History of Science and Technology Q&A (January 10, 2024)

Sam. Right. Hello there. Welcome to another episode in Q and A about history of science and technology. I am still not in my natural habitat, so weird things might happen, but we'll do our best. All right, let's see a bunch of questions that got saved up here. One from Eric. How often do separate ideas emerge, like convergent evolution and merged either complement each other or make whole ideas that didn't have all the answers themselves? That's an interesting question. When did things kind of sort of surprisingly fit together? For example, you know, I'm kind of thinking there are examples in the history of physics where one had kind of a clue that things were going on. And you know, sometimes like for example, an example would be Brownian motion observed in 1830 or so. Something under a microscope is kicking pollen grains around. What is it? Now? That wasn't a terribly famous effect. It was kind of a thing where that was something that was sort of an obscure effect that was in the textbooks, but nobody really cared about it. Then by 1900, people realized, oh, there's this quite separate thing of the development of the idea of molecules and these things merged together. Another example a bit like that, where again, it's an obscure effect which wasn't really known, I suppose, until was the discovery of the cosmic microwave background where people had discussed the idea of kind of big Bang hot early universe cosmology. And then 1964ish there were actual projects to communicate with communication satellites and there was kind of this background radio noise that was observed. But again, that wasn't like that was a known phenomenon from a long time ago. Let's think there probably are examples of places where things had been known for a long time and now it fit together, so to speak. Well, you know, I suppose one could argue that things about the origin of species and natural selection people had known for a long time there are all these different critters on the Earth. I'm not sure that that was fully explained by natural selection. I mean, that's still an ongoing issue. But it was certainly something where there was this sort of one thing was known. And then these ideas came in and there had been ideas about kind of the kind of the sort of the breeding of species and so on that had predated this kind of notion of actual origin of species. I don't think these are great examples. I kind of feel like there are examples of this. Probably there are even examples in my own life of places where there's sort of convergent evolution of ideas and where you need different Pieces to come together to make the whole. Maybe it's even something that we can see happening. Yeah. I mean, you know, it's constantly the case in our physics project and in things we're doing. Yeah. Okay, I'll give you an example. Right. This is. Yes, there's a much better example, okay. About the second law of thermodynamics, something I've studied a lot for more than 50 years, actually, and recently put out a book on and so on. This question of how does randomness originate? How does heat get generated from systematic mechanical processes? That's the story of thermodynamics. And it was very confusing to people how one could go from something where, in principle, all these molecules have sort of determined motions and so on, to something where we just say the motion seems random. That's the tradition of the second order of thermodynamics that originated in the. Well, in the 1820s and more seriously in the 1860s and sort of continued to today. And it was quite mysterious how this all worked. Tradition, number one. Tradition, number two, the origins of computation and the ideas of computation. And that was originally Godel's theorem, turing machines. That's 1931, 1936. These are ideas of how sort of processes take place that correspond to computations. Okay. It's only in my own efforts, first in the 1980s and now very recently, that one's seen that these two very different traditions of kind of this computational processes, things like undecidability, things like what I call computational irreducibility. This is things from the kind of computation tradition, things from the physics and statistical mechanics tradition of the second law. Finally, we now understand how those merge together and how both we can understand the second law with these computational ideas and how the second law helps us to get intuition about these computational kinds of processes. So I think that's a pretty good example of where after, well, sort of 100 years for the computation ideas, 150 years for the second law ideas, these things finally have merged together. So that's perhaps an example. Let's see. Question from Jamie here. What surprises you most about the history of science and technology? What is there to learn? One thing that often surprises me is many ideas have precursors. There are things where you say, this is new. This has never happened before. You realize, well, actually, it did happen. That's one thing that surprises me. Another is when you see that an idea has a precursor. It often had a precursor without the current context, and the idea was a raw idea that didn't really fit into other Things and people ignored it at the time. And then 50 years, 100 years go by, and then, my gosh, it's a thing. Another thing that surprises me is the timescales for absorption of big ideas are very long. I mean, there are ideas that come in where there's sort of an enthusiasm for something that comes in quickly, five or 10 years, but then the full absorption of those ideas takes 50 or 100 years. And I think the other thing that you always notice in the history of science is in retrospect, people say, oh, yes, that idea was accepted immediately on the ground. It was a generation. On the ground, it was 20, 30 years, whatever. You see that with relativity, for example. You see that with most major ideas. I mean, these ideas about computation as a foundation for thinking about science, which I've been kind of developing since the early 1980s. It, you know, when I first developed them, people were like, oh, that's kind of cool. And in some particular fields, people are like, oh, that's interesting. We're going to adopt it. But the full sort of, yes, that's really the way things work. That's finally kind of. It's been 40 years or more. That's finally a thing where people are like, oh, yeah, you know, that's kind of obviously the way things work. It's kind of ironic. I wrote in the. In the preface to my book A New Kind of Science that came out in 2002, I wrote because I knew it would be the case that the ideas that are in this book at first now will seem shocking, but in time they will come to seem obvious. And 22 years or something later, we're in very much in the. We're riding down the obviousness curve, so to speak, to younger people, to people who were sort of first exposed to this in the context of these kinds of ideas, they do come to. They have come to seem quite obvious, even though at the time they were like, shocking. And people couldn't sort of often couldn't get their. Get their minds around them. So that's one kind of thing. I think another thing that is also sort of interesting about the history of science and technology is how much individual contributions matter. That is, there are times when science develops in a very collective way where there's just a lot of detail to fill in, lots of genomes to work out, lots of chemicals to study, things like this, lots of detailed things to study. But many of the big advances are very small numbers of people. And that's something that in kind of some version of the history of science, it's just like throw in more people, more things will happen. Often not the case. Often, kind of when you want something really unusual and unexpected to happen, it's only one person, two people, whatever, who are going to go out on that limb and make that new thing happen. If you say let's get the big collective to do it, the big collective is not going to do it. The big collective is going to be kind of voting to do what the sort of to do the average thing. And that's the story of a lot of large scale science funding, et cetera, et cetera. Those are things where particularly in theoretical ideas is. It's kind of the story of small numbers of people and sometimes even small numbers of people, where those individuals repeatedly do things in a particular direction. Another thing I suppose I could say is that at some sense, most people who've made significant contributions in science, they have a certain shtick. And that shtick may be one that. And there's sort of a question of does that shtick resonate with what represents progress at that particular time in history? And that shtick may be a very kind of abstracted one where you can use the same meta method, so to speak, across a bunch of different areas and make progress. But I think all of us, for better or worse, end up developing certain patterns of thought. And there's a question of sort of applying those patterns of thought across different areas. For myself, I could say that sort of in lots of different areas where I've worked, it's all sort of a story of, well, what's the foundation? What are the underlying primitives? How can you build up from those underlying primitives into a big structure? That's what I've tried to do both in science and in technology. And I've been lucky that that kind of shtick has worked out really well in a bunch of different areas. And I think there are even more areas where it can work well. But it's sort of the same pattern of work and sort of repeated in different areas. And that's what you see in most people. It's kind of like there's a particular approach to doing things and you get to try that over and over again. I think it's partly a question of once that approach has worked and you really understand it, it's sort of, there's a certain economy of scale to try the same thing again. And it doesn't tend to be the case that it's sort of something quite different that you try next. Let's see another question Here from Lola. History of timekeeping. How did civilizations create the calendar and clocks? What science supports this? The story of the calendar is a long and complicated one. I think a lot of what we have, civilization getting organized, was, so far as we know, largely a story of ancient Babylon, because that was the time when cities were first coming into existence. And that was a time when sort of people had to get organized. It wasn't just, oh, yeah, I know everybody who's involved and, you know, I'll just trade my sheep and my barley and things like this. And it's like we're all kind of, we're all friends and we just sort of know what's going on. It then was there started to be, you know, 100,000 people, and you had to have these organized ways of saying, you know, a price for this and you're exchanging it with money. And how much barley am I getting? Oh, I can weigh it in some standard way, you know, how long is it going to be? Rather than, oh, it's kind of going to be roughly, you know, I'll pay you back in next season type thing. It started to be the need to be more precise. And I think the, the thing that we certainly get from, from the Babylonians, I mean, they believed there were, at least for a while, there were 360 days in the year. That's where we get the angles, so to speak. 360 degrees in a full circle. The idea of 24 hours in a day, 60 minutes in an hour. Those were, I believe, Babylonian constructs. I'm not sure about seconds in a minute. That may have been Babylonian. That may have been later. At the time, the forms of timekeeping were. There were water clocks where you're just, you know, you put a bunch of water in something and you let it stream out and it takes a few hours. And that's kind of how you, how you determine time. And that's good for a day's worth of time. Then there were astronomical ways of observing time, and those astronomical ways were on much longer timescales. I mean, clearly there was a day was a significant thing. There were also sundials where you could kind of mark off the hours of the day. And of course, those sundials changed their character with seasons. And that was a thing that was significant. Now it may have been important that sort of some early civilization was a bit closer to the equator than lots of people live today. That probably had an effect on sort of. The sundials don't have to change as much in those Latitudes, I think. So those are sort of two methods of timekeeping. And when it comes to sort of longer scale times like the lunar months, where people could perfectly well see it's a full moon, it's a new moon, that was a good way of measuring sort of longer periods of time. And people were also, I think, very attuned to what was happening in the heavens. I mean, you know, clearly if the only form of light at night is fires, you tend to see much darker, night skies, you don't tend to see. You tend to be much more aware of what's happening in the heavens, so to speak. And I think people were, you know, when's the solstice, when's the equinox? Those were things that I think loomed much larger in people's lives or when's the new moon, when's the full moon and so on, those loomed much larger in people's lives back in antiquity and so on than they do today. And so a lot of kind of observation of kind of what, you know, how did those things work? How long was a lunar month, you know, how many lunar months were there in a year, how many days were there in a year? These kinds of things, people really paid attention to that. I think it was quite early. I mean, even certainly in Babylonian times and certainly by the time of people like Ptolemy, around 1st century A.D. there was lots known about, lots of details known about astronomy, lots of details known about different forms of lunar month, the Draconic month. There are different ways of measuring when does the Moon come back to where it was before, and that is affected by where the Moon is in its orbit and where the Earth is in its orbit and so on. All these different things were starting to be understood. The Saros series of the 18 year and a bit kind of way in which the configuration of the Moon and sun and Earth came back to something sort of similar enough that the eclipses would be the same. That was another kind of thing that was already known around 2,000 years ago. So those are all things that were understood now. There were, in terms of sort of the more detailed kind of measurement of time. There were a couple of different dimensions. I mean, one was, there's a lot of interest in kind of time on ships because that was important for navigation. But it was really tough to get, you know, to keep time properly on ship. And that was sort of a big challenge that survived until, what, the 1700s of, you know, how do you get, if you want to measure longitude, if you measure latitude pretty easily by just Observing the position of the sun and so on. But if you want to measure longitude, you need to know the time at which things happen, the time that the sun rises, et cetera, et cetera, et cetera. And for that you have to have something that reliably keeps time even though your ship is pitching up and down. So thing that happened in the 1600s was clockwork and the idea of clocks that would have some kind of clockwork mechanism. I suppose what happened before that was pendulums. And people certainly knew about pendulums in antiquity. I wonder whether seconds originated even in antiquity through a pendulum swinging back and forth. I know Galileo, for example, when he was interested in measuring time, he had a pendulum where he could see how many swings of the pendulum. He also used his own pulse. And you know, I think he was a. Must have been in a good, in good shape, cool cucumber or something. You know, he was like, my heart rate is 60 beats per, per minute. You know, one second per heartbeat. I think. Well, Galileo was a small red haired chap, quite pugnacious. So I don't know what that tells one about some what knowing that his heart rate, he thinks, he claimed at least because he used it to, to measure different kinds of things was, you know, he assumed it was one beat per second, so to speak. But I mean, the idea that one could, you know, one had pendulum clocks and so on that existed and then one had kind of the notion of clockwork to turn the motion of the pendulum into the kind of rotary motion of clock faces, I think, I don't know actually when the sort of standard clock face was invented, I'm guessing 1600s. And then kind of later on came the idea of having springs to drive things and having this sort of little tiny back and forth thing driven by a spring that could be inside a watch, as opposed to the big kind of grandfather clock thing with a pendulum swinging back and forth. One of the key things about timekeeping is a pendulum. In a first approximation, it doesn't matter how much the pendulum is swinging. It only matters how long the pendulum is, how long it takes to go from one side to the other. In other words, you might think as a pendulum slows down of not swinging quite as far as on from one side to the other, that the time it would take to swing from one side to the other would, would change. But it doesn't. In a first approximation. In a first approximation, it's just a formula for the period that's independent of the, of how, of the amplitude of the swings that only depends on the. On the length of the pendulum and the. And the amount and the strength of gravity and things like this in. In the sort of. The fancier version involves elliptic functions and things, and it does depend on the amplitude, but. But for small oscillations, the pendulum is still accurate, even though it might be sort of running down and going less to each side than the other. So in terms of things like the calendar, at different times, people sort of wanted to reform the calendar because things had gone wrong with the calendar. It's worth saying that back in antiquity, most dates were so called regnal dates. They were like in the reign of king, so and so, in the reign of emperor, so and so the first year of that emperor's reign and so on. The notion of a sort of an absolute timescale for dates is a more recent idea. But then the question was, what about the months of the year? Well, famously, Julius Caesar added, I guess, added August, although July is the kind of the Julius month, but August is the Augustus month, so to speak. And he did that because things had sort of gotten out of whack with the previous months that have been put in there. And then things ran. And at that time, leap years were added, and at that time, sort of all was running just fine. By the 1500s, things hadn't gone quite right, because I think in the 1500s what had happened is because the length of a year is 365.2481 days, I think, rather than 365.25 days, which is what you would get with the standard rule for leap years, where you just say add a leap day out of February 29th every four years. That doesn't quite correctly give you the right number of days in the year. So what you've got to DO is approximate 365.2481 by, you know, you could say, well, I'm going to add a February 29th at that time. I'm going to not have a February 29th every hundred years. Let's say I'm going to have, you know, I'm going to gradually adjust, you know, I'm going to have this date added and this date subtracted every so often. And in 15, what was it? 1582, if I'm remembering correctly, I have that date wrong. Pope Gregory had sort of noticed that things had gotten very out of whack with the calendar. I think one of the things was that Christmas, you know, December 25th, give or take, had sort of swung into the summer by that time. In other Words, the days of the year weren't aligned properly with the seasons. So he got together a group of astronomers and so on and said, we're going to reform the calendar. That led from the Julian calendar, which is what had been used, the Julius Caesar calendar, had been used in kind of the West. And then that led to the Gregorian calendar. The Gregorian calendar came in very gradually. I mean, there were places that were adding the Gregorian calendar even in the early 20th century. And it's very confusing because there are dates like Newton's date of birth, which was Christmas Day in 1642, give or take, but that was in the old style calendar. But by the time Newton was out and about, and particularly by the time he died in 1727, the calendar had been changed in England from the Julian calendar to the Gregorian calendar. And so his date of birth is a different date. For if you have this particular day, that day is labeled differently in the original Julian calendar, which was enforced when Newton was born, and the Gregorian calendar, which was enforced by the time Newton was an adult. So the confusing thing. But anyway, the Gregorian calendar is what we've used to today. Although there are gradual things that have to be updated. There are leap seconds that come in because in fact, the length of the year, that is the time it takes the Earth to go around the sun relative to the length of the day. The time it takes the Earth to have one rotation that's continually changing, those relative lengths are continually changing. In fact, every few years one has to add or subtract a leap second because the Earth is roughly slowing down in its rotation. But how much it slows down depends on what earthquakes happen. It might depend on climate issues, all kinds of things like this. I think there hasn't been a leap second added for maybe a decade or two. But in terms of that's sort of how one defines time. There are all kinds of other issues in the definition of time. I mean, one thing to say is, is up until the early 1800s, different places could sort of have their own time zone, could have their own time, and mostly that was determined by the sun. And there was this notion of so called local mean time, which was, that's what we will call it today, which was kind of the sundial time of a particular place. But as soon as people started being able to communicate across large distances, telegraphs, there were trains going back and forth. By the early 1800s, then it became important to actually have sort of a uniform way of describing times. And you know, the US was the place where time zones, because it was a country big enough and with railroads going far enough and telegraph lines going far enough, that it became important to define the notion of time zones. And there were all kinds of features of time zones. And when I was growing up in England, I barely knew about time zones because England is a small enough country. There's just one time. The only thing one did know about is the notion of summertime, the notion that one would have daylight savings time, one would switch the clocks so that it was always said so that the farmers would be. So it was convenient for the farmers. I'm not sure there have been different arguments for daylight savings time at different times, some of them more convincing than others. The thing that always used to happen in England, which doesn't happen in the US in the us, Although there are different states that can sort of decide to use daylight savings time, Arizona being a famous one, that makes different choices, different times and different parts and so on, but there are different. The notion of there is a well defined algorithm in the US or at least there has been for when daylight savings time comes into effect in England. When I was growing up, it kind of depended on which political party was in power, whether there was summertime or double summertime or whatever else. I have to say I didn't follow quite what the arguments were for what kind of time, but. But it's probably just as well that computers weren't set up by that time where there was kind of a. Computers without networking would have a hard time with all of these sort of arbitrary choices of when there is summertime, daylight savings time or not. You know, somewhere in all of this, there's a question of sort of how does time get kept accurately? And, you know, it was all clockwork and pendula and things like that until. Until the 1950s, when atomic clocks. Well, actually there were quartz crystal clocks where you were using the vibration of quartz crystal that was probably 1940s, maybe 1950s. But then subsequently, the notion of an atomic clock where you're making use of the actual detailed frequency of atomic excitation levels and things to determine time, where you're basically just counting how many oscillations of this occur. And that gives you the passage of time. And now, for example, the definition, the official definition of the second is based on the particular details of the cesium atom, a particular frequency of the transitions in a cesium atom, and that kind of gives you this time that's based purely on the characteristics of any old cesium atom. Now, having said any old cesium atom, there is actually a bit of a detail because it does matter. There's gravitational redshift. It's affected by the presence of gravitational fields. Things are. It's a little trickier than that, but that's kind of the modern way of keeping time that is independent of looking at the motion of the moon, the rotation of the Earth, and independent of kind of the mechanics of a pendulum swinging back and forth, The. Well, let's see. I was asking the history of daylight savings time, and I don't know that in detail. The Kelly is asking, how would you keep track of sync up all your devices before they were all networked together? Yeah, I mean, not all my devices are networked together. And. And I have to say there are some that haven't made the change from when the last transition of daylight savings time. And. And sometimes they get left for six months before they make the change. And I just have to remember that's off by an hour. You know, in modern times, there's this thing called nntp, the Network Time Protocol. And there's this. It's in Colorado, I think, is the. The big source of NNTP associated with National Institute of Standards and Technology there, based on an atomic clock, is kind of this propagation of time signals to all the Internet devices. But of course, that's tricky because it takes time for that signal to propagate to different devices. So there's a whole elaborate story of kind of how do you know? How do you know when is now, so to speak. By the way, that's kind of the story of sort of relativity and Einstein and all this kind of thing. And when Einstein invented special relativity in 1905, one of the big questions was, what counts as simultaneity? How do you know that these two things happened at the same time? And the only way you can know sort of the relative times is you send a signal from one thing to the other. And kind of the concept is the fastest you can send that signal is the speed of light. And that kind of determines what definitions of simultaneity you can have. But at the time, people were pretty interested in definitions of simultaneity. In Switzerland, where Einstein lived, there was sort of a, let's be very precise about our train times and things like that. And there were all kinds of issues of are the clocks at different train stations along the train line? Are they all synchronized? Right. And they were synchronized by electrical signals going from one to another. And it was sort of a matter of discussion kind of, you know, would the electrical Signals go fast enough to synchronize the clock so that they were genuinely at the same time. Of course, Einstein realized that genuinely at the same time is not really something you can define in an absolute way. That's something that you have to define by actually sending signals from one to the other, and hence relativity and so on. So. But that's a thing that sort of shows up in synchronizing sort of clocks on the Internet today. We have the same issue that people had back in those days, synchronizing the train clocks and so on. LCQ says rather, rather complementarily. How do you get to know so much in such depth about how many different, so many different historical topics? I don't know. I think I have a decent memory and I sort of gradually pick up more and more facts. And the trick is always to understand sort of these broader narratives because if it was just individual facts, there's no chance that I would remember them. The way that one ends up remembering things is by kind of fitting them into broader, at least for me, is by fitting them into kind of broader narratives. And then there are some things where it's like, okay, that's a thing I'm just going to remember because it's a useful thing to know. Like 1642 is a good year to remember. It's the year Galileo died, Newton was born, Pascal invented a mechanical calculator. Kind of gives you a sense of sort of what was happening at that time, I think. So there are useful sort of anchor points to remember, I think also I've been lucky enough to work on a lot of different things. And so any given kind of topic, I will often have done a very deep dive into something sort of close to that topic. And in doing that deep dive, I will have done my homework well enough to have learned sort of the slightly broader area around that topic. And that's how one gets to know a bunch of things. I've often done sort of deep dives into the biographies of various historical scientific figures. And there's always that deep dive has many details, but that deep dive there are always ambient pieces of science history that you pick up along the way there. Let's see. LAB is commenting. Blockchains might be the. The evolution of agreed upon ledgers with one single agreed upon time. That's an interesting point I haven't seen. You know, people have tried to tokenize a zillion things. You know, they, they tokenize the things like network bandwidth. You know, it's kind of like I'm going to Instead of, instead of just, I'm going to get tokens for making network bandwidth be used, I'm going to get tokens for storing things and so on. Interesting to think about. Could you get tokens for helping to synchronize time, you know, by, by propagating the NNTP protocol through your devices, things like this. So maybe I have this vague recollection that somebody was trying to promote a blockchain on that basis. But this notion of simultaneity, blockchains actually do simultaneity in a rather boring way, typically because the notion is in something like in typical blockchains, it's a distributed ledger. And what does that mean? Well, typically that means there are many copies of the same ledger. There are many copies of the kind of recording of what happened. And the question and sort of the idea is, oh, there are 10,000 copies or I don't know how many there are for bitcoin these days, maybe let's say 5,000. I'm not sure how many. There are different copies of that same ledger that says this is the sequence of transactions that happened on the bitcoin blockchain. And the way it works is that any a new transaction comes in, it will get propagated through this network of, of, well, miners, people who have copies of the blockchain, copies of the ledger. And then it's a question of does everybody come to agreement about, yes, this was a valid transaction, let's add it to all copies of the ledger. That takes a surprisingly long time. I mean, every block is the transactions are put together in blocks. There's maybe 10 minutes per block on a fairly active blockchain. And then there's the question of, well, do we really get full agreement? And often there's a sort of 24 hour timeout for that. And so this notion of there is a moment when everybody kind of agrees. I suppose there is a notion of simultaneity there, but it's very slow simultaneity. The much more interesting thing is a distributed blockchain where you really have the idea that there is only local agreement. Let's imagine all of those blockchain ledgers were distributed around the earth or the solar system or whatever else. And you've got a thing where you locally agree every second. Let's say the things that are local nearby agree that they have the same transactions listed, but they don't necessarily agree with something further away. Just as the question of what already happened, did that star go supernova? Well, you know, locally to the, the the folks that are there, they know very well that it went supernova. But do we know, and at what time do we say that, you know, do we say it went supernova at 12 noon on August, you know, 28th or something? What does that mean? Does that mean when did we notice that it went supernova? Does that mean, do we have a, a notion of time where we've given dates that are sort of somehow correspond to our dates? We what does it mean? What does that simultaneity mean? And so similarly, one can imagine for a blockchain to have something which is locally coherent, but globally not coherent. And it gradually, just like in physics, it gradually kind of comes to global agreement. And actually I've tried to work out sort of schemes for distributed blockchain that work using physics type methods to have sort of local coherence, globally not coherent. That leads you to things like you can, if you want to know sort of your, your bank balance, if you want to know it quickly, you can know it approximately, if you want to know it exactly, you have to wait for sort of all the signals to come in from everywhere. But that's, that's a kind of a, some thoughts about blockchains and time. Let's see, go back to some of these other questions. Kalman asks, do you think the Fourier transform is fundamental to nature historically? It appears in quantum field theory, quantum computing, signal processing, et cetera. Well, what is a Fourier transform? So when I'm talking to you, my vocal cords are vibrating. We're producing all these sounds. Those sounds have different frequencies combined into them. So for example, on a piano, every note of the piano at least has a basic frequency associated with it, and each different note has a different basic frequency. If you play a chord, you're going to get two basic frequencies combined. Fourier analysis is the story of, given that you know what the sort of the pressure wave from the sound looks like as a function of time, decompose that into sort of the individual frequencies associated with particular notes. In actuality, in a piano, any given note has a fundamental frequency, but it has a bunch of harmonics of that frequency and a bunch of other detailed sort of extra frequencies and that which give the kind of the timbre of the note. And just like with a human, if I tried to whistle a definite frequency, I probably wouldn't hit a single frequency. And there will be this distribution of frequencies. And Fourier analysis is the story of taking a signal and decomposing it into these different frequencies. And any signal you can represent either by this is what happens as a function of time. Or this is what happens at different frequencies. And when you take the sort of pure tones of those different frequencies and combine them together, you'll get the thing that corresponds to the signal as a function of time. Another example of this is with, for example, the tides. Tides, the water is going up and down at different times of day. And you can just look at the tide as a function of time. In this harbor, the tide was plus 6ft at this time of day and minus 3ft at that time of day. And in the course of a day it does this or that. In the course of a lunar month it does this or that. In the course of different amounts of time, it goes up and down different ways. In addition to looking at the tide as a function of time, you can say, well, what are the frequency components and the tides? And so then there are definite, I think there's an 18 year piece, there's a bunch of different frequencies of things going up and down in the tides. So Fourier analysis is the story of, well, what frequencies are there in the signal? And it's any given signal you can represent in the time domain as just, oh, it's doing this, it's going louder, softer. As a function of time or in the frequency domain, it's mostly at, I don't know, 300 hertz versus it's mostly at 800 hertz and so on. These are equivalent representations. Now so that duality between representing things in the time domain and the frequency domain is important in lots of areas of physics. Because, for example, if you have something like I was talking about a pendulum earlier, a pendulum of a certain length has a certain characteristic frequency. So if you want to know this signal, how much effect does it have on that pendulum? It matters what component of that signal is in the range of frequencies which are the natural frequencies of the pendulum. So there are places where it's useful to analyze things in terms of frequency and ones where it's useful to analyze things in terms of, as a function of time. The original invention of Fourier analysis by Joseph Fourier, that was, oh boy, it must have been 1810 ish. Fourier was a kind of a person who worked with Napoleon. He was partly an Egyptologist who went with Napoleon on his Egyptian efforts, but he was also a mathematician. He was particularly interested in the theory of heat and the question of sort of how heat, how to analyze how heat would flow in. For example, if you have, if you heat one end of a metal bar, how long does it take for the heat to get to the other end, so to speak. And he invented Fourier analysis as a way to talk about the different kinds of the solutions to the heat equation that would determine how that, how that sort of heat propagates down the metal bar. People had known about the idea of frequencies, discrete frequencies in music and things. The Pythagoreans knew about that and they knew about sort of the ratios. An octave is a factor of two in frequency. A perfect fifth is three halves ratio frequency. All those kinds of things that was known to the Pythagoreans in the 5th century BC and the Thing that, but sort of the Fourier story was at first, how do you represent something in terms of a discrete set of frequencies? Then later on it was how do you make sort of this signal represented either in the frequency domain or in the time domain? So that was the thing from the early 1800s, I would say that the way in which that entered other areas of science, a big place where it entered as a quantum mechanics, because it turns out that in quantum mechanics you can. The position and momentum are sort of like the time domain and the frequency domain. So when you have, if you have a particle that is in kind of standard quantum mechanics, the momentum of that particle, the particle has a wave function and the wave function has all these wiggles in it. And essentially the frequency of those wiggles gives the momentum of the corresponding particle. And so this idea. So momentum is associated with frequency in quantum mechanics and in quantum field theory and so on, same story. It's always the frequency domain is what gives you the kind of things with definite momenta that is sort of complementary to the usually called configuration space representation, where it's the actual positions of things. And so when you work out sort of calculations about scattering of particles and things like that, you'll be often operating in, oh, I'm going to keep track of the momentum of these particles. That's a Fourier component of the quantum field, so to speak. So those are places. Now in signal processing, the main place where Fourier analysis comes in is you've got, you know, you're talking, you've got a microphone. There are pressure waves in the air that correspond, that are generated by the motion of your vocal cords and things like this. Or if you're playing a musical instrument by a string moving or, or air being blown in a tube or something like this that's generating pressure waves. And that pressure, those pressure waves in a loudspeaker, the loudspeaker cone is wiggling back and forth and pushing the air in these pressure waves. Well, now the question is, okay, so maybe some of those pressure waves are for us. When we perceive the sound, we're like, oh, that's a high frequency sound, that's a low frequency sound. For example, I don't know, you might have a hum from something like a 60 Hz hum from something. And you might say, I don't want to hear sounds that are at 60 hertz, I only want to hear sounds that are at, let's say, 1500 hertz, where lots of speech sounds are, or something like this. And so then how do I do that? Well, I have to filter out the sounds that are at low frequencies and, and leave the sounds at higher frequencies. And so then I might have a high pass filter which passes only high frequency sounds. And that's again a story of fur analysis. And the whole development of signal processing, which is sort of a story of how do you make, for example, an electric circuit that will sort of get rid of low frequency sounds. And the big idea there is capacitors. The capacitor is something where you've got an electrical signal and the capacitor keeps on just sort of storing charge and then releasing it. And that's kind of the way in which you sort of buffer up the individual kind of amounts of current and things. And that's sort of the way that you smooth things out. If you want to just pass the. In that case, that would be just passing the low frequencies. But this whole idea about how do you design a filter that will pass only certain frequencies, that ends up being a story of Fourier analysis. When you analyze electric circuits, it's often convenient to do that in the frequency domain. And that's a Fourier analysis story. In digital signal processing, one is not using capacitors and inductors and things like that to do things with signals. One is instead using one's instead taking the signal as a digital signal and one's doing mathematical operations on it. And that's a whole other story. Digital signal processing, I guess, got big. When was it when electronics had gotten fast enough? Probably 1980s. I think that was when sort of typical signal processing started to become digital and use computers rather than using discrete circuit components. Let's see, Question here. Coming back to time, when did time become an important variable in science? Interesting question. I mean, the very notion of a variable is really a concept of mathematics. And that sort of development of mathematics didn't really come into existence until, well, until 1600s and so on. But actually there's a different thing to say, which is when you make a Plot, for example, you plot a thing as a function of time, you start talking about things happening as a function of time. I think there was a. Erasmus, I think was his name, that must have been 1200, something like that. That was a person who started talking about kind of the progression of things with time as a kind of a pre scientific type of notion. Something where there was a kind of a, a things happening through time as opposed to sort of. And things like sort of making a plot of the position of something as a function of time. That seems totally obvious to us today. I don't think it was obvious in antiquity. I don't think anybody would have drawn such a thing. I mean people drew geometrical figures, but they were just like, here's the triangle. It is what it is right now. The idea that you might draw sort of the progression of the position of the sun as a function of time. I believe that was something that didn't come in until maybe as late as the 1400s actually. And this idea that you are looking at sort of how systems behave through time, certainly that is present in what Galileo was talking about. When Galileo discovered kind of the fact that there's this sort of parabolic relationship between position and time as something falls under gravity there you absolutely need a notion of how does it behave as a function of time. The idea that time would be sort of a variable, I think that's sort of a Galileo type construct. Sort of gets more sophisticated as soon as you have calculus with Newton and so on that really time is the. You have this, you know, these, these. You're looking at. Well, Newton had this idea of fluxions which were kind of variables that were showing their change through time. You know, X dots and things like this that were kind of a thing that was not a thing, an X. So in a sense, I suppose that's a Newton kind of concept of that, that one would have sort of the. The thing X and then the fluxion of X X dot, which is the time variation of X. So I suppose that's a Newton and calculus kind of story. And this notion that one could have the instantaneous change of the thing with time, which is again not an obvious concept. You could say, okay, I've got this happening today, that happening tomorrow. I've got sort of discrete moments in time. But this idea that something could be continuously changing with time, my guess is that's pretty much a construct of Newton. And I think this idea of kind of variables as a thing that you could really distinguish the notion of variables, I think that Came in only with Newton. I think that the idea that you could have sort of a disembodied algebraic kind of variable was something needed by Newton for his studies in mechanics, but it hadn't really been explicitly enunciated before that time. Let's see, Question here about. Let's see, Question from Matt about. Why do you suppose no one tried to continue with Tesla's, Nikola Tesla's incomplete inventions? I don't know that much about Tesla. I think I remember a number of years ago visiting Tesla's birthplace in Croatia and realizing you couldn't drive a Tesla car there, at least at that time, because you couldn't keep it charged in that part of the world. But I'm sure that's been rectified in the years since. But the, I mean, Tesla was a person with all kinds of crazy ideas and occasionally some of them landed in sensible ways. I don't really know enough about the level of definiteness. I mean, somehow there are people like for example, Edison, Marconi, these kinds of people who took what were sort of idea inventions and turned them into deployment and companies and all this kind of thing. Tesla did much less of that. And so it's often hard to tell. You have the idea for. Oh, I don't know. There are lots of things where the idea existed a long time before it was reduced to practice. The telephone is a good example. The idea of transmitting voice over electrical cables and things, that was an idea that had existed for many years, but you couldn't quite make it work. And there's sort of engineering detail to make it actually work. And sometimes sort of the core idea, I mean, we could say today that, oh, I don't know, you know, the Star Trek communicator became like the flip phone, so to speak. And it kind of. But the Star Trek communicator didn't invent the cell phone. There had to be lots of details about how, you know, signal handoff worked and this and that and the other to get to the cell phone. So it's always difficult to go from sort of the raw idea to the engineering deployment. And I don't know, you know, I think some of Tesla's ideas about, for example, wirelessly transmitting electricity and which you could say is kind of the wireless charging of today. But I don't know how, you know, I don't know whether the engineering problems that had to be solved, whether it's kind of 90 engineering problems that had to be solved and 10% the idea of transmitting power wirelessly, that. That was what's the story? So, and I think, I don't know all of Tesla's inventions by any means. But, you know, I think there were a bunch of kind of directed energy weaponry type things and so on. And I, I, you know, again, the reduction of that to practice I think is probably in those cases, 99% of the story. So it's kind of like there are, I mean, one could as well say, let's take a bunch of science fiction and say, let's take every invention in 2001 a space odyssey and try and make it real. And, you know, that's sort of a. There's a lot of effort in making it real. So that would be my guess as to why things didn't, quote, get followed up, because there just wasn't enough there that it was sort of enough of a reduction to practice. But that may be quite unfair. I mean, it may be that there was certainly, you know, at any given time, there's always a certain amount of human competitiveness going on. And, you know, people saying, I've got my patent, you've got your patent. You know, how does this work? And I don't know, you know, sometimes, sometimes it happens that there are things that in science and technology that go the way they go for sort of purely human. Somebody was annoyed at somebody and so they ignored something. I think that that tends to work out over the course of time, but I'm not sure how long it takes. See, they wrap up soon here. But. Steve Felipe says, as a software engineer, I discover elegant academic programming languages all the time, but they never seem to gain much traction in industry. On the other hand, we have languages like JavaScript, which was pretty much developed as a prototype, but is now ubiquitous in web development. So I'd be curious to hear your thoughts on the history of organic development of programming languages. Yeah, I mean, the thing to say is most programming languages at their core are quite small. And, you know, the claim that, you know, JavaScript was written over a weekend is not wholly inconceivable because the core is quite small. To make them efficient, that's one thing. But the bigger thing is what's the ecosystem around them. I mean, for example, Haskell famously, originally was a very theoretical language which had no input output. It's like it could sit there and it could do things internally and it could, it's kind of like the disembodied brain. It could be, it could think all these deep thoughts, but it could never communicate them with the outside world or get anything from the outside. World to say what to do. So there's one thing. How does the ecosystem develop of practicality? In my own efforts to build a computational language, it's been a very different story from the programming languages. The programming languages tend to be, yes, it's going to be. I can put it together, there's a small number of components. I can just sort of assemble the thing. What we've tried to do with our computational language over the last 36 years or so is put in all of these, all of these different capabilities, all sort of coherently organized, whether it's dealing with video or combinatorial optimization or knowledge about chemistry or whatever else, to fit all these things together. So there is a sort of a full scale, uniform computational way of thinking about the world. That's a very different kind of idea than most programming languages. Most programming languages, it's like, let's wrap some things around the intrinsic operations of a computer with loops and variables and things like that. And then that's the core programming language that's pretty easy to construct, at least easy to construct in a first approximation. And then there are all these libraries that start getting added and different people add different libraries and there's this sort of giant, well, mess typically of capabilities that get sort of grafted on that aren't part of the core language but are just sort of added for practicality of various kinds. Most academic languages never get those things added. They never have. They never have the deployment. They don't, you know, they're getting the thing to run in all these different environments and you know, and even these different kinds of platforms and so on, getting it to be, you know, in a server configuration or this configuration, that it's typically those things aren't done for sort of academic languages because it's a whole bunch of work and it's a whole bunch of software engineering. And typically the creation of those languages is done for a reason of sort of the theory of programming languages, not the practicality of, oh, I'm going to get a bunch of software engineers to make this run and all these different platforms and server configurations and how do we deal with interrupts and what do we do with this and, and what about IO in that situation and how does it, how does it work across parallel machines or all those kinds of things. Those are, those are not, you know, there is a, it's kind of a, it tends to be a let's do this thing to emphasize this particular theoretical idea. I think the, this usually one of the things that happens with languages is people if people use them, you can't really change them because it's kind of like, well, there's all this code out there that works this way. And if you've got it wrong at the beginning, you're kind of in a bad situation because you've got to say, oh, we're going to break compatibility. Python has done that, for example, of breaking compatibility and has just horrendous consequences. We fortunately have in the last 36 years, touch wood, so to speak, never had to make a major break of compatibility. The things that, you know in version one, Mathematica program will still run in version 14 today. And that's been something. I think we were both. It's a combination of luck and judgment, so to speak. It really helped that when I was building the first version of what's now Wolfram language, I had built a previous system, smp, and had made many of the mistakes in that system. So by the time I was building what's now Wolfram language, didn't make those mistakes. So we were able to just take what we did 36 years ago and we've been able to kind of keep compatibility all that time. But that's something that happens. I would say that this question of, of some languages that have been developed for very pragmatic reasons get propelled by their use case, for example, C, the C programming language was the language used to implement the Unix operating system. And it really got propelled by that, by the fact that people were starting to use the Unix operating system. It was then. It was a nice language, but it was then sort of the natural thing, and people sort of knew. Well, Unix had been developed in C, that was in the late 1970s, and that was a boost to it. I have to say. One of the things that sometimes disappoints me today is there's an awful lot of things that have been implemented in Wolfram language, like Wolfram Alpha, for example, like a lot of systems out there in the world have been implemented in Wolfram language, but nobody knows it. It's kind of like, you might say we get a big boost by people knowing. Gosh, when I go into this kind of retail store and I'm buying this, well, it's a Wolfram language system that's generating all the data for that, but nobody knows that. And I'm not sure people care at this point. They just say, oh, the system works in some way. So the sort of. The boost languages from. Yes, it got used to do this. It got used to discover this, invent this, whatever else isn't so much there and it tends to be the case that if the language sort of hangs out in, in a particular case. So, for example JavaScript sort of hanging out on, in web browsers and things. Well, Java famously, you know, Sun Microsystems really was pushing, you know, Java as the language of the web. Right when the web was coming into prominence at the beginning of the 1990s. It kind of, it ran up Sun's market cap and so on to say, you know, sun has invented Java. Java is the language of the web. That was a great piece of marketing. I'm not sure that Java really was. I mean for a while it kind of had, it was all very confused because there was Java that was being run in sort of client side and there was Java that was being run on servers and it was, it was just, it was all a bit, a bit confused for a while. I mean even Java itself had originated in this thing called Ginny I guess which was a. Intended for set top boxes for sort of the, the thing to run inside the inside the thing that went along with your television to decode television signals, satellite signals, things like this, cable signals and so on and add additional features. But I think, you know, different languages have been propelled by their sort of being part of some system that people use as kind of a. Used for other reasons. I mean, I think for example the Lua language, very small language, was propelled a bit by its use in games. And sometimes again it's a bit of a self fulfilling thing that something gets. A language gets used for some purpose and that brings it sort of more visibility than it would otherwise have. And I think sometimes languages, and arguably it happened with JavaScript kind of, they get much more usage than they deserve based on the structure of the language. And sort of crazy things start happening like that. You're compiling C code into JavaScript which is kind of a weird and crazy thing to do. And sometimes there are features like security features and things, but some language might have that is sort of the reason to build a lot of stuff on top of it. But I think this idea that programming languages end up sort of developing all these tentacles of all these libraries and things. I don't think you ever come back from the tentacles. I don't think you know what we've done in building our computational language. Sort of my big effort over the last, well, majority of my life by now the Last words now 40 something years of sort of trying to keep coherence of this language. That's sort of a unique thing and it's something where there aren't at this point, now that we have this giant coherent thing, it becomes possible for us to add little tentacles and not have those tentacles as a little tentative tentacles, so to speak of. Yes, we can integrate some piece of Python code or something. And even though, and because it will integrate so well with the big thing that we already have it, you know, we have well defined ways of representing images and geopositions and all this kind of thing. And once you're living in that sort of environment on that platform, the fact that there's this little tentacle that works in a slightly weird way is not, you know, it's. It doesn't destroy the coherence of the whole thing. We've got a big enough coherent thing that we can start to do that. Although it's certainly our preference to just grow the coherent piece, but that grows a bit more slowly. You can grow a few tentacles a bit faster than you can grow the big coherent thing. But I don't think one goes back from the tentacles. I think that's a level of kind of heavy lifting that is just not realistic, particularly not in the context of open source development efforts where there's complicated motivation structures about, you know, how are these things getting pulled together or not, and why are people doing things and so on. And so I think that's, you know, we've kind of been the unique example of where we're building a very big computational language, more so than just a programming language that is that sort of maintains this consistency. And it's been a lot of work different from the sort of organic growth kind of, let's build a library for this, let's build a library for that kind of kind of approach. All right, maybe one last thing and then I should. Okay, let's see, There's a question here from Hive. Are there any pros to using historical technology or is newer or is better? I don't know. There are people I know who are using versions of our Wolfram language or Mathematica that are many versions back. And it's like, why are you doing this? You're missing everything we've developed in the last 15 years. Oh, well, I understand how the previous thing works and I know it works. I don't want to do something newer. The fact is that this is the story of whether one actually maintains compatibility, whether one. Whether the new is always better than the old or not. There are plenty of cases where this is the whole story of I want the classic retro type thing rather than the modern version I mean, I suppose what can often happen is that the new is a bit untested. The old, the classic architecture or something. People are used to it. It's kind of been well debugged over the years. It's more convincing than that piece of wild modern architecture where you didn't think, oh, the roof might leak or whatever else, because it wasn't sort of a well debugged, people have been doing it that way for thousands of years type story. So I think people. There's, you know, there are places. I'm always. It's always interesting for me because I always like buying the latest gadgets and so on and using the latest stuff. But I also am quite well aware of the fact that the latest, maybe the flakiest, so to speak. I think when it comes to. I mean, there are places where just things get developed and the new ideas are just not very good. There are things in user interfaces where people develop them and it's like, yeah, somebody might have thought this was a good idea, but it's really not. The old version was actually much better. I'll give you an example of a weird one. This was in the early days of workstation computers. This is early 1980s. And I was interested in cellular automata and in putting these sort of blocks of black and white squares on a computer screen. And at the beginning, it was really very easy to tell your computer, just stick this collection of pixels on the screen in this place, make this picture. As operating systems and sort of graphics subsystems became more sophisticated, it became more and more difficult to just say, put this pixel, make it black, make it white on the screen. And you ended up with these giant stacks of software to do what should have been a very simple operation. And that's something which happened because, well, people were interested in different things, more general things, more sophisticated things. This particular use case was kind of left behind and actually got more complicated. And that's not an uncommon thing. People say we need all these extra features and something which was originally this very simple user interface with three buttons or something becomes this giant airplane cockpit kind of thing that's much harder to use. So those are places where, you know, the earlier version is better. I mean, I think, you know, it's, in a sense, it's in the skill of the functional designer, whether you can maintain the streamlined efficiency of earlier versions while still adding those extra features that people want on top of that. And that's something certainly we spend a whole bunch of time thinking about is how do we keep. If something was nice and simple before. How do we make sure that nice, simple path still exists? That nice, simple functionality path exists even when there are more capabilities that have been added separately? All right, I should probably wrap up here, and thanks for joining me and look forward to chatting with you another time. So bye for now.