History of Science and Technology Q&A (February 28, 2024)

Sam. Hello, everyone. Welcome to another Q and A about history of science and technology. And I see a variety of questions here. I also notice people seem to have noticed our series of posts on Instagram and X and so on about various historical, scientific and technical figures and asking questions about what would various different people have done with our technology stack and how would their sort of progression of work have been different? And I see several questions here. One about Aristotle. All right, let me say a few things about Aristotle. I mean, the thing that I suppose I find striking about Aristotle is that he was sort of an information organizer. I mean, in a much different period of history, he would have been some kind of encyclopedist. You know, he was fond of making lists of things, causes of things in the world, things, types of animals, you know, types of argument and so on. And I think more than anything else, he was sort of a. There's all this information about the world, let's try to categorize it and organize it. And sometimes he was able to sort of identify these very structured ways to organize things, and sometimes he wasn't. So one of the things that he got a certain distance with was organizing arguments and writing down syllogisms and these forms of valid kind of statements about things that turned into logic. I mean, the actual development. I mean, what Aristotle had was things like all men immortal. Socrates is a man, therefore Socrates is mortal. That's a particular form of argument. And those got categorized, the forms of syllogism got categorized by the time of the Middle Ages, maybe earlier than that. But people was part of sort of standard education, logic was part of standard education. And people were memorizing these forms of argument, just like people memorize things in school today. In those days they were memorizing these patterns of valid argument. I think two of the famous ones were called Barbara and Selorunt, and those are essentially acronyms for the pieces of the construction in Latin, I think, of sentences that correspond to these forms of argument that all got much more mathematicised in the 1830s by George Boole, who kind of realized that you could make sort of a generalization of algebra that covered these kinds of logical propositions. I mean, the main thing was that sort of and is times that. Well, first of all, false is zero, true is one and is times. So you need both X and y to be non zero. For x times y to be non zero, Then the only big glitch is, or you might think that was x plus y. But the problem is if both X and Y are true. That's one plus one, which is two, not one. And so to make Boolean algebra, you have to say we're going to have one plus one being equal to one, right, Rather than being equal to two, and so on. But that was sort of a mathematicization of logic. What Aristotle had developed was this kind of more classificatory form of logic. Just saying these are valid types of arguments. And in the time of the Middle Ages, the kids were just memorizing. These are valid arguments, I don't think. I think education in those days was a very rote memorization kind of thing. And this idea of sort of let's figure it out was more, let's remember, does it follow the pattern of one of these kind of standard syllogisms and so on. But I think for Aristotle, Aristotle kind of had the pre version of sort of this idea of computational language, the idea of formalizing everything in the world. But the only medium in which he could formalize things was, was essentially inventing categories and giving them names in Greek or whatever and being able to describe them. So I think he would have had a great time, I think, in modern times with trying to figure out some of the kinds of things I've been interested in figuring out, for example, about how to represent the world computationally in a sort of structured way. And I kind of feel like some of the things we're doing right now with, for example, our symbolic discourse language project, trying to have a kind of precise, symbolic representation of the kinds of things we talk about in normal everyday speech, including things like human mental states and so on, that is what Aristotle had kind of started on. He got as far as doing logic for arguments. He had some notions of categories and so on of different kinds of things. In modern times, that's kind of what. It's the extension of what he was trying to do. Now, in a sense, the fact that the LLMs do so well in making kind of meaningful text is an indication that there is some kind of structure there that is actually not even potentially that hard to discover. There is a. A well defined, narratively describable structure that in a sense, once we really have it nailed down, it might almost be, well, Aristotle might have been drat. I should have been able to see that. I just didn't have LLMs. I didn't have orphan language. I didn't have computers. And so these are not things I could have seen back 2,400 years ago or whatever. So anyway, it's a little bit on. On Aristotle we can kind of talk about different kinds of characters and what they would have been able to see and not see at that time. I mean, Archimedes. I have to say that I've always wondered to what extent Archimedes was sort of in the same business that we're in today of providing tools for computation. I mean, I've kind of wondered. The Antikythera device, for example, the one example we have from antiquity of a computational device, it's a gear cog based thing that computes at least approximately things like when eclipses can happen and so on. That's a thing that comes from a little bit after Archimedes actually, probably. I mean, it's not really clear. It comes from a shipwreck that was discovered around 1900, but the shipwreck happened 2000 years earlier. But it's not completely clear whether it's 2000 years or 1900 years or whatever earlier. But the question of how did. This is one example from antiquity of kind of a computational device. It happens that that device probably was connected with the city state of Syracuse in Sicily, which was where Archimedes lived. So it's sort of some slight connection maybe to Archimedes and his tradition there. But I've kind of always had the whimsical view that Archimedes might have been running a little company, so to speak, that was making computational devices in his day, so to speak. I mean, Archimedes had some very clever, particularly geometrical kinds of arguments for things. He had sort of a lot of pre calculus kinds of results that were purely geometrical in origin. And he also had things where he was interested in kind of making structured ways to describe things of the world. I mean, I think he was sort of a structured thinker. And for example, he has a famous little piece called the Sand Reckoner, which is trying to work out, for example, how many grains of sand would fit in the universe. But for that he had to invent kind of a structure for describing extremely large numbers. And that was sort of a challenging thing because he didn't really have scientific notation. He didn't have a lot of the things that we have today. But he had sort of a way of trying to build up what might be thought of as a symbolic representation for very large numbers. It's interesting in Wolfram language, for example, we can deal with very large numbers, but there's a limit on the numbers we can deal with because we're fundamentally representing numbers in floating point notation where, well, for an integer, we're just saying here are all the digits in base 2 or base 10 or whatever. And it's just a big long list of digits. But if we want an approximate number, we're saying here's the Mantissa 3.78 and then times 10 to the sum power. Actually, internally we're representing it as times two to some power. But there's a question of do you need sort of arbitrarily big numbers or not? Right now we can have numbers up to size two to the two to the 64. So that's a very big number. That's. I mean, remember, the number of particles in the universe is around 10 to the 90th. So that's just. And that is absolutely infinitesimal compared to 2 to 2 to the 64. In our physics project, for example, we kind of have this vague guess that there might be 10 to the 400 atoms of space in our universe. If we look at the whole rulead of all possible evolutions, then we're looking at more like 10 to the 10 to the some number of hundreds of possibilities. And that is a bit more comparable to the maximum size number that we can represent in Wolfram language. So we probably could represent everything in the universe, including sort of the full rule out of all possible computations or possible histories of the universe in the numbers that we have. But we can certainly imagine, as Archimedes tried to do, even bigger numbers that are sort of bigger than our representation. And for that, we can imagine sort of a tower of representations. The 2 to the 2 to the 2 to the 2 To the 2 arbitrary number of times. That's a tetration operation. That's sort of a generalization. Just as multiplication is repeated, additional powers are repeated multiplication, tetration is repeated powers. And that allows us to represent very, very big numbers. And then we can imagine sort of developing a calculus for combining numbers represented symbolically in that kind of way. But Aristotle was. Archimedes was sort of going in that direction with this sand reckoner kinds of things, I think. Interesting question is to what extent? Well, that's a few thoughts there. Let's see. Calais asks, what would Ada Lovelace have done with current computing? You know, Ada was doing her things in the 1840s and had sort of understood this idea that you should be able to make a universal computer. Famous quote from her was talking about sort of the programmability of this mechanical analytical engine concept of Charles Babbage's. He didn't quite get to build that. He got to build a difference engine, which is a sort of simpler version of that. But the analytical engine could have a program for what operations it could do that was specified by a punch card. And the punch cards had been invented by Jacquard back in 1800 or so as a way of specifying the kind of weaving patterns to be used on a loom. And so when you're doing those weaving patterns, you're making sort of art that would go on woven pieces and so on. And Ada sort of says, well, you know, the analytical engine will be able to weave algebraical patterns as the Jacquard loom weaves patterns of birds and flowers. So she had kind of the idea of sort of this representing lots of things in the world in this kind of computational way. That was sort of a thing that I think she did in some sense fundamentally understand. And that's at some level, that's the beginning of the story of universal computation. It's the beginning of the story of things I've tried to do of sort of representing the world computationally. In the end, discovering that sort of physics and the fundamental sort of structure of the universe is ultimately computational. It's sort of computational all the way down. That was the path that got started in those days, I think, at the time. There is a lovely letter that Ada Lovelace wrote to Charles babbage sometime around 1840, something in which Charles Babbage has been trying to build the analytical engine. He's been trying to raise money from the UK British government to do this. The British government hasn't been giving him the money and he's kind of. He's generally making a big fuss about it. He did get some money, but then he kind of didn't manage the engineers very well. And it's all sort of a bad story. And Ada Lovelace writes him this letter saying, hey, why don't we sort of basically start a company? And she, Ada will be the CEO and Charles Babbage will be the cto. And together they will make essentially a cloud computing system where people make. Where they make some analytical engines. They would have been the size of large locomotives or something steam powered at that time and chugging away computing things. In those days, the things of most interest to compute were things like navigation tables. Charles Babbage was actually involved in a life insurance company. So there were calculations of insurance premiums and so on. These were the thing to be computed in those days. And sort of they had the idea of, let's provide these centralized services where people could send in, we want the senuity table computed, go compute it and the machine would crank up and they get some number of hours of time on the machine and it would be crunching away and a steam powered thing and people would be shoveling coal into it and it would be huffing and puffing away and eventually printing, because that was the output medium that Babbage had, was essentially a printer of things like tables and so on. That was how the difference engine was supposed to be set up. So that was kind of an idea. And it almost happened. I mean, it only didn't happen because Ada got sick. Otherwise it probably would have happened. One would have had powered computing where it would have been, you know, there would have been puffs of smoke from the. Or steam from the steam engine, so to speak. They actually did know people like Wheatstone and so on who were doing electricity and Faraday also who were doing things with electricity at that time. And so they might have been able to actually get it to the point where instead of doing a huffing, puffing steam engine, they had an electrical, a system of electrical switches making the analytical engine. But none of that happened. And I think that the kind of conceptualization of sort of computing as a service was something that Ada Lovelace, I think did have. And had that, had it been modern times, that would have been a thing that, you know, the, the concept of computing as a central way of thinking about the world, I suspect is something that Ada Lovelace would have picked up on quite well. I mean, she was very much a person who liked to think. She would describe herself as doing poetical science, I suppose in those days, the ical ending, like algebraical and so on. I suppose that was a feature of Victorian English that, you know, there are these trends in language and I think the removal of the extra ornamental syllable. There is one that's sort of been a trend that we've seen. And even in modern times that happens that there are words. There's one that I just was doing recently. Oh my gosh. Well, numerical computation versus numeric computation or symbolical computation, which one doesn't say, versus symbolic computation and so on. But any case, I think Ada Lovelace sort of did understand in this sense her poetical science was this kind of way of thinking about the world at a foundational level, about what are the real structures that are, that are involved there. And the translation of that to what we now think of as something computational is something that I think she had sort of begun. So that would be something that I think would fit in very much to today's world. Yes, I mean, it is to say the, you know, Ada Lovelace was something of a kind of a, a, a former day hacker or something. I mean, she, she would tell these kind of very nerdy mathematical jokes about herself and, and, and other things. I'm trying to remember one of them. But. And, and she had a, quite a, A habit of. Well, as I say, of, of using kind of mathematical language to describe herself, you know, to say a little bit about, about Ada Lovelace. I, I've studied her a bit, quite a bit actually. She. Bit of the life story. I mean, she was. Oh, gosh, what was her mother's first name? Milbank was her last name. Oh my gosh, I forget any case began with a. I forget it. The Ada's father was. Was Lord Byron, the poet who was kind of a celebrity of the time. He was kind of the. A top celebrity. I mean, in today's world, poets don't get to be top celebrities as both rap artists who are in some sense the modern poets get to be top celebrities of the day. But he was also sort of a definite kind of bad boy type celebrity doing all kinds of wild things. Annabelle, that was, I think Annabel Milibank, if I remember right, was Ada's mother, who came from a sort of distinguished, rather starchy family in England. Those two got together in a fiery kind of way, produced Ada. By the time Ada was born, Byron was gone and she never met him and he was off running around continental Europe particularly. I always find it amusing that he rented a house along with Shelley at some point. In fact, I think the Frankenstein book was written by Mary Shelley during a time when they were sort of all locked in this house in some storm or something. And at least the idea for the Frankenstein book came from this. And they were kind of making up sort of ghost stories or something. But the description of that house is kind of like it was a big kind of thing with all kinds of crazy stuff going on, including five peacocks on the grand staircase, so to speak. I mean, actual peacocks running around. In fact, Byron had had quite a tradition of keeping animals. I think he kept them. When he was in Cay, Cambridge, in university, he kept a bear in his room there. But in any case, a kind of a wild character. I think late in his life, one of the notable things was there was the Greek War of Independence at that time. And he ended up being sort of a leader of some military leader in that effort. I mean, it kind of reminds one a bit of modern times where some people who are, I don't know, Silicon Valley operatives and so on, would go off and help some kind of war effort somewhere. And they're kind of plopped into that situation, even though they're not people with necessarily any military background. So it was with Byron, I believe there's a statue of him somewhere in Athens leading some whole Greek independence effort, which he did. I think he actually got sick at that time and died shortly after. But in any case, that was a be an adventurer type thing, which was a thing that was something that he seemed to do much of his life. But anyway, he was long gone from Ada's life. And Ada's mother was the person who kind of raised Ada. And Ada's mother was, I think, a rather stiff character. I mean, I think she was a sort of social reformer type person with a lot of kind of, you know, educate the local poor, so to speak. But with Ada, her biggest fear was that Ada would be like her father and some kind of crazy person, you know, crazy poet type person or something. And so she really concentrated on sort of having Ada learn. Ada was taught at home, as was the typical thing for the aristocracy in those days. But Ada was kind of. She really pushed Ada in the math science direction partly in order to avoid her becoming a poet. And I think Ada perhaps had some poet tendencies. And that sort of came out even later in her life. And she was quite given to sort of creative kinds of things. I know there's some early Ada sort of kid thing that she wrote about flyology, the idea of flying machines and so on. And she had all kinds of interesting imaginative flights of fancy about that kind of thing. She had various. She did learn a certain amount of math. She didn't get as far as calculus at that time. She did algebra and things like that. Not untypical of the time. I mean, calculus wasn't a thing. Calculus was a university level subject in those days. And until fairly recently, actually. Then let's see what happened. She must have been 17 years old, I think she was, you know, she mostly lived on some country estate, but then she went in for a season in London and it was the convention of the time that, you know, the young women of the time, young aristocratic ladies of the time, would be kind of would have a sort of whole coming out extravaganza that would include being presented to the Queen, Queen Victoria at the time and those sorts of things. And as sort of part of that whole swirl of activity, she ended up going to this party put on by Charles Babbage. Charles Babbage was by that point Must have been in his 40s. He had been a. He'd been sort of a Cambridge educated chap, very much into kind of the future and so on. I think he had a quote from his college days of, I want to leave the world a little better than I have found it. But he got interested at that time. He got involved with the, I guess, making astronomical tables and figuring out how you would compute what was the position of the moon. And astronomical tables in those days also have mathematical tables as part of them. And actually this must have been in the 1820s or 1810s. But any case, Babbage took a trip to France where he found that Napoleon had set a bunch of people up to go compute tables. And he got very freaked out. He said, there's going to be a tables gap between France and England and we better do something in England that sort of matches this French effort in creating books of tables, mathematical tables and so on. At the time, sort of tables seemed particularly important for navigation. And people would say things like, if you don't have the tables correct, a ship is going to crash and lots of things are going to get destroyed and so on. And so that seemed like a very important kind of thing to be working on. And there was a famous comment from Babbage, you know, it's, I wish by God this could be done by steam. He said, well, steam was sort of the metaphor at that time for automation. You know, can one make mathematical tables automatically? And so that got Babbage started on this whole effort of seeing whether you could get correct tables produced in some mechanical way by some device with cogs and so on that would just work out the tables. Now, it had been known since antiquity actually that you could have sort of an odometer like thing where you had a bunch of cogs and you would count up, and when you get to a 10 or something, that cog would have a pin that would move another cog a bit. And so you could sort of count up and you could do positional notation. It was not known until way after way, way after Babbage's time that in antiquity people had known how to make things like the Antikythera device. As far as Babbage was concerned. The earliest devices that were sort of computational devices had been made in the 1600s. Famous one was made by Blaise Pascal in 1642. That one still exists. It's a brass kind of thing that does addition with wheels and so on. There was actually an earlier device made by a person called Chicard, who was A friend of Kepler's and he made a thing out of wood. It hasn't survived that. It's known about from letters and so on that exist with Kepler. That was a thing to help Kepler do computations for astronomy and celestial mechanics. But any case, the idea of mechanical calculators sort of developed progressively from the 1600s on. By the late 1600s, people like Leibniz made a four function calculator. I've seen it, it's a brass thing. It took him, he had a lot of trouble. There was a lot of difficulty in the engineering of these devices particularly. Well, carry bits are the real killer because you're putting a certain amount of force on these wheels. But at the 99999 plus one, you have to get all these wheels to twist a bit and get that final wheel to move. And it's hard to get to sort of have forces that work both for, oh, you're just moving one wheel and oh, you're moving all these wheels together. And that was a continuing source of trouble. And there's endless difficulty that for example, Leibniz had in getting his calculator to work. Babbage also had some difficulty later on. But Leibniz actually, somewhat amusingly, one can find in his papers these ads that he wrote for his calculator that read kind of depressingly similarly to at least our early Mathematica ads of do calculations automatically type thing. But in any case, little changes in the world. Perhaps Archimedes had had these ads a couple of thousand years earlier, I'm not sure. But in any case, the thing that this sort of tradition of mechanical calculators had existed and it got fairly well developed by Babbage's time just to sort of add more history to that. When I was a kid in the 1960s, the mechanical calculators were still a thing. I mean, I used one. And you know, the choice of automation for doing arithmetic was really three things. You could use tables, like logarithm tables, where you're using the fact that you add the logarithms to multiply numbers together. You use books of tables. You could use a slide rule that was sort of approximate, or you could use a mechanical calculator, a big thing made of metal, you know, big sort of size of a laptop, I suppose you could say a lot heavier than a laptop where you were, where it was cogs and so on inside. Actually, the finest development of that was a thing called the Kurta calculator developed in Liechtenstein right around the end of World War II. I think that is really a handheld thing that's just full of cogs and it's quite light. And it was finally really, really perfected by the 1960s. And they're pretty cool things. You can kind of twist them around and they make all kinds of. Of kind of cog noises. And you can do calculations of least four function calculator calculations. That thing finally got perfected right around the time, around 1972 and so on, when electronic calculators came out. Kind of a bit of a sad story of very elaborate technology development. One can only hope that that technology, as so often happens in the history of technology, the technology will be back at some point. One will need a purely mechanical way to do those calculations. I know there was a fun project to send a spacecraft to Venus where the surface temperature is what, 350 degrees or something, and most things just melt. But if you could only make. And things like semiconductor electronics doesn't work because the heat makes the charge carriers jump into the conduction band or whatever and not act like a semiconductor. And so the idea was, well, let's just have a mechanical computer and put it on Venus. So maybe the technology of the Curta calculator and the Babbage difference engine, all these kinds of things will be back on Venus. We'll see. Or maybe there'll be a case where it will turn out that when we get molecular scale circuitry, that it makes sense to use some of these techniques again. It is one of these tendencies in the history of technology that these ideas, they are hibernated, but they eventually recur and one needs to care about them again. But any case, in terms of the history of what happened, there were mechanical calculators. Babbage really wanted to make a thing for essentially computing polynomials. He was going to make polynomial approximations to mathematical functions and then compute values of polynomials. And so he wanted this difference engineering. It's called the difference engine, because when you have a polynomial take enough differences and you'll get a constant, constant, constant. If you take it's a degree N polynomial, take what, n minus one differences or something, and you'll get that. And so his idea was sort of build up the polynomial from these differences, so to speak, and do that by this mechanical mechanism and in the end have it so that it will print the tables so nothing could go wrong. It's actually made the final tables. He was working in base 10. He didn't have the idea of binary. Leibniz had certainly known about binary, but that wasn't a thing that was carried sort of down in history and it wasn't a thing where people were thinking about. I think Leibniz had thought about binary and the idea of by just using ones and zeros, you can make everything. And he thought that was a big deal. Babbage, I don't think will have known about that. He could have known about it, but I don't think he did. In any case, he didn't have that idea. So by the time Ada came to his party, Babbage had built a small difference engine. There's the. And pieces of it. I think the London Science Museum has. Has a reproduction of the difference engine and. And it also has pieces from the original and a bunch of the plans from the original. Babbage went through many, many, many different plans. It's not completely clear what got built at different times and so on. But in any case, he built this difference. A piece of this difference engine. Ada came to this party, Ada saw the difference engine. Babbage thought, oh, you know, I'm sorry, it's a. You know, it's gender roles of the Victorian period, you know, thought, oh, it's a young gal, she's not going to be interested in these kind of technical mathematical things, you know, she's only going to be interested in this sort of automaton thing that he had that was some kind of. I forget it was some kind of automaton that he dressed up with different clothes and so on. But actually he was wrong because Ada was actually more interested in the difference engine and got really interested in that. Then she, I guess, sort of went off and she had. I'm trying to remember the sequence of events here. She married a chap called. His last name was William King, I guess, and he later became Lord King and then Count Lovelace. He'd been a British civil servant somehow working particularly on the kind of management of the Greek islands. But in any case, he had a sort of fairly distinguished career and eventually got all these various honorifics and so on. He was anyway, Ada, he married Ada and they had three kids. I think after the third kid was born, Ada sort of decided she should go back to more intellectual kinds of pursuits and contacted. She wanted to kind of learn more advanced math. And she somewhat, I suppose it was not considered a societally appropriate thing for her to be doing or something, but she somewhat quietly contacted a chap called Augustus de Morgan, who was a professor of mathematics in London and sort of a mathematics tutoring person, and said, I want to learn math. And so he ended up Teaching her a bunch of math. He was a person who's most famous for de Morgan's laws, which are laws of logic. He's also a person who encouraged George Boole actually to go push on the thing that became Boolean algebra. But anyway, he was kind of a mathematical teacher type person who Ada learned a bunch of stuff from, and it's an, I guess from him. Learnt a reasonable amount of mathematics and so on. And then at some point she was friends with Babbage. Babbage. I'm trying to remember the. Yeah, so there's a lot of, kind of. There's a lot of correspondence between Ada Lovelace and Babbage. One of the things that, you know, one thinks of the ancient worlds, or not ancient, but the. Those times as being very things where things happen more slowly and so on, and people were riding around in horse carriages and such like. But an interesting fact is that Ada and Babbage lived, I don't know, a couple of miles apart in London. And there are days when they were exchanging mail very rapidly. In fact, in those days in central London, there were 14 mail deliveries per day. And so they were able to send letters through the mail system. They could also just have somebody carry a letter from one to the other. But there are times when you can see kind of in the course of a day the letters have been preserved and it's backwards and forwards in the morning, in the afternoon and so on. But in any case, Babbage had all these plans for this. Well, he had this difference engine which was just computing polynomials. Then he had the idea of, well, why doesn't one just use these punch cards to determine what operation the engine will do? He called the main part of the engine, and by the way, the term engine came from kind of locomotive type engine. He had the main sort of CPU he called the mill, which was kind of like a mill for making bread and so on. That was the place where things. One would take the data from the memory. Did he call that the store? I'm not sure. And then he would mill it to turn it into some other arithmetic thing and then he would eventually print it. So he had this idea that you could kind of control what operations were done in the mill using punch cards. And he had many designs for that and interacted with Ada. He wanted the British Admiralty particularly to pay for this machine that wasn't successful. They kept on being new politicians that came in, new prime ministers and so on, and Babbage would talk to them and he wouldn't quite convince people to, to give him the money. Actually, Babbage always thought that he never really, I think, understood how much money he had. Well, I'm sure he didn't understand how much he had, but he always thought other people had more. And Babbage's father had been a banker, was a rather austere man. But he left Babbage a lot of money. And Babbage. You can look at Babbage's account books are in the British Library now. And I looked at them and he was quite a well off fellow. He later on he got involved in various startups. He was involved in a life insurance startup and he was kind of the techie in the life insurance startup, trying to figure out premiums and mortality curves, things like this. But he always believed that Ada was much richer than he was. I don't think this was in fact true. In fact, Ada's husband was given to constructing, to doing all kinds of real estate projects which were of dubious, somewhat dubious kind of success. I mean, he had various houses where he would construct these elaborate turrets and things and underground stuff and so on. It cost a lot of money. And I think Babbage in the end, because Ada was a kind of a peer, you know, she was, you know, eventually Countess of Lovelace and so on. And that was a very sort of, that was kind of in the pecking order of British society. That was sort of an aristocratic role that was more highly pecking than Babbage as a sort of a pure commoner and an engineer and so on. So he always believed that Ada was somehow in a level above him, particularly financially. And that was important. I mean, I think partly he imagined that Ada was sort of the conduit through which he could actually get his analytical engine funded. And that might have been true partly because Ada was a much more effective people person than Babbage was. Babbage was a kind of a rather kind of difficult, bad tempered character. You know, he, he had a whole effort developing his, well, difference engine and so on. It was in his, you know, people nowadays have startups in garages in those days. Babbage had his startup in his stable, which was I suppose the direct analog. But he was constantly having arguments with his engineers and they were leaving and there were all kinds of problems there. And I think the, and he was also changing his mind about how to do things and so on. Very, very sort of typical complaints about startup CEOs and such like. But in any case, the, well, as it was, eventually people didn't really. Babbage was always upset that people didn't appreciate him. Babbage wrote about all kinds of things. I mean, he wrote about, you know, extensive diatribes about the decline of British science. Somewhat amusing that he was doing that in the mid-1800s, right when things were very much about to be on the upswing. And he was writing, you know, he was a Fellow of the Royal Society, but he would write about how terrible the Royal Society was. He was not a great kind of. You know, his ingratiation skills were not spectacular. But any case, the. At least in England, people were not very appreciative of the whole Analytical Engine thing. Babbage ended up giving a series of lectures in Italy that were about the Analytical Engine. Actually, the person who organized them was a chap called Menabrea, who was at that time a civil engineer, I think, working on things like bridges and so on. Years later, became the president of Italy. President, I think, and after Italy was unified and so on. And I think the. But any case, Menabrea wrote up, kind of in Italian, sort of a summary of Babbage's lectures about the Analytical Engine. And then Ada ended up deciding she was going to translate these into English. Ada, I think, thought of herself at that time as something of a kind of a literary explainer of science. Particularly, she'd been kind of friends with a person called Mary Somerville, who was, I guess, the translator of Laplace's Mechanic Celeste Celestial Mechanics book from French into English and have become kind of a fairly distinguished sort of expositor of science. And somehow, gosh, what is the story? Maybe one of Mary Somervell's kids was somehow a lawyer that Ada Lovelace dealt with. I forget there was some connection like that. Mary Somerville was considerably older than Ada Lovelace. But in any case, Ada had sort of got this idea that she would be an expositor of science. And one of her exposition efforts was going to be translating this thing of Babbage's from, I guess it was Italian, into English. As it turned out, she thought it was pretty badly written, and she thought she better actually explain what was going on with the Analytical Engine. So she wrote this kind of supplement to this translation. The supplement is much better than the actual document. And the supplement basically explains kind of the story of how the Analytical Engine works and contains these quotes about algebraical patterns and so on. And also, I guess, for the purpose of making that supplement, she decided she would write a program basically, for the Analytical Engine. And she decided to write a program for computing Bernoulli numbers. Bernoulli Numbers had been developed by one of the Bernoullis. It's all about kind of if you're multiplying out polynomials, then you can just do that by explicitly multiplying things and you get sort of combinatorial number of calculations to do. Bernoulli numbers are a kind of compression of that, but they still require sort of recurrence. There's a recurrence relation that computes the Bernoulli numbers. Anyway, Ada decided to use that as her sample for a thing to compute. And so she's like, okay, how's the analytical engine going to compute Bernoulli numbers? And you can see the correspondence going back and forth with Babbage about how does this work, how does that work, how can it do this, et cetera, et cetera, et cetera. And she ended up inventing these collection of nested loops that there's a kind of a coding sheet that is the series of steps that are needed to compute the Bernoulli numbers. When you're storing things in memory locations and so on and computing those things, it's kind of interesting correspondence to see. She's kind of all frustrated about how this is all rather difficult and she's having trouble making it all work and so on. And so she writes this thing saying, I'm frustrated with the day, I'm just off to go and ride my horse and I'll be back to this later type thing. But any case, she does eventually finish it. And Babbage sort of says, yeah, it looks right to him. And that is, in a sense, an explicit version of how the Analytical Engine, how a program could be written for the Analytical Engine, and that ended up being published there. At the time, this piece was just signed, I think, aal, which were her initials. And there was no kind of the kind of, oh, a society lady has written this mathematical treatise was kind of out of place and wasn't said at the time. Ada herself was quite proud of the thing and in very Victorian ways, she would describe, I think she wrote something to her mother. She had a very difficult relationship with her mother. Her mother was always making. Her mother was always kind of complaining about this and that thing and Ada's child rearing practices and Ada's this and that and the other. And the mother was also always, I think, sort of very much in the. I'm sick and frail and, you know, going to have all kinds of quacky rest cures and so on. As it turned out, Ada's mother outlived Ada by many years. In any case, the Thing that was, I think she wrote about her. Her first publication, she sends it to her mother and she's talking about it as the. Describing it as something like the head of a household of which there will be many more generations or something. I forget exactly how it's put, but she saw it as sort of a first step in kind of a career in kind of explaining and clarifying science. She also had this thing I mentioned earlier of kind of interacting with Babbage and saying she would help Babbage to actually get this thing built and make a cloud computing company, more or less. None of that happened because Ada got sick. She got, let's see, either cervical or ovarian cancer. I forget which. I think it wasn't known at the time, which. But something like that. And that was sort of a bad story. And she has a lot of very kind of sad correspondence towards the end. She ended up getting very much using opium a whole lot as a painkiller. But she also was talking about. There's a lot of correspondence about how she understands dying is not a thing that happens all at once. It's a thing that happens piece by piece type thing. Actually, a friend of hers was Florence Nightingale, who came to see her quite a lot in her last years, and I think has a rather touching piece about how the strength of Ada's mind was such that, you know, it was hard for her to die because her mind kind of was keeping her going for longer than one would have expected would be possible, so to speak. But in any case, I think many different things would have happened, I think, if Ada had not died young, as it was, there was. Ada's sort of reputation was a bit spotty because, well, there was sort of a big PR campaign that was raging for 100 years between the supporters of Byron, the celebrity poet, and the supporters of Annabel Milibank, I guess Ada's mother, sort of part of a whole social reform movement and so on. And they were all throwing mud at each other and there were all kinds of books published and so on. And so Ada was somewhere submerged in the mud, so to speak, and didn't really reappear until it must have been 1940s or so, when people like, for example, Alan Turing knew about Ada Lovelace. But I think he. Let's see, I traced how this happened. He learned about her from somebody who knew Ada's, maybe granddaughter, Ada's daughter. Ada had. A daughter who was notable for bringing. I think she was the person who brought. It was an Arabian horses breeder and brought Those sort of racehorses to England and so on. And charmingly has all kinds of very sort of mathematical like kind of analysis of breeding patterns, which I think kind of uses binary numbers in some way. And people have sort of said, oh, she used binary numbers because her mother was Ada, who was a computer person. Well, actually, Ada didn't use binary in computing. And that wasn't a correct connection. I mean, there are many things that went wrong in the biographies of Ada. One of the ones that's sort of a telling one was this correspondence between Ada and Babbage in which Ader is one of them, is talking about the vexing problem of the three bodies. And somehow this was interpreted by some biographer to be some kind of romantic triangle story with Ada and Ada's husband and Charles Babbage and so on. I don't believe anything like that ever happened. It was nothing. There was no such story. The problem of the three bodies turns out to be the three body problem of celestial mechanics. The Earth, moon, sun type problem of bodies moving under gravity. And that's kind of revealed by the fact that there's a subsequent letter in which Ada or Babaji, I can't remember, which is saying, oh, yeah, I'll return your copy of mechanic Celeste Laplace's book about celestial mechanics. So it's obvious that they were talking about the three body problem of mechanics. And some biographer made a lot out of kind of the. The psychological analysis of this whole romantic story, which is complete nonsense so far as I can tell. And subsequently, partly as a result of the sort of PR campaign between the Ada mother and Ada father camps, there was an awful lot of sort of Ada bashing of. Oh, there was a famous one, that the claim was that Babbage and Ada had had this method for betting on horse races which hadn't worked out very well. And Ada had kind of pawned the family jewels not once but twice, betting on horses in a bad way. So far as I can tell, this was completely false. No such thing ever happened. And there's not even any evidence that Ada had any notable engagement with horse race. Well, some horse racing, but not extensive elaborate betting schemes on horse racing. And I think most of the money being kind of money problems of the Ada family were a result of her husband's peculiar real estate adventures. Not anything to do with Ada herself. But any case, that was a very long description of the story of. Ada Lovelace and so on. Gosh, there's a question from M here. Did Galileo have mechanical mathematical tools? I don't believe So I mean, Galileo's father had been a professor of music and Galileo certainly knew about things about kind of ratios of lengths and harmonics and so on. But I don't think Galileo ever had mathematical construction tools. He will have had. Well, I don't know how much of that he would have ever done. I mean, he invented certain things. He invented a kind of early thermometer like device that was based on expansion of maybe not mercury, but something else. I don't think so. Hylo asks, how does the abacus fit into the story of calculators? The abacus was an Eastern tradition and I think it was certainly something that was known in the West. For example, Fibonacci's book that was sort of his manual of arithmetic. I believe this book as such has been lost, but it was called Liber Abaci the Book of the Abacus. And it was a book about sort of practical arithmetic from like 1200 teaching merchants how to do practical arithmetic. By the way, just more comments perhaps about. Ada. I see RBS commenting about if ADA had been asked about her coding style, she would have said her code is like poetry, logical, elegant and never divided by zero. I think her code was definitely very machine code because it had to be. It was describing things to do on a machine. Although I guess it was reasonably abstracted from that, now that I would say it. I mean, it definitely had the idea of there are variables, registers that store things independent of their actual physical location in the machine and anything like that. I think there's sort of a. I mean, recently someone was making an AI generated ADA Lovelace sort of reproduction type video. And I was wondering to myself, what would ADA have been like to talk to and even what accent would she have had? She would have had, I think, a very upper class British accent. I think she would have had a very ornate style of speaking would be my guess. You can see that already in her letters. I think that she would have, in a sense it would have been very incongruous because she would have been telling kind of nerdy mathematical jokes with this very sort of ornate Victorian kind of presentation of things, which I think would have been quite bizarre. And my guess is that she was kind of more into the kind of nerdy jokes than many of the kind of, you know, I don't think people like Michael Faraday were into that, in fact. And you would have been able to tell, you know, my guess is from my knowledge of sort of British cultural history that ADA would have, would have had a much more sort of Upper classy type accent than somebody like Michael Faraday who had been, you know, who, who didn't come from that, that kind of background. And that was sort of a. There still is sort of a. A strange marker of social origins in, In England, I think that it would be, you know, Ada was in some ways quite an emotional character. And there were all kinds of scandals that unrolled about her father even into her at least twenties. There was some illegitimate child who was thought to not really be a child, but was actually a child. And that all sort of unraveled at some point. And that led to a whole, a whole embarrassment. All kinds of things about this and all kinds of interactions with Ada's mother that were fraught with difficulty. I think Ada's husband was quite a steady fellow and very sort of a calm, anything goes kind of guy, from what I can gather. And. The. How did she refer to him? Ada, in her letters refers to her husband, I think, as Lord King, or I think maybe she has an acronym for him. But it's also very charming and Victorian to see that of, you know, he's not my husband, Bill or something. He's, you know, Lord King. In any case, I think there's some nice correspondence, actually from Ada, maybe in her late teens, early 20s, where she's trying to sort of teach math to some younger cousins. And I remember there's some kind of nice explanations of things there. And there's also interesting stuff in her interactions with Augustus de Morgan in which she's confused about various things to do with variables and naming of variables and so on. And she's right to be confused in a sense. And in a sense one sees from that a kind of a. You know, she's a very kind of foundationally oriented thinker. You know, like, let's put together these pieces in a very precise way. Something which I think Babbage was really not. Babbage was much more of an engineer than of let's hack this and put another cog on here and so on and try and make this work. I don't think Babbage ever understood the kind of. The bigger picture of the idea of computation, which I think Ada did understand. I think Babbage was like, we are going to print tables and that's what we're trying to do. And in any case, that's a little bit on that. Let's see. Well, I should probably wrap up soon here. Let's see. Oh, boy. Asking about all kinds of things. That's an interesting one from Juan here. Would Authors like Shakespeare find a use for our technology. How might he react to technology in general? I think the thing to understand about those times is that learned people learnt all kinds of stuff. I mean, it was a regular thing maybe in slightly earlier years, but even by that time to be a doctor of law and a doctor of medicine and to just be a person who knew about a lot of different things, I don't know, for example, both Dante and Chaucer, knowledge of astronomy and those kinds of things. And that was pretty typical of the time that this idea of today's world of, oh, you're going to be a physicist and that's what you do, and you're not even going to know about chemistry and you're not going to know about philosophy and you're not going to know about other things. That wasn't really a thing of that time. I think that it was really. It's like you'd know about everything that was kind of known about. Now, I think in the case of. Interesting question with Shakespeare, you know, I think. I don't think he has as much kind of techie stuff in his plays as some do, but I think that sort of a question of what? Oh, I don't know. In a slightly less savory world, so to speak, not unsavory, but just a little bit less cultured or something, I don't know what. But people who create things like soap operas and so on, there is, you know, there's a definite rhythm of the story and people have tried. I remember there was a product actually that was based on our tech. I don't know if it's still in use. That was had to do with kind of mapping out the arc of a story to be used for things like a soap opera and so on. I don't think. My guess is that Shakespeare was a much more efficient artisan than to kind of need that kind of thing. And I don't think. I think it might have been interesting, I suppose, in modern times when it comes to. Well, if you want to invent sort of names for functions in computational language. I found that LLMs are quite a good source for those kinds of things. Shakespeare was famous for having introduced lots of words into the English language. One might be amused to know to what extent he would have been able to use computational methods to home in on what those words should be. I don't know. It's kind of like. I'm not sure that people really use those kinds of techniques much even to make product names and so on. Even in today's world. So I don't know in that, in that case, I think people are asking about. Plato, Socrates, you know, Plato. I think the whole computational idea, computational language, computational representations of the world, I think Plato would have found that of great interest. I think that sort of this question about formalism and the reality of formalism and so on is a very Plato oriented kind of thing. I think that in fact, one of the things that has become clear in the efforts that I've had in sort of the physicalization of metamathematics is Plato sort of had this view that there was some kind of notion of ideal forms, that there was some reality to the abstract thing that was inside things like mathematics. And I think that we now can see finally, a couple of thousand years later, that yes, that's really true, that the stuff from which the abstraction of mathematics is made is the same stuff from which the reality of our physical universe is made. That it's the same ruliad kind of construct that is this purely computational thing which when viewed in a certain way becomes mathematics, when viewed in another way is physical reality. I think Plato would have been really into that, actually. I think he would have found that quite lovely. And that would be. And I think at the time Plato was doing all kinds of political philosophy stuff and talking about, I think he has some 5040 maybe as his ideal size for a number of people, for some kind of democratic state because it has all these different ways to be divided up and so on. I think perhaps from Plato we would have got kind of a computational version of political philosophy which we still don't have today. And that would have been sort of an interesting direction, perhaps in those times. All right, I should probably, even though I'm having fun and you guys will feed me perhaps all kinds of other characters to try and. Gosh, a lot of interesting questions here. Well, anyway, you're tempting me, but I've got to go back to my day job and take care of that. And we'll have to continue this another time. But thanks for all the questions and I look forward to chatting with you all another time. Bye for now.