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Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe | Lex Fridman Podcast #124


small model | large model

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The following is a conversation with Stephen Wolfram,
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his second time on the podcast.
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He's a computer scientist, mathematician,
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theoretical physicist, and the founder and CEO
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of Wolfram Research, a company behind Mathematica,
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Wolfram Alpha, Wolfram Language,
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and the new Wolfram Physics Project.
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He's the author of several books,
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including A New Kind of Science, and the new book,
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A Project to Find the Fundamental Theory of Physics.
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This second round of our conversation is primarily focused
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on this latter endeavor of searching for the physics
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of our universe in simple rules that do their work
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on hypergraphs and eventually generate the infrastructure
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from which space, time, and all of modern physics can emerge.
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Quick summary of the sponsors,
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SimpliSafe, Sunbasket, and Masterclass.
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Please check out these sponsors in the description
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to get a discount and to support this podcast.
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As a side note, let me say that to me,
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the idea that seemingly infinite complexity can arise
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from very simple rules and initial conditions
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is one of the most beautiful and important
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mathematical and philosophical mysteries in science.
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I find that both cellular automata
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and the hypergraph data structure
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that Stephen and team are currently working on
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to be the kind of simple, clear mathematical playground
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within which fundamental ideas about intelligence,
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consciousness, and the fundamental laws of physics
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can be further developed in totally new ways.
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In fact, I think I'll try to make a video or two
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about the most beautiful aspects of these models
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in the coming weeks, especially, I think,
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trying to describe how fellow curious minds like myself
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can jump in and explore them either just for fun
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or potentially for publication of new innovative research
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in math, computer science, and physics.
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But honestly, I think the emerging complexity
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in these hypergraphs can capture the imagination
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of everyone, even if you're someone
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who never really connected with mathematics.
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That's my hope, at least, to have these conversations
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that inspire everyone to look up to the skies
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and into our own minds in awe of our amazing universe.
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Let me also mention that this is the first time
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I ever recorded a podcast outdoors
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as a kind of experiment to see if this is an option
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in times of COVID.
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I'm sorry if the audio is not great.
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I did my best and promise to keep improving
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and learning as always.
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If you enjoy this thing, subscribe on YouTube,
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review it with Five Stars and Apple Podcast,
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follow on Spotify, support on Patreon,
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or connect with me on Twitter at Lex Friedman.
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As usual, I'll do a few minutes of ads now
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and no ads in the middle.
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I tried to make these interesting,
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but I do give you timestamps, so you're welcome to skip,
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but still, please do check out the sponsors
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It's the best way to support this podcast.
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Also, let me say, even though I'm talking way too much,
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that I did a survey and it seems like over 90% of people
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either enjoy these ad reads somehow magically
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or don't mind them, at least.
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That honestly just warms my heart
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that people are that supportive.
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This show is sponsored by SimpliSafe,
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Go to SimpliSafe.com to get a free HD camera.
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I have it set up in my apartment.
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Of course, I also welcome intruders.
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One of my favorite movies is Leon or The Professional
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with Jean Reno, Gary Oldman,
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and the brilliant young Natalie Portman.
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If you haven't seen the movie,
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he's a hit man with a minimalist life that resembles my own.
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In fact, when I was younger, the idea of being a hit man
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or targeting evil in a skilled way,
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which is how I thought about it, really appealed to me.
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The skill of it, the planning, the craftsmanship.
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00:04:03.720
In another life, perhaps,
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if I didn't love engineering and science so much,
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I could see myself being something like a Navy SEAL.
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And in general, I love the idea of serving my country,
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of serving society by contributing my skill
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in some small way.
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Anyway, go to Simplisafe.com slash Lex
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They're a new sponsor, and this is a trial run,
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This show is also sponsored by Sun Basket,
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Visit SunBasket.com slash Lex
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and use code LEX to get $30 off your order
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This is the last read of the trial they're doing,
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so this is the time to get them if you're considering it.
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And if you do, it'll help ensure
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a nice break from the minimalist meals of meat
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and vegetables that I usually eat.
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Maybe on a personal note,
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one of my favorite things to do is watch people cook,
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00:05:03.720
especially people who love cooking,
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and hang out with people over amazing meals.
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I still tend to be strict in my diet no matter what,
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even in fancy restaurants,
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but it brings me joy to see friends and family indulge
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something like a cake that has way too many calories
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or ice cream or whatever.
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My mom, in fact, for much of my life,
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made this cake called an anthill on my birthday
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that brings me a lot of joy and way too many calories.
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I was thinking of doing a video with my mom as she makes it.
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I thought it'd be a fun thing to do together.
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Anyway, go to SunBasket.com slash Lex and use code LEX.
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Do it now.
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So they signed a longterm contract for this podcast.
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I'm thinking of doing a few solo podcast episodes
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on difficult topics, especially in history,
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like the rise and fall of the Third Reich or Stalin, Putin,
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and many other difficult topics that I'm fascinated by.
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I have a worldview that seeks inspiring positive insights,
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even and perhaps especially from periods of tragedy and evil
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that perhaps some folks may find value in.
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If I can only learn to convey the ideas in my mind
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as clearly as I think them.
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I think deeply and rigorously and precisely,
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but to be honest, have trouble speaking in a way
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that reflects that rigor of thought.
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So it really does mean a lot, the love and support I get
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as I try to get better at this thing,
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at this talking thing.
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Anyway, go to masterclass.com slash LEX to get a discount
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And now finally, here's my conversation with Stephen Wolfram.
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You said that there are moments in history of physics
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and maybe mathematical physics or even mathematics
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where breakthroughs happen
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and then a flurry of progress follows.
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So if you look back through the history of physics,
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what moments stand out to you as important such breakthroughs
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where a flurry of progress follows?
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So the big famous one was 1920s,
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the invention of quantum mechanics,
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where in about five or 10 years,
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lots of stuff got figured out.
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That's now quantum mechanics.
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Can you mention the people involved?
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Yeah, it was kind of the Schrodinger, Heisenberg,
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Einstein had been a key figure, originally Planck,
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then Dirac was a little bit later.
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That was something that happened at that time,
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that's sort of before my time, right?
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In my time was in the 1970s,
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there was this sort of realization
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that quantum field theory was actually going to be useful
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in physics and QCD, quantum thermodynamics theory
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of quarks and gluons and so on was really getting started.
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And there was again, sort of big flurry of things
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happened then, I happened to be a teenager at that time
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and happened to be really involved in physics.
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And so I got to be part of that, which was really cool.
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Who were the key figures
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aside from your young selves at that time?
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You know, who won the Nobel Prize for QCD, okay?
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People, David Gross, Frank Wilczek, you know, David Politzer.
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The people who are the sort of the slightly older generation,
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Dick Feynman, Murray Gellman, people like that,
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who were Steve Weinberg, Gerhard Hoft, he's younger,
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he's in the younger group actually.
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But these are all, you know, characters who were involved.
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I mean, it's funny because those are all people
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who are kind of in my time and I know them
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and they don't seem like sort of historical,
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you know, iconic figures.
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They seem more like everyday characters, so to speak.
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And so it's always, you know, when you look at history
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from long afterwards, it always seems like
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everything happened instantly.
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And that's usually not the case.
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There was usually a long buildup,
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but usually there's, you know,
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there's some methodological thing happens
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and then there's a whole bunch of low hanging fruit
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to be picked.
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And that usually lasts five or 10 years.
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You know, we see it today with machine learning
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and, you know, deep learning neural nets and so on.
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You know, methodological advance,
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things actually started working in, you know, 2011, 2012
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and so on.
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And, you know, there's been this sort of rapid
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picking of low hanging fruit, which is probably, you know,
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some significant fraction of the way done, so to speak.
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Do you think there's a key moment?
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Like if I had to really introspect,
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like what was the key moment
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for the deep learning, quote unquote, revolution?
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I mean.
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It's probably the AlexNet business.
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AlexNet with ImageNet.
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So is there something like that with physics
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where, so deep learning neural networks
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have been around for a long time.
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Absolutely, since the 1940s, yeah.
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There's a bunch of little pieces that came together
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and then all of a sudden everybody's eyes lit up.
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Like, wow, there's something here.
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Like even just looking at your own work,
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just your thinking about the universe,
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that there's simple rules can create complexity.
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You know, at which point was there a thing
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where your eyes light up?
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It's like, wait a minute, there's something here.
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Is it the very first idea
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or is it some moment along the line of implementations
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and experiments and so on?
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There's a couple of different stages to this.
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I mean, one is the think about the world computationally.
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Can we use programs instead of equations
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to make models of the world?
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That's something that I got interested in
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in the beginning of the 1980s.
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I did a bunch of computer experiments.
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When I first did them, I didn't really,
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I could see some significance to them,
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but it took me a few years to really say,
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wow, there's a big important phenomenon here
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that lets sort of complex things arise
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from very simple programs.
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That kind of happened back in 1984 or so.
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Then, you know, a bunch of other years go by,
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then I start actually doing a lot
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of much more systematic computer experiments and things
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and find out that the, you know,
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this phenomenon that I could only have said occurs
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in one particular case
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is actually something incredibly general.
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And then that led me to this thing called
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principle of computational equivalence.
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And that was a long story.
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And then, you know, as part of that process,
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I was like, okay, you can make simple programs,
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can make models of complicated things.
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What about the whole universe?
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That's our sort of ultimate example of a complicated thing.
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And so I got to thinking, you know,
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could we use these ideas to study fundamental physics?
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You know, I happen to know a lot about,
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you know, traditional fundamental physics.
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My first, you know, I had a bunch of ideas
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about how to do this in the early 1990s.
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I made a bunch of technical progress.
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I figured out a bunch of things
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I thought were pretty interesting.
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You know, I wrote about them back in 2002.
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With the new kind of science
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in the cellular automata world.
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And there's echoes in the cellular automata world
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with your new Wolfram physics project.
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We'll get to all that.
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Allow me to sort of romanticize a little more
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on the philosophy of science.
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So Thomas Kuhn, philosopher of science,
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describes that, you know, the progress in science
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is made with these paradigm shifts.
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And so to link on the sort of original line of discussion,
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do you agree with this view
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that there is revolutions in science
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that just kind of flip the table?
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What happens is it's a different way
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of thinking about things.
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It's a different methodology for studying things.
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And that opens stuff up.
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There's this idea of,
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he's a famous biographer,
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but I think it's called the innovators.
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There's a biographer of Steve Jobs, of Albert Einstein.
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He also wrote a book,
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I think it's called the innovators,
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where he discusses how a lot of the innovations
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in the history of computing has been done by groups.
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There's a complicated group dynamic going on,
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but there's also a romanticized notion
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that the individual is at the core of the revolution.
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Like where does your sense fall?
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Is ultimately like one person responsible
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for these revolutions that creates the spark
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or one or two, whatever,
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or is it just the big mush and mess and chaos
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of people interacting, of personalities interacting?
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I think it ends up being like many things,
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there's leadership and there ends up being,
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it's a lot easier for one person to have a crisp new idea
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than it is for a big committee to have a crisp new idea.
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And I think, but I think it can happen
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that you have a great idea,
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but the world isn't ready for it.
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And you can, I mean, this has happened to me plenty, right?
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It's, you have an idea, it's actually a pretty good idea,
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but things aren't ready,
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either you're not really ready for it,
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or the ambient world isn't ready for it.
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And it's hard to get the thing to get traction.
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It's kind of interesting.
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I mean, when I look at a new kind of science,
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you're now living inside the history,
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so you can't tell the story of these decades,
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but it seems like the new kind of science
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has not had the revolutionary impact
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I would think it might.
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Like, it feels like at some point, of course it might be,
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but it feels at some point people will return to that book
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and say, that was something special here.
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This was incredible.
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What happened?
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Or do you think that's already happened?
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Oh, yeah, it's happened, except that people aren't,
link |
00:15:16.400
the sort of the heroism of it may not be there,
link |
00:15:19.480
but what's happened is for 300 years,
link |
00:15:22.760
people basically said,
link |
00:15:24.520
if you want to make a model of things in the world,
link |
00:15:27.040
mathematical equations are the best place to go.
link |
00:15:29.760
Last 15 years, doesn't happen.
link |
00:15:32.480
New models that get made of things
link |
00:15:34.600
most often are made with programs, not with equations.
link |
00:15:38.600
Now, was that sort of going to happen anyway?
link |
00:15:42.320
Was that a consequence of my particular work
link |
00:15:45.600
and my particular book?
link |
00:15:47.240
It's hard to know for sure.
link |
00:15:48.800
I mean, I am always amazed at the amounts of feedback
link |
00:15:51.560
that I get from people where they say,
link |
00:15:52.960
oh, by the way, I started doing this whole line of research
link |
00:15:56.080
because I read your book, blah, blah, blah, blah, blah.
link |
00:15:58.520
It's like, well, can you tell that
link |
00:15:59.920
from the academic literature?
link |
00:16:01.880
Was there a chain of academic references?
link |
00:16:04.520
Probably not.
link |
00:16:05.800
One of the interesting side effects of publishing
link |
00:16:09.040
in the way you did this tome
link |
00:16:11.920
is it serves as an education tool and an inspiration
link |
00:16:15.320
to hundreds of thousands, millions of people,
link |
00:16:19.200
but because it's not a single,
link |
00:16:21.680
it's not a chain of papers with spiffy titles,
link |
00:16:25.200
it doesn't create a splash of citations.
link |
00:16:29.320
It's had plenty of citations, but it's, you know,
link |
00:16:31.440
I think that people think of it as probably more,
link |
00:16:36.440
you know, conceptual inspiration than kind of a,
link |
00:16:41.640
you know, this is a line from here to here to here
link |
00:16:43.880
in our particular field.
link |
00:16:45.440
I think that the thing which I am disappointed by
link |
00:16:49.520
and which will eventually happen
link |
00:16:51.440
is this kind of study of the sort of pure computationalism,
link |
00:16:55.840
this kind of study of the abstract behavior
link |
00:16:58.600
of the computational universe.
link |
00:17:00.520
That should be a big thing that lots of people do.
link |
00:17:03.960
You mean in mathematics purely, almost like.
link |
00:17:06.320
It's like pure mathematics, but it isn't mathematics.
link |
00:17:08.840
But it isn't, it isn't.
link |
00:17:10.440
It's a new kind of mathematics.
link |
00:17:12.320
Is it a new title of the book?
link |
00:17:14.360
Yeah, right.
link |
00:17:15.200
That's why the book is called that.
link |
00:17:17.040
Right, that's not coincidental.
link |
00:17:19.160
Yeah.
link |
00:17:20.160
It's interesting that I haven't seen
link |
00:17:22.840
really rigorous investigation
link |
00:17:24.960
by thousands of people of this idea.
link |
00:17:26.880
I mean, you look at your competition around rule 30.
link |
00:17:30.080
I mean, that's fascinating.
link |
00:17:31.320
If you can say something.
link |
00:17:34.320
Right.
link |
00:17:35.160
Is there some aspect of this thing that could be predicted?
link |
00:17:38.800
That's the fundamental question of science.
link |
00:17:40.960
That's the core.
link |
00:17:41.800
Well, that has been a question of science.
link |
00:17:42.880
I think that is some people's view of what science is about
link |
00:17:47.440
and it's not clear that's the right view.
link |
00:17:48.960
In fact, as we live through this pandemic
link |
00:17:51.520
full of predictions and so on,
link |
00:17:53.320
it's an interesting moment to be pondering
link |
00:17:55.360
what science's actual role in those kinds of things is.
link |
00:17:58.440
Or you think it's possible that in science,
link |
00:18:02.080
clean, beautiful, simple prediction
link |
00:18:04.920
may not even be possible in real systems.
link |
00:18:07.240
That's the open question.
link |
00:18:08.800
I don't think it's open.
link |
00:18:09.640
I think that question is answered and the answer is no.
link |
00:18:12.240
Well, no, no.
link |
00:18:13.120
The answer could be just humans are not smart enough yet.
link |
00:18:16.680
Like we don't have the tools yet.
link |
00:18:17.520
No, that's the whole point.
link |
00:18:18.680
I mean, that's sort of the big discovery
link |
00:18:20.680
of this principle of computational equivalence of mine.
link |
00:18:23.320
And this is something which is kind of a follow on
link |
00:18:26.880
to Gödel's theorem, to Turing's work
link |
00:18:28.920
on the halting problem, all these kinds of things.
link |
00:18:31.680
That there is this fundamental limitation
link |
00:18:34.720
built into science,
link |
00:18:36.360
this idea of computational irreducibility
link |
00:18:39.120
that says that even though you may know the rules
link |
00:18:42.480
by which something operates,
link |
00:18:44.160
that does not mean that you can readily sort of
link |
00:18:47.600
be smarter than it and jump ahead
link |
00:18:49.760
and figure out what it's going to do.
link |
00:18:51.640
Yes, but do you think there's a hope
link |
00:18:53.800
for pockets of computational reducibility?
link |
00:18:56.960
Computational reducibility.
link |
00:19:02.480
And then a set of tools and mathematics
link |
00:19:04.840
that help you discover such pockets.
link |
00:19:07.040
That's where we live is in the pockets of reducibility.
link |
00:19:10.160
That's why, and this is one of the things
link |
00:19:12.560
that sort of come out of this physics project
link |
00:19:14.080
and actually something that, again,
link |
00:19:15.480
I should have realized many years ago, but didn't,
link |
00:19:18.680
is it could very well be that everything about the world
link |
00:19:23.440
is computationally reducible and completely unpredictable.
link |
00:19:26.560
But in our experience of the world,
link |
00:19:29.720
there is at least some amount of prediction we can make.
link |
00:19:32.520
And that's because we have sort of chosen a slice of,
link |
00:19:36.560
probably talk about this in much more detail,
link |
00:19:38.320
but I mean, we've kind of chosen a slice
link |
00:19:39.920
of how to think about the universe
link |
00:19:41.760
in which we can kind of sample
link |
00:19:43.960
a certain amount of computational reducibility.
link |
00:19:46.640
And that's sort of where we exist.
link |
00:19:51.640
And it may not be the whole story of how the universe is,
link |
00:19:55.920
but it is the part of the universe that we care about
link |
00:19:59.240
and we sort of operate in.
link |
00:20:01.000
And that's, you know, in science,
link |
00:20:03.600
that's been sort of a very special case of that.
link |
00:20:05.720
That is science has chosen to talk a lot about places
link |
00:20:09.360
where there is this computational reducibility
link |
00:20:12.120
that it can find, you know,
link |
00:20:13.640
the motion of the planets can be more or less predicted.
link |
00:20:16.400
You know, something about the weather
link |
00:20:19.080
is much harder to predict.
link |
00:20:20.640
Something about, you know, other kinds of things
link |
00:20:22.760
that are much harder to predict.
link |
00:20:25.160
And it's, these are, but science has tended to,
link |
00:20:29.160
you know, concentrate itself on places
link |
00:20:31.040
where its methods have allowed successful prediction.
link |
00:20:35.080
So you think rule 30, if we could linger on it,
link |
00:20:39.160
because it's just such a beautiful, simple formulation
link |
00:20:41.600
of the essential concept underlying
link |
00:20:43.520
all the things we're talking about.
link |
00:20:45.000
Do you think there's pockets of reducibility
link |
00:20:47.240
inside rule 30?
link |
00:20:48.480
Yes, that is the question of how big are they?
link |
00:20:51.600
What will they allow you to say?
link |
00:20:53.120
And so on.
link |
00:20:53.960
And that's, and figuring out where those pockets are,
link |
00:20:56.960
I mean, in a sense, that's the, that's sort of a,
link |
00:21:00.480
you know, that is an essential thing
link |
00:21:02.640
that one would like to do in science.
link |
00:21:05.760
But it's also, the important thing to realize
link |
00:21:08.800
that has not been, you know, is that science,
link |
00:21:13.760
if you just pick an arbitrary thing,
link |
00:21:15.400
you say, what's the answer to this question?
link |
00:21:18.120
That question may not be one
link |
00:21:20.200
that has a computationally reducible answer.
link |
00:21:22.880
That question, if you choose, you know,
link |
00:21:26.360
if you walk along the series of questions
link |
00:21:28.880
and you've got one that's reducible
link |
00:21:30.280
and you get to another one that's nearby
link |
00:21:31.680
and it's reducible too,
link |
00:21:33.000
if you stick to that kind of stick to the land,
link |
00:21:36.080
so to speak, then you can go down this chain
link |
00:21:39.640
of sort of reducible, answerable things.
link |
00:21:41.960
But if you just say, I'm just pick a question at random,
link |
00:21:44.440
I'm gonna have my computer pick a question at random.
link |
00:21:47.400
Most likely it's gonna be reducible.
link |
00:21:49.280
Most likely it will be reducible.
link |
00:21:50.960
And what we're thrown in the world, so to speak,
link |
00:21:54.720
we, you know, when we engineer things,
link |
00:21:56.440
we tend to engineer things to sort of keep
link |
00:21:58.320
in the zone of reducibility.
link |
00:22:00.280
When we're throwing things by the natural world,
link |
00:22:02.280
for example, not at all certain
link |
00:22:05.520
that we will be kept in this kind of zone of reducibility.
link |
00:22:08.680
Can we talk about this pandemic then?
link |
00:22:11.240
Sure.
link |
00:22:12.080
For a second, is a, so how do we,
link |
00:22:16.000
there's obviously huge amount of economic pain
link |
00:22:18.920
that people are feeling.
link |
00:22:19.800
There's a huge incentive and medical pain,
link |
00:22:23.960
health, just all kind of psychological.
link |
00:22:26.760
There's a huge incentive to figure this out,
link |
00:22:28.760
to walk along the trajectory of reducible, of reducibility.
link |
00:22:34.440
There's a lot of disparate data.
link |
00:22:38.040
You know, people understand generally how viruses spread,
link |
00:22:40.520
but it's very complicated
link |
00:22:43.240
because there's a lot of uncertainty.
link |
00:22:45.320
There's a, there could be a lot of variability also,
link |
00:22:49.320
like so many, obviously a nearly infinite number
link |
00:22:52.920
of variables that represent human interaction.
link |
00:22:57.920
And so you have to figure out,
link |
00:22:59.920
from the perspective of reducibility,
link |
00:23:02.680
figure out which variables are really important
link |
00:23:06.600
in this kind of, from an epidemiological perspective.
link |
00:23:10.600
So why aren't we, you kind of said
link |
00:23:13.800
that we're clearly failing.
link |
00:23:15.960
Well, I think it's a complicated thing.
link |
00:23:17.320
So, I mean, you know, when this pandemic started up,
link |
00:23:20.200
you know, I happened to be in the middle
link |
00:23:21.800
of being about to release this whole physics project thing,
link |
00:23:24.800
but I thought, you know.
link |
00:23:25.640
The timing is just cosmically absurd.
link |
00:23:28.280
A little bit bizarre, but you know,
link |
00:23:30.440
but I thought, you know,
link |
00:23:31.360
I should do the public service thing of, you know,
link |
00:23:33.960
trying to understand what I could about the pandemic.
link |
00:23:36.000
And, you know, we'd been curating data about it
link |
00:23:38.160
and all that kind of thing.
link |
00:23:39.280
But, you know, so I started looking at the data
link |
00:23:41.680
and started looking at modeling
link |
00:23:43.600
and I decided it's just really hard.
link |
00:23:46.000
You need to know a lot of stuff that we don't know
link |
00:23:48.240
about human interactions.
link |
00:23:49.840
It's actually clear now that there's a lot of stuff
link |
00:23:51.600
we didn't know about viruses
link |
00:23:53.480
and about the way immunity works and so on.
link |
00:23:56.000
And it's, you know, I think what will come out in the end
link |
00:23:58.840
is there's a certain amount of what happens
link |
00:24:02.000
that we just kind of have to trace each step
link |
00:24:04.320
and see what happens.
link |
00:24:05.800
There's a certain amount of stuff
link |
00:24:06.960
where there's going to be a big narrative
link |
00:24:08.280
about this happened because, you know, of T cell immunity.
link |
00:24:12.240
This could happen because there's this whole giant
link |
00:24:14.320
sort of field of asymptomatic viral stuff out there.
link |
00:24:18.640
You know, there will be a narrative
link |
00:24:20.120
and that narrative, whenever there's a narrative,
link |
00:24:22.400
that's kind of a sign of reducibility.
link |
00:24:24.600
But when you just say,
link |
00:24:26.000
let's from first principles figure out what's going on,
link |
00:24:28.880
then you can potentially be stuck
link |
00:24:30.880
in this kind of a mess of irreducibility
link |
00:24:33.720
where you just have to simulate each step
link |
00:24:35.680
and you can't do that unless you know details about,
link |
00:24:38.240
you know, human interaction networks
link |
00:24:40.120
and so on and so on and so on.
link |
00:24:41.360
The thing that has been very sort of frustrating to see
link |
00:24:46.440
is the mismatch between people's expectations
link |
00:24:48.920
about what science can deliver
link |
00:24:50.760
and what science can actually deliver, so to speak.
link |
00:24:53.680
Because people have this idea that, you know, it's science.
link |
00:24:56.760
So there must be a definite answer
link |
00:24:58.480
and we must be able to know that answer.
link |
00:25:00.520
And, you know, this is, it is both, you know,
link |
00:25:05.040
when you've, after you've played around
link |
00:25:07.600
with sort of little programs in the computational universe,
link |
00:25:10.080
you don't have that intuition anymore.
link |
00:25:11.840
You know, it's, I always, I'm always fond of saying,
link |
00:25:14.520
you know, the computational animals
link |
00:25:17.040
are always smarter than you are.
link |
00:25:18.240
That is, you know, you look at one of these things
link |
00:25:20.240
and it's like, it can't possibly do such and such a thing.
link |
00:25:23.240
Then you run it and it's like, wait a minute,
link |
00:25:25.280
it's doing that thing.
link |
00:25:26.200
How does that work?
link |
00:25:27.520
Okay, now I can go back and understand it.
link |
00:25:29.320
But that's the brave thing about science
link |
00:25:31.520
is that in the chaos of the irreducible universe,
link |
00:25:35.880
we nevertheless persist to find those pockets.
link |
00:25:38.600
That's kind of the whole point.
link |
00:25:40.240
That's like, you say that the limits of science,
link |
00:25:43.000
but that, you know, yes, it's highly limited,
link |
00:25:46.800
but there's a hope there.
link |
00:25:48.800
And like, there's so many questions I want to ask here.
link |
00:25:51.960
So one, you said narrative, which is really interesting.
link |
00:25:54.160
So obviously from a, at every level of society,
link |
00:25:58.040
you look at Twitter, everybody's constructing narratives
link |
00:26:00.400
about the pandemic, about not just the pandemic,
link |
00:26:03.120
but all the cultural tension that we're going through.
link |
00:26:06.000
So there's narratives,
link |
00:26:07.000
but they're not necessarily connected
link |
00:26:10.200
to the underlying reality of these systems.
link |
00:26:17.400
So our human narratives, I don't even know if they're,
link |
00:26:22.440
I don't like those pockets of reducibility
link |
00:26:25.360
because we're, it's like constructing things
link |
00:26:29.480
that are not actually representative of reality,
link |
00:26:33.360
and thereby not giving us like good solutions
link |
00:26:36.360
to how to predict the system.
link |
00:26:39.520
Look, it gets complicated because, you know,
link |
00:26:41.120
people want to say, explain the pandemic to me,
link |
00:26:43.840
explain what's going to happen.
link |
00:26:45.320
In the future.
link |
00:26:46.360
Yes, but also, can you explain it?
link |
00:26:48.200
Is there a story to tell?
link |
00:26:49.520
What already happened in the past?
link |
00:26:51.440
Yeah, or what's going to happen,
link |
00:26:53.040
but I mean, you know, it's similar to sort of
link |
00:26:55.280
explaining things in AI or in any computational system.
link |
00:26:58.560
It's like, you know, explain what happened.
link |
00:27:00.960
Well, it could just be this happened
link |
00:27:03.000
because of this detail and this detail and this detail,
link |
00:27:05.240
and a million details,
link |
00:27:06.880
and there isn't a big story to tell.
link |
00:27:08.600
There's no kind of big arc of the story that says,
link |
00:27:12.000
oh, it's because, you know, there's a viral field
link |
00:27:14.480
that has these properties
link |
00:27:15.640
and people start showing symptoms.
link |
00:27:17.680
You know, when the seasons change,
link |
00:27:20.040
people will show symptoms
link |
00:27:21.000
and people don't even understand, you know,
link |
00:27:22.480
seasonal variation of flu, for example.
link |
00:27:24.640
It's something where, you know,
link |
00:27:28.480
there could be a big story,
link |
00:27:29.920
or it could be just a zillion little details that mount up.
link |
00:27:33.800
See, but, okay, let's pretend that this pandemic,
link |
00:27:38.200
like the coronavirus, resembles something
link |
00:27:41.080
like the 1D rule 30 cellular automata, okay?
link |
00:27:45.840
So, I mean, that's how epidemiologists model virus spread.
link |
00:27:51.880
Indeed, yes.
link |
00:27:52.720
They sometimes use cellular automata, yes.
link |
00:27:54.320
Yeah, and okay, so you could say it's simplistic,
link |
00:27:57.280
but okay, let's say it's representative
link |
00:28:00.520
of actually what happens.
link |
00:28:02.320
You know, the dynamic of,
link |
00:28:06.240
you have a graph,
link |
00:28:07.480
it probably is closer to the hypergraph model.
link |
00:28:09.760
It is, yes.
link |
00:28:10.600
It's actually, that's another funny thing.
link |
00:28:13.280
As we were getting ready to release this physics project,
link |
00:28:15.320
we realized that a bunch of things we'd worked out
link |
00:28:17.200
about foliations of causal graphs and things
link |
00:28:20.680
were directly relevant to thinking about contact tracing.
link |
00:28:23.520
Yeah, exactly.
link |
00:28:24.360
And interactions with cell phones and so on,
link |
00:28:25.920
which is really weird.
link |
00:28:27.200
But like, it just feels like,
link |
00:28:29.680
it feels like we should be able to get
link |
00:28:31.000
some beautiful core insight about the spread
link |
00:28:34.960
of this particular virus
link |
00:28:36.720
on the hypergraph of human civilization, right?
link |
00:28:40.040
I tried, I didn't manage to figure it out.
link |
00:28:42.360
But you're one person.
link |
00:28:43.520
Yeah, but I mean, I think actually it's a funny thing
link |
00:28:46.240
because it turns out the main model,
link |
00:28:48.360
you know, this SIR model,
link |
00:28:49.960
I only realized recently was invented by the grandfather
link |
00:28:53.280
of a good friend of mine from high school.
link |
00:28:55.160
So that was just a, you know, it's a weird thing, right?
link |
00:28:58.800
The question is, you know, okay, so you know,
link |
00:29:02.240
on this graph of how humans are connected,
link |
00:29:04.400
you know something about what happens
link |
00:29:05.880
if this happens and that happens.
link |
00:29:07.520
That graph is made in complicated ways
link |
00:29:09.680
that depends on all sorts of issues
link |
00:29:11.480
that where we don't have the data
link |
00:29:13.120
about how human society works well enough
link |
00:29:15.200
to be able to make that graph.
link |
00:29:17.160
There's actually, one of my kids did a study
link |
00:29:20.480
of sort of what happens on different kinds of graphs
link |
00:29:23.320
and how robust are the results, okay?
link |
00:29:25.720
His basic answer is there are a few general results
link |
00:29:28.760
that you can get that are quite robust.
link |
00:29:30.720
Like, you know, a small number of big gatherings
link |
00:29:33.080
is worse than a large number of small gatherings, okay?
link |
00:29:36.280
That's quite robust.
link |
00:29:37.680
But when you ask more detailed questions,
link |
00:29:40.120
it seemed like it just depends.
link |
00:29:42.960
It depends on details.
link |
00:29:44.200
In other words, it's kind of telling you in that case,
link |
00:29:47.240
you know, the irreducibility matters, so to speak.
link |
00:29:49.760
It's not, there's not gonna be this kind of one
link |
00:29:53.040
sort of master theorem that says,
link |
00:29:55.040
and therefore this is how things are gonna work.
link |
00:29:57.520
Yeah, but there's a certain kind of,
link |
00:29:59.040
from a graph perspective,
link |
00:30:01.480
the certain kind of dynamic to human interaction.
link |
00:30:04.720
So like large groups and small groups,
link |
00:30:08.640
I think it matters who the groups are.
link |
00:30:10.520
For example, you could imagine large,
link |
00:30:12.600
depends how you define large,
link |
00:30:13.720
but you can imagine groups of 30 people,
link |
00:30:17.120
as long as they are cliques or whatever.
link |
00:30:22.440
Right.
link |
00:30:23.280
As long as the outgoing degree of that graph is small
link |
00:30:27.640
or something like that,
link |
00:30:28.480
like you can imagine some beautiful underlying rule
link |
00:30:31.360
of human dynamic interaction where I can still be happy,
link |
00:30:34.640
where I can have a conversation with you
link |
00:30:36.520
and a bunch of other people that mean a lot to me in my life
link |
00:30:39.640
and then stay away from the bigger, I don't know,
link |
00:30:42.560
not going to a Miley Cyrus concert or something like that
link |
00:30:45.600
and figuring out mathematically some nice.
link |
00:30:49.840
See, this is an interesting thing.
link |
00:30:51.080
So I mean, this is the question of what you're describing
link |
00:30:54.760
is kind of the problem of the many situations
link |
00:30:59.320
where you would like to get away
link |
00:31:00.600
from computational irreducibility.
link |
00:31:02.040
A classic one in physics is thermodynamics.
link |
00:31:05.080
The second law of thermodynamics,
link |
00:31:06.840
the law that says entropy tends to increase things
link |
00:31:09.880
that start orderly tend to get more disordered,
link |
00:31:13.240
or which is also the thing that says,
link |
00:31:15.040
given that you have a bunch of heat,
link |
00:31:16.640
it's hard, heat is the microscopic motion of molecules,
link |
00:31:19.800
it's hard to turn that heat into systematic mechanical work.
link |
00:31:23.600
It's hard to just take something being hot
link |
00:31:26.240
and turn that into, oh, all the atoms are gonna line up
link |
00:31:29.840
in the bar of metal and the piece of metal
link |
00:31:31.520
is gonna shoot in some direction.
link |
00:31:33.600
That's essentially the same problem
link |
00:31:35.800
as how do you go from this computationally irreducible
link |
00:31:40.040
mess of things happening
link |
00:31:41.680
and get something you want out of it.
link |
00:31:43.560
It's kind of mining, you're kind of,
link |
00:31:45.760
now, actually I've understood in recent years
link |
00:31:48.320
that the story of thermodynamics
link |
00:31:50.880
is actually precisely a story of computational irreducibility,
link |
00:31:54.400
but it is a, it is already an analogy.
link |
00:31:58.600
You can kind of see that as can you take the,
link |
00:32:02.080
what you're asking to do there
link |
00:32:03.560
is you're asking to go from the kind of,
link |
00:32:07.840
the mess of all these complicated human interactions
link |
00:32:10.080
and all this kind of computational processes going on
link |
00:32:12.360
and you say, I want to achieve
link |
00:32:14.120
this particular thing out of it.
link |
00:32:15.240
I want to kind of extract from the heat of what's happening.
link |
00:32:18.680
I want to kind of extract this useful piece
link |
00:32:22.160
of sort of mechanical work that I find helpful.
link |
00:32:25.240
I mean.
link |
00:32:26.080
Do you have a hope for the pandemic?
link |
00:32:27.320
So we'll talk about physics,
link |
00:32:28.600
but for the pandemic, can that be extracted?
link |
00:32:31.320
Do you think?
link |
00:32:32.160
What's your intuition?
link |
00:32:33.120
The good news is the curves basically,
link |
00:32:36.520
for reasons we don't understand,
link |
00:32:38.480
the curves, the clearly measurable mortality curves
link |
00:32:42.560
and so on for the Northern Hemisphere have gone down.
link |
00:32:46.360
Yeah, but the bad news is that it could be a lot worse
link |
00:32:50.320
for future viruses.
link |
00:32:51.640
And what this pandemic revealed is we're highly unprepared
link |
00:32:55.200
for the discovery of the pockets of reducibility
link |
00:32:59.840
within a pandemic that's much more dangerous.
link |
00:33:02.560
Well, my guess is the specific risk of viral pandemics,
link |
00:33:07.400
you know, that the pure virology
link |
00:33:10.400
and immunology of the thing,
link |
00:33:12.760
this will cause that to advance to the point
link |
00:33:14.720
where this particular risk
link |
00:33:16.640
is probably considerably mitigated.
link |
00:33:19.040
But is the structure of modern society robust
link |
00:33:25.160
to all kinds of risks?
link |
00:33:26.920
Well, the answer is clearly no.
link |
00:33:29.160
And it's surprising to me the extent to which people,
link |
00:33:34.120
as I say, it's kind of scary actually
link |
00:33:37.320
how much people believe in science.
link |
00:33:39.360
That is people say, oh, you know,
link |
00:33:41.560
because the science says this, that and the other,
link |
00:33:43.160
we'll do this and this and this,
link |
00:33:44.320
even though from a sort of common sense point of view,
link |
00:33:46.760
it's a little bit crazy and people are not prepared
link |
00:33:50.440
and it doesn't really work in society
link |
00:33:52.600
as it is for people to say,
link |
00:33:53.600
well, actually we don't really know how the science works.
link |
00:33:56.520
People say, well, tell us what to do.
link |
00:33:58.600
Yeah, because then, yeah, what's the alternative?
link |
00:34:01.600
For the masses, it's difficult to sit,
link |
00:34:04.960
it's difficult to meditate on computational reducibility.
link |
00:34:08.560
It's difficult to sit,
link |
00:34:10.280
it's difficult to enjoy a good dinner meal
link |
00:34:13.120
while knowing that you know nothing about the world.
link |
00:34:15.600
Well, I think this is a place where, you know,
link |
00:34:17.800
this is what politicians and political leaders do
link |
00:34:21.160
for a living, so to speak,
link |
00:34:22.120
is you've got to make some decision about what to do.
link |
00:34:24.880
And it's...
link |
00:34:25.840
Tell some narrative that while amidst the mystery
link |
00:34:29.760
and knowing not much about the past or the future,
link |
00:34:33.760
still telling a narrative that somehow gives people hope
link |
00:34:37.240
that we know what the heck we're doing.
link |
00:34:39.200
Yeah, and get society through the issue.
link |
00:34:41.520
You know, even though, you know,
link |
00:34:43.440
the idea that we're just gonna, you know,
link |
00:34:45.560
sort of be able to get the definitive answer from science
link |
00:34:48.600
and it's gonna tell us exactly what to do.
link |
00:34:50.600
Unfortunately, you know, it's interesting
link |
00:34:54.360
because let me point out that if that was possible,
link |
00:34:56.880
if science could always tell us what to do,
link |
00:34:59.200
then in a sense, our, you know,
link |
00:35:01.920
that would be a big downer for our lives.
link |
00:35:03.960
If science could always tell us
link |
00:35:05.080
what the answer is gonna be,
link |
00:35:06.760
it's like, well, you know,
link |
00:35:08.720
it's kind of fun to live one's life
link |
00:35:10.120
and just sort of see what happens.
link |
00:35:11.720
If one could always just say,
link |
00:35:12.960
let me check my science.
link |
00:35:15.080
Oh, I know, you know,
link |
00:35:16.760
the result of everything is gonna be 42.
link |
00:35:18.320
I don't need to live my life and do what I do.
link |
00:35:21.000
It's just, we already know the answer.
link |
00:35:23.000
It's actually good news in a sense
link |
00:35:24.840
that there is this phenomenon
link |
00:35:25.960
of computational irreducibility
link |
00:35:27.640
that doesn't allow you to just sort of jump through time
link |
00:35:30.760
and say, this is the answer, so to speak.
link |
00:35:33.680
And that's, so that's a good thing.
link |
00:35:35.160
The bad thing is it doesn't allow you to jump through time
link |
00:35:38.120
and know what the answer is.
link |
00:35:39.640
It's scary.
link |
00:35:40.960
Do you think we're gonna be okay as a human civilization?
link |
00:35:44.160
You said, we don't know.
link |
00:35:46.120
Absolutely.
link |
00:35:47.920
Do you think we'll prosper or destroy ourselves?
link |
00:35:53.920
In general?
link |
00:35:54.760
In general.
link |
00:35:55.720
I'm an optimist.
link |
00:35:57.760
No, I think that, you know,
link |
00:35:59.200
it'll be interesting to see, for example,
link |
00:36:01.000
with this, you know, pandemic,
link |
00:36:02.480
I, you know, to me, you know,
link |
00:36:05.720
when you look at like organizations, for example,
link |
00:36:08.320
you know, having some kind of perturbation,
link |
00:36:10.920
some kick to the system,
link |
00:36:12.840
usually the end result of that is actually quite good.
link |
00:36:16.120
You know, unless it kills the system,
link |
00:36:17.720
it's actually quite good usually.
link |
00:36:19.520
And I think in this case, you know, people,
link |
00:36:22.280
I mean, my impression, you know,
link |
00:36:23.840
it's a little weird for me because, you know,
link |
00:36:25.400
I've been a remote tech CEO for 30 years.
link |
00:36:28.000
It doesn't, you know, this is bizarrely, you know,
link |
00:36:30.720
and the fact that, you know, like this coming to see you here
link |
00:36:33.920
is the first time in six months that I've been like,
link |
00:36:39.160
you know, in a building other than my house, okay?
link |
00:36:41.360
So, you know, I'm a kind of ridiculous outlier
link |
00:36:46.160
in these kinds of things.
link |
00:36:47.040
But overall, your sense is when you shake up the system
link |
00:36:50.920
and throw in chaos that you challenge the system,
link |
00:36:55.200
we humans emerge better.
link |
00:36:57.720
Seems to be that way.
link |
00:36:58.800
Who's to know?
link |
00:36:59.640
I think that, you know, people, you know,
link |
00:37:01.920
my sort of vague impression is that people are sort of,
link |
00:37:05.040
you know, oh, what's actually important?
link |
00:37:07.280
You know, what is worth caring about and so on?
link |
00:37:10.400
And that seems to be something that perhaps is more,
link |
00:37:14.280
you know, emergent in this kind of situation.
link |
00:37:16.840
It's so fascinating that on the individual level,
link |
00:37:19.840
we have our own complex cognition.
link |
00:37:22.320
We have consciousness, we have intelligence,
link |
00:37:24.080
we're trying to figure out little puzzles.
link |
00:37:25.960
And then that somehow creates this graph
link |
00:37:28.280
of collective intelligence.
link |
00:37:30.280
Well, we figure out, and then you throw in these viruses
link |
00:37:33.920
of which there's millions different, you know,
link |
00:37:36.600
there's entire taxonomy and the viruses are thrown
link |
00:37:39.360
into the system of collective human intelligence.
link |
00:37:42.640
And when little humans figure out what to do about it,
link |
00:37:45.680
we get like, we tweet stuff about information.
link |
00:37:48.680
There's doctors as conspiracy theorists.
link |
00:37:50.720
And then we play with different information.
link |
00:37:53.120
I mean, the whole of it is fascinating.
link |
00:37:55.680
I am like you also very optimistic,
link |
00:37:58.080
but you said the computational reducibility.
link |
00:38:04.120
There's always a fear of the darkness
link |
00:38:06.440
of the uncertainty before us.
link |
00:38:09.760
Yeah, I know. And it's scary.
link |
00:38:11.120
I mean, the thing is, if you knew everything,
link |
00:38:13.400
it will be boring.
link |
00:38:15.280
And it would be, and then, and worse than boring,
link |
00:38:19.720
so to speak.
link |
00:38:20.560
It would reveal the pointlessness, so to speak.
link |
00:38:24.120
And in a sense, the fact that there is
link |
00:38:26.540
this computational irreducibility,
link |
00:38:28.000
it's like as we live our lives, so to speak,
link |
00:38:30.360
something is being achieved.
link |
00:38:31.660
We're computing what our lives, you know,
link |
00:38:35.520
what happens in our lives.
link |
00:38:36.900
That's funny.
link |
00:38:37.740
So the computational reducibility is kind of like,
link |
00:38:40.520
it gives the meaning to life.
link |
00:38:41.980
It is the meaning of life.
link |
00:38:43.360
Computational reducibility is the meaning of life.
link |
00:38:45.720
There you go.
link |
00:38:46.560
It gives it meaning, yes.
link |
00:38:47.480
I mean, it's what causes it to not be something
link |
00:38:51.580
where you can just say, you know,
link |
00:38:53.540
you went through all those steps to live your life,
link |
00:38:55.760
but we already knew what the answer was.
link |
00:38:58.560
Hold on one second.
link |
00:38:59.400
I'm going to use my handy Wolfram Alpha sunburn
link |
00:39:03.120
computation thing, so long as I can get network here.
link |
00:39:06.120
There we go.
link |
00:39:08.240
Oh, actually, you know what?
link |
00:39:09.460
It says sunburn unlikely.
link |
00:39:11.460
This is a QA moment.
link |
00:39:12.680
This is a good moment.
link |
00:39:16.720
Okay, well, let me just check what it thinks.
link |
00:39:20.560
See why it thinks that.
link |
00:39:22.000
It doesn't seem like my intuition.
link |
00:39:23.540
This is one of these cases where we can,
link |
00:39:25.360
the question is, do we trust the science
link |
00:39:27.800
or do we use common sense?
link |
00:39:30.360
The UV thing is cool.
link |
00:39:32.000
Yeah, yeah, well, we'll see.
link |
00:39:32.880
This is a QA moment, as I say.
link |
00:39:35.040
It's, do we trust the product?
link |
00:39:37.960
Yes, we trust the product, so.
link |
00:39:39.560
And then there'll be a data point either way.
link |
00:39:42.240
If I'm desperately sunburned,
link |
00:39:43.560
I will send in an angry feedback.
link |
00:39:46.840
Because we mentioned the concept so much
link |
00:39:50.760
and a lot of people know it,
link |
00:39:51.960
but can you say what computational reducibility is?
link |
00:39:54.480
Yeah, right.
link |
00:39:55.320
The question is, if you think about things
link |
00:39:58.760
that happen as being computations,
link |
00:40:01.160
you think about some process in physics,
link |
00:40:06.080
something that you compute in mathematics, whatever else,
link |
00:40:09.120
it's a computation in the sense it has definite rules.
link |
00:40:11.920
You follow those rules.
link |
00:40:13.640
You follow them many steps and you get some result.
link |
00:40:18.360
So then the issue is,
link |
00:40:20.080
if you look at all these different kinds of computations
link |
00:40:21.960
that can happen,
link |
00:40:22.800
whether they're computations
link |
00:40:23.760
that are happening in the natural world,
link |
00:40:24.880
whether they're happening in our brains,
link |
00:40:26.560
whether they're happening in our mathematics,
link |
00:40:28.080
whatever else,
link |
00:40:29.040
the big question is, how do these computations compare?
link |
00:40:32.120
Is, are there dumb computations and smart computations
link |
00:40:35.560
or are they somehow all equivalent?
link |
00:40:37.520
And the thing that I kind of was sort of surprised to realize
link |
00:40:41.720
from a bunch of experiments that I did in the early nineties
link |
00:40:43.960
and now we have tons more evidence for it,
link |
00:40:46.080
this thing I call the principle of computational equivalence,
link |
00:40:48.880
which basically says, when one of these computations,
link |
00:40:51.920
one of these processes that follows rules,
link |
00:40:54.280
doesn't seem like it's doing something obviously simple,
link |
00:40:57.640
then it has reached the sort of equivalent level
link |
00:41:00.120
of computational sophistication of everything.
link |
00:41:03.720
So what does that mean?
link |
00:41:04.560
That means that, you might say, gosh,
link |
00:41:07.560
I'm studying this little tiny program on my computer.
link |
00:41:11.600
I'm studying this little thing in nature,
link |
00:41:14.280
but I have my brain
link |
00:41:15.360
and my brain is surely much smarter than that thing.
link |
00:41:18.440
I'm gonna be able to systematically outrun
link |
00:41:20.520
the computation that it does
link |
00:41:22.120
because I have a more sophisticated computation
link |
00:41:24.000
that I can do.
link |
00:41:25.160
But what the principle of computational equivalence says
link |
00:41:27.400
is that doesn't work.
link |
00:41:29.000
Our brains are doing computations
link |
00:41:31.800
that are exactly equivalent to the kinds of computations
link |
00:41:34.600
that are being done in all these other sorts of systems.
link |
00:41:36.920
And so what consequences does that have?
link |
00:41:38.320
Well, it means that we can't systematically
link |
00:41:40.640
outrun these systems.
link |
00:41:42.240
These systems are computationally irreducible
link |
00:41:45.840
in the sense that there's no sort of shortcut
link |
00:41:47.800
that we can make that jumps to the answer.
link |
00:41:50.440
Now the general case.
link |
00:41:51.880
Right, right.
link |
00:41:52.920
But the, so what has happened,
link |
00:41:55.280
what science has become used to doing
link |
00:41:58.760
is using the little sort of pockets
link |
00:42:00.720
of computational reducibility,
link |
00:42:02.840
which by the way are an inevitable consequence
link |
00:42:04.800
of computational irreducibility,
link |
00:42:06.680
that there have to be these pockets
link |
00:42:08.640
scattered around of computational reducibility
link |
00:42:11.480
to be able to find those particular cases
link |
00:42:14.440
where you can jump ahead.
link |
00:42:15.280
I mean, one thing sort of a little bit
link |
00:42:17.320
of a parable type thing that I think is fun to tell.
link |
00:42:20.440
If you look at ancient Babylon,
link |
00:42:22.440
they were trying to predict three kinds of things.
link |
00:42:25.120
They tried to predict where the planets would be,
link |
00:42:27.960
what the weather would be like,
link |
00:42:29.440
and who would win or lose a certain battle.
link |
00:42:32.160
And they had no idea which of these things
link |
00:42:34.560
would be more predictable than the other.
link |
00:42:36.480
That's funny.
link |
00:42:37.320
And it turns out where the planets are
link |
00:42:40.920
is a piece of computational reducibility
link |
00:42:43.600
that 300 years ago or so we pretty much cracked.
link |
00:42:46.680
I mean, it's been technically difficult
link |
00:42:48.000
to get all the details right,
link |
00:42:49.040
but it's basically, we got that.
link |
00:42:52.160
Who's gonna win or lose the battle?
link |
00:42:54.160
No, we didn't crack that one.
link |
00:42:55.400
That one, that one, right.
link |
00:42:57.600
Game theorists are trying.
link |
00:42:58.920
Yes. And then the weather.
link |
00:43:00.800
It's kind of halfway on that one.
link |
00:43:02.480
Halfway?
link |
00:43:03.320
Yeah, I think we're doing okay on that one.
link |
00:43:05.520
Long term climate, different story.
link |
00:43:07.360
But the weather, we're much closer on that.
link |
00:43:10.040
But do you think eventually we'll figure out the weather?
link |
00:43:11.920
So do you think eventually most think
link |
00:43:15.120
we'll figure out the local pockets in everything,
link |
00:43:17.600
essentially the local pockets of reducibility?
link |
00:43:19.800
No, I think that it's an interesting question,
link |
00:43:22.720
but I think that there is an infinite collection
link |
00:43:25.560
of these local pockets.
link |
00:43:26.720
We'll never run out of local pockets.
link |
00:43:28.560
And by the way, those local pockets
link |
00:43:30.600
are where we build engineering, for example.
link |
00:43:33.120
That's how we, if we want to have a predictable life,
link |
00:43:36.880
so to speak, then we have to build
link |
00:43:40.520
in these sort of pockets of reducibility.
link |
00:43:43.000
Otherwise, if we were sort of existing
link |
00:43:46.520
in this kind of irreducible world,
link |
00:43:48.720
we'd never be able to have definite things
link |
00:43:51.800
to know what's gonna happen.
link |
00:43:53.240
I have to say, I think one of the features,
link |
00:43:55.400
when we look at sort of today from the future, so to speak,
link |
00:43:59.920
I suspect one of the things where people will say
link |
00:44:02.120
I can't believe they didn't see that
link |
00:44:04.440
is stuff to do with the following kind of thing.
link |
00:44:07.000
So if we describe, oh, I don't know,
link |
00:44:10.160
something like heat, for instance,
link |
00:44:12.880
we say, oh, the air in here, it's this temperature,
link |
00:44:17.880
this pressure, that's as much as we can say.
link |
00:44:20.320
Otherwise, just a bunch of random molecules bouncing around.
link |
00:44:23.240
People will say, I just can't believe they didn't realize
link |
00:44:26.080
that there was all this detail
link |
00:44:27.240
and how all these molecules were bouncing around
link |
00:44:29.320
and they could make use of that.
link |
00:44:31.800
And actually, I realized there's a thing
link |
00:44:32.920
I realized last week, actually,
link |
00:44:34.720
was a thing that people say, one of the scenarios
link |
00:44:37.680
for the very long term history of our universe
link |
00:44:40.040
is a so called heat death of the universe,
link |
00:44:42.560
where basically everything just becomes
link |
00:44:44.840
thermodynamically boring.
link |
00:44:47.160
Everything's just this big kind of gas
link |
00:44:48.840
and thermal equilibrium.
link |
00:44:50.080
People say, that's a really bad outcome.
link |
00:44:52.640
But actually, it's not a really bad outcome.
link |
00:44:54.960
It's an outcome where there's all this computation going on
link |
00:44:57.360
and all those individual gas molecules
link |
00:44:58.920
are all bouncing around in very complicated ways
link |
00:45:01.440
doing this very elaborate computation.
link |
00:45:03.520
It just happens to be a computation that right now,
link |
00:45:06.360
we haven't found ways to understand.
link |
00:45:09.560
We haven't found ways, our brains haven't,
link |
00:45:12.560
and our mathematics and our science and so on,
link |
00:45:14.960
haven't found ways to tell an interesting story about that.
link |
00:45:17.960
It just looks boring to us.
link |
00:45:19.560
So you're saying there's a hopeful view
link |
00:45:23.080
of the heat death, quote unquote, of the universe
link |
00:45:26.320
where there's actual beautiful complexity going on.
link |
00:45:30.400
Similar to the kind of complexity we think of
link |
00:45:34.440
that creates rich experience in human life and life on Earth.
link |
00:45:38.120
So those little molecules interacting complex ways,
link |
00:45:40.720
that could be intelligence in that, there could be.
link |
00:45:43.320
Absolutely.
link |
00:45:44.160
I mean, this is what you learn from this principle.
link |
00:45:46.120
Wow, that's a hopeful message.
link |
00:45:48.000
Right.
link |
00:45:48.840
I mean, this is what you kind of learn
link |
00:45:49.680
from this principle of computational equivalence.
link |
00:45:51.720
You learn it's both a message of sort of hope
link |
00:45:56.200
and a message of kind of, you know,
link |
00:45:59.040
you're not as special as you think you are, so to speak.
link |
00:46:01.120
I mean, because, you know, we imagine that
link |
00:46:03.520
with sort of all the things we do with human intelligence
link |
00:46:06.360
and all that kind of thing,
link |
00:46:07.640
and all of the stuff we've constructed in science,
link |
00:46:09.880
it's like, we're very special.
link |
00:46:12.000
But actually it turns out, well, no, we're not.
link |
00:46:15.200
We're just doing computations
link |
00:46:17.000
like things in nature do computations,
link |
00:46:19.480
like those gas molecules do computations,
link |
00:46:21.280
like the weather does computations.
link |
00:46:23.280
The only thing about the computations that we do
link |
00:46:26.120
that's really special is that we understand
link |
00:46:30.000
what they are, so to speak.
link |
00:46:31.160
In other words, we have a, you know,
link |
00:46:33.120
to us they're special because kind of,
link |
00:46:35.320
they're connected to our purposes,
link |
00:46:37.040
our ways of thinking about things and so on.
link |
00:46:39.160
And that's some, but so.
link |
00:46:41.000
That's very human centric.
link |
00:46:42.560
That's, we're just attached to this kind of thing.
link |
00:46:45.520
So let's talk a little bit of physics.
link |
00:46:48.280
Maybe let's ask the biggest question.
link |
00:46:50.960
What is a theory of everything in general?
link |
00:46:55.320
What does that mean?
link |
00:46:56.160
Yeah, so I mean, the question is,
link |
00:46:58.000
can we kind of reduce what has been physics
link |
00:47:01.720
as a something where we have to sort of pick away and say,
link |
00:47:05.680
do we roughly know how the world works
link |
00:47:08.280
to something where we have a complete formal theory
link |
00:47:11.040
where we say, if we were to run this program
link |
00:47:14.240
for long enough, we would reproduce everything,
link |
00:47:17.680
you know, down to the fact that we're having
link |
00:47:19.600
this conversation at this moment,
link |
00:47:21.160
et cetera, et cetera, et cetera.
link |
00:47:22.800
Any physical phenomena, any phenomena in this world?
link |
00:47:25.480
Any phenomenon in the universe.
link |
00:47:27.040
But the, you know, because of computational irreducibility,
link |
00:47:30.320
it's not, you know, that's not something where you say,
link |
00:47:33.720
okay, you've got the fundamental theory of everything.
link |
00:47:36.160
Then, you know, tell me whether, you know,
link |
00:47:39.920
lions are gonna eat tigers or something.
link |
00:47:42.480
You know, that's a, no, you have to run this thing
link |
00:47:45.440
for, you know, 10 to the 500 steps or something
link |
00:47:48.560
to know something like that, okay?
link |
00:47:50.800
So at some moment, potentially, you say,
link |
00:47:54.200
this is a rule and run this rule enough times
link |
00:47:57.560
and you will get the whole universe, right?
link |
00:47:59.760
That's what it means to kind of have
link |
00:48:02.400
a fundamental theory of physics as far as I'm concerned
link |
00:48:04.720
is you've got this rule.
link |
00:48:06.600
It's potentially quite simple.
link |
00:48:07.720
We don't know for sure it's simple,
link |
00:48:09.360
but we have various reasons to believe it might be simple.
link |
00:48:12.560
And then you say, okay, I'm showing you this rule.
link |
00:48:15.800
You just run it only 10 to the 500 times
link |
00:48:18.720
and you'll get everything.
link |
00:48:20.080
In other words, you've kind of reduced the problem
link |
00:48:22.800
of physics to a problem of mathematics, so to speak.
link |
00:48:25.600
It's like, it's as if, you know, you'd like,
link |
00:48:27.760
you generate the digits of pi.
link |
00:48:29.760
There's a definite procedure.
link |
00:48:30.920
You just generate them and it'd be the same thing
link |
00:48:33.720
if you have a fundamental theory of physics
link |
00:48:35.600
of the kind that I'm imagining, you know,
link |
00:48:38.640
you get this rule and you just run it out
link |
00:48:42.760
and you get everything that happens in the universe.
link |
00:48:45.880
So a theory of everything is a mathematical framework
link |
00:48:52.160
within which you can explain everything that happens
link |
00:48:55.360
in the universe, it's kind of in a unified way.
link |
00:48:58.640
It's not, there's a bunch of disparate modules of,
link |
00:49:01.600
does it feel like if you create a rule
link |
00:49:07.120
and we'll talk about the Wolfram physics model,
link |
00:49:11.200
which is fascinating, but if you have a simple set
link |
00:49:16.280
of rules with a data structure, like a hypergraph,
link |
00:49:21.840
does that feel like a satisfying theory of everything?
link |
00:49:25.120
Because then you really run up against the irreducibility,
link |
00:49:29.320
computational irreducibility.
link |
00:49:32.360
Right, so that's a really interesting question.
link |
00:49:34.240
So I, you know, what I thought was gonna happen
link |
00:49:38.200
is I thought we, you know, I thought we had a pretty good,
link |
00:49:42.280
I had a pretty good idea for what the structure
link |
00:49:45.480
of this sort of theory that sort of underneath space
link |
00:49:47.960
and time and so on might be like.
link |
00:49:50.200
And I thought, gosh, you know, in my lifetime,
link |
00:49:52.920
so to speak, we might be able to figure out what happens
link |
00:49:55.040
in the first 10 to the minus 100 seconds of the universe.
link |
00:49:58.160
And that would be cool, but it's pretty far away
link |
00:50:01.480
from anything that we can see today.
link |
00:50:03.840
And it will be hard to test whether that's right
link |
00:50:05.760
and so on and so on and so on.
link |
00:50:07.520
To my huge surprise, although it should have been obvious
link |
00:50:10.480
and it's embarrassing that it wasn't obvious to me,
link |
00:50:12.600
but to my huge surprise,
link |
00:50:15.600
we managed to get unbelievably much further than that.
link |
00:50:18.400
And basically what happened is that it turns out
link |
00:50:21.520
that even though there's this kind of bed
link |
00:50:23.160
of computational irreducibility,
link |
00:50:25.280
that sort of these, all these simple rules run into,
link |
00:50:30.040
there are certain pieces of computational reducibility
link |
00:50:34.240
that quite generically occur
link |
00:50:36.200
for large classes of these rules.
link |
00:50:38.400
And, and this is the really exciting thing
link |
00:50:40.960
as far as I'm concerned,
link |
00:50:42.400
the big pieces of computational reducibility
link |
00:50:46.000
are basically the pillars of 20th century physics.
link |
00:50:49.320
That's the amazing thing,
link |
00:50:50.280
that general relativity and quantum field theory
link |
00:50:52.680
is sort of the pillars of 20th century physics
link |
00:50:55.480
turn out to be precisely the stuff you can say.
link |
00:50:59.720
There's a lot you can't say,
link |
00:51:00.840
there's a lot that's kind of at this irreducible level
link |
00:51:03.360
where you kind of don't know what's going to happen,
link |
00:51:05.120
you have to run it, you know,
link |
00:51:06.400
you can't run it within our universe,
link |
00:51:07.840
et cetera, et cetera, et cetera, et cetera.
link |
00:51:10.240
But the thing is there are things you can say
link |
00:51:13.560
and the things you can say turn out to be very beautifully
link |
00:51:17.840
exactly the structure that was found
link |
00:51:19.760
in 20th century physics,
link |
00:51:21.520
namely general relativity and quantum mechanics.
link |
00:51:24.040
And general relativity and quantum mechanics
link |
00:51:26.960
are these pockets of reducibility that we think of as,
link |
00:51:32.000
that 20th century physics
link |
00:51:34.120
is essentially pockets of reducibility.
link |
00:51:36.880
And then it is incredibly surprising
link |
00:51:39.400
that any kind of model that's generative
link |
00:51:43.440
from simple rules would have such pockets.
link |
00:51:47.960
Yeah, well, I think what's surprising
link |
00:51:49.920
is we didn't know where those things came from.
link |
00:51:52.680
It's like general relativity,
link |
00:51:53.920
it's a very nice mathematically elegant theory.
link |
00:51:56.840
Why is it true?
link |
00:51:58.400
You know, quantum mechanics, why is it true?
link |
00:52:00.960
What we realized is that from this,
link |
00:52:04.160
that these theories are generic
link |
00:52:07.080
to a huge class of systems
link |
00:52:09.280
that have these particular
link |
00:52:10.440
very unstructured underlying rules.
link |
00:52:13.480
And that's the thing that is sort of remarkable
link |
00:52:16.920
and that's the thing to me
link |
00:52:18.280
that's just, it's really beautiful.
link |
00:52:20.320
I mean, it's, and the thing that's even more beautiful
link |
00:52:22.800
is that it turns out that, you know,
link |
00:52:24.400
people have been struggling for a long time.
link |
00:52:26.120
You know, how does general relativity theory of gravity
link |
00:52:29.000
relate to quantum mechanics?
link |
00:52:30.080
They seem to have all kinds of incompatibilities.
link |
00:52:32.400
It turns out what we realized is
link |
00:52:34.400
at some level they are the same theory.
link |
00:52:37.040
And that's just, it's just great as far as I'm concerned.
link |
00:52:40.840
So maybe like taking a little step back
link |
00:52:43.160
from your perspective, not from the low,
link |
00:52:47.120
not from the beautiful hypergraph,
link |
00:52:50.680
well, from physics model perspective,
link |
00:52:52.480
but from the perspective of 20th century physics,
link |
00:52:55.440
what is general relativity?
link |
00:52:57.240
What is quantum mechanics?
link |
00:52:58.320
How do you think about these two theories
link |
00:53:00.880
from the context of the theory of everything?
link |
00:53:04.000
Like just even definition.
link |
00:53:05.720
Yeah, yeah, yeah, right.
link |
00:53:06.560
So I mean, you know, a little bit of history of physics,
link |
00:53:08.800
right?
link |
00:53:09.640
So, I mean the, you know, okay,
link |
00:53:12.040
very, very quick history of this, right?
link |
00:53:14.200
So, I mean, you know, physics, you know,
link |
00:53:16.240
in ancient Greek times, people basically said,
link |
00:53:19.000
we can just figure out how the world works.
link |
00:53:21.200
As you know, we're philosophers,
link |
00:53:22.560
we're gonna figure out how the world works.
link |
00:53:24.560
You know, some philosophers thought there were atoms.
link |
00:53:26.600
Some philosophers thought there were,
link |
00:53:28.600
you know, continuous flows of things.
link |
00:53:30.600
People had different ideas about how the world works.
link |
00:53:33.000
And they tried to just say,
link |
00:53:33.840
we're gonna construct this idea of how the world works.
link |
00:53:36.840
They didn't really have sort of notions
link |
00:53:38.200
of doing experiments and so on quite the same way
link |
00:53:40.640
as developed later.
link |
00:53:41.480
So that was sort of an early tradition
link |
00:53:43.320
for thinking about sort of models of the world.
link |
00:53:46.600
Then by the time of 1600s, time of Galileo and then Newton,
link |
00:53:51.200
sort of the big idea there was, you know,
link |
00:53:55.280
title of Newton's book, you know, Principia Mathematica,
link |
00:53:57.640
mathematical principles of natural philosophy.
link |
00:54:00.440
We can use mathematics to understand natural philosophy,
link |
00:54:04.240
to understand things about the way the world works.
link |
00:54:07.080
And so that then led to this kind of idea that, you know,
link |
00:54:10.480
we can write down a mathematical equation
link |
00:54:12.760
and have that represent how the world works.
link |
00:54:14.960
So Newton's one of his most famous ones
link |
00:54:16.800
is his universal law of gravity,
link |
00:54:19.240
inverse square law of gravity
link |
00:54:21.160
that allowed him to compute all sorts of features
link |
00:54:23.360
of the planets and so on.
link |
00:54:24.920
Although some of them he got wrong
link |
00:54:26.240
and it took another hundred years
link |
00:54:28.000
for people to actually be able to do the math
link |
00:54:30.200
to the level that was needed.
link |
00:54:31.240
But so that had been this sort of tradition
link |
00:54:34.560
was we write down these mathematical equations.
link |
00:54:36.280
We don't really know where these equations come from.
link |
00:54:38.640
We write them down.
link |
00:54:39.960
Then we figure out, we work out the consequences
link |
00:54:42.480
and we say, yes, that agrees with what we actually observe
link |
00:54:45.320
in astronomy or something like this.
link |
00:54:47.320
So that tradition continued.
link |
00:54:49.480
And then the first of these two
link |
00:54:51.440
sort of great 20th century innovations was,
link |
00:54:55.480
well, the history is actually a little bit more complicated,
link |
00:54:57.320
but let's say that there were two,
link |
00:55:01.600
quantum mechanics and general relativity.
link |
00:55:03.440
Quantum mechanics kind of 1900
link |
00:55:05.400
was kind of the very early stuff done by Planck
link |
00:55:08.400
that led to the idea of photons, particles of light.
link |
00:55:12.320
But let's take general relativity first.
link |
00:55:14.880
One feature of the story is that special relativity
link |
00:55:19.240
thing Einstein invented in 1905
link |
00:55:21.800
was something which surprisingly
link |
00:55:24.240
was a kind of logically invented theory.
link |
00:55:27.040
It was not a theory where it was something where
link |
00:55:29.880
given these ideas that were sort of axiomatically
link |
00:55:32.960
thought to be true about the world,
link |
00:55:34.760
it followed that such and such a thing would be the case.
link |
00:55:38.360
It was a little bit different
link |
00:55:39.400
from the kind of methodological structure
link |
00:55:42.000
of some existing theories in the more recent times,
link |
00:55:45.920
where it's just been, we write down an equation
link |
00:55:47.640
and we find out that it works.
link |
00:55:49.960
So what happened there.
link |
00:55:51.560
So there's some reasoning about the light.
link |
00:55:53.680
The basic idea was the speed of light
link |
00:55:57.720
appears to be constant.
link |
00:55:59.960
Even if you're traveling very fast,
link |
00:56:01.920
you shine a flashlight, the light will come out.
link |
00:56:05.080
Even if you're going at half the speed of light,
link |
00:56:07.120
the light doesn't come out of your flashlight
link |
00:56:08.920
at one and a half times the speed of light.
link |
00:56:11.160
It's still just the speed of light.
link |
00:56:13.080
And to make that work,
link |
00:56:14.680
you have to change your view of how space and time work
link |
00:56:18.040
to be able to account for the fact
link |
00:56:20.200
that when you're going faster,
link |
00:56:21.480
it appears that length is foreshortened
link |
00:56:24.440
and time is dilated and things like this.
link |
00:56:26.240
And that's special relativity.
link |
00:56:27.200
That's special relativity.
link |
00:56:28.560
So then Einstein went on with sort of
link |
00:56:33.160
vaguely similar kinds of thinking.
link |
00:56:34.800
In 1915, invented general relativity,
link |
00:56:37.960
which is the theory of gravity.
link |
00:56:39.920
And the basic point of general relativity
link |
00:56:42.480
is it's a theory that says,
link |
00:56:44.840
when there is mass in space, space is curved.
link |
00:56:49.680
And what does that mean?
link |
00:56:52.320
Usually you think of what's the shortest distance
link |
00:56:55.160
between two points.
link |
00:56:56.000
Like ordinarily on a plane in space, it's a straight line.
link |
00:57:00.840
Photons, light goes in straight lines.
link |
00:57:04.640
Well, then the question is,
link |
00:57:06.440
is if you have a curved surface,
link |
00:57:10.280
a straight line is no longer straight.
link |
00:57:12.160
On the surface of the earth,
link |
00:57:13.560
the shortest distance between two points is a great circle.
link |
00:57:16.200
It's a circle.
link |
00:57:18.600
So, you know, Einstein's observation was
link |
00:57:21.040
maybe the physical structure of space
link |
00:57:24.520
is such that space is curved.
link |
00:57:26.800
So the shortest distance between two points,
link |
00:57:29.640
the path, the straight line in quotes,
link |
00:57:32.880
won't be straight anymore.
link |
00:57:34.160
And in particular, if a photon is, you know,
link |
00:57:37.160
traveling near the sun or something,
link |
00:57:39.320
or if a particle is going,
link |
00:57:40.600
something is traveling near the sun,
link |
00:57:42.400
maybe the shortest path will be one
link |
00:57:45.320
that is something which looks curved to us
link |
00:57:48.840
because it seems curved to us
link |
00:57:50.160
because space has been deformed by the presence of mass
link |
00:57:53.240
associated with that massive object.
link |
00:57:55.480
So the kind of the idea there is,
link |
00:57:59.240
think of the structure of space
link |
00:58:01.000
as being a dynamical changing kind of thing.
link |
00:58:03.680
But then what Einstein did
link |
00:58:04.840
was he wrote down these differential equations
link |
00:58:07.120
that basically represented the curvature of space
link |
00:58:10.240
and its response to the presence of mass and energy.
link |
00:58:13.040
And that ultimately is connected to the force of gravity,
link |
00:58:18.280
which is one of the forces that seems to,
link |
00:58:20.600
based on its strength,
link |
00:58:21.480
operate on a different scale than some of the other forces.
link |
00:58:24.800
So it operates in a scale that's very large.
link |
00:58:27.760
What happens there is just this curvature of space,
link |
00:58:32.160
which causes, you know, the paths of objects to be deflected.
link |
00:58:35.960
That's what gravity does.
link |
00:58:37.200
It causes the paths of objects to be deflected.
link |
00:58:39.720
And this is an explanation for gravity, so to speak.
link |
00:58:43.160
And the surprise is that from 1915 until today,
link |
00:58:47.280
everything that we've measured about gravity
link |
00:58:49.680
precisely agrees with general relativity.
link |
00:58:52.160
And that, you know, it wasn't clear black holes
link |
00:58:55.720
were sort of a predict,
link |
00:58:56.560
well, actually the expansion of the universe
link |
00:58:57.720
was an early potential prediction,
link |
00:58:59.560
although Einstein tried to sort of patch up his equations
link |
00:59:02.720
to make it not cause the universe to expand,
link |
00:59:05.080
because it was kind of so obvious
link |
00:59:06.320
the universe wasn't expanding.
link |
00:59:08.160
And, you know, it turns out it was expanding
link |
00:59:10.480
and he should have just trusted the equations.
link |
00:59:11.960
And that's a lesson for those of us
link |
00:59:14.480
interested in making fundamental theories of physics
link |
00:59:16.680
is you should trust your theory and not try and patch it
link |
00:59:19.840
because of something that you think might be the case
link |
00:59:22.000
that might turn out not to be the case.
link |
00:59:25.280
Even if the theory says something crazy is happening.
link |
00:59:28.360
Yeah, right.
link |
00:59:29.200
Like the universe is expanding.
link |
00:59:30.040
Like the universe is expanding, right, which is,
link |
00:59:31.880
but, you know, then it took until the 1940s,
link |
00:59:35.160
probably even really until the 1960s,
link |
00:59:36.840
until people understood that black holes
link |
00:59:38.600
were a consequence of general relativity and so on.
link |
00:59:42.200
But that's, you know, the big surprise has been
link |
00:59:45.640
that so far this theory of gravity has perfectly agreed
link |
00:59:50.000
with, you know, these collisions of black holes
link |
00:59:51.880
seen by their gravitational waves, you know,
link |
00:59:54.480
it all just works.
link |
00:59:55.880
So that's been kind of one pillar of the story of physics
link |
00:59:59.160
it's mathematically complicated to work out
link |
01:00:01.120
the consequences of general relativity,
link |
01:00:03.080
but it's not, there's no, I mean,
link |
01:00:05.720
and some things are kind of squiggly and complicated.
link |
01:00:09.400
Like people believe, you know, energy is conserved.
link |
01:00:12.120
Okay, well, energy conservation doesn't really work
link |
01:00:14.480
in general activity in the same way as it ordinarily does.
link |
01:00:16.840
And it's all a big mathematical story
link |
01:00:19.300
of how you actually nail down something that is definitive
link |
01:00:22.840
that you can talk about it and not specific to the,
link |
01:00:25.320
you know, reference frames you're operating in
link |
01:00:27.200
and so on and so on and so on.
link |
01:00:28.420
But fundamentally, general relativity is a straight shot
link |
01:00:31.360
in the sense that you have this theory,
link |
01:00:32.960
you work out its consequences.
link |
01:00:34.960
And that theory is useful in terms of basic science
link |
01:00:39.300
and trying to understand the way black holes work,
link |
01:00:41.220
the way the creation of galaxies work,
link |
01:00:43.580
sort of all of these kinds of cosmological things,
link |
01:00:45.840
understanding what happened, like you said, at the Big Bang.
link |
01:00:49.200
Yeah. Like all those kinds of,
link |
01:00:50.560
well, no, not at the Big Bang actually, right?
link |
01:00:52.800
But the...
link |
01:00:53.860
Well, features of the expansion of the universe, yes.
link |
01:00:55.880
I mean, and there are lots of details
link |
01:00:58.220
where we don't quite know how it's working, you know,
link |
01:00:59.920
is there, you know, where's the dark matter,
link |
01:01:02.040
is there dark energy, you know, et cetera, et cetera, et cetera.
link |
01:01:04.400
But fundamentally, the, you know,
link |
01:01:06.320
the testable features of general relativity,
link |
01:01:08.440
it all works very beautifully.
link |
01:01:10.080
And it's in a sense, it is mathematically sophisticated,
link |
01:01:13.720
but it is not conceptually hard to understand in some sense.
link |
01:01:17.160
Okay. So that's general relativity.
link |
01:01:18.720
And what's its friendly neighbor, like you said,
link |
01:01:21.240
there's two theories, quantum mechanics.
link |
01:01:22.800
Right. So quantum mechanics,
link |
01:01:24.320
the sort of the way that that originated was,
link |
01:01:28.240
one question was, is the world continuous or is it discrete?
link |
01:01:31.360
You know, in ancient Greek times,
link |
01:01:32.480
people have been debating this.
link |
01:01:34.000
People debated it, you know, throughout history.
link |
01:01:36.400
Is light made of waves?
link |
01:01:38.360
Is it continuous? Is it discrete?
link |
01:01:39.820
Is it made of particles, corpuscles, whatever.
link |
01:01:43.380
You know, what had become clear in the 1800s is that atoms,
link |
01:01:47.760
that, you know, materials are made of discrete atoms.
link |
01:01:51.360
You know, when you take some water,
link |
01:01:53.940
the water is not a continuous fluid,
link |
01:01:55.560
even though it seems like a continuous fluid
link |
01:01:57.360
to us at our scale.
link |
01:01:58.880
But if you say, let's look at it,
link |
01:02:00.760
smaller and smaller and smaller and smaller scale,
link |
01:02:02.480
eventually you get down to these, you know,
link |
01:02:04.400
these molecules and then atoms.
link |
01:02:06.320
It's made of discrete things.
link |
01:02:07.960
The question is sort of how important is this discreteness?
link |
01:02:10.960
Just what's discrete, what's not discrete?
link |
01:02:12.900
Is energy discrete?
link |
01:02:14.040
Is, you know, what's discrete, what's not?
link |
01:02:17.400
And so.
link |
01:02:18.240
Does it have mass?
link |
01:02:19.560
Those kinds of questions.
link |
01:02:20.880
Yeah, yeah, right.
link |
01:02:21.700
Well, there's a question, I mean, for example,
link |
01:02:23.640
is mass discrete is an interesting question,
link |
01:02:26.040
which is now something we can address.
link |
01:02:28.140
But, you know, what happened in the coming up to the 1920s,
link |
01:02:35.720
there was this kind of mathematical theory developed
link |
01:02:37.720
that could explain certain kinds of discreteness
link |
01:02:40.500
in particularly in features of atoms and so on.
link |
01:02:44.340
And, you know, what developed was this mathematical theory
link |
01:02:47.780
that was the theory of quantum mechanics,
link |
01:02:50.200
theory of wave functions, Schrodinger's equation,
link |
01:02:52.520
things like this.
link |
01:02:53.680
That's a mathematical theory that allows you to calculate
link |
01:02:57.320
lots of features of the microscopic world,
link |
01:02:59.260
lots of things about how atoms work,
link |
01:03:01.480
et cetera, et cetera, et cetera.
link |
01:03:03.000
Now, the calculations all work just great.
link |
01:03:05.760
The question of what does it really mean
link |
01:03:09.400
is a complicated question.
link |
01:03:11.300
Now, I mean, to just explain a little bit historically,
link |
01:03:14.280
the, you know, the early calculations of things like atoms
link |
01:03:17.040
worked great in 1920s, 1930s and so on.
link |
01:03:20.320
There was always a problem.
link |
01:03:21.400
There were, in quantum field theory,
link |
01:03:24.200
which is a theory of, in quantum mechanics,
link |
01:03:27.300
you're dealing with a certain number of electrons
link |
01:03:30.480
and you fix the number of electrons.
link |
01:03:31.940
You say, I'm dealing with a two electron thing.
link |
01:03:34.900
In quantum field theory,
link |
01:03:35.800
you allow for particles being created and destroyed.
link |
01:03:38.880
So you can emit a photon that didn't exist before.
link |
01:03:41.200
You can absorb a photon, things like that.
link |
01:03:43.440
That's a more complicated,
link |
01:03:44.560
mathematically complicated theory.
link |
01:03:46.280
And it had all kinds of mathematical issues
link |
01:03:47.960
and all kinds of infinities that cropped up.
link |
01:03:49.980
And it was finally figured out more or less
link |
01:03:51.400
how to get rid of those.
link |
01:03:52.920
But there were only certain ways of doing the calculations
link |
01:03:55.940
and those didn't work for atomic nuclei among other things.
link |
01:03:59.640
And that led to a lot of development up until the 1960s
link |
01:04:03.840
of alternative ideas for how one could understand
link |
01:04:07.160
what was happening in atomic nuclei, et cetera,
link |
01:04:09.080
et cetera, et cetera.
link |
01:04:10.120
End result, in the end,
link |
01:04:12.280
the kind of most quotes obvious mathematical structure
link |
01:04:16.000
of quantum field theory seems to work.
link |
01:04:18.360
Although it's mathematically difficult to deal with,
link |
01:04:20.680
but you can calculate all kinds of things.
link |
01:04:22.980
You can calculate to a dozen decimal places,
link |
01:04:26.140
certain things, you can measure them.
link |
01:04:27.800
It all works.
link |
01:04:28.640
It's all beautiful.
link |
01:04:29.600
Now you say...
link |
01:04:30.440
The underlying fabric is the model
link |
01:04:32.520
of that particular theory is fields.
link |
01:04:34.800
Like you keep saying fields.
link |
01:04:37.000
Those are quantum fields.
link |
01:04:37.940
Those are different from classical fields.
link |
01:04:40.400
A field is something like you say,
link |
01:04:44.640
like you say the temperature field in this room.
link |
01:04:46.920
It's like there is a value of temperature
link |
01:04:49.520
at every point around the room.
link |
01:04:51.360
That's some, or you can say the wind field
link |
01:04:53.980
would be the vector direction of the wind at every point.
link |
01:04:56.920
It's continuous.
link |
01:04:57.880
Yes, and that's a classical field.
link |
01:05:00.200
The quantum field is a much more
link |
01:05:01.360
mathematically elaborate kind of thing.
link |
01:05:04.280
And I should explain that one of the pictures
link |
01:05:06.400
of quantum mechanics that's really important is,
link |
01:05:09.360
in classical physics, one believes
link |
01:05:11.760
that sort of definite things happen in the world.
link |
01:05:13.800
You pick up a ball, you throw it,
link |
01:05:16.160
the ball goes in a definite trajectory
link |
01:05:17.980
that has certain equations of motion.
link |
01:05:20.200
It goes in a parabola, whatever else.
link |
01:05:22.240
In quantum mechanics, the picture is
link |
01:05:25.320
definite things don't happen.
link |
01:05:26.880
Instead, sort of what happens is this whole
link |
01:05:29.720
sort of structure of all many different paths being followed
link |
01:05:34.840
and we can calculate certain aspects of what happens,
link |
01:05:37.840
certain probabilities of different outcomes and so on.
link |
01:05:40.560
And you say, well, what really happened?
link |
01:05:42.440
What's really going on?
link |
01:05:43.440
What's the sort of, what's the underlying,
link |
01:05:45.680
what's the underlying story?
link |
01:05:47.120
How do we turn this mathematical theory
link |
01:05:50.640
that we can calculate things with
link |
01:05:52.400
into something that we can really understand
link |
01:05:54.760
and have a narrative about?
link |
01:05:56.360
And that's been really, really hard for quantum mechanics.
link |
01:05:58.920
My friend, Dick Feynman, always used to say,
link |
01:06:01.500
nobody understands quantum mechanics,
link |
01:06:03.640
even though he'd made his whole career
link |
01:06:06.400
out of calculating things about quantum mechanics.
link |
01:06:10.160
And so it's a little bit.
link |
01:06:11.720
Nevertheless, it's what the quantum field theory is very,
link |
01:06:16.840
very accurate at predicting a lot of the physical phenomena.
link |
01:06:20.640
So it works.
link |
01:06:21.720
Yeah.
link |
01:06:22.560
But there are things about it, it has certain,
link |
01:06:25.240
when we apply it, the standard model of particle physics,
link |
01:06:27.780
for example, we, which we apply to calculate
link |
01:06:31.500
all kinds of things that works really well.
link |
01:06:33.440
And you say, well, it has certain parameters.
link |
01:06:34.880
It has a whole bunch of parameters actually.
link |
01:06:36.900
You say, why is the, why does the muon particle exist?
link |
01:06:41.540
Why is it 206 times the mass of the electron?
link |
01:06:44.880
We don't know, no idea.
link |
01:06:46.680
But so the standard model of physics is one of the models
link |
01:06:50.020
that's very accurate for describing
link |
01:06:51.720
three of the fundamental forces of physics.
link |
01:06:55.200
And it's looking at the world of the very small.
link |
01:06:58.240
Right.
link |
01:06:59.080
And then there's back to the neighbor of gravity,
link |
01:07:03.140
of general relativity.
link |
01:07:04.760
So, and then in the context of a theory of everything,
link |
01:07:07.660
what's traditionally the task of the unification
link |
01:07:13.560
of these theories?
link |
01:07:15.160
And why is it hard?
link |
01:07:16.000
The issue is you try to use the methods
link |
01:07:18.160
of quantum field theory to talk about gravity
link |
01:07:20.840
and it doesn't work.
link |
01:07:22.000
Just like there are photons of light.
link |
01:07:24.000
So there are gravitons,
link |
01:07:25.320
which are sort of the particles of gravity.
link |
01:07:27.960
And when you try and compute sort of the properties
link |
01:07:30.280
of the particles of gravity,
link |
01:07:32.680
the kind of mathematical tricks that get used
link |
01:07:36.040
in working things out in quantum field theory don't work.
link |
01:07:39.280
And that's, so that's been a sort of fundamental issue.
link |
01:07:43.000
And when you think about black holes,
link |
01:07:44.800
which are a place where sort of the structure of space
link |
01:07:48.960
is, you know, has sort of rapid variation
link |
01:07:52.800
and you get kind of quantum effects mixed in
link |
01:07:55.320
with effects from general relativity,
link |
01:07:57.520
things get very complicated
link |
01:07:58.720
and there are apparent paradoxes and things like that.
link |
01:08:01.320
And people have, you know,
link |
01:08:02.840
there've been a bunch of mathematical developments
link |
01:08:05.040
in physics over the last, I don't know, 30 years or so,
link |
01:08:08.600
which have kind of picked away at those kinds of issues
link |
01:08:11.560
and got hints about how things might work.
link |
01:08:15.200
But it hasn't been, you know,
link |
01:08:17.280
and the other thing to realize is,
link |
01:08:19.040
as far as physics is concerned,
link |
01:08:20.680
it's just like here's general relativity,
link |
01:08:22.840
here's quantum field theory, you know, be happy.
link |
01:08:25.840
Yeah, so do you think there's a quantization of gravity,
link |
01:08:28.760
so quantum gravity, what do you think of efforts
link |
01:08:31.100
that people have tried to, yeah,
link |
01:08:33.760
what do you think in general of the efforts
link |
01:08:36.340
of the physics community to try to unify these laws?
link |
01:08:39.600
So I think what's, it's interesting.
link |
01:08:41.320
I mean, I would have said something very different
link |
01:08:43.360
before what's happened with our physics project.
link |
01:08:46.400
I mean, you know, the remarkable thing is
link |
01:08:48.880
what we've been able to do is to make
link |
01:08:51.720
from this very simple, structurally simple,
link |
01:08:55.560
underlying set of ideas,
link |
01:08:57.960
we've been able to build this, you know,
link |
01:09:00.940
very elaborate structure that's both very abstract
link |
01:09:04.480
and very sort of mathematically rich.
link |
01:09:06.880
And the big surprise, as far as I'm concerned,
link |
01:09:09.240
is that it touches many of the ideas that people have had.
link |
01:09:12.960
So in other words, things like string theory and so on,
link |
01:09:15.520
twister theory, it's like the, you know,
link |
01:09:18.160
we might've thought, I had thought we're out on a prong,
link |
01:09:21.020
we're building something that's computational,
link |
01:09:22.640
it's completely different from what other people have done.
link |
01:09:25.060
But actually it seems like what we've done
link |
01:09:27.320
is to provide essentially the machine code that, you know,
link |
01:09:30.820
these things are various features
link |
01:09:33.080
of domain specific languages, so to speak,
link |
01:09:35.460
that talk about various aspects of this machine code.
link |
01:09:37.920
And I think this is something that to me is very exciting
link |
01:09:41.800
because it allows one both for us to provide
link |
01:09:45.540
sort of a new foundation for what's been thought about there
link |
01:09:48.440
and for all the work that's been done in those areas
link |
01:09:52.000
to give us, you know, more momentum
link |
01:09:55.760
to be able to figure out what's going on.
link |
01:09:57.140
Now, you know, people have sort of hoped,
link |
01:09:58.840
oh, we're just gonna be able to get, you know,
link |
01:10:01.200
string theory to just answer everything.
link |
01:10:03.400
That hasn't worked out.
link |
01:10:04.920
And I think we now kind of can see a little bit about
link |
01:10:07.920
just sort of how far away certain kinds of things are
link |
01:10:10.360
from being able to explain things.
link |
01:10:12.520
Some things, one of the big surprises to me,
link |
01:10:14.720
actually I literally just got a message
link |
01:10:16.600
about one aspect of this is the, you know,
link |
01:10:20.800
it's turning out to be easier.
link |
01:10:22.640
I mean, this project has been so much easier
link |
01:10:24.880
than I could ever imagine it would be.
link |
01:10:26.680
That is, I thought we would be, you know,
link |
01:10:29.720
just about able to understand
link |
01:10:31.360
the first 10 to the minus 100 seconds of the universe.
link |
01:10:34.120
And, you know, it would be a hundred years
link |
01:10:35.800
before we get much further than that.
link |
01:10:37.640
It's just turned out, it actually wasn't that hard.
link |
01:10:40.440
I mean, we're not finished, but, you know.
link |
01:10:42.480
So you're seeing echoes of all the disparate theories
link |
01:10:45.840
of physics in this framework.
link |
01:10:47.400
Yes, yes.
link |
01:10:48.440
I mean, it's a very interesting, you know,
link |
01:10:50.840
sort of history of science like phenomenon.
link |
01:10:53.300
I mean, the best analogy that I can see
link |
01:10:55.920
is what happened with the early days
link |
01:10:58.240
of computability and computation theory.
link |
01:11:00.600
You know, Turing machines were invented in 1936.
link |
01:11:03.520
People sort of understand computation
link |
01:11:06.040
in terms of Turing machines,
link |
01:11:07.280
but actually there had been preexisting theories
link |
01:11:09.920
of computation, combinators, general recursive functions,
link |
01:11:12.920
Lambda calculus, things like this.
link |
01:11:14.880
But people hadn't, those hadn't been concrete enough
link |
01:11:18.280
that people could really wrap their arms around them
link |
01:11:20.320
and understand what was going on.
link |
01:11:21.800
And I think what we're gonna see in this case
link |
01:11:23.480
is that a bunch of these mathematical theories,
link |
01:11:26.000
including some very,
link |
01:11:28.080
I mean, one of the things that's really interesting
link |
01:11:29.720
is one of the most abstract things
link |
01:11:31.840
that's come out of sort of mathematics,
link |
01:11:36.240
higher category theory, things about infinity group voids,
link |
01:11:39.680
things like this, which to me always just seemed
link |
01:11:41.640
like they were floating off into the stratosphere,
link |
01:11:44.160
ionosphere of mathematics, turn out to be things
link |
01:11:48.300
which our sort of theory anchors down
link |
01:11:52.000
to something fairly definite and says are super relevant
link |
01:11:56.240
to the way that we can understand how physics works.
link |
01:11:59.240
Give me a sec.
link |
01:12:00.080
By the way, I just threw a hat on.
link |
01:12:01.560
You've said that with this metaphor analogy
link |
01:12:06.400
that the theory of everything is a big mountain
link |
01:12:09.360
and you have a sense that however far we are up the mountain,
link |
01:12:14.360
that the Wolfram physics model view of the universe
link |
01:12:21.280
is at least the right mountain.
link |
01:12:22.600
We're the right mountain, yes, without question.
link |
01:12:25.440
Which aspect of it is the right mountain?
link |
01:12:27.880
So for example, I mean, so there's so many aspects
link |
01:12:31.000
to just the way of the Wolfram physics project,
link |
01:12:34.560
the way it approaches the world that's clean, crisp,
link |
01:12:39.560
and unique and powerful, so there's a discreet nature to it,
link |
01:12:45.320
there's a hypergraph, there's a computational nature,
link |
01:12:48.960
there's a generative aspect, you start from nothing,
link |
01:12:51.600
you generate everything, do you think the actual model
link |
01:12:56.920
is actually a really good one,
link |
01:12:58.320
or do you think this general principle
link |
01:13:00.160
from simplicity generating complexity is the right,
link |
01:13:02.880
like what aspect of the mountain is the correct?
link |
01:13:05.040
Yeah, right, I think that the kind of the meta idea
link |
01:13:10.080
about using simple computational systems to do things,
link |
01:13:14.080
that's the ultimate big paradigm
link |
01:13:18.080
that is sort of super important.
link |
01:13:21.560
The details of the particular model are very nice and clean
link |
01:13:25.560
and allow one to actually understand what's going on.
link |
01:13:27.880
They are not unique, and in fact, we know that.
link |
01:13:30.600
We know that there's a very, very, very, very,
link |
01:13:34.680
there's a large number of different ways
link |
01:13:37.160
to describe essentially the same thing.
link |
01:13:38.600
I mean, I can describe things in terms of hypergraphs,
link |
01:13:41.120
I can describe them in terms of higher category theory,
link |
01:13:43.520
I can describe them in a bunch of different ways.
link |
01:13:45.240
They are in some sense all the same thing,
link |
01:13:47.480
but our sort of story about what's going on
link |
01:13:50.240
and the kind of cultural mathematical resonances
link |
01:13:53.600
are a bit different.
link |
01:13:54.720
And I think it's perhaps worth sort of saying a little bit
link |
01:13:57.600
about kind of the foundational ideas
link |
01:14:00.600
of these models and things.
link |
01:14:04.800
Great, so can you maybe, can we like rewind?
link |
01:14:09.920
We've talked about it a little bit,
link |
01:14:11.120
but can you say like what the central idea is
link |
01:14:14.080
of the Wolfram Physics Project?
link |
01:14:16.680
Right, so the question is we're interested
link |
01:14:19.200
in finding sort of simple computational rule
link |
01:14:21.920
that describes our whole universe.
link |
01:14:24.040
Can we just pause on that?
link |
01:14:25.480
It's just so beautiful, that's such a beautiful idea
link |
01:14:30.920
that we can generate our universe
link |
01:14:32.440
from a data structure, a simple structure,
link |
01:14:39.400
simple set of rules, and we can generate our entire universe.
link |
01:14:42.680
Yes, that's the idea. That's awe inspiring.
link |
01:14:44.840
Right, but so the question is how do you actualize that?
link |
01:14:50.480
What might this rule be like?
link |
01:14:52.560
And so one thing you quickly realize is
link |
01:14:55.160
if you're gonna pack everything about our universe
link |
01:14:57.200
into this tiny rule, not much that we are familiar with
link |
01:15:01.240
in our universe will be obvious in that rule.
link |
01:15:05.000
So you don't get to fit all these parameters of the universe,
link |
01:15:07.920
all these features of, you know, this is how space works,
link |
01:15:10.080
this is how time works, et cetera, et cetera, et cetera.
link |
01:15:12.000
You don't get to fit that all in.
link |
01:15:13.080
It all has to be sort of packed in to this thing,
link |
01:15:16.680
something much smaller, much more basic,
link |
01:15:18.640
much lower level machine code, so to speak, than that.
link |
01:15:22.040
And all the stuff that we're familiar with
link |
01:15:23.520
has to kind of emerge from the operation.
link |
01:15:26.240
So the rule in itself,
link |
01:15:27.840
because of the computational reducibility,
link |
01:15:30.440
is not gonna tell you the story.
link |
01:15:32.320
It's not gonna give you the answer to,
link |
01:15:36.600
it's not gonna let you predict
link |
01:15:38.360
what you're gonna have for lunch tomorrow,
link |
01:15:40.600
and it's not going to let you predict
link |
01:15:42.160
basically anything about your life, about the universe.
link |
01:15:44.800
Right, and you're not going to be able to see in that rule,
link |
01:15:47.880
oh, there's the three
link |
01:15:49.160
for the number of dimensions of space and so on.
link |
01:15:51.240
That's not gonna be there.
link |
01:15:52.080
Spacetime is not going to be obviously.
link |
01:15:54.560
Right, so the question is then,
link |
01:15:55.720
what is the universe made of?
link |
01:15:57.760
That's a basic question.
link |
01:16:00.200
And we've had some assumptions
link |
01:16:01.640
about what the universe is made of
link |
01:16:02.960
for the last few thousand years
link |
01:16:04.840
that I think in some cases just turn out not to be right.
link |
01:16:08.680
And the most important assumption
link |
01:16:11.040
is that space is a continuous thing.
link |
01:16:13.960
That is that you can, if you say,
link |
01:16:17.040
let's pick a point in space.
link |
01:16:19.200
We're gonna do geometry.
link |
01:16:20.120
We're gonna pick a point.
link |
01:16:21.520
We can pick a point absolutely anywhere in space.
link |
01:16:24.320
Precise numbers we can specify of where that point is.
link |
01:16:28.080
In fact, Euclid who kind of wrote down
link |
01:16:30.320
the original kind of axiomatization of geometry
link |
01:16:32.960
back in 300 BC or so,
link |
01:16:36.000
his very first definition, he says,
link |
01:16:38.320
a point is that which has no part.
link |
01:16:40.640
A point is this indivisible infinitesimal thing.
link |
01:16:47.520
Okay, so we might've said that about material objects.
link |
01:16:50.440
We might've said that about water, for example.
link |
01:16:52.880
We might've said water is a continuous thing
link |
01:16:54.800
that we can just pick any point we want in some water,
link |
01:16:59.160
but actually we know it isn't true.
link |
01:17:00.760
We know that water is made of molecules that are discrete.
link |
01:17:04.120
And so the question, one fundamental question
link |
01:17:06.560
is what is space made of?
link |
01:17:08.360
And so one of the things that's sort of a starting point
link |
01:17:10.880
for what I've done is to think of space as a discrete thing,
link |
01:17:15.600
to think of there being sort of atoms of space
link |
01:17:18.560
just as there are atoms of material things,
link |
01:17:20.600
although very different kinds of atoms.
link |
01:17:23.120
And by the way, I mean, this idea,
link |
01:17:25.000
you know, there were ancient Greek philosophers
link |
01:17:27.200
who had this idea.
link |
01:17:28.360
There were, you know, Einstein actually thought
link |
01:17:30.280
this is probably how things would work out.
link |
01:17:31.840
I mean, he said, you know, repeatedly he thought
link |
01:17:34.320
that's the way it would work out.
link |
01:17:35.520
We don't have the mathematical tools in our time,
link |
01:17:38.680
which was 1940s, 1950s and so on to explore this.
link |
01:17:42.520
Like the way he thought,
link |
01:17:44.120
you mean that there is something very, very small
link |
01:17:48.280
and discrete that's underlying space.
link |
01:17:52.240
Yes.
link |
01:17:53.080
And that means that, so, you know, the mathematical theory,
link |
01:17:56.600
mathematical theories in physics assume that space
link |
01:17:59.960
can be described just as a continuous thing.
link |
01:18:02.400
You can just pick coordinates
link |
01:18:04.000
and the coordinates can have any values.
link |
01:18:06.000
And that's how you define space.
link |
01:18:07.840
Space is this just sort of background sort of theater
link |
01:18:11.680
on which the universe operates.
link |
01:18:13.600
But can we draw a distinction between space
link |
01:18:17.240
as a thing that could be described by three values,
link |
01:18:22.280
coordinates, and how you're,
link |
01:18:25.400
are you using the word space more generally when you say?
link |
01:18:29.320
No, I'm just talking about space
link |
01:18:30.960
as in what we experience in the universe.
link |
01:18:34.320
So that you think this 3D aspect of it is fundamental.
link |
01:18:38.440
No, I don't think that 3D is fundamental at all, actually.
link |
01:18:40.840
I think that the thing that has been assumed
link |
01:18:45.160
is that space is this continuous thing
link |
01:18:48.200
where you can just describe it by,
link |
01:18:49.480
let's say three numbers, for instance.
link |
01:18:51.320
But most important thing about that
link |
01:18:53.160
is that you can describe it by precise numbers
link |
01:18:56.080
because you can pick any point in space
link |
01:18:58.200
and you can talk about motions,
link |
01:18:59.640
any infinitesimal motion in space.
link |
01:19:01.800
And that's what continuous means.
link |
01:19:03.320
That's what continuous means.
link |
01:19:04.240
That's what, you know, Newton invented calculus
link |
01:19:06.120
to describe these kind of continuous small variations
link |
01:19:08.600
and so on.
link |
01:19:09.440
That was, that's kind of a fundamental idea
link |
01:19:11.400
from Euclid on that's been a fundamental idea about space.
link |
01:19:15.360
And so.
link |
01:19:16.200
Is that right or wrong?
link |
01:19:18.800
It's not right.
link |
01:19:20.000
It's not right.
link |
01:19:20.960
It's right at the level of our experience most of the time.
link |
01:19:25.720
It's not right at the level of the machine code,
link |
01:19:27.760
so to speak.
link |
01:19:28.920
And so.
link |
01:19:29.760
Machine code.
link |
01:19:31.040
Yeah, of the simulation.
link |
01:19:32.200
That's right.
link |
01:19:33.040
That's right.
link |
01:19:33.880
They're the very lowest level of the fabric of the universe,
link |
01:19:36.960
at least under the Wolfram physics model
link |
01:19:41.960
is your senses is discrete.
link |
01:19:44.240
Right.
link |
01:19:45.080
So now what does that mean?
link |
01:19:46.320
So it means what is space then?
link |
01:19:49.160
So in models, the basic idea is you say
link |
01:19:54.160
there are these sort of atoms of space.
link |
01:19:56.400
They're these points that represent,
link |
01:19:59.080
you know, represent places in space,
link |
01:20:02.040
but they're just discrete points.
link |
01:20:03.960
And the only thing we know about them
link |
01:20:06.120
is how they're connected to each other.
link |
01:20:08.000
We don't know where they are.
link |
01:20:09.480
They don't have coordinates.
link |
01:20:10.520
We don't get to say this is a position, such and such.
link |
01:20:12.920
It's just, here's a big bag of points.
link |
01:20:15.280
Like in our universe,
link |
01:20:16.120
there might be 10 to the 100 of these points.
link |
01:20:18.440
And all we know is this point is connected
link |
01:20:21.640
to this other point.
link |
01:20:22.480
So it's like, you know,
link |
01:20:23.480
all we have is the friend network, so to speak.
link |
01:20:25.560
We don't have, you know, people's, you know,
link |
01:20:27.960
physical addresses.
link |
01:20:29.120
All we have is the friend network of these points.
link |
01:20:31.560
Yeah.
link |
01:20:32.400
The underlying nature of reality is kind of like a Facebook.
link |
01:20:35.240
We don't know their location, but we have the friends.
link |
01:20:37.240
Yeah, yeah, right.
link |
01:20:38.080
We know which point is connected to which other points.
link |
01:20:41.960
And that's all we know.
link |
01:20:43.480
And so you might say, well,
link |
01:20:44.320
how on earth can you get something
link |
01:20:46.040
which is like our experience of, you know,
link |
01:20:49.200
what seems like continuous space?
link |
01:20:50.560
Well, the answer is,
link |
01:20:51.640
by the time you have 10 to the 100 of these things,
link |
01:20:54.520
those connections can work in such a way
link |
01:20:57.840
that on a large scale,
link |
01:20:59.720
it will seem to be like continuous space
link |
01:21:02.320
in let's say three dimensions
link |
01:21:03.800
or some other number of dimensions
link |
01:21:05.240
or 2.6 dimensions or whatever else.
link |
01:21:07.760
Because they're much, much, much, much larger.
link |
01:21:10.360
So like the number of relationships here we're talking about
link |
01:21:15.200
is just a humongous amount.
link |
01:21:16.480
So the kind of thing you're talking about
link |
01:21:18.880
is very, very, very small relative
link |
01:21:20.640
to our experience of daily life.
link |
01:21:22.720
Right, so I mean, you know,
link |
01:21:23.760
we don't know exactly the size,
link |
01:21:25.080
but maybe 10 to the minus,
link |
01:21:30.400
maybe around 10 to the minus 100 meters.
link |
01:21:32.760
So, you know, the size of, to give a comparison,
link |
01:21:34.960
the size of a proton is 10 to the minus 15 meters.
link |
01:21:38.480
And so this is something incredibly tiny compared to that.
link |
01:21:42.440
And the idea that from that would emerge
link |
01:21:45.960
the experience of continuous space is mind blowing.
link |
01:21:51.040
Well, what's your intuition why that's possible?
link |
01:21:53.520
Like, first of all, I mean, we'll get into it,
link |
01:21:57.480
but I don't know if we will
link |
01:21:59.320
through the medium of conversation,
link |
01:22:01.840
but the construct of hypergraphs is just beautiful.
link |
01:22:06.400
Right.
link |
01:22:07.240
Cellular automata are beautiful.
link |
01:22:08.200
We'll talk about it.
link |
01:22:09.040
But this thing about, you know,
link |
01:22:11.120
continuity arising from discrete systems
link |
01:22:14.160
is in today's world is actually not so surprising.
link |
01:22:17.240
I mean, you know, your average computer screen, right?
link |
01:22:19.480
Every computer screen is made of discrete pixels.
link |
01:22:21.920
Yet we have the, you know,
link |
01:22:23.680
we have the idea that we're seeing
link |
01:22:25.440
these continuous pictures.
link |
01:22:27.000
I mean, it's, you know,
link |
01:22:27.840
the fact that on a large scale,
link |
01:22:29.480
continuity can arise from lots of discrete elements.
link |
01:22:33.120
This is at some level unsurprising now.
link |
01:22:35.640
Wait, wait, wait, wait, wait, wait.
link |
01:22:37.000
But the pixels have a very definitive structure
link |
01:22:42.360
of neighbors on a computer screen.
link |
01:22:46.000
Right.
link |
01:22:46.840
There's no concept of spatial,
link |
01:22:50.520
of space inherent in the underlying fabric of reality.
link |
01:22:55.760
Right, right, right.
link |
01:22:56.600
So the point is that, but there are cases where there are.
link |
01:22:59.920
So for example, let's just imagine you have a square grid.
link |
01:23:03.400
Okay, and at every point on the grid,
link |
01:23:05.360
you have one of these atoms of space
link |
01:23:07.680
and it's connected to four other,
link |
01:23:09.480
four other atoms of space on the, you know,
link |
01:23:11.440
Northeast, Southwest corners, right?
link |
01:23:14.480
There you have something where if you zoom out from that,
link |
01:23:17.600
it's like a computer screen.
link |
01:23:19.040
Yeah, so the relationship creates the spatial,
link |
01:23:23.240
like the relationship creates a constraint,
link |
01:23:26.720
which then in an emergent sense creates a like,
link |
01:23:33.080
yeah, like basically a spatial coordinate for that thing.
link |
01:23:37.720
Yeah, right.
link |
01:23:38.560
Even though the individual point doesn't have a space.
link |
01:23:40.560
Even though the individual point doesn't know anything,
link |
01:23:42.320
it just knows what its neighbors are.
link |
01:23:45.000
On a large scale, it can be described by saying,
link |
01:23:48.840
oh, it looks like it's a, you know,
link |
01:23:50.960
this grid is zoomed out grid.
link |
01:23:52.800
You can say, well, you can describe these different points
link |
01:23:54.920
by saying they have certain positions,
link |
01:23:56.480
coordinates, et cetera.
link |
01:23:57.840
Now, in the sort of real setup,
link |
01:23:59.920
it's more complicated than that.
link |
01:24:00.920
It isn't just a square grid or something.
link |
01:24:03.040
It's something much more dynamic and complicated,
link |
01:24:05.720
which we'll talk about.
link |
01:24:07.200
But so, you know, the first idea,
link |
01:24:10.800
the first key idea is, you know,
link |
01:24:12.720
what's the universe made of?
link |
01:24:13.840
It's made of atoms of space basically
link |
01:24:15.720
with these connections between them.
link |
01:24:17.760
What kind of connections do they have?
link |
01:24:19.320
Well, so the simplest kind of thing you might say is,
link |
01:24:23.000
we've got something like a graph
link |
01:24:25.200
where every atom of space,
link |
01:24:28.440
where we have these edges that go between,
link |
01:24:31.200
these connections that go between atoms of space.
link |
01:24:33.120
We're not saying how long these edges are.
link |
01:24:34.960
We're just saying there is a connection
link |
01:24:36.360
from this place, from this atom to this atom.
link |
01:24:39.080
Just a quick pause,
link |
01:24:40.600
because there's a lot of very people that listen to this.
link |
01:24:44.520
Just to clarify, because I did a poll actually,
link |
01:24:46.920
what do you think a graph is a long time ago?
link |
01:24:49.640
And it's kind of funny how few people
link |
01:24:52.080
know the term graph outside of computer science.
link |
01:24:55.920
It's good.
link |
01:24:56.760
Let's call it a network.
link |
01:24:57.600
I think that's it.
link |
01:24:58.440
Let's call it a network is better.
link |
01:24:59.280
So, but every time, I like the word graph though.
link |
01:25:00.920
So let's define, let's just say that a graph
link |
01:25:03.880
will use terms nodes and edges maybe.
link |
01:25:06.680
And it's just the nodes represent some abstract entity
link |
01:25:11.600
and then the edges represent relationships
link |
01:25:13.960
between those entities.
link |
01:25:14.840
Right, exactly.
link |
01:25:15.880
So that's what a graph says.
link |
01:25:16.800
Sorry, so there you go.
link |
01:25:18.480
So that's the basic structure.
link |
01:25:20.600
That is the simplest case of a basic structure.
link |
01:25:23.360
Actually, it tends to be better to think about hypergraphs.
link |
01:25:27.840
So a hypergraph is just, instead of saying
link |
01:25:31.560
there are connections between pairs of things,
link |
01:25:34.600
we say there are connections between any number of things.
link |
01:25:37.160
So there might be ternary edges.
link |
01:25:39.200
So instead of just having two points
link |
01:25:42.920
are connected by an edge,
link |
01:25:44.520
you say three points are all associated with a hyperedge,
link |
01:25:48.320
are all connected by a hyperedge.
link |
01:25:50.200
That's just, at some level, that's a detail.
link |
01:25:54.120
It's a detail that happens to make the, for me,
link |
01:25:57.880
sort of in the history of this project,
link |
01:26:00.000
the realization that you could do things that way
link |
01:26:02.320
broke out of certain kinds of arbitrariness
link |
01:26:04.360
that I felt that there was in the model
link |
01:26:06.080
before I had seen how this worked.
link |
01:26:07.880
I mean, a hypergraph can be mapped to a graph.
link |
01:26:12.440
It's just a convenient representation.
link |
01:26:14.360
Mathematical speaking.
link |
01:26:15.320
That's correct. That's correct.
link |
01:26:16.920
But so then, so, okay, so the first question,
link |
01:26:19.680
the first idea of these models of ours is
link |
01:26:22.720
space is made of these connected sort of atoms of space.
link |
01:26:26.520
The next idea is space is all there is.
link |
01:26:29.800
There's nothing except for this space.
link |
01:26:31.840
So in traditional ideas in physics,
link |
01:26:33.880
people have said there's space, it's kind of a background.
link |
01:26:36.960
And then there's matter, all these particles, electrons,
link |
01:26:39.200
all these other things, which exist in space, right?
link |
01:26:43.360
But in this model, one of the key ideas is
link |
01:26:46.200
there's nothing except space.
link |
01:26:48.400
So in other words, everything that exists in the universe
link |
01:26:52.160
is a feature of this hypergraph.
link |
01:26:54.640
So how can that possibly be?
link |
01:26:55.920
Well, the way that works is
link |
01:26:58.040
that there are certain structures in this hypergraph
link |
01:27:01.640
where you say that little twisty knotted thing,
link |
01:27:05.760
we don't know exactly how this works yet,
link |
01:27:07.240
but we have sort of idea about how it works mathematically.
link |
01:27:10.960
This sort of twisted knotted thing,
link |
01:27:13.000
that's the core of an electron.
link |
01:27:14.840
This thing over there that has this different form,
link |
01:27:17.360
that's something else.
link |
01:27:18.520
So the different peculiarities of the structure
link |
01:27:21.040
of this graph are the very things
link |
01:27:24.800
that we think of as the particles inside the space,
link |
01:27:29.000
but in fact, it's just a property of the space.
link |
01:27:31.760
Mind blowing, first of all, that it's mind blowing,
link |
01:27:34.960
and we'll probably talk in its simplicity and beauty.
link |
01:27:38.520
Yes, I think it's very beautiful.
link |
01:27:40.480
I mean, this is, I'm...
link |
01:27:41.320
But okay, but that's space,
link |
01:27:43.080
and then there's another concept
link |
01:27:44.560
we didn't really kind of mention,
link |
01:27:45.880
but you think it of computation as a transformation.
link |
01:27:50.480
Let's talk about time in a second.
link |
01:27:51.680
Let's just, I mean, on the subject of space,
link |
01:27:55.360
there's this question of kind of what,
link |
01:27:57.680
there's this idea, there is this hypergraph,
link |
01:27:59.880
it represents space,
link |
01:28:01.760
and it represents everything that's in space.
link |
01:28:03.640
The features of that hypergraph,
link |
01:28:05.320
you can say certain features in this part we do know,
link |
01:28:08.320
certain features of the hypergraph
link |
01:28:09.680
represent the presence of energy, for example,
link |
01:28:11.800
or the presence of mass or momentum,
link |
01:28:13.960
and we know what the features of the hypergraph
link |
01:28:16.080
that represent those things are,
link |
01:28:17.920
but it's all just the same hypergraph.
link |
01:28:20.320
So one thing you might ask is,
link |
01:28:22.040
you know, if you just look at this hypergraph and you say,
link |
01:28:24.280
and we're gonna talk about sort of what the hypergraph does,
link |
01:28:27.160
but if you say, you know,
link |
01:28:28.600
how much of what's going on in this hypergraph
link |
01:28:31.320
is things we know and care about,
link |
01:28:34.040
like particles and atoms and electrons
link |
01:28:36.520
and all this kind of thing,
link |
01:28:37.560
and how much is just the background of space?
link |
01:28:40.880
So it turns out, so far as in one rough estimate of this,
link |
01:28:45.440
everything that we care about in the universe
link |
01:28:47.880
is only one part in 10 to the 120
link |
01:28:50.800
of what's actually going on.
link |
01:28:52.040
The vast majority of what's happening
link |
01:28:54.040
is purely things that maintain the structure of space.
link |
01:28:57.360
That, in other words, that the things that are
link |
01:28:59.760
the features of space that are the things
link |
01:29:03.280
that we consider notable,
link |
01:29:04.640
like the presence of particles and so on,
link |
01:29:06.480
that's a tiny little piece of froth
link |
01:29:08.760
on the top of all this activity
link |
01:29:10.680
that mostly is just intended to,
link |
01:29:13.560
you know, mostly, I can't say intended,
link |
01:29:15.160
there's no intention here,
link |
01:29:16.480
that just maintains the structure of space.
link |
01:29:20.600
Let me load that in.
link |
01:29:24.160
It just makes me feel so good as a human being.
link |
01:29:27.880
To be the froth on the one in a 10 to the 120
link |
01:29:31.800
or something of, well.
link |
01:29:33.120
And also just humbling how,
link |
01:29:37.960
in this mathematical framework,
link |
01:29:39.880
how much work needs to be done
link |
01:29:41.400
on the infrastructure of our universe.
link |
01:29:44.840
Right, to maintain the infrastructure of our universe
link |
01:29:46.840
is a lot of work.
link |
01:29:47.960
We are merely writing a little tiny things
link |
01:29:51.560
on top of that infrastructure.
link |
01:29:53.360
But you were just starting to talk a little bit about,
link |
01:29:57.480
we talked about space,
link |
01:29:59.800
that represents all the stuff that's in the universe.
link |
01:30:03.280
The question is, what does that stuff do?
link |
01:30:06.080
And for that, we have to start talking about time
link |
01:30:09.200
and what is time and so on.
link |
01:30:11.440
And, you know, one of the basic idea of this model
link |
01:30:15.240
is time is the progression of computation.
link |
01:30:18.000
So in other words, we have a structure of space
link |
01:30:21.040
and there is a rule that says
link |
01:30:23.000
how that structure of space will change.
link |
01:30:25.120
And it's the application,
link |
01:30:26.160
the repeated application of that rule
link |
01:30:28.480
that defines the progress of time.
link |
01:30:32.400
And what does the rule look like
link |
01:30:34.040
in the space of hypergraphs?
link |
01:30:36.000
Right, so what the rule says is something like,
link |
01:30:38.640
if you have a little tiny piece of hypergraph
link |
01:30:40.440
that looks like this,
link |
01:30:42.200
then it will be transformed into a piece of hypergraph
link |
01:30:44.720
that looks like this.
link |
01:30:46.640
So that's all it says.
link |
01:30:47.880
It says you pick up these elements of space
link |
01:30:51.280
and you can think of these edges,
link |
01:30:54.360
these hyper edges as being relations
link |
01:30:56.040
between elements in space.
link |
01:30:57.720
You might pick up these two relations
link |
01:31:01.200
between elements in space.
link |
01:31:03.280
And we're not saying where those elements are
link |
01:31:04.840
or what they are,
link |
01:31:05.680
but every time there's a certain arrangement
link |
01:31:07.520
of elements in space,
link |
01:31:09.240
then arrangement in the sense of the way they're connected,
link |
01:31:12.200
then we transform it into some other arrangement.
link |
01:31:14.640
So there's a little tiny pattern
link |
01:31:16.280
and you transform it into another little pattern.
link |
01:31:18.520
That's right.
link |
01:31:19.360
And then because of this,
link |
01:31:20.840
I mean, again, it's kind of similar to cellular automata
link |
01:31:23.280
in that like on paper, the rule looks like super simple.
link |
01:31:26.840
It's like, yeah, okay.
link |
01:31:30.480
Yeah, right, from this, the universe can be born.
link |
01:31:33.680
But like once you start applying it,
link |
01:31:36.720
beautiful structure starts being,
link |
01:31:39.040
potentially can be created.
link |
01:31:41.000
And what you're doing is you're applying that rule
link |
01:31:43.560
to different parts,
link |
01:31:45.400
like anytime you match it within the hypergraph.
link |
01:31:49.320
And then one of the like incredibly beautiful
link |
01:31:53.160
and interesting things to think about
link |
01:31:55.640
is the order in which you apply that rule,
link |
01:31:59.280
because that pattern appears all over the place.
link |
01:32:02.000
Right, so this is a big complicated thing,
link |
01:32:04.400
very hard to wrap one's brain around, okay?
link |
01:32:06.200
So you say the rule is every time you see this little pattern
link |
01:32:10.680
transform it in this way.
link |
01:32:12.520
But yet, as you look around the space
link |
01:32:15.800
that represents the universe,
link |
01:32:17.400
there may be zillions of places
link |
01:32:18.760
where that little pattern occurs.
link |
01:32:20.600
So what it says is just do this,
link |
01:32:24.440
apply this rule wherever you feel like.
link |
01:32:26.920
And what is extremely non trivial is,
link |
01:32:31.360
well, okay, so this is happening sort of
link |
01:32:33.520
in computer science terms, sort of asynchronously,
link |
01:32:35.920
you're just doing it wherever you feel like doing it.
link |
01:32:39.000
And the only constraint is
link |
01:32:41.120
that if you're going to apply the rule somewhere,
link |
01:32:43.880
the things to which you apply the rule,
link |
01:32:46.760
the little elements to which you apply the rule,
link |
01:32:50.080
if they have to be,
link |
01:32:54.200
okay, well, you can think of each application of the rule
link |
01:32:56.560
as being kind of an event that happens in the universe.
link |
01:32:59.840
And the input to an event has to be ready
link |
01:33:04.760
for the event to occur.
link |
01:33:06.240
That is, if one event occurred,
link |
01:33:08.240
if one transformation occurred,
link |
01:33:10.000
and it produced a particular atom of space,
link |
01:33:12.720
then that atom of space has to already exist
link |
01:33:17.200
before another transformation that's going to apply
link |
01:33:20.880
to that atom of space can occur.
link |
01:33:23.240
So that's like the prerequisite for the event.
link |
01:33:25.840
That's right, that's right.
link |
01:33:26.920
So that defines a kind of,
link |
01:33:30.520
this sort of set of causal relationships between events.
link |
01:33:33.840
It says, this event has to have happened before this event.
link |
01:33:38.000
But that is...
link |
01:33:40.200
But that's not a very limiting constraint.
link |
01:33:42.960
No, it's not.
link |
01:33:44.080
And what's interesting...
link |
01:33:44.960
You still get the zillion,
link |
01:33:47.200
that's a technical term, options.
link |
01:33:49.760
That's correct.
link |
01:33:50.680
But, okay, so this is where things get a little bit more
link |
01:33:53.760
elaborate, but...
link |
01:33:54.600
But they're mind blowing, so...
link |
01:33:56.640
Right, but so what happens is,
link |
01:33:59.120
so the first thing you might say is,
link |
01:34:01.160
you know, let's...
link |
01:34:02.520
Well, okay, so this question about the freedom
link |
01:34:04.800
of which event you do when.
link |
01:34:07.200
Well, let me sort of state an answer and then explain it.
link |
01:34:10.200
Okay, the validity of special relativity
link |
01:34:14.120
is a consequence of the fact that in some sense,
link |
01:34:17.000
it doesn't matter in what order you do
link |
01:34:19.240
these underlying things, so long as they respect
link |
01:34:22.160
this kind of set of causal relationships.
link |
01:34:25.400
So...
link |
01:34:26.240
And that's the part that's in a certain sense
link |
01:34:30.640
is a really important one,
link |
01:34:31.800
but the fact that it sometimes doesn't matter,
link |
01:34:35.640
that's a...
link |
01:34:37.080
I don't know what to...
link |
01:34:37.920
That's another, like, beautiful thing.
link |
01:34:38.760
Well, okay, so there's this idea
link |
01:34:40.520
of what I call causal invariance.
link |
01:34:42.560
Causal invariance, exactly.
link |
01:34:44.080
So that's a...
link |
01:34:44.920
Really, really powerful idea.
link |
01:34:46.240
Right, it's a powerful idea,
link |
01:34:47.640
which has actually arisen in different forms
link |
01:34:50.080
many times in the history of mathematics,
link |
01:34:52.040
mathematical logic, even computer science,
link |
01:34:54.880
has many different names.
link |
01:34:56.800
I mean, our particular version of it
link |
01:34:58.200
is a little bit tighter than other versions,
link |
01:35:00.240
but it's basically the same idea.
link |
01:35:01.480
Here's how to think about that idea.
link |
01:35:03.680
So imagine that...
link |
01:35:05.440
Well, let's talk about it in terms of math for a second.
link |
01:35:08.120
Let's say you're doing algebra and you're told,
link |
01:35:10.600
you know, multiply out this series of polynomials
link |
01:35:14.280
that are multiplied together, okay?
link |
01:35:16.800
You say, well, which order should I do that in?
link |
01:35:19.120
Say, well, do I multiply the third one by the fourth one
link |
01:35:21.480
and then do it by the first one?
link |
01:35:22.640
Or do I do the fifth one by the sixth one and then do that?
link |
01:35:25.920
Well, it turns out it doesn't matter.
link |
01:35:27.800
You can multiply them out in any order,
link |
01:35:29.720
you'll always get the same answer.
link |
01:35:31.560
That's a property...
link |
01:35:33.760
If you think about kind of making a kind of network
link |
01:35:36.240
that represents in what order you do things,
link |
01:35:38.720
you'll get different orders
link |
01:35:40.680
for different ways of multiplying things out,
link |
01:35:42.760
but you'll always get the same answer.
link |
01:35:44.880
Same thing if you...
link |
01:35:45.720
Let's say you're sorting.
link |
01:35:46.680
You've got a bunch of A's and B's.
link |
01:35:48.880
They're in random, some random order,
link |
01:35:50.280
you know, BAA, BBBAA, whatever.
link |
01:35:53.400
And you have a little rule that says,
link |
01:35:55.240
every time you see BA, flip it around to AB, okay?
link |
01:36:00.000
Eventually you apply that rule enough times,
link |
01:36:02.280
you'll have sorted the string
link |
01:36:03.800
so that it's all the A's first and then all the B's.
link |
01:36:07.400
Again, there are many different orders
link |
01:36:10.040
in which you can do that to many different sort of places
link |
01:36:13.200
where you can apply that update.
link |
01:36:15.280
In the end, you'll always get the string sorted the same way.
link |
01:36:18.520
I know with sorting the string, it sounds obvious.
link |
01:36:22.320
That's to me surprising
link |
01:36:24.680
that there is in complicated systems,
link |
01:36:28.320
obviously with a string,
link |
01:36:29.840
but in a hypergraph that the application of the rule,
link |
01:36:33.760
asynchronous rule can lead to the same results sometimes.
link |
01:36:36.720
Yes, yes, that is not obvious.
link |
01:36:39.080
And it was something that, you know,
link |
01:36:40.720
I sort of discovered that idea for these kinds of systems
link |
01:36:44.080
and back in the 1990s.
link |
01:36:45.520
And for various reasons, I was not satisfied
link |
01:36:50.360
by how sort of fragile finding that particular property was.
link |
01:36:54.320
And let me just make another point,
link |
01:36:56.360
which is that it turns out that even if the underlying rule
link |
01:37:01.120
does not have this property of causal invariance,
link |
01:37:03.880
it can turn out that every observation
link |
01:37:06.200
made by observers of the rule can,
link |
01:37:09.240
they can impose what amounts to causal invariance
link |
01:37:12.680
on the rule.
link |
01:37:13.880
We can explain that.
link |
01:37:14.720
It's a little bit more complicated.
link |
01:37:15.560
I mean, technically that has to do with this idea
link |
01:37:18.000
of completions, which is something that comes up
link |
01:37:20.160
in term rewriting systems,
link |
01:37:21.760
automated theorem proving systems and so on.
link |
01:37:24.040
But let's ignore that for a second.
link |
01:37:26.320
We can come to that later.
link |
01:37:27.560
But is it useful to talk about observation?
link |
01:37:29.840
Not yet.
link |
01:37:30.680
Not yet.
link |
01:37:31.720
It's so great.
link |
01:37:33.160
So there's some concept of causal invariance
link |
01:37:35.560
as you apply these rules in an asynchronous way,
link |
01:37:39.480
you can think of those transformations as events.
link |
01:37:42.200
So there's this hypergraph that represents space
link |
01:37:44.400
and all of these events happening in the space
link |
01:37:47.000
and the graph grows in interesting complicated ways.
link |
01:37:50.440
And eventually the froth arises of what we experience
link |
01:37:54.560
as human existence.
link |
01:37:56.200
So that's it.
link |
01:37:57.440
That's some version of the picture,
link |
01:37:58.920
but let's explain a little bit more.
link |
01:38:00.800
Exactly.
link |
01:38:01.640
What's a little more detail like?
link |
01:38:03.600
Right.
link |
01:38:04.440
Well, so one thing that is sort of surprising
link |
01:38:06.760
in this theory is one of the sort of achievements
link |
01:38:10.080
of 20th century physics was kind of bringing
link |
01:38:12.000
space and time together.
link |
01:38:13.880
That was, you know, special relativity.
link |
01:38:15.720
People talk about space time, this sort of unified thing
link |
01:38:19.320
where space and time kind of a mixed
link |
01:38:21.880
and there's a nice mathematical formalism
link |
01:38:24.680
that in which, you know, space and time sort of appear
link |
01:38:28.040
as part of the space time continuum,
link |
01:38:30.760
the space time, you know, four vectors and things like this.
link |
01:38:34.480
You know, we talk about time as the fourth dimension
link |
01:38:37.320
and all these kinds of things.
link |
01:38:38.800
It's, you know, and it seems like the theory of relativity
link |
01:38:42.200
sort of says space and time are fundamentally
link |
01:38:44.040
the same kind of thing.
link |
01:38:45.400
So one of the things that took a while to understand
link |
01:38:48.680
in this approach of mine is that in my kind of approach,
link |
01:38:54.880
space and time are really not fundamentally
link |
01:38:56.680
the same kind of thing.
link |
01:38:57.520
Space is the extension of this hypergraph.
link |
01:39:00.480
Time is the kind of progress of this inexorable computation
link |
01:39:04.440
of these rules getting applied to the hypergraph.
link |
01:39:07.040
So it's, they seem like very different kinds of things.
link |
01:39:10.000
And so that at first seems like
link |
01:39:12.760
how can that possibly be right?
link |
01:39:14.160
How can that possibly be Lorentz invariant?
link |
01:39:16.440
That's the term for things being, you know,
link |
01:39:18.840
following the rules of special relativity.
link |
01:39:21.600
Well, it turns out that when you have causal invariants
link |
01:39:26.120
that, and let's see, we can, it's worth explaining
link |
01:39:30.120
a little bit how this works.
link |
01:39:31.000
It's a little bit elaborate,
link |
01:39:32.440
but the basic point is that even though space and time
link |
01:39:38.960
sort of come from very different places,
link |
01:39:41.640
it turns out that the rules of sort of space time
link |
01:39:45.360
that special relativity talks about come out of this model
link |
01:39:51.080
when you're looking at large enough systems.
link |
01:39:53.680
So a way to think about this, you know,
link |
01:39:56.080
in terms of when you're looking at large enough systems,
link |
01:39:59.480
the part of that story is when you look at some fluid
link |
01:40:03.800
like water, for example, there are equations
link |
01:40:06.280
that govern the flow of water.
link |
01:40:08.920
Those equations are things that apply on a large scale.
link |
01:40:12.720
If you look at the individual molecules,
link |
01:40:14.400
they don't know anything about those equations.
link |
01:40:16.280
It's just the sort of the large scale effect
link |
01:40:19.360
of those molecules turns out to follow those equations.
link |
01:40:22.800
And it's the same kind of thing happening in our models.
link |
01:40:25.960
I know this might be a small point,
link |
01:40:27.960
but it might be a very big one.
link |
01:40:29.600
We've been talking about space and time
link |
01:40:32.560
at the lowest level of the model, which is space.
link |
01:40:35.960
The hypergraph time is the evolution of this hypergraph.
link |
01:40:39.860
But there's also space time that we think about
link |
01:40:43.160
and general relativity for your special relativity.
link |
01:40:47.400
Like how do you go from the lowest source code
link |
01:40:54.080
of space and time as we're talking about
link |
01:40:55.960
to the more traditional terminology of space and time?
link |
01:40:58.720
So the key thing is this thing we call the causal graph.
link |
01:41:01.840
So the causal graph is the graph
link |
01:41:03.760
of causal relationships between events.
link |
01:41:06.660
So every one of these little updating events,
link |
01:41:08.980
every one of these little transformations
link |
01:41:10.320
of the hypergraph happens somewhere in the hypergraph,
link |
01:41:13.360
happens at some stage in the computation.
link |
01:41:16.800
That's an event.
link |
01:41:18.240
That event has a causal relationship to other events
link |
01:41:22.280
in the sense that if another event needs as its input,
link |
01:41:27.360
the output from the first event,
link |
01:41:29.440
there will be a causal relationship
link |
01:41:31.140
of the future event will depend on the past event.
link |
01:41:35.220
So you can say it has a causal connection.
link |
01:41:37.960
And so you can make this graph
link |
01:41:39.760
of causal relationships between events.
link |
01:41:42.440
That graph of causal relationships,
link |
01:41:44.240
causal invariance implies that that graph is unique.
link |
01:41:47.680
It doesn't matter even though you think,
link |
01:41:51.280
oh, I'm, let's say we were sorting a string, for example,
link |
01:41:54.160
I did that particular transposition of characters
link |
01:41:57.720
at this time, then I did that one, then I did this one.
link |
01:42:00.180
Turns out if you look at the network of connections
link |
01:42:03.000
between those updating events, that network is the same.
link |
01:42:06.680
It's the, if you were to, the structure.
link |
01:42:11.040
So in other words, if you were to draw that,
link |
01:42:13.360
if you were to put that network on a picture
link |
01:42:15.440
of where you're doing all the updating,
link |
01:42:17.100
the places where you put the nodes of the network
link |
01:42:20.080
will be different, but the way the nodes are connected
link |
01:42:22.440
will always be the same.
link |
01:42:23.560
So, but the causal graph is, I don't know,
link |
01:42:27.320
it's kind of an observation, it's not enforced,
link |
01:42:31.080
it's just emergent from a set of events.
link |
01:42:33.760
It's a feature of, okay, so what it is is.
link |
01:42:36.440
The characteristic, I guess, of the way events happen.
link |
01:42:38.860
Right, it's an event can't happen
link |
01:42:40.800
until its input is ready.
link |
01:42:42.520
And so that creates this network of causal relationships.
link |
01:42:46.360
And that's the causal graph.
link |
01:42:48.280
And the thing that the next thing to realize is,
link |
01:42:51.560
okay, we, when you're going to observe
link |
01:42:54.480
what happens in the universe,
link |
01:42:56.400
you have to sort of make sense of this causal graph.
link |
01:42:59.560
So, and you are an observer who yourself
link |
01:43:02.840
is part of this causal graph.
link |
01:43:05.040
And so that means, so let me give you an example
link |
01:43:07.520
of how that works.
link |
01:43:08.360
So imagine we have a really weird theory of physics
link |
01:43:11.160
of the world where it says this updating process,
link |
01:43:15.100
there's only gonna be one update at every moment in time.
link |
01:43:18.180
And there's just gonna be like a Turing machine.
link |
01:43:19.720
It has a little head that runs around
link |
01:43:21.520
and just is always just updating one thing at a time.
link |
01:43:23.680
So you say, I have a theory of physics
link |
01:43:26.040
and the theory of physics says,
link |
01:43:27.480
there's just this one little place where things get updated.
link |
01:43:30.440
You say, that's completely crazy because,
link |
01:43:32.960
it's plainly obvious that things are being updated
link |
01:43:35.860
sort of at the same time.
link |
01:43:37.120
Async obviously, yeah, at the same time, yeah.
link |
01:43:39.280
But the fact is that the thing is that if I'm talking to you
link |
01:43:44.240
and you seem to be being updated as I'm being updated,
link |
01:43:47.200
but if there's just this one little head
link |
01:43:48.960
that's running around updating things,
link |
01:43:51.000
I will not know whether you've been updated or not
link |
01:43:53.440
until I'm updated.
link |
01:43:55.440
So in other words, draw this causal graph
link |
01:43:58.640
of the causal relationship between the updatings in you
link |
01:44:01.000
and the updatings in me,
link |
01:44:02.440
it'll still be the same causal graph,
link |
01:44:04.400
whether even though the underlying sort of story
link |
01:44:07.120
of what happens is, oh, there's just this one little thing
link |
01:44:10.120
and it goes and updates in different places in the universe.
link |
01:44:12.840
So is that clear or is that a hypothesis?
link |
01:44:18.040
Is that clear that there's a unique causal graph?
link |
01:44:21.440
If there's causal invariance, there's unique causal graph.
link |
01:44:24.880
So it's okay to think of what we're talking about
link |
01:44:28.060
as a hypergraph and the operations on it
link |
01:44:30.600
as a kind of touring machine with a single head,
link |
01:44:32.960
like a single guy running around updating stuff.
link |
01:44:37.120
Is that safe to intuitively think of it this way?
link |
01:44:40.520
Let me think about that for a second.
link |
01:44:41.680
Yes, I think so.
link |
01:44:42.560
I think there's nothing, it doesn't matter.
link |
01:44:44.800
I mean, you can say, okay, there is one,
link |
01:44:47.980
the reason I'm pausing for a second is that I'm wondering,
link |
01:44:52.880
well, when you say running around,
link |
01:44:55.840
depends how far it jumps every time it runs.
link |
01:44:57.960
Yeah, yeah, that's right.
link |
01:44:59.160
But I mean like one operation at a time.
link |
01:45:02.000
Yeah, you can think of it as one operation at a time.
link |
01:45:03.760
It's easier for the human brain to think of it that way
link |
01:45:06.680
as opposed to simultaneous.
link |
01:45:08.240
Well, maybe it's not, okay, but the thing is
link |
01:45:10.720
that's not how we experience the world.
link |
01:45:12.720
What we experience is we look around,
link |
01:45:15.760
everything seems to be happening
link |
01:45:17.880
at successive moments in time everywhere in space.
link |
01:45:21.000
Yes.
link |
01:45:21.840
That is the, and that's partly a feature
link |
01:45:23.880
of our particular construction.
link |
01:45:25.580
I mean, that is the speed of light is really fast
link |
01:45:28.480
compared to, you know, we look around, you know,
link |
01:45:30.680
I can see maybe a hundred feet away right now.
link |
01:45:33.800
You know, it's the, my brain does not process very much
link |
01:45:38.800
in the time it takes light to go a hundred feet.
link |
01:45:41.280
The brain operates at a scale of hundreds of milliseconds
link |
01:45:44.040
or something like that, I don't know.
link |
01:45:45.320
Right.
link |
01:45:46.160
And speed of light is much faster.
link |
01:45:47.600
Right, you know, light goes,
link |
01:45:49.160
in a billionth of a second light has gone afoot.
link |
01:45:51.000
So it goes a billion feet every second.
link |
01:45:53.720
There's certain moments through this conversation
link |
01:45:56.480
where I imagine the absurdity of the fact
link |
01:46:01.200
that there's two descendants of apes modeled by a hypergraph
link |
01:46:05.080
that are communicating with each other
link |
01:46:06.400
and experiencing this whole thing
link |
01:46:09.160
as a real time simultaneous update with,
link |
01:46:13.440
I'm taking in photons from you right now,
link |
01:46:15.440
but there's something much, much deeper going on here.
link |
01:46:19.160
Right, it does have a.
link |
01:46:20.000
It's paralyzing sometimes to just.
link |
01:46:22.560
Yes.
link |
01:46:23.400
To remember that.
link |
01:46:24.220
Right, no, I mean, you know, it's a, you know.
link |
01:46:26.400
Sorry.
link |
01:46:27.240
Yes, yes, no.
link |
01:46:28.080
As a small little tangent, I just remembered
link |
01:46:30.800
that we're talking about,
link |
01:46:32.360
I mean, about the fabric of reality.
link |
01:46:37.080
Right, so we've got this causal graph
link |
01:46:40.080
that represents the sort of causal relationships
link |
01:46:41.920
between all these events in the universe.
link |
01:46:43.760
That causal graph kind of is a representation of space time,
link |
01:46:47.680
but our experience of it requires
link |
01:46:50.800
that we pick reference frames.
link |
01:46:52.960
This is kind of a key idea.
link |
01:46:54.200
Einstein had this idea that what that means is
link |
01:46:57.440
we have to say, what are we going to pick
link |
01:47:01.040
as being the sort of what we define
link |
01:47:04.540
as simultaneous moments in time?
link |
01:47:07.680
So for example, we can say, you know,
link |
01:47:11.400
how do we set our clocks?
link |
01:47:13.040
You know, if we've got a spacecraft landing on Mars,
link |
01:47:16.420
you know, do we say that, you know,
link |
01:47:17.840
what time is it landing at?
link |
01:47:19.480
Was it, you know, even though there's a 20 minute
link |
01:47:21.640
speed of light delay or something, you know,
link |
01:47:23.760
what time do we say it landed at?
link |
01:47:25.340
How do we set up sort of time coordinates for the world?
link |
01:47:30.020
And that turns out to be that there's kind of
link |
01:47:32.400
this arbitrariness to how we set these reference frames
link |
01:47:35.960
that defines sort of what counts as simultaneous.
link |
01:47:39.200
And what is the essence of special relativity
link |
01:47:42.020
is to think about reference frames going at different speeds
link |
01:47:45.880
and to think about sort of how they assign,
link |
01:47:48.760
what counts as space, what counts as time and so on.
link |
01:47:52.320
That's all a bit technical, but the basic bottom line is
link |
01:47:55.680
that this causal invariance property,
link |
01:47:58.920
that means that it's always the same causal graph,
link |
01:48:01.800
independent of how you slice it with these reference frames,
link |
01:48:04.760
you'll always sort of see the same physical processes go on.
link |
01:48:07.840
And that's basically why special relativity works.
link |
01:48:10.380
So there's something like special relativity,
link |
01:48:14.620
like everything around space and time
link |
01:48:17.680
that fits this idea of the causal graph.
link |
01:48:22.900
Right, well, you know, one way to think about it is
link |
01:48:24.900
given that you have a basic structure
link |
01:48:27.280
that just involves updating things in these,
link |
01:48:31.040
you know, connected updates and looking at
link |
01:48:33.280
the causal relationships between connected updates,
link |
01:48:35.640
that's enough when you unravel the consequences of that,
link |
01:48:39.760
that together with the fact that there are lots
link |
01:48:41.500
of these things and that you can take a continuum limit
link |
01:48:43.880
and so on implies special relativity.
link |
01:48:46.900
And so that, it's kind of not a big deal
link |
01:48:51.000
because it's kind of a, you know,
link |
01:48:52.920
it was completely unobvious when you started off
link |
01:48:56.520
with saying, we've got this graph,
link |
01:48:57.860
it's being updated in time, et cetera, et cetera, et cetera,
link |
01:49:00.200
that just looks like nothing to do with special relativity.
link |
01:49:03.280
And yet you get that.
link |
01:49:05.040
And what, I mean, then the thing,
link |
01:49:08.080
I mean, this was stuff that I figured out back in the 1990s.
link |
01:49:11.160
The next big thing you get is general relativity.
link |
01:49:16.200
And so in this hypergraph,
link |
01:49:18.920
the sort of limiting structure,
link |
01:49:20.700
when you have a very big hypergraph,
link |
01:49:22.440
you can think of as being just like, you know,
link |
01:49:24.480
water seems continuous on a large scale.
link |
01:49:27.040
So this hypergraph seems continuous on a large scale.
link |
01:49:30.140
One question is, you know,
link |
01:49:31.660
how many dimensions of space does it correspond to?
link |
01:49:35.200
So one question you can ask is,
link |
01:49:36.440
if you've just got a bunch of points
link |
01:49:38.000
and they're connected together,
link |
01:49:39.480
how do you deduce what effective dimension of space
link |
01:49:43.160
that bundle of points corresponds to?
link |
01:49:46.000
And that's pretty easy to explain.
link |
01:49:47.680
So basically if you say you've got a point
link |
01:49:50.520
and you look at how many neighbors does that point have?
link |
01:49:52.760
Okay, imagine it's on a square grid.
link |
01:49:54.680
Then it'll have four neighbors.
link |
01:49:56.260
Go another level out.
link |
01:49:58.280
How many neighbors do you get then?
link |
01:50:00.000
What you realize is as you go more and more levels out,
link |
01:50:02.800
as you go more and more distance on the graph out,
link |
01:50:05.920
you're capturing something which is essentially a circle
link |
01:50:09.700
in two dimensions so that, you know,
link |
01:50:11.920
the number of the area of a circle is pi R squared.
link |
01:50:14.720
So it's the number of points that you get to
link |
01:50:18.400
goes up like the distance you've gone squared.
link |
01:50:21.540
And in general, in D dimensional space,
link |
01:50:24.440
it's R to the power D.
link |
01:50:25.940
It's the number of points you get to
link |
01:50:28.680
if you go R steps on the graph grows like
link |
01:50:32.720
the number of steps you go to the power of the dimension.
link |
01:50:35.560
And that's a way that you can estimate
link |
01:50:37.760
the effective dimension of one of these graphs.
link |
01:50:39.960
So what does that grow to?
link |
01:50:41.080
So how does the dimension grow?
link |
01:50:42.540
There's a, I mean, obviously the visual aspect
link |
01:50:45.900
of these hypergraphs,
link |
01:50:47.380
they're often visualized in three dimensions.
link |
01:50:50.120
Right.
link |
01:50:50.960
So there's a certain kind of structure,
link |
01:50:54.640
like you said, there's, I mean, a circle, a sphere,
link |
01:50:58.880
there's a planar aspect to it,
link |
01:51:02.360
to this graph to where it kind of,
link |
01:51:04.680
it almost starts creating a surface,
link |
01:51:06.760
like a complicated surface, but a surface.
link |
01:51:09.120
So how does that connect to effective dimension?
link |
01:51:11.880
Okay, so if you can lay out the graph
link |
01:51:14.400
in such a way that the points in the graph that,
link |
01:51:18.880
you know, the points that are neighbors on the graph
link |
01:51:21.360
are neighbors as you lay them out,
link |
01:51:23.520
and you can do that in two dimensions,
link |
01:51:25.680
then it's gonna approximate a two dimensional thing.
link |
01:51:28.360
If you can't do that in two dimensions,
link |
01:51:29.760
if everything would have to fold over a lot
link |
01:51:31.240
in two dimensions,
link |
01:51:32.240
then it's not approximating a two dimensional thing.
link |
01:51:34.080
Maybe you can lay it out in three dimensions.
link |
01:51:36.200
Maybe you have to lay it out in five dimensions
link |
01:51:38.640
to have it be the case
link |
01:51:39.640
that it sort of smoothly lays out like that.
link |
01:51:42.000
Well, but okay, so I apologize
link |
01:51:44.720
for the different tangent questions,
link |
01:51:46.060
but you know, there's an infinity number of possible rules.
link |
01:51:51.320
So we have to look for rules
link |
01:51:54.600
that create the kind of structures
link |
01:51:58.520
that are reminiscent for,
link |
01:52:01.560
that have echoes of the different physics theories in them.
link |
01:52:05.080
So what kind of rules,
link |
01:52:06.600
is there something simple to be said
link |
01:52:08.240
about the kind of rules that you have found beautiful,
link |
01:52:12.080
that you have found powerful?
link |
01:52:13.480
Right, so I mean, what, you know,
link |
01:52:15.400
one of the features of computational irreducibility is,
link |
01:52:18.760
it's very, you can't say in advance,
link |
01:52:21.980
what's gonna happen with any particular,
link |
01:52:23.960
you can't say, I'm gonna pick these rules
link |
01:52:26.000
from this part of rule space, so to speak,
link |
01:52:28.900
because they're gonna be the ones that are gonna work.
link |
01:52:30.960
That's, you can make some statements along those lines,
link |
01:52:33.360
but you can't generally say that.
link |
01:52:35.200
Now, you know, the state of what we've been able to do
link |
01:52:38.280
is, you know, different properties of the universe,
link |
01:52:40.680
like dimensionality, you know, integer dimensionality,
link |
01:52:44.600
features of other features of quantum mechanics,
link |
01:52:47.960
things like that.
link |
01:52:48.960
At this point, what we've got is,
link |
01:52:50.600
we've got rules that any one of those features,
link |
01:52:55.380
we can get a rule that has that feature.
link |
01:52:58.080
Yeah, so the.
link |
01:52:58.920
We don't have the sort of, the final,
link |
01:53:00.720
here's a rule which has all of these features,
link |
01:53:02.640
we do not have that yet.
link |
01:53:03.680
So if I were to try to summarize
link |
01:53:06.960
the Wolfram physics project, which is, you know,
link |
01:53:11.380
something that's been in your brain for a long time,
link |
01:53:13.920
but really has just exploded in activity,
link |
01:53:17.280
you know, only just months ago.
link |
01:53:19.160
Yes.
link |
01:53:20.040
So it's an evolving thing, and next week,
link |
01:53:23.480
I'll try to publish this conversation
link |
01:53:24.920
as quickly as possible, because by the time it's published,
link |
01:53:27.840
already new things will probably have come out.
link |
01:53:29.640
So if I were to summarize it,
link |
01:53:33.180
we've talked about the basics of,
link |
01:53:35.940
there's a hypergraph that represents space,
link |
01:53:38.360
there is transformations in that hypergraph
link |
01:53:42.360
that represents time.
link |
01:53:44.720
The progress of time.
link |
01:53:45.560
The progress of time, there's a causal graph
link |
01:53:47.840
that's a characteristic of this,
link |
01:53:49.640
and the basic process of science,
link |
01:53:53.720
of, yeah, of science within the Wolfram physics model
link |
01:53:58.640
is to try different rules and see which properties
link |
01:54:02.560
of physics that we know of, known physical theories,
link |
01:54:06.120
are, appear within the graphs that emerge from that rule.
link |
01:54:10.700
That's what I thought it was going to be.
link |
01:54:12.400
Uh oh, okay.
link |
01:54:13.660
So what is it?
link |
01:54:16.080
It turns out we can do a lot better than that.
link |
01:54:18.200
It turns out that using kind of mathematical ideas,
link |
01:54:21.400
we can say, and computational ideas,
link |
01:54:25.140
we can make general statements,
link |
01:54:28.400
and those general statements turn out to correspond
link |
01:54:31.520
to things that we know from 20th century physics.
link |
01:54:34.080
In other words, the idea of you just try a bunch of rules
link |
01:54:36.940
and see what they do,
link |
01:54:37.780
that's what I thought we were gonna have to do.
link |
01:54:40.240
But in fact, we can say, given causal invariance
link |
01:54:43.760
and computational irreducibility, we can derive,
link |
01:54:47.480
and this is where it gets really pretty interesting,
link |
01:54:49.480
we can derive special relativity,
link |
01:54:51.120
we can derive general relativity,
link |
01:54:52.920
we can derive quantum mechanics.
link |
01:54:55.140
And that's where things really start to get exciting,
link |
01:54:58.280
is, you know, it wasn't at all obvious to me
link |
01:55:01.340
that even if we were completely correct,
link |
01:55:03.360
and even if we had, you know, this is the rule,
link |
01:55:05.240
you know, even if we found the rule,
link |
01:55:06.920
to be able to say, yes, it corresponds
link |
01:55:08.940
to things we already know,
link |
01:55:10.360
I did not expect that to be the case.
link |
01:55:12.660
And...
link |
01:55:13.500
So for somebody who is a simple mind
link |
01:55:16.920
and definitely not a physicist, not even close,
link |
01:55:19.460
what does derivation mean in this case?
link |
01:55:22.760
Okay, so let me, this is an interesting question.
link |
01:55:26.940
Okay, so there's, so one thing...
link |
01:55:29.160
In the context of computational irreducibility.
link |
01:55:31.880
Yeah, yeah, right, right.
link |
01:55:32.920
So what you have to do, let me go back to, again,
link |
01:55:36.840
the mundane example of fluids and water
link |
01:55:39.000
and things like that, right?
link |
01:55:40.400
So you have a bunch of molecules bouncing around.
link |
01:55:44.040
You can say, just as a piece of mathematics,
link |
01:55:47.340
I happen to do this from cellular automata
link |
01:55:49.260
back in the mid 1980s, you can say,
link |
01:55:52.160
just as a matter of mathematics,
link |
01:55:54.200
you can say the continuum limit
link |
01:55:57.240
of these little molecules bouncing around
link |
01:55:59.240
is the Navier Stokes equations.
link |
01:56:01.640
That's just a piece of mathematics.
link |
01:56:03.260
It's not, it doesn't rely on...
link |
01:56:06.640
You have to make certain assumptions
link |
01:56:08.480
that you have to say there's enough randomness
link |
01:56:10.880
in the way the molecules bounce around
link |
01:56:12.400
that certain statistical averages work,
link |
01:56:14.240
et cetera, et cetera, et cetera.
link |
01:56:15.680
Okay, it is a very similar derivation
link |
01:56:18.320
to derive, for example, the Einstein equations.
link |
01:56:21.220
Okay, so the way that works, roughly,
link |
01:56:23.720
the Einstein equations are about curvature of space.
link |
01:56:26.740
Curvature of space, I talked about sort of
link |
01:56:29.080
how you can figure out dimension of space.
link |
01:56:31.840
There's a similar kind of way of figuring out
link |
01:56:34.260
if you just sort of say, you know,
link |
01:56:37.240
you're making a larger and larger ball
link |
01:56:39.040
or larger and larger, if you draw a circle
link |
01:56:40.920
on the surface of the earth, for example,
link |
01:56:42.940
you might think the area of a circle is pi r squared,
link |
01:56:45.980
but on the surface of the earth,
link |
01:56:47.940
because it's a sphere, it's not flat,
link |
01:56:50.560
the area of a circle isn't precisely pi r squared.
link |
01:56:53.360
As the circle gets bigger, the area is slightly smaller
link |
01:56:56.240
than you would expect from the formula pi r squared
link |
01:56:58.160
as a little correction term that depends on the ratio
link |
01:57:01.040
of the size of the circle to the radius of the earth.
link |
01:57:03.700
Okay, so it's the same basic thing,
link |
01:57:05.680
allows you to measure from one of these hypergraphs
link |
01:57:08.240
what is its effective curvature.
link |
01:57:11.240
And that's...
link |
01:57:12.080
So the little piece of mathematics
link |
01:57:15.440
that explains special general relativity
link |
01:57:20.960
can map nicely to describe fundamental property
link |
01:57:25.400
of the hypergraphs, the curvature of the hypergraphs.
link |
01:57:27.560
So special relativity is about the relationship
link |
01:57:31.280
of time to space.
link |
01:57:32.720
General relativity is about curvature
link |
01:57:35.280
and this space represented by this hypergraph.
link |
01:57:38.600
So what is the curvature of a hypergraph?
link |
01:57:40.760
Okay, so first I have to explain,
link |
01:57:43.120
what we're explaining is,
link |
01:57:44.680
first thing you have to have is a notion of dimension.
link |
01:57:47.120
You don't get to talk about curvature of things.
link |
01:57:49.280
If you say, oh, it's a curved line,
link |
01:57:51.800
but I don't know what a line is yet.
link |
01:57:53.800
So...
link |
01:57:54.640
Yeah, what is the dimension of a hypergraph then?
link |
01:57:56.960
From where, we've talked about effective dimension, but...
link |
01:58:00.580
Right, that's what this is about.
link |
01:58:03.080
What this is about is, you have your hypergraph,
link |
01:58:05.180
it's got a trillion nodes in it.
link |
01:58:07.380
What is it roughly like?
link |
01:58:08.740
Is it roughly like a grid, a two dimensional grid?
link |
01:58:11.460
Is it roughly like all those nodes are arranged online?
link |
01:58:15.240
What's it roughly like?
link |
01:58:16.740
And there's a pretty simple mathematical way
link |
01:58:19.600
to estimate that by just looking at this thing
link |
01:58:23.960
I was describing, this sort of the size of a ball
link |
01:58:26.340
that you construct in the hypergraph.
link |
01:58:28.240
That's a, you just measure that,
link |
01:58:29.800
you can just compute it on a computer for a given hypergraph
link |
01:58:33.000
and you can say, oh, this thing is wiggling around,
link |
01:58:35.160
but it's roughly corresponds to two or something like that,
link |
01:58:38.240
or roughly corresponds to 2.6 or whatever.
link |
01:58:41.440
So that's how you have a notion of dimension
link |
01:58:44.080
in these hypergraphs.
link |
01:58:45.640
Curvature is something a little bit beyond that.
link |
01:58:48.600
If you look at how the size of this ball increases
link |
01:58:52.120
as you increase its radius,
link |
01:58:53.960
curvature is a correction
link |
01:58:55.400
to the size increase associated with dimension.
link |
01:58:58.920
It's a sort of a second order term
link |
01:59:01.120
in determining the size.
link |
01:59:03.360
Just like the area of a circle is roughly pi R squared.
link |
01:59:07.000
So it goes up like R squared.
link |
01:59:08.520
The two is because it's in two dimensions,
link |
01:59:11.080
but when that circle is drawn on a big sphere,
link |
01:59:14.440
the actual formula is pi R squared times one minus
link |
01:59:19.400
R squared over A squared and some coefficient.
link |
01:59:22.640
So in other words, there's a correction to,
link |
01:59:25.000
and that correction term, that gives you curvature.
link |
01:59:28.240
And that correction term
link |
01:59:29.720
is what makes this hypergraph correspond,
link |
01:59:32.880
have the potential to correspond to curved space.
link |
01:59:35.840
Now, the next question is, is that curvature,
link |
01:59:38.480
is the way that curvature works
link |
01:59:40.400
the way that Einstein's equations for general relativity,
link |
01:59:43.800
is it the way they say it should work?
link |
01:59:46.040
And the answer is yes.
link |
01:59:49.160
And so how does that work?
link |
01:59:54.560
The calculation of the curvature of this hypergraph
link |
01:59:57.240
for some set of rules?
link |
01:59:59.760
No, it doesn't matter what the rules are.
link |
02:00:01.800
So long as they have causal invariance
link |
02:00:03.360
and computational irreducibility,
link |
02:00:05.440
and they lead to finite dimensional space,
link |
02:00:09.360
noninfinite dimensional space.
link |
02:00:11.600
Noninfinite dimensional.
link |
02:00:13.600
It can grow infinitely,
link |
02:00:14.760
but it can't be infinite dimensional.
link |
02:00:16.560
So what is a infinitely dimensional hypergraph look like?
link |
02:00:19.840
So that means, for example, so in a tree,
link |
02:00:22.600
you start from one root of the tree,
link |
02:00:25.400
it doubles, doubles again, doubles again, doubles again.
link |
02:00:28.360
And that means if you ask the question,
link |
02:00:30.720
starting from a given point,
link |
02:00:32.360
how many points do you get to?
link |
02:00:34.160
Remember, in like a circle,
link |
02:00:35.360
you get to R squared, the two there.
link |
02:00:37.840
On a tree, you get to, for example, two to the R.
link |
02:00:41.240
It's exponential dimensional, so to speak,
link |
02:00:43.320
or infinite dimensional.
link |
02:00:44.360
Do you have a sense of, in the space of all possible rules,
link |
02:00:48.480
how many lead to infinitely dimensional hypergraphs?
link |
02:00:53.720
Is that? No.
link |
02:00:55.280
Okay.
link |
02:00:56.120
Is that an important thing to know?
link |
02:00:57.920
Yes, it's an important thing to know.
link |
02:00:59.520
I would love to know the answer to that.
link |
02:01:01.560
But it gets a little bit more complicated
link |
02:01:03.520
because, for example, it's very possibly the case
link |
02:01:05.720
that in our physical universe,
link |
02:01:07.440
that the universe started infinite dimensional.
link |
02:01:10.000
And it only, as the Big Bang,
link |
02:01:13.800
it was very likely infinite dimensional.
link |
02:01:16.080
And as the universe sort of expanded and cooled,
link |
02:01:21.280
its dimension gradually went down.
link |
02:01:23.720
And so one of the bizarre possibilities,
link |
02:01:25.400
which actually there are experiments you can do
link |
02:01:27.120
to try and look at this,
link |
02:01:28.520
the universe can have dimension fluctuations.
link |
02:01:31.000
So in other words,
link |
02:01:31.840
we think we live in a three dimensional universe,
link |
02:01:33.400
but actually there may be places
link |
02:01:35.600
where it's actually 3.01 dimensional,
link |
02:01:37.920
or where it's 2.99 dimensional.
link |
02:01:40.520
And it may be that in the very early universe,
link |
02:01:43.320
it was actually infinite dimensional,
link |
02:01:45.200
and it's only a late stage phenomenon
link |
02:01:47.200
that we end up getting three dimensional space.
link |
02:01:49.240
But from your perspective of the hypergraph,
link |
02:01:51.920
one of the underlying assumptions you kind of implied,
link |
02:01:55.240
but you have a sense, a hope set of assumptions
link |
02:01:59.640
that the rules that underlie our universe,
link |
02:02:03.120
or the rule that underlies our universe is static.
link |
02:02:08.200
Is that one of the assumptions
link |
02:02:10.160
you're currently operating under?
link |
02:02:11.840
Yes, but there's a footnote to that,
link |
02:02:14.840
which we should get to,
link |
02:02:15.680
because it requires a few more steps.
link |
02:02:17.560
Well, actually then, let's backtrack to the curvature,
link |
02:02:19.920
because we're talking about as long as it's finite dimensional.
link |
02:02:25.320
Finite dimensional computational irreducibility
link |
02:02:28.000
and causal invariance,
link |
02:02:29.680
then it follows that the large scale structure
link |
02:02:35.800
will follow Einstein's equations.
link |
02:02:37.880
And now let me again, qualify that a little bit more,
link |
02:02:40.720
there's a little bit more complexity to it.
link |
02:02:43.120
The, okay, so Einstein's equations in their simplest form
link |
02:02:48.120
apply to the vacuum, no matter, just the vacuum.
link |
02:02:51.720
And they say, in particular, what they say is,
link |
02:02:54.200
if you have, so there's this term GD6,
link |
02:02:58.520
that's a term that means shortest path,
link |
02:03:00.920
comes from measuring the shortest paths on the Earth.
link |
02:03:03.680
So you look at a bunch of, a bundle of GD6,
link |
02:03:07.600
a bunch of shortest paths,
link |
02:03:09.520
it's like the paths that photons
link |
02:03:11.040
would take between two points.
link |
02:03:13.040
Then the statement of Einstein's equations,
link |
02:03:14.960
it's basically a statement about a certain the,
link |
02:03:18.040
that as you look at a bundle of GD6,
link |
02:03:20.360
the structure of space has to be such that,
link |
02:03:22.920
although the cross sectional area of this bundle may,
link |
02:03:27.800
although the actual shape of the cross section may change,
link |
02:03:30.000
the cross sectional area does not.
link |
02:03:31.800
That's a version, that's the most simple minded version
link |
02:03:35.280
of R mu nu minus a half R G mu nu equals zero,
link |
02:03:38.960
which is the more mathematical version
link |
02:03:41.040
of Einstein's equations.
link |
02:03:42.440
It's a statement of the thing called the Ritchie tensor
link |
02:03:45.360
is equal to zero.
link |
02:03:46.840
That's Einstein's equations for the vacuum.
link |
02:03:50.080
Okay, so we get that as a result of this model,
link |
02:03:54.400
but footnote, big footnote,
link |
02:03:57.840
because all the matter in the universe
link |
02:04:00.280
is the stuff we actually care about.
link |
02:04:01.680
The vacuum is not stuff we care about.
link |
02:04:03.560
So the question is, how does matter come into this?
link |
02:04:06.440
And for that, you have to understand what energy is
link |
02:04:09.720
in these models.
link |
02:04:11.120
And one of the things that we realized, you know,
link |
02:04:15.280
late last year was that there's a very simple interpretation
link |
02:04:20.360
of energy in these models, okay?
link |
02:04:22.560
And energy is basically, well, intuitively,
link |
02:04:28.000
it's the amount of activity in these hypergraphs
link |
02:04:32.720
and the way that that remains over time.
link |
02:04:36.840
So a little bit more formally,
link |
02:04:38.640
you can think about this causal graph
link |
02:04:41.560
as having these edges that represent causal relationships.
link |
02:04:44.880
You can think about, oh boy,
link |
02:04:46.120
there's one more concept that we didn't get to.
link |
02:04:47.920
It's the notion of space like hypersurfaces.
link |
02:04:51.800
So this is not as scary as it sounds.
link |
02:04:55.800
It's a common notion in general activity.
link |
02:04:59.720
The notion is you are defining what is a possibly,
link |
02:05:04.720
where in space time might be a particular moment in time.
link |
02:05:13.960
So in other words, what is a consistent set of places
link |
02:05:18.200
where you can say, this is happening now, so to speak.
link |
02:05:21.760
And you make the series of sort of slices
link |
02:05:25.600
through the space time, through this causal graph
link |
02:05:29.200
to represent sort of what we consider
link |
02:05:32.000
to be successive moments in time.
link |
02:05:34.680
It's somewhat arbitrary because you can deform that
link |
02:05:37.720
if you're going at a different speed in a special activity,
link |
02:05:39.880
you tip those things, there are different kinds
link |
02:05:44.520
of deformations, but only certain deformations
link |
02:05:46.800
are allowed by the structure of the causal graph.
link |
02:05:48.400
Anyway, be that as it may, the basic point is
link |
02:05:52.360
there is a way of figuring out,
link |
02:05:54.880
you say, what is the energy associated
link |
02:05:57.120
with what's going on in this hypergraph?
link |
02:06:00.400
And the answer is there is a precise definition of that.
link |
02:06:04.360
And it is the formal way to say it is,
link |
02:06:06.840
it's the flux of causal edges
link |
02:06:08.560
through space like hypersurfaces.
link |
02:06:10.680
The slightly less formal way to say it,
link |
02:06:12.280
it's basically the amount of activity.
link |
02:06:14.480
See, the reason it gets tricky is you might say
link |
02:06:18.000
it's the amount of activity per unit volume
link |
02:06:21.000
in this hypergraph, but you haven't defined what volume is.
link |
02:06:25.280
So it's a little bit, you have to be a little more careful.
link |
02:06:27.520
But this hypersurface gives some more formalism to that.
link |
02:06:30.600
Yeah, yeah, it gives a way to connect that.
link |
02:06:32.840
But intuitive, we should think about as the just activity.
link |
02:06:36.400
Right, so the amount of activity that kind of remains
link |
02:06:39.640
in one place in the hypergraph corresponds to energy.
link |
02:06:42.800
The amount of activity that is kind of where an activity here
link |
02:06:45.800
affects an activity somewhere else,
link |
02:06:48.160
corresponds to momentum.
link |
02:06:50.480
And so one of the things that's kind of cool
link |
02:06:53.840
is that I'm trying to think about
link |
02:06:55.600
how to say this intuitively.
link |
02:06:56.680
The mathematics is easy,
link |
02:06:57.720
but the intuitive version, I'm not sure.
link |
02:06:59.800
But basically the way that things sort of stay
link |
02:07:01.640
in the same place and have activity
link |
02:07:03.960
is associated with rest mass.
link |
02:07:05.920
And so one of the things that you get to derive
link |
02:07:08.080
is E equals MC squared.
link |
02:07:10.800
That is a consequence of this interpretation of energy
link |
02:07:14.840
in terms of the way the causal graph works,
link |
02:07:18.040
which is the whole thing is sort of a consequence
link |
02:07:20.160
of this whole story about updates and hypergraphs and so on.
link |
02:07:23.720
So can you linger on that a little bit?
link |
02:07:26.280
How do we get E equals MC squared?
link |
02:07:28.840
So where does the mass come from?
link |
02:07:31.280
Okay, okay.
link |
02:07:32.240
I mean, is there an intuitive, it's okay.
link |
02:07:35.000
First of all, you're pretty deep
link |
02:07:37.720
in the mathematical explorations of this thing right now.
link |
02:07:41.600
We're in a very, we're in a flux currently.
link |
02:07:45.920
So maybe you haven't even had time
link |
02:07:47.960
to think about intuitive explanations, but.
link |
02:07:51.680
Yeah, I mean, this one is, look, roughly what's happening,
link |
02:07:56.320
that derivation is actually rather easy.
link |
02:07:58.400
And everybody, and I've been saying
link |
02:07:59.840
we should pay more attention to this derivation
link |
02:08:01.600
because it's such, you know,
link |
02:08:02.480
cause people care about this one.
link |
02:08:04.320
But everybody says, it's just easy.
link |
02:08:05.880
It's easy.
link |
02:08:07.200
So there's some concept of energy
link |
02:08:09.320
that can be intuitively thought of as the activity,
link |
02:08:12.880
the flux, the level of changes that are occurring
link |
02:08:16.760
based on the transformations within a certain volume,
link |
02:08:19.400
however the heck do you find the volume.
link |
02:08:21.240
Okay, so, and then mass.
link |
02:08:23.560
Well, mass is associated with kind of the energy
link |
02:08:28.560
that does not cause you to,
link |
02:08:30.440
that does not somehow propagate through time.
link |
02:08:34.000
Yeah, I mean, one of the things that was not obvious
link |
02:08:35.960
in the usual formulation of special relativity
link |
02:08:38.400
is that space and time are connected in a certain way.
link |
02:08:42.800
Energy and momentum are also connected in a certain way.
link |
02:08:46.280
The fact that the connection of energy to momentum
link |
02:08:49.080
is analogous to the connection to space
link |
02:08:50.800
between space and time
link |
02:08:52.400
is not self evident in ordinary relativity.
link |
02:08:54.920
It is a consequence of this, of the way this model works.
link |
02:08:58.360
It's an intrinsic consequence of the way this model works.
link |
02:09:00.960
And it's all to do with that,
link |
02:09:02.800
with unraveling that connection
link |
02:09:05.240
that ends up giving you this relationship
link |
02:09:07.720
between energy and, well, it's energy, momentum, mass,
link |
02:09:12.480
they're all connected.
link |
02:09:13.760
And so like, that's hence the general relativity.
link |
02:09:19.560
You have a sense that it appears to be baked in
link |
02:09:24.600
to the fundamental properties
link |
02:09:27.000
of the way these hypergraphs are evolved.
link |
02:09:29.320
Well, I didn't yet get to,
link |
02:09:30.360
so I got as far as special relativity and equals MC squared.
link |
02:09:33.680
The one last step is, in general relativity,
link |
02:09:37.320
the final connection is energy and mass
link |
02:09:41.800
cause curvature in space.
link |
02:09:44.440
And that's something that when you understand
link |
02:09:47.720
this interpretation of energy,
link |
02:09:49.760
and you kind of understand the correspondence
link |
02:09:52.080
to curvature and hypergraphs,
link |
02:09:54.000
then you can finally sort of, the big final answer is,
link |
02:09:57.640
you derive the full version of Einstein's equations
link |
02:10:00.440
for space, time and matter.
link |
02:10:03.320
And that's some.
link |
02:10:04.480
Is that, have you, that last piece with curvature,
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02:10:09.520
have, is that, have you arrived there yet?
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02:10:12.320
Oh yeah, we're there, yes.
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02:10:13.760
And here's the way that we,
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02:10:15.480
here's how we're really, really going to know
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02:10:17.200
we've arrived, okay?
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02:10:18.480
So, you know, we have the mathematical derivation,
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02:10:20.720
it's all fine, but, you know,
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02:10:22.720
mathematical derivations, okay.
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02:10:25.000
So one thing that's sort of a,
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02:10:27.720
you know, we're taking this limit
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02:10:29.240
of what happens when you, the limit,
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02:10:31.160
you have to look at things which are large
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02:10:32.920
compared to the size of an elementary length,
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02:10:35.240
small compared to the whole size of the universe,
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02:10:37.440
large compared to certain kinds of fluctuations,
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02:10:40.480
blah, blah, blah.
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02:10:41.600
There's a, there's a, there's a tower
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02:10:43.360
of many, many of these mathematical limits
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02:10:45.160
that have to be taken.
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02:10:46.440
So if you're a pure mathematician saying,
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02:10:48.720
where's the precise proof?
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02:10:50.520
It's like, well, there are all these limits,
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02:10:52.480
we can, you know, we can try each one of them
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02:10:54.880
computationally and we could say, yeah, it really works,
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02:10:57.520
but the formal mathematics is really hard to do.
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02:11:00.560
I mean, for example, in the case of deriving
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02:11:03.120
the equations of fluid dynamics from molecular dynamics,
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02:11:06.200
that derivation has never been done.
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02:11:09.000
There is no rigorous version of that derivation.
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02:11:11.360
So, so that could be.
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02:11:12.200
Because you can't do the limits?
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02:11:13.760
Yeah, because you can't do the limits.
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02:11:15.920
But so the limits allow you to try to describe
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02:11:18.320
something general about the system
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02:11:20.280
and very, very particular kinds of limits that you need
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02:11:22.520
to take with these very.
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02:11:23.640
Right, and the limits will definitely work
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02:11:26.000
the way we think they work.
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02:11:27.200
And we can do all kinds of computer experiments.
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02:11:28.760
It's just a hard derivation.
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02:11:29.760
Yeah, it's just, it's just the mathematical structure
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02:11:32.760
kind of, you know, ends up running right into
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02:11:35.240
computational irreducibility.
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02:11:37.080
And you end up with a bunch of, a bunch of difficulty there.
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02:11:39.560
But here's the way that we're getting really confident
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02:11:42.320
that we know completely what we're talking about,
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02:11:43.960
which is when people study things like black hole mergers,
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02:11:47.880
using Einstein's equations, what do they actually do?
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02:11:51.000
Well, they actually use Mathematica or a whole bunch
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02:11:52.800
to analyze the equations and so on.
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02:11:54.440
But in the end, they do numerical relativity,
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02:11:57.360
which means they take these nice mathematical equations
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02:12:01.440
and they break them down so that they can run them
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02:12:03.280
on a computer.
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02:12:04.360
And they break them down into something
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02:12:05.920
which is actually a discrete approximation
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02:12:07.680
to these equations.
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02:12:08.920
Then they run them on a computer, they get results.
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02:12:11.560
Then you look at the gravitational waves
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02:12:12.880
and you see if they match, okay?
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02:12:14.840
It turns out that our model gives you a direct way
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02:12:18.240
to do numerical relativity.
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02:12:19.800
So in other words, instead of saying,
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02:12:21.120
you start from these continuum equations from Einstein,
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02:12:23.960
you break them down into these discrete things,
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02:12:26.280
you run them on a computer,
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02:12:27.600
you say, we're doing it the other way around.
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02:12:28.920
We're starting from these discrete things
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02:12:30.680
that come from our model.
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02:12:31.880
And we're just running big versions on the computer.
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02:12:34.520
And, you know, what we're saying is,
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02:12:37.080
and this is how things will work.
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02:12:39.560
So the way I'm calling this is proof by compilation,
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02:12:43.760
so to speak, that is, in other words,
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02:12:46.480
you're taking something where, you know,
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02:12:49.320
we've got this description of a black hole system.
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02:12:52.320
And what we're doing is we're showing that the, you know,
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02:12:56.120
what we get by just running our model agrees
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02:12:59.320
with what you would get by doing the computation
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02:13:02.720
from the Einstein equations.
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02:13:04.320
As a small tangent or actually a very big tangent,
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02:13:08.360
but proof by compilation is a beautiful concept.
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02:13:15.200
In a sense, the way of doing physics with this model
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02:13:21.400
is by running it or compiling it.
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02:13:26.040
And have you thought about,
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02:13:29.800
and these things can be very large,
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02:13:32.000
is there a totally new possibilities of computing hardware
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02:13:37.000
and computing software,
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