Future of Science and Technology Q&A (October 27, 2023)

Hello, everyone. Welcome to another episode of Q and A about future of science and technology. And I see there are lots of questions here. Question here. Not sure if I've talked about this another time, but I'm happy to talk about it. From Larry. How will the future of mathematics change? So partly depends on what one means by mathematics. There's kind of an activity of exploring kind of mathematical kinds of ideas, and then there's the sort of social practice among mathematicians of doing what they call mathematics. And these are not necessarily quite the same thing. I mean, I think one thing to say about mathematics is there's this methodology that tends to exist that says kind of, you write a math paper and it's like your goal is invent a theorem and then give a proof of that theorem. And, well, why is the theorem true? Well, in the end, the theorem has to rest on certain axioms, at least implicitly. Certain things that you kind of state are true. Like Euclid was an original person a couple of thousand years ago who started stating axioms. So he had axioms like statements like, for instance, on a line between any two points, there's another point, or another very famous axiom that he had was two parallel lines can never cross. His fifth postulate. Well, that was something you can prove a lot of stuff from the assumption that two parallel lines never cross. But you can still ask the question, is that axiom actually true in. In some, for example, for our universe? And what became clear in 1915 with Einstein's general theory of relativity, is that, no, actually in the space time that exists, space that exists in our actual universe, it can be curved. So two parallel lines can in fact cross in space in our universe. So that axiom of Euclid's isn't true for our universe. It's a perfectly reasonable thing to set up a mathematics to prove things on the basis of that axiom. But it isn't something which will be true in our physical universe. And this is sort of a general feature of mathematics. You set up axioms and then you prove what's true. At least, that's how people sort of imagine mathematics is set up. And they've been imagining that for about a bit more than 100 years. This idea that mathematics is this kind of effort to define formal axioms, then prove what you can from those formal axioms, whether or not those formal axioms are, for example, in any sense true about our physical universe. They're just kind of statements of formal things from which you can make proofs. Now, back when that was all being started when people were really excited about those things. From the 1880s to early part of the 20th century, this was kind of where it was at in terms of formalism leads to consequences. But then starting in 1920, developing in the 1930s, then really developing in the last few decades, computation, the idea of having something where you could start from rules and then work out the consequences of those rules, but do it in this very direct way. You've got these rules for how, for example, the state of a system should be transformed. You just apply the rules over and over and over again. It makes a computation, it gives you a series of results. That's something very much more direct than what you're doing in mathematics, where you say, well, I've got this theorem and I kind of want to see that I can piece together from axioms to get to that theorem. And you kind of have to find this path from. It's kind of a non deterministic computation problem of finding this path from the axioms to the theorem you happen to want to prove. But more to the point, as I say, mathematics as conceived 100 years ago was kind of this idea of we've got formal rules, formal axioms, and then we see what their consequences are. And this was the environment, the framework in which that type of idea was played out. More recently, that type of idea is played out much more powerfully in computation, very much more direct. You've just got these rules, you see their consequences and so on. So one of the things that I think is a feature of mathematics is when you think about doing experimental mathematics, just try and run things based on these mathematical rules and so on, and see what's true. That's more like doing computations. What has been more the tradition of mathematics is assert from somewhere, come up with something you think is true, some theorem, and then find this path by which you can prove that from the axioms. But this idea of experimental mathematics, which has been sort of an undercurrent in a lot of the great mathematical work that's been done over the course of centuries, I think that experimental mathematics, the idea of just find what's true computationally, is a key part of what can be the future of mathematics. Now, one question is, is that field which consists of finding out what's true and on the basis of various kinds of rules, and is that what people would normally call mathematics? Well, when it comes to computational rules, that's the field that I've recently been calling ruliology. Start with a computational rule, see its consequences when Those rules are things about, oh, you have just this array of cells and you do this thing updating the array of cells based on colors of neighboring cells and so on. That feels more like ruleology. If I were to state that same kind of thing as a rule in terms of what you do to some mathematical formula, how you iterate some mathematical formula, it will sound more like traditional mathematics. It will sound more like something stated in the language of mathematics. But I think that this idea of just find out what's true computationally is sort of a key direction in mathematics which really has not been pursued as much as it could be. I mean, I myself have made a bunch of discoveries with that methodology. I've encouraged other people over decades to do that, and some have really made great careers out of doing that. But it's surprisingly untypical. It's kind of a. Mathematics is this strange field of science like stuff where the purely theoretical field is much bigger than the experimental field. In most areas like physics or something, there are many more people doing experiments than sort of trying to invent theory. But mathematics isn't that way. Now, if you ask, well, what is the sort of picture of mathematics as it is? So one point is when you start talking about formal, about axiom systems and formalization of mathematics and the idea that you can start with arbitrary axioms, and those axioms are really uncoupled with what's actually true in the world, actual practicing mathematicians will find that for the most part, an alien view of mathematics. That's not what they think they're doing. They think they are taking the sort of mathematics as it has been developed and sort of building on what's been developed and sort of adding pieces to what's been developed, rather than going down to these micro axioms. My kind of analogy is if you're doing, studying a fluid like water or something, you can go all the way down to the molecules and be studying what each individual molecule does. It's kind of like the axiomatic approach to mathematics. Or you can be trying to work out the equations of fluid flow and study the fluid at the level of kind of like large scale motions and so on. And that second thing is more what the typical mathematician thinks they're doing. When you drop down to the level of axioms and to this kind of sub microscopic, this sort of microscopic level, then you've got all kinds of different metamathematical phenomena that go on. But even the possibility of doing mathematics consistently sort of at this fluid dynamics level, it's not obvious that that would be possible. And one of the things I just wrote this book actually, what is it nearly a year ago now about the physicalization of metamathematics, which is all about trying to understand this idea of kind of higher level mathematics as compared to things like axiomatic mathematics. And part of the starting point for that book is kind of looking at the network of all possible theorems of mathematics. I mean, in the published literature of mathematics, there are 3 or 4 million theorems there's have been accumulated over the last couple of thousand years. And from one theorem, one axiom, axioms are just theorems you assume to be true, rather than ones you imagine you can prove. From the axioms or theorems that we already have established. You're building up this whole network. You can build up an infinite network of possible theorems of mathematics. And then the question is, well, what is that structure of that space of possible theorems? And one of the things that I think is kind of you can ask that question analogously to the way you can ask that question about the structure of physical space. We now think in our physics project that physical space underneath is just this network of relations between atoms of space. So it too is discrete. And what in physical space is an atom of space in mathemathematics is a theorem. But they're both just sort of things that are out there connected together by various kinds of relations. And so one of the big things that we notice about physical space is that for us humans, it seems to be continuous. And that's because we, as sort of finite minds, observing all of this complexity of these atoms of space, we aggregate that to the point where what we notice is just this continuous structure of space. And so it is, I think, with mathematics, the fact is that the human mathematical observer is kind of most of the time not going down to the level of sort of the axioms or below the axioms, but is rather aggregating things. So they can talk about things like the Pythagorean theorem as just a theorem that we can just intuitively have a sense of. Even though there are ways to drill down and turn that theorem into micro axioms. There may be many ways to do that, but. But that doesn't matter. We don't have to know exactly what we mean by a number and things like this. We have an intuitive sense of how the Pythagorean theorem works. So the possibility of doing higher level mathematics is a feature, I think, that is something for sort of human mathematicians with finite minds, just as the belief that There is a continuous space in the universe is a feature of us, with finite minds observing the physical world. So in any case, what does that mean for the future of mathematics? Well, those three or four million theorems of mathematics, we can explore an infinite number of theorems. There's the question of which of those theorems do we humans care about? It's kind of like in the physical space that exists on the surface of the Earth, where do we actually hang out and colonize, so to speak, where do we put our cities? And where is just sort of space that's sitting on the surface of the Earth without humans hanging out there? So the same thing in metamathematical space. Where do we choose to sort of put the places where we're kind of populating it with actual mathematics, that we make theorems and put them in papers and so on? Well, I think what we're seeing is sort of the steady sort of growth in this metamathematical space of these sort of towers of theorems that we build, that we decide we care about and that we write down in the publications of mathematics and so on. And I think that we will see these sort of. These prongs of mathematics continue to grow out. One thing that is sort of an observation about a lot of kind of the leading edge of mathematics is these remarkable kind of dualities between different areas of mathematics. It's been known for, well, three, 400 years now that algebra and geometry have a certain duality, things that you can represent geometrically. You know, I've got a circle, and it's got lines going through it, and it intersects another circle and so on. You can write down algebraic equations that represent that situation. And similarly, many algebraic equations you can also represent in terms of geometrical figures and their properties. So that's a duality that has been known for a long time. What's sort of emerged in the last few decades is these grand dualities between different areas of mathematics. And we're seeing lots of dualities. And my guess is that that's sort of a feature of the structure of mathematical space, that it's kind of like physical space. It's kind of homogeneous. You can move a thing from one place to another. So similarly in mathematical space, you can move from one place to another. And that represents this kind of dualities between different areas of mathematics. And I think that's a thing we'll see more of. And we'll see kind of the ultimate unity of mathematics, which is ultimately computational, ultimately deeply related to this object I call the rouliad. Which is this kind of entangled limit of all possible computations. In a sense, that's the ultimate future of mathematics, is to fill out the ruliad. But the fact is that if we were to do that, they would not be things that we can connect to in a human kind of way. We will be kind of filling out everything and sort of have nothing as a result. So in a sense, part of what mathematics is is this human activity of kind of filling out different areas for which we can, which we describe as being mathematics we care about. Just like we have words for certain concepts in natural language that we care about. And there are other sort of interconcept objects, things in interconcept space that are different kinds of constructs for which we don't have words. And I think it's the same kind of thing in mathematics. So as a practical matter, my guess is there will be more sort of unification in mathematics at the sort of abstract level. There will be, I hope, more experimental mathematics of finding things that are true. And where it's really what's at issue is which things do we humans care about? And I think those are things we can see happen. I think the effort to just sort of say, let's turn all of mathematics into a formalized system where we can just kind of go from axioms we choose and just grind out everything, I think that's kind of a fool's errand, because I think that what will happen is that most of what really matters in mathematics is this very human aesthetic question of what do we humans care about? And so on. Simply grinding out the theorems mechanically is not what we usually think of as human. Like mathematics, it's kind of the. It's something alien, something kind of. It's like saying, imagine all possible concepts. Imagine all possible things that can computationally happen. Most of those are not things that we have a human connection to. And so I don't think those get to be what we will normally call mathematics. Now, in terms of what will happen sort of sociologically in mathematics, I think the typical mathematical paper, for example, can say what I think should happen. I mean, one of the things that is often very missing is the why are you doing this? Type question. A mathematics paper will start off by saying, these are the definitions. Now we're going to do the following thing. It's like, why are we doing this? We have no idea. There's a certain trend to make mathematics more explain why it's doing what it's doing, which I think is very good that's the sort of more humanization of mathematics because that's in the end, what's what true mathematics is really about. To say it's this mechanical thing that just comes from axioms, is to kind of deny what is, I think, important about mathematics for us humans. Well, I think there's this question of whether questions that we have in mathematics, whether they have to be ground down to the level of kind of mechanical axiomatic work. If that happens, there will be things like undecidability. The fact that you given a particular set of axioms, there may not be any finite proof you can give of either a statement or the negation of that statement. It may be something that's independent of those axioms. And there's sort of a question of will that happen a lot? Well, I always was for decades actually curious about why that didn't happen more than it does. And I think the answer is that this human level mathematics is almost defined to not drop down to the sort of axiomatic level where that's a common phenomenon. It's defined to operate sort of at this fluid dynamics level where those kinds of things don't go on. Now, another question you can ask is, with all the emphasis on AI and LLMs and all this kind of thing, you can ask the question, given that we know through 4 million theorems of mathematics and we have this mechanical process for producing new theorems, can we make the LLMs be sort of proxies for us humans and decide what directions we will think are interesting? And that's a good question. And we've been doing some experiments on that. And I don't think I know the answer yet. I know a few cases where, yes, there is kind of a good heuristic for deciding what theorems humans will care about. Essentially one case of that heuristic is for the theorems of Boolean algebra of logic, where the ones we put in our textbooks are precisely the ones, it turns out there are only 14 of them. Where those theorems are simpler statements of what they contain than they're the simplest statements of sort of the mathematical content they contain. And everything else is an embellishment on that. And it's the sort of the minimal ones that we actually put in our textbook. So that's one particular heuristic. But I think an interesting question is, is there a more general thing that the AIs have sort of picked up from looking at human mathematics that says, oh, these are things that humans are going to care about? Just like if you're Doing image generation. It's like the AI can say this is a picture the human is going to think is beautiful in some way. And you can kind of prompt it to say show me a beautiful picture of. And it will have some idea of what that means based on pictures, billions of pictures it's seen which have been tagged in various ways by humans. All right, long, answer that question. There's a question here from Cloud asking would there be a way to use the moon as a gravitational tugboat to slowly tow the Earth away from the expanding surface of the sun when it becomes a red giant so we can stay in a nice temperate zone of the solar system? Well, when does the sun. I think the sun. What do we have about another 4 billion years before the sun turns into a red giant? I'm not sure of that order, but I think eventually it will expand to more or less get out to the orbit of Jupiter. So the question is, what do we do with the Earth at that point? I don't know. There's the science fiction story wandering Earth where people have put rocket engines on the Earth, so to speak, to slowly move it out of the solar system. I think it's getting the Earth to sort of go fast enough to sort of move to a different orbit around the sun means you have to make it go not quite a hundred thousand miles an hour, which is the escape velocity of the sun, but something close to that. And how would you achieve that? I don't know. I think it's quite challenging. Certainly with, I don't think it works to. I'd be, I think the, yes, the Earth moon system. I mean, I don't think we get to change much about is what it is and to move it around would require all sorts of pushing, so to speak. Now an interesting question is if we knew we had, if we knew we had a million years before anything needed to be done, is there a way that we could set up a pretty weak kind of rocket engine on the Earth that would slowly, slowly start to push the Earth in a different way? I don't entirely know the answer to that. Although as I say, I think in the end I mean that, that that rocket engine would have to be gradually increasing the momentum of the Earth so that eventually it reaches that roughly 100,000 miles an hour speed in order to be able to move around in the gravitational well of the Sun. So I think that's a, it's kind of a long range plan, so to speak. You know, it's kind of funny, somebody was showing me just A couple of days ago, some for organization showing their 2030 plans and I'm like, that's a fairly long way away. And then I was remembering back in the 1980s, I remember visiting some group in the Netherlands where they were making plans for the dikes in the Netherlands because they're parts of the country are below sea level and they use dikes to keep the ocean out. Kind of like what people say is going to happen if sea level rises in other places you have to have dikes. The Netherlands has had them for a very, very long time. But in terms of long term planning, those guys were telling me they have a 400 year plan for their dikes. So that's sort of a longer range plan than one usually hears about. So maybe in the case of the Earth moving around in the solar system, a million year plan would be in order. Let's see. Kevani asks, what future applications do you think will come out? Being able to measure attosecond timescales. So attosecond means 10 to the minus 18 seconds, which is a million trillionth of a second. And it's, let's see what happens in that. A lot of things. For example, in chemistry there are a lot of things happening at the femtosecond scale. 10 to minus 15 seconds. By the time you're down at the 10 to the minus 18 seconds scale, that's higher energy things are happening at that scale. What will happen from being able to measure things at that scale? It's a good question. You know, I think being able to see sort of processes in action, like chemical reactions is, is something that, with sort of femtosecond laser pulses and things where we're being able to see. And I think as you get down to even shorter timescales, that's more of a. Well, we get to see how things happen rather than just seeing. Typically in both chemistry and in physics, particle physics, for example, when we see reactions between things, we just say there are these molecules going in. And by golly, after eventually those molecules come out. In particle physics, we say two protons, you know, collide and outcome a cascade of, you know, pions and other things. We, we just get to see what goes in, what comes out. If we have some way to kind of, you know, sort of click the shutter in effect for our detector more and more quickly, we get to see more of the process by which things occur. Now, you know, I would say that there are pieces of science that will be very interesting to understand more about will that. For example, if we knew more about how fission, spontaneous fission works in nuclear physics. What would that tell us? And are there kind of engineering hacks that we can use? If we knew more about how molecules actually interact in the reactions that they have, and we knew how the molecules kind of danced around, changed their shape, electron clouds moved, and so on, would that allow us to have different pathways that we can invent for having processes as go on? I think the answer is quite possibly yes. In terms of what the world will look like at that kind of scale. It's an interesting question. I think one thing I was kind of curious about thinking about a couple of weeks ago is if we could think a million times faster than we do, imagine our brains are largely replaced by digital electronics. That's sort of thinking a million times faster than we do. And what would we sense in the world? And it's pretty clear that, for example, light goes one foot in a nanosecond. And for us, a nanosecond is a really short time. For us, with our current brains, a nanosecond is a really short time. But if our brains were running a million times faster, a nanosecond would be kind of more like the time it takes to form a thought, which for us now is more in the many tens to hundreds of milliseconds. So if you can form a thought in a nanosecond, then you don't get to sort of aggregate the structure of space in the same way that we typically do. You're much more seeing the world in these kind of sort of individual pieces of light from different parts of the scene that you're seeing are sort of arriving at perceptibly different times. And no doubt phenomena of the kind that you experience with sound, with echoes and things like that. Whenever a photon kind of is arriving somewhere, it's often sort of bouncing around the room. I mean, that's why we can see objects in the room, is because photons are being reflected from those objects. That's what we're actually seeing when we see the objects. And so your average photon is bouncing around a bunch of times in the room. If there are mirrors, it's even more sort of convincingly sort of bouncing from place to place. And we get to see that if we were on an attosecond time scale, if we were thinking a million times faster than we do those kinds of things, we'll get to see all of that. We'll get to see sort of the full complexity of what's actually happening. The physics of the scenes we're dealing with. The fact that we see things in this much more aggregated way is, I think, important for us generating this kind of human level narrative about those things. We're not used to seeing things at the true physics level, and it will be very confusing to us with what we currently know. So it's sort of an interesting question what that would really be like. Well, Rebel is asking, do you see new conjectures that could be made by AIs or AGIs? I'm not so keen on that term because I'm not sure quite what it means, but AI systems, and how will humans tackle the abstraction and complexity of these conjectures? Well, it's easy to do this. I've done it a lot in my life. You just go out into the computational universe of possible programs and you run these programs and they do all kinds of wild things. And if you say, what's really going on? Can I understand at a sort of human level of narrative what's going on? The answer is often no. I mean, in a sense, work I've done has been about sort of taking that ruliology and pulling it in at some level to be a thing about which we can have some level of human narrative, some level of description of, you know, there's four classes of cellular automata, there's these particular structures, and so on that occurrence. It's a thing. Actually, I'm interested to see whether, with modern AIs, whether we're able to take sort of some of those things from the computational world and say, can we fit them to things which are more sort of known human concepts? How does that work? Again, I don't know how well that's going to work. The very initial experiments from a couple of days ago were not promising. But these things tend to have to mature a bit. It's kind of like you don't get a large language model in a day. It takes lots of engineering and sort of trying different things before you discover how to do something like a large language model. So when it comes to things that AIs invent and our ability to understand them, I think that we kind of gradually expand our understanding. We gradually invent some new concept. We give it a name, we give some, you know, we eventually invent some new paradigm for thinking about things. That's a gradual process and we're always connecting the next thing we learn to the things we already knew. And in a sense, that's a feature of sort of the growth of science people. That's what people find it easy to do. If you say, let's jump into this completely alien world where you have no connection to anything you already knew, that's a very difficult thing to do. Very difficult to kind of reason about things that are far away from things you've reasoned about before. So I kind of think that this question of. I mean, gradually people get more used to going out on some sort of abstraction prong. And it's kind of like this question about how come education doesn't take much more time than it does. Given that we know so much more in our civilization, why is it that even though we know more, that the time to get educated has not changed that much in thousands of years? And I think the answer is because there's more levels of abstraction in what we learn now than what we learned before. If before we had to learn separately the characteristics of every animal that we now describe as being a mammal, now we just have to use this abstract concept of a mammal, and immediately we know a lot of things about that particular kind of organism. Let's see, there's some questions here about physics and science. I just tweeted out a couple of days ago, and I just posted, in a TED Talk thing that I gave from last week, just posted some videos that we just made about features of our physics project. One of them was about a rendering sort of of the beginning of the universe. Well, let's see. This is kind of a complicated story, but. But kind of in our view of what the universe. What's in the universe. What's the universe made of? First statement is the only thing in the universe is space. Everything is just a feature of the structure of space. All the particles, all the. The gravity, all those kinds of things, they're all features of the structure of space. Just like if all we have was a fluid, it's made of molecules. But all these things, these eddies in the fluid, these different motions and so on, they're all made of combinations of those molecules. And so similarly, what we think is that in the structure of the universe, that everything is just made of this kind of space, which is this kind of giant network where there are discrete atoms of space and just relations which we can indicate as a graph with edges that join the atoms of space. And that this view of space, In a sense, 100 years ago, a little bit more than 100 years ago, this view of space would have been very uncontroversial. That is, people were wondering, you know, is matter continuous, so discrete? Is light continuous or discrete? Well, it turns out matter was discovered around 1900 really is made of molecules. It's discrete. Light, a little bit later really is made of photons. It's discrete space. Well, people kind of thought it might be discrete, too, but nobody ever figured out how to make that work, made a consistent theory based on that. And that's what we managed to do in the last few years. And so we have this view that space is discrete. And what this video is showing is the first few, starting from sort of what can be the very beginning of the universe. And when I. When I say what can be. Slightly complicated story, because many different things can be the beginning of the universe. They're all different threads of time that kind of go from those different beginnings. And the whole point is that for us humans, we are sort of embedded in the thing that is our universe, including its many threads of time. And when we, with our many threads of time, try to see how we perceive the universe, we at least believe that there's a definite thread of time. We believe we have to conflate together those actual underlying threads of time. And so we're with that belief, with that way of looking at the universe, we are sort of combining all these different initial conditions for the universe and so on. But that video is showing just one of those initial conditions, and it's showing the kind of the updating of the structure of this network that represents space and everything in space in the universe and the time in our models is this sort of inexorable computational updating of the structure of space. So the fact that relativity works with these connections between space and time is sort of an emergent feature of how things work in our models. But what that video is showing is kind of this successive, kind of successive kind of moments of time and kind of the updating of the structure of space that represents our whole universe as time progresses. And actually, there's sort of a red parts of the network. Those are the ones that just got updated. And it's sort of a big, big issue which ones get updated when. Because the rule for updating just says you can update whenever you feel like, but the actual rendering of this depends on how you're observing it. And so in that particular video, what was done was to say, everything that can be updated now consistently, without overlapping something else that could be updated. Just go ahead and update all those at this moment. And that sort of has this idea that all of space is updated at successive moments in time. You don't have to do it that way. A different observer would observe something different happening, though, underneath the sort of causal graph of what? The sequence of events that update that correspond to the updates that will always be the same. But our perception of it and the way we render it is very different. And of course, that rendering is just based on taking the connectivity of the atoms of space and just laying out the graph in a nice sort of human, Human understandable way. It's not. There's nothing intrinsic about those atoms of space being placed at the particular places they're placed. The only thing that's intrinsic is how those atoms of space are connected to other atoms of space. So this is. That's kind of the idea. And then this particular. In this particular branch, to an observer of the kind that is being used to make that video, their conclusion about the structure of space is that it will be about 2.6 dimensional, which is kind of weird. To a different kind of observer, you would see something different there. But that's kind of the most generic observer and the one that's used for that particular rendering. Let's see. Well, I mean, there's an awful lot to say about a physics project. One more question about that, then I'll talk about some other things. Saurav is asking. Could I talk a bit about energy as a flux of causal edges through space, like hypersurfaces? That's kind of the formal statement of what energy is in our models. Here's the intuition. Energy is basically the amount of activity in the network. So energy is kind of the rate at which things are changing in time. It's the rate at which updates are happening. But when you try and make that a little bit more precise, it's like, well, rate at which they're happening, you know, density of updates. What does it mean, density? Space. We haven't defined space yet. Space is being defined by the things that are being updated and so on. So you have to be a little bit more precise. And what happens is you're looking at this causal graph of this update happened, then this one happened. There's certain updates that must happen in a certain order because the input to one update uses the output from another update. So that output, the update whose output is being used, has to have happened before that output is used to the input to some other event. So you build up this causal graph of how these events are related. And some have to be in these kind of timelike sequences of one, then another, then another. Some can be space, like separate in the sense that those events could be sort of just happening at different places in space at the same time simultaneously. So the flux of causal edges is basically saying, imagine that you've got this causal graph and you're saying, okay, there are these things which are space like separated in the sense that they don't have to follow each other. Now, there are different ways that you can make a foliation of this causal graph. There are different ways that you can decide what are the surfaces of simultaneity. What, what, which events are the ones we should say happen simultaneously, even though they're happening at different places in space. So once we define this series of simultaneity surfaces, this foliation of the causal graph, those are our space like hypersurfaces. Those are our all of space at a moment in time. And when we talk about flux of causal edges, we're saying that there are causal edges which go from one space, like hypersurface, to the next. There are other causal edges that we're looking at sort of the projection of these causal edges into the direction that corresponds to the successive space, like hypersurfaces. And essentially what that's doing is it's giving us a more invariant, more mathematically defined way to basically see how much activity there is in the network. And that activity in the network we identify with energy. I'm really surprised that the identification is as simple as that, but it is. And once we have that, we can start saying, well, how does the presence of energy affect, for example, geodesics, shortest paths in this network? And we can discover that the presence of energy deflects these geodesics. And that's exactly what the Einstein equations say should happen, because they're relating the curvature of space, which is what determines the curving of those shortest paths. The curvature of space is proportional to essentially the energy density. So that, that's kind of how that works. Gosh. Rudy is asking on the topic of conferences, do you think technology will change the format? Will panels and standard talks remain constant? Will AIs one day be participants? Well, you know, even a combination of pandemic plus technology changed conferences a lot from. And, you know, virtual. I have been doing kind of video conference conferences for, let's see, 26 years at least. Well, I had been doing at the beginning of the pandemic, maybe 23 years or whatever, but for a long time. But sort of the virtual became much more common. And that has advantages that there are lots of conferences and get togethers where sort of the, the cost of doing it as a thing where everybody flies into a place is just way too high. It will never happen and it will never work with people's schedules and things like that. So things can happen that couldn't have happened, get togethers can happen that couldn't have happened before. And just like, you know, I'm, I'm talking to you in this live stream and that's a thing of this sort of modern virtualized times that, you know, I've given lots of talks in person, but at a much lower density than these live streams. And this is a, this is a thing of modern times now. You know, to what extent will AI be relevant to this? I don't know. I think that there's sort of very practical things like summarizing things that are going on. Like you can come in late to a talk, you can say, give me to the AI, give me a summary of what's been said so far. That's the thing that sort of changes the human dynamic of that in terms of the sort of the value of sort of human interaction. I have to say I think that what we've seen, well, for very specialized conferences, it's kind of like people are just going to get sort of fact, fact, fact. Maybe there's a clique of people who little community of people who like to hang out together because they all study this particular, very specific area. But I think that the things that I often find the most valuable are these kind of conferences where there's all kinds of people milling around and they all do different kinds of things and you get to meet those people and that becomes in a sense the focus of the conference rather than, oh, there's going to be a talk here, a talk there. I think the other thing that maybe is becoming more common is kind of interview style presentations at conferences, so to speak, which are, I think both are a lot easier for the speaker. And I think they're often a lot more gets communicated and a lot. Because in a sense if you're giving a talk, there's a whole arc of that talk. And often you feel like you have to give, you really do need to give that full arc. But actually if it was just like there's this question, okay, given the answer you've given to that question, there's another question might be in a different direction that can the sort of total density of information communicated is actually higher than in that kind of whole arc of the talk. Now in terms of AIs doing interviews, that's an interesting possibility. I don't know. I mean, if really the point is just draw out the speaker or for example organize questions people are asking through some AI, that's an Interesting thought. I've not really, not really considered that. So. Right. I think that's my immediate thoughts on that subject. Stephen is asking here what is it like to actually run a task on a supercomputer? Most supercomputers are these days very parallel computers. They have, you know, tens of thousands of CPUs and so on. And you know, actually in Wolfram language there's quite simply functions like parallel table, make a table of things where each element of the table is being worked out on a different computer. And you know, I, I do this routinely. My, my personal mini supercomputer is about 150 separate CPU cores on computers that are dotted around. Actually not even all of them, but the particular set of computers kind of at my house. And I routinely say sort of parallelize this computation across all these computers. I have to say it's often a pain in the neck because these computers, by the time you're connecting to all these computers and there's some, one of them is down and there's an issue and it has to back up and it has to retry and so on. That can be kind of an annoying piece of usually largely automated but sort of computer wrangling. But then it's like, then it just, you know, things are happening on these different parallel pieces. It's then important to know sort of how is the distribution of the task working. Because if the whole task requires a thousand different pieces to be completed and one of them is a holdout and it takes a year of CPU time to complete, you're not going to have a happy time because all your other 999 already finished, but you're just waiting for that one holdout. So it's sort of a complicated art to distribute sort of the load as well as possible. I think other than that, I mean, I would say that most supercomputer systems have these job submission systems that. Well, isn't true for the ones that I have personally because I'm sort of in a first approximation their only user. And so it's like, well, I have to just remember, am I already running something? All these things. If I am, if I try and run a second thing, it's not going to run very fast. But so I'm a very simple kind of job submission program. It's just me remembering, oh, I'm doing an overnight run on all these computers, I can't do a second one. But in the more sort of official case where many people are trying to use a supercomputer, there tend to be these job management job submission systems that handle that. Actually in Morphem language, for example, there's a function remote batch submit, which submits kind of just lumps of orphan language code to be run on batch in a batch way on cloud services or supercomputers. And that's something where the only difference from what I was describing is the answer doesn't come back to you immediately. You're sort of sending it, you're submitting this batch job and it goes off and maybe a few hours later it sends you mail and says it's finished. Now you can click somewhere or you can go into a Wolfram language notebook and you can start looking at the results that you got. But that's, that's kind of the experience. Let's see, Rebel is asking, don't you fear humans will start to live mostly in digital worlds and most of cognitive energy will be spent on problems there and not in natural science? Well, I mean, welcome to the world of video games. I think it's an interesting question whether there is, and I'm not a video game player really actually at all. I'm hopeless and not adequately knowledgeable in that area. But it's like we can do an experiment in natural science or we can go into Minecraft and we could do an experiment. Now, turns out the physics there is kind of a simple imitation of the physics that we see in real life. We can certainly imagine a game in which the physics is utterly different from what we see in real life. And we could be spending our sort of game time trying to reverse engineer the physics that's been put into the game. Just like we try to quote reverse engineer the laws of nature to see how our physical universe is put together or how we perceive it's operating. So this question of, well, will we eventually get to a point where most of our effort is spent kind of exploring what we would today see as video games? Yes, I think that's a likely possibility. And I think the thing that to me right now as a non video game player, not well connected to that kind of paradigm, that's like, boy, that's a really bad outcome for humanity. But I think one of the features of history is that any given time people say I'm doing this because, and the because changes. And sometimes in a different age, that because seems just bizarre. I mean, one that's not terribly bizarre but dominated a bunch of a thousand years ago or something is like, I'm doing this for the greater glory of God. And what does that mean? Well, if you have certain religious beliefs. That has a definite meaning, but it's also quite abstract. At some level, at some level it might be a statement or another statement that's very common, I would say in modern times in the tech industry is we're doing this to make the world a better place, which I view as being kind of a modern version, but of. For the greater glory of God. But you know, it's kind of a. These are all things that are sort of explanations why are we doing this? You know, at some other times in history it might have been like, what do you wish for people? Do you wish for people to, for example, lead a fulfilled life? Okay, that might be a current desire. Do you wish for them to lead at a different time in history? It might have been to die well and you know, for the next life, so to speak, or just as a matter of honor. Or do you want, you know, at different times in history, people have had very different sets of goals which at another time in history just look bizarre. So for example, in, you know, the individualist kind of self helpish kind of push start, I suppose, 1950, 1960s, where it's kind of like, you know, do the best for yourself, so to speak. Whereas at other times in history and other cultures perhaps it's kind of do the best for the community, that's the important thing, as opposed to do the best for yourself. And each of these things has a. They each have a different kind of. So that's what the real point is. Do this, you know, make the world a better place, you know, feel us, feel as at peace with yourself as you can. Whatever the goal is, those goals have changed over time and there is no absolute to what those goals are. Those are just the goals that we decide are the goals we should have. And so similarly, if we imagine a future world in which kind of it's all sort of uploaded souls playing video games, so to speak, in that environment, there will surely also be objectives, just as there are today of people wanting to, you know, maintain their streak in some social media platform or achieve things that I wouldn't necessarily even know or understand to my detriment in, you know, in video games, you know, get to the next level in this video game, do, you know, achieve this objective in this video game. I think the only difference right now is, is that we still feel like, I think for the most part games are kind of like there was a puppet master who defined the game. But I think it is not a far reach. And it's already happened with lots of Games that like the story of computational irreducibility, the original puppeteer made the game, made the rules, but the consequences of those rules, they could not foresee. And in fact, the only way to get to the consequences is essentially to play the game and see what happens. And so that then makes gameplay much more like the sort of the process of living in the world and experiencing nature. And so I think, and in that situation, many of the things that we now say, that's the point, that's what's, you know, that's the objective that we're satisfying, will seem much more similar between the sort of video game case and the case in nature. So this question of, for example, given that there were rules put into the game, but then we had to sort of just play the game to see what happens. Well, so it is with nature. There were rules put into nature. We don't necessarily know what they are. We have a much better idea now than we did a few years ago. But the consequences of those rules, what can happen in nature as a result? Is it possible for us to go faster than light? Is it possible for us to do this or that? These are things which, just from knowing the rules, it's extremely difficult, usually impossible to determine that for certain. We really have to just try out lots of experiments, invent lots of technology, those kinds of things. And I think so it will be in the case of video games, or, you know, what I'm referring to as video games, the virtualized world, that it will still be the case that it's like, well, can we build this thing? Can we make this, know what are they called? Mods? No, that's, that's a little different. But can we make these, these features in the game that allow us to do this or that thing, and that will be kind of the environment. It won't be the true environment of nature and it'll be the environment of our experienced nature. And by the way, there is no true environment of nature. It's all what we experience. It's all kind of, kind of where we, how we perceive the ruliad, I don't think, and, and how we perceive it with our current biological, physical instantiation versus how we will perceive the ruliad. Same ruliad, different perception when we're hanging out in the video game is, is, it's interesting. And this, My assumption is that there needs to be a continuity between our experience of the physical world in our biological form and the experience of the kind of virtual world in our virtualized form, or we won't even recognize it as being sort of the same thing. We won't recognize that. Yes, we've successfully transplanted our kind of consciousness from the biological world to the purely virtual computational world. And how that will work, I mean, my guess is that to make that work, it will have to be a gradual process that will gradually have the neural connections and this and that and the other. And it'll gradually be like, what does it feel like to have part of your brain be just sort of executing digitally somewhere else? And then we kind of feel like this and then more of it is executing digitally. And eventually it's kind of, we made the transition, so to speak. My guess is that's how it will work. Just as if you take somebody from a thousand years ago and you plonk them in modern society, modern technology, they will be somewhat lost. But if you have to give them a path. Actually it's sort of an interesting case in point of this, and it makes me feel a little bit of self improvement for myself is with video games, I. If you plunked me down in front of a modern advanced video game, I would not have a clue what to do. You know, it takes me, it would take me sort of. There's a learning path that I would have to go through that goes. Which I should do because it's kind of embarrassing. I don't know these things, but I have so many things I want to do. I don't feel like I should be doing these things where I'm sort of. I like to play a game where I invent the whole game, so to speak, rather than when some part of it is invented for me. But in a sense you might say, well, why am I interested in natural science? Because that too is a game where part of it has been invented for me. And I mean, I suppose if I'm to really be introspective, I'm actually more interested in cases where I get to define the formal rules than I am in sort of reverse engineering the actualities of natural science. So I suppose it is a consistent, you know, if, if, if, if sort of I don't know what personality trait that. It's kind of like I'm the same thing that makes me interested in and not so interested in video games makes me sort of all the more interested in rules that I define myself and what the consequences are. So I think, you know, a very. An interesting question would be if you are looking from the outside at this box with a trillion souls in it that are all kind of interpreting the Universe in certain ways. And you look at what is happening in that box and you say, do these souls have an inner experience? You're looking from the outside. Do these souls have an inner experience of understanding the world in which they're living or not? Same thing you can ask for a human. Does that human whose brain we can probe only in very coarse ways with kind of, you know, brain recording of various kinds, does that human have an inner experience of understanding what's going on in the world? Hard to tell. But it will be interesting to know if there is sort of a mechanism for if there's sort of a test of. You see these bits that are representing the innards of the brain, whether they're a human brain with biological one or whether they're a virtualized brain. You know, you see the bits, can you tell what the inner experience, what can you tell about the inner experience of that brain? Challenging. But I suspect there are some things one can say and that would be an interesting challenge in kind of to what extent? Well, to what extent we can attribute other minds in other things because it's kind of a thing that has. One of our fundamental assumptions about the world is we have an inner experience of what's happening inside our minds, but we don't know for sure that there even is an inner experience in another mind. We talk to a person, they seem to be doing mind like things that remind us of the sensations that we have ourselves. We try and talk to a cat. Does the cat have a mind like experience like ours? Probably not so much so, you know, it's a question of, to what extent can we make this assumption of mind likeness in another thing. And if we could see that in sort of the bit patterns of the disembodied soul in this kind of virtualized sort of game like environment, that would be an interesting thing to know whether there's a signature of that kind of I am a, a mind with an internal view of things. Let's see, Jamie is asking, would it be possible at some point to have both a digital and a physical consciousness simultaneously, and when you sleep they combine to sort of absorb the knowledge of both experiences. It's kind of interesting. Look, I think that in some sense we are outsourcing all kinds of our capabilities to computers. Whether it's a remote webcam that's watching something, whether it's the memory of, you know, my big archives of everything I've done that are on my computer, we're sort of outsourcing things that were just in our brains and I think the sort of, one of the features of human experience is that we do feel like we experience a single thread of time. So there is ultimately the attention system of brains which says this is what I'm experiencing, this is what I'm paying attention to. And it's in one thread. And so when we see that remote webcam, we're still pulling that remote webcam into that one thread of experience. I think it's an interesting question whether what it would feel like to have more than one thread of experience. I think there may be some things that we consider to be sort of psychiatric issues where people sort of dissociate multiple threads of experience. And for better or worse, I fortunately don't have that personal experience. So, you know, it's hard to know what that really feels like from the inside. So it, I think, you know, that that's a case where what would it be like to have multiple threads of experience and really have them sort of rattling around in one's mind? I don't know. And maybe some people do have that kind of experience. Maybe it does not match well with kind of operating in the world as the world is currently built. I mean, it's kind of like people discuss. The world is built in a certain way and society is built in a certain way and society is built in a way that's good for hopefully many of the people in the society. It may not be good for the not so what people, whatever it is, the non neurotypical, whatever that might mean. One can imagine there are other parts of society maybe which are well built for that. And it's a different part from the part that's well built for the usual experience. And so most of our human experience is this kind of single threaded human experience. And that's kind of the thing that seems to work well in the world for how things operate. And I don't know what it would be like when we're. My guess is it's going to be single thread of experiences in charge. Now when that single thread of experience is digital and when it's just probing, for example, let's say we replace biological brains with digital brains, but we still have bodies with biological things and we've got nerve fibers going out from the brain to wiggle our fingers and things like this, what will that be like? And then occasionally that will be signals coming back from the biological us to the digital us, saying by the way, you just stubbed your toe or something. Or by the way, this, you know, your hunger sensor, which wasn't Part of your digital brain is now firing, so to speak. So it'll be an interesting thing what that, you know, what that feels like. And so many things about the human condition will change when we have sort of a major digital way of existing. And I'm not sure that civilization as it currently exists, whether it will survive that transition in a form that will be recognizable to us today is quite unclear to me now. Whether to the entities of the time, they'll say, oh my gosh, the roof is caving in. You know, the sky is falling. It's. It's all disastrous. Or whether they'll say, hey, we're having a great time here. You know, we're doing all kinds of cool things. We're. We're. Even though there's a lot of. The value system that we had from our biological experience is no longer relevant, we're having a great time over here. I think that. But yet to us today, it's like, my gosh, what a. What a disaster. There, There are, you know, all these, you know, these trillion souls in a box playing video games. You know, that looks really bad. It looks like something, you know, it looks like the end of history. And it's all, it's all sort of. It's all gone to hell, so to speak. But, you know, it's worth remembering that if you were to look at sort of today's society from the point of view of society a thousand years ago, you would, oh, I don't know, to pick on religion again, for example, you would, oh, my gosh, people are not praying for some fraction of the time or most are not of the day. That's a shocker. You know, that's what we would have expected. That's part of humanity as of, you know, a thousand years ago or something. It doesn't happen to be in much of the world today. But similarly, people saying, oh, you know, I'm. Well, even from longer ago, you know, I'm trying to accumulate more stuff as I go through life to other people of long ago or different cultures and so on. It's like private property. What is that? That doesn't make any sense. They might say, you know, it's all about kind of the community or something. And then at different times, one has different. There's different principles about what seems to be the worthwhile thing to do. And I think it's hard to project to say this is an issue always with judging history and judging the future and so on. It's like at the time when people did X, you might Say today, that was a shocking thing to have done, but the time it was done, that was just part of the culture of what was going on. And so similarly, there are things that we might imagine about the future where we say that will be a shocking outcome. But yet to the future, to the entities of the future, so to speak, it will seem like a fine outcome. It will seem to make kind of cultural sense in that moment of time. And I think that. So, you know, I think the. It's very hard to judge the future from the present, to judge the past from the present. I think it's worth just remembering that to the entity in the moment, there is a certain perception, there's a certain feeling. And you can sort of recurse on this question is what they're feeling at that time. Something good to feel. And that's, you know, even the feeling that. Oh, I don't know, you. The feeling. Some. Some feeling that you might have at a certain moment, you might. At another time in history, that feeling might have been a shocking feeling. I mean, for instance, I don't know, I won that battle. I killed my opponent. Okay, but sometimes in history, that's like, you feel good about that. At other times in history, that's like, no, that's not how things, you know, that. That's. That's terrible. That would be, you know, that would be incredibly traumatic to be in that, you know, in with that feeling of that. Of that having happened at a different time, like now in. In history, so to speak, and much of. Of what happens now. So anyway, a few thoughts on that. Let's see, Pro is asking what if you take someone's videos, articles, life notes, lots of things, feed them into a specialized AI, make it answer the questions, behave almost like that person. That technology is not so far away. It feels like sort of a consciousness transfer. Do you think it can be trans. Classified as that? Yes. I mean, I've certainly thought about that even for myself. It's kind of like I've put like 50 million words of stuff out there and that's probably enough to reconstruct a pretty good approximation to me. Actually, somebody just sent me some once. One thing that was produced by an LLM that was supposed to be sounding like me. They just sent it to me this morning. It was terrible, awful. It didn't sound like me. To me, maybe other people, it does sound like me. I have noticed before that things that. To other people, when I see what an LLM produces, that's supposed to sound like somebody else. I often say that's pretty good. But when it's, for me, I kind of know that's not how I talk. That's not what I say, that's not what I would say in that case. So I don't know what it takes to get above that bar, but my guess is it's going to be possible to get above that bar. And then there are many interesting ethical questions. I mean, there's all sorts of questions. I was just exposed to one of these in a discussion recently about what is the term now being used? Griefbots. I think that is an avatar of a person who's died and under what circumstances, who gets to determine that that thing exists? What do you get to do with it? How does it, you know, is it good for people to have that? Under what circumstances it good for people to have that? How does that all work? That's something that I think is a. Is an increasingly relevant question. I mean, for somebody like me, for example, because I do have an awful lot of stuff that is raw material from which such a thing could be made. That certainly is an interesting question. And I suppose it's kind of like in the time of ancient Egypt. It's kind of like unless it was written down, kind of, it doesn't have a long time life, so to speak. And that worked out really well for the Egyptians, as in, we can now read their, you know, in their. We can read their inscriptions and we can know things about their lives 4,000 years later. And so maybe the answer is, well, you know, insofar as one seeking the eternal life, which has been something that us humans have been often interested in, it's kind of like, well, put up that, you know, let that avatar of yourself exist as well as possible, as far into the future as possible. You know, perhaps that's the analog of put away those things in the, you know, put all those extra bits around the mummy or inside the mummy or whatever for the Egyptians, so to speak. And maybe that's the analog of that. Elsie is commenting. Imagine those entities perfectly conscious and everything, but only digital come to vastly outnumber us biological ones. Yeah, I mean, that will surely happen because it is much easier to clone a digital thing than to clone a biological thing, at least for now. I mean, it's always amazing to me, you know, we have an awful lot of cells in our bodies. 100 trillion. That's a lot. And it's awfully, you know, the number when things are molecular scale. Even cells are much bigger than molecular scale, although there's a big variation of the sizes of cells. But you know, when there's an awful lot of stuff, awful lot of distinct things that fit in, things that are kind of human scaled. And so I think it's not clear. Yeah, I mean, also what counts as biological is going to get complicated. I mean, we're going to have more and more, kind of more and more of these. More and more sort of things like artificial tissues and so on. We'll have more and more sort of interaction between nanotechnology and biology. More and more things where we can kind of replace that blood cell by some kind of manufactured, engineered thing. It's not completely clear what the difference is because it's kind of like, well, that blood cell was made by some molecular processes and out at the end of that plopped a blood cell and then we have this kind of set of molecular manufacturing and out of the end of the molecular factory, so to speak, plops an artificial red blood cell. It's not clear how different those kinds of things are. So in any case, yes, this question about sort of. Well, there are all kinds of questions about insofar as collective decisions have to be made about the world and insofar as there is sort of, there are all sorts of digital entities that are starting to populate the world, you know, how does that all work? And how does one, and you know, at what point does one decide that the happiness of digital entities is important? Well, certainly by the time it is reasonable to think that by the time the future of some human thread of experience for a human is in that digital form, that its happiness is relevant. But now imagine that you've converted your sort of consciousness somehow to the digital form. You're disconnected from the biological one. You've got the digital one. It, it's your future, so to speak, and it's you at some level, and then you copied a million times. Well, does each of those million copies have the same right to life, liberty and the pursuit of happiness, so to speak, as the one original one? Or does it get diluted by a factor of a million? Or what happens? These are complicated issues. We've had the idea for our species that seems like the obvious idea, that for every human, every individual human, it's kind of like there's a certain bundle of rights and a certain bundle of things that it's like human by human. But when you take that one human and you clone it, effectively you digitally clone it a million times, what happens to that? And how does that compare? And let's say you've got. If you decided that for every one of those digital clones, it's got as much right to decide what's happening as any other one. Then you say, well, it becomes a clone war, so to speak. Not to sound too Star wars like, but a digital clone war, as in, I've got a quadrillion clones, therefore my views are more important than you, who's only got a trillion clones. And actually, it's kind of interesting as I, as I'm talking this through, that that is so bizarrely similar to the struggle for life in biological evolution. That is the winner is the one who has the most progeny. It's kind of like the traits you have are going to be the winning traits. If you have the most children, so to speak, over at least over the course of generations. You know, the butterfly that has the purple wings that does better than the butterfly that has the green wings, and the purple winged butterfly tends to have purple winged butterfly kids, then that's going to win out. And that's the story of biological evolution. But if what you say is in the kind of struggle for digital life, in the case of AIs, it's like you've got the one that's cloned a million times, the one that's cloned a billion times. If the one that's cloned a billion times, it feels like you can clone as much as you want. Now that's sort of interesting because in the end you hit resource boundaries. In the end you're cloning, you have clones of you expanding at the speed of light, and then you are hitting kind of the raw edges of what is kind of physically possible. I suppose it's an interesting thing to think through. Imagine a kind of. I haven't thought about this before, but imagine kind of a digital existence that is kind of in the ruliad. There's only one ruliad. You don't get to escape the ruliad. You're always existing there. You're always computations taking place in the ruliad. But you say, I'm going to, you know, my thread of experience, my thread of meanness is going to somehow be spread through all these different kind of pieces of the ruliad. And somebody else's thread of meanness is spread through some other pieces of the rule I had. And in a sense it's kind of like, how does the ruliad become more about me, me, me, so to speak, rather than about some other entity? And sort of how does that work? And there are clearly constraints like the meanness can only spread at the speed of light in physical space, it can only spread at maximum entanglement speed. And branchial space it can only spread at the maximum rulial speed. In rulial space those speeds are very high, but there is a limit. And there are in a sense it's telling you that there's a. That sort of. Those are some constraints. Now what happens when there's sort of competition between the me and the you? I'm not sure how to think about that. And maybe the way to think about it is incredibly similar to the way that we actually think about biological evolution. Maybe it turns out natural selection is actually something that is sort of will be played out at that level as well. I mean, I, I've sort of thought a little bit about the kind of the society of the AIs. But you know, this is one of the things that one kind of learns from doing computational stuff is, or learns from actually from physics as well. It's like there can be an awful lot of things that is, you know, you have to, once you've got to. Example, one of the things that held me back in our physics project was that I had this view of physics as being somehow computational, but I could not imagine that physics was the unbelievably profligate waster of computational resources that it is. That there are all these branches of history and they're all branching out and branching out and at every moment there's many, many more branches being made. And it's just unbelievable amounts of computation happening. And for me, I still had this kind of was holding on to this idea. Computation is kind of a valuable kind of thing. The universe can't just waste it in that completely crazy way. But actually it does. And I think this kind of, this is part of sort of overcoming one's sort of existing paradigms and realizing that yes, sort of things like when have you thought about, okay, we've got an AI, we got one AI, it's really cool, but what about if we had a million AIs or a billion AIs or we filled every fragment of the universe with what we can think of as an AI? That's sort of an interesting kind of end point that I guess, you know, we're still a little bit stuck in that we've got one AI and we're very proud of it, rather than the what happens when there's a whole society of AIs or kind of a whole RDs worth of AIs. So anyway, that's a few thoughts actually. I have not so thank you guys for leading me in this particular direction in the ruliad of understanding these kinds of things. It's an interesting thing to think through. And by the way, I see somebody commenting that this is like mini science fiction adventures. Yeah. And I. I must say that I think some of these things about thinking through alien minds. I think that is a very important thing for us, particularly right now as AIs come more on the scene. Understanding what alien minds are like, it's sort of. In some sense, it's a little bit like the. I mean, I suppose it's the ultimate multiculturalism, so to speak. Understand the alien minds. And it's something which, even within sort of the cultures of the world, it's something that sort of getting inside that way of thinking is always challenging. Very difficult in many cases. But to kind of imagine what it's like to be in an alien mind is yet more, but somehow revealing, I think, of both what one can know and what one cannot know, even within sort of human minds and different human cultures. So I think it's a really interesting exercise and one that is particularly pertinent right now with the kind of arrival of the AIs to think that through. And I can imagine being able to express those ideas as much in science fiction as one can in kind of the sort of cold facts of what will go on. I mean, imagine what it's like to be some sort of struggle for life with. Or struggle for. We don't call it life. I don't know what you should call it. The struggle for existence with all of these other competing sort of digital, cloned minds. You know, what's. What does that feel like? What can we describe that? Can we humanize that experience? Is it. You know, what's it like? I mean, I could even imagine. I don't think one hasn't seen this really too much is kind of what does it really feel like to be an ant or something? I know there's the Bug's Life movie, which I haven't seen in a very long time, which has some versions of that, particularly about scale and so on. But what does it really feel like to be sort of in part of some collective species like that? I'm not sure, you know, I don't know how to think about that. And perhaps sort of the fictionalized account helps one potentially to sort of be able to get a better internal feeling for what that would be like. But it's something I think is know it's a. It's a challenging thing to do. All right, I should wrap up there and. And go back to some much more prosaic things in my. In my day job here. But thanks. Thanks for prompting all kinds of interesting thoughts here, and I look forward to seeing you guys. Another live stream, or at least imagining. And this is again, a very digitalized virtualized experience for me. And interestingly, I don't know, maybe I should. Will, you know, for some reason, it is still a human experience of some kind, even though this is sort of a deeply virtualized situation. By the way, I might say for next week, it is the time of our annual Wolfram Technology Conference, which is online this year and so accessible to people more easily. Somebody was asking about the evolution of conferences, and we have one coming up just next week where. It's all virtual, so it's quite accessible. You know, I have to say, things we've experimented with, for example, having people in sort of a physical space and moving around a virtualized physical space. I really thought that was going to be very compelling. I pushed very hard for a company I've been an advisor to deploy at the beginning of the pandemic, such a thing. I think it could have been slightly better deployed, but they did not. Terrible job. But it's sort of interesting the extent to which people can or cannot interact well in that kind of virtualized simulacrum of physical space, so to speak. I'm not sure if we're doing an experiment like that at our upcoming conference, but in any case, there will be certainly various opportunities to interact virtually at our conference next week. All right, well, thanks very much and bye for now.