back to index## Stephen 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 GÃ¶del'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.

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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,

link |

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,