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

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“It is very nice. It's very beautiful. It's so clean. I mean, it's really, you know, it tells one, okay, so anyway, so then this Branchill space has this sort of map of the entanglements between quantum states. So in physical space, so you can say”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“But what you get is by making the slice, what you call it Branchial space, the space of branches. And in this branchial space, you have a graph that represents the relationships between these quantum states in Branchell space. You have this notion of distance in Branchhill space.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, but then, okay, so the important thing that you are quickly picking up on is that what matters is kind of how these leaves are related to each other. So a good way to tell how leaves are related is just to say on the step before do they have a common ancestor. So two leaves might be, they might have just branched from one thing, or they might be far away, you know, way, far apart in this graph where to get to a common ancestor, maybe you have to go all the way back to the beginning of the graph, all the way back to the beginning.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Then we're asking, and okay, we take the slice, this slice represents each of these different paths corresponds to a different quantum possibility for what's happening. When we take the slice, we're saying, What are the set of quantum”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So that idea, okay, so then. So that's one thing, and that's closely related to the sort of objectivity in quantum mechanics, the fact that we believe definite things happen. It's because although there are all these different paths, in some sense, because of causal invariance, they all imply the same thing. I'm cheating a little bit and saying that, but that's roughly the essence of what's going on. Okay, next thing to think about is you have this multi-weight graph. It has all these different possible things that are happening. we ask this multi-way graph is sort of evolving with time. Over time it's branching, it's merging, it's doing all these things. The question we can ask is if we slice it at a particular time, what do we see? And that slice represents in a sense something to do with the state of the universe at a particular time. So in other words, we've got this multi-way graph of all these possibilities.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“A little bit. Let me explain a couple of things first. The structure of quantum mechanics is mathematically quite complicated. One of the features, let's see, how to describe this. Okay, so first point is there's this multi-way graph of all these different paths of things that can happen in the world. And the important point is that you can have branchings and you can have mergings. Okay, so this property turns out causal invariance is the statement that the number of mergings is equal to the number of branchings. So, in other words, every time there's a branch, eventually there will also be a merge. In other words, every time there were two possibilities for what might have happened, eventually those will merge.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“You know, all this mathematical structure and so on. How do you get that mathematical structure? Okay, a couple of things to say. So quantum mechanics is actually, in a sense, two different theories glued together. Quantum mechanics is the theory of how quantum amplitudes work that more or less give you the probabilities of things happening. And it's the theory of quantum measurement, which is the theory of how we actually conclude definite things because the mathematics just gives you these quantum amplitudes, which are more or less probabilities of things happening, but yet we actually observe definite things in the world. Quantum measurement has always been a bit mysterious. It's always been something where people just say, well, the mathematics says this, but then you do a measurement and the philosophical arguments about what the measurement is, but it's not something where there's a theory of the measurement.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So TikTok toe, you start off with some board that knows everything is blank, and then somebody can put down an X somewhere, an O somewhere. And then there are different possibilities. At each stage, there are different possibilities. And so you build up this multi-way graph of all those possibilities. Now, notice that even in Tic Tac-Toe, you have the feature that there can be something where you have two different things that happen and then those branches merge because you end up with the same configuration of the board, even though you got there in two different ways. So the thing that sort of inevitable feature of our models is that just like quantum mechanics suggests, definite things don't happen. Instead, you get this whole multi-way graph of all these possibilities. Okay, so then the question is, okay, so that's sort of a picture of what's going on. Now you say, okay, well, quantum mechanics has all these features of...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, for example, you go this way, go that way. Those are two different edges in the multiway graph. And you're building up this set of possibilities. So actually, like, for example, I just made the one, the multi-way graph for tic-tac-toe.”
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, the key idea of quantum mechanics, the typical interpretation is classical physics says a definite thing happens. Quantum physics says there's this whole set of paths of things that might happen, and we are just observing some overall probability of how those paths work. Okay, so when you think about our hypergraphs and all these little updates that are going on, there's a very remarkable thing to realize, which is If you say, well, which particular sequence of updates should you do? Say, well, it's not really defined. You can do any of a whole collection of possible sequences of updates. Okay, that set of possible sequences of updates defines yet another kind of graph that we call a multi-way graph. And a multi-way graph just is a graph where at every node there is a choice of several different possible things that could happen.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“There's a bunch of sort of bulk information about the world, the thing that I'm excited about last few days is the idea of fermions versus bosons, fundamental idea that, I mean, the reason we have matter that doesn't just self-destruct is because of the exclusion principle that means that two electrons can never be in the same quantum state.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Good question. I mean, there's probably certain things. You know, the fact that we can deduce anything, okay, the question is, how deep does the reducibility go? And I keep on being surprised it's a lot deeper than I thought. One of the things is that That there's a question of sort of how much of the whole of physics do we have to be able to get in order to explain certain kinds of phenomena? Like, for example, if we want to study quantum interference, do we have to know what an electron is? Turns out I thought we did. Turns out we don't. I thought to know what energy is. We would have to know what electrons were. We don't.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Is a question of how many sort of atoms of space might there be? Maybe 10 to the 400. We don't know exactly how to estimate these numbers. I mean, this is based on some, I would say somewhat rickety way of estimating things. When they start to be able to be experiments done, if we're lucky, there will be experiments that can actually nail down some of these numbers.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, right. So because it turns out in the end, there will be 10 to the 500 or from language operations per second, I think. I think it's of that order. So that's the scale of the computation.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“The inevitable features of having a rule that has only a finite amount of information in the rule. So long as you have a rule that only involves a bounded amount, a limited amount of only involving a limited number of elements, limited number of relations, it is inevitable that there are these speed constraints. We knew about the one for speed of light. We didn't know about the one for maximum entanglement speed, which is actually something that is possibly measurable, particularly in black hole systems and things like this. But anyway, this is long story short. You're asking what the processing specs of the universe of the sort of computation of the universe. There's a question of even what are the units of some of these measurements. So the units I'm using are Wolfram language instructions per second because you've got to have some quad computation that you're doing.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, the ratio of the elementary distance to the elementary time is the speed of light. Perfect. And so there's another, there are two other levels of this. So there is a thing which we can talk about, which is the maximum entanglement speed, which is a thing that happens at another level in this whole sort of story of how these things get constructed. That's a sort of maximum speed in the space of quantum states, just as the speed of light is a maximum speed in physical space. This is a maximum speed in the space of quantum states. There's another level, which is associated with what we call roule space, which is another one of these maximum speeds. We'll get to this.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“It doesn't matter. But what does matter is the ratio, what we can, the ratio of the spatial distance and this hypergraph to this moment of time, again, that's an arbitrary thing, but we measure that in meters per second, for example, and that ratio is the speed of light.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, it doesn't matter what it is because we could be it could be slow, it's just a number which we use to convert that to second, so to speak, because we are experiencing things and we say this amount of time has elapsed 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
“The specs underneath, so I have an estimate. So the question is what are the units? So we've got these different fundamental constants about the world. So one of them is the speed of light, which is the, so the thing that's always the same in all these different ways of thinking about the universe is the notion of time, because time is computation. And so there's an elementary time, which is sort of the amount of time that we ascribe to elapsing in a single computational step. So that's the elementary time. So then there's an elementary”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes. But the layers are, you know, you might be asking me how do we get the difference between fermions and bosons, the difference between particles that can be all in the same state and particles that exclude each other. Last three days, we've kind of figured that out. And it's very interesting, it's very cool, and it's very”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Small objects, and there's 10 to the 120 something. Yeah, right. It is conceptually deep. And one of the things that's happening sort of structurally in this project is there were ideas, there's another layer of ideas, there's another layer of ideas to get to the different things that correspond to physics. They're just different layers of ideas. And they are, you know, it's actually probably, if anything, getting harder to explain this project because I'm realizing that the fraction of way through that I am so far and explaining this to you is less than, you know, it might be because we know more now. Every week, basically, we know a little bit more.”
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 actually, I did try to estimate that, and we actually have to go a couple more stages before we can really get to that answer because we're talking about this thing. This is what happens when you build these abstract systems and you're trying to explain the universe that quite a number of levels deep, so to speak. But the...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“How long has it taken me to figure stuff out? But back in the 1980s, I worked on trying to make up languages for parallel computation. I thought about doing graph rewriting. I thought about doing these kinds of things, but I couldn't see how to actually make the connections to actually do something useful. I think now physics is kind of showing us how to make those things useful. And so my guess is that in time, we'll be talking about, you know, we do parallel programming, we'll be talking about programming in a certain reference frame, just as we think about thinking about physics in a certain reference frame. It's a certain coordination of what's going on. We say, we're going to program in this reference frame. Oh, let's change the reference frame to this reference frame. And then our program will seem different and we'll have a different way to think about it, but it's still the same program underneath.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I mean, I was also thinking about look, the fact is, you know, I've spent much of my life as a language designer, right? So I can't possibly not think about, you know, what does this mean for designing languages for parallel computation? In fact, another thing that's one of these I'm always embarrassed at.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Absolutely. No, I mean, you know, what's eventual consistency in distributed databases is essentially the causal invariance idea So that's, but”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, causal invariance is the built in protection. Causal invariance is what means that even though things happen in different orders, it doesn't matter in the end.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“The ways that we are simulating it, we're just starting to be able to use that deep parallelism to be able to be more efficient in the way that we simulate things. But in fact, the structure of the model itself allows us to think about parallel computation in different ways. And one of my realizations is that it's very hard to get in your brain how you deal with parallel computation. And you're always worrying about if multiple things can happen at different on different computers at different times. Oh, what happens if this thing happens before that thing and we've really got, you know, we have these race conditions where something can race to get to the answer before another thing and you get all tangled up. Because you don't know which thing is going to come in first. And usually when you do parallel computing, there's a big obsession to lock things down to the point where you've had locks and mutexes and God knows what else where you've arranged it so that there can only be one sequence of things that can happen.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, first comment is these models seem to give one a lot of intuition about distributed computing, a lot of different intuition about how to think about parallel computation. And that particularly comes from the quantum mechanics side of things, which we didn't talk about much yet. But the question of what, given our current computer hardware, how can we most efficiently simulate things, that's actually partly a story of the model itself, because the model itself has deep parallelism in it.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Turns out that our model gives you a direct way to do numerical relativity. So in other words, instead of saying you start from these continuum equations for Einstein, you break them down into these discrete things, you run them on a computer, you say, we're doing it the other way around. We're starting from these discrete things that come from our model, and we're just running big versions of them on the computer. What we're saying is, and this is how things will work. So the way I'm calling this is proof by compilation, so to speak. In other words, you're taking something where we've got this description of a black hole system, and what we're doing is we're showing that what we get by just running our model Agrees with what you would get by doing the computation from the Einstein equations.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, it's just the mathematical structure kind of ends up running right into computational irreducibility and you end up with a bunch of difficulty there. But here's the way that we're getting really confident that we know completely what we're talking about, which is when people study things like black hole mergers using Einstein's equations, what do they actually do? Well, they actually use mathematica a whole bunch to analyze the equations and so on. But in the end, they do numerical relativity, which means they take these nice mathematical equations and they break them down so that they can run them on a computer and they break them down into something which is actually a discrete approximation to these equations. Then they run them on a computer, they get results, then you look at the gravitational waves and you see if they match.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And the limits will definitely work the way we think they work, and we can do all kinds of computer experiments. It's just a hard derivation.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Oh, yeah, we're with her. Yes. And here's the way that we're how we're really, really going to know we've arrived. We have the mathematical derivation. It's all fine. But mathematical derivations, okay, so one thing that's sort of, you know, we're taking this limit of what happens when the limit, you have to look at things which are large compared to the size of an elementary length, small compared to the whole size of the universe, large compared to certain kinds of fluctuations, blah, blah, blah. There's a tower of many, many of these mathematical limits that have to be taken. So if you're a pure mathematician saying, where's the precise proof? It's like, well, there are all these limits. We can try each one of them computationally and we can say, yeah, it really works. But the formal mathematics is really hard to do. I mean, for example, in the case of deriving the equations of fluid dynamics from molecular dynamics, that derivation has never been done.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, I didn't yet get to, so I got as far as special relativity and equals mc squared. The one last step is in general relativity, the final connection is energy, mass cause curvature in space. And that's something that when you understand this interpretation of energy and you kind of understand the correspondence to curvature in hypergraphs, then you can finally sort of the big final answer is you derive the full version of Einstein's equations for space-time and matter. And that's...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Mass is associated with kind of the energy that does not cause you somehow propagate through time. One of the things that was not obvious in the usual formulation of special relativity is that space and time are connected in a certain way. Energy momentum and momentum are also connected in a certain way. The fact that the connection of energy to momentum is analogous to the connection to space between space and time is not self-evident in ordinary relativity. It is a consequence of the way this model works. It's an intrinsic consequence of the way this model works. And it's all to do with that with unraveling that connection that ends up giving you this relationship between energy and, well, energy, momentum, mass, they're all connected.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, I mean, this one is, look, roughly what's happening. That derivation is actually rather easy. And everybody, and I've been saying we should pay more attention to this derivation because it's such, you know, because people care about this one. And everybody says, it's just easy. It's easy.”
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 amount of activity that kind of remains in one place in the hypergraph corresponds to energy. The amount of activity that is kind of where an activity here affects an activity somewhere else corresponds to momentum. And so one of the things that's kind of cool is that I'm trying to think about how to say this intuitively. The mathematics is easy, but the intuitive version, I'm not sure. But basically the way that things sort of stay in the same place and have activity is associated with rest mass. And so one of the things that you get to derive is E equals MC squared. That is a consequence of this interpretation of energy in terms of the way the causal graph works, which is the whole thing is sort of a consequence of this whole story about updates and hypergraphs and so on.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Somewhat arbitrary because you can deform that if you're going at a different speed and special activity, you tip those things, there are different kinds of deformations, but only certain deformations are allowed by the structure of the causal graph. Anyway, be there as it may. The basic point is there is a way of figuring out, you know, you say what is the energy associated with what's going on in this hypergraph? And the answer is there is a precise definition of that and it is the formal way to say it is it's the flux of causal edges through space like hypersurfaces, the slightly less formal way to say it, it's basically the amount of activity. See, the reason it gets tricky is you might say it's the amount of activity per unit volume in this hypergraph, but you haven't defined what volume is. So it's a little bit that you have to be able to this hypersurface.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Is basically well, intuitively, it's the amount of activity in these hypergraphs and the way that that remains over time. So a little bit more formally, you can think about this causal graph as having these edges that represent causal relationships. You can think about, oh boy, there's one more concept that we didn't get to. What's that? The notion of space like hypersurfaces. So it's not as scary as it sounds. It's a common notion in general. The notion is you are defining what is a possibly... Where in space time might be a particular moment in time? So in other words, what is a consistent set of places where you can say this is happening now, so to speak. And you make this series of slices through the space-time, through this causal graph to represent sort of what we consider to be successive moments in time.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Gmu equals zero, which is the more mathematical version of Einstein's equations. It's a statement of the thing called the Ricci tensor is equal to zero. That's Einstein's equations for the vacuum. So we get that as a result of this model. But big footnote because all the matter in the universe is the stuff we actually care about. The vacuum is not stuff we care about. So the question is, how does matter come into this? And for that, you have to understand what energy is in these models. And one of the things that we realized last year was that there's a very simple interpretation of energy in these models. And energy”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“The structure of space has to be such that although the cross sectional area of this bundle may, although the actual shape of the cross-section may change, the cross-sectional area does not. That's a version. That's the most simple-minded version of Army New Minus a half hour.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Finite dimensional computational irreducibility and causal invariance, then it follows that the large-scale structure will follow Einstein's equations. Now, let me again qualify that a little bit more. There's a little bit more complexity to it. So Einstein's equations in their simplest form apply to the vacuum, no matter just the vacuum. And they say, in particular, what they say is if you have, so there's this term GD sick, that's a term that means shortest path, comes from measuring shortest paths on the earth. So you look at a bunch of a bundle of JD6, a bunch of shortest paths. It's like the paths that photons would take between two points. Then the statement of Einstein's equations is basically a statement about that as you look at a bundle of GD6.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, it's an important thing to know. I would love to know the answer to that. But it gets a little bit more complicated because, for example, it's very possibly the case that in our physical universe, that the universe started infinite dimensional and it only, as the Big Bang, it was very likely infinite dimensional. And as the universe sort of expanded and cooled, its dimension gradually went down. And so one of the bizarre possibilities, which actually their experiments you can do to try and look at this, the universe can have dimension fluctuations. So in other words, we think we live in a three-dimensional universe, but actually there may be places where it's actually 3.01 dimensional or where it's 2.99 dimensional. And it may be that in the very early universe, it was actually infinite dimensional, and it's only a late stage phenomenon that we end up getting three-dimensional space.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“For example, so in a tree, you start from one root of the tree. Doubles again, doubles again, doubles again. And that means if you ask the question, starting from a given point, how many points do you get to? Remember like a circle, you get to r squared with a two there. On a tree, you get to, for example, 2 to the r. It's exponential dimensional, so to speak, or infinite dimensional.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“No, it doesn't matter what the rules are. It doesn't. So long as they have causal invariance and computational irreducibility and they lead to finite dimensional space.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Determining the size, just like the area of a circle is roughly pi r squared, so it goes up like r squared. The two is because it's in two dimensions. But when that circle is drawn on a big sphere, the actual formula is pi r squared times 1 minus r squared over a squared and some coefficient. So in other words, there's a correction, and that correction term, that gives you curvature. And that correction term is what makes this hypergraph correspond, have the potential to correspond to curved space. The next question is, is that covature? Is the way that coverture works, the way that Einstein's equations of general relativity, you know, is it the way they say it should work? And the answer is yes. And so, how does that work? I mean, the”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, that's what this is about. What this is about is you have your hypergraph, it's got a trillion nodes in it. What is it roughly like? Is it roughly like a grid, a two-dimensional grid? Is it roughly like all those nodes are arranged online? What's it roughly like? And there's a pretty simple mathematical way to estimate that by just looking at this thing I was describing, this sort of the size of a ball that you construct in the hypergraph. You just measure that. You can just compute it on a computer for a given hypergraph. And you can say, oh, this thing is wiggling around, but it's roughly corresponds to two or something like that. It roughly corresponds to 2.6 or whatever. So that's how you have a notion of dimension in these hypergraphs. Curvature is something a little bit beyond that. If you look at the how the size of this ball increases as you increase its radius, curvature is a correction to the size increase associated with dimension. It's a sort of a second order term.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Okay, so first I have to explain. What I was explaining is first thing you have to have is a notion of dimension. You don't get to talk about curvature of things. If you say, oh, it's a curved line, but I don't know what a line is yet.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Special relativity is about the relationship of time to space. General relativity is about curvature in this space represented by this hypergraph.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Expect from the formula pi r squared has a little correction term that depends on the ratio of the size of the circle to the radius to the earth. So it's the same basic thing, allows you to measure from one of these hypergraphs what is its effective curvature”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“It's just a piece of mathematics. It doesn't rely on, you have to make certain assumptions that you have to say there's enough randomness in the way the molecules bounce around, that certain statistical averages work, et cetera, et cetera, et cetera. Okay, it is a very similar derivation to derive, for example, the Einstein equations. So the way that works roughly, the Einstein equations are about curvature of space. Curvature of space, I talked about sort of how you can figure out dimension of space. There's a similar kind of way of figuring out if you just sort of say you're making a larger and larger ball or if you draw a circle on the surface of the earth, for example, you might think the area of a circle is pi r squared, but on the surface of the earth, because it's a sphere, it's not flat, the area of a circle isn't precisely pi r squared. Does the circle get bigger? The area is slightly smaller than you would expect.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source