History of Science and Technology Q&A (August 30, 2023)

Sam. Hello everyone. Welcome to another episode of Q and A about history of science and technology. I see there are a bunch of questions here. Let me see. Eng asks, do you believe we had an exploration age? Sometimes the hype feels exponential, but maybe it's just linear. What are your thoughts? You know, it's a funny thing. People have often commented on the fact that sort of discovery in the world seems to be speeding up and kind of, you know, it seems like there's just more and more being learned and more and more papers and more and more patents, all this kind of thing. One set of people says that says it's all exponential and it's heading for sort of the singularity of infinite kind of speed of acquiring knowledge. And another set of people say, oh, you know, I'm a venture capitalist and I've heard a million pitches and they're now all the same. And, you know, or I think there's one quote, you know, I was, we were expecting flying cars, but all we got was, you know, 140 character tweets or something. How can both of these be right? I think it's really very simple. The point is that there are sort of domains which we already know are a thing, and there are emerging areas that are not already a thing. So for example, you can have fields of science or something where it's a well established field. It's physics, for example, it's, you know, it's, I don't know, it's, it's biology, chemistry, whatever else. And those fields, they build a lot of institutional structure. They can, you know, there are prizes in those fields, et cetera, et cetera, et cetera. It's possible for thousands of people to pile into those fields and do more and more and more work, publish more and more papers, you know, start more and more journals in those fields. But then you have some new area like, I don't know, LLM science that just came on the scene, but that doesn't have any of that institutional structure. And if you are tracking how many papers are being produced, being published in academic journals, for example, you don't detect that because maybe the things that are being done in that field aren't really quite the same academic way. Maybe they're things that are done by tech companies or something like that and are presented in different ways. They just don't show up as signals on the kind of thing where everybody knew, oh, we're looking for the number of academic papers published or something like this. So I think what tends to happen is, and this is Kind of the long rerunning story of the development of science and technology and so on, is there will be some new area that's opened up, a new paradigm, a new methodology, something like this. That's the place where there's rapid growth. Then after a certain period of time, you know, maybe a little bit less than a generation or so, you will get to the point where that field is institutionalized. It's got a lot of engines running, but the really innovative stuff has probably already happened and maybe another hundred years before really innovative stuff happens in that field again, over several hundred years. And so this idea that kind of there's a. So what happens is when you say, I've got a metric, and it's based on things that already exist in the world, that metric will often say, on the one hand, there's more and more activity, there's more and more papers being published and so on, and on the other hand, it will. But when you look at them, that many of them are quite incremental and not really adding. They're not really accelerating things in a major way. But the things that are accelerating things in a major way aren't yet defined how to make metrics for them. And so those things which become the future, so to speak, become the really important sort of new directions in the future, tend to sort of go under the radar of whatever metrics you have, saying, is it exponential? Is it not? And so on. So I think I myself have been lucky enough to be involved in a few things which I think are, you know, at least the seeds of things which will grow dramatically in years and centuries to come. But I think in. And, you know, you can kind of watch those things happening, like, for example, the exploration of the computational universe of possible programs, this field that I now call ruleology, the study of simple rules. And abstractly, what do they do? You know, there's a certain amount of work that's been done on that, and there's certain growth in that area. There are a number of sort of major things that emerged from things I did and so on in the 1980s and so on that are somewhat known by people. But this field, somehow there'll come a time when there are just zillions and zillions of papers about this field, and some people will say, oh, that's a sign of amazing growth. And other people will say, oh, no, you know, it's all. They're all, you know, incremental and so on. So I think that's the way I see it, that there is at Any given time in history, there are these kind of emerging areas. They are the growth hotspots, but they're not as visible as they might be. They're only visible to people who happen to be kind of paying attention to those things. It's often not clear how big they're going to get. But those are the places, you know, rapid growth happens in these areas where they aren't that big. By the time they're big and really noticeable, the growth is not nearly as rapid. And so I think that's how sort of this sort of seemingly paradoxical situation arises. There both is rapid growth and there isn't rapid growth. And I think that if you ask the question, what's the rate of major new science ideas, let's say, or technology ideas over the course of history, it'd be an interesting thing to try and figure out. I don't think it's super easy to figure that out. I think that whatever thing you make, you know, whatever big wall chart you make, that's a history of this or that thing, the thing it won't take account of is the stuff that is a new type of thing. And so it doesn't, you know, it's not going to appear on the wall chart that will be a different wall chart for the future, so to speak. So it's kind of hard to, to compare these things in a clear way. You know, there is a question of as the world gets bigger and there are just more people and more people doing more stuff, why isn't it the case that that leads to more rapid growth? I think I've talked about this a bunch of times before. I think the challenge is always as soon as things get big, they get slow because they get institutionalized. There's all kinds of structure, there's all kinds of kind of built in conservatism of, yes, the 50,000 people who do this field all believe this. And so when somebody comes along and says, well, actually there might be something else, that's true. All those 50,000 people are going to say, no, no, no, we don't believe that. It's going to be much more difficult for that lone voice to actually get anywhere with what they're saying. Whereas if it's a small young field, there's much more potential for sort of major new directions to be taken. But it's not nearly as visible when it's at that point. All right, let me see another question here from Vivala. Okay. It's about the weather. When was it learned about the weather being essentially mathematics? And physics which could be utilized. Okay. And then asking about making weapons that control weather and weather conditions and so on. So the question of, you know, predicting the weather. Okay, so first of all, the sort of the systematic recording of weather is not that old. And the people who most cared about that were navies and particularly the British Navy. And there were, I think, Captain later, Admiral Fitzroy, who was the chap who was the captain of the Beagle, the ship that Charles Darwin kind of traveled around the world on and found his finches and the Galapagos Islands and all the other cool things. His later career was all about kind of setting up a systematic weather reporting network for the British Navy. And that was probably 1860s, 1870s, that that was done. And so there were kind of that idea of systematic weather reporting that came in in the latter half of the 19th century. And then there was a long sort of tradition of weather forecasting. And when I was a kid in England, for example, England is a place where weather forecasting is comparatively hard because it's a place where there's enough sort of pieces of ocean and topography and so on that you don't just get a weather system that just translates just blown by the wind from one place to another without changing. It's more detailed and it's more difficult to predict the weather. And the. But certainly, you know, in the 1960s, for example, there would be, you know, the. On the television, there'd be the weather predicting people. And they were quite. It's quite kind of funny because they were. There was a certain kind of theory about, oh, there's a hot front, there's a cold front, there's a this, there's a that. And it was kind of an art of how can you see all these things where. Oh yes, I've seen a hot front and a cold front come together like that before. And so I think it's going to rain tomorrow type thing. I mean, the joke was always that the typical weather forecasting that was done in England, at least in the 1960s, you would do better just looking out the window and seeing what was happening now to predict the weather than by listening to the weather forecasters. I'm not sure if that was really true. And they also, they were still at that time. I don't know if it's still true. You know, on the, on the radio, for example, they would read off these kind of boring seeming, a little bit like financial news. They would kind of read off the. The wind speed at all these weather stations around the country and particularly ones out in the, you know, in the North Sea or whatever else. So that was, you know, there was this whole tradition of kind of sort of history based weather forecasting as an art form, so to speak. It kind of reminds one of sort of lots of investing kinds of things in financial markets where people say, oh yes, I've seen that pattern before. Whenever this goes up in the winter, then it comes down in the summer and this or that thing happens. It's kind of a, a piece of experiential kind of history based, kind of artistic prediction, so to speak. But the first time when people sort of really thought seriously about, well, the atmosphere has a bunch of fluids and it's mostly, you know, it's air and it's water vapor and so on. When that started to get thought about was John von Neumann and a person called Charney in 1950 maybe wrote a paper or something about weather forecasting. But they tried to do weather forecasting on an early computer. On the computer at the Institute for Advanced Study in Princeton. They were setting up kind of the differential equations to describe kind of the motion of the air and to try and do other forecasting. And at the beginning they were like, it's just physics, we can predict it. But very quickly they realized, well, actually, no, it's much more complicated than that. It's actually quite hard to predict. And they didn't really make that much progress in predicting it. And then so that was sort of a little bit the beginning of that story of can we just run codes to predict the weather, so to speak. And then I think that picked up a certain amount of steam. But then there was sort of a bit of a wrench thrown in those works by ed Lorenz in 1963, 1964. I don't know how influential the paper he wrote was in the practice of weather forecasting. It had perhaps more influence in mathematical physics in general. But what Ed Lorentz, who I knew actually was, he was a meteorologist at mit. Earth scientist in general, but I think primarily meteorologist at mit. And what he did was he took the equations of fluid dynamics in the atmosphere and he did so called modal truncation. So he said, let's just imagine that there's just one or two kind of big eddies in the atmosphere that and that that's kind of what's mostly going on. Let's write down the equations for those for the whole atmosphere where you have all these different motions and things happening in different places. You get a big partial differential equation that's telling you the time variation as compared to the space variation and so on. What Ed Lorentz did was he kind of truncated that. So he got a system of just pure ordinary differential equations. Just these variables depend on these variables, and there's no dependence on space where there's sort of an infinite number of different places where we have to account for things. So he ended up with a small system of equations that later got called Lorenz equations. And what he showed is that those equations have sensitive dependence on initial conditions. The equations in general, if you run them, you will. For most initial conditions, well, you'll eventually, on a large scale, you evolve to an attractor that is, it's kind of like, you know, there are many ways you can roll downhill, but in the end, you always get to the bottom of the hill. Always get to this one sort of lowest point at the bottom of the hill. That's kind of an attractor story. And similarly with Lorenz equations, you always get to this attractor. It's a kind of complicated thing that has two sort of two holes in it, and it looks kind of complicated. On a large scale, you always get to the attractor. You always get to kind of circulate around these two holes and make sort of figure eight type patterns and so on. That's always what happens from essentially any. Well, essentially any initial condition. However, the details of where you go are very different. Even two initial conditions that are very, very nearby, they end up at different phases in the attractor. So the detailed position they end up at, they're always on the attractor, and they're always just chasing around the attractor. But the details of where they end up is different. And that was a thing that was kind of this idea of sensitive dependence on initial conditions. That idea had originated. Well, it originated actually. James Clerk Maxwell talked about that idea in the mid-1800s in connection with things like you have two spheres, and he was interested in this for the kinetic theory of gases. You have two spheres. They bounce off each other. If they're exactly aligned so they're exactly on axis. The two spheres, if they're elastic, they're like billiard balls or something. They hit and they bounce back exactly the way they came. But as soon as they're at all off axis and they'll hit and they'll be moving away at a certain angle. If they're then reflected from sort of the edges of the billiard table or something, they come back and hit again. They'll be. Every time they hit, they'll be progressively exponentially further off Axis. So even if they were perfectly on axis at the beginning and they're one million billionth of an inch off axis, the next time around the there'll be 10 million billionths of an inch and then 100 and then 1,000 and so on. And after a while they'll not be hitting, they'll not even be hitting at all, so to speak. So James Clerk Maxwell knew that phenomenon in the 1800s. But that phenomenon was sort of then highlighted particularly by Henri Poincare around 1900 in connection with celestial mechanics, where again there can be this effect that, oh, if the planet was sort of at exactly this position, then it will kind of line up correctly and it'll get gravitationally attracted to this and it will follow this orbit. But if it's even a tiny bit off, that amount off will grow exponentially and eventually the thing will be going in completely different direction. So Poincare wrote about this. Then subsequently a chap called Garrett Berkhoff at Harvard studied. Well, this became this kind of field of so called. This kind of merged into this field of so called dynamical systems theory, which was kind of a study of these kinds of typically ordinary differential equations. There were a whole series of these kinds of things that got studied. The van der Poel equation was another one which arose in the 1930s, I think in connection with studying electronic amplifiers. And people wondered, you know, if you have this amplifier, it's kind of like the thing with the balls bouncing back and forth, every sort of iteration, the effect gets bigger, so to speak. And what does that mean? Does that mean if the, if things were just a tiny bit different at the beginning, they will diverge rapidly, so to speak. Well, the thing that. So there'd been this kind of history in dynamical systems theory of the mathematics. And in fact, I think Ed Lorentz was somehow a student of Garrett Berkhoff's or some such other thing. And so he meteorologist, he writes this paper about how there is sense of dependence on initial conditions in something that affects the weather. And so some set of people said, well then it's hopeless, you can't predict the weather. There'll always be the sensory dependence on initial conditions. Now actually that became a whole kind of tradition, the whole sort of chaos theory tradition. It's funny how these things work out. I mean there was a certain group of people that were very big on this. Some had come out of the sort of mathematics of dynamical systems theory. Then there are a bunch of kind of young physicists, all of whom I knew no, and they kind of were really the sort of the chaos theory promoters, so to speak. And there were things like the work that my friend Mitchell Feigenbaum did, showing that there was sensory dependence on initial conditions, but in his case, in iterative maps, just things like X goes to A times X times 1 minus X and so on, that there was sense of dependence on initial conditions, but yet there were global statements you could make in his case about the scaling of period doubling and so on. So there was this whole sort of tradition of, oh, there's sense of dependence on initial conditions that also sort of fed into all sorts of things about how roulette wheels work and how games of chance work. Because when you flip a coin, the fact that it's hard to predict which way it will come up is because a small change in velocity can flip you over to a small change in initial velocity can flip you over from being, oh, it's going to land on heads to, oh, it's going to land on tails. And because you, when you flip, you know, when you flip the coin with your finger or whatever, can't control that velocity precisely enough. That's why it's a reasonably good source of randomness. So there are many of these kinds of situations where this happened. Sometime in the middle of this, there was a. A popular book written by Jim Glick called Chaos, which kind of sort of fueled this kind of chaos theory as a thing idea. It's actually very confusing because Jim Glick interviewed me for that book and wrote a certain amount about things about my. I don't know whether he wrote about Rule 30, but he wrote about a bunch of stuff that came from me. I'm not sure whether it was properly attributed to me, but that's a different story. But about kind of systems where you get, for sort of purely computational reasons, you get complex behavior, but it's a completely different phenomenon from the sensor dependence phenomenon in this. So just to explain when something comes out random, like I just mentioned with coin flipping, the reason coin flipping seems random is because we don't have precise control over the initial conditions and the initial conditions matter. So then what people said was, well, the reason there's randomness in the world is because we don't have perfect control over initial conditions. And they said, well, maybe there's randomness because there's an initial condition. And depending on whether the initial condition is 0.100000200000 or whether it's that with an extra, you know, Instead of the two, it's a, you know, 0.1999 or something. A very tiny numerical change. That tiny numerical change could be the thing that gets amplified. And because we don't know the value of that initial condition, that's sort of why things look random. It's actually something that makes very little sense because this question, well, why is the initial condition unknown? It's something which, if you believe in continuous numbers and real numbers and so on, you say, well, you know, you just throw down a real number. We don't know which real number it is. And as you excavate it further and further, you're seeing things that we don't know. But the fact that we don't know it doesn't mean that it isn't precisely defined, so to speak. And it gets very kind of weird because you're starting to say, well, actually, kind of the. When you have randomness in, let's say, fluid dynamics, fluid turbulence, things like that, you're excavating down to the position of an individual atom, and then you go below that because, you know, after a while it will be sensitive to even more detail about the initial conditions. So this kind of idea that, well, it's random because there's something we didn't know about the initial conditions, that's kind of a, A, it's sort of random because there's something we didn't know. And that's kind of the question is, if you have a really closed system where you kind of know everything, can you still have randomness? And this is part of the whole thing that I discovered in the early 80s with things like the Rule 30 cellular automaton, that even when you completely know, you've completely nailed down what are the rules for the system, what's the initial condition? It's just one black cell. We can say exactly what it is. Even when you know all of those things, you can still get apparently random behavior. Same kind of thing that happens with the digits of PI. We know exactly how to compute them. Yet if you just take a slab of digits of PI, they'll seem random when you look at them. So anyway, this phenomenon of kind of randomness for computational reasons, intrinsic randomness generation, as I've called it, closely related to computational irreducibility, is a thing that was not understood. And in fact, I remember talking to Ed Lorentz at length about it, and I think he did actually understand it in the end. But in any case, what Ed Lorentz did was widely quoted as, so you can't predict the weather because there is sensor Dependence on initial conditions in systems like the weather. And, and then this was very confusing because in fact, when you make a small perturbation in a fluid, most of the time it just dies out. That's the nature of viscosity. You know, you, you make, you, you have your, your water and you wiggle, you know, you put your hand in, you flap it around for a while, the water will be all sort of flapping around, but after a while the water will calm down, it'll be perfectly flat if there are no other perturbations as a result of viscosity, as a result of essentially the analog of friction for a liquid. And so it actually isn't the case that most small perturbations in the fluid grow and eventually take over and dominate the behavior of the system. In fact, what happens is it's only at those points that, that are very kind of on a knife edge where, you know, just a tiny thing pushing one way or the other will flip it into one situation or the other. Those are the only cases where there's this kind of sensory dependence and there are sort of mathematical setups that you can make where, where you've sort of amplified that. And what Ed Lorentz did with his modal truncation thing was he got rid of viscosity. You have to go to sort of all the modes to see all the viscosity. So he specifically had a case where there's a lot more sort of knife edging that goes on. So in any case, that led to this belief on the part of some people like physicists, oh, you can never predict the weather for this reason. But in practice, people went right along at national center for Atmospheric Research at the European Weather Prediction outfit in, I think it was in Reading, England, at least at some point it was the, they, you know, getting computers, supercomputers and so on to just try and solve those differential equations and see what you could say about the weather. And it gradually got better and better and it got to the point where at least over a few day period you could make pretty decent predictions. Now, it was certainly true that if you go further in the future, you are more and more sensitive to whether you got all the measurements right at the beginning, not in quite the Lorentz sensitive dependence on initial conditions. It's all going to go one way or the other. I mean, the typical thing that people would say is if a butterfly flapped its wings one way, there'd be a hurricane. If it flapped its wings another way, there won't be a Hurricane? Well, yes, but only one in a gazillion, gazillion, gazillion cases only. Most butterflies, they'll never have an effect. Most butterflies will go through their lives and all the flappings that they'll do will not have any measurable effect in the future of the world, so to speak. It's only that one super lucky one in a gazillion, gazillion, gazillion butterflies that will flap their wing at just the right moment to push you over from the knife edge from have hurricane to not have hurricane. So that sort of got quite confusing. But it's still the case that the more accurate measurements help in these, in these simulations. Now it's also pretty difficult to do these simulations. And there are, there's a, you know, the forecasts have gradually gotten better. Typically what's done is you'll run multiple forecasts that have certain detailed differences and you'll kind of see where do they all line up. Like you'll run a dozen forecasts. And so one of them was going to say it's going to rain like crazy. Another one's going to say it's beautifully sunny. And then when you'll see people quoting, you know, there's a 5% chance of rain or something, that's often essentially coming from the fact that, well, of these forecasts we ran, it rained in 5% of them. And so that's kind of the chance of it raining in the actual world. But so, you know, the state of the art has gradually improved in terms of weather prediction. That's a different thing from large scale climate prediction, which is a whole more complicated can of worms that. And there are a lot of things about modeling the atmosphere, like, for example, the number of layers of the atmosphere. I don't remember how many it is, but I think it's less than 10 still layers that get modeled. And it's like when there's a cloud, that's a big problem because a cloud is sort of a feature on a fairly small scale that can have a big effect on things. And it's hard to model that, hard to model clouds in a bunch of these kinds of settings. And clouds have complicated physics about when they start to rain, how the raindrops get bigger, all these kinds of things. That's a whole separate thing to talk about, but hard to model. But so the question that was asked here is as we try and learn to predict the weather, can we kind of weaponize the weather and things like this? One of the things I always Find an interesting feature of the history of science is this question about can you predict the weather? It's an old question. And back in Babylonian times, people were doing sort of astrology type things and they were predicting sort of, well, where's this planet going to be next? They were predicting sort of who's going to win or lose the next battle. And they were predicting the weather. And the thing that's sort of interesting is of those three things, predicting the planets, predicting the battles, predicting the weather, we learned, we managed to develop mathematical science that did a pretty good job of predicting the planets for the weather. Took another few thousand years, but we've gotten to the point where we can do an okay job at predicting that for the battles. I don't think we've got there yet. And it's sort of interesting to realize that back in Babylonian times would have been very hard for somebody to know which of those was going to be easy and which of those was going to be hard. But any case, back to the weather. And there's always a question of, okay, can we change the weather? People talk about changing the overall climate. That's a different issue. That's much longer timescales. It's just like, can we make sure that it doesn't rain on our parade, so to speak, today? And there's been, since the 1950s, I think, maybe even earlier than that, there have been a bunch of ideas about how you might do that, mostly around this concept of cloud seeding. And the issue is, we talked about how clouds make rain. Well, the question is, what starts the raindrops getting bigger to the point where they actually fall out of the cloud? Because there's always water vapor. That's what a cloud is. It's a thing of water vapor. But most of the time that water vapor is being held up by updrafts of air and so on. And the water and the particles are small enough that that works. But sometimes the particles grow by kind of the opposite of evaporation, of condensing of water, condensing from steam onto these growing drops. They grow to a certain size. Beyond that size, they start crashing into each other. And they then start growing by sort of coalescing. And then eventually they get big enough that the updrafts of air can't hold them up and they fall down as rain. But there's sort of a question of can you make that process happen faster? And for example, when a drop starts forming, it's probably the case that inside every drop there's a little nucleus that started the formation. It might be a grain of pollen, might be a grain of dust. Maybe for some things it's even the result of a cosmic ray going through. But there's something in there. If you took apart that water drop, there would be something very, very small in there. That was the thing that caused the water vapor to, at a particular place, start nucleating into a drop of water. And so kind of the idea was, well, let's just put artificial nuclei that will sort of seed water drops and then get this cloud that is approaching our parade to drop its water somewhere else. So it doesn't rain on our parade, it rains somewhere else. And there were a bunch of experiments done, I think, in the 1950s on that in the U.S. i think in Israel there were a bunch done. I don't know about other places. I think, I mean, in more recent years, China's done a bunch of things on this. The concept of sort of weather modification and, you know, would there be a systematic way to do it? Is one that, particularly in the 1950s, in sort of the Cold War period, the US was like, let's try everything as a way to sort of get ahead. And a lot of kind of wild scientific ideas were investigated. And one of them was cloud seeding and weather modification. There were also ideas about sort of large scale weather modification. I mean, I know there was this facility in Alaska that got closed down, I don't know, 15 years ago now called HARP H A R A R P, which was High Altitude Atmospheric. Not sure what the rest of the abbreviation stood for, but it was something which was kind of making an artificial aurora. It was kind of shooting electrical pulses into the atmosphere and kind of seeing what happened. And, you know, the conspiracy theory was that it was some kind of global weather modification thing. Not really. I think it was for studying sort of electrical effects in the upper atmosphere. But, you know, that was kind of in the direction of, oh, is there something we can do to just sort of switch the weather to do different things? My impression is that it really has not been clear how to do weather modification and that while there are some sort of claimed successes of, oh, stop it raining on the Olympics in Beijing or something, or whatever else, they're sort of claimed successes. I'm not sure how convincing they are. And it's one of these kinds of things where the weather sort of has a mind of its own, so to speak, and goes off and does different things and you see an effect happen and you can very quickly say, oh, my rain dance caused it to Rain, because it just happened to rain, so to speak, after you did your rain dance. So I don't know how convincing any of that is. And I think the general problem of the sort of the physics of how to control weather is complicated. And I don't think it's. I don't think it's clear how that can work. I think there are some approaches that are kind of like more local versions of geoengineering approaches that one might make to climate change. I don't know enough about how those would play out on a small scale. Let's see. All right, you guys give me a lot of challenging questions here. There's one from Chris here. Are you aware of efforts, past or present, of using nature to understand mathematics instead of the other way around? Well, at some level, the Pythagoreans, who originated a bunch of what we now have in mathematics, particularly things related to numbers and so on, in a sense, they were observing things like musical harmonies of strings of different lengths, and that's what led to rational numbers and all this kind of thing. So in a sense, they were taking the natural world and using that as a clue to, well, let's look at rational numbers. Let's look at these ratios of integers. They might be interesting things to look at. I mean, I would say that a lot of things about physics, for example, have led to thinking about mathematics. I would say that there's sort of a question of are there cases where. So, I mean, whether it's the invention of calculus or something which was done. Well, at least the Newton version of it was done in support of thinking about physics and as a way to sort of describe the physical world. I suppose a question you could ask is, are there things where somebody said, aha, now I understand the math because I saw something work that way in nature. And there are things that come to mind that aren't examples of that. For instance, the phyllotaxis spirals of lots and lots of plants, where you form these Fibonacci sequences when you count up, for example, the stamens in a daisy or something like this. I think I've talked about before what the actual sort of science behind that is, and the 137.5 degrees and so on of angles between stalks of plants. But I have to say that wasn't how Fibonacci sequences were discovered, invented, whatever else. They were actually probably first invented by some Indian folk who were studying around 2,000 years ago, studying kind of the patterns of the counting, the number of different ways you could make kind of a piece of prosody, a kind of a way of kind of ancient rap music or something of different kinds of rhythms for saying things. But I'm trying to think about cases where people had sort of a problem in mathematics and then people said, aha, we can see this thing in the natural world. And it sort of reveals the answer to what's happening in the mathematics. I'm trying to think about that and I'm not coming up with great examples. There's certainly many cases where what you observe in the natural world leads you to a particular kind of mathematics or particular to ask certain questions in mathematics. But the questions once asked in mathematics. Are there places where you kind of go to nature and see what the answer is? I'm not sure. I think you could ask. I'm thinking perhaps something I was mentioning earlier, the van der Poel oscillator, that. No, I'm. I'm not coming up with anything immediately. I probably, I'll. If I stop talking about this, I'd probably think of something, but I, I don't immediately think of something there. Let's see. Salas wishing me a happy birthday. Thank you very much. That was yesterday. And is asking notable things to say about my history. Oh my gosh, I don't know. I keep on writing things about pieces of the history of my ideas. I wrote quite a big chunk about the history of my work on the second law of thermodynamics, which kind of started when I was 12 years old and was still going 50 years later. But I think I kind of figured out what I wanted to figure out there. I suppose one of the things that is both a big advantage and something that makes things difficult is that I have pretty good archives. So I have, you know, I've kept material for the last 50 years or so and I have it pretty decently searchable, if not decently organized. I'm hoping eventually to expose a bunch of that material because there's a lot of things, if one's interested in the history of science and technology. I've been lucky enough to be kind of involved with know people who were sort of key figures in, in all of that going back, well now I don't know, 45 years at least. And I'm sort of hoping to be able to expose a bunch of that material. It's just a lot of work to do that and there aren't really good systems. We're trying to build a Wolfram language based system for doing sort of archival management and hopefully that will allow us to expose a bunch of things. It's a tricky thing because, for example, I have 3 million emails and archived. And some of those emails are interesting history of science emails. Some of those emails are complicated pieces of sort of proprietary information being exchanged with some technology company 25 years ago. I don't even know if the company still exists. I don't know if that information is still, you know, proprietary to that company. There are things that are about, you know, people and so on where it's kind of like, well, you know, it's, you know, detailed interactions with people about, you know, let me give you a piece of advice about this or that type thing. Those are not things which probably one feels okay exposing in the near term. Eventually, sort of, when all the people involved are dead, you might as well expose them. But the. I think, you know, I just did a thing, actually, I wrote a rather long piece about a chap I knew for 40 years named Ed Fredkin, who had a very interesting, improbable kind of life, which I kind of explored quite a bit of in the last month or two. And that exposed a bunch of email that I had with Ed Fredkin that was kind of, kind of complicated. I mean, kind of. And I don't know at what point it would be right or would have been right to have exposed that email. I think now it's fair game and an interesting history. But. So this question of you take 3 million emails and what do you expose? When is a difficult one? I don't really know. A great answer. And reading through 3 million emails, well, it takes one. Would take one a very long time to do that, and one needs some kind of criteria. And I don't know quite what they should be. And that's one of the issues in these kinds of things. Now, the other point is you've got millions of emails. Again, this is both the. The blessing and the curse of having a good archive is that I know that there's a lot of material about something like, let's say, my interactions with Ed Fredkin that is there in my archive. And I can search for it, I can pull it up, but there's a lot of it. And then one has to kind of parse through it. If one is doing something where there's much less information, in a sense, the history is easier. One's more likely to get it wrong, but the history is sort of easier because there's less of it. But so I have the sort of. The feature that I really have stored a lot of material and so many things can be pieced together, but it's also not very interesting to just look at all those individual pieces. What I think becomes more interesting is seeing the arc of various kinds of intellectual development that I've been lucky enough to be involved in and seeing how that plays out over decades and trying to understand what one might learn from sort of the way that development played out. I mean, for me personally, a lot of studying this kind of history is all about being in a better position to sort of make decisions and predict the future. It's kind of like if I can know this is the pattern of how kind of particular sorts of ideas get diffused and come to exist in the world. It helps me to see the pattern of how that's going to come, how that's going to happen in the future, where, if I know this is what it looks like. When there's this kind of hype in the technology industry, it helps me to understand what's going to happen with the LLM hype bubble, so to speak, how is it going to evolve over time and so on. And so that, for me, is an important reason to study history, even my own personal history, because, you know, when I recognize this is something, this is the kind of mistake I've made before, so to speak, that's a very useful thing to know. Or this is something where I kind of remember things that I kind of remember what happened 35 years ago, 40 years ago, whatever, on such and such a thing. But when I really look at it in more detail, it helps me to know something about what's going to happen now. One thing that's kind of funny in very recent times is there are a bunch of questions that I kind of started asking, oh, beginning of the 1980s, for example. And I'm finally in a position to answer these questions. And so several of the things that I'm doing, it kind of feels. It feels terrible because it's kind of like I don't think I'm getting old, but it's kind of like, you know, I'm sort of putting certain kind of intellectual affairs in order, so to speak, because they're things that I kind of started wondering about the beginning of the 1980s. And it's like, now I can actually answer that, so I'm going to go do it. And I have several pieces that I've been writing recently that are of exactly that kind. For example, there's one I'm working on right now that probably will get called something like the Physics of Expression Evaluation that Has to do with the question of when you have a system like Wolfram language where you type in some expression and it gets evaluated and turned into some big arithmetic thing or some big thing with a bunch of functions that. That compute things and then the end, the answer is 42 or whatever. What does the process of evaluation. What is going on in that process of evaluation, particularly when the process of evaluation might not terminate. And I thought about this a bunch. When I was building smp, the kind of forerunner to Mathematica and Wolfram language that I built starting in 1979. I thought about this a bunch. At that time I was really quite obsessed with this question of how do you deal with these layers of recursion? How do you control that? How do you build this kind of evaluation control system and so on. And now I finally understand this, I think as a result of looking at things in the physics project and understanding about kind of time, like evaluation chains, space, like evaluation processes, branch like evaluation processes. It's very beautiful and very, very aligned with physics. And it kind of helps one even in understanding the physics to see this example in expression evaluation. But the thing that's a bit funny for me is that I really did work pretty hard on this around 1980 and tried to figure it out, and I couldn't figure it out. And in fact, I put into SMP these mechanisms for controlling recursion, controlling the evaluation process, which I really didn't understand that well at that time. I put them in because they're a piece of. You can implement them. But what do they really mean? I really didn't understand them, nor did anybody else. Over the years, every so often I come back and say, can I understand these things now? Finally, I think I can. And they were sort of, maybe not quite aligned in the right direction, but sort of interesting in what they tried to do. But now I can finally do this. The thing that is kind of the last laugh on me, I suppose, is that right when I was doing that work back in 1980, I was also working on quantum field theory and in particular on gauge theories and in particular on all these questions about sort of gauge invariance and under what circumstances? It's kind of like relativistic invariance. Under what circumstances can you kind of. How do you assign simultaneity to different events? How do you say which event is simultaneous with which event? That's kind of a choice of what's called gauge. And so I was pretty interested in those kinds of things back then, was studying kind of that in the concepts of quantum field theory. And if you'd asked me back then, is this thing you're studying about evaluation, does it have anything to do with what you're studying in quantum field theory? I would instantly have said, of course not. It has absolutely nothing to do with those two things are completely unrelated. Well, now it turns out they are basically the same question. And this is sort of a deep connection between physics and computation that manifests itself in a thing like that. See, Gosh. The question from the lala, what is the history of naming mathematical terms? How has this branched off into other areas of naming? So, you know, mathematics, one of the things about mathematics is it's pretty global. Human languages, there are lots of them, 5,000, whatever it is, 10,000 if we're lucky. Some are going. They're going extinct at a certain rate. But there are many different human languages. There are even quite a lot of languages that have been used for higher learning over the course of time. And so there are things that get names in different languages and so on. Mathematics has. The time for progress in mathematics is slow compared to the time it takes for knowledge to kind of diffuse around the world. And so there is just one mathematics, at least there has been for a long time, probably for a couple of thousand years. And so the notation and so on is pretty uniform. It's not like, okay, there are things, you know, there are few countries or things like the number system can be different in different countries, and there are a few kind of sort of little extra twiddles that exist in some places, but pretty much by the time you're even in arithmetic, it's pretty global. And so a lot of things that got named in mathematics, at least at the level of the symbolism and so on, it became pretty global. It took a while. Sometimes, for example, people had different approaches to different kinds of mathematical notation. For instance, the greater than sign in the 1600s, that was still sort of getting worked out. Leibniz, Gottfried Leibniz was a big person pushing for kind of standardization in mathematical notation. He was, in part, a sort of diplomat kind of diplomat. He was kind of the geek, end of diplomacy, I would say. He was the guy who's kind of the back office guy who would try to find a complicated historical story that explained why it was okay for person A to marry person B or for some country to do this or that thing. He was kind of the staff support for diplomacy, so to speak, more than the frontline diplomat. But he lived at a time when Latin was kind of going out of fashion as the sort of global language of learning. And. But he was really keen to kind of have a global language that he thought would sort of bring people together and be a kind of common way to talk about things. And so that was one of the reasons he pushed quite hard for mathematical notation and saw this opportunity for sort of a global mathematical notation. But he invented various ideas. For example, for greater than signs and less than signs and equal signs. He had this idea, well, it's like weighing things on a scale. If you're, you know, if one side is heavier, that side of the scale goes down, the other side's heavier, it goes up, or if it's balanced, it's kind of, you know, in the middle. So he had a notation for sort of almost hieroglyphic in some sense, notation for kind of greater than, less than equal, which were kind of a scale tipped one side of the other. Kind of an amusing idea. Didn't catch on. He had other. He had a bunch of other notational ideas, but he had many notational ideas that did work. For example, he had the notational idea of an integral sign, you know, an extended S. And one can find in his notes the very place where he first wrote that down. Now he also had the idea of, you know, DY by DX for derivatives. And he worried at the very beginning, he said, people are going to cancel the Ds, they're going to think it's like multiplication, they're going to cancel the Ds, that sort of calculus error 101 type thing that's happened for the last 300 years as a result of that sort of rather bad notational choice. Also, there's a fun correspondence that he had with a chap called William Outred, who's the person who invented the multiplication sign, in which Leibniz says this is a really bad idea because your multiplication sign looks like an X and people are going to confuse is it 2 times 3 or 2x3 type thing. But nevertheless, that notation kind of got burnt in when it comes to naming things. I think what tends to happen is somebody comes up with a name and often it makes it and sometimes it doesn't. And it's kind of a natural selection of names. I know in my own life I've come up with some names that have made it well, and some names that I thought were pretty good at the time that didn't make it. One of the ones that I thought was pretty good at the time was the homoplectic and autoplectic for systems Actually, a little bit like what we were talking about earlier. Homoplectic systems are systems where the complexity you see in the system comes from something that you inject into the system from the outside. It's kind of a same complexity type system, something like sensor of dependence on initial conditions, where you are injecting those initial conditions. And that's where the complexity comes from. Autoplectic. The idea was the system itself intrinsically as a self thing, you know, it's. Auto in Greek is sort of the self prefix that. That is where the complexity comes from. But those names, I invented those in the. In the mid-1980s, they didn't catch on the. And you know, it's. People try and make names. In some fields, there's pretty standardized naming and often those names come from Latin and Greek roots. There's a nice book I think I have about the origin of scientific terms which kind of goes through, you know, if you want, you know, assists a trans. Whatever. It is a different kinds of, you know, that there are. There are many Greek prefixes. For example, you know, an anti, a hyper, a sub. It's Latin, a super, a whatever. There are all these things that have sort of. That often become part of mathematical naming that come into a. That used. And in medicine, for example, you know, there are many of these names that come from, well, from Hippocrates, from Galen, from, you know, Greek Latin roots, you know, the ventral side of the whatever. I don't know all these terms. You know, for me as a kind of amateur sort of reader of biomedical literature and, you know, person who interacts with those kinds of things, it's always fun that the fact that I know sort of know decently well Latin and ancient Greek is really useful because I can sort of. When somebody says, you know, erythema or something, it's like, okay, that means something about redness and so on, because I kind of know the Greek roots. And that's very useful. And a lot of these terms, particularly in sort of biomedical areas, come from that. In something like mathematics, there have been periods of time when people have really pushed for these kind of Latinized roots that happen in the Bourbaki group in France in the 1930s, 40s and so on, where that was a lot of sort of formalization of mathematics was pushing for those kinds of things. I think when it comes to, for example, things named after people, there's a certain, certain amount of yes, it got the right person and a certain amount of no, it absolutely didn't get the right person that was named after the wrong person. And there's been a certain tendency in modern times to try and sort of right the wrongs. And there are things which used to be called, I don't know, the Friedman universe, and then it became the Friedman, Robertson Walker universe, the Friedman, Robertson Walker lemaitre universe. And I think it's sort of gradually adding names on. And sometimes, often I think the detailed history of these things gets quite complicated, and maybe there should be even more names added on. And that's been sort of a recent trend in these kinds of things. But I think people have tried to name things. I don't know, like a recent name that I came up with was the name Ruliad. And I like that name. It seems to have caught on quite well. And a friend of mine said to me, after seeing that name, which they thought was pretty good, thank goodness you didn't make it an oid. It noted that many things in modern mathematics, it's kind of oid means sort of like. And it's like a. You know, you tack oid onto something as a kind of. Well, it's sort of like this, but it's not quite that. It is, I think, an interesting, you know, place. There are places in modern mathematics that, like category theory where there are all kinds of names, like, you know, the endofunctor and things like this, where, again, knowing a bit of Greek, you can kind of translate a bunch of these things, and there's a certain tendency to use those things. But what's sort of interesting is that things like endo, you know, hetero, tran, whatever, all these different terms that are prefixes that have been used enough times in, for enough purposes in language in general, that when we see them somewhere, we can associate with something, you know, hyper, whatever it is, you know, meta. All these prefixes, they originally came from Greek, for example, but they are fairly familiar. And I think that I have certainly tried for many purposes to mine kind of ancient Greek for concepts like, for example, The concept of kind of knowledge, which is sort of around the logos, et cetera, et cetera, et cetera term, or the concept of rules around the arcos kind of term. The problem is that things that begin with log, they're an awful lot of things, from logic to logistics to all sorts of things. It's a. Well, mind, you know, you don't get to. You kind of have a choice. You can pick up a Greek word that is kind of not very familiar to people, and then you can kind of attach it and say, oh, look, there's this cute Greek origin, but nobody knows that you know the Greek term or you can pick something where there are enough sort of English derivatives of that term that it has some immediate cognitive connection and that, but that has the problem that's in some areas it's very infested with concepts that are already there. You know, an example of one that wasn't, and I don't really know, cybernetics, which comes from gubernator, which is a Latin word, maybe there's a Greek one as well, which means a steersman, somebody who kind of steers the ship and sort of cybernetics is the study originally of control in machines and animals. And so this idea, I don't know, maybe it was Norbert Wiener, maybe it was somebody else who came up with this term cybernetics. And of course there's a certain development because in the original Latin it will be gub, but that was sort of morphed into cyb. And that term, I don't know the extent to which that term was sort of a known term and the extent to which it was sort of plucked out of obscure Latin and placed in this place and then had to fight for itself, so to speak. Just like a brand where, you know, if you call your company, you know, you know, Floxicon or something, nobody knows what that means. It doesn't have a maybe, I don't know, I just made that word up. But you know, maybe if it's called Fluxicon, one would immediately think it was some thing about change or magnetic fields or something like that. But you know, sometimes you have a strong word that has sort of never been heard before and that has to fight for itself. And when it manages, if it manages to make it, it becomes something where it, it kind of is a, is a, is a strong thing or sometimes it's something which is very much derived from something one already knows. But, but I think in, you know, maybe there are issues with naming because there was a time when, you know, most people who were in the kind of intellectual sphere, new Latin, for example. And so you could expect that a name that was sort of Latin derived would be immediately sort of recognizable to people in the same way that an English derived name is recognizable to people today. So I think, and I've ended up, despite having tried pretty hard to have Latinized names for things like Mathematica is obviously Latinized name, and I've had plenty of others. Some things like Ruliad is very sort of, I don't know, Anglo Saxon, Modern English derived, rather than having sort of classical roots. I don't know that the precise, right way to think about sort of the theory of doing those kinds of things. Often, you know, there are weird origins for names. I mean, I don't know even a term like revolution in science or other things. I think that came from sort of the Copernican experience where he had a book called De Revolutionibus. Oh, I forget the whole title. But it's about, you know, the. The Earth going around the sun and so on. It's revolution in a very, very direct sense, but yet kind of the sort of the baggage that came with that led that word to be used for many other purposes. And I think the same thing has happened in some other places. I'm trying to think of examples in mathematics and in science. I mean, I would say that there are words which are pretty weird. I mean, like determinant for a matrix. You know, you compute the determinant. I think that originated in the late 1800s. And probably at the time when it originated, that was. Yes, it was the. I had never thought of this before. I'm sure it was the determinant that determines whether an equation will have solutions of this kind or that kind. But then it just gets called the determinant. And that sort of floats off as a name, independent name of its own. I think there are weird ones, like the absolute value of something. I don't know. I suppose that one maybe is sort of understandable the norm of something. I don't know. There are things that sort of have. Maybe that comes from norm. Probably comes from normalizing things, and then it got shortened to that. And I suppose there are different origins of that kind. Yeah, it's a complicated world of where these names come from. I know I've obviously been deeply involved in coming up with names for things in a very kind of forced situation of naming the functions in Wolfram language, of which there are now nearly 7,000. And each of those names, it's an attempt to kind of sort of crush a little tiny piece of poetry into that name. Of what can you crush? What kinds of ideas can you crush into? You know, a name like Nest List? You're kind of trying to crush the concept of what's going on into something which is recognizable from. From English words. And that's kind of been an extreme example of that. One of the things one learns from that is the number of weird words that are de novo. You know, never seen that word before that one gets away with using is quite small. People can learn just a few. But really not very many. This was one of the big mistakes made, for example, in apl, early and quite visionary programming language made by Ken Iverson in the early 1960s. That was kind of a. He thought of it as kind of a notation for computation, as mathematical notation, as a notation for mathematics. I would kind of say that that's a little bit what we've now achieved with Wolfram language, but in a very different way. Because what Ken Iverson, the mistake he made. I talked to him at length about this in past years, is that he invented all these symbols. He needed a special keyboard to type APL and so on. Of course, that wouldn't be an issue today. Now that sort of. All keyboards are kind of soft in some sense, or many keyboards can be made sort of soft. But, you know, the problem was the amount that people could learn of these sort of funny symbols of triangles with lines through them and so on. People just didn't have a very big buffer or patience for learning all those special symbols. And so it really didn't work. If there had been just one special funky symbol. Yes, you can learn it, but many you cannot. You know, it reminds me of another thing which is the use of things like Greek letters and so on to denote various kinds of concepts and quantities in mathematics and elsewhere. And it's sort of fun. We did a survey once of sort of how often are different Greek letters used? How many Greek letters are used for many things. I've always. In my sort of life in science, occasionally I have to make up a notation for an exotic thing. And I. I have often used the capital xi, which is three parallel horizontal lines, the middle line usually a bit shorter than the other two. And I've always used that for kind of these very exotic things. You know, it's used. It has various uses, like the grand canonical ensemble. I've used it for a kind of complexity measure for finite automata. And it's the thing you kind of. It's the thing you roll out that has a certain exotic ness to it. And there are other kinds of things where. Oh, yes, a parameter that's sort of an eigenvalue of some kind. It gets the name lambda, usually. And there's a certain whole ethos that's developed around all these different Greek letters. Something which is vaguely. Something small. It might be a delta or an epsilon. There's nothing about delta or epsilon that makes it. In the abstract. It's like D and E. What's small about D and E? But delta and epsilon developed this kind of sort of association in mathematics to small things like for instance, oh, I don't know, capital sigma is the whole summation. Well, okay, that makes some sense because it's an S for sum. Something like a tau is sort of a variant of time and things like this. Then there are Greek letters that don't make it very often. Like I was the capital upsilon, which is a kind of a Y shaped letter. I was looking at a friend of mine's book on mathematical economics and I was impressed that on page one it had a capital epsilon. I'm not sure what that really says about the level of obscurity or not of the mathematical economics, but the capital upsilon is an endangered, you know, it's a not endangered. It's a very minority kind of Greek character, so to speak, rarely used. Or something like iota, which is somewhat confusing because it's really like an I without a dot on it. I've sometimes found there are Greek letters. Sometimes when I want to go really exotic and it works better in modern times than it did in the past, I'll use some of the antiquated Greek letters that went out of circulation before the kind of golden age of ancient Greek. So, for example, if you are doing something like you have PQR English letters and you want corresponding Greek letters, well, it's PI for P, rho for R. What is it for Q? Well, there's a Greek letter called copper, K, O, P, P, A, which is like a circle with a line, actually looks surprisingly like a Q now that I think about it. That is. That is sort of the analog of a cue in some sense. I mean, we don't know how these things were pronounced, but it seems to be somewhat plausible that that's the case. Or for example, a digamma, that's a kind of a W like sign sound. That's this sort of peak thing with. It's kind of like an F written backwards, so to speak. But you know, those are the things that. But people don't usually use the digamma or the copper. It's very exotic that you'll see those in. In mathematical notation. Actually, there's another one worth mentioning which is always very confusing. It's like, you may know a lowercase omega is kind of like a little W like thing. There's a thing that kind of looks a bit like a lowercase omega, but it kind of closes at the top and it's used in astronomy and it's used for the periapsis. I think of an orbit and I Had not known for years what the heck that thing actually was. And I now discover that it is a curly pie. It's kind of a script, like PI symbol. But that's an example of something got used in astronomy and hasn't really been used elsewhere. It's kind of a fun thing if one has to make up notation for something. I suppose it's a fun thing to use. There also are other letters that sometimes get used. For example, Russian characters, Cyrillic characters. There is, oh, gosh, there's one. The Shafarevich group, I think. Tate Shafarevich. I'm forgetting. Am I remembering the right person? I'm not sure. But anyway, there's a, you know, the Russian character which is kind of like the. Like a squared off W with a tail on it, I think is. I think there's this one place where people tend to use that in that particular area of mathematics. There are notations that have caught on. Haven't caught on. For example, in Alan Turing's time, when he wrote his original paper on turing machines in 1936, he needed to use all sorts of notation, but he needed to use notation for computation, which was a new thing at the time, and for describing his Turing machine. So he used what he called German letters. He had Greek letters and he had German letters which were in fact Gothic letters. And I suppose maybe the term German letters went out of popularity when the Second World War started, I'm not sure. Or maybe that was just an Alan Turing special, I don't know. But that was another thing where people use Gothic letters for certain particular things. And at the very beginning, Turing used them to represent computational kinds of things that did not catch on. Otherwise we would be seeing, you know, every paper on theoretical computer science would be full of Gothic letters, but didn't catch on. The. Okay, I see a comment here that from Evangelos, rather Greek sounding name, the major reason Greek is overused, they say, in science, is the fact that ancient Greek vocabulary has literally a word for everything. I would dispute that. You know, it's sort of interesting. You go and look at a Greek dictionary and you say, well, is it a word for computer? Well, obviously not. Well, not so obviously not, because there was the Antikythera device that existed and probably there was a word for that. But, you know, there's no instruction manual that came with the Antikythera device. So it doesn't say. This is a, you know, a. I don't know what the word would be, but I don't know. It'd be actually nice If I could come up with a word for computer, I mean, certainly computare. Computo. Computare is a Latin word for to reckon. And there's these weird things that happen, and one of the ones that's sort of a favorite of mine of naming is calculus. What on earth is calculus? Well, calculus is a thing that not only in mathematics but also in dentistry, because it's this kind of, you know, it's this hard plaque and so on that you kind of get to get to scrape off, and it's. But how on earth did those two names end up being the same? Well, the reason is because these calcul were little stones that people would use for reckoning. And so when it came to name, kind of this method for reckoning that Newton and Leibniz and so on had back in the 1600s, it's, well, let's use this thing that comes from these little stones and so on. But the last laugh there is that calculus of the kind that, you know, Newton, Leibniz type calculus is all about continuous quantities, not discrete kinds of things. And yet now, for example, as we work on the physics project and lots of other things, and we work on computation in general, it's all about discrete things. So it's actually the original calculi, the original little hard stones that you would use for reckoning. That's what we want to be talking about. But the term calculus was used, was taken by this thing that's all about continuous mathematics. So it's kind of an ironic thing. But, you know, I think it is sort of interesting that the names. There really weren't as many things in the world. Well, I don't know. This is one of these things that you can kind of dispute because, you know, I say there weren't as many things in the world back in ancient Greek times as there are today. But, you know, I'm sure in ancient Greek times there were all kinds of different words for the sort of the hood, ornament on a ship or something, and all those terms kind of disappeared, or maybe they only exist in some very specialized area today. And so I don't know whether in fact, the number of terms. I think the number of terms that were used in sort of ancient Greek vocabulary was significantly smaller than the 50,000 or so that are used in modern English, for instance. That's an interesting question, an easy question to answer. I think it was much smaller. Certainly when I was learning something like Ancient Greek, you could learn a vocabulary that wasn't huge and yet you could pick out the words for pretty much your average, at least, Herodotus level. Ancient Greek author. And I think when it got more creative, like the Shakespeare in English, and they were perhaps making up their own words, it becomes more challenging. But my impression is that the collection of words used was somewhat smaller. I think the thing that I've sort of wondered, I was considering at one time when we made image identifiers that can say, this is what, 5,000 different picturable nouns in English I can recognize a cat, a dog, a teacup, a chair, whatever else. I had kind of wondered what would be involved if you trained an image identifier on only words that appear in an ancient Greek dictionary. So you get to, you know, for example, that doesn't include something like a car. And then what you do is you train it on that. You give it images of all those things, including all the different wine flasks and all this kind of stuff, and then you show it something from the modern world. What does it say it is? And I think that would be, you know, that would be sort of a fun thing to do. And it kind of speaks to the difference in kind of language from ancient Greek times to today. I mean, there's, of course, famous examples of changes in language and what one can describe. Famous example, I've never really dug into this one myself, but the. Color words, like, you know, I think it's claimed that in ancient Greek, the blue and green aren't really distinguished in the color words yet. For example, there's a famous line from the beginning of the first main book of the Odyssey, I think, which talks about how kind of, you know, rosy fingered dawn, you know, found its way across the plains of Troy, so to speak. And that word for, you know, rosy fingered, who knows how that's, you know, that the translation of that word is difficult because we don't know kind of the mapping of what color they thought that was versus what we would now describe it. And that's sort of a place where it's hard to make the alignment. You know, it's always interesting that as you start thinking about translating ancient languages and so on, this question of how do you align what was going on then with what exists today? I know, for example, a chap whose work I've studied quite a bit, named Darcy Thompson, who mostly was famous for his book on growth and form that was about the kind of shapes of biological organisms and so on, but he was kind of a classical scholar, and he wrote one book called Greek Fishes and another one called Greek Birds and What he was trying to do was he was trying to match up the species that were mentioned in something like the Odyssey, let's say, with a modern species. You know, was that a whale or was it a shark? You know, what was this word in ancient Greek? And how did it map onto modern times? And, you know, who knows? Maybe there were species that were still extant in those days that have gone extinct today for which there's a word, you know, a kind of bird or something, a dodo or a dodo plus plus or whatever that existed at that time doesn't exist today. And it's hard to translate. Let's see. I think I'm going to have to wrap up soon here. But. The, you know, this question, I mean, I have to say, as we're talking about languages and words and so on, there is always this question, what comes first, the word or the concept kind of thing? And it's something I've thought about quite a bit, and I think about a lot in terms of kind of how do we, as we sort of expand our domain in science and so on, to what extent is that enabled by the invention of words for things? In a sense, that's what makes me feel important as a language designer, that I'm kind of making up words for things that then become concepts that people can think in terms of. That helps kind of lead the possibility of thought out in different directions. But there's sort of this complicated loop between things which become common in the world, for which people make up names and can remember what those names are, and things where one makes up names for things, and that leads one to go in that direction. Typically, the making up of a name for a thing will greatly enhance the extent to which that thing gets talked about, because if you don't have a name for it, it's really pretty hard to talk about it. And I think this question of whether there were times in history where the lack of a name, for want of a name, so to speak, a concept, was lost. And I bet there have been. I mean, there are also places where kind of the notation for things has made a surprising difference. Like, for example, I'm pretty sure that the fact that algebra didn't get invented until the 1400s is in no small part a consequence of the fact that in antiquity, in, for example, Roman times, numbers had letters associated with them. And so distinguishing a letter that stands for a number is an obscure thing. When we're doing Roman numerals, as soon as you have Hindu, Arabic numerals, where the symbols for Numbers are different from the letters. It becomes much easier to imagine what we can have a letter that stands for a number. A confusing thing about that is in Euclid, surviving manuscripts of Euclid. Not manuscripts, not original ones, but surprising. I mean, surviving things from antiquity that involve figures, geometric figures do have labels for those geometric figures. They label an angle with an alpha or something like this, or more, or perhaps a theta. I mean, again, how theta became the name for an angle, I have no idea. Maybe Euclid off in, you know, back in Alexandria in, you know, what is it, 2nd century BC or something, was just kind of hanging out one day. He's like, I got to pick a name for this. Let me pick a theta. And, you know, that's how these things start. And then we're 2,000 years later, and it's like, yes, the angle is called theta. Let's pick theta as the name for an angle. One example of this is lambda functions and lambda calculus and lambda expressions and so on. It's a name invented by Alonzo Church. And people asked Alonzo Church, why did you call it lambda? And he said, well, it's completely arbitrary, and it could have perfectly well been called a sigma function or something instead of a lambda function. But it's sort of fun to see how the term lambda has found its way into all sorts of places, even though it's really quite meaningless. It's not like Church said, oh, I called it lambda because it stood for L. It was really just an arbitrary choice. But I think this question, it's always interesting also when I have written kind of, when I used to write sort of papers that use mathematical notation a lot, I've. For the last 30 years, I've kind of tried to use computational notation much more than mathematical notation, because I think it's clearer. And you can also run it on a computer, and it allows you to talk about a much broader range of things. But back when I used to primarily use mathematical notation, it's always an art form to figure out, how do you name things? Like, you know, how do you name objects that you're talking about to sort of not be obscure? You know, you can easily, if you make up a bunch of things and you say, I'm going to call things A, B, C, D, E, F. It's incredibly easy to get a mathematical description that is just unreadable because it's just like, it's an F, it's an A, it's a B. I don't know what those mean, but yet if you called One of those things sigma and you call one of them kappa and you called one of them, you know, capital Q. Each of those things has a certain, I wouldn't say emotional, but a certain conceptual baggage that comes with it from all its uses in different areas of mathematics. You know, another thing that's quite interesting is, is the use of multi letter things. So for example, most mathematical functions, a Bessel function is a J, sub something or other, an elliptic function, a K, an E, a PI, whatever those are A theta for other kinds of elliptic functions. But then I remember when I was, well, a kid actually the first time I saw a mathematical function that wasn't a single letter function was the function erf E, R, F which is the error function, the integral of a Gaussian distribution. It's kind of a term that came in from statistics, I think. But for me it was very wonderfully exotic to have a mathematical function that was in mathematical notation. It didn't have a single letter name. And then there was started to be more like the li for logarithmic integral and so on. And it's kind of interesting again there's sort of an ethos associated with these different, different names. For example, in, in engineering it's quite common to have, you know, I don't know, Reynolds number, re, things like this. It's, it also shows up in physics, but it came from more from the engineering side. And you know, in these different fields there's a different sort of ethos of how you name things and that, that's, it's always. And you have to, when you're, when you're building out some new area, you have to kind of be mindful of this. You know, you either have to invent your own conventions or you have to kind of decide what are you buying into. And, and you can make things go from, you know, from very clear and easy to understand to being completely obscure by getting that stuff wrong. All right, I see a lot of other interesting questions and comments here and I'm looking forward to talking about them. Oh, I see just one more I have to dive into now and then I really need to go from calliope asking which are better autobiographies or biographies? Which gives a better historical record of a person? You know, that's interesting. I have encountered that many times because I have studied people where there are autobiographies, there are biographies. I think they show different things. I mean the, and it depends a lot on the personality of the person. I mean the. Somehow I've seen even for Myself, I remember a certain narrative of how certain things happened, and it's roughly right, but the big picture often is not part of that narrative. So for example, in my own life, if I look at, oh, I don't know, there's one I figured out years ago and say, how did I come to start thinking about simple programs like cellular automata and essentially building science up from programs one looks at, rather than being a reductionist? And going from the phenomena of the world down to this kind of description of the world in terms of primitive elements. How did I end up doing this kind of build stuff up rather than reduce stuff down? Okay, well, I never really, you know, I just like, well, I did it, you know, that's what I did back in, you know, 1981 or so. That was a. Just a thing I started working on. And then I realized at some point, wait a minute, there's more historical arc to this than that. What was I doing around 1981? Well, I was building a computer system. I was building a computer language. And. Okay, that's interesting. Then I realized, look, the reason I was thinking about building things up from primitives is because that's what you do when you build a computer language. Before that, I'd been doing physics, where you're mostly doing the reductionist thing of going down from the thing that you. From the, from the world and trying to grind down and figure out what its elements are. But in building a computer language, you're going up from the elements and seeing what it's consequent, what their consequences are. At least that's a large part of what you're doing. So I kind of realized from outside my personal experience, I kind of realized that, you know, the picture of what was going on was I thought of doing that because I had had this experience in building a computer language. I realized only very recently that back in a few years after that, when I was studying these simple programs and finding out how complicated their behavior was, a number of very good mathematicians started working on the kinds of things I was looking at. And after a couple years, they got very frustrated. They just sort of went away. They said, the methods we have for mathematics, they just don't help. We can't say anything about these systems. But what I realized is what I managed to do, which again, I didn't feel like anything at the time, was I realized the very fact that it is difficult to say something is the most interesting fact. It's not what the mathematicians were looking for, which is we want to say something using our Mathematical methods. What I realized was that it's kind of the inability to do that that leads to phenomena like computational irreducibility and and so on. Now that's something it took me several decades to realize after it actually happened. Sort of a good historian would see those pieces and realize that's what actually happened. But from inside you don't get to see that. I think another thing I realized very recently is ridiculously recently is I've worked on a bunch of different things. And one of the things that's true about most fields is that there's a certain sort of guild that builds up within that field. There are people who learn the field and then they have students, and then they have grand students and so on. And there's a certain sort of human connection, human social connection between the people who do that field. Well, I've worked on a bunch of things where for whatever reason I've ended up not being involved with the field, but making use of sort of ideas from that field, sometimes making sort of contributions to the fundamentals of the field. But I've come from outside the field. And I was realizing recently that's totally weird. It doesn't usually happen that way. Hadn't really internalized that. It's something I happen to have done and done repeatedly, but it isn't very common. I didn't realize that wasn't very common. Probably I could go back and look at why do I end up doing that and other people don't do it so much. And it might have to do with being entrepreneurially oriented in some way. I don't know. I have to think about it. But my point is there are these things that you can realize about the sort of the arc of history, that even though you lived it, you don't know it. And if you are a good historian or biographer, you can see that arc even from sort of, you know, better from the outside sometimes than from the inside. Maybe. I'm not sure. I mean, I think, for example, people have asked me another one of these questions about, you know, how can you know. There are things that I've figured out scientifically that seem completely at odds with my personal way in which I conduct my life, so to speak. Like, for example, I'm very, you know, I like people, I interact with people, et cetera, et cetera, et cetera. I talk to people on live streams, I do all kinds of people oriented things. Yet some part of my science is a, is a sort of deconstruction of everything, a very non, seemingly non Human. Let's grind everything down to its fundamental elements that don't have anything like people in them. But yet I realize that. And by the way, one of the challenges in doing science is to do science independent of what your prejudices about what has to be true are. And mistakes that I've made in the past, slowed me down by decades, have been things where I'm like, I think I know how this works because I have this kind of general view about how the world must work. But then the actual evidence shows me something different, and I kind of ignore the evidence until, you know, that's a big part of being able to do these things and discover what you didn't expect is to notice that evidence you didn't expect. But so I think, you know, I have to say, in biographies, autobiographies, there are, I would say, the number one mistake in terms of intellectual biographies and autobiographies is the failure to realize that there is an explanation for things. That is that people will write a biography and they'll say magically, on this day, somebody had a brilliant idea and they solved this. It never happens that way. As you trace back, there is a thread that goes back a decade or more, and it's like, they did this, they did this, they did this. And that led to the possibility that they were in the right place at the right time to have this epiphany that led to this. And, you know, in the efforts that I've done in sort of biography and so on and even autobiography, I have been sort of very insistent on trying to find these threads. And I think often people don't do that. And so they end up writing things that sort of don't make sense and where they end up with. With. Well, with things which don't really. They don't really give the most interesting picture because they haven't really put together kind of the. The arc of the narrative, so to speak. So, you know, when people do that, sometimes people from the inside, autobiographically are more able to do that than biographers can do it. I think the, you know, the. The. A good biographer who's done a bunch of work in biography should be able to do a better job than the typical autobiography, so long as the material is actually accessible. But there's some material where the only way you know what happened is because you were there and you remember it, and there just isn't any external material. Of course, that has the risk that you remember it, but you remember it wrong. And I find for myself, I have a pretty decent Memory, I think. And, you know, these live streams are a great test of memory. But the, you know, in, in the. I always find that, you know, I have a pretty good memory, but there's a little bit more detail in, you know, in what actually happened than the, the gloss that I remember on it anyway. So I have to say I find both biographies and autobiographies interesting to read. I am more often frustrated by biographies than I am by autobiographies. I mean, autobiographies, they say something. Even if the whole thing is a total gloss, even if I know it's a whitewash, it's interesting that it is a whitewash. Whereas if it's a biography, that it's a whitewash, it's like, who cares? Or if it's a biography, that's an attack biography. I was very frustrated recently. I was looking at, I'm trying to understand the biography of a founder of immunology, and there's a kind of an attack biography of him. And I don't know why it's an attack biography. I don't really understand, but it's hard to actually get through that to what actually happened. But I think if that was written by the person themselves, it would tell me. And it's a biography with a certain slant that gives me. An autobiography with a certain slant, it gives me information, whereas a biography with a certain slant gives me very little information. The slant is irrelevant, so to speak. Anyway, a few thoughts, but thank you for asking lots of interesting questions and look forward to doing this another time. Bye for now.