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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,
link |
02:10:09.520
have, is that, have you arrived there yet?
link |
02:10:12.320
Oh yeah, we're there, yes.
link |
02:10:13.760
And here's the way that we,
link |
02:10:15.480
here's how we're really, really going to know
link |
02:10:17.200
we've arrived, okay?
link |
02:10:18.480
So, you know, we have the mathematical derivation,
link |
02:10:20.720
it's all fine, but, you know,
link |
02:10:22.720
mathematical derivations, okay.
link |
02:10:25.000
So one thing that's sort of a,
link |
02:10:27.720
you know, we're taking this limit
link |
02:10:29.240
of what happens when you, the limit,
link |
02:10:31.160
you have to look at things which are large
link |
02:10:32.920
compared to the size of an elementary length,
link |
02:10:35.240
small compared to the whole size of the universe,
link |
02:10:37.440
large compared to certain kinds of fluctuations,
link |
02:10:40.480
blah, blah, blah.
link |
02:10:41.600
There's a, there's a, there's a tower
link |
02:10:43.360
of many, many of these mathematical limits
link |
02:10:45.160
that have to be taken.
link |
02:10:46.440
So if you're a pure mathematician saying,
link |
02:10:48.720
where's the precise proof?
link |
02:10:50.520
It's like, well, there are all these limits,
link |
02:10:52.480
we can, you know, we can try each one of them
link |
02:10:54.880
computationally and we could say, yeah, it really works,
link |
02:10:57.520
but the formal mathematics is really hard to do.
link |
02:11:00.560
I mean, for example, in the case of deriving
link |
02:11:03.120
the equations of fluid dynamics from molecular dynamics,
link |
02:11:06.200
that derivation has never been done.
link |
02:11:09.000
There is no rigorous version of that derivation.
link |
02:11:11.360
So, so that could be.
link |
02:11:12.200
Because you can't do the limits?
link |
02:11:13.760
Yeah, because you can't do the limits.
link |
02:11:15.920
But so the limits allow you to try to describe
link |
02:11:18.320
something general about the system
link |
02:11:20.280
and very, very particular kinds of limits that you need
link |
02:11:22.520
to take with these very.
link |
02:11:23.640
Right, and the limits will definitely work
link |
02:11:26.000
the way we think they work.
link |
02:11:27.200
And we can do all kinds of computer experiments.
link |
02:11:28.760
It's just a hard derivation.
link |
02:11:29.760
Yeah, it's just, it's just the mathematical structure
link |
02:11:32.760
kind of, you know, ends up running right into
link |
02:11:35.240
computational irreducibility.
link |
02:11:37.080
And you end up with a bunch of, a bunch of difficulty there.
link |
02:11:39.560
But here's the way that we're getting really confident
link |
02:11:42.320
that we know completely what we're talking about,
link |
02:11:43.960
which is when people study things like black hole mergers,
link |
02:11:47.880
using Einstein's equations, what do they actually do?
link |
02:11:51.000
Well, they actually use Mathematica or a whole bunch
link |
02:11:52.800
to analyze the equations and so on.
link |
02:11:54.440
But in the end, they do numerical relativity,
link |
02:11:57.360
which means they take these nice mathematical equations
link |
02:12:01.440
and they break them down so that they can run them
link |
02:12:03.280
on a computer.
link |
02:12:04.360
And they break them down into something
link |
02:12:05.920
which is actually a discrete approximation
link |
02:12:07.680
to these equations.
link |
02:12:08.920
Then they run them on a computer, they get results.
link |
02:12:11.560
Then you look at the gravitational waves
link |
02:12:12.880
and you see if they match, okay?
link |
02:12:14.840
It turns out that our model gives you a direct way
link |
02:12:18.240
to do numerical relativity.
link |
02:12:19.800
So in other words, instead of saying,
link |
02:12:21.120
you start from these continuum equations from Einstein,
link |
02:12:23.960
you break them down into these discrete things,
link |
02:12:26.280
you run them on a computer,
link |
02:12:27.600
you say, we're doing it the other way around.
link |
02:12:28.920
We're starting from these discrete things
link |
02:12:30.680
that come from our model.
link |
02:12:31.880
And we're just running big versions on the computer.
link |
02:12:34.520
And, you know, what we're saying is,
link |
02:12:37.080
and this is how things will work.
link |
02:12:39.560
So the way I'm calling this is proof by compilation,
link |
02:12:43.760
so to speak, that is, in other words,
link |
02:12:46.480
you're taking something where, you know,
link |
02:12:49.320
we've got this description of a black hole system.
link |
02:12:52.320
And what we're doing is we're showing that the, you know,
link |
02:12:56.120
what we get by just running our model agrees
link |
02:12:59.320
with what you would get by doing the computation
link |
02:13:02.720
from the Einstein equations.
link |
02:13:04.320
As a small tangent or actually a very big tangent,
link |
02:13:08.360
but proof by compilation is a beautiful concept.
link |
02:13:15.200
In a sense, the way of doing physics with this model
link |
02:13:21.400
is by running it or compiling it.
link |
02:13:26.040
And have you thought about,
link |
02:13:29.800
and these things can be very large,
link |
02:13:32.000
is there a totally new possibilities of computing hardware
link |
02:13:37.000
and computing software,
link |
02:13:38.960
which allows you to perform this kind of compilation?
link |
02:13:42.200
Well, algorithms, software, hardware.
link |
02:13:44.920
So first comment is these models seem to give one
link |
02:13:49.440
a lot of intuition about distributed computing,
link |
02:13:52.480
a lot of different intuition about how to think
link |
02:13:54.680
about parallel computation.
link |
02:13:56.640
And that particularly comes from the quantum mechanics
link |
02:13:58.960
side of things, which we didn't talk about much yet.
link |
02:14:01.880
But the question of what, you know,
link |
02:14:04.720
given our current computer hardware,
link |
02:14:07.760
how can we most efficiently simulate things?
link |
02:14:10.120
That's actually partly a story of the model itself,
link |
02:14:12.920
because the model itself has deep parallelism in it.
link |
02:14:16.160
The ways that we are simulating it,
link |
02:14:17.760
we're just starting to be able to use that deep parallelism
link |
02:14:21.080
to be able to be more efficient
link |
02:14:22.600
in the way that we simulate things.
link |
02:14:24.400
But in fact, the structure of the model itself
link |
02:14:27.880
allows us to think about parallel computation
link |
02:14:30.280
in different ways.
link |
02:14:31.520
And one of my realizations is that, you know,
link |
02:14:34.600
so it's very hard to get in your brain
link |
02:14:37.000
how you deal with parallel computation.
link |
02:14:38.520
And you're always worrying about, you know,
link |
02:14:40.240
if multiple things can happen on different computers
link |
02:14:42.720
at different times, oh, what happens
link |
02:14:44.640
if this thing happens before that thing?
link |
02:14:46.440
And we've really got, you know,
link |
02:14:47.520
we have these race conditions where something can race
link |
02:14:49.720
to get to the answer before another thing.
link |
02:14:51.800
And you get all tangled up because you don't know
link |
02:14:54.040
which thing is gonna come in first.
link |
02:14:55.960
And usually when you do parallel computing,
link |
02:14:58.320
there's a big obsession to lock things down
link |
02:15:00.480
to the point where you've had locks and mutexes
link |
02:15:03.920
and God knows what else,
link |
02:15:05.240
where you've arranged it so that there can only be
link |
02:15:09.600
one sequence of things that can happen.
link |
02:15:11.560
So you don't have to think about
link |
02:15:12.640
all the different kinds of things that can happen.
link |
02:15:14.760
Well, in these models, physics is throwing us into,
link |
02:15:18.200
forcing us to think about all these possible things
link |
02:15:20.240
that can happen.
link |
02:15:21.240
But these models together with what we know from physics
link |
02:15:24.640
is giving us new ways to think about
link |
02:15:26.520
all possible things happening,
link |
02:15:28.560
about all these different things happening in parallel.
link |
02:15:30.680
And so I'm guessing...
link |
02:15:31.680
They have built in protection for some of the parallelism.
link |
02:15:34.640
Well, causal invariance is the built in protection.
link |
02:15:37.280
Causal invariance is what means that
link |
02:15:39.720
even though things happen in different orders,
link |
02:15:41.680
it doesn't matter in the end.
link |
02:15:43.440
As a person who struggled with concurrent programming
link |
02:15:46.520
in like Java,
link |
02:15:50.240
with all the basic concepts of concurrent programming,
link |
02:15:53.760
that if there could be built up
link |
02:15:55.760
a strong mathematical framework for causal invariance,
link |
02:16:00.080
that's so liberating.
link |
02:16:01.760
And that could be not just liberating,
link |
02:16:03.680
but really powerful for massively distributed computation.
link |
02:16:08.320
Absolutely.
link |
02:16:09.160
No, I mean, what's eventual consistency
link |
02:16:11.800
in distributed databases
link |
02:16:14.000
is essentially the causal invariance idea.
link |
02:16:16.160
Yeah. Okay.
link |
02:16:17.000
So that's...
link |
02:16:17.840
But have you thought about,
link |
02:16:22.160
like really large simulations?
link |
02:16:26.000
Yeah. I mean, I'm also thinking about,
link |
02:16:28.080
look, the fact is I've spent much of my life
link |
02:16:30.400
as a language designer, right?
link |
02:16:31.640
So I can't possibly not think about,
link |
02:16:34.360
what does this mean for designing languages
link |
02:16:37.240
for parallel computation?
link |
02:16:38.320
In fact, another thing that's one of these...
link |
02:16:41.640
I'm always embarrassed at how long it's taken me
link |
02:16:44.400
to figure stuff out.
link |
02:16:45.680
But back in the 1980s,
link |
02:16:47.360
I worked on trying to make up languages
link |
02:16:49.600
for parallel computation.
link |
02:16:50.960
I thought about doing graph rewriting.
link |
02:16:53.080
I thought about doing these kinds of things,
link |
02:16:54.440
but I couldn't see how to actually make the connections
link |
02:16:57.160
to actually do something useful.
link |
02:16:59.320
I think now physics is kind of showing us
link |
02:17:02.520
how to make those things useful.
link |
02:17:04.200
And so my guess is that in time,
link |
02:17:06.320
we'll be talking about, we do parallel programming.
link |
02:17:09.000
We'll be talking about programming
link |
02:17:10.360
in a certain reference frame,
link |
02:17:12.080
just as we think about thinking about physics
link |
02:17:14.120
in a certain reference frame.
link |
02:17:15.080
It's a certain coordination of what's going on.
link |
02:17:17.640
We say, we're gonna program in this reference frame.
link |
02:17:19.960
Oh, let's change the reference frame
link |
02:17:21.280
to this reference frame.
link |
02:17:22.680
And then our program will seem different
link |
02:17:25.240
and we'll have a different way to think about it.
link |
02:17:27.120
But it's still the same program underneath.
link |
02:17:28.960
So let me ask on this topic,
link |
02:17:30.760
cause I put out that I'm talking to you.
link |
02:17:32.360
I got way more questions than I can deal with,
link |
02:17:34.560
but what pops to mind is a question somebody asked
link |
02:17:37.520
on Reddit I think is, please ask Dr. Wolfram,
link |
02:17:42.560
what are the specs of the computer running the universe?
link |
02:17:46.200
So we're talking about specs of hardware and software
link |
02:17:51.480
for simulations of a large scale thing.
link |
02:17:54.080
What about a scale that is comparative
link |
02:17:57.520
to something that eventually leads
link |
02:17:59.720
to the two of us talking and about?
link |
02:18:01.560
Right, right, right.
link |
02:18:02.400
So actually I did try to estimate that.
link |
02:18:05.080
And we actually have to go a couple more stages
link |
02:18:07.280
before we can really get to that answer
link |
02:18:08.680
because we're talking about this thing.
link |
02:18:14.200
This is what happens when you build these abstract systems
link |
02:18:16.920
and you're trying to explain the universe,
link |
02:18:19.560
they're quite a number of levels deep, so to speak.
link |
02:18:23.640
But the...
link |
02:18:25.520
You mean conceptually or like literally?
link |
02:18:27.280
Cause you're talking about small objects
link |
02:18:28.800
and there's 10 to the 120 something.
link |
02:18:31.600
Yeah, right.
link |
02:18:33.840
It is conceptually deep.
link |
02:18:35.120
And one of the things that's happening sort of structurally
link |
02:18:37.920
in this project is, you know, there were ideas,
link |
02:18:40.600
there's another layer of ideas,
link |
02:18:41.760
there's another layer of ideas
link |
02:18:43.240
to get to the different things that correspond to physics.
link |
02:18:46.960
They're just different layers of ideas.
link |
02:18:49.280
And they are, you know, it's actually probably,
link |
02:18:52.360
if anything, getting harder to explain this project
link |
02:18:54.480
cause I'm realizing that the fraction of way through
link |
02:18:56.520
that I am so far and explaining this to you is less than,
link |
02:18:59.760
than, you know, it might be because we know more now,
link |
02:19:02.840
you know, every week basically we know a little bit more.
link |
02:19:06.200
And like...
link |
02:19:07.040
Those are just layers on the initial fundamental structure.
link |
02:19:10.480
Yes, but the layers are, you know,
link |
02:19:12.640
you might be asking me, you know,
link |
02:19:14.320
how do we get the difference between fermions and bosons,
link |
02:19:18.680
the difference between particles
link |
02:19:19.880
that can be all in the same state
link |
02:19:21.760
and particles that exclude each other, okay.
link |
02:19:24.080
Last three days, we've kind of figured that out.
link |
02:19:26.600
Okay.
link |
02:19:27.440
But, and it's very interesting.
link |
02:19:29.440
It's very cool.
link |
02:19:31.080
And it's very...
link |
02:19:32.040
And those are some kind of properties at a certain level,
link |
02:19:35.800
layer of abstraction on the graph.
link |
02:19:37.880
Yes, yes.
link |
02:19:38.720
And there's, but the layers of abstraction are kind of,
link |
02:19:41.640
they're compounding.
link |
02:19:42.760
Stacking up.
link |
02:19:43.600
So it's difficult, but...
link |
02:19:45.320
But okay.
link |
02:19:46.160
But the specs nevertheless remain the same.
link |
02:19:47.920
Okay, the specs underneath.
link |
02:19:49.560
So I have an estimate.
link |
02:19:50.960
So the question is, what are the units?
link |
02:19:52.440
So we've got these different fundamental constants
link |
02:19:54.840
about the world.
link |
02:19:56.160
So one of them is the speed of light, which is the...
link |
02:19:58.520
So the thing that's always the same
link |
02:20:00.200
in all these different ways of thinking about the universe
link |
02:20:02.720
is the notion of time, because time is computation.
link |
02:20:06.200
And so there's an elementary time,
link |
02:20:08.080
which is sort of the amount of time that we ascribe
link |
02:20:12.240
to elapsing in a single computational step.
link |
02:20:16.160
Yeah.
link |
02:20:17.000
Okay.
link |
02:20:17.840
So that's the elementary time.
link |
02:20:18.680
So then there's an elementary...
link |
02:20:19.520
That's a parameter or whatever.
link |
02:20:20.440
That's a constant.
link |
02:20:21.880
It's whatever we define it to be,
link |
02:20:23.360
because I mean, we don't, you know...
link |
02:20:25.360
I mean, it's all relative, right?
link |
02:20:26.840
It doesn't matter.
link |
02:20:27.680
Yes, it doesn't matter what it is,
link |
02:20:28.520
because we could be, it could be slower.
link |
02:20:30.360
It's just a number which we use to convert that
link |
02:20:33.840
to seconds, so to speak,
link |
02:20:35.000
because we are experiencing things
link |
02:20:37.160
and we say this amount of time has elapsed, so to speak.
link |
02:20:39.880
But we're within this thing.
link |
02:20:41.400
Absolutely.
link |
02:20:42.240
So it doesn't matter, right?
link |
02:20:43.680
But what does matter is the ratio,
link |
02:20:46.000
what we can, the ratio of the spatial distance
link |
02:20:49.520
and this hypergraph to this moment of time.
link |
02:20:54.320
Again, that's an arbitrary thing,
link |
02:20:55.800
but we measure that in meters per second, for example,
link |
02:20:58.720
and that ratio is the speed of light.
link |
02:21:00.880
So the ratio of the elementary distance
link |
02:21:03.160
to the elementary time is the speed of light, okay?
link |
02:21:06.640
Perfect.
link |
02:21:07.480
And so there's another,
link |
02:21:08.320
there are two other levels of this, okay?
link |
02:21:11.360
So there is a thing which we can talk about,
link |
02:21:13.880
which is the maximum entanglement speed,
link |
02:21:16.520
which is a thing that happens at another level
link |
02:21:19.320
in this whole sort of story
link |
02:21:20.680
of how these things get constructed.
link |
02:21:22.840
That's a sort of maximum speed in quantum,
link |
02:21:24.840
in the space of quantum states.
link |
02:21:26.920
Just as the speed of light
link |
02:21:28.040
is a maximum speed in physical space,
link |
02:21:30.200
this is a maximum speed in the space of quantum states.
link |
02:21:32.680
There's another level which is associated
link |
02:21:35.000
with what we call ruleal space,
link |
02:21:36.600
which is another one of these maximum speeds.
link |
02:21:39.120
We'll get to this.
link |
02:21:40.360
So these are limitations on the system
link |
02:21:42.120
that are able to capture the kind of physical universe
link |
02:21:45.280
which we live in.
link |
02:21:46.280
The quantum mechanical.
link |
02:21:47.120
There are inevitable features of having a rule
link |
02:21:51.800
that has only a finite amount of information in the rule.
link |
02:21:54.600
So long as you have a rule that only involves
link |
02:21:57.280
a bounded amount, a limited amount of,
link |
02:22:01.560
only involving a limited number of elements,
link |
02:22:03.280
limited number of relations,
link |
02:22:04.760
it is inevitable that there are these speed constraints.
link |
02:22:07.320
We knew about the one for speed of light.
link |
02:22:08.800
We didn't know about the one for maximum entanglement speed,
link |
02:22:11.440
which is actually something that is possibly measurable,
link |
02:22:14.040
particularly in black hole systems and things like this.
link |
02:22:17.000
Anyway, this is long, long story short.
link |
02:22:19.600
You're asking what the processing specs of the universe,
link |
02:22:23.120
of the sort of computation of the universe.
link |
02:22:25.120
There's a question of even what are the units
link |
02:22:27.400
of some of these measurements, okay?
link |
02:22:29.000
So the units I'm using are Wolfram language instructions
link |
02:22:31.960
per second, okay?
link |
02:22:33.280
Because you gotta have some,
link |
02:22:34.840
what computation are you doing?
link |
02:22:37.000
There gotta be some kind of frame of reference.
link |
02:22:38.360
Right, right.
link |
02:22:39.200
So, because it turns out in the end,
link |
02:22:41.800
there will be, there's sort of an arbitrariness
link |
02:22:44.240
in the language that you use to describe the universe.
link |
02:22:46.960
So in those terms, I think it's like 10 to the 500,
link |
02:22:51.600
Wolfram language operations per second, I think,
link |
02:22:54.320
is the, I think it's of that order.
link |
02:22:56.480
You know, basically.
link |
02:22:57.320
So that's the scale of the computation.
link |
02:22:58.760
What about memory?
link |
02:22:59.920
If there's an interesting thing to say
link |
02:23:01.360
about storage and memory.
link |
02:23:02.720
Well, there's a question of how many sort of atoms
link |
02:23:04.360
of space might there be?
link |
02:23:06.280
You know, maybe 10 to the 400.
link |
02:23:08.680
We don't know exactly how to estimate these numbers.
link |
02:23:11.320
I mean, this is based on some, I would say,
link |
02:23:14.680
somewhat rickety way of estimating things.
link |
02:23:17.960
You know, when there start to be able to be experiments done,
link |
02:23:20.240
if we're lucky, there will be experiments
link |
02:23:21.840
that can actually nail down some of these numbers.
link |
02:23:24.160
And because of computation reducibility,
link |
02:23:27.920
there's not much hope for very efficient compression,
link |
02:23:31.520
like very efficient representation
link |
02:23:34.080
of this atom space? Good question.
link |
02:23:35.680
I mean, there's probably certain things, you know,
link |
02:23:37.960
the fact that we can deduce anything,
link |
02:23:40.560
okay, the question is how deep does the reducibility go?
link |
02:23:44.560
Right. Okay.
link |
02:23:45.400
And I keep on being surprised
link |
02:23:46.600
that it's a lot deeper than I thought.
link |
02:23:48.560
Okay, and so one of the things is that,
link |
02:23:52.120
that there's a question of sort of how much
link |
02:23:53.840
of the whole of physics do we have to be able to get
link |
02:23:57.480
in order to explain certain kinds of phenomena?
link |
02:23:59.280
Like for example, if we want to study quantum interference,
link |
02:24:02.840
do we have to know what an electron is?
link |
02:24:05.800
Turns out I thought we did, turns out we don't.
link |
02:24:08.480
I thought to know what energy is,
link |
02:24:10.400
we would have to know what electrons were.
link |
02:24:12.320
We don't.
link |
02:24:13.160
So you get a lot of really powerful shortcuts.
link |
02:24:15.560
Right.
link |
02:24:16.400
There's a bunch of sort of bulk information about the world.
link |
02:24:19.240
The thing that I'm excited about last few days, okay,
link |
02:24:22.960
is the idea of fermions versus bosons, fundamental idea
link |
02:24:27.560
that I mean, it's the reason we have matter
link |
02:24:29.800
that doesn't just self destruct,
link |
02:24:31.920
is because of the exclusion principle
link |
02:24:33.800
that means that two electrons can never be
link |
02:24:36.360
in the same quantum state.
link |
02:24:38.280
Is it useful for us to maybe first talk
link |
02:24:41.000
about how quantum mechanics fits
link |
02:24:44.240
into the Wolfram physics model?
link |
02:24:46.480
Yes.
link |
02:24:47.320
Let's go there.
link |
02:24:48.160
So we talked about general relativity.
link |
02:24:49.680
Now, what have you found from quantum mechanics
link |
02:24:56.960
within and outside of the Wolfram physics?
link |
02:24:59.920
Right, so I mean, the key idea of quantum mechanics
link |
02:25:04.200
that sort of the typical interpretation
link |
02:25:06.600
is classical physics says a definite thing happens.
link |
02:25:09.960
Quantum physics says there's this whole set of paths
link |
02:25:12.880
of things that might happen.
link |
02:25:14.600
And we are just observing some overall probability
link |
02:25:17.760
of how those paths work.
link |
02:25:19.680
Okay, so when you think about our hypergraphs
link |
02:25:22.480
and all these little updates that are going on,
link |
02:25:24.680
there's a very remarkable thing to realize,
link |
02:25:27.040
which is if you say, well,
link |
02:25:29.240
which particular sequence of updates should you do?
link |
02:25:32.360
Say, well, it's not really defined.
link |
02:25:33.760
You can do any of a whole collection
link |
02:25:35.400
of possible sequences of updates.
link |
02:25:37.440
Okay, that set of possible sequences of updates
link |
02:25:42.000
defines yet another kind of graph
link |
02:25:44.240
that we call a multiway graph.
link |
02:25:46.120
And a multiway graph just is a graph
link |
02:25:48.680
where at every node, there is a choice
link |
02:25:52.800
of several different possible things that could happen.
link |
02:25:55.320
So for example, you go this way, you go that way.
link |
02:25:57.720
Those are two different edges in the multiway graph.
link |
02:26:00.920
And you're building up the set of possibilities.
link |
02:26:02.640
So actually, like, for example, I just made the one,
link |
02:26:04.880
the multiway graph for tic tac toe, okay?
link |
02:26:07.400
So tic tac toe, you start off with some board
link |
02:26:11.000
that, you know, is everything is blank,
link |
02:26:12.280
and then somebody can put down an X somewhere,
link |
02:26:15.240
an O somewhere, and then there are different possibilities.
link |
02:26:18.200
At each stage, there are different possibilities.
link |
02:26:20.320
And so you build up this multiway graph
link |
02:26:22.760
of all those possibilities.
link |
02:26:23.760
Now notice that even in tic tac toe,
link |
02:26:25.960
you have the feature that there can be something
link |
02:26:28.160
where you have two different things that happen
link |
02:26:31.000
and then those branches merge
link |
02:26:33.400
because you end up with the same shape,
link |
02:26:35.280
you know, the same configuration of the board,
link |
02:26:37.440
even though you got there in two different ways.
link |
02:26:40.000
So the thing that's sort of an inevitable feature
link |
02:26:42.840
of our models is that just like quantum mechanics suggests,
link |
02:26:47.360
definite things don't happen.
link |
02:26:48.880
Instead, you get this whole multiway graph
link |
02:26:50.880
of all these possibilities.
link |
02:26:52.760
Okay, so then the question is, so, okay,
link |
02:26:55.680
so that's sort of a picture of what's going on.
link |
02:26:58.320
Now you say, okay, well, quantum mechanics
link |
02:27:00.520
has all these features of, you know,
link |
02:27:02.720
all this mathematical structure and so on.
link |
02:27:04.880
How do you get that mathematical structure?
link |
02:27:07.160
Okay, a couple of things to say.
link |
02:27:08.880
So quantum mechanics is actually, in a sense,
link |
02:27:11.680
two different theories glued together.
link |
02:27:13.960
Quantum mechanics is the theory
link |
02:27:15.680
of how quantum amplitudes work
link |
02:27:18.120
that more or less give you the probabilities
link |
02:27:19.440
of things happening.
link |
02:27:20.720
And it's the theory of quantum measurement,
link |
02:27:22.800
which is the theory of how we actually
link |
02:27:25.200
conclude definite things.
link |
02:27:27.000
Because the mathematics just gives you
link |
02:27:29.080
these quantum amplitudes, which are more or less
link |
02:27:30.760
probabilities of things happening,
link |
02:27:32.480
but yet we actually observe definite things in the world.
link |
02:27:36.920
Quantum measurement has always been a bit mysterious.
link |
02:27:39.120
It's always been something where people just say,
link |
02:27:41.160
well, the mathematics says this,
link |
02:27:42.400
but then you do a measurement,
link |
02:27:43.480
and there are philosophical arguments
link |
02:27:45.120
about what the measurement is.
link |
02:27:46.600
But it's not something where there's a theory
link |
02:27:48.800
of the measurement.
link |
02:27:49.720
Somebody on Reddit also asked,
link |
02:27:53.080
please ask Stephen to tell his story
link |
02:27:56.800
of the double slit experiment.
link |
02:27:59.840
Okay, yeah, I can.
link |
02:28:01.160
Is that, does that make sense?
link |
02:28:02.880
Oh yeah, it makes sense.
link |
02:28:03.960
Absolutely makes sense.
link |
02:28:05.000
Why, is this like a good way to discuss?
link |
02:28:07.760
A little bit.
link |
02:28:08.600
Let me go, let me explain a couple of things first.
link |
02:28:10.560
So the structure of quantum mechanics
link |
02:28:13.840
is mathematically quite complicated.
link |
02:28:16.240
One of the features, let's see,
link |
02:28:18.600
well, how to describe this.
link |
02:28:20.520
Okay, so first point is there's this multiway graph
link |
02:28:23.800
of all these different paths of things
link |
02:28:26.880
that can happen in the world.
link |
02:28:28.760
And the important point is that these,
link |
02:28:32.600
you can have branchings and you can have mergings.
link |
02:28:35.600
Okay, so this property turns out causal invariance
link |
02:28:39.680
is the statement that the number of mergings
link |
02:28:43.360
is equal to the number of branchings.
link |
02:28:45.520
Yeah.
link |
02:28:46.360
So in other words, every time there's a branch,
link |
02:28:48.720
eventually there will also be a merge.
link |
02:28:50.640
In other words, every time there were two possibilities
link |
02:28:52.600
for what might've happened, eventually those will merge.
link |
02:28:55.120
Beautiful concept by the way, but yeah, yeah, yeah.
link |
02:28:57.400
So that idea, okay, so then, so that's one thing
link |
02:29:03.920
and that's closely related to the sort of objectivity
link |
02:29:07.680
in quantum mechanics.
link |
02:29:08.520
The fact that we believe definite things happen,
link |
02:29:10.720
it's because although there are all these different paths,
link |
02:29:13.200
in some sense, because of causal invariance,
link |
02:29:15.600
they all imply the same thing.
link |
02:29:17.640
I'm cheating a little bit in saying that,
link |
02:29:19.400
but that's roughly the essence of what's going on.
link |
02:29:22.120
Okay, next thing to think about
link |
02:29:24.560
is you have this multiway graph,
link |
02:29:27.440
it has all these different possible things
link |
02:29:28.840
that are happening.
link |
02:29:30.040
Now we ask, this multiway graph
link |
02:29:32.440
is sort of evolving with time.
link |
02:29:34.120
Over time, it's branching, it's merging,
link |
02:29:36.680
it's doing all these things, okay?
link |
02:29:39.840
Question we can ask is if we slice it at a particular time,
link |
02:29:44.680
what do we see?
link |
02:29:46.120
And that slice represents in a sense,
link |
02:29:48.840
something to do with the state of the universe
link |
02:29:51.240
at a particular time.
link |
02:29:53.080
So in other words, we've got this multiway graph
link |
02:29:55.080
of all these possibilities,
link |
02:29:56.680
and then we're asking, okay, we take the slice,
link |
02:30:01.320
this slice represents, okay,
link |
02:30:04.440
each of these different paths
link |
02:30:05.640
corresponds to a different quantum possibility
link |
02:30:07.760
for what's happening.
link |
02:30:09.320
When we take the slice, we're saying,
link |
02:30:11.440
what are the set of quantum possibilities
link |
02:30:13.120
that exist at a particular time?
link |
02:30:14.960
And when you say slice, you slice the graph
link |
02:30:17.640
and then there's a bunch of leaves.
link |
02:30:19.720
A bunch of leaves.
link |
02:30:20.560
Those represent the state of things.
link |
02:30:23.440
Right, but then, okay, so the important thing
link |
02:30:26.240
that you are quickly picking up on
link |
02:30:29.040
is that what matters is kind of
link |
02:30:31.960
how these leaves are related to each other.
link |
02:30:34.600
So a good way to tell how leaves are related
link |
02:30:37.560
is just to say on the step before
link |
02:30:39.920
do they have a common ancestor?
link |
02:30:42.160
So two leaves might be,
link |
02:30:43.960
they might have just branched from one thing
link |
02:30:45.800
or they might be far away,
link |
02:30:47.920
way far apart in this graph
link |
02:30:50.720
where to get to a common ancestor,
link |
02:30:52.320
maybe you have to go all the way back
link |
02:30:53.400
to the beginning of the graph,
link |
02:30:54.240
all the way back to the beginning.
link |
02:30:55.080
So there's some kind of measure of distance.
link |
02:30:57.160
Right, but what you get is by making the slice,
link |
02:31:02.000
we call it branchial space, the space of branches.
link |
02:31:05.880
And in this branchial space,
link |
02:31:08.360
you have a graph that represents the relationships
link |
02:31:11.240
between these quantum states in branchial space.
link |
02:31:14.640
You have this notion of distance in branchial space.
link |
02:31:18.000
Okay, so.
link |
02:31:18.840
It's connected to quantum entanglement.
link |
02:31:20.880
Yes, yes, it's basically,
link |
02:31:23.520
the distance in branchial space
link |
02:31:25.640
is kind of an entanglement distance.
link |
02:31:27.840
So this.
link |
02:31:28.680
That's a very nice model.
link |
02:31:29.880
Right, it is very nice, it's very beautiful.
link |
02:31:33.240
I mean, it's so clean.
link |
02:31:35.520
I mean, it's really, and it tells one,
link |
02:31:38.920
okay, so anyway, so then this branchial space
link |
02:31:42.840
has this sort of map of the entanglements
link |
02:31:46.080
between quantum states.
link |
02:31:47.760
So in physical space, we have,
link |
02:31:50.360
so you can say, take, let's say the causal graph,
link |
02:31:54.680
and we can slice that at a particular time,
link |
02:31:57.800
and then we get this map
link |
02:31:58.840
of how things are laid out in physical space.
link |
02:32:01.400
When we do the same kind of thing,
link |
02:32:02.720
there's a thing called the multiway causal graph,
link |
02:32:04.840
which is the analog of a causal graph
link |
02:32:06.360
for the multiway system.
link |
02:32:07.760
We slice that, we get essentially the relationships
link |
02:32:11.360
between things, not in physical space,
link |
02:32:13.720
but in the space of quantum states.
link |
02:32:15.720
It's like which quantum state
link |
02:32:17.040
is similar to which other quantum state.
link |
02:32:19.360
Okay, so now I think next thing to say
link |
02:32:22.280
is just to mention how quantum measurement works.
link |
02:32:24.800
So quantum measurement has to do with reference frames
link |
02:32:27.560
in branchial space.
link |
02:32:29.760
So, okay, so measurement in physical space,
link |
02:32:33.720
it matters whether how we assign spatial position
link |
02:32:38.720
and how we define coordinates in space and time.
link |
02:32:42.520
And that's how we make measurements in ordinary space.
link |
02:32:45.360
Are we making a measurement based on us sitting still here?
link |
02:32:48.240
Are we traveling at half the speed of light
link |
02:32:49.880
and making measurements that way?
link |
02:32:51.600
These are different reference frames
link |
02:32:53.080
in which we're making our measurements.
link |
02:32:54.760
And the relationship between different events
link |
02:32:57.840
and different points in space and time
link |
02:33:00.760
will be different depending on what reference frame we're in.
link |
02:33:04.200
Okay, so then we have this idea
link |
02:33:06.480
of quantum observation frames,
link |
02:33:08.880
which are the analog of reference frames,
link |
02:33:11.040
but in branchial space.
link |
02:33:13.040
And so what happens is what we realize
link |
02:33:15.880
is that a quantum measurement is the observer
link |
02:33:19.960
is sort of arbitrarily determining this reference frame.
link |
02:33:23.000
The observer is saying, I'm going to understand the world
link |
02:33:26.840
by saying that space and time are coordinated this way.
link |
02:33:30.560
I'm gonna understand the world by saying
link |
02:33:32.600
that quantum states and time are coordinated in this way.
link |
02:33:36.520
And essentially what happens is
link |
02:33:38.280
that the process of quantum measurement
link |
02:33:40.920
is a process of deciding how you slice up
link |
02:33:44.920
this multiway system in these quantum observation frames.
link |
02:33:48.560
So in a sense, the observer, the way the observer enters
link |
02:33:51.760
is by their choice of these quantum observation frames.
link |
02:33:55.600
And what happens is that the observer,
link |
02:33:58.880
because, okay, this is again,
link |
02:34:00.480
another stack of other concepts, but anyway,
link |
02:34:03.120
because the observer is computationally bounded,
link |
02:34:06.200
there is a limit to the type of quantum observation frames
link |
02:34:08.880
that they can construct.
link |
02:34:09.960
Interesting, okay, so there's some constraints,
link |
02:34:12.600
some limit on the choice of observation frames.
link |
02:34:17.760
Right, and by the way, I just want to mention
link |
02:34:19.960
that there's a, I mean, it's bizarre,
link |
02:34:21.840
but there's a hierarchy of these things.
link |
02:34:23.640
So in thermodynamics,
link |
02:34:27.440
the fact that we believe entropy increases,
link |
02:34:29.600
we believe things get more disordered,
link |
02:34:31.480
is a consequence of the fact
link |
02:34:32.520
that we can't track each individual molecule.
link |
02:34:34.280
If we could track every single molecule,
link |
02:34:36.160
we could run every movie in reverse, so to speak,
link |
02:34:38.240
and we would not see that things are getting more disordered.
link |
02:34:42.200
But it's because we are computationally bounded,
link |
02:34:44.800
we can only look at these big blobs
link |
02:34:46.720
of what all these molecules collectively do,
link |
02:34:49.560
that we think that things are,
link |
02:34:52.280
that we describe it in terms of entropy increasing
link |
02:34:54.920
and so on.
link |
02:34:55.800
And it's the same phenomenon, basically,
link |
02:34:58.560
and also a consequence of computational irreducibility
link |
02:35:01.520
that causes us to basically be forced to conclude
link |
02:35:04.800
that definite things happen in the world,
link |
02:35:06.920
even though there's this quantum,
link |
02:35:08.720
this set of all these different quantum processes
link |
02:35:10.680
that are going on.
link |
02:35:11.880
So, I mean, I'm skipping a little bit,
link |
02:35:15.400
but that's a rough picture.
link |
02:35:18.560
And in the evolution of the Wolfram Physics Project,
link |
02:35:21.880
where do you feel we stand on some of the puzzles
link |
02:35:24.280
that are along the way?
link |
02:35:25.120
See, you're skipping along a bunch of stuff.
link |
02:35:28.080
It's amazing how much these things are unraveling.
link |
02:35:30.440
I mean, you know, these things, look,
link |
02:35:32.480
it used to be the case that I would agree with Dick Feynman,
link |
02:35:35.640
nobody understands quantum mechanics, including me, okay?
link |
02:35:38.840
I'm getting to the point where I think
link |
02:35:40.120
I actually understand quantum mechanics.
link |
02:35:41.560
My exercise, okay, is can I explain quantum mechanics
link |
02:35:45.720
for real at the level of kind of middle school
link |
02:35:48.800
type explanation?
link |
02:35:50.320
And I'm getting closer, it's getting there.
link |
02:35:52.600
I'm not quite there, I've tried it a few times,
link |
02:35:54.960
and I realized that there are things
link |
02:35:57.640
where I have to start talking about
link |
02:35:59.080
elaborate mathematical concepts and so on.
link |
02:36:00.920
But I think, and you've got to realize
link |
02:36:03.000
that it's not self evident that we can explain
link |
02:36:06.280
at an intuitively graspable level,
link |
02:36:09.240
something which, about the way the universe works,
link |
02:36:12.400
the universe wasn't built for our understanding,
link |
02:36:14.760
so to speak.
link |
02:36:16.280
But I think then, okay, so another important idea
link |
02:36:21.720
is this idea of branchial space, which I mentioned,
link |
02:36:25.280
this sort of space of quantum states.
link |
02:36:27.400
It is, okay, so I mentioned Einstein's equations
link |
02:36:31.240
describing the effect of mass and energy
link |
02:36:37.400
on trajectories of particles, on GD6.
link |
02:36:40.840
The curvature of physical space is associated
link |
02:36:44.920
with the presence of energy,
link |
02:36:47.040
according to Einstein's equations, okay?
link |
02:36:49.400
So it turns out that, rather amazingly,
link |
02:36:51.920
the same thing is true in branchial space.
link |
02:36:54.880
So it turns out the presence of energy
link |
02:36:57.360
or more accurately Lagrangian density,
link |
02:36:59.440
which is a kind of relativistic invariant version of energy,
link |
02:37:03.200
the presence of that causes essentially deflection of GD6
link |
02:37:08.560
in this branchial space, okay?
link |
02:37:11.160
So you might say, so what?
link |
02:37:12.560
Well, it turns out that the sort of the best formulation
link |
02:37:17.040
we have of quantum mechanics,
link |
02:37:18.800
this Feynman path integral,
link |
02:37:21.360
is a thing that describes quantum processes
link |
02:37:26.200
in terms of mathematics that can be interpreted as,
link |
02:37:31.480
well, in quantum mechanics, the big thing
link |
02:37:33.880
is you get these quantum amplitudes,
link |
02:37:35.360
which are complex numbers that represent,
link |
02:37:38.280
when you combine them together,
link |
02:37:39.400
represent probabilities of things happening.
link |
02:37:41.560
And so the big story has been,
link |
02:37:42.840
how do you derive these quantum amplitudes?
link |
02:37:45.320
And people think these quantum amplitudes,
link |
02:37:47.480
they have a complex number,
link |
02:37:49.160
has a real part and an imaginary part.
link |
02:37:51.200
You can also think of it as a magnitude and a phase.
link |
02:37:53.920
And people have sort of thought these quantum amplitudes
link |
02:37:57.160
have magnitude and phase, and you compute those together.
link |
02:38:00.040
Turns out that the magnitude and the phase
link |
02:38:03.680
come from completely different places.
link |
02:38:06.120
The magnitude comes, okay, so how do you compute things
link |
02:38:10.080
in quantum mechanics?
link |
02:38:10.920
Roughly, I'm telling you, I'm getting there
link |
02:38:13.360
to be able to do this at a middle school level,
link |
02:38:15.080
but I'm not there yet.
link |
02:38:17.720
Roughly what happens is you're asking,
link |
02:38:20.440
does this state in quantum mechanics
link |
02:38:24.160
evolve to this other state in quantum mechanics?
link |
02:38:27.080
And you can think about that like a particle traveling
link |
02:38:30.600
or something traveling through physical space,
link |
02:38:33.240
but instead it's traveling through branchial space.
link |
02:38:36.160
And so what's happening is, does this quantum state evolve
link |
02:38:38.920
to this other quantum state?
link |
02:38:39.920
It's like saying, does this object move
link |
02:38:42.160
from this place in space to this other place in space?
link |
02:38:45.160
Okay, now the way that these quantum amplitudes
link |
02:38:49.360
characterize kind of to what extent the thing
link |
02:38:54.000
will successfully reach some particular point
link |
02:38:56.400
in branchial space, just like in physical space,
link |
02:38:58.560
you could say, oh, it had a certain velocity
link |
02:39:00.720
and it went in this direction.
link |
02:39:02.400
In branchial space, there's a similar kind of concept.
link |
02:39:05.160
Is there a nice way to visualize for me now
link |
02:39:08.280
mentally branchial space?
link |
02:39:10.560
It's just, you have this hypergraph,
link |
02:39:13.720
sorry, you have this multiway graph.
link |
02:39:15.720
It's this big branching thing, branching and merging thing.
link |
02:39:18.440
But I mean, like moving through that space,
link |
02:39:21.800
I'm just trying to understand what that looks like.
link |
02:39:25.920
You know, that space is probably exponential dimensional,
link |
02:39:29.280
which makes it again, another can of worms
link |
02:39:32.280
in understanding what's going on.
link |
02:39:33.880
That space as in an ordinary space,
link |
02:39:36.920
this hypergraph, the spatial hypergraph
link |
02:39:39.160
limits to something which is like a manifold,
link |
02:39:42.600
like something like three dimensional space.
link |
02:39:45.040
Almost certainly the multiway graph limits
link |
02:39:48.720
to a Hilbert space, which is something that,
link |
02:39:52.360
I mean, it's just a weird exponential dimensional space.
link |
02:39:55.560
And by the way, you can ask, I mean,
link |
02:39:57.400
there are much weirder things that go on.
link |
02:39:58.880
For example, one of the things I've been interested in
link |
02:40:00.720
is the expansion of the universe in branchial space.
link |
02:40:03.920
So we know the universe is expanding in physical space,
link |
02:40:07.080
but the universe is probably also expanding
link |
02:40:09.200
in branchial space.
link |
02:40:10.920
So that means the number of quantum states
link |
02:40:13.280
of the universe is increasing with time.
link |
02:40:15.760
The diameter of the thing is growing.
link |
02:40:17.880
Right, so that means that the,
link |
02:40:19.480
and by the way, this is related
link |
02:40:22.760
to whether quantum computing can ever work.
link |
02:40:28.200
Why?
link |
02:40:29.040
Okay, so let me explain why.
link |
02:40:30.440
So let's talk about, okay, so first of all,
link |
02:40:32.840
just to finish the thought about quantum amplitudes,
link |
02:40:35.320
that the incredibly beautiful thing,
link |
02:40:37.320
but I'm just very excited about this.
link |
02:40:40.680
The fine path integral is this formula.
link |
02:40:44.640
It says that the amplitude, the quantum amplitude
link |
02:40:47.360
is E to the I S over H bar,
link |
02:40:49.480
where S is the thing called the action.
link |
02:40:51.560
And it, okay, so that can be thought of
link |
02:40:55.720
as representing a deflection of the angle
link |
02:40:59.280
of this path in the multiway graph.
link |
02:41:02.200
So it's a deflection of a geodesic in the multiway path
link |
02:41:05.040
that is caused by this thing called the action,
link |
02:41:06.960
which is essentially associated with energy, okay?
link |
02:41:10.040
And so this is a deflection of a path in branchial space
link |
02:41:13.760
that is described by this path integral,
link |
02:41:15.520
which is the thing that is the mathematical essence
link |
02:41:17.760
of quantum mechanics.
link |
02:41:19.440
Turns out that deflection is,
link |
02:41:22.760
the deflection of geodesics in branchial space
link |
02:41:25.240
follows the exact same mathematical setup
link |
02:41:28.720
as the deflection of geodesics in physical space,
link |
02:41:31.880
except the deflection of geodesics in physical space
link |
02:41:34.280
is described with Einstein's equations.
link |
02:41:36.480
The deflection of geodesics in branchial space
link |
02:41:38.600
is defined by the Feynman path integral,
link |
02:41:40.880
and they are the same.
link |
02:41:42.800
In other words, they are mathematically the same.
link |
02:41:45.760
So that means that general relativity
link |
02:41:48.360
is a story of essentially motion in physical space.
link |
02:41:53.200
Quantum mechanics is a story of essentially motion
link |
02:41:55.560
in branchial space.
link |
02:41:57.320
And the underlying equation for those two things,
link |
02:42:01.360
although it's presented differently
link |
02:42:02.560
because one's interested in different things
link |
02:42:04.160
in branchial space than physical space,
link |
02:42:06.080
but the underlying equation is the same.
link |
02:42:08.720
So in other words, it's just these two theories,
link |
02:42:13.440
which are those two sort of pillars
link |
02:42:14.600
of 20th century physics,
link |
02:42:16.320
which have seemed to be off in different directions,
link |
02:42:19.080
are actually facets of the exact same theory.
link |
02:42:24.280
That's exciting to see where that evolves
link |
02:42:26.960
and exciting that that just is there.
link |
02:42:29.120
Right, I mean, to me,
link |
02:42:31.000
look, having spent some part of my early life
link |
02:42:34.480
working in the context of these theories
link |
02:42:37.040
of 20th century physics,
link |
02:42:39.400
it's, they just, they seem so different.
link |
02:42:41.960
And the fact that they're really the same
link |
02:42:44.080
is just really amazing.
link |
02:42:46.480
Actually, you mentioned double slit experiment, okay?
link |
02:42:49.120
So the double slit experiment
link |
02:42:50.280
is an interference phenomenon where you say there are,
link |
02:42:54.360
you can have a photon or an electron,
link |
02:42:56.600
and you say there are these two slits
link |
02:42:58.240
that could have gone through either one,
link |
02:43:00.320
but there is this interference pattern
link |
02:43:02.560
where there's destructive interference,
link |
02:43:05.080
where you might've said in classical physics,
link |
02:43:07.200
oh, well, if there are two slits,
link |
02:43:09.000
then there's a better chance
link |
02:43:10.440
that it gets through one or the other of them.
link |
02:43:12.120
But in quantum mechanics,
link |
02:43:13.240
there's this phenomenon of destructive interference
link |
02:43:15.720
that means that even though there are two slits,
link |
02:43:18.120
two can lead to nothing,
link |
02:43:20.240
as opposed to two leading to more
link |
02:43:22.560
than, for example, one slit.
link |
02:43:25.240
And what happens in this model,
link |
02:43:27.480
and we've just been understanding this
link |
02:43:29.040
in the last few weeks, actually,
link |
02:43:30.760
is that what essentially happens
link |
02:43:34.400
is that the double slit experiment
link |
02:43:38.040
is a story of the interface
link |
02:43:39.360
between branchial space and physical space.
link |
02:43:41.960
And what's essentially happening
link |
02:43:43.080
is that the destructive interference
link |
02:43:45.520
is the result of the two possible paths
link |
02:43:48.520
associated with photons going through those two slits
link |
02:43:51.200
winding up at opposite ends of branchial space.
link |
02:43:53.960
And so that's why there's sort of nothing there
link |
02:43:57.120
when you look at it,
link |
02:43:58.440
is because these two different sort of branches
link |
02:44:02.120
couldn't get merged together
link |
02:44:03.920
to produce something that you can measure
link |
02:44:06.240
in physical space.
link |
02:44:07.680
Is there a lot to be understood about branchial space?
link |
02:44:10.680
I guess, mathematically speaking.
link |
02:44:13.920
Yes, it's a very beautiful mathematical thing.
link |
02:44:16.400
And it's very, I mean, by the way,
link |
02:44:18.280
this whole theory is just amazingly rich
link |
02:44:22.000
in terms of the mathematics that it says should exist.
link |
02:44:24.920
Okay, so for example,
link |
02:44:26.120
calculus is a story of infinitesimal change
link |
02:44:30.320
in integer dimensional space,
link |
02:44:32.000
one dimensional, two dimensional, three dimensional space.
link |
02:44:34.880
We need a theory of infinitesimal change
link |
02:44:37.960
in fractional dimensional and dynamic dimensional space.
link |
02:44:41.440
No such theory exists.
link |
02:44:42.640
So there's tools of mathematics that are needed here.
link |
02:44:45.280
Right.
link |
02:44:46.120
And this is a motivation for that actually.
link |
02:44:47.040
Right, and there are indications
link |
02:44:50.320
and we can do computer experiments
link |
02:44:51.760
and we can see how it's gonna come out,
link |
02:44:53.560
but we need to, the actual mathematics doesn't exist.
link |
02:44:58.040
And in branchial space, it's actually even worse.
link |
02:45:00.720
There's even more sort of layers of mathematics that are,
link |
02:45:04.720
we can see how it works roughly
link |
02:45:06.240
by doing computer experiments,
link |
02:45:07.960
but to really understand it,
link |
02:45:10.120
we need more sort of mathematical sophistication.
link |
02:45:13.320
So quantum computers.
link |
02:45:14.880
Okay, so the basic idea of quantum computers,
link |
02:45:17.800
the promise of quantum computers
link |
02:45:19.960
is quantum mechanics does things in parallel.
link |
02:45:23.640
And so you can sort of intrinsically do computations
link |
02:45:26.960
in parallel.
link |
02:45:27.880
And somehow that can be much more efficient
link |
02:45:30.160
than just doing them one after another.
link |
02:45:33.280
And I actually worked on quantum computing a bit
link |
02:45:36.240
with Dick Feynman back in 1981, two, three,
link |
02:45:40.680
that kind of timeframe.
link |
02:45:41.800
And we...
link |
02:45:42.640
It's a fascinating image.
link |
02:45:43.680
You and Feynman working on quantum computers.
link |
02:45:46.600
Well, we tried to work,
link |
02:45:47.880
the big thing we tried to do was invent a randomness chip
link |
02:45:51.040
that would generate randomness at a high speed
link |
02:45:53.800
using quantum mechanics.
link |
02:45:55.480
And the discovery that that wasn't really possible
link |
02:45:58.920
was part of the story of,
link |
02:46:01.520
we never really wrote anything about it.
link |
02:46:03.000
I think maybe he wrote some stuff,
link |
02:46:04.240
but we didn't write stuff about what we figured out
link |
02:46:07.520
about sort of the fact that it really seemed like
link |
02:46:10.080
the measurement process in quantum mechanics
link |
02:46:12.320
was a serious damper on what was possible to do
link |
02:46:15.680
in sort of the possible advantages of quantum mechanics
link |
02:46:19.600
for computing.
link |
02:46:20.760
But anyway, so the sort of the promise of quantum computing
link |
02:46:24.800
is let's say you're trying to factor an integer.
link |
02:46:28.320
Well, you can, instead of,
link |
02:46:30.040
when you factor an integer, you might say,
link |
02:46:31.560
well, does this factor work?
link |
02:46:32.720
Does this factor work?
link |
02:46:33.560
Does this factor work?
link |
02:46:35.680
In ordinary computing,
link |
02:46:37.160
it seems like we pretty much just have to try
link |
02:46:39.120
all these different factors,
link |
02:46:41.680
kind of one after another.
link |
02:46:43.160
But in quantum mechanics, you might have the idea,
link |
02:46:45.200
oh, you can just sort of have the physics,
link |
02:46:48.360
try all of them in parallel, okay?
link |
02:46:51.320
And there's this algorithm, Shor's algorithm,
link |
02:46:56.120
which allows you,
link |
02:46:58.760
according to the formalism of quantum mechanics,
link |
02:47:01.080
to do everything in parallel
link |
02:47:02.400
and to do it much faster than you can on a classical computer.
link |
02:47:05.320
Okay, the only little footnote is
link |
02:47:08.120
you have to figure out what the answer is.
link |
02:47:09.920
You have to measure the result.
link |
02:47:12.000
So the quantum mechanics internally has figured out
link |
02:47:13.960
all these different branches,
link |
02:47:15.520
but then you have to pull all these branches together
link |
02:47:17.880
to say, and the classical answer is this, okay?
link |
02:47:21.040
The standard theory of quantum mechanics
link |
02:47:22.600
does not tell you how to do that.
link |
02:47:24.200
It tells you how the branching works,
link |
02:47:26.160
but it doesn't tell you the process
link |
02:47:27.880
of corralling all these things together.
link |
02:47:30.240
And that process, which intuitively you can see
link |
02:47:32.800
is gonna be kind of tricky,
link |
02:47:34.400
but our model actually does tell you
link |
02:47:37.080
how that process of pulling things together works.
link |
02:47:40.200
And the answer seems to be, we're not absolutely sure.
link |
02:47:42.880
We've only got to two times three so far
link |
02:47:46.720
which is kind of in this factorization
link |
02:47:50.520
in quantum computers.
link |
02:47:51.360
But we can, what seems to be the case
link |
02:47:55.440
is that the advantage you get from the parallelization
link |
02:47:58.520
from quantum mechanics is lost
link |
02:48:01.200
from the amount that you have to spend
link |
02:48:03.520
pulling together all those parallel threads
link |
02:48:05.320
to get to a classical answer at the end.
link |
02:48:07.680
Now, that phenomenon is not unrelated
link |
02:48:10.280
to various decoherence phenomena
link |
02:48:11.880
that are seen in practical quantum computers and so on.
link |
02:48:14.320
I mean, I should say as a very practical point,
link |
02:48:16.760
I mean, it's like, should people stop bothering
link |
02:48:19.080
to do quantum computing research?
link |
02:48:20.760
No, because what they're really doing
link |
02:48:23.120
is they're trying to use physics
link |
02:48:25.240
to get to a new level of what's possible in computing.
link |
02:48:28.720
And that's a completely valid activity.
link |
02:48:30.920
Whether you can really put, you know,
link |
02:48:33.400
whether you can say,
link |
02:48:34.240
oh, you can solve an NP complete problem.
link |
02:48:36.000
You can reduce exponential time to polynomial time.
link |
02:48:39.120
You know, we're not sure.
link |
02:48:40.600
And I'm suspecting the answer is no,
link |
02:48:43.080
but that's not relevant to the practical speed ups
link |
02:48:46.080
you can get by using different kinds of technologies,
link |
02:48:48.520
different kinds of physics to do basic computing.
link |
02:48:52.320
But you're saying, I mean,
link |
02:48:53.680
some of the models you're playing with,
link |
02:48:55.280
the indication is that to get all the sheep back together
link |
02:49:02.640
and, you know, to corral everything together,
link |
02:49:05.960
to get the actual solution to the algorithm is...
link |
02:49:10.120
You lose all the...
link |
02:49:10.960
You lose all of the...
link |
02:49:12.240
By the way, I mean, so again, this question,
link |
02:49:14.400
do we actually know what we're talking about
link |
02:49:16.600
about quantum computing and so on?
link |
02:49:18.240
So again, we're doing proof by compilation.
link |
02:49:22.440
So we have a quantum computing framework
link |
02:49:24.880
in Wolfram language,
link |
02:49:26.080
and which is, you know,
link |
02:49:26.920
a standard quantum computing framework
link |
02:49:28.360
that represents things in terms of the standard,
link |
02:49:31.080
you know, formalism of quantum mechanics.
link |
02:49:32.840
And we have a compiler that simply compiles
link |
02:49:36.920
the representation of quantum gates into multiway systems.
link |
02:49:41.520
So, and in fact, the message that I got
link |
02:49:43.920
was from somebody who's working on the project
link |
02:49:46.000
who has managed to compile one of the sort of
link |
02:49:50.360
a core formalism based on category theory
link |
02:49:53.200
and core quantum formalism into multiway systems.
link |
02:49:57.520
So this is...
link |
02:49:58.360
When you say multiway system, these multiway graphs?
link |
02:50:00.160
Yes.
link |
02:50:01.000
So you're compiling...
link |
02:50:02.000
Yeah, okay, that's awesome.
link |
02:50:03.200
And then you can do all kinds of experiments
link |
02:50:05.200
on that multiway graph.
link |
02:50:06.280
Right, but the point is that what we're saying is
link |
02:50:08.640
the thing we've got this representation
link |
02:50:10.400
of let's say Shor's algorithm
link |
02:50:12.000
in terms of standard quantum gates.
link |
02:50:14.040
And it's just a pure matter of sort of computation
link |
02:50:17.480
to just say that is equivalent.
link |
02:50:19.240
We will get the same result as running this multiway system.
link |
02:50:23.360
Can you do complexity analysis on that multiway system?
link |
02:50:26.640
Well, that's what we've been trying to do, yes.
link |
02:50:28.600
We're getting there.
link |
02:50:29.440
We haven't done that yet.
link |
02:50:30.280
I mean, there's a pretty good indication
link |
02:50:32.520
of how that's gonna work out.
link |
02:50:33.480
We've done, as I say, our computer experiments.
link |
02:50:36.280
We've unimpressively gotten to about two times three
link |
02:50:39.440
in terms of factorization,
link |
02:50:41.080
which is kind of about how far people have got
link |
02:50:43.120
with physical quantum computers as well.
link |
02:50:45.440
But yes, we will be able to do...
link |
02:50:48.040
We definitely will be able to do complexity analysis
link |
02:50:50.480
and we will be able to know.
link |
02:50:51.800
So the one remaining hope for quantum computing
link |
02:50:55.240
really, really working at this formal level
link |
02:50:58.200
of quantum brand exponential stuff being done
link |
02:51:01.120
in polynomial time and so on.
link |
02:51:03.080
The one hope, which is very bizarre,
link |
02:51:05.280
is that you can kind of piggyback
link |
02:51:09.000
on the expansion of branchial space.
link |
02:51:11.240
So here's how that might work.
link |
02:51:13.480
So you think, you know, energy conservation,
link |
02:51:17.160
standard thing in high school physics,
link |
02:51:18.720
energy is conserved, right?
link |
02:51:20.600
But now you imagine, you think about energy
link |
02:51:23.640
in the context of cosmology
link |
02:51:25.000
and the context of the whole universe.
link |
02:51:26.920
It's a much more complicated story.
link |
02:51:28.680
The expansion of the universe kind of violates
link |
02:51:30.800
energy conservation.
link |
02:51:32.520
And so for example, if you imagine you've got two galaxies,
link |
02:51:35.000
they're receding from each other very quickly.
link |
02:51:37.080
They've got two big central black holes.
link |
02:51:39.400
You connect a spring between these two central black holes.
link |
02:51:43.040
Not easy to do in practice,
link |
02:51:44.640
but let's imagine you could do it.
link |
02:51:46.600
Now that spring is being pulled apart.
link |
02:51:49.200
It's getting more potential energy in the spring
link |
02:51:52.400
as a result of the expansion of the universe.
link |
02:51:55.120
So in a sense, you are piggybacking on the expansion
link |
02:51:59.040
that exists in the universe
link |
02:52:00.520
and the sort of violation of energy conservation
link |
02:52:03.120
that's associated with that cosmological expansion
link |
02:52:05.840
to essentially get energy.
link |
02:52:07.160
You're essentially building a perpetual motion machine
link |
02:52:09.680
by using the expansion of the universe.
link |
02:52:12.400
And that is a physical version of that.
link |
02:52:15.280
It is conceivable that the same thing can be done
link |
02:52:17.640
in branchial space to essentially mine the expansion
link |
02:52:22.640
of the universe in branchial space
link |
02:52:24.880
as a way to get sort of quantum computing for free,
link |
02:52:29.880
so to speak, just from the expansion of the universe
link |
02:52:32.280
in branchial space.
link |
02:52:33.520
Now, the physical space version is kind of absurd
link |
02:52:35.840
and involves springs between black holes and so on.
link |
02:52:39.520
It's conceivable that the branchial space version
link |
02:52:42.080
is not as absurd
link |
02:52:43.560
and that it's actually something you can reach
link |
02:52:45.840
with physical things you can build in labs and so on.
link |
02:52:48.600
We don't know yet.
link |
02:52:49.680
Okay, so like you were saying,
link |
02:52:51.320
the branch of space might be expanding
link |
02:52:54.040
and there might be something that could be exploited.
link |
02:52:57.120
Right, in the same kind of way
link |
02:52:59.040
that you can exploit that expansion of the universe
link |
02:53:03.720
in principle, in physical space.
link |
02:53:06.560
You just have like a glimmer of hope.
link |
02:53:08.520
Right, I think that the,
link |
02:53:09.640
look, I think the real answer is going to be
link |
02:53:11.800
that for practical purposes,
link |
02:53:13.960
the official brand that says you can do exponential things
link |
02:53:18.240
in polynomial time is probably not gonna work.
link |
02:53:20.480
For people curious to kind of learn more,
link |
02:53:22.320
so this is more like, it's not middle school,
link |
02:53:24.680
we're gonna go to elementary school for a second.
link |
02:53:27.880
Maybe middle school, let's go to middle school.
link |
02:53:31.320
So if I were to try to maybe write a pamphlet
link |
02:53:38.280
of like Wolfram physics project for dummies,
link |
02:53:42.760
AKA for me, or maybe make a video on the basics,
link |
02:53:47.280
but not just the basics of the physics project,
link |
02:53:51.240
but the basics plus the most beautiful central ideas.
link |
02:53:59.280
How would you go about doing that?
link |
02:54:01.200
Could you help me out a little bit?
link |
02:54:02.720
Yeah, yeah, I mean, as a really practical matter,
link |
02:54:05.760
we have this kind of visual summary picture that we made,
link |
02:54:10.280
which I think is a pretty good,
link |
02:54:12.320
when I've tried to explain this to people
link |
02:54:14.520
and it's a pretty good place to start.
link |
02:54:17.120
As you got this rule, you apply the rule,
link |
02:54:19.800
you're building up this big hypergraph,
link |
02:54:22.760
you've got all these possibilities,
link |
02:54:24.560
you're kind of thinking about that
link |
02:54:25.960
in terms of quantum mechanics.
link |
02:54:27.680
I mean, that's a decent place to start.
link |
02:54:30.640
So basically the things we've talked about,
link |
02:54:33.000
which is space represented as a hypergraph,
link |
02:54:37.120
transformation of that space is kind of time.
link |
02:54:40.760
Yes.
link |
02:54:41.600
And then...
link |
02:54:43.040
Structure of that space,
link |
02:54:45.080
the curvature of that space has gravity.
link |
02:54:47.840
That can be explained without going anywhere
link |
02:54:49.440
near quantum mechanics.
link |
02:54:51.240
I would say that's actually easier to explain
link |
02:54:53.120
than special relativity.
link |
02:54:55.200
Oh, so going into general, so go into curvature.
link |
02:54:58.440
Yeah, I mean, special relativity,
link |
02:54:59.880
I think it's a little bit elaborate to explain.
link |
02:55:03.520
And honestly, you only care about it
link |
02:55:05.600
if you know about special relativity,
link |
02:55:06.840
if you know how special relativity
link |
02:55:08.000
is ordinarily derived and so on.
link |
02:55:09.920
So general relativity is easier.
link |
02:55:11.800
Is easier, yes.
link |
02:55:12.800
And then what about quantum?
link |
02:55:13.800
What's the easiest way to reveal...
link |
02:55:16.320
I think the basic point is just this.
link |
02:55:19.320
This fact that there are all these different branches,
link |
02:55:22.160
that there's this kind of map of how the branches work.
link |
02:55:25.320
And that, I mean, I think actually the recent things
link |
02:55:30.600
that we have about the double slit experiment
link |
02:55:32.280
are pretty good, because you can actually see this.
link |
02:55:34.920
You can see how the double slit phenomenon arises
link |
02:55:39.080
from just features of these graphs.
link |
02:55:41.360
Now, having said that,
link |
02:55:43.880
there is a little bit of sleight of hand there
link |
02:55:47.080
because the true story of the way
link |
02:55:49.880
that double slit thing works
link |
02:55:51.800
depends on the coordination of branchial space
link |
02:55:55.080
that, for example, in our internal team,
link |
02:55:57.800
there is still a vigorous battle going on
link |
02:56:00.200
about how that works.
link |
02:56:01.560
And what's becoming clear is...
link |
02:56:04.320
I mean, what's becoming clear
link |
02:56:05.880
is that it's mathematically really quite interesting.
link |
02:56:08.840
I mean, that is that there's a...
link |
02:56:10.720
It involves essentially putting space filling curves.
link |
02:56:13.120
You'll basically have a thing
link |
02:56:14.120
which is naturally two dimensional,
link |
02:56:15.840
and you're sort of mapping it into one dimension
link |
02:56:18.800
with a space filling curve.
link |
02:56:20.000
And it's like, why is it this space filling curve
link |
02:56:21.640
and another space filling curve?
link |
02:56:23.360
And that becomes a story about Riemann surfaces and things,
link |
02:56:26.560
and it's quite elaborate.
link |
02:56:29.200
But there's a more, a little bit sleight of hand way
link |
02:56:32.640
of doing it where it's surprisingly direct.
link |
02:56:36.680
It's...
link |
02:56:37.520
So a question that might be difficult to answer,
link |
02:56:42.520
but for several levels of people,
link |
02:56:46.120
could you give me advice on how we can learn more?
link |
02:56:50.360
Specifically, there is people that are completely outside
link |
02:56:54.640
and just curious and are captivated
link |
02:56:57.080
by the beauty of hypergraphs, actually.
link |
02:57:00.880
So people that just wanna explore, play around with this.
link |
02:57:04.040
Second level is people from, say, people like me
link |
02:57:09.040
who somehow got a PhD in computer science,
link |
02:57:12.720
but are not physicists.
link |
02:57:14.240
But fundamentally, the work you're doing
link |
02:57:16.600
is of computational nature.
link |
02:57:18.720
So it feels very accessible.
link |
02:57:20.480
So what can a person like that do to learn enough physics
link |
02:57:27.480
or not to be able to, one, explore the beauty of it,
link |
02:57:31.640
and two, the final level of contribute something
link |
02:57:36.640
of a level of even publishable,
link |
02:57:40.280
like strong, interesting ideas.
link |
02:57:43.240
So at all those layers, complete beginner,
link |
02:57:46.200
a CS person, and the CS person that wants to publish.
link |
02:57:49.560
I mean, I think that, I've written a bunch of stuff,
link |
02:57:53.120
a person called Jonathan Gorod,
link |
02:57:54.440
who's been a key person working on this project,
link |
02:57:56.160
has also written a bunch of stuff.
link |
02:57:58.040
And some other people started writing things too.
link |
02:58:00.800
And he's a physicist.
link |
02:58:02.120
Physicist.
link |
02:58:02.960
Well, he's, I would say, a mathematical physicist.
link |
02:58:05.240
Mathematical.
link |
02:58:06.080
Mathematical physicist.
link |
02:58:06.920
He's pretty mathematically sophisticated.
link |
02:58:08.800
He regularly outmathematicizes me.
link |
02:58:11.640
Yeah, strong mathematical physicist.
link |
02:58:14.720
Yeah, I looked at some of the papers.
link |
02:58:16.560
Right, but so, I mean,
link |
02:58:19.440
I wrote this kind of original announcement blog post
link |
02:58:22.440
about this project, which people seem to have found.
link |
02:58:25.480
I've been really happy, actually, that people who,
link |
02:58:30.880
people seem to have grokked key points from that,
link |
02:58:34.760
much deeper key points, people seem to have grokked
link |
02:58:37.400
than I thought they would grokk.
link |
02:58:39.520
And that's a kind of a long blog post
link |
02:58:41.600
that explains some of the things we talked about,
link |
02:58:43.120
like the hypergraph and the basic rules.
link |
02:58:45.360
And I don't, does it, I forget,
link |
02:58:47.920
it doesn't have any quantum mechanics in here.
link |
02:58:49.880
It does. It does.
link |
02:58:51.920
But we know a little bit more since that blog post
link |
02:58:54.720
that probably clarifies,
link |
02:58:56.480
but that blog post does a pretty decent job.
link |
02:58:59.560
And, you know, talking about things like, again,
link |
02:59:02.160
something we didn't mention,
link |
02:59:03.000
the fact that the uncertainty principle
link |
02:59:04.960
is a consequence of curvature in branchial space.
link |
02:59:07.760
How much physics should a person know
link |
02:59:10.120
to be able to understand the beauty of this framework
link |
02:59:14.480
and to contribute something novel?
link |
02:59:16.880
Okay, so I think that those are different questions.
link |
02:59:20.200
So, I mean, I think that the, why does this work?
link |
02:59:23.840
Why does this make any sense?
link |
02:59:27.440
To really know that,
link |
02:59:28.480
you have to know a fair amount of physics, okay?
link |
02:59:32.040
And for example, have a decent understanding.
link |
02:59:33.520
When you say, why does this work?
link |
02:59:35.040
You're referring to the connection between this model
link |
02:59:38.480
and general relativity, for example.
link |
02:59:40.600
You have to understand something about general relativity.
link |
02:59:43.160
There's also a side of this where just
link |
02:59:45.240
as the pure mathematical framework is fascinating.
link |
02:59:47.880
Yes.
link |
02:59:48.720
If you throw the physics out completely.
link |
02:59:50.360
Then it's quite accessible to, I mean, you know,
link |
02:59:52.520
I wrote this sort of long technical introduction
link |
02:59:55.280
to the project, which seems to have been very accessible
link |
02:59:58.480
to people who are, you know, who understand computation
link |
03:00:01.400
and formal abstract ideas, but are not specialists
link |
03:00:04.960
in physics or other kinds of things.
link |
03:00:07.240
I mean, the thing with the physics part of it is,
link |
03:00:10.280
you know, there's both a way of thinking
link |
03:00:14.600
and literally a mathematical formalism.
link |
03:00:16.840
I mean, it's like, you know,
link |
03:00:18.040
to know that we get the Einstein equations,
link |
03:00:19.960
to know we get the energy momentum tensor,
link |
03:00:22.120
you kind of have to know what the energy momentum tensor is.
link |
03:00:24.800
And that's physics.
link |
03:00:25.880
I mean, that's kind of graduate level physics basically.
link |
03:00:29.240
And so that, you know, making that final connection
link |
03:00:33.360
is requires some depth of physics knowledge.
link |
03:00:37.440
I mean, that's the unfortunate thing,
link |
03:00:38.880
the difference in machine learning and physics
link |
03:00:40.600
in the 21st century.
link |
03:00:42.880
Is it really out of reach of a year or two worth of study?
link |
03:00:47.440
No, you could get it in a year or two,
link |
03:00:49.920
but you can't get it in a month.
link |
03:00:51.600
Right.
link |
03:00:52.440
I mean.
link |
03:00:53.280
So, but it doesn't require necessarily like 15 years.
link |
03:00:56.160
No, it does not.
link |
03:00:57.000
And in fact, a lot of what has happened with this project
link |
03:01:00.240
makes a lot of this stuff much more accessible.
link |
03:01:02.800
There are things where it has been quite difficult
link |
03:01:04.800
to explain what's going on.
link |
03:01:06.040
And it requires much more, you know,
link |
03:01:09.160
having the concreteness of being able to do simulations,
link |
03:01:11.840
knowing that this thing that you might've thought
link |
03:01:15.160
was just an analogy is really actually what's going on,
link |
03:01:19.000
makes one feel much more secure
link |
03:01:21.040
about just sort of saying, this is how this works.
link |
03:01:24.240
And I think it will be, you know,
link |
03:01:26.240
the, I'm hoping the textbooks of the future,
link |
03:01:28.520
the physics textbooks of the future,
link |
03:01:30.480
there will be a certain compression.
link |
03:01:32.120
There will be things that used to be
link |
03:01:33.360
very much more elaborate because for example,
link |
03:01:35.240
even doing continuous mathematics
link |
03:01:36.720
versus this discrete mathematics,
link |
03:01:38.880
that, you know, to know how things work
link |
03:01:40.680
in continuous mathematics,
link |
03:01:41.800
you have to be talking about stuff
link |
03:01:43.120
and waving your hands about things.
link |
03:01:44.760
Whereas with discrete, the discrete version,
link |
03:01:47.120
it's just like, here is a picture.
link |
03:01:49.280
This is how it works.
link |
03:01:50.920
And there's no, oh, do we get the limit right?
link |
03:01:53.240
Did this, you know, did this thing that is of,
link |
03:01:55.560
you know, zero, you know, measure zero object,
link |
03:01:59.440
you know, interact with this thing in the right way.
link |
03:02:01.960
You don't have to have that whole discussion.
link |
03:02:03.400
It's just like, here's a picture, you know,
link |
03:02:05.520
this is what it does.
link |
03:02:07.160
And, you know, you can, then it takes more effort to say,
link |
03:02:09.560
what does it do in the limit when the picture gets very big?
link |
03:02:12.040
But you can do experiments
link |
03:02:13.120
to build up an intuition actually.
link |
03:02:14.360
Yes, right.
link |
03:02:15.200
And you can get sort of core intuition for what's going on.
link |
03:02:17.480
Now, in terms of contributing to this, the, you know,
link |
03:02:20.160
I would say that the study of the computational universe
link |
03:02:23.240
and how all these programs work
link |
03:02:24.520
in the computational universe,
link |
03:02:26.000
there's just an unbelievable amount to do there.
link |
03:02:28.760
And it is very close to the surface.
link |
03:02:31.320
That is, you know, high school kids,
link |
03:02:34.400
you can do experiments.
link |
03:02:36.080
It's not, you know, and you can discover things.
link |
03:02:38.960
I mean, you know, we, you can discover stuff about,
link |
03:02:42.600
I don't know, like this thing about expansion
link |
03:02:44.320
of branchial space.
link |
03:02:45.160
That's an absolutely accessible thing to look at.
link |
03:02:47.760
Now, you know, the main issue with doing these things
link |
03:02:50.680
is not, there isn't a lot of technical depth difficulty
link |
03:02:55.200
there.
link |
03:02:56.040
The actual doing of the experiments, you know,
link |
03:02:58.040
all the code is all on our website to do all these things.
link |
03:03:01.360
The real thing is sort of the judgment
link |
03:03:03.880
of what's the right experiment to do.
link |
03:03:05.600
How do you interpret what you see?
link |
03:03:07.800
That's the part that, you know,
link |
03:03:09.920
people will do amazing things with.
link |
03:03:11.840
And that's the part that, but,
link |
03:03:13.520
but it isn't like you have to have done 10 years of study
link |
03:03:17.040
to get to the point where you can do the experiments.
link |
03:03:18.840
You don't.
link |
03:03:19.680
That's a cool thing you can do experiments day one,
link |
03:03:21.840
basically.
link |
03:03:22.680
That's the amazing thing about,
link |
03:03:25.040
and you've actually put the tools out there.
link |
03:03:27.240
It's beautiful.
link |
03:03:28.080
It's mysterious.
link |
03:03:29.640
There's still, I would say, maybe you can correct me.
link |
03:03:32.720
It feels like there's a huge number of log hanging fruit
link |
03:03:36.440
on the mathematical side, at least not the physics side,
link |
03:03:39.440
perhaps.
link |
03:03:40.280
No, there's, look on the, on the, okay.
link |
03:03:42.800
On the physics side, we are,
link |
03:03:45.160
we're definitely in harvesting mode, you know.
link |
03:03:48.440
Of which, which fruit, the low hanging ones or?
link |
03:03:50.960
The low hanging ones, yeah, right.
link |
03:03:52.560
I mean, basically here's the thing.
link |
03:03:54.200
There's a certain list of, you know,
link |
03:03:56.120
here are the effects in quantum mechanics.
link |
03:03:57.800
Here are the effects in general activity.
link |
03:03:59.760
It's just like industrial harvesting.
link |
03:04:02.240
It's like, can we get this one, this one, this one,
link |
03:04:04.480
this one, this one?
link |
03:04:05.560
And the thing that's really, you know,
link |
03:04:07.560
interesting and satisfying, and it's like, you know,
link |
03:04:10.120
is one climbing the right mountain?
link |
03:04:11.520
Does one have the right model?
link |
03:04:12.920
The thing that's just amazing is, you know,
link |
03:04:15.920
we keep on like, are we going to get this one?
link |
03:04:18.280
How hard is this one?
link |
03:04:19.920
It's like, oh, you know, it looks really hard.
link |
03:04:22.920
It looks really hard.
link |
03:04:23.800
Oh, actually we can get it.
link |
03:04:26.760
And.
link |
03:04:27.600
And you're, you're continually surprised.
link |
03:04:29.040
I mean, it seems like I've been following your progress.
link |
03:04:31.520
It's kind of exciting.
link |
03:04:32.520
All the, in harvesting mode,
link |
03:04:34.320
all the things you're picking up along the way.
link |
03:04:35.880
Right, right.
link |
03:04:36.720
No, I mean, it's, it's the thing that is,
link |
03:04:38.320
I keep on thinking it's going to be more difficult
link |
03:04:40.200
than it is.
link |
03:04:41.040
Now that's a, you know, that's a, who knows what,
link |
03:04:43.360
I mean, the one thing, so the, the, the,
link |
03:04:45.880
the thing that's been a, was a big thing
link |
03:04:48.640
that I think we're, we're pretty close to.
link |
03:04:50.900
I mean, I can give you a little bit of the roadmap.
link |
03:04:52.480
It's sort of interesting to see, it's like,
link |
03:04:54.640
what are particles?
link |
03:04:55.720
What are things like electrons?
link |
03:04:56.880
How do they really work?
link |
03:04:58.520
Are you close to get like, what, what's a,
link |
03:05:01.400
are you close to trying to understand like the atom,
link |
03:05:03.800
the electrons, neutrons, protons?
link |
03:05:06.480
Okay, so this is, this is the stack.
link |
03:05:08.080
So the first thing we want to understand is
link |
03:05:11.680
the quantization of spin.
link |
03:05:13.360
So particles, they, they kind of spin,
link |
03:05:15.960
they have a certain angular momentum,
link |
03:05:18.120
that angular momentum,
link |
03:05:19.400
even though the masses of particles are all over the place,
link |
03:05:22.280
you know, the electron has a mass of 0.511 MeV,
link |
03:05:25.920
but you know, the proton is 938 MeV, et cetera, et cetera,
link |
03:05:28.760
et cetera, they're all kind of random numbers.
link |
03:05:30.640
The, the spins of all these particles
link |
03:05:32.720
are either integers or half integers.
link |
03:05:34.880
And that's a fact that was discovered in the 1920s, I guess.
link |
03:05:38.440
The, I think that we are close to understanding
link |
03:05:44.120
why spin is quantized.
link |
03:05:45.800
And that's a, and it, it appears to be
link |
03:05:48.280
a quite elaborate mathematical story
link |
03:05:50.280
about homotopic groups in twister space
link |
03:05:53.040
and all kinds of things.
link |
03:05:54.400
But bottom line is that seems within reach.
link |
03:05:58.000
And that's, that's a big deal
link |
03:05:59.200
because that's a very core feature of understanding
link |
03:06:01.680
how particles work in quantum mechanics.
link |
03:06:04.160
Another core feature is this difference between particles
link |
03:06:07.280
that obey the exclusion principle and sort of stay apart,
link |
03:06:10.600
that leads to the stability of matter and things like that,
link |
03:06:13.680
and particles that love to get together
link |
03:06:15.360
and be in the same state, things like photons,
link |
03:06:18.120
that, and that's what leads to phenomena like lasers,
link |
03:06:22.160
where you can get sort of coherently
link |
03:06:23.800
everything in the same state.
link |
03:06:25.280
That difference is the particles of integer spin
link |
03:06:29.240
are bosons like to get together in the same state,
link |
03:06:31.760
the particles of half integer spin are fermions,
link |
03:06:34.440
like electrons that they tend to stay apart.
link |
03:06:37.520
And so the question is, can we get that in our models?
link |
03:06:41.800
And, oh, just the last few days, I think we made,
link |
03:06:45.400
I mean, I think the story of,
link |
03:06:47.920
I mean, it's one of these things where we're really close.
link |
03:06:51.400
Is this connected fermions and bosons?
link |
03:06:53.680
Yeah, yeah.
link |
03:06:54.520
So this was what happens is what seems to happen, okay?
link |
03:06:57.720
It's, you know, subject to revision in the next few days.
link |
03:07:01.440
But what seems to be the case is that
link |
03:07:04.200
bosons are associated with essentially
link |
03:07:06.360
merging in multiway graphs,
link |
03:07:08.400
and fermions are associated with branching
link |
03:07:10.440
in multiway graphs.
link |
03:07:11.920
And that essentially the exclusion principle
link |
03:07:15.120
is the fact that in branchial space,
link |
03:07:18.320
things have a certain extent in branchial space
link |
03:07:21.360
that in which things are being sort of forced apart
link |
03:07:24.000
in branchial space, whereas the case of bosons,
link |
03:07:26.280
they get, they come together in branchial space.
link |
03:07:29.400
And the real question is, can we explain the relationship
link |
03:07:32.360
between that and these things called spinners,
link |
03:07:34.520
which are the representation of half integer spin particles
link |
03:07:37.440
that have this weird feature that usually when you go
link |
03:07:39.320
around 360 degree rotation,
link |
03:07:41.520
you get back to where you started from.
link |
03:07:43.400
But for a spinner, you don't get back
link |
03:07:44.760
to where you started from.
link |
03:07:46.040
It takes 720 degrees of rotation to get back
link |
03:07:48.800
to where you started from.
link |
03:07:50.240
And we are just, it feels like we are,
link |
03:07:53.160
we're just incredibly close to actually having that,
link |
03:07:55.440
understanding how that works.
link |
03:07:57.160
And it turns out, it looks like,
link |
03:07:59.000
my current speculation is that it's as simple
link |
03:08:01.640
as the directed hypergraphs versus undirected hypergraphs,
link |
03:08:07.760
the relationship between spinners and vectors.
link |
03:08:10.240
So, which is just interesting.
link |
03:08:11.800
Yeah, that would be interesting if these are all these kind
link |
03:08:13.840
of nice properties of this multi way graphs of branching
link |
03:08:18.600
and rejoining.
link |
03:08:19.920
Spinners have been very mysterious.
link |
03:08:21.760
And if that's what they turn out to be,
link |
03:08:23.880
there's going to be an easy explanation
link |
03:08:25.240
of what's going on.
link |
03:08:26.080
Directive versus undirective.
link |
03:08:27.160
It's just, and that's why there's only two different cases.
link |
03:08:30.600
It's why are spinners important in quantum mechanics?
link |
03:08:34.160
Can you just give a...
link |
03:08:35.680
Yeah, so spinners are important because they are,
link |
03:08:39.040
they're the representation of electrons
link |
03:08:41.480
which have half an inch of spin.
link |
03:08:43.400
They are, the wave functions of electrons are spinners.
link |
03:08:48.320
Just like the wave functions of photons are vectors,
link |
03:08:51.280
the wave functions of electrons are spinners.
link |
03:08:54.280
And they have this property that when you rotate
link |
03:08:58.040
by 360 degrees, they come back to minus one of themselves
link |
03:09:02.880
and take 720 degrees to get back to the original value.
link |
03:09:06.760
And they are a consequence of,
link |
03:09:10.640
we usually think of rotation in space as being,
link |
03:09:15.160
when you have this notion of rotational invariance
link |
03:09:18.720
and rotational invariance, as we ordinarily experience it,
link |
03:09:22.160
doesn't have the feature.
link |
03:09:23.280
If you go through 360 degrees,
link |
03:09:24.760
you go back to where you started from,
link |
03:09:26.440
but that's not true for electrons.
link |
03:09:28.480
And so that's why understanding how that works is important.
link |
03:09:32.480
Yeah, I've been playing with Mobius Strip
link |
03:09:34.920
quite a bit lately, just for fun.
link |
03:09:37.000
Yes, yes.
link |
03:09:37.840
It adds some funk, it has the same kind of funky properties.
link |
03:09:41.000
Yes, right, exactly.
link |
03:09:41.840
You can have this so called belt trick,
link |
03:09:43.560
which is this way of taking an extended object
link |
03:09:45.960
and you can see properties like spinners
link |
03:09:47.600
with that kind of extended object that...
link |
03:09:50.200
Yeah, it would be very cool if there's,
link |
03:09:51.720
it somehow connects the directive versus undirective.
link |
03:09:53.840
I think that's what it's gonna be.
link |
03:09:54.680
I think it's gonna be as simple as that, but we'll see.
link |
03:09:57.480
I mean, this is the thing that,
link |
03:09:59.680
this is the big sort of bizarre surprise is that,
link |
03:10:03.200
because I learned physics as probably, let's say,
link |
03:10:07.720
let's say a fifth generation in the sense that,
link |
03:10:10.080
if you go back to the 1920s and so on,
link |
03:10:11.960
there were the people who were originating
link |
03:10:13.720
quantum mechanics and so on.
link |
03:10:15.400
Maybe it's a little less than that.
link |
03:10:16.280
Maybe I was like a third generation or something.
link |
03:10:19.760
I don't know, but the people from whom I learned physics
link |
03:10:23.560
were the people who had been students of the students
link |
03:10:26.760
of the people who originated
link |
03:10:28.920
the current understanding of physics.
link |
03:10:31.240
And we're now at probably the seventh generation
link |
03:10:33.920
of physicists or something
link |
03:10:35.080
from the early days of 20th century physics.
link |
03:10:38.320
And whenever a field gets that many generations deep,
link |
03:10:43.360
it seems the foundations seem quite inaccessible.
link |
03:10:46.640
And they seem, it seems like
link |
03:10:48.160
you can't possibly understand that.
link |
03:10:49.800
We've gone through seven academic generations
link |
03:10:52.720
and that's been, you know, that's been this thing
link |
03:10:55.320
that's been difficult to understand for that long.
link |
03:10:58.600
It just can't be that simple.
link |
03:11:01.240
But in a sense, maybe that journey takes you
link |
03:11:03.800
to a simple explanation that was there all along.
link |
03:11:07.640
That's the whole. Right, right, right.
link |
03:11:08.480
I mean, you know, and the thing for me personally,
link |
03:11:10.640
the thing that's been quite interesting is, you know,
link |
03:11:13.200
I didn't expect this project to work in this way.
link |
03:11:16.200
And I, you know, but I had this sort of weird piece
link |
03:11:19.080
of personal history that I used to be a physicist
link |
03:11:21.840
and I used to do all this stuff.
link |
03:11:23.040
And I know, you know, the standard canon of physics,
link |
03:11:26.880
I knew it very well.
link |
03:11:28.760
And, you know, but then I'd been working
link |
03:11:31.280
on this kind of computational paradigm
link |
03:11:33.000
for basically 40 years.
link |
03:11:35.120
And the fact that, you know, I'm sort of now coming back
link |
03:11:38.800
to, you know, trying to apply that in physics,
link |
03:11:42.240
it kind of felt like that journey was necessary.
link |
03:11:44.920
Was this, when did you first try to play with a hypergraph?
link |
03:11:49.040
So what happened is,
link |
03:11:50.520
yeah, so what I had was, okay, so this is again,
link |
03:11:53.320
you know, one always feels dumb after the fact.
link |
03:11:56.320
It's obvious after the fact.
link |
03:11:58.800
But so back in the early 1990s,
link |
03:12:02.240
I realized that using graphs
link |
03:12:05.240
as a sort of underlying thing underneath space and time
link |
03:12:07.760
was going to be a useful thing to do.
link |
03:12:09.720
I figured out about multiway systems.
link |
03:12:12.760
I figured out the things about general relativity
link |
03:12:14.960
I'd figured out by the end of the 1990s.
link |
03:12:17.400
But I always felt there was a certain inelegance
link |
03:12:20.040
because I was using these graphs
link |
03:12:21.880
and there were certain constraints on these graphs
link |
03:12:23.880
that seemed like they were kind of awkward.
link |
03:12:26.440
It was kind of like, you can pick,
link |
03:12:28.320
it's like you couldn't pick any rule.
link |
03:12:30.240
It was like pick any number, but the number has to be prime.
link |
03:12:33.360
It was kind of like you couldn't,
link |
03:12:34.600
it was kind of an awkward special constraint.
link |
03:12:36.920
I had these trivalent graphs,
link |
03:12:38.400
graphs with just three connections from every node.
link |
03:12:41.440
Okay, so, but I discovered a bunch of stuff with that.
link |
03:12:44.280
And I thought it was kind of inelegant.
link |
03:12:46.280
And, you know, the other piece of sort of personal history
link |
03:12:48.680
is obviously I spent my life
link |
03:12:50.160
as a computational language designer.
link |
03:12:52.960
And so the story of computational language design
link |
03:12:55.160
is a story of how do you take all these random ideas
link |
03:12:58.000
in the world and kind of grind them down
link |
03:13:00.720
into something that is computationally
link |
03:13:02.720
as simple as possible.
link |
03:13:04.760
And so, you know, I've been very interested
link |
03:13:06.680
in kind of simple computational frameworks
link |
03:13:09.280
for representing things and have, you know,
link |
03:13:12.600
ridiculous amounts of experience in trying to do that.
link |
03:13:15.800
And actually all of those trajectories of your life
link |
03:13:18.280
kind of came together.
link |
03:13:19.320
So you make it sound like you could have come up
link |
03:13:21.600
with everything you're working on now decades ago,
link |
03:13:24.640
but in reality.
link |
03:13:26.440
Look, two things slowed me down.
link |
03:13:28.080
I mean, one thing that slowed me down was
link |
03:13:30.280
I couldn't figure out how to make it elegant.
link |
03:13:32.840
And that turns out hypergraphs were the key to that.
link |
03:13:35.600
And that I figured out about less than two years ago now.
link |
03:13:40.160
And the other, I mean, I think,
link |
03:13:43.360
so that was sort of a key thing.
link |
03:13:46.160
Well, okay, so the real embarrassment of this project, okay,
link |
03:13:49.760
is that the final structure that we have
link |
03:13:52.680
that is the foundation for this project
link |
03:13:55.840
is basically a kind of an idealized version,
link |
03:14:00.000
a formalized version of the exact same structure
link |
03:14:03.560
that I've used to build computational languages
link |
03:14:05.640
for more than 40 years.
link |
03:14:07.160
But it took me, but I didn't realize that.
link |
03:14:09.840
And, you know.
link |
03:14:11.280
And there yet may be others.
link |
03:14:12.840
So we're focused on physics now,
link |
03:14:14.360
but I mean, that's what the new kind of science was about.
link |
03:14:17.720
Same kind of stuff.
link |
03:14:19.120
And this, in terms of mathematically,
link |
03:14:21.720
well, the beauty of it.
link |
03:14:22.960
So there could be entire other kind of objects
link |
03:14:26.160
that are useful for,
link |
03:14:27.600
like we're not talking about, you know,
link |
03:14:29.760
machine learning, for example.
link |
03:14:31.760
Maybe there's other variants of the hypergraph
link |
03:14:33.880
that are very useful for reasoning.
link |
03:14:35.720
Well, we'll see whether the multiway graph
link |
03:14:37.440
or machine learning system is interesting.
link |
03:14:40.320
Okay.
link |
03:14:41.480
Let's leave it at that.
link |
03:14:42.320
That's conversation number three.
link |
03:14:43.640
That's, we're not gonna go there right now, but.
link |
03:14:47.440
One of the things you've mentioned
link |
03:14:49.040
is the space of all possible rules
link |
03:14:52.640
that we kind of discussed a little bit.
link |
03:14:55.200
That, you know, that could be, I guess,
link |
03:14:58.000
the set of possible rules is infinite.
link |
03:15:00.800
Right.
link |
03:15:01.640
Well, so here's the big sort of one of the conundrums
link |
03:15:04.200
that I'm kind of trying to deal with is,
link |
03:15:07.840
let's say we think we found the rule for the universe
link |
03:15:11.720
and we say, here it is.
link |
03:15:13.160
You know, write it down.
link |
03:15:14.200
It's a little tiny thing.
link |
03:15:15.800
And then we say, gosh, that's really weird.
link |
03:15:18.000
Why did we get that one?
link |
03:15:20.640
Right.
link |
03:15:21.480
And then we're in this whole situation
link |
03:15:23.240
because let's say it's fairly simple.
link |
03:15:25.480
How did we come up the winners
link |
03:15:27.680
getting one of the simple possible universe rules?
link |
03:15:30.400
Why didn't we get what some incredibly complicated rule?
link |
03:15:33.600
Why do we get one of the simpler ones?
link |
03:15:34.880
And that's a thing which, you know,
link |
03:15:36.560
in the history of science, you know,
link |
03:15:38.800
the whole sort of story of Copernicus and so on was,
link |
03:15:42.680
you know, we used to think the earth
link |
03:15:43.920
was the center of the universe,
link |
03:15:44.960
but now we find out it's not.
link |
03:15:46.320
And we're actually just in some, you know,
link |
03:15:47.760
random corner of some random galaxy
link |
03:15:50.480
out in this big universe, there's nothing special about us.
link |
03:15:53.800
So if we get, you know, universe number 317
link |
03:15:58.120
out of all the infinite number of possibilities,
link |
03:16:00.400
how do we get something that small and simple?
link |
03:16:02.720
Right, so I was very confused by this.
link |
03:16:05.040
And it's like, what are we going to say about this?
link |
03:16:06.720
How are we going to explain this?
link |
03:16:08.560
And I thought it was, might be one of these things
link |
03:16:10.320
where you just, you know, you can get it to the threshold,
link |
03:16:13.320
and then you find out its rule number, such and such,
link |
03:16:15.480
and you just have no idea why it's like that.
link |
03:16:17.760
Okay, so then I realized
link |
03:16:20.040
it's actually more bizarre than that, okay?
link |
03:16:22.560
So we talked about multiway graphs.
link |
03:16:25.040
We talked about this idea that
link |
03:16:26.760
you take these underlying transformation rules
link |
03:16:29.040
on these hypergraphs, and you apply them
link |
03:16:31.840
wherever the rule can apply, you apply it.
link |
03:16:34.720
And that makes this whole multiway graph of possibilities.
link |
03:16:37.680
Okay, so let's go a little bit weirder.
link |
03:16:39.960
Let's say that at every place,
link |
03:16:42.800
not only do you apply a particular rule
link |
03:16:45.240
in all possible ways it can apply,
link |
03:16:47.160
but you apply all possible rules
link |
03:16:49.520
in all possible ways they can apply.
link |
03:16:51.920
As you say, that's just crazy.
link |
03:16:53.760
That's way too complicated.
link |
03:16:54.920
You're never going to be able to conclude anything.
link |
03:16:57.240
Okay, however, turns out that...
link |
03:17:00.800
Don't tell me there's some kind of invariance.
link |
03:17:02.880
Yeah, yeah.
link |
03:17:04.000
So what happens is...
link |
03:17:06.440
And that would be amazing.
link |
03:17:08.080
Right, so this thing that you get
link |
03:17:11.240
is this kind of ruleal multiway graph,
link |
03:17:13.360
this multiway graph that is a branching of rules
link |
03:17:15.880
as well as a branching of possible applications of rules.
link |
03:17:19.760
This thing has causal invariance.
link |
03:17:22.080
It's an inevitable feature that it shows causal invariance.
link |
03:17:25.320
And that means that you can take different reference frames,
link |
03:17:28.640
different ways of slicing this thing,
link |
03:17:30.920
and they will all in some sense be equivalent.
link |
03:17:33.920
If you make the right translation, they will be equivalent.
link |
03:17:37.360
So, okay, so the basic point here is...
link |
03:17:40.360
If that's true, that would be beautiful.
link |
03:17:43.040
It is true, and it is beautiful.
link |
03:17:45.640
It's not just an intuition, there is some...
link |
03:17:47.480
No, no, no, there's real mathematics behind this,
link |
03:17:50.120
and it is...
link |
03:17:53.360
Okay, so here's where it comes in.
link |
03:17:55.160
Yeah, that's amazing.
link |
03:17:57.360
Right, so by the way, I mean,
link |
03:17:58.800
the mathematics it's connected to
link |
03:18:00.240
is the mathematics of higher category theory
link |
03:18:02.360
and group voids and things like this,
link |
03:18:04.240
which I've always been afraid of,
link |
03:18:05.880
but now I'm finally wrapping my arms around it.
link |
03:18:09.960
But it's also related to...
link |
03:18:13.120
It also relates to computational complexity theory.
link |
03:18:16.160
It's also deeply related to the P versus NP problem
link |
03:18:19.200
and other things like this.
link |
03:18:20.440
Again, it seems completely bizarre
link |
03:18:21.880
that these things are connected,
link |
03:18:22.960
but here's why it's connected.
link |
03:18:25.160
This space of all possible...
link |
03:18:28.000
Okay, so a Turing machine, very simple model of computation.
link |
03:18:32.080
You know, you just got this tape
link |
03:18:34.280
where you write down, you know, ones and zeros
link |
03:18:36.480
or something on the tape,
link |
03:18:37.400
and you have this rule that says, you know,
link |
03:18:40.120
you change the number,
link |
03:18:41.520
you move the head on the tape, et cetera.
link |
03:18:44.320
You have a definite rule for doing that.
link |
03:18:46.040
A deterministic Turing machine
link |
03:18:47.880
just does that deterministically.
link |
03:18:50.000
Given the configuration of the tape,
link |
03:18:51.760
it will always do the same thing.
link |
03:18:53.600
A non deterministic Turing machine
link |
03:18:55.760
can have different choices that it makes at every step.
link |
03:18:58.960
And so, you know, you know this stuff,
link |
03:19:01.840
you probably teach this stuff.
link |
03:19:04.440
It, you know, so a non deterministic Turing machine
link |
03:19:09.200
has the set of branching possibilities,
link |
03:19:11.680
which is in fact, one of these multiway graphs.
link |
03:19:14.360
And in fact, if you say,
link |
03:19:16.240
imagine the extremely non deterministic Turing machine,
link |
03:19:19.520
the Turing machine that can just do,
link |
03:19:22.560
that takes any possible rule at each step,
link |
03:19:25.440
that is this real multiway graph.
link |
03:19:27.520
The set of possible histories
link |
03:19:31.280
of that extreme non deterministic Turing machine
link |
03:19:33.720
is a Rulio multiway graph.
link |
03:19:35.880
And you're, what term are you using?
link |
03:19:37.680
Rulio?
link |
03:19:38.520
Rulio.
link |
03:19:39.360
Rulio, I like it.
link |
03:19:40.200
It's a weird word.
link |
03:19:41.040
Yeah, it's a weird word, right?
link |
03:19:41.880
Rulio multiway graph.
link |
03:19:44.160
Okay, so this, so that.
link |
03:19:45.880
I'm trying to think of,
link |
03:19:48.880
I'm trying to think of the space of rules.
link |
03:19:51.800
So these are basic transformations.
link |
03:19:54.240
So in a Turing machine,
link |
03:19:55.760
it's like it says, move left, move, you know,
link |
03:19:58.280
if it's a one, if it's a black square under the head,
link |
03:20:02.320
move left and right to green square.
link |
03:20:04.840
That's a rule.
link |
03:20:05.720
That's a very basic rule,
link |
03:20:06.720
but I'm trying to see the rules on the hypergraphs,
link |
03:20:09.880
how rich of the programs can they be?
link |
03:20:12.200
Or do they all ultimately just map into something simple?
link |
03:20:15.520
Yeah, they're all, I mean, hypergraphs,
link |
03:20:18.000
that's another layer of complexity on this whole thing.
link |
03:20:20.200
You can think about these in transformations of hypergraphs,
link |
03:20:23.040
but Turing machines are a little bit simpler.
link |
03:20:24.360
You just think of it Turing machines, okay.
link |
03:20:25.600
Right, they're a little bit simpler.
link |
03:20:27.280
So if you look at these extreme
link |
03:20:29.120
non deterministic Turing machines,
link |
03:20:30.920
you're mapping out all the possible non deterministic paths
link |
03:20:35.120
that the Turing machine can follow.
link |
03:20:37.160
And if you ask the question, can you reach, okay,
link |
03:20:41.040
so a deterministic Turing machine follows a single path.
link |
03:20:44.800
The non deterministic Turing machine fills out
link |
03:20:46.960
this whole sort of ball of possibilities.
link |
03:20:50.680
And so then the P versus MP problem
link |
03:20:53.280
ends up being questions about,
link |
03:20:55.160
and we haven't completely figured out
link |
03:20:56.760
all the details of this,
link |
03:20:57.600
but it's basically has to do with questions
link |
03:20:59.920
about the growth of that ball relative
link |
03:21:03.320
to what happens with individual paths and so on.
link |
03:21:05.800
So essentially there's a geometrization
link |
03:21:07.800
of the P versus MP problem that comes out of this.
link |
03:21:10.120
That's a sideshow, okay.
link |
03:21:12.000
The main event here is the statement
link |
03:21:14.960
that you can look at this multiway graph
link |
03:21:19.960
where the branches correspond
link |
03:21:21.800
not just to different applications of a single rule,
link |
03:21:24.200
but to different applications of different rules, okay.
link |
03:21:28.200
And that then that when you say,
link |
03:21:31.960
I'm going to be an observer embedded in that system
link |
03:21:35.440
and I'm going to try and make sense
link |
03:21:36.960
of what's going on in the system.
link |
03:21:38.760
And to do that, I essentially am picking a reference frame
link |
03:21:43.040
and that turns out to be, well, okay.
link |
03:21:46.560
So the way this comes out essentially
link |
03:21:48.600
is the reference frame you pick
link |
03:21:50.720
is the rule that you infer is what's going on
link |
03:21:53.800
in the universe, even though all possible rules
link |
03:21:57.440
are being run, although all those possible rules
link |
03:22:01.240
are in a sense giving the same answer
link |
03:22:02.720
because of causal invariance.
link |
03:22:04.560
But what you see could be completely different.
link |
03:22:08.480
If you pick different reference frames,
link |
03:22:10.360
you essentially have a different description language
link |
03:22:12.920
for describing the universe.
link |
03:22:14.960
Okay, so what does this really mean in practice?
link |
03:22:17.320
So imagine there's us.
link |
03:22:19.640
We think about the universe in terms of space and time
link |
03:22:22.280
and we have various kinds of description models and so on.
link |
03:22:25.000
Now let's imagine the friendly aliens, for example, right?
link |
03:22:29.040
How do they describe their universe?
link |
03:22:31.320
Well, you know, our description of the universe
link |
03:22:33.440
probably is affected by the fact that, you know,
link |
03:22:36.160
we are about the size we are, you know,
link |
03:22:37.920
a meter ish tall, so to speak.
link |
03:22:40.240
We have brain processing speeds,
link |
03:22:41.840
we're about the speeds we have.
link |
03:22:43.680
We're not the size of planets, for example,
link |
03:22:46.320
where the speed of light really would matter.
link |
03:22:48.600
You know, in our everyday life,
link |
03:22:50.040
the speed of light doesn't really matter.
link |
03:22:51.800
Everything can be, you know,
link |
03:22:52.920
the fact that the speed of light is finite is irrelevant.
link |
03:22:55.200
It could as well be infinite.
link |
03:22:56.720
We wouldn't make any difference.
link |
03:22:58.480
You know, it affects the ping times on the internet.
link |
03:23:01.240
That's about the level of how we notice the speed of light.
link |
03:23:06.040
In our sort of everyday existence,
link |
03:23:07.400
we don't really notice it.
link |
03:23:09.360
And so we have a way of describing the universe
link |
03:23:12.240
that's based on our sensory, you know, our senses,
link |
03:23:17.240
these days also on the mathematics we've constructed
link |
03:23:19.760
and so on, but the realization is
link |
03:23:22.520
it's not the only way to do it.
link |
03:23:24.160
There will be completely, utterly incoherent descriptions
link |
03:23:28.200
of the universe, which correspond
link |
03:23:30.840
to different reference frames in this sort of ruleal space.
link |
03:23:34.240
In the ruleal space, that's fascinating.
link |
03:23:36.080
So we have some kind of reference frame
link |
03:23:38.200
in this ruleal space, and from that.
link |
03:23:41.680
That's why we are attributing this rule to the universe.
link |
03:23:45.600
So in other words, when we say,
link |
03:23:47.320
why is it this rule and not another,
link |
03:23:49.440
the answer is just, you know,
link |
03:23:52.280
shine the light back on us, so to speak.
link |
03:23:54.600
It's because of the reference frame that we've picked
link |
03:23:57.240
in our way of understanding what's happening
link |
03:23:58.960
in this sort of space of all possible rules and so on.
link |
03:24:02.320
But also in the space from this reference frame,
link |
03:24:06.120
because of the ruleal, the invariance,
link |
03:24:12.200
that simple, that the rule on which the universe,
link |
03:24:17.200
with which you can run the universe,
link |
03:24:19.840
might as well be simple.
link |
03:24:21.360
Yes, yes, but okay, so here's another point.
link |
03:24:23.720
So this is, again, these are a little bit mind twisting
link |
03:24:26.800
in some ways, but the, okay, another thing that's sort of,
link |
03:24:31.400
we know from computation is this idea
link |
03:24:34.640
of computation universality.
link |
03:24:36.480
The fact that given that we have a program
link |
03:24:38.880
that runs on one kind of computer, we can as well,
link |
03:24:42.320
you know, we can convert it to run
link |
03:24:44.280
on any other kind of computer.
link |
03:24:45.380
We can emulate one kind of computer with another.
link |
03:24:47.880
So that might lead you to say, well,
link |
03:24:50.640
you think you have the rule for the universe,
link |
03:24:52.800
but you might as well be running it on a Turing machine
link |
03:24:54.840
because we know we can emulate any computational rule
link |
03:24:59.000
on any kind of machine.
link |
03:25:00.920
And that's essentially the same thing
link |
03:25:02.300
that's being said here.
link |
03:25:03.680
That is that what we're doing is we're saying
link |
03:25:07.320
these different interpretations of physics correspond
link |
03:25:11.280
to essentially running physics
link |
03:25:13.400
on different underlying, you know,
link |
03:25:16.040
thinking about the physics as running in different
link |
03:25:18.140
with different underlying rules
link |
03:25:19.540
as if different underlying computers were running them.
link |
03:25:22.980
And, but because of computation universality
link |
03:25:26.060
or more accurately, because of this principle
link |
03:25:27.720
of computational equivalence thing of mine,
link |
03:25:30.360
there's that they are,
link |
03:25:33.520
these things are ultimately equivalent.
link |
03:25:35.760
So the only thing that is the ultimate fact
link |
03:25:38.120
about the universe, the ultimate fact that doesn't depend
link |
03:25:40.920
on any of these, you know, we don't have to talk
link |
03:25:42.760
about specific rules, et cetera, et cetera, et cetera.
link |
03:25:44.640
The ultimate fact is the universe is computational
link |
03:25:48.360
and it is the things that happen in the universe
link |
03:25:52.640
are the kinds of computations that the principle
link |
03:25:54.920
of computational equivalence says should happen.
link |
03:25:57.560
Now that might sound like you're not really saying
link |
03:26:00.440
anything there, but you are because you can,
link |
03:26:03.920
you could in principle have a hyper computer
link |
03:26:06.640
that things that take an ordinary computer
link |
03:26:09.720
an infinite time to do the hyper computer can just say,
link |
03:26:12.000
oh, I know the answer.
link |
03:26:13.480
It's this immediately.
link |
03:26:15.720
What this is saying is the universe is not a hyper computer.
link |
03:26:19.600
It's not simpler than a,
link |
03:26:21.800
an ordinary Turing machine type computer.
link |
03:26:24.040
It's exactly like an ordinary Turing machine type computer.
link |
03:26:28.080
And so that's the, that's in the end,
link |
03:26:30.040
the sort of net net conclusion is that's the thing
link |
03:26:34.000
that is the sort of the hard immovable fact
link |
03:26:36.600
about the universe.
link |
03:26:38.000
That's sort of the fundamental principle of the universe
link |
03:26:41.600
is that it is computational and not hyper computational
link |
03:26:45.440
and not sort of infra computational.
link |
03:26:47.280
It is this level of computational ability
link |
03:26:50.360
and it's, it kind of has,
link |
03:26:53.080
and that's sort of the, the, the core fact, but now,
link |
03:26:57.080
you know, this, this idea that you can have these different
link |
03:26:59.800
kind of a rule reference frames,
link |
03:27:02.280
these different description languages for the universe.
link |
03:27:05.280
It makes me, you know, I used to think, okay, you know,
link |
03:27:08.840
imagine the aliens,
link |
03:27:09.840
imagine the extraterrestrial intelligence thing, you know,
link |
03:27:12.560
at least they experienced the same physics.
link |
03:27:15.560
And now I've realized it isn't true.
link |
03:27:17.440
They could have a different rule frame.
link |
03:27:19.240
That's fascinating.
link |
03:27:20.480
That they can end up with a, a, a,
link |
03:27:23.920
a description of the universe that is utterly,
link |
03:27:26.040
utterly incoherent with ours.
link |
03:27:28.040
And that's also interesting in terms of how we think about,
link |
03:27:31.320
well, intelligence, the nature of intelligence and so on.
link |
03:27:33.600
You know, I'm, I'm fond of the quote, you know,
link |
03:27:35.440
the weather has a mind of its own because these are,
link |
03:27:38.640
you know, these are sort of computationally that,
link |
03:27:41.040
that system is computationally equivalent to the system
link |
03:27:44.760
that is our brains and so on.
link |
03:27:46.560
And what's different is we don't have a way to understand,
link |
03:27:49.960
you know, what the weather is trying to do, so to speak.
link |
03:27:52.520
We have a story about what's happening in our brains.
link |
03:27:54.880
We don't have a sort of connection
link |
03:27:56.680
to what's happening there.
link |
03:27:57.800
So we actually, it's funny,
link |
03:27:59.680
last time we talked maybe over a year ago,
link |
03:28:04.160
we talked about how it was more based on your work
link |
03:28:08.080
with Arrival.
link |
03:28:09.920
We talked about how would we communicate
link |
03:28:11.600
with alien intelligences.
link |
03:28:14.160
Can you maybe comment on how we might,
link |
03:28:18.000
how the Wolfram Physics Project changed your view,
link |
03:28:20.720
how we might be able to communicate
link |
03:28:22.200
with alien intelligence?
link |
03:28:23.280
Like if they showed up,
link |
03:28:25.040
is it possible that because of our comprehension
link |
03:28:30.080
of the physics of the world might be completely different,
link |
03:28:33.640
we would just not be able to communicate at all?
link |
03:28:36.600
Here's the thing, you know, intelligence is everywhere.
link |
03:28:41.520
The fact this idea that there's this notion of,
link |
03:28:43.800
oh, there's gonna be this amazing
link |
03:28:45.080
extraterrestrial intelligence
link |
03:28:46.400
and it's gonna be this unique thing.
link |
03:28:48.760
It's just not true.
link |
03:28:50.080
It's the same thing.
link |
03:28:51.360
You know, I think people will realize this
link |
03:28:53.240
about the time when people decide
link |
03:28:54.840
that artificial intelligences are kind of
link |
03:28:57.280
just natural things that are like human intelligences.
link |
03:29:01.160
They'll realize that extraterrestrial intelligences
link |
03:29:04.520
or intelligences associated with physical systems
link |
03:29:07.720
and so on, it's all the same kind of thing.
link |
03:29:09.760
It's ultimately computation.
link |
03:29:11.160
It's all the same.
link |
03:29:12.080
It's all just computation.
link |
03:29:13.280
And the issue is, can you, are you sort of inside it?
link |
03:29:17.160
Are you thinking about it?
link |
03:29:19.200
Do you have sort of a story you're telling yourself
link |
03:29:22.200
about it?
link |
03:29:23.160
And you know, the weather could have a story
link |
03:29:25.200
it's telling itself about what it's doing.
link |
03:29:27.560
We just, it's utterly incoherent with the stories
link |
03:29:30.920
that we tell ourselves based on how our brains work.
link |
03:29:33.560
I mean, ultimately it must be a question
link |
03:29:37.080
whether we can align.
link |
03:29:39.280
Exactly.
link |
03:29:40.120
Align with the kind of intelligence.
link |
03:29:41.960
Right, right, right.
link |
03:29:42.800
So there's a systematic way of doing it.
link |
03:29:44.200
Right, so the question is in the space
link |
03:29:45.520
of all possible intelligences,
link |
03:29:47.240
what's the, how do you think about the distance
link |
03:29:50.440
between description languages
link |
03:29:52.400
for one intelligence versus another?
link |
03:29:54.680
And needless to say, I have thought about this
link |
03:29:57.120
and you know, I don't have a great answer yet,
link |
03:30:00.880
but I think that's a thing
link |
03:30:02.920
where there will be things that can be said
link |
03:30:04.440
and there'll be things that where you can sort of
link |
03:30:06.000
start to characterize, you know,
link |
03:30:08.400
what is the translation distance between this,
link |
03:30:12.880
you know, version of the universe
link |
03:30:15.120
or this kind of set of computational rules
link |
03:30:17.840
and this other one.
link |
03:30:18.800
In fact, okay, so this is a, you know,
link |
03:30:21.480
there's this idea of algorithmic information theory.
link |
03:30:23.560
There's this question of sort of what is the,
link |
03:30:25.800
when you have something,
link |
03:30:28.680
what is the sort of shortest description you can make of it
link |
03:30:31.520
where that description could be saying,
link |
03:30:33.320
run this program to get the thing, right?
link |
03:30:36.480
So I'm pretty sure that there will be a physicalization
link |
03:30:45.280
of the idea of algorithmic information
link |
03:30:47.720
and that, okay, this is again, a little bit bizarre,
link |
03:30:51.560
but so I mentioned that there's the speed of light,
link |
03:30:54.480
maximum speed of information transmission in physical space.
link |
03:30:57.560
There's a maximum speed of information transmission
link |
03:30:59.840
in branchial space, which is a maximum entanglement speed.
link |
03:31:02.920
There's a maximum speed of information transmission
link |
03:31:05.240
in ruleal space, which is,
link |
03:31:07.160
has to do with a maximum speed of translation
link |
03:31:10.600
between different description languages.
link |
03:31:14.480
And again, I'm not fully wrapped my brain around this one.
link |
03:31:17.440
Yeah, that one just blows my mind to think about that,
link |
03:31:20.080
but that starts getting closer to the, yeah,
link |
03:31:22.800
the intelligence. It's kind of a physicalization.
link |
03:31:25.280
Right, and it's also a physicalization
link |
03:31:27.840
of algorithmic information.
link |
03:31:29.920
And I think there's probably a connection between,
link |
03:31:32.320
I mean, there's probably a connection
link |
03:31:33.600
between the notion of energy and some of these things,
link |
03:31:36.600
which again, I hadn't seen all this coming.
link |
03:31:39.400
I've always been a little bit resistant
link |
03:31:41.120
to the idea of connecting physical energy
link |
03:31:43.480
to things in computation theory,
link |
03:31:45.640
but I think that's probably coming.
link |
03:31:47.200
And that's what essentially at the core
link |
03:31:48.560
with the physics project is
link |
03:31:50.680
that you're connecting information theory with physics.
link |
03:31:55.560
Yeah, it's computation.
link |
03:31:56.880
Computation with our physical universe.
link |
03:31:59.560
Yeah, right.
link |
03:32:00.400
I mean, the fact that our physical universe is,
link |
03:32:03.480
right, that we can think of it as a computation
link |
03:32:05.720
and that we can have discussions like,
link |
03:32:08.760
the theory of the physical universe
link |
03:32:11.000
is the same kind of a theory as the P versus MP problem
link |
03:32:14.520
and so on is really, I think that's really interesting.
link |
03:32:18.640
And the fact that, well, okay,
link |
03:32:21.520
so this kind of brings me to one more thing
link |
03:32:24.240
that I have to in terms of this sort of unification
link |
03:32:26.120
of different ideas, which is metamathematics.
link |
03:32:29.640
Yeah, let's talk about that.
link |
03:32:30.520
You mentioned that earlier.
link |
03:32:31.680
What the heck is metamathematics and...
link |
03:32:34.760
Okay, so here's what, okay.
link |
03:32:36.880
So what is mathematics?
link |
03:32:38.840
Mathematics, sort of at a lowest level,
link |
03:32:43.840
one thinks of mathematics as you have certain axioms.
link |
03:32:47.400
You say things like X plus Y is the same as Y plus X.
link |
03:32:51.840
That's an axiom about addition.
link |
03:32:55.360
And then you say, we've got these axioms
link |
03:32:57.360
and from these axioms, we derive all these theorems
link |
03:33:00.560
that fill up the literature of mathematics.
link |
03:33:02.880
The activity of mathematicians
link |
03:33:04.760
is to derive all these theorems.
link |
03:33:06.800
Actually, the axioms of mathematics are very small.
link |
03:33:10.360
You can fit, when I did my new kind of science book,
link |
03:33:13.520
I fit all of the standard axioms of mathematics
link |
03:33:16.000
on basically a page and a half.
link |
03:33:18.760
Not much stuff.
link |
03:33:19.640
It's like a very simple rule
link |
03:33:21.400
from which all of mathematics arises.
link |
03:33:24.000
The way it works though is a little different
link |
03:33:26.640
from the way things work in sort of a computation
link |
03:33:31.720
because in mathematics, what you're interested in
link |
03:33:33.440
is a proof and the proof says,
link |
03:33:36.160
from here, you can use, from this expression, for example,
link |
03:33:40.360
you can use these axioms to get to this other expression.
link |
03:33:43.040
So that proves these two things are equal.
link |
03:33:45.440
Okay, so we can begin to see how this has been going to work.
link |
03:33:49.040
What's gonna happen is there are paths
link |
03:33:51.360
in metamathematical space.
link |
03:33:53.400
So what happens is each, two different ways to look at it.
link |
03:33:57.640
You can just look at it as mathematical expressions
link |
03:33:59.880
or you can look at it as mathematical statements,
link |
03:34:02.640
postulates or something.
link |
03:34:04.120
But either way, you think of these things
link |
03:34:06.440
and they are connected by these axioms.
link |
03:34:11.480
So in other words, you have some fact
link |
03:34:14.760
or you have some expression, you apply this axiom,
link |
03:34:16.960
you get some other expression.
link |
03:34:18.840
And in general, given some expression,
link |
03:34:21.600
there may be many possible different expressions
link |
03:34:23.880
you can get.
link |
03:34:24.840
You basically build up a multiway graph
link |
03:34:27.320
and a proof is a path through the multiway graph
link |
03:34:31.120
that goes from one thing to another thing.
link |
03:34:34.200
The path tells you how did you get from one thing
link |
03:34:36.920
to the other thing.
link |
03:34:37.760
It's the story of how you got from this to that.
link |
03:34:40.680
The theorem is the thing at one end
link |
03:34:42.840
is equal to the thing at the other end.
link |
03:34:44.640
The proof is the path you go down
link |
03:34:46.880
to get from one thing to the other.
link |
03:34:48.600
You mentioned that Gödel's incompleteness theorem
link |
03:34:52.600
fits naturally there.
link |
03:34:53.560
How does it fit?
link |
03:34:54.400
Yeah, so what happens there is that the Gödel's theorem
link |
03:34:57.160
is basically saying that there are paths of infinite length.
link |
03:35:01.240
That is that there's no upper bound.
link |
03:35:03.120
If you know these two things,
link |
03:35:04.240
you say, I'm trying to get from here to here,
link |
03:35:06.200
how long do I have to go?
link |
03:35:07.920
You say, well, I've looked at all the paths of length 10.
link |
03:35:10.800
Somebody says, that's not good enough.
link |
03:35:12.600
That path might be of length a billion.
link |
03:35:14.720
And there's no upper bound on how long that path is.
link |
03:35:17.400
And that's what leads to the incompleteness theorem.
link |
03:35:19.760
So I mean, the thing that is kind of an emerging idea
link |
03:35:24.480
is you can start asking,
link |
03:35:26.160
what's the analog of Einstein's equations
link |
03:35:27.840
in metamathematical space?
link |
03:35:29.720
What's the analog of a black hole
link |
03:35:31.160
in metamathematical space?
link |
03:35:33.120
What's the hope of this?
link |
03:35:33.960
So yeah, it's fascinating to model all the mathematics
link |
03:35:36.840
in this way.
link |
03:35:37.680
So here's what it is.
link |
03:35:38.520
This is mathematics in bulk.
link |
03:35:40.320
So human mathematicians have made a few million theorems.
link |
03:35:44.000
They've published a few million theorems.
link |
03:35:45.800
But imagine the infinite future of mathematics.
link |
03:35:48.400
Apply something to mathematics
link |
03:35:50.440
that mathematics likes to apply to other things.
link |
03:35:52.360
Take a limit.
link |
03:35:53.520
What is the limit of the infinite future of mathematics?
link |
03:35:56.320
What does it look like?
link |
03:35:57.560
What is the continuum limit of mathematics?
link |
03:35:59.560
What is the, as you just fill in
link |
03:36:01.560
more and more and more theorems,
link |
03:36:03.120
what does it look like?
link |
03:36:04.040
What does it do?
link |
03:36:05.040
How does, what kinds of conclusions can you make?
link |
03:36:07.360
So for example, one thing I've just been doing
link |
03:36:09.800
is taking Euclid.
link |
03:36:10.960
So Euclid, very impressive.
link |
03:36:12.760
He had 10 axioms, he derived 465 theorems, okay?
link |
03:36:17.400
His book, you know,
link |
03:36:19.120
that was the sort of defining book of mathematics
link |
03:36:21.960
for 2000 years.
link |
03:36:24.120
So you can actually map out,
link |
03:36:25.640
and I actually did this 20 years ago,
link |
03:36:28.800
but I've done it more seriously now.
link |
03:36:30.720
You can map out the theorem dependency
link |
03:36:32.640
of those 465 theorems.
link |
03:36:34.760
So from the axioms, you grow this graph,
link |
03:36:37.520
it's actually a multiway graph,
link |
03:36:39.200
of how all these theorems get proved from other theorems.
link |
03:36:42.400
And so you can ask questions about, you know,
link |
03:36:45.240
well, you can ask things like,
link |
03:36:46.080
what's the hardest theorem in Euclid?
link |
03:36:47.520
The answer is, the hardest theorem
link |
03:36:48.840
is that there are five platonic solids.
link |
03:36:50.960
That turns out to be the hardest theorem in Euclid.
link |
03:36:52.800
That's actually his last theorem in all his books.
link |
03:36:55.320
That's the final.
link |
03:36:56.160
What's the hardness, the distance you have to travel?
link |
03:36:58.440
Yeah, let's say it's 33 steps from the,
link |
03:37:01.080
the longest path in the graph is 33 steps.
link |
03:37:03.720
So that's the, there's a 33 step path you have to follow
link |
03:37:07.400
to go from the axioms, according to Euclid's proofs,
link |
03:37:10.920
to the statement there are five platonic solids.
link |
03:37:13.560
So, okay, so then the question is,
link |
03:37:17.480
in, what does it mean if you have this map?
link |
03:37:22.360
Okay, so in a sense, this metamathematical space
link |
03:37:26.400
is the infrastructural space of all possible theorems
link |
03:37:29.200
that you could prove in mathematics.
link |
03:37:31.560
That's the geometry of metamathematics.
link |
03:37:34.360
There's also the geography of mathematics.
link |
03:37:37.120
That is, where did people choose to live in space?
link |
03:37:40.760
And that's what, for example,
link |
03:37:42.240
exploring the sort of empirical metamathematics
link |
03:37:44.320
that Euclid is doing.
link |
03:37:45.160
You could put each individual, like, human mathematician,
link |
03:37:48.360
you can embed them into that space.
link |
03:37:49.840
I mean, they kind of live.
link |
03:37:51.000
They represent a path in the space.
link |
03:37:52.320
The little path.
link |
03:37:53.160
The things they do.
link |
03:37:54.000
Maybe a set of paths.
link |
03:37:54.820
Right.
link |
03:37:55.660
So like a set of axioms that are chosen.
link |
03:37:58.480
Right, so for example,
link |
03:37:59.400
here's an example of a thing that I realized.
link |
03:38:01.960
So one of the surprising things about,
link |
03:38:03.920
well, there are two surprising facts about math.
link |
03:38:06.040
One is that it's hard,
link |
03:38:07.520
and the other is that it's doable, okay?
link |
03:38:10.200
So first question is, why is math hard?
link |
03:38:12.640
You know, you've got these axioms.
link |
03:38:13.800
They're very small.
link |
03:38:14.980
Why can't you just solve every problem in math easily?
link |
03:38:17.640
Yeah, it's just logic.
link |
03:38:19.120
Right, yeah.
link |
03:38:19.960
Well, logic happens to be a particular special case
link |
03:38:22.560
that does have certain simplicity to it.
link |
03:38:25.280
But general mathematics, even arithmetic,
link |
03:38:27.580
already doesn't have the simplicity that logic has.
link |
03:38:30.360
So why is it hard?
link |
03:38:31.720
Because of computational irreducibility.
link |
03:38:33.840
Right.
link |
03:38:35.560
Because what happens is, to know what's true,
link |
03:38:38.900
and this is this whole story about the path
link |
03:38:40.720
you have to follow and how long is the path,
link |
03:38:43.000
and Gödel's theorem is the statement
link |
03:38:44.520
that the path is not a bounded length,
link |
03:38:47.680
but the fact that the path is not always compressible
link |
03:38:50.440
to something tiny is a story of computational irreducibility.
link |
03:38:54.480
So that's why math is hard.
link |
03:38:56.800
Now, the next question is, why is math doable?
link |
03:38:59.520
Because it might be the case that most things you care about
link |
03:39:02.260
don't have finite length paths.
link |
03:39:04.200
Most things you care about might be things
link |
03:39:06.720
where you get lost in the sea of computational irreducibility
link |
03:39:10.160
and worse, undecidability.
link |
03:39:12.520
That is, there's just no finite length path
link |
03:39:14.760
that gets you there.
link |
03:39:17.000
Why is mathematics doable?
link |
03:39:19.040
Gödel proved his incompleteness theorem in 1931.
link |
03:39:22.200
Most working mathematicians don't really care about it.
link |
03:39:25.240
They just go ahead and do mathematics,
link |
03:39:27.240
even though it could be that the questions they're asking
link |
03:39:29.720
are undecidable.
link |
03:39:31.040
It could have been that Fermat's last theorem
link |
03:39:32.880
is undecidable.
link |
03:39:33.720
It turned out it had a proof.
link |
03:39:35.120
It's a long, complicated proof.
link |
03:39:36.960
The twin prime conjecture might be undecidable.
link |
03:39:40.200
The Riemann hypothesis might be undecidable.
link |
03:39:43.020
These things might be, the axioms of mathematics
link |
03:39:45.920
might not be strong enough to reach those statements.
link |
03:39:49.020
It might be the case that depending on what axioms
link |
03:39:51.400
you choose, you can either say that's true
link |
03:39:53.440
or that's not true.
link |
03:39:54.760
So...
link |
03:39:55.600
And by the way, from Fermat's last theorem,
link |
03:39:57.640
there could be a shorter path.
link |
03:39:59.420
Absolutely.
link |
03:40:00.360
Yeah, so the notion of geodesics in metamathematical space
link |
03:40:03.720
is the notion of shortest proofs in metamathematical space.
link |
03:40:07.260
And that's a, you know, human mathematicians
link |
03:40:09.400
do not find shortest paths,
link |
03:40:11.400
nor do automated theorem provers.
link |
03:40:13.940
But the fact, and by the way, the, I mean,
link |
03:40:16.840
this stuff is so bizarrely connected.
link |
03:40:18.760
I mean, if you're into automated theorem proving,
link |
03:40:21.640
there are these so called critical pair lemmas
link |
03:40:23.500
and automated theorem proving.
link |
03:40:24.900
Those are precisely the branch pairs in our,
link |
03:40:28.600
that in multiway graphs.
link |
03:40:30.600
Let me just finish on the why mathematics is doable.
link |
03:40:32.920
Oh yes, the second part.
link |
03:40:34.120
So you know why it's hard, why is it doable?
link |
03:40:36.680
Right, why do we not just get lost
link |
03:40:38.120
in undecidability all the time?
link |
03:40:39.520
Yeah.
link |
03:40:40.560
So, and here's another fact,
link |
03:40:43.160
is in doing computer experiments
link |
03:40:45.400
and doing experimental mathematics,
link |
03:40:47.020
you do get lost in that way.
link |
03:40:49.020
When you just say, I'm picking a random integer equation.
link |
03:40:53.860
How do I, does it have a solution or not?
link |
03:40:56.200
And you just pick it at random
link |
03:40:57.400
without any human sort of path getting there.
link |
03:41:00.900
Often, it's really, really hard.
link |
03:41:03.280
It's really hard to answer those questions.
link |
03:41:04.760
We just pick them at random from the space of possibilities.
link |
03:41:07.840
But what I think is happening is,
link |
03:41:10.720
and that's a case where you just fell off
link |
03:41:12.460
into this ocean of sort of irreducibility and so on.
link |
03:41:15.560
What's happening is human mathematics
link |
03:41:18.220
is a story of building a path.
link |
03:41:19.920
You started off, you're always building out
link |
03:41:23.220
on this path where you are proving things.
link |
03:41:25.720
You've got this proof trajectory
link |
03:41:28.120
and you're basically, the human mathematics
link |
03:41:30.320
is the sort of the exploration of the world
link |
03:41:34.160
along this proof trajectory, so to speak.
link |
03:41:36.760
You're not just parachuting in from anywhere.
link |
03:41:42.840
You're following Lewis and Clark or whatever.
link |
03:41:44.840
You're actually going, doing the path.
link |
03:41:48.160
And the fact that you are constrained to go along that path
link |
03:41:52.080
is the reason you don't end up with,
link |
03:41:53.760
every so often you'll see a little piece of undecidability
link |
03:41:55.840
and you'll avoid that part of the path.
link |
03:41:57.980
But that's basically the story of why human mathematics
link |
03:42:00.960
has seemed to be doable.
link |
03:42:02.640
It's a story of exploring these paths
link |
03:42:05.200
that are by their nature,
link |
03:42:07.240
they have been constructed to be paths that can be followed.
link |
03:42:10.480
And so you can follow them further.
link |
03:42:12.260
Now, why is this relevant to anything?
link |
03:42:14.920
So, okay, so here's my belief.
link |
03:42:19.480
The fact that human mathematics works that way
link |
03:42:22.640
is I think there's some sort of connections
link |
03:42:26.080
between the way that observers work in physics
link |
03:42:29.720
and the way that the axiom systems of mathematics are set up
link |
03:42:32.980
to make mathematics be doable in that kind of way.
link |
03:42:36.360
And so, in other words, in particular,
link |
03:42:38.880
I think there is an analog of causal invariance,
link |
03:42:41.720
which I think is, and this is again,
link |
03:42:44.800
it's sort of the upper reaches of mathematics
link |
03:42:46.620
and stuff that it's a thing,
link |
03:42:50.680
there's this thing called homotopy type theory,
link |
03:42:52.900
which is an abstract, it's came out of category theory,
link |
03:42:56.120
and it's sort of an abstraction of mathematics.
link |
03:42:58.380
Mathematics itself is an abstraction,
link |
03:43:00.360
but it's an abstraction of the abstraction of mathematics.
link |
03:43:03.980
And there is the thing called the univalence axiom,
link |
03:43:06.620
which is a sort of a key axiom in that set of ideas.
link |
03:43:12.220
And I'm pretty sure the univalence axiom
link |
03:43:14.200
is equivalent to causal invariance.
link |
03:43:16.220
What was the term you used again?
link |
03:43:18.120
Univalence.
link |
03:43:19.000
Is that something for somebody like me accessible?
link |
03:43:21.560
Or is this?
link |
03:43:23.200
There's a statement of it that's fairly accessible.
link |
03:43:25.560
I mean, the statement of it is,
link |
03:43:29.680
basically it says things which are equivalent
link |
03:43:32.760
can be considered to be identical.
link |
03:43:35.520
In which space?
link |
03:43:38.160
Yeah, it's in higher category.
link |
03:43:40.720
In category.
link |
03:43:41.720
Okay, so it's a, but I mean,
link |
03:43:43.880
the thing just to give a sketch of how that works.
link |
03:43:46.160
So category theory is an attempt to idealize,
link |
03:43:49.680
it's an attempt to sort of have a formal theory
link |
03:43:52.060
of mathematics that is at a sort of higher level
link |
03:43:54.400
than mathematics.
link |
03:43:55.600
It's where you just think about these mathematical objects
link |
03:43:59.560
and these categories of objects and these morphisms,
link |
03:44:03.720
these connections between categories.
link |
03:44:05.600
Okay, so it turns out the morphisms and categories,
link |
03:44:08.640
at least weak categories,
link |
03:44:10.840
are very much like the paths in our hypergraphs and things.
link |
03:44:14.820
And it turns out, again, this is where it all gets crazy.
link |
03:44:18.480
I mean, the fact that these things are connected
link |
03:44:20.800
is just bizarre.
link |
03:44:22.000
So category theory, our causal graphs
link |
03:44:27.080
are like second order category theory.
link |
03:44:29.940
And it turns out you can take the limits
link |
03:44:32.640
of infinite order category theory.
link |
03:44:34.160
So just give roughly the idea.
link |
03:44:36.480
This is a roughly explainable idea.
link |
03:44:39.120
So a mathematical proof will be a path
link |
03:44:43.400
that says you can get from this thing to this other thing.
link |
03:44:45.920
And here's the path that you get from this thing
link |
03:44:47.480
to this other thing.
link |
03:44:48.720
But in general, there may be many paths,
link |
03:44:51.160
many proofs that get you many different paths
link |
03:44:53.960
that all successfully go from this thing
link |
03:44:55.800
to this other thing, okay?
link |
03:44:57.700
Now you can define a higher order proof,
link |
03:45:00.400
which is a proof of the equivalence of those proofs.
link |
03:45:03.840
Okay, so you're saying there's a...
link |
03:45:05.440
A path between those proofs essentially.
link |
03:45:07.120
Yes, a path between the paths, okay?
link |
03:45:09.800
And so you do that.
link |
03:45:10.960
That's the sort of second order thing.
link |
03:45:12.300
That path between the paths is essentially related
link |
03:45:16.120
to our causal graphs.
link |
03:45:18.240
Then you can take the limit.
link |
03:45:19.560
Wow, okay.
link |
03:45:20.400
The path between path, between path, between path.
link |
03:45:23.040
The infinite limit.
link |
03:45:24.640
That infinite limit turns out to be
link |
03:45:26.340
our Rulial Multiway System.
link |
03:45:28.800
Yeah, the Rulial Multiway System,
link |
03:45:31.600
that's a fascinating, both in the physics world
link |
03:45:33.860
and as you're saying now, that's fast.
link |
03:45:36.920
I'm not sure I've loaded it in completely, but...
link |
03:45:39.120
Well, I'm not sure I have either.
link |
03:45:40.320
And it may be one of these things where,
link |
03:45:42.560
in another five years or something, it's like,
link |
03:45:45.160
it was obvious, but I didn't see it.
link |
03:45:47.120
No, but the thing which is sort of interesting to me
link |
03:45:49.360
is that there's sort of an upper reach of mathematics,
link |
03:45:53.080
of the abstraction of mathematics.
link |
03:45:55.880
This thing, there's this mathematician called Grothendieck
link |
03:45:59.000
who's generally viewed as being sort of one
link |
03:46:00.680
of the most abstract,
link |
03:46:02.320
sort of creator of the most abstract mathematics
link |
03:46:04.800
of 1970s ish timeframe.
link |
03:46:09.360
And one of the things that he constructed was this thing
link |
03:46:11.560
he called the Infinity Grupoid.
link |
03:46:13.280
And he has this sort of hypothesis
link |
03:46:15.820
about the inevitable appearance of geometry
link |
03:46:18.380
from essentially logic in the structure of this thing.
link |
03:46:22.420
Well, it turns out this Rulial Multiway System
link |
03:46:24.660
is the Infinity Grupoid.
link |
03:46:26.620
So it's this limiting object.
link |
03:46:29.700
And this is an instance of that limiting object.
link |
03:46:33.560
So what to me is, I mean, again,
link |
03:46:35.460
I've been always afraid of this kind of mathematics
link |
03:46:37.980
because it seemed incomprehensibly abstract to me.
link |
03:46:42.260
But what I'm sort of excited about with this
link |
03:46:45.620
is that we've sort of concretified the way
link |
03:46:49.540
that you can reach this kind of mathematics,
link |
03:46:51.860
which makes it, well, both seem more relevant
link |
03:46:55.260
and also the fact that I don't yet know exactly
link |
03:46:58.820
what mileage we're gonna get from using
link |
03:47:01.120
the sort of the apparatus that's been built
link |
03:47:03.340
in those areas of mathematics to analyze what we're doing.
link |
03:47:06.500
But the thing that's.
link |
03:47:07.340
So both ways.
link |
03:47:08.180
So using mathematics to understand what you're doing
link |
03:47:10.020
and using what you're doing computationally
link |
03:47:12.340
to understand that.
link |
03:47:13.180
Right, so for example,
link |
03:47:14.020
the understanding of metamathematical space,
link |
03:47:17.860
one of the reasons I really want to do that
link |
03:47:19.860
is because I want to understand quantum mechanics better.
link |
03:47:22.620
And that, what you see,
link |
03:47:25.980
we live that kind of the multiway graph of mathematics
link |
03:47:30.260
because we actually know this is a theorem we've heard of.
link |
03:47:32.540
This is another one we've heard of.
link |
03:47:34.020
We can actually say these are actual things in the world
link |
03:47:36.900
that we relate to,
link |
03:47:38.480
which we can't really do as readily for the physics case.
link |
03:47:43.100
And so it's kind of a way to help my intuition.
link |
03:47:45.180
It's also, there are bizarre things
link |
03:47:47.820
like what's the analog of Einstein's equations
link |
03:47:50.020
in metamathematical space?
link |
03:47:51.880
What's the analog of a black hole?
link |
03:47:53.980
It turns out it looks like not completely sure yet,
link |
03:47:57.660
but there's this notion of nonconstructive proofs
link |
03:48:00.180
in mathematics.
link |
03:48:01.500
And I think those relate to,
link |
03:48:03.540
well, actually they relate to things
link |
03:48:07.780
related to event horizons.
link |
03:48:10.420
So the fact that you can take ideas from physics
link |
03:48:13.500
like event horizons.
link |
03:48:14.460
And map them into the same kind of space, metamath.
link |
03:48:17.100
It's really.
link |
03:48:17.940
So do you think there'll be,
link |
03:48:19.460
do you think you might stumble upon
link |
03:48:22.140
some breakthrough ideas in theorem proving?
link |
03:48:25.860
Like for, from the other direction?
link |
03:48:28.700
Yeah, yeah, yeah.
link |
03:48:29.540
No, I mean, what's really nice is that we are using,
link |
03:48:32.180
so this absolutely directly maps to theorem proving.
link |
03:48:35.640
So pods and multiway graphs,
link |
03:48:37.240
that's what a theorem prover is trying to do.
link |
03:48:38.540
But I also mean like automated theorem.
link |
03:48:40.780
Yeah, yeah, yeah.
link |
03:48:41.620
That's what, right.
link |
03:48:42.440
So the finding of pods, the finding of shortest pods
link |
03:48:45.180
or finding of pods at all
link |
03:48:46.840
is what automated theorem provers do.
link |
03:48:48.780
And actually what we've been doing.
link |
03:48:51.020
So we've actually been using automated theorem proving
link |
03:48:53.760
both in the physics project to prove things
link |
03:48:56.340
and using that as a way to understand multiway graphs.
link |
03:49:00.540
And because what an automated theorem prover is doing
link |
03:49:04.080
is it's trying to find a path through a multiway graph
link |
03:49:07.380
and its critical pair lemmas
link |
03:49:09.300
are precisely little stubs of branch pairs
link |
03:49:12.960
going off into branchial space.
link |
03:49:15.080
And that's, I mean, it's really weird.
link |
03:49:16.860
You know, we have these visualizations in Wolfram language
link |
03:49:19.100
of proof graphs from our automated theorem proving system.
link |
03:49:24.180
And they look reminiscent of.
link |
03:49:25.660
Well, it's just bizarre
link |
03:49:26.860
because we made these up a few years ago
link |
03:49:28.820
and they have these little triangle things
link |
03:49:30.740
and they are, we didn't quite get it right.
link |
03:49:33.020
We didn't quite get the analogy perfectly right,
link |
03:49:35.100
but it's very close.
link |
03:49:36.220
You know, just to say,
link |
03:49:37.460
in terms of how these things are connected.
link |
03:49:39.940
So there's another bizarre connection
link |
03:49:41.520
that I have to mention because which is,
link |
03:49:46.160
which again, we don't fully know,
link |
03:49:47.940
but it's a connection to something else
link |
03:49:51.140
you might not have thought was in the slightest
link |
03:49:52.660
but connected, which is distributed blockchain like things.
link |
03:49:56.840
Now you might figure out that that's,
link |
03:49:58.140
you would figure out that that's connected
link |
03:49:59.900
because it's a story of distributed computing.
link |
03:50:02.860
And the issue, you know, with the blockchain,
link |
03:50:04.860
you're saying there's going to be this one ledger
link |
03:50:07.580
that globally says, this is what happened in the world.
link |
03:50:11.700
But that's a bad deal.
link |
03:50:14.000
If you've got all these different transactions
link |
03:50:15.640
that are happening and you know,
link |
03:50:17.300
this transaction in country A
link |
03:50:20.660
doesn't have to be reconciled with the transaction
link |
03:50:23.380
in country B, at least not for a while.
link |
03:50:26.220
And that story is just like what happens
link |
03:50:29.380
with our causal graphs.
link |
03:50:31.000
That whole reconciliation thing is just like
link |
03:50:33.220
what happens with light cones and all this kind of thing.
link |
03:50:35.740
That's where the causal awareness comes into play.
link |
03:50:37.420
I mean, that's, you know,
link |
03:50:39.180
most of your conversations are about physics,
link |
03:50:41.380
but it's kind of funny that this probably
link |
03:50:46.000
and possibly might have even bigger impact
link |
03:50:49.340
and revolutionary ideas and totally other disciplines.
link |
03:50:53.980
Right, well, you see, yeah, right.
link |
03:50:55.400
So the question is, why is that happening, right?
link |
03:50:57.640
And the reason it's happening,
link |
03:50:59.140
I've thought about this obviously,
link |
03:51:00.700
because I like to think about these meta questions of,
link |
03:51:03.300
you know, what's happening is this model that we have
link |
03:51:06.380
is an incredibly minimal model.
link |
03:51:08.740
And once you have an incredibly minimal model,
link |
03:51:11.360
and this happened with cellular automata as well,
link |
03:51:13.620
cellular automata are an incredibly minimal model.
link |
03:51:16.040
And so it's inevitable that it gets you,
link |
03:51:19.100
it's sort of an upstream thing
link |
03:51:20.600
that gets used in lots of different places.
link |
03:51:22.720
And it's like, you know, the fact that it gets used,
link |
03:51:25.280
you know, cellular automata is sort of a minimal model
link |
03:51:27.380
of let's say road traffic flow or something.
link |
03:51:29.140
And they're also a minimal model of something in,
link |
03:51:31.340
you know, chemistry,
link |
03:51:32.180
and they're also a minimal model of something
link |
03:51:33.560
in epidemiology, right?
link |
03:51:35.860
It's because they're such a simple model that they can,
link |
03:51:38.140
that they apply to all these different things.
link |
03:51:40.300
Similarly, this model that we have with the physics project
link |
03:51:43.060
is another, cellular automata are a minimal model
link |
03:51:47.300
of parallel, of basically of parallel computation
link |
03:51:50.580
where you've defined space and time.
link |
03:51:52.840
These models are minimal models
link |
03:51:54.820
where you have not defined space and time.
link |
03:51:57.180
And they have been very hard to understand in the past,
link |
03:52:00.340
but the, I think the,
link |
03:52:01.980
perhaps the most important breakthrough there
link |
03:52:04.500
is the realization that these are models of physics.
link |
03:52:07.440
And therefore that you can use everything
link |
03:52:09.180
that's been developed in physics
link |
03:52:11.140
to get intuition about how things like that work.
link |
03:52:13.880
And that's why you can potentially use ideas from physics
link |
03:52:17.500
to get intuition about how to do parallel computing.
link |
03:52:20.140
And because the underlying model is the same.
link |
03:52:24.940
But we have all of this achievement in physics.
link |
03:52:27.060
I mean, you know, you might say,
link |
03:52:28.500
oh, you've come up with the fundamental theory of physics
link |
03:52:30.160
that throws out what people have done in physics before.
link |
03:52:32.500
Well, it doesn't, but also the real power
link |
03:52:35.540
is to use what's been done before in physics
link |
03:52:37.940
to apply it in these other places.
link |
03:52:39.620
Yes, absolutely.
link |
03:52:41.500
This kind of brings up,
link |
03:52:43.020
I know you probably don't particularly love commenting
link |
03:52:47.900
on the work of others,
link |
03:52:48.820
but let me bring up a couple of personalities
link |
03:52:51.260
just because it's fun and people are curious about it.
link |
03:52:53.660
So there's Sabine Hassenfelder.
link |
03:52:58.700
I don't know if you're familiar with her.
link |
03:53:00.460
She wrote this book that I need to read,
link |
03:53:04.920
but I forget what the title is,
link |
03:53:06.980
but it's Beauty Leads Us Astray in Physics
link |
03:53:10.480
is a subtitle or something like that.
link |
03:53:12.420
Which so much about what we're talking about now,
link |
03:53:15.100
like this simplification,
link |
03:53:17.860
to us humans seems to be beautiful.
link |
03:53:20.440
Like there's a certain intuition with physicists,
link |
03:53:23.540
with people that a simple theory,
link |
03:53:26.700
like this reducibility,
link |
03:53:28.060
pockets of reducibility is the ultimate goal.
link |
03:53:30.580
And I think what she tries to argue is no,
link |
03:53:34.780
we just need to come up with theories
link |
03:53:37.740
that are just really good at predicting physical phenomena.
link |
03:53:40.620
It's okay to have a bunch of disparate theories
link |
03:53:44.360
as opposed to trying to chase this beautiful theory
link |
03:53:48.580
of everything is the ultimate beautiful theory,
link |
03:53:51.140
a simple one.
link |
03:53:52.140
What's your response to that?
link |
03:53:54.620
Well, so what you're quoting,
link |
03:53:56.340
I don't know the Sabine Hassenfelder's,
link |
03:53:59.820
exactly what she said,
link |
03:54:00.660
but I mean that you're quoting the title of her book.
link |
03:54:03.780
Okay.
link |
03:54:04.620
Let me respond to what you were describing,
link |
03:54:07.780
which may or may not have nothing to do with
link |
03:54:09.620
what Sabine Hassenfelder says or thinks.
link |
03:54:14.660
Sorry, Sabine.
link |
03:54:16.460
Right.
link |
03:54:17.300
Sorry for misquoting.
link |
03:54:18.420
But I mean, the question is,
link |
03:54:23.300
is beauty a guide to whether something is correct?
link |
03:54:26.540
Which is kind of also the story of Occam's razor.
link |
03:54:29.180
If you've got a bunch of different explanations of things,
link |
03:54:32.140
is the thing that is the simplest explanation
link |
03:54:34.500
likely to be the correct explanation?
link |
03:54:36.580
And there are situations where that's true
link |
03:54:38.100
and there are situations where it isn't true.
link |
03:54:39.940
Sometimes in human systems, it is true
link |
03:54:41.900
because people have kind of,
link |
03:54:43.140
in evolutionary systems, sometimes it's true
link |
03:54:45.220
because it's sort of been kicked
link |
03:54:46.780
to the point where it's minimized.
link |
03:54:49.340
But in physics, does Occam's razor work?
link |
03:54:53.580
Is there a simple, quotes, beautiful explanation for things
link |
03:54:57.420
or is it a big mess?
link |
03:54:59.780
We don't intrinsically know.
link |
03:55:01.940
I think that the, I wouldn't,
link |
03:55:03.660
before I worked on the project in recent times,
link |
03:55:07.180
I would have said,
link |
03:55:08.220
we do not know how complicated
link |
03:55:09.900
the rule for the universe will be.
link |
03:55:12.100
And I would have said, the one thing we know,
link |
03:55:15.940
which is a fundamental fact about science,
link |
03:55:17.780
that's the thing that makes science possible,
link |
03:55:19.740
is that there is order in the universe.
link |
03:55:21.860
I mean, early theologians would have used that
link |
03:55:24.860
as an argument for the existence of God
link |
03:55:27.140
because it's like, why is there order in the universe?
link |
03:55:29.420
Why doesn't every single particle in the universe
link |
03:55:31.500
just do its own thing?
link |
03:55:33.980
Something must be making there be order in the universe.
link |
03:55:37.180
We, in the sort of early theology point of view,
link |
03:55:41.820
that's the role of God is to do that, so to speak.
link |
03:55:45.180
In our, we might say,
link |
03:55:47.580
it's the role of a formal theory to do that.
link |
03:55:50.140
And then the question is,
link |
03:55:51.060
but how simple should that theory be?
link |
03:55:53.260
And should that theory be one that,
link |
03:55:57.060
where I think the point is, if it's simple,
link |
03:56:00.620
it's almost inevitably somewhat beautiful
link |
03:56:03.180
in the sense that, because all the stuff that we see
link |
03:56:06.460
has to fit into this little tiny theory.
link |
03:56:08.740
And the way it does that has to be,
link |
03:56:11.380
it depends on your notion of beauty,
link |
03:56:13.300
but I mean, for me, the sort of the surprising
link |
03:56:17.940
connectivity of it is, at least in my aesthetic,
link |
03:56:21.980
that's something that responds to my aesthetic.
link |
03:56:25.100
But the question is, I mean,
link |
03:56:27.780
you're a fascinating person in the sense that
link |
03:56:31.060
you're at once talking about computational,
link |
03:56:34.460
the fundamental computational reducibility of the universe,
link |
03:56:37.940
and on the other hand,
link |
03:56:40.380
trying to come up with a theory of everything,
link |
03:56:42.540
which simply describes the,
link |
03:56:47.740
the simple origins of that computational reducibility.
link |
03:56:51.460
I mean, both of those things are kind of,
link |
03:56:53.820
it's paralyzing to think that we can't make any sense
link |
03:56:56.340
of the universe in the general case,
link |
03:56:58.580
but it's hopeful to think like,
link |
03:57:01.060
one, we can think of a rule
link |
03:57:03.060
and that generates this whole complexity,
link |
03:57:05.980
and two, we can find pockets of reducibility
link |
03:57:10.980
that are powerful for everyday life
link |
03:57:13.420
to do different kinds of predictions.
link |
03:57:15.540
I suppose Sabine wants to find,
link |
03:57:19.060
focus on the finding of small pockets of reducibility
link |
03:57:22.940
versus the theory of everything.
link |
03:57:26.780
You know, it's a funny thing because,
link |
03:57:29.300
you know, a bunch of people have started working
link |
03:57:30.780
on this physics project,
link |
03:57:32.980
people who are physicists, basically,
link |
03:57:36.780
and it is really a fascinating sociological phenomenon
link |
03:57:39.820
because what, you know,
link |
03:57:41.780
when I was working on this before in the 1990s,
link |
03:57:45.300
you know, wrote it up, put it,
link |
03:57:47.900
it's 100 pages of this 1200 page book
link |
03:57:50.060
that I wrote, New Kind of Science,
link |
03:57:51.300
is, you know, 100 pages of that is about physics,
link |
03:57:54.140
but I saw it at that time,
link |
03:57:57.380
not as a pinnacle achievement,
link |
03:57:59.620
but rather as a use case, so to speak.
link |
03:58:01.820
I mean, my main point was this new kind of science,
link |
03:58:04.100
and it's like, you can apply it to biology,
link |
03:58:05.940
you can apply it to, you know, other kinds of physics,
link |
03:58:08.420
you can apply it to fundamental physics,
link |
03:58:09.900
it's just an application, so to speak,
link |
03:58:12.420
it's not the core thing.
link |
03:58:14.740
But then, you know, one of the things that was interesting
link |
03:58:18.100
with that book was, you know,
link |
03:58:21.180
book comes out, lots of people think it's pretty interesting
link |
03:58:24.580
and lots of people start using what it has
link |
03:58:26.460
in different kinds of fields.
link |
03:58:28.100
The one field where there was sort of a heavy pitchforking
link |
03:58:32.500
was from my friends, the fundamental physics people,
link |
03:58:35.940
which was, it's like, no,
link |
03:58:37.460
this can't possibly be right.
link |
03:58:38.700
And, you know, it's like, you know,
link |
03:58:40.180
if what you're doing is right,
link |
03:58:41.540
it'll overturn 50 years of what we've been doing.
link |
03:58:44.220
And it's like, no, it won't, was what I was saying.
link |
03:58:46.980
And it's like, but, you know, for a while,
link |
03:58:50.820
when I started, you know, I was going to go on back in 2002,
link |
03:58:54.380
well, 2004, actually, I was going to go on
link |
03:58:57.060
working on this project.
link |
03:58:58.500
And I actually stopped,
link |
03:58:59.820
partly because it's like, why am I, you know,
link |
03:59:03.100
this is like, I've been in business a long time, right?
link |
03:59:05.380
I'm building a product for a target market
link |
03:59:08.100
that doesn't want the product.
link |
03:59:09.700
And it's like.
link |
03:59:10.700
Why work, yeah, yeah, why work against the,
link |
03:59:13.260
swim against the current or whatever.
link |
03:59:14.620
Right, but you see what's happened,
link |
03:59:16.100
which is sort of interesting is that,
link |
03:59:18.060
so a couple of things happened and it was like,
link |
03:59:22.580
you know, it was like, I don't want to do this project
link |
03:59:25.700
because I can do so many other things,
link |
03:59:28.540
which I'm really interested in where, you know,
link |
03:59:31.820
people say, great, thanks for those tools.
link |
03:59:34.100
Thanks for those ideas, et cetera.
link |
03:59:36.380
Whereas, you know, if you're dealing with kind of a,
link |
03:59:40.020
you know, a sort of a structure where people are saying,
link |
03:59:42.820
no, no, we don't want this new stuff.
link |
03:59:44.220
We don't need any new stuff.
link |
03:59:45.300
We're really fine with what we're doing.
link |
03:59:46.660
Yeah, there's like literally like, I don't know,
link |
03:59:48.300
millions of people who are thankful for Wolfram Alpha.
link |
03:59:51.140
A bunch of people wrote to me, how thankful,
link |
03:59:53.260
they are a different crowd
link |
03:59:55.460
than the theoretical physics community, perhaps.
link |
03:59:57.820
Yeah, well, but you know,
link |
03:59:58.900
the theoretical physics community
link |
04:00:00.260
pretty much uniformly uses Wolfram language
link |
04:00:03.180
and Mathematica, right?
link |
04:00:04.380
And so it's kind of like, you know, and that's,
link |
04:00:08.340
but the thing is what happens, you know,
link |
04:00:11.180
this is what happens, mature fields do not, you know,
link |
04:00:14.980
it's like, we're doing what we're doing.
link |
04:00:16.420
We have the methods that we have
link |
04:00:18.220
and we're just fine here.
link |
04:00:20.220
Now what's happened in the last 18 years or so,
link |
04:00:23.380
I think there's a couple of things have happened.
link |
04:00:25.460
First of all, the hope that, you know,
link |
04:00:29.260
string theory or whatever would deliver
link |
04:00:31.300
the fundamental theory of physics,
link |
04:00:32.460
that hope has disappeared.
link |
04:00:34.540
That the, another thing that's happened
link |
04:00:36.820
is the sort of the interest in computation around physics
link |
04:00:41.020
has been greatly enhanced
link |
04:00:42.460
by the whole quantum information,
link |
04:00:44.020
quantum computing story.
link |
04:00:46.020
People, you know, the idea there might be something
link |
04:00:47.940
sort of computational related to physics
link |
04:00:51.100
has somehow grown.
link |
04:00:53.060
And I think, you know, it's sort of interesting.
link |
04:00:55.820
I mean, right now, if we say, you know,
link |
04:00:58.060
it's like, if you're like,
link |
04:00:59.700
who else is trying to come up
link |
04:01:00.820
with the fundamental theory of physics?
link |
04:01:02.420
It's like, there aren't professional,
link |
04:01:04.460
no professional physicists, no professional physicists.
link |
04:01:07.220
What are your, I mean, you've talked with him,
link |
04:01:10.820
but just as a matter of personalities,
link |
04:01:12.820
cause it's a beautiful story.
link |
04:01:13.820
What are your thoughts about Eric Weinstein's work?
link |
04:01:17.100
You know, I think his, I mean,
link |
04:01:20.580
he did a PhD thesis in mathematical physics at Harvard.
link |
04:01:23.420
He's a mathematical physicist.
link |
04:01:24.580
And, you know, it seems like it's kind of,
link |
04:01:28.900
you know, it's in that framework.
link |
04:01:30.940
And it's kind of like,
link |
04:01:32.820
I'm not sure how much further it's got than his PhD thesis,
link |
04:01:35.940
which was 20 years ago or something.
link |
04:01:37.580
And I think that, you know, the, you know,
link |
04:01:40.740
it's a fairly specific piece of mathematical physics.
link |
04:01:43.780
That's quite nice.
link |
04:01:44.940
And...
link |
04:01:45.780
What trajectory do you hope it takes?
link |
04:01:47.540
I mean...
link |
04:01:48.620
Well, I think in his particular case,
link |
04:01:50.100
I mean, from what I understand,
link |
04:01:51.380
which is not everything at all,
link |
04:01:52.940
but, you know, I think I know the rough tradition,
link |
04:01:54.820
at least what he's operating in is sort of theory of gauge theories.
link |
04:01:58.980
Gauge theories, yeah.
link |
04:01:59.740
Local gauge invariants and so on.
link |
04:02:01.100
Okay, we are very close to understanding
link |
04:02:04.180
how local gauge invariants works in our models.
link |
04:02:06.220
And it's very beautiful.
link |
04:02:07.620
And it's very...
link |
04:02:09.420
And, you know, does some of the mathematical structure
link |
04:02:12.260
that he's enthusiastic about fit?
link |
04:02:14.340
Quite possibly, yes.
link |
04:02:15.820
So there might be a possibility of trying to understand
link |
04:02:17.740
how those things fit, how gauge theory fits.
link |
04:02:19.780
Yeah, very well.
link |
04:02:20.620
I mean, the question is, you know,
link |
04:02:21.980
so there are a couple of things
link |
04:02:22.820
one might try to get in the world.
link |
04:02:24.100
So for example, it's like,
link |
04:02:25.660
can we get three dimensions of space?
link |
04:02:27.100
We haven't managed to get that yet.
link |
04:02:28.860
Gauge theory, the standard model of particle physics says,
link |
04:02:32.380
but it's SU3 cross SU2 cross U1.
link |
04:02:35.620
Those are the designations of these Lie groups.
link |
04:02:39.980
It doesn't, but anyway,
link |
04:02:41.340
so those are sort of representations
link |
04:02:43.700
of symmetries of the theory.
link |
04:02:46.460
And so, you know, it is conceivable
link |
04:02:50.060
that it is generically true.
link |
04:02:52.660
Okay, so all those are subgroups of a group called E8,
link |
04:02:55.340
which is a weird, exceptional Lie group, okay?
link |
04:02:59.620
It is conceivable, I don't know whether it's the case,
link |
04:03:02.100
that that will be generic in these models,
link |
04:03:05.100
that it will be generic,
link |
04:03:06.780
that the gauge invariance of the model has this property,
link |
04:03:12.020
just as things like general relativity,
link |
04:03:15.100
which corresponds to the thing called general covariance,
link |
04:03:20.100
which is another gauge like invariance.
link |
04:03:23.100
It could conceivably be the case
link |
04:03:25.340
that the kind of local gauge invariance
link |
04:03:27.460
that we see in particle physics is somehow generic.
link |
04:03:30.580
And that would be a, you know,
link |
04:03:32.300
the thing that's really cool, I think, you know,
link |
04:03:35.380
sociologically, although this hasn't really hit yet,
link |
04:03:38.100
is that all of these different things,
link |
04:03:40.020
all these different things people have been working on
link |
04:03:41.660
in these, in some cases,
link |
04:03:43.260
quite abstruse areas of mathematical physics,
link |
04:03:46.500
an awful lot of them seem to tie into what we're doing.
link |
04:03:49.420
And, you know, it might not be that way.
link |
04:03:51.460
Yeah, absolutely.
link |
04:03:52.300
That's a beautiful thing, I think.
link |
04:03:53.740
I mean, but the reason Eric Weinstein is important
link |
04:03:58.100
is to the point that you mentioned before,
link |
04:04:00.180
which is, it's strange that the theory of everything
link |
04:04:04.380
is not at the core of the passion, the dream,
link |
04:04:09.780
the focus, the funding of the physics community.
link |
04:04:14.140
It's too hard.
link |
04:04:16.420
It's too hard and people gave up.
link |
04:04:17.980
I mean, basically what happened is ancient Greece,
link |
04:04:21.420
people thought we're nearly there.
link |
04:04:23.060
You know, the world is made of platonic solids.
link |
04:04:25.100
It's, you know, water is a tetrahedron or something.
link |
04:04:27.700
We're almost there, okay?
link |
04:04:29.700
Long period of time where people were like,
link |
04:04:32.180
no, we don't know how it works.
link |
04:04:34.020
You know, time of Newton, you know, we're almost there.
link |
04:04:36.980
Everything is gravitation.
link |
04:04:38.740
You know, time of Faraday and Maxwell, we're almost there.
link |
04:04:42.380
Everything is fields, everything is the ether, you know?
link |
04:04:45.500
Then...
link |
04:04:46.340
And the whole time we're making big progress though.
link |
04:04:48.940
Oh yes, absolutely.
link |
04:04:50.140
But the fundamental theory of physics is almost a footnote
link |
04:04:53.860
because it's like, it's the machine code.
link |
04:04:56.900
It's like we're operating in the high level languages.
link |
04:04:59.340
Yeah.
link |
04:05:00.180
You know, that's what we really care about.
link |
04:05:01.700
That's what's relevant for our everyday physics.
link |
04:05:03.660
You talked about different centuries
link |
04:05:05.020
and the 21st century will be everything is computation.
link |
04:05:08.820
Yes.
link |
04:05:09.660
If that takes us all the way, we don't know,
link |
04:05:11.500
but it might take us pretty far.
link |
04:05:13.260
Yes, right, that's right.
link |
04:05:14.580
And I, but I think the point is that it's like, you know,
link |
04:05:17.060
if you're doing biology, you might say,
link |
04:05:18.700
how can you not be really interested in the origin of life
link |
04:05:21.140
and the definition of life?
link |
04:05:22.700
Well, it's irrelevant.
link |
04:05:23.540
You know, you're studying the properties of some virus.
link |
04:05:26.020
It doesn't matter, you know, where, you know,
link |
04:05:28.020
you're operating at some much higher level.
link |
04:05:30.620
And it's the same, what's happening with physics is,
link |
04:05:34.180
I was sort of surprised actually.
link |
04:05:35.420
I was sort of mapping out this history of people's efforts
link |
04:05:38.780
to understand the fundamental theory of physics.
link |
04:05:41.180
And it's remarkable how little has been done on this question.
link |
04:05:45.220
And it's, you know, because, you know,
link |
04:05:47.100
there've been times when there's been bursts of enthusiasm.
link |
04:05:49.340
Oh, we're almost there.
link |
04:05:50.940
And then it decays and people just say,
link |
04:05:54.940
oh, it's too hard, but it's not relevant anyway.
link |
04:05:57.260
And I think that the thing that, you know,
link |
04:06:01.140
so the question of, you know, one question is,
link |
04:06:04.860
why does anybody, why should anybody care, right?
link |
04:06:07.420
Why should anybody care
link |
04:06:08.500
what the fundamental theory of physics is?
link |
04:06:10.420
I think it's intellectually interesting,
link |
04:06:13.140
but what will be the sort of,
link |
04:06:14.820
what will be the impact of this?
link |
04:06:16.460
What, I mean, this is the key question.
link |
04:06:18.900
What do you think will happen
link |
04:06:20.660
if we figure out the fundamental theory of physics?
link |
04:06:25.260
Right.
link |
04:06:26.100
Outside of the intellectual curiosity of us.
link |
04:06:28.140
Okay, so here's my best guess, okay?
link |
04:06:31.340
So if you look at the history of science,
link |
04:06:33.540
I think a very interesting analogy is Copernicus.
link |
04:06:37.420
Okay, so what did Copernicus do?
link |
04:06:39.740
There'd been this Ptolemaic system
link |
04:06:41.340
for working out the motion of planets.
link |
04:06:43.260
It did pretty well.
link |
04:06:44.740
It used epicycles, et cetera, et cetera, et cetera.
link |
04:06:47.100
It had all this computational ways
link |
04:06:49.340
of working out where planets will be.
link |
04:06:51.180
When we work out where planets are today,
link |
04:06:52.740
we're basically using epicycles.
link |
04:06:54.860
But Copernicus had this different way of formulating things
link |
04:06:58.060
in which he said, you know,
link |
04:07:00.260
and the earth is going around the sun,
link |
04:07:02.980
and that had a consequence.
link |
04:07:04.180
The consequence was you can use this mathematical theory
link |
04:07:07.900
to conclude something which is absolutely not
link |
04:07:10.740
what we can tell from common sense, right?
link |
04:07:14.180
So it's like, trust the mathematics, trust the science, okay?
link |
04:07:18.420
Now fast forward 400 years,
link |
04:07:21.060
and now we're in this pandemic,
link |
04:07:23.900
and it's kind of like everybody thinks the science
link |
04:07:26.500
will figure out everything.
link |
04:07:28.260
It's like from the science,
link |
04:07:30.020
we can just figure out what to do.
link |
04:07:31.380
We can figure out everything.
link |
04:07:32.940
That was before Copernicus.
link |
04:07:34.820
Nobody would have thought if the science says something
link |
04:07:37.700
that doesn't agree with our everyday experience,
link |
04:07:40.780
where we just have to compute the science
link |
04:07:43.180
and then figure out what to do,
link |
04:07:44.420
people would say that's completely crazy.
link |
04:07:46.380
And so your sense is,
link |
04:07:47.580
once we figure out the framework of computation
link |
04:07:49.820
that can basically do any,
link |
04:07:51.780
understand the fabric of reality,
link |
04:07:53.780
we'll be able to derive totally counterintuitive things.
link |
04:07:58.900
No, the point I think is the following.
link |
04:08:01.580
That right now, you know,
link |
04:08:03.020
I talk about computational irreducibility.
link |
04:08:05.740
People, you know, I was very proud
link |
04:08:07.820
that I managed to get the term computational irreducibility
link |
04:08:10.140
into the congressional record last year.
link |
04:08:13.020
That's right, by the way,
link |
04:08:13.860
that's a whole nother topic we could talk about.
link |
04:08:15.460
Fascinating. Different topic.
link |
04:08:17.140
Different topic.
link |
04:08:18.180
But Tim, in any case, you know,
link |
04:08:20.420
but so computational irreducibility
link |
04:08:22.140
is one of these sort of concepts
link |
04:08:23.900
that I think is important in understanding
link |
04:08:25.420
lots of things in the world.
link |
04:08:26.980
But the question is, it's only important
link |
04:08:29.180
if you believe the world is fundamentally computational.
link |
04:08:32.100
Right?
link |
04:08:33.140
But if you know the fundamental theory of physics
link |
04:08:35.940
and it's fundamentally computational,
link |
04:08:38.260
then you've rooted the whole thing.
link |
04:08:40.180
That is, you know the world is computational.
link |
04:08:43.140
And while you can discuss whether, you know,
link |
04:08:47.260
it's not the case that people would say,
link |
04:08:48.820
well, you have this whole computational irreducibility,
link |
04:08:50.940
all these features of computation.
link |
04:08:52.580
We don't care about those
link |
04:08:54.100
because after all the world isn't computational,
link |
04:08:56.180
you might say.
link |
04:08:57.300
But if you know, you know, base, base, base thing,
link |
04:09:01.260
physics is computational,
link |
04:09:03.220
then you know that that stuff is, you know,
link |
04:09:05.540
that that's kind of the grounding for that stuff.
link |
04:09:07.700
Just as in a sense Copernicus was the grounding
link |
04:09:10.540
for the idea that you could figure out something
link |
04:09:12.900
with math and science
link |
04:09:14.620
that was not what you would intuitively think
link |
04:09:18.820
from your senses.
link |
04:09:20.100
So now we've got to this point where, for example,
link |
04:09:22.780
we say, you know, once we have the idea
link |
04:09:25.220
that computation is the foundational thing
link |
04:09:27.940
that explains our whole universe,
link |
04:09:30.100
then we have to say, well, what does it mean
link |
04:09:32.020
for other things?
link |
04:09:32.860
Like it means there's computational irreducibility.
link |
04:09:35.220
That means science is limited in certain ways.
link |
04:09:37.860
That means this, that means that.
link |
04:09:39.740
But the fact that we have that grounding means that,
link |
04:09:43.260
you know, and I think, for example, for Copernicus,
link |
04:09:45.660
for instance, the implications of his work
link |
04:09:49.140
on the set of mathematics of astronomy were cool,
link |
04:09:52.340
but they involved a very small number of people.
link |
04:09:54.540
The implications of his work for sort of the philosophy
link |
04:09:56.900
of how you think about things were vast
link |
04:09:59.820
and involved, you know, everybody more or less.
link |
04:10:02.820
But do you think, so that's actually the way scientists
link |
04:10:05.740
and people see the world around us.
link |
04:10:08.540
So it has a huge impact in that sense.
link |
04:10:10.580
Do you think it might have an impact more directly
link |
04:10:14.220
to engineering derivations from physics,
link |
04:10:18.100
like propulsion systems, our ability to colonize the world?
link |
04:10:21.980
Like, for example, okay, this is like sci fi,
link |
04:10:24.580
but if you understand the computational nature, say,
link |
04:10:30.420
of the different forces of physics, you know,
link |
04:10:34.300
there's a notion of being able to warp gravity,
link |
04:10:38.420
things like this.
link |
04:10:39.260
Yeah, can we make warp drive?
link |
04:10:40.500
Warp drive, yeah.
link |
04:10:41.700
So like, would we be able to, will, you know,
link |
04:10:45.660
will like Elon Musk start paying attention?
link |
04:10:47.580
Like it's awfully costly to launch these rockets.
link |
04:10:50.460
Do you think we'll be able to, yeah, create warp drive?
link |
04:10:52.820
And, you know, I set myself some homework.
link |
04:10:55.340
I agreed to give a talk at some NASA workshop
link |
04:10:57.580
in a few weeks about faster than light travel.
link |
04:10:59.860
So I haven't figured it out yet, but no, but.
link |
04:11:02.700
You got two weeks.
link |
04:11:03.540
Yeah, right.
link |
04:11:04.380
But do you think that kind of understanding
link |
04:11:06.260
of fundamental theory of physics can lead
link |
04:11:07.980
to those engineering breakthroughs?
link |
04:11:09.540
Okay, I think it's far away, but I'm not certain.
link |
04:11:12.020
I mean, you know, this is the thing that,
link |
04:11:14.660
I set myself an exercise when gravity waves,
link |
04:11:16.940
gravitational waves were discovered, right?
link |
04:11:19.220
I set myself the exercise of what would black hole
link |
04:11:22.020
technology look like?
link |
04:11:23.780
In other words, right now, you know,
link |
04:11:25.260
black holes are far away.
link |
04:11:26.420
They're, you know, how on earth can we do things with them?
link |
04:11:28.100
But just imagine that we could get, you know,
link |
04:11:30.060
pet black holes right in our backyard.
link |
04:11:32.460
You know, what kind of technology could we build with them?
link |
04:11:34.500
I got a certain distance, not that far,
link |
04:11:36.700
but I think in, you know, so there are ideas, you know,
link |
04:11:40.020
I have this, one of the weirder ideas is things
link |
04:11:42.340
I'm calling space tunnels,
link |
04:11:44.140
which are higher dimensional pieces of space time,
link |
04:11:47.820
where basically you can, you know,
link |
04:11:50.020
in our three dimensional space,
link |
04:11:51.980
there might be a five dimensional, you know,
link |
04:11:54.620
region, which actually will appear as a white hole
link |
04:11:57.020
at one end and a black hole at the other end,
link |
04:11:59.300
you know, who knows whether they exist.
link |
04:12:01.060
And then the questions, another one,
link |
04:12:02.700
okay, this is another crazy one,
link |
04:12:04.420
is the thing that I'm calling a vacuum cleaner, okay?
link |
04:12:07.620
So, I mentioned that, you know,
link |
04:12:10.620
there's all this activity in the universe,
link |
04:12:12.580
which is maintaining the structure of space.
link |
04:12:14.980
And that leads to a certain energy density
link |
04:12:18.260
effectively in space.
link |
04:12:20.100
And so the question, in fact, dark energy
link |
04:12:23.620
is a story of essentially negative mass
link |
04:12:26.820
produced by the absence of energy
link |
04:12:30.900
you thought would be there, so to speak.
link |
04:12:33.180
And we don't know exactly how it works
link |
04:12:34.820
in either our model or the physical universe,
link |
04:12:37.700
but this notion of a vacuum cleaner is a thing where,
link |
04:12:41.860
you know, you have all these things
link |
04:12:43.060
that are maintaining the structure of space,
link |
04:12:44.500
but what if you could clean out some of that stuff
link |
04:12:47.580
that's maintaining the structure of space
link |
04:12:49.460
and make a simpler vacuum somewhere?
link |
04:12:51.860
You know, what would that do?
link |
04:12:52.700
A totally different kind of vacuum.
link |
04:12:54.220
Right, and that would lead to negative energy density,
link |
04:12:57.180
which would need to, so gravity is usually
link |
04:12:59.420
a purely attractive force, but negative mass
link |
04:13:02.420
would lead to repulsive gravity
link |
04:13:06.180
and lead to all kinds of weird things.
link |
04:13:08.540
Now, can it be done in our universe?
link |
04:13:11.220
You know, my immediate thought is no,
link |
04:13:14.820
but you know, the fact is that, okay, so here's the thing.
link |
04:13:18.420
Well, once you understand the fact,
link |
04:13:19.620
because you're saying like, at this level of abstraction,
link |
04:13:21.580
can we reach to the lower levels and mess with it?
link |
04:13:25.420
Yes.
link |
04:13:26.260
Once you understand the levels, I think you can start to.
link |
04:13:27.940
I know, and I'm, you know, I have to say
link |
04:13:30.700
that this reminds me of people telling one years ago
link |
04:13:34.660
that, you know, you'll never transmit data
link |
04:13:36.300
over a copper wire at more than 1,000,
link |
04:13:38.740
you know, 1,000 board or something, right?
link |
04:13:41.460
And this is, why did that not happen?
link |
04:13:43.940
You know, why do we have this much,
link |
04:13:45.580
much faster data transmission?
link |
04:13:46.940
Because we've understood many more of the details
link |
04:13:48.820
of what's actually going on.
link |
04:13:50.380
And it's the same exact story here.
link |
04:13:52.540
And it's the same, you know, I think that this,
link |
04:13:54.740
as I say, I think one of the features of sort of,
link |
04:13:58.580
one of the things about our time
link |
04:14:00.540
that will seem incredibly naive in the future
link |
04:14:03.020
is the belief that, you know, things like heat
link |
04:14:06.220
is just random motion of molecules,
link |
04:14:08.380
that it's just throw up your hands, it's just random.
link |
04:14:12.460
We can't say anything about it.
link |
04:14:14.060
That will seem naive.
link |
04:14:15.660
Yeah, at the heat death of the universe,
link |
04:14:18.100
those particles would be laughing at us humans thinking.
link |
04:14:20.980
Yes, right.
link |
04:14:22.380
That life is not beautiful.
link |
04:14:23.220
I'll have a whole civilization, you know.
link |
04:14:25.900
Humans used to think they're special
link |
04:14:27.580
with their little brains.
link |
04:14:28.980
Well, right, but also, and they used to think
link |
04:14:31.260
that this would just be random and uninteresting.
link |
04:14:33.940
But that's, but so this question about whether you can,
link |
04:14:37.620
you know, mess with the underlying structure
link |
04:14:39.980
and how you find a way to mess with the underlying structure,
link |
04:14:42.860
that's a, you know, I have to say, you know,
link |
04:14:45.660
my immediate thing is, boy, that seems really hard,
link |
04:14:48.820
but then, and you know,
link |
04:14:50.980
possibly computational irreducibility will bite you,
link |
04:14:54.020
but then there's always some path
link |
04:14:55.540
of computational reducibility.
link |
04:14:57.380
And that path of computational reducibility
link |
04:14:59.740
is the engineering invention that has to be made.
link |
04:15:02.540
Those little pockets can have huge engineering impact.
link |
04:15:05.980
Right, and I think that that's right.
link |
04:15:07.780
And I mean, we live in, you know, we make use of so many
link |
04:15:10.380
of those pockets.
link |
04:15:11.420
And the fact is, you know, I, you know, this is, yes,
link |
04:15:16.980
it's a, you know, it's one of these things where,
link |
04:15:20.380
where, you know, I'm a person who likes to figure out ideas
link |
04:15:24.740
and so on, and the sort of tests of my level of imagination,
link |
04:15:28.060
so to speak.
link |
04:15:29.180
And so a couple of places where there's sort of serious
link |
04:15:32.700
humility in terms of my level of imagination,
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04:15:35.460
one is this thing about different reference frames
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04:15:38.220
for understanding the universe,
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04:15:39.860
where like, imagine the physics of the aliens,
link |
04:15:42.260
what will it be like?
link |
04:15:43.660
And I'm like, that's really hard.
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04:15:45.780
I don't know, you know?
link |
04:15:47.500
And I mean, I think that...
link |
04:15:48.340
But once you have the framework in place,
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04:15:49.980
you can at least reason about the things you don't know,
link |
04:15:53.940
maybe can't know, or like, it's too hard for you to know,
link |
04:15:57.620
but then the mathematics can, that's exactly it,
link |
04:16:01.620
allow you to reach beyond where you can reason about.
link |
04:16:05.900
So I'm, you know, I'm trying to not have, you know,
link |
04:16:09.340
if you think back to Alan Turing, for example,
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04:16:11.660
and, you know, when he invented Turing machines, you know,
link |
04:16:14.260
and imagining what computers would end up doing,
link |
04:16:16.980
so to speak.
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04:16:17.820
Yeah.
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04:16:18.660
You know, and it's...
link |
04:16:19.500
It's very difficult.
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04:16:20.340
It's difficult, right.
link |
04:16:21.180
And it's, and I mean, this thing...
link |
04:16:22.020
Made a few reasonable predictions,
link |
04:16:23.460
but most of it, he couldn't predict, possibly.
link |
04:16:25.500
By the time, by 1950, he was making reasonable predictions
link |
04:16:28.300
about some things.
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04:16:29.140
But not the 30s, yeah.
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04:16:30.140
Right, not when he first, you know, conceptualized,
link |
04:16:34.660
you know, and he conceptualized universal computing
link |
04:16:37.380
for a very specific mathematical reason
link |
04:16:39.180
that wasn't as general.
link |
04:16:41.340
But yes, it's a good sort of exercise in humility
link |
04:16:44.220
to realize that it's kind of like,
link |
04:16:46.860
it's really hard to figure these things out.
link |
04:16:49.580
The engineering of the universe,
link |
04:16:52.260
if we know how the universe works, how can we engineer it?
link |
04:16:55.860
That's such a beautiful vision.
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04:16:57.580
That's such a beautiful vision.
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04:16:58.420
By the way, I have to mention one more thing,
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04:16:59.740
which is the ultimate question from physics is,
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04:17:04.300
okay, so we have this abstract model of the universe.
link |
04:17:07.380
Why does the universe exist at all, right?
link |
04:17:11.260
So, you know, we might say there is a formal model
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04:17:15.220
that if you run this model, you get the universe,
link |
04:17:18.100
or the model gives you, you know, a model of the universe,
link |
04:17:21.900
right, you run this mathematical thing
link |
04:17:25.300
and the mathematics unfolds in the way
link |
04:17:27.820
that corresponds to the universe.
link |
04:17:29.420
But the question is, why was that actualized?
link |
04:17:32.460
Why does the actual universe actually exist?
link |
04:17:35.980
And so this is another one of these humility
link |
04:17:39.220
and it's like, can you figure this out?
link |
04:17:41.700
I have a guess, okay, about the answer to that.
link |
04:17:44.780
And my guess is somewhat unsatisfying,
link |
04:17:47.820
but my guess is that it's a little bit similar
link |
04:17:50.380
to Gödel's second incompleteness theorem,
link |
04:17:52.740
which is the statement that from within,
link |
04:17:55.180
as an axiomatic theory like piano arithmetic,
link |
04:17:58.060
you cannot from within that theory
link |
04:17:59.780
prove the consistency of the theory.
link |
04:18:02.420
So my guess is that for entities within the universe,
link |
04:18:08.140
there is no finite determination that can be made
link |
04:18:11.540
of the statement the universe exists
link |
04:18:15.260
is essentially undecidable to any entity
link |
04:18:18.580
that is embedded in the universe.
link |
04:18:19.900
Within that universe, how does that make you feel?
link |
04:18:22.780
Does that put you at peace that it's impossible,
link |
04:18:27.980
or is it really ultimately frustrating?
link |
04:18:30.940
Well, I think it just says that it's not a kind of question
link |
04:18:35.460
that, you know, there are things that it is reasonable.
link |
04:18:40.140
I mean, there's kinds of, you know,
link |
04:18:42.780
you can talk about hyper computation as well.
link |
04:18:44.580
You can say, imagine there was a hyper computer,
link |
04:18:46.500
here's what it would do.
link |
04:18:47.700
So okay, great, it would be lovely to have a hyper computer,
link |
04:18:49.940
but unfortunately we can't make it in the universe.
link |
04:18:52.300
Like it would be lovely to answer this,
link |
04:18:53.540
but unfortunately we can't do it in the universe.
link |
04:18:56.300
And you know, this is all we have, so to speak.
link |
04:18:59.100
And I think it's really just a statement.
link |
04:19:02.340
It's sort of, in the end, it'll be a kind of a logical,
link |
04:19:06.180
logically inevitable statement, I think.
link |
04:19:08.380
I think it will be something where it is,
link |
04:19:10.700
as you understand what it means to have,
link |
04:19:13.260
what it means to have a sort of predicate of existence
link |
04:19:16.220
and what it means to have these kinds of things,
link |
04:19:17.780
it will sort of be inevitable that this has to be the case,
link |
04:19:20.460
that from within that universe, you can't establish
link |
04:19:23.460
the reason for its existence, so to speak.
link |
04:19:25.060
You can't prove that it exists and so on.
link |
04:19:26.900
And nevertheless, because of computational reducibility,
link |
04:19:29.940
the future is ultimately not predictable, full of mystery,
link |
04:19:34.140
and that's what makes life worth living.
link |
04:19:36.860
Right, I mean, right.
link |
04:19:37.780
And you know, it's funny for me,
link |
04:19:39.340
because as a pure sort of human being doing what I do,
link |
04:19:43.100
it's, you know, like I'm interested in people,
link |
04:19:46.780
I like sort of the whole human experience, so to speak.
link |
04:19:51.020
And yet, it's a little bit weird when I'm thinking,
link |
04:19:53.980
you know, it's all hypergraphs down there,
link |
04:19:56.460
and it's all just.
link |
04:19:57.780
Hypergraphs all the way down.
link |
04:19:59.580
Right.
link |
04:20:00.420
It's like turtles all the way down.
link |
04:20:01.380
Yeah, yeah, right.
link |
04:20:02.540
And it's kind of, you know, to me, it is a funny thing,
link |
04:20:06.580
because every so often I get this, you know,
link |
04:20:08.220
as I'm thinking about, I think we've really gotten,
link |
04:20:10.620
you know, we've really figured out kind of the essence
link |
04:20:12.500
of how physics works, and I'm like thinking to myself,
link |
04:20:14.780
you know, here's this physical thing,
link |
04:20:16.420
and I'm like, you know,
link |
04:20:17.780
this feels like a very definite thing.
link |
04:20:19.900
How can it be the case that this is just
link |
04:20:21.460
some rule or reference frame of, you know,
link |
04:20:23.980
this infinite creature that is so abstract and so on?
link |
04:20:28.420
And I kind of, it is a, it's a funny sort of feeling
link |
04:20:32.980
that, you know, we are, we're sort of, it's like,
link |
04:20:37.620
in the end, it's just sort of,
link |
04:20:39.580
we're just happy we're just humans type thing.
link |
04:20:42.220
And it's kind of like, but we're making,
link |
04:20:44.980
we make things as, it's not like we're just a tiny speck.
link |
04:20:50.020
We are, in a sense, the, we are more important
link |
04:20:54.500
by virtue of the fact that, in a sense,
link |
04:20:58.340
it's not like there's, there is no ultimate, you know,
link |
04:21:02.780
it's like, we're important because,
link |
04:21:06.540
because, you know, we're here, so to speak,
link |
04:21:08.900
and we're not, it's not like there's a thing
link |
04:21:10.900
where we're saying, you know, we are just but one
link |
04:21:15.780
sort of intelligence out of all these other intelligences.
link |
04:21:18.380
And so, you know, ultimately there'll be
link |
04:21:20.860
the super intelligence, which is all of these put together
link |
04:21:23.980
and they'll be very different from us.
link |
04:21:25.260
No, it's actually going to be equivalent to us.
link |
04:21:27.540
And the thing that makes us a sort of special
link |
04:21:31.380
is just the details of us, so to speak.
link |
04:21:34.740
It's not something where we can say,
link |
04:21:36.700
oh, there's this other thing, you know,
link |
04:21:38.980
just, you think humans are cool,
link |
04:21:40.900
just wait until you've seen this.
link |
04:21:43.260
You know, it's going to be much more impressive.
link |
04:21:45.100
Well, no, it's all going to be
link |
04:21:47.020
kind of computationally equivalent.
link |
04:21:48.900
And the thing that, you know, it's not going to be,
link |
04:21:51.380
oh, this thing is amazingly much more impressive
link |
04:21:53.980
and amazingly much more meaningful, let's say.
link |
04:21:56.860
No, we're it.
link |
04:21:58.980
I mean, that's the...
link |
04:22:01.460
And the symbolism of this particular moment.
link |
04:22:04.380
So this has been one of the,
link |
04:22:07.020
one of the favorite conversations I've ever had, Stephen.
link |
04:22:10.860
It's a huge honor to talk to you,
link |
04:22:12.700
to talk about a topic like this for four plus hours
link |
04:22:16.660
on the fundamental theory of physics.
link |
04:22:18.620
And yet we're just two finite descendants of apes
link |
04:22:22.900
that have to end this conversation
link |
04:22:24.940
because darkness have come upon us.
link |
04:22:28.020
Right, and we're going to get bitten by mosquitoes
link |
04:22:29.980
and all kinds of terrible things.
link |
04:22:30.820
The symbolism of that,
link |
04:22:32.540
we're talking about the most basic fabric of reality
link |
04:22:36.220
and having to end because of the fact that things end.
link |
04:22:40.900
It's tragic and beautiful, Stephen.
link |
04:22:42.580
Thank you so much.
link |
04:22:43.420
Huge honor.
link |
04:22:44.380
I can't wait to see what you do in the next couple of days
link |
04:22:47.100
and next week, a month.
link |
04:22:48.580
We're all watching with excitement.
link |
04:22:50.700
Thank you so much.
link |
04:22:51.540
Thanks.
link |
04:22:53.020
Thanks for listening to this conversation
link |
04:22:54.500
with Stephen Wolfram.
link |
04:22:55.660
And thank you to our sponsors,
link |
04:22:57.540
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04:23:00.940
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link |
04:23:03.220
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link |
04:23:06.020
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04:23:08.220
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04:23:10.420
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link |
04:23:12.980
or connect with me on Twitter at Lex Friedman.
link |
04:23:16.580
And now let me leave you with some words
link |
04:23:19.100
from Richard Feynman.
link |
04:23:21.220
Physics isn't the most important thing, love is.
link |
04:23:25.340
Thank you for listening and hope to see you next time.