History of Science and Technology Q&A (July 24, 2024)

Hello there. Welcome to another episode of Q and A about history of science and technology. And I see that we have a bunch of questions that have been submitted or saved up here. So let's save. See where should we start off? Alex asks what was more important to ancient civilizations, philosophy or science? I don't think that there was that. The word science is a pretty recent origin. I mean, in Latin there's scientia, which just meant knowledge. But the notion of science, the notion of like a scientist, I think dates from as late as the 1800s. So this idea of kind of the term science is of fairly recent origin as a distinct thing, meaning the kind of thing we now mean by science as opposed to knowledge in general. Now I think philosophy, on the other hand, was a much more ancient term. I mean, it's from Greek, love of wisdom. And I think that in ancient Greek times, people, many people will have thought about themselves as philosophers, from Aristotle, Plato, all those kinds of people. There were also mathematicians, people who thought of themselves as mathematicians. And then there were astrologers. For some reason, astrology in Babylon seem to be very closely connected. And I think people will even have talked about Chaldeans, which is folks from Chaldea, which is, I guess, geographically. I think that was a. I'm not sure if that was a race or whether that was an area, but it was closely associated with Babylon. And what did the astrologers do? Well, they would do divination. They would be able to, they would try to predict things, I think usually by looking at, oh, what, bones from sheep? Maybe the, the kind of the, the shoulder bone of a sheep or something, and looking at the number of nicks in the shoulder bone of a sheep, things like that, to try and predict the future. Now, what did they try to predict? I mean, famously they were trying to predict things like where will the planets be in the sky, what will the weather be like, who will win or lose this battle? These are all things that were sort of part of the astrologer portfolio. I mean, I think at some level astrologers, I suspect, were a bit like kind of strategy consultants of modern times. And they would show up at courts and be like, let me tell you something about what will happen in the future as kind of a way of providing advice about what to do in the present, so to speak. So astrologers were kind of a feature of kind of thinking about what to do. I mean, thinking about, I suppose, the strategy of what to do. I mean, probably in later times and medieval times, there will also be things like the court jesters and so on, who would sort of say interesting random things. And I don't know what the relationship between sort of the interesting random things said and hey, why don't you think about this as kind of a form of consultant or something. But then there were other activities that were done, for example, in ancient Babylon, like their astronomical observations, which were done for probably 800 years every day. I think originally that was sort of commissioned by the king, but I think maybe had some slightly different kind of municipal or state kind of character in later years. But that's something which is not completely clear why this was done. Presumably it was done to somehow support the practice of astrology. But exactly how, I don't think one knows. So those are kind of early forms of what one might think of as science. Meanwhile, there was mathematics. Mathematics was in those days largely something relevant for sort of organization and commerce. So things like, well, let's, you know, count the number of thises that you have or let's work out something where, you know, where, where this, this commercial mathematics had to work out. And then there was also land surveying, just, you know, how much. What is the area of land that you actually have? Things like this. If we look at kind of the exercises that Babylonian students of mathematics did, which we still have because they're preserved on little clay tablets and so on, it's kind of funny because many of those exercises are just like the word problems of today, except that a few of the terms and issues have changed. It's things like if I ask X number of people to dig a ditch and the ditches of such and such a size, and they're digging such and such an amount per hour, how long will it take them to dig the whole ditch? These kinds of things? And there are geometrical problems. They seem to have a. They're very keen on various geometrical shapes. Like I think the cow's nose shape, which is the kind of shape formed by four circles coming together. That's a shape that is often discussed. And they talk about finding the area of that shape, things like this. I think the. So there was a kind of a mathematical tradition that was very relevant for commerce and for taxation and for kind of things like land transactions and so on. That wasn't really a scientific tradition, that was a mathematical tradition. The intersection of that with something scientific came, I suppose, through people like Archimedes 1st century BC and people like 2nd century 150 BC I think. And then people like Euclid, where they were kind of using sort of the Mathematics of geometry, to figure out things that were relevant for sort of engineering and those kinds of purposes. So I think now meanwhile, on the side, I mean, this is all kind of complicated because the distinction between these different fields really didn't emerge until much, much later. I mean, if you think about Plato, for example, a lot of what he discussed was philosophy, what we would now call philosophy, things like political philosophy. But in the middle of that, he was talking about philosophy of mathematics and occasionally about mathematics itself, and occasionally linking kind of mathematics to things about political philosophy, like discussing the idea that, I think, what is it? 5040 is the ideal size for a state according to Plato, because of the divisibility properties of that number, things like this. And so I don't know whether one would say that that was a political science. I think it seems more mathematical than most of sort of what one would normally think of as philosophy. Meanwhile, then there were people like Aristotle who were trying to figure out things about how the world works. I mean, Aristotle was a huge maker of lists of sea creatures and forms of argument that turned into logic and different kinds of things about the way the world is set up. It was sort of, in some sense, quite an encyclopedist of ideas. But he also had a bunch of ideas about how the mind works, physics works, these kinds of things. He made an assumption about how you could figure out those sorts of things, and he assumed that you could figure them out by pure thought. If you wanted to know how did mechanics work? He had the idea that, for example, things tend to go to the place where they sort of will best be, which means things tend to go towards the center of the earth. That is, things fall under gravity. But he didn't have the idea that there will be a formal structure around that. He had the idea that there would be kind of a. Those were things that could be worked out by pure thought, so to speak. The idea that there would be some kind of formal structure around those kinds of things that we would now call science was a vastly later idea that really didn't come into play until the 1600s. And people like Galileo and then Newton finding, as Newton would describe it, you know, the mathematical principles of natural philosophy. Where before the thinking about how nature works was purely on the basis of thinking, not on the basis of kind of a formalism and mathematical equations and so on. Somewhere in the middle of all of that was Francis Bacon, a bit earlier than those folk who was talking about kind of using the scientific method, as he called it. I think he was an advisor To Elizabeth I and, and had the bright idea that if you called things kind of a scientific, logical type method, then you could sort of get away with telling people things and they wouldn't say, no, no, no, you're wrong, because it was somehow scientifically proved. It was kind of originally, I think, introduced as almost a political idea rather than sort of something that just as a matter of intellectual development. Then I guess around the same time was Copernicus who was again doing something which was sort of breaking away from the let's work out how the world works purely by thinking about it and saying, well, there's this mathematical structure that you can describe. And this mathematical structure leads us to kind of be able to talk about the Earth going around the sun and so on. I mean, yes, this is an interesting question and a muddy answer. I would say that the distinction between philosophy and science didn't really emerge until much later. Although maybe the right distinction to make is that philosophy could be thought of as something where you can sort of put it together by pure thought, whereas science, at least in some forms, has the feature that it is formally constructed or perhaps constructed by doing explicit experiments. And in that sense that kind of idea is really an idea of sort of a post renaissance type idea rather than something that existed as such in antiquity. Now, in terms of what would the typical person think was important back in antiquity? I think that technology there was technology, technology particularly important for warfare. You know, if you were attacking some city with a bunch of city walls which had been carefully built in some way, you know, what was the right way to set up a catapult, to, to do the right thing there. That was sort of a matter of, of what one could think of as technology and of science in a sense. I mean, Archimedes was, was big on being sort of a consultant for war machines and so on, and presumably used some of his geometry to figure out things like sort of what to do with catapults and so on. But I think that the, in sort of the. Was there a thought that there would be sort of a scientific basis for technology? I'm not sure. I mean, certainly folks like Archimedes being pulled into sort of developing technology, one would think that that led to a certain amount of formal structure, at least in the way that Archimedes was thinking about these things. But I have the impression, I mean, I don't think that most of the time there were sort of things like calculations being done. I think that was a thing that really didn't happen until perhaps the late midd ages or something and the stone masons who were responsible for sort of figuring out how to make a cathedral that wouldn't fall down. Things like this. My impression, maybe it's not right. I'm thinking about this. Maybe the Egyptians, for example, certainly knew a certain amount about things like trigonometry and potentially used it in figuring out things about the construction of pyramids and so on. So I'm not sure. What to say about that. Boy, this was a question I thought, you know, it's a funny thing as I try and answer various different kinds of questions. I saw this question, I thought that's a question that's pretty easy to answer. And I realize as I'm trying to tell you answers to it, that's a pretty hard question actually. Let's see. Ollie asks what have been my observations on the role of history in current science and research? Is it still relevant or are we advancing fast enough to make it irrelevant? Well, you know, I was just looking at some history today which was helping me to understand some things about science in the present. I think the most important thing for me about scientific history is the way that it contextualizes scientific ideas and lets you know, things like is this idea really a solid idea or is it an idea that people came to through some historical process that we can now see no longer makes sense. Even though people may be absolutely convinced in some field of some particular fact, some particular result, it might not be true. And you can see that by knowing sort of how they got to that result. The other thing that I find very helpful is to see sort of the arc of how fields develop and how ideas, sort of learning about sort of the meta progression of ideas is helpful to understand ideas today. I mean, I find it useful to think about analogies, particularly places where things have gone astray in the history of science, to think things mistakes we might be making today, so to speak. I mean, I think that the. And also places where I'll give you an example that I mentioned before, I think from Sadi Kano, 1824, 100 years ago, 200 years ago, coming up with what ended up being things like the second law of thermodynamics. He had this kind of notion of talking about kind of the pure dynamics of heat. Well, at that time there was a standard theory of heat, the so called caloric theory of heat that had the idea that heat was a fluid that suffused substances and when something got hotter it was because it had more caloric fluid in it and so on. Carnot believed that theory, at least at first, his original construction of thermodynamics and his calculations about the efficiency of heat engines were based on the caloric theory of heat. Well, turns out the caloric theory of heat is not correct. Heat is not a fluid that suffuses substances. Heat is a feature of the microscopic mechanics of materials and the motion of molecules and so on. But nevertheless, the kind of logical structure of Carnot's arguments was strong enough to survive the fact that the underlying ontology and that he was working with was completely wrong. And that's an interesting thing to see in the history of science, that you can have sort of a theory where the conclusions are right but the underpinnings are completely wrong. And my guess is, by the way, that things that people talk about right now with dark matter, for example, probably the assumption that's being made that it's all particles because everything must be made of particles, is probably completely wrong. But nevertheless, one might think, oh, if that's completely wrong, every other conclusion about how dark matter works must similarly be wrong. But knowing the example of Carnot and knowing the fact that you can have, that you can, for example, have completely sort of correct worked out dynamics of what quotes cold dark matter does, even though the thing for which that dynamics is worked out isn't cold dark, or matter, so to speak. Well, it's dark in some sense, but isn't made of something like particles. The fact that there can be a sort of a feature, that you can have sort of a theory whose structure is right but whose underpinnings are wrong is interesting. It's also worth remembering that, that in the history of science there have been many times when people have been quite convinced about how a certain thing works and it just turns out not to be true. That was the case, for example, in the endless back and forth about was light a wave or a particle? Well, actually, it turns out to be both. By the way, that's another thing that quite often happens in the history of science, that you have two kind of polar opposite theories and they're sort of majorly at odds with each other. And what turns out actually to be true is something that nobody could see but was something that sort of merges those two theories, like for example, Darwin versus Lamarck in heredity. And we know now that it's mostly Darwin, but there's a little bit of Lamarck there, a little bit of kind of what can happen in the life of one organism can get passed to its progeny, although it's mostly the genetic story. But it's again, one of the things that's pretty common actually in history of science is when people have very strongly believed something and even if that thing is debunked, there will be something to the thing that they believed that one shouldn't just completely throw out. For example, the caloric theory of heat, even though the underpinnings of that aren't right, the idea that you can have fluid like equations like the heat equation that govern sort of the motion of heat, is still a surviving thing. And I think this kind of pattern, there are these patterns from history which I think are interesting and informative for what one thinks about today. I mean, another pattern is when things are sort of very dogmatically believed, but yet it doesn't quite fit. That's usually a sign that it isn't just a small hack that has to be added. It's usually a crack that's going to be eventually blown wide open. Example when Boole, George Boole, 1830s was thinking about kind of could you make kind of a system, a formal system like arithmetic that would apply to logic? Well, you might say, let's take true to be one, false to be zero. Then we have kind of sort of or is a plus and it's like one plus zero, true or false is true. But then we have the glitch one plus one. Well, that shouldn't be two, it should be one. How does that work? Boole kind of hacked around that. But in a sense that, but realized that it was reasonable to sort of set up an algebra where 1 plus 1 would be equal to 1. But that was a little crack that eventually opened out into what became things like universal algebra and a whole kind of a whole sort of formalization of mathematics that went beyond the mere sort of practical features of arithmetic and addition and so on. So I think that's another thing that when there are little cracks often get bigger. Another thing that happens is that when a theory is first constructed, when one is first sort of hacking through the jungle in a new area, often the formalism that's created is not particularly clean. Come back a few decades later and what was, oh, that special feature that was just. Oh yes, this trick fact that, you know, becomes something which is part of the mainstream and it's all very sort of organized. And that's just a piece of the whole organized story. So the thing that was the obscure fact when the field was new becomes kind of this thing that just fits into the whole pattern when the field gets older. Another thing one learns from the History of science is about the personal arcs of scientific discovery. I mean, there's a certain tendency for people to say, to write the kind of storybook version of scientific discovery where on this particular day an apple fell on Isaac Newton's head and he figured out gravity, or on this particular day this or that happened. This is essentially never the story. The story is there was a long period of development where somebody was thinking about things and trying to fit things together and accumulating facts and so on. And then maybe there was a particular moment, a particular day when they realized, yes, all these things that they've been figuring out, they all fit together in this particular way. This happened to me a bunch of times in my life. And I suppose perhaps in my efforts in history of science, I'm helped by the fact that I've discovered, I'm happy to say, a few things in science. And I kind of know the pattern of those discoveries, which often after the fact is kind of embarrassing because it's like, look, I basically had this, but I didn't understand what I had and it took me years to understand what I had. I'll give you an example. My favorite kind of all time, favorite science discovery, the Rule 30 cellular automaton, which I could say I discovered on June 1, 1984, but that really wouldn't be quite correct because I had published a paper in 1982 which had a picture of Rule 30 doing its thing and making complicated behavior from simple rules and so on. It wasn't a very big picture, but it was still a picture. But I didn't know what I had and I didn't understand its significance. And it took building on a bunch of different observations to really come back and on June 1, 1984, to have this high resolution printout that I made, because I happened to just have got a fancy laser printer that could make those kinds of printouts. I made this high resolution printout. I took it with me on a plane, was going to Europe that day, and was kind of realized, oh, yes, then I realized what I had, so to speak. And it's kind of fun because within a couple of days after that I was at some conference and there was a discussion at that conference which was recorded, and there's a transcript from it. And there I am confidently Talking about Rule 30 and so on as if I'd known about it for years. But actually I had known about it for years, but I'd only internalized its significance sort of a couple of days earlier. So this. But that's a common Thing that one's sort of, you know, slowly going towards things. And maybe at some moment there is a kind of a realization this is how it all fits together. But it doesn't come out of nothing. It comes out of a sort of a long development. I mean, the same thing happened with our physics project. I started thinking about kind of discrete space, time and networks to represent the structure, the underlying structure of space. I started thinking about that at the beginning of the 1990s, made a bunch of progress on it, got to a certain point, was a little bit frustrated. I couldn't kind of get further. And then in 2018, made sort of a. What seemed like kind of a technical kind of advance, which in the end was not. Not really that significant, but it sort of opened up for me something that fit together. A lot of things that I've been thinking about for a long time. You know, I think in very recent times, I've been working on a bunch of things that I had worked on in the 1980s. And in fact, in those cases, I'd kind of particularly things about, for example, biological evolution now things about the foundations of machine learning, where I had kind of done things about them. But in that particular case, I was blocked because I didn't do quite the right experiment because I was so sure that those experiments wouldn't work. And I only came to do those right experiments very recently because my intuition about things had changed enough that I could actually believe that those experiments might be worth doing. So, you know, one thing to. To realize is that there are ideas that have emerged in the history of science that are still good ideas and which were. Which sort of modern sort of beliefs and practice no longer take seriously. But actually they were good ideas. And one is well served if one knows what those ideas are. I learned an idea just today which I don't yet know all the details of. I've been working, as I mentioned, on the foundations of machine learning. And I got interested in understanding more about the origin of neural nets and kind of how people started thinking about neural nets, since there's a famous paper written by Warren McCulloch and Walter Pitts in 1943 about kind of a logical calculus of the nervous system, which kind of presented kind of what is very close to our modern neural net formalism. But where did that come from? Well, I learned just today, actually, that Warren McCulloch in the 1920s was already trying to think about how one would make a kind of a logic of the brain. Now, remember, that was at a time when, for example, Whitehead And Russell had done their thing in 1910, their Principia Mathematica, trying to sort of derive all of mathematics from logic. A bit of a show off project that, you know, famously managed to prove 1 +1 equals 2 by about page 150 or something. Full of ornate formalism, very badly constructed formalism in my opinion. But in any case, that was a thing that was sort of around at the time and this idea. And also the 1920s was a time when quantum mechanics was coming in. Photons had been talked about, electrons had been discovered 20 years earlier or something. It was a time when it seemed like there was going to be a kind of a way of making particles out of everything. And so Warren McCulloch, as I learned today, invented this idea of a psychon P, S Y C H O N, a unit of thought, an atom of thought. And his idea was that in the brain there are atoms of thought that somehow are operating in the brain and that somehow atoms of thought correspond to propositions in logic. And he got very confused by the fact that he thought there were cycles of nerves in the brain. He didn't understand what that meant in terms of sort of the derivation of logic. The idea that there could be a sort of a cycle in logic was something that just confused him. Now, if he'd understood more about computation and by 1920, Schoen Finkel had invented combinators. Not that anybody really knew about them or understood them. But in the end, this idea that you can have a sort of cycle of logical operations is kind of one corner of thinking about the idea of computation. But Warren McCulloch didn't have that idea at that time. He's quite confused by it. But this notion of an atom of thought, an elementary event that could be recorded in the brain McCulloch was talking about. Well, that's something bizarrely similar to kinds of things that we think about in terms of elementary events in physics and the kind of ideas in our physics project. And it's kind of interesting that reflecting sort of all the way back to ideas that are more kind of theological ideas about in areas like Buddhism, where it's sort of a question of what's inside the mind versus what's happening outside. That's something that's reflected also in philosophy and Descartes and other people, kind of what's the construction you make in your mind versus what's actually going on outside? Well, it's sort of interesting then to think about these psychons, which are kind of the elementary events in the brain. And Thinking about the elementary events happening in the world and what the correspondence between those is. And sort of fun. I hadn't really thought about elementary events recorded in the brain, although it's an obvious idea. And I still have to learn more about what exactly Warren McCulloch did. And I might have to go and look at some of his original papers to original manuscript documents to find out how those ideas developed. Let's hope his handwriting is readable. That's always a challenge. Although for somebody like me who grew up in the old world, somehow reading handwriting seems a lot easier than it does for the younger New World folk. Well, so. Let's see a little bit. I don't think that the fact that science is advancing quickly is a reason one shouldn't study history. In fact, to the contrary, sort of, if one wants to understand what advances make sense and what are sort of merely, you know, one should learn from history. The same is true with general history in the world, that many things about the world tend to repeat themselves. And one is going to repeat the mistakes or the misinterpretations, misunderstandings, if one doesn't know the history. There are some fields that are more oriented towards history than others. For example, economics, which doesn't get to do very many experiments. I suppose it could do more experiments in virtual worlds and things like this. But what happens when you don't have the gold standard anymore? Well, that really just sort of happened once, or what happened when one had the idea of paper money. That kind of more or less just happened once. So economics necessarily is a field that must look back to history because that's sort of its raw material for thinking about things. Other fields you can say, well, let's, you know, we could have done the experiment yesterday, but we don't have to know sort of the history of what happened. It's something which is sort of the experiment is going to be doable and doable anytime we want, so to speak. So I think. But I tend to feel, I think perhaps the most important thing to say about learning about history is the way that it contextualizes ideas. And when people just tell you, oh, this is how things work in such and such a field, If you really want to understand what that means, it's almost always necessary to go back and look at the history to see the contextualization of the idea. What would be an example? I think something in, oh, well, in lots of things about quantum mechanics, for example, where people just confidently assert this or that thing about the way that quantum mechanics works. And you Say, why is that true? Can you explain that to me? And people just say, well, we've known it's true, it's true, it's established. Well, where did it come from? And sometimes you realize that people sort of said, well, this is a provisional idea. And they said it in 1920 or something, and the provisional idea never got revised. It's still a provisional idea, but the people who work with those ideas just take it for granted, so to speak. And things sort of become true, in a sense through repetition, even though they really have never been properly established. And it's only by looking at the history that you find that out. And if you are blind to the history and look only at the present, you just will never know that. Let's see, Nori asks a question that I should know the answer to, which is, can you tell us about the history of the Wolfram summer School? How did it start? So we just had the 22nd of our Wolfram summer schools just a few weeks ago now. How did it start? So I had published my big book, A New Kind of Science, in 2002. It was a project I had started in 1991, trying to kind of sort of organize the things that I had figured out about kind of the computational universe of simple programs, the things I'd figured out in the 1980s about that. I wanted to kind of put it all together and kind of package it up as something that would be kind of a clear exposition of what I'd figured out. Meanwhile, I had built Mathematica, what's now Wolfram language, in part as a tool to do that kind of science. Well, in 1991, I started doing that science. And the thing that happened was I just started discovering more and more and more stuff. And what I thought would be a one year project, a one year sort of sabbatical from my energetic CEOing of our then still a quite young company, turned into a 10 year extravaganza because I just kept on discovering more and more things. And I had this kind of fixed table of contents for the book. I was trying to write 12 chapters and I was like, well, now I'm going to talk. In this chapter, chapter eight, for example, I'm going to talk about what this means for biology. In chapter nine, I'm going to talk about what this means for physics and so on. And what kept on happening is I thought I would just have some vague, simple things to say, and then I would actually do the experiments, do the figuring out of things. And I discovered there's this vast Array of, of things to talk about. So the book took me a decade. It's finally finished in 2002. I, I think I, I finished writing it in January of 2002. It was published in May of 2002. Well, the nice thing was a bunch of people read it, a lot of people read it. The and a lot of people were like, hey, this is interesting. I want to work on something related to this from my particular field. I think the book was probably the least popular among my best friends in physics because at that time physics was riding very high and it was like, we don't need a new kind of science. We have everything we need to find the fundamental theory of physics or whatever. Twenty years later that kind of the shine came off that idea. And people have been vastly more receptive to our, our physics project in recent times and, and the project has also gotten a lot further. But any case, at the time, one of the things that happened was a lot of people said, you know, we want to study this and you know, like, what was the mechanism going to be through which that would happen? I mean, my day job was I was CEOing a tech company, which I'm still CEOing, and you know, we make tools and things, but our company doesn't do basic research except in a few very specific areas. And it wasn't, you know, it's like somebody writes to us and says, I want to work with you. I'm a biologist, studying this or that. And I think the things you're doing are relevant. Yes, they probably are relevant, but what do we do about that? Well, actually the. I. So, so that, so then the summer school was sort of an answer to that question. It was, you want to know about the science, come to the summer school and let's talk about it. And the kind of, the concept from the very beginning was people would come to the summer school and everybody would do their own independent original project. The original expectation was that those projects would be kind of applying the methods of the NKS book, new kind of science book to this or that area and then sort of peel that off and do whatever you do with it. The idea of a summer school was sort of an obvious idea, but it was a little bit encouraged by some friends of mine who had, in the, in the. What was it? I guess in the 1980s had started a summer school related to neural nets. Actually at the time when neural nets were kind of reborn at the beginning of the 1980s, the so called parallel distributed processing PDP kind of initiative, they had this issue as well, that people were like, oh, we want to work on this. And how is that going to happen? Well, they organized a summer school to kind of give people a jump start about working on those kinds of things. And it's something which in a lot of kind of emergent fields has been a thing to do. I think the. So that was kind of the concept there, and it worked really well. And over the years it kind of gradually expanded into things that make use of our technology stack, make use of the ideas we have, as well as specifically kind of things based on the book New Kind of Science. I would say that there's been a kind of continual thread of what I would now call ruleology, studying simple programs and what they do. And it's been kind of nice to see that quite a few careers have been minted in that particular area over the years from the summer school, as well as careers in lots of other areas. But that's sort of different. About a decade ago, somebody who was working with me at the time was like, why don't we do a high school program that's kind of related a little bit more to technology than specifically to science. So we started that. That's now our summer research program for high school students. We started one for middle school students as well. But they've all been kind of. Well, at least the main summer school and the high school summer research program are very much based on the idea of everybody will do an independent project and most of them will be projects. Well, certainly for the summer school, they're projects that are sort of original projects that are things that haven't been done before. Often they're things where I kind of, you know, provide the. I kind of suggest the project. I just did that for like 130 projects a few weeks ago for our summer school and high school summer program. So that's the story behind that. I've been very happy with what's happened there. And it's been a great kind of way to sort of, well, a way for us to meet people, for people to meet each other, for ideas to be communicated and things to move forward. It's kind of like perhaps the original conception of universities and so on as a way to take sort of a corpus of knowledge and pass it on. I think that some of the sort of credentialing aspects of universities are a different thing. And that's not what we've been concentrating on or the social aspects. Maybe we have achieved some of that too. But anyway, that's a little bit of the story of that questions here. Gosh. Smiling asks, what's the history of formal verification in computer security? Especially how is it related to automated theorem proving and symbolic computation? Do people use Wolfram language for formal verification? Interesting. Well, let's see. The idea that you can kind of prove a program correct is something that I think originated kind of in the 1960s. And it's a little bit of a complicated story because the sort of formalization of mathematics around proof came before computation existed. And in fact, the very conception of computation in the hands of people like Schoenfinkel and Church and Turing and so on from the 1920s and 1930s came out of kind of how do we formalize this process that corresponds to things like mathematical proof? It's a little bit confusing because when people actually do mathematical computation, they're mostly not doing proofs. That was one of the things that. Where Mathematica is very different from Principia Mathematica, the Whitehead Russell conception of mathematics was mathematics is this process of making proofs. Whereas what Mathematica does is it just computes things. It may implicitly prove things internally, but mostly what it's about is just computing things, sort of forward computation rather than filling in the bureaucracy of oh yes, and we can establish, we can paper this result, we can kind of give evidence that it's true. But in. So sort of proof and formalized proof came before computation. And in the 1960s, there were various efforts to kind of make sort of symbolic systems that would be associated with proof. There was a project called Automath done by a person called de Bruyne in the Netherlands that was a particularly notable example of this, where kind of the idea was one could take what was otherwise written down in mathematics and formalize it. It's what turned into modern proof assistants, where one has kind of this formal statement that one can verify it's correct even though the statement is written by humans. But it's not a program in the usual sense of a sort of forward compute something and get a result type program. It's more a fill in the steps that one can verify correct. So the question of people got interested in various kinds of formal verification for various purposes. There were efforts in the 1960s, 1970s. There were various kinds of languages where people said, we will be able to formally verify programs. I remember there was a famous story, it might be a bit apocryphal of a fighter plane, I think, which had had. This was probably in the 1970s, which supposedly had formally verified code for its flight control system or Something like this. And it all went great until the fighter plane flew over the equator and turned upside down. And so what is that? Because what are you formally verifying? It's always a tricky thing because there's a program that defines how something will work. And then you say, well now I want to formally verify that. Well, the formal verification needs a description of what you want to have happen, but the program is a description of what you want to have happen. So it's always this kind of complicated dance of what is just the program that says what you want to have happen versus the formal verifier that also says what you want to have happen. And famous examples of things like this that have happened in the Ethereum blockchain when this thing was created called the DAO Distributed Autonomous Organization that was supposed to be, I think, a venture capital operation on the Ethereum blockchain that was very proud of the fact that everything about it is defined by code, by computational code. It's all just smart contracts all the way down. And there's no kind of human sort of legal framework, it's just code. Well then somebody just Transferred I think $50 million or something to their own account. And people said that's wrong, you can't do that. And the person correctly said, well the thing said, it's all governed by code. I use this code. You might say the code has a bug, but the code defines what the code should do, so you can't say it has a bug, so to speak. Now from the outside you might say that wasn't what we intended, but that's something that is sort of a meta claim and it's not the sort of the formal verification. In that case, the formal description was the code itself. And so this idea that then well, actually the code isn't enough. Same thing with formal verification. It's always a question of when is the program itself is doing what it does. The verifier has to be something that is also saying what it should do, but in a different way than the program. Now there are cases where you can expect to do things. For example, you might say, well, there's a meta fact about a program. If you use some low level programming language, not Wolfram language, we don't have this issue. And you scribble on memory because you had an overflow in some pointer move past the end of an array or something like this, you could say meta fact, you shouldn't scribble on memory. And so then you can imagine having a formal verifier that Goes in and says, given this program, could it ever scribble on memory? Now, obviously, in a language like C, you can just scribble on memory. In languages like Rust, you can't do that. It's more structured and more from language. You can't do that. It. It has its much higher level kind of construction, but that's the kind of thing which you can expect to sort of formally verify. There were a number of efforts to. It all was a bit muddled, this question of how do you. You've got a verifier. But the program itself was specifying what it should do. That's been kind of a repeated muddle. But there were efforts, I think. What is it? The Z? What is it? T3? Maybe. Maybe that was a. There have been a series of projects in France, the uk, places like this, of creating kind of theorem provers that apply to code, I think. And in fact, even some of the things like Lean, which has become a popular proof assistant system, I think that was originally developed for code verification, not for anything to do with mathematical proof assistance and so on. In terms of the verification of things like protocols, the Holy Grail for a while has been to verify something like a blockchain protocol. I don't think anybody has achieved that. It's something where you could say, well, what do we want to verify? We want to verify there's no double spending, for example, of tokens or some other property. We say, does this property hold for this program? It's awfully difficult to figure that out. Now, what tends to happen is there have been areas. In the 1970s and 1980s, a lot of work was done on things like Boolean functions, being able to describe some big system, some undercarriage of a plane or something in terms of some giant collection of Boolean functions. And then being able to verify there is no arrangement, there is no set of values for these Boolean variables, for example, that will cause the plane to land without its wheels down, or something like this. And there was a technology, the whole technology of exploring very large Boolean functions, things like Boolean decision diagrams and so on were introduced to make it easier to do that. And that was a thing that has had quite a bit of success, I would say. Related to that are Petri nets, which are a slightly more dynamic version of kind of descriptions of systems and how they work. Related to that, finite automata. These are all kind of in the same general bucket, Boolean functions, finite automata, petri nets and so on. They're all systems that have the feature that they're quite rich, but yet they're limited, and their limitation makes verification possible. None of those systems is computation universal. None of those systems allow you to specify and run an arbitrary program. And that's been important in the fact that they are verifiable is a consequence of the fact that they are not universal and the fact that you can readily figure out certain properties in general. If you want to know some property, like, for example, let's take a Turing machine. You say, I want to verify that this Turing machine will always halt in any computation. Well, that was something Alan turing proved in 1936. You can't make a finite program, at least with a Turing machine. Or as we now believe, any computational system that will guarantee to answer the question, will the Turing machine ever halt? It could be like, well, I can tell it didn't halt after a million steps or a billion steps. But there's no way to kind of jump ahead and guarantee to be able to say, even after an infinite number of steps, it won't halt. So for a general Turing machine, it becomes very difficult to make statements like that. It is possible for something like Boolean functions, Petri nets, finite automata, those kinds of things, to make those kinds of global statements. And verification often sits on this kind of border between that which is sort of rich enough to be interesting and that which is so rich that it's full of computational irreducibility, undecidability, and so on. A place where this comes up is type theory. One of the things that one often does in programming is to say, well, the idea, the theory of types, was originally introduced by Bertrand Russell as a hack to get around some definitional problems in set theory and so on. But in its later instantiation, it was, oh, we want to represent integers on a computer, we want to represent real numbers on a computer. Want to represent strings on a computer. We will consider these as different types, and we will say that certain operations work only on certain types. In building Wolfram Language and its predecessor SMP, back in 1979, I was very big on the idea that one should think of everything as just a symbolic expression and not kind of slice the world into these very specific types. This idea of symbolic expressions has been super powerful and is really the basis for a lot of the technology we've built. But nevertheless, the idea of types, particularly when you're dealing with computers at the hardware level, where there really is a register that can store an integer or store a real number or whatever else, it matters that you specify what type of thing you're going to be operating on in the computer. So for example, in our compiler for Wolfram language, it's full of type specifications because it's trying to compile down to the raw hardware of a computer. But when it comes to the theory of types, which has become more popular in recent years, and things like homotopy type theory as kind of a foundational theory for mathematics and so on, in that case, people say, oh well, when you have types you can do verification, you can take a program, you can say, do the types match? Does this work given type specifications? In fact, in our compiler, a large part of the effort is in type inference, is in essentially theorem proving that when you do this operation, the only types that can occur are this and that. Why do you need that? Well, you need that if you're making a compiler that's going to be compiled down to low level code, but because you need to be able to guarantee in the operation of this function, the only things that can happen are you get pairs of integers. So that's all you need to be able to store. You can never get a triple of integers, but you wouldn't be able to store the same way. And so on. You've proved what the types are. Well, there's an escape hatch though, and it's a difficult one, which is usually this theory of types when you're just talking about integers, arrays of integers, functions that return integers, functions that map integers to integers and so on. These are all sort of well defined types. But then there's so called dependent type theory where you say, well, it's an integer, but it's an integer that has this or that property. It's an integer that has the property that it's a property. An integer N such that X to the n plus y to the n equals z to the N never has solutions for those values of N that we're considering as integer solutions. Well, that's a statement of Fermat's last theorem and figuring out just what kind of a thing can N be, you'd have to know how to prove Fermat's. We'd have to know Fermat's last theorem to be able to establish that. So as soon as you get into the sort of dependent type theory where you're saying not just it's this kind of structural type, an integer, a function returning an integer, things like that, you end up with sort of the slippery slope of arbitrary computation. And so what happens is, yes, you can prove things about kind of independent types, but as soon as you have these kind of parameter, these types that are defined by computations, so to speak, you end up being in a morass of things that are unprovable. So it's tricky. Formal verification, as I say, lives in this weird kind of zone between things that are trivial, where there's not even a reason to say let's formally verify it, and things that have enough computation going on that the things you might want to ask about them are typically undecidable, and so on. So there's a question, do people use Wolfram language for formal verification? Absolutely. And it's been done for various microprocessor architectures and all sorts of other things. Oh, I might say a few other things about the history of formal verification. The automated theorem proving that kind of came out of quite a lot of enthusiasm for automated theorem proven Even in the 1950s, very early computers and even the Boolean satisfiability, given a Boolean expression, a logic expression, other assignments of truth values to the variables such that the whole thing is true. Thing called the Davis Putnam algorithm. It's a pretty nice algorithm, still very useful. Algorithm that originated in the 1950s was a surprisingly cheap algorithm for determining the answer to that. Even though formally that problem is NP complete and is in some sense exponential time, et cetera, et cetera, et cetera, in practice you can often solve it rather easily. So the thing that, that was kind of an early example of a theorem proving like thing, then so called resolution theorem provers that. Well, more or less what is theorem proving? Theorem proving is about you're given a certain set of axioms, a certain set of relations between things. And basically a theorem is a sequence of relations, a sequence of axioms you're applying to get from one thing to another. In more detail, it tends to be the case that it's like pairs of theorems kind of combined together to make another theorem, but. But in a simpler case it's just you go from one expression, apply axiom to get another expression, keep going. And so a theorem becomes this fact that these two things are connected just through axioms, through things you assume are true. And theorem proving is a story of finding a path in this network of connected things. And so how do you find that path? Well, that's sort of the art of theorem proving and pathfinding. The main problem of pathfinding is what if you took a wrong turn, you might never get to the destination. And so there are a variety of tricks. One thing is to go both from the beginning and from the end. And Kind of try and meet in the middle. Another is to use the concept of completions, where you're basically saying, if it was the case that this set of paths had a property called confluence, that. Let me give an example. If you're simplifying an algebraic expression, it's got a bunch of parentheses and other things, and you're kind of trying to, you're trying to simplify it down to whatever it can be simplified down to. And eventually you're going to get rid of all those parentheses, you're going to multiply them all out. Interesting algebraic fact. It doesn't matter in what order you multiply out those parentheses, we're always going to get the same answer. If you imagine drawing a graph, we call it a multi way graph these days, of all the different moves you can make in simplifying that algebraic expression, there'd be a whole bunch of branches. But the point is that every branch that happens merges again, leading to the same final expression. Well, that property of confluence means that if you're trying to do theorem proving, you can never make a wrong turn, because any wrong turn you make, you'll always be able to fix it up later. You'll always end up in the same place as taking the other turn you could have taken. So a big approach in theorem proving is to try and sort of introduce completions which sort of make things more confluent. And it's an idea that's been rediscovered multiple times with multiple different names. But that's kind of a common approach. All of these things have a certain number of heuristics of what completion should you do, what branches should you go on, and so on. But that's been the story of automated theorem proving. Now, automated theorem proving is a somewhat different tradition from the kind of proof assistant, proof type tradition. Automated theorem proving tends to be. Okay, we've got this. Well, okay, there are the proof assistants where a person is going to put down those elements and the machine is going to check that those elements really fit together correctly, as opposed to, here's a thing, just come up with an automated proof. In practice, it's pretty difficult to come up with automated proofs. And the vast, vast majority of all automated proofs that have ever been done are of things that people sort of already knew were true. I think the only example of a case where something was discovered by automated theorem proving and one didn't already suspect it was true is the thing that I found in the year 2000, which was the minimal axiom for Boolean algebra Given the logic, you can say things like P and Q is the same as Q and P and so on. You can write down a bunch of different axioms for logic. The question is, what's the absolute minimum collection of such axioms? And you can just use the single NAND operation rather than using and, and, or not. And you can say, well, what is the simplest version of this? And people have looked for this for, I don't know, 50 years or so. And some people had spent their whole lives actually pretty much trying to simplify more complicated axioms to get simpler ones. I kind of had this suspicion that there might be a really simple axiom that you could find just by searching the set of possible axioms with a certain amount of filtering. And so I did that, and it turned out that about the 50,000th axiom that I looked at, just starting from the very simplest one and sort of enumerating up to more complicated ones, the 50,000th one I could prove with automated theorem proving was actually an axiom for Boolean algebra. So we know it's the simplest one. So that was a thing that was discovered by automated theorem proving and had not really been suspected or believed to be there before that. I had a guess that it was there, but that was what was needed to establish it. But other than that, I don't know of any other example where automated theorem proving has been used for sort of discovery of something that wasn't already thought to be true. Now, I suppose miniature automated theorem proving is used all the time in type inference, in things like our compiler and so on, but for things that are sort of mathematical type interest, that's the only example that I know of where automated theorem proving has been used to sort of discover something. Now, you know, the one time when sort of automated verification got a bit of a boost was the FDIV bug, the FDIV Pentium bug. This must have been, oh, when was it? Early 1990s, 1993 maybe. Here's what happened. Intel had come out with this Pentium microprocessor. It was the 8086 and then it was the 586. And it was a proud new microprocessor. And one day somebody noticed that a particular bit pattern, when put into the division operation, floating point, division operation, gave the wrong answer. And it was a big shocker. It was, you know, for three or four days it was the top story in the news everywhere. And everybody kept on saying things like, oh, my spreadsheet must be wrong because I must have hit The FDIV bug. Well, that was all complete nonsense because it was a bug associated with a particular weird pattern of bits in this that you could give in a floating point number. And you know, most of the time you're mostly interested in the overall size of a floating point number. The fact that in its 16 decimal digit it has a 1 instead of a 2 is mostly never relevant for practical purposes. And actually an interesting question that I only. It was one of these cases where there was a lot of news about this Pentium bug and people were asking us for our comment on it because after all, we made mathematical software. Actually, I discovered at that time a shocking fact that all the companies that made floating point units at the time were using Mathematica as the sort of gold standard to check that the arithmetic they were doing was correct. And they obviously were all doing this independently because they were all competing companies. But I eventually traced down they were all using this one sort of single source of truth about arithmetic. Well, I think we got it right, so it was probably all good. But it was an interesting thing to realize. It may very well still be true. But in any case, at the time there was sort of a question. You know, a lot of people have been kind of talking about this thing. And as a result of that bug, intel and other companies put a lot more resources into automated verification for something like arithmetic. You can expect to kind of. You can hope that you can verify a microprocessor design and say, yes, will it always do the arithmetic the way it's supposed to do the arithmetic? I think the. By the way, in that particular case, one of the things that was interesting, which I realized after a few days of, of this being in the news every day, was like, how common are the numbers that would lead to this bug? Like, if it was a very round number, like the number 2.500000 or the same thing in binary, then yes, people might actually run into this bug. But if it's a number that's 2.5764-82483, blah blah, blah, blah, blah, blah. Not a thing that was sort of a readily generated number from an actual computation, then people wouldn't run into it. And so it was an interesting thing. You know, how widespread is this number? If it's related to PI, if it's related to E, if it's related to square root of two, it might be more common. It didn't seem to be related to any of those things. It was a number, a really quotes random number that was A number that kind of was not something that would sort of naturally be generated by a simple formula, so to speak. But in any case, that led to the more interest, particularly in microprocessors of design, in verification of these kinds of things. There's another whole branch which has to do with. In computer security, sort of the classic kind of computer security mistake is buffer overflow. This was from the 1960s. People were discovering, oh, there's a password that's being requested. What if I type in something that's way too long? Oh, they'll only have a certain number of characters in the buffer where that password is being put in. Oh, if I put in all this other stuff, it's going to get scribbled randomly on memory. And that could allow us to break into some computer system. I think that first happened on a system at MIT sometime in the 1960s. But that kind of thing is something where you can potentially expect. Well, you can hope that you can do automated verification on those kinds of things. I don't know the current state of being able to do that. As I say, I know that for things like blockchain, it's been sort of the holy grail to do things of that kind that hasn't yet been possible. And again, I think it is a tricky thing because it's one of these cases where there's a trade off between the level of functionality of the system and, and its verifiability. In other words, the fancier the system, the fancier the firewall, the fancier the rules, et cetera, et cetera, et cetera, the more difficult they will be to verify. So it's kind of like the same thing that happens in AI ethics. If you want your AIs to be able to do a lot of fancy things, then you can't lock them down and know that they'll never do the wrong thing. You kind of have that choice. You can either lock it down, no, it'll never do the wrong thing, but. But then it can't do much at all. Or you say, I wanted to do a lot of stuff, but there will be some surprises that can happen. That's a sort of a computational irreducibility story. Let's see. I noticed. Sorry, I haven't been looking at the recent questions that have been coming in. There's one from Grizzleby. Would you consider using one AI to formally verify software now? Maybe formally verify another AI? One of the challenges has been that we're used to doing software testing where we generate millions of tests. And we can run those automated tests. We are able to do a certain amount of testing at the level of verification of source code verification and coverage analysis, things like this. But mostly we're dealing with the phenomena of what does the software do? Well, that's a fine thing when the software is deterministic and it'll always do the same thing. And you can expect that it will always give sort of the same. The function you're computing will always give the same answer. But when the function says write an essay about this or that, there's no single right answer. And so doing regression testing where you say it was right before, is it going to stay right? Doesn't really work. And so there's this question, when you're doing sort of LLM testing and so on, can you test whether the thing you get out is reasonable or whether the thing just went completely off the deep end and maybe some prompt went off a skew or the way the prompt interacted with some new model went wrong or something like this. The best thing we've been able to find is to use an LLM to test an LLM. So you're basically saying this is the new result, this is the old result. Are they this, are they similar enough? Ask an LLM to determine that. So that's a kind of recursive way to try and verify these sorts of things. Let's see. Gosh, let me see. Question from Sentient here. What are some examples of scientific technological dead ends other than alchemy? Well, you know, alchemy just turned into chemistry. The, the particular holy grail of the field of turning lead into gold didn't work out. But an awful lot of what was done under the name of alchemy basically turned into chemistry. And I think that's an interesting question when kind of sometimes fields develop these kind of our holy grail is blah, blah, blah, and it's never achieved. AI would be an example of that. The original kind of idea from 1956 was let's just make computers that do what brains do. And that objective led to a great many things over the course of many years, even though the objective wasn't sort of slam dunk achieved. Now I think one might have said, oh, AI is a dead end. It didn't achieve its objective. But still it did achieve a bunch of things along the way. Same with cybernetics. Cybernetics was about sort of communication and control in sort of humans, animals, machines, etc. Well, you know, it had a bunch of lofty objectives in terms of understanding Minds and humans and so on, but it actually achieved a bunch of things in control theory and in the construction of mechanisms and so on. So again, even though you might have said it was a dead end, because it didn't get to the end that it intended to get to, it did get somewhere. Now there are theories that get very elaborated, where it's kind of lots of angels dancing on lots of heads of pins working on something which really doesn't make a lot of sense. This happened with the phlogiston theory associated with heat and chemicals and so on. It happened a bit with the caloric theory of heat. But as I was mentioning earlier, it's surprising that a lot of those things, when they were elaborate sort of formal constructions, they weren't really dead ends. The underpinnings were wrong, but the formal constructions were in many cases not wrong. Now you can ask, let me give some other examples. I mean, there are examples in mathematics where people said the most important thing is blah, blah. And that didn't seem to be the case. Like for example, for the Pythagoreans, they were talking about prime numbers. They were also talking about perfect numbers, numbers which are the sum of their divisors. Well, prime numbers became a big thing. Perfect numbers didn't really turn into much. So you could say the study of perfect numbers was sort of a dead end, at least for now. Whereas the study of prime numbers has led to endless number theory and so on. You could say there are things that have been invented in mathematics that were sort of dead end ideas, like, let's say, transfinite numbers. Well, it's not really a dead end idea. It hasn't sort of made it into major application areas, but it's informed all kinds of things in sort of abstract mathematics. And I don't think the story has ended yet of whether transfinite numbers will end up being of practical importance, for example, in thinking about infinite computations, all those kinds of things. So I'm kind of a believer in there are very few dead ends actually in the end, there are things where people get the wrong idea for the objective. And I'll give you another example. Expert systems, a methodology for AI from the 1980s. Go and interview an expert and encode their knowledge as rules, which will then allow you to reproduce everything the expert can do. Didn't work out very well, but now we're doing things that are really tantamount to that idea. It just wasn't technically possible at that time. Its objectives didn't really pan out. But I wouldn't call it. It was temporarily a dead end. But I wouldn't say that the, that the sort of the idea of thinking about it was a bad idea. Maybe I'm not thinking of other cases where. Well, there are things where people just decide it's a super bad idea for other reasons. I mean, a good example of that would be eugenics, breeding humans, so to speak. People decided that was a really bad idea and they decided that for external reasons, so to speak. So you could say that was sort of a dead end. And you could say the same thing about. Well, a lot of, kind of, you know, there are developments like the idea from the 1800s, beginning of the 1800s, of a social physics, the idea, you know, we now are beginning to understand as of that time, kind of mechanics. We have a mathematical theory of mechanics and physics and so on. Surely we must be able to have people said a mathematical theory of the operation of society. Well, it didn't work out at the time, but I think that that idea wasn't obviously bad idea. There are issues with it. There are questions of computational irreducibility, things like this, but it's not, you know, at the time, temporarily it was a dead end. You know, in the, in 1800, it wasn't a thing you could do. As it's turned out, same one could say about, oh, I don't know, you know, Leibnitz, late 1600s. Let's resolve legal cases using logic. Let's build a machine that can sort of solve, you know, resolve kind of legal disputes by some kind of structured logical means. Well, it was a few hundred years too early, but the dynamics of those kinds of things played into computational contracts is not really such a bad idea. I think that what often happens is that there's kind of a giant, you know, people say this is the most amazing thing. We're gonna, you know, everything's gonna work out this way. And usually it often doesn't. It. It doesn't, you know, immediately the hype bubble isn't really supported, but often there was something inside it that was perfectly worthwhile. And I think that tends to be much more the lesson than things really went in the wrong direction. I mean, there are things, as I mentioned before, where people come to believe things that may turn out not to be true and it can inhibit the field for decades, maybe even centuries, where people say that isn't the way things work, even though people maybe at one time did think it was the way things work. In a sense, things get squashed all the more strongly if people at One time believed them. For example, the idea of discrete space was probably more squashed because it had been believed at the beginning of the 20th century. It's like, no, no, no, that's not true or something. The. So, you know, if nothing was known about something, it might be that it is less kind of. People are less dogmatically certain that it isn't that way than they are if it was once believed and then sort of fell into disrepute. Maybe one more thing, and then I've got to go to my day job here. Satiri asks, related to a very early question here. What about Pythagoras, philosophy or science? Yeah, good question. I mean, I think. Good question. I mean, Pythagoras started thinking about numbers and how the world was constructed in terms of numbers, but he started thinking about that noticing musical harmonies, which are not really the stuff of. They're more the stuff of perception than the stuff of what we would nowadays think of as objective science. So, yeah, it's a good question. I mean, that was certainly in the period when those things had not sort of separated out. Oh, and Rudo asks, we have enough information to answer the question of philosophy versus science for ancient south and Middle American civilization. I think, no, I think not enough is known. I mean, I certainly. We know about the Mayan calendar, things like this, but I don't think, you know, it's funny, because civilizations think some things are worth recording and other things are not. The Babylonians tended to want to record everything other civilizations did not. Babylonians were also lucky that they recorded things on clay tablets which survived. But it's interesting that things like, I don't know, documentation for computer systems, people just go, oh, that's just a thing that comes with a computer, and you throw it away when you. When you've read it, type thing. Whereas somebody might say, this book of poetry, that's a thing we preserve. There are things where people bother to write it down and others where they don't. There are things, for example, in, I think, a lot of, you know, Indian science and so on, we don't know when it came from because none of it was written down for a millennium or more. It was all an oral tradition, and when it was put down, it didn't include. There's some civilizations where every tablet was dated with such and such a year of the reign of so and so, and there are other civilizations where that wasn't included. It was just like, here's a thing, and there's no kind of date stamp on it. So some things people think are worth recording, some things people have not thought were worth recording. I think there's a lot of. So, you know, for example, another thing, you know, the antikythera device, the mechanical computer from around 2,000 years ago, we've only got this one instance of such a thing. Maybe they were very common, but people just didn't record the fact that they were being used. They didn't. And there were no instruction manuals that have survived and so on. It's like, what does a civilization preserve and what does it not preserve? And I think I've been an enthusiast of kind of preserving sort of personal analytics data. And I tend to collect data on everything, every keystroke I type and all these kinds of things, and all the paper documents I've had, I've scanned and I've got all my emails for 35 years and so on and lots of other things like this. So I'm a kind of preserve everything. But I think that it is, you know, a lot of things people just sort of say, oh, like social media postings, let's say some people would say, you know, some of those are just like they're gone and some of them are like it's preserved. And I think that the question of what gets preserved, what does not get preserved in civilization is a tricky one. And often the sort of the practices by which things are done are not preserved. They're just everybody knows it and so nobody ever writes it down. We're lucky that I don't know etiquette books exist from a certain period of time because then we know how things worked. Well, maybe in more modern times we might have TV shows that illustrate the etiquette, so to speak, or we might have novels from the past even that illustrate the etiquette. But the fact that certain things were know it was written down that you should in, I don't know, in British etiquette, you know, you should squash peas onto the back of your fork when you eat them or something. That was one I never really got. But the, you know, some things get written down, some things do not. So in terms of Central and South America, my impression is that we really don't know because quite possibly there were lots of sophisticated things, but there isn't written evidence of those things. And when they're abstract ideas, that's all we get to have to know that those ideas were figured out. Now sometimes we may be able to deduce that that idea was figured out because by golly, they set up this sort of engineering structure in a particular way. But, for example, particularly when it comes to, oh, they must have understood astronomy very well because there's this coincidence of this thing and that thing right at the vernal equinox or something. Those are very tricky to interpret. And without, I think, some sort of. Without what amounts to writing or markings or something like this that really indicate that was the point. Knowing that this happened to be lined up with that, in this case is a pretty difficult thing to interpret because by the end of it, kind of every alignment of things is special in some way, and it's a question of was it special enough and did they have an interpretation that made it special to them and so on. So I think another thing I might say about archeology, and it's very unintuitive in a sense, is that one might think that whatever we know about the past is what we're ever going to know, that we never learn more about the past. But that's consistently not true. Consistently. There's more and more discovered in archaeology. I mean, for example, one thing I'm sure is true is that beneath any city like Athens or something that's been lived in for a long time, there are many, many layers of archaeological material which have never been excavated. And of course, when there's a modern city built on top of it, it's hard to do the excavation. One imagines one day there'll be some kind of earth submarine or something that some little thing that can kind of drill its way underneath the city and gradually go and explore what's there and take pictures of all the artifacts or something, and hopefully not run into some critical electrical cable that was laid 100 years ago or something like this and that nobody has a map of. But one imagines maybe one day one will know what's underneath the city like Athens, and one will have the complete story of, well, this was a layer that was put down in the 5th century BC, and by golly, we found this extra little piece of, you know, we found this inscription that was from such and such a thing or something like this, or we found, you know, I think it is. And even places where it's just sort of somewhere got buried, you know, I don't know, the inscriptions that the Pythagoreans made in exile in Italy, so to speak, where they were, you know, figuring out something about the square root of 2, it might be found one day. I don't think we can say it will not be. I mean, a lovely example that has been the subject of this scroll prize is these scrolls that were in a villa that was covered in the eruption of Vesuvius in 79 AD. I guess it was a villa that was a very fancy villa that at one time had been owned by Julius Caesar's father in law, at least the father of his later wife Julia. That villa, it wasn't even known to exist. It was sort of rediscovered in the 1800s, 1700s maybe was actually, I think, one of the first places where any systematic archaeological excavation was done. But this villa, it was thought, oh, he discovered one floor of this villa, actually there are three floors altogether, two are still underground because there was a lot of material that was piled on top by this eruption. Well, in this villa were found in the 1800s, these carbonized rolled up scrolls and people tried to unroll them and they broke into fragments, a few of them. You could kind of see some pieces of them. They clearly had writing in them, was clearly a big library, maybe 10,000 scrolls. And there's an effort now to use modern CT scanning and machine learning to read what's in these scrolls. And it's pretty exciting because it's clear there was a philosopher who was probably hung out in that library at some point in its history. And that philosopher was an enthusiast of the Epicureans and folks like Democritus, who originally started talking about atoms and so on, was an Epicurean connected to the Epicurean school of philosophy and so on. And I think it's very possible that if the rest of that villa is excavated and if one manages to read those scrolls, there's this prize that's been put up for being able to make progress in the machine learning of decoding. They're very difficult to decode because it's kind of like the whole thing is carbonized, but there's sort of a little bit of an imprint left by where the ink was put, which changes a little bit the structure of the fibers in the paper and so on. And that's what you have to kind of tease out. And it's a difficult thing to do to. But some progress was made. There's an announcement of it. I happened to go to a few months ago at the reproduction of that villa, that is the Getty Villa in the la, Los Angeles area, is a reproduction of what was known of one floor of that villa that was the villa near Vesuvius, so to speak. So in any case, the point of this is that probably in some period of time we'll have all of those scrolls, maybe 10,000 scrolls. And it will be an amazing sort of discovery of lots of history, lots of works that were believed to have been lost, lots of things where in the future we will know more history, which is a surprising thing. You might just think that whatever we know is what we're going to know, but it isn't true. And then there's another challenge, which is when, as we have better technology, we can scrape off the little DNA and sequence it from every kind of object that was touched at some time in the past, or we can do all these very fine kind of molecular scale archaeological things. Do we go ahead and excavate things in 2025, let's say, or do we wait until 2100 when we might have better technology? Because if we excavate in 2025, we might destroy those wonderful little traces of molecular imperfections or something that by 2100 we'll know how to interpret with some kind of large scale atomic force microscope or something. That's a challenge. And it's kind of like, do we want to know now and potentially lose the material, or do we want to wait and not know for 100 years, but have a better chance to know at some point in the future? I think that's a difficult thing to know for sure. And one tends to want to know. One tends to be impatient and say, hey, if we can, let's do what we can do now and learn more about history. And perhaps that's the right approach, because as we discover more ways to discover things, so to speak, we'll find more archaeological artifacts that we couldn't find because they're buried in some random field somewhere which we don't have a way to surveil right now. And it's kind of reminiscent of drilling for oil. It's kind of like you find the oil you can find, and then if you're prepared to spend more money and more effort, there's probably always more oil to find. And it's probably true with archaeological artifacts as well, that if you put more effort in, there's probably always more to find. And so maybe the right approach, it's an interesting sort of, I don't know, question of ethics or something. And the right approach is whatever we know now, use the best methods we have today and try and sort of analyze it, even if it might destroy some of what we, we have now relative to the methods that we have in 100 years. Because in 100 years, those enhanced methods will allow us to find more stuff that hasn't been soiled, so to speak, by the by, the things that we do with it today. But I think so. You know, the fact that we don't know about some particular, you know, piece of history right now, like. Like Central and South America and its history of its science and its philosophy, I wouldn't count it as out. I wouldn't say that means we'll never know. That means it's lost to history. I doubt that's true. I think it'll be an interesting thing to know. One imagines one day maybe there'll be enough sort of molecular scale reconstruction and there'll be enough kind of rigidity to solid objects that one imagines one day maybe one will be able to find something where the sound waves that hit this piece of clay as it was drying 3,000 years ago was somehow recorded in the molecular structure of the clay. And we'll be able to replay what a person said right at that moment. And that doesn't seem outside the domain of physical possibility. But these are things that will sort of allow us to excavate more of history, so to speak, so. So that we can know those kinds of things. All right, I think. I think we should wrap up here. Thank you for asking lots of interesting questions. And I see there are many more that I didn't get a chance to get to today, and I look forward to getting to them another time. So thanks for joining me, and bye for now. Sa.