if you ask the question,
02:00:30 starting from a given point,
02:00:32 how many points do you get to?
02:00:34 Remember, in like a circle,
02:00:35 you get to R squared, the two there.
02:00:37 On a tree, you get to, for example, two to the R.
02:00:41 It’s exponential dimensional, so to speak,
02:00:43 or infinite dimensional.
02:00:44 Do you have a sense of, in the space of all possible rules,
02:00:48 how many lead to infinitely dimensional hypergraphs?
02:00:53 Is that? No.
02:00:55 Okay.
02:00:56 Is that an important thing to know?
02:00:57 Yes, it’s an important thing to know.
02:00:59 I would love to know the answer to that.
02:01:01 But it gets a little bit more complicated
02:01:03 because, for example, it’s very possibly the case
02:01:05 that in our physical universe,
02:01:07 that the universe started infinite dimensional.
02:01:10 And it only, as the Big Bang,
02:01:13 it was very likely infinite dimensional.
02:01:16 And as the universe sort of expanded and cooled,
02:01:21 its dimension gradually went down.
02:01:23 And so one of the bizarre possibilities,
02:01:25 which actually there are experiments you can do
02:01:27 to try and look at this,
02:01:28 the universe can have dimension fluctuations.
02:01:31 So in other words,
02:01:31 we think we live in a three dimensional universe,
02:01:33 but actually there may be places
02:01:35 where it’s actually 3.01 dimensional,
02:01:37 or where it’s 2.99 dimensional.
02:01:40 And it may be that in the very early universe,
02:01:43 it was actually infinite dimensional,
02:01:45 and it’s only a late stage phenomenon
02:01:47 that we end up getting three dimensional space.
02:01:49 But from your perspective of the hypergraph,
02:01:51 one of the underlying assumptions you kind of implied,
02:01:55 but you have a sense, a hope set of assumptions
02:01:59 that the rules that underlie our universe,
02:02:03 or the rule that underlies our universe is static.
02:02:08 Is that one of the assumptions
02:02:10 you’re currently operating under?
02:02:11 Yes, but there’s a footnote to that,
02:02:14 which we should get to,
02:02:15 because it requires a few more steps.
02:02:17 Well, actually then, let’s backtrack to the curvature,
02:02:19 because we’re talking about as long as it’s finite dimensional.
02:02:25 Finite dimensional computational irreducibility
02:02:28 and causal invariance,
02:02:29 then it follows that the large scale structure
02:02:35 will follow Einstein’s equations.
02:02:37 And now let me again, qualify that a little bit more,
02:02:40 there’s a little bit more complexity to it.
02:02:43 The, okay, so Einstein’s equations in their simplest form
02:02:48 apply to the vacuum, no matter, just the vacuum.
02:02:51 And they say, in particular, what they say is,
02:02:54 if you have, so there’s this term GD6,
02:02:58 that’s a term that means shortest path,
02:03:00 comes from measuring the shortest paths on the Earth.
02:03:03 So you look at a bunch of, a bundle of GD6,
02:03:07 a bunch of shortest paths,
02:03:09 it’s like the paths that photons
02:03:11 would take between two points.
02:03:13 Then the statement of Einstein’s equations,
02:03:14 it’s basically a statement about a certain the,
02:03:18 that as you look at a bundle of GD6,
02:03:20 the structure of space has to be such that,
02:03:22 although the cross sectional area of this bundle may,
02:03:27 although the actual shape of the cross section may change,
02:03:30 the cross sectional area does not.
02:03:31 That’s a version, that’s the most simple minded version
02:03:35 of R mu nu minus a half R G mu nu equals zero,
02:03:38 which is the more mathematical version
02:03:41 of Einstein’s equations.
02:03:42 It’s a statement of the thing called the Ritchie tensor
02:03:45 is equal to zero.
02:03:46 That’s Einstein’s equations for the vacuum.
02:03:50 Okay, so we get that as a result of this model,
02:03:54 but footnote, big footnote,
02:03:57 because all the matter in the universe
02:04:00 is the stuff we actually care about.
02:04:01 The vacuum is not stuff we care about.
02:04:03 So the question is, how does matter come into this?
02:04:06 And for that, you have to understand what energy is
02:04:09 in these models.
02:04:11 And one of the things that we realized, you know,
02:04:15 late last year was that there’s a very simple interpretation
02:04:20 of energy in these models, okay?
02:04:22 And energy is basically, well, intuitively,
02:04:28 it’s the amount of activity in these hypergraphs
02:04:32 and the way that that remains over time.
02:04:36 So a little bit more formally,
02:04:38 you can think about this causal graph
02:04:41 as having these edges that represent causal relationships.
02:04:44 You can think about, oh boy,
02:04:46 there’s one more concept that we didn’t get to.
02:04:47 It’s the notion of space like hypersurfaces.
02:04:51 So this is not as scary as it sounds.
02:04:55 It’s a common notion in general activity.
02:04:59 The notion is you are defining what is a possibly,
02:05:04 where in space time might be a particular moment in time.
02:05:13 So in other words, what is a consistent set of places
02:05:18 where you can say, this is happening now, so to speak.
02:05:21 And you make the series of sort of slices
02:05:25 through the space time, through this causal graph
02:05:29 to represent sort of what we consider
02:05:32 to be successive moments in time.
02:05:34 It’s somewhat arbitrary because you can deform that
02:05:37 if you’re going at a different speed in a special activity,
02:05:39 you tip those things, there are different kinds
02:05:44 of deformations, but only certain deformations
02:05:46 are allowed by the structure of the causal graph.
02:05:48 Anyway, be that as it may, the basic point is
02:05:52 there is a way of figuring out,
02:05:54 you say, what is the energy associated
02:05:57 with what’s going on in this hypergraph?
02:06:00 And the answer is there is a precise definition of that.
02:06:04 And it is the formal way to say it is,
02:06:06 it’s the flux of causal edges
02:06:08 through space like hypersurfaces.
02:06:10 The slightly less formal way to say it,
02:06:12 it’s basically the amount of activity.
02:06:14 See, the reason it gets tricky is you might say
02:06:18 it’s the amount of activity per unit volume
02:06:21 in this hypergraph, but you haven’t defined what volume is.
02:06:25 So it’s a little bit, you have to be a little more careful.
02:06:27 But this hypersurface gives some more formalism to that.
02:06:30 Yeah, yeah, it gives a way to connect that.
02:06:32 But intuitive, we should think about as the just activity.
02:06:36 Right, so the amount of activity that kind of remains
02:06:39 in one place in the hypergraph corresponds to energy.
02:06:42 The amount of activity that is kind of where an activity here
02:06:45 affects an activity somewhere else,
02:06:48 corresponds to momentum.
02:06:50 And so one of the things that’s kind of cool
02:06:53 is that I’m trying to think about
02:06:55 how to say this intuitively.
02:06:56 The mathematics is easy,
02:06:57 but the intuitive version, I’m not sure.
02:06:59 But basically the way that things sort of stay
02:07:01 in the same place and have activity
02:07:03 is associated with rest mass.
02:07:05 And so one of the things that you get to derive
02:07:08 is E equals MC squared.
02:07:10 That is a consequence of this interpretation of energy
02:07:14 in terms of the way the causal graph works,
02:07:18 which is the whole thing is sort of a consequence
02:07:20 of this whole story about updates and hypergraphs and so on.
02:07:23 So can you linger on that a little bit?
02:07:26 How do we get E equals MC squared?
02:07:28 So where does the mass come from?
02:07:31 Okay, okay.
02:07:32 I mean, is there an intuitive, it’s okay.
02:07:35 First of all, you’re pretty deep
02:07:37 in the mathematical explorations of this thing right now.
02:07:41 We’re in a very, we’re in a flux currently.
02:07:45 So maybe you haven’t even had time
02:07:47 to think about intuitive explanations, but.
02:07:51 Yeah, I mean, this one is, look, roughly what’s happening,
02:07:56 that derivation is actually rather easy.
02:07:58 And everybody, and I’ve been saying
02:07:59 we should pay more attention to this derivation
02:08:01 because it’s such, you know,
02:08:02 cause people care about this one.
02:08:04 But everybody says, it’s just easy.
02:08:05 It’s easy.
02:08:07 So there’s some concept of energy
02:08:09 that can be intuitively thought of as the activity,
02:08:12 the flux, the level of changes that are occurring
02:08:16 based on the transformations within a certain volume,
02:08:19 however the heck do you find the volume.
02:08:21 Okay, so, and then mass.
02:08:23 Well, mass is associated with kind of the energy
02:08:28 that does not cause you to,
02:08:30 that does not somehow propagate through time.
02:08:34 Yeah, I mean, one of the things that was not obvious
02:08:35 in the usual formulation of special relativity
02:08:38 is that space and time are connected in a certain way.
02:08:42 Energy and momentum are also connected in a certain way.
02:08:46 The fact that the connection of energy to momentum
02:08:49 is analogous to the connection to space
02:08:50 between space and time
02:08:52 is not self evident in ordinary relativity.
02:08:54 It is a consequence of this, of the way this model works.
02:08:58 It’s an intrinsic consequence of the way this model works.
02:09:00 And it’s all to do with that,
02:09:02 with unraveling that connection
02:09:05 that ends up giving you this relationship
02:09:07 between energy and, well, it’s energy, momentum, mass,
02:09:12 they’re all connected.
02:09:13 And so like, that’s hence the general relativity.
02:09:19 You have a sense that it appears to be baked in
02:09:24 to the fundamental properties
02:09:27 of the way these hypergraphs are evolved.
02:09:29 Well, I didn’t yet get to,
02:09:30 so I got as far as special relativity and equals MC squared.
02:09:33 The one last step is, in general relativity,
02:09:37 the final connection is energy and mass
02:09:41 cause curvature in space.
02:09:44 And that’s something that when you understand
02:09:47 this interpretation of energy,
02:09:49 and you kind of understand the correspondence
02:09:52 to curvature and hypergraphs,
02:09:54 then you can finally sort of, the big final answer is,
02:09:57 you derive the full version of Einstein’s equations
02:10:00 for space, time and matter.
02:10:03 And that’s some.
02:10:04 Is that, have you, that last piece with curvature,
02:10:09 have, is that, have you arrived there yet?
02:10:12 Oh yeah, we’re there, yes.
02:10:13 And here’s the way that we,
02:10:15 here’s how we’re really, really going to know
02:10:17 we’ve arrived, okay?
02:10:18 So, you know, we have the mathematical derivation,
02:10:20 it’s all fine, but, you know,
02:10:22 mathematical derivations, okay.
02:10:25 So one thing that’s sort of a,
02:10:27 you know, we’re taking this limit
02:10:29 of what happens when you, the limit,
02:10:31 you have to look at things which are large
02:10:32 compared to the size of an elementary length,
02:10:35 small compared to the whole size of the universe,
02:10:37 large compared to certain kinds of fluctuations,
02:10:40 blah, blah, blah.
02:10:41 There’s a, there’s a, there’s a tower
02:10:43 of many, many of these mathematical limits
02:10:45 that have to be taken.
02:10:46 So if you’re a pure mathematician saying,
02:10:48 where’s the precise proof?
02:10:50 It’s like, well, there are all these limits,
02:10:52 we can, you know, we can try each one of them
02:10:54 computationally and we could say, yeah, it really works,
02:10:57 but the formal mathematics is really hard to do.
02:11:00 I mean, for example, in the case of deriving
02:11:03 the equations of fluid dynamics from molecular dynamics,
02:11:06 that derivation has never been done.
02:11:09 There is no rigorous version of that derivation.
02:11:11 So, so that could be.
02:11:12 Because you can’t do the limits?
02:11:13 Yeah, because you can’t do the limits.
02:11:15 But so the limits allow you to try to describe
02:11:18 something general about the system
02:11:20 and very, very particular kinds of limits that you need
02:11:22 to take with these very.
02:11:23 Right, and the limits will definitely work
02:11:26 the way we think they work.
02:11:27 And we can do all kinds of computer experiments.
02:11:28 It’s just a hard derivation.
02:11:29 Yeah, it’s just, it’s just the mathematical structure
02:11:32 kind of, you know, ends up running right into
02:11:35 computational irreducibility.
02:11:37 And you end up with a bunch of, a bunch of difficulty there.
02:11:39 But here’s the way that we’re getting really confident
02:11:42 that we know completely what we’re talking about,
02:11:43 which is when people study things like black hole mergers,
02:11:47 using Einstein’s equations, what do they actually do?
02:11:51 Well, they actually use Mathematica or a whole bunch
02:11:52 to analyze the equations and so on.
02:11:54 But in the end, they do numerical relativity,
02:11:57 which means they take these nice mathematical equations
02:12:01 and they break them down so that they can run them
02:12:03 on a computer.
02:12:04 And they break them down into something
02:12:05 which is actually a discrete approximation
02:12:07 to these equations.
02:12:08 Then they run them on a computer, they get results.
02:12:11 Then you look at the gravitational waves
02:12:12 and you see if they match, okay?
02:12:14 It turns out that our model gives you a direct way
02:12:18 to do numerical relativity.
02:12:19 So in other words, instead of saying,
02:12:21 you start from these continuum equations from Einstein,
02:12:23 you break them down into these discrete things,
02:12:26 you run them on a computer,
02:12:27 you say, we’re doing it the other way around.
02:12:28 We’re starting from these discrete things
02:12:30 that come from our model.
02:12:31 And we’re just running big versions on the computer.
02:12:34 And, you know, what we’re saying is,
02:12:37 and this is how things will work.
02:12:39 So the way I’m calling this is proof by compilation,
02:12:43 so to speak, that is, in other words,
02:12:46 you’re taking something where, you know,
02:12:49 we’ve got this description of a black hole system.
02:12:52 And what we’re doing is we’re showing that the, you know,
02:12:56 what we get by just running our model agrees
02:12:59 with what you would get by doing the computation
02:13:02 from the Einstein equations.
02:13:04 As a small tangent or actually a very big tangent,
02:13:08 but proof by compilation is a beautiful concept.
02:13:15 In a sense, the way of doing physics with this model
02:13:21 is by running it or compiling it.
02:13:26 And have you thought about,
02:13:29 and these things can be very large,
02:13:32 is there a totally new possibilities of computing hardware
02:13:37 and computing software,
02:13:38 which allows you to perform this kind of compilation?
02:13:42 Well, algorithms, software, hardware.
02:13:44 So first comment is these models seem to give one
02:13:49 a lot of intuition about distributed computing,
02:13:52 a lot of different intuition about how to think
02:13:54 about parallel computation.
02:13:56 And that particularly comes from the quantum mechanics
02:13:58 side of things, which we didn’t talk about much yet.
02:14:01 But the question of what, you know,
02:14:04 given our current computer hardware,
02:14:07 how can we most efficiently simulate things?
02:14:10 That’s actually partly a story of the model itself,
02:14:12 because the model itself has deep parallelism in it.
02:14:16 The ways that we are simulating it,
02:14:17 we’re just starting to be able to use that deep parallelism
02:14:21 to be able to be more efficient
02:14:22 in the way that we simulate things.
02:14:24 But in fact, the structure of the model itself
02:14:27 allows us to think about parallel computation
02:14:30 in different ways.
02:14:31 And one of my realizations is that, you know,
02:14:34 so it’s very hard to get in your brain
02:14:37 how you deal with parallel computation.
02:14:38 And you’re always worrying about, you know,
02:14:40 if multiple things can happen on different computers
02:14:42 at different times, oh, what happens
02:14:44 if this thing happens before that thing?
02:14:46 And we’ve really got, you know,
02:14:47 we have these race conditions where something can race
02:14:49 to get to the answer before another thing.
02:14:51 And you get all tangled up because you don’t know
02:14:54 which thing is gonna come in first.
02:14:55 And usually when you do parallel computing,
02:14:58 there’s a big obsession to lock things down
02:15:00 to the point where you’ve had locks and mutexes
02:15:03 and God knows what else,
02:15:05 where you’ve arranged it so that there can only be
02:15:09 one sequence of things that can happen.
02:15:11 So you don’t have to think about
02:15:12 all the different kinds of things that can happen.
02:15:14 Well, in these models, physics is throwing us into,
02:15:18 forcing us to think about all these possible things
02:15:20 that can happen.
02:15:21 But these models together with what we know from physics
02:15:24 is giving us new ways to think about
02:15:26 all possible things happening,
02:15:28 about all these different things happening in parallel.
02:15:30 And so I’m guessing…
02:15:31 They have built in protection for some of the parallelism.
02:15:34 Well, causal invariance is the built in protection.
02:15:37 Causal invariance is what means that
02:15:39 even though things happen in different orders,
02:15:41 it doesn’t matter in the end.
02:15:43 As a person who struggled with concurrent programming
02:15:46 in like Java,
02:15:50 with all the basic concepts of concurrent programming,
02:15:53 that if there could be built up
02:15:55 a strong mathematical framework for causal invariance,
02:16:00 that’s so liberating.
02:16:01 And that could be not just liberating,
02:16:03 but really powerful for massively distributed computation.
02:16:08 Absolutely.
02:16:09 No, I mean, what’s eventual consistency
02:16:11 in distributed databases
02:16:14 is essentially the causal invariance idea.
02:16:16 Yeah. Okay.
02:16:17 So that’s…
02:16:17 But have you thought about,
02:16:22 like really large simulations?
02:16:26 Yeah. I mean, I’m also thinking about,
02:16:28 look, the fact is I’ve spent much of my life
02:16:30 as a language designer, right?
02:16:31 So I can’t possibly not think about,
02:16:34 what does this mean for designing languages
02:16:37 for parallel computation?
02:16:38 In fact, another thing that’s one of these…
02:16:41 I’m always embarrassed at how long it’s taken me
02:16:44 to figure stuff out.
02:16:45 But back in the 1980s,
02:16:47 I worked on trying to make up languages
02:16:49 for parallel computation.
02:16:50 I thought about doing graph rewriting.
02:16:53 I thought about doing these kinds of things,
02:16:54 but I couldn’t see how to actually make the connections
02:16:57 to actually do something useful.
02:16:59 I think now physics is kind of showing us
02:17:02 how to make those things useful.
02:17:04 And so my guess is that in time,
02:17:06 we’ll be talking about, we do parallel programming.
02:17:09 We’ll be talking about programming
02:17:10 in a certain reference frame,
02:17:12 just as we think about thinking about physics
02:17:14 in a certain reference frame.
02:17:15 It’s a certain coordination of what’s going on.
02:17:17 We say, we’re gonna program in this reference frame.
02:17:19 Oh, let’s change the reference frame
02:17:21 to this reference frame.
02:17:22 And then our program will seem different
02:17:25 and we’ll have a different way to think about it.
02:17:27 But it’s still the same program underneath.
02:17:28 So let me ask on this topic,
02:17:30 cause I put out that I’m talking to you.
02:17:32 I got way more questions than I can deal with,
02:17:34 but what pops to mind is a question somebody asked
02:17:37 on Reddit I think is, please ask Dr. Wolfram,
02:17:42 what are the specs of the computer running the universe?
02:17:46 So we’re talking about specs of hardware and software
02:17:51 for simulations of a large scale thing.
02:17:54 What about a scale that is comparative
02:17:57 to something that eventually leads
02:17:59 to the two of us talking and about?
02:18:01 Right, right, right.
02:18:02 So actually I did try to estimate that.
02:18:05 And we actually have to go a couple more stages
02:18:07 before we can really get to that answer
02:18:08 because we’re talking about this thing.
02:18:14 This is what happens when you build these abstract systems
02:18:16 and you’re trying to explain the universe,
02:18:19 they’re quite a number of levels deep, so to speak.
02:18:23 But the…
02:18:25 You mean conceptually or like literally?
02:18:27 Cause you’re talking about small objects
02:18:28 and there’s 10 to the 120 something.
02:18:31 Yeah, right.
02:18:33 It is conceptually deep.
02:18:35 And one of the things that’s happening sort of structurally
02:18:37 in this project is, you know, there were ideas,
02:18:40 there’s another layer of ideas,
02:18:41 there’s another layer of ideas
02:18:43 to get to the different things that correspond to physics.
02:18:46 They’re just different layers of ideas.
02:18:49 And they are, you know, it’s actually probably,
02:18:52 if anything, getting harder to explain this project
02:18:54 cause I’m realizing that the fraction of way through
02:18:56 that I am so far and explaining this to you is less than,
02:18:59 than, you know, it might be because we know more now,
02:19:02 you know, every week basically we know a little bit more.
02:19:06 And like…
02:19:07 Those are just layers on the initial fundamental structure.
02:19:10 Yes, but the layers are, you know,
02:19:12 you might be asking me, you know,
02:19:14 how do we get the difference between fermions and bosons,
02:19:18 the difference between particles
02:19:19 that can be all in the same state
02:19:21 and particles that exclude each other, okay.
02:19:24 Last three days, we’ve kind of figured that out.
02:19:26 Okay.
02:19:27 But, and it’s very interesting.
02:19:29 It’s very cool.
02:19:31 And it’s very…
02:19:32 And those are some kind of properties at a certain level,
02:19:35 layer of abstraction on the graph.
02:19:37 Yes, yes.
02:19:38 And there’s, but the layers of abstraction are kind of,
02:19:41 they’re compounding.
02:19:42 Stacking up.
02:19:43 So it’s difficult, but…
02:19:45 But okay.
02:19:46 But the specs nevertheless remain the same.
02:19:47 Okay, the specs underneath.
02:19:49 So I have an estimate.
02:19:50 So the question is, what are the units?
02:19:52 So we’ve got these different fundamental constants
02:19:54 about the world.
02:19:56 So one of them is the speed of light, which is the…
02:19:58 So the thing that’s always the same
02:20:00 in all these different ways of thinking about the universe
02:20:02 is the notion of time, because time is computation.
02:20:06 And so there’s an elementary time,
02:20:08 which is sort of the amount of time that we ascribe
02:20:12 to elapsing in a single computational step.
02:20:16 Yeah.
02:20:17 Okay.
02:20:17 So that’s the elementary time.
02:20:18 So then there’s an elementary…
02:20:19 That’s a parameter or whatever.
02:20:20 That’s a constant.
02:20:21 It’s whatever we define it to be,
02:20:23 because I mean, we don’t, you know…
02:20:25 I mean, it’s all relative, right?
02:20:26 It doesn’t matter.
02:20:27 Yes, it doesn’t matter what it is,
02:20:28 because we could be, it could be slower.
02:20:30 It’s just a number which we use to convert that
02:20:33 to seconds, so to speak,
02:20:35 because we are experiencing things
02:20:37 and we say this amount of time has elapsed, so to speak.
02:20:39 But we’re within this thing.
02:20:41 Absolutely.
02:20:42 So it doesn’t matter, right?
02:20:43 But what does matter is the ratio,
02:20:46 what we can, the ratio of the spatial distance
02:20:49 and this hypergraph to this moment of time.
02:20:54 Again, that’s an arbitrary thing,
02:20:55 but we measure that in meters per second, for example,
02:20:58 and that ratio is the speed of light.
02:21:00 So the ratio of the elementary distance
02:21:03 to the elementary time is the speed of light, okay?
02:21:06 Perfect.
02:21:07 And so there’s another,
02:21:08 there are two other levels of this, okay?
02:21:11 So there is a thing which we can talk about,
02:21:13 which is the maximum entanglement speed,
02:21:16 which is a thing that happens at another level
02:21:19 in this whole sort of story
02:21:20 of how these things get constructed.
02:21:22 That’s a sort of maximum speed in quantum,
02:21:24 in the space of quantum states.
02:21:26 Just as the speed of light
02:21:28 is a maximum speed in physical space,
02:21:30 this is a maximum speed in the space of quantum states.
02:21:32 There’s another level which is associated
02:21:35 with what we call ruleal space,
02:21:36 which is another one of these maximum speeds.
02:21:39 We’ll get to this.
02:21:40 So these are limitations on the system
02:21:42 that are able to capture the kind of physical universe
02:21:45 which we live in.
02:21:46 The quantum mechanical.
02:21:47 There are inevitable features of having a rule
02:21:51 that has only a finite amount of information in the rule.
02:21:54 So long as you have a rule that only involves
02:21:57 a bounded amount, a limited amount of,
02:22:01 only involving a limited number of elements,
02:22:03 limited number of relations,
02:22:04 it is inevitable that there are these speed constraints.
02:22:07 We knew about the one for speed of light.
02:22:08 We didn’t know about the one for maximum entanglement speed,
02:22:11 which is actually something that is possibly measurable,
02:22:14 particularly in black hole systems and things like this.
02:22:17 Anyway, this is long, long story short.
02:22:19 You’re asking what the processing specs of the universe,
02:22:23 of the sort of computation of the universe.
02:22:25 There’s a question of even what are the units
02:22:27 of some of these measurements, okay?
02:22:29 So the units I’m using are Wolfram language instructions
02:22:31 per second, okay?
02:22:33 Because you gotta have some,
02:22:34 what computation are you doing?
02:22:37 There gotta be some kind of frame of reference.
02:22:38 Right, right.
02:22:39 So, because it turns out in the end,
02:22:41 there will be, there’s sort of an arbitrariness
02:22:44 in the language that you use to describe the universe.
02:22:46 So in those terms, I think it’s like 10 to the 500,
02:22:51 Wolfram language operations per second, I think,
02:22:54 is the, I think it’s of that order.
02:22:56 You know, basically.
02:22:57 So that’s the scale of the computation.
02:22:58 What about memory?
02:22:59 If there’s an interesting thing to say
02:23:01 about storage and memory.
02:23:02 Well, there’s a question of how many sort of atoms
02:23:04 of space might there be?
02:23:06 You know, maybe 10 to the 400.
02:23:08 We don’t know exactly how to estimate these numbers.
02:23:11 I mean, this is based on some, I would say,
02:23:14 somewhat rickety way of estimating things.
02:23:17 You know, when there start to be able to be experiments done,
02:23:20 if we’re lucky, there will be experiments
02:23:21 that can actually nail down some of these numbers.
02:23:24 And because of computation reducibility,
02:23:27 there’s not much hope for very efficient compression,
02:23:31 like very efficient representation
02:23:34 of this atom space? Good question.
02:23:35 I mean, there’s probably certain things, you know,
02:23:37 the fact that we can deduce anything,
02:23:40 okay, the question is how deep does the reducibility go?
02:23:44 Right. Okay.
02:23:45 And I keep on being surprised
02:23:46 that it’s a lot deeper than I thought.
02:23:48 Okay, and so one of the things is that,
02:23:52 that there’s a question of sort of how much
02:23:53 of the whole of physics do we have to be able to get
02:23:57 in order to explain certain kinds of phenomena?
02:23:59 Like for example, if we want to study quantum interference,
02:24:02 do we have to know what an electron is?
02:24:05 Turns out I thought we did, turns out we don’t.
02:24:08 I thought to know what energy is,
02:24:10 we would have to know what electrons were.
02:24:12 We don’t.
02:24:13 So you get a lot of really powerful shortcuts.
02:24:15 Right.
02:24:16 There’s a bunch of sort of bulk information about the world.
02:24:19 The thing that I’m excited about last few days, okay,
02:24:22 is the idea of fermions versus bosons, fundamental idea
02:24:27 that I mean, it’s the reason we have matter
02:24:29 that doesn’t just self destruct,
02:24:31 is because of the exclusion principle
02:24:33 that means that two electrons can never be
02:24:36 in the same quantum state.
02:24:38 Is it useful for us to maybe first talk
02:24:41 about how quantum mechanics fits
02:24:44 into the Wolfram physics model?
02:24:46 Yes.
02:24:47 Let’s go there.
02:24:48 So we talked about general relativity.
02:24:49 Now, what have you found from quantum mechanics
02:24:56 within and outside of the Wolfram physics?
02:24:59 Right, so I mean, the key idea of quantum mechanics
02:25:04 that sort of the typical interpretation
02:25:06 is classical physics says a definite thing happens.
02:25:09 Quantum physics says there’s this whole set of paths
02:25:12 of things that might happen.
02:25:14 And we are just observing some overall probability
02:25:17 of how those paths work.
02:25:19 Okay, so when you think about our hypergraphs
02:25:22 and all these little updates that are going on,
02:25:24 there’s a very remarkable thing to realize,
02:25:27 which is if you say, well,
02:25:29 which particular sequence of updates should you do?
02:25:32 Say, well, it’s not really defined.
02:25:33 You can do any of a whole collection
02:25:35 of possible sequences of updates.
02:25:37 Okay, that set of possible sequences of updates
02:25:42 defines yet another kind of graph
02:25:44 that we call a multiway graph.
02:25:46 And a multiway graph just is a graph
02:25:48 where at every node, there is a choice
02:25:52 of several different possible things that could happen.
02:25:55 So for example, you go this way, you go that way.
02:25:57 Those are two different edges in the multiway graph.
02:26:00 And you’re building up the set of possibilities.
02:26:02 So actually, like, for example, I just made the one,
02:26:04 the multiway graph for tic tac toe, okay?
02:26:07 So tic tac toe, you start off with some board
02:26:11 that, you know, is everything is blank,
02:26:12 and then somebody can put down an X somewhere,
02:26:15 an O somewhere, and then there are different possibilities.
02:26:18 At each stage, there are different possibilities.
02:26:20 And so you build up this multiway graph
02:26:22 of all those possibilities.
02:26:23 Now notice that even in tic tac toe,
02:26:25 you have the feature that there can be something
02:26:28 where you have two different things that happen
02:26:31 and then those branches merge
02:26:33 because you end up with the same shape,
02:26:35 you know, the same configuration of the board,
02:26:37 even though you got there in two different ways.
02:26:40 So the thing that’s sort of an inevitable feature
02:26:42 of our models is that just like quantum mechanics suggests,
02:26:47 definite things don’t happen.
02:26:48 Instead, you get this whole multiway graph
02:26:50 of all these possibilities.
02:26:52 Okay, so then the question is, so, okay,
02:26:55 so that’s sort of a picture of what’s going on.
02:26:58 Now you say, okay, well, quantum mechanics
02:27:00 has all these features of, you know,
02:27:02 all this mathematical structure and so on.
02:27:04 How do you get that mathematical structure?
02:27:07 Okay, a couple of things to say.
02:27:08 So quantum mechanics is actually, in a sense,
02:27:11 two different theories glued together.
02:27:13 Quantum mechanics is the theory
02:27:15 of how quantum amplitudes work
02:27:18 that more or less give you the probabilities
02:27:19 of things happening.
02:27:20 And it’s the theory of quantum measurement,
02:27:22 which is the theory of how we actually
02:27:25 conclude definite things.
02:27:27 Because the mathematics just gives you
02:27:29 these quantum amplitudes, which are more or less
02:27:30 probabilities of things happening,
02:27:32 but yet we actually observe definite things in the world.
02:27:36 Quantum measurement has always been a bit mysterious.
02:27:39 It’s always been something where people just say,
02:27:41 well, the mathematics says this,
02:27:42 but then you do a measurement,
02:27:43 and there are philosophical arguments
02:27:45 about what the measurement is.
02:27:46 But it’s not something where there’s a theory
02:27:48 of the measurement.
02:27:49 Somebody on Reddit also asked,
02:27:53 please ask Stephen to tell his story
02:27:56 of the double slit experiment.
02:27:59 Okay, yeah, I can.
02:28:01 Is that, does that make sense?
02:28:02 Oh yeah, it makes sense.
02:28:03 Absolutely makes sense.
02:28:05 Why, is this like a good way to discuss?
02:28:07 A little bit.
02:28:08 Let me go, let me explain a couple of things first.
02:28:10 So the structure of quantum mechanics
02:28:13 is mathematically quite complicated.
02:28:16 One of the features, let’s see,
02:28:18 well, how to describe this.
02:28:20 Okay, so first point is there’s this multiway graph
02:28:23 of all these different paths of things
02:28:26 that can happen in the world.
02:28:28 And the important point is that these,
02:28:32 you can have branchings and you can have mergings.
02:28:35 Okay, so this property turns out causal invariance
02:28:39 is the statement that the number of mergings
02:28:43 is equal to the number of branchings.
02:28:45 Yeah.
02:28:46 So in other words, every time there’s a branch,
02:28:48 eventually there will also be a merge.
02:28:50 In other words, every time there were two possibilities
02:28:52 for what might’ve happened, eventually those will merge.
02:28:55 Beautiful concept by the way, but yeah, yeah, yeah.
02:28:57 So that idea, okay, so then, so that’s one thing
02:29:03 and that’s closely related to the sort of objectivity
02:29:07 in quantum mechanics.
02:29:08 The fact that we believe definite things happen,
02:29:10 it’s because although there are all these different paths,
02:29:13 in some sense, because of causal invariance,
02:29:15 they all imply the same thing.
02:29:17 I’m cheating a little bit in saying that,
02:29:19 but that’s roughly the essence of what’s going on.
02:29:22 Okay, next thing to think about
02:29:24 is you have this multiway graph,
02:29:27 it has all these different possible things
02:29:28 that are happening.
02:29:30 Now we ask, this multiway graph
02:29:32 is sort of evolving with time.
02:29:34 Over time, it’s branching, it’s merging,
02:29:36 it’s doing all these things, okay?
02:29:39 Question we can ask is if we slice it at a particular time,
02:29:44 what do we see?
02:29:46 And that slice represents in a sense,
02:29:48 something to do with the state of the universe
02:29:51 at a particular time.
02:29:53 So in other words, we’ve got this multiway graph
02:29:55 of all these possibilities,
02:29:56 and then we’re asking, okay, we take the slice,
02:30:01 this slice represents, okay,
02:30:04 each of these different paths
02:30:05 corresponds to a different quantum possibility
02:30:07 for what’s happening.
02:30:09 When we take the slice, we’re saying,
02:30:11 what are the set of quantum possibilities
02:30:13 that exist at a particular time?
02:30:14 And when you say slice, you slice the graph
02:30:17 and then there’s a bunch of leaves.
02:30:19 A bunch of leaves.
02:30:20 Those represent the state of things.
02:30:23 Right, but then, okay, so the important thing
02:30:26 that you are quickly picking up on
02:30:29 is that what matters is kind of
02:30:31 how these leaves are related to each other.
02:30:34 So a good way to tell how leaves are related
02:30:37 is just to say on the step before
02:30:39 do they have a common ancestor?
02:30:42 So two leaves might be,
02:30:43 they might have just branched from one thing
02:30:45 or they might be far away,
02:30:47 way far apart in this graph
02:30:50 where to get to a common ancestor,
02:30:52 maybe you have to go all the way back
02:30:53 to the beginning of the graph,
02:30:54 all the way back to the beginning.
02:30:55 So there’s some kind of measure of distance.
02:30:57 Right, but what you get is by making the slice,
02:31:02 we call it branchial space, the space of branches.
02:31:05 And in this branchial space,
02:31:08 you have a graph that represents the relationships
02:31:11 between these quantum states in branchial space.
02:31:14 You have this notion of distance in branchial space.
02:31:18 Okay, so.
02:31:18 It’s connected to quantum entanglement.
02:31:20 Yes, yes, it’s basically,
02:31:23 the distance in branchial space
02:31:25 is kind of an entanglement distance.
02:31:27 So this.
02:31:28 That’s a very nice model.
02:31:29 Right, it is very nice, it’s very beautiful.
02:31:33 I mean, it’s so clean.
02:31:35 I mean, it’s really, and it tells one,
02:31:38 okay, so anyway, so then this branchial space
02:31:42 has this sort of map of the entanglements
02:31:46 between quantum states.
02:31:47 So in physical space, we have,
02:31:50 so you can say, take, let’s say the causal graph,
02:31:54 and we can slice that at a particular time,
02:31:57 and then we get this map
02:31:58 of how things are laid out in physical space.
02:32:01 When we do the same kind of thing,
02:32:02 there’s a thing called the multiway causal graph,
02:32:04 which is the analog of a causal graph
02:32:06 for the multiway system.
02:32:07 We slice that, we get essentially the relationships
02:32:11 between things, not in physical space,
02:32:13 but in the space of quantum states.
02:32:15 It’s like which quantum state
02:32:17 is similar to which other quantum state.
02:32:19 Okay, so now I think next thing to say
02:32:22 is just to mention how quantum measurement works.
02:32:24 So quantum measurement has to do with reference frames
02:32:27 in branchial space.
02:32:29 So, okay, so measurement in physical space,
02:32:33 it matters whether how we assign spatial position
02:32:38 and how we define coordinates in space and time.
02:32:42 And that’s how we make measurements in ordinary space.
02:32:45 Are we making a measurement based on us sitting still here?
02:32:48 Are we traveling at half the speed of light
02:32:49 and making measurements that way?
02:32:51 These are different reference frames
02:32:53 in which we’re making our measurements.
02:32:54 And the relationship between different events
02:32:57 and different points in space and time
02:33:00 will be different depending on what reference frame we’re in.
02:33:04 Okay, so then we have this idea
02:33:06 of quantum observation frames,
02:33:08 which are the analog of reference frames,
02:33:11 but in branchial space.
02:33:13 And so what happens is what we realize
02:33:15 is that a quantum measurement is the observer
02:33:19 is sort of arbitrarily determining this reference frame.
02:33:23 The observer is saying, I’m going to understand the world
02:33:26 by saying that space and time are coordinated this way.
02:33:30 I’m gonna understand the world by saying
02:33:32 that quantum states and time are coordinated in this way.
02:33:36 And essentially what happens is
02:33:38 that the process of quantum measurement
02:33:40 is a process of deciding how you slice up
02:33:44 this multiway system in these quantum observation frames.
02:33:48 So in a sense, the observer, the way the observer enters
02:33:51 is by their choice of these quantum observation frames.
02:33:55 And what happens is that the observer,
02:33:58 because, okay, this is again,
02:34:00 another stack of other concepts, but anyway,
02:34:03 because the observer is computationally bounded,
02:34:06 there is a limit to the type of quantum observation frames
02:34:08 that they can construct.
02:34:09 Interesting, okay, so there’s some constraints,
02:34:12 some limit on the choice of observation frames.
02:34:17 Right, and by the way, I just want to mention
02:34:19 that there’s a, I mean, it’s bizarre,
02:34:21 but there’s a hierarchy of these things.
02:34:23 So in thermodynamics,
02:34:27 the fact that we believe entropy increases,
02:34:29 we believe things get more disordered,
02:34:31 is a consequence of the fact
02:34:32 that we can’t track each individual molecule.
02:34:34 If we could track every single molecule,
02:34:36 we could run every movie in reverse, so to speak,
02:34:38 and we would not see that things are getting more disordered.
02:34:42 But it’s because we are computationally bounded,
02:34:44 we can only look at these big blobs
02:34:46 of what all these molecules collectively do,
02:34:49 that we think that things are,
02:34:52 that we describe it in terms of entropy increasing
02:34:54 and so on.
02:34:55 And it’s the same phenomenon, basically,
02:34:58 and also a consequence of computational irreducibility
02:35:01 that causes us to basically be forced to conclude
02:35:04 that definite things happen in the world,
02:35:06 even though there’s this quantum,
02:35:08 this set of all these different quantum processes
02:35:10 that are going on.
02:35:11 So, I mean, I’m skipping a little bit,
02:35:15 but that’s a rough picture.
02:35:18 And in the evolution of the Wolfram Physics Project,
02:35:21 where do you feel we stand on some of the puzzles
02:35:24 that are along the way?
02:35:25 See, you’re skipping along a bunch of stuff.
02:35:28 It’s amazing how much these things are unraveling.
02:35:30 I mean, you know, these things, look,
02:35:32 it used to be the case that I would agree with Dick Feynman,
02:35:35 nobody understands quantum mechanics, including me, okay?
02:35:38 I’m getting to the point where I think
02:35:40 I actually understand quantum mechanics.
02:35:41 My exercise, okay, is can I explain quantum mechanics
02:35:45 for real at the level of kind of middle school
02:35:48 type explanation?
02:35:50 And I’m getting closer, it’s getting there.
02:35:52 I’m not quite there, I’ve tried it a few times,
02:35:54 and I realized that there are things
02:35:57 where I have to start talking about
02:35:59 elaborate mathematical concepts and so on.
02:36:00 But I think, and you’ve got to realize
02:36:03 that it’s not self evident that we can explain
02:36:06 at an intuitively graspable level,
02:36:09 something which, about the way the universe works,
02:36:12 the universe wasn’t built for our understanding,
02:36:14 so to speak.
02:36:16 But I think then, okay, so another important idea
02:36:21 is this idea of branchial space, which I mentioned,
02:36:25 this sort of space of quantum states.
02:36:27 It is, okay, so I mentioned Einstein’s equations
02:36:31 describing the effect of mass and energy
02:36:37 on trajectories of particles, on GD6.
02:36:40 The curvature of physical space is associated
02:36:44 with the presence of energy,
02:36:47 according to Einstein’s equations, okay?
02:36:49 So it turns out that, rather amazingly,
02:36:51 the same thing is true in branchial space.
02:36:54 So it turns out the presence of energy
02:36:57 or more accurately Lagrangian density,
02:36:59 which is a kind of relativistic invariant version of energy,
02:37:03 the presence of that causes essentially deflection of GD6
02:37:08 in this branchial space, okay?
02:37:11 So you might say, so what?
02:37:12 Well, it turns out that the sort of the best formulation
02:37:17 we have of quantum mechanics,
02:37:18 this Feynman path integral,
02:37:21 is a thing that describes quantum processes
02:37:26 in terms of mathematics that can be interpreted as,
02:37:31 well, in quantum mechanics, the big thing
02:37:33 is you get these quantum amplitudes,
02:37:35 which are complex numbers that represent,
02:37:38 when you combine them together,
02:37:39 represent probabilities of things happening.
02:37:41 And so the big story has been,
02:37:42 how do you derive these quantum amplitudes?
02:37:45 And people think these quantum amplitudes,
02:37:47 they have a complex number,
02:37:49 has a real part and an imaginary part.
02:37:51 You can also think of it as a magnitude and a phase.
02:37:53 And people have sort of thought these quantum amplitudes
02:37:57 have magnitude and phase, and you compute those together.
02:38:00 Turns out that the magnitude and the phase
02:38:03 come from completely different places.
02:38:06 The magnitude comes, okay, so how do you compute things
02:38:10 in quantum mechanics?
02:38:10 Roughly, I’m telling you, I’m getting there
02:38:13 to be able to do this at a middle school level,
02:38:15 but I’m not there yet.
02:38:17 Roughly what happens is you’re asking,
02:38:20 does this state in quantum mechanics
02:38:24 evolve to this other state in quantum mechanics?
02:38:27 And you can think about that like a particle traveling
02:38:30 or something traveling through physical space,
02:38:33 but instead it’s traveling through branchial space.
02:38:36 And so what’s happening is, does this quantum state evolve
02:38:38 to this other quantum state?
02:38:39 It’s like saying, does this object move
02:38:42 from this place in space to this other place in space?
02:38:45 Okay, now the way that these quantum amplitudes
02:38:49 characterize kind of to what extent the thing
02:38:54 will successfully reach some particular point
02:38:56 in branchial space, just like in physical space,
02:38:58 you could say, oh, it had a certain velocity
02:39:00 and it went in this direction.
02:39:02 In branchial space, there’s a similar kind of concept.
02:39:05 Is there a nice way to visualize for me now
02:39:08 mentally branchial space?
02:39:10 It’s just, you have this hypergraph,
02:39:13 sorry, you have this multiway graph.
02:39:15 It’s this big branching thing, branching and merging thing.
02:39:18 But I mean, like moving through that space,
02:39:21 I’m just trying to understand what that looks like.
02:39:25 You know, that space is probably exponential dimensional,
02:39:29 which makes it again, another can of worms
02:39:32 in understanding what’s going on.
02:39:33 That space as in an ordinary space,
02:39:36 this hypergraph, the spatial hypergraph
02:39:39 limits to something which is like a manifold,
02:39:42 like something like three dimensional space.
02:39:45 Almost certainly the multiway graph limits
02:39:48 to a Hilbert space, which is something that,
02:39:52 I mean, it’s just a weird exponential dimensional space.
02:39:55 And by the way, you can ask, I mean,
02:39:57 there are much weirder things that go on.
02:39:58 For example, one of the things I’ve been interested in
02:40:00 is the expansion of the universe in branchial space.
02:40:03 So we know the universe is expanding in physical space,
02:40:07 but the universe is probably also expanding
02:40:09 in branchial space.
02:40:10 So that means the number of quantum states
02:40:13 of the universe is increasing with time.
02:40:15 The diameter of the thing is growing.
02:40:17 Right, so that means that the,
02:40:19 and by the way, this is related
02:40:22 to whether quantum computing can ever work.
02:40:28 Why?
02:40:29 Okay, so let me explain why.
02:40:30 So let’s talk about, okay, so first of all,
02:40:32 just to finish the thought about quantum amplitudes,
02:40:35 that the incredibly beautiful thing,
02:40:37 but I’m just very excited about this.
02:40:40 The fine path integral is this formula.
02:40:44 It says that the amplitude, the quantum amplitude
02:40:47 is E to the I S over H bar,
02:40:49 where S is the thing called the action.
02:40:51 And it, okay, so that can be thought of
02:40:55 as representing a deflection of the angle
02:40:59 of this path in the multiway graph.
02:41:02 So it’s a deflection of a geodesic in the multiway path
02:41:05 that is caused by this thing called the action,
02:41:06 which is essentially associated with energy, okay?
02:41:10 And so this is a deflection of a path in branchial space
02:41:13 that is described by this path integral,
02:41:15 which is the thing that is the mathematical essence
02:41:17 of quantum mechanics.
02:41:19 Turns out that deflection is,
02:41:22 the deflection of geodesics in branchial space
02:41:25 follows the exact same mathematical setup
02:41:28 as the deflection of geodesics in physical space,
02:41:31 except the deflection of geodesics in physical space
02:41:34 is described with Einstein’s equations.
02:41:36 The deflection of geodesics in branchial space
02:41:38 is defined by the Feynman path integral,
02:41:40 and they are the same.
02:41:42 In other words, they are mathematically the same.
02:41:45 So that means that general relativity
02:41:48 is a story of essentially motion in physical space.
02:41:53 Quantum mechanics is a story of essentially motion
02:41:55 in branchial space.
02:41:57 And the underlying equation for those two things,
02:42:01 although it’s presented differently
02:42:02 because one’s interested in different things
02:42:04 in branchial space than physical space,
02:42:06 but the underlying equation is the same.
02:42:08 So in other words, it’s just these two theories,
02:42:13 which are those two sort of pillars
02:42:14 of 20th century physics,
02:42:16 which have seemed to be off in different directions,
02:42:19 are actually facets of the exact same theory.
02:42:24 That’s exciting to see where that evolves
02:42:26 and exciting that that just is there.
02:42:29 Right, I mean, to me,
02:42:31 look, having spent some part of my early life
02:42:34 working in the context of these theories
02:42:37 of 20th century physics,
02:42:39 it’s, they just, they seem so different.
02:42:41 And the fact that they’re really the same
02:42:44 is just really amazing.
02:42:46 Actually, you mentioned double slit experiment, okay?
02:42:49 So the double slit experiment
02:42:50 is an interference phenomenon where you say there are,
02:42:54 you can have a photon or an electron,
02:42:56 and you say there are these two slits
02:42:58 that could have gone through either one,
02:43:00 but there is this interference pattern
02:43:02 where there’s destructive interference,
02:43:05 where you might’ve said in classical physics,
02:43:07 oh, well, if there are two slits,
02:43:09 then there’s a better chance
02:43:10 that it gets through one or the other of them.
02:43:12 But in quantum mechanics,
02:43:13 there’s this phenomenon of destructive interference
02:43:15 that means that even though there are two slits,
02:43:18 two can lead to nothing,
02:43:20 as opposed to two leading to more
02:43:22 than, for example, one slit.
02:43:25 And what happens in this model,
02:43:27 and we’ve just been understanding this
02:43:29 in the last few weeks, actually,
02:43:30 is that what essentially happens
02:43:34 is that the double slit experiment
02:43:38 is a story of the interface
02:43:39 between branchial space and physical space.
02:43:41 And what’s essentially happening
02:43:43 is that the destructive interference
02:43:45 is the result of the two possible paths
02:43:48 associated with photons going through those two slits
02:43:51 winding up at opposite ends of branchial space.
02:43:53 And so that’s why there’s sort of nothing there
02:43:57 when you look at it,
02:43:58 is because these two different sort of branches
02:44:02 couldn’t get merged together
02:44:03 to produce something that you can measure
02:44:06 in physical space.
02:44:07 Is there a lot to be understood about branchial space?
02:44:10 I guess, mathematically speaking.
02:44:13 Yes, it’s a very beautiful mathematical thing.
02:44:16 And it’s very, I mean, by the way,
02:44:18 this whole theory is just amazingly rich
02:44:22 in terms of the mathematics that it says should exist.
02:44:24 Okay, so for example,
02:44:26 calculus is a story of infinitesimal change
02:44:30 in integer dimensional space,
02:44:32 one dimensional, two dimensional, three dimensional space.
02:44:34 We need a theory of infinitesimal change
02:44:37 in fractional dimensional and dynamic dimensional space.
02:44:41 No such theory exists.
02:44:42 So there’s tools of mathematics that are needed here.
02:44:45 Right.
02:44:46 And this is a motivation for that actually.
02:44:47 Right, and there are indications
02:44:50 and we can do computer experiments
02:44:51 and we can see how it’s gonna come out,
02:44:53 but we need to, the actual mathematics doesn’t exist.
02:44:58 And in branchial space, it’s actually even worse.
02:45:00 There’s even more sort of layers of mathematics that are,
02:45:04 we can see how it works roughly
02:45:06 by doing computer experiments,
02:45:07 but to really understand it,
02:45:10 we need more sort of mathematical sophistication.
02:45:13 So quantum computers.
02:45:14 Okay, so the basic idea of quantum computers,
02:45:17 the promise of quantum computers
02:45:19 is quantum mechanics does things in parallel.
02:45:23 And so you can sort of intrinsically do computations
02:45:26 in parallel.
02:45:27 And somehow that can be much more efficient
02:45:30 than just doing them one after another.
02:45:33 And I actually worked on quantum computing a bit
02:45:36 with Dick Feynman back in 1981, two, three,
02:45:40 that kind of timeframe.
02:45:41 And we…
02:45:42 It’s a fascinating image.
02:45:43 You and Feynman working on quantum computers.
02:45:46 Well, we tried to work,
02:45:47 the big thing we tried to do was invent a randomness chip
02:45:51 that would generate randomness at a high speed
02:45:53 using quantum mechanics.
02:45:55 And the discovery that that wasn’t really possible
02:45:58 was part of the story of,
02:46:01 we never really wrote anything about it.
02:46:03 I think maybe he wrote some stuff,
02:46:04 but we didn’t write stuff about what we figured out
02:46:07 about sort of the fact that it really seemed like
02:46:10 the measurement process in quantum mechanics
02:46:12 was a serious damper on what was possible to do
02:46:15 in sort of the possible advantages of quantum mechanics
02:46:19 for computing.
02:46:20 But anyway, so the sort of the promise of quantum computing
02:46:24 is let’s say you’re trying to factor an integer.
02:46:28 Well, you can, instead of,
02:46:30 when you factor an integer, you might say,
02:46:31 well, does this factor work?
02:46:32 Does this factor work?
02:46:33 Does this factor work?
02:46:35 In ordinary computing,
02:46:37 it seems like we pretty much just have to try
02:46:39 all these different factors,
02:46:41 kind of one after another.
02:46:43 But in quantum mechanics, you might have the idea,
02:46:45 oh, you can just sort of have the physics,
02:46:48 try all of them in parallel, okay?
02:46:51 And there’s this algorithm, Shor’s algorithm,
02:46:56 which allows you,
02:46:58 according to the formalism of quantum mechanics,
02:47:01 to do everything in parallel
02:47:02 and to do it much faster than you can on a classical computer.
02:47:05 Okay, the only little footnote is
02:47:08 you have to figure out what the answer is.
02:47:09 You have to measure the result.
02:47:12 So the quantum mechanics internally has figured out
02:47:13 all these different branches,
02:47:15 but then you have to pull all these branches together
02:47:17 to say, and the classical answer is this, okay?
02:47:21 The standard theory of quantum mechanics
02:47:22 does not tell you how to do that.
02:47:24 It tells you how the branching works,
02:47:26 but it doesn’t tell you the process
02:47:27 of corralling all these things together.
02:47:30 And that process, which intuitively you can see
02:47:32 is gonna be kind of tricky,
02:47:34 but our model actually does tell you
02:47:37 how that process of pulling things together works.
02:47:40 And the answer seems to be, we’re not absolutely sure.
02:47:42 We’ve only got to two times three so far
02:47:46 which is kind of in this factorization
02:47:50 in quantum computers.
02:47:51 But we can, what seems to be the case
02:47:55 is that the advantage you get from the parallelization
02:47:58 from quantum mechanics is lost
02:48:01 from the amount that you have to spend
02:48:03 pulling together all those parallel threads
02:48:05 to get to a classical answer at the end.
02:48:07 Now, that phenomenon is not unrelated
02:48:10 to various decoherence phenomena
02:48:11 that are seen in practical quantum computers and so on.
02:48:14 I mean, I should say as a very practical point,
02:48:16 I mean, it’s like, should people stop bothering
02:48:19 to do quantum computing research?
02:48:20 No, because what they’re really doing
02:48:23 is they’re trying to use physics
02:48:25 to get to a new level of what’s possible in computing.
02:48:28 And that’s a completely valid activity.
02:48:30 Whether you can really put, you know,
02:48:33 whether you can say,
02:48:34 oh, you can solve an NP complete problem.
02:48:36 You can reduce exponential time to polynomial time.
02:48:39 You know, we’re not sure.
02:48:40 And I’m suspecting the answer is no,
02:48:43 but that’s not relevant to the practical speed ups
02:48:46 you can get by using different kinds of technologies,
02:48:48 different kinds of physics to do basic computing.
02:48:52 But you’re saying, I mean,
02:48:53 some of the models you’re playing with,
02:48:55 the indication is that to get all the sheep back together
02:49:02 and, you know, to corral everything together,
02:49:05 to get the actual solution to the algorithm is…
02:49:10 You lose all the…
02:49:10 You lose all of the…
02:49:12 By the way, I mean, so again, this question,
02:49:14 do we actually know what we’re talking about
02:49:16 about quantum computing and so on?
02:49:18 So again, we’re doing proof by compilation.
02:49:22 So we have a quantum computing framework
02:49:24 in Wolfram language,
02:49:26 and which is, you know,
02:49:26 a standard quantum computing framework
02:49:28 that represents things in terms of the standard,
02:49:31 you know, formalism of quantum mechanics.
02:49:32 And we have a compiler that simply compiles
02:49:36 the representation of quantum gates into multiway systems.
02:49:41 So, and in fact, the message that I got
02:49:43 was from somebody who’s working on the project
02:49:46 who has managed to compile one of the sort of
02:49:50 a core formalism based on category theory
02:49:53 and core quantum formalism into multiway systems.
02:49:57 So this is…
02:49:58 When you say multiway system, these multiway graphs?
02:50:00 Yes.
02:50:01 So you’re compiling…
02:50:02 Yeah, okay, that’s awesome.
02:50:03 And then you can do all kinds of experiments
02:50:05 on that multiway graph.
02:50:06 Right, but the point is that what we’re saying is
02:50:08 the thing we’ve got this representation
02:50:10 of let’s say Shor’s algorithm
02:50:12 in terms of standard quantum gates.
02:50:14 And it’s just a pure matter of sort of computation
02:50:17 to just say that is equivalent.
02:50:19 We will get the same result as running this multiway system.
02:50:23 Can you do complexity analysis on that multiway system?
02:50:26 Well, that’s what we’ve been trying to do, yes.
02:50:28 We’re getting there.
02:50:29 We haven’t done that yet.
02:50:30 I mean, there’s a pretty good indication
02:50:32 of how that’s gonna work out.
02:50:33 We’ve done, as I say, our computer experiments.
02:50:36 We’ve unimpressively gotten to about two times three
02:50:39 in terms of factorization,
02:50:41 which is kind of about how far people have got
02:50:43 with physical quantum computers as well.
02:50:45 But yes, we will be able to do…
02:50:48 We definitely will be able to do complexity analysis
02:50:50 and we will be able to know.
02:50:51 So the one remaining hope for quantum computing
02:50:55 really, really working at this formal level
02:50:58 of quantum brand exponential stuff being done
02:51:01 in polynomial time and so on.
02:51:03 The one hope, which is very bizarre,
02:51:05 is that you can kind of piggyback
02:51:09 on the expansion of branchial space.
02:51:11 So here’s how that might work.
02:51:13 So you think, you know, energy conservation,
02:51:17 standard thing in high school physics,
02:51:18 energy is conserved, right?
02:51:20 But now you imagine, you think about energy
02:51:23 in the context of cosmology
02:51:25 and the context of the whole universe.
02:51:26 It’s a much more complicated story.
02:51:28 The expansion of the universe kind of violates
02:51:30 energy conservation.
02:51:32 And so for example, if you imagine you’ve got two galaxies,
02:51:35 they’re receding from each other very quickly.
02:51:37 They’ve got two big central black holes.
02:51:39 You connect a spring between these two central black holes.
02:51:43 Not easy to do in practice,
02:51:44 but let’s imagine you could do it.
02:51:46 Now that spring is being pulled apart.
02:51:49 It’s getting more potential energy in the spring
02:51:52 as a result of the expansion of the universe.
02:51:55 So in a sense, you are piggybacking on the expansion
02:51:59 that exists in the universe
02:52:00 and the sort of violation of energy conservation
02:52:03 that’s associated with that cosmological expansion
02:52:05 to essentially get energy.
02:52:07 You’re essentially building a perpetual motion machine
02:52:09 by using the expansion of the universe.
02:52:12 And that is a physical version of that.
02:52:15 It is conceivable that the same thing can be done
02:52:17 in branchial space to essentially mine the expansion
02:52:22 of the universe in branchial space
02:52:24 as a way to get sort of quantum computing for free,
02:52:29 so to speak, just from the expansion of the universe
02:52:32 in branchial space.
02:52:33 Now, the physical space version is kind of absurd
02:52:35 and involves springs between black holes and so on.
02:52:39 It’s conceivable that the branchial space version
02:52:42 is not as absurd
02:52:43 and that it’s actually something you can reach
02:52:45 with physical things you can build in labs and so on.
02:52:48 We don’t know yet.
02:52:49 Okay, so like you were saying,
02:52:51 the branch of space might be expanding
02:52:54 and there might be something that could be exploited.
02:52:57 Right, in the same kind of way
02:52:59 that you can exploit that expansion of the universe
02:53:03 in principle, in physical space.
02:53:06 You just have like a glimmer of hope.
02:53:08 Right, I think that the,
02:53:09 look, I think the real answer is going to be
02:53:11 that for practical purposes,
02:53:13 the official brand that says you can do exponential things
02:53:18 in polynomial time is probably not gonna work.
02:53:20 For people curious to kind of learn more,
02:53:22 so this is more like, it’s not middle school,
02:53:24 we’re gonna go to elementary school for a second.
02:53:27 Maybe middle school, let’s go to middle school.
02:53:31 So if I were to try to maybe write a pamphlet
02:53:38 of like Wolfram physics project for dummies,
02:53:42 AKA for me, or maybe make a video on the basics,
02:53:47 but not just the basics of the physics project,
02:53:51 but the basics plus the most beautiful central ideas.
02:53:59 How would you go about doing that?
02:54:01 Could you help me out a little bit?
02:54:02 Yeah, yeah, I mean, as a really practical matter,
02:54:05 we have this kind of visual summary picture that we made,
02:54:10 which I think is a pretty good,
02:54:12 when I’ve tried to explain this to people
02:54:14 and it’s a pretty good place to start.
02:54:17 As you got this rule, you apply the rule,
02:54:19 you’re building up this big hypergraph,
02:54:22 you’ve got all these possibilities,
02:54:24 you’re kind of thinking about that
02:54:25 in terms of quantum mechanics.
02:54:27 I mean, that’s a decent place to start.
02:54:30 So basically the things we’ve talked about,
02:54:33 which is space represented as a hypergraph,
02:54:37 transformation of that space is kind of time.
02:54:40 Yes.
02:54:41 And then…
02:54:43 Structure of that space,
02:54:45 the curvature of that space has gravity.
02:54:47 That can be explained without going anywhere
02:54:49 near quantum mechanics.
02:54:51 I would say that’s actually easier to explain
02:54:53 than special relativity.
02:54:55 Oh, so going into general, so go into curvature.
02:54:58 Yeah, I mean, special relativity,
02:54:59 I think it’s a little bit elaborate to explain.
02:55:03 And honestly, you only care about it
02:55:05 if you know about special relativity,
02:55:06 if you know how special relativity
02:55:08 is ordinarily derived and so on.
02:55:09 So general relativity is easier.
02:55:11 Is easier, yes.
02:55:12 And then what about quantum?
02:55:13 What’s the easiest way to reveal…
02:55:16 I think the basic point is just this.
02:55:19 This fact that there are all these different branches,
02:55:22 that there’s this kind of map of how the branches work.
02:55:25 And that, I mean, I think actually the recent things
02:55:30 that we have about the double slit experiment
02:55:32 are pretty good, because you can actually see this.
02:55:34 You can see how the double slit phenomenon arises
02:55:39 from just features of these graphs.
02:55:41 Now, having said that,
02:55:43 there is a little bit of sleight of hand there
02:55:47 because the true story of the way
02:55:49 that double slit thing works
02:55:51 depends on the coordination of branchial space
02:55:55 that, for example, in our internal team,
02:55:57 there is still a vigorous battle going on
02:56:00 about how that works.
02:56:01 And what’s becoming clear is…
02:56:04 I mean, what’s becoming clear
02:56:05 is that it’s mathematically really quite interesting.
02:56:08 I mean, that is that there’s a…
02:56:10 It involves essentially putting space filling curves.
02:56:13 You’ll basically have a thing
02:56:14 which is naturally two dimensional,
02:56:15 and you’re sort of mapping it into one dimension
02:56:18 with a space filling curve.
02:56:20 And it’s like, why is it this space filling curve
02:56:21 and another space filling curve?
02:56:23 And that becomes a story about Riemann surfaces and things,
02:56:26 and it’s quite elaborate.
02:56:29 But there’s a more, a little bit sleight of hand way
02:56:32 of doing it where it’s surprisingly direct.
02:56:36 It’s…
02:56:37 So a question that might be difficult to answer,
02:56:42 but for several levels of people,
02:56:46 could you give me advice on how we can learn more?
02:56:50 Specifically, there is people that are completely outside
02:56:54 and just curious and are captivated
02:56:57 by the beauty of hypergraphs, actually.
02:57:00 So people that just wanna explore, play around with this.
02:57:04 Second level is people from, say, people like me
02:57:09 who somehow got a PhD in computer science,
02:57:12 but are not physicists.
02:57:14 But fundamentally, the work you’re doing
02:57:16 is of computational nature.
02:57:18 So it feels very accessible.
02:57:20 So what can a person like that do to learn enough physics
02:57:27 or not to be able to, one, explore the beauty of it,
02:57:31 and two, the final level of contribute something
02:57:36 of a level of even publishable,
02:57:40 like strong, interesting ideas.
02:57:43 So at all those layers, complete beginner,
02:57:46 a CS person, and the CS person that wants to publish.
02:57:49 I mean, I think that, I’ve written a bunch of stuff,
02:57:53 a person called Jonathan Gorod,
02:57:54 who’s been a key person working on this project,
02:57:56 has also written a bunch of stuff.
02:57:58 And some other people started writing things too.
02:58:00 And he’s a physicist.
02:58:02 Physicist.
02:58:02 Well, he’s, I would say, a mathematical physicist.
02:58:05 Mathematical.
02:58:06 Mathematical physicist.
02:58:06 He’s pretty mathematically sophisticated.
02:58:08 He regularly outmathematicizes me.
02:58:11 Yeah, strong mathematical physicist.
02:58:14 Yeah, I looked at some of the papers.
02:58:16 Right, but so, I mean,
02:58:19 I wrote this kind of original announcement blog post
02:58:22 about this project, which people seem to have found.
02:58:25 I’ve been really happy, actually, that people who,
02:58:30 people seem to have grokked key points from that,
02:58:34 much deeper key points, people seem to have grokked
02:58:37 than I thought they would grokk.
02:58:39 And that’s a kind of a long blog post
02:58:41 that explains some of the things we talked about,
02:58:43 like the hypergraph and the basic rules.
02:58:45 And I don’t, does it, I forget,
02:58:47 it doesn’t have any quantum mechanics in here.
02:58:49 It does. It does.
02:58:51 But we know a little bit more since that blog post
02:58:54 that probably clarifies,
02:58:56 but that blog post does a pretty decent job.
02:58:59 And, you know, talking about things like, again,
02:59:02 something we didn’t mention,
02:59:03 the fact that the uncertainty principle
02:59:04 is a consequence of curvature in branchial space.
02:59:07 How much physics should a person know
02:59:10 to be able to understand the beauty of this framework
02:59:14 and to contribute something novel?
02:59:16 Okay, so I think that those are different questions.
02:59:20 So, I mean, I think that the, why does this work?
02:59:23 Why does this make any sense?
02:59:27 To really know that,
02:59:28 you have to know a fair amount of physics, okay?
02:59:32 And for example, have a decent understanding.
02:59:33 When you say, why does this work?
02:59:35 You’re referring to the connection between this model
02:59:38 and general relativity, for example.
02:59:40 You have to understand something about general relativity.
02:59:43 There’s also a side of this where just
02:59:45 as the pure mathematical framework is fascinating.
02:59:47 Yes.
02:59:48 If you throw the physics out completely.
02:59:50 Then it’s quite accessible to, I mean, you know,
02:59:52 I wrote this sort of long technical introduction
02:59:55 to the project, which seems to have been very accessible
02:59:58 to people who are, you know, who understand computation
03:00:01 and formal abstract ideas, but are not specialists
03:00:04 in physics or other kinds of things.
03:00:07 I mean, the thing with the physics part of it is,
03:00:10 you know, there’s both a way of thinking
03:00:14 and literally a mathematical formalism.
03:00:16 I mean, it’s like, you know,
03:00:18 to know that we get the Einstein equations,
03:00:19 to know we get the energy momentum tensor,
03:00:22 you kind of have to know what the energy momentum tensor is.
03:00:24 And that’s physics.
03:00:25 I mean, that’s kind of graduate level physics basically.
03:00:29 And so that, you know, making that final connection
03:00:33 is requires some depth of physics knowledge.
03:00:37 I mean, that’s the unfortunate thing,
03:00:38 the difference in machine learning and physics
03:00:40 in the 21st century.
03:00:42 Is it really out of reach of a year or two worth of study?
03:00:47 No, you could get it in a year or two,
03:00:49 but you can’t get it in a month.
03:00:51 Right.
03:00:52 I mean.
03:00:53 So, but it doesn’t require necessarily like 15 years.
03:00:56 No, it does not.
03:00:57 And in fact, a lot of what has happened with this project
03:01:00 makes a lot of this stuff much more accessible.
03:01:02 There are things where it has been quite difficult
03:01:04 to explain what’s going on.
03:01:06 And it requires much more, you know,
03:01:09 having the concreteness of being able to do simulations,
03:01:11 knowing that this thing that you might’ve thought
03:01:15 was just an analogy is really actually what’s going on,
03:01:19 makes one feel much more secure
03:01:21 about just sort of saying, this is how this works.
03:01:24 And I think it will be, you know,
03:01:26 the, I’m hoping the textbooks of the future,
03:01:28 the physics textbooks of the future,
03:01:30 there will be a certain compression.
03:01:32 There will be things that used to be
03:01:33 very much more elaborate because for example,
03:01:35 even doing continuous mathematics
03:01:36 versus this discrete mathematics,
03:01:38 that, you know, to know how things work
03:01:40 in continuous mathematics,
03:01:41 you have to be talking about stuff
03:01:43 and waving your hands about things.
03:01:44 Whereas with discrete, the discrete version,
03:01:47 it’s just like, here is a picture.
03:01:49 This is how it works.
03:01:50 And there’s no, oh, do we get the limit right?
03:01:53 Did this, you know, did this thing that is of,
03:01:55 you know, zero, you know, measure zero object,
03:01:59 you know, interact with this thing in the right way.
03:02:01 You don’t have to have that whole discussion.
03:02:03 It’s just like, here’s a picture, you know,
03:02:05 this is what it does.
03:02:07 And, you know, you can, then it takes more effort to say,
03:02:09 what does it do in the limit when the picture gets very big?
03:02:12 But you can do experiments
03:02:13 to build up an intuition actually.
03:02:14 Yes, right.
03:02:15 And you can get sort of core intuition for what’s going on.
03:02:17 Now, in terms of contributing to this, the, you know,
03:02:20 I would say that the study of the computational universe
03:02:23 and how all these programs work
03:02:24 in the computational universe,
03:02:26 there’s just an unbelievable amount to do there.
03:02:28 And it is very close to the surface.
03:02:31 That is, you know, high school kids,
03:02:34 you can do experiments.
03:02:36 It’s not, you know, and you can discover things.
03:02:38 I mean, you know, we, you can discover stuff about,
03:02:42 I don’t know, like this thing about expansion
03:02:44 of branchial space.
03:02:45 That’s an absolutely accessible thing to look at.
03:02:47 Now, you know, the main issue with doing these things
03:02:50 is not, there isn’t a lot of technical depth difficulty
03:02:55 there.
03:02:56 The actual doing of the experiments, you know,
03:02:58 all the code is all on our website to do all these things.
03:03:01 The real thing is sort of the judgment
03:03:03 of what’s the right experiment to do.
03:03:05 How do you interpret what you see?
03:03:07 That’s the part that, you know,
03:03:09 people will do amazing things with.
03:03:11 And that’s the part that, but,
03:03:13 but it isn’t like you have to have done 10 years of study
03:03:17 to get to the point where you can do the experiments.
03:03:18 You don’t.
03:03:19 That’s a cool thing you can do experiments day one,
03:03:21 basically.
03:03:22 That’s the amazing thing about,
03:03:25 and you’ve actually put the tools out there.
03:03:27 It’s beautiful.
03:03:28 It’s mysterious.
03:03:29 There’s still, I would say, maybe you can correct me.
03:03:32 It feels like there’s a huge number of log hanging fruit
03:03:36 on the mathematical side, at least not the physics side,
03:03:39 perhaps.
03:03:40 No, there’s, look on the, on the, okay.
03:03:42 On the physics side, we are,
03:03:45 we’re definitely in harvesting mode, you know.
03:03:48 Of which, which fruit, the low hanging ones or?
03:03:50 The low hanging ones, yeah, right.
03:03:52 I mean, basically here’s the thing.
03:03:54 There’s a certain list of, you know,
03:03:56 here are the effects in quantum mechanics.
03:03:57 Here are the effects in general activity.
03:03:59 It’s just like industrial harvesting.
03:04:02 It’s like, can we get this one, this one, this one,
03:04:04 this one, this one?
03:04:05 And the thing that’s really, you know,
03:04:07 interesting and satisfying, and it’s like, you know,
03:04:10 is one climbing the right mountain?
03:04:11 Does one have the right model?
03:04:12 The thing that’s just amazing is, you know,
03:04:15 we keep on like, are we going to get this one?
03:04:18 How hard is this one?
03:04:19 It’s like, oh, you know, it looks really hard.
03:04:22 It looks really hard.
03:04:23 Oh, actually we can get it.
03:04:26 And.
03:04:27 And you’re, you’re continually surprised.
03:04:29 I mean, it seems like I’ve been following your progress.
03:04:31 It’s kind of exciting.
03:04:32 All the, in harvesting mode,
03:04:34 all the things you’re picking up along the way.
03:04:35 Right, right.
03:04:36 No, I mean, it’s, it’s the thing that is,
03:04:38 I keep on thinking it’s going to be more difficult
03:04:40 than it is.
03:04:41 Now that’s a, you know, that’s a, who knows what,
03:04:43 I mean, the one thing, so the, the, the,
03:04:45 the thing that’s been a, was a big thing
03:04:48 that I think we’re, we’re pretty close to.
03:04:50 I mean, I can give you a little bit of the roadmap.
03:04:52 It’s sort of interesting to see, it’s like,
03:04:54 what are particles?
03:04:55 What are things like electrons?
03:04:56 How do they really work?
03:04:58 Are you close to get like, what, what’s a,
03:05:01 are you close to trying to understand like the atom,
03:05:03 the electrons, neutrons, protons?
03:05:06 Okay, so this is, this is the stack.
03:05:08 So the first thing we want to understand is
03:05:11 the quantization of spin.
03:05:13 So particles, they, they kind of spin,
03:05:15 they have a certain angular momentum,
03:05:18 that angular momentum,
03:05:19 even though the masses of particles are all over the place,
03:05:22 you know, the electron has a mass of 0.511 MeV,
03:05:25 but you know, the proton is 938 MeV, et cetera, et cetera,
03:05:28 et cetera, they’re all kind of random numbers.
03:05:30 The, the spins of all these particles
03:05:32 are either integers or half integers.
03:05:34 And that’s a fact that was discovered in the 1920s, I guess.
03:05:38 The, I think that we are close to understanding
03:05:44 why spin is quantized.
03:05:45 And that’s a, and it, it appears to be
03:05:48 a quite elaborate mathematical story
03:05:50 about homotopic groups in twister space
03:05:53 and all kinds of things.
03:05:54 But bottom line is that seems within reach.
03:05:58 And that’s, that’s a big deal
03:05:59 because that’s a very core feature of understanding
03:06:01 how particles work in quantum mechanics.
03:06:04 Another core feature is this difference between particles
03:06:07 that obey the exclusion principle and sort of stay apart,
03:06:10 that leads to the stability of matter and things like that,
03:06:13 and particles that love to get together
03:06:15 and be in the same state, things like photons,
03:06:18 that, and that’s what leads to phenomena like lasers,
03:06:22 where you can get sort of coherently
03:06:23 everything in the same state.
03:06:25 That difference is the particles of integer spin
03:06:29 are bosons like to get together in the same state,
03:06:31 the particles of half integer spin are fermions,
03:06:34 like electrons that they tend to stay apart.
03:06:37 And so the question is, can we get that in our models?
03:06:41 And, oh, just the last few days, I think we made,
03:06:45 I mean, I think the story of,
03:06:47 I mean, it’s one of these things where we’re really close.
03:06:51 Is this connected fermions and bosons?
03:06:53 Yeah, yeah.
03:06:54 So this was what happens is what seems to happen, okay?
03:06:57 It’s, you know, subject to revision in the next few days.
03:07:01 But what seems to be the case is that
03:07:04 bosons are associated with essentially
03:07:06 merging in multiway graphs,
03:07:08 and fermions are associated with branching
03:07:10 in multiway graphs.
03:07:11 And that essentially the exclusion principle
03:07:15 is the fact that in branchial space,
03:07:18 things have a certain extent in branchial space
03:07:21 that in which things are being sort of forced apart
03:07:24 in branchial space, whereas the case of bosons,
03:07:26 they get, they come together in branchial space.
03:07:29 And the real question is, can we explain the relationship
03:07:32 between that and these things called spinners,
03:07:34 which are the representation of half integer spin particles
03:07:37 that have this weird feature that usually when you go
03:07:39 around 360 degree rotation,
03:07:41 you get back to where you started from.
03:07:43 But for a spinner, you don’t get back
03:07:44 to where you started from.
03:07:46 It takes 720 degrees of rotation to get back
03:07:48 to where you started from.
03:07:50 And we are just, it feels like we are,
03:07:53 we’re just incredibly close to actually having that,
03:07:55 understanding how that works.
03:07:57 And it turns out, it looks like,
03:07:59 my current speculation is that it’s as simple
03:08:01 as the directed hypergraphs versus undirected hypergraphs,
03:08:07 the relationship between spinners and vectors.
03:08:10 So, which is just interesting.
03:08:11 Yeah, that would be interesting if these are all these kind
03:08:13 of nice properties of this multi way graphs of branching
03:08:18 and rejoining.
03:08:19 Spinners have been very mysterious.
03:08:21 And if that’s what they turn out to be,
03:08:23 there’s going to be an easy explanation
03:08:25 of what’s going on.
03:08:26 Directive versus undirective.
03:08:27 It’s just, and that’s why there’s only two different cases.
03:08:30 It’s why are spinners important in quantum mechanics?
03:08:34 Can you just give a…
03:08:35 Yeah, so spinners are important because they are,
03:08:39 they’re the representation of electrons
03:08:41 which have half an inch of spin.
03:08:43 They are, the wave functions of electrons are spinners.
03:08:48 Just like the wave functions of photons are vectors,
03:08:51 the wave functions of electrons are spinners.
03:08:54 And they have this property that when you rotate
03:08:58 by 360 degrees, they come back to minus one of themselves
03:09:02 and take 720 degrees to get back to the original value.
03:09:06 And they are a consequence of,
03:09:10 we usually think of rotation in space as being,
03:09:15 when you have this notion of rotational invariance
03:09:18 and rotational invariance, as we ordinarily experience it,
03:09:22 doesn’t have the feature.
03:09:23 If you go through 360 degrees,
03:09:24 you go back to where you started from,
03:09:26 but that’s not true for electrons.
03:09:28 And so that’s why understanding how that works is important.
03:09:32 Yeah, I’ve been playing with Mobius Strip
03:09:34 quite a bit lately, just for fun.
03:09:37 Yes, yes.
03:09:37 It adds some funk, it has the same kind of funky properties.
03:09:41 Yes, right, exactly.
03:09:41 You can have this so called belt trick,
03:09:43 which is this way of taking an extended object
03:09:45 and you can see properties like spinners
03:09:47 with that kind of extended object that…
03:09:50 Yeah, it would be very cool if there’s,
03:09:51 it somehow connects the directive versus undirective.
03:09:53 I think that’s what it’s gonna be.
03:09:54 I think it’s gonna be as simple as that, but we’ll see.
03:09:57 I mean, this is the thing that,
03:09:59 this is the big sort of bizarre surprise is that,
03:10:03 because I learned physics as probably, let’s say,
03:10:07 let’s say a fifth generation in the sense that,
03:10:10 if you go back to the 1920s and so on,
03:10:11 there were the people who were originating
03:10:13 quantum mechanics and so on.
03:10:15 Maybe it’s a little less than that.
03:10:16 Maybe I was like a third generation or something.
03:10:19 I don’t know, but the people from whom I learned physics
03:10:23 were the people who had been students of the students
03:10:26 of the people who originated
03:10:28 the current understanding of physics.
03:10:31 And we’re now at probably the seventh generation
03:10:33 of physicists or something
03:10:35 from the early days of 20th century physics.
03:10:38 And whenever a field gets that many generations deep,
03:10:43 it seems the foundations seem quite inaccessible.
03:10:46 And they seem, it seems like
03:10:48 you can’t possibly understand that.
03:10:49 We’ve gone through seven academic generations
03:10:52 and that’s been, you know, that’s been this thing
03:10:55 that’s been difficult to understand for that long.
03:10:58 It just can’t be that simple.
03:11:01 But in a sense, maybe that journey takes you
03:11:03 to a simple explanation that was there all along.
03:11:07 That’s the whole. Right, right, right.
03:11:08 I mean, you know, and the thing for me personally,
03:11:10 the thing that’s been quite interesting is, you know,
03:11:13 I didn’t expect this project to work in this way.
03:11:16 And I, you know, but I had this sort of weird piece
03:11:19 of personal history that I used to be a physicist
03:11:21 and I used to do all this stuff.
03:11:23 And I know, you know, the standard canon of physics,
03:11:26 I knew it very well.
03:11:28 And, you know, but then I’d been working
03:11:31 on this kind of computational paradigm
03:11:33 for basically 40 years.
03:11:35 And the fact that, you know, I’m sort of now coming back
03:11:38 to, you know, trying to apply that in physics,
03:11:42 it kind of felt like that journey was necessary.
03:11:44 Was this, when did you first try to play with a hypergraph?
03:11:49 So what happened is,
03:11:50 yeah, so what I had was, okay, so this is again,
03:11:53 you know, one always feels dumb after the fact.
03:11:56 It’s obvious after the fact.
03:11:58 But so back in the early 1990s,
03:12:02 I realized that using graphs
03:12:05 as a sort of underlying thing underneath space and time
03:12:07 was going to be a useful thing to do.
03:12:09 I figured out about multiway systems.
03:12:12 I figured out the things about general relativity
03:12:14 I’d figured out by the end of the 1990s.
03:12:17 But I always felt there was a certain inelegance
03:12:20 because I was using these graphs
03:12:21 and there were certain constraints on these graphs
03:12:23 that seemed like they were kind of awkward.
03:12:26 It was kind of like, you can pick,
03:12:28 it’s like you couldn’t pick any rule.
03:12:30 It was like pick any number, but the number has to be prime.
03:12:33 It was kind of like you couldn’t,
03:12:34 it was kind of an awkward special constraint.
03:12:36 I had these trivalent graphs,
03:12:38 graphs with just three connections from every node.
03:12:41 Okay, so, but I discovered a bunch of stuff with that.
03:12:44 And I thought it was kind of inelegant.
03:12:46 And, you know, the other piece of sort of personal history
03:12:48 is obviously I spent my life
03:12:50 as a computational language designer.
03:12:52 And so the story of computational language design
03:12:55 is a story of how do you take all these random ideas
03:12:58 in the world and kind of grind them down
03:13:00 into something that is computationally
03:13:02 as simple as possible.
03:13:04 And so, you know, I’ve been very interested
03:13:06 in kind of simple computational frameworks
03:13:09 for representing things and have, you know,
03:13:12 ridiculous amounts of experience in trying to do that.
03:13:15 And actually all of those trajectories of your life
03:13:18 kind of came together.
03:13:19 So you make it sound like you could have come up
03:13:21 with everything you’re working on now decades ago,
03:13:24 but in reality.
03:13:26 Look, two things slowed me down.
03:13:28 I mean, one thing that slowed me down was
03:13:30 I couldn’t figure out how to make it elegant.
03:13:32 And that turns out hypergraphs were the key to that.
03:13:35 And that I figured out about less than two years ago now.
03:13:40 And the other, I mean, I think,
03:13:43 so that was sort of a key thing.
03:13:46 Well, okay, so the real embarrassment of this project, okay,
03:13:49 is that the final structure that we have
03:13:52 that is the foundation for this project
03:13:55 is basically a kind of an idealized version,
03:14:00 a formalized version of the exact same structure
03:14:03 that I’ve used to build computational languages
03:14:05 for more than 40 years.
03:14:07 But it took me, but I didn’t realize that.
03:14:09 And, you know.
03:14:11 And there yet may be others.
03:14:12 So we’re focused on physics now,
03:14:14 but I mean, that’s what the new kind of science was about.
03:14:17 Same kind of stuff.
03:14:19 And this, in terms of mathematically,
03:14:21 well, the beauty of it.
03:14:22 So there could be entire other kind of objects
03:14:26 that are useful for,
03:14:27 like we’re not talking about, you know,
03:14:29 machine learning, for example.
03:14:31 Maybe there’s other variants of the hypergraph
03:14:33 that are very useful for reasoning.
03:14:35 Well, we’ll see whether the multiway graph
03:14:37 or machine learning system is interesting.
03:14:40 Okay.
03:14:41 Let’s leave it at that.
03:14:42 That’s conversation number three.
03:14:43 That’s, we’re not gonna go there right now, but.
03:14:47 One of the things you’ve mentioned
03:14:49 is the space of all possible rules
03:14:52 that we kind of discussed a little bit.
03:14:55 That, you know, that could be, I guess,
03:14:58 the set of possible rules is infinite.
03:15:00 Right.
03:15:01 Well, so here’s the big sort of one of the conundrums
03:15:04 that I’m kind of trying to deal with is,
03:15:07 let’s say we think we found the rule for the universe
03:15:11 and we say, here it is.
03:15:13 You know, write it down.
03:15:14 It’s a little tiny thing.
03:15:15 And then we say, gosh, that’s really weird.
03:15:18 Why did we get that one?
03:15:20 Right.
03:15:21 And then we’re in this whole situation
03:15:23 because let’s say it’s fairly simple.
03:15:25 How did we come up the winners
03:15:27 getting one of the simple possible universe rules?
03:15:30 Why didn’t we get what some incredibly complicated rule?
03:15:33 Why do we get one of the simpler ones?
03:15:34 And that’s a thing which, you know,
03:15:36 in the history of science, you know,
03:15:38 the whole sort of story of Copernicus and so on was,
03:15:42 you know, we used to think the earth
03:15:43 was the center of the universe,
03:15:44 but now we find out it’s not.
03:15:46 And we’re actually just in some, you know,
03:15:47 random corner of some random galaxy
03:15:50 out in this big universe, there’s nothing special about us.
03:15:53 So if we get, you know, universe number 317
03:15:58 out of all the infinite number of possibilities,
03:16:00 how do we get something that small and simple?
03:16:02 Right, so I was very confused by this.
03:16:05 And it’s like, what are we going to say about this?
03:16:06 How are we going to explain this?
03:16:08 And I thought it was, might be one of these things
03:16:10 where you just, you know, you can get it to the threshold,
03:16:13 and then you find out its rule number, such and such,
03:16:15 and you just have no idea why it’s like that.
03:16:17 Okay, so then I realized
03:16:20 it’s actually more bizarre than that, okay?
03:16:22 So we talked about multiway graphs.
03:16:25 We talked about this idea that
03:16:26 you take these underlying transformation rules
03:16:29 on these hypergraphs, and you apply them
03:16:31 wherever the rule can apply, you apply it.
03:16:34 And that makes this whole multiway graph of possibilities.
03:16:37 Okay, so let’s go a little bit weirder.
03:16:39 Let’s say that at every place,
03:16:42 not only do you apply a particular rule
03:16:45 in all possible ways it can apply,
03:16:47 but you apply all possible rules
03:16:49 in all possible ways they can apply.
03:16:51 As you say, that’s just crazy.
03:16:53 That’s way too complicated.
03:16:54 You’re never going to be able to conclude anything.
03:16:57 Okay, however, turns out that…
03:17:00 Don’t tell me there’s some kind of invariance.
03:17:02 Yeah, yeah.
03:17:04 So what happens is…
03:17:06 And that would be amazing.
03:17:08 Right, so this thing that you get
03:17:11 is this kind of ruleal multiway graph,
03:17:13 this multiway graph that is a branching of rules
03:17:15 as well as a branching of possible applications of rules.
03:17:19 This thing has causal invariance.
03:17:22 It’s an inevitable feature that it shows causal invariance.
03:17:25 And that means that you can take different reference frames,
03:17:28 different ways of slicing this thing,
03:17:30 and they will all in some sense be equivalent.
03:17:33 If you make the right translation, they will be equivalent.
03:17:37 So, okay, so the basic point here is…
03:17:40 If that’s true, that would be beautiful.
03:17:43 It is true, and it is beautiful.
03:17:45 It’s not just an intuition, there is some…
03:17:47 No, no, no, there’s real mathematics behind this,
03:17:50 and it is…
03:17:53 Okay, so here’s where it comes in.
03:17:55 Yeah, that’s amazing.
03:17:57 Right, so by the way, I mean,
03:17:58 the mathematics it’s connected to
03:18:00 is the mathematics of higher category theory
03:18:02 and group voids and things like this,
03:18:04 which I’ve always been afraid of,
03:18:05 but now I’m finally wrapping my arms around it.
03:18:09 But it’s also related to…
03:18:13 It also relates to computational complexity theory.
03:18:16 It’s also deeply related to the P versus NP problem
03:18:19 and other things like this.
03:18:20 Again, it seems completely bizarre
03:18:21 that these things are connected,
03:18:22 but here’s why it’s connected.
03:18:25 This space of all possible…
03:18:28 Okay, so a Turing machine, very simple model of computation.
03:18:32 You know, you just got this tape
03:18:34 where you write down, you know, ones and zeros
03:18:36 or something on the tape,
03:18:37 and you have this rule that says, you know,
03:18:40 you change the number,
03:18:41 you move the head on the tape, et cetera.
03:18:44 You have a definite rule for doing that.
03:18:46 A deterministic Turing machine
03:18:47 just does that deterministically.
03:18:50 Given the configuration of the tape,
03:18:51 it will always do the same thing.
03:18:53 A non deterministic Turing machine
03:18:55 can have different choices that it makes at every step.
03:18:58 And so, you know, you know this stuff,
03:19:01 you probably teach this stuff.
03:19:04 It, you know, so a non deterministic Turing machine
03:19:09 has the set of branching possibilities,
03:19:11 which is in fact, one of these multiway graphs.
03:19:14 And in fact, if you say,
03:19:16 imagine the extremely non deterministic Turing machine,
03:19:19 the Turing machine that can just do,
03:19:22 that takes any possible rule at each step,
03:19:25 that is this real multiway graph.
03:19:27 The set of possible histories
03:19:31 of that extreme non deterministic Turing machine
03:19:33 is a Rulio multiway graph.
03:19:35 And you’re, what term are you using?
03:19:37 Rulio?
03:19:38 Rulio.
03:19:39 Rulio, I like it.
03:19:40 It’s a weird word.
03:19:41 Yeah, it’s a weird word, right?
03:19:41 Rulio multiway graph.
03:19:44 Okay, so this, so that.
03:19:45 I’m trying to think of,
03:19:48 I’m trying to think of the space of rules.
03:19:51 So these are basic transformations.
03:19:54 So in a Turing machine,
03:19:55 it’s like it says, move left, move, you know,
03:19:58 if it’s a one, if it’s a black square under the head,
03:20:02 move left and right to green square.
03:20:04 That’s a rule.
03:20:05 That’s a very basic rule,
03:20:06 but I’m trying to see the rules on the hypergraphs,
03:20:09 how rich of the programs can they be?
03:20:12 Or do they all ultimately just map into something simple?
03:20:15 Yeah, they’re all, I mean, hypergraphs,
03:20:18 that’s another layer of complexity on this whole thing.
03:20:20 You can think about these in transformations of hypergraphs,
03:20:23 but Turing machines are a little bit simpler.
03:20:24 You just think of it Turing machines, okay.
03:20:25 Right, they’re a little bit simpler.
03:20:27 So if you look at these extreme
03:20:29 non deterministic Turing machines,
03:20:30 you’re mapping out all the possible non deterministic paths
03:20:35 that the Turing machine can follow.
03:20:37 And if you ask the question, can you reach, okay,
03:20:41 so a deterministic Turing machine follows a single path.
03:20:44 The non deterministic Turing machine fills out
03:20:46 this whole sort of ball of possibilities.
03:20:50 And so then the P versus MP problem
03:20:53 ends up being questions about,
03:20:55 and we haven’t completely figured out
03:20:56 all the details of this,
03:20:57 but it’s basically has to do with questions
03:20:59 about the growth of that ball relative
03:21:03 to what happens with individual paths and so on.
03:21:05 So essentially there’s a geometrization
03:21:07 of the P versus MP problem that comes out of this.
03:21:10 That’s a sideshow, okay.
03:21:12 The main event here is the statement
03:21:14 that you can look at this multiway graph
03:21:19 where the branches correspond
03:21:21 not just to different applications of a single rule,
03:21:24 but to different applications of different rules, okay.
03:21:28 And that then that when you say,
03:21:31 I’m going to be an observer embedded in that system
03:21:35 and I’m going to try and make sense
03:21:36 of what’s going on in the system.
03:21:38 And to do that, I essentially am picking a reference frame
03:21:43 and that turns out to be, well, okay.
03:21:46 So the way this comes out essentially
03:21:48 is the reference frame you pick
03:21:50 is the rule that you infer is what’s going on
03:21:53 in the universe, even though all possible rules
03:21:57 are being run, although all those possible rules
03:22:01 are in a sense giving the same answer
03:22:02 because of causal invariance.
03:22:04 But what you see could be completely different.
03:22:08 If you pick different reference frames,
03:22:10 you essentially have a different description language
03:22:12 for describing the universe.
03:22:14 Okay, so what does this really mean in practice?
03:22:17 So imagine there’s us.
03:22:19 We think about the universe in terms of space and time
03:22:22 and we have various kinds of description models and so on.
03:22:25 Now let’s imagine the friendly aliens, for example, right?
03:22:29 How do they describe their universe?
03:22:31 Well, you know, our description of the universe
03:22:33 probably is affected by the fact that, you know,
03:22:36 we are about the size we are, you know,
03:22:37 a meter ish tall, so to speak.
03:22:40 We have brain processing speeds,
03:22:41 we’re about the speeds we have.
03:22:43 We’re not the size of planets, for example,
03:22:46 where the speed of light really would matter.
03:22:48 You know, in our everyday life,
03:22:50 the speed of light doesn’t really matter.
03:22:51 Everything can be, you know,
03:22:52 the fact that the speed of light is finite is irrelevant.
03:22:55 It could as well be infinite.
03:22:56 We wouldn’t make any difference.
03:22:58 You know, it affects the ping times on the internet.
03:23:01 That’s about the level of how we notice the speed of light.
03:23:06 In our sort of everyday existence,
03:23:07 we don’t really notice it.
03:23:09 And so we have a way of describing the universe
03:23:12 that’s based on our sensory, you know, our senses,
03:23:17 these days also on the mathematics we’ve constructed
03:23:19 and so on, but the realization is
03:23:22 it’s not the only way to do it.
03:23:24 There will be completely, utterly incoherent descriptions
03:23:28 of the universe, which correspond
03:23:30 to different reference frames in this sort of ruleal space.
03:23:34 In the ruleal space, that’s fascinating.
03:23:36 So we have some kind of reference frame
03:23:38 in this ruleal space, and from that.
03:23:41 That’s why we are attributing this rule to the universe.
03:23:45 So in other words, when we say,
03:23:47 why is it this rule and not another,
03:23:49 the answer is just, you know,
03:23:52 shine the light back on us, so to speak.
03:23:54 It’s because of the reference frame that we’ve picked
03:23:57 in our way of understanding what’s happening
03:23:58 in this sort of space of all possible rules and so on.
03:24:02 But also in the space from this reference frame,
03:24:06 because of the ruleal, the invariance,
03:24:12 that simple, that the rule on which the universe,
03:24:17 with which you can run the universe,
03:24:19 might as well be simple.
03:24:21 Yes, yes, but okay, so here’s another point.
03:24:23 So this is, again, these are a little bit mind twisting
03:24:26 in some ways, but the, okay, another thing that’s sort of,
03:24:31 we know from computation is this idea
03:24:34 of computation universality.
03:24:36 The fact that given that we have a program
03:24:38 that runs on one kind of computer, we can as well,
03:24:42 you know, we can convert it to run
03:24:44 on any other kind of computer.
03:24:45 We can emulate one kind of computer with another.
03:24:47 So that might lead you to say, well,
03:24:50 you think you have the rule for the universe,
03:24:52 but you might as well be running it on a Turing machine
03:24:54 because we know we can emulate any computational rule
03:24:59 on any kind of machine.
03:25:00 And that’s essentially the same thing
03:25:02 that’s being said here.
03:25:03 That is that what we’re doing is we’re saying
03:25:07 these different interpretations of physics correspond
03:25:11 to essentially running physics
03:25:13 on different underlying, you know,
03:25:16 thinking about the physics as running in different
03:25:18 with different underlying rules
03:25:19 as if different underlying computers were running them.
03:25:22 And, but because of computation universality
03:25:26 or more accurately, because of this principle
03:25:27 of computational equivalence thing of mine,
03:25:30 there’s that they are,
03:25:33 these things are ultimately equivalent.
03:25:35 So the only thing that is the ultimate fact
03:25:38 about the universe, the ultimate fact that doesn’t depend
03:25:40 on any of these, you know, we don’t have to talk
03:25:42 about specific rules, et cetera, et cetera, et cetera.
03:25:44 The ultimate fact is the universe is computational
03:25:48 and it is the things that happen in the universe
03:25:52 are the kinds of computations that the principle
03:25:54 of computational equivalence says should happen.
03:25:57 Now that might sound like you’re not really saying
03:26:00 anything there, but you are because you can,
03:26:03 you could in principle have a hyper computer
03:26:06 that things that take an ordinary computer
03:26:09 an infinite time to do the hyper computer can just say,
03:26:12 oh, I know the answer.
03:26:13 It’s this immediately.
03:26:15 What this is saying is the universe is not a hyper computer.
03:26:19 It’s not simpler than a,
03:26:21 an ordinary Turing machine type computer.
03:26:24 It’s exactly like an ordinary Turing machine type computer.
03:26:28 And so that’s the, that’s in the end,
03:26:30 the sort of net net conclusion is that’s the thing
03:26:34 that is the sort of the hard immovable fact
03:26:36 about the universe.
03:26:38 That’s sort of the fundamental principle of the universe
03:26:41 is that it is computational and not hyper computational
03:26:45 and not sort of infra computational.
03:26:47 It is this level of computational ability
03:26:50 and it’s, it kind of has,
03:26:53 and that’s sort of the, the, the core fact, but now,
03:26:57 you know, this, this idea that you can have these different
03:26:59 kind of a rule reference frames,
03:27:02 these different description languages for the universe.
03:27:05 It makes me, you know, I used to think, okay, you know,
03:27:08 imagine the aliens,
03:27:09 imagine the extraterrestrial intelligence thing, you know,
03:27:12 at least they experienced the same physics.
03:27:15 And now I’ve realized it isn’t true.
03:27:17 They could have a different rule frame.
03:27:19 That’s fascinating.
03:27:20 That they can end up with a, a, a,
03:27:23 a description of the universe that is utterly,
03:27:26 utterly incoherent with ours.
03:27:28 And that’s also interesting in terms of how we think about,
03:27:31 well, intelligence, the nature of intelligence and so on.
03:27:33 You know, I’m, I’m fond of the quote, you know,
03:27:35 the weather has a mind of its own because these are,
03:27:38 you know, these are sort of computationally that,
03:27:41 that system is computationally equivalent to the system
03:27:44 that is our brains and so on.
03:27:46 And what’s different is we don’t have a way to understand,
03:27:49 you know, what the weather is trying to do, so to speak.
03:27:52 We have a story about what’s happening in our brains.
03:27:54 We don’t have a sort of connection
03:27:56 to what’s happening there.
03:27:57 So we actually, it’s funny,
03:27:59 last time we talked maybe over a year ago,
03:28:04 we talked about how it was more based on your work
03:28:08 with Arrival.
03:28:09 We talked about how would we communicate
03:28:11 with alien intelligences.
03:28:14 Can you maybe comment on how we might,
03:28:18 how the Wolfram Physics Project changed your view,
03:28:20 how we might be able to communicate
03:28:22 with alien intelligence?
03:28:23 Like if they showed up,
03:28:25 is it possible that because of our comprehension
03:28:30 of the physics of the world might be completely different,
03:28:33 we would just not be able to communicate at all?
03:28:36 Here’s the thing, you know, intelligence is everywhere.
03:28:41 The fact this idea that there’s this notion of,
03:28:43 oh, there’s gonna be this amazing
03:28:45 extraterrestrial intelligence
03:28:46 and it’s gonna be this unique thing.
03:28:48 It’s just not true.
03:28:50 It’s the same thing.
03:28:51 You know, I think people will realize this
03:28:53 about the time when people decide
03:28:54 that artificial intelligences are kind of
03:28:57 just natural things that are like human intelligences.
03:29:01 They’ll realize that extraterrestrial intelligences
03:29:04 or intelligences associated with physical systems
03:29:07 and so on, it’s all the same kind of thing.
03:29:09 It’s ultimately computation.
03:29:11 It’s all the same.
03:29:12 It’s all just computation.
03:29:13 And the issue is, can you, are you sort of inside it?
03:29:17 Are you thinking about it?
03:29:19 Do you have sort of a story you’re telling yourself
03:29:22 about it?
03:29:23 And you know, the weather could have a story
03:29:25 it’s telling itself about what it’s doing.
03:29:27 We just, it’s utterly incoherent with the stories
03:29:30 that we tell ourselves based on how our brains work.
03:29:33 I mean, ultimately it must be a question
03:29:37 whether we can align.
03:29:39 Exactly.
03:29:40 Align with the kind of intelligence.
03:29:41 Right, right, right.
03:29:42 So there’s a systematic way of doing it.
03:29:44 Right, so the question is in the space
03:29:45 of all possible intelligences,
03:29:47 what’s the, how do you think about the distance
03:29:50 between description languages
03:29:52 for one intelligence versus another?
03:29:54 And needless to say, I have thought about this
03:29:57 and you know, I don’t have a great answer yet,
03:30:00 but I think that’s a thing
03:30:02 where there will be things that can be said
03:30:04 and there’ll be things that where you can sort of
03:30:06 start to characterize, you know,
03:30:08 what is the translation distance between this,
03:30:12 you know, version of the universe
03:30:15 or this kind of set of computational rules
03:30:17 and this other one.
03:30:18 In fact, okay, so this is a, you know,
03:30:21 there’s this idea of algorithmic information theory.
03:30:23 There’s this question of sort of what is the,
03:30:25 when you have something,
03:30:28 what is the sort of shortest description you can make of it
03:30:31 where that description could be saying,
03:30:33 run this program to get the thing, right?
03:30:36 So I’m pretty sure that there will be a physicalization
03:30:45 of the idea of algorithmic information
03:30:47 and that, okay, this is again, a little bit bizarre,
03:30:51 but so I mentioned that there’s the speed of light,
03:30:54 maximum speed of information transmission in physical space.
03:30:57 There’s a maximum speed of information transmission
03:30:59 in branchial space, which is a maximum entanglement speed.
03:31:02 There’s a maximum speed of information transmission
03:31:05 in ruleal space, which is,
03:31:07 has to do with a maximum speed of translation
03:31:10 between different description languages.
03:31:14 And again, I’m not fully wrapped my brain around this one.
03:31:17 Yeah, that one just blows my mind to think about that,
03:31:20 but that starts getting closer to the, yeah,
03:31:22 the intelligence. It’s kind of a physicalization.
03:31:25 Right, and it’s also a physicalization
03:31:27 of algorithmic information.
03:31:29 And I think there’s probably a connection between,
03:31:32 I mean, there’s probably a connection
03:31:33 between the notion of energy and some of these things,
03:31:36 which again, I hadn’t seen all this coming.
03:31:39 I’ve always been a little bit resistant
03:31:41 to the idea of connecting physical energy
03:31:43 to things in computation theory,
03:31:45 but I think that’s probably coming.
03:31:47 And that’s what essentially at the core
03:31:48 with the physics project is
03:31:50 that you’re connecting information theory with physics.
03:31:55 Yeah, it’s computation.
03:31:56 Computation with our physical universe.
03:31:59 Yeah, right.
03:32:00 I mean, the fact that our physical universe is,
03:32:03 right, that we can think of it as a computation
03:32:05 and that we can have discussions like,
03:32:08 the theory of the physical universe
03:32:11 is the same kind of a theory as the P versus MP problem
03:32:14 and so on is really, I think that’s really interesting.
03:32:18 And the fact that, well, okay,
03:32:21 so this kind of brings me to one more thing
03:32:24 that I have to in terms of this sort of unification
03:32:26 of different ideas, which is metamathematics.
03:32:29 Yeah, let’s talk about that.
03:32:30 You mentioned that earlier.
03:32:31 What the heck is metamathematics and…
03:32:34 Okay, so here’s what, okay.
03:32:36 So what is mathematics?
03:32:38 Mathematics, sort of at a lowest level,
03:32:43 one thinks of mathematics as you have certain axioms.
03:32:47 You say things like X plus Y is the same as Y plus X.
03:32:51 That’s an axiom about addition.
03:32:55 And then you say, we’ve got these axioms
03:32:57 and from these axioms, we derive all these theorems
03:33:00 that fill up the literature of mathematics.
03:33:02 The activity of mathematicians
03:33:04 is to derive all these theorems.
03:33:06 Actually, the axioms of mathematics are very small.
03:33:10 You can fit, when I did my new kind of science book,
03:33:13 I fit all of the standard axioms of mathematics
03:33:16 on basically a page and a half.
03:33:18 Not much stuff.
03:33:19 It’s like a very simple rule
03:33:21 from which all of mathematics arises.
03:33:24 The way it works though is a little different
03:33:26 from the way things work in sort of a computation
03:33:31 because in mathematics, what you’re interested in
03:33:33 is a proof and the proof says,
03:33:36 from here, you can use, from this expression, for example,
03:33:40 you can use these axioms to get to this other expression.
03:33:43 So that proves these two things are equal.
03:33:45 Okay, so we can begin to see how this has been going to work.
03:33:49 What’s gonna happen is there are paths
03:33:51 in metamathematical space.
03:33:53 So what happens is each, two different ways to look at it.
03:33:57 You can just look at it as mathematical expressions
03:33:59 or you can look at it as mathematical statements,
03:34:02 postulates or something.
03:34:04 But either way, you think of these things
03:34:06 and they are connected by these axioms.
03:34:11 So in other words, you have some fact
03:34:14 or you have some expression, you apply this axiom,
03:34:16 you get some other expression.
03:34:18 And in general, given some expression,
03:34:21 there may be many possible different expressions
03:34:23 you can get.
03:34:24 You basically build up a multiway graph
03:34:27 and a proof is a path through the multiway graph
03:34:31 that goes from one thing to another thing.
03:34:34 The path tells you how did you get from one thing
03:34:36 to the other thing.
03:34:37 It’s the story of how you got from this to that.
03:34:40 The theorem is the thing at one end
03:34:42 is equal to the thing at the other end.
03:34:44 The proof is the path you go down
03:34:46 to get from one thing to the other.
03:34:48 You mentioned that Gödel’s incompleteness theorem
03:34:52 fits naturally there.
03:34:53 How does it fit?
03:34:54 Yeah, so what happens there is that the Gödel’s theorem
03:34:57 is basically saying that there are paths of infinite length.
03:35:01 That is that there’s no upper bound.
03:35:03 If you know these two things,
03:35:04 you say, I’m trying to get from here to here,
03:35:06 how long do I have to go?
03:35:07 You say, well, I’ve looked at all the paths of length 10.
03:35:10 Somebody says, that’s not good enough.
03:35:12 That path might be of length a billion.
03:35:14 And there’s no upper bound on how long that path is.
03:35:17 And that’s what leads to the incompleteness theorem.
03:35:19 So I mean, the thing that is kind of an emerging idea
03:35:24 is you can start asking,
03:35:26 what’s the analog of Einstein’s equations
03:35:27 in metamathematical space?
03:35:29 What’s the analog of a black hole
03:35:31 in metamathematical space?
03:35:33 What’s the hope of this?
03:35:33 So yeah, it’s fascinating to model all the mathematics
03:35:36 in this way.
03:35:37 So here’s what it is.
03:35:38 This is mathematics in bulk.
03:35:40 So human mathematicians have made a few million theorems.
03:35:44 They’ve published a few million theorems.
03:35:45 But imagine the infinite future of mathematics.
03:35:48 Apply something to mathematics
03:35:50 that mathematics likes to apply to other things.
03:35:52 Take a limit.
03:35:53 What is the limit of the infinite future of mathematics?
03:35:56 What does it look like?
03:35:57 What is the continuum limit of mathematics?
03:35:59 What is the, as you just fill in
03:36:01 more and more and more theorems,
03:36:03 what does it look like?
03:36:04 What does it do?
03:36:05 How does, what kinds of conclusions can you make?
03:36:07 So for example, one thing I’ve just been doing
03:36:09 is taking Euclid.
03:36:10 So Euclid, very impressive.
03:36:12 He had 10 axioms, he derived 465 theorems, okay?
03:36:17 His book, you know,
03:36:19 that was the sort of defining book of mathematics
03:36:21 for 2000 years.
03:36:24 So you can actually map out,
03:36:25 and I actually did this 20 years ago,
03:36:28 but I’ve done it more seriously now.
03:36:30 You can map out the theorem dependency
03:36:32 of those 465 theorems.
03:36:34 So from the axioms, you grow this graph,
03:36:37 it’s actually a multiway graph,
03:36:39 of how all these theorems get proved from other theorems.
03:36:42 And so you can ask questions about, you know,
03:36:45 well, you can ask things like,
03:36:46 what’s the hardest theorem in Euclid?
03:36:47 The answer is, the hardest theorem
03:36:48 is that there are five platonic solids.
03:36:50 That turns out to be the hardest theorem in Euclid.
03:36:52 That’s actually his last theorem in all his books.
03:36:55 That’s the final.
03:36:56 What’s the hardness, the distance you have to travel?
03:36:58 Yeah, let’s say it’s 33 steps from the,
03:37:01 the longest path in the graph is 33 steps.
03:37:03 So that’s the, there’s a 33 step path you have to follow
03:37:07 to go from the axioms, according to Euclid’s proofs,
03:37:10 to the statement there are five platonic solids.
03:37:13 So, okay, so then the question is,
03:37:17 in, what does it mean if you have this map?
03:37:22 Okay, so in a sense, this metamathematical space
03:37:26 is the infrastructural space of all possible theorems
03:37:29 that you could prove in mathematics.
03:37:31 That’s the geometry of metamathematics.
03:37:34 There’s also the geography of mathematics.
03:37:37 That is, where did people choose to live in space?
03:37:40 And that’s what, for example,
03:37:42 exploring the sort of empirical metamathematics
03:37:44 that Euclid is doing.
03:37:45 You could put each individual, like, human mathematician,
03:37:48 you can embed them into that space.
03:37:49 I mean, they kind of live.
03:37:51 They represent a path in the space.
03:37:52 The little path.
03:37:53 The things they do.
03:37:54 Maybe a set of paths.
03:37:54 Right.
03:37:55 So like a set of axioms that are chosen.
03:37:58 Right, so for example,
03:37:59 here’s an example of a thing that I realized.
03:38:01 So one of the surprising things about,
03:38:03 well, there are two surprising facts about math.
03:38:06 One is that it’s hard,
03:38:07 and the other is that it’s doable, okay?
03:38:10 So first question is, why is math hard?
03:38:12 You know, you’ve got these axioms.
03:38:13 They’re very small.
03:38:14 Why can’t you just solve every problem in math easily?
03:38:17 Yeah, it’s just logic.
03:38:19 Right, yeah.
03:38:19 Well, logic happens to be a particular special case
03:38:22 that does have certain simplicity to it.
03:38:25 But general mathematics, even arithmetic,
03:38:27 already doesn’t have the simplicity that logic has.
03:38:30 So why is it hard?
03:38:31 Because of computational irreducibility.
03:38:33 Right.
03:38:35 Because what happens is, to know what’s true,
03:38:38 and this is this whole story about the path
03:38:40 you have to follow and how long is the path,
03:38:43 and Gödel’s theorem is the statement
03:38:44 that the path is not a bounded length,
03:38:47 but the fact that the path is not always compressible
03:38:50 to something tiny is a story of computational irreducibility.
03:38:54 So that’s why math is hard.
03:38:56 Now, the next question is, why is math doable?
03:38:59 Because it might be the case that most things you care about
03:39:02 don’t have finite length paths.
03:39:04 Most things you care about might be things
03:39:06 where you get lost in the sea of computational irreducibility
03:39:10 and worse, undecidability.
03:39:12 That is, there’s just no finite length path
03:39:14 that gets you there.
03:39:17 Why is mathematics doable?
03:39:19 Gödel proved his incompleteness theorem in 1931.
03:39:22 Most working mathematicians don’t really care about it.
03:39:25 They just go ahead and do mathematics,
03:39:27 even though it could be that the questions they’re asking
03:39:29 are undecidable.
03:39:31 It could have been that Fermat’s last theorem
03:39:32 is undecidable.
03:39:33 It turned out it had a proof.
03:39:35 It’s a long, complicated proof.
03:39:36 The twin prime conjecture might be undecidable.
03:39:40 The Riemann hypothesis might be undecidable.
03:39:43 These things might be, the axioms of mathematics
03:39:45 might not be strong enough to reach those statements.
03:39:49 It might be the case that depending on what axioms
03:39:51 you choose, you can either say that’s true
03:39:53 or that’s not true.
03:39:54 So…
03:39:55 And by the way, from Fermat’s last theorem,
03:39:57 there could be a shorter path.
03:39:59 Absolutely.
03:40:00 Yeah, so the notion of geodesics in metamathematical space
03:40:03 is the notion of shortest proofs in metamathematical space.
03:40:07 And that’s a, you know, human mathematicians
03:40:09 do not find shortest paths,
03:40:11 nor do automated theorem provers.
03:40:13 But the fact, and by the way, the, I mean,
03:40:16 this stuff is so bizarrely connected.
03:40:18 I mean, if you’re into automated theorem proving,
03:40:21 there are these so called critical pair lemmas
03:40:23 and automated theorem proving.
03:40:24 Those are precisely the branch pairs in our,
03:40:28 that in multiway graphs.
03:40:30 Let me just finish on the why mathematics is doable.
03:40:32 Oh yes, the second part.
03:40:34 So you know why it’s hard, why is it doable?
03:40:36 Right, why do we not just get lost
03:40:38 in undecidability all the time?
03:40:39 Yeah.
03:40:40 So, and here’s another fact,
03:40:43 is in doing computer experiments
03:40:45 and doing experimental mathematics,
03:40:47 you do get lost in that way.
03:40:49 When you just say, I’m picking a random integer equation.
03:40:53 How do I, does it have a solution or not?
03:40:56 And you just pick it at random
03:40:57 without any human sort of path getting there.
03:41:00 Often, it’s really, really hard.
03:41:03 It’s really hard to answer those questions.
03:41:04 We just pick them at random from the space of possibilities.
03:41:07 But what I think is happening is,
03:41:10 and that’s a case where you just fell off
03:41:12 into this ocean of sort of irreducibility and so on.
03:41:15 What’s happening is human mathematics
03:41:18 is a story of building a path.
03:41:19 You started off, you’re always building out
03:41:23 on this path where you are proving things.
03:41:25 You’ve got this proof trajectory
03:41:28 and you’re basically, the human mathematics
03:41:30 is the sort of the exploration of the world
03:41:34 along this proof trajectory, so to speak.
03:41:36 You’re not just parachuting in from anywhere.
03:41:42 You’re following Lewis and Clark or whatever.
03:41:44 You’re actually going, doing the path.
03:41:48 And the fact that you are constrained to go along that path
03:41:52 is the reason you don’t end up with,
03:41:53 every so often you’ll see a little piece of undecidability
03:41:55 and you’ll avoid that part of the path.
03:41:57 But that’s basically the story of why human mathematics
03:42:00 has seemed to be doable.
03:42:02 It’s a story of exploring these paths
03:42:05 that are by their nature,
03:42:07 they have been constructed to be paths that can be followed.
03:42:10 And so you can follow them further.
03:42:12 Now, why is this relevant to anything?
03:42:14 So, okay, so here’s my belief.
03:42:19 The fact that human mathematics works that way
03:42:22 is I think there’s some sort of connections
03:42:26 between the way that observers work in physics
03:42:29 and the way that the axiom systems of mathematics are set up
03:42:32 to make mathematics be doable in that kind of way.
03:42:36 And so, in other words, in particular,
03:42:38 I think there is an analog of causal invariance,
03:42:41 which I think is, and this is again,
03:42:44 it’s sort of the upper reaches of mathematics
03:42:46 and stuff that it’s a thing,
03:42:50 there’s this thing called homotopy type theory,
03:42:52 which is an abstract, it’s came out of category theory,
03:42:56 and it’s sort of an abstraction of mathematics.
03:42:58 Mathematics itself is an abstraction,
03:43:00 but it’s an abstraction of the abstraction of mathematics.
03:43:03 And there is the thing called the univalence axiom,
03:43:06 which is a sort of a key axiom in that set of ideas.
03:43:12 And I’m pretty sure the univalence axiom
03:43:14 is equivalent to causal invariance.
03:43:16 What was the term you used again?
03:43:18 Univalence.
03:43:19 Is that something for somebody like me accessible?
03:43:21 Or is this?
03:43:23 There’s a statement of it that’s fairly accessible.
03:43:25 I mean, the statement of it is,
03:43:29 basically it says things which are equivalent
03:43:32 can be considered to be identical.
03:43:35 In which space?
03:43:38 Yeah, it’s in higher category.
03:43:40 In category.
03:43:41 Okay, so it’s a, but I mean,
03:43:43 the thing just to give a sketch of how that works.
03:43:46 So category theory is an attempt to idealize,
03:43:49 it’s an attempt to sort of have a formal theory
03:43:52 of mathematics that is at a sort of higher level
03:43:54 than mathematics.
03:43:55 It’s where you just think about these mathematical objects
03:43:59 and these categories of objects and these morphisms,
03:44:03 these connections between categories.
03:44:05 Okay, so it turns out the morphisms and categories,
03:44:08 at least weak categories,
03:44:10 are very much like the paths in our hypergraphs and things.
03:44:14 And it turns out, again, this is where it all gets crazy.
03:44:18 I mean, the fact that these things are connected
03:44:20 is just bizarre.
03:44:22 So category theory, our causal graphs
03:44:27 are like second order category theory.
03:44:29 And it turns out you can take the limits
03:44:32 of infinite order category theory.
03:44:34 So just give roughly the idea.
03:44:36 This is a roughly explainable idea.
03:44:39 So a mathematical proof will be a path
03:44:43 that says you can get from this thing to this other thing.
03:44:45 And here’s the path that you get from this thing
03:44:47 to this other thing.
03:44:48 But in general, there may be many paths,
03:44:51 many proofs that get you many different paths
03:44:53 that all successfully go from this thing
03:44:55 to this other thing, okay?
03:44:57 Now you can define a higher order proof,
03:45:00 which is a proof of the equivalence of those proofs.
03:45:03 Okay, so you’re saying there’s a…
03:45:05 A path between those proofs essentially.
03:45:07 Yes, a path between the paths, okay?
03:45:09 And so you do that.
03:45:10 That’s the sort of second order thing.
03:45:12 That path between the paths is essentially related
03:45:16 to our causal graphs.
03:45:18 Then you can take the limit.
03:45:19 Wow, okay.
03:45:20 The path between path, between path, between path.
03:45:23 The infinite limit.
03:45:24 That infinite limit turns out to be
03:45:26 our Rulial Multiway System.
03:45:28 Yeah, the Rulial Multiway System,
03:45:31 that’s a fascinating, both in the physics world
03:45:33 and as you’re saying now, that’s fast.
03:45:36 I’m not sure I’ve loaded it in completely, but…
03:45:39 Well, I’m not sure I have either.
03:45:40 And it may be one of these things where,
03:45:42 in another five years or something, it’s like,
03:45:45 it was obvious, but I didn’t see it.
03:45:47 No, but the thing which is sort of interesting to me
03:45:49 is that there’s sort of an upper reach of mathematics,
03:45:53 of the abstraction of mathematics.
03:45:55 This thing, there’s this mathematician called Grothendieck
03:45:59 who’s generally viewed as being sort of one
03:46:00 of the most abstract,
03:46:02 sort of creator of the most abstract mathematics
03:46:04 of 1970s ish timeframe.
03:46:09 And one of the things that he constructed was this thing
03:46:11 he called the Infinity Grupoid.
03:46:13 And he has this sort of hypothesis
03:46:15 about the inevitable appearance of geometry
03:46:18 from essentially logic in the structure of this thing.
03:46:22 Well, it turns out this Rulial Multiway System
03:46:24 is the Infinity Grupoid.
03:46:26 So it’s this limiting object.
03:46:29 And this is an instance of that limiting object.
03:46:33 So what to me is, I mean, again,
03:46:35 I’ve been always afraid of this kind of mathematics
03:46:37 because it seemed incomprehensibly abstract to me.
03:46:42 But what I’m sort of excited about with this
03:46:45 is that we’ve sort of concretified the way
03:46:49 that you can reach this kind of mathematics,
03:46:51 which makes it, well, both seem more relevant
03:46:55 and also the fact that I don’t yet know exactly
03:46:58 what mileage we’re gonna get from using
03:47:01 the sort of the apparatus that’s been built
03:47:03 in those areas of mathematics to analyze what we’re doing.
03:47:06 But the thing that’s.
03:47:07 So both ways.
03:47:08 So using mathematics to understand what you’re doing
03:47:10 and using what you’re doing computationally
03:47:12 to understand that.
03:47:13 Right, so for example,
03:47:14 the understanding of metamathematical space,
03:47:17 one of the reasons I really want to do that
03:47:19 is because I want to understand quantum mechanics better.
03:47:22 And that, what you see,
03:47:25 we live that kind of the multiway graph of mathematics
03:47:30 because we actually know this is a theorem we’ve heard of.
03:47:32 This is another one we’ve heard of.
03:47:34 We can actually say these are actual things in the world
03:47:36 that we relate to,
03:47:38 which we can’t really do as readily for the physics case.
03:47:43 And so it’s kind of a way to help my intuition.
03:47:45 It’s also, there are bizarre things
03:47:47 like what’s the analog of Einstein’s equations
03:47:50 in metamathematical space?
03:47:51 What’s the analog of a black hole?
03:47:53 It turns out it looks like not completely sure yet,
03:47:57 but there’s this notion of nonconstructive proofs
03:48:00 in mathematics.
03:48:01 And I think those relate to,
03:48:03 well, actually they relate to things
03:48:07 related to event horizons.
03:48:10 So the fact that you can take ideas from physics
03:48:13 like event horizons.
03:48:14 And map them into the same kind of space, metamath.
03:48:17 It’s really.
03:48:17 So do you think there’ll be,
03:48:19 do you think you might stumble upon
03:48:22 some breakthrough ideas in theorem proving?
03:48:25 Like for, from the other direction?
03:48:28 Yeah, yeah, yeah.
03:48:29 No, I mean, what’s really nice is that we are using,
03:48:32 so this absolutely directly maps to theorem proving.
03:48:35 So pods and multiway graphs,
03:48:37 that’s what a theorem prover is trying to do.
03:48:38 But I also mean like automated theorem.
03:48:40 Yeah, yeah, yeah.
03:48:41 That’s what, right.
03:48:42 So the finding of pods, the finding of shortest pods
03:48:45 or finding of pods at all
03:48:46 is what automated theorem provers do.
03:48:48 And actually what we’ve been doing.
03:48:51 So we’ve actually been using automated theorem proving
03:48:53 both in the physics project to prove things
03:48:56 and using that as a way to understand multiway graphs.
03:49:00 And because what an automated theorem prover is doing
03:49:04 is it’s trying to find a path through a multiway graph
03:49:07 and its critical pair lemmas
03:49:09 are precisely little stubs of branch pairs
03:49:12 going off into branchial space.
03:49:15 And that’s, I mean, it’s really weird.
03:49:16 You know, we have these visualizations in Wolfram language
03:49:19 of proof graphs from our automated theorem proving system.
03:49:24 And they look reminiscent of.
03:49:25 Well, it’s just bizarre
03:49:26 because we made these up a few years ago
03:49:28 and they have these little triangle things
03:49:30 and they are, we didn’t quite get it right.
03:49:33 We didn’t quite get the analogy perfectly right,
03:49:35 but it’s very close.
03:49:36 You know, just to say,
03:49:37 in terms of how these things are connected.
03:49:39 So there’s another bizarre connection
03:49:41 that I have to mention because which is,
03:49:46 which again, we don’t fully know,
03:49:47 but it’s a connection to something else
03:49:51 you might not have thought was in the slightest
03:49:52 but connected, which is distributed blockchain like things.
03:49:56 Now you might figure out that that’s,
03:49:58 you would figure out that that’s connected
03:49:59 because it’s a story of distributed computing.
03:50:02 And the issue, you know, with the blockchain,
03:50:04 you’re saying there’s going to be this one ledger
03:50:07 that globally says, this is what happened in the world.
03:50:11 But that’s a bad deal.
03:50:14 If you’ve got all these different transactions
03:50:15 that are happening and you know,
03:50:17 this transaction in country A
03:50:20 doesn’t have to be reconciled with the transaction
03:50:23 in country B, at least not for a while.
03:50:26 And that story is just like what happens
03:50:29 with our causal graphs.
03:50:31 That whole reconciliation thing is just like
03:50:33 what happens with light cones and all this kind of thing.
03:50:35 That’s where the causal awareness comes into play.
03:50:37 I mean, that’s, you know,
03:50:39 most of your conversations are about physics,
03:50:41 but it’s kind of funny that this probably
03:50:46 and possibly might have even bigger impact
03:50:49 and revolutionary ideas and totally other disciplines.
03:50:53 Right, well, you see, yeah, right.
03:50:55 So the question is, why is that happening, right?
03:50:57 And the reason it’s happening,
03:50:59 I’ve thought about this obviously,
03:51:00 because I like to think about these meta questions of,
03:51:03 you know, what’s happening is this model that we have
03:51:06 is an incredibly minimal model.
03:51:08 And once you have an incredibly minimal model,
03:51:11 and this happened with cellular automata as well,
03:51:13 cellular automata are an incredibly minimal model.
03:51:16 And so it’s inevitable that it gets you,
03:51:19 it’s sort of an upstream thing
03:51:20 that gets used in lots of different places.
03:51:22 And it’s like, you know, the fact that it gets used,
03:51:25 you know, cellular automata is sort of a minimal model
03:51:27 of let’s say road traffic flow or something.
03:51:29 And they’re also a minimal model of something in,
03:51:31 you know, chemistry,
03:51:32 and they’re also a minimal model of something
03:51:33 in epidemiology, right?
03:51:35 It’s because they’re such a simple model that they can,
03:51:38 that they apply to all these different things.
03:51:40 Similarly, this model that we have with the physics project
03:51:43 is another, cellular automata are a minimal model
03:51:47 of parallel, of basically of parallel computation
03:51:50 where you’ve defined space and time.
03:51:52 These models are minimal models
03:51:54 where you have not defined space and time.
03:51:57 And they have been very hard to understand in the past,
03:52:00 but the, I think the,
03:52:01 perhaps the most important breakthrough there
03:52:04 is the realization that these are models of physics.
03:52:07 And therefore that you can use everything
03:52:09 that’s been developed in physics
03:52:11 to get intuition about how things like that work.
03:52:13 And that’s why you can potentially use ideas from physics
03:52:17 to get intuition about how to do parallel computing.
03:52:20 And because the underlying model is the same.
03:52:24 But we have all of this achievement in physics.
03:52:27 I mean, you know, you might say,
03:52:28 oh, you’ve come up with the fundamental theory of physics
03:52:30 that throws out what people have done in physics before.
03:52:32 Well, it doesn’t, but also the real power
03:52:35 is to use what’s been done before in physics
03:52:37 to apply it in these other places.
03:52:39 Yes, absolutely.
03:52:41 This kind of brings up,
03:52:43 I know you probably don’t particularly love commenting
03:52:47 on the work of others,
03:52:48 but let me bring up a couple of personalities
03:52:51 just because it’s fun and people are curious about it.
03:52:53 So there’s Sabine Hassenfelder.
03:52:58 I don’t know if you’re familiar with her.
03:53:00 She wrote this book that I need to read,
03:53:04 but I forget what the title is,
03:53:06 but it’s Beauty Leads Us Astray in Physics
03:53:10 is a subtitle or something like that.
03:53:12 Which so much about what we’re talking about now,
03:53:15 like this simplification,
03:53:17 to us humans seems to be beautiful.
03:53:20 Like there’s a certain intuition with physicists,
03:53:23 with people that a simple theory,
03:53:26 like this reducibility,
03:53:28 pockets of reducibility is the ultimate goal.
03:53:30 And I think what she tries to argue is no,
03:53:34 we just need to come up with theories
03:53:37 that are just really good at predicting physical phenomena.
03:53:40 It’s okay to have a bunch of disparate theories
03:53:44 as opposed to trying to chase this beautiful theory
03:53:48 of everything is the ultimate beautiful theory,
03:53:51 a simple one.
03:53:52 What’s your response to that?
03:53:54 Well, so what you’re quoting,
03:53:56 I don’t know the Sabine Hassenfelder’s,
03:53:59 exactly what she said,
03:54:00 but I mean that you’re quoting the title of her book.
03:54:03 Okay.
03:54:04 Let me respond to what you were describing,
03:54:07 which may or may not have nothing to do with
03:54:09 what Sabine Hassenfelder says or thinks.
03:54:14 Sorry, Sabine.
03:54:16 Right.
03:54:17 Sorry for misquoting.
03:54:18 But I mean, the question is,
03:54:23 is beauty a guide to whether something is correct?
03:54:26 Which is kind of also the story of Occam’s razor.
03:54:29 If you’ve got a bunch of different explanations of things,
03:54:32 is the thing that is the simplest explanation
03:54:34 likely to be the correct explanation?
03:54:36 And there are situations where that’s true
03:54:38 and there are situations where it isn’t true.
03:54:39 Sometimes in human systems, it is true
03:54:41 because people have kind of,
03:54:43 in evolutionary systems, sometimes it’s true
03:54:45 because it’s sort of been kicked
03:54:46 to the point where it’s minimized.
03:54:49 But in physics, does Occam’s razor work?
03:54:53 Is there a simple, quotes, beautiful explanation for things
03:54:57 or is it a big mess?
03:54:59 We don’t intrinsically know.
03:55:01 I think that the, I wouldn’t,
03:55:03 before I worked on the project in recent times,
03:55:07 I would have said,
03:55:08 we do not know how complicated
03:55:09 the rule for the universe will be.
03:55:12 And I would have said, the one thing we know,
03:55:15 which is a fundamental fact about science,
03:55:17 that’s the thing that makes science possible,
03:55:19 is that there is order in the universe.
03:55:21 I mean, early theologians would have used that
03:55:24 as an argument for the existence of God
03:55:27 because it’s like, why is there order in the universe?
03:55:29 Why doesn’t every single particle in the universe
03:55:31 just do its own thing?
03:55:33 Something must be making there be order in the universe.
03:55:37 We, in the sort of early theology point of view,
03:55:41 that’s the role of God is to do that, so to speak.
03:55:45 In our, we might say,
03:55:47 it’s the role of a formal theory to do that.
03:55:50 And then the question is,
03:55:51 but how simple should that theory be?
03:55:53 And should that theory be one that,
03:55:57 where I think the point is, if it’s simple,
03:56:00 it’s almost inevitably somewhat beautiful
03:56:03 in the sense that, because all the stuff that we see
03:56:06 has to fit into this little tiny theory.
03:56:08 And the way it does that has to be,
03:56:11 it depends on your notion of beauty,
03:56:13 but I mean, for me, the sort of the surprising
03:56:17 connectivity of it is, at least in my aesthetic,
03:56:21 that’s something that responds to my aesthetic.
03:56:25 But the question is, I mean,
03:56:27 you’re a fascinating person in the sense that
03:56:31 you’re at once talking about computational,
03:56:34 the fundamental computational reducibility of the universe,
03:56:37 and on the other hand,
03:56:40 trying to come up with a theory of everything,
03:56:42 which simply describes the,
03:56:47 the simple origins of that computational reducibility.
03:56:51 I mean, both of those things are kind of,
03:56:53 it’s paralyzing to think that we can’t make any sense
03:56:56 of the universe in the general case,
03:56:58 but it’s hopeful to think like,
03:57:01 one, we can think of a rule
03:57:03 and that generates this whole complexity,
03:57:05 and two, we can find pockets of reducibility
03:57:10 that are powerful for everyday life
03:57:13 to do different kinds of predictions.
03:57:15 I suppose Sabine wants to find,
03:57:19 focus on the finding of small pockets of reducibility
03:57:22 versus the theory of everything.
03:57:26 You know, it’s a funny thing because,
03:57:29 you know, a bunch of people have started working
03:57:30 on this physics project,
03:57:32 people who are physicists, basically,
03:57:36 and it is really a fascinating sociological phenomenon
03:57:39 because what, you know,
03:57:41 when I was working on this before in the 1990s,
03:57:45 you know, wrote it up, put it,
03:57:47 it’s 100 pages of this 1200 page book
03:57:50 that I wrote, New Kind of Science,
03:57:51 is, you know, 100 pages of that is about physics,
03:57:54 but I saw it at that time,
03:57:57 not as a pinnacle achievement,
03:57:59 but rather as a use case, so to speak.
03:58:01 I mean, my main point was this new kind of science,
03:58:04 and it’s like, you can apply it to biology,
03:58:05 you can apply it to, you know, other kinds of physics,
03:58:08 you can apply it to fundamental physics,
03:58:09 it’s just an application, so to speak,
03:58:12 it’s not the core thing.
03:58:14 But then, you know, one of the things that was interesting
03:58:18 with that book was, you know,
03:58:21 book comes out, lots of people think it’s pretty interesting
03:58:24 and lots of people start using what it has
03:58:26 in different kinds of fields.
03:58:28 The one field where there was sort of a heavy pitchforking
03:58:32 was from my friends, the fundamental physics people,
03:58:35 which was, it’s like, no,
03:58:37 this can’t possibly be right.
03:58:38 And, you know, it’s like, you know,
03:58:40 if what you’re doing is right,
03:58:41 it’ll overturn 50 years of what we’ve been doing.
03:58:44 And it’s like, no, it won’t, was what I was saying.
03:58:46 And it’s like, but, you know, for a while,
03:58:50 when I started, you know, I was going to go on back in 2002,
03:58:54 well, 2004, actually, I was going to go on
03:58:57 working on this project.
03:58:58 And I actually stopped,
03:58:59 partly because it’s like, why am I, you know,
03:59:03 this is like, I’ve been in business a long time, right?
03:59:05 I’m building a product for a target market
03:59:08 that doesn’t want the product.
03:59:09 And it’s like.
03:59:10 Why work, yeah, yeah, why work against the,
03:59:13 swim against the current or whatever.
03:59:14 Right, but you see what’s happened,
03:59:16 which is sort of interesting is that,
03:59:18 so a couple of things happened and it was like,
03:59:22 you know, it was like, I don’t want to do this project
03:59:25 because I can do so many other things,
03:59:28 which I’m really interested in where, you know,
03:59:31 people say, great, thanks for those tools.
03:59:34 Thanks for those ideas, et cetera.
03:59:36 Whereas, you know, if you’re dealing with kind of a,
03:59:40 you know, a sort of a structure where people are saying,
03:59:42 no, no, we don’t want this new stuff.
03:59:44 We don’t need any new stuff.
03:59:45 We’re really fine with what we’re doing.
03:59:46 Yeah, there’s like literally like, I don’t know,
03:59:48 millions of people who are thankful for Wolfram Alpha.
03:59:51 A bunch of people wrote to me, how thankful,
03:59:53 they are a different crowd
03:59:55 than the theoretical physics community, perhaps.
03:59:57 Yeah, well, but you know,
03:59:58 the theoretical physics community
04:00:00 pretty much uniformly uses Wolfram language
04:00:03 and Mathematica, right?
04:00:04 And so it’s kind of like, you know, and that’s,
04:00:08 but the thing is what happens, you know,
04:00:11 this is what happens, mature fields do not, you know,
04:00:14 it’s like, we’re doing what we’re doing.
04:00:16 We have the methods that we have
04:00:18 and we’re just fine here.
04:00:20 Now what’s happened in the last 18 years or so,
04:00:23 I think there’s a couple of things have happened.
04:00:25 First of all, the hope that, you know,
04:00:29 string theory or whatever would deliver
04:00:31 the fundamental theory of physics,
04:00:32 that hope has disappeared.
04:00:34 That the, another thing that’s happened
04:00:36 is the sort of the interest in computation around physics
04:00:41 has been greatly enhanced
04:00:42 by the whole quantum information,
04:00:44 quantum computing story.
04:00:46 People, you know, the idea there might be something
04:00:47 sort of computational related to physics
04:00:51 has somehow grown.
04:00:53 And I think, you know, it’s sort of interesting.
04:00:55 I mean, right now, if we say, you know,
04:00:58 it’s like, if you’re like,
04:00:59 who else is trying to come up
04:01:00 with the fundamental theory of physics?
04:01:02 It’s like, there aren’t professional,
04:01:04 no professional physicists, no professional physicists.
04:01:07 What are your, I mean, you’ve talked with him,
04:01:10 but just as a matter of personalities,
04:01:12 cause it’s a beautiful story.
04:01:13 What are your thoughts about Eric Weinstein’s work?
04:01:17 You know, I think his, I mean,
04:01:20 he did a PhD thesis in mathematical physics at Harvard.
04:01:23 He’s a mathematical physicist.
04:01:24 And, you know, it seems like it’s kind of,
04:01:28 you know, it’s in that framework.
04:01:30 And it’s kind of like,
04:01:32 I’m not sure how much further it’s got than his PhD thesis,
04:01:35 which was 20 years ago or something.
04:01:37 And I think that, you know, the, you know,
04:01:40 it’s a fairly specific piece of mathematical physics.
04:01:43 That’s quite nice.
04:01:44 And…
04:01:45 What trajectory do you hope it takes?
04:01:47 I mean…
04:01:48 Well, I think in his particular case,
04:01:50 I mean, from what I understand,
04:01:51 which is not everything at all,
04:01:52 but, you know, I think I know the rough tradition,
04:01:54 at least what he’s operating in is sort of theory of gauge theories.
04:01:58 Gauge theories, yeah.
04:01:59 Local gauge invariants and so on.
04:02:01 Okay, we are very close to understanding
04:02:04 how local gauge invariants works in our models.
04:02:06 And it’s very beautiful.
04:02:07 And it’s very…
04:02:09 And, you know, does some of the mathematical structure
04:02:12 that he’s enthusiastic about fit?
04:02:14 Quite possibly, yes.
04:02:15 So there might be a possibility of trying to understand
04:02:17 how those things fit, how gauge theory fits.
04:02:19 Yeah, very well.
04:02:20 I mean, the question is, you know,
04:02:21 so there are a couple of things
04:02:22 one might try to get in the world.
04:02:24 So for example, it’s like,
04:02:25 can we get three dimensions of space?
04:02:27 We haven’t managed to get that yet.
04:02:28 Gauge theory, the standard model of particle physics says,
04:02:32 but it’s SU3 cross SU2 cross U1.
04:02:35 Those are the designations of these Lie groups.
04:02:39 It doesn’t, but anyway,
04:02:41 so those are sort of representations
04:02:43 of symmetries of the theory.
04:02:46 And so, you know, it is conceivable
04:02:50 that it is generically true.
04:02:52 Okay, so all those are subgroups of a group called E8,
04:02:55 which is a weird, exceptional Lie group, okay?
04:02:59 It is conceivable, I don’t know whether it’s the case,
04:03:02 that that will be generic in these models,
04:03:05 that it will be generic,
04:03:06 that the gauge invariance of the model has this property,
04:03:12 just as things like general relativity,
04:03:15 which corresponds to the thing called general covariance,
04:03:20 which is another gauge like invariance.
04:03:23 It could conceivably be the case
04:03:25 that the kind of local gauge invariance
04:03:27 that we see in particle physics is somehow generic.
04:03:30 And that would be a, you know,
04:03:32 the thing that’s really cool, I think, you know,
04:03:35 sociologically, although this hasn’t really hit yet,
04:03:38 is that all of these different things,
04:03:40 all these different things people have been working on
04:03:41 in these, in some cases,
04:03:43 quite abstruse areas of mathematical physics,
04:03:46 an awful lot of them seem to tie into what we’re doing.
04:03:49 And, you know, it might not be that way.
04:03:51 Yeah, absolutely.
04:03:52 That’s a beautiful thing, I think.
04:03:53 I mean, but the reason Eric Weinstein is important
04:03:58 is to the point that you mentioned before,
04:04:00 which is, it’s strange that the theory of everything
04:04:04 is not at the core of the passion, the dream,
04:04:09 the focus, the funding of the physics community.
04:04:14 It’s too hard.
04:04:16 It’s too hard and people gave up.
04:04:17 I mean, basically what happened is ancient Greece,
04:04:21 people thought we’re nearly there.
04:04:23 You know, the world is made of platonic solids.
04:04:25 It’s, you know, water is a tetrahedron or something.
04:04:27 We’re almost there, okay?
04:04:29 Long period of time where people were like,
04:04:32 no, we don’t know how it works.
04:04:34 You know, time of Newton, you know, we’re almost there.
04:04:36 Everything is gravitation.
04:04:38 You know, time of Faraday and Maxwell, we’re almost there.
04:04:42 Everything is fields, everything is the ether, you know?
04:04:45 Then…
04:04:46 And the whole time we’re making big progress though.
04:04:48 Oh yes, absolutely.
04:04:50 But the fundamental theory of physics is almost a footnote
04:04:53 because it’s like, it’s the machine code.
04:04:56 It’s like we’re operating in the high level languages.
04:04:59 Yeah.
04:05:00 You know, that’s what we really care about.
04:05:01 That’s what’s relevant for our everyday physics.
04:05:03 You talked about different centuries
04:05:05 and the 21st century will be everything is computation.
04:05:08 Yes.
04:05:09 If that takes us all the way, we don’t know,
04:05:11 but it might take us pretty far.
04:05:13 Yes, right, that’s right.
04:05:14 And I, but I think the point is that it’s like, you know,
04:05:17 if you’re doing biology, you might say,
04:05:18 how can you not be really interested in the origin of life
04:05:21 and the definition of life?
04:05:22 Well, it’s irrelevant.
04:05:23 You know, you’re studying the properties of some virus.
04:05:26 It doesn’t matter, you know, where, you know,
04:05:28 you’re operating at some much higher level.
04:05:30 And it’s the same, what’s happening with physics is,
04:05:34 I was sort of surprised actually.
04:05:35 I was sort of mapping out this history of people’s efforts
04:05:38 to understand the fundamental theory of physics.
04:05:41 And it’s remarkable how little has been done on this question.
04:05:45 And it’s, you know, because, you know,
04:05:47 there’ve been times when there’s been bursts of enthusiasm.
04:05:49 Oh, we’re almost there.
04:05:50 And then it decays and people just say,
04:05:54 oh, it’s too hard, but it’s not relevant anyway.
04:05:57 And I think that the thing that, you know,
04:06:01 so the question of, you know, one question is,
04:06:04 why does anybody, why should anybody care, right?
04:06:07 Why should anybody care
04:06:08 what the fundamental theory of physics is?
04:06:10 I think it’s intellectually interesting,
04:06:13 but what will be the sort of,
04:06:14 what will be the impact of this?
04:06:16 What, I mean, this is the key question.
04:06:18 What do you think will happen
04:06:20 if we figure out the fundamental theory of physics?
04:06:25 Right.
04:06:26 Outside of the intellectual curiosity of us.
04:06:28 Okay, so here’s my best guess, okay?
04:06:31 So if you look at the history of science,
04:06:33 I think a very interesting analogy is Copernicus.
04:06:37 Okay, so what did Copernicus do?
04:06:39 There’d been this Ptolemaic system
04:06:41 for working out the motion of planets.
04:06:43 It did pretty well.
04:06:44 It used epicycles, et cetera, et cetera, et cetera.
04:06:47 It had all this computational ways
04:06:49 of working out where planets will be.
04:06:51 When we work out where planets are today,
04:06:52 we’re basically using epicycles.
04:06:54 But Copernicus had this different way of formulating things
04:06:58 in which he said, you know,
04:07:00 and the earth is going around the sun,
04:07:02 and that had a consequence.
04:07:04 The consequence was you can use this mathematical theory
04:07:07 to conclude something which is absolutely not
04:07:10 what we can tell from common sense, right?
04:07:14 So it’s like, trust the mathematics, trust the science, okay?
04:07:18 Now fast forward 400 years,
04:07:21 and now we’re in this pandemic,
04:07:23 and it’s kind of like everybody thinks the science
04:07:26 will figure out everything.
04:07:28 It’s like from the science,
04:07:30 we can just figure out what to do.
04:07:31 We can figure out everything.
04:07:32 That was before Copernicus.
04:07:34 Nobody would have thought if the science says something
04:07:37 that doesn’t agree with our everyday experience,
04:07:40 where we just have to compute the science
04:07:43 and then figure out what to do,
04:07:44 people would say that’s completely crazy.
04:07:46 And so your sense is,
04:07:47 once we figure out the framework of computation
04:07:49 that can basically do any,
04:07:51 understand the fabric of reality,
04:07:53 we’ll be able to derive totally counterintuitive things.
04:07:58 No, the point I think is the following.
04:08:01 That right now, you know,
04:08:03 I talk about computational irreducibility.
04:08:05 People, you know, I was very proud
04:08:07 that I managed to get the term computational irreducibility
04:08:10 into the congressional record last year.
04:08:13 That’s right, by the way,
04:08:13 that’s a whole nother topic we could talk about.
04:08:15 Fascinating. Different topic.
04:08:17 Different topic.
04:08:18 But Tim, in any case, you know,
04:08:20 but so computational irreducibility
04:08:22 is one of these sort of concepts
04:08:23 that I think is important in understanding
04:08:25 lots of things in the world.
04:08:26 But the question is, it’s only important
04:08:29 if you believe the world is fundamentally computational.
04:08:32 Right?
04:08:33 But if you know the fundamental theory of physics
04:08:35 and it’s fundamentally computational,
04:08:38 then you’ve rooted the whole thing.
04:08:40 That is, you know the world is computational.
04:08:43 And while you can discuss whether, you know,
04:08:47 it’s not the case that people would say,
04:08:48 well, you have this whole computational irreducibility,
04:08:50 all these features of computation.
04:08:52 We don’t care about those
04:08:54 because after all the world isn’t computational,
04:08:56 you might say.
04:08:57 But if you know, you know, base, base, base thing,
04:09:01 physics is computational,
04:09:03 then you know that that stuff is, you know,
04:09:05 that that’s kind of the grounding for that stuff.
04:09:07 Just as in a sense Copernicus was the grounding
04:09:10 for the idea that you could figure out something
04:09:12 with math and science
04:09:14 that was not what you would intuitively think
04:09:18 from your senses.
04:09:20 So now we’ve got to this point where, for example,
04:09:22 we say, you know, once we have the idea
04:09:25 that computation is the foundational thing
04:09:27 that explains our whole universe,
04:09:30 then we have to say, well, what does it mean
04:09:32 for other things?
04:09:32 Like it means there’s computational irreducibility.
04:09:35 That means science is limited in certain ways.
04:09:37 That means this, that means that.
04:09:39 But the fact that we have that grounding means that,
04:09:43 you know, and I think, for example, for Copernicus,
04:09:45 for instance, the implications of his work
04:09:49 on the set of mathematics of astronomy were cool,
04:09:52 but they involved a very small number of people.
04:09:54 The implications of his work for sort of the philosophy
04:09:56 of how you think about things were vast
04:09:59 and involved, you know, everybody more or less.
04:10:02 But do you think, so that’s actually the way scientists
04:10:05 and people see the world around us.
04:10:08 So it has a huge impact in that sense.
04:10:10 Do you think it might have an impact more directly
04:10:14 to engineering derivations from physics,
04:10:18 like propulsion systems, our ability to colonize the world?
04:10:21 Like, for example, okay, this is like sci fi,
04:10:24 but if you understand the computational nature, say,
04:10:30 of the different forces of physics, you know,
04:10:34 there’s a notion of being able to warp gravity,
04:10:38 things like this.
04:10:39 Yeah, can we make warp drive?
04:10:40 Warp drive, yeah.
04:10:41 So like, would we be able to, will, you know,
04:10:45 will like Elon Musk start paying attention?
04:10:47 Like it’s awfully costly to launch these rockets.
04:10:50 Do you think we’ll be able to, yeah, create warp drive?
04:10:52 And, you know, I set myself some homework.
04:10:55 I agreed to give a talk at some NASA workshop
04:10:57 in a few weeks about faster than light travel.
04:10:59 So I haven’t figured it out yet, but no, but.
04:11:02 You got two weeks.
04:11:03 Yeah, right.
04:11:04 But do you think that kind of understanding
04:11:06 of fundamental theory of physics can lead
04:11:07 to those engineering breakthroughs?
04:11:09 Okay, I think it’s far away, but I’m not certain.
04:11:12 I mean, you know, this is the thing that,
04:11:14 I set myself an exercise when gravity waves,
04:11:16 gravitational waves were discovered, right?
04:11:19 I set myself the exercise of what would black hole
04:11:22 technology look like?
04:11:23 In other words, right now, you know,
04:11:25 black holes are far away.
04:11:26 They’re, you know, how on earth can we do things with them?
04:11:28 But just imagine that we could get, you know,
04:11:30 pet black holes right in our backyard.
04:11:32 You know, what kind of technology could we build with them?
04:11:34 I got a certain distance, not that far,
04:11:36 but I think in, you know, so there are ideas, you know,
04:11:40 I have this, one of the weirder ideas is things
04:11:42 I’m calling space tunnels,
04:11:44 which are higher dimensional pieces of space time,
04:11:47 where basically you can, you know,
04:11:50 in our three dimensional space,
04:11:51 there might be a five dimensional, you know,
04:11:54 region, which actually will appear as a white hole
04:11:57 at one end and a black hole at the other end,
04:11:59 you know, who knows whether they exist.
04:12:01 And then the questions, another one,
04:12:02 okay, this is another crazy one,
04:12:04 is the thing that I’m calling a vacuum cleaner, okay?
04:12:07 So, I mentioned that, you know,
04:12:10 there’s all this activity in the universe,
04:12:12 which is maintaining the structure of space.
04:12:14 And that leads to a certain energy density
04:12:18 effectively in space.
04:12:20 And so the question, in fact, dark energy
04:12:23 is a story of essentially negative mass
04:12:26 produced by the absence of energy
04:12:30 you thought would be there, so to speak.
04:12:33 And we don’t know exactly how it works
04:12:34 in either our model or the physical universe,
04:12:37 but this notion of a vacuum cleaner is a thing where,
04:12:41 you know, you have all these things
04:12:43 that are maintaining the structure of space,
04:12:44 but what if you could clean out some of that stuff
04:12:47 that’s maintaining the structure of space
04:12:49 and make a simpler vacuum somewhere?
04:12:51 You know, what would that do?
04:12:52 A totally different kind of vacuum.
04:12:54 Right, and that would lead to negative energy density,
04:12:57 which would need to, so gravity is usually
04:12:59 a purely attractive force, but negative mass
04:13:02 would lead to repulsive gravity
04:13:06 and lead to all kinds of weird things.
04:13:08 Now, can it be done in our universe?
04:13:11 You know, my immediate thought is no,
04:13:14 but you know, the fact is that, okay, so here’s the thing.
04:13:18 Well, once you understand the fact,
04:13:19 because you’re saying like, at this level of abstraction,
04:13:21 can we reach to the lower levels and mess with it?
04:13:25 Yes.
04:13:26 Once you understand the levels, I think you can start to.
04:13:27 I know, and I’m, you know, I have to say
04:13:30 that this reminds me of people telling one years ago
04:13:34 that, you know, you’ll never transmit data
04:13:36 over a copper wire at more than 1,000,
04:13:38 you know, 1,000 board or something, right?
04:13:41 And this is, why did that not happen?
04:13:43 You know, why do we have this much,
04:13:45 much faster data transmission?
04:13:46 Because we’ve understood many more of the details
04:13:48 of what’s actually going on.
04:13:50 And it’s the same exact story here.
04:13:52 And it’s the same, you know, I think that this,
04:13:54 as I say, I think one of the features of sort of,
04:13:58 one of the things about our time
04:14:00 that will seem incredibly naive in the future
04:14:03 is the belief that, you know, things like heat
04:14:06 is just random motion of molecules,
04:14:08 that it’s just throw up your hands, it’s just random.
04:14:12 We can’t say anything about it.
04:14:14 That will seem naive.
04:14:15 Yeah, at the heat death of the universe,
04:14:18 those particles would be laughing at us humans thinking.
04:14:20 Yes, right.
04:14:22 That life is not beautiful.
04:14:23 I’ll have a whole civilization, you know.
04:14:25 Humans used to think they’re special
04:14:27 with their little brains.
04:14:28 Well, right, but also, and they used to think
04:14:31 that this would just be random and uninteresting.
04:14:33 But that’s, but so this question about whether you can,
04:14:37 you know, mess with the underlying structure
04:14:39 and how you find a way to mess with the underlying structure,
04:14:42 that’s a, you know, I have to say, you know,
04:14:45 my immediate thing is, boy, that seems really hard,
04:14:48 but then, and you know,
04:14:50 possibly computational irreducibility will bite you,
04:14:54 but then there’s always some path
04:14:55 of computational reducibility.
04:14:57 And that path of computational reducibility
04:14:59 is the engineering invention that has to be made.
04:15:02 Those little pockets can have huge engineering impact.
04:15:05 Right, and I think that that’s right.
04:15:07 And I mean, we live in, you know, we make use of so many
04:15:10 of those pockets.
04:15:11 And the fact is, you know, I, you know, this is, yes,
04:15:16 it’s a, you know, it’s one of these things where,
04:15:20 where, you know, I’m a person who likes to figure out ideas
04:15:24 and so on, and the sort of tests of my level of imagination,
04:15:28 so to speak.
04:15:29 And so a couple of places where there’s sort of serious
04:15:32 humility in terms of my level of imagination,
04:15:35 one is this thing about different reference frames
04:15:38 for understanding the universe,
04:15:39 where like, imagine the physics of the aliens,
04:15:42 what will it be like?
04:15:43 And I’m like, that’s really hard.
04:15:45 I don’t know, you know?
04:15:47 And I mean, I think that…
04:15:48 But once you have the framework in place,
04:15:49 you can at least reason about the things you don’t know,
04:15:53 maybe can’t know, or like, it’s too hard for you to know,
04:15:57 but then the mathematics can, that’s exactly it,
04:16:01 allow you to reach beyond where you can reason about.
04:16:05 So I’m, you know, I’m trying to not have, you know,
04:16:09 if you think back to Alan Turing, for example,
04:16:11 and, you know, when he invented Turing machines, you know,
04:16:14 and imagining what computers would end up doing,
04:16:16 so to speak.
04:16:17 Yeah.
04:16:18 You know, and it’s…
04:16:19 It’s very difficult.
04:16:20 It’s difficult, right.
04:16:21 And it’s, and I mean, this thing…
04:16:22 Made a few reasonable predictions,
04:16:23 but most of it, he couldn’t predict, possibly.
04:16:25 By the time, by 1950, he was making reasonable predictions
04:16:28 about some things.
04:16:29 But not the 30s, yeah.
04:16:30 Right, not when he first, you know, conceptualized,
04:16:34 you know, and he conceptualized universal computing
04:16:37 for a very specific mathematical reason
04:16:39 that wasn’t as general.
04:16:41 But yes, it’s a good sort of exercise in humility
04:16:44 to realize that it’s kind of like,
04:16:46 it’s really hard to figure these things out.
04:16:49 The engineering of the universe,
04:16:52 if we know how the universe works, how can we engineer it?
04:16:55 That’s such a beautiful vision.
04:16:57 That’s such a beautiful vision.
04:16:58 By the way, I have to mention one more thing,
04:16:59 which is the ultimate question from physics is,
04:17:04 okay, so we have this abstract model of the universe.
04:17:07 Why does the universe exist at all, right?
04:17:11 So, you know, we might say there is a formal model
04:17:15 that if you run this model, you get the universe,
04:17:18 or the model gives you, you know, a model of the universe,
04:17:21 right, you run this mathematical thing
04:17:25 and the mathematics unfolds in the way
04:17:27 that corresponds to the universe.
04:17:29 But the question is, why was that actualized?
04:17:32 Why does the actual universe actually exist?
04:17:35 And so this is another one of these humility
04:17:39 and it’s like, can you figure this out?
04:17:41 I have a guess, okay, about the answer to that.
04:17:44 And my guess is somewhat unsatisfying,
04:17:47 but my guess is that it’s a little bit similar
04:17:50 to Gödel’s second incompleteness theorem,
04:17:52 which is the statement that from within,
04:17:55 as an axiomatic theory like piano arithmetic,
04:17:58 you cannot from within that theory
04:17:59 prove the consistency of the theory.
04:18:02 So my guess is that for entities within the universe,
04:18:08 there is no finite determination that can be made
04:18:11 of the statement the universe exists
04:18:15 is essentially undecidable to any entity
04:18:18 that is embedded in the universe.
04:18:19 Within that universe, how does that make you feel?
04:18:22 Does that put you at peace that it’s impossible,
04:18:27 or is it really ultimately frustrating?
04:18:30 Well, I think it just says that it’s not a kind of question
04:18:35 that, you know, there are things that it is reasonable.
04:18:40 I mean, there’s kinds of, you know,
04:18:42 you can talk about hyper computation as well.
04:18:44 You can say, imagine there was a hyper computer,
04:18:46 here’s what it would do.
04:18:47 So okay, great, it would be lovely to have a hyper computer,
04:18:49 but unfortunately we can’t make it in the universe.
04:18:52 Like it would be lovely to answer this,
04:18:53 but unfortunately we can’t do it in the universe.
04:18:56 And you know, this is all we have, so to speak.
04:18:59 And I think it’s really just a statement.
04:19:02 It’s sort of, in the end, it’ll be a kind of a logical,
04:19:06 logically inevitable statement, I think.
04:19:08 I think it will be something where it is,
04:19:10 as you understand what it means to have,
04:19:13 what it means to have a sort of predicate of existence
04:19:16 and what it means to have these kinds of things,
04:19:17 it will sort of be inevitable that this has to be the case,
04:19:20 that from within that universe, you can’t establish
04:19:23 the reason for its existence, so to speak.
04:19:25 You can’t prove that it exists and so on.
04:19:26 And nevertheless, because of computational reducibility,
04:19:29 the future is ultimately not predictable, full of mystery,
04:19:34 and that’s what makes life worth living.
04:19:36 Right, I mean, right.
04:19:37 And you know, it’s funny for me,
04:19:39 because as a pure sort of human being doing what I do,
04:19:43 it’s, you know, like I’m interested in people,
04:19:46 I like sort of the whole human experience, so to speak.
04:19:51 And yet, it’s a little bit weird when I’m thinking,
04:19:53 you know, it’s all hypergraphs down there,
04:19:56 and it’s all just.
04:19:57 Hypergraphs all the way down.
04:19:59 Right.
04:20:00 It’s like turtles all the way down.
04:20:01 Yeah, yeah, right.
04:20:02 And it’s kind of, you know, to me, it is a funny thing,
04:20:06 because every so often I get this, you know,
04:20:08 as I’m thinking about, I think we’ve really gotten,
04:20:10 you know, we’ve really figured out kind of the essence
04:20:12 of how physics works, and I’m like thinking to myself,
04:20:14 you know, here’s this physical thing,
04:20:16 and I’m like, you know,
04:20:17 this feels like a very definite thing.
04:20:19 How can it be the case that this is just
04:20:21 some rule or reference frame of, you know,
04:20:23 this infinite creature that is so abstract and so on?
04:20:28 And I kind of, it is a, it’s a funny sort of feeling
04:20:32 that, you know, we are, we’re sort of, it’s like,
04:20:37 in the end, it’s just sort of,
04:20:39 we’re just happy we’re just humans type thing.
04:20:42 And it’s kind of like, but we’re making,
04:20:44 we make things as, it’s not like we’re just a tiny speck.
04:20:50 We are, in a sense, the, we are more important
04:20:54 by virtue of the fact that, in a sense,
04:20:58 it’s not like there’s, there is no ultimate, you know,
04:21:02 it’s like, we’re important because,
04:21:06 because, you know, we’re here, so to speak,
04:21:08 and we’re not, it’s not like there’s a thing
04:21:10 where we’re saying, you know, we are just but one
04:21:15 sort of intelligence out of all these other intelligences.
04:21:18 And so, you know, ultimately there’ll be
04:21:20 the super intelligence, which is all of these put together
04:21:23 and they’ll be very different from us.
04:21:25 No, it’s actually going to be equivalent to us.
04:21:27 And the thing that makes us a sort of special
04:21:31 is just the details of us, so to speak.
04:21:34 It’s not something where we can say,
04:21:36 oh, there’s this other thing, you know,
04:21:38 just, you think humans are cool,
04:21:40 just wait until you’ve seen this.
04:21:43 You know, it’s going to be much more impressive.
04:21:45 Well, no, it’s all going to be
04:21:47 kind of computationally equivalent.
04:21:48 And the thing that, you know, it’s not going to be,
04:21:51 oh, this thing is amazingly much more impressive
04:21:53 and amazingly much more meaningful, let’s say.
04:21:56 No, we’re it.
04:21:58 I mean, that’s the…
04:22:01 And the symbolism of this particular moment.
04:22:04 So this has been one of the,
04:22:07 one of the favorite conversations I’ve ever had, Stephen.
04:22:10 It’s a huge honor to talk to you,
04:22:12 to talk about a topic like this for four plus hours
04:22:16 on the fundamental theory of physics.
04:22:18 And yet we’re just two finite descendants of apes
04:22:22 that have to end this conversation
04:22:24 because darkness have come upon us.
04:22:28 Right, and we’re going to get bitten by mosquitoes
04:22:29 and all kinds of terrible things.
04:22:30 The symbolism of that,
04:22:32 we’re talking about the most basic fabric of reality
04:22:36 and having to end because of the fact that things end.
04:22:40 It’s tragic and beautiful, Stephen.
04:22:42 Thank you so much.
04:22:43 Huge honor.
04:22:44 I can’t wait to see what you do in the next couple of days
04:22:47 and next week, a month.
04:22:48 We’re all watching with excitement.
04:22:50 Thank you so much.
04:22:51 Thanks.
04:22:53 Thanks for listening to this conversation
04:22:54 with Stephen Wolfram.
04:22:55 And thank you to our sponsors,
04:22:57 SimplySafe, Sun Basket, and Masterclass.
04:23:00 Please check out our sponsors in the description
04:23:03 to get a discount and to support this podcast.
04:23:06 If you enjoy this thing, subscribe on YouTube,
04:23:08 review it with five stars on Apple Podcasts,
04:23:10 follow on Spotify, support on Patreon,
04:23:12 or connect with me on Twitter at Lex Friedman.
04:23:16 And now let me leave you with some words
04:23:19 from Richard Feynman.
04:23:21 Physics isn’t the most important thing, love is.
04:23:25 Thank you for listening and hope to see you next time.