back to indexStephen Wolfram: Fundamental Theory of Physics, Life, and the Universe | Lex Fridman Podcast #124
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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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by clicking the links in the description.
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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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a home security company.
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Go to SimpliSafe.com to get a free HD camera.
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It's simple, no contracts, 15 bucks a month, easy setup.
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Even I figured it out.
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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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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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to get a free HD camera and to support this podcast.
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They're a new sponsor, and this is a trial run,
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so you know what to do.
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This show is also sponsored by Sun Basket,
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a meal delivery service.
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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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and to support this podcast.
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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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that they decide to support this podcast long term.
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Their meals are healthy and delicious,
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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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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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So they signed a longterm contract for this podcast.
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This show is also sponsored by Masterclass.
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Sign up at masterclass.com slash LEX.
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180 bucks a year, you get an all access pass
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to watch lessons from Chris Hadfield,
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and many more brilliant world experts.
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Masterclass has been a really special sponsor.
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They believe in this podcast in a way that gives me strength
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and motivation to take intellectual risks.
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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 to support this podcast.
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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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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, 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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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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Or do you think that's already happened?
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Oh, yeah, it's happened, except that people aren't,
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the sort of the heroism of it may not be there,
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but what's happened is for 300 years,
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people basically said,
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if you want to make a model of things in the world,
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mathematical equations are the best place to go.
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Last 15 years, doesn't happen.
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New models that get made of things
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most often are made with programs, not with equations.
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Now, was that sort of going to happen anyway?
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Was that a consequence of my particular work
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and my particular book?
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It's hard to know for sure.
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I mean, I am always amazed at the amounts of feedback
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that I get from people where they say,
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oh, by the way, I started doing this whole line of research
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because I read your book, blah, blah, blah, blah, blah.
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It's like, well, can you tell that
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from the academic literature?
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Was there a chain of academic references?
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One of the interesting side effects of publishing
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in the way you did this tome
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is it serves as an education tool and an inspiration
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to hundreds of thousands, millions of people,
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but because it's not a single,
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it's not a chain of papers with spiffy titles,
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it doesn't create a splash of citations.
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It's had plenty of citations, but it's, you know,
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I think that people think of it as probably more,
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you know, conceptual inspiration than kind of a,
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you know, this is a line from here to here to here
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in our particular field.
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I think that the thing which I am disappointed by
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and which will eventually happen
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is this kind of study of the sort of pure computationalism,
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this kind of study of the abstract behavior
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of the computational universe.
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That should be a big thing that lots of people do.
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You mean in mathematics purely, almost like.
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It's like pure mathematics, but it isn't mathematics.
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But it isn't, it isn't.
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It's a new kind of mathematics.
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Is it a new title of the book?
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That's why the book is called that.
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Right, that's not coincidental.
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It's interesting that I haven't seen
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really rigorous investigation
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by thousands of people of this idea.
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I mean, you look at your competition around rule 30.
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I mean, that's fascinating.
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If you can say something.
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Is there some aspect of this thing that could be predicted?
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That's the fundamental question of science.
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Well, that has been a question of science.
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I think that is some people's view of what science is about
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and it's not clear that's the right view.
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In fact, as we live through this pandemic
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full of predictions and so on,
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it's an interesting moment to be pondering
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what science's actual role in those kinds of things is.
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Or you think it's possible that in science,
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clean, beautiful, simple prediction
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may not even be possible in real systems.
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That's the open question.
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I don't think it's open.
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I think that question is answered and the answer is no.
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The answer could be just humans are not smart enough yet.
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Like we don't have the tools yet.
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No, that's the whole point.
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I mean, that's sort of the big discovery
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of this principle of computational equivalence of mine.
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And this is something which is kind of a follow on
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to Gödel's theorem, to Turing's work
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on the halting problem, all these kinds of things.
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That there is this fundamental limitation
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built into science,
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this idea of computational irreducibility
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that says that even though you may know the rules
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by which something operates,
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that does not mean that you can readily sort of
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be smarter than it and jump ahead
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and figure out what it's going to do.
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Yes, but do you think there's a hope
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for pockets of computational reducibility?
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Computational reducibility.
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And then a set of tools and mathematics
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that help you discover such pockets.
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That's where we live is in the pockets of reducibility.
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That's why, and this is one of the things
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that sort of come out of this physics project
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and actually something that, again,
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I should have realized many years ago, but didn't,
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is it could very well be that everything about the world
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is computationally reducible and completely unpredictable.
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But in our experience of the world,
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there is at least some amount of prediction we can make.
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And that's because we have sort of chosen a slice of,
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probably talk about this in much more detail,
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but I mean, we've kind of chosen a slice
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of how to think about the universe
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in which we can kind of sample
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a certain amount of computational reducibility.
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And that's sort of where we exist.
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And it may not be the whole story of how the universe is,
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but it is the part of the universe that we care about
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and we sort of operate in.
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And that's, you know, in science,
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that's been sort of a very special case of that.
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That is science has chosen to talk a lot about places
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where there is this computational reducibility
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that it can find, you know,
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the motion of the planets can be more or less predicted.
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You know, something about the weather
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is much harder to predict.
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Something about, you know, other kinds of things
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that are much harder to predict.
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And it's, these are, but science has tended to,
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you know, concentrate itself on places
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where its methods have allowed successful prediction.
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So you think rule 30, if we could linger on it,
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because it's just such a beautiful, simple formulation
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of the essential concept underlying
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all the things we're talking about.
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Do you think there's pockets of reducibility
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Yes, that is the question of how big are they?
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What will they allow you to say?
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And that's, and figuring out where those pockets are,
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I mean, in a sense, that's the, that's sort of a,
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you know, that is an essential thing
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that one would like to do in science.
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But it's also, the important thing to realize
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that has not been, you know, is that science,
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if you just pick an arbitrary thing,
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you say, what's the answer to this question?
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That question may not be one
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that has a computationally reducible answer.
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That question, if you choose, you know,
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if you walk along the series of questions
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and you've got one that's reducible
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and you get to another one that's nearby
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and it's reducible too,
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if you stick to that kind of stick to the land,
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so to speak, then you can go down this chain
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of sort of reducible, answerable things.
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But if you just say, I'm just pick a question at random,
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I'm gonna have my computer pick a question at random.
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Most likely it's gonna be reducible.
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Most likely it will be reducible.
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And what we're thrown in the world, so to speak,
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we, you know, when we engineer things,
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we tend to engineer things to sort of keep
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in the zone of reducibility.
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When we're throwing things by the natural world,
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for example, not at all certain
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that we will be kept in this kind of zone of reducibility.
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Can we talk about this pandemic then?
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For a second, is a, so how do we,
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there's obviously huge amount of economic pain
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that people are feeling.
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There's a huge incentive and medical pain,
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health, just all kind of psychological.
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There's a huge incentive to figure this out,
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to walk along the trajectory of reducible, of reducibility.
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There's a lot of disparate data.
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You know, people understand generally how viruses spread,
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but it's very complicated
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because there's a lot of uncertainty.
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There's a, there could be a lot of variability also,
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like so many, obviously a nearly infinite number
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of variables that represent human interaction.
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And so you have to figure out,
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from the perspective of reducibility,
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figure out which variables are really important
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in this kind of, from an epidemiological perspective.
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So why aren't we, you kind of said
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that we're clearly failing.
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Well, I think it's a complicated thing.
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So, I mean, you know, when this pandemic started up,
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you know, I happened to be in the middle
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of being about to release this whole physics project thing,
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but I thought, you know.
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The timing is just cosmically absurd.
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A little bit bizarre, but you know,
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but I thought, you know,
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I should do the public service thing of, you know,
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trying to understand what I could about the pandemic.
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And, you know, we'd been curating data about it
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and all that kind of thing.
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But, you know, so I started looking at the data
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and started looking at modeling
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and I decided it's just really hard.
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You need to know a lot of stuff that we don't know
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about human interactions.
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It's actually clear now that there's a lot of stuff
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we didn't know about viruses
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and about the way immunity works and so on.
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And it's, you know, I think what will come out in the end
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is there's a certain amount of what happens
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that we just kind of have to trace each step
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and see what happens.
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There's a certain amount of stuff
link |
where there's going to be a big narrative
link |
about this happened because, you know, of T cell immunity.
link |
This could happen because there's this whole giant
link |
sort of field of asymptomatic viral stuff out there.
link |
You know, there will be a narrative
link |
and that narrative, whenever there's a narrative,
link |
that's kind of a sign of reducibility.
link |
But when you just say,
link |
let's from first principles figure out what's going on,
link |
then you can potentially be stuck
link |
in this kind of a mess of irreducibility
link |
where you just have to simulate each step
link |
and you can't do that unless you know details about,
link |
you know, human interaction networks
link |
and so on and so on and so on.
link |
The thing that has been very sort of frustrating to see
link |
is the mismatch between people's expectations
link |
about what science can deliver
link |
and what science can actually deliver, so to speak.
link |
Because people have this idea that, you know, it's science.
link |
So there must be a definite answer
link |
and we must be able to know that answer.
link |
And, you know, this is, it is both, you know,
link |
when you've, after you've played around
link |
with sort of little programs in the computational universe,
link |
you don't have that intuition anymore.
link |
You know, it's, I always, I'm always fond of saying,
link |
you know, the computational animals
link |
are always smarter than you are.
link |
That is, you know, you look at one of these things
link |
and it's like, it can't possibly do such and such a thing.
link |
Then you run it and it's like, wait a minute,
link |
it's doing that thing.
link |
How does that work?
link |
Okay, now I can go back and understand it.
link |
But that's the brave thing about science
link |
is that in the chaos of the irreducible universe,
link |
we nevertheless persist to find those pockets.
link |
That's kind of the whole point.
link |
That's like, you say that the limits of science,
link |
but that, you know, yes, it's highly limited,
link |
but there's a hope there.
link |
And like, there's so many questions I want to ask here.
link |
So one, you said narrative, which is really interesting.
link |
So obviously from a, at every level of society,
link |
you look at Twitter, everybody's constructing narratives
link |
about the pandemic, about not just the pandemic,
link |
but all the cultural tension that we're going through.
link |
So there's narratives,
link |
but they're not necessarily connected
link |
to the underlying reality of these systems.
link |
So our human narratives, I don't even know if they're,
link |
I don't like those pockets of reducibility
link |
because we're, it's like constructing things
link |
that are not actually representative of reality,
link |
and thereby not giving us like good solutions
link |
to how to predict the system.
link |
Look, it gets complicated because, you know,
link |
people want to say, explain the pandemic to me,
link |
explain what's going to happen.
link |
Yes, but also, can you explain it?
link |
Is there a story to tell?
link |
What already happened in the past?
link |
Yeah, or what's going to happen,
link |
but I mean, you know, it's similar to sort of
link |
explaining things in AI or in any computational system.
link |
It's like, you know, explain what happened.
link |
Well, it could just be this happened
link |
because of this detail and this detail and this detail,
link |
and a million details,
link |
and there isn't a big story to tell.
link |
There's no kind of big arc of the story that says,
link |
oh, it's because, you know, there's a viral field
link |
that has these properties
link |
and people start showing symptoms.
link |
You know, when the seasons change,
link |
people will show symptoms
link |
and people don't even understand, you know,
link |
seasonal variation of flu, for example.
link |
It's something where, you know,
link |
there could be a big story,
link |
or it could be just a zillion little details that mount up.
link |
See, but, okay, let's pretend that this pandemic,
link |
like the coronavirus, resembles something
link |
like the 1D rule 30 cellular automata, okay?
link |
So, I mean, that's how epidemiologists model virus spread.
link |
They sometimes use cellular automata, yes.
link |
Yeah, and okay, so you could say it's simplistic,
link |
but okay, let's say it's representative
link |
of actually what happens.
link |
You know, the dynamic of,
link |
it probably is closer to the hypergraph model.
link |
It's actually, that's another funny thing.
link |
As we were getting ready to release this physics project,
link |
we realized that a bunch of things we'd worked out
link |
about foliations of causal graphs and things
link |
were directly relevant to thinking about contact tracing.
link |
And interactions with cell phones and so on,
link |
which is really weird.
link |
But like, it just feels like,
link |
it feels like we should be able to get
link |
some beautiful core insight about the spread
link |
of this particular virus
link |
on the hypergraph of human civilization, right?
link |
I tried, I didn't manage to figure it out.
link |
But you're one person.
link |
Yeah, but I mean, I think actually it's a funny thing
link |
because it turns out the main model,
link |
you know, this SIR model,
link |
I only realized recently was invented by the grandfather
link |
of a good friend of mine from high school.
link |
So that was just a, you know, it's a weird thing, right?
link |
The question is, you know, okay, so you know,
link |
on this graph of how humans are connected,
link |
you know something about what happens
link |
if this happens and that happens.
link |
That graph is made in complicated ways
link |
that depends on all sorts of issues
link |
that where we don't have the data
link |
about how human society works well enough
link |
to be able to make that graph.
link |
There's actually, one of my kids did a study
link |
of sort of what happens on different kinds of graphs
link |
and how robust are the results, okay?
link |
His basic answer is there are a few general results
link |
that you can get that are quite robust.
link |
Like, you know, a small number of big gatherings
link |
is worse than a large number of small gatherings, okay?
link |
That's quite robust.
link |
But when you ask more detailed questions,
link |
it seemed like it just depends.
link |
It depends on details.
link |
In other words, it's kind of telling you in that case,
link |
you know, the irreducibility matters, so to speak.
link |
It's not, there's not gonna be this kind of one
link |
sort of master theorem that says,
link |
and therefore this is how things are gonna work.
link |
Yeah, but there's a certain kind of,
link |
from a graph perspective,
link |
the certain kind of dynamic to human interaction.
link |
So like large groups and small groups,
link |
I think it matters who the groups are.
link |
For example, you could imagine large,
link |
depends how you define large,
link |
but you can imagine groups of 30 people,
link |
as long as they are cliques or whatever.
link |
As long as the outgoing degree of that graph is small
link |
or something like that,
link |
like you can imagine some beautiful underlying rule
link |
of human dynamic interaction where I can still be happy,
link |
where I can have a conversation with you
link |
and a bunch of other people that mean a lot to me in my life
link |
and then stay away from the bigger, I don't know,
link |
not going to a Miley Cyrus concert or something like that
link |
and figuring out mathematically some nice.
link |
See, this is an interesting thing.
link |
So I mean, this is the question of what you're describing
link |
is kind of the problem of the many situations
link |
where you would like to get away
link |
from computational irreducibility.
link |
A classic one in physics is thermodynamics.
link |
The second law of thermodynamics,
link |
the law that says entropy tends to increase things
link |
that start orderly tend to get more disordered,
link |
or which is also the thing that says,
link |
given that you have a bunch of heat,
link |
it's hard, heat is the microscopic motion of molecules,
link |
it's hard to turn that heat into systematic mechanical work.
link |
It's hard to just take something being hot
link |
and turn that into, oh, all the atoms are gonna line up
link |
in the bar of metal and the piece of metal
link |
is gonna shoot in some direction.
link |
That's essentially the same problem
link |
as how do you go from this computationally irreducible
link |
mess of things happening
link |
and get something you want out of it.
link |
It's kind of mining, you're kind of,
link |
now, actually I've understood in recent years
link |
that the story of thermodynamics
link |
is actually precisely a story of computational irreducibility,
link |
but it is a, it is already an analogy.
link |
You can kind of see that as can you take the,
link |
what you're asking to do there
link |
is you're asking to go from the kind of,
link |
the mess of all these complicated human interactions
link |
and all this kind of computational processes going on
link |
and you say, I want to achieve
link |
this particular thing out of it.
link |
I want to kind of extract from the heat of what's happening.
link |
I want to kind of extract this useful piece
link |
of sort of mechanical work that I find helpful.
link |
Do you have a hope for the pandemic?
link |
So we'll talk about physics,
link |
but for the pandemic, can that be extracted?
link |
What's your intuition?
link |
The good news is the curves basically,
link |
for reasons we don't understand,
link |
the curves, the clearly measurable mortality curves
link |
and so on for the Northern Hemisphere have gone down.
link |
Yeah, but the bad news is that it could be a lot worse
link |
for future viruses.
link |
And what this pandemic revealed is we're highly unprepared
link |
for the discovery of the pockets of reducibility
link |
within a pandemic that's much more dangerous.
link |
Well, my guess is the specific risk of viral pandemics,
link |
you know, that the pure virology
link |
and immunology of the thing,
link |
this will cause that to advance to the point
link |
where this particular risk
link |
is probably considerably mitigated.
link |
But is the structure of modern society robust
link |
to all kinds of risks?
link |
Well, the answer is clearly no.
link |
And it's surprising to me the extent to which people,
link |
as I say, it's kind of scary actually
link |
how much people believe in science.
link |
That is people say, oh, you know,
link |
because the science says this, that and the other,
link |
we'll do this and this and this,
link |
even though from a sort of common sense point of view,
link |
it's a little bit crazy and people are not prepared
link |
and it doesn't really work in society
link |
as it is for people to say,
link |
well, actually we don't really know how the science works.
link |
People say, well, tell us what to do.
link |
Yeah, because then, yeah, what's the alternative?
link |
For the masses, it's difficult to sit,
link |
it's difficult to meditate on computational reducibility.
link |
It's difficult to sit,
link |
it's difficult to enjoy a good dinner meal
link |
while knowing that you know nothing about the world.
link |
Well, I think this is a place where, you know,
link |
this is what politicians and political leaders do
link |
for a living, so to speak,
link |
is you've got to make some decision about what to do.
link |
Tell some narrative that while amidst the mystery
link |
and knowing not much about the past or the future,
link |
still telling a narrative that somehow gives people hope
link |
that we know what the heck we're doing.
link |
Yeah, and get society through the issue.
link |
You know, even though, you know,
link |
the idea that we're just gonna, you know,
link |
sort of be able to get the definitive answer from science
link |
and it's gonna tell us exactly what to do.
link |
Unfortunately, you know, it's interesting
link |
because let me point out that if that was possible,
link |
if science could always tell us what to do,
link |
then in a sense, our, you know,
link |
that would be a big downer for our lives.
link |
If science could always tell us
link |
what the answer is gonna be,
link |
it's like, well, you know,
link |
it's kind of fun to live one's life
link |
and just sort of see what happens.
link |
If one could always just say,
link |
let me check my science.
link |
Oh, I know, you know,
link |
the result of everything is gonna be 42.
link |
I don't need to live my life and do what I do.
link |
It's just, we already know the answer.
link |
It's actually good news in a sense
link |
that there is this phenomenon
link |
of computational irreducibility
link |
that doesn't allow you to just sort of jump through time
link |
and say, this is the answer, so to speak.
link |
And that's, so that's a good thing.
link |
The bad thing is it doesn't allow you to jump through time
link |
and know what the answer is.
link |
Do you think we're gonna be okay as a human civilization?
link |
You said, we don't know.
link |
Do you think we'll prosper or destroy ourselves?
link |
No, I think that, you know,
link |
it'll be interesting to see, for example,
link |
with this, you know, pandemic,
link |
I, you know, to me, you know,
link |
when you look at like organizations, for example,
link |
you know, having some kind of perturbation,
link |
some kick to the system,
link |
usually the end result of that is actually quite good.
link |
You know, unless it kills the system,
link |
it's actually quite good usually.
link |
And I think in this case, you know, people,
link |
I mean, my impression, you know,
link |
it's a little weird for me because, you know,
link |
I've been a remote tech CEO for 30 years.
link |
It doesn't, you know, this is bizarrely, you know,
link |
and the fact that, you know, like this coming to see you here
link |
is the first time in six months that I've been like,
link |
you know, in a building other than my house, okay?
link |
So, you know, I'm a kind of ridiculous outlier
link |
in these kinds of things.
link |
But overall, your sense is when you shake up the system
link |
and throw in chaos that you challenge the system,
link |
we humans emerge better.
link |
Seems to be that way.
link |
I think that, you know, people, you know,
link |
my sort of vague impression is that people are sort of,
link |
you know, oh, what's actually important?
link |
You know, what is worth caring about and so on?
link |
And that seems to be something that perhaps is more,
link |
you know, emergent in this kind of situation.
link |
It's so fascinating that on the individual level,
link |
we have our own complex cognition.
link |
We have consciousness, we have intelligence,
link |
we're trying to figure out little puzzles.
link |
And then that somehow creates this graph
link |
of collective intelligence.
link |
Well, we figure out, and then you throw in these viruses
link |
of which there's millions different, you know,
link |
there's entire taxonomy and the viruses are thrown
link |
into the system of collective human intelligence.
link |
And when little humans figure out what to do about it,
link |
we get like, we tweet stuff about information.
link |
There's doctors as conspiracy theorists.
link |
And then we play with different information.
link |
I mean, the whole of it is fascinating.
link |
I am like you also very optimistic,
link |
but you said the computational reducibility.
link |
There's always a fear of the darkness
link |
of the uncertainty before us.
link |
Yeah, I know. And it's scary.
link |
I mean, the thing is, if you knew everything,
link |
it will be boring.
link |
And it would be, and then, and worse than boring,
link |
It would reveal the pointlessness, so to speak.
link |
And in a sense, the fact that there is
link |
this computational irreducibility,
link |
it's like as we live our lives, so to speak,
link |
something is being achieved.
link |
We're computing what our lives, you know,
link |
what happens in our lives.
link |
So the computational reducibility is kind of like,
link |
it gives the meaning to life.
link |
It is the meaning of life.
link |
Computational reducibility is the meaning of life.
link |
It gives it meaning, yes.
link |
I mean, it's what causes it to not be something
link |
where you can just say, you know,
link |
you went through all those steps to live your life,
link |
but we already knew what the answer was.
link |
Hold on one second.
link |
I'm going to use my handy Wolfram Alpha sunburn
link |
computation thing, so long as I can get network here.
link |
Oh, actually, you know what?
link |
It says sunburn unlikely.
link |
This is a QA moment.
link |
This is a good moment.
link |
Okay, well, let me just check what it thinks.
link |
See why it thinks that.
link |
It doesn't seem like my intuition.
link |
This is one of these cases where we can,
link |
the question is, do we trust the science
link |
or do we use common sense?
link |
The UV thing is cool.
link |
Yeah, yeah, well, we'll see.
link |
This is a QA moment, as I say.
link |
It's, do we trust the product?
link |
Yes, we trust the product, so.
link |
And then there'll be a data point either way.
link |
If I'm desperately sunburned,
link |
I will send in an angry feedback.
link |
Because we mentioned the concept so much
link |
and a lot of people know it,
link |
but can you say what computational reducibility is?
link |
The question is, if you think about things
link |
that happen as being computations,
link |
you think about some process in physics,
link |
something that you compute in mathematics, whatever else,
link |
it's a computation in the sense it has definite rules.
link |
You follow those rules.
link |
You follow them many steps and you get some result.
link |
So then the issue is,
link |
if you look at all these different kinds of computations
link |
whether they're computations
link |
that are happening in the natural world,
link |
whether they're happening in our brains,
link |
whether they're happening in our mathematics,
link |
the big question is, how do these computations compare?
link |
Is, are there dumb computations and smart computations
link |
or are they somehow all equivalent?
link |
And the thing that I kind of was sort of surprised to realize
link |
from a bunch of experiments that I did in the early nineties
link |
and now we have tons more evidence for it,
link |
this thing I call the principle of computational equivalence,
link |
which basically says, when one of these computations,
link |
one of these processes that follows rules,
link |
doesn't seem like it's doing something obviously simple,
link |
then it has reached the sort of equivalent level
link |
of computational sophistication of everything.
link |
So what does that mean?
link |
That means that, you might say, gosh,
link |
I'm studying this little tiny program on my computer.
link |
I'm studying this little thing in nature,
link |
but I have my brain
link |
and my brain is surely much smarter than that thing.
link |
I'm gonna be able to systematically outrun
link |
the computation that it does
link |
because I have a more sophisticated computation
link |
But what the principle of computational equivalence says
link |
is that doesn't work.
link |
Our brains are doing computations
link |
that are exactly equivalent to the kinds of computations
link |
that are being done in all these other sorts of systems.
link |
And so what consequences does that have?
link |
Well, it means that we can't systematically
link |
outrun these systems.
link |
These systems are computationally irreducible
link |
in the sense that there's no sort of shortcut
link |
that we can make that jumps to the answer.
link |
Now the general case.
link |
But the, so what has happened,
link |
what science has become used to doing
link |
is using the little sort of pockets
link |
of computational reducibility,
link |
which by the way are an inevitable consequence
link |
of computational irreducibility,
link |
that there have to be these pockets
link |
scattered around of computational reducibility
link |
to be able to find those particular cases
link |
where you can jump ahead.
link |
I mean, one thing sort of a little bit
link |
of a parable type thing that I think is fun to tell.
link |
If you look at ancient Babylon,
link |
they were trying to predict three kinds of things.
link |
They tried to predict where the planets would be,
link |
what the weather would be like,
link |
and who would win or lose a certain battle.
link |
And they had no idea which of these things
link |
would be more predictable than the other.
link |
And it turns out where the planets are
link |
is a piece of computational reducibility
link |
that 300 years ago or so we pretty much cracked.
link |
I mean, it's been technically difficult
link |
to get all the details right,
link |
but it's basically, we got that.
link |
Who's gonna win or lose the battle?
link |
No, we didn't crack that one.
link |
That one, that one, right.
link |
Game theorists are trying.
link |
Yes. And then the weather.
link |
It's kind of halfway on that one.
link |
Yeah, I think we're doing okay on that one.
link |
Long term climate, different story.
link |
But the weather, we're much closer on that.
link |
But do you think eventually we'll figure out the weather?
link |
So do you think eventually most think
link |
we'll figure out the local pockets in everything,
link |
essentially the local pockets of reducibility?
link |
No, I think that it's an interesting question,
link |
but I think that there is an infinite collection
link |
of these local pockets.
link |
We'll never run out of local pockets.
link |
And by the way, those local pockets
link |
are where we build engineering, for example.
link |
That's how we, if we want to have a predictable life,
link |
so to speak, then we have to build
link |
in these sort of pockets of reducibility.
link |
Otherwise, if we were sort of existing
link |
in this kind of irreducible world,
link |
we'd never be able to have definite things
link |
to know what's gonna happen.
link |
I have to say, I think one of the features,
link |
when we look at sort of today from the future, so to speak,
link |
I suspect one of the things where people will say
link |
I can't believe they didn't see that
link |
is stuff to do with the following kind of thing.
link |
So if we describe, oh, I don't know,
link |
something like heat, for instance,
link |
we say, oh, the air in here, it's this temperature,
link |
this pressure, that's as much as we can say.
link |
Otherwise, just a bunch of random molecules bouncing around.
link |
People will say, I just can't believe they didn't realize
link |
that there was all this detail
link |
and how all these molecules were bouncing around
link |
and they could make use of that.
link |
And actually, I realized there's a thing
link |
I realized last week, actually,
link |
was a thing that people say, one of the scenarios
link |
for the very long term history of our universe
link |
is a so called heat death of the universe,
link |
where basically everything just becomes
link |
thermodynamically boring.
link |
Everything's just this big kind of gas
link |
and thermal equilibrium.
link |
People say, that's a really bad outcome.
link |
But actually, it's not a really bad outcome.
link |
It's an outcome where there's all this computation going on
link |
and all those individual gas molecules
link |
are all bouncing around in very complicated ways
link |
doing this very elaborate computation.
link |
It just happens to be a computation that right now,
link |
we haven't found ways to understand.
link |
We haven't found ways, our brains haven't,
link |
and our mathematics and our science and so on,
link |
haven't found ways to tell an interesting story about that.
link |
It just looks boring to us.
link |
So you're saying there's a hopeful view
link |
of the heat death, quote unquote, of the universe
link |
where there's actual beautiful complexity going on.
link |
Similar to the kind of complexity we think of
link |
that creates rich experience in human life and life on Earth.
link |
So those little molecules interacting complex ways,
link |
that could be intelligence in that, there could be.
link |
I mean, this is what you learn from this principle.
link |
Wow, that's a hopeful message.
link |
I mean, this is what you kind of learn
link |
from this principle of computational equivalence.
link |
You learn it's both a message of sort of hope
link |
and a message of kind of, you know,
link |
you're not as special as you think you are, so to speak.
link |
I mean, because, you know, we imagine that
link |
with sort of all the things we do with human intelligence
link |
and all that kind of thing,
link |
and all of the stuff we've constructed in science,
link |
it's like, we're very special.
link |
But actually it turns out, well, no, we're not.
link |
We're just doing computations
link |
like things in nature do computations,
link |
like those gas molecules do computations,
link |
like the weather does computations.
link |
The only thing about the computations that we do
link |
that's really special is that we understand
link |
what they are, so to speak.
link |
In other words, we have a, you know,
link |
to us they're special because kind of,
link |
they're connected to our purposes,
link |
our ways of thinking about things and so on.
link |
And that's some, but so.
link |
That's very human centric.
link |
That's, we're just attached to this kind of thing.
link |
So let's talk a little bit of physics.
link |
Maybe let's ask the biggest question.
link |
What is a theory of everything in general?
link |
What does that mean?
link |
Yeah, so I mean, the question is,
link |
can we kind of reduce what has been physics
link |
as a something where we have to sort of pick away and say,
link |
do we roughly know how the world works
link |
to something where we have a complete formal theory
link |
where we say, if we were to run this program
link |
for long enough, we would reproduce everything,
link |
you know, down to the fact that we're having
link |
this conversation at this moment,
link |
et cetera, et cetera, et cetera.
link |
Any physical phenomena, any phenomena in this world?
link |
Any phenomenon in the universe.
link |
But the, you know, because of computational irreducibility,
link |
it's not, you know, that's not something where you say,
link |
okay, you've got the fundamental theory of everything.
link |
Then, you know, tell me whether, you know,
link |
lions are gonna eat tigers or something.
link |
You know, that's a, no, you have to run this thing
link |
for, you know, 10 to the 500 steps or something
link |
to know something like that, okay?
link |
So at some moment, potentially, you say,
link |
this is a rule and run this rule enough times
link |
and you will get the whole universe, right?
link |
That's what it means to kind of have
link |
a fundamental theory of physics as far as I'm concerned
link |
is you've got this rule.
link |
It's potentially quite simple.
link |
We don't know for sure it's simple,
link |
but we have various reasons to believe it might be simple.
link |
And then you say, okay, I'm showing you this rule.
link |
You just run it only 10 to the 500 times
link |
and you'll get everything.
link |
In other words, you've kind of reduced the problem
link |
of physics to a problem of mathematics, so to speak.
link |
It's like, it's as if, you know, you'd like,
link |
you generate the digits of pi.
link |
There's a definite procedure.
link |
You just generate them and it'd be the same thing
link |
if you have a fundamental theory of physics
link |
of the kind that I'm imagining, you know,
link |
you get this rule and you just run it out
link |
and you get everything that happens in the universe.
link |
So a theory of everything is a mathematical framework
link |
within which you can explain everything that happens
link |
in the universe, it's kind of in a unified way.
link |
It's not, there's a bunch of disparate modules of,
link |
does it feel like if you create a rule
link |
and we'll talk about the Wolfram physics model,
link |
which is fascinating, but if you have a simple set
link |
of rules with a data structure, like a hypergraph,
link |
does that feel like a satisfying theory of everything?
link |
Because then you really run up against the irreducibility,
link |
computational irreducibility.
link |
Right, so that's a really interesting question.
link |
So I, you know, what I thought was gonna happen
link |
is I thought we, you know, I thought we had a pretty good,
link |
I had a pretty good idea for what the structure
link |
of this sort of theory that sort of underneath space
link |
and time and so on might be like.
link |
And I thought, gosh, you know, in my lifetime,
link |
so to speak, we might be able to figure out what happens
link |
in the first 10 to the minus 100 seconds of the universe.
link |
And that would be cool, but it's pretty far away
link |
from anything that we can see today.
link |
And it will be hard to test whether that's right
link |
and so on and so on and so on.
link |
To my huge surprise, although it should have been obvious
link |
and it's embarrassing that it wasn't obvious to me,
link |
but to my huge surprise,
link |
we managed to get unbelievably much further than that.
link |
And basically what happened is that it turns out
link |
that even though there's this kind of bed
link |
of computational irreducibility,
link |
that sort of these, all these simple rules run into,
link |
there are certain pieces of computational reducibility
link |
that quite generically occur
link |
for large classes of these rules.
link |
And, and this is the really exciting thing
link |
as far as I'm concerned,
link |
the big pieces of computational reducibility
link |
are basically the pillars of 20th century physics.
link |
That's the amazing thing,
link |
that general relativity and quantum field theory
link |
is sort of the pillars of 20th century physics
link |
turn out to be precisely the stuff you can say.
link |
There's a lot you can't say,
link |
there's a lot that's kind of at this irreducible level
link |
where you kind of don't know what's going to happen,
link |
you have to run it, you know,
link |
you can't run it within our universe,
link |
et cetera, et cetera, et cetera, et cetera.
link |
But the thing is there are things you can say
link |
and the things you can say turn out to be very beautifully
link |
exactly the structure that was found
link |
in 20th century physics,
link |
namely general relativity and quantum mechanics.
link |
And general relativity and quantum mechanics
link |
are these pockets of reducibility that we think of as,
link |
that 20th century physics
link |
is essentially pockets of reducibility.
link |
And then it is incredibly surprising
link |
that any kind of model that's generative
link |
from simple rules would have such pockets.
link |
Yeah, well, I think what's surprising
link |
is we didn't know where those things came from.
link |
It's like general relativity,
link |
it's a very nice mathematically elegant theory.
link |
You know, quantum mechanics, why is it true?
link |
What we realized is that from this,
link |
that these theories are generic
link |
to a huge class of systems
link |
that have these particular
link |
very unstructured underlying rules.
link |
And that's the thing that is sort of remarkable
link |
and that's the thing to me
link |
that's just, it's really beautiful.
link |
I mean, it's, and the thing that's even more beautiful
link |
is that it turns out that, you know,
link |
people have been struggling for a long time.
link |
You know, how does general relativity theory of gravity
link |
relate to quantum mechanics?
link |
They seem to have all kinds of incompatibilities.
link |
It turns out what we realized is
link |
at some level they are the same theory.
link |
And that's just, it's just great as far as I'm concerned.
link |
So maybe like taking a little step back
link |
from your perspective, not from the low,
link |
not from the beautiful hypergraph,
link |
well, from physics model perspective,
link |
but from the perspective of 20th century physics,
link |
what is general relativity?
link |
What is quantum mechanics?
link |
How do you think about these two theories
link |
from the context of the theory of everything?
link |
Like just even definition.
link |
Yeah, yeah, yeah, right.
link |
So I mean, you know, a little bit of history of physics,
link |
So, I mean the, you know, okay,
link |
very, very quick history of this, right?
link |
So, I mean, you know, physics, you know,
link |
in ancient Greek times, people basically said,
link |
we can just figure out how the world works.
link |
As you know, we're philosophers,
link |
we're gonna figure out how the world works.
link |
You know, some philosophers thought there were atoms.
link |
Some philosophers thought there were,
link |
you know, continuous flows of things.
link |
People had different ideas about how the world works.
link |
And they tried to just say,
link |
we're gonna construct this idea of how the world works.
link |
They didn't really have sort of notions
link |
of doing experiments and so on quite the same way
link |
as developed later.
link |
So that was sort of an early tradition
link |
for thinking about sort of models of the world.
link |
Then by the time of 1600s, time of Galileo and then Newton,
link |
sort of the big idea there was, you know,
link |
title of Newton's book, you know, Principia Mathematica,
link |
mathematical principles of natural philosophy.
link |
We can use mathematics to understand natural philosophy,
link |
to understand things about the way the world works.
link |
And so that then led to this kind of idea that, you know,
link |
we can write down a mathematical equation
link |
and have that represent how the world works.
link |
So Newton's one of his most famous ones
link |
is his universal law of gravity,
link |
inverse square law of gravity
link |
that allowed him to compute all sorts of features
link |
of the planets and so on.
link |
Although some of them he got wrong
link |
and it took another hundred years
link |
for people to actually be able to do the math
link |
to the level that was needed.
link |
But so that had been this sort of tradition
link |
was we write down these mathematical equations.
link |
We don't really know where these equations come from.
link |
We write them down.
link |
Then we figure out, we work out the consequences
link |
and we say, yes, that agrees with what we actually observe
link |
in astronomy or something like this.
link |
So that tradition continued.
link |
And then the first of these two
link |
sort of great 20th century innovations was,
link |
well, the history is actually a little bit more complicated,
link |
but let's say that there were two,
link |
quantum mechanics and general relativity.
link |
Quantum mechanics kind of 1900
link |
was kind of the very early stuff done by Planck
link |
that led to the idea of photons, particles of light.
link |
But let's take general relativity first.
link |
One feature of the story is that special relativity
link |
thing Einstein invented in 1905
link |
was something which surprisingly
link |
was a kind of logically invented theory.
link |
It was not a theory where it was something where
link |
given these ideas that were sort of axiomatically
link |
thought to be true about the world,
link |
it followed that such and such a thing would be the case.
link |
It was a little bit different
link |
from the kind of methodological structure
link |
of some existing theories in the more recent times,
link |
where it's just been, we write down an equation
link |
and we find out that it works.
link |
So what happened there.
link |
So there's some reasoning about the light.
link |
The basic idea was the speed of light
link |
appears to be constant.
link |
Even if you're traveling very fast,
link |
you shine a flashlight, the light will come out.
link |
Even if you're going at half the speed of light,
link |
the light doesn't come out of your flashlight
link |
at one and a half times the speed of light.
link |
It's still just the speed of light.
link |
And to make that work,
link |
you have to change your view of how space and time work
link |
to be able to account for the fact
link |
that when you're going faster,
link |
it appears that length is foreshortened
link |
and time is dilated and things like this.
link |
And that's special relativity.
link |
That's special relativity.
link |
So then Einstein went on with sort of
link |
vaguely similar kinds of thinking.
link |
In 1915, invented general relativity,
link |
which is the theory of gravity.
link |
And the basic point of general relativity
link |
is it's a theory that says,
link |
when there is mass in space, space is curved.
link |
And what does that mean?
link |
Usually you think of what's the shortest distance
link |
between two points.
link |
Like ordinarily on a plane in space, it's a straight line.
link |
Photons, light goes in straight lines.
link |
Well, then the question is,
link |
is if you have a curved surface,
link |
a straight line is no longer straight.
link |
On the surface of the earth,
link |
the shortest distance between two points is a great circle.
link |
So, you know, Einstein's observation was
link |
maybe the physical structure of space
link |
is such that space is curved.
link |
So the shortest distance between two points,
link |
the path, the straight line in quotes,
link |
won't be straight anymore.
link |
And in particular, if a photon is, you know,
link |
traveling near the sun or something,
link |
or if a particle is going,
link |
something is traveling near the sun,
link |
maybe the shortest path will be one
link |
that is something which looks curved to us
link |
because it seems curved to us
link |
because space has been deformed by the presence of mass
link |
associated with that massive object.
link |
So the kind of the idea there is,
link |
think of the structure of space
link |
as being a dynamical changing kind of thing.
link |
But then what Einstein did
link |
was he wrote down these differential equations
link |
that basically represented the curvature of space
link |
and its response to the presence of mass and energy.
link |
And that ultimately is connected to the force of gravity,
link |
which is one of the forces that seems to,
link |
based on its strength,
link |
operate on a different scale than some of the other forces.
link |
So it operates in a scale that's very large.
link |
What happens there is just this curvature of space,
link |
which causes, you know, the paths of objects to be deflected.
link |
That's what gravity does.
link |
It causes the paths of objects to be deflected.
link |
And this is an explanation for gravity, so to speak.
link |
And the surprise is that from 1915 until today,
link |
everything that we've measured about gravity
link |
precisely agrees with general relativity.
link |
And that, you know, it wasn't clear black holes
link |
were sort of a predict,
link |
well, actually the expansion of the universe
link |
was an early potential prediction,
link |
although Einstein tried to sort of patch up his equations
link |
to make it not cause the universe to expand,
link |
because it was kind of so obvious
link |
the universe wasn't expanding.
link |
And, you know, it turns out it was expanding
link |
and he should have just trusted the equations.
link |
And that's a lesson for those of us
link |
interested in making fundamental theories of physics
link |
is you should trust your theory and not try and patch it
link |
because of something that you think might be the case
link |
that might turn out not to be the case.
link |
Even if the theory says something crazy is happening.
link |
Like the universe is expanding.
link |
Like the universe is expanding, right, which is,
link |
but, you know, then it took until the 1940s,
link |
probably even really until the 1960s,
link |
until people understood that black holes
link |
were a consequence of general relativity and so on.
link |
But that's, you know, the big surprise has been
link |
that so far this theory of gravity has perfectly agreed
link |
with, you know, these collisions of black holes
link |
seen by their gravitational waves, you know,
link |
it all just works.
link |
So that's been kind of one pillar of the story of physics
link |
it's mathematically complicated to work out
link |
the consequences of general relativity,
link |
but it's not, there's no, I mean,
link |
and some things are kind of squiggly and complicated.
link |
Like people believe, you know, energy is conserved.
link |
Okay, well, energy conservation doesn't really work
link |
in general activity in the same way as it ordinarily does.
link |
And it's all a big mathematical story
link |
of how you actually nail down something that is definitive
link |
that you can talk about it and not specific to the,
link |
you know, reference frames you're operating in
link |
and so on and so on and so on.
link |
But fundamentally, general relativity is a straight shot
link |
in the sense that you have this theory,
link |
you work out its consequences.
link |
And that theory is useful in terms of basic science
link |
and trying to understand the way black holes work,
link |
the way the creation of galaxies work,
link |
sort of all of these kinds of cosmological things,
link |
understanding what happened, like you said, at the Big Bang.
link |
Yeah. Like all those kinds of,
link |
well, no, not at the Big Bang actually, right?
link |
Well, features of the expansion of the universe, yes.
link |
I mean, and there are lots of details
link |
where we don't quite know how it's working, you know,
link |
is there, you know, where's the dark matter,
link |
is there dark energy, you know, et cetera, et cetera, et cetera.
link |
But fundamentally, the, you know,
link |
the testable features of general relativity,
link |
it all works very beautifully.
link |
And it's in a sense, it is mathematically sophisticated,
link |
but it is not conceptually hard to understand in some sense.
link |
Okay. So that's general relativity.
link |
And what's its friendly neighbor, like you said,
link |
there's two theories, quantum mechanics.
link |
Right. So quantum mechanics,
link |
the sort of the way that that originated was,
link |
one question was, is the world continuous or is it discrete?
link |
You know, in ancient Greek times,
link |
people have been debating this.
link |
People debated it, you know, throughout history.
link |
Is light made of waves?
link |
Is it continuous? Is it discrete?
link |
Is it made of particles, corpuscles, whatever.
link |
You know, what had become clear in the 1800s is that atoms,
link |
that, you know, materials are made of discrete atoms.
link |
You know, when you take some water,
link |
the water is not a continuous fluid,
link |
even though it seems like a continuous fluid
link |
to us at our scale.
link |
But if you say, let's look at it,
link |
smaller and smaller and smaller and smaller scale,
link |
eventually you get down to these, you know,
link |
these molecules and then atoms.
link |
It's made of discrete things.
link |
The question is sort of how important is this discreteness?
link |
Just what's discrete, what's not discrete?
link |
Is energy discrete?
link |
Is, you know, what's discrete, what's not?
link |
Does it have mass?
link |
Those kinds of questions.
link |
Yeah, yeah, right.
link |
Well, there's a question, I mean, for example,
link |
is mass discrete is an interesting question,
link |
which is now something we can address.
link |
But, you know, what happened in the coming up to the 1920s,
link |
there was this kind of mathematical theory developed
link |
that could explain certain kinds of discreteness
link |
in particularly in features of atoms and so on.
link |
And, you know, what developed was this mathematical theory
link |
that was the theory of quantum mechanics,
link |
theory of wave functions, Schrodinger's equation,
link |
That's a mathematical theory that allows you to calculate
link |
lots of features of the microscopic world,
link |
lots of things about how atoms work,
link |
et cetera, et cetera, et cetera.
link |
Now, the calculations all work just great.
link |
The question of what does it really mean
link |
is a complicated question.
link |
Now, I mean, to just explain a little bit historically,
link |
the, you know, the early calculations of things like atoms
link |
worked great in 1920s, 1930s and so on.
link |
There was always a problem.
link |
There were, in quantum field theory,
link |
which is a theory of, in quantum mechanics,
link |
you're dealing with a certain number of electrons
link |
and you fix the number of electrons.
link |
You say, I'm dealing with a two electron thing.
link |
In quantum field theory,
link |
you allow for particles being created and destroyed.
link |
So you can emit a photon that didn't exist before.
link |
You can absorb a photon, things like that.
link |
That's a more complicated,
link |
mathematically complicated theory.
link |
And it had all kinds of mathematical issues
link |
and all kinds of infinities that cropped up.
link |
And it was finally figured out more or less
link |
how to get rid of those.
link |
But there were only certain ways of doing the calculations
link |
and those didn't work for atomic nuclei among other things.
link |
And that led to a lot of development up until the 1960s
link |
of alternative ideas for how one could understand
link |
what was happening in atomic nuclei, et cetera,
link |
et cetera, et cetera.
link |
End result, in the end,
link |
the kind of most quotes obvious mathematical structure
link |
of quantum field theory seems to work.
link |
Although it's mathematically difficult to deal with,
link |
but you can calculate all kinds of things.
link |
You can calculate to a dozen decimal places,
link |
certain things, you can measure them.
link |
It's all beautiful.
link |
The underlying fabric is the model
link |
of that particular theory is fields.
link |
Like you keep saying fields.
link |
Those are quantum fields.
link |
Those are different from classical fields.
link |
A field is something like you say,
link |
like you say the temperature field in this room.
link |
It's like there is a value of temperature
link |
at every point around the room.
link |
That's some, or you can say the wind field
link |
would be the vector direction of the wind at every point.
link |
Yes, and that's a classical field.
link |
The quantum field is a much more
link |
mathematically elaborate kind of thing.
link |
And I should explain that one of the pictures
link |
of quantum mechanics that's really important is,
link |
in classical physics, one believes
link |
that sort of definite things happen in the world.
link |
You pick up a ball, you throw it,
link |
the ball goes in a definite trajectory
link |
that has certain equations of motion.
link |
It goes in a parabola, whatever else.
link |
In quantum mechanics, the picture is
link |
definite things don't happen.
link |
Instead, sort of what happens is this whole
link |
sort of structure of all many different paths being followed
link |
and we can calculate certain aspects of what happens,
link |
certain probabilities of different outcomes and so on.
link |
And you say, well, what really happened?
link |
What's really going on?
link |
What's the sort of, what's the underlying,
link |
what's the underlying story?
link |
How do we turn this mathematical theory
link |
that we can calculate things with
link |
into something that we can really understand
link |
and have a narrative about?
link |
And that's been really, really hard for quantum mechanics.
link |
My friend, Dick Feynman, always used to say,
link |
nobody understands quantum mechanics,
link |
even though he'd made his whole career
link |
out of calculating things about quantum mechanics.
link |
And so it's a little bit.
link |
Nevertheless, it's what the quantum field theory is very,
link |
very accurate at predicting a lot of the physical phenomena.
link |
But there are things about it, it has certain,
link |
when we apply it, the standard model of particle physics,
link |
for example, we, which we apply to calculate
link |
all kinds of things that works really well.
link |
And you say, well, it has certain parameters.
link |
It has a whole bunch of parameters actually.
link |
You say, why is the, why does the muon particle exist?
link |
Why is it 206 times the mass of the electron?
link |
We don't know, no idea.
link |
But so the standard model of physics is one of the models
link |
that's very accurate for describing
link |
three of the fundamental forces of physics.
link |
And it's looking at the world of the very small.
link |
And then there's back to the neighbor of gravity,
link |
of general relativity.
link |
So, and then in the context of a theory of everything,
link |
what's traditionally the task of the unification
link |
of these theories?
link |
And why is it hard?
link |
The issue is you try to use the methods
link |
of quantum field theory to talk about gravity
link |
and it doesn't work.
link |
Just like there are photons of light.
link |
So there are gravitons,
link |
which are sort of the particles of gravity.
link |
And when you try and compute sort of the properties
link |
of the particles of gravity,
link |
the kind of mathematical tricks that get used
link |
in working things out in quantum field theory don't work.
link |
And that's, so that's been a sort of fundamental issue.
link |
And when you think about black holes,
link |
which are a place where sort of the structure of space
link |
is, you know, has sort of rapid variation
link |
and you get kind of quantum effects mixed in
link |
with effects from general relativity,
link |
things get very complicated
link |
and there are apparent paradoxes and things like that.
link |
And people have, you know,
link |
there've been a bunch of mathematical developments
link |
in physics over the last, I don't know, 30 years or so,
link |
which have kind of picked away at those kinds of issues
link |
and got hints about how things might work.
link |
But it hasn't been, you know,
link |
and the other thing to realize is,
link |
as far as physics is concerned,
link |
it's just like here's general relativity,
link |
here's quantum field theory, you know, be happy.
link |
Yeah, so do you think there's a quantization of gravity,
link |
so quantum gravity, what do you think of efforts
link |
that people have tried to, yeah,
link |
what do you think in general of the efforts
link |
of the physics community to try to unify these laws?
link |
So I think what's, it's interesting.
link |
I mean, I would have said something very different
link |
before what's happened with our physics project.
link |
I mean, you know, the remarkable thing is
link |
what we've been able to do is to make
link |
from this very simple, structurally simple,
link |
underlying set of ideas,
link |
we've been able to build this, you know,
link |
very elaborate structure that's both very abstract
link |
and very sort of mathematically rich.
link |
And the big surprise, as far as I'm concerned,
link |
is that it touches many of the ideas that people have had.
link |
So in other words, things like string theory and so on,
link |
twister theory, it's like the, you know,
link |
we might've thought, I had thought we're out on a prong,
link |
we're building something that's computational,
link |
it's completely different from what other people have done.
link |
But actually it seems like what we've done
link |
is to provide essentially the machine code that, you know,
link |
these things are various features
link |
of domain specific languages, so to speak,
link |
that talk about various aspects of this machine code.
link |
And I think this is something that to me is very exciting
link |
because it allows one both for us to provide
link |
sort of a new foundation for what's been thought about there
link |
and for all the work that's been done in those areas
link |
to give us, you know, more momentum
link |
to be able to figure out what's going on.
link |
Now, you know, people have sort of hoped,
link |
oh, we're just gonna be able to get, you know,
link |
string theory to just answer everything.
link |
That hasn't worked out.
link |
And I think we now kind of can see a little bit about
link |
just sort of how far away certain kinds of things are
link |
from being able to explain things.
link |
Some things, one of the big surprises to me,
link |
actually I literally just got a message
link |
about one aspect of this is the, you know,
link |
it's turning out to be easier.
link |
I mean, this project has been so much easier
link |
than I could ever imagine it would be.
link |
That is, I thought we would be, you know,
link |
just about able to understand
link |
the first 10 to the minus 100 seconds of the universe.
link |
And, you know, it would be a hundred years
link |
before we get much further than that.
link |
It's just turned out, it actually wasn't that hard.
link |
I mean, we're not finished, but, you know.
link |
So you're seeing echoes of all the disparate theories
link |
of physics in this framework.
link |
I mean, it's a very interesting, you know,
link |
sort of history of science like phenomenon.
link |
I mean, the best analogy that I can see
link |
is what happened with the early days
link |
of computability and computation theory.
link |
You know, Turing machines were invented in 1936.
link |
People sort of understand computation
link |
in terms of Turing machines,
link |
but actually there had been preexisting theories
link |
of computation, combinators, general recursive functions,
link |
Lambda calculus, things like this.
link |
But people hadn't, those hadn't been concrete enough
link |
that people could really wrap their arms around them
link |
and understand what was going on.
link |
And I think what we're gonna see in this case
link |
is that a bunch of these mathematical theories,
link |
including some very,
link |
I mean, one of the things that's really interesting
link |
is one of the most abstract things
link |
that's come out of sort of mathematics,
link |
higher category theory, things about infinity group voids,
link |
things like this, which to me always just seemed
link |
like they were floating off into the stratosphere,
link |
ionosphere of mathematics, turn out to be things
link |
which our sort of theory anchors down
link |
to something fairly definite and says are super relevant
link |
to the way that we can understand how physics works.
link |
By the way, I just threw a hat on.
link |
You've said that with this metaphor analogy
link |
that the theory of everything is a big mountain
link |
and you have a sense that however far we are up the mountain,
link |
that the Wolfram physics model view of the universe
link |
is at least the right mountain.
link |
We're the right mountain, yes, without question.
link |
Which aspect of it is the right mountain?
link |
So for example, I mean, so there's so many aspects
link |
to just the way of the Wolfram physics project,
link |
the way it approaches the world that's clean, crisp,
link |
and unique and powerful, so there's a discreet nature to it,
link |
there's a hypergraph, there's a computational nature,
link |
there's a generative aspect, you start from nothing,
link |
you generate everything, do you think the actual model
link |
is actually a really good one,
link |
or do you think this general principle
link |
from simplicity generating complexity is the right,
link |
like what aspect of the mountain is the correct?
link |
Yeah, right, I think that the kind of the meta idea
link |
about using simple computational systems to do things,
link |
that's the ultimate big paradigm
link |
that is sort of super important.
link |
The details of the particular model are very nice and clean
link |
and allow one to actually understand what's going on.
link |
They are not unique, and in fact, we know that.
link |
We know that there's a very, very, very, very,
link |
there's a large number of different ways
link |
to describe essentially the same thing.
link |
I mean, I can describe things in terms of hypergraphs,
link |
I can describe them in terms of higher category theory,
link |
I can describe them in a bunch of different ways.
link |
They are in some sense all the same thing,
link |
but our sort of story about what's going on
link |
and the kind of cultural mathematical resonances
link |
are a bit different.
link |
And I think it's perhaps worth sort of saying a little bit
link |
about kind of the foundational ideas
link |
of these models and things.
link |
Great, so can you maybe, can we like rewind?
link |
We've talked about it a little bit,
link |
but can you say like what the central idea is
link |
of the Wolfram Physics Project?
link |
Right, so the question is we're interested
link |
in finding sort of simple computational rule
link |
that describes our whole universe.
link |
Can we just pause on that?
link |
It's just so beautiful, that's such a beautiful idea
link |
that we can generate our universe
link |
from a data structure, a simple structure,
link |
simple set of rules, and we can generate our entire universe.
link |
Yes, that's the idea. That's awe inspiring.
link |
Right, but so the question is how do you actualize that?
link |
What might this rule be like?
link |
And so one thing you quickly realize is
link |
if you're gonna pack everything about our universe
link |
into this tiny rule, not much that we are familiar with
link |
in our universe will be obvious in that rule.
link |
So you don't get to fit all these parameters of the universe,
link |
all these features of, you know, this is how space works,
link |
this is how time works, et cetera, et cetera, et cetera.
link |
You don't get to fit that all in.
link |
It all has to be sort of packed in to this thing,
link |
something much smaller, much more basic,
link |
much lower level machine code, so to speak, than that.
link |
And all the stuff that we're familiar with
link |
has to kind of emerge from the operation.
link |
So the rule in itself,
link |
because of the computational reducibility,
link |
is not gonna tell you the story.
link |
It's not gonna give you the answer to,
link |
it's not gonna let you predict
link |
what you're gonna have for lunch tomorrow,
link |
and it's not going to let you predict
link |
basically anything about your life, about the universe.
link |
Right, and you're not going to be able to see in that rule,
link |
oh, there's the three
link |
for the number of dimensions of space and so on.
link |
That's not gonna be there.
link |
Spacetime is not going to be obviously.
link |
Right, so the question is then,
link |
what is the universe made of?
link |
That's a basic question.
link |
And we've had some assumptions
link |
about what the universe is made of
link |
for the last few thousand years
link |
that I think in some cases just turn out not to be right.
link |
And the most important assumption
link |
is that space is a continuous thing.
link |
That is that you can, if you say,
link |
let's pick a point in space.
link |
We're gonna do geometry.
link |
We're gonna pick a point.
link |
We can pick a point absolutely anywhere in space.
link |
Precise numbers we can specify of where that point is.
link |
In fact, Euclid who kind of wrote down
link |
the original kind of axiomatization of geometry
link |
back in 300 BC or so,
link |
his very first definition, he says,
link |
a point is that which has no part.
link |
A point is this indivisible infinitesimal thing.
link |
Okay, so we might've said that about material objects.
link |
We might've said that about water, for example.
link |
We might've said water is a continuous thing
link |
that we can just pick any point we want in some water,
link |
but actually we know it isn't true.
link |
We know that water is made of molecules that are discrete.
link |
And so the question, one fundamental question
link |
is what is space made of?
link |
And so one of the things that's sort of a starting point
link |
for what I've done is to think of space as a discrete thing,
link |
to think of there being sort of atoms of space
link |
just as there are atoms of material things,
link |
although very different kinds of atoms.
link |
And by the way, I mean, this idea,
link |
you know, there were ancient Greek philosophers
link |
who had this idea.
link |
There were, you know, Einstein actually thought
link |
this is probably how things would work out.
link |
I mean, he said, you know, repeatedly he thought
link |
that's the way it would work out.
link |
We don't have the mathematical tools in our time,
link |
which was 1940s, 1950s and so on to explore this.
link |
Like the way he thought,
link |
you mean that there is something very, very small
link |
and discrete that's underlying space.
link |
And that means that, so, you know, the mathematical theory,
link |
mathematical theories in physics assume that space
link |
can be described just as a continuous thing.
link |
You can just pick coordinates
link |
and the coordinates can have any values.
link |
And that's how you define space.
link |
Space is this just sort of background sort of theater
link |
on which the universe operates.
link |
But can we draw a distinction between space
link |
as a thing that could be described by three values,
link |
coordinates, and how you're,
link |
are you using the word space more generally when you say?
link |
No, I'm just talking about space
link |
as in what we experience in the universe.
link |
So that you think this 3D aspect of it is fundamental.
link |
No, I don't think that 3D is fundamental at all, actually.
link |
I think that the thing that has been assumed
link |
is that space is this continuous thing
link |
where you can just describe it by,
link |
let's say three numbers, for instance.
link |
But most important thing about that
link |
is that you can describe it by precise numbers
link |
because you can pick any point in space
link |
and you can talk about motions,
link |
any infinitesimal motion in space.
link |
And that's what continuous means.
link |
That's what continuous means.
link |
That's what, you know, Newton invented calculus
link |
to describe these kind of continuous small variations
link |
That was, that's kind of a fundamental idea
link |
from Euclid on that's been a fundamental idea about space.
link |
Is that right or wrong?
link |
It's right at the level of our experience most of the time.
link |
It's not right at the level of the machine code,
link |
Yeah, of the simulation.
link |
They're the very lowest level of the fabric of the universe,
link |
at least under the Wolfram physics model
link |
is your senses is discrete.
link |
So now what does that mean?
link |
So it means what is space then?
link |
So in models, the basic idea is you say
link |
there are these sort of atoms of space.
link |
They're these points that represent,
link |
you know, represent places in space,
link |
but they're just discrete points.
link |
And the only thing we know about them
link |
is how they're connected to each other.
link |
We don't know where they are.
link |
They don't have coordinates.
link |
We don't get to say this is a position, such and such.
link |
It's just, here's a big bag of points.
link |
Like in our universe,
link |
there might be 10 to the 100 of these points.
link |
And all we know is this point is connected
link |
to this other point.
link |
So it's like, you know,
link |
all we have is the friend network, so to speak.
link |
We don't have, you know, people's, you know,
link |
physical addresses.
link |
All we have is the friend network of these points.
link |
The underlying nature of reality is kind of like a Facebook.
link |
We don't know their location, but we have the friends.
link |
Yeah, yeah, right.
link |
We know which point is connected to which other points.
link |
And that's all we know.
link |
And so you might say, well,
link |
how on earth can you get something
link |
which is like our experience of, you know,
link |
what seems like continuous space?
link |
Well, the answer is,
link |
by the time you have 10 to the 100 of these things,
link |
those connections can work in such a way
link |
that on a large scale,
link |
it will seem to be like continuous space
link |
in let's say three dimensions
link |
or some other number of dimensions
link |
or 2.6 dimensions or whatever else.
link |
Because they're much, much, much, much larger.
link |
So like the number of relationships here we're talking about
link |
is just a humongous amount.
link |
So the kind of thing you're talking about
link |
is very, very, very small relative
link |
to our experience of daily life.
link |
Right, so I mean, you know,
link |
we don't know exactly the size,
link |
but maybe 10 to the minus,
link |
maybe around 10 to the minus 100 meters.
link |
So, you know, the size of, to give a comparison,
link |
the size of a proton is 10 to the minus 15 meters.
link |
And so this is something incredibly tiny compared to that.
link |
And the idea that from that would emerge
link |
the experience of continuous space is mind blowing.
link |
Well, what's your intuition why that's possible?
link |
Like, first of all, I mean, we'll get into it,
link |
but I don't know if we will
link |
through the medium of conversation,
link |
but the construct of hypergraphs is just beautiful.
link |
Cellular automata are beautiful.
link |
We'll talk about it.
link |
But this thing about, you know,
link |
continuity arising from discrete systems
link |
is in today's world is actually not so surprising.
link |
I mean, you know, your average computer screen, right?
link |
Every computer screen is made of discrete pixels.
link |
Yet we have the, you know,
link |
we have the idea that we're seeing
link |
these continuous pictures.
link |
I mean, it's, you know,
link |
the fact that on a large scale,
link |
continuity can arise from lots of discrete elements.
link |
This is at some level unsurprising now.
link |
Wait, wait, wait, wait, wait, wait.
link |
But the pixels have a very definitive structure
link |
of neighbors on a computer screen.
link |
There's no concept of spatial,
link |
of space inherent in the underlying fabric of reality.
link |
Right, right, right.
link |
So the point is that, but there are cases where there are.
link |
So for example, let's just imagine you have a square grid.
link |
Okay, and at every point on the grid,
link |
you have one of these atoms of space
link |
and it's connected to four other,
link |
four other atoms of space on the, you know,
link |
Northeast, Southwest corners, right?
link |
There you have something where if you zoom out from that,
link |
it's like a computer screen.
link |
Yeah, so the relationship creates the spatial,
link |
like the relationship creates a constraint,
link |
which then in an emergent sense creates a like,
link |
yeah, like basically a spatial coordinate for that thing.
link |
Even though the individual point doesn't have a space.
link |
Even though the individual point doesn't know anything,
link |
it just knows what its neighbors are.
link |
On a large scale, it can be described by saying,
link |
oh, it looks like it's a, you know,
link |
this grid is zoomed out grid.
link |
You can say, well, you can describe these different points
link |
by saying they have certain positions,
link |
coordinates, et cetera.
link |
Now, in the sort of real setup,
link |
it's more complicated than that.
link |
It isn't just a square grid or something.
link |
It's something much more dynamic and complicated,
link |
which we'll talk about.
link |
But so, you know, the first idea,
link |
the first key idea is, you know,
link |
what's the universe made of?
link |
It's made of atoms of space basically
link |
with these connections between them.
link |
What kind of connections do they have?
link |
Well, so the simplest kind of thing you might say is,
link |
we've got something like a graph
link |
where every atom of space,
link |
where we have these edges that go between,
link |
these connections that go between atoms of space.
link |
We're not saying how long these edges are.
link |
We're just saying there is a connection
link |
from this place, from this atom to this atom.
link |
Just a quick pause,
link |
because there's a lot of very people that listen to this.
link |
Just to clarify, because I did a poll actually,
link |
what do you think a graph is a long time ago?
link |
And it's kind of funny how few people
link |
know the term graph outside of computer science.
link |
Let's call it a network.
link |
I think that's it.
link |
Let's call it a network is better.
link |
So, but every time, I like the word graph though.
link |
So let's define, let's just say that a graph
link |
will use terms nodes and edges maybe.
link |
And it's just the nodes represent some abstract entity
link |
and then the edges represent relationships
link |
between those entities.
link |
So that's what a graph says.
link |
Sorry, so there you go.
link |
So that's the basic structure.
link |
That is the simplest case of a basic structure.
link |
Actually, it tends to be better to think about hypergraphs.
link |
So a hypergraph is just, instead of saying
link |
there are connections between pairs of things,
link |
we say there are connections between any number of things.
link |
So there might be ternary edges.
link |
So instead of just having two points
link |
are connected by an edge,
link |
you say three points are all associated with a hyperedge,
link |
are all connected by a hyperedge.
link |
That's just, at some level, that's a detail.
link |
It's a detail that happens to make the, for me,
link |
sort of in the history of this project,
link |
the realization that you could do things that way
link |
broke out of certain kinds of arbitrariness
link |
that I felt that there was in the model
link |
before I had seen how this worked.
link |
I mean, a hypergraph can be mapped to a graph.
link |
It's just a convenient representation.
link |
Mathematical speaking.
link |
That's correct. That's correct.
link |
But so then, so, okay, so the first question,
link |
the first idea of these models of ours is
link |
space is made of these connected sort of atoms of space.
link |
The next idea is space is all there is.
link |
There's nothing except for this space.
link |
So in traditional ideas in physics,
link |
people have said there's space, it's kind of a background.
link |
And then there's matter, all these particles, electrons,
link |
all these other things, which exist in space, right?
link |
But in this model, one of the key ideas is
link |
there's nothing except space.
link |
So in other words, everything that exists in the universe
link |
is a feature of this hypergraph.
link |
So how can that possibly be?
link |
Well, the way that works is
link |
that there are certain structures in this hypergraph
link |
where you say that little twisty knotted thing,
link |
we don't know exactly how this works yet,
link |
but we have sort of idea about how it works mathematically.
link |
This sort of twisted knotted thing,
link |
that's the core of an electron.
link |
This thing over there that has this different form,
link |
that's something else.
link |
So the different peculiarities of the structure
link |
of this graph are the very things
link |
that we think of as the particles inside the space,
link |
but in fact, it's just a property of the space.
link |
Mind blowing, first of all, that it's mind blowing,
link |
and we'll probably talk in its simplicity and beauty.
link |
Yes, I think it's very beautiful.
link |
I mean, this is, I'm...
link |
But okay, but that's space,
link |
and then there's another concept
link |
we didn't really kind of mention,
link |
but you think it of computation as a transformation.
link |
Let's talk about time in a second.
link |
Let's just, I mean, on the subject of space,
link |
there's this question of kind of what,
link |
there's this idea, there is this hypergraph,
link |
it represents space,
link |
and it represents everything that's in space.
link |
The features of that hypergraph,
link |
you can say certain features in this part we do know,
link |
certain features of the hypergraph
link |
represent the presence of energy, for example,
link |
or the presence of mass or momentum,
link |
and we know what the features of the hypergraph
link |
that represent those things are,
link |
but it's all just the same hypergraph.
link |
So one thing you might ask is,
link |
you know, if you just look at this hypergraph and you say,
link |
and we're gonna talk about sort of what the hypergraph does,
link |
but if you say, you know,
link |
how much of what's going on in this hypergraph
link |
is things we know and care about,
link |
like particles and atoms and electrons
link |
and all this kind of thing,
link |
and how much is just the background of space?
link |
So it turns out, so far as in one rough estimate of this,
link |
everything that we care about in the universe
link |
is only one part in 10 to the 120
link |
of what's actually going on.
link |
The vast majority of what's happening
link |
is purely things that maintain the structure of space.
link |
That, in other words, that the things that are
link |
the features of space that are the things
link |
that we consider notable,
link |
like the presence of particles and so on,
link |
that's a tiny little piece of froth
link |
on the top of all this activity
link |
that mostly is just intended to,
link |
you know, mostly, I can't say intended,
link |
there's no intention here,
link |
that just maintains the structure of space.
link |
Let me load that in.
link |
It just makes me feel so good as a human being.
link |
To be the froth on the one in a 10 to the 120
link |
or something of, well.
link |
And also just humbling how,
link |
in this mathematical framework,
link |
how much work needs to be done
link |
on the infrastructure of our universe.
link |
Right, to maintain the infrastructure of our universe
link |
We are merely writing a little tiny things
link |
on top of that infrastructure.
link |
But you were just starting to talk a little bit about,
link |
we talked about space,
link |
that represents all the stuff that's in the universe.
link |
The question is, what does that stuff do?
link |
And for that, we have to start talking about time
link |
and what is time and so on.
link |
And, you know, one of the basic idea of this model
link |
is time is the progression of computation.
link |
So in other words, we have a structure of space
link |
and there is a rule that says
link |
how that structure of space will change.
link |
And it's the application,
link |
the repeated application of that rule
link |
that defines the progress of time.
link |
And what does the rule look like
link |
in the space of hypergraphs?
link |
Right, so what the rule says is something like,
link |
if you have a little tiny piece of hypergraph
link |
that looks like this,
link |
then it will be transformed into a piece of hypergraph
link |
that looks like this.
link |
So that's all it says.
link |
It says you pick up these elements of space
link |
and you can think of these edges,
link |
these hyper edges as being relations
link |
between elements in space.
link |
You might pick up these two relations
link |
between elements in space.
link |
And we're not saying where those elements are
link |
but every time there's a certain arrangement
link |
of elements in space,
link |
then arrangement in the sense of the way they're connected,
link |
then we transform it into some other arrangement.
link |
So there's a little tiny pattern
link |
and you transform it into another little pattern.
link |
And then because of this,
link |
I mean, again, it's kind of similar to cellular automata
link |
in that like on paper, the rule looks like super simple.
link |
It's like, yeah, okay.
link |
Yeah, right, from this, the universe can be born.
link |
But like once you start applying it,
link |
beautiful structure starts being,
link |
potentially can be created.
link |
And what you're doing is you're applying that rule
link |
to different parts,
link |
like anytime you match it within the hypergraph.
link |
And then one of the like incredibly beautiful
link |
and interesting things to think about
link |
is the order in which you apply that rule,
link |
because that pattern appears all over the place.
link |
Right, so this is a big complicated thing,
link |
very hard to wrap one's brain around, okay?
link |
So you say the rule is every time you see this little pattern
link |
transform it in this way.
link |
But yet, as you look around the space
link |
that represents the universe,
link |
there may be zillions of places
link |
where that little pattern occurs.
link |
So what it says is just do this,
link |
apply this rule wherever you feel like.
link |
And what is extremely non trivial is,
link |
well, okay, so this is happening sort of
link |
in computer science terms, sort of asynchronously,
link |
you're just doing it wherever you feel like doing it.
link |
And the only constraint is
link |
that if you're going to apply the rule somewhere,
link |
the things to which you apply the rule,
link |
the little elements to which you apply the rule,
link |
if they have to be,
link |
okay, well, you can think of each application of the rule
link |
as being kind of an event that happens in the universe.
link |
And the input to an event has to be ready
link |
for the event to occur.
link |
That is, if one event occurred,
link |
if one transformation occurred,
link |
and it produced a particular atom of space,
link |
then that atom of space has to already exist
link |
before another transformation that's going to apply
link |
to that atom of space can occur.
link |
So that's like the prerequisite for the event.
link |
That's right, that's right.
link |
So that defines a kind of,
link |
this sort of set of causal relationships between events.
link |
It says, this event has to have happened before this event.
link |
But that's not a very limiting constraint.
link |
And what's interesting...
link |
You still get the zillion,
link |
that's a technical term, options.
link |
But, okay, so this is where things get a little bit more
link |
But they're mind blowing, so...
link |
Right, but so what happens is,
link |
so the first thing you might say is,
link |
you know, let's...
link |
Well, okay, so this question about the freedom
link |
of which event you do when.
link |
Well, let me sort of state an answer and then explain it.
link |
Okay, the validity of special relativity
link |
is a consequence of the fact that in some sense,
link |
it doesn't matter in what order you do
link |
these underlying things, so long as they respect
link |
this kind of set of causal relationships.
link |
And that's the part that's in a certain sense
link |
is a really important one,
link |
but the fact that it sometimes doesn't matter,
link |
I don't know what to...
link |
That's another, like, beautiful thing.
link |
Well, okay, so there's this idea
link |
of what I call causal invariance.
link |
Causal invariance, exactly.
link |
Really, really powerful idea.
link |
Right, it's a powerful idea,
link |
which has actually arisen in different forms
link |
many times in the history of mathematics,
link |
mathematical logic, even computer science,
link |
has many different names.
link |
I mean, our particular version of it
link |
is a little bit tighter than other versions,
link |
but it's basically the same idea.
link |
Here's how to think about that idea.
link |
So imagine that...
link |
Well, let's talk about it in terms of math for a second.
link |
Let's say you're doing algebra and you're told,
link |
you know, multiply out this series of polynomials
link |
that are multiplied together, okay?
link |
You say, well, which order should I do that in?
link |
Say, well, do I multiply the third one by the fourth one
link |
and then do it by the first one?
link |
Or do I do the fifth one by the sixth one and then do that?
link |
Well, it turns out it doesn't matter.
link |
You can multiply them out in any order,
link |
you'll always get the same answer.
link |
That's a property...
link |
If you think about kind of making a kind of network
link |
that represents in what order you do things,
link |
you'll get different orders
link |
for different ways of multiplying things out,
link |
but you'll always get the same answer.
link |
Same thing if you...
link |
Let's say you're sorting.
link |
You've got a bunch of A's and B's.
link |
They're in random, some random order,
link |
you know, BAA, BBBAA, whatever.
link |
And you have a little rule that says,
link |
every time you see BA, flip it around to AB, okay?
link |
Eventually you apply that rule enough times,
link |
you'll have sorted the string
link |
so that it's all the A's first and then all the B's.
link |
Again, there are many different orders
link |
in which you can do that to many different sort of places
link |
where you can apply that update.
link |
In the end, you'll always get the string sorted the same way.
link |
I know with sorting the string, it sounds obvious.
link |
That's to me surprising
link |
that there is in complicated systems,
link |
obviously with a string,
link |
but in a hypergraph that the application of the rule,
link |
asynchronous rule can lead to the same results sometimes.
link |
Yes, yes, that is not obvious.
link |
And it was something that, you know,
link |
I sort of discovered that idea for these kinds of systems
link |
and back in the 1990s.
link |
And for various reasons, I was not satisfied
link |
by how sort of fragile finding that particular property was.
link |
And let me just make another point,
link |
which is that it turns out that even if the underlying rule
link |
does not have this property of causal invariance,
link |
it can turn out that every observation
link |
made by observers of the rule can,
link |
they can impose what amounts to causal invariance
link |
We can explain that.
link |
It's a little bit more complicated.
link |
I mean, technically that has to do with this idea
link |
of completions, which is something that comes up
link |
in term rewriting systems,
link |
automated theorem proving systems and so on.
link |
But let's ignore that for a second.
link |
We can come to that later.
link |
But is it useful to talk about observation?
link |
So there's some concept of causal invariance
link |
as you apply these rules in an asynchronous way,
link |
you can think of those transformations as events.
link |
So there's this hypergraph that represents space
link |
and all of these events happening in the space
link |
and the graph grows in interesting complicated ways.
link |
And eventually the froth arises of what we experience
link |
as human existence.
link |
That's some version of the picture,
link |
but let's explain a little bit more.
link |
What's a little more detail like?
link |
Well, so one thing that is sort of surprising
link |
in this theory is one of the sort of achievements
link |
of 20th century physics was kind of bringing
link |
space and time together.
link |
That was, you know, special relativity.
link |
People talk about space time, this sort of unified thing
link |
where space and time kind of a mixed
link |
and there's a nice mathematical formalism
link |
that in which, you know, space and time sort of appear
link |
as part of the space time continuum,
link |
the space time, you know, four vectors and things like this.
link |
You know, we talk about time as the fourth dimension
link |
and all these kinds of things.
link |
It's, you know, and it seems like the theory of relativity
link |
sort of says space and time are fundamentally
link |
the same kind of thing.
link |
So one of the things that took a while to understand
link |
in this approach of mine is that in my kind of approach,
link |
space and time are really not fundamentally
link |
the same kind of thing.
link |
Space is the extension of this hypergraph.
link |
Time is the kind of progress of this inexorable computation
link |
of these rules getting applied to the hypergraph.
link |
So it's, they seem like very different kinds of things.
link |
And so that at first seems like
link |
how can that possibly be right?
link |
How can that possibly be Lorentz invariant?
link |
That's the term for things being, you know,
link |
following the rules of special relativity.
link |
Well, it turns out that when you have causal invariants
link |
that, and let's see, we can, it's worth explaining
link |
a little bit how this works.
link |
It's a little bit elaborate,
link |
but the basic point is that even though space and time
link |
sort of come from very different places,
link |
it turns out that the rules of sort of space time
link |
that special relativity talks about come out of this model
link |
when you're looking at large enough systems.
link |
So a way to think about this, you know,
link |
in terms of when you're looking at large enough systems,
link |
the part of that story is when you look at some fluid
link |
like water, for example, there are equations
link |
that govern the flow of water.
link |
Those equations are things that apply on a large scale.
link |
If you look at the individual molecules,
link |
they don't know anything about those equations.
link |
It's just the sort of the large scale effect
link |
of those molecules turns out to follow those equations.
link |
And it's the same kind of thing happening in our models.
link |
I know this might be a small point,
link |
but it might be a very big one.
link |
We've been talking about space and time
link |
at the lowest level of the model, which is space.
link |
The hypergraph time is the evolution of this hypergraph.
link |
But there's also space time that we think about
link |
and general relativity for your special relativity.
link |
Like how do you go from the lowest source code
link |
of space and time as we're talking about
link |
to the more traditional terminology of space and time?
link |
So the key thing is this thing we call the causal graph.
link |
So the causal graph is the graph
link |
of causal relationships between events.
link |
So every one of these little updating events,
link |
every one of these little transformations
link |
of the hypergraph happens somewhere in the hypergraph,
link |
happens at some stage in the computation.
link |
That event has a causal relationship to other events
link |
in the sense that if another event needs as its input,
link |
the output from the first event,
link |
there will be a causal relationship
link |
of the future event will depend on the past event.
link |
So you can say it has a causal connection.
link |
And so you can make this graph
link |
of causal relationships between events.
link |
That graph of causal relationships,
link |
causal invariance implies that that graph is unique.
link |
It doesn't matter even though you think,
link |
oh, I'm, let's say we were sorting a string, for example,
link |
I did that particular transposition of characters
link |
at this time, then I did that one, then I did this one.
link |
Turns out if you look at the network of connections
link |
between those updating events, that network is the same.
link |
It's the, if you were to, the structure.
link |
So in other words, if you were to draw that,
link |
if you were to put that network on a picture
link |
of where you're doing all the updating,
link |
the places where you put the nodes of the network
link |
will be different, but the way the nodes are connected
link |
will always be the same.
link |
So, but the causal graph is, I don't know,
link |
it's kind of an observation, it's not enforced,
link |
it's just emergent from a set of events.
link |
It's a feature of, okay, so what it is is.
link |
The characteristic, I guess, of the way events happen.
link |
Right, it's an event can't happen
link |
until its input is ready.
link |
And so that creates this network of causal relationships.
link |
And that's the causal graph.
link |
And the thing that the next thing to realize is,
link |
okay, we, when you're going to observe
link |
what happens in the universe,
link |
you have to sort of make sense of this causal graph.
link |
So, and you are an observer who yourself
link |
is part of this causal graph.
link |
And so that means, so let me give you an example
link |
of how that works.
link |
So imagine we have a really weird theory of physics
link |
of the world where it says this updating process,
link |
there's only gonna be one update at every moment in time.
link |
And there's just gonna be like a Turing machine.
link |
It has a little head that runs around
link |
and just is always just updating one thing at a time.
link |
So you say, I have a theory of physics
link |
and the theory of physics says,
link |
there's just this one little place where things get updated.
link |
You say, that's completely crazy because,
link |
it's plainly obvious that things are being updated
link |
sort of at the same time.
link |
Async obviously, yeah, at the same time, yeah.
link |
But the fact is that the thing is that if I'm talking to you
link |
and you seem to be being updated as I'm being updated,
link |
but if there's just this one little head
link |
that's running around updating things,
link |
I will not know whether you've been updated or not
link |
until I'm updated.
link |
So in other words, draw this causal graph
link |
of the causal relationship between the updatings in you
link |
and the updatings in me,
link |
it'll still be the same causal graph,
link |
whether even though the underlying sort of story
link |
of what happens is, oh, there's just this one little thing
link |
and it goes and updates in different places in the universe.
link |
So is that clear or is that a hypothesis?
link |
Is that clear that there's a unique causal graph?
link |
If there's causal invariance, there's unique causal graph.
link |
So it's okay to think of what we're talking about
link |
as a hypergraph and the operations on it
link |
as a kind of touring machine with a single head,
link |
like a single guy running around updating stuff.
link |
Is that safe to intuitively think of it this way?
link |
Let me think about that for a second.
link |
I think there's nothing, it doesn't matter.
link |
I mean, you can say, okay, there is one,
link |
the reason I'm pausing for a second is that I'm wondering,
link |
well, when you say running around,
link |
depends how far it jumps every time it runs.
link |
Yeah, yeah, that's right.
link |
But I mean like one operation at a time.
link |
Yeah, you can think of it as one operation at a time.
link |
It's easier for the human brain to think of it that way
link |
as opposed to simultaneous.
link |
Well, maybe it's not, okay, but the thing is
link |
that's not how we experience the world.
link |
What we experience is we look around,
link |
everything seems to be happening
link |
at successive moments in time everywhere in space.
link |
That is the, and that's partly a feature
link |
of our particular construction.
link |
I mean, that is the speed of light is really fast
link |
compared to, you know, we look around, you know,
link |
I can see maybe a hundred feet away right now.
link |
You know, it's the, my brain does not process very much
link |
in the time it takes light to go a hundred feet.
link |
The brain operates at a scale of hundreds of milliseconds
link |
or something like that, I don't know.
link |
And speed of light is much faster.
link |
Right, you know, light goes,
link |
in a billionth of a second light has gone afoot.
link |
So it goes a billion feet every second.
link |
There's certain moments through this conversation
link |
where I imagine the absurdity of the fact
link |
that there's two descendants of apes modeled by a hypergraph
link |
that are communicating with each other
link |
and experiencing this whole thing
link |
as a real time simultaneous update with,
link |
I'm taking in photons from you right now,
link |
but there's something much, much deeper going on here.
link |
Right, it does have a.
link |
It's paralyzing sometimes to just.
link |
Right, no, I mean, you know, it's a, you know.
link |
As a small little tangent, I just remembered
link |
that we're talking about,
link |
I mean, about the fabric of reality.
link |
Right, so we've got this causal graph
link |
that represents the sort of causal relationships
link |
between all these events in the universe.
link |
That causal graph kind of is a representation of space time,
link |
but our experience of it requires
link |
that we pick reference frames.
link |
This is kind of a key idea.
link |
Einstein had this idea that what that means is
link |
we have to say, what are we going to pick
link |
as being the sort of what we define
link |
as simultaneous moments in time?
link |
So for example, we can say, you know,
link |
how do we set our clocks?
link |
You know, if we've got a spacecraft landing on Mars,
link |
you know, do we say that, you know,
link |
what time is it landing at?
link |
Was it, you know, even though there's a 20 minute
link |
speed of light delay or something, you know,
link |
what time do we say it landed at?
link |
How do we set up sort of time coordinates for the world?
link |
And that turns out to be that there's kind of
link |
this arbitrariness to how we set these reference frames
link |
that defines sort of what counts as simultaneous.
link |
And what is the essence of special relativity
link |
is to think about reference frames going at different speeds
link |
and to think about sort of how they assign,
link |
what counts as space, what counts as time and so on.
link |
That's all a bit technical, but the basic bottom line is
link |
that this causal invariance property,
link |
that means that it's always the same causal graph,
link |
independent of how you slice it with these reference frames,
link |
you'll always sort of see the same physical processes go on.
link |
And that's basically why special relativity works.
link |
So there's something like special relativity,
link |
like everything around space and time
link |
that fits this idea of the causal graph.
link |
Right, well, you know, one way to think about it is
link |
given that you have a basic structure
link |
that just involves updating things in these,
link |
you know, connected updates and looking at
link |
the causal relationships between connected updates,
link |
that's enough when you unravel the consequences of that,
link |
that together with the fact that there are lots
link |
of these things and that you can take a continuum limit
link |
and so on implies special relativity.
link |
And so that, it's kind of not a big deal
link |
because it's kind of a, you know,
link |
it was completely unobvious when you started off
link |
with saying, we've got this graph,
link |
it's being updated in time, et cetera, et cetera, et cetera,
link |
that just looks like nothing to do with special relativity.
link |
And yet you get that.
link |
And what, I mean, then the thing,
link |
I mean, this was stuff that I figured out back in the 1990s.
link |
The next big thing you get is general relativity.
link |
And so in this hypergraph,
link |
the sort of limiting structure,
link |
when you have a very big hypergraph,
link |
you can think of as being just like, you know,
link |
water seems continuous on a large scale.
link |
So this hypergraph seems continuous on a large scale.
link |
One question is, you know,
link |
how many dimensions of space does it correspond to?
link |
So one question you can ask is,
link |
if you've just got a bunch of points
link |
and they're connected together,
link |
how do you deduce what effective dimension of space
link |
that bundle of points corresponds to?
link |
And that's pretty easy to explain.
link |
So basically if you say you've got a point
link |
and you look at how many neighbors does that point have?
link |
Okay, imagine it's on a square grid.
link |
Then it'll have four neighbors.
link |
Go another level out.
link |
How many neighbors do you get then?
link |
What you realize is as you go more and more levels out,
link |
as you go more and more distance on the graph out,
link |
you're capturing something which is essentially a circle
link |
in two dimensions so that, you know,
link |
the number of the area of a circle is pi R squared.
link |
So it's the number of points that you get to
link |
goes up like the distance you've gone squared.
link |
And in general, in D dimensional space,
link |
it's R to the power D.
link |
It's the number of points you get to
link |
if you go R steps on the graph grows like
link |
the number of steps you go to the power of the dimension.
link |
And that's a way that you can estimate
link |
the effective dimension of one of these graphs.
link |
So what does that grow to?
link |
So how does the dimension grow?
link |
There's a, I mean, obviously the visual aspect
link |
of these hypergraphs,
link |
they're often visualized in three dimensions.
link |
So there's a certain kind of structure,
link |
like you said, there's, I mean, a circle, a sphere,
link |
there's a planar aspect to it,
link |
to this graph to where it kind of,
link |
it almost starts creating a surface,
link |
like a complicated surface, but a surface.
link |
So how does that connect to effective dimension?
link |
Okay, so if you can lay out the graph
link |
in such a way that the points in the graph that,
link |
you know, the points that are neighbors on the graph
link |
are neighbors as you lay them out,
link |
and you can do that in two dimensions,
link |
then it's gonna approximate a two dimensional thing.
link |
If you can't do that in two dimensions,
link |
if everything would have to fold over a lot
link |
in two dimensions,
link |
then it's not approximating a two dimensional thing.
link |
Maybe you can lay it out in three dimensions.
link |
Maybe you have to lay it out in five dimensions
link |
to have it be the case
link |
that it sort of smoothly lays out like that.
link |
Well, but okay, so I apologize
link |
for the different tangent questions,
link |
but you know, there's an infinity number of possible rules.
link |
So we have to look for rules
link |
that create the kind of structures
link |
that are reminiscent for,
link |
that have echoes of the different physics theories in them.
link |
So what kind of rules,
link |
is there something simple to be said
link |
about the kind of rules that you have found beautiful,
link |
that you have found powerful?
link |
Right, so I mean, what, you know,
link |
one of the features of computational irreducibility is,
link |
it's very, you can't say in advance,
link |
what's gonna happen with any particular,
link |
you can't say, I'm gonna pick these rules
link |
from this part of rule space, so to speak,
link |
because they're gonna be the ones that are gonna work.
link |
That's, you can make some statements along those lines,
link |
but you can't generally say that.
link |
Now, you know, the state of what we've been able to do
link |
is, you know, different properties of the universe,
link |
like dimensionality, you know, integer dimensionality,
link |
features of other features of quantum mechanics,
link |
At this point, what we've got is,
link |
we've got rules that any one of those features,
link |
we can get a rule that has that feature.
link |
We don't have the sort of, the final,
link |
here's a rule which has all of these features,
link |
we do not have that yet.
link |
So if I were to try to summarize
link |
the Wolfram physics project, which is, you know,
link |
something that's been in your brain for a long time,
link |
but really has just exploded in activity,
link |
you know, only just months ago.
link |
So it's an evolving thing, and next week,
link |
I'll try to publish this conversation
link |
as quickly as possible, because by the time it's published,
link |
already new things will probably have come out.
link |
So if I were to summarize it,
link |
we've talked about the basics of,
link |
there's a hypergraph that represents space,
link |
there is transformations in that hypergraph
link |
that represents time.
link |
The progress of time.
link |
The progress of time, there's a causal graph
link |
that's a characteristic of this,
link |
and the basic process of science,
link |
of, yeah, of science within the Wolfram physics model
link |
is to try different rules and see which properties
link |
of physics that we know of, known physical theories,
link |
are, appear within the graphs that emerge from that rule.
link |
That's what I thought it was going to be.
link |
It turns out we can do a lot better than that.
link |
It turns out that using kind of mathematical ideas,
link |
we can say, and computational ideas,
link |
we can make general statements,
link |
and those general statements turn out to correspond
link |
to things that we know from 20th century physics.
link |
In other words, the idea of you just try a bunch of rules
link |
and see what they do,
link |
that's what I thought we were gonna have to do.
link |
But in fact, we can say, given causal invariance
link |
and computational irreducibility, we can derive,
link |
and this is where it gets really pretty interesting,
link |
we can derive special relativity,
link |
we can derive general relativity,
link |
we can derive quantum mechanics.
link |
And that's where things really start to get exciting,
link |
is, you know, it wasn't at all obvious to me
link |
that even if we were completely correct,
link |
and even if we had, you know, this is the rule,
link |
you know, even if we found the rule,
link |
to be able to say, yes, it corresponds
link |
to things we already know,
link |
I did not expect that to be the case.
link |
So for somebody who is a simple mind
link |
and definitely not a physicist, not even close,
link |
what does derivation mean in this case?
link |
Okay, so let me, this is an interesting question.
link |
Okay, so there's, so one thing...
link |
In the context of computational irreducibility.
link |
Yeah, yeah, right, right.
link |
So what you have to do, let me go back to, again,
link |
the mundane example of fluids and water
link |
and things like that, right?
link |
So you have a bunch of molecules bouncing around.
link |
You can say, just as a piece of mathematics,
link |
I happen to do this from cellular automata
link |
back in the mid 1980s, you can say,
link |
just as a matter of mathematics,
link |
you can say the continuum limit
link |
of these little molecules bouncing around
link |
is the Navier Stokes equations.
link |
That's just a piece of mathematics.
link |
It's not, it doesn't rely on...
link |
You have to make certain assumptions
link |
that you have to say there's enough randomness
link |
in the way the molecules bounce around
link |
that certain statistical averages work,
link |
et cetera, et cetera, et cetera.
link |
Okay, it is a very similar derivation
link |
to derive, for example, the Einstein equations.
link |
Okay, so the way that works, roughly,
link |
the Einstein equations are about curvature of space.
link |
Curvature of space, I talked about sort of
link |
how you can figure out dimension of space.
link |
There's a similar kind of way of figuring out
link |
if you just sort of say, you know,
link |
you're making a larger and larger ball
link |
or larger and larger, if you draw a circle
link |
on the surface of the earth, for example,
link |
you might think the area of a circle is pi r squared,
link |
but on the surface of the earth,
link |
because it's a sphere, it's not flat,
link |
the area of a circle isn't precisely pi r squared.
link |
As the circle gets bigger, the area is slightly smaller
link |
than you would expect from the formula pi r squared
link |
as a little correction term that depends on the ratio
link |
of the size of the circle to the radius of the earth.
link |
Okay, so it's the same basic thing,
link |
allows you to measure from one of these hypergraphs
link |
what is its effective curvature.
link |
So the little piece of mathematics
link |
that explains special general relativity
link |
can map nicely to describe fundamental property
link |
of the hypergraphs, the curvature of the hypergraphs.
link |
So special relativity is about the relationship
link |
General relativity is about curvature
link |
and this space represented by this hypergraph.
link |
So what is the curvature of a hypergraph?
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Okay, so first I have to explain,
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what we're explaining is,
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first thing you have to have is a notion of dimension.
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You don't get to talk about curvature of things.
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If you say, oh, it's a curved line,
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but I don't know what a line is yet.
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Yeah, what is the dimension of a hypergraph then?
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From where, we've talked about effective dimension, but...
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Right, that's what this is about.
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What this is about is, you have your hypergraph,
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it's got a trillion nodes in it.
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What is it roughly like?
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Is it roughly like a grid, a two dimensional grid?
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Is it roughly like all those nodes are arranged online?
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What's it roughly like?
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And there's a pretty simple mathematical way
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to estimate that by just looking at this thing
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I was describing, this sort of the size of a ball
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that you construct in the hypergraph.
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That's a, you just measure that,
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you can just compute it on a computer for a given hypergraph
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and you can say, oh, this thing is wiggling around,
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but it's roughly corresponds to two or something like that,
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or roughly corresponds to 2.6 or whatever.
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So that's how you have a notion of dimension
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in these hypergraphs.
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Curvature is something a little bit beyond that.
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If you look at how the size of this ball increases
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as you increase its radius,
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curvature is a correction
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to the size increase associated with dimension.
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It's a sort of a second order term
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in determining the size.
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Just like the area of a circle is roughly pi R squared.
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So it goes up like R squared.
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The two is because it's in two dimensions,
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but when that circle is drawn on a big sphere,
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the actual formula is pi R squared times one minus
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R squared over A squared and some coefficient.
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So in other words, there's a correction to,
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and that correction term, that gives you curvature.
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And that correction term
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is what makes this hypergraph correspond,
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have the potential to correspond to curved space.
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Now, the next question is, is that curvature,
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is the way that curvature works
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the way that Einstein's equations for general relativity,
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is it the way they say it should work?
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And the answer is yes.
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And so how does that work?
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The calculation of the curvature of this hypergraph
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for some set of rules?
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No, it doesn't matter what the rules are.
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So long as they have causal invariance
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and computational irreducibility,
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and they lead to finite dimensional space,
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noninfinite dimensional space.
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Noninfinite dimensional.
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It can grow infinitely,
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but it can't be infinite dimensional.
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So what is a infinitely dimensional hypergraph look like?
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So that means, for example, so in a tree,
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you start from one root of the tree,
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it doubles, doubles again, doubles again, doubles again.
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And that means if you ask the question,
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starting from a given point,
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how many points do you get to?
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Remember, in like a circle,
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you get to R squared, the two there.
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On a tree, you get to, for example, two to the R.
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It's exponential dimensional, so to speak,
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or infinite dimensional.
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Do you have a sense of, in the space of all possible rules,
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how many lead to infinitely dimensional hypergraphs?
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Is that an important thing to know?
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Yes, it's an important thing to know.
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I would love to know the answer to that.
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But it gets a little bit more complicated
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because, for example, it's very possibly the case
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that in our physical universe,
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that the universe started infinite dimensional.
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And it only, as the Big Bang,
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it was very likely infinite dimensional.
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And as the universe sort of expanded and cooled,
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its dimension gradually went down.
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And so one of the bizarre possibilities,
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which actually there are experiments you can do
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to try and look at this,
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the universe can have dimension fluctuations.
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So in other words,
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we think we live in a three dimensional universe,
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but actually there may be places
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where it's actually 3.01 dimensional,
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or where it's 2.99 dimensional.
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And it may be that in the very early universe,
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it was actually infinite dimensional,
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and it's only a late stage phenomenon
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that we end up getting three dimensional space.
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But from your perspective of the hypergraph,
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one of the underlying assumptions you kind of implied,
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but you have a sense, a hope set of assumptions
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that the rules that underlie our universe,
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or the rule that underlies our universe is static.
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Is that one of the assumptions
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you're currently operating under?
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Yes, but there's a footnote to that,
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which we should get to,
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because it requires a few more steps.
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Well, actually then, let's backtrack to the curvature,
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because we're talking about as long as it's finite dimensional.
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Finite dimensional computational irreducibility
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and causal invariance,
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then it follows that the large scale structure
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will follow Einstein's equations.
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And now let me again, qualify that a little bit more,
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there's a little bit more complexity to it.
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The, okay, so Einstein's equations in their simplest form
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apply to the vacuum, no matter, just the vacuum.
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And they say, in particular, what they say is,
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if you have, so there's this term GD6,
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that's a term that means shortest path,
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comes from measuring the shortest paths on the Earth.
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So you look at a bunch of, a bundle of GD6,
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a bunch of shortest paths,
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it's like the paths that photons
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would take between two points.
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Then the statement of Einstein's equations,
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it's basically a statement about a certain the,
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that as you look at a bundle of GD6,
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the structure of space has to be such that,
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although the cross sectional area of this bundle may,
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although the actual shape of the cross section may change,
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the cross sectional area does not.
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That's a version, that's the most simple minded version
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of R mu nu minus a half R G mu nu equals zero,
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which is the more mathematical version
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of Einstein's equations.
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It's a statement of the thing called the Ritchie tensor
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That's Einstein's equations for the vacuum.
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Okay, so we get that as a result of this model,
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but footnote, big footnote,
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because all the matter in the universe
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is the stuff we actually care about.
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The vacuum is not stuff we care about.
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So the question is, how does matter come into this?
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And for that, you have to understand what energy is
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And one of the things that we realized, you know,
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late last year was that there's a very simple interpretation
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of energy in these models, okay?
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And energy is basically, well, intuitively,
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it's the amount of activity in these hypergraphs
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and the way that that remains over time.
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So a little bit more formally,
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you can think about this causal graph
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as having these edges that represent causal relationships.
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You can think about, oh boy,
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there's one more concept that we didn't get to.
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It's the notion of space like hypersurfaces.
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So this is not as scary as it sounds.
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It's a common notion in general activity.
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The notion is you are defining what is a possibly,
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where in space time might be a particular moment in time.
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So in other words, what is a consistent set of places
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where you can say, this is happening now, so to speak.
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And you make the series of sort of slices
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through the space time, through this causal graph
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to represent sort of what we consider
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to be successive moments in time.
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It's somewhat arbitrary because you can deform that
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if you're going at a different speed in a special activity,
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you tip those things, there are different kinds
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of deformations, but only certain deformations
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are allowed by the structure of the causal graph.
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Anyway, be that as it may, the basic point is
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there is a way of figuring out,
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you say, what is the energy associated
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with what's going on in this hypergraph?
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And the answer is there is a precise definition of that.
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And it is the formal way to say it is,
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it's the flux of causal edges
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through space like hypersurfaces.
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The slightly less formal way to say it,
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it's basically the amount of activity.
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See, the reason it gets tricky is you might say
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it's the amount of activity per unit volume
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in this hypergraph, but you haven't defined what volume is.
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So it's a little bit, you have to be a little more careful.
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But this hypersurface gives some more formalism to that.
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Yeah, yeah, it gives a way to connect that.
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But intuitive, we should think about as the just activity.
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Right, so the amount of activity that kind of remains
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in one place in the hypergraph corresponds to energy.
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The amount of activity that is kind of where an activity here
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affects an activity somewhere else,
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corresponds to momentum.
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And so one of the things that's kind of cool
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is that I'm trying to think about
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how to say this intuitively.
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The mathematics is easy,
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but the intuitive version, I'm not sure.
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But basically the way that things sort of stay
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in the same place and have activity
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is associated with rest mass.
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And so one of the things that you get to derive
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is E equals MC squared.
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That is a consequence of this interpretation of energy
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in terms of the way the causal graph works,
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which is the whole thing is sort of a consequence
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of this whole story about updates and hypergraphs and so on.
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So can you linger on that a little bit?
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How do we get E equals MC squared?
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So where does the mass come from?
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I mean, is there an intuitive, it's okay.
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First of all, you're pretty deep
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in the mathematical explorations of this thing right now.
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We're in a very, we're in a flux currently.
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So maybe you haven't even had time
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to think about intuitive explanations, but.
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Yeah, I mean, this one is, look, roughly what's happening,
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that derivation is actually rather easy.
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And everybody, and I've been saying
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we should pay more attention to this derivation
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because it's such, you know,
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cause people care about this one.
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But everybody says, it's just easy.
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So there's some concept of energy
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that can be intuitively thought of as the activity,
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the flux, the level of changes that are occurring
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based on the transformations within a certain volume,
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however the heck do you find the volume.
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Okay, so, and then mass.
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Well, mass is associated with kind of the energy
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that does not cause you to,
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that does not somehow propagate through time.
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Yeah, I mean, one of the things that was not obvious
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in the usual formulation of special relativity
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is that space and time are connected in a certain way.
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Energy and momentum are also connected in a certain way.
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The fact that the connection of energy to momentum
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is analogous to the connection to space
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between space and time
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is not self evident in ordinary relativity.
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It is a consequence of this, of the way this model works.
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It's an intrinsic consequence of the way this model works.
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And it's all to do with that,
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with unraveling that connection
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that ends up giving you this relationship
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between energy and, well, it's energy, momentum, mass,
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they're all connected.
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And so like, that's hence the general relativity.
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You have a sense that it appears to be baked in
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to the fundamental properties
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of the way these hypergraphs are evolved.
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Well, I didn't yet get to,
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so I got as far as special relativity and equals MC squared.
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The one last step is, in general relativity,
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the final connection is energy and mass
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cause curvature in space.
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And that's something that when you understand
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this interpretation of energy,
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and you kind of understand the correspondence
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to curvature and hypergraphs,
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then you can finally sort of, the big final answer is,
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you derive the full version of Einstein's equations
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for space, time and matter.
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Is that, have you, that last piece with curvature,
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have, is that, have you arrived there yet?
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Oh yeah, we're there, yes.
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And here's the way that we,
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here's how we're really, really going to know
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we've arrived, okay?
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So, you know, we have the mathematical derivation,
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it's all fine, but, you know,
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mathematical derivations, okay.
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So one thing that's sort of a,
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you know, we're taking this limit
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of what happens when you, the limit,
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you have to look at things which are large
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compared to the size of an elementary length,
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small compared to the whole size of the universe,
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large compared to certain kinds of fluctuations,
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There's a, there's a, there's a tower
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of many, many of these mathematical limits
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that have to be taken.
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So if you're a pure mathematician saying,
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where's the precise proof?
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It's like, well, there are all these limits,
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we can, you know, we can try each one of them
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computationally and we could say, yeah, it really works,
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but the formal mathematics is really hard to do.
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I mean, for example, in the case of deriving
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the equations of fluid dynamics from molecular dynamics,
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that derivation has never been done.
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There is no rigorous version of that derivation.
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So, so that could be.
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Because you can't do the limits?
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Yeah, because you can't do the limits.
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But so the limits allow you to try to describe
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something general about the system
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and very, very particular kinds of limits that you need
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to take with these very.
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Right, and the limits will definitely work
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the way we think they work.
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And we can do all kinds of computer experiments.
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It's just a hard derivation.
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Yeah, it's just, it's just the mathematical structure
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kind of, you know, ends up running right into
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computational irreducibility.
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And you end up with a bunch of, a bunch of difficulty there.
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But here's the way that we're getting really confident
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that we know completely what we're talking about,
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which is when people study things like black hole mergers,
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using Einstein's equations, what do they actually do?
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Well, they actually use Mathematica or a whole bunch
link |
to analyze the equations and so on.
link |
But in the end, they do numerical relativity,
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which means they take these nice mathematical equations
link |
and they break them down so that they can run them
link |
And they break them down into something
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which is actually a discrete approximation
link |
to these equations.
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Then they run them on a computer, they get results.
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Then you look at the gravitational waves
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and you see if they match, okay?
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It turns out that our model gives you a direct way
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to do numerical relativity.
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So in other words, instead of saying,
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you start from these continuum equations from Einstein,
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you break them down into these discrete things,
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you run them on a computer,
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you say, we're doing it the other way around.
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We're starting from these discrete things
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that come from our model.
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And we're just running big versions on the computer.
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And, you know, what we're saying is,
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and this is how things will work.
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So the way I'm calling this is proof by compilation,
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so to speak, that is, in other words,
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you're taking something where, you know,
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we've got this description of a black hole system.
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And what we're doing is we're showing that the, you know,
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what we get by just running our model agrees
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with what you would get by doing the computation
link |
from the Einstein equations.
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As a small tangent or actually a very big tangent,
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but proof by compilation is a beautiful concept.
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In a sense, the way of doing physics with this model
link |
is by running it or compiling it.
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And have you thought about,
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and these things can be very large,
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is there a totally new possibilities of computing hardware
link |
and computing software,