History of Science and Technology Q&A (April 26, 2023)

Sam. Hi everyone. Welcome to another episode of Q and A about history of science and technology. I think for some reason Wednesdays have emerged as my heavy live streaming day and I've got three live streams about different things all in in series. But let's see, I see a question here from Ryan on the submission form. Can you discuss the history of programming languages? Is programming always associated with computers or were there other forms of programming? Interesting question. So it's kind of what's the history of systematically stated rules for things? So just to be clear, programming in the form of computers that store their own programs, that was a phenomenon of the 1940s, mid to late 1940s, and really started being properly developed in the 1950s. The idea that is an idea where a computer, a so called stored program computer, where the program is stored like the data of the computer, in the electronic memory of the computer. But in many computers and early computers, electronic computers, there was an idea that in many ways the program was being fed from the outside, very commonly through cards, punch cards, or through paper tape. And so the idea of a punch card is you have a bunch of, well, let's say it's, I don't know, representation of numbers or something. And every column of the punch card has holes punched out of it, square holes in the case of punch card punched out of it in a certain pattern that corresponds to that particular number. And then the computer reads the punch card by either some mechanical device or some optical device. And then that determines what the computer computes. And the idea of storing the program for what the computer should be, the operations the computer should be doing, as well as the data, like the numbers the computer should be working on. The idea of storing those things on punch cards is actually quite an old idea. And sort of the big jump for computers went when computers started being able to store their programs in the memory of the computer. So that in effect, among other things, you could operate on the programs just like you can operate on the data that the computers were dealing with. So this idea of punch cards, that particular idea dates to 1800 with a guy called Marie Jacquard. And Jacquard invented this loom that would control the where threads go in weaving that one's doing based on where the holes were punched out of a punch card. And so there were machines that were making designs, you know, whatever it was that you were trying to weave, you know, some picture of some natural scene with animals in it or something like this, you would represent that scene in terms of a set of actions to be taken by the machine that was deciding where to put the threads. And you would encode those actions in terms of how you punch out the punch card. And as the machine is trying to weave, the would be reading the punch card, moving the threads around to eventually produce this kind of pattern. So historically, the idea of using that to do things like mathematical computation, that idea was around by the 1830s. Charles Babbage kind of got that idea in connection with his notion of an analytical engine. So he built this difference engine that was for computing polynomials using mechanical computation. And then he had a plan to build an analytical engine that would use punch cards as a way to decide what operations. It should perform. And I guess he had very charming things, like his name for the CPU was the mill, because this was a time when mills, like on powered by water wheels and things like that were kind of a big place where things got made. Famously then, Ada Lovelace had seen the difference engine back in the 1830s or so, when she was maybe 17 years old or something. 18 years old, perhaps. And then a number of years later ended up being sort of the big expositor of what Babbage was trying to do with the analytical engine. Babbage never ended up being able to build the analytical engine, but Ada Lovelace wrote this exposition of the analytical engine, called kind of nominally, as an introduction to a translation of lectures that Babbage had given in Italian, not his native language. He was British, and not Ada's native language either. But she translated it, and actually, I guess, no, a person called Manabrea maybe translated it. And then Ada Lovelace wrote a kind of introduction which ended up being longer than the actual piece itself, and was actually the much clearer exposition of what the sort of key point of the analytical engine was. And famously, she has a place where she says the analytical engine will weave algebraical patterns, much as a jacquard loom weaves patterns of birds and flowers. So it's kind of the notion that one would have this way of programming sort of these mathematical operations, these abstract operations. And she also thought about things like being able to compose music and so on this way, these kinds of much more abstract things. Babbage had gotten the idea of computing values of polynomials for making mathematical tables, and then eventually having the machine print those out. But this was a kind of a more abstracted version of that in which. So that was kind of the way that. So, you know, the implementation layer of that would have been kind of the punch cards, the actual sort of original design for the analytical engine. Was going to be sort of a steam powered thing. Although by that time both Ada Lovelace and Charles Babbage didn't know a bunch of people who were involved in the sort of Faraday orbit of thinking about electricity. So had the Analytical Engine actually been built, it would quite possibly have been an electrical device, not a steam powered device, not a giant locomotive sized steam powered thing. I mean, the, the actual story of the Analytical Engine was Babbage was. Well, Babbage had, had in fact inherited quite a lot of money because his father was a banker and he was in fact quite wealthy. And I, I some years ago, looked at his account books which are now to be found in the British Library, and you could see that he was, you know, he, he had, he had substantial assets. In fact, he also was involved in a startup which was a life insurance company and he was involved in computing the actuarial tables for that which he would have liked to use. Well, I think he did use his difference engine to compute some of those tables, a thing for computing values of polynomials and so on. But then for a long time Babbage was kind of wanted the British government to pay for the creation of the Analytical Engine and went through many cycles of, of, you know, this politician was in power and he was friends with them and then he would make a presentation and try and get this to happen and so on and so on and so on. Ada Lovelace, who was significantly younger than Charles Babbage, was very interested in what he was doing. And Ada had already been, you know, she was the daughter of Lord Byron, the poet. And then she married a person. His last name was King, I forget his first name now, who was a count or who became a count. He was actually, he'd been a kind of a civil servant in the British government and for apparently fairly effective. And he had inherited a title. And I think he also got sort of elevated a bit further from his services to the government. But anyway, Ada became a countess and Charles Babbage, for his whole life, I think, believed that Ada was much wealthier than he was and was capable of sort of funding his Analytical Engine or at least convincing Queen Victoria to fund the Analytical Engine upon actual investigation. I think if you look at the account books of Charles Babbage and Ada Lovelace, I think Charles Babbage was wrong about his estimate of Ada's net worth versus his net worth. Ada had the issue that her husband was very much into real estate and very much into kind of elaborate construction projects. They had a house in the country where he was building towers and turrets and things like this. And those finances were not as rosy as they might have been. And Charles Babbage was much more conservative in these things and had made, I think, reasonable investments and so on. And so his whole sort of effort to convince Ada to be the, in part, sort of the marketer for the Analytical Engine project. While it might have been relevant in terms of the British government, and certainly Ada was much more politic and dealing with people and much better at explaining what was going on, Charles Babbage was much more down at the level of the specific engineering details. I mean, in, in a kind of a, a modern version of the Silicon Valley. Let's start a company in the garage. The, the Charles Babbage version of that was he had his workshop set up in his stable because there were horses, not cars in those days. And he had been, he had had a bunch of engineers who'd worked on the actual, you know, making of the difference engine and so on, and making the whole brass sort of elaborate construction. And there were a lot of difficult mechanical problems to do with, you know, how do you, how do you make the carry bits propagate without having so much force that you break the metal, things like this. And he'd had engineers who'd worked on that. He was not, I think, a tremendously good manager of these projects. And he had a tremendous habit of thinking he was the high flying mathematical person and he would delegate the stuff to the engineers. Then he would be upset that the engineers weren't doing it very well and would say, he's got a better idea of how to do the engineering, which quite possibly he did have. And it kind of went in a not very positive loop. Ada Lovelace, actually, at one point there's a nice letter she wrote to Babbage where she basically says, you're messing up this Analytical Engine project. Let me, Ada, take over the project and sort of become its CEO and you become the cto, and then we'll make this work. And it's kind of a fun thing because I, you know, I found all these letters. And in those days there were, I think Ada Lovelace and Charles Babbage lived maybe a mile and a half apart in London. And there were in those days, 14 million mail deliveries per day in that part of London. And so they were able to kind of exchange messages, you know, much like email today, so to speak, but through a combination of the postal service and having, you know, people couriers just take the letters from one place to another. But you see this lovely thing where Ada has written this giant, you know, this letter proposing that she take over the project. And Charles Babbage annotates the letter, you know, saw Aal, his name for Ada Lovelace, you know, this morning and refused all her requests. These scribbles in the margin. Well, I think by that afternoon he'd kind of agreed. Yes, actually her suggestion was pretty good. She should do this. Unfortunately, she got sick and it never happened. Had it happened, possibly the era of computing would have occurred at a very different time. And certainly Babbage had this kind of idea. And I think Ada Lovelace was sort of into this as well, of the sort of cloud computing of the 1840s, of having the various difficult problems of the time, whether they're about navigation or actuarial tables or artillery tables and so on, have these things all be fed in into the central analytical engine that would be puffing away if it was steam powered, generating those results. That was kind of the notion at the time. Now by that time there were telegraph machines and so on. And so quite possibly it really would have been a very Victorian cloud computing story of people. You know, the question is tapped in with a telegraph and then the machine runs and you know, the result is tapped back by, by telegraph, so to speak, to give the answer. But I think the original question here was sort of the origin of this notion of specifying rules for things and having them be executed. And was that kind of a thing of computation? I think the answer is no. That idea goes back a long way. I mean, anytime one's had sort of plans for doing something that is a sort of a specification of rules that then get followed. And you know, back in military drills, military operations, people had, you know, the Romans no doubt had their, you know, let's go into a tortoise configuration, let's do this, let's do that. These were things which were essentially rules that defined, executed by humans in that case rather than by machines. But they were sort of rules that defined how one would do something like a program. Same is true. I mean, whether it's recipes for food or whether it's kind of things for defining knitting patterns or whatever else. You know, there are many places where people have defined rules for things. Similarly in architecture, there are certain cases where people would have, oh, let's make a fort and you know, all the forts look the same and maybe they have some elaborate fractal pattern. There are these so called star forts that had these sort of the big, the big tower and then the smaller towers. And so on around them, and people would work out all the sort of lines of visibility for these things. But those were cases where there was sort of, there was a plan and then the plan was going to be executed in some way with people actually building the thing. And one certainly knows even from Babylonian times, there were cases where there was a sort of an abstract representation of an architectural plan which was then built. So I think those are examples of sort of rule based things. Another type of rule based thing is games where, you know, the rules for chess or something, and you then get to sort of follow those rules. And that's something a little bit like programming too. I think the concept, I mean, when programming was first out and about, it was really very much in the style of there are certain set of operations that the computer can do. Kind of let's have a sequence of things defined that says, do this, you know, run the adding, adding, you know, the adding machine and the adding system, run the multiplying system. Take these pieces from here and there. And in the analytical engine those things all existed. One of the things I think Ada Lovelace figured out was the idea of loops where you could have sort of this contingent loop that would go around a different number of times and so on. But this idea of do this, then that, then that, it gets more elaborated by the time you can have a loop which says, keep doing this until something happens, and so on. That idea of keep doing this until something happens. For instance, in mathematics, the idea that you would iterate until you reach a fixed point or something like this, that idea did exist in a variety of places. For example, Newton's method for finding a square root, a variant of which was actually known in antiquity of just sort of iteratively going and getting, you know, closer and closer to the square root. That's an example of one of these rule based things which kind of iterates until. Until the answer is good enough, so to speak. Subsequently, when people kind of tried to idealize sort of what is, what does mathematics do, how does mathematics work? The sort of earliest version of this involved just a fixed loop. That is saying just go this number of times where we know how many times it will be, rather than go until something happens. That was the idea of primitive recursion, which arose in the late, as an idealization for a certain class of mathematical operations. People thought until the 1920s that that might be sort of all of the things you need, that that might be the only sort of iterative type operation that you needed to sort of specify standard Mathematical functions got kind of blown up in 1920 by this thing called the Ackerman function, which is a function that can be defined recursively in terms of. The function is defined in terms of values of the function at smaller arguments, but it doesn't have the feature that you can always go a fixed number of steps and it grows too. You can prove from the rapid growth that it has that it doesn't work that way. And so that was an example where one had to do something beyond primitive recursion. And for example, Kurt Godel, in proving Godel's theorem in 1931, had this thing called the general recursion, the so called mu operator, which was a thing which said keep going until something happens. And that was sort of a new idea that when computers sort of first started being out and about in the 1940s and 1950s, that sort of idea of the do this until something happens was a pretty early idea. I think there are other notions of kind of things based on rules. Another area will be logic, where this was a thing invented presumably by Aristotle, where it's kind of lifted out of the sort of arguments that were given in text and finding a sort of generalization of, oh, this argument is given in terms of cats. It could also be given in terms of dogs. It could also be given abstractly in terms of P's. If you have this particular pattern of ands and ors and nots and so on, then it follows this other pattern of ands and ors and nots. One could think of that as another example of kind of a rule based system. And by the way, by the 1830s, when George Boole had sort of cleaned up and mathematicized the notion of logic, had come up with Boolean algebra. And this sort of formalization of logic, formal logic that people like Lewis Carroll, Charles Dodson were into and so on. By that point, people started actually making machines for mechanical devices that would kind of resolve simple logic, you know, would give you the answers. You know, you say, make a machine that computes P and Q and not R or something. And you would set things to represent P and Q and R. And then you'd look at another part of the machine and it would have the. And it would have the results from that. And that was. That was kind of another. An early form of mechanical computer. So that's. Yeah, so those are a few examples. Let's see. Desk comment. Didn't IBM have its own extremely labor intensive telegraph system? I. Well, telegraphs were invented long before IBM as A company came into existence. I mean telegraphs were invented. What Samuel Morse was like 1833, something like that. By the time, I mean IBM's was originally something like the. Something rather the Hollerith Tabulating Company, something like that. This person, Herman Hollerith, who was involved in punch cards and I think their first big contract was the census, the US census around 19, maybe the 1910 census, I'm not sure. And where the big idea was to have census forms be encoded by punch cards. And then if you wanted to tabulate to count the number of people who have this characteristic or that characteristic, you could do that almost mechanically by looking at sort of the holes in the punch cards, so to speak. Let's see. Well, there are lots of questions here about different kinds of things. Ollie asks, how do you think ADA would view the current age of AI? That's an interesting question. You know, that is an interesting question. You know, LLMs large language models of which ChatGPT is, is an example. Sort of their big story is how do you continue a piece of text? You know, you've given a prompt. What's the way to continue that? I suspect that Ada would have seen that. I mean she was the. She kind of, you know, her father had been Lord Byron, the poet, she never really knew him and the. But she. Much to her mother's dismay because her mother had the sort of ugly divorce from Lord Byron and the kind of the repercussions of that lasted a century with the, you know, attacks on both sides from the people trying to claim that Anna Millibank I guess was her name, Anne bank was a terrible person and that Byron was a terrible person and so on. And there were all these attacks on Ada that resulted from that and it's just a horrible mess that goes back and forth in the kind of gossip columns, the Victorian gossip columns and books and so on. I mean there were all these claims about how, you know, Ada was an out of control gambler and she gambled away the family jewels three times and things. This is not true so far as I could tell. It's in fact completely false. But this was part of the kind of the gossip that came from the pro Lord Byron anti and Millibank faction. In any case, the thing that Millbank, Millibank, I've forgotten. I think Ada would have perhaps thought about this idea of completions as being a little bit like what it takes to fill in a piece of poetry because it's like, okay, what word could go next? Well, there's a limited set of possibilities, given that you want the poem to scan in a particular way, rhyme in a particular way, and so on. So I think that piece of sort of the construction of a large language model might have been somewhat familiar to her in terms of the ability for a. You know, I think this notion of. Well, to me, there are sort of two sides of what's going on. One is the kind of the statistical learn from what is out there on the Web and do kind of completions and things like this. That's, you know, the LLM story. The other side of the story is kind of the Wolfram language side of, you know, compute what can be computed based on having a very structured view of the world. Certainly that second part had a long tradition going back to people like Leibniz who thought about doing that. I think Charles Babbage would have been quite into that kind of idea. He was very much of a sort of organized knowledge, although he was kind of stuck to things like make mathematical tables, astronomical tables, things of this kind. So. So I think that. And the idea of let's just compute mechanically. I think one of his famous quotes when he was trying to build some logarithm tables back in probably the 1820s or something, I think the quote is, I wish by God this could be done by steam, which is translated into modern terminology. That would be done automatically, so to speak. And so I think that would be, you know, the idea that one could sort of compute things automatically would be sort of more his thing. But I think Ada would kind of probably associate the kind of, you know, how do you continue based on how things were continued before, as something not that dissimilar to her sort of family business of poetry. She at one point sort of thought of herself as a sort of a. A poetess of science, of kind of the exposition of science. I mean, I think her big, In a sense, both her big skill and her big point was to kind of see the big picture of what was going on, which turned out in the case of computation, there was a very big picture to see which she managed to get a reasonable glimpse of, even as, you know, folks like Babbage were seeing much more the micro details of, you know, we're going to get this thing and it's going to turn this crank so that this number will come out in this way and so on. So, Yeah, I think the. I mean, this whole notion of kind of entrepreneurism and so on, which people think of as being terribly modern is really. I mean, the fact that Charles Babbage was involved in this insurance startup is an example of that. That's not such a modern thing. And I think, although it is the case that the kind of the complexity of like starting a company and the sort of the bureaucracy around it has definitely gone way down, at least in most countries over the last century or so. And that's kind of a different story. Let's see. Satoshi comments. I wonder what would have happened if Newton or Gauss had had access to digital computers. Yeah, I think Gauss was a pretty decent hand calculator. One can find his places where he was trying to figure out properties of primes, where he just enumerated a whole bunch of primes and was trying to empirically work things out. Of course, many mathematicians don't realize that people like Gauss did those kinds of experiments because all that Gauss sort of published was I proved this theorem, here's this result rather than, you know, I tried it on 10,000 numbers and this is the result I got. I don't know about Newton's. I've never looked. How have I looked at Newton's? I don't know whether the handwritten calculation and so on. I know Leibniz. I have looked at his handwriting calculation. He was pretty bad at it. He made a lot of mistakes. He was better at algebra, which was much more. Something that was a more newfangled thing and probably more exciting than these big tables of numbers and so on. I think the answer, for example, for Gauss surely is that just a huge number of things that Gauss might have wondered whether they were true about prime numbers or other kinds of mathematical things would be. Would have been worked out differently. You know, I'm reminded when Mathematica first came out in 1988, a rather lovely review of Mathematica written by a mathematician had a title like, you know, if Gauss had a mouse and was talking about this question, I think that might have been written by a. Was a mathematical logic person now no longer alive. But I'm also reminded by just, I have to tell this story because I thought it was amusing. When we first announced Mathematica, June 23, 1988 was a different time. The web didn't exist. The way you communicated things was with press conferences. So we had such a thing in Silicon Valley, actually in Santa Clara, and invited lots of newspapers and such like and, you know, most of which had written most of their story because we briefed them beforehand and, you know, they dutifully showed up and then filed their story and off it went to the newspaper but we had invited a number of things like mathematicians to the press conference and one of them wrote some rather lovely account of, of that event. A number of interesting people showed up to the press conference. Among them actually quite a few kind of, I would say even warring chieftains of Silicon Valley. Steve Jobs was there and who hadn't been out in public much because he was in the middle of working on his NEXT company called Next, that hadn't yet released its computer. And there were, gosh, lots of people, were lots of interesting people. Gordon Bell, the developer of the VAX for Digital, was there. There's people from IBM, Sun Microsystems, Andy Bechtelsheim, Bill Joy, I think. Yeah, and a variety, variety of other people, all sorts of interesting crowd. Chap from sun actually had the bright idea of making sure that everybody who was there kind of signed a copy of the Mathematica book, which had just came out. So that's kind of a nice collection of interesting signatures of the time. In any case, the person who was there, as I think representing some math publication actually, but really a mathematician, wrote that he'd sort of expected he was coming to this thing that was going to be a math talk, so to speak. And it rapidly became clear that this was not a kind of math talk that this person had ever seen before. I think this was probably the first and perhaps only press conference that they ever went to. But it was rather a charming clash of worlds that worked out quite nicely. But any case, there's a question here from Brian. Any thoughts about Planck Talcool? So. That was a thing created by a person called Conrad Zuse, Z U S E and I don't know that much about it. I know a certain amount about Konrad Zuse. Conrad Zuse was an early computer pioneer in Germany who after the Second World War, built up a company, the Zuse Computer Company, that made a series of computers and had some degree of commercial success, but I think was eventually overtaken by sort of a different generation of electronic computers. But I suppose one of Conrad Zuse's claims to fame was something he did during the Second World War. I mean, I should say in kind of the connectivity of history. Conrad Zusa was also interested in kind of versions of cellular automata, though primarily more like finite difference models, where you have a grid of values and there's a discrete grid, but every value on the grid is a real number, whereas in cellular automata the values on the grid are discrete numbers. But towards the end of Zuse's life, this was in the 1980s, I actually exchanged some letters with him and I think his very last papers were actually much more in line with things I've done on cellular automata because he'd read a bunch of things I wrote. And so there's sort of a confusing thing because as happily his lifespan many decades and in the final decade so to speak, it sort of overlapped with things that I'd done and sort of as a related area. So that's led to a certain degree of confusion about sort of what was he doing earlier on. Well, it wasn't actually quite the same thing as cellular automata. He had this idea of what he called calculating space, the German name for it, which I can't say, but that was something I think he'd maybe written in the 60s, 1960s or so. But that was kind of an idea of discrete space. He wasn't really very much into physics. I mean he talked about physics but I don't think he ever had learned that much about physics. In any case, the thing that was an earlier sort of adventure of his was during the Second World War he made a binary mechanical computer presumably. And it's a little bit unclear what happened because the computer, there's one photograph of it, he made it in his sort of parents house in Berlin and it was. Well the standard story is that house was bombed, the computer was destroyed and the only thing that remains is this photograph. And then many, many years later, I think 1980s, probably Konrad Zuse and his son Horst Zuse were responsible for sort of making a reconstruction of that computer for the Deutsche Museum in Berlin. And that reconstruction doesn't look that much like what's in the photograph. But supposedly it worked the same way as what's in the photograph. And a number of years ago I actually met up with Horstzer and looked at that machine and it's not very easy to tell that much from it. But the real question that I got very curious about is so what did happen to the Z1, the very first computer built around 1944 and what were its origins and what physically happened to it? Because it's a big metal object and you know, you can we, we did find out in, I think we even got a photograph of the, from aerial reconnaissance of the bomb site where a bomb had been dropped on that, you know, on that house. But the question then was so what really happens to a computer when it's, you know, in a house that's bombed? Is it vaporized? Is it, you know, what happens to it? It's a big lump of metal, it Was already mysterious to me. Where did a big lump of metal come from in 1944? Because metal was, you know, of great strategic value and you know, wasn't self evident how you would get, how you get a big chunk of metal. What I learned actually much more recently, Conor Zuza was not officially in the military and quite why, I'm not sure. I mean, he was a college student at that time, but apparently he had a friend in, well, I think in the SS actually, and also had some connection, I learned recently from somebody had some connection with the German Air force. And so presumably that had something to do with how he managed to get a giant lump of metal to make a computer out of. But in any case, the question, I mean, for me, the sort of an interesting story fragment, this must have been, oh, how long ago? A decade ago or something. Now I was visiting this museum in Germany and looking at this computer, talking to the son of Konrad Zusa and the woman who is the curator of that part of the museum. And it's like, you know, oh, what happened to the original computer? Well, it was in this house, it was bombed. And eventually it's like, where is that house? Oh, well, actually it's five blocks from here. Unfortunately, I had to kind of leave that point and couldn't go and do that investigation. But we have subsequently done a bit more investigation and had many more conversations about what really happened to the computer. And the computer has still not been tracked down because it was an early story was, well, the computer was in the basement of the house. It had been moved to the basement because there were air raids and so on. And okay, so then I asked people who know about urban archaeology and so on, what happens if you have a house that collapses? There's a computer, it's made of metal, it's in the basement. And you know what happens? And it's like most people said, well, it'll still be there. You know, it might be smooshed a bit, but it'll still be there. You don't, it doesn't, you know, it's not, you know, that's no worse of a situation than many things that have happened to things that are still preserved from antiquity. So then further investigation, further discussions. It turned out there was an air raid shelter nearby and there was a. Well, maybe it was moved to the air raid shelter. Well, maybe not. Where was that? Well, there were two houses that were next to each other, they'd been rebuilt. And it's kind of like, you know, so I for a while was thinking about Sort of mounting some kind of urban archaeology expedition. Because I think it'd be really cool to actually unearth, you know, a computer from 1944 that was perhaps the first sort of binary mechanical computer. But I never got around to doing it. And it became clear that there were. It wasn't clear. You might think everybody would be like very gung ho to find this computer, but it was clear that that wasn't really the case. And it's sort of a question of why. And I don't know the answer. I mean, it's one of these things that one can speculate on. But I think the generally one speculation would be the computer didn't really exist. I think that's not correct because there is a photograph. The photograph seems fairly convincing. I think the computer existed. Did the computer work? Who knows? Maybe it didn't work. Maybe it was. Did the computer have components that had come from some unsavory source? Possibly, yes. These are some of the things one might think about. But anyway, so the answer is, I don't know about what happened to that computer. It's a mystery. Somebody can go out and solve it, go find that computer. Playing CAL Cool, I think was a programming scheme for that computer. And I really don't know much about it. I'm telling you only the ambient story, so to speak. RBS comments here. Isn't mathematics itself following rules? Yes, I suppose one could say that it was, although in a sense the Euclidean. The tradition that started with Euclid of let us prove this. If you read what Euclid says, it's mostly things like construct a pentagon. It's like you're defining the goal, but you're not saying how you get there. One of the great things about computation and computers is it's all about the steps that let you get to something and defining those steps. And then a thing I've spent some part of my life doing is, okay, computer, here are the rules. Now go run with them and see what happens, so to speak. Which is very different from sort of the Euclid. To construct, you know, a typical form in his. In Greek is something like to construct a pentagon, a regular pentagon. And then it's like, okay, now you've got the goal. Now go figure out how to do that with these. With these sort of set of other goals that you have achieved in the past. And so in a sense, that's the notion of the, you know, a view of mathematics is it's all about proofs and you've got, you know, the theorems are out there and you are defining what those theorems are. And then the process of mathematics is to go find that proof, to go build the scaffolding that gets to the place where you're trying to get to. That is really different from the computation idea, which is you've defined the program, now you run it and you see what happens. And for example, when Whitehead And Russell in 1910 wrote their big Principia Mathematica effort to sort of formalize mathematics, to have a. To derive mathematics from logic, I think one of the things that they got wrong was they thought the process of mathematics was the process of proof. And I think that in what became clear and in a sense our own efforts with Mathematica and what's now Wolfram Language and so on make clear is that it is much more valuable to be able to do the forward computation, to figure out what's true, than to say, I've got this thing, it's a theorem. I'm pretty sure it's true. Now go find me the steps that fills that in from the axioms that I started from. So I think mathematics in a sense is a rule following thing. Now there are examples that are more rule based. So, for example, the Fibonacci sequence, you know, F of N is equal to F of N minus 1 plus F of N minus 2. That was defined with some clarity by Leonardo Fibonacci in the first decade of the, of the 1200s, 1205, maybe, in his book Liber Abaci, the Book of the Abacus, which was actually a book, kind of a manual for merchants in Italy and in Venice and Pisa and so on for how to use an abacus. And really its big innovation was bringing Hindu Arabic base 10 numerals to the west where it had been that Roman numerals had been used previously. And so in a sense, the Fibonacci sequence, which he put at the very end of his Liber of Arche as kind of an exercise. Imagine rabbits in this enclosure and they have this successive baby rabbits and successive years and so on. And that was sort of defining a rule, a recursive rule that's kind of a little bit more like the sort of forward definition that we're used to from programs. Let's, Let's see. Oh boy. Lots of interesting questions here. All right, question from spare here. Can you talk about the history of cybernetics and the idea of feedback loops? Cybernetics as a name came from Norbert wiener in the 1930s or 40s. You know, his big thing I think I've talked about this here before was sort of control of machines and animals and so on. And how do you do, how do you manage to, you know, put your finger in a particular place? It involves sort of a. You look at your finger, where is it going? Well, it's going too far that way. Oh no, pull it back the other way. And you know, it's kind of this feedback process of looking at what happened and then sort of feeding it back. Now this notion of kind of how do you get a system that kind of. It tries to home in on a particular thing like it tries to home in on. Do you get the device to precisely follow this place? Do you get the autopilot to precisely go at this particular altitude and so on. How do you get that kind of feedback mechanism to work? I think the earliest examples of these kinds of things were various kinds of governors that were used. For example, James Watt, I believe had a form of governor that was used on steam engines. And I think the way that one worked was it has this thing that spins around and it has these weights on it. And depending on how fast it's spinning, the weights will be pulled out by centrifugal force and that will cause it to, I think maybe close a valve or something that makes it run slower. And that mechanism of kind of the, you know, when the thing is going too fast, the, the thing closes itself down. That mechanism was certainly known that the, the Watt governor was a thing back in the 17, I think 1776. That was a famous date for a memorable date from the American founding and also from the founding of the sort of Watt steam engine and so on. But I think that was one of the innovations that Watt had was this idea of governors. Now I know James Maxwell picked that up and has a paper he wrote. He didn't write that many papers and they were pretty hard hitting. But he wrote one called On Governors. And I'm pretty sure that contained some sort of early control theory kinds of kinds of methods that must have been written in the 1840s, I would guess 1850s maybe, I'm not sure. In any case. So those kinds of things were around the sort of mechanical governor devices were around then. Wiener famously worked on an anti aircraft gun that used those kinds of things in World War II. And I think really kind of got more into the, the electronic version of that kind of feedback. I'm trying to think about other examples of that type of thing because I think that the. Let me think about this. The amplifiers, electronic amplifiers that came into existence in, let me see, in the. Originally. Well, let's see. The vacuum tube was invented. Well, There were the 1920s and 1930s, I think was when the first kind of. Now there's something I'm confusing in my history here because for radio you need amplifiers. And there were. Oh yeah, that's right. There were crystal amplifiers, first of all. But I'm now little bit confused about how that works because hertz in the 1880s had 1890s maybe had demonstrated kind of radio transmission. I mean, Hertz, Heinrich Hertz had this idea, okay, we've got Maxwell's equations for electromagnetic field. That implies that there must exist these electromagnetic waves. That was known. And then Hertz said, well, let me do a physics experiment and see if I can pick up an electromagnetic wave generated by a spark here, pick it up somewhere else. And yes, he managed to do that. People asked him famously, you know, is there any use for this kind of physics experiment? Oh, no, he said, no, I don't. There's no use at all. Well, of course, that turned into radio in the hands of people like Marconi, who developed its kind of large scale commercial applications. But any case, the amplifiers. Oh my, that was invented. I just wrote a little bit about this chap recently actually, the inventor of the triode. Oh my gosh, the person who founded RCA Radio Corporation of America and. Oh, I'm blanking on the name. But in any case, that person strangely showed up in my recent writings because he was a student of Josiah Willard Gibbs, big wheel in thermodynamics in the late 1800s and so on, and professor at Yale. And that was one of his few graduate students. Was that person. In any case, that was. I think by the time you have electronic amplifiers and so on, there is sort of a feedback loop in those electronic circuits. That's another example. The whole idea of sort of the importance of feedback. I mean, Ouino is very big on promoting that then, in terms of sort of feedback as a mechanism for everything in the world. The whole system dynamics development, particularly around Jay Forrester, among other things, the inventor of magnetic core memory. Long time MIT person. I met him a few times. He was very big on the whole idea of system dynamics and this whole idea of sort of feedback as a key feature of sort of general systems in the world. In fact, I think out near where I live in Concord, Massachusetts, there was sort of an effort for quite a while to teach system dynamics in K through 12 schools as sort of key ideas for understanding how the world works in terms of these kinds of, you know, a series of feedback loops and so on. I don't know how. I mean, I think that whole enterprise of sort of finding these global kind of sort of loops for how the world works, which revolved around some of these economic models in the 1960s, didn't really pan out as well as people had hoped. And it hasn't really developed as strongly as might have been expected. There's a question here about, from Quinn. How are the history of education and programming connected? When did degrees in programming become significant? Oh, that's an interesting question with a lot of modern tentacles, I have to say. Look, in education, the sort of the codification of what's worth learning had there were versions of this in antiquity. I mean, the scribal schools, for example, in Babylon, where people were being taught to be scribes and to learn to write. I think once you'd learned basic writing, there were like five different kinds of things. You also learned, whether it was astronomy or astrology or whether it was something else. There were things you would write about on the little tablets you were using. And then by the time of Plato's academy and things like this, there was some codification of sort of what was worth learning. I think the. What is it, the trivium or something, and the various different combinations of rhetoric and mathematics and so on and logic managed to make its way in there. And I think sort of through the Middle Ages, there was a pretty well defined set of things one learned, at least in the Western tradition. And some of those revolved around sort of read the Bible, read Aristotle. Aristotle was sort of an early encyclopedist, in effect, having written about things from kind of the sea creatures to a theory of physics to kind of the idea of logic and so on. He really covered, you know, his works were sort of encyclopedic works. And some of what he. Much of what he wrote was sort of somewhat factual and not a bad summary, but he also kind of segued into the much more theoretical and hypothetical. And some of that is, you know, to modern eyes, just utterly wrong. I mean, the views of kind of very much anthropomorphizing nature, in many ways of nature abhors a vacuum and so on, these kinds of ideas of what nature wants, which seem out of place in much of modern thinking. And also, Aristotle didn't have the idea of connecting mathematics to nature. In fact, he didn't even have the idea of connecting logic to nature. Had he had that idea, that would have been something much closer to things. I've tried to do in sort of thinking about computation as models of nature, but he didn't do that. For him, logic was a kind of a codification of rhetoric of the ways that arguments got made. But any case, the sort of tradition of teaching continued in that way. There were, it's worth remembering that universities in the west, you know, which originate in the 1200s in Bologna and, and Paris and Oxford and so on. Those universities were mostly for training for the church. And that was really their main, you know, it's. You learned the things that were relevant for that. There were also quite separate from the sort of the scholars at universities and so on, who often ended up going from town to town because they were sometimes became not well liked in the local area. Which is why an awful lot of ramparts and things on early universities that make one feel like the academy is under attack. But in any case, I don't really quite know what. Well, in any case, the separate story of the sort of the politics of academia from the 1200s on, so to speak. But one of the things there was quite separately from the academic world and the kind of church training type world was the merchant world and the world of guilds and the worlds of craftspeople and tradespeople and so on. And I think somewhat separate from that again was the banking world. But this idea of merchants and merchants who dealt with money and so on, that was an area. And there were people who made a living essentially teaching merchants, for example, how to do mathematics. Like that was what Fibonacci had been doing later on in English, I think the first book that was sort of the Secret Art of Reckoning of Calculating. A person called Richard Record was the author of that. And it's interesting to see these things because there have been all these fads and math teaching about what's the right way to teach long multiplication or whatever, what's the right way to teach these different kinds of things back in the day. Those fads were alive and well in the 1600s and so on. Richard Record was out talking about the rule of Z's, I think, which was, you know, you had this whole scheme, or you can see in his book, has this whole thing where you're calculating by sort of putting numbers in some particular pattern and then doing this thing and magically the result pops out and you can you, the merchant have an advantage over the other merchants because you can calculate faster. I mean, it's kind of. It's quant finance from the 1600s, so to speak. But at that time it was Like, I don't know, calculating interest rates and things of this kind of. But the training of merchants, so to speak, and learning about how to do calculation. Quite separate from the universities, there were things, the astrologers who were sort of segued into the astronomers again, yet separate again. And insofar as their work was used for navigation yet separate again. So this idea, now it's worth remembering that sort of the whole kind of the streamlining of sort of learning at universities, things like law came in, medicine came in. That was in some places that was slowed down by, for example, bans on human dissection in England, as opposed to Scotland, that kind of slowed down the sort of ingestion of medicine into universities, at least in that place for that time. But then gradually these things kind of came in. Now, by the time Galileo, for example, was a university professor, and he was a sort of a mixed. I think he'd done medical stuff and he did mathematics. His father had been a music professor. So by the 1600s, there was a certain sort of, you know, tradition there of things being done and taught at universities. You know, Newton was also a professor at Cambridge University of Mathematics. But, okay, but so there are these traditions of teaching at universities. By the time there started to be sort of organized K through 12 schools, I think the first of those that one knows about were. Well, there's certainly one in England that dates to the 1600s. What is it? Christ's hospital school or something like that. Famously, Newton was one of the consultants who worked on curriculum for that school and suggested calculus, I believe, as one of the things to teach there. But there have been these traditions, like the high school I went to, Eton, was started in 1450, I think. But it was for the, you know, for the education of poor scholars, so to speak, and paid for by the king. When I was there, the. The. The scholars were still getting supposedly a piece of the endowment that had been put down in 1450. And there was this. There had been a tradition that on a particular day they would give the scholars their little piece of the endowment for that year. And I think back in the early 1900s, there had been a choice of you could either get threepence, three pennies or a pig and. No, actually, much earlier than that. Sorry, much earlier than that. That had been the threepence or a pig was the sort of choice for the kids. And I know the story that was circulating, at least when I was at Eton was that back in the. Must have been what, 1920s, perhaps, two of the students who were There as scholar kids were, yeah, I think Harold Macmillan who later became prime minister in England and John Maynard Keynes who became a well known economist. And the story which, who knows whether the story told by kids, passed down by generations of kids is accurate. But the story was that everybody was confused at the time about how could it be the case that there was a choice between threepence and a pig, but yet by that time a pig cost a lot more than threepence. And of course Keynes was keen to, to note apparently according to the story that yes, well, there's this thing inflation that happens in economies. And perhaps at that point as a 13 year old or something, he might have given his explanation of why inflation happens which may or may not have developed as time went on. But any case, by the time, I mean just to give a sense of Eaton for example, taught classics, Latin, Greek, taught things like that, mathematics education at Eton had been pretty much non existent. It consisted of reading, Euclid and Greek. And that persisted right up until the 1950s. And that was kind of. So you know, mathematics education wasn't really much of a thing there I think. But you know, that was. Eton was an unusual, you know, one of the unusual so called public schools where kids would go to be educated not at home but in public so to speak, at an outside school. Now of course that all changed. For example In England in 1870 there was the. An Education act which sort of brought in the idea of what we would now call public education. That is sort of the government provides schools for everybody to go to. And at that time there's sort of a question about what fields would be included in public education. And you know, the three Rs, you know, reading, writing, arithmetic were kind of the big things that yeah, writing doesn't start with an R I know. With sort of the big things that were being taught. And in a sense that sort of curriculum setup has persisted in the K12 world until today. And I think one of the things that I find really interesting is that computation is the first really important new idea that has come into existence, come into the world since the time when public education was developed. And sort of how that merges is really an interesting question. But then, so, okay, the question was asked about programming education. What a mess that is. So at. Well, okay, so when computers were first being built in the 1950s, for example, you know, IBM, which was building a bunch of these computers would provide programming courses and people would do them. People who'd studied mathematics, chemistry people would then do these programming courses and that's how they learned to program. And the early books of Fortran, programming and things, they came out of those courses. The idea that there would be sort of an academic subject of learning to program, it was seen much more, I think, as a trade, an intellectual trade, but a trade nevertheless, rather than a sort of academic kind of thing. And very few universities had, you know, some universities got computers, and by the time they had computers, they had sort of a computer center. And sometimes there would be things that sort of revolved around that computer center. And I think, I mean, one could talk about individual universities and how they kind of got online with having some sort of computer activities. But the idea of a kind of computer science as a field, really what had happened, you know, it sometimes, it occasionally grew a little bit out of mathematics, but mathematicians usually pushed it aside. That's certainly what happened at, for example, the Institute for Advanced Study where I worked back in the early 80s. John von Neumann had built a computer there in the 1950s. When he died in 1957, I guess the mathematicians at the institute, he was officially there as a mathematician, were like, let's get rid of this computer. It's a big messy thing. And Tom Watson, then CEO of IBM, sort of kindly offered to get it taken away, so to speak. And von Neumann had been a consultant for IBM on computer design for a while, in any case. And by the way, I can say that I was at an event with some mathematicians and some people who'd gone to IBM from von Neumann's computer project. It was sort of a reunion for some of these people back must have been 1984, 85, something like that. And I kind of initiated the questioning of what really had the mathematicians thought was going to happen with computers back when von Neumann was around. And there was, let's say, a vigorous discussion about what their expectations had been and that they hadn't really been as hopeless as, as, as people had made out. But any case, there was, you know, computers, they sort of arose sometimes out of, a little bit out of math, but not so much more often out of electrical engineering, where people were thinking about the actual building of the computer. Oh, you're going to run a computer, it needs electrical engineers keep it running. Sometimes out of business schools where it was kind of more a. A story of kind of, well, computers are going to be used in the workplace. They're used for doing kind of financial calculations and so on. So that's a thing relevant to business students, things like that. But it's sort of a messy history. And the Thing that became computer science in universities really had originated, I think in probably the 1960s or so, a lot of theoretical computer science. Different places in different ways. Like, you know, MIT had really, I think that got, kind of got launched with the lab for computer science, which was from the early 1960s, and then the AI lab. These were both big government contracts that sort of caused an effort in these areas to get planted in that case at mit. You know, Harvard just down the street, didn't have a computer science department for the longest time. I mean, I remember when that university was trying to hire me back in the early, early 1980s, they really didn't have, you know, they had an applied sciences area that was, you know, in which there was sort of a few people, in fact, at least one of whom is still there, maybe two even, who were sort of computer science professors, but not even completely. I think they used that term. I think they were not mathematics professors, but they were very theoretical. And actually there have been other people there who did theoretical work in computer science. But any case, that was very much of a. Computer science is a theoretical area. You know, they've been worked on a finite automata there. And again, now I'm. I'm. It's. The history is always confusing. There was another person, Howard Aiken, who had been there in the 1940s, working on kind of a mechanical electromechanical computer that I don't think connected. That was part of the engineering effort. And I don't think connected to the work that was done on what became called computer science that was quite theoretical. But this was typical of many universities that there were sort of theoretical computer science. There were a set of courses people did. This was true in the 1970s and so on, where people would study finite automata, they would study compiler design, they would study logic, Boolean algebra, things like this. This sort of was computer science. And I suppose the most of the work that had been done on algorithm development, the sorting algorithms, Quicksort and things invented at companies. Now you can kind of see a bit of a snapshot of the history of computer science in Don Knuth's Art of Computer Programming series of books which he kind of. Whose design was set down, whose kind of architecture of those books I think was from 1964. And it was planned as a series of eight books. And the. What is it? I think there's one about sorting and searching, there's one about numerical algorithms and so on. And this kind of was the idea of computer science. Now Don has now reached volume four out of his eight volumes, some of the subsequent volumes were about languages in the sense of parsing, compiling, you know, finite optometer, things like this. It is a little bit. I mean, I consider Don Knuth a friend, and I certainly am both inspired by and horrified by his effort of building this sort of the definitive scholarly work on computer science started so long ago. And he's now at volume four, and I think even volume four keeps on expanding into more and more subparts of volume four. And I wonder whether I need to ask him whether he actually has even drafts of volumes 5, 6, 7, 8. I think he did say to me recently that the field had evolved a bit and maybe he would change his plan a bit for the other volumes. I can say that when I was at Caltech, actually, this is late 1970s, and I decided when I was going to build my first big computer system, SMP, that was in 1979, I decided I better learn some computer science. So I went to the Caltech bookstore and I thought, I'm going to buy all the books on the shelf on computer science. And it was a, you know, a small, you know, a foot and a half of books maybe. And I sort of read through them over a weekend, so to speak, and they were. That was sort of a. That was computer science. And it was all theoretical stuff about compilers and, and so on at that time. So, you know, the early education of computer science in universities really was of that kind. And even when I started our company in 1986, it was hard to hire people who'd come through computer science because they knew a bunch of this theoretical stuff. We didn't really need that theoretical stuff, although I thought it was interesting. I'd worked on things related to that myself, but it wasn't what we needed for software development. And then this huge pivot happened in the 1990s, I guess, when there was a big pressure of students who wanted to study computer science because they knew that there were jobs to be had in programming this huge pivot as universities, you know, started hiring computer science faculty in droves. I mean, I could tell you about many different universities that really didn't have any effort in computer science back in the 1980s. And, you know, then that sort of all developed in the 1990s and beyond. I think that. And then the question was, well, how do you teach? You know, what is computer science? Well, a lot of computer science, as people want to be learning it, is about programming and about how do you program? Well, it turns out a lot of good programmers didn't go to computer science school and you know, so it's a very strange thing that it's kind of like, you know, lots of good actors didn't go to acting school either. It's, it's one of these things where it's not obvious that sort of knowing the, the kind of the, the, the sort of the, the, the, the, the kind of the, the template for how to program and learning that in a kind of mechanical learning kind of way is not necessarily the best thing. But anyway, that's been a, it's been a big thing and that's been sort of a huge sort of effort of universities is to train all these programmers because after all, people say programming is this job that is going to be a nice, stable, well paying job and so on because the world always needs more programmers. Well, of course that was a great idea until 2023. And for myself, I've spent the last 40 years or more trying to as much as possible automate the process of programming. That's why our company has been able to build as much technology as it has with as comparatively few people as we have, because it's, we've automated many, many layers of what amounts to programming. And that's what sort of, that's one of the ideas of our computational language is, you know, make it so that it is from sort of human thinking. That's where the language is kind of connected. It's kind of this general way of formalizing things which by the way happens to be implemented by computer. And. But it is not something where it's kind of the low level. You're taking all the steps according to the way you want the computer or the way that the computer is fundamentally set up. And as I was explaining kind of the things that came from Babbage and Lovelace and you know, the very early computers, Atanasoft and the ENIAC and all this kind of thing. You know, much of the thinking about what a programming language should be comes from the thinking about those very early computers. There are these operations, the computer does them. We're going to write down the recipe for what the computer should do. My approach in thinking about computational language has been a different approach. It's been how do we think about things, maybe in mathematics, maybe thinking about the world in general. And how do we write that in a formal way, much like logic as a formalization of arguments. This is sort of a formalization of things you want to have happen in the world, so to speak. How do you make a language like that? And then it's the job of our team to kind of build all of the, what you need to achieve the things that you can describe in that computational language. Well, in any case, until 2023 it looked like a pretty good bet to just, you know, you learn your Java programming, you can be a professional Java programmer for decades and all is good. Of course, now people realize that LLMs can write low level languages. They can write Wolfram language code as well. They do a lot better at writing Wolfram language code than they can at these lower level languages for very practical reasons right now to do with context sizes and so on, but also because, you know, in Wolfram language, everything they learned from all of that general knowledge on the web and so on that involves words and such like that is sort of encapsulated and condensed in Wolfram language where we're using words to represent these sort of computational operations. And it's something where it's realistic for an LLM to learn that well and so on. But the fact is when you're building a substantial tower of functionality, you can't expect that the things you've just described in pure language to an LLM will be correctly represented. And that's why it's become very clear that Wolfram language is this great kind of way of, of you look at what you describe something to the LLM. It produces a piece of Wolf language code. You can read it because it's a language intended for humans to read as well as computers. You see what you've got, you decide, okay, that part is good. That's a solid kind of foundation brick. Now we can build a series of, you know, build a big tower on top of that. And that's, that seems to be a really good workflow that we're just learning now. But so then the question is, okay, we've got all these sort of programmers and who are learning these low level languages and what's going to happen to them? Well, the answer is they're going to get automated away. And in a sense that is absolutely no surprise to somebody like me because that's the path we've been on for 40 years of building these layers of automation. Now what does that mean for universities that have tooled up to program to, to program the programmers, so to speak, to provide all of that kind of trade school education? In a sense, much of that education is a bizarre kind of, you know, it's sort of a plug in to the university in many ways because the kind of, the, the kind of the flow of learning in kind of just learn to program is a bit different from the flow of learning in some of these. More, less trade and skill oriented and more academic and intellectually oriented fields. Now, you know, like the scribal schools of ancient Babylon, the, you know, the scribes learned how to write and then they had to figure out what were they going to write about. In computer science departments there has been a certain amount of sort of attaching these areas, like, I don't know, cryptography, machine learning, What are some others? Oh my gosh, I'm blanking on. You know, maybe a little bit of data science, although that's had a complicated history at universities. Data science has sort of in some cases grown out of business schools. Statistics departments, which have kind of budded off from math departments, sometimes from, from kind of a social science area where people were doing sort of, kind of statistical analysis and social sciences and things, different kinds of places. And quite often data sciences has sort of emerged in business schools. But that's again a sort of a separate tradition from the learn to program computer science tradition, which is yet a separate tradition from the theoretical computer science tradition. But there's been this question of what really is computer science. Now the thing that is very clear is that there's a kind of computational X for all X. There's a computational way to think about all these different fields. I mean, the way I see it these days, sort of a computational thinking about a field is about formalizing that field. It's the same as what logic did for argument, so to speak. It's a formalization of whatever it is, archeology, zoology, whatever it is. It's a formalization which happens to have the great feature that can be assisted by computers. Once you formalize things, then your computer is off and running and can help you. And so I see this as being kind of this whole idea of formalizing fields, formalizing one's way of thinking about things. This is a tremendously general thing and it has little to do with kind of low level programming. And so the thing that I think is perhaps computer science somewhat, I don't know, it's has become identified with this learn to program tradition. Computer science as an academic intellectual area is something rather different from that. But the learn to program thing is a, and learn, you know, methodologies for managing large programming software, things and so on. That's in the kind of learn to program strand which is now what people call computer science. I kind of think there's a computational X cx, not CS that is kind of this whole learn to Think formally, learn to think computationally. And it's necessary to know how to formulate things in a kind of formal computational way. Even if your goal is even if you're basically going to tell an LLM to write all the steps of the program, or you might write a little piece of orphan language code, then you plug it into something LLM has produced for you and keep going. It's really a tremendously powerful possibility. It's something that will be the future of kind of the way people think about kind of this is formalizing things is the way you build big towers of ideas. Without that, it's kind of like always at the always as kind of a surface level thing to formalize is to make sort of a solid block that you can build in a big tower. And that's what in mathematics has been done in a particularly successful way. It's something that we are getting to do in this computationalization of all these different fields. So it's a very interesting question, what will happen as computation changes its character away from the need for large numbers of low level programmers? Because that is something that got automated away, or is going to get automated away just as assembly language programming long ago got largely automated away by compilers from C and other languages. And so the good news about sort of what can be done with LLMs and computation is many more people can make use of computation. It's a great broadening of the access to computation. And that will be true at universities as well as other places. There are many departments and people and professors and so on who will now routinely be able to do things computationally and formalize what they're thinking about in computational terms and get a computer to help them than were possible before. That's the good news. The bad news is the demand for straight sort of trade like programmers is going to go down. And this big sort of bubble, I think it will be seen as of, you know, everybody wants to go to school to learn to be a programmer. That's probably over or will be over. And I think that the. So sort of it's a challenge at this point because more people want to know about kind of the ideas of computation. But the kind of mechanical teaching of, you know, learn to write, you know, loops in Python or something is just going to go away. I mean, it's just that's, that's sort of not, not going to be a thing going forward except for a small group of people, just like there's a small group of people that absolutely know an assembly language and program in IT and so on. But. And that's necessary for kind of the big stack of technology that we have in the world. But I think so, you know, it's a very interesting question. What will happen, for example, at universities as these shifts occur. Now there's also the K through 12 world, and the K 12 world has a terrible history in terms of programming because there have been many rounds of efforts to really teach coding, programming, whatever you call it, in the K12 sector. Each one has kind of sort of largely failed. I think the first serious one was in the 1960s with basic and John Kameny at Dartmouth, mathematician, who had this time sharing system and developed this language called basic, which is quite good. And that was a sort of an early way people learned some programming. Then there was kind of a more sort of a bring it to even earlier ages. This was. Well, that was programming sort of at the college level. That extended a bit to some high school students in New York City and other places. Then I think Also in the 1960s, Seymour Pappert worked on sort of using computers for younger kids, invented Logo and you know, the turtle moving around the screen and so on. That was kind of based on a turtle that a person called Gray Walter had made in the 1950s as an example of robotics and feedback control actually and things like this. But that was another initiative which got some, some momentum and continues to have in the form of Scratch and other things that have come from, from Logo. But it's not really quite the same. You know, I think the transferability of the skills that you learn from scratch to sort of serious computational thinking seems to me a bit unconvincing, was more convincing in days when the average kid had never seen a computer. And the idea that you could get a computer to do something you told it to do was very novel. But that idea is obviously not novel to any kid who's been born in the last 20 years or more. And so I think the thing that. Then there were these different waves of, you know, let's teach. Oh gosh, I can't even remember them. There was a. Oh, there was a Pascal wave, there was a. I think there was a. Was there a C programming wave? I'm not sure. There was a Java wave, there was a JavaScript wave, there's a Python wave, there's a. Oh, what other ones? There's, you know, there are little wave mini waves of. I know Swift, I think has some push in that direction. Lots of different things. It tends to be the case that very few of these, you know, first of all, it's hard to write an interesting program in raw Java, let's say. And the programs tend to be very desiccated. And kind of one of the takeaways for kids ends up being, oh, gosh, this coding thing is really dull. Just like kind of mechanical math is really dull. Now there'll be some subset of kids who say this is great and they're going to become software engineers, whatever else, working and writing Java code, for example. But for the vast majority, it's like, why am I doing this? It's incredibly mechanical. It's really boring. And I think the thing that we've seen with what's been done with, you know, with Wolven language and so on is that it's a place where kids can use the exact same technology as the fanciest, you know, research scientists and so on. Use. But kids can also immediately, because it's a computational language that talks about real things in the world, kids can immediately kind of look at things with a computer that are things they care about. Whether it's geography or whether it's music or whether it's whatever else. These are things that the language knows about. It's not just dealing with arrays of numbers and things like that. It's not, you know, it knows the words in English. It's not, oh, you have to find a dictionary to import from somewhere, et cetera, et cetera, et cetera. It's. And so that makes it, at least in my observation, just vastly more compelling as a, as a medium for teaching. And I think, you know, a lot has been done on that. Vastly more could be done. I think that the thing that is, I've been interested in, well, okay, so, so that's kind of a, a, a different play, so to speak, on what you can teach. But what's tended to happen in using low level programming languages for teaching is that to make them interesting, you have to kind of embed them in things like a game environment, at which point you are barely talking about the actual programming language. You're really talking about the particular setup of this game. And it becomes something much more like Scratch, where you've got just these particular things moving the cat around or whatever else it is, which are, I don't know how related they are to sort of true computational thinking. To me, computational thinking is all about how do you take the things you are otherwise thinking about in the world and, and represent them in some formal way. And I think that's really different from what you get, given that you are constrained by the particular operations that you've been provided by your sort of low level programming language. That's a different way of thinking about things than let me take the things I'm really thinking about in the world at large and put them into sort of a formal structure. Now, you know, when you look at what people actually do in things like Scratch and so on, you often find, well, they're, they're doing things that are like representations of pictures and they're sort of animating some picture or something like this. In a sense, a large part of that story is kind of the picture and a much smaller part of the story is the formalization of the process and so on that goes into it. Let's see. Well, I think, okay, so there's a question about what will happen with kind of the new age of AI and so on. And certainly what seems to be the case. I mean, it's really quite remarkable how well LLMs can do things like explain what went wrong in a piece of Wolfram language code. And I fully expect that the sort of personalized education, writing computational language will become a thing and that will again broaden the set of people who can be exposed to this kind of computational way of thinking about things. I think one of the things that's sort of a challenge, which I probably will end up having to work on, is, okay, you're going to tell people about how do you think about the world computationally? What does that actually mean? It doesn't mean teaching for loops. It doesn't mean talking about variables. It means sort of what are the things that, I don't know, somebody like me who spent their life basically working on sort of computationally thinking about the world? What are the kinds of things that one knows that are worth kind of explaining to other people because it allows them to be able to make sort of a computational way to think about the world, a way to formalize what they see in the world and to kind of build from there. And I think that's an important definition. Now, how that plugs into the existing world of university education, K12 education, that's a horribly complicated challenge. I think the specific question that was asked here about when did degrees in programming become significant? You know, I think that's one of these things where there was a period of time for many kinds of degrees. There have been these periods where that's the hot thing to have is a this or that degree. There's always a tail, it always lasts, you know, But a degree in programming which isn't, you know, it's not like a. It's actually funny that that hasn't developed. You know, it's like you can be a Master of Public Health or something, or you can be a, you know, and that's a different degree, designation, name than, you know, a generic master's degree or some. Some such other thing. I do find it amusing, actually, now that I think about it, that there is no, to my knowledge, professional certification of I'm a, you know, a BCS or something that is sort of I'm now. And perhaps that's a consequence of the fact that, thankfully, the idea of sort of certifying programmers, which was floated in the 1970s and early 1980s, didn't come to pass, because I think it's a deeply undefined thing. I mean, it reminds me of Register your AI. What's an AI? I mean, you know, it's. It's like saying, oh, you've got to, you know, some government, you know, some place where it's like the government insists you register every AI, just like you register every cat. A cat is a much better defined object than an AI. And exactly what that means is quite unclear. All right, I should probably wrap up in a moment. You guys are asking just all sorts of interesting questions here. There's a question from Des about Wittgenstein and language and have any relevance to LLMs and AI. I know probably a lot less about Wittgenstein than I know about AI. So. But I think this kind of. The idea of the extent to which language is defined by thought and thought is defined by language, so to speak, is an interesting one. And in a sense, the LLMs very much do the kind of linguistic philosophy kind of, you know, thought is defined by language type of thing, because they really are a language model. They're a model in which all they know is how to complete sentences in the way that they are typically completed. Now, the thing we realize upon looking at this is that's kind of what Aristotle knew about and what caused him to invent logic. And there are, no doubt I've written about this, this kind of idea of semantic grammar where there are these kind of forms of meaning that are abstractable from natural language. But as it is, the AIs just know about how to complete pieces of natural language. And that's their whole story. And they very much give evidence for the fact that you can get a long way by just thinking in terms of language, so to speak. And what you can't get to are certain kinds of things that involve deeper computation, that involve These kind of whole stacks of computation. That's not something where just knowing this is the way to complete this sentence, that's not really enough for that. And in fact, in the case of AN LLM Like ChatGPT, the sort of the outer loop that says, now you put down the next token, now you put down the next word, whatever it is, that outer loop, which seems almost trivial because the main machinery is the neural net, the 175 billion weights that are all computed with every time you figure out the probabilities for new words. But turns out that outer loop is pretty important. And it is, I think, the development of that outer loop, the further development of that outer loop, in a sense, the, you know, a serious deep computation is all outer loop and much less inner, you know, flow through a neural net. The operations inside are much, in a sense, simpler, better defined, but there's a lot more, you know, there's a much bigger kind of sort of sequentialization or, you know, longer chain of those operations that are done. Whereas in an LLM, it's kind of like the big effort is making putting out each token and. But there's this sort of outer loop that's defining which tokens should be put out. And when an LLM, you know, calls a tool like the wolfram plugin for ChatGPT, what's happening is that the LLM is actually just generating a piece of language, like stuff that you as a user don't happen to see, because the front end of the whole thing thing. But for the language model, it's just like it put down something saying, call the Wolfram plugin, and then goes off, it does a computation, then our plugin writes back a piece of essentially text, which becomes the next thing that the language model sees. It reads that, and then it doesn't show you any of that stuff unless you open those little boxes in the user interface. And then it keeps going and makes use of the results it got. But this idea, I think we're beginning to see in much sharper form, this kind of idea of what language is versus what thinking is versus what computation is. And I think that really is all clarifying. And I should learn more about what Wittgenstein actually wrote about those kinds of things. And I should wrap up here for now. Thank you for all these interesting questions and comments. And I got to go to my day job and do another live stream here, so thanks for joining me and bye for now.