History of Science and Technology Q&A (September 4, 2024)

Hello, everyone. Welcome to another Q and A about history of science and technology. And I see a bunch of questions saved up here. There's one from Peter here. When for you, he asks, was a computational approach introduced to the scientific process or scientific culture? Well, there's sort of the notion of computing things is super old. That is, you know, in Babylonian times, when people were first using kind of formal methods to do anything, people were interested in doing things like figuring out whether a planet is going to show up in a particular place. And that is, in a sense, a computational representation of something about the natural world. The concept that the natural world was capable of human computation is something that's really old. When it came to figuring out why the world is the way it is, that was mostly thought of as being something that you reasoned about philosophically. The question of which planet will be in this place at this time in the sky was something that, I think from very earliest times that we have recorded history, people were kind of imagining that that was something that you would sort of work out by some kind of computational process, a bit like the kind of process that you would use to add numbers up or some other thing like that. Now, the idea that you would. Well, the kind of notion that lots of things in natural science could be worked out using mathematical methods, that was something that really rose in the mid to late 1600s. I mean, famously, as I've said many times here, Isaac Newton's 1687 Principia Mathematica, its sort of full title is Mathematical Principles of Natural Philosophy. Can we wheel in kind of these methods that were invented for mathematics, for working out things with equations and so on, for doing things that were relevant for commerce and land surveying and the kind of more almost kind of sporting kind of character of mathematics, of, you know, can you find the. This number that will solve this equation and so on, as a kind of sporting event type thing? Can one use those kinds of methods, these methods of formal mathematics, and apply them to natural science? That was sort of the big idea of Newton's efforts and to make that work, had to invent calculus. Because the mathematics that existed of algebra and so on wasn't enough to deal with the kinds of processes that one saw in the heavens, so to speak, and in mechanics and such like. And so then the idea of, well, can you compute something about what's going to happen? Can you compute when Halley's comet is going to return? Can you compute the orbit of the moon? That was something that, yes, the idea was there was mathematics and you could work through the mathematics and compute from it things. And you'll see. I mean, I haven't looked at Newton's actually I have, but not in as much detail. But Leibniz for example, I looked at his manuscript archive and it's full of sort of calculation where it's like lots of long arithmetic and so on being done to work stuff out. Now Leibniz wasn't so much interested in natural science, he was more interested in kind of formal mathematical questions. But nevertheless he was doing a lot of, kind of just working things out by hand. He was pretty bad at it, by the way. He made a lot of mistakes. He made fewer mistakes in algebra, he made many more mistakes in just sort of chasing numbers and twos and threes and sevens and so on around. But that was a thing that definitely Newton will have done many such calculations to work out, you know, just what is the what, what would be the expected orbit of a planet and so on. Notably Kepler, who predated Newton and Galileo for that matter, Was also involved with calculating things to try to work out. He did many calculations, but in celestial mechanics he was calculating kind of the properties of orbits of planets and discovered Kepler's laws and so on. And actually a friend of his named Shakad built a mechanical calculator to help Kepler do these astronomical computations. So definitely at that time, this is now must be 1630s, maybe 1640s, maybe even a little earlier than that, there was actual computation being done. It's probably the earliest non antiquity mechanical calculator that was produced was the one produced for Kepler. It was made of wood, so it didn't survive. The first one of those that has survived is the one made by Pascal, BLAISE Pascal, in 1642, I think, which is made of brass. And you can see it in a museum in Paris. And it's a little thing, it's about so big and it's very nicely kind of turned out in brass and has these little wheels that you can turn to set numbers and then you can do addition by sort of odometer style, turning these wheels and so on. But in any case, that was used presumably by Kepler to do various kinds of astronomical computation. So that was a place where computation sort of was certainly entering the lexicon of natural science. Now there was then certainly people through the 1700s to 1800s were doing various kinds of hand calculations, but they were much more concerned with can we solve the equation, can we use algebraic methods and can we sort of figure things out as a matter of sort of pure Thought to solve these equations and so on. More so than like, let's just work out the specifics of what these particular numerical results should be. Certainly people were doing that when they were building iron bridges and ships and so on, where you had to do engineering calculations. Certainly people were doing those engineering calculations. I think for science that was probably, well, actually somewhat less prevalent. Although one case I can certainly think of is the discovery of Neptune, for example, by Adams and Le Verrier. That is a giant calculation done using Newtonian mechanics and using these approximations, various kinds of series approximations to represent the effect of gravity and so on. And that fills a whole book of calculations to figure out what was the pull on Uranus and other planets. And could you deduce from that that there was another planet in the picture and where would it be? And then it was looked for and it was found. And that was the discovery of Neptune, which was a great sort of computational in a sense discovery that made use of the laws of Newtonian mechanics and then computed things from them. Now subsequently, as one gets towards the end of the 1800s, there were things like Kelvin produced a tide calculator and that was a sort of semi empirical thing because it was known that the configuration of the Earth and the moon and the sun and so on repeated every 18 years or something like this. And there were other cycles from lunar months and things of this kind. And you could empirically work out what the effect that was sort of what tide tables did. And Kelvin made a thing with wheels and so on that would compute the tides in this approximate way. That machine is actually in the London Science Museum. Hopefully they still have it on display. They did the last time I was there, which is quite a while ago. Hopefully it's a fine example of sort of early computational activity. And then well after that the kind of notion that you would be able to compute things that were useful for let's say physics. For example. Famously Hartree atomic physicist made a computer out of Meccano construction kit stuff that was a. And there was a. Was kind of funny that one of the early sort of papers about computing was published in Meccano magazine. That will have been probably in the 20s or 30s, I think 1920s, 1930s. But any case then sort of where did computers get used next? Well, the original development of things like the ENIAC in the US in 1940, well 5, 6 type timeframe that was originally done to compute ballistics tables. So I mean that was one of its sort of early applications. And the motivation for building it was given that you're going to use Newtonian mechanics. You're firing some big gun and it's going to fire a shell that goes 15 miles or something like this. You have to actually calculate what angle do you put it out. You have to take care of figuring out air resistance, the Coriolis force from rotation of the Earth, all these kinds of things. And that was a job for using sort of physics to then do a computation that was then for an applied purpose, so to speak. And that was sort of. The original development of the ENIAC was driven by that. Now, once the ENIAC existed, people did use it for other things. People used it very quickly to try and do mathematical calculations like work out digits of square root of two and see how random they were. Those kinds of things were done quickly. I think some things with primes were also done on it. Some things like working out linear congruence relations, kind of early random number generators. That was another thing that was done on those very first electronic machines, electronic computers. And then. Well, what happened next there in terms of basic science? I think some of the early things that were done were things like trying to simulate. Well, it was of great interest to simulate things related to kind of the behavior of matter in extreme circumstances. That was particularly relevant to nuclear weapons development in the 1940s to 1950s. And that one of the things that sort of came out of that was an attempt to simulate kind of what would happen if you had a bunch of sort of hard sphere, billiard ball like particles bouncing around in a box. And what would happen? What would be the kind of. What would happen as they got more crushed together? Would they eventually form some kind of regular crystal? Would they form something like a liquid? What would be the sort of transitions between those things? That was a thing that was being done in the mid-1950s, I guess, particularly at things like US government labs and so on, using the computers that existed at that time. I mean, by that point, there were plenty of computers used for sort of commercial purposes and sort of tabulation purposes, not so much for science. That was one of the early uses. There were other places where computers were used. I mean, when computers existed and scientists were there, the computers got used for science. Like at Los Alamos, Enrico Fermi, for example, by the mid-1950s, was trying to study things about nonlinear oscillators. And the question of whether you could get, when you have a linear oscillator, just a thing on a spring, for example, where the spring is a nice linear spring that doesn't dissipate energy, doesn't do anything weird. The thing just bounces up and down, makes a sine wave, whatever. By the time, it's nonlinear. And if you have an array of nonlinear oscillators, that was sort of the question of what would happen. That's something firmly investigated. That time, even cellular automata were getting simulated by. Let's see, by 1960 or so, it's again, one of these where there were scientists and computers together, which was things like US Government labs. People would use them for various kinds of science. But a pretty early use was this hard sphere gas use. And amusingly enough, I mean, in terms of the sort of connectivity of history, that led to simulations that ended up in. At the beginning of the 1960s, on the COVID of this textbook about statistical mechanics, it was kind of a simulated movie strip of what happens to particles bouncing around in a box. I saw that picture in 1972, and that was kind of the first thing that kind of got me interested in simulating sort of natural systems on a computer. I didn't succeed in doing that simulation. Many years later, I found out that the actual simulation that was shown there was kind of a fake. I didn't find that out for a few more decades, but that was, for me, that was sort of a story there. Now, the question of when. So the use of computers to simulate things of relevance to physics by, I would say, the 1970s, that was somewhat commonplace. Different kinds of things where you took the equations of physics, for example, and you tried to simulate them on a computer. You tried to work out their consequences on a computer. And that typically involved. Because the equations tended to be continuous things. Computers are discrete and digital, that tended to involve kind of breaking things up into discrete bins or discrete increments and hoping that when those increments were small enough, you would approximate the actual behavior of these equations. And so lots of things got done along those lines. Now, a different question is when people started thinking that you could actually use computational ideas as foundations for natural science. And that's a thing. That was kind of one of my big sort of initiatives by the beginning of the 1980s. And that was something which I will say at the time, it was very much in terms of sort of physical scientists. It was like, no, no, that's not. That's not a thing. Even, for example, Alan Turing in 1952, very early computer, he had gotten interested in simulating biological morphogenesis, the formation of form in biology. And he was interested in things like how would the dappling pattern of a cow develop Which I believe is the origin of the, consider a spherical cow kind of thing that's quite commonly quoted in sort of idealizations in science. But anyway, he was considering a spherical cow, and then he actually tried to work out on a computer at that time. His code is awful. That's a different issue. The effect of sort of the diffusion of material on the surface of a spherical cow and what it would lead to, these dappling patterns and so on. But what he did at that time, even though he'd invented Turing Machines, you know, 15 years earlier, he was like, oh, well, now we're doing physics. We're going to use differential equations and the standard apparatus of physical models, not something computational like Turing machines. So that was kind of the absolutely uniform belief of physical scientists coming into, I would say, the 1980s and my own efforts, kind of through a somewhat circuitous route, I ended up, well, realizing that you could do more than just use sort of the mathematical equations, differential equations and so on. Mainly that happened because I was studying kind of how did you get complex behavior in the world, whether it's snowflake patterns or turbulent fluid flows or whatever else. And I had the fortunate experience of the fact that I started doing that around 1981, which happened to be right after I had been putting a lot of effort into building my first big sort of computational language at that time, really computer language, a thing called smp, Symbolic Manipulation Program that was intended to be something to do symbolic computations, like algebraic computations and so on. And to build that system, I had kind of gone back and invented this idea, which we still use in Wolfram language of transformations for symbolic expressions and so on. But that idea, which is sort of a foundational computational idea, had been what led me to build this language. And when you build a language, it's like you just set up the rules, and then you hope people can use them and do something useful with them. But that idea had given me sort of a different view of how one should think about natural science. In thinking about natural science, kind of the traditional way, it's like nature gives you something, and then it is the job of the natural scientist to kind of reverse engineer what nature has given you and find out what kind of rules can give those, what nature shows. And that approach, people had said from Newton and Galileo on, had said, let's use mathematical equations to do that. But my experience from sort of building something computational and then just putting it out there and seeing how it was used was to kind of take a different approach to sort of Foundations of science. And instead of saying, we've got what nature gives us, now let's reverse engineer it. I was interested in can we make kind of an artificial nature? Can we just enumerate possible rules and see what they do and see whether they correspond to what one sees in nature? And that's what led me to start studying simple cellular automata and so on, and led me to discover that, yes, even though the rules are simple, the behavior can be very complex. That's something I knew certainly by the end of 1981, I think. But that got me to the idea that really one should think about sort of systems in nature as following computational rules. A special case of that being the mathematical rules that people had thought about for the preceding 300 years. But I can say that sort of on the ground, sort of the saying, yes, you should think about things in computational terms. There are models for the natural world, whether it's for snowflake growth, whether it's for fluid flow and so on, that can be based on purely computational constructs, not traditional equations and derivatives and calculus and so on. That idea was not an idea at that time. That was really my thing to push. And so I did many things with that. I mean, for example, by 1986, I guess I'd invented this way of doing fluid dynamics that sort of started from computation, so to speak, rather than starting from the standard equations of fluid mechanics, and had done the same kind of thing for other kinds of models. I have to say I didn't push the, here's a particular model for this particular thing. I didn't push that as hard as I might have done. I was more interested in the kind of overall theory of what models like this do. And part of the reason I didn't push kind of individual models so hard is because modeling is an incredibly controversial business. Because when you make a model of something, you say, I'm going to capture the features of this thing that I care about. And yes, there are going to be features I don't capture, because that's the nature of models. Models aren't the thing itself. They're some kind of idealization of the thing. So, for example, a good example of this is in snowflakes. When I made models of snowflakes, they did a pretty good job of capturing kind of the overall form and shape of snowflakes. And the way that snowflakes go from hexagonal plates to these very tree like dendritic forms back to hexagonal plates again. When they fill in, they have little holes in them and so on, did really pretty well at capturing that. But if you ask the question at a given humidity and temperature and so on, what will the growth rate of the arms of a snowflake be? The models that I developed had nothing to say about that. But there were other models that were based on differential equations that were all about the growth rate at the tip of the arm. And they gave good results for the growth rate of the tip of the arm. Of course, those models said, for example, in some cases, snowflakes will be spherical, which is completely crazy. But it's a question of what one is concentrating on. So when one makes models of things, one's always in this situation of having to argue, well, there's the part that I care about that it does well, even if the part that you might care about, it doesn't do well. So that's part of the reason that I was not as keen on generating all these models of different kinds of things. There were but plenty of others that I generated, but some of them were kind of at the level of qualitative models, like the distribution of patterns that you get on mollusk shells, things like this, where it wasn't so much a question of measuring this is however many microns it was across this piece of pigment on a mollusk shell. It was more. Is this pattern roughly right or completely wrong? So Anyway, in the 1980s, I would say that the. The absolutely uniform belief of sort of physicists was there are computers and they do discrete kinds of things, and there's the physical world. And in the end, the physical world is based on equations and real numbers and so on. And that belief took a long time to shift. I would say that when I published my big book, A New Kind of science, in 2002, people outside of kind of the core of physics had pretty much were grokking that idea by that time. That is, people who were making models in, I don't know, social science or even, in some cases in biology. That even happened in the 80s actually, was something people pretty keen on. My work on cellular automata in biology at that time, and there have been a few other discrete models in biology as well. But in these areas outside of the core, mathematics has worked really well for us for 300 years kind of area, there was plenty of kind of. It might be sort of more computational like. But in this core area of sort of physical science, even by 2002, it was still to many people sort of shocking that you would think that nature was somehow fundamentally computational. So it's then I Suppose what happened is there was a bit more enthusiasm about sort of quantum computing, which had been around since the early 80s. I even worked on it back then, and it was sort of when you have quantum things, the natural way to set up quantum mechanics is with discrete constructs. I mean, the actual formalism of quantum mechanics is sort of still, in many ways, sort of differential equations, Schrodinger equations, quantum quantum field theories, things like this still have a lot of continuous mathematics in them. But nevertheless, at least in the simple idealization that's relevant for some kinds of quantum mechanics and quantum information and so on, one is dealing with discrete things. And that was very physicsy, and that sort of drove a certain amount of. Yes, there could be something computational that was thought about in physics now, in know I had, I must say that I had thought in. I had worked on sort of fundamental physics and particle physics and things in the 1970s. And I, I, I always thought, well, maybe there's something sort of computational one could think about, about truly fundamental physics. But I didn't see how it would work. By the beginning of the 90s, I had a definite idea about how it should work. I mean, I kind of realized that if you're going to go sort of to something more fundamental than we knew, we had to go underneath space and time as we know it, to something sort of lower level than space and time. I'd had the experience of doing that for fluid mechanics in 1986, of seeing that one could have just these discrete elements that sort of approximated things like molecules, but that on a large scale you would then get ordinary continuous fluid mechanics. So that sort of encouraged the idea that one could do something similar for space and time. And so I had ideas about that and space as a network and things like this. At the beginning of the 90s, I started working on it. By the mid-90s, I'd managed to make quite a bit of progress. And a number of really suggestive cool things came out about sort of the correspondence with general relativity, the theory of gravity and so on. I published a bunch of those things in New Kind of Science in 2002. And I would say that, well, I wouldn't say nobody cared. I would say even more than that, people who were in physics, my friends in physics, many of them were outraged. How could you say that the foundations of the physical world might not be quantum field theories and the kinds of things that we studied for 50 years and so on? Well, I didn't work on that for quite a few years, partly because I thought the market for theories of fundamental physics is physicists, and the physicists didn't want this product. And so I went and worked on other things like Wolfram Alpha and Wolfram language and so on. But anyway, came back to these things in 20. Well, I'd been sort of poking away at them for years, but in 2018, made a little bit of technical progress, and then a couple of young physicists were really, really insistent in 2019, you got to work on this. And also I was, like, getting old and decided if I was ever going to do this, it was now was the time. So kind of got started on, okay, can we really take this seriously and find a serious model of physics that's based on hypergraphs and that sort of discrete computational structure? And the answer was, heck, yes. And by the end of 2019, it was like, wow, this is really going to work. There really is a truly computational foundation for the way the universe works. And that's, you know, we sort of, I think, have found the outline of the sort of machine code of the universe. And so we now know that. We now know that this idea that. Can the universe be thought of computationally? The answer is absolutely yes. Is that the only useful way to think about the universe? No. There are many layers above. It's just like if we're describing a fluid, we can talk about it in terms of its individual molecules, but for many purposes, we want to talk about it in terms of the continuous flow of fluid. And that's the stuff of traditional mathematical physics, and there's plenty to do there. But if you really want to know what's it ultimately based on, it's ultimately something computational and occasionally that will shine through to things that we observe at a larger scale and so on. And also it gives you sort of the confidence to say, yes, we can really use computational ideas in lots of places because that's really the way things work. I mean, a bit like when before Copernicus, there was sort of the idea, well, you could use mathematics to kind of describe things about the world, but it wasn't really mathematics down there. And then after Copernicus, it was kind of like, well, just trust the mathematics. Even though it doesn't feel like the Earth is moving, the mathematics say that what we experience can be correspond to the Earth moving and so on. And I think it was sort of interesting because when Newton was describing the motion of the Earth with calculus, all that kind of thing, there was definitely a contingent of people were saying, but what's pushing the Earth around? Where are the Angels that are mechanically pushing the earth around. And a few hundred years later, the tables had turned and people were now saying to me, for example, in the early 80s, what do you mean that there are mechanisms? There are computational mechanisms by which things work in the world. There can't be mechanisms. The world is just described abstractly by equations which you solve. The idea of a notion of a mechanism isn't really a part of science. That seems wrong, that seems primitive, to talk about mechanisms. But in a sense, whenever you have a computational system, you are talking about mechanism, maybe very abstractly. And that's what we now realize is really at the foundation of things. I see Turbo commenting. Consider a qubit like cow. That's interesting. All right, let me see. Well, the question from Paula here. Is there a historical figure that you feel you relate to? Share a journey with who I've looked to for inspiration. I think I am interested in kind of the whole arc of intellectual history, and I certainly look to a lot of that for inspiration. Some of it is inspiration about kind of the relationship between ideas and the world, which is often complicated. And I think one of the things that's been really striking to me recently is a huge number of things that I've done recently have been essentially follow ups to things that were hot 100 years ago. And it's sort of an interesting thing because a lot of what I've been trying to do is to sort of develop formalization for the way the world works, whether it's fundamental physics, whether it's metamathematics, whether it's foundations of biology. Recently, these kinds of things. A lot of these things were sort of started about 100 years ago, a little bit more than 100 years ago, in some cases were somewhat abandoned. And now we're coming back to them. I mentioned actually one other thing that also relates to the previous answer. A place where it's like, how computational is it? Another place where that shows up is in neural networks. People got the idea that sort of the. Even though people knew that there were discrete firings of neurons in the brain, they got the idea that somehow the way that neurons are set up is based on continuous weights that you could sort of change. Instead of it being the case that we remember things in discrete units. There was the idea in the 1920s of Cycons of kind of units of thought. But mostly people had the idea that was sort of continuous thing. There were continuous numbers that describe neural networks. And that's been a thing that a trillion dollars is kind of riding on. So to Speak right now of we're using kind of continuous numbers to represent what happens in neural nets. We train neural nets that way. I kind of thought, well, yes, that what you have to do to make sort of incremental progress, to incrementally train a neural net. I thought that until a few weeks ago, when I finally got around to trying to see, is it possible to do the things that you do in machine learning in a purely discrete, sort of purely computational way. And the answer turns out to be yes, so far as we can tell. So it's a case where sort of it looked not so computational. It looked like, oh, you've still got to compute things with real numbers and so on, albeit on a computer. But now even that seems to be something where this completely sort of discrete bit like approach seems to be quite, quite viable. And whether that's a good specific model for how brains do it, I'm not sure whether it is functionally equivalent. I think it's very likely. But in a case back to sort of the inspiration of things, I think a thing that has really been striking to me is if you look at a bunch of different areas, I mean, the 1800s was the period when a lot of stuff was sort of formalized. Beginning of the 1800s, you ask people, what does math do? Math was really something which described the world. Euclid was idealizing how triangles worked, but you could imagine actually making a triangle out of pieces of wood or whatever else, and the triangle would operate the way that Euclid said triangles operate. Beginning of the 1800s, there started to be places where people said, well, let's make things work in a way that was more abstract. So, for instance, that was what happened with Lobachevsky and the idea of curved space. Even though real space, people thought at the time, had the property that it would follow Euclid's fifth postulate, which says two parallel lines never cross. Lobachevsky imagined a kind of space in which actually there was curvature and those lines could cross. Now, later on with, with Einstein and So on, in 1915, it became clear that actual space in the universe works that way too, and didn't work the way that Euclid assumed that space would work. But that was one sort of little piece of abstractification, so to speak, that happened. Another one was galois1830ish, where he was looking at a pretty concrete problem of looking at solutions to quantic equations, trying to determine kind of the symmetries of those solutions. Invented group theory, which is something that's sort Of a bit like arithmetic. You have elements, they get multiplied, things like this, but it doesn't follow the laws of arithmetic. Same with George Boole, around the same time invented Boolean algebra where it was kind of like you can think of and, and, or as you know, and is roughly like times or is roughly like plus, except that the, you know, true plus true one plus one doesn't equal two, it equals one in logic, so to speak. But Boole thought that he was making a model for as he called it, the laws of thought. Again, he thought it was not mathematics in the abstract. He thought it was mathematics as applied to something in the world. In his case the laws of thought, rather than something about geometry or something like this. And then another thing that came around the same time was Hamilton, William Rowland Hamilton, 1840 ish, looking at quaternions again, a sort of a departure from the way ordinary arithmetic works. But by around the 1870s, 1880s it was becoming, in a bunch of different threads of development were leading to this idea of let's, let's abstract things, let's have a formal abstract way of setting things up, which in a sense Euclid had done by coming up with axioms and saying we'll deduce things from axioms. But Euclid imagined that his axioms were merely a representation of the world as it is not sort of arbitrarily human constructed axioms. So this notion that things would be just you construct formal axioms and then you see their consequences. That was an idea which really became big in 1860s-1880s type time frame. Lots of different people, people contributing to that. Schroeder in algebra and universal algebra and so on, Grassman, but bunch of people. Then Frege Cantor, all sorts of people doing all sorts of different things. But by 1900, David Hilbert, mathematician, was talking about, well, mathematics really is just this set of rules. He said mathematics could be about tables and chairs as much as it being about integers and addition and so on. And so this idea that everything could be formalized like that. Okay, so that notion of formalization came to. Well, it came to physics, it came to mathematics. Well, in mathematics it led to sort of this, the kind of metamathematics, the study of the overall structure of mathematics, which kind of got started in serious way around that time and then kind of kind of stopped. It had various assertions that were kind of shot down by Godel's theorem, but it kind of stopped. And I've tried to pick it up again. And then on the physics side, the Big thing that happened is one was finding kind of discrete elements for things. Finally, after many, many centuries, it became clear by the end of the 1800s that matter is discrete. It's made of discrete molecules, atoms, whatever else. Then light could be thought of as being made from photons. People thought that space was discrete because they said everything must be discrete if, you know, if we have. People were thinking, like I mentioned cycons. People thought must be discrete as well. It's kind of like we've cracked the code and things are discrete. By the way, discrete mathematics was not developing very much yet at that time. Discrete mathematics was something that took another 50 years to really get big. But people were nevertheless looking at discrete kinds of things, and they sort of thought, well, maybe everything is discrete. They couldn't make it work to have space be discreet. So that was abandoned by the 1920s and at least 1930s. And that's again something that I had the opportunity to pick up again in recent times. And it's been a funny experience because a lot of things that I've looked at have been things that have been kind of thought about another one second law of thermodynamics. Thought about a lot, heading for 1900 or so, and then kind of dropped after that. So all sorts of things like this similarly kind of theoretical foundations for evolution. Another thing that was kind of thought about a little bit there wasn't really the right apparatus to think about that question and have had a chance to look at that again with this kind of modern computational paradigm. So it's been sort of an interesting thing to see. There were things that were started 100 years ago or so and then stopped, and now we have a chance to restart them. And it's kind of, in a sense, shocking how far people got and how much they were oriented in this direction. But then they got stuck. And even, for example, David Hilbert spent a long time trying to do something which spent about a decade trying to derive things like fluid mechanics from underlying molecular dynamics. Now, in the end, I think that that requires sort of computational understanding. And I think that's what. For example, I've worked on a bunch in recent times of the second law of thermodynamics. I think we really understand how that works now. But, you know, Hilbert tried to do that 120 years ago, and he didn't succeed. Einstein tried to figure out how you could make space be discrete. Heisenberg, same thing. These people didn't manage it. And it's pretty cool that one can now come in with sort of A new layer of paradigm and method and actually kind of do what people tried to do at that time. And it's also interesting that a lot of those people had the right intuition about what one should try to do. They just were not technically able to do it. And it kind of makes one wonder about these things that one wonders, well, does it work this way? We have the intuition that it works this way, but. But do we have the technical machinery to actually get there, or is that technical machinery too far away? And so those are. I think it's. I mean, I always find there's these questions about how hard do you push? You know, Hilbert spent a decade trying to solve this problem about discrete underlying molecules and so on, and it just wasn't doable at that time because the sort of ambient technology didn't exist. But should Hilbert only have spent a couple of months on it and concluded it was impossible, or was it right to spend that amount of time? These are things where it's interesting to think about how much effort should you spend? I mean, I think with our physics project, I was kind of lucky that I didn't try it seriously a lot earlier than I did, because by the time I was trying it, I had all kinds of tooling intuition, mathematical methods and so on that were sort of able to be wheeled in and were sort of ready to actually attack it at that time, 20, 30 years earlier. Didn't have those things even at the level of doing good graph theory computations. Graph computation and Wolf language, things like that, which existed by the time I was really trying to use it. Let's see. Jay's asked who began the trend of naming discoveries, inventions after themselves. You know, most people, sometimes people name things after themselves. I mean, companies, things like that, products and so on. I've ended up doing that partly because I saw too many mistakes and even perhaps made them myself. Where you name a thing after what you think it's for, and it turns out that's not what it's actually for. You know, we're fighting that a bit with Mathematica where people say, oh, that's for doing math, which it long, long ago transcended that. I mean, the, the Mathematica is great for doing math. It's very universally used for doing math. But that math represents, I don't know what 10, 20% of what Mathematica does. And so better you just throw it a name like Wolfram Language, where you don't know anything about it from its name alone, so to speak. So that's a place where naming companies is sort of an interesting club of people who've named companies after themselves. It turns out not to be the egotists. It turns out to be people, in large part who really sort of care about the things that their companies do and the products that they make and so on. But it's sort of an interesting club. But any case, in terms of scientific discoveries and so on, most often those things, well, they're often misnamed. I mean, they are, you know, more often than not, the name given to something by the world is not the name that is not the correct kind of historically correct name. I mean, you know, the Fibonacci sequence. Absolutely. Definitively not invented by Leonardo Fibonacci, for what it's worth. But in a sense, it's just a tag. So, you know, it's useful to call it a Fibonacci sequence rather than to call it thing invented by unknown, unnamed Indian studier of the Vedas and prosody and so on sometime around 2000 years ago or something. That wouldn't be a. You know, it's just a tag. And I think the convention of using those kinds of tags. It's an interesting question. When did that start coming in? Let's see. I mean, Certainly by the 1700s, people were routinely referring to it as so and so's, whatever it was. I think, yeah, I think even another case of this is creatures when people were naming. When people were naming organisms. I suspect even in Linnaeus, there are names that were given that are called Fred's lizard and things like this. So that's another case. The. So I think that the idea of. Yeah, so I think that's sort of a natural idea, and it's an idea that originated pretty early. It's something where people don't usually do the history very well. And it's not even clear. You know, it's a complicated, almost moral question about sort of what history do you do and how much do you do and how much do you care? And, you know, what happens if it's wrong and so on. And. And there's been a certain tendency in recent times to try and right the wrongs. I have to say, I know there are things I've invented that got named after other people, and I haven't yet seen anybody trying to right those wrongs, But I don't know. I'm not sure how much it matters, but it's wrong, so to speak. And I think there are cases where things used to get called. One that immediately comes to mind is the Friedman Universe, which is a particular solution for the expanding universe verse. And it then became the Friedman Robertson Walker, and then the Friedman Robertson Walker lemaitre. And I think it's even got another one added to it. And you know, it's always complicated. And I think that sort of, you know, there's a tag and there's historical correctness and if those align, it's great. If they don't align, it kind of might be annoying to the person who's. Who, you know, who didn't get attached to the thing. But it's one of those. In the end, it's like words. It's like, where does a word come from? It's, you know, a word is just something that got plucked somehow out of the air and perhaps it got invented by somebody. I mean, for example, I've. Right, right now I happen to be working on this area that I'm calling infra geometry, which is kind of the, the lower level version of the thing, the sort of computational layer from which ordinary geometry emerges. And I'm realizing I'm having to invent a ton of words there, which are cases where it's just like I think of the word, and unless the word is horrible, the word will probably get used for that particular to represent that particular kind of thing. Let's see, Let's see. Well, let's see. I'm looking at some of these things here. The more or something became clear how pretty sure no one ever solved the three body problem. I think that must be referring to a different comment that I had there. The people commenting about naming conventions. Look, I have to say a few other things about naming. Naming of biological species is an interesting story because there is an entity international. What is it called? Committee on Biological Nomenclature, I think it's called. If you are out in the jungle somewhere and you discover a new kind of beetle, then you get naming rights for that beetle. And you typically deposit a type specimen somewhere and you say this is in such and such a mutuseum, in formaldehyde or whatever. It is preserved in a bottle. Darwin specimens are still out there, preserved, I think mostly in the Natural History Museum in London. Sitting there, the actual first specimen that he got of such and such kind of barnacle or whatever is still right there. It is the type specimen for that species. But anyway, you get kind of the naming rights. To the creature. And people have had all kinds of crazy names for creatures they're named after. Sometimes they're named for what they look like, sometimes they're named for some sort of Cool character, et cetera, et cetera, et cetera. There was a period of time about 20 years ago now where, where people who sponsored expeditions and so on got to get naming rights and you could kind of buy. There were websites where it was like, here are creatures for sale. Sponsor this creature and get it named after you type thing. Most of the creatures were kind of ugly beetles and so on. There would be an occasional more elegant creature that was correspondingly more expensive. I think that kind of went out of style. But that was a case where it's kind of like what are you going to call these? What are you going to call these creatures? And I think there are sort of, you can't call them. There are various kinds of, you know, obscenities and things you can't have and a few other things like that that are kind of, you know, no nos for species naming. I think, you know, when it comes to that kind of naming, there's also asteroid naming, crater naming, all these kinds of things where there's an awful lot to name and it's mostly honorary naming in those cases rather than the discovery of it was so and so. I would say that in some creature names, dinosaur names, things like that include the name of the discoverer and some are just the name of a rock group that somebody thought was cool or something like this. I think there was an interesting trend a while ago like sponsor a mathematical theorem. I don't think that really got anywhere and kind of get the naming rights to a mathematical theorem. There are a few examples I know in history, I think orreries these things for sort of making models of solar systems and things. I think that was made by somebody and named after, if I'm not mistaken, Duke of something or other. In fact, when Galileo discovered the moons of Jupiter, I think he was thinking of calling them the Medicean stars after the Medici who were his sponsors. But for some reason he didn't do that. I'm not sure quite why. I think he was a fairly argumentative fellow and maybe by that time he'd had a fight with those guys or something. I'm not sure exactly what now, by the way, I'm now wondering when, for example, the Trojan asteroids were named. I assume they were named after the ancient city of Troy. And I don't actually know why, but that will have been an honorary naming. It wasn't like, I don't think Mr. Troy discovered it. Now there are weird cases like for example, gray code used and you know, when you have a number represented in binary, gray code is something where instead of there being sort of a. Successive numbers always differ by just one bit. So you might have thought gray code was called that because of something to do with it being gray as opposed to black and white or something like that. But no, there was a person named Gray. I think he worked at Bell Labs after whom gray code was named. So it's sometimes super confusing in that regard. And there are cases which I always find somewhat amusing where people worked on things that are very related to their name. It's kind of this strange phenomenon of sort of nominative determinism that, you know, the person who works on plants is named Green, or the person who, you know lots of other kinds of things like that. And then you end up with these names for things which are named after people who discovered them, but they sound like the thing because of this bizarre phenomenon of people. Maybe it's coincidence, maybe it's kind of the way that people are encouraged or something, that the name of the person aligns with the thing they worked on. Let's see. I think, you know, there have been different naming conventions. I mean, in. In physics, for example, there were. People would name things routinely. And James Clerk Maxwell was quite a namer, named a bunch of things, and some of his names stuck and some didn't. A famous one is Curl in vector analysis. Dell Cross, whatever he called Maxwell was going to call that Twirl, but that didn't stick. It became called Curl instead. I think that various people have been prolific namers. I've contributed some names myself, some of which have worked out very well, some of which have not. I say it's a bit frustrating because some names that I thought of in five seconds or something have caught on very well. Like totalistic rules, for example, and names that I really worked on, like autoplectic processors, didn't catch on. And I think the. It's a funny thing when words, names and so on are going to catch on and when they're not. I would say I've done pretty well in getting names that I've invented to be ones that people end up using. I think another thing. Well, I'm trying to think about other. I mean, there are. Yeah, there's. Oh, yeah. Other other kinds of naming things like naming of elementary particles that was, you know, oh, there's a mu, there's a PI, there's a this, there's a that. And it was really just letters being used to name particles. And then, for example, there would be. There was a horrible collision in 1974 where two different groups discovered the same particle. One called it the J particle, one called it the psi particle. So it got called the J psi particle. But most particles have single letter names. Now what happened in physics was there had been fairly serious, I mean the word twirl, maybe it is not as serious as some, but physics names were fairly staid and stodgy. And then in 1950s, Murray Garman invented this name strangeness for this attribute of particles. Various kinds of particles have been discovered at that time, hyperons, the K masons, things like this called the attribute that they had strangeness. And that kind of led to a you can't be serious type thing. You know, how can we take physics seriously if we have names like this? And then later on came by 19, when was it 70ish. Charm was sort of the next follow on from strangeness. Oh my gosh, now we've got charm. Then there's B and T which were either bottom and top or beautiful and don't know what T stood for at that time, but these things sort of the whimsicalization of physics happened. Now some other fields are routinely whimsical. I mean some other fields have had kind of, I would say in some areas of sort of towards computer science. There's been kind of a whimsy for a long time and perhaps that's a consequence of whimsy in kind of engineering naming of things. I know well, to tell a funky story. Well, a lot of kind of the, the early sort of names of programs and languages and so on would be puns and things like this. To tell a funky story. This is probably 19, when was it? 1979, maybe 1980. I was working on S and P and I was working at Caltech at that time. And I invited this whole series of people who'd worked on sort of precursor systems to come and give talks. One chap comes to give a talk and actually he was a. Fairly young fellow at that time who had this system that was a Lisp system and so on. And he was explaining that, you know, it was called Franz after the. And they sort of asked the audience, you know, why do you think it's called Franz? And you know, because the answer is because it's like Franz Liszt and that's like Lisp and so on. And I happened to be. One person who was in that audience happened to be sitting next to me was Dick Feynman, physicist, who at that moment kind of stands up and says, if this is what computer science is about, it's all nonsense. And walks out. And so that was sort of an example. I mean that. I'm afraid that incident had many bizarre repercussions, but that's not for this stream. But I think that what that was an example of was kind of a very different naming convention in one field than another. And the feeling from physics that, oh, this field, which has these incredibly whimsical naming ideas must be not a serious field, so to speak. I have to say, when my children were young, I had the sort of idea that I would try and write a children's book. No, I've never done that. Probably never will. And my, my concept was a book about my dinosaur needs a name. I was kind of imagining the, the, you know, dinosaurs found by some kid. And, and then there are lots of different adventures of different kinds of conventions for how you should name it. Like somebody says, well, you know, one has a theory that it rolls up in a ball, so it should be called, you know, whatever it is, ballasaurus or something. And then they're like the, the people who are trying to promote some consumer product based on its name and this and that, the other. But I could never quite find the right ending for this. So I, So I never wr. Maybe I will one day, any case. Okay, there's a comment here that Trojan asteroids were named after characters from Trojan War. Doesn't surprise me. And. Yeah, well, astronomers decided to name them after people from the Trojan War. I have no idea why. When it comes to naming things and new things, it's always a funky business. Like for example, when I first had networked computers, which was 1982. Is that right? Yeah, 1981. 1982. First had these networked workstation computers and they all needed names. And so my first generation names were names of stars like Sirius and Vega and so on. And that was the first computer network I had, was All Stars. Then actually at, at our company, when our company was young, starting 1986, 87, we. We named them because we were doing software development. We named them after various kinds of bugs, insects, beetles, things like that. I think that was the next one. And then, then I've gone through, over the course of my life, I've gone through various different conventions about how you name these things. And you always notice, you know, I always notice. And when, you know, I, I'm connecting to WI fi in some, in some spot and I see all the names that people have assigned to their networks, it's another one of these, what are you going to call it? Type things. Okay, so let's See. Real asks in response to my comment about nominative determinism, I think, do I have any planned work with tungsten? Yeah, that's an amusing question. So far as I know, the Wolfram, which is the name for tungsten, it's the thing that gives it the W on the periodic table is it certainly was not because tungsten was discovered by a relative of mine. Actually the story is that tungsten is usually called wolfram in a bunch of European countries and I believe in the mid-1950s. I just learned this recently was sort of a. There's this niobium is called columbium. Was called columbium in the US Sort of a Columbus based name. So it was columbium in the U.S. niobium in Europe and tungsten. Was tungsten in the U.S. and wolfram in Europe. And there was some agreement in the international chemical union, I guess union of. Well, whatever. In. In the mid-1950s, sort of the agreement was reached. Okay, the US will get niobium and Europe will get. Am I. No, I'm sorry. The Europe will get niobium and the US will get tungsten. So I had it not been for the ca for that. Even though it, it got left with. With W as the symbol in the periodic table. I think the derivation is tungsten comes out along with aluminum as an ore. It comes out as an orc or wolframite. W04 I think that is. And it was some kind of wolf, you know, wolf vomit type thing. Wolf ram and I think Germanic languages. That was the sort of thing that came out, the sort of froth that came out along with the. With aluminum and being mined. And that's where that name for the, for the material came from. I don't know where the name, my last name, who knows what its history is. It's a comparatively common sort of Anglo Saxonish, Germanic ish name even became popular as a first name at one point. I do know that There was a Saint Wolfram from the 7th century AD who was a rather undistinguished saint who I think lived primarily in France. And in a piece of utter bizarre trivia, it turns out there are very few churches of St. Wolfram around the place. But there is one in Lincolnshire in England, which is where Isaac Newton grew up. And so the elementary school that Isaac Newton went to was at the St. Wolfram's Church in his local town in Lincolnshire. So just one of those pieces of utter trivia that doesn't really affect the course of the world. But anyway, so I Don't know. So the answer is I, I haven't had, I don't believe I've ever, I've ever used tungsten for any, for any particular purpose. I know at various times various different elements become important for random studies I've done. I remember when I was a kid being interested in the, the isotope that has the smallest Q value, smallest energy difference when it decays to emit neutrinos because I was interested in that for studying neutrino background radiation in the universe. And I went through all these books at that time because that was the only way you could do it. And that was rhenium187. That's been my all time favorite isotope is rhenium187. But I haven't chanced upon tungsten as a thing of significance in anything I've done so far. Okay, let me see, maybe one last. There's a question from Gollagatz here about naming. Yeah, there's also the question of naming programs in naming functions in your programs. And that's always so difficult. I mean I, I, I guess I have this terrible convention of I have the name of something and then I want a modified version, I'll add an X at the end. And I think that came from when I first was using computers. I was writing in machine code and assembler language and a very primitive computer. And for some reason programs, I don't remember why I started doing this, but programs that were intrinsic programs that were sort of a core part of what I was doing, I would call Q something or other programs. I'm not sure why I started doing this. It may be from the Q source word in Latin, I'm not sure. But anyway. So I've personally ended up with some bizarre and terrible conventions in that regard. It's a thing where LLMs sometimes do a reasonable job saying what should I call this function? And if they can tell at all what the thing is doing. And they find it easier involving language because there's a lot of actual words in the names of functions and so there's much more clue about what's going on. And sometimes they can come up with reasonable names for functions. It's something as we roll out various kind of code assistance features in the next few months there'll probably be some good ability to do that in Wolfram language. Well, let's see, one more thing. Perhaps there's a question from Eri here. What's your view in innovation in economic science? We're nearly 250 years since Adam Smith's wealth of Nations. What's the story of sort of the development of economics? I think there was an earlier question from Brady about history of minimal models of economics, and computer models of economics seem to be instead quite maximal. I don't know as much about this as I hope I soon will, because economics is an area that I'm sort of actively interested in studying and specifically in finding what minimal models might exist in economics. I think it is my impression that bizarrely enough, around the same time that I was mentioning earlier of formalization, there were a bunch of efforts to kind of find more minimal models of economics around 100 years ago. And I don't know as much about these as I should with people like Menger and so on. I just don't know this field well enough. I mean, it is a. It's a remarkable thing that even very fundamental questions like sort of fundamentally is money? Do cryptocurrencies have fundamental value or not? Do, do you need, you know, what, what's the way to think about all these kinds of. All these kinds of economic dynamics in the world? That those things, we really don't know those things yet. And there are wildly different theories about what is sort of really going on now? You know, usually when there are wildly different theories about what's really going on, they're all correct at some level or they're all incorrect at some level. It's kind of like the argument, you know, is light a wave or a particle which. Which raged for for centuries, and in the end, well, it's partly a wave and partly a particle. You can think about it both ways. I think that. And I've seen that same thing in a lot of different situations where there are sort of heavily held beliefs. And it turns out in the end, the thing that is the best way to think about it is something that kind of slices it in some different way. I suppose the. And that the things that have been thought about both are kind of right. We've seen that a lot with our physics project, that we have a very different, very paradigmatically different way of thinking about what the underlying kind of what's really there in the universe. But yet that plugs into a lot of things about different kind of models of mathematical physics and so on that people have studied. And you can really say, well, underneath that is this machine code, but you can sort of plug it into these things that have been thought about. And my guess is that something similar will happen with economics. But this question about, well, what really is economics? That's Another one of these challenges is economics a field in which you are merely describing what happens in kind of a statistical way? Or are you kind of. Are you instead having something where you say there are these axioms maybe of human behavior, and from these axioms we can derive how economics works? You know, I have to say that they're very different. The beliefs about different ways that economics work have consequences for economic policies. I mean, there are, you know, in some traditions, like in various kinds of Marxist traditions and so on, it's kind of like there is control of the economy. You just pull this lever and this happens. I mean, that's obviously also believed in capitalist world too. There are certain levers that you have which you can pull to make things happen. You know, I have to say that for me, kind of a particularly striking version of this was something I saw in 1991, I guess, when mathematical and wolf and language were young and they were getting used in lots of different places and lots of different finance and economics applications. And I happen to be visiting the Federal Reserve, I think, in Washington, D.C. sometime, and I go visit them, and the only thing they want to talk about is statistics. It's like there is the economy. It's flapping around, it's doing its thing. We want to understand it using kind of econometric, statistical type techniques. Okay, so happened pretty much the next week I was in Moscow visiting the central economic whatever planning bureau I suspect it was called, and talking to those guys. And the only thing they want to talk about is linear programming and operations research and so on, and how you basically determine what happens by changing parameters and so on. So it was a nice example, very on the ground example, of the difference between two different systems for thinking about economics and thinking about the degree of control that one does or does not have. I mean, I think it's an interesting thing, but certainly is related to the whole sort of story of computational irreducibility. Even if you know the rules, you kind of just have to follow each step to see what happens. And the discovery that that's important. I've recently kind of really made, I think, with more clarity than I've ever had before in biological evolution and now very recently, last couple of weeks in machine learning. That sort of machine learning is a story of taking these lumps of computational irreducibility and finding ways to fit them together so that they usefully achieve the objectives one wants. So now the question is, well, in economics, is it sort of a similar story is a lot of what happens in economics computationally Irreducible. Is the. Is the randomness of the market or something, some piece of computational irreducibility where you merely get to, as you try to sort of put things together in economics, take these lumps of computational irreducibility and try and fit them together in some way. I'm not sure. I'm not sure how one should best think about that working. I do tend to think that there are sort of ideas. Well, I will say that I think the idea of computational irreducibility, you know the rules, you can't see what's going to happen. That idea does show up, I think, in some strands of economic thought. I don't know this history as well as I should, but I think Hayek, for example, Friedrich Hayek, no, F. Hayek, I can't remember the first name, in the 1940s, maybe in 1950s, is talking about sort of as an attack on communism. I think more than anything else is talking about it just isn't going to work to kind of, you know, even if you set the rules, you can't know what's going to happen type thing. I have to say I'm reminded of visiting Soviet Union in the 80s and the person who was my sort of assigned tour guide was explaining to me how. How hopeless things were there. And they had a refrigerator factory that had not made a working refrigerator in seven years. And the system is. And then when you think about kind of what people would say about, well, you can control everything, but actually things go horribly wrong type thing. And in a sense, that was sort of, I think, what Hayek was getting at in his sort of proto versions of computational irreducibility. I think at that time there were even descriptions that people like Hayek gave about, which I haven't really understood, I have to say, about sort of Godel's Theorem, like stories about the system. I think they were very keen on the idea that once you try to control the system, can you control the control, so to speak. And I think it sort of is a little bit reflective of my friends who run hedge funds and so on, where it's kind of like given any set of rules in the system, you can sort of find ways to do things that leverage those rules in some sense. And I think there were some arguments about sort of recursion type arguments about how you had to have inevitable unpredictability. I don't think those arguments are at the core of computational irreducibility. I think that those arguments are kind of very much revolve around Godel's theorem. And I don't think really quite capture the. The same idea, but the conclusion is more or less the same. Just because you know the rules doesn't mean you know how the system will actually behave. And I think. The. I see a comment from George here, who. Hello, George who? This is about naming again. And this is in Wolfram language, built in function names, which we didn't talk about here. That's sort of a big activity of mine. But the function apply, which will take a function and you have a list of arguments, and it will apply that function to the arguments. So F applied to the list ABC would be F of A, B, C. And a possible name for that function was recapitate. That is the. We call F in F of A, B, C the head. And so recapitate would be re. Put the head on, so to speak, a terrible name which fortunately we didn't use. But anyway, back to economics, the question is, is there a theory of economics? And what would that even mean? And it's like, is there a theory of machine learning? Is there a theory of biological evolution? What I found rather recently for both biological evolution and machine learning is they've got lots of computational irreducibility in them. They work by leveraging computational irreducibility. So in a sense, when you've got a lump of computational irreducibility, you don't have what we normally think of as a theory. Because normally when we say theory, we mean take a thing that's out there in the world and find a kind of human narrative, a kind of way of describing what's going on in the world, what's going on, a way of describing it that kind of fits in a finite mind like ours, a way that we can tell a story about what's happening so we understand it. When we have computational irreducibility, there's a lump where we're not really going to be able to do that other than just saying, run these rules, see what happens. But typically that run these rules, see what happens is not something that sort of fits in a human brain, a human mind, to do. So insofar as these fields have computational irreducibility inside them, there will be a limit to the explainability of what's going on. It's kind of like in biological evolution. Why did it work that way? Well, it's just because it found that lump of computational irreducibility, and that lump of computational irreducibility works that way. Why did. It's the analogy I've been using for machine Learning is you're building a wall. If you're building it out of regular shaped bricks, you can say, why do the bricks arrange themselves that way? Well, because that's the way you arrange bricks that are cuboids like that. But if you're building the wall out of stones you happen to find lying around on the ground, there isn't really a good. Why is the wall that shape, that pattern of stones? Well, it's because those are the ones that happen to be lying around and that fit. So in economics, my guess is there's quite a lot of computational irreducibility where it works that way, because it happens to work that way. Now the question is, is there an overarching theory? So, for example, in, let's say, fluid mechanics, the molecules bounce around in all sorts of computationally irreducible ways. But yet, if we're looking at just the large scale aggregate velocity field of the fluid, we have a theory of that that doesn't have to get into all that computational irreducibility. So the question for economics would be, what are the kinds of things about which we might have an aggregated theory? And by the way, my guess is that the actual dynamics of economics follows this whole story of the ruliad that shows up in our physics project, in metamathematics and so on, that in fact there will be inevitably kind of global laws of economics. The question is, are those laws of economics things that are actually useful to us? I mean, it could be that there's a global law of economics that says that whenever the velocity of money in this corner of this is that then this happens and that happens. And people say that's not something that we care about. Now, I have to say, in the world of quantitative finance, sort of everything is something you care about. So if you find one of those kinds of regularities, kind of the, the goal in most cases is to leverage that piece of regularity that you find, to leverage that, to be able to sort of take advantage of that to build more value or to build to generate more. Well, in the end, to extract more money from the system. I have to say one of the things that I'm suspecting is that value in economics is associated with computational reducibility, that there's a lot of irreducibility of this happens just because it happens to happen, so to speak. But that there are. We know that in any computationally irreducible system there are always pockets of reducibility, places where you can say things. The pattern is mostly quite random, but you can see that there are these triangles that are, that behave in certain ways, or there's this piece of periodic stuff on the edge or something like this. And so there are always pockets of reducibility. And what does a pocket of reducibility do? Well, it lets you get to the end more quickly. It also lets you control it, which is an interesting point, but it mostly says you don't have to go through all those steps. You can just jump to the end. Instead of having to personally collect all the different materials that make a smartphone, somebody has already done that for you. There's sort of a jump forward. There's a piece of, for you at least, it's like there's a piece of reducibility. So I kind of have the suspicion that value is about pockets of reducibility. And that in a sense the somewhat surprising to most areas of economics observation that the overall value of the world seems to be going up. The overall GDP of the world seems to be going up in real terms, so to speak. And maybe that's because as we discover more, we are gradually finding more pockets of reducibility and that's the driver of sort of increase of value. And why does it matter that we find pockets of reducibility? My current proto theory is that it's because we have finite lifetimes. In other words, time is something that is fundamentally valuable to us because any one of us only has a limited amount of it. And so to be able to do something quicker is somehow fundamentally valuable. If we were living forever, then who cares that we're going to spend five years picking up the components to make this thing or whatever. But if we only live a certain amount of time, then it really matters that we can just buy that thing from a store and use it rather than having to spend five years of our life picking up the pieces and putting them together. Now it's an interesting question in the theory that kind of value in the world is associated with pockets of reducibility. Pockets of reducibility are the story of science. Science is about kind of the dynamics of sort of how you take, you know, how you take what's out there and make a narrative that sort of fits in human minds and so on. So there's, it's, well, there's this question of, okay, science is doing that. Basic science is finding pockets of reducibility. New intellectual paradigms are finding pockets of reducibility. Often the economic value of those pockets of reducibility is far in the future. Calculus was invented. I don't know when calculus started making Money, but It probably took 100 years. I thought our physics project would take 100 years before it generated anything of kind of commercial value. Actually, I was wrong. And there are things of commercial value that it's generating, even starting to now. So very few years in, and it's very clear there's a path to do that. But most of the time, basic science is a very long term bet. And so there's a sort of very, you know, if one understands more about economics, maybe one understands more about how sort of the value proposition of basic science can be pulled into today's world. Because one of the issues, it's certainly something we think about in connection with this Wolfram Institute that we've started in recent times is, okay, we're doing lots of great basic science. How does that work from an economic point of view? I mean, one can do philanthropy and sort of just say, I'm going to give money to basic science because it's good for the world. And that can be fun and a good idea. But really that basic science might have a huge amount of value. Take machine learning, for example. Take neural nets, neural nets in more or less their current form, invented in 1943. People working on machine learning for many years. But it wasn't until very recent times that there's trillions of dollars of perceived value in machine learning. But what do you do if you're in 1943 and you're trying to move machine learning, neural nets and so on forwards, but you imagine that 80 years later there's a trillion dollars of value in it? How does that work? What can you do to kind of accelerate the, the sort of going into that pocket of reducibility and so on? How does that work? And how do you get sort of, how do you build dynamics in the world so that you can cause those things to happen? Because right now those dynamics are really not there. I mean, the dynamics of kind of commercial intellectual property, all these kinds of things, they operate on much shorter time scales than the kinds of timescales. I mean, very little operates on a century long timescale. It is interesting to think about the fact that there are some things that operate on those timescales. And can you use kind of the value that happens on those timescales that are relevant to some things, to kind of walk backwards into things that are relevant to today for purpose of, for example, sort of accelerating the rate at which we can do basic science? Anyway, we should probably wrap up there and perhaps in a little while I will have more cogent things to say about economics. I mean, I think that economics has a terrible It's a place where governments get to potentially do things, or at least they imagine they do things, or people imagine that governments do things. And certainly they achieve some things. They achieve positive, negatively, some things. In economics, governments can make horrible mistakes, and things can go horribly wrong. Governments can probably make things go righter. I'm not sure. But it's a place where it often segues into the many other sort of the economic things that governments do are certainly tied to other things that governments do. And that's a whole different horrifying can of worms that. Tends to lead to all sorts of strife and so on. Anyway, we should probably wrap up there, and I'll look forward to chatting with you another time. So bye for now.