Future of Science and Technology Q&A (September 29, 2023)

Sam. Hello, everyone. Welcome to another episode of Q and A about future of science and technology. And I see a bunch of interesting questions here. Where should we start? Olmer is asking, what can you say about the future of physics? Well, gosh, I'm a funny person to ask that, because last three years we've really done a bunch of things which I think define kind of a very new direction for physics in terms of its methodology, at least. I mean, if we look at the history of physics, there have been, well, antiquity. People started talking about maybe there are definite laws that govern the world, maybe there are definite regularities to the world, maybe the world is made up of lots of identical things. There's sort of definite regular things that one can say about the world. Then sort of the thing that launched kind of what became much of physics as it has been, is what happened in the 1600s, first with Galileo, then with Newton and so on, which was the mathematicization of physics, that one could take mathematical formulas, one could take algebra and so on and apply this to physics. And then calculus was invented. Then that became sort of the main methodology of physics is describe the world using mathematical equations, particularly calculus. And it had a great run. I mean, what happened at first was mechanics. There was a lot of development of mechanics. The big problem was the three body problem. Things like Earth, moon, sun, with gravitational attractions between them come unsolved for their motions. And that was finally done respectably, much by the beginning of the 20th century. But it took a while after Newton's 1687 Principia, which with his universal law of gravitation and so on, it took a while for those formulas to actually sort of get worked out. But then after that came lots of other physics, whether that was the physics of fluids, fluid dynamics, the equations of fluid mechanics, the equations of solid mechanics, the equations of electromagnetism, lots of equations for things got developed. And then when quantum mechanics started in the 1920s, again, it was a story of equations, the Schrodinger equation, the Dirac equation, the equations for describing things. And that's kind of been the dominant paradigm is this kind of mathematical equations type paradigm. Now, there were some things that didn't quite fit that. I mean, for example, in the development of statistical mechanics, in the development of trying to understand thermodynamics, trying to understand the second law of thermodynamics, those were things that were happening in the 1860s and so on, and they were not so much kind of, let's just write down an equation. People certainly tried to do that. They didn't succeed in deriving the second order of thermodynamics in a sort of equational type way. And actually, then I suppose a different tradition of. Of physics emerged that had kind of had a precursor in the second law of thermodynamics. Because when people like Ludwig Boltzmann were trying to prove the second law of thermodynamics, the thing that he realized one had to do is to start thinking in terms of discrete atoms. Nobody knew discrete atoms existed. But to think about kind of the formal structure that you get, if discrete atoms existed, and you're starting to count things combinatorially, you're starting to be able to make very different kinds of arguments from the kinds of arguments that have been made on the basis of algebra and calculus and so on previously in physics. And those arguments were things about, well, we have this whole collection of different possible states, and there's a certain kind of randomness, and we take averages and things like this. And that was kind of a new way of thinking about physics, more, in a sense, a way that went back to kind of philosophical traditions of kind of, let's just figure it out, rather than, as Leibniz would say, calculamus, let us calculate, by which he meant, you know, do algebra and calculus and so on. And so then that tradition, the kind of the big prize, was, can you prove the second law of thermodynamics from pure mechanics, from just knowing the dynamics of individual molecules bouncing around? Can you prove that in the aggregate entropy will tend to increase, that things will tend to get more random, et cetera, et cetera, et cetera? That was attempted for the latter half of the 19th century and failed. And one of the later people who tried to do it was a certain Albert Einstein, who, starting in about 1903, wrote a series of papers trying to prove the second order of thermodynamics using arguments that were, in a sense, kind of sort of philosophical, logical arguments. If you have a box that is connect, that has this temperature and it's connected to one with this temperature, and they come to equilibrium and they do this and this and this, then it must follow sort of logically that the second law of thermodynamics is correct. Okay? He never succeeded at that. In fact, what he did was kind of a bit off track. Then in 1905, he kind of took the same methodology of just, let's set down essentially some axioms for how the world must work and work out their logical consequences, and let's see where that takes Us. And so the first place it took him was special relativity, which was a story of assume the speed of light is constant, assume that things appear the same in all states, states of motion, then logically we can deduce that there will be time dilation, et cetera, et cetera, et cetera. So, big win there. Similar thing with Brownian motion, analyzing kind of what the dynamics of sort of random motion of particles in a random walk would be. And then somewhat similarly with the idea of photons and the kind of taking seriously the quantization of the electromagnetic field. Again, sort of an argument by this is the way things have to be, with in that case, a certain amount of mathematics dressing it up, so to speak. But this idea that you could sort of figure things out from this in the structural way, which had emerged from the work in working on the second law of thermodynamics in the 19th century with Pope Bill, like Boltzmann, kind of translated into that, okay, so there was this big burst of interest in activity and physics starting in the beginning of the 20th century. And another piece of that same kind of story was Einstein's 1915 general relativity. And then in the 1920s, sort of lots of development of the idea of quantum mechanics in a fairly traditional mathematical framework. So that led to, in the 20th century, three big ideas in physics. Statistical mechanics, of which the core is the second law of thermodynamics, general relativity, theory of gravity and mechanics, and quantum mechanics, and later quantum field theory, the theory of how things on the very small kind of work. So those have been the three dominant theories across the last century. And a certain amount of development has been done. Those theories have been extremely successful. And it's been something where. But it's reconciling those theories a little bit complicated, and particularly between general relativity and quantum mechanics, been challenging to kind of fit those two theories together. The thing that got really exciting was our physics project, which kind of got launched in 2020, where we really can understand kind of how all three of these big theories of 20th century physics, how they fit together. And actually, in the end, they are in some sense the same theory. They all work the same way. They all are a result of the interplay between underlying computational sophistication of the processes going on in the world and our computational limitations as observers of those processes. So for me, it's kind of a really exciting sort of convergence that these three things where we thought, well, statistical mechanics might be derivable, but general relativity, we didn't imagine that was derivable. From anything sort of more fundamental and similarly quantum mechanics. And now what we realize is they're all sort of equally derivable from in the end, sort of necessary features of formalism. So, okay, so what does that mean? Well, it's a tremendously fertile moment because it means we've got a new methodology. And in a sense the core of that methodology is just the description of everything in computational terms. What is space? It's not some mathematical thing where we have some manifold that we described with mathematics and calculus. It's this hypergraph, this thing made of atoms of space, where in principle we could just say it's this particular hypergraph and well, not quite this particular one because it ends up being a multi way system, et cetera, et cetera, et cetera, but roughly you could sort of conceptually pick it up and grab onto it. It's a thing where in the end everything is represented computationally. We can run simulations, little simulations where we can actually they're big enough that we can see black holes and dynamics of black holes, things like that, but they're still very small compared to sort of our everyday experience of the world. But so it's a fantastically, it's just great. There was a, as I say, there been a couple of big advances in sort of the paradigms for physics. One late 1600s, kind of the introduction of mathematics into physics to kind of the, the early 20th century, this kind of introduction of kind of this almost logical way of thinking about physics and how things in physics get put together, which I think Einstein was a key sort of contributor. And now we have another one in which we're kind of thinking about physics in fundamentally computational terms. And that doesn't mean taking the existing equations of physics and putting it on a computer, something people do with our technology, with Mathematica, modern language and so on all the time I'm talking about thinking about physics in a fundamentally computational way where the actual mechanics of the universe is computational processes sort of all the way up and down. And what's going to happen from that? Well, we're just at the point. It's a difficult thing to actually work through, through the formal consequences of. It involves the sort of very upper reaches of abstract mathematics. It involves, well, a lot of kind of practical computer simulation. It involves a bunch of new figuring out like, you know, we've got calculus and we've got, you know, one variable calculus and multivariable calculus, but it's integer numbers of variables. We need the generalization of calculus to fractional dimensional space for Example, something which just not been worked out in the history of mathematics. And we have to work it out to be able to understand the consequences of these models. So it's a thing where that's sort of the direction. Now what is happening in more detail is one is kind of really developing the formalism. That's a story of pretty much all the different methods of mathematical physics that have been developed plug into the sort of foundational approach that we're taking, whether that is string theory or causal set theory or all sorts of other kinds of approaches to mathematical physics that have been taken. Unless those approaches are really completely off track, and most of them are not, they plug in as some kind of limit of what we're doing. And understanding that is an important direction. And I think then the thing that we can then do is say, well, okay, what are the consequences of this model? How does it, what kinds of predictions does it make? What kinds of things does it manage to say the world must be this way, it must have an electron, a mule on a tau lepton. We don't know that yet. But to be able to show from this underlying model what its consequences are, and we're starting to be able to see a big frontier that I'd like to find more people to help with actually is sort of understanding the sort of everyday astrophysics, condensed matter physics, consequences of our models of physics. What does a dimension fluctuation look like to a space telescope? What is the consequence in a black hole merger of the discreteness of space, these kinds of things? We're starting to get some idea of that. But that's a lot of hard work of physics to do those things. Once we are at a point where we really know what the space telescope should see or what this experiment should observe, there seemed to be rather nicely a very good collection of experimentalists who are interested in exploring these things and actually going to look for these effects. But we don't really know what the effects that will be observable. As opposed to very low level things in the model, what those are like. So there are a lot of directions there and a lot of things that have been thought about in physics and where people got really stuck understanding kind of quantum gravity and things like this. It's clear we have a definite path forward. The actual going forward of that path is difficult. It's both sort of mathematically formally difficult, it's computationally difficult, it's difficult to give the interpretations and so on. But there is at least a path which is something we haven't had for a very long time in physics. So that's sort of an exciting thing that I think a lot of stuff is going to fall into place. A lot of things about the universe that have seemed kind of random. We don't know why it is that way. I think we will understand why it is that way, why it has to be that way. And in particular, the structure of the theory will end up being, for observers like us, the universe that we observe must look this way. Observers very different from us will observe a different universe, even though at a sort of formal underlying level of the level of this thing we call the ruliad. It's all the same, but the slice that is taken by different kinds of observers is different. And so really the question is, it's kind of an introspective question in many ways, what features of us as observers are there? So, for example, one thing I've been thinking about recently, don't have good things to say about yet. What if we could think a million times faster than we do? Our cycle time of our neurons is maybe a millisecond. Typical computer, it's nanosecond, more like. And what if we could think a million times faster? What would the world look like at a million times faster? The speed of light delays are significant. Even looking around this room, light only goes a foot in a nanosecond. And so one would see sort of strobing arrival of photons and so on. One would have a different view of what is going on in the world. And so it's kind of an interesting question. What laws of physics would be useful to a thing that thinks a million times faster than we do? What laws of physics will be useful to something which exists on a scale, the scale of a proton, for example, or the scale of a galaxy? There are different laws of physics that would be useful to describe the kinds of things one observes there. And so that's a sort of a. And then what I think we're going to discover is that the laws of physics as we have them and the kinds of descriptive parameters that we use depend on sort of a great detail of us as observers. It's kind of like you could say, well, you know, the universe we observe is one where it depends on the fact that we are sitting on this particular planet, in this particular solar system, in this particular galaxy. Were we to be somebody somewhere else, we would have a different observation and experience of the universe. But we happen to be here. And so it is with what we call rulial space. And so it is with what we call branchial space. These are both more abstract kinds of spaces that we happen to exist at a particular place in those spaces. And so we observe things the way we observe them. And I think that's sort of an important part of understanding. It's sort of this introspection part of understanding how one can deduce things about physics. But, you know, what consequences does all this have? Well, for fundamental physics, I think it has dramatic consequences about understanding the way things are put together. I think the methods that we've developed that are these what we call multi computational methods are also applicable to a lot of things that are about more practical kinds of physics and the application, the interplay between physics and metamathematics, physics and economics, physics and molecular biology, all these kinds of things. We now have a new kind of methodology that in a sense, we can anchor to the things that we've learned in physics so far and apply to other fields. So that's another kind of direction. There's a close interplay, for example, between distributed computing. I'm just about to actually post something about that very topic and these ideas in fundamental physics. But what's the future of physics? I think that we now have a new form of sort of way to construct physical theories. And I think there will be new kinds of questions that can be asked. I don't know so much what those are yet. I know more the way in which one can reconstruct what's already known about physics. From something more lower level, I think when it comes to what kinds of physics experiments will be doable. I mean, a lot of the advance of physics has come both from these paradigmatic advances and from advances in instrumentation of now there are electronic amplifiers, so we can do this or that. Now there are particle accelerators, so we can do this or that. I think it's an interesting question, as we have these different methodologies and paradigms for thinking about physics, what new kinds of experiments will become possible? Right now, there's not a huge amount that's super exciting. I think on the horizon, in terms of qualitatively different kinds of experiments, we can build bigger particle accelerators. I'm not sure that that's the right way to do sort of that frontier. Whether it's like a smaller number of particles to a higher energy, rather than just a sort of continuing the direction we have. I'm not sure. I think in quantum mechanics, for example, I think that the sort of big effort that's been spent on quantum computing has. I mean, I don't think it's going to be successful from the point of view of practical delivery of something truly quantum branded. I think it'll be successful as a way to make computers out of physical devices other than semiconductors. And also the formalism of quantum computing is very interesting and has lots of mileage and plugs in very nicely with our models. But I think there are questions about whether there are different kinds of experiments that become possible when you're dealing with very large numbers of atoms and so on that we don't yet know how to do. And maybe we will learn how to do that when we understand distributed computing better. And sort of there'll be this way of. It's a little bit of a choice. You can either be running the simulation or the measurement inside your computer, and in which case it's not clear as you do a sophisticated measurement, it's almost as if you're doing a piece of simulation as part of the measurement and then as compared to what you're actually observing in the physical world. But I think there's probably some mileage to be gotten in that direction. Let's see. Gosh, Lola is asking something practical. Do you think pens and pencils still have room for improvement, or has writing technology been perfected? You know, one thing that frustrates me about, about pen pens is I like to keep sort of archives of everything. And I've sort of been surprised that there isn't a pen with mems with accelerometers inside it where it can just record everything you write. You know, forget about actually seeing the piece of paper. It just knows where the pen is, and it can somehow detect that it's on a piece of paper and writing and then can send it to your computer. I mean, there are things where you can. I think there maybe is one device that does something like that, but it's based on sort of having a pad of. With a bunch of wires that measure where the pen is underneath. I just want to be able to do it just from my pen, so to speak. Now, you know, you might ask the question that there's sort of this issue of how does technology advance given that we humans are not advancing, so to speak? We still have our ten fingers, we still have certain things that we're able to do and other things we're not able to do. One of the constraints on technology was that, you know, you can build. We could build something that was an interface to some very sophisticated device that had a thousand levers and 10,000 buttons, but humans wouldn't be able to use it. And the thing that ends up happening is that through kind of user interface design and so on, through various kinds of sort of physical devices, we end up being able to sort of pull into the domain of human accessibility different kinds of technical modalities. And so, for example, a good example, one that we don't yet have, is sort of molding things in three dimensional space. When you want to specify a three dimensional object on a computer, it's kind of a pain. It's a lot of detailed stuff you have to give. Now there have been attempts and they're not quite there. And maybe with the next generation of augmented reality, it'll finally arrive where you can just have sort of virtual clay in your hands and you can just sort of sculpt this thing and it'll have sort of snap grids that say, oh, you're making roughly a sphere. Let's just do this to make it exactly a sphere, something like that. But that's something where, you know, we have an interface modality which is kind of our fingers moving things around in space. We've got our fingers, we can do what we can do with our fingers. That's so, you know, how do we connect to the things that we intrinsically are able to deal with, like moving our fingers around. So, you know, when it comes to writing, there's something we're sort of intrinsically able to do which is move things around in two dimensions. You know, there's. Can we write in 3D? There was, I think for a while there was some kind of 3D pen that people were talking about. What would that be like? Is it useful? Right now it doesn't seem terribly useful. But each of these things needs a certain kind of creativity of interface to be able to make something that really works well with humans. So for example, when smartphones came into existence, there were know at the beginning, touch screens and so on had existed for a while. There was a lot of kind of janky stuff. And then finally, perhaps in no small measure due to Steve Jobs, actually the kind of, the sort of idea that you could really make a smooth, clean interface that was just a touchscreen on a phone like device was, you know, was realized. And the idea, the crazy idea, I think it was Philippe Kahn's idea of put a camera into a phone. It's like, what a crazy thing to do. But then it turns out that once you do that there are all kinds of possibilities because you have a camera typically with you at all times and et cetera, et cetera. Et cetera. And so I think these things about, well, what can you do with the humble pen, so to speak? Well, I think there are, you know, depending on what you know, there are all kinds of things that I can imagine doing, from recording everything you Write to the 3D Pen, to all sorts of things. So I think that's, you know, those are most of these. I mean the idea of a pen, something you hold in your hand and you sort of make something, you know, you are doing sort of repeatable two dimensional squiggles or whatever, that seems to be a good sort of human user interface thing. If we were octopuses, we might have a different point of view, but given the way we are, there are certain things that work well. Now my guess is that over the course of time we will discover more things that work well. I mean, people didn't know about touch screens with pinch zoom. They didn't know there are different kinds of things. For example, one thing that isn't quite here yet is what are they called? Electro. Oh, what is it called? The, the way that you can feel a different texture based on electrical effects on essentially a touch screen. That, oh, it went, you know, it went, you know, felt like a rough piece of rock or it felt like a piece of fabric or something. And you know, how useful is that? And there's also things like force feedback which exist in things like joysticks and so on. There's more kind of, or you know, as you move your finger, it kind of, you kind of feel as if you're hitting the edge of the screen. People have done some of that. Even though what you're feeling is just some electrical effect, it's not a physical boundary at all. But I think there are a lot of these things where there will be sort of more advances in kind of plugging into the way we humans are. So for example, the sense of touch, there's quite a bit with texture that hasn't really been properly developed. I think will get developed. The sense of three dimensionality is still kind of not really well developed. As augmented reality goes further, we'll get more ability to sort of interact with the three dimensionality of the world. Let's see, EPI is asking, should we prioritize adding new senses to ourselves, like a magnetic sense, for example, for better observation of the world? I think it'd be really interesting to routinely have additional senses and that will be possible when we have sort of routinely have augmented reality, when it becomes fashionable to wear glasses again, because that's where you put your augmented Reality, so to speak. And I think, you know, I think I talked about it another time that know when if you can sort of see in the infrared and ultraviolet and you're kind of superimposing some, you know, flashing thing on your scene of the world, so to speak, we'll get intuition. I don't have intuition for what the typical scene I'm in, what it's like in the ultraviolet. I don't have intuition for what the. You know, when I see something that looks red, I just think it's red. I don't think, you know, what's its frequency spectrum. I don't know whether it has little discrete pieces to its frequency spectrum. If I had routinely saw that in the world, I would get intuition about that. And routinely, one would start to have words to describe things that are a particular. I mean, you might say that looks like a rough surface, okay, that's in visual form, but that looks like a surface that is hot at one end and cold at the other and has this characteristic and that characteristic. We don't have simple words for those kinds of things because they're not part of our everyday experience. But if they became part of our everyday experience, we'd get lots of other sort of descriptions, and we might end up realizing that there are things that are kind of worth describing sort of scientifically that we haven't been paying attention with that. I think people are asking here about direct neural connections. And yes, that's obviously. I think I've talked about that several times before. You know, that's. That's another form of user interface and figuring out kind of what it feels like to have a direct neural connection, just like as you. Kind of as you. If you, you know, it's kind of like if you've been sort of blind for a while and now you get sight again, what is it like to start to see again, and so on. And that's kind of what one expects it to be like when one can have sort of a more direct connection. There'll be a lot. There'll be a certain amount that the connector can learn and a certain amount our brains can learn about how to achieve things from that. Let's see. Okay. C asks, when will it become mainstream, mainstream view that mathematics is merely a branch or form of computational work, and as such, sort of a physical science. Every field of human endeavor develops certain methodology, and that methodology comes to define the field. And when a radically new methodology is invented, often the field with its name and so on will ride off into the sunset and Kind of go extinct and something new will come in its place. So, for example, when computer science, as we now call it, was starting to develop ideas about computers and programming of computers and so on, was starting to develop much of what was done. Well, there were sort of two branches. There was the electrical engineering branch, maybe three branches, the electrical engineering branch, the mathematics branch, and the kind of business systems, data collection type of branch. And I think the fact that the methodology of mathematics could have developed in the direction of being sort of deeply computational, but it didn't. And mathematics stayed as it was and continues to sort of move along. But computer science and the theoretical aspects of that really broke off as a separate discipline with a different name and so on. And so for mathematics, one of the things about mathematics is that it is done as a constructive theoretical discipline where you're sort of trying to say, let me imagine a theorem, let me create a proof, and those kinds of things. It's not an empirical science. For example, in most of the way that people claim it's practiced physics, some part of physics has to do with looking at the actual natural world and seeing what it's like. I have to say that our own efforts in kind of seeing the consequences of the ruliad and so on are less of that kind. They're more. This is the foundation. And now the difficulty is to understand what the consequence of that foundation is. Some of the way one does that is through computer experiment. But that's different from experiment, looking at the natural world as it is. Although in the end, I think they will turn out to be the same because the natural world is ultimately computational. But in mathematics, people have. It's been a very funny thing because the methodology of mathematics doesn't say, oh, in your paper you write about how I did this experiment. No, in your paper you write, I invented this theorem from who knows where. I pulled it out of the air. And now I have this proof that you can understand, that I've written down. Now, the fact is, an awful lot of, particularly the world's sort of top mathematicians over the course of history have been in the back room, so to speak, doing experiments these days, using Mathematica, in the past, using pencil and paper, these kinds of things. They do experiments and they come up with empirical conclusions. And then they say, now I've guessed what the theorem is, let me go try and prove the theorem. And then I'll just write down the theorem and I'll not show anybody those experiments which were kind of messy and just indicative and they weren't the true mathematics. They were just a way of helping me develop my intuition. That's the way people talk about mathematics today. I don't think that's the right way to do it. I think there's an awful lot that is possible by studying empirically this sort of computational mathematical universe. And that's a valid field in its own right. Just as most fields of science. For example, the experimental part of the field is much bigger than the theoretical part of the field field in biology there's practically no theoretical part, it's all experiment. In physics it's a bit more matched. But I think that that's a big piece of the story of the future of mathematics. Now there are different vectors leading to that kind of thing. There's the whole sort of tradition of automated theorem proving, proof assistance. Those are still not at all. They're not absorbed into mainstream mathematics because they are kind of methodologically very different from mathematics. I mean, doing sort of the aesthetics of mathematics, the elegance of the proof and so on. It's like who cares if it's automated theorem proving and there's just a grindy machine that's going and saying yes, I can in principle prove it, it's true, but you humans don't even want to look at the proof because it's way too mess. So let's see. Harry comments. I like the thought that there are kids now playing four dimensional multiplayer games where the next generation won't even be able to understand the trivial stuff we were thinking about. I have to say, with computer games and so on, I'm probably a good data point for somebody who is incapable of understanding sophisticated modern games because I really haven't ever played video games. And as they have advanced in their sophistication, they become quite incomprehensible in many cases to me. So I'm kind of a. It's an example and I'm not saying it from pride, I'm just saying it from laziness in a sense that I haven't gone and explored this domain particularly. It's kind of an indication of what it feels like to be sort of technologically left behind, at least for me, that I don't understand. I see this stuff and sort of things are flashing on the screen and people are pressing buttons and things are happening and I don't know what's going on. And I think that that's sort of a little bit of an indication of you transport yourself to the future and then the whole world looks like that to one. And just like if you've never seen a, A smartphone, and you're sort of plopped into the world full of phones. It's kind of shocking. What's possible there, I think, in this whole question about what seems obvious now to us and what we can routinely do and what is. There's sort of a question of what's learnable and what's not learnable. If you went back to the 1600s and gave our friends like Leibniz and Newton and so on, you handed them a laptop, what would happen? Would they be just totally confused or would they be able to learn reasonably quickly? Give them Wolfram language. Let's invert the history of the development of calculus, and let's say the computation came first. We've got Wolfram language running. It's able to compute things, and then we're kind of going back and then what does old Isaac Newton do, given that, so to speak. And sort of an interesting question. What is readily learnable by people and what is difficult to learn? What may be most impossible to learn? I mean, we know that there are manual tasks and there are cognitive tasks that humans just can't really do. I mean, you show somebody some tangled ball of string that represents some graph that hasn't been properly laid out and you say, lay this graph out. Most people find that super difficult to do. I mean, it's kind of an ultimate example of kind of mental rotation, something or other. Imagining it's hard to do and people find it hard to do. Or you give people some control of the, like the, the old quadricopters of. Fly this drone. Well, it wouldn't be a drone because you're flying it yourself, but fly this thing with four rotors, control it so it doesn't go unstable. Nobody could do. Can now be done with technology, with microprocessors and so on. But that was not something that humans with, oh, you've got these seven levers that you're pulling. People couldn't keep that in stable flight. And so there are things people just can't do, given our current sort of biological construction. And I think there's sort of. There are things where people can learn it over time. There are things where people will never be able to do it. And there are things which, as soon as you show it to them, it's like, oh, that's obvious. Like, I suspect, you know, pinch zoom on a smartphone. Pretty obvious to most people once you show it to them. I mean, there are other things where there are different kinds of. Oh, you, you. Different kinds of things which are or not intuitive once you're shown them. So it's interesting question whether there are things where they can be educated to, but they are not intuitively obvious. And that's a case where the kids of today, so to speak, who have been educated through that can get to it and somebody just being sort of dropped into it cannot. And the same is absolutely true with scientific paradigms, with learning computational language and so on. I see lots of kids who are fluent in Wolfram language, very fluent in it, and who can really take the test of fluency in Wolfram languages. Can you start typing before you can explain what you're going to do? And I certainly can do that. And I see a whole bunch of kids who can do that, and older people too, but, but it's an interesting process. And one of the things that we've, it's sort of a fascinating thing because you have with Wolfram language you have this kind of superpower of taking things that you can formulate computationally in your mind and getting them implemented. I sort of realized recently that there's, over the course of the last 35 years, there are just an amazing number of kind of intellectual leaders in all sorts of different fields and organizations and domains and so on who use a language every day very often to do things. And yet there's a huge bolus of sort of traditional software engineering programmers who are like, oh no, it's too difficult for me. I just write my low level code in some, in some low level programming language. And I kind of have been confused and I sort of realized this recently. Why is it that sort of the intellectual leader crowd so routinely and so enthusiastically uses our technology and the kind of rank and file programming crowd is so kind of in a sense resistant to it. And I think the thing that I realized is if you're a typical programmer who just sort of shows up to work every day, most of what you do does not involve conceptualizing sort of what you should do. It mostly involves just, you know, write the lines of code type thing. And maybe once a month you're like, okay, now I have to sort of figure out a bigger picture. But when you use Wolfram language, for example, it's all about bigger picture because we've automated all of that, you know, most of that sort of grind, grind, grind, part of the kind of programming process. And so it's kind of a thing where, where it's kind of a, a daunting effort to some people of sort of actually thinking or a very invigorating and energizing thing for people who routinely can sort of think computationally about things. And so, you know, we see people who are typically kind of intellectual leaders of some kind or another or are becoming so who sort of routinely are doing the think implement thing in Wolfram language immediately, so to speak, very different from sort of the typical I'm just writing a big lump of code type thing that is happening in much of the kind of software engineering world. And I think that it's really quite interesting to see to what extent how much faster, how much more effective the sort of the people with a superpower are relative to everybody else. But the superpower is challenging to yield, to wield, because it has. You have to actually know what direction to think in, so to speak. So why am I saying this? I'm saying this partly because I think that there will be a. As more people begin to understand how to think computationally, how to think in terms of computational language, how to delegate to a computer all that stuff that the programmers are spending all their effort writing, then that becomes the possibility of going much further. And that as I can see from people who are young, fluent Wolfram language programmers, so to speak, that it must look like magic to many people. In fact, I know people say that it's like, how can you do that? How can you make this computational thing in a matter of a few minutes that is sort of singing and dancing in these ways? And so to the people who just don't get it, don't know that, don't know how to think computationally about these kinds of things, it's going to look like something out of reach just as. And I think that's kind of a. That's a major sort of future trend, I have to say, you know, as somebody in the middle of this whole thing, this kind of development of computational language, which I've been doing now for 40 years, it is amazing how slow the process of seeing these things widely absorbed is. Although, I mean, of course there are millions of people who use our tech every day, but there should be many, many more than that. And it is also true that the kind of the leading edge, so to speak, which is full of people who use our tech all the time, is kind of that there's sort of an interesting separation and an interesting set of timescales of what's the diffusion time from those folk to sort of everybody. And the answer is it's many decades. And it's kind of, you know, I don't know how many decades. It's always, I think, I'VE said this a bunch of times before. It's much easier for me, at least to predict what will happen than how long it will take to happen. And for me, it's just, it's completely inexorable. That sort of computational language, it's sort of the, the analog of mathematical notation for the future. And it's the thing, what one thinks in terms of, if one wants to formalize one's thoughts, make them computational and so on. That is the future. Some people are sort of living in the future today, but for many people, that future is probably going to be a while away. So a few thoughts there. Elsie is asking, how do you envision mathematics being practiced in the long term future? Look, the question is, what should mathematics be? What is the long, what is the. You know, right now there are 3 or 4 million theorems that have been written down in the history of mathematics, history of human mathematics. There is a vast network of all possible theorems. Those are the ones we have chosen, we've decided are interesting enough that we're going to write down, put in papers or books or whatever else. What does the infinite future of mathematics look like as we expand on the theorems that we already thought were interesting, build new, you know, go out into this sort of metamathematical space of all possible theorems and decide what we should populate. And I, I wrote this book recently about metamathematics and have a bunch of pictures and so on about sort of empirical mathematics, looking at what parts of metamathematical space have people populated. And there's this sort of question of as we just, like we go explore the solar system or something, we send out spacecraft, we are exploring metamathematical space as we do mathematics, as we extend mathematics. And there's a question of sort of which direction do we choose to go in exploring mathematical space? And I think that's what we see happening is that there are these kind of towers of mathematical development, these kind of directions that one's going in. And once one's gone a certain distance in that direction, one has kind of built up a certain set of technology and abstraction and so on. And then there's further to go in that direction. But there are sort of prongs developing in mathematical space. There are limitations to do with what we humans are capable of sort of understanding, as opposed to just saying, go, computer, go prove every theorem. We can do that. But most of those theorems will not be ones that we humans have much to say about or have some sort of intrinsic understanding of. So I think the. It's in terms of. So, you know, there's the mathematics that we choose to study in pure mathematics as a matter of what sort of direction, what is the aesthetic human direction that's being created? And there's also kind of. Well, there's then the question of, well, this formalization, which is one of the concepts of mathematics. How do we apply that throughout things in the world? I think computational language is the answer to that. I think that is the generalization of mathematics that gets to be an application, a way that you can apply formalization to sort of everything in the world. Now, if you ask about what will mathematics look like in the future, one of the things that the study of mathematical space gives one is some sense of what the bulk theory of mathematics looks like. Instead of 3 or 4 million theorems, let's say we have a trillion theorems. What's mathematics going to look like? When mathematicians, you know, it's been a few million people so far they've worked on mathematics in the history of human civilization. Let's say there's lots more, and there are a trillion theorems that have been written down in the papers of the future. What will that structure look like? Here's one very important thing, I think. I think mathematical space is in some sense homogeneous. So in physical space, our planet has certain features, and so on and so on and so on. But the fact is, we expect that if we were to tool off in a spacecraft to some other part of the universe, the nature of the universe there will be very similar. The laws of physics would be the same, many of the things we would observe as observers like us would be the same, etc. So now the question is, as we go around metamathematical space, how similar is it? So, for example, we might go from geometry to algebra. Those are two different points in mathematical space. The theorems of algebra, the theorems of geometry, they're just these little regions of metamathematical space. But the thing that's interesting is that I'm pretty sure that there's a certain homogeneity in metamathematical space, and that in a sense, the structure of algebra and the structure of geometry are unsurprisingly similar. And that in a sense, any human constructed, any human observed area of mathematics will have certain commonality, which means that there will be these giant dualities between different areas of mathematics, these giant correspondences where we get to move stuff from algebra to geometry or whatever else it is, and across different areas. And there are things like the Langlands program, which attempt to do that for specific kinds of areas of mathematics. But my feeling is one of the biggest big stories of the future of mathematics will be the one that instead of all these different prongs of, oh, I'm doing algebraic number theory, I'm doing representation theory, whatever else, there will be more and more kind of commonalities seen between these different areas. It's kind of a little bit like what's happened in computation where there was a time, not for very long actually, when there were Turing machines and lambda calculus and recursive functions and, and so on, and these were all different prongs which could have all had their own, in a sense, branch of theory of computation, branch of mathematical logic developed for them. But what became clear in the 1930s and beyond was that actually these are all fundamentally equivalent. They're all universal computers. So there's some kind of uniform thing that can be said about all of them. I think that same thing will happen in mathematics. I think that the kind of the prong of algebraic number theory is kind of like the prong of lambda calculus and it will be mergeable with these other prongs and there will be these kinds of ways to leverage sort of the big success in one area in another area. So it's similar to the fact that we can use the success of our physics project and use the fact that it shows that the underlying formalism between physics and, let's say, metamathematics is the same. And so that means that if we can say things about singularity theorems and event horizons and physics, we can import those results into metamathematics. And that's kind of a. That's, I think, an important direction for mathematics going into the future. Let's see. Memes comments. I think World of Warcraft, they say, may have helped me understand calculus better. You have a goal with a particular group set up. What is the optimal scenario for victory given one's resources? This is where I am such a naive. I have never played World of Warcraft. I'm sorry, I think I've seen it being played, but that's about as close as I've got. So it is an interesting question to what extent one could develop intuition for physicses other than our own by playing video games and so on. I don't know to what extent people have really. For example, even a very simple thing which I've often thought should be done is the relativistic video game of, you know, you're zipping around at close to the Speed of light. What do things look like? We know that perfectly well. You know, you're going down a road and you're going close to the speed of light. Okay, the street lights all sort of bend inwards. Things that you're going towards turn blue. Things that you're going away from turn red kind of, you know, things like, things, you know, get compressed in a particular direction. Strangely enough, things like cubes will tend to rotate because the time it takes light to get from one side to the other starts mattering as you get closer. During the time that sort of the light is going from one part of the cube to another and so on. So even getting, I mean, I don't have intuition for this. What it really would be like to live in one's everyday world, so to speak, at relativistic speeds, going close to the speed of light. If I were kind of zipping around, you know, if I, you know, I'm going to go to some event this evening and if I could zip there at close to the speed of light, you know, what would the streets of, of Cambridge, Massachusetts or something look like close to the speed of light? I don't know. I mean, it will be interesting to get that intuition and maybe it would help me even in understanding things about physics to get that. In fact, right now we're making some videos about a physics project and it's beginning to be, it's sort of interesting what one can, you know, kind of the intuition that one begins to get from kind of seeing these things in action. But yeah, I think, I think I'm curious. I mean, as a matter of fact, one kind of game that somebody should make is I wrote this thing recently about kind of the rule space of generative AIs. Kind of. It was, you tell a generative AI sort of make a picture of a cat in a party hat. It has a certain place in its kind of concept space that corresponds to that. You move away from that into kind of inter concept space. You have all these different images that get generated. And it's kind of like, get an intuition. What would it be like to kind of drive a rule spacecraft around that space of possible concepts, an interconcept space? And you know, what is it like? I don't know. That's something. It's kind of, from a very practical point of view, just takes a while for a GPU to generate a picture using modern generative AI. And so, you know, the navigating your spacecraft in real time with a joystick type thing is not quite as exciting as it will one day be because it's still quite slow, but to me it's kind of an interesting. So if anybody wants to go out and build such a video game, let me know, I've got ideas about it. Let's see, maybe a couple more things here and then I need to run away here. Let's see. Hela asks which area of tech is advancing the fastest. Will this change in the future? It always changes at any given time. I think I've talked about this before. I think there's a sort of a pattern of history which is new methodology is invented, opens up a bunch of possibilities. Five to 10 to maybe a few more years, lots of low hanging fruit to be picked, very rapid advance. Then 100 years of grinding to get to the next moment of methodological expansion. And so we see that in large language models, a methodological idea, a surprise that it worked. There's low hanging fruit, it will get picked for a short while, it's rapidly changing right now, but that will slow down and then there'll be a long slow grind. And you see that everywhere. So knowing what the hot new thing is is often challenging. And it is often the result of very practical technological stuff. Sometimes it's the result of ideas, sometimes it's the result of the bizarre phenomenon of the sudden acceptance of ideas. Like people invented something and nobody cared. And then 25, 50 years later, people say, wow, that thing is really cool. We're really going to go in that direction. And it really wasn't a kind of a major conceptual advance. It was just people decided it was interesting. Now I mean that happened with number theory in probably the middle part of the 20th century. People have been like, who cares? And then it's like, oh, this is really exciting. Now maybe to some extent that was because there was sort of a clustering of results that were being got in that area, but it was more of a sociological phenomenon. I would say that one particular one I'm not as, I haven't really thought through the history as clearly as perhaps I might, but there are lots of places where it's kind of like people suddenly it's kind of like everybody there, even things I've invented where they went for decades with people like who knows, who cares? And then suddenly the world discovers them and everybody thinks they're really cool. And it's like, well, why didn't you know that? I, I already said that 25 years earlier, you know, why weren't you paying attention type thing. But it's just not the way things work, there's this sort of gathering social momentum that happens around things and I think. So, you know, when you say what's, what's new, what's coming, et cetera, it's a, that's, that's curve. At any given time, there's always new stuff happening. When you see the very first murmurings of new stuff to the time when it's in full bloom, maybe five years, maybe ten, I'm not sure. Then there's this period when it's in rapid growth and then it slows down. And if we say what are their murmurings about? I have to say all the stuff around our physics project and its consequences, that to me is a pretty seismic piece of murmuring. I mean, it's really obvious that there's just a huge amount of stuff that becomes possible there. And we are just beginning to see what's possible. I mean, we made a bunch of progress. Some people understand that progress, more people understand it every month. But it's a big, very fertile thing that is going to have high growth when it really does its most energetic. In physics, for example, one of the things that I think was a sign of a not so totally healthy field way back was there used to be these kind of fads in physics. Everybody would say, oh, this is exciting now, this kind of new type of string theory or this type of gauge theory or whatever else it was. And some fraction of the physics community would rush into that fad for six months, a year, maybe more. And I think people even started plotting. Back when I was doing physics for a living, people were plotting the fraction of physicists who went into each fad versus the length of the fad. And it was getting to be a larger fraction of all physicists, a shorter time. And I don't think that was terribly healthy in the field. I think that was kind of a death throes type thing for the paradigms that existed at that time. But the, you know, that that's a thing where finding the murmurs that will then turn into something big. That's an interesting thing. And sometimes, sometimes they're hiding in plain sight. I mean, like it could be the case that augmented reality will suddenly take off after it's been not taking off for 30, 40 years and suddenly that will kind of really develop. Let's see. Well, we should probably wrap up here. I think I'm being told I am maybe one more. If there's something quick, he says, Crucial flow asks, will you ever invent a new language again? Me personally, you know, it's been interesting. I. I built my first computer language starting in 1979, thing called SMP. A lot of interesting ideas. I was just. In fact, the thing I'm just writing probably post today reflects back to a bunch of things that I did in S and P, where I almost figured out some things which I think I now can actually figure out. S and P was very interesting and had things that were not as easy to use as they could have been in building Mathematica in Wolfram language, I kind of got the opportunity to do that again. So that was kind of. That was 1986-88 to now, that whole process of building more and more and more on that stack. The stack has done very, very well. The idea of symbolic programming, the kind of design methodologies and so on. In a sense I had it easy because I'd already kind of got to do a trial run with SMP before and so it was easier to not make mistakes. But that stack has been quite wonderful to build on for the last 36 years. But you know, I did a different thing in the early 2000s, decided we're going to build WolframAlpha. And WolframAlpha is going to be something that has a very different design methodology. It's going to take natural language input, it's going to have no documentation, it's going to have no precision. It's just going to be something where the user says what the user feels like saying. And it's up to us to kind of untangle that. Just like in a sense for Wolfram language, it's up to us to go compute. We're not asking the user to go tell us how to do things like you would in some low level language. You're just saying what you want to have happen. And it's up to us to get Wolfram language to actually do that. So now you ask will I ever do such a thing again? Well, there is something that's actually a project that's quite active right now building what I call symbolic discourse language. It may yet change its name, which is kind of a symbolic representation of the things people sort of say every day in the world. And that design methodology is probably going to be different from the things I've had before. So it's probably how it exactly plugs into the WolframAlpha story and the Wolfram language story. We don't yet completely know. It will certainly attach to both of those stories. But the thing that was really important in building WolframAlpha was the idea that we're going to do a different design methodology. It's not the sort of precision, precise kind of formal specification structure of orphan language. It's going to be something which is just a sort of do what the user wants based on the yakking that they're making. And I think that's a piece. The whole thing we're doing with symbolic discourse language is all deeply tied up with LLMs, but in perhaps ways people might not expect the thing. So yes, I'm, I am planning that. And another thing that I'm interested in, I've been interested in this for just forever is kind of programming using graphs. And is there a way of representing things? In a sense, Wolfram language takes its cue from human natural language. It's a string of word like things that are connected in a sort of grammatical way, way, but it's not obvious. And that by the way, is a very powerful thing to do because that is sort of the thing that plugs into our highest levels of thinking is human language. So that's a great model to use for computational language. But the thing that I sort of wonder is, is it the only model and are there things that involve graphs and sort of dimension, you know, three dimensionality and spatiality and so on that are an alternative way to kind of sort of organize one's thoughts? Now people often argue, you know, thinking and language are deeply connected. We don't think without language and so on. Maybe that's right. Maybe we can think sort of spatially and maybe we can think in terms of, you know, graphs, networks, things like that. I don't know whether I can. I mean, I don't know whether it's the kind of thing where one learns to be able to do that. I mean, I've certainly done quite my tour of duty with graphs and networks for all kinds of purposes. So maybe I have as good a chance as anybody to be able to do that. But it's still the question is, is there a way of expressing oneself and thinking about things that is fundamentally sort of in terms of graphs and networks rather than in terms of something that's essentially linguistically based? I don't know. I've been wondering about that since the early 1980s. I've done a bunch of experiments. They've typically not been successful because basically it's like, well, you can do this, but I don't understand what's going on. It's not useful for me as a way to organize and formalize my thoughts. So the answer is I don't know. I think in Some sense, yes. Invent something. But whether you call it a language will be an interesting question. All right, we should. Oh boy. There's a question here I almost can't resist. Is there anything you've recently changed your mind about? I will say one quick thing and then we'll maybe talk about this another time. But, but you know, I had no, you know back. If you'd asked me this time last year, are language models going to be able to write reasonable text, I would have said no particular indication they can. They're just babbling and writing things which are sort of statistically reasonable but don't make a lot of sense. That's something where clearly the aliens landed and the LLMs were able to start producing very human like lumps of text. So that was a thing that definitely changed my mind about something. And I have to say in our physics project as well, one big thing was I didn't think we'd get nearly as far as we've got. I thought it'd be 100 years before one can get to the place where we've got to now. And I think that it is a thing where some of the predictions. I think there may be some things which turn out to be really hard and we can't get anywhere with them and there may be some low hanging fruit that's lower hanging than I expect that allow us to, to really make all sorts of interesting progress. All right, with that, I should probably wrap up for today. Thanks for lots of interesting questions and comments and I look forward to doing this another time. Bye for now.