History of Science and Technology Q&A (November 8, 2023)

Sam. Hello, everyone. Welcome to another episode of Q and A about history of science and technology. So I see a variety of questions that have come in here. Gosh, all sorts of interesting things. Question from Des here, not particularly my area of expertise, but asks how did taxation work before money was invented? I think it was pretty direct. It was like you need to send a person to fight in our army, or you need to deliver kind of this amount of grain to the imperial operative, so to speak. I think that was before there was a concept of money. Then it becomes a lot more circular and more complicated because the money is issued by the government, and then you're paying the money back to the government and so on. And it's all a bit more complicated. And I know people didn't understand a lot of how that worked back in Roman times and things. And people would print money to pay armies and things like this. And it was all quite confused, the concept of. And then they would print money to pay armies, but they would have sort of, in a sense, printed lists of how much things cost. And you can't both print money and have a list of how much things cost, because when you are printing money, you're going to lead to inflation. But then it's all rather complicated and I think was not well understood and maybe even still not that well understood. All the kind of machinery of economics and so on. And I get the impression that more is understood. Much more has been measured. There are situations like virtual worlds where you can kind of see the flow of all the money and where there's at least a certain amount known about, kind of the intersection between sort of human behavior and the machinery of economics, so to speak. But I think that was not understood until quite recently. Stasis asks, how did trading happen between nations that use different number systems? Well, you know, the big issue was weights and measures. That was the thing that, you know, in ancient Babylon, I mean, a lot of our standardization of things started in ancient Babylon or Babylonian cities like Ur and so on, because they were the places where cities grew up. And you needed to be much more organized if you had a city. And you needed to be able to sort of have systematic commerce. You'd have people coming from other places trying to buy and sell goods and so on. You needed to standardize things. That's where standardization of calendars, well, that was invented multiple times, but standardization of things like weights and measures. I'm selling you this amount of barley and I will buy. I don't know what it is, 2 pounds of barley or 20 pounds of barley or something and it will cost this number of credits, so to speak. But you have to know what that number of pounds of barley is. And when people were presumably weighing things when with balances and you had to have these sort of standardized weights and if somebody could cheat they could say well this is a standardized 1 pound weight or whatever it is. But actually it wasn't. So you had to have this whole elaborate system which sort of still exists today of kind of standardizing the standards for weights. So for example, in the US what used to be the National Bureau of Standards, now the National Institute of Standards and Technology essentially provides ways of standardizing things like, oh, I don't know, when you buy a gallon of gasoline, is it really a gallon? Well, that's sort of a, that's in the end that's determined by some standard that eventually flows all the way back to nist. I think the cold sort of notion of sort of distribution channel for weights and measures. Interesting one. And I think that was one of the things that was sort of established in a variety of kind of. That was something that the state provided. I mean, I remember when I was a kid in England, you know, in the US you might learn about the US Constitution or something. Well, England doesn't have a constitution as such. And so school kids would learn about the Magna carta from the 1200s, which definitely had some non modern provisions in it. I mean it was basically the barons said to King John or whatever, if you don't play ball, we're going to have a big coup. And so this was kind of a deal made with them. But one of the things that always used to amuse me when I was a kid was one of the provisions of the Magna Carta is that an inch shall be the length of the king's thumb. And clearly this is fraught with difficulty because which king and how do you get from the king's thumb to determine all the different uses of that inch measuring out fabric, measuring out this, measuring out that. But so this idea of standardizing weights and measures is important when you want to have organized commerce. It sort of arose with cities and so on. Now what happened for a long, long time is that different city states would just have different units. And so, for example, things like pounds and ounces and so on. There were certainly way into the 1800s there were sort of, I don't know, Belgian pounds weight and French pound weight, British pound weight, et cetera, et cetera, et cetera, all these different places. And there are books I have Some of these books that. That literally list by city state. The different city states in Germany, for example, would have different values for their standardized measures. And I'm sure it was a big can of worms kind of doing trade across those things. Now, in today's world, we've obviously got things like the metric system, the imperial system, feet and inches versus meters and so on. And there's a certain amount of sort of dealing with the standardization across that. I mean, there's sort of an effort to define international standards. The ISO, International Standards Organization in Geneva, I guess it is, you know, has this habit of producing these sort of proclamations of, you know, ISO. Some number that is kind of supposed to be the world standard for how, you know, for the size of a credit card or the world's standard for some unit of this, that and the other. Or even in some cases in things like ISO 9000, the world's standard for the procedures that should be used within a company. That one I find more peculiar. And really what that ends up being is a definition of how you kind of. Of how you define what you're doing more so than actually sort of what you're doing, so to speak. It's a kind of a specification of a bureaucratic structure, so to speak. But in any case, this whole question of sort of how do you standardize things and how does that all work is one that in the past, it was very much once there was a state and it said, we're, you know, we're setting things up for our particular state. There's no guarantee of compatibility. And that meant all kinds of things were incompatible. I don't know, the. The gauges of railways different in different countries in Europe, and you would have situations where you would have. When a train wanted to go from one part of Europe to another, it would have to kind of be. Be, you know, stop for a long time, be pulled off the tracks, you know, different rolling stock installed, and then off it goes on the different gauge of tracks in the different country. And obviously more basic things like which still haven't been standardized today, like which side of the road you drive on and things like what the outlets are, the voltage for the outlets. Voltage doesn't matter so much because we have transformers that deal with giving. Get. Taking in sort of a wide range of input voltages and giving out the output voltage that different kinds of electronics needs. But it's still the case that one ends up with different shaped plugs in different countries, so to speak. And these are things where at some moment there'll never be sort of a further standardization because the difficulty of sort of working across standards is not so great that it makes it worthwhile to go to the extreme difficulty of changing the standard. You know, I think Sweden, I guess it was, was a country that made a change from driving on the left hand side of the road to driving on the right hand side of the road. And it's just one of those charming stories about change is they did it at like, I don't know, midnight or two in the morning or something someday, and they figured that would be a good time to do it because nobody will be out on the road and there wouldn't be anybody sort of being confused by the fact that all this changeover was happening. Of course, if it's the one moment where a country changes what side of the road it's driving on, everybody's out for tourist value to see that happen. But I don't think anything too bad happened. I think people just had their tourist moment. But in any case, now a question would be why did, why did it get to be standardization, for example, the metric system? Well, that was Napoleon who invented, caused the metric system as it is now to get set up. And I guess the success of Napoleon spreading across a bunch of countries is probably what spread the metric system. I mean, these different kinds of standardizations. Another famous one is for the calendar, which in the time of the Roman Empire it kind of got standardized to the Julian calendar, kind of put in place by Julius Caesar with months like August being added and so on. And with the most basic formula for leap years being added by the 1500s, the lack of precision in leap years, it was just assume the year is 365 and a quarter days long. But it isn't quite. It's, I think 365.2481 days is the actual length of a year in terms of the number of rotations of the Earth that happen during the time when the Earth goes once around the sun. And so by getting that wrong, you end up with something where the seasons start slipping around the year. So I think Christmas was by that point in the summer and things like this. And it was kind of bad. And then Pope Gregory kind of got this whole collection of consultant astronomers and so on to come up with, okay, how should the calendar be revised? And that led to the Gregorian calendar that was introduced in, if I remember right, 1580s, but I might be wrong about the precise date. And that sort of gradually spread throughout the world. But there are places where it spread very, very late like in Russia, I think it was still at the beginning of the 20th century, still was using the Julian calendar. And in England, for example, notably happened during Isaac Newton's life from whatever it was, 1642-1727 or so. His date of birth is in the old style calendar, the Julian calendar, and his date of death is in the new style, Gregorian calendar. So again, the standardization of are you Julian, are you Gregorian? Obviously these things start to matter when there's longer range trade. And if you're only sort of dealing with people in your own city state, it doesn't really matter whether you have compatibility. It kind of reminds me if we want to think very physically about it. When you set up a gauge theory in physics, you have this notion of different kind of coordinate systems that are operating in different places. And you have this notion of a connection which is actualized in the gauge fields and so on. That kind of converts you from one coordinate system to another. And I suppose this is a charming human example of that is we're using one system of units in one city and one system of units in another city. And somehow there has to be a translation between those systems of units sort of by merchants traveling from one city to the other. That's sort of a bizarre analogy there. But with respect to the. I mean, I think one thing that was true about merchants back in the day is people who were traveling merchants spoke many languages and were very much sort of able to operate in the. You know, one of the things they did was this translation from systems of units, number systems, dates, whatever. That was part of the story. I mean, I know when I was younger, sort of this notion of import export companies, it still exists, not perhaps as prominent as it was in the time right after the second World War. That was kind of one of the kind of high tech industries in places like the UK and so on was we'll buy stuff from one country and sell it in another country. Like you could do that with textiles or something like that. You'd buy them from, you know, folks in Peru who were actually kept the llamas in their, on their farm type thing to people in, you know, in, in Italy who were making fine alpaca scarves or something. And this whole mechanism of how you actually did trade across different countries was quite non trivial. And it involved all of this elaborate stuff about letters of credit and all these things about how you convert things and how you arrange for this thing that you're buying from here and it's in this currency and that currency. And so On, I mean, one part that was easier was at some moment before currencies started to float in value with respect to each other, there were fixed known conversion rates like 2.$8 to the pound, for example. And that stopped in the 1970s, I guess. But this idea of how do you do trade across different countries, it was pretty high tech back in the 1950s, 1960s, even 1970s and so on. Gradually things got more and more standardized, more and more organized. Things like the SWIFT system for bank transfers between countries and so on got established. Things eventually kind of the credit card companies went global. That must have been in the 1980s and so on. 70s maybe to 80s? No, it must have been in the, let's see, I first got a credit card when I was maybe 14, 15 years old, so that's mid-1970s. But they were, you know, there was Diners Club and a few other credit card companies. But the big expansion I think was probably the 80s. And then, you know, it started to be the case that lots of different countries took these things. Now it's still the case. And this is, you know, when you, for example, we sell things as a company in lots of different countries and it's really complicated and even, you know, to take consumer payments, it's not very complicated for payments from organizations and institutions and so on, but for consumer payments, it's kind of like there are places where, you know, it's very well standardized and where it's just there are sort of, there are kind of payment processors who can deal with, oh, there's somebody has a Visa card and they're in Singapore or something and they're buying something. And it's all very easy. Then the places where it's still very difficult, like India, for example, China, lots of these countries, it's really very difficult for to actually get consumers to buy things in those countries and make payments for them. And it's quite an elaborate and baroque system even to this day. And perhaps in some cases that's, you know, it's a sort of geopolitical fact about the world that maybe in some cases that's even getting more difficult as countries try to sort of close these things in. But anyway, a few thoughts on that subject. Let's see, Patrick asks. He discussed the role of ancient civilizations such as the Greeks, in laying the foundations of modern science and technology. I think the Greeks in particular, well, the kind of one thing we have a certain lack of knowledge about some ancient civilizations because they didn't leave kind of permanent written records. So we know a bunch about the Babylonians because they left a lot of clay tablets. We know a bunch about the Greeks. We know about the Romans. We know much less about about the Phoenicians, for example, because they just didn't leave a lot of kind of written artifacts behind. I mean, the Phoenicians presumably gave us an Alphabet and things like this. But we know that sort of rather indirectly. It's not because we have a lot of actual tangible documents and so on. I think the. The Babylonians had sort of quite an organized way of thinking about, I don't know, number systems. They did things in astronomy. They cared about astronomy. They recorded data about astronomy. They had kind of math problems that we know what they were because they're on clay tablets. And people would solve these math problems, and they're very similar to the math problems that you would find people solving in middle school to high school today. They would accept that a little bit of the vernacular, the word problems are different. X number of people are going to dig a ditch, and the ditch has these properties. Probably in most countries, digging ditches is not what the word problems in math are about. But in ancient Babylon, that was a thing for those to be about. And they had a few kind of geometrical kind of figures that were not as common today. Like, they had a thing, they called it, what was it, the cow's nose or ox's nose, which is this thing that is kind of the intersection the figure made. When you put four circles right next to each other, there's this kind of hole that's cut out between them. And they were very keen on that particular geometrical figure. And I'm working out its area and things like this. But I think what you see is these kind of math exercises that were used primarily to support commerce. And as a kind of a side effect, there was some sort of models, mathematical interpolation models, effectively used to figure out things like the positions of planets and so on. Why did one care about positions of planets for astrology, for being able to cast horoscopes? Because it was believed at that time that kind of the conduct of human affairs was affected by the. The configuration of planets and so on. And that, if I don't know, Aries was in the Ascendant or something, that meant it was a good time to declare war on the neighboring city state or something like this. No, not Aries. I think its planets were in the Ascendant and so on. But in any case, I would say that the thing that really happened with Greeks, and particularly the Athenians, well, actually, more generally, a whole bunch of Greek city states was kind of this, in a sense, commitment to philosophy and the concept that it was kind of worth recording and worth kind of trying to understand the world by pure thought. And there were many different sort of pieces of that. The pre Socratic philosophers, Plato, Aristotle, all these folk, the Epicureans, lots of different groups that sort of all got this idea that one might be able to understand the world by thinking about it. Now, maybe other people had that idea too, but didn't bother to write it down. I think that. And I would say in Greek times it was. It wasn't like everybody was thinking about that. It was particular people. But somehow that became a cool thing to do. And so sort of records of it got preserved and propagated and so on. And I think this kind of notion that let's think about how the world works and kind of come up with human ideas about how the world works. That's a very Greek kind of concept. And I don't think the Babylonians really had that concept. We don't know, at least of kind of an abstract layer of their kind of description of the world. It was very much people are digging a ditch. This is this number of people. And it takes this amount of time to dig this number of feet or whatever they called them. I think they had stadia, I think were a unit of length at that time. But it's very pragmatic stuff. At least that's what's recorded. We don't know, maybe there was sort of more abstraction that was happening kind of on the ground. But what's recorded for us is just the pragmatic stuff. Whereas in Greek times the description of the abstraction is also recorded. And I think that it's something where that sort of. Okay, so once one starts thinking about can one figure out the world just by thought? Then one has questions like, what's the world made of? And the idea that arose pretty early in Greek times is it's made of a large number of copies of discrete things. And that's kind of the idea of sort of atomic theory and so on. That was something that. Democritus was a pre Socratic philosopher who had a fairly clear statement, it seems, although most of his actual works have been lost, but sort of commentators on his works make it seem like had a pretty clear idea that the world might be made of lots of copies of identical atoms. And I'm not sure sort of how people got that idea. Later on in like 1st century AD Lucretius in Roman Sort of science poet type person who wrote this book called De rerum Natura on the nature of things. It's a kind of a topic that I might have picked for myself on the nature of things as a kind of description of kind of how the world works. But he used as his kind of model of this kind of atoms being put together in different ways. He used kind of grammar and the grammar of sentences. And so for him it was like they're a discrete set of possible words. And similarly there is a discrete set of possible atoms somehow. And there are rules for how these get put together, which are like the rules by which words can get put together in sentences. It's perhaps an ultimate irony descending deep into the rabbit hole here, that in our ideas about the ruliad and ideas about kind of rulial space and motion in rulial space and so on, when we talk about physical space, the sort of carriers of motion are particles, things like electrons, where an electron can go from one place to another and still be the same electron, while in rulial space the what can go from one place to another and still be the same thing. It seems like it's concepts which are very closely related to words. And so it would be an ultimate irony that I hadn't realized until this moment of describing it to you, if in fact what for us is the origin of sort of discrete things that are like the particles, et cetera, et cetera, that the sort of precursor of that really is the idea of discrete concepts. And that Lucretius in his kind of poetic description of the atoms that make up our universe, like the words and sentences, he might be closer than one might think that those words and sentences might be like the concepts that are the particle like entities that exist in rulial space. That's a very bizarre rabbit hole type concept, but yeah, concept about concepts and so on. But any case, I think this notion of thinking about things abstractly, very Greek oriented idea, led to things like Euclid trying to state sort of geometry in an abstract way, rather than just saying look, I can draw this figure and it's obvious it has this or that shape. It was like, let us abstractly consider this and deduce things by pure thought. I mean, it's kind of really putting sort of human thought at the center of things in a much greater way than than one had, than appears to have been done before. But we're a little bit prejudiced because we don't have such good records from lots of civilizations. I mean, Egyptian civilization, I Don't think there's a lot that is. There aren't the same kinds of mathematical papyruses, tablets, whatever, that exist from ancient Babylon, where there are tables, for example, of arithmetic constructs, some of them coming from the Babylonian education system. We don't, I think, have similar things in the Egyptian case, at least not as systematically. And I don't know what the sort of system of. If you'd gone to some Egyptian and ancient Egypt person in ancient Egypt and said, so how does the world work? I think the kind of answer you would have got would be Ra makes the sun come up type thing. You wouldn't have got this more kind of less anthropomorphized version of things that I think you would have seen in the Greek case, where most of the story was, well, it might be made of atoms type thing, even though there was a separate sort of thread of the kind of mythology of Zeus throws the thunderbolts and so on. But I think there was a sort of philosophical layer that was much more seriously kind of thinking about, which might have said, just for kind of a manner of speech or a way of talking about things, yes, Zeus throws the thunderbolts, but really they were thinking in a more abstract way about sort of how the world was put together. And I think that idea that there is an abstract way to think about the world is something which has very much informed and created a lot of modern sort of formalistic thinking and science, mathematics, et cetera. I mean, I think the sort of the earliest formalism of our species is probably the invention of words and language, where it wasn't just pointing at things, but having a word that abstractly described those things in an aggregate way. And then in ancient Greek times, one had things like logic being sort of lifted out of the details of specific sentences and so on. And from Babylon and then more developed in Greece, the idea of mathematics and the sort of abstractions of mathematics. I mean, I like to believe that in modern times, you know, 20 centuries later, where we have another form of abstraction that's really very important, which is kind of this idea of computation and this idea of defining things according to rules and seeing what the consequences of those rules are. I think one of the things that's important there is this notion of symbolic structure, the idea that there can be kind of a. A way of representing things that is precise. We have that in mathematics and the very restricted examples of mathematics. But this question of how do we represent sort of things in the world in an abstract, symbolic, computational way, how do we Talk about things like cities or paths on the earth or sort of the interactions between chemicals and so on. How do we talk about these kinds of things in a way that has some sort of uniform structure? I mean, as we get logic, for example, it gives us kind of a uniform structure for talking about arguments, let's say, about lots of different kinds of things. Arguments about whether to go to war, arguments about whether this sheep is prettier than that sheep. The subject matter doesn't matter. There's this framework of logic that allows you to talk about these different things. Well, I think computation is a framework that allows you to talk about lots of kinds of things in the world in a sort of formal way, in a way where one can make use of the same machinery to go and make deductions, go and work out consequences from those structures, where one doesn't have to reinvent things. For every different kind of things one's talking about, one has a certain uniformity of structure that allows one to apply the same kinds of rules, the same kinds of functions effectively to different kinds of structures that represent different kinds of things. Now, I have to say that's kind of my longtime life effort is building our computational language, Wolfram language, to be able to represent the world computationally in that way, to give one a way to set up these structures, to apply certain standardized functions to these structures, and to essentially work things out in the world that way, by the way, making use of sort of the automation of our computers to be able to do that. And I think that's kind of the modern version of the ancient Greek idea of let's invent abstraction for things, let's start talking about atoms, let's start talking about logic. That was kind of a notion, an early notion of abstraction. What we have now with computational language is the modern 20 something, centuries later version of that abstraction that has the extremely powerful feature that not only is it something we humans can talk about, write about, et cetera, it's also something that we can get our computers to go actually compute with. And we then have, I've been describing it as kind of a superpower that we get. Once we can describe things in computational language, we get to sort of apply the superpower of actual implemented Wolfram language and computers in general to be able to see the consequences of what we've defined. And so I view that as being in some ways the next step after probably that sort of idea of formalization invented in ancient Greek times. There's sort of an intermediate piece which was sort of the idea of applying mathematics to the world in general, which is a kind of a 1600s type idea. But this notion of sort of being able to represent the world in terms of symbolic structures is a. That this is sort of an idea of the computational age, so to speak. An idea of computational language. I think it's pretty important. I think it's something that sort of will drive the future of kind of what we might think of as science, where in a sense, what is the role of science? Science is about taking what's out there in the world and sort of connecting it to narratives that we humans can think in terms of. It's like, well, these things happen in the world, but we can have a scientific discussion of what's going on. We don't just sort of say, well, it just happened. We say we can give some narrative, some scientific narrative about why it happened, what's going on. We can reduce the complexities of the world to something that is more at the level of a human narrative. That's what the story of science is. And in a sense, as we try and represent more things computationally, we give ourselves the opportunity to have more things that we can describe in a way that we humans can kind of understand through computational language. In a sense, we can think of the operation of the whole world as being deeply computational. That's kind of the idea that started with my new kind of science efforts and now in our physics project, that you really can represent the processes that go on in the world as computations. Now, many of those computations are ones that are very non human. They're things that we don't really have a way to connect to the kinds of things we think about. And the role of computational language is to somehow provide that bridge, to have a sort of a concrete version of the things we can think about, that then we can connect to the things that happen in the world. And I think that's kind of a. An idea that leverages kind of the original sort of ancient Greek idea, but with this major extra kicker that we have actual computers to automate it. And that's why I think what we're doing with computational language and so on is important. It is the next phase in kind of the formalization of things and going beyond merely, well, it seemed that way to me, type thinking rather something where you can actually build the sort of tower of consequences in a solid way. Let's see. Gosh. Okay. David asks, did Isaac Newton spend a significant amount of time attempting to transmute lead into gold? Did he believe in all the Miracles described in the Old Testament. I don't know all of those things. Newton lived at a time when chemistry was alchemy. And alchemy, the kind of the holy grail of alchemy, was to transmute lead into gold, to take a base metal and turn it into, into gold. Because that was kind of gold was seen as having some kind of intrinsic value, as it still sort of has today. And the question was, could you just, could you just invent money? Could you create money? Well, sort of. Ironically, Newton in his later years became controller of the Mint, essentially chairman of the Federal Reserve in modern American terms in England, sort of dealing with the management of the currency. And he had all kinds of cool ideas. I mean he had, I think these are all genuinely attributed to Newton. I don't know if it's still, gosh, on a British currency, at least when I was a kid. The edges of the coins were always serrated and that was done so you couldn't clip the edge of the coin off. Because if things went wrong with the value of the currency, it could be the case that those pennies that were made of copper, that the copper in them was worth more than the pennies were worth. And so given that it was worth just clipping a little piece of the copper off, actually you could do that, you could clip a piece of copper off and just sort of still say, this is worth a penny, but I've got some copper that I can separately sell. And so that was a sort of, I don't know, debase. That was. What was, I think it was the debasing the currency. Is that the. No, that, that's a slightly different concept. But that was anyway, that was a. People clipping little pieces of currency. So, so old Isaac, I, I think it was him, said, well, let's put serrations around the edge of the coins so you can tell if people clip things off. Another thing that was one of his contributions was non commensurate weights for coins. So if you want to know you've got a big pile of coins and you want to know how much it's all worth. Well, if the coins, if a coin was, I mean one thing you could do is just make sort of one penny, weigh this amount and then a tuppence, a two penny piece or something weigh twice that amount. But people didn't want to do that for all kinds of reasons. But then the question was, if you've got a big pile of currency, a big pile of coins, can you just weigh them all and figure out by Sort of numerics, how much of each coin there was? Well, if you have non commensurate numbers. So for example, if you've got coins that weigh one unit and coins that wear square root of two units, then you can tell if you've got ten plus seven times square root of two, that number is something where you can sort of take the pieces apart and see how many ones and how many square root of twos there were. Well, Newton apparently did that for the British currency. And back in Certainly the early 1970s, I could say I had the experience of. I had somehow accumulated a large number of coins and I thought, okay, I'm going to take these into a bank and I'm going to convert them into some other, into paper money or put them in a bank account or something like this. And I thought, you know, I'm going to be very clever, I'm going to sort these coins into, you know, this denomination of coin and that denomination of coin and the other, and the, I take them all into this bank and they, I think they were still just, they, they said, oh, we don't care about the fact you sorted these, just, you know, unsort them and put them all in this, this machine and it will just tell us how much of each coin there was. And I think that was still at that time working using non commensurate weights. I mean, later on there were just coin sorters that would just take the coins and just automatically sort them by a more complicated mechanical device. But that was a contribution there. So it's sort of ironic that Newton was concerned with, I mean, he was very concerned with preventing forgery of coins and things like this. So it's ironic that he spent some of his life trying to do the exact sort of the ultimate forgery in a sense of turning lead into gold. He was certainly a do it yourself kind of scientist. I mean, he ground his own lenses, he did his own experiments looking at the sun, doing various chemical kinds of things. Some of them were not terribly safe experiments, although he lived to a ripe old age, into his 80s. But, and he had, I think that was. So he definitely had a strand of doing the kind of experiments that other people were doing in alchemy and I think also chemistry, although I don't think he made that much progress in chemistry or in alchemy for that matter. And obviously the fact that the word chemistry has the same root pieces as alchemy is not a coincidence in terms of the Old Testament and Newton's beliefs about those kinds of things. Newton did have some somewhat unusual religious beliefs for the time, things to do with the Holy Trinity. And I don't remember exactly what they were. I think his beliefs weren't sort of too far out there. I mean, he was a sort of post Henry VIII time person. So there was. The Church of England was there. And he was the Lucasian professor in Cambridge for a bunch of his life. And I'm sure that he had to sort of officially sign on to the Church of England as being part of Cambridge University. I think he was also later a Member of Parliament. I don't know exactly what the relationship between that and Church of England was. But you know, he was a. I think maybe he was a Trinitarian or something. I don't remember what the whole religious structure that he believed in or talked about was, but he wasn't very far out in that regard. In terms of his view of biblical descriptions of things, one of the things that is kind of interesting, he was very interested in dating different kinds of events. Like one knew when various eclipses took place. He wanted to know when did that actually happen? In what year did it happen? And so he went back and tried to sort of figure out the, you know, in what year did. In sort of in the modern reckoning of years, which was by then the Gregorian calendar, in the modern reckoning of years and so on. You know, when exactly did the Great Pyramid get built or whatever else, or when exactly did the, you know, the Jews migrate from Egypt or something? When did all these particular things happen that were described, for example, in the Bible? And so he did go and try and make an effort to piece together the timeline of the Bible. In fact, the very last book he wrote, published after his death is a book called the Chronology of Ancient Kingdoms. And it's kind of a hokey book because it sort of has this rather face value belief about oh, the Hittites did this because it's described in this book in the Bible, et cetera, et cetera, et cetera. And I don't know whether he quite goes into this person lived for 900 years and so on, but he definitely has. He's taking it seriously as a thing to build this astronomical timeline that he wants to build. And I don't know whether he did that because what else could he do or whether he did that because he sort of firmly believed that that was the way things were. I think that like many kinds of situations, one is he was primarily interested in kind of the science and figuring out the math of figuring out when would Halley's Comet return and all these kinds of things. And I think he was operating in the kind of political and religious world of his time. I think that there were things where he was just kind of going with the flow on those types of things as opposed to inventing the new, in the case of the mathematics and physics he was doing. And I think, I don't know, I think as a member of Parliament. He was a Member of Parliament for Cambridge and I think he spoke only once in the recorded record of Parliament during the time he was there. I think he was just. I don't even know why. I mean, I think the main reason probably that he eventually became controller of the Mint is because he made a better living that way, was a better job. It's like in today's world you can go into finance and it pays better than being a professor probably. And I think it was probably true, that was true in the late 1600s, just as it's true today. And I think Newton, he was a bachelor his whole life and he sort of set up house in London and actually his niece, Catherine Barton was kind of the person who sort of kept his house for him. And he had certainly an extended family that kind of, I suppose hung out with him to some extent. Although he was rather a, you know, it's said that he was a rather dour fellow, although when he went to the local pub apparently and was sort of interacting with the townsfolk, he livened up. It's sad. But in any case, I think he became controller of the Mint for the money and perhaps for the prestige because he didn't know that Newtonian science would be a thing for hundreds of years later. I mean, in his time he was a well known kind of scientist, but he definitely wasn't kind of the prominence in those days was much more in, kind of in the government circles than in doing science. I think it's sort of an interesting thing in the course of history that different professions get to be the cool profession that everybody says I want to be a whatever. I mean, it always amuses me that, for example, tech entrepreneurs were not really particularly cool. Back in the, for example, early 80s, it was not really particularly cool. Then they became much cooler. And there's always these periods of time when, you know, being a consultant is cool, being a venture capitalist is cool, or being a physicist is cool. You know, I think being a physicist has been reasonably consistently cool since the Second World War. I would say being a mathematician, I don't know, some countries like France, it's Been cool. You know, it's had a lot of coolness factor, but it's always like, what are the top professions as a function of time? And in some countries today, being in the government, the civil service, whatever, is sort of the tippy top profession. That's been true historically in different countries. It goes up and down in popularity depending on kind of the structure of the country and the government and all those kinds of things. I mean, I think it is always interesting to see what do the cool kids want to do, you know, in. In. Even when I was growing up in England, it was, you know, going into the army was a. Was kind of a cool kid thing to do in England. Being a journalist was a cool kid thing to do. These kinds of things that, you know, that's. That shifts and changes over time. And being a scientist, well, at least some kinds of scientists has. Has, you know, in some ways increased in coolness probably. I think in Newton's day, being a scientist, being a science professor, a mathematic professor of mathematics as he was, was not a particularly high coolness activity. And being the controller of the mint was definitely much higher on the pecking order. Giovanni asks, what was the greatest technological advancement to come out of the Roman Empire? You know, I think a lot of civil engineering kinds of things, whether it's the aqueducts or the roads, these are kind of major infrastructure building ideas. And the Roman roads, they still. The freeway system in England is still sort of built on. A lot of it is built on the paths of Roman roads, partly because when the Romans were there and they wanted to build a road, the fact that people owned the land in the way was irrelevant. They just built a road anyway. And that became more difficult in subsequent years. But. The fact that there are aqueducts that are still operating, I think in Italy that were built by the Romans is remarkable. Now, it helps when you build things out of stone, but the whole civil engineering story, the idea of the arches you can build, the things you can do to construct stone buildings and so on, those are all very. They were all things that were done in a very, I would say, artisanal way. I mean, we don't know. It wasn't like people were computing things. It was, you know, I don't think it was. Somebody was sitting there doing calculations with Roman numerals and working out sines and cosines. The Egyptians did know a little bit about sines and cosines and so on. In fact, I think the word sine is a mistransliteration through Arabic of Ancient Egyptian into going into Latin. But in any case, and it has to do with arcs and chords. And when you make the sine function, the arc sine is kind of the distance on the circumference of the circle. The chord is the thing that is going straight across. And I think the word for chord, I believe it's in ancient Egyptian transliterated into Arabic, then into Latin, is the thing that gives us the name of the sine function. But we don't know, I think of abstract science being done in Roman times. We know mostly of the practical things that they built. Now there are mysterious things like the Antikythera device, this kind of cog based computer from sometime during the first century bc, the first century AD that is presumably of Greek origin. It has inscriptions in the Greek in the sort of vernacular of the island of Sicily. But that was an example of a piece of kind of Roman era technology that was very singular. We don't really understand how it fits in with other kinds of things. Even though, for example, Cicero does make some reference to the existence of an object like this in something he wrote. But I would say that the Romans civil engineering was the big, big thing. I suspect there's some military technology or at least some, I don't know whether you call it technology, but ways to organize one's army and so on. That was also big for Romans. I mean, I think it just depends on what, you know, what a civilization emphasizes. And Rome definitely emphasized having conquering things, provinces, having highly organized setup where you could have these roads going out all leading to Rome or whatever is the case, those kinds of things. All right, I probably should wrap up in a moment now because I have to go to something else. Oh, I'll try and take one more here from Elsie. Asking about symbolic representations and languages. What you make of the break from computable mathematics in 1800s and 1900s and our current set theoretic foundations. Honestly, I think they're kind of a wrong turn. I think that the set theory, the idea, you know, what is mathematics? Well, one can argue that I've written recently a whole book about the sort of physicalization of metamathematics and the extent to which mathematics ultimately is a particular way of looking at the ruliad, the entangled limit of all possible computations. And there are certain sort of human friendly ways to look at that. Some that lead to physics, some that lead to mathematics. There are ways to look at it that are sort of the types of things that we humans can stick in our minds and think about. As mathematicians. And there are ones that, for which we can't do that, for which really have to grind it down to all those micro details of all the things that are at the level of axioms or even below axioms. Kind of this notion that arose in the late 1800s, early 1900s, was Mathematics is just this formal game where you're putting things down and you can build anything up from them. Hilbert famously talked about you could make mathematics out of tables and chairs, just as you can make it out of this algebraic construct and that algebraic construct. I think that's basically wrong. I think that's not what mathematics as we usefully think of mathematics is now. One particular foundation for mathematics that became popular in the early 1900s was set theory. And set theory had arisen in the work of Gorg Cantor originally on the convergence of trigonometric series. You have some sums of cosines and sines and infinite series, and you say for what values of these parameters does the series converge to a definite value? And the set of places where it converges can be a very elaborate complicated set. And that led Cantor to this sort of elaborate theory of elaborate set theory, which dovetailed with his whole transfinite numbers story. But any case, it came from the rather obscure place, but then it kind of got consumerized. And by the 1960s even people were imagining in the new math it should be taught to all school kids and so on in its rather finite simple form. But the notion that sort of mathematics should be based on this rather obscure kind of thing, that's very non human, that one. This set theory I think is really weird. I mean, there are questions like the Continuum hypothesis, can talk about what it is some other time, but it's a potential axiom of set theory. And we humans have no intuition for whether it's true or not true. I tend to think that there is a way to understand that for us humans it basically will be true, but that it's true of our way of perceiving things, but in any case, or of the things we can construct that sort of fit in with our way of perceiving things. But any case, the fact that we can't sort of. There's no intuitive way to decide it, or so it normally seems. It's something where we just have to assume it or not assume it. And it's very weird to me to base kind of this thing that we want to have kind of an intuitive understanding of in mathematics on this thing which we, which is fundamentally kind of not, you know, doesn't come from those kinds of places. I mean, it almost feels like it's one of these things where people say, well, the foundations of mathematics is important. We should. There should be very solid foundations. Let's make the foundations incomprehensible so they'll seem more solid, so to speak. So we don't have to kind of. So we don't have to engage on this question about are they intuitively obvious? Because they're so obscure that they'd never be intuitively obvious. They never have a chance to be intuitively obvious. So I tend to think that this approach to mathematics that's very much based on. This rather obscure wheeled in set of axioms of set theory is kind of a mistake. I think that thinking about mathematics more as one of the many kinds of things that one can get from just applying explicit kind of symbolic rules is a much better kind of approach. It may be equivalent to set theory in many, many cases, although it probably has a definite thing to say about something like the continuum hypothesis. It's sort of equivalent in the same sense that the gas molecules can have different shapes, yet the gas is still a gas that obeys the gas laws even though it has those different shapes. So similarly, you may be able to use set theory as the axioms or some other quite different foundation that's more explicitly computational as the axioms and end up at sort of this human level, at the kind of fluid dynamics level, with something that is very much the same type of thing. All right, with that, I think I should wrap up and thank you for joining me today and I will be back again another time. See you then. Bye for now.