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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“So it's a, but I mean, the thing just to give a sketch of how that works. So category theory is an attempt to idealize, it's an attempt to sort of have a formal theory of mathematics that is at a sort of higher level than mathematics. It's where you just think about these mathematical objects and these categories of objects and these morphisms, these connections between categories. Okay, so it turns out the morphisms and categories at least weak categories are very much like the paths in our hypergraphs and things. And it turns out, again, this is where it all gets crazy. I mean, the fact that these things are connected is just bizarre. So category theory, our causal graphs are like second order category theory.”
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 statement of it that's fairly accessible. I mean, the statement of it is basically it says things which are equivalent can be considered to be identical.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Think there's some sort of connections between the way that observers work in physics and the way that the axiom systems of mathematics are set up to make mathematics be doable in that kind of way. And so, in other words, in particular, I think there is an analog of causal invariance, which I think is, and this is again in sort of the upper reaches of mathematics and stuff that... It's a thing, there's this thing called homotopy type theory, which is an abstract came out of category theory, and it's sort of an abstraction of mathematics. Mathematics itself is an abstraction, but it's an abstraction of the abstraction of mathematics. And there is a thing called the univalence axiom, which is a sort of a key axiom in that set of ideas. And I'm pretty sure the univalence axiom is equivalent to causal invariance.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Trajectory, so to speak. You're not just parachuting in from anywhere. You're following Lewis and Clark or whatever. You're actually going the path. And the fact that you are constrained to go along that path is the reason you don't end up with. So often you'll see a little piece of undecidability and you'll avoid that part of the path. But that's basically the story of why human mathematics has seemed to be doable. It's a story of exploring these paths that are by their nature, they have been constructed to be paths that can be followed. And so you can follow them further. Now, you know, why is this relevant to anything? So, okay, so here's the belief. The fact that human mathematics works that way is”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, why do we not just get lost in undecidability all the time And here's another fact in doing computer experiments and doing experimental mathematics, you do get lost in that way. When you just say, I'm picking a random integer equation, does it have a solution or not? And you just pick it at random without any human sort of path getting there. Often it's really, really hard. It's really hard to answer those questions when you just pick them up random from the space of possibilities. What I think is happening is, and that's a case where you just fell off into this ocean of sort of irreducibility and so on, what's happening is human mathematics is a story of building a path. You started off, you're always building out on this path where you are proving things. You've got this proof trajectory, and you're basically that human mathematics is the sort of the exploration of the world along this proof truth.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Absolutely. Yeah. So the notion of Godes in mathematical space is the notion of shortest proofs in mathematical space. And human mathematicians do not find shortest paths. Nodo automated theorem provers, but the fact and by the way, this stuff is so bizarrely connected. I mean, if you're into automated theorem proving, there are the so-called critical pair lammas and automated theorem proving. Those are precisely the branch pairs in multi-weight graphs. Let me just finish on the why mathematics is doable.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“It could have been that Formats Law's theorem is undecidable. It turned out it had a proof. It's a long, complicated proof. The twin prime conjecture might be undecidable. The Riemann hypothesis might be undecidable. These things might be the axioms of mathematics might not be strong enough to reach those statements. It might be the case that depending on what axioms you choose, you can either say that's true or that's not true.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Because of computational irreducibility Because what happens is to know what's true, and this is this whole story about the path you have to follow and how long is the path and godel's theorem is the statement there could be that the path is not a bounded length, but the fact that the path is not always compressible to something tiny is a story of computational irreducibility. So that's why math is hard. Now the next question is, why is math doable? Because it might be the case that most things you care about don't have finite length paths. Most things you care about might be things where you get lost in the sea of computational irreducibility and worse undecidability. That is, there's just no finite length path that gets you there. Why is mathematics doable? Girdle proved his incompleteness theorem in 1931. Most working mathematicians don't really care about it. They just go ahead and do mathematics, even though it could be that the questions they're asking are undecidable.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. Yeah. Well, logic happens to be a particular special case that does have certain simplicity to it. But general mathematics, even arithmetic, already doesn't have the simplicity that logic has”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So, for example, here's an example of a thing that I realized. So, one of the surprising things about, well, the two surprising facts about math. One is that it's hard and the other is that it's doable. So, first question is why is math hard? You know, you've got these axioms, they're very small. Why can't you just solve every problem in math easily?”
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 33 steps from the longest path in the graph is 33 steps. So that's a 33-step path you have to follow to go from the axioms according to Euclid's proofs to the statement there are five platonic solids. So, okay, so then the question is, what does it mean? If you have this map, okay, so in a sense, this meta-mathematical space is the infrastructural space of all possible theorems that you could prove in mathematics. That's the geometry of metamathematics. There's also the geography of mathematics. That is where did people choose to live? In space. And that's what, for example,”
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 actually map out, and I actually did this 20 years ago, but I've done it more seriously now, you can map out the theorem dependency of those 465 theorems. So from the axioms, you grow this graph. It's actually a multi-way graph, of how all these theorems get proved from other theorems. And so you can ask questions about you can ask things like, what's the hardest theorem in Euclid? The answer is the hardest theorem is that there are five platonic solids. That turns out to be the hardest theorem in Euclid. That's actually his last theorem in all his books. That's the final.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Well, so here's what it is this is mathematics in bulk. So human mathematicians have made a few million theorems. They published a few million theorems. But imagine the infinite future of mathematics. Apply something to mathematics that mathematics likes to apply to other things. Take a limit. What is the limit of the infinite future of mathematics? What does it look like? What is the continuum limit of mathematics? What is the, as you just fill in more and more and more theorems, what does it look like? What does it do? What kinds of conclusions can you make? So, for example, one thing I've just been doing is taking Euclid. So Euclid, very impressive. He had 10 axioms. He derived 465 theorems. Okay, his book, you know, that was the sort of defining book of mathematics for 2000 years.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so what happens there is that Girdell's theorem is basically saying that there are paths of infinite length. That is, that there's no upper bound. If you know these two things, you say, I'm trying to get from here to here. How long do I have to go? You say, well, I've looked at all the parse of length 10. Somebody says, that's not good enough. That path might be of length a billion. And there's no upper bound on how long that path is. And that's what leads to the incompleteness theorem. So, I mean, the thing that is kind of an emerging idea is you can start asking, what's the analog of Einstein's equations in metamathematical space? What's the analog of a black hole in metaphematical space?”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“You basically build up a multiway graph, and a proof is a path through the multiway graph that goes from one thing to another thing. The path tells you how did you get from one thing to the other thing. It's the story of how you got from this to that. The theorem is the thing at one end is equal to the thing at the other end. The proof is the path you go down to get from one thing to the other.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“A computation because in mathematics, what you're interested in is a proof, and the proof says from here, you can use from this expression, for example, you can use these axioms to get to this other expression. So that proves these two things are equal. Okay, so we can begin to see how this is going to work. What happened is there are paths in metamathematical space. So what happens is each two different ways to look at it, you can just look at it as mathematical expressions or you can look at it as mathematical statements, postulates, or something. But either way, you think of these things and they are connected by these axioms. So in other words, you have some fact or you have some expression, you apply this axiom, you get some other expression. And in general, given some expression, there may be many possible different expressions you can get.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So here's what his okay. So, what is mathematics? Mathematics sort of at a lowest level, one thinks of mathematics as you have certain axioms, you say things like x plus y is the same as y plus x. That's an axiom about addition. And then you say we've got these axioms. And from these axioms, we derive all these theorems that fill up the literature of mathematics, the activity of mathematicians is to derive all these theorems. Actually, the axioms of mathematics are very small. You can fit, you know, when I did my new kind of science book, I fit all of the standard axioms of mathematics on basically a page and a half. It's not much stuff. It's like a very simple rule from which all of mathematics arises. The way it works, though, is a little different from the way things work in sort of”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“With our physical universe. Yeah, right. I mean, the fact that our physical universe is a computation and that we can have discussions like the theory of the physical universe is the same kind of a theory as the p versus mp problem and so on is really, I think that's really interesting. And the fact that, well, okay, so this kind of brings me to one more thing that I have to, in terms of this sort of unification of different ideas, which is metamathematics.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And it's also a physicalization of algorithmic information. And I think there's probably a connection between, I mean, there's probably a connection between the notion of energy and some of these things, which again, I hadn't seen all this coming. I've always been a little bit resistant to the idea of connecting physical energy to things in computation theory, but I think that's probably coming.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“There will be a physicalization of the idea of algorithmic information and that, okay, this is again a little bit bizarre, but so I mentioned that there's the speed of light, maximum speed of information transmission in physical space. There's a maximum speed of information transmission in Branchield space, which is a maximum entanglement speed. There's a maximum speed of information transmission in Roule space, which has to do with a maximum speed of translation between different description languages. And again, I'm not fully wrapped my brain around this one.”
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. That's a systematic way of doing it. Right. So the question is in the space of all possible intelligences, how do you think about the distance between description languages? For one intelligence versus another. And needless to say, I have thought about this. And I don't have a great answer yet, but I think that's a thing where there will be things that can be said. And there'll be things that where you can sort of start to characterize what is the translation distance between this”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“A use of inside it. Are you thinking about it? Do you have sort of a story you're telling yourself about it? And the weather could have a story it's telling itself about what it's doing. We just, it's utterly incoherent with the stories that we tell ourselves based on how our brains work.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Just not Here's the thing. Intelligence is everywhere. The fact this idea that there's this notion of, oh, there's going to be this amazing extraterrestrial intelligence and it's going to be this unique thing. It's just not true. It's the same thing. I think people will realize this about the time when people decide that artificial intelligence is a kind of just natural things that are like human intelligences. They'll realize that extraterrestrial intelligences or intelligences associated with physical systems and so on, it's all the same kind of thing.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That's fascinating, they can end up with a description of the universe that is utterly, utterly incoherent with ours. And that's also interesting in terms of how we think about intelligence, the nature of intelligence, and so on. I'm fond of the quote, you know, the weather has a mind of its own because these are sort of computationally that system is computationally equivalent to the system that is our brains and so on. And what's different is we don't have a way to understand what the weather is trying to do, so to speak. We have a story about what's happening in our brains. We don't have a sort of connection to what's happening there.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“I used to think, okay, imagine the aliens, imagine the extraterrestrial intelligence thing. At least they experience the same physics And now I've realized this isn't true.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Can just say, Oh, I know the answer. It's this immediately. What this is saying is the universe is not a hypercomputer, it's not simpler than an ordinary Turing machine type computer. It's exactly like an ordinary Turing machine type computer. And so that's in the end the sort of net, net conclusion is that's the thing that is the sort of the hard immovable fact about the universe. That's sort of the fundamental principle of the universe is that it is computational and not hypercomputational and not sort of infra-computational. It is this level of computational ability. And it kind of has, and that's sort of the core fact. But now, you know, this idea that you can have these different kind of rule reference frames, these different description languages for the universe, it makes me...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“About the physics as running with different underlying rules as if different underlying computers were running them. But because of computation universality, or more accurately because of this principle of computational equivalence thing of mine, they are these things are ultimately equivalent. So the only thing that is the ultimate fact about the universe, the ultimate fact that doesn't depend on any of these, you know, we don't have to talk about specific rules, et cetera, et cetera, et cetera. The ultimate fact is the universe's computational and it is the things that happen in the universe are the kinds of computations that the principle of computational equivalence says should happen. Now, that might sound like you're not really saying anything there, but you are because you could in principle have a hypercomputer that things that take an ordinary computer an infinite time to do, the hypercomputer”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, yes, but okay, so here's another point. So this is again these are a little bit mind twisting in some ways, but another thing that's sort of we know from computation is this idea of computation universality, the fact that given that we have a program that runs on one kind of computer, we can as well convert it to run on any other kind of computer. We can emulate one kind of computer with another. So that might lead you to say, well, you think you have the rule for the universe, but you might as well be running it on a Turing machine because we know we can emulate any computational rule on any kind of machine. And that's essentially the same thing that's being said here. That is that what we're doing is we're saying these different interpretations of physics correspond to essentially running physics on different underlying thinking.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“That's why we are attributing this rule to the universe. So in other words, when we say, why is it this rule and not another, the answer is just, you know, shine the light back on us, so to speak. It's because of the reference frame that we've picked in our way of understanding what's happening in this sort of space of all possible rules 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
“But what you see could be completely different if you pick different reference frames. You essentially have a different description language for describing the universe. Okay, so how does this really mean in practice? So imagine there's us. We think about the universe in terms of space and time, and we have various kinds of description models and so on. Now let's imagine the friendly aliens, for example. How do they describe their universe? Well, you know, our description of the universe probably is affected by the fact that we are about the size we are, you know, a meter-ish tall, so to speak. We have brain processing speeds of about the”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Going to be an observer embedded in that system, and I'm going to try and make sense of what's going on in the system. And to do that, I essentially am picking a reference frame. And that turns out to be, well, okay, so the way this comes out essentially is the reference frame you pick is the rule that you infer is what's going on in the universe, even though all possible rules are being run, although all those possible rules are in a sense giving the same answer because of causal invariance.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, they're a little bit simpler. So if you look at these extreme non deterministic Turing machines, you're mapping out all the possible non-deterministic paths that the Turing machine can follow. And if you ask the question, can you reach so a deterministic Turing machine follows a single path? The non-deterministic Turing machine fills out this whole sort of ball of possibilities. And so then the P versus MP problem ends up being questions about, and we haven't completely figured out all the details of this, but it's basically has to do with questions about the growth of that ball relative to what happens with individual paths and so on. So essentially there's a geometrization of the P versus MP problem that comes out of this. That's a sideshow. The main event here is the statement that you can look at this multi-way graph where the branches correspond not just to different applications of a single rule, but to different applications of different rules. And that then that when you say, I'm”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, they're all. I mean, hypergraphs, that's another layer of complexity on this whole thing. You can think about these in transformations of hypergraphs, but Turing machines are a little bit of a...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, in a Turing machine It's like it says move left, move, you know, if it's a one, if it's a black square under the head, move left and write a green square. That's a rule.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Same thing a non deterministic Turing machine can have different choices that it makes at every step. And so, you know, you know this stuff, you probably teach this stuff. So a non-deterministic Turing machine has this set of branching possibilities, which is in fact one of these multi-way graphs. And in fact, if you say, imagine the extremely non-deterministic Turing machine, the Turing machine that can just do that takes any possible rule at each step, that is this Roule multi-way graph, the set of possible histories of that extreme non-deterministic Turing machine is a Roulet multi-way graph.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right. So, by the way, I mean, the mathematics that's connected to is the mathematics of higher category theory and groupoids and things like this, which I've always been afraid of, but now I'm finally wrapping my arms around it. But it's also related to computational complexity theory. It's also deeply related to the P versus NP problem and other things like this. Again, seems completely bizarre that these things are connected, but here's why it's connected. space of all possible, okay, so a Turing machine, very simple model of computation, you know, you just got this tape where you write down, you know, ones and zeros or something on the tape and you have this rule that says you change the number, you move the head on the tape, etc. You have a definite rule for doing that. A deterministic Turing machine just does that deterministically, given the configuration of the tape, it will always do the”
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 thing that you get is this kind of rule multiway graph, this multiway graph that is a branching of rules as well as a branching of possible applications of rules. This thing has causal invariance. It's an inevitable feature that it shows causal invariance. And that means that you can take different reference frames, different ways of slicing this thing, and they will all, in some sense, be equivalent. If you make the right translation, they will be equivalent. So, okay. So the basic point here is”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Have no idea what it's like that Okay, so then I realized it's actually more bizarre than that. Okay, so we talked about multiway graphs. We talked about this idea that you take these underlying transformation rules on these hypergraphs and you apply them wherever the rule can apply, you apply it. And that makes this whole multi-way graph of possibilities. Okay, so let's go a little bit weirder. Let's say that at every place, not only do you apply a particular rule in all possible ways it can apply, but you apply all possible rules in all possible ways they can apply. So you say, that's just crazy. That's way too complicated. You're never going to be able to conclude anything. Okay. However, it turns out... Don't tell me there's”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“And then we're in this whole situation because let's say it's fairly simple. How did we come up the winners getting one of the simple possible universe rules? Why didn't we get some incredibly complicated rule? Why do we get one of the simpler ones? And that's a thing which, you know, in the history of science, the whole sort of story of Copernicus and so on was we used to think the Earth was the center of the universe, but now we find out it's not, and we're actually just in some, you know, random corner of some random galaxy out in this big universe. There's nothing special about us. So if we get universe number 317 out of all the infinite number of possibilities, how do we get something that small and simple? So I was very confused by this. And it's like, what are we going to say about this? How are we going to explain this? And I thought it might be one of these things where you just, you know, you can get it to the threshold and then you find out its rule number such and such.”
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 here's the big set of one of the conundrums that I'm kind of trying to deal with is let's say we think we found the rule for the universe and we say, here it is, you know, write it down. It's a little tiny thing. And then we say, gosh, that's really weird. Why did we get that one?”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Look, two things slowed me down. I mean, one thing that slowed me down was I couldn't figure out how to make it elegant. And that turns out hypergraphs were the key to that. And that I figured out about less than two years ago now. And the other, I mean, I think that was sort of a key thing. Well, okay, so the real embarrassment of this project. Is that the final structure that we have that is the foundation for this project is basically a kind of an idealized version, a formalized version of the exact same structure that I've used to build computational languages for more than 40 years. But it took me, but I didn't realize that, and you know”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“But I thought it was kind of inelegant. And the other piece of sort of personal history is obviously, I've spent my life as a computational language designer. And so the story of computational language design is a story of how do you take all these random ideas in the world and kind of grind them down into something that is computationally as simple as possible. And so, you know, I've been very interested in kind of simple computational frameworks for representing things and have ridiculous amounts of experience in trying to do that.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So what happens is what I had was, okay, so this is again, one always feels dumb after the fact. It's obvious after the fact. But so back in the early 1990s, I realized that using graphs as a sort of underlying thing underneath space and time was going to be a useful thing to do. I figured out about multiway systems. I figured out the things about general relativity. I'd figured out by the end of the 1990s. I always felt there was a certain inelegance because I was using these graphs and there were certain constraints on these graphs that seemed like they were kind of awkward. It was kind of like you can pick, it's like you couldn't pick any rule. It was like pick any number, but the number has to be prime. It was kind of like you couldn't, it was kind of an awkward special constraint. I had these trivalent graphs, graphs with just three connections from every node. But I discovered a bunch of stuff with that.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Right, right. I mean, you know, and the thing for me personally, the thing that's been quite interesting is I didn't expect this project to work in this way. And I, you know, but I had this sort of weird piece of personal history that I used to be a physicist and I used to do all this stuff. And I know the standard canon of physics. I knew it very well. And then I'd been working on this kind of computational paradigm for basically 40 years. And the fact that, you know, I'm sort of now coming back to trying to apply that in physics, it kind of felt like that journey was necessary.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Seems the foundations seem quite inaccessible, and they seem, you know, it seems like you can't possibly understand that. We've gone through seven academic generations and that's been this thing that's been difficult to understand for that long. It just can't be that simple.”
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 it's going to be as simple as that, but we'll see. I mean, this is the thing that, you know, this is the big sort of bizarre surprise is that, you know, because I learnt physics as probably, let's say, let's say a fifth generation in the sense that, you know, if you go back to the 1920s and so on, there were the people who were originating quantum mechanics and so on, maybe it's a little less than that. Maybe I was like a third generation or something. I don't know. But the people from whom I learnt physics were the people who had been students of the students of the people who originated the current understanding of physics. And we're now at probably the seventh generation of physicists or something from the early days of 20th century physics. And whenever a field gets that many generations deep.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yes, yes. Yes, right, exactly. You can have the so called belt trick, which is this way of taking an extended object, and you can see properties like spinners with that kind of extended object that would be very...”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“Yeah, so spinners are important because they're the representation for electrons, which have half initiative spin. They are the wave functions of electrons are spinners. Just like the wave functions of photons are vectors. The wave functions of electrons are spinners. And they have this property that when you rotate by 360 degrees, they come back to minus one of themselves and take 720 degrees to get back to the original value. And they are a consequence of, and we usually think of rotation in space as being, you know, when you have this notion of rotational invariance and rotational invariance, as we ordinarily experience it, doesn't have the feature. If you go through 360 degrees, you go back to where you started from. But that's not true for electrons. And so that's why under Understanding how that works is important”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“So, this was what happens what seems to happen. It's subject to revision even next few days. But what seems to be the case is that bosons are associated with essentially merging in multi-way graphs and fermions are associated with branching in multiway graphs. And that essentially the exclusion principle is the fact that in Branchield space things have a certain extent in Branchield space that in which things are being sort of forced apart in Branchial space, whereas the case of bosons, they come together in branch hill space. And the real question is, can we explain the relationship between that and these things called spinners, which are the representation of half integer spin particles that have this weird feature that usually when you go around 360 degree rotation, you get back to where you start?”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source
“How particles work in quantum mechanics. Another core feature is this difference between particles that obey the exclusion principle and sort of stay apart that leads to the stability of matter and things like that. And particles that love to get together and be in the same state, things like photons. And that's what leads to phenomena like lasers, where you can get sort of coherently everything in the same state. That difference is the particles of integer spin are bosons like to get together in the same state. The particles of half integer spin are fermions like electrons that they tend to stay apart. And so the question is, can we get that in our models? And just the last few days, I think we've made, I mean, I think the story of, I mean, it's one of these things we're really close.”
2020-09-15 · Lex Fridman Podcast · #124 – Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe · IDENTIFIED FROM THE TRANSCRIPT · source