History of Science and Technology Q&A (May 1, 2024)

Sam. Hello everyone. Welcome to another episode of Q and A about history of science and technology. And, well, let's see, lots of questions here. Querious asks, are there exact matches or just similarities between complexity in nature, biology and evolution, society, political, religious and technology? Interesting question. I've just actually been studying. I sort of surprised myself by coming up with a model for biological evolution which hopefully I will get to post about in the next few days. But these questions about sort of how evolution happens and particularly things like natural selection, in other words, what is the sort of variation and selection are two key elements of kind of evolutionary processes, adaptive evolutionary processes like that, it's like you make many possibilities, you pick particular ones and then you keep going. Given the ones that you have, you make more variations, you pick more, you go and select from that. And it is interesting to see in biological evolution one kind of has this notion that things get discovered in biological evolution. The, the concept of a leaf or something, the concept of branching structures, the concept of, I don't know, using of eyes, of photo sensors, things like that. These things get discovered and then they get built on. And I think it is not totally obvious that one will have a situation where one discovers something and it gets built on as opposed to one discovers something and one just goes backwards, so to speak. It's sort of like discovering something opens up this new vista of possibilities that then allow one to build on that. It's kind of analogous to, oh, I don't know if you're, I mean, there are many different kinds of places where there's sort of, There are many possibilities and you go down a particular path. You're trying to prove a theorem in mathematics. You can say there are different steps we can take at this stage and, and some of them will eventually get to the theorem and others we won't. Chemical synthesis, same kind of thing. You do these chemical operations. You're trying to get to some particular end product and maybe you'll get there, maybe you won't. You have to pick the particular path. But I think in sort of biology there's a question of sort of what is the selection mechanism and in something like technology. So again, what's the selection mechanism? I mean, it's like products go extinct if nobody buys them. It's a little different, but not so different from organisms go extinct if they don't have enough descendants. My impression is that the phenomenon of sort of evolution by the selection process is robust enough that you will see similarities. I have to say that the things I've done very recently with studying biological evolution, it's something I'd kind of, well, I almost did it like 40 years ago, but didn't figure it out at that time. And then quite by chance a few weeks ago, I managed to find some things that sort of have unlocked understanding that. And there's kind of a trade off between you've got sort of a specification for how to build something, then you follow these kind of rules for building it. And the thing you end up building has sort of lots of complexity that is a result of just sort of the computational irreducibility of finding those, of following those rules. So, okay, so maybe said a different way. When you look at a thing that has been sort of adaptively evolved and it's complicated, question is, why is it complicated? Is it complicated because it's been gradually tweaked through this sort of adaptive evolution process, or is it complicated because the dynamics of it growing from its rules typically leads to it looking complicated? So actually it's sort of an interesting question because in engineered technology it really tends to be the case that one's gradually tweaking the thing in a way that one could foresee what those tweaks are going to do. Whereas in biology it's more you change the genes and then the thing will go through some different growth process. And that growth process has a certain autonomy to it. It's not like we tweak every single step, it's like we point it in this direction and then it goes and it evolves that way. And it isn't the case that it is that we didn't get to do all the tweaking, we get to point in that direction and then it autonomously builds a bunch of things. So I think in technology, for example, that is less true. It is more the case that one is in a situation where one is sort of progressively tweaking everything. I mean, the same thing is true with, I don't know, the forms that one uses for this or that thing. They're gradually tweaked or legal kind of contract type things, they're sort of gradually tweaked to deal with different cases. So it's sort of an interesting question to what extent those end up looking the same when it's tweaked with understanding versus change the gene and all sorts of different things happen. And it turns out that with certain tweakings you get a successful result, even though you couldn't foresee every detail the result when it comes to society. It's another interesting question of Sort of the evolution of society. My guess is that that is sort of intermediate between those two cases. I mean, now that I think about it, I think that the sort of technological engineering case is you are much more seeing a reflection of sort of the history of the adaptive process, whereas in biology you're much more seeing kind of the adaptive process underneath, but then lots of autonomous creation of things by virtue of the actual growth processes. My guess is society is intermediate, that there are things where, okay, you can change the culture, the laws, whatever else, and that to some extent you can sort of foresee what will happen there. But to some extent things will happen that you didn't expect. Interesting question, very interesting question. Thank you. Let's see. RBS asks how did the development of atomic theory by scientists such as Democritus, Dalton and Rutherford influence our understanding of discrete structures and the behavior of matter at the atomic scale? Well, I mean, the history of sort of, in antiquity people were arguing as a sort of philosophical matter, is the world made of discrete things like atoms or is it all continuous flow, so to speak. And at the time there wasn't really a clear basis for deciding between those two things. And I'm not even sure people had conceptualized what it would mean to make a sort of experimental determination. It's kind of like we can see it and it's obvious and we can argue for it. But this idea of you do this sort of carefully set up experiment and then you conclude something that was a, you know, that was a much later stage phenomenon. Although the idea of kind of the workflow, the logical workflow of kind of you set up a hypothesis, you try and verify or falsify it, that was a much more 1500s type, Francis Bacon type story, I think, than that kind of idea of that sort of workflow of you assert something and then you check it experimentally. I don't think that workflow really existed in antiquity. I think it's sort of interesting that in antiquity there were concepts of logic, syllogistic logic and so on. This implies that all those kinds of things, but nature I don't think got in that loop. It wasn't a thing where we're sort of betting against nature and trying to establish that by virtue of some experiment and so on, I think that if you ask a question about the relationship between kind of the study of discrete structures at an abstract level, let's say in mathematics, combinatorics, graph theory, things like that, and the relationship of those things to the history of kind of discrete models of the world, well, we can talk about that. I think the, I mean, one notable example is there was a theory that people like Kelvin and Maxwell and so on had in the 1860s, 1870s, about the possibility that there could be atoms that are. Maybe it was later than that, maybe later than that. If there are atoms, if there are different kinds of chemical elements, it was known there were different kinds of chemical elements. What are they? Maybe the atoms of these different chemicals are different knots in the ether, in the continuous thing that was those days in a very Victorian way, the so called luminiferous ether, the light carrying ether, the substance that was supposed to suffuse the universe and be the thing which was the analog for light of the air transmitting sound and so on. So I mean, it is sort of ironic that the ether was kind of, people said, oh, there isn't an ether. But because in 1900 the Michelson Morley experiment got done to do with whether there was an ether drift, whether there was a difference in the speed of propagation of light in different directions as the earth goes around the sun and so on, and no such thing was found. And so people said, oh, well, there isn't anything like that. And then relativity came along and people said there's no preferred reference frame in the universe. It doesn't matter what your absolute speed is. What all that matters is the relative speed of things. And that was sort of what became the physics textbook story. Of course, in modern times we know that the universe does have a definite sort of center of mass. The cosmic microwave background defines essentially a center of mass frame for the universe. The Earth is moving at about a thousandth of the speed of light with respect to that. And also as we start thinking about kind of the, the actual how space is knitted together, for example, in our models of physics, we get to again see that there is in some sense a definite rest frame of the universe, so to speak. That doesn't mean that most phenomena that we experience indeed have the feature that they have relativistic invariance. They are independent of the absolute frame in which one is. But nevertheless there is a small effect of that. But in any case, back to. Back to knots in the ether. So that was a thing where that was kind of discrete mathematics of what knots could you make? And there was sort of a hypothesis, maybe the elements we know, whatever there were 80 something at the time, maybe the elements that we know are precisely the distinct knots that you can make. And Maxwell and Kelvin both had knew a chap called Peter Guthrie Tate, who was a, well, natural Natural scientist and mathematician in Scotland. And I think he'd been a childhood friend of Maxwell's. But any case, he ended up being the person who tried to enumerate knots. Say when are two knots, you know, what are the distinct knots? You know, you can clearly arrange the string in different ways in space, but somehow they're equivalent. They're topologically equivalent knots. A trefoil knot, a knot with a, you know, a 4:1 knot, a 4:2 knot, et cetera, et cetera, et cetera. These are knots that are sort of correspond to a certain number of crossings and so on. What it means to have a crossing, it depends on how you project the knot. Let's not get into knot theory in detail here, but with respect to this question, it is true that knot theory was kind of born out of a, as it turned out, not quite correct theory of atomic sort of theory of matter. I think in terms of other kind of discrete mathy things. I suppose whenever you're doing stoichiometry and you're trying to match up this amount of this chemical with that amount of that chemical and so on. Ultimately those are equations involving linear equations, involving integers and trying to match up those integer equations, that's so called diophantine equations, studied by Diophantus in the first second century A.D. but I don't think people formulated. When people like Dalton were talking about kind of chemistry in terms of atoms and matching up numbers of atoms and reactions and so on. I think that the. Oh yes, you can get out this power tool of diophantine equations. I don't think that was really a thing. I mean, I think people from school children on, so to speak, have been doing sort of by hand, can you puzzle through the stoichiometry of, oh, we need seven of this molecule and three of molecule and so on. I know when we've done these things for wolframalpha and for Wolfram language, now the way we do stoichiometry is just with a power tool of just using the general Darfuntine equation solving techniques that we have to just say, well, that's the answer. So that's a case there. Yeah. A few comments. I would say that the, you know, the history of kind of knowing that matter is discrete is, I don't think Democritus and the Epicureans and folks in antiquity beyond just philosophically saying, oh, and matter is discrete. I don't think they had much in detail to predict or say about how matter would work. Certainly things like the kinetic theory of Gases. The idea that a gas was made of discrete things that had sort of some premonitions in the 1600s, but it really didn't get serious until, what, the 1800s and so on. That was a. People didn't understand the. The idea that, yes, you could actually make a gas out of things bouncing around and that was how you got pressure in air. You know, Robert bole, in the 16, oh, gosh, mid-1600s, I think, had studied kind of the pressure of air and he had these different theories about what air was. How would there be spring? He called it the spring of the air. What was it he talked about? Maybe it was like the content of the air was like a set of microscopic kind of things that were like a fleece of wool, I don't know quite, you know, which we can have some wool and you squash it and it's only somewhat squashable. And he had other kinds of ideas that they were sort of things twirling around each other. Like Descartes had his sort of vortex model of the world. But it wasn't for another 150 years that it really became established that those were discrete molecules bouncing around. I think when it comes to Dalton, I don't know that history as well as I probably should, but, I mean, quite a lot of what was done in chemistry was just sort of counting. Oh, this reaction happens, that reaction happens, this amount of this gas is produced. We can make that all match up if we assume that. That there are molecules where there are certain numbers of atoms with chemical formulas and so on. And it was kind of a numerology type story. It's sort of interesting that when that came about later on, when lots of particles were being discovered in the late 1950s, early 1960s, all these particles being discovered in particle accelerators, and there were all these sort of ideas for what these particles might be. Oh, well. Well, first they were discovered in cosmic rays, then in particle accelerators. There's protons and neutrons, but then there's lambda particles and sigma hyperons and psi cascade hyperons and all kinds of other things. And there's just this sort of complicated zoo of particles. And at first, the kind of understanding why there was this complicated zoo was done very much in terms of group theory and in terms of very abstract mathematics. It's kind of like, well, just as you can say, we can take this thing and sort of rotate it and we've got, I don't know, an icosahedron or something. It has certain symmetry where the icosahedron looks the same when we rotate it this way and that way. People sort of imagine there was some kind of internal degree of freedom that you could sort of rotate to get from a proton to a neutron to a sigma particle, et cetera, et cetera, et cetera. And it was really analyzed in a very theoretical mathematical way that looked very kind of non Mechanical until 1964 or so when Mari Galman and Georges Vaig and so on. And it kind of came up with this idea of quarks and that where we just say, okay, a proton is two up quarks and a down quark, a sigma particle is a sigma plus would be a strange quark, an up quark and an up quark. And then it became rather straightforward to just sort of numerologically say, oh, there must be these particles and not those. And Murray Galman famously predicted the omega minus particle. Three stange quarks altogether a charge. See that will be a. It's charge minus 1, that's right, strangeness 2, strangeness 3 particle. And that was duly observed I think in 1968 in a particle accelerator, I think Brookhaven National Lab. The little track of an omega minus decaying into a psi particle and so on was observed. There was a great sort of triumph of, well, particularly the quark model of being able to predict, yes, there will be this thing. By the way, that idea that there would be that thing I think was much less clear when it was couched in terms of group theory and so on than when it was couched in terms of just add up these quarks as discrete things. But so that was a case where what came first was the abstract group theory. What came later was. Was just the counting type argument. I think in. I mean it's worth remembering that discrete mathematics was not particularly. Was not a particularly significant area of mathematics for the first part of the 20th century comics was, you know, it had come about, people like the Bernoullis had thought about it in terms of the theory of games. In the 1600s, 1700s there were sort of isolated pieces like, you know, Euler 1700s sort of invented graph theory for solving this problem of the afternoon strolls over the bridges of the city of Konigsberg. And this question of kind of could you kind of have a path where you go over all the bridges without crossing any bridge more than once? And that turned into so called Euler circuit for a graph. And he kind of idealized the bridges of Konigsberg into this abstract graph. But they were isolated examples of things like this. The real sort of enthusiastic Interest in discrete mathematics didn't develop until really way into the kind of computer period. A lot of discrete mathematics had also shown up in kind of recreational mathematics. Again, that was somewhat separated from the mainstream of mathematics with its emphasis on algebra and geometry and so on. I suppose another sort of place where discrete mathematics had entered sort of a back doorway was in mathematical logic, where sort of an attempt to mathematicize, to take kind of the logic that had come from Aristotle through Boole in the 1800s and been sort of mathematicized. But to sort of build on that, that amounted to discrete mathematics, although it wasn't really talked about in those terms. And certainly the power tools of discrete mathematics were not used there. So a few thoughts about that. So question here from how do historians know with certainty the identities of prominent historical figures? Could there have been more to the Socrates, Plato, Aristotle, timeline? I think absolutely. I think that, you know, the way that the memory of people and their works and so on gets preserved over the course of millennia is very messy, very arbitrary. I mean, Aristotle was really sort of lucky that his works were picked up by Aquinas and really promoted that way. Otherwise Aristotle would not be nearly as famous. If the Catholic Church and so on had not picked up Aristotle through Aquinas and such like, had not picked up Aristotle, kind of, well, not quite a patron saint, but sort of a key originator of kind of ideas about how to think about the world. I don't think Aristotle would have had nearly the reach that Aristotle had. I think it's always funny when people say, oh, this is a bust of so and so. Well, sometimes it is and sometimes it isn't. Sometimes it's something that was made long after the fact. I mean, kings and such like had the advantage that they often got their image, presumably accurate image on coins, and there were lots of coins. Or maybe they also got their image on some grand monument that was built, that survived. But coins are a really good bet because they're just lots of them. And so somewhere there's going to be a picture of Alexander the Great because he was on a coin. So that becomes a clear sort of. That's distributed. You think about, I don't know, the blockchain pitch of distributed ledgers and so on. When you have coins and you've got lots and lots of coins distributed all over the place, that's a way that you're going to survive in some form or another. I think that the question of kind of a thing that people would often do is they would comment on other people's work. So, for example, Democritus, we just mentioned very little of his work. Essentially, none of his work, except for aphorism, survives, because the only thing that survived is things that other people quoted from him. So one kind of knows he existed. Now, there are even more confusing things because there are people have the same name, like Euclid. There are many Euclids in antiquity. But was it the same Euclid? Was it a different Euclid? One gets confused. I mean, I know even in much more recent times, the Sadi Carnot, the person who first sort of started Talking about the second law of thermodynamics in 1824 or so, he had a cousin, also named Sadi Carnot, who became president of France in the later 1800s. And I was looking at a thermodynamics textbook recently, and by golly, they have a picture of the wrong Sadi Karno there. So even in recent times with, you know, expensive, you know, college textbooks and so on, these things, it's like, well, that isn't really a bust of Socrates. It was somebody completely different who maybe even had the name Socrates, but was not the Socrates who we know. So things can get very, very confused. I think there are sort of rare moments when there is clarity because something gets discovered. I mean, right now, there's this lovely project to try and recover these scrolls that were kind of carbonized in the eruption of Vesuvius in 79 AD that were kind of buried in this library that had originally been part of.