YouSaid · the spoken record

Stephen Wolfram

lines on the record: 331
first: 2020-09-15
most recent: 2020-09-15
sittings or episodes: 1
sources: podcast

Every line below is reproduced as it was said and linked to the record it came from. Nothing here is summarised or generated. Directory · Search · Corrections

“Yeah, yeah, right, right. So, what you have to do, let me go back to, again, the mundane example of fluids and water and things like that, right? So you have a bunch of molecules bouncing around. You can say, just as a piece of mathematics, I happen to do this from cellular automata back in the mid-1980s, you can say, just as a matter of mathematics, you can say the continuum limit of these little molecules bouncing around is the Navier-Stokes equations”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, what is it? It turns out we can do a lot better than that. It turns out that using kind of mathematical ideas, we can say and computational ideas, we can make general statements. And those general statements turn out to correspond to things that we know from 20th century physics. In other words, the idea of you just try a bunch of rules and see what they do. That's what I thought we were going to have to do. But in fact, we can say given causal invariance and computational irreducibility, we can derive, and this is where it gets really pretty interesting, we can derive special relativity, we can derive general relativity, we can derive quantum mechanics. And that's where things really start to get exciting is, you know, it wasn't at all obvious to me that even if we were completely correct and even if we had, you know, this is the rule, you know, even if we found the rule to be able to say, yes, it corresponds to things we already know.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So, I mean, one of the features of computational irreducibility is it's very, you can't say in advance what's going to happen with any particular, you can't say, I'm going to pick these rules from this part of rule space, so to speak, because they're going to be the ones that are going to work. You can make some statements along those lines, but you can't generally say that. Now, the state of what we've been able to do is, you know, different properties of the universe, like dimensionality. Any one of those features, we can get a rule that has that feature. We don't have the sort of the final here's a rule which has all of these features. We do not have that yet.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And you can do that in two dimensions, then it's going to approximate a two-dimensional thing. If you can't do that in two dimensions of everything would have to fold over a lot in two dimensions, then it's not approximating a two-dimensional thing. Maybe you can lay it out in three dimensions. Maybe you have to lay it out in five dimensions to have it be the case that it sort of smoothly lays out like that.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So Okay, so if you can lay out the graph in such a way that the points in the graph that the points that are neighbors on the graph are neighbors as you lay them out”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So that the number of the area of a circle is pi r squared. So it's the number of points that you get to goes up like the distance you've gone squared. And in general, in dimensional space, it's r to the power d. It's the number of points you get to if you go r steps on the graph grows like the number of steps you go to the power of the dimension. And that's a way that you can estimate the effective dimension of one of these graphs.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And so in this hypograph, the sort of limiting structure when you have a very big hypergraph, you can think of as being just like water seems continuous on a large scale. So this hypergraph seems continuous on a large scale. One question is how many dimensions of space does it correspond to? So one question you can ask is if you've just got a bunch of points and they're connected together, how do you deduce what effective dimension of space that bundle of points corresponds to? And that's pretty easy to explain. So basically if you say you've got a point and you look at how many neighbors does that point have, okay, imagine it's on a square grid. Then it'll have four neighbors. Go another level out. How many neighbors do you get then? What you realize is as you go more and more levels out, as you go more and more distance on the graph out, you're capturing something which is essentially a circle in two dimensions.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, well, you know, one way to think about it is given that you have a basic structure that just involves updating things in these connected updates and looking at the causal relationships between connected updates, that's enough when you unravel the consequences of that, that together with the fact that there are lots of these things and that you can take continuum limits and so on, implies special relativity. not a big deal because it's kind of a you know it was completely unobvious when you started off with saying we've got this graph it's being updated in time etc etc etc that just looks like nothing to do with special relativity and yet you get that and and what i mean then the thing i mean this was stuff that i figured out back in the 1990s the um the the next big thing you get as general art of day”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Speed of light delay or something. What time do we say it landed at? How do we set up sort of time coordinates for the world? And that turns out to be that there's kind of this arbitrariness to how we set these reference frames that define sort of what councils simultaneous and what is the essence of special relativity is to think about reference frames going at different speeds and to think about sort of how they assign what counts as space, what counts as time, and so on. That's all a bit technical, but the basic bottom line is that this causal invariance property that means that it's always the same causal graph, independent of how you slice it with these reference frames, you'll always sort of see the same physical processes go on. And that's basically why special relativity works.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, so we've got this causal graph that represents the sort of causal relationships between all these events in the universe. That causal graph kind of is a representation of space-time, but our experience of it requires that we pick reference frames. This is kind of a key idea Einstein had this idea that what that means is we have to say, what are we going to pick as being the sort of what we define as simultaneous moments in time? So, for example, we can say, how do we set our clocks? If we've got a spacecraft landing on Mars, do we say that what time is it landing at? Was it, you know, even though there's a 20 minute...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And speed of light is much faster. Right. You know, light goes in a billionth of a second. Light has gone afoot. So it goes a billion feet every second.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, you can think of it as one opera right now It's not okay, but the thing is that that's not how we experience the world. That is, and that's partly a feature of our particular construction. I mean, that is the speed of light is really fast compared to, you know, we look around. I can see maybe 100 feet away right now. My brain does not process very much in the time it takes light to go 100 feet.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Let me think about that for a second. Yes, I think so. I think that there's nothing, it doesn't matter. I mean, you can say, okay, there is one, the reason I'm pausing for a second is that I'm wondering, well, when you say running around depends how far it jumps every time it runs around”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“But the fact is that the thing is that if I'm talking to you and you seem to be being updated as I'm being updated, but if there's just this one little head that's running around updating things, I will not know whether you've been updated or not until I'm updated. So in other words, when you draw this causal graph of the causal relationship between the updatings and you and the updatings in me, it'll still be the same causal graph, whether even though the underlying sort of story of what happens is, oh, there's just this one little thing and it goes and updates in different places in the universe.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“You have to sort of make sense of this causal graph. And you are an observer who yourself is part of this causal graph. And so that means, so let me give you an example of how that works. So imagine we have a really weird theory of physics, of the world, where it says this updating process, there's only going to be one update at every moment in time. And there's just going to be like a Turing machine. It has a little head that runs around and just is always just updating one thing at a time. So you say, you know, I have a theory of physics, and the theory of physics says there's just this one little place where things get updated. You say, that's completely crazy because, you know, it's plainly obvious that things are being updated sort of, you know, at the same time.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, it's an event can't happen until its input is ready. And so that creates this network of causal relationships. And that's the causal graph. And the thing, the next thing to realize is, okay, when you're going to observe what happens in the universe,”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“The structure, so in other words, if you were to draw that, if you were to put that network on a picture of where you're doing all the updating, the places where you put the nodes of the network will be different, but the way the nodes are connected will always be the same.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So you can say it has a causal connection. And so you can make this graph of causal relationships between events. That graph of causal relationships, causal invariance, implies that that graph is unique. It doesn't matter, even though you think, oh, let's say we were sorting a string, for example. I did that particular transposition of characters at this time. Then I did that one, then I did this one. Turns out if you look at the network of connections between those updating events, that network is the same. If you were to...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, right. So the key thing is this thing we call the causal graph. So the causal graph is the graph of causal relationships between events. So every one of these little updating events, every one of these little transformations of the hypergraph happens somewhere in the hypergraph happens at some stage in the computation. That's an event. That event has a causal relationship to other events in the sense that if another event needs as its input the output from the first event, there will be a causal relationship of the future event will depend on the past event.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, a way to think about this in terms of when you're looking at large enough systems, part of that story is when you look at some fluid like water, for example, there are equations that govern the flow of water. Those equations are things that apply on a large scale. If you look at the individual molecules, they don't know anything about those equations. It's just the sort of the large scale effect of those molecules turns out to follow those equations. And it's the same kind of thing happening in our models”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“The extension of this hypergraph, time is the kind of progress of this inexorable computation of these rules getting applied to the hypergraph. So they seem like very different kinds of things. And so that at first seems like, how can that possibly be right? How can that possibly be Lorentz invariant? That's the term for things being following the rules of special relativity. Well, it turns out that when you have causal invariance that And let's see we can it's worth it's worth explaining a little bit how this works it's a little bit little bit elaborate but but the basic point is that even though space and time sort of come from very different places it turns out that the rules of sort of space time that special relativity talks about come out of this model when you're looking at large enough systems”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. Well, so one thing that is sort of surprising in this theory is one of the sort of achievements of 20th century physics was kind of bringing space and time together. That was, you know, special relativity people talk about space-time, this sort of unified thing where space and time kind of a mixed, and there's a nice mathematical formalism in which space and time sort of appear as part of this space-time continuum, the space-time four vectors and things like this. We talk about time as the fourth dimension and all these kinds of things. And it seems like the theory relativity sort of says space and time are fundamentally the same kind of thing. So one of the things that took a while to understand in this approach of mine is that in my kind of approach, space and time are really not fundamentally the same kind of thing. Space is”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, yes. It is not obvious, and it was something that I sort of discovered that idea for these kinds of systems. And back in the 1990s, and for various reasons, I was not satisfied by how sort of fragile finding that particular property was. And let me just make another point, which is that it turns out that even if the underlying rule does not have this property of causal invariance, it can turn out that every observation made by observers of the rule can, they can impose what amounts to causal invariance on the rule. We can explain that. It's a little bit more complicated. I mean, technically, that has to do with this idea of completions, which is something that comes up in term rewriting systems, automated theorem proving systems, and so on. But let's ignore that for a second. We can come to that later.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Of multiplying things out, but you'll always get the same answer. Same thing if you let's say you're sorting, you've got a bunch of A's and B's. They're in some random order, you know, BAA, BBBA, whatever. And you have a little rule that says every time you see BA, flip it around to AB. Eventually, you apply that rule enough times, you'll have sorted the string so that it's all the A's first and then all the B's. Again, there are many different orders in which you can do that, many different sort of places where you can apply that update. In the end, you'll always get the string sorted the same way.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“A powerful idea which has actually arisen in different forms many times in the history of mathematics, mathematical logic, even computer science, has many different names. I mean, our particular version of it is a little bit tighter than other versions, but it's basically the same idea. Here's how to think about that idea. So imagine that, well, let's talk about it in terms of math for a second. Let's say you're doing algebra and you're told, you know, multiply out this series of polynomials that are multiplied together. You say, well, which order should I do that in? Say, well, do I multiply the third one by the fourth one and then do it by the first one or do I do the fifth one by the sixth one? And then do that? Well, it turns out it doesn't matter. You can multiply them out in any order. You always get the same answer. That's a property. If you think about kind of making a kind of network that represents in what order you do things, you'll get different orders for different ways.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, but so what happens is, so the first thing you might say is, you know, let's, well, okay, so this question about the freedom of which event you do when let me sort of state an answer and then explain it, okay? The validity of special relativity is a consequence of the fact that in some sense it doesn't matter in what order you do these underlying things so long as they respect this kind of set of causal relationships.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Technical term options. That's correct. But okay, so this is where things get a little bit more elaborate. But they're mind-blowing.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That's right. So that defines a kind of this sort of set of causal relationships between events. It says this event has to have happened before this event. But that is”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And what is extremely non trivial is, well, okay, so this is happening sort of in computer science terms, sort of asynchronously. You're just doing it wherever you feel like doing it. And the only constraint is that if you're going to apply the rules somewhere, the things to which you apply the rule, the little elements to which you apply the rule, if they have to be, okay, you can think of each application of the rule as being kind of an event that happens in the universe. And the input to an event has to be ready for the event to occur. That is, if one event occurred, if one transformation occurred, and it produced a particular atom of space, then that atom of space has to already exist before another transformation that's going to apply to that atom of space can occur.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, so this is a big complicated thing, very hard to wrap one's brain around. Okay, so you say the rule is every time you see this little pattern transform it in this way But yet, you know, as you look around the space that represents the universe, there may be zillions of places where that little pattern occurs. So what it says is just do this, apply this rule wherever you feel like.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So, what the rule says is something like if you have a little tiny piece of hypergraph that looks like this, then it will be transformed into a piece of hypergraph that looks like this. So that's all it says. It says you pick up these elements of space and you can think of these edges, these hyperedges as being relations between elements in space. You might pick up these two relations between elements in space. And we're not saying where those elements are or what they are, but every time there's a certain arrangement of elements in space, then arrangement in the sense of the way they're connected, then we transform it into some other arrangement.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, to maintain the infrastructure of our universe is a lot of work. We are merely riding little tiny things on top of that infrastructure. But you were just starting to talk a little bit about, we talked about space, that represents all the stuff that's in the universe. The question is, what does that stuff do? And for that, we have to start talking about time and what is time and so on. And what is the rule?”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So it turns out so far in one rough estimate of this, or everything that we care about in the universe is only one part in 10 to the 120 of what's actually going on. The vast majority of what's happening is purely things that maintain the structure of space. In other words, the things that are the features of space that are the things that we consider notable, like the presence of particles and so on, that's a tiny little piece of froth on the top of all this activity that mostly is just intended to mostly, I can't say intended. There's no intention here that just maintains the structure of space.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Talk about time in a second. Let's just, I mean, on the subject of space, there's this question of kind of what is this hypergraph. It represents space and it represents everything that's in space. The features of that hypergraph, you can say certain features in this part we do know, certain features of the hypergraph represent the presence of energy, for example, or the presence of mass or momentum. And we know what the features of the hypergraph that represent those things are. But it's all just the same hypergraph. So one thing you might ask is, you know, if you just look at this hypergraph and you say, and we're going to talk about sort of what the hypergraph does, but if you say how much of what's going on in this hypergraph is things we know and care about like particles and atoms of electrons and all this kind of thing, and how much is just the background of space?”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Mathematically, this sort of twisted knotted thing, that's the core of an electron. This thing over there that has this different form, that's something else.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That's correct. That's correct. So then, so, okay, so the first question, the first idea of these models of ours is space is made of these connected sort of atoms of space. The next idea is space is all there is. There's nothing except for this space. So in traditional ideas in physics, people have said there's space. It's kind of a background. And then there's matter, all these particles, electrons, all these other things, which exist in space, right? But in this model, one of the key ideas is there's nothing except space. So in other words, everything that exists in the universe is a feature of this hypergraph. So how can that possibly be? Well, the way that works is that there are certain structures in this hypergraph where you say that little twisty knotted thing, we don't know exactly how this works yet, but we have sort of idea about how it works.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That is the simplest case of a basic structure. Actually, it tends to be better to think about hypergraphs. So a hypergraph is just, instead of saying there are connections between pairs of things, we say there are connections between any number of things. So there might be ternary edges. So instead of just having two points are connected by an edge, you say three points are all associated with a hyperedge, are all connected by a hyper edge. That's just at some level that's a detail. It's a detail that happens to make the, for me, sort of in the history of this project, the realization that you could do things that way broke out of certain kinds of arbitrariness that I felt that there was in the model before I had seen how this worked.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That thing, yeah, right Even though the individual point doesn't know anything, it just knows what its neighbors are, on a large scale, it can be described by saying, oh, it looks like it's this grid, zoomed out grid. You can say, well, you can describe these different points by saying they have certain positions, coordinates, et cetera. Now, in the sort of real setup, it's more complicated than that. It isn't just a square grid or something. It's something much more dynamic and complicated, which we'll talk about. So the first idea, the first key idea is what's the universe made of? It's made of atoms of space basically with these connections between them. What kind of connections do they have? Well, so the simplest kind of thing you might say is we've got something like a graph where every atom of space where we have these edges that go between these connections that go between atoms of space. We're not saying how long these edges are just saying.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, right, right. So the point is, but there are cases where there are. So, for example, let's just imagine you have a square grid. And at every point on the grid, you have one of these atoms of space. And it's connected to four other atoms of space on the northeast, southwest corners. There you have something where if you zoom out from that, it's like a computer screen.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“But this thing about continuity arising from discrete systems is in today's world is actually not so surprising. I mean, your average computer screen, right? Every computer screen is made of discrete pixels, yet we have the idea that we're seeing these continuous pictures. I mean, the fact that on a large scale continuity can arise from lots of discrete elements, this is at some level unsurprising.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So, I mean, we don't know exactly the size, but maybe 10 to the minus, maybe around 10 to the minus 100 meters. So the size of to give a comparison, size of a proton is 10 to the minus 15 meters. And so this is something incredibly tiny compared to that.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, yeah, right. We know which point is connected to which other points, 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 what seems like continuous space? Well, the answer is by the time you have 10 to the 100 of these things, 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.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So now, what does that mean? So it means what is space then? So in our models, the basic idea is you say there are these sort of atoms of space. There are these points that 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 all we have is the friend network, so to speak. We don't have people's physical addresses. All we have is the friend network of these points”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“It's not right. It's not right. 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.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That's what continuous means. That's what Newton invented calculus to describe these kind of continuous small variations and so on. That's kind of a fundamental idea from Euclid on. That's been a fundamental idea about space.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“No, I don't think a 3D is fundamental at all, actually. I think that 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 the 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 continues.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes. And that means that so, you know, the mathematical theory is 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 just sort of background theater on which the universe operates.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“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 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.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“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, Euclid, who kind of wrote down the original kind of axiomatization of geometry back in 300 BC or so, his very first definition, he says, a point is that which has no part. A point is this indivisible infinitesimal thing. 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 pick any point we want 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 sort of a starting point for what I've done is to think of space.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So the question is then what is the universe made of? That'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 just turn out not to be right. And the most important assumption is that space is a continuous thing. That is that you can, if you say, let's pick a point.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source