斯蒂芬·沃爾夫勒姆：ChatGPT 與真理、現實和計算的本質

Lex Fridman Podcast #376 – Stephen Wolfram: ChatGPT and the Nature of Truth, Reality & Computation Machine transcription by Qwen3-ASR 0.6B (MLX, local, Apache-2.0). May contain recognition errors. The following is a conversation with Stephen Wolfram, his fourth time on this podcast. He's a computer scientist, mathematician, theoretical physicist, and the founder of Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the Wolfram Physics and Metamathematics projects. He has been a pioneer in exploring the computational nature of reality, and so he's the perfect person to explore with together the new, quickly evolving landscape of large language models as human civilization journeys towards building super intelligent AGI. And now a quick view second mention of his sponsor. Check them out in the description. It's the best way to support this podcast. 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This is the Lex Friedman podcast to support it. Please check out our sponsors in the description. And now dear friends, here's Stephen Wolfram. You announced the integration of ChatGPT and Wolfram Alpha and Wolfram Language. So let's talk about that integration. What are the key differences from the high philosophical level? Maybe the technical level between the capabilities of. Broadly speaking, the two kinds of systems large language models and this computational gigantic computational system infrastructure that is Wolfram Alpha. Yeah, so what does something like ChatGPT do? It's it's mostly focused on make language like the language that humans have made and put on the web and so on. So you know it's it's primary sort of underlying technical thing is you've given a prompt. It's trying to continue that prompt in a way that's somehow typical of what it's seen based on a trillion words of text that humans have written on the web, and the way it's doing that is. With something which is probably quite similar to the way we humans do the first stages of that using a neuron that and so on and just saying given these given this piece of text, let's ripple through the neuron that one word and get one word at a time of output, and it's kind of a shallow computation on a large amount of kind of training data that is what we humans have put on the web. That's a different thing from sort of the computational stack that I spent the last I don't know forty years or so building, which has to do with what can you compute many steps potentially a very deep computation. It's not sort of taking the statistics of what we humans have produced and trying to continue things based on that statistics instead. It's trying to take kind of the formal structure that we've created in our civilization whether it's from mathematics or whether it's from kind of systematic knowledge of all kinds and use that to do arbitrarily deep computations to figure out things that that aren't just let's match what's already been kind of said on the web, but let's potentially be able to compute something new and different that's never been computed before. So as a practical matter, you know the the what we're you know our goal is to have made as much as possible of the world computable in the sense that if there's a question that in principle is answerable from some sort of expert knowledge that's been accumulated, we can compute the answer of that question and we can do it in a sort of reliable way that's that's the best one can do given what the expertise that our civilization has accumulated. It's a very it's a it's a much more sort of labor intensive on the side of kind of being creating kind of the the computational system to do that. Obviously the in the the kind of the ChatGPT world, it's like take things which were produced for quite other purposes namely all the things we've written out on the web and so on and sort of forage from that things which were are like what's been written on the web. So I think you know as a practical point of view, I view sort of the ChatGPT thing as being wide and shallow, and what we're trying to do with sort of building out computation as being this sort of deep also broad but but most importantly kind of deep type of thing. I think another way to think about this is if you go back in human history, you know I don't know thousand years or something, and you say what what can the typical person what's the typical person going to figure out. Well the answer is there certain kinds of things that we humans can quickly figure out that's sort of what what our you know our neural architecture and the kinds of things we learn in our lives let us do. But then there's this whole layer of kind of formalization that got developed in which is you know the kind of whole sort of story of intellectual history and whole kind of depth of learning that formalization turned into things like logic, mathematics, science and so on, and that's the kind of thing that allows one to kind of build these towers of of of sort of towers of things you work out. It's not just I can immediately figure this out. It's no I can use this kind of formalism to go step by step and work out something which was not immediately obvious to me, and that's kind of the story of what what we're trying to do computationally is to be able to build those kind of tall towers of what implies what implies what and so on, and as opposed to kind of the yes I can immediately figure it out. It's just like what I saw somewhere else in something that I heard or remembered or something like this. What can you say about the kind of formal structure, the kind of formal foundation you can build such a formal structure on, about the kinds of things you would start on in order to build this kind of deep computable knowledge trees. So the question is sort of how do you how do you think about computation, and there's there's a couple of points here. One is what computation intrinsically is like, and the other is what aspects of computation we humans with our minds and with the kinds of things we've learned can sort of relate to in that computational universe. So if we start on the kind of what can computation be like, it's something I've spent some big chunk of my life studying. Is imagine that you're you know we we usually write programs where we kind of know what we want the program to do and we carefully write you know many lines of code and we hope that the program does what we what we intended it to do. But the thing I've been interested in is if you just look at the kind of natural science of programs. So you just say I'm going to make this program it's a really tiny program maybe I even pick the pieces of the program at random but it's really tiny and by really tiny I mean you know less than a line of code type thing. You say what does this program do and you run it and big discovery that I made in the early 80s is that even extremely simple programs when you run them can do really complicated things. Really surprised me it took me several years to kind of realize that that was a thing so to speak, but that that realization that even very simple programs can do incredibly complicated things that we very much don't expect. That discovery I mean I realized that that's very much I think how nature works that is nature has simple rules but yet does all sorts of complicated things that we might not expect. You know as big thing of the last few years has been understanding that that's how the whole universe and physics works, but that's a quite separate topic. But so there's this whole world of programs and what they do and very rich sophisticated things that these programs can do. But when we look at many of these programs, we look at them and say well that's kind of I don't really know what that's doing. It's not a very human kind of thing. So on the one hand we have sort of what's possible in the computational universe, on the other hand we have the kinds of things that we humans think about the kinds of things that have developed in kind of our intellectual history, and that's and really the challenge to sort of making things computational is to connect what's computationally possible out in the computational universe with the things that we humans sort of typically think about with our minds. Now that's a complicated kind of moving target because the things that we think about change over time. We've learned more stuff. We've invented mathematics. We've invented various kinds of ideas and structures and so on. So it's it's gradually expanding. We're kind of gradually colonizing more and more of this kind of intellectual space of possibilities. But the the real thing the real challenge is how do you take what is computationally possible. How do you take how do you encapsulate the kinds of things that we think about in a way that kind of plugs in to what's computationally possible, and and actually the the the big sort of idea there is this idea of kind of symbolic programming symbolic representations of things, and so the question is when you look at sort of everything in the world and you kind of you know you take some visual scene or something looking at, and you say well how do I turn that into something that I can kind of stuff into my mind. You know there are lots of pixels in my visual scene but the things that I remembered from that visual scene are you know there's a there's a chair in this place. It's a kind of a symbolic representation of the visual scene. There are two chairs on a table or something rather than there are all these pixels arranged in all these detailed ways. And so the question then is how do you take sort of all the all the things in the world and make some kind of representation that corresponds to the types of ways that we think about things and human language is is sort of one form of representation that we have. We talk about chairs that's a word in human language and so on. How do we how do we take but human language is not in and of itself something from that plugs in very well to sort of computation. It's not something from which you can immediately compute consequences and so on, and so you have to kind of find a way to take sort of the the the stuff we understand from human language and make it more precise, and that's really this story of symbolic programming and you know what what that turns into is something which I didn't know at the time it was going to work as well as it has, but back in the 1979 or so I was trying to build my first big computer system and trying to figure out you know how should I represent computations at a high level, and I kind of invented this idea of using kind of symbolic expressions you know structured as it's kind of like a a function and a bunch of arguments, but that function doesn't necessarily evaluate to anything. It's just a a thing that sits there representing a structure, and so building up that structure and it's turned out that structure has been extremely it's it's a good match for the way that we humans it seems to be a good match for the way that we humans kind of conceptualize higher level things, and it's been for the last I don't know forty five years or something, it's served me remarkably well. So building up that structure using this kind of symbolic representation, but what can you say about abstractions here because you could just start with your physics project you could start at a hypergraph at a very very low level and build up everything from there but you don't you take shortcuts, right? You take the highest level of abstraction, convert that, the kind of abstraction that's convertible into something computable using symbolic representation, and then that's your new foundation for that little piece of knowledge. Somehow all that is integrated, right? So the sort of a very important phenomenon that that is kind of a thing that I've sort of realized is just it's one of these things that sort of in the in the future of kind of everything is going to become more and more important is this phenomenon of computational irreducibility, and the the question is if you know the rules for something you have a program you're going to run it. You might say I know the rules, great I know everything about what's going to happen. Well, in principle you do because you can just run those rules out and just see what they do. You might run them a million steps, you see what happens, et cetera. The question is can you like immediately jump ahead and say I know what's going to happen after a million steps, and the answer is 13 or something. Yes, and the the one of the very critical things to realize is if you could reduce that computation, there is in a sense no point in doing the computation. The place where you really get value out of doing a computation is when you had to do the computation to find out the answer, but this phenomenon that you have to do the computation to find out the answer this phenomenon of computational irreducibility seems to be tremendously important for thinking about lots of kinds of things. So one of the things that happens is okay you've got a model of the universe at the low level in terms of atoms of space and hypergraphs and rewriting hypergraphs and so on, and it's happening you know 10 to the 100 times every second let's say. Well you say great then we've we've nailed it we we know how the universe works. Well the problem is the universe can figure out what it's going to do. It does those 10 to the 100 you know steps, but for us to work out what it's going to do we have no way to reduce that computation. The only way to do the computation to see the result of the computation is to do it, and if we're operating within the universe we're kind of there's no there's no opportunity to do that because the universe is doing it as fast as the universe can do it, and that's you know that's what's happening. So what we're trying to do and a lot of the story of science and a lot of other kinds of things is finding pockets of reducibility. That is you could have a situation where everything in the world is full of computational irreducibility. We never know what's going to happen next. The only way we can figure out what's going to happen next is just let the system run and see what happens. So in a sense the story of of most kinds of science inventions a lot of kinds of things is the story of finding these places where we can locally jump ahead, and one of the features of computational irreducibility is there are always pockets of reducibility. There are always. Places there are always an infinite number of places where you can jump ahead. There is no way where you can jump completely ahead, but there are little little patches, little places where you can jump ahead a bit. And I think you know we can talk about physics project and so on, but I think the thing we realize is we kind of exist in a slice of all the possible computational irreducibility in the universe. We exist in a slice where there is a reasonable amount of predictability, and in a sense as we try and construct these kind of higher levels of of abstraction symbolic representations and so on. What we're doing is we're finding these lumps of reducibility that we can kind of attach ourselves to and about which we can kind of have fairly simple narrative things to say. Because in principle you know I say what's going to happen in the next few seconds you know oh there are these molecules moving around in the air in this room and oh gosh it's an incredibly complicated story and that's a whole computationally reducible thing most of which I don't care about and most of it is well you know the air is still going to be here and nothing much is going to be different about it and that's a kind of reducible fact about what is ultimately at an underlying level of computational irreducible process. And life would not be possible if we didn't have a large number of such reducible pockets. Yes, pockets amenable to reduction into something symbolic. Yes, I think so. I mean life in in the way that we experience it, that I mean you know one might you know depending on what we mean by life so to speak the the experience that we have of sort of consistent things happening in the world the idea of space for example where there's you know we can just say you're here you move there it's kind of the same thing it's still you in that different place even though you're made of different atoms of space and so on. This is this idea that it's that there's sort of this level of predictability of what's going on that's us finding a slice of reducibility in what is underneath this computationally reducible kind of system and I think that's that sort of the thing which is actually my favorite discovery of the last few years is the realization that it is sort of the interaction between this sort of underlying computational irreducibility and our nature as kind of observers who sort of have to key into computational reducibility. That fact leads to the main laws of physics that we discovered in the twentieth century. So this is we talk about this in in more detail but this is a to me it's kind of our nature as observers the fact that we are computationally bounded observers we don't get to follow all those little pieces of computational irreducibility to stuff what is about out there in the world into our minds. Requires that we are looking at things that are reducible we are compressing kind of we're extracting just some essence some kind of symbolic essence of what's the detail of what's going on in the world that together with one other condition that at first seems sort of trivial but isn't which is that we believe we are persistent in time. That is yes you know so so that's the causality. Here's the thing at every moment according to our theory we're made of different atoms of space at every moment sort of the microscopic detail of what what the universe is made of is being rewritten and that's and in fact the very fact that there's coherence between different parts of space is a consequence of the fact that there are all these little processes going on that kind of knit together the structure of space. It's kind of like if you wanted to have a fluid with a bunch of molecules in it if those molecules weren't interacting you wouldn't have this fluid that would pour and do all these kinds of things it would just be sort of a free floating collection of molecules. So similarly it is with space that the fact that space is kind of knitted together is a consequence of all this activity in space and the fact that kind of what we consist of sort of this this series of of you know we're continually being rewritten. And the question is why is it the case that we think of ourselves as being the same us through time that's kind of a key assumption I think it's a key aspect of what we see as sort of our consciousness so to speak is that we have this kind of consistent thread of experience. Well isn't that just another limitation of our mind that we want to reduce reality into some that kind of temporal consistency is just a nice narrative to tell ourselves. Well the fact is I think it's critical to the way we humans typically operate is that we have a single thread of experience you know if you if you imagine sort of a mind where you have you know maybe that's what's happening in various kinds of minds that aren't working the same way other minds work is that you're splitting into multiple threads of experience. It's also it's also something where you know when you look at I don't know quantum mechanics for example in the insides of quantum mechanics it's splitting into many threads of experience but in order for us humans to interact with it you kind of have to have to knit all those different threads together so that we say oh yeah definite thing happened and now the next definite thing happens and so on. And I think you know sort of inside it it's it's sort of interesting to try and imagine what's it like to have kind of these fundamentally multiple threads of experience going on. I mean right now different human minds have different threads of experience we just have a bunch of minds that are interacting with each other but we don't have a you know within each mind there's a single thread and that's a that is indeed a simplification. I think it's a it's a thing you know the general computational system does not have that simplification and it's one of the things you know I people often seem to think that you know consciousness is the highest level of kind of things that can happen in the universe so to speak. But I think that's not true I think it's actually a a specialization in which among other things you have this idea of a single thread of experience which is not a general feature of anything that could kind of computationally happen in the universe. So it's a feature of a computationally limited system that's only able to observe reducible pockets. So so I mean this word observer it means something in quantum mechanics it means something in a lot of places it means something to us humans as conscious beings. So what what's the importance of the observer what is the observer and what's the importance of the observer in the computational universe. So this question of what is an observer what's the general idea of an observer is actually one of my next projects which got somewhat derailed by the the current sort of AI mania but is there a connection there or is that do you do you think the observer is primarily a physics phenomenon. Is it related to the whole AI thing yes yes it is related so one question is what is a general observer so you know we know we have an idea what is a general computational system we think about Turing machines we think about other models of computation. There's a question what is a general model of an observer and there's kind of observers like us which is kind of the observers we're interested in you know we could imagine an alien observer that deals with computational irreducibility and it has a mind that's utterly different from ours and and completely incoherent with what what we're like. But the fact is that that you know if we are talking about observers like us that one of the key things is this idea of kind of taking all the detail of the world and being able to stuff it into a mind being able to take all the detail and kind of you know extract out of it a smaller set of of kind of degrees of freedom a smaller number of elements that will sort of fit in our minds. And I think this this question so I've been interested in trying to characterize what is the general observer and the general observer is I think in part there are many let me give an example of a you know you have a gas it's got a bunch of molecules bouncing around and the thing you're measuring about the gas is its pressure. And the only thing you as an observer care about is pressure and that means you have a piston on the side of this box and the piston is being pushed by the gas and there are many many different ways that molecules can hit that piston but all that matters is the kind of aggregate of all those molecular impacts because that's what determines pressure. So there's a huge number of different configurations of the gas which are all equivalent. So I think one key aspect of observers is this equilibrating of many different configurations of a system saying all I care about is this aggregate feature all I care about is this this overall thing and that's that sort of one one aspect and we see that in lots of different again it's the same story over and over again that there's there's a lot of detail in the world but what we are extracting from it is something a sort of a thin a thin summary of that of that detail. Is that thin summary nevertheless true is can it be a crappy approximation that on average is is correct I mean if we look at the observer that's the human mind it seems like there's a lot of very as represented by natural language for example there's a lot of really crappy approximation. Sure and that could be maybe a feature of it. Well there's ambiguity. Right right you don't know you know it could be the case you're just measuring the aggregate impact of these molecules but there is some tiny tiny probability that the molecules will arrange themselves in some really funky way and that just measuring that average isn't going to be the main point. By the way an awful lot of science is very confused about this because you know you look at you look at papers and people are really keen they draw this curve and they have these you know these bars on the curve and things. It's just this curve and it's this one thing and it's supposed to represent some system that has all kinds of details in it and this is a way that lots of science has gotten wrong because people say I remember years ago I was studying snowflake growth. You know you have a snowflake and it's growing it has all these arms it's doing complicated things but there was a literature on this stuff and it talked about you know what's the rate of snowflake growth and you know it it got pretty good answers for the rate of the growth of the snowflake and then I looked at it more carefully and and they had these nice curves of you know snowflake growth rates and so on. I looked at it more carefully and I realized according to their models the snowflake will be spherical and so they got the growth rate right but the detail was just utterly wrong and you know not only the detail the the whole thing was was not capturing you know it was capturing this aspect of the system that was in a sense missing the main point of what was going on and what is the geometric shape of a snowflake. Snowflakes start in in the phase of water that's relevant to formation of snowflakes it's a phase of ice which starts with a hexagonal arrangement of of water molecules and so it starts off growing as a hexagonal plate and then what happens is it's a plate oh oh versus sphere sphere well no no but it's it's much more than that. I mean snowflakes are fluffy you know typical snowflakes have little little dendritic arms. Okay yeah and what actually happens is it's kind of kind of cool because you can make these very simple discrete models with cellular automata and things that that figure this out. You start off with this you know hexagonal thing and then the places it it starts to grow little arms and every time a little piece of ice adds itself to the snowflake. The fact that that ice condensed from the water vapor heats the snowflake up locally and so it makes it less likely for for another piece of ice to accumulate right nearby. This leads to a kind of growth inhibition so you grow an arm and it is a a separated arm because right around the arm it got a little bit hot and it didn't add more ice there. So what happens is it grows you have a hexagon it grows out arms the arms grow arms and then the arms grow arms grow arms and eventually actually it's kind of cool because it it actually fills in another hexagon a bigger hexagon and when I first looked at this you had a very simple model for this I realized you know when it fills in that hexagon it actually leaves some holes behind. So I thought well you know is that really right so I look at these pictures of snowflakes and sure enough they have these little holes in them that are kind of scars of the way that these arms grow out. So you can't fill in backfill holes. They don't backfill and presumably there's a limitation on how big like you can't arbitrarily grow. I'm not sure I mean the thing falls through the I mean I think it does you know it hits the ground at some point. I think you can grow I think you can grow in the lab I think you can grow pretty big ones I think you can grow many many iterations of this kind of goes from hexagon it grows out arms it turns back it fills back into a hexagon it grows more arms again in 3D. No it's flat usually. Why is it flat why doesn't it span out? Okay okay wait a minute you said it's fluffy and fluffy is a three dimensional property no or no it's it's fluffy snow is okay so you know what makes we're really we're really in a in a detail but but as multiple snowflakes become fluffy a single snowflake is not fluffy. No no a single snowflake is fluffy and what happens is you know if if you have snow that it's just pure hexagons they they can you know they they fit together pretty well it's not it doesn't it doesn't make it doesn't have a lot of air in it and they can also slide against each other pretty easily and so the snow can be pretty you know can I think avalanches happen sometimes when when the things tend to be these you know hexagonal plates and it kind of slides but then when the thing has all these arms that have grown out it's not they don't fit together very well and that's why the snow has lots of air in it and if you look at one of these snowflakes you know if you catch one you'll see it has little arms and people actually people often say you know no two snowflakes are alike. That's mostly because as a snowflake grows they do grow pretty consistently with these different arms and so on but you capture them at different times as they you know they fell through through the air in a different way you'll catch this one at this stage and as it goes through different stages they look really different and so that's why you know kind of looks like no two snowflakes are alike because you caught them at different a different time. So the rules under which they grow are the same it's just the timing is. Yes okay so the point is science is not able to describe the full complexity of snowflake growth. Well science if you if you do what people might often do which is say okay let's make it scientific let's turn into one number and that one number is kind of the growth rate of the arms or some such other thing that fails to capture sort of the detail of what's going on inside the system and that's in a sense a big challenge for science is how do you extract from the natural world for example those aspects of it that you are interested in talking about. Now you might just say I don't really care about the fluffiness of the snowflakes all I care about is the growth rate of the arms in which case you know you have you can have a good model without knowing anything about the fluffiness. But the fact is as a practical you know if you if you say what's the what is the most obvious feature of a snowflake oh that it has this complicated shape. Well then you've got a different story about what you model I mean this is one of the features of of sort of modeling in science that you know what is a model a model is some way of reducing the actuality of the world to something where you can readily sort of give a narrative for what's happening or you can basically make some kind of abstraction of what's happening and answer questions that you care about answering. If you wanted to answer all possible questions about the system you'd have to have the whole system because you might care about this particular molecule where did it go and you know your model which is some big abstraction of that has nothing to say about that. So you know one of the things that's that's often confusing in science is people will have I've got a model somebody says somebody else will say I don't believe in your model because it doesn't capture the feature of the system that I care about. You know there's always this controversy about you know is is it a correct model well no model is except for the actual system itself is a correct model in the sense that it captures everything. Questions does it capture what you care about capturing sometimes that's ultimately defined by what you're going to build technology out of things like this. The one counter example to this is if you think you're modeling the whole universe all the way down then there is a notion of a correct model but even that is more complicated because it depends on kind of how observers sample things and so on that's a that's a separate story but at least at the first level to say you know this thing about oh it's an approximation you're capturing one aspect you're not capturing other aspects. When you really think you have a complete model for the whole universe you better be capturing ultimately everything even though to actually run that model is impossible because of computational irreducibility. The only the only thing that successfully runs that model is the actual running of the universe. Is the universe itself but okay so what you care about is an interesting concept so that's a that's a human concept so that's what you're doing with Wolfram Alpha and Wolfram Language is you're trying to come up with symbolic representations. Yes as simple as possible. So a model that's as simple as possible that fully captures stuff we care about. Yes so I mean for example you know we could we'll have a thing about you know data about movies let's say we could be describing every individual pixel in every movie and so on but that's not the level that people care about and it's yes this is a I mean and and that level that people care about is somewhat related to what's described in natural language. But what what we're trying to do is to find a way to sort of represent precisely so you can compute things. See one thing we say you give a piece of natural language question is you feed it to a computer you say does the computer understand this natural language. Well you know the computer processes it in some way it does this maybe it can make a continuation of the natural language you know maybe it can go on from the prompt and say what it's going to say you say does it really understand it. Hard to know but for in this kind of computational world there is a very definite definition of does it understand. Which is could it be turned into this symbolic computational thing from which you can compute all kinds of consequences and that's the that's the sense in which one has sort of a target for the understanding of natural language and that's kind of our goal is to have as much as possible about the world that can be computed in a in a reasonable way so to speak. Be able to be sort of captured by this kind of computational language that's that's kind of the goal and and I think for us humans the the main thing that's important is as we formalize what we're talking about it gives us a way of kind of building a structure where we can sort of build this tower of consequences of things. So if we're just saying well let's talk about it in natural language it doesn't really give us some hard foundation that lets us you know build step by step to work something out