The machine code of the universe is discrete | Stephen Wolfram and Lex Fridman

you've said that um with this metaphor analogy that theory of everything is a big mountain and you have a sense that however far we're up the mountain that the the wolfram physics model a view of the universe is at least the right mountain we're the right mountain yes without the question so i'm which aspect of it is the right mountain so for example i mean so there's so many aspects to just the way of the wolfram physics project the way it approaches the world that's um that's clean crisp and uh unique and powerful so you know there's a there's discrete nature to it there's a hypergraph there's a computational nature there's a generative aspect you start from nothing you generate everything which do you think the actual model is actually a really good one or do you think this general principle of from simplicity generating complexity is the right like what aspect of the mountain yeah right i mean i i think that the the kind of the meta idea about using simple computational systems to do things that's you know that's the ultimate big paradigm that is you know sort of super important the details of the particular model are very nice and clean and allow one to actually understand what's going on they are not unique and in fact we know that we know that there's a there's a large number of different ways to describe essentially the same thing i mean i can describe things in terms of hypergraphs i can describe them in terms of higher category theory i can describe them in a bunch of different ways they are in some sense all the same thing but our sort of story about what's going on and the kind of kind of cultural mathematical resonances are a bit different i mean i think it's it's it's perhaps worth sort of saying a little bit about kind of the the you know foundational ideas of of uh of uh you know these of these models and things great so can you maybe uh can we like rewind we've talked about a little bit but can you say like what the central idea is of the wolfram physics project right so so the question is we're interested in finding a sort of simple computational rule that describes our whole universe can we just pause on that it's just so beautiful that's such a beautiful that's such a beautiful idea that we can generate our universe from from uh from a data structure a simple structure simple set of rules and we can generate our entire universe yes that's awe-inspiring right but but so so you know the question is how do you actualize that what might this rule be like and so one thing you quickly realize is if you're going to pack everything about our universe into this tiny rule not much that we are familiar with in our universe will be obvious in that rule so you don't get to fit all these parameters of the universe all these features of you know this is how space works this is our timer et cetera et cetera et cetera you don't get to fit that all it all has to be sort of packed in to this this thing something much smaller much more basic much lower level machine code so to speak than that and all the stuff that we're familiar with has to kind of emerge from the operation so the rule in itself because of the computational reducibility is not going to tell you the story it's not going to give you the answer to uh it's not going to let you predict what you're going to have for lunch tomorrow right it's not going to let you predict basically anything about your life about the universe right but and you're not going to be able to see in that rule oh there's the three for the number of dimensions of space and so on right that's not going to be so space time is not going to be obviously right so the question is then what what is the universe made of that's that's a it's a basic question and we've had some assumptions about what the universe is made of for the last few thousand years that i think in some cases i just turned out not to be right and you know the most important assumption is that space is a continuous thing that is that you can if you say let's pick a point in space we're going to do geometry we're going to pick a point we can pick a point absolutely anywhere in space precise numbers we can specify of where that point is in fact you know euclid who kind of wrote down the original kind of axiomatization of geometry back in 300 bc or so um you know his his very first definition he says a point is that which has no part a point is this is this you know uh this indivisible you know infinitesimal thing okay so we might have said that about material objects we might have said that about water for example we might have said water is a continuous thing that we can just uh you know pick any point we want in in some water but actually we know it isn't true we know that water is made of molecules that are discrete and so the question one fundamental question is what is space made of and so one of the things that's sort of a starting point for what i've done is to think of space as a discrete thing to think of there being sort of atoms of space just as there are atoms of material things although very different kinds of atoms and by the way i mean this idea you know there were ancient greek philosophers who had this idea there were you know einstein actually thought this is probably how things would work out i mean he said you know repeatedly he thought this is where it would work out we don't have the mathematical tools in our time which was 1940s 1950s and so on to explore this like the way he thought you mean that there is something very very small and discreet that's underlying space space yes and that means that so you know the mathematical theory mathematical theories in physics assume that space can be described just as a continuous thing you can just pick coordinates and the coordinates can have any values and that's how you define space space is this just sort of background uh sort of theater on which the universe operates but can we draw a distinction between space as a thing that could be described by uh three values coordinates and how you're are you are you using the word space more generally when you say no i'm just talking about what we spaces in in the universe so you think this 3d aspect of it is fundamental no i don't think that 3d is fundamental at all actually i think that the what's the the thing that has been assumed is that space is this continuous thing where you can just describe it by let's say three numbers for instance but most important thing about that is that you can describe it by precise numbers because you can pick any point in space and you can talk about motions any infinitesimal motion in space and that's what continuous means that's what continuous means that's what you know newton invented calculus to describe these kind of continuous small variations and so on that was that's kind of a fundamental idea from euclid on that's been a fundamental idea about space and so right or wrong uh it's not right it's not right it's it's it's it's right at the level of our experience most of the time it's not right at the level of the machine code so to speak and so machine code yeah of the simulation that's right that's right the the very lowest level of the fabric of the universe at least under the the the wolfram physics model is your senses is discrete right so so now what does that mean so it means what what is space then so in in our models the basic idea is you say there are these sort of atoms of space they're these points that represent you know represent places in space but they're just discrete points and the only thing we know about them is how they're connected to each other we don't know where they are they don't have coordinates we don't get to say this is a position such and such it's just here's a big bag of points like in our universe there might be 10 to the 100 of these points and all we know is this point is connected to this other point so it's like you know all we have is the friend network so to speak we don't we don't have you know people's you know physical addresses all we have is the friend network of these points yeah the underlying nature of reality is kind of like a facebook uh we don't know their location but we have the friends yeah yeah right we we know which point is connected to which other points and and that's all we know and so you might say well how on earth can you get something which is like our experience of of you know what seems like continuous space well the answer is by the time you have 10 to the 100 of these things there those connections can work in such a way that on a large scale it will seem to be like continuous space in let's say three dimensions or some other number of dimensions or 2.6 dimensions or whatever else because they're much much much much larger so like the uh the number of relationships here we're talking about is just a humongous amount so the the kind of thing you're talking about is very very very small relative to our experience of daily life right so i mean you know we don't know exactly the size but maybe maybe uh uh 10 to the minus uh maybe around 10 to the minus 100 meters so you know the size of to give a comparison the size of a of a proton is 10 to the minus 15 meters and so this is something incredibly tiny compared to that um and and the idea that from that would emerge the experience of continuous space is mind-blowing well what's your intuition why that's possible like first of all i mean we'll get in into it but i don't know if we will through the medium of conversation but the construct of hypergraphs is just beautiful right let's tell your automator beautiful we'll talk about it but right but this thing about you know continuity arising from discrete systems is in today's world is actually not so surprising i mean you know your average computer screen right every computer screen is made of discrete pixels yet we have the you know we have the idea that we're seeing these continuous pictures i mean it's you know the fact that on a large scale continuity can arise from lots of discrete elements this is at some level unsurprising now like but the pixels have a very definitive structure of neighbors on a computer screen right there is no concept of spatial of space inherent in the underlying fabric of reality right right right so so the the point is but there are cases where there are so for example let's just imagine you have a square grid okay and at every point on the grid you have one of these atoms of space and it's connected to four other four other atoms of space on the you know north northeast southwest corners right um there you have something where if you zoom out from that it's like a computer screen yeah so the relationship creates the the spatial like the relationship creates a constraint which then [Music] in an emergent sense creates a like yeah like a sp uh basically a spatial coordinate yeah that thing yeah right even though the individual point doesn't have a special even though the individual point doesn't know anything it just knows what it's you know what its neighbors are they on a large scale it can be described by saying oh it looks like it's a you know this grid zoomed out grid you can say well you can describe these different points by saying they have certain positions coordinates etc now in the in the sort of real setup it's more complicated than that isn't just a square grid or something it's something much more dynamic and complicated which we'll talk about you

Channel: Lex Clips

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Keywords: stephen wolfram, lex fridman podcast, artificial intelligence, ai, ai podcast, artificial intelligence podcast, lex clips, lex fridman, lex friedman, joe rogan, elon musk, lex podcast, lex mit, lex ai, mit ai, ai podcast clips, ai clips, deep learning, machine learning, computer science, engineering, physics, science, tech, technology, tech podcast, physics podcast, mathematics, math, math podcast, friedman, consciousness, philosophy, turing, einstein

Id: GuGIawc1IW4

Length: 12min 28sec (748 seconds)

Published: Wed Sep 16 2020