200th Anniversary of Sadi Carnot's Book on Heat & the Introduction of the 2nd Law of Thermodynamics

Hello there. Well, we're going to do something a little bit different today. We are here to celebrate the 200th anniversary of the publication of show you of this book. In many ways, this was the book that launched the science of thermodynamics, a field that I've been interested in now for half a century. And I wanted to tell you a little bit about, about this book and the history around it and about the person who wrote this book named Sadi Kano. That's a picture of him a little bit younger than the time when he wrote that book. That's a picture of him a bit older than when he wrote that book. And that's his rather ornate signature of the time. So we're going to be talking about this book. It was published in 1824. It was published on this date in 1824, or at least within this week. We know that from a digest of books published in France at that time. And in many ways, this book was the origin story or the second law of thermodynamics. It was in many ways also the origin story of the abstract science of thermodynamics, the abstract science of heat and its dynamics. Although in retrospect, the book was based on scientific ideas that were completely wrong, yet the conclusions of the book were completely valid. And that's an interesting story in its own right that has all sorts of resonance with all kinds of things that are happening today. So let me give you a little bit more context about, about this book. Person who wrote it. Sadi Kano was 28 years old when, when he wrote the book. And he had a. This was the only thing he ever published in his whole, whole life. And he was in many ways did not have a particularly distinguished story. He was nominally a French military engineer. He was sort of retired at the time when he wrote this book. We'll explain why later. But he had been well educated at the ecolepal technique in Paris. But he was mostly just tooling around, being a military engineer and then produced this book. Now, as we'll talk about later, his father, Lazare Carnot, was both a distinguished politician and a distinguished scientist. And much of what Lazare Carnot had done was kind of a setup that let one get to the point of being able to write this book. Sort of the key, in a sense was to take what was then the high tech. The high tech of the time was steam engines. Steam engines were sort of the technology that was taking the world by storm right at that time. And the big question that Sadiq Hanaud concerned himself with was just how efficient can a steam engine be? And people have been building all kinds of different steam engines. And the issue was if you use steam, you use air as the working fluid, you use this kind of piston, use that kind of piston, what can you do to make the steam engine as efficient as possible? Now, just to give some history of steam engines, I mean, there had been steam engines kind of developed in the. Well, there have been some even sort of precursors in antiquity. But by the 1710s there were already some kinds of steam engine, kinds of things that were emerging. But 1776 was the big year for steam engines as well as for the American Revolution and so on. But 1776 was the year when James Watt introduced his, his version of the steam engine, vastly more efficient than previous ones, with a lot of clever ideas about kind of clever science related engineering ideas, including maybe some precursors of what Kano ended up doing, although not presented in a kind of scientific, formal way. But so Carnot's effort was to figure out, we got these steam engines, they're made in practical ways, how efficient can we make a steam engine be? And what he ended up doing was developing what amounts to kind of an almost logical argument, almost philosophical argument. People would describe it later as kind of a matter of philosophy, what he had figured out about the possible efficiency of steam engines. Now he also was laboring under a kind of a misimpression about the nature of heat, because a steam engine is all about taking heat and making it do mechanical work. In fact, the title of Connot's book is Reflections on the Motive Power of Heat and on Machines Intended to Make Use of this power. So he was interested in the motive power of heat. To what extent can you take heat and make it do mechanical work, which is what a steam engine is all about? But the question was, one of the questions was, well, what is heat? Well, the theory that was dominant at that time was the so called caloric theory of heat. That was the theory that pretty much everybody believed that heat was a fluid, that heat was something that flowed from one material to another. People had sort of the idea that maybe there were molecules nobody knew, that matter was made of discrete particles. That wasn't known, but it had been kind of imagined a bit even since antiquity. And people thought that maybe there was a special kind of particle that was heat and that was the thing that was flowing from one material to another. But in any case, this caloric theory of heat was the dominant theory of what heat was. It was A fluid that suffused substances and would flow from one to another. And so, for example, when Fourier, Joseph Fourier in 1810s, I think was developing kind of his theory of heat, he was, he had the idea that it was something that flowed like a fluid, would have differential equations that it satisfied, like the equations of fluid dynamics. And that was kind of the, the story of the motion of heat, so to speak. So in Carnot's time, that was kind of Carnot's view in, in 1824 of the nature of heat was it was this fluid like thing, caloric fluid. And so in a sense what Carnot thought he was doing was, was to say, well, I don't really care if the caloric fluid is in steam or it's in air or it's in water, where it is. All I care about is that there's a certain amount of caloric fluid. And so what he thought he was doing was developing a theory for essentially the dynamics of caloric fluid. And that's in a sense why he ended up coming up with this kind of abstract view of what was going on in the dynamics of heat, because he thought heat was this thing that was sort of abstracted away from matter and was just caloric fluid. The big thing that Carnot established, well, he made some assumptions. He made the assumption that mechanical motion tends to degrade into heat. He also made the assumption that perpetual motion is impossible, that it's not possible to have something which will just sort of keep going forever and will, will keep generating mechanical work from nothing, so to speak. He made those two assumptions. And from those assumptions he then kind of derived the idea that the efficiency of a steam engine wouldn't depend on things like whether it was using steam or this or pistons or that. All it depended on. In the end, the ultimate efficiency of a steam engine would depend only on the temperature, the hottest temperature and the coldest temperature, that there was sort of heat in the steam engine and there was kind of a sink outside that was of lower temperature. And although he didn't get the actual formula for this, the so called Carnot efficiency, which is the higher temperature minus the lower temperature divided by the lower temperature, to get that formula, you have to understand things about absolute scales of temperature and so on. But he was kind of edging towards that formula and the kind of this that was kind of his achievement was to say, when you do this, however good you make your steam engine, this will be the limit of its efficiency. Now he had another point to make which we'll see has all Sorts of interesting historical resonance for him and so on, which was he said the way you make your steam engine most efficient is to have it run really slowly, to have it run so that the actual operation of it is reversible, so that you can just, you're just making a little tiny change to where the piston is and so on. So you could also make a change back. And he kind of used as an analogy the differential calculus where you're just making infinitesimal changes. It's kind of like you make this infinitesimal movement of the piston in the steam engine and then you can always move it back. And he argued that sort of the maximum efficiency was at the point where there wasn't kind of all sorts of irreversible stuff going on, where everything was happening reversibly. And so that was what he set up. Now what happened to this book? Well, Carnot paid for the printing of this book himself. It was printed through a bookseller called Bachelier. And amusingly, you can see on the actual book that it was. What is it? I think 55. Say here it's. I'm sorry, my French accent is absolutely terrible. I apologize for that in advance. But Kada Augustin, number 55 was on the book. It says that's, that's where its bookseller was. And that's a, that's a location on the bank of the Seine River. And amusingly, at least the last time I visited Paris, there were still booksellers actually sort of hanging out, including ones who were selling kind of old books right at that same spot on the banks of the Seine. So, so little changes in a couple of hundred years. But any case, the, the book was published through this kind of high end bookseller paid for by Kano. 600 copies were printed. It was priced at three franks of the time, which turns out to be about 20 bucks today. It was a fairly short book and when it came out, nobody really cared. There was, it was actually presented by Carnot at the Academy of Sciences on July 26, 1824. Again, no particular sign of any kind of response to it. There was one kind of little review that was printed of the book that said it was a kind of a bold, courageous, intellectual book, but basically vanished without trace. Now, as we'll talk about, after Carnot published this book, he was 28 years old, 1824, he, he lived quite a few more years. He died at the age of 36 and he never published anymore. He was kind of a, a bit of a loner kind of person. He did write some notes that were found 50 years after he died and which we'll talk about later. The. He had the misfortune of dying in a cholera epidemic. Actually, the same one that sort of immortalized, I suppose, in. Oh, my gosh, the general who's talked about General Lamarck in Les Miserables. That same cholera epidemic was also the one in which Sadi Kano died. One of the issues of dying from cholera at the time was cholera was a sufficiently infectious disease that the thing was burn everything that was involved. So a whole bunch of his papers were probably burnt at the time. And so less survives than might have done. But a few notes that are quite interesting do survive that indicate what Connaught was interested in in the last eight years of his life. But in any case, this book about the motive power of heat that Carnot wrote in 1824 would have vanished without trace were it not for the fact that a certain Emile Claparon, who was a engineering professor and a steam engine maker, kind of knew about it and really paid attention to it. And then in. See, when was that? That will have been in. In the 18. Beginning of the 1830s, the. Yeah, 1834, Clapeyron published a paper that sort of built directly on Carnot's ideas. Claparan, you know, says that he will present these original ideas, et cetera, et cetera, et cetera. Actually, it's basically just a recapitulation of what Carnot did, together with some diagrams which have become kind of standard diagrams in thermodynamics books. We'll look at those a bit later. But again, things didn't really take root yet. Waited until 1845. In 1845, an ambitious young Scotsman named William Thompson was in Paris kind of working at a lab that was a kind of a lab studying the properties of steam. And he heard about Clapeyron's paper and he tried to get a copy of Connot's book. And those 600 copies, they hadn't sold through in the bookstore, but they were hard to get. And it took William Thompson a while to find a copy of those books. William Thompson was later Lord Kelvin, but at the time he was still William Thompson. But in 1845, William Thompson got interested in the question of inventing a thermodynamic scale of temperature. People had said, well, you can measure the temperature of something by saying, well, how much does mercury expand? How much does water expand when the temperature is this or that relative to this or that. But William Thompson wanted an absolute scale of temperature, a scale of Temperature, which would depend not at all on the particular substances that were involved, but was just features of heat. And for that he, he imagined that what he was doing was having features of caloric and that he wanted to have, like Carnot, he wanted to have something that would just be talking about the, the features of heat alone, not a particular substance that was getting hot. And in, in doing this, he started studying carnot's work. Then 1849, William Thompson wrote a review of Carnot. We'll look at that a little bit later. And that was really what got started with sort of the formalization of thermodynamics. And pretty soon, for other reasons, people had come to imagine that heat was a form of energy. That wasn't something Carnot knew, although it was something that in a sense, he kind of intuited. And in fact, in the notes that he left late in his life, it was clear that he was really homing in on this idea that heat was a form of energy and that there was an energy conservation and that you could sort of exchange energy between heat and mechanical work, but you would fix the total amount of energy. That became the first law of thermodynamics. And very soon thereafter, William Thompson, Lord Kelvin, was formulating the second law of thermodynamics. But the second law he really rooted in Carnot's work. And he thought of Carnot's work as being philosophical axiomatic, inevitable. And this is how 150 year confusion got started. Because from what Kelvin, William Thompson said, it looked like the second law was something that was inevitable, something that was not really a law of physics. It was more something that was rooted in kind of mathematical necessity. It really wasn't. And in fact, Carnot had effectively assumed the second law. He kind of just assumed that mechanical work degrades into heat, which is sort of an essential point of the second law. He assumed that perpetual motion was impossible, another version of the second law. He just took those for granted as matters of sort of intuitive physics and then built his kind of logical structure on that basis. But when Kelvin picked it up, he kind of referred back to Carnot and said, look, Carnot axiomatically proved these things. And then Kelvin was taking it as essentially a necessary feature of the world that the second law of thermodynamics should be true. And within a few years, Kelvin was talking about the heat death of the universe and all sorts of other things which were felt to be kind of the inevitable consequences of this completely axiomatically grounded second law that was believed to be grounded in that way because it came from Carnot, who had derived it from intuitive thinking based on a wrong theory of heat, namely the caloric theory of heat. And, and so anyway, 150 year confusion got started as a result of this. And I mean it, it certainly wasn't Carnot's fault that that confusion got started. If anybody's fault, it was Kelvin's fault. But that, that's, that's how it worked. Now subsequently, people like Boltzmann tried to sort of nail that down and prove the second law of thermodynamics from something lower level. And that didn't work out well. And in fact sort of the mystery of the origins of the second law. Why is the second law true? Is the second law derivable? What is its status? Is something. Well, I got interested in back when I was a kid and have worked on for about 50 years and, and finally last year produced this book on the second law, which I think finally, I hope kind of as a result of thinking about things in kind of computational terms, finally provides sort of a resolution of why the second law is true. And essentially a derivation of the second law that depends in part only on abstract concepts about computation and so on, but in part has a very important dependence on the nature of us as observers of the world. And the conclusion is if we were different from the way we are, if we were sort of organisms that could trace the computations of all the collisions between molecules, we wouldn't believe in the second law. It's just a consequence of our character as kind of computationally bounded observers of molecular dynamics that we believe in the second law. So in some sense the second law really is derivable. It is formally derivable for observers like us, but it depends on our nature as observers that it works that way. But that's the sort of 150 years later story here. But what I wanted to talk about here today was Carnot and the publication of this book 200 years ago today, or at least this week, about the motive power of heat. So maybe a good way to start would be actually to read a little bit of what Kano said. I'll give the English version of it because I can more or less read French, but it's more useful to give this in English. I'm going to read quite a bit of this because it's kind of interesting and it has quite a lot of sort of historical content. So the English translations given here, reflections on the motive power of heat and on machines fitted to develop that power. Everyone knows, says Carnot, that heat can produce motion. That it possesses vast motive power. No one can doubt in these days, when the steam engine is everywhere so well known. Steam engine in this translation from the late 1800s is hyphenated kind of charmingly to heat also. Adieu. The vast movements which take place on the earth. It causes the agitations of the atmosphere, the ascension of clouds, the fall of rain out of meteors. I don't quite understand. The meteors part the currents of water which channel the surface of the globe and of which man has thus far employed but a small portion. Even earthquakes and volcanic eruptions are the result, says Carnot, of heat. Not clear. That's true for earthquakes. From this immense reservoir we may draw the moving force necessary for our purposes. Nature, in providing us with combustibles on all sides, has given us the power to produce at all times and in all places heat. And the impelling power which is the result of it. To develop this power, to appropriate it to our uses, is the object of heat engines. The study of these engines is of the greatest interest. Their importance is enormous. Their use is continually increasing, and they seem destined to produce a great revolution in the civilized world. We'll talk later about Connot's interest in economics and in and in kind of engineering work. Already the steam engine works our minds, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grains, spins and weaves our clothes, transports the heaviest burdens, etc. It appears that it must someday serve as a universal motor and be substituted for animal power, waterfalls and air currents. Of course, we only go backwards here with now we've got hydroelectric power and wind power and so on. Not sure it's backwards. Over the first of these motors it has the advantage of economy that is relative to animal power. Over the other two, the inestimable advantage that it can be used at all times and places without interruption. If someday the steam engine shall be so perfected that it can be set up and supplied with fuel at small cost, it will combine all desirable qualities and will afford to the industrial arts a range the extent of which can scarcely be predicted. It is not merely that a powerful and convenient motor that can be procured and carried anywhere is substituted for the motors already in use, but that it causes rapid extension in the arts in which it is applied and, and even create entirely new arts. The most signal service that the steam engine has rendered to England. Is undoubtedly the revival of the working of the coal mines, which had declined and threatened to cease entirely in consequence of the continually increasing difficulty of drainage and of raising the coal. Here's a footnote here. It may be said that coal mining has increased tenfold in England since the invention of the steam engine. It is almost equally true in regard to the mining of copper, tin and iron. The results produced in a half century by the steam engine in the mines of England are today paralleled in the gold and silver mines of the new world mines, of which the working declined from day to day Principally on account of the insufficiently the motors employed in the draining and extraction of minerals. Very, very practical stuff. We should rank, he says. Second, the benefit to iron manufacture, both by the abundant supply of coal substituted for wood, Just when the latter had begun to grow scarce because people had chopped down all the forests and by the powerful machines of all kinds, the use of which the introduction of the steam engine has permitted or facilitated. And he goes on to talk about the importance of iron in the economy of England. England is where James Watt had lived and developed the steam engine. And there was the usual kind of rivalry between France and England at the time. Let's see, he talks again about the safe and rapid navigation by steamships May be regarded as entirely new art due to the steam engine. Already this art has permitted the establishment of prompt and regular communication across the arms of the sea and on the great rivers of the old and new continents. It has made it possible to traverse savage regions where before we could scarcely penetrate. It has enabled us to carry the fruits of civilization over portions of the globe where they would else have been wanting for years. Steam navigation brings nearer together the most distant nations. It tends to unite the nations of the earth as inhabitants of one country. In fact, to lessen the time, the fatigues, the uncertainties and the dangers of travel. Is the not this the same as greatly to shorten distances? He says in any case, it's sort of interesting to. To read through these things because, you know, this is. Things have changed in the world in 200 years. Lots has not changed. It's. Let's see, the talks a bit about who discovered the steam engine, that it's not really known. And then he goes on to talk about. The question has often been raised whether the motive power of heat is unbounded, whether the possible improvements in steam engines have an assignable limit, a limit which the nature of things will not allow to be passed by any means whatever, or whether, on the contrary, these improvements may be carried on indefinitely. We have long sought, and are seeking today to ascertain whether they're in existence, are in existence agents preferable to the vapor of water for developing the motor power of heat, whether atmospheric air, for example, would not present in this respect great advantages. We propose now to submit these questions to a deliberate examination. And then, he says, the phenomenon of the production of motion by heat has not been considered from a sufficiently general point of view. We have considered it only in machines, the nature and mode of action of which have not allowed us to take it in the whole extent of application of which it is susceptible. In such machines, the phenomenon is in a way incomplete. It becomes difficult to recognize its principles and study its laws. He says, let's. In order to consider in the most general way the principle of the production of motion by heat, it must be considered independently of any mechanism or particular agent. It is necessary to establish principles applicable not only to steam engines, but to all imaginable heat engines, whatever the working substance and whatever the method by which it is operated. Machines which do not receive their motion from heat, those which have for a motor the force of men or animals, a waterfall, an air current, et cetera, can be studied even to their smallest details. By mechanical theory. All cases are foreseen, all imaginable movements are referred to. These general principles firmly established and applicable under all circumstances. This is the character of a complete theory. A similar theory is evidently needed for heat engines. We shall have it only when the laws of physics shall be extended enough, generalized enough, to make known beforehand all the effects of heat acting in a determined manner on any body. We will suppose, in what follows, at least a superficial knowledge of the different parts which compose an ordinary steam engine. And we consider it unnecessary to explain what are the furnace, the boiler, the steam cylinder, the piston, the condenser, and so on. I'm not sure that's so unnecessary to at least me today. The production of motion in steam engines is always accompanied by a circumstance on which we should fix our attention. This circumstance is the reestablishing of equilibrium in the caloric, that is, its passage from a body in which the temperature is more or less elevated to another in which it is lower. What happens, in fact, in a steam engine actually in motion, the caloric develops in the furnace. You can read that as the heat developed in the furnace by the effect of the combustion traverses the walls of the boiler, produces steam in some way incorporates itself with it. In other words, the sort of the heat gets mixed into the steam in some way. The latter steam, carrying it away, takes it first into the cylinder where it performs some function, and from thence into the condenser, where it is liquefied by contact with cold water which it encounters there. Then, as a final result, the cold water of the condenser takes possession of the caloric developed by the combustion. It is heated by the intervention of the steam as if it had been placed directly over the furnace. The steam is here only a means of transporting the caloric. It fills the same office as the heating of baths by steam, except that in this case its motion is rendered useful. So what he's saying is all that really matters is the motion of the heat, the thermodynamics, the motion of the raw heat, the caloric fluid, which, as it turns out, doesn't exist. But at the time, he was imagining there was a thing that was pure heat that was being moved around, and the steam was merely a carrier of that pure heat. We easily recognize in the operations that we have just described the reestablishment of equilibrium in the caloric, its passage from a more or less heated body to a cooler one. The first of these bodies, in this case, is the heated air of the furnace. The second is the condensing water. The reestablishment of equilibrium of the caloric takes place between them and the. If not completely, at least partially, et cetera, et cetera, et cetera. So again, then he goes on to say, and this is the very important point for him, the production of motive power is then due in steam engines not to an actual consumption of caloric. It's not that the heat fluid got converted to motion, but instead, he says, to its transportation from a warm body to a cold body, that is, to its re. Establishment of equilibrium, an equilibrium considered as destroyed by any cause whatever by chemical actions such as combustion or by any other, we shall see shortly that this principle is applicable to any machine set in motion by heat. So in other words, again, the sort of. The key idea is there is the pure heat caloric fluid, as he thought. And the pure heat is something which, when operating in a cycle, can lead to motion. And again, an idea that he had which was important was that steam engines operate in cycles. Now, you watch a steam engine running. It's having its piston go up and down and so on. It's kind of like, yeah, well, obviously it's in a cycle. You can see it mechanically in a cycle. But the point that he was making was that this idea of the operation being a closed cycle was where at some point the state of the machine returns to what it originally was, was critical. Because if the caloric was being consumed to make mechanical work, then there wouldn't be a closed cycle. The machine would, you know, you'd feed it in a certain amount of caloric and then the caloric would have been sort of burnt off and turned into mechanical work and then you're done. But what he said is, no, actually the machine can operate on a closed cycle in which one is merely moving this caloric around. And the result of that is to produce mechanical work. Well, so if we take a look here. Let's see if I can bring this up. Second. Okay, so let's take a look at the actual book in French. Just scroll through it a bit. So it's mostly words, a lot of words. There's not much math in it. He intended this book to be kind of a book that anybody could read. I suppose it's the new kind of science tradition of new science books, so to speak. And so he intended it to be kind of a book that would be of interest to people who were concerned with the high tech of the time, steam engines. And anyway, there's keeps going. At the time the gas laws were known, PV equals rt, Boyle's law, all that kind of thing, they were known. And he made some use of those in talking about what was going on. And then here is. So this is the specific heats of gases. So he's listing for some reason, I'm not quite sure. Okay, so this is various features of gas because he's interested in sort of the concrete realization of the steam engine in terms of this kind of cycle of activities where the gas is kept at constant temperature. Isothermal. And then the gas is kept without any heat coming in or out. Adiabatic. And this thing that became what is in the physics textbooks and the engineering textbooks is the Carnot cycle of different things that happen to the gas. But so he's giving some details. You know, here it's the. The rise of temperature through the reduction of volume by one part in 116. I don't know exactly why that's the number he's picking. But so then he's here he's kind of describing. He's referring to some figures which just show pictures of cylinders going up and down. But he's describing this kind of operation from one state to another and going back again in this closed cycle. So I'm not sure what this is. That's probably adiabatic expansion. That depends on the specific heat of the ratio of specific heats and keeps going. Okay, we got some logarithms here. And then he's talking about, I guess at that time. Well, this is just more of some pretty elementary mathematics of what was going on. Let's see what else happens here. It's not a terribly long book, but it just gives you a sense of what kind of thing he's talking about here. Let's see. Okay. Okay. Fraction of the. Wall during the rise of the cylinder. I'm not quite sure what this is that. I guess that's to do with his efforts to calculate the efficiency of steam engine. I think there's a little bit more that comes up here. Okay, there we go. There are at the end. Okay. Here are figures not particularly inspiring, just pictures of cylinders going up and down. So this is kind of the. It's 818 page book and that's what it was. And if we look kind of at the end of that, he's talking about by the time he reaches the end of the book. Let's see if we can find the English translation of the end of the book. Yeah, so he's talking about some details of steam engines. And he ends. We should not expect ever to utilize in practice all the motor power of combustibles. The attempts made to attain this result would be far more harmful, hurtful than useful if they caused other important considerations to be neglected. The economy of the combustible is only one of the conditions to be fulfilled in heat engines in many cases. In other words, do not use more combustible than you need to. In many cases it is only secondary. It should often give precedence to safety, to strength, to the durability of the engine, to the sole small space which it must occupy, to small cost of installation, et cetera. To know how to appreciate in each case at their true value the considerations of convenience and economy which may present themselves. To know how to discern the more important of those which are only accessories to balance them properly against each other in order to attain the best results by the simplest means. Such should be the leading characteristics of the man called to direct, to coordinate among themselves the labors of his comrades, to make them cooperate towards one useful end of whatsoever sort it may be. Well, so, okay, so that was the book and I said a little bit about kind of what happened later. Let's talk about how Sadi Carnot in 1824 got to write this book. Well, actually we have to start with his father, Lazar Carnot. And let's talk a little bit about Lazar Carnot and for a second. And so. Let's see, that's a picture of Lazar Carnot. That's another slightly more energetic picture of Lazar Carnot. So what was the story of Lazar Carnot? Lazar Carnot was actually a pretty prominent person in France. He didn't come from a particularly aristocratic background. He was trained as an engineer. And he kind of gradually rose through the ranks and eventually was kind of a practical guy who got stuff done. And see here he. One of the things. But he was, as I say, educated as an engineer. And in those days, and to some extent today, but particularly in France, in those days, being educated as an engineer meant you got to know the latest mathematics and so on. Engineering was very connected, as it, I think still is, particularly in countries like France, with kind of. With mathematics, even fairly high end mathematics. So Lazar Carnot was well educated in the mathematics of his day. Calculus, all those kinds of things. And to sort of improve his lot as a working military engineer in the later decades of the 1700s, Lazar Carnot started competing in these various essay competitions which were put up by the French Academy of Sciences. And he started sending in essays about different kinds of things. So one of the essays that he sent him was about the foundations of the infinitesimal calculus. Another one, which actually was his first really successful one, was about fortifications in the style of a particular kind of French general of the past and the geometry of fortifications. But in 1789, was that right? 17. No, I'm sorry, 17. 1778, he competed in a. In a. An essay competition about the science of machines. And that became, in 1783, Lazar Carnot's first book. I have a picture of that. Let me. That, Hold on. There we go. An essay on Machines in General by Monsieur Carnot, Captain of the Corps of Engineers and member of the Academy of Sciences, Arts and Letters of Dijon, et cetera, et cetera, et cetera, Correspondent of the Museum of Paris, et cetera. This is actually a second edition, but this is the first edition was published in 1783. So what is this? Well, this is a book which attempts to mathematicize the operation of mechanical devices. And it was at the time there were all these machines that had been built and they were doing their thing and they were clanking around and they were being. Having various degrees of efficiency and so on. Lazar Carnot decided he would mathematicize the operation of machines. He would have an abstract way of describing machines. Now, if that reminds you of what Sadi Cano later did. Yes, there is a strong resonance of these things and we'll try and explain what the relationship seems to have been between them. But Lazar Carnot had the idea, let's describe machines in this abstract way. And if you flip through his book, it's also very much a words book, but it's a book that starts to kind of talk about the kind of how machines are sort of things whose abstract effect is to transfer force from one place to another. You see a little bit of calculus showing up here. So he kind of had this notion of abstraction, of abstracting the operation of machines. Now, we also had various other things, by the way. This is particular laws of equilibrium in machines. Notice that Carnot Jr. Savi Carnot, also was talking about the notion of equilibrium, Though by that he meant equilibrium of the steam engine with respect to the motion of heat. Here, Lazar Carnot is meaning the equilibrium of machines and forces and machines and so on. So one of the things that Lazar Carnot, I guess he had an even shorter book than his son, 107 pages here. One of the things that Carnot Sr kind of was established was this idea of what became known as Carnot's principle. And this is again something deeply confusing in the history of this subject, because Even in the 1830s, after the publication of Sardi Carnot's book on principles of what became known later as thermodynamics, what was at that time called Carnot's principle, was actually a principle due to Lazar Carnot that had to do with general machines, not with anything to do with heat. So Lazare Carnot's principle, Carnot's principle, as it was called at the time, was basically this. If the machine is clanking, it's not as efficient as it might be. If there are accelerations or shocks in the operation of the machine, it will have inefficiency. And so the best way to operate a machine, and this again resonates with the later work of Sadi Kano, is sort of reversibly just a tiny bit. Keep it slow, keep it so that everything is kind of moving smoothly, as Lazar Carnot would describe it. There was no loss of moment of activity associated with smooth motions. It was only these shocks and accelerations that would lead to that. And also Lazar Carnot made it as kind of an axiom of what he believed was going on with machines, that perpetual motion is impossible. Okay, so Lazar Carnot was, as I say, an engineer. He was kind of rising in the ranks of the French army and so on. And eventually he was a pretty senior guy who was commanding large Numbers of forces and so on. And he became friends with a young Robespierre, for example. And well, in 1795, he did something which would turn out to be a good career move, which is he appointed a chap called Napoleon to be the general in chief of the army of Italy. And well, at that point, Italy was a separate. Separate place, hadn't been unified, but it was a separate. It was separate from France. But after Lazar Carnot appointed Napoleon general in chief of the army of Italy, the army of Italy went on the rampage, so to speak, and invaded in the next year, basically invaded Italy. And that was Napoleon's sort of first. That. That had been Napoleon's first commission in first real position in the French army. And that was his first big achievement was. Was the invasion of Italy. And Lazar Carnot was the person who kind of put him up to that. Well, meanwhile, I should have explained that the. In the. The time of the French Revolution, Lazar Carnot was. Was a big figure in that. I think he was mostly a guy who made stuff actually work. I don't think he was part of the sort of activism front. I think he was much more of a. A make stuff work kind of guy. But nevertheless, when you find sort of illustrations of the French Revolution, you'll. You'll find. Did I show the right thing here? Let me see the. You'll find pictures like this. This says intellectuals of the French Revolution. And in that picture, five people there is down. That one is supposed to be Lazare Carnot. So he was a major figure in the French Revolution, but somehow managed to navigate it without kind of running afoul of the various political winds. Now in fact, that was something that was an important trait throughout his life. Basically, when things got too hot in France, he hightailed out of there to Switzerland and Germany and kind of hung out in exile for a few years until the political winds changed in France. One feature of those exiles was he did lots of math during those exiles. But any case, back to Lazar Cano. So. He was at that point he had kind of. He put Napoleon in that position. And then as Napoleon kind of rose, he was in important positions. He actually kind of quit. The. He kind of left. The. Let's see. I'm trying to remember how this all works. The. There was some coup in 1797, which was one of the times when Lazar Carnot went into exile. But then he was back and the. Then in 1796, Sadi Kano was born in Paris, actually, confusingly enough. And we'll run into this again. There was an earlier Sadi Carnot. Lazar Carnot had had a first child who died after a few months, but was named Sadi Kano. When his second child came along, he also named that child, the one we're talking about, Sadi Kano. Five years later, a brother arrived, Hippolyte Carnot, who again we'll talk about. And later on, Hippolyte Carnot had a son who he named Sadi Carnot. And that son became President of France. And again, confusingly enough, you'll find in physics textbooks there is a not small incidence of pictures of the Sardi Carnot who was President of France being attributed as the inventor of thermodynamics. So lots of confusion here. There are three Sodi Carnots. We're talking about the middle one, the one who was born in 1796. So for the first 16 years of his life he was kind of educated at home. His father, Lazar Carnot was kind of in charge of things there. By the way, Lazar Connot at the time was kind of an inspector of devices for Napoleon. He was kind of the person, kind of almost the patent office person for Napoleon. Napoleon, by the way, had this interesting habit of insisting that if you were patenting an invention, you had to actually send a version of the invention, a physical version of the invention, which Napoleon then put in a museum somewhere. But in any case, Lazar Carnot was sort of an inspector of devices and apparently there were all kinds of steam engine like things which were being tested on the Seine river and so on. And the young Sadi Kano will certainly have seen those kinds of things. Maybe we'll talk a little bit later about more details of the young Sadi Carnot. There's one nice story that Madame Bonaparte was sort of a babysitter of the young Lazare Carnot at some point when he was like 4 years old or so. And there were various interactions between Napoleon and the young Sadi Carnot that happened at that time. But any case, by the time in, in 1812, Sadi Kano entered the ecopole technique and was sort of off being educated and was off in college. Basically Napoleon had been defeated in Moscow and was sort of on the retreat. And by after a couple of years when Paris was under siege and at that point and Sadiqano kind of in 1814 left the accel Pol technique and in those days the Accel Pole technique was, it was in large part a military training operation and the, the students there went off to, to fight and, and, and Sadi Kano was, was one of those. And he then kind of joined the equivalent of the core of engineers and was, was a military engineer, basically having grad, basically graduated from college now. So for a while he was just doing the thing of being a military engineer. There's not a lot that's known. Time. 1820, Napoleon's out. The king is back. Lazar Carnot is out. Went off to place in Germany during the time that Sadi Carnot had been kind of military engineer. He was sort of a favored military engineer because people knew that his dad was famous and all this kind of thing. But by the time the king was back, he was sort of out of favor. He was sent to sort of random garrison duty and pretty soon he was retired to Paris at half pay. That was 1820. So at that point he kind of, he was living in this apartment which had been owned by his father in Paris. And he was hanging out at various colleges around Paris, learning various kinds of things, particularly interested in physics and economics. And he was visiting factories, trying to learn about industry, things like this. Apparently the biggest interaction that he had with Lazare Carnot at that time, I mean, since after he went off to College in 1812, Lazar Carnot was sort of out of the picture as far as Sadi Kano was concerned. But in 1821, he spent a bunch of time with Lazar Connot in Magdeburg, I think, in, in Germany. And exactly what was discussed at that time will be interesting to know. Presumably Lazar Carnot and Sadi Carnot would discuss thermodynamics or discussed heat engines and so on, because that will have been a topic of interest. And it's also known that Lazar Carnot kind of encouraged Sadi Kano to study economics and made the statement that there would be a mathematics of economics that would emerge and that might be a good thing to study. Well, in 1823, Lazar Connot died. Hippolyte, who had been living with Lazar Connot, moved back to Paris, moved in with Sadi Carnot. And then Sadi Kano started writing this book and apparently he gave it to Hippolyte Kano to read because Hippolyte Kano was not technically educated and he thought that he would check that it was sort of accessible to the general reader. Well, and so, as I say, after that book, I mean, Sadi Carnot pretty much hung out on his own doing various kinds of research. There's evidence that he was at least interested in doing a bunch of physical experiments. And then he died eight years later. Well, let's talk about. What we know of. So that's kind of the interaction between Lazar Carnot and Sadi Carnot. Carnot as a person, very little was known about him. Eventually, pretty much 50 years after he died, Hippolyte Carnot wrote a biographical sketch of. Of Sadiq. I know, and let me tell you a little bit about what that said. See if I can pull this up. Just a moment here. It's rather a charming biographical sketch. And then, let's see. There we go. It's about the life of Sadiq Hanaud. As the life of Sadi Carnot was, says Hippolyte Carnot, not marked by any notable event, his biography would have occur, occupied only a few lines. But a scientific work by him, after remaining long in obscurity, brought again to light many years after his death, has caused his name to be placed among those of the great inventors. In regard to his person, his mind, his character, nothing whatever has been known since. There remains a witness of his private life, the sole witness, that is Hippolyte Carnau. Has he not a duty to fulfill? Ought he not to satisfy the natural and legitimate interest which attaches to any man whose work has deserved a portion of glory? Nicholas Leonard Sardi Connot was born on June 1, 1796, in the smaller Luxembourg. This was that part of the palace, palace de Luxembourg, where our father then dwelt as a member of the Directory, the sort of executive committee, I suppose, of France. Our father had a predilection for the name of Sadi, which recalled to his mind ideas of wisdom and poetry. His firstborn had borne this name. And despite the fate of this poor child, who lived but a few months, he called the second also Sa'di, in memory of the celebrated Persian poet and moralist. Scarcely a year had passed when the proscription, which included the director, obliged him to give up his life, or at least his liberty, to the conspirators of the fluctidor. A mother carried her son far from the palace in which violation of law had just triumphed. So this was one of the coup stories. She fled to Saint Omer with her family, while her husband was exiled to Switzerland and then to Germany. Our mother often said to me, thy brother was born in the midst of the cares and agitations of grandeur. Thou, you, Hippolyte, in the calm of an obscure retreat. Your constitutions show this difference of origin. So Hippolyte Kano was born about five years after Sadi Kano, my brother. He's referring to Sadi Kano, in fact, was of delicate constitution. He increased his strength later by means of varied and judicious bodily exercises. He was of medium size, endowed with extreme sensibility, and at the same time with extreme energy. More than reserved, almost rude, but singularly courageous on occasion, when he felt himself to be contending against injustice, nothing could restrain him. The following is an anecdote and illustration. The Directory had given place to the Consulate. Carnot, after two years of exile, that's Lazar Carnot, returned to his country and was appointed Minister of War. Bonaparte, at the same time, was still in favor with the Republicans. He remembered that Carnot had assisted him in the beginning of his military career, and he resumed the intimate relation which had existed between them during the Directory, when the Minister went to Malmaison to work with the First Consul. So that's when Lazare Carnot had gone to work with Napoleon, who themed himself as First Consul. He often took with him his son, then about 4 years old, to stay with Madame Bonaparte, who was greatly attached to him. She was one day with some other ladies in a small boat on a pond, the ladies rowing the boat themselves, when Bonaparte unexpectedly appearing, amused himself by picking up stones and throwing them near the boat, spattering water on the fresh toilettes of the rowers. The the ladies dared not manifest their displeasure. But the little Sadi, having looked on the affair for some time, suddenly placed himself boldly before the conqueror of Marengo, Napoleon, and threatening him with his fist, he cried, beast of a first console. Will you stop tormenting those ladies. Bonapart, at this unexpected attack, stopped and looked in astonishment at the child. Then he was seized with a fit of laughter in which all the spectators of the scene joined. Kind of sounds like Napoleon was a bit of a jerk there. Anyway, at another time, when the minister, that's Lazare Carnot, wishing to return to Paris, sought his son, who had been left with Madame Bonaparte, it was discovered that he had run away. They found him a long way off in a mill, the mechanism of which he was trying to understand. This desire had been in the child's mind for days, and the honest miller, not knowing who he was, was kindly answering all his questions. Curiosity, especially in regard to mechanics and physics, was one of the essential traits of Sardi's mind. On account of this disposition so early manifested, Carnot did not hesitate, that's the Tsar. Carnot did not hesitate to give a scientific direction to the studies of his son. He was able to undertake the task himself. When the monarchic Tendencies of the new government had determined him to retire for a few months only. Saudi followed the course of Monsieur Bourdon at the Charlemagne Laissez to prepare himself for the polytechnique. The pupil made rapid progress. He was just 16 years old when he was admitted to the 24th on the list. I think this is a tradition in France. Everybody takes exams and there are ranks of everything. So I guess Sadiq Hanaud was the 24th in that year. I'm curious. He was the first. This was in 1812. The following year he left it first in artillery. But he was considered too young for the school. Okay. For the artillery school continued his. This is more details about his schooling. Let's see. The. This is various efforts of the Polytechnic School, the students of the Polytechnic School to enter the war effort. Things have changed, I suppose. Let's see. And then meanwhile his father, Lazar Kano was by that point themed as General Carnot and wow. So I guess general connoisseur in 1814 was. Was. Was pretty seriously in the military business as at Anvers, apparently defending against the Confederate English, Prussians and Swedes where the French flag yet floated when he wrote in 1814. This is Lazar Connot writing to Sadi. My dear Sadi, I have learnt with extreme pleasure that the battalion of the Polytechnic School has distinguished itself and you have performed your first military exploits with honor. When I am recalled, I shall be very glad if the Minister of War will give you permission to come to me. You will become acquainted with a fine country and a beautiful city where I've had the satisfaction of remaining in peace while disaster has overwhelmed so many places. So Sadi Kano did indeed go to Anvers and then back to Paris. Let's see. That's a lot of stuff about the all the winds of political change and how Lazar Kano and Sadi Kano kind of. Navigated that. But this is now about 1823, when Lazar Kano had died and Hippolyte Kano is writing. When two years later death took from us this revered father and I returned alone to France. I found Sori devoting himself to his scientific studies, which he alternated with the culture of the arts. In this way also his tastes had marked out for him an original direction. For no one was more opposed than he to the traditional and the conventional. On his music desk was seen only the compositions of Lully. I have no idea who that was that he studied. And the concerti of Viotti which he executed on his table was seen only Pascal Moliere or La Fontaine, and he knew his favorite books almost by heart. I call this direction original because it was anterior to the artistic and literary movement which preceded the Revolution of 1830. As to the sympathy of Sardi for the author of the Provinciales, it was not due to only to the respect of the young mathematician for one of the masters of science, but his devoutly religious mind, regarded with horror, hypocrisy and hypocrites appreciating the useful and the beautiful. Sardi frequented the museum of the Louvre and the Italian theater, as well as the Jardin des Plantes and the Conservatoire des Arts et Metier. Music was almost a passion for him. He probably inherited this from our mother, who was an excellent pianist and who learned from various distinguished people. Not content with being able to play well on the violin, Sadi carried to great length his theoretical studies. His insatiable intellect, moreover, would not allow him to remain a stranger to any branch of knowledge. He diligently followed the course of the College de France and of the Sorbonne, of the Ecole de Mine, of the Museum and of the Bibliotheque. He visited the workshops, factories, I guess with eager interest, and made himself familiar with the processes of manufacturer mathematical sciences, natural history, industrial art, political economy. All of these he cultivated with equal ardor. I have seen him not only practice as an amusement, but search theoretically into gymnastics, fencing, swimming, dancing, and even skating. In even these things, Sa'di acquired a superiority which astonished specialists when, by chance he forgot himself enough to speak of them, for the satisfaction of his own mind was the only aim that he sought. He had such a repugnance to bringing himself forward that in his intimate conversations with a few friends he kept them ignorant of the treasures of science which he had accumulated. They never knew of more than a small part of them. How was it that he determined to formulate his ideas about the motive power of heat and especially to publish them? I shall ask myself this question. I, who lived with him in the little apartment where our father was confined in the Rue du Parc Royal, while the police of the first restoration were threatening him. Anxious to be perfectly clear, Saudi made me read some. Anxious that his writing would be perfectly clear, Sadi made me, Hippolyte, read some passages of his manuscript in order to convince himself that it will be understood by persons occupied with other studies. Perhaps a solitary life in small garrisons, in the workroom and in the chemical laboratory had increased his natural reserve. In small companies, however, he was not at all taciturn. He took part voluntarily in the gayest plays abandoning himself to lively chat, the time passed in laughing is well spent, he once wrote. His language was at times full of wit, keen without malice, original without eccentricity, sometimes paradoxical, but without other pretension than that of an innocent activity of intelligence. He had a very warm heart. Under a cold banner, he was obliging and devoted, sincere and true in his dealings. Towards the end of 1826, that's after the publication of his book a new royal ordinance having obliged the staff lieutenants to return to the ranks, Sadi asked and obtained a return to the engineer corps, in which he received the following year as his rank of seniority, the grade of captain. So he went back to being a working military engineer. Military service, however, weighed upon him. Jealous of his liberty in 1828, a couple years later, he laid aside his uniform that he might be free to come and go at will. He took advantage of his leisure to make journeys and to visit our principal centers of industry. He frequently visited Clement Desorme, professor at the Conservatoire des Artsier, the school of. I guess that's engineering Arts and engineering, Right. Arts and matters. Okay. This is my poor French, who had made great advances. Des Hommes had made great advances in applied chemistry. It's a person once heard of even today. Monsieur des Hommes willingly took counsel with him. He was a native of Bourgogne, a family country, which circumstance, I believe, brought them together. So. Okay. It was before this period in 1824, that Sadi had published his reflection sur le poiss froissons motrice de faut the Reflections on the Motive Power of Heat. He had seen how little progress had been made in the theory of machines in which this power was employed. He had ascertained that the improvements made in their arrangement were affected. Tentatively and almost by chance, he comprehended that it, comprehended that in order to raise the important art above empiricism and to give it the rank of a science, it was necessary to study the phenomena of the production of motion by heat from the most general point of view, independently of any mechanism, of any special agent. And such had been the thought of his life. Did he foresee that this small brochure would become the foundation of a new science? He must have attached much importance to it to publish it and bring himself out of his voluntary obscurity. In fact, as his working notes prove, he perceived the existing relation between heat and mechanical work. And after having established the principle to which savants, scientists, I guess, have given his name, he devoted himself. Now, this is again super confusing, because Hippolyte Carnot is talking about having established the principle that Sa'di had Carnot had established, to which people have given the name of Carnot. But in fact, the thing that was called Carnot's principle was something that Lazar Carnot had invented to do with the operation of abstract machines. It was not. There wasn't really a Carnot's principle. That was a different thing. Just one of these. Yet another one of these confusions. In any case, as Hippolytes Kano says, established establishment enable him to establish with certainty the second principle, which that of equivalence, which he already clearly divined. Thermodynamics was established from that time. I think Hippolyte Carnot is a bit confused here. But these researches were rudely interrupted by a great event, another piece of political turbulence, the revolution of July 1830. It's hard for me to keep track of all these revolutions in France at that time. Sadi welcomed it enthusiastically. Not, however, it is evident, as a personal advantage, Several old members of the Convention, Convention, Directory, they're all sorts of names, I'm sure I would know if I knew my French history better. Several old members of the Convention were still living. Even of those who had become celebrated, no favor of the new government was accorded them. To the, let's see, various kinds of commentary about the politics of the time. Let's see. However, it may be, some of those about him vaguely question my brother, that's Sadi Carnot, as to his desires in case one of us should be called to the Chamber of Peers of which Carnot had been a member. Carnot, Lazar Kano. So in other words, there was, you know, Would. Would. Would Sadi Kano somehow help out his friends or his brother if they became members of Parliament, basically, in 1815? Oh, no. Of which, which members of Parliament, which Lazar Kano had been a Member of Parliament in 1815, we had on this occasion a brief conference, a brief meeting. Unknown to us both, this distinction could be offered only to a title in some sort hereditary. We could not accept it without forsaking the principles of Carnot. Okay, so the point being made here was that Lazare Carnot in 1815 had been a Member of Parliament, and Hippolyte Carnot wondered if that meant that he had a right to also be a member of Parliament. But apparently this could only be done if there was some kind of hereditary title which they couldn't accept without forsaking the principles of Carnot. Another principle of Carnot, not about abstract machines, not about thermodynamics. This is a principle that was a principle that was combating the heredity of the peerage. The paternal opinion therefore came to second our distaste for the proposition and dictated our reply. Sa'di frequented the popular reunions at this period without forsaking his role of a simple observer. Nevertheless, he was, one occasion demanded, a man of prompt and energetic action. One incident will suffice to prove this and to show the sang froid which characterized him. On the day of the funeral of General Lamarque, later of miserable of fame, Sardi was walking thoughtfully in the vicinity of the insurrection riot that had been going on. A horseman preceding a company, and who was evidently intoxicated, passed along the streak on the gallop, brandishing his saber and striking down the passersby, sounds rather terrible. Sa'di darted forward, cleverly avoided the weapon of the soldier, seized him by the leg, threw him to the earth and laid him in the gutter, then continued on his way to escape from the cheers of the crowd, amazed at this daring deed. So, before 1830, Sardi had formed part of the Reunion Polytechnique Industrial, made up of old pupils of cole Polytechnique, with a plan to study in common. After 1830, he was a member of a similar association. And. I think. Let's see. So this goes on to talk about the hopes of the democracy. Meanwhile, seeming to be in abeyance, Sadi devoted himself anew to study and pursued his scientific labors with all the greater energy as he brought to bear upon them the political ardor now so completely repressed. So he was, according to Hippolyte Carnot, who I'm not sure is completely to be trusted on this issue. Sadi Carnot kind of had very definite political views that, you know, were sometimes the ones that were in favor, sometimes not. So he says of Sardi Kono. He undertook profound researches on the physical properties of gases and vapors and especially on their elastic tensions. And unfortunately, the tables which he prepared from his comparative experiments were not completed. But happily, the excellent works of Victor Renaud, so remarkable for their accuracy of supply to science in this respect, the blanks of which Sardi Carnot was conscious now in the small world that it was Victor Regnault was the person in whose lab William Thompson ended up working in the 1840s, that led him to the connection with Carnot, that led him to start talking about thermodynamics. So this then goes on for, say, Hipolit Kano goes on to say about Sadi Cano, his excessive application affected his health towards the end of June 1832, feeling temporarily better, he wrote gaily to one of his friends who had written several letters to him. My delay this time is not without excuse. I have been sick for a long time in a very wearisome way. I have had an inflammation of the lungs followed by scarlet fever. Perhaps you know what this horrible disease is. I had to remain 12 days in bed without sleep or food, without any occupation, amusing myself with leeches. That was at that time a. A sort of a. That was one of. One of the medical. Medical interventions of the time was put leeches on yourself and have them suck your blood. And that was thought to be a. A good thing. It says, anyway, without any occupation, amusing myself with leeches, with drinks, with bars and other toys out of the same shop. This little diversion is not yet ended, for I am still very feeble. This letter was written at the end of July. This is 1832. There was a relapse then. Brain fever, presumably. Encephalitis, I suppose. Then finally, hardly recovering from so many violent illnesses which had weakened him morally and physically, Sardi was carried off in a few hours on August 24, 1832, by an attack of cholera. Towards the last, as if from a dark presentiment, he'd given much attention to the prevailing epidemic following its course with the attention and penetration that he gave to everything. So an early epidemiologist, I suppose, Sadi Kano died in the vigor of life, in the brightness of a career that he bade fair to run with glory, leaving memory of profound esteem and affection in the hearts of many friends. Sir. His copy books filled with memoranda attest the activity of his mind, the variety of his knowledge, his love of humanity, his clear sentiments of justice and of liberty. Now again, let me comment that Hippolyte Carnot, by this time 50 years after Sadi Kano died. By this point, Hippolyte Kano was a serious politician himself and had become Minister of Education in France. So there's a certain sort of license of back projection, I suppose, of the. The importance of justice and liberty and so on attributed to his brother. So it's a little unclear to what extent that was something that could really be said to be there in Sadiq Arnaud, who, as I say, seems to have been a pretty keep to himself kind of person. Anyway, we can follow therein in these notes the traces of all his various studies. But the only work that he actually completed is that which is published. It will suffice to preserve his name from oblivion. His moral Character has other claims on our recognition. Our only ambition here, Hippolyte Kano says, is to present a sketch of it. But much better than through the perusal of these few pages. Sadi Kano can be appreciated by reading the thoughts scattered through his memoranda which are to be carefully collected. There are many practical rules of conduct which he records for himself, many observations that he desires to fix in his memory, sometimes in impression that has just come to him grave or gay, sometimes, though too rarely, a trace of ill humor directed against men or society. He never thought that these notes, the outpouring of his mind, will be read by other eyes than his own, or that they would someday be used to judge him. I find in them, for my part, touching analogies with the thoughts of my father, Hippolyte's father, Lazar Carnau, although the father and son had unfortunately lived almost always apart by the force of circumstances. Okay, so that was Hippolyte Carnot writing about Sadi Kano. Now, I suppose the last thing maybe I'll talk about is Saadi Kano's unpublished notes that were left over that were not burnt when he died of cholera. I should comment that Hippolyte Kano, as I mentioned, had a son who he named Sadi Carnot, who became president of France at the end of the 1800s. That sadi kano was had the misfortune of being assassinated in 1894 by an Italian anarchist. And at the time that Sadi Carnot, one of the things he'd done in France was to try to outlaw the French anarchists. But he was then killed by an Italian anarchist. And the anarchists, ironically enough, were organizing themselves, so to speak. So let's just kind of a little bit to finish off here, and I'm happy to try and have some discussion after this. But to finish off, let's have a look at some of Sadi Kano's unpublished notes, which, as his brother Hippolyte points out, didn't really intend anybody ever to read. See if I can find these here. So there are a number of pages of notes and they make kind of interesting reading. Here we go. They're cataloged into various different sections. So starts off by talking about daily occupations. So here are some sort of aphorisms of Sonny Connell. Plan in the morning the work of the day and reflect in the evening on what has been done. It's kind of an early personal analytics enthusiast, it seems. Carry when walking a book and a notebook to preserve the ideas and a piece of bread in order to prolong the walk, if need be. So he's a walking enthusiast like some of the rest of us. I just have a little piece of paper in my pocket. He went further and had a whole notebook. Sadiq I know says vary the mental and bodily exercises with dancing, horsemanship, swimming, fencing with sword and with saber, shooting with gun and pistol, skating the slings, stilts, tennis bowls. Hop on one foot, cross the arms, jump high and far. Turn on one foot propped against the wall. Exercise and shirt in the evening to get up a perspiration before going to bed. Turning joinery, gardening, reading while walking deck. That's interesting. It must have been an early person who was doing what one sometimes does today. Reading one's phone while one walks. Reading while walking. Declamation, singing, violin, Versification. That's writing. Writing, verse, musical composition. Eight hours of sleep, a walk on awakening before and after eating a. A great sobriety. Eat slowly, little and often. Avoid idleness and useless meditation. Quite a. Quite a health nut, actually. He goes on. Other aphorisms. Adopt good habits. When I change my method of life. Never turn to the past unless to enlighten the future. Regrets are useless. Form resolutions in advance in order not to reflect during action. Then obey thyself blindly. The promptitude of resolutions must most frequently accords with their justice. Not quite sure what that means. Yield frequently to the first inspiration. Too much meditation on the same subject ends by suggesting the worst part, or at least causes loss of precious time. Suffer slight disagreeables without seeming to perceive them. But repulse decisively anyone who evidently intends to injure or humiliate you. One should never feign a character that he has not or affect a character that he cannot sustain. Let's see. Make intimate acquaintances only with much circumspection. Perfect confidence in those who have been thoroughly tested. Nothing to do with others. Interesting principle. Question thyself to learn what will please others. I guess that's empathy for the possibly slightly spectrum type person. No. Useless discourse. All conversations which do not serve to enlighten others or ourselves or others to interest the heart or amuse the mind. Is hurtful. Seems not to have been into small talk, it seems. Ah, yes, this is a good one. Speak a little of what you know and not at all of what you do not. Why not say more frequently? I do not know. Speak to everyone of that which he knows best. This will put him at ease and be profitable to you, boy. I believe in some of these principles. Abstain from all pleasantry which could wound. Employ only expressions of the most Perfect propriety. Listen attentively to your interlocutor. And so prepare him to listen in the same way to your reply. And predispose him in favor of your arguments. Show neither passion nor weariness in discussion. Never direct an argument against anyone. If you know some particulars against your adversary, you have a right to make him aware of it, to keep him under control. But proceed with discretion. And do not wound him before others. When discussion degenerates into dispute, be silent. This is not. This is not to declare yourself beaten. How much modesty adds to merit. A man of talents who conceals his knowledge is like a branch bending under the weight of fruit. Interesting analogy. Why try to be witty? I would rather be thought stupid and modest than witty and pretentious. These are interesting comments on a personality. Men desire nothing so much as to make themselves envied. Egotism is the most common and most hated of all vices. Properly speaking, it is the only one which should be hated. The pleasures of self love are the only ones that can really be turned into ridicule. I do not know why these two expressions, good sense and common sense, are confounded. There is nothing less common than good sense. Talks about the strain of suffering causes the mind to decay. This is another interesting one. It must be that all honest people are in the galleys. Only knaves are to be met with elsewhere. I suppose he's saying only the people working in the kitchens are the only people who are honest. All the people who are off in high society are. Are not. Anyway, he. He goes on and. It's. He has a comment here which I suppose sadly turned out not to be true. Life is a short enough passage. I am half the journey. I will complete the remainder as I can. But he didn't live so many more years. Hope being the greatest of all blessings. It is necessary in order to be happy to sacrifice the present to the future. Let us not be exacting. Perfection is so rare. The more an object approaches perfection, the more we notice its slightest defects. To neglect the opportunity of an innocent pleasure is a loss to ourselves. It is to act like a spendthrift. By the way, I should say that Sadi Kano, so far as we know, was always a bachelor and lived alone his whole adult life. He says here, do nothing that all the world may not know. It's an interesting principle I kind of tend to agree with. The truly wise man is he who loves virtue for its own sake. Let's see. Various other comments here from Sadiq Arnaud. The laws of war do they Say, as if war were not the destruction of all laws. War has been represented as necessary to prevent the 2 rapid increase of the population. That's interesting claim. But war mows down the flower of the young men while it spares the men disgraced by nature. Hence it tends to the degeneration of the species. Interesting argument. He also talks about medicine here. In some respects, medicine is directly opposed to the will of nature, which tends to perpetuate the strongest and best of the species and to abandon the delicate to a thousand forms of destruction. This is what occurs among animals and savage men. Only the most robust attain the adult age and these only reproduce the species. This is kind of a. Remember this is before Darwin's Origin of Species, long before. Sort of interesting that he's talking about only the most robust attain adult age. I mean, this was obviously known, but not emphasized from a science point of view. Medicine and the aids of social state prolong the lives of feeble creatures whose posterity is usually equally feeble. Among the Spartans, barbarous regulations put an end to the existence of malformed infants that the strength and beauty of the race might be preserved. Such regulations are antipathetic, it says to our customs. Nevertheless, it might be desirable that we should devote ourselves to the preservation of the human race from the causes of weakness and degeneracy. It's an early eugenics pitch, I suppose, that we don't like very much today. The decadence of the Greeks and Romans without change of race proves the influence of institutions upon customs. Let's see. Oh boy, this is interesting. Okay, so this is a comment about economics. According to the system of modern economists, it will be desirable that the government should interfere as little as possible in the commerce and industry of the country. That's a. Well, I won't give my own commentary on that. Nevertheless, we cannot deny that in certain circumstances this intervention of the government in commerce and industry is very useful. Taxes, says Sadi Kano, are recorded by economists as an evil, but a necessary evil since they provide for public expenses. Consequently, economists think that if the government possess sufficient revenues in domains, for example, this. In domains, for example. I'm not sure what that means. Anyway, if the government possessed sufficient revenues, the suppression of all taxes would be a desirable measure. Taxes are a means of influencing production and commerce to give them a direction which they would not naturally have taken. Yes, so people say. Such an influence may undoubtedly have disagreeable consequences if the taxes are imposed without discrimination or exclusively for a fiscal purpose. But it is entirely otherwise if wisdom and fact preside at their institution. Definitely a definite political point of view by Monsieur Carnot in the probably around 1830. A tax on the rent of a farm will be much better than a tax on the land itself. Proprietors then could only avoid taxes by themselves improving their property. As it is, they merely collect the rents and usually employ their surplus in unproductive expenditure, while the proprietary farmers voluntarily devote theirs to the improvement of the land. This is definitely a nudge people with taxes kind of theory. Attacks on the farms would then result in the proprietors themselves working the lands. And this would mean better cultivation and improvements which would yield returns indeed. But at too remote a period for the tenant it would tend to a division of landed property. Men of small fortune uniting in the purchase with capitalists who seek only the rent or payment for the land. So clearly he was thinking about these kind of dynamics of economics and their effect on policies and so on. Great capitalists could not themselves cultivate vast extensive land and not wanting to diminish their revenues by renting them, were being induced to sell portions suitable for cultivation by their new owners and would then carry their money into new industrial and commercial enterprises. So I guess this is a farm, your own land kind of theory. This is a have the founders run the company, don't sell it to private equity and have somebody else run it kind of thing. Interesting point of view from 1830. The competition of the sellers would cause a momentary fall in the price of the lands and would enable small farmers to become landowners. The number of vast estates, often badly managed, would then be diminished and considerable fortunes changing hands more easily would naturally pass into those which would be most likely to increase their value. Proprietors becoming cultivators to escape the taxes would settle in the country where their presence would disseminate intelligence and comfort. And their revenues before spent unprofitably would then pay expenses and improvements on their property. Boy, I don't know what the Karl Marx version of some of these kinds of thoughts would have been in later years. Well, anyway, the establishment of such tax would certainly find many opponents among proprietors, landed non cultivators who form in fact the influential personnel in the state. For it is they who usually make the laws. Yeah, well, so, so he goes on. This is, this is definitely a. A certain political point of view. It's a lot of detail about his scheme for, for taxes on farms and so on and, and some terms I don't actually understand here. Let's see, proprietors of lands then after all have to bear the mutation taxes. I'm not sure what that means some piece of taxation that maybe has survived under a different name. All increase of these taxes are lost for them. And these taxes are heavier on the small proprietors than on the large because their changes are more frequent. Oh, I see. That must be mutation. Taxes must be. Oh my gosh. The taxes one pays, one real estate is transferred and has different names in different countries. The tax on the farms on the country would bear more heavily on larger states, etc. Etc. Etc. Anyway, it kind of goes on. These are again the unpublished notes of Sadiq Hanaud, so he didn't expect anybody to read them, but it gives some impression of what his point of view was. So there are a few thoughts here about religion. Men attribute to chance those events of the causes of which they are ignorant. If they succeed in divining these causes, chance disappears. To say that a thing has happened by chance is to say that we have not been able to foresee it. I do not myself believe that any other acceptation can be given to this word. What to an ignorant man is chance cannot be chance to one better instructed. If human reason is incapable of discovering the mysteries of divinity, and why has not divinity God basically made human reason more clear sighted? Asks Sadiq Hanaud. God cannot punish man for not believing when he could so easily have enlightened him and convinced him. If God is absolutely good, why should he punish the sinner for all eternity, since he does not lead him to good? Or give him an example. According to the doctrine of the Church, God resembles a sphinx, posing, proposing enigmas and devouring those who cannot guess them. The Church attributes to God all human passions, anger, desire for vengeance, curiosity, tyranny, partiality, idleness. If Christianity were pruned of all which is not Christ, this religion would be the simplest in the world. He says. What motives have influenced the writers who have rejected all religious systems? Is it the conviction that the ideas which they oppose are all injurious to society? Have they not rather included in in the same prescription religion and the abuse of it? The belief in an all powerful being who loves us and watches over us gives to the mind great strength to endure misfortune. A religion suited to the soul and preached by men worthy of respect would exercise the most salutary influence upon society and customs. Well then there are a bunch of unpublished notes about mathematics, physics and so on. There's something about collision of bodies, let's see. And the fact that he knows that when there's a collision of bodies there's expenditure of motive power. And this is so as I recall, one of the things that comes out in these notes, in these notes about physics that were written probably several years after his book from 1824, Sadi Carnot is beginning to doubt the caloric theory of heat, even though his great work had been based on the caloric theory of heat, Is kind of was there. So he comments. He says when a hypothesis no longer suffices to explain phenomena, it should be abandoned. This is the case with a hypothesis which regards caloric as matter, as a subtle fluid. The experimental facts tending to destroy this theory are as follows. The development of heat by percussion or the friction of bodies. Experiments by Rumford. Friction of wheels on their spindles, on the axles. Experiments to be made. Oh, I see. Perhaps he's imagining doing those experiments here. The elevation of temperature takes place at the same time in the body rubbing and the body rubber. Moreover, they do not change perceptibly in form or nature. And he says to be proved thus, heat is produced by motion. If it is matter, it must be admitted that the matter is created by motion. So he's beginning to realize that this idea that heat is a form of matter, a caloric fluid, doesn't make sense. He says when an air pump is worked and at the same time air is emitted into the receiver, the temperature remains constant and the receiver remains constant on the outside. Consequently, the air compressed by the pumps must rise in temperature above the air outside, etc. Etc. Etc. Thus again he says heat has been created by motion. This is all his evidence for the inadequacy of the caloric theory of heat. He talks again about experiments he can make. And let's see. We may be allowed to express here a hypothesis in regard to the nature of heat. At present, light is generally regarded as the result of a vibratory movement of the ethereal fluid. Light produces heat, or at least accompanies the radiating heat and moves with the same velocity as heat. So that he's talking about infrared radiant heat. Radiating heat is then a vibratory movement. It would be ridiculous to suppose that it is an emission of matter, while the light which accompanies it could be only a movement. In other words, he says radiant heat seems to be something just like light, as he's describing it, a vibratory motion of the ethereal fluid. That was at a time when people imagined that electromagnetic waves would be something that were. I mean, that wasn't understood until much later. But the concept was that light was kind of a, A, a vibration in the, in the ether, that that pervades all of space, or was imagined at the time to pervade all of space, much as sound, as a vibration in something like air. So anyway, so he says, so it seems silly to think that basically radiating heat, that if ordinary heat is a form of matter, that radiating heat is more like light, that it seems like those two forms of heat should be sort of more the same kind of thing. Okay, so then he says, could a motion that of radiating heat produce matter per an caloric? No, Undoubtedly it can only produce a motion. Heat is then the result of a motion. Then it is plain that it could be produced by the consumption of motor power and that it could produce this power. All the other phenomena, composition and decomposition of bodies, passage to the gaseous state, specific heat, equilibrium heat, it's more or less easy transmission, its constancy in experiments with the calorimeter could be explained by this hypothesis. Would it be difficult to explain why in the development of motor power by heat, a cold body is necessary? Why, in consuming the heat of a warm body, motion cannot be produced? It appears very difficult to penetrate into the real essence of bodies. To avoid erroneous reasoning, it will be necessary to investigate carefully the source of our knowledge in regard to the nature of bodies, their form, their forces, to see what the primitive notions are, to see what form of impressions they are derived, to see how it is raised successively to different degrees of abstraction. So he's basically saying what is matter made of? That wasn't known at the time. People had imagined things like atoms from antiquity. But at the time, 1830 or so, it wasn't known what matter was made of. And he says to understand so the relationship between radiant heat, heat, light and so on, one needs to know more about what matter is made of, which is a very, very perceptive comment. If heat, the result of a vibratory motion, is heat the result of a vibratory motion of molecules, the ding. You got it. So if this is so, quantity of heat is simply quantity of motive power. Very good. In other words, he's saying, he's asking the question, this caloric fluid thing, maybe that's all nonsense. Maybe there is no matter. Is heat really the result of a vibratory motion of molecules? If this is so, he says quantity of heat is simply quantity of motive power. So that, by the way, is already not a trivial kind of thing to connect. Because, as I say, at the time when he was writing this, people didn't know that heat was a form of energy. But he's saying, if so, the quantity of heat Is simply a quantity of motive power. As long as motor power is employed to produce vibratory movements, the quantity of heat must be unchangeable, which seems to follow from experiments with a calorimeter. But when it passes into movements of sensible extent, the quantity of heat can no longer remain constant. In other words, when the. I mean, really. This note. He's got it. I mean, that's the correct theory of what heat is. That heat is these vibratory movements of the molecules. And when it is only at some times that it passes into movements of sensible extent, that is movements you can sense, that is kind of systematic motion mechanical work. So that paragraph is really, really quite, you know, kind of nailed what's really going on with heat and ultimately with thermodynamics. But of course, this was in unpublished notes which weren't found for 50 years after Carnot's death, By which point other people had come in and thought about these kinds of things. Can examples be found of the production of motor power, the actual consumption of heat? It seems we may find production of heat with consumption of motor power re entrance of air into vacuum. So he's thinking about how would you get evidence of this idea that heat is really the motor power associated with the vibratory motion of molecules? He's talking about what is the production of heat and the combinations of substances, chemical reactions and so on. What is radiant caloric liquefaction of bodies? Yeah, he's talking about liquefaction of bodies, solidification of liquids, crystallization. Are they not forms of combination of integrant molecules? Yep, that's true. Supposing heat due to a vibratory movement, how can the passage from the solid or the liquid to the gaseous state be explained? That's cool. Well, yeah, that. That got figured out. When motive power is produced by the passage of heat from a body from body A to body B is the quantity of this heat which arrives at B. If it is not the same as that which has been taken from A. If a portion of it has been consumed to produce motive power, the same whatever may be the substance employed to realize the motive power. In other words, when all these. If heat is this form of vibrations, why is it that sort of it works the same in all different materials? Is there any way of using more heat in the production of motive power and of causing less to reach body B, could we even utilize it entirely, allowing none to go to body B? In other words, could we take all the heat and energy that's in one body and make it go to mechanical work. If this were possible, motive power could be created without consumption of combustible and by mere destruction of the heat of bodies. So there he's kind of denying the second law of thermodynamics. He's saying if this was possible, if we could take all the heat in a body and turn it to mechanical work, could that be something that would happen? If that could happen, then the second law of thermodynamics doesn't work. Is it absolutely certain that steam, after having operated an engine and produced motive power, can raise the temperature of the water of condensation as if it had been conducted directly into it? So that's sort of thinking about the experiments here. Reasoning shows us that there cannot be loss of living force or, which is the same thing, of motive power. So living force was the vis viva, was the term that I think Leibniz had given to kinetic energy, a bit of a confusing term, as the bodies act upon each other without directly touching each other, without actual collision. Now everything leads us to believe that the molecules of bodies are always separated from each other by some space, that they are never actually in contact. If they touched each other, they would remain united and consequently change form. So he's saying molecules are. He's imagining that the molecules and substances are never actually stuck together, as they kind of a little bit are in solids. So, but he's imagining they always just have space between them and are bouncing around. If the molecules of bodies are never in close contact with each other, whatever, maybe the forces which separate or attract them, there can never be either production or loss of motor power in nature. So in other words, he's saying if the things can stick together, if there's binding energy, what we now call binding energy, that can take away from the kinetic energy. But if what's happening is the molecules are always just bouncing elastically, then they must keep the same energy. Living force viva. This power must be as unchangeable in quantity as matter. That's an interesting statement because he's basically saying this thing that is essentially energy must be as unchangeable in quantity as matter, which is kind of speaking to the conservation of energy, which was a principle that was understood only years after this. Well, at least a decade after this, then the direct re establishment of equilibrium of the caloric and its re establishment with the production of motor power will be essentially different from each other. Heat, he says, is simply motive power, rather motion, which has changed form. That's a good thing to say. It is a movement among the Particles of bodies. Wherever there is destruction of motor power. There is at the same time production of heat and quantity. Exactly proportional to the quantity of motive power destroyed. Boy, that's pretty good. That's energy conservation. Reciprocally, wherever there is destruction of heat. There is production of motive power. He says. Very cool. We can then establish the general proposition. That motive power is in quantity, invariable in nature. That it is, correctly speaking, neither produced or destroyed. It is true that it changes form. That is, it produces sometimes one sort of motion, sometimes another. But it is never annihilated. So that's pretty good. That's really conservation of energy. Before people like Joule and so on started talking about that. So he has some calculations here. According to my ideas, I formed on theory of heat. The production of a unit of motive power. Necessitates the destruction of 2.7 units of heat. Well, that, of course, depends a lot on the units that you're using. And he's talking about unit of motive power, the dyname, which I've never heard of. Representing the weight of 1 cubic meter of water. Raised to the height of 1 meter. So that's a quantity that a system of units we don't have anymore. Well, anyway, so then he talks about various experiments he might do. Experiments to be made on surface tension, et cetera, et cetera, et cetera. But I'm pretty impressed with the fact that he really seems to have figured out kind of the molecular theory of heat there. But sadly didn't tell anybody about it at the time. And it died with him. So, let's see. So that's kind of the story of what Carnot said. I'll just show you a couple more things. And then I want to comment on sort of the history of science resonance with all of this. So just to give a sense. Let me see here. Just to give a sense of sort of the other things happening in thermodynamics at this time. So these are sort of some big figures of thermodynamics. There's Sadi Carnot at the beginning here. And sort of after Saudi Carnot, there was Clausius, Kelvin, who we mentioned before. And then Maxwell, Boltzmann, Gibbs, all coming in later. These are sort of the people who established thermodynamics. And the second law of thermodynamics by the 1860s or so. And so just to give a sense of what happened from Connot's work. Let me just show you a few other items here. So this was pages from Carnot's books that I showed earlier, this was I mentioned in 1834, Emile Clapperin had sort of written his version of what Carnot said and then included this diagram, which is kind of the first sort of diagrammatic representation of the Carnot cycle, sort of the idealized cycle for a steam engine. And by the way, in Cat Laurent's work, he's starting to use notation like DQ and so on for the change of the absolute quantity of heat, as he calls it, Q, which is the same symbol that we use today to represent the quantity of heat. So that was all established as Clapeyron tried to sort of more mathematically present what Carnot had done. So this is now Kelvin. This is. I mentioned that Kelvin had really been introduced to Carnot by his desire to make a thermodynamic scale of temperature, a scale of temperature which didn't depend on the details of sort of the expansion of one material or another. This is on an absolute thermometric scale founded on Carnot's theory of the motive power of heat. And that's an early work, so he says, here published in 1824 in a work entitled Reflections sur lauriste de Foi by Monsieur S. Carnot, having never met with the original work, says William Thomson, later Lord Kelvin at the time, it is only through a paper by Monsieur Clapeyron on the same subject, published in the Journal de la Colpole Technique and translated into the first volume of Taylor's Scientific Memoirs, that the author has become acquainted with Carnot's theory. In those days, typically papers in French, significant papers in French, there were journals in English which translated those papers fairly rapidly into English. So then, 1849, I mentioned this before. This is Kelvin basically giving an account of Carnot's theory of motive power of heat. So this is kind of the recapitulation by Kelvin of what Carnot wrote, what Carnot had written in 1824, this is now Kelvin, a quarter of a century later, kind of recapitulating that and beginning the kind of clear formulation of the laws of thermodynamics. Kelvin says, thus it is that Carnot, in accordance with the strictest principles of philosophy, enters upon the investigation of the theory of the motor power of heat. So Kelvin is kind of imagining that Carnot has kind of based his. That it's all based on bedrock, that there's no kind of intuition involved, that it's all based on the strictest princip of philosophy. Let's see. And then he says, so generally is Carnot's principle. Again, total confusion about the term Carnot's principle tacitly admitted as an axiom that its application in this case has never, so far as I am aware, been questioned by practical engineers. So in other words, he's saying that, you know, it's a very circular kind of thing. He says Carnot is based on sort of philosophical principles, but actually it's really an axiom that we choose arbitrarily. But no engineer has ever disputed it. But this is the second law of thermodynamics, which we're taking as a law of physics, even though we're assigning, we're saying that the engineers never dispute it. And then later we imagine that it's a law of physics that necessarily is that way. And we argue it so vehemently that we believe that it explains that the things about kind of the end of the universe and so on. And pretty soon Calvin has convinced himself that sort of the second law kind of just has to be that way. And so it stays for many years to come with great confusion over the course of a century and a half. So let's just reflect a little bit on what Carnot did and kind of the nature of it. One of the things that's interesting, I think, about what Connot did was sort of wrong theory, right answer. He managed now to be fair to Carnot, as we see from his unpublished notes, late in life, he groked it. He figured out the caloric theory. He probably wasn't right and that heat really was motion of molecules. But at the time when his known work that sort of had a historical place was based on the caloric theory of heat, that heat was a fluid, heat was a form of matter, which is not the case. But nevertheless, the sort of strength of his logical argument was great enough that even though its kind of intuitive foundation was wrong, the logical argument was correct. Now, I have to say that I find it very interesting that there are things in today's world where in today's physics, where one sees very close analogies. I think one is dark matter. Dark matter, by its name is thought to be a form of matter, just as caloric was thought to be a form of matter. But caloric heat turned out not to be a form of matter. It turned out to be a feature of the microscopic structure of all matter. It turned out to be a feature of the microscopic motion of molecules and so on. So it's my own suspicion that dark matter will go the same way. We've known that there were anomalies in the way that gravity works in galaxies and now in Lots of other things. We've known that for basically 100 years, since the 1930s, it's been known that the rotation curves of galaxies aren't accounted for by the luminous matter in galaxies and so on. But yet, knowing only about matter particles being the sort of the things that we talk about in fundamental physics, people say it must be matter, it must be a form of matter, it must be dark matter that is causing these essentially gravitational anomalies. My guess is that's not true. My guess is that in fact, history of science will sort of recapitulate itself and that just as caloric fluid turned out not to be a kind of matter, it turned out to be a feature of the microscopic structure of all matter. So similarly, that dark matter will turn out not to be matter at all, but will turn out to be a feature of the microscopic structure of space. And in fact, in our models of physics, space is discrete. It's made of actual sort of networks of atoms of space. And one can imagine a kind of space time form of heat in which there are sort of microscopic aspects. It's not quite motion, because motion is a thing that gets only defined at a much larger scale, but essentially microscopic features of the structure of space that leads to the anomalies of gravity that we now call dark matter. And it is interesting that thinking of cold dark matter as the thing that produces that gravity has been a correct way or seems to accord with experiment in terms of studying cosmology and so on, just as the caloric theory of heat seemed to accord with experiment as a description of how heat worked. But in fact, the kind of intuitive basis of it is wrong, the nature of it is wrong. So I think it will be with dark matter. And my guess is that what will happen is really a very close recapitulation that the matter won't be matter at all. It'll be a feature of sort of the microstructure of the medium. Now, another thing that sort of a resonance with today's world is this question of just how efficient can things be? When we're looking at what Carnot was interested in was how efficient can you make a steam engine? What is the fundamental limits on steam engine efficiency? Well, in today's world, we've got other issues of that kind. We might be looking at, you know, machine learning and, and efficiency there and, and the laws for that. But I think more physics oriented, one's looking at things like quantum computing and one's asking questions about sort of what is the ultimate ability of a quantum computer. What, you know, can one make a Carnot like argument for what sort of the ultimate effectiveness of a quantum computer can be? There is kind of an idealization, it's kind of a Lazar Carnot type stage of study of quantum mechanics where one has these kind of idealizations of quantum mechanics in which there is sort of a mathematical theory of quantum mechanics. And then this process of measurement is something which is kind of a bolt on to that. Just as in the time of Lazar Carnot, one knew about kind of the mechanics of machinery, but when it came to the role of heat in the operation of machinery, that was kind of a bolt on thing that wasn't really accounted for for. And so I think that there is a, there's sort of this question and we see in quantum computers and so on, we see the sort of mystery of the fact that there is a limit. There seems to be in practice limits to the efficiency and effect of quantum computers as a result of noise, decoherence times, things like this. When people actually try and build quantum computers and sort of a question of where do those, what are those fundamental limits come one have a theory of those fundamental limits. My own guess right now is that perhaps the most interesting thing about quantum computing today is what we have learned about fundamental limits on quantum measurement. I mean, the analogy I've been using is imagine you want to make a telescope that's going to look at sand dunes on Mars. Well, you know, you could say it's just an engineering problem, but we don't have enough resolution to be able to see those sand dunes. But in fact, as we know from a time around, actually the time when Connor was working, as we know from diffraction, we know that in fact there is an ultimate limit on the effectiveness of a telescope that has to do with the angular resolution being proportional to the wavelength divided by wavelength of the light that's being used in the telescope divided by the diameter of the telescope. That there is a piece of physics which is that ultimate limitation. We don't know that piece of physics for quantum measurement, but I think it's a Carnot like study that has to be done to try and understand that, that, that thing. My own guess is that it will reveal some sort of fundamental physics. My, my hope is that it will reveal the thing that shows up in our theory. Just as there's a speed of light in physical space, so there is a maximum entanglement speed in what we call branchial space, the space of quantum branches. And it is my hope that that maximum entanglement speed will show up as sort of a constant of nature, which is contributing to this sort of ultimate limit on. On quantum measurement. And if we can find the maximum entanglement speed, then that will tell us the elementary time and the elementary length, the actual sort of scale of granularity of space and of time in the universe. All right, well, so to wrap up here, as I say, it's the Today, or at least this week, we don't know. Absolutely to the day is the 200th anniversary of the publication of Sadi Kano's book on the motive power of heat. And really the launching point for what became the science of thermodynamics. Also a certain kind of almost philosophical approach to the derivation of results in physics. Something which had existed before, kind of the mathematization of these things in the late 1600s, and something which came back again in the work of Boltzmann and following from that, the work of Einstein in 1905 and so on. When gives arguments for special relativity and so on, those are arguments couched in somewhat the same kind of almost philosophical terms that Carnot was using. And I kind of wonder what the line is between Carnot and Boltzmann. And there's a clear line from Boltzmann to Einstein, even though they never met. And although Einstein was the, you know, Boltzmann had long pushed the molecular theory of matter and towards the end of his life had sort of given up and said, you know, this is. It's. I think his famous quote is something like, you know, one man cannot turn back the tide of history. And by which he meant that the tide of history was against the molecular theory, matter. And Einstein kind of turned that around with his analysis of Brownian motion in 1905. All right, well, I should wrap up there. Let's see. I'm happy to try and answer questions and things if I can. Let me just take a look at what we have. There's a comment here from. From rbs. So Carnot was the original new kind of science guy of his time, perhaps. So one can certainly speculate on what would have happened if Carnot had lived longer and what kinds of things he would have invented. Let's see. Harry. Comments. If you think about it, we still mostly live in the steam age. Most energy we get is steam at some point. Yeah, I suppose, except for the electrical motors. Except for. I mean, that's kind of the transition from fluids to. From physical fluids of molecules bouncing around in gases to just the motion of electrons and what we might think of electron gases. Harry is asking why was Carnot's book printed with such wasteful borders? Only a few lines per page, it had fairly generous borders. I think that was pretty typical of the time. I think books were usually, I think still by that time, certainly earlier printed books. When you bought a book, you bought a block of paper and it was up to you to bind that paper and so there was space being left over for the binding that you would do as the purchaser of the book. I'm not sure if that was still happening by the time of, by 1824. Certainly happened earlier than that. Castle Comments what does it mean to discuss the heat death of the universe if entropy only pertains to closed systems? The heat death of the universe is simply saying that as time goes on, what is orderly structure will degrade into kind of just the random motions of molecules. I've sort of pointed this out a bunch of times, but with my Interinterpretation of the second law of thermodynamics as sort of this thing that is only perceived by computationally bounded observers, what one's saying is, yes, the things that exist today will have been sort of ground down into the detailed motions of molecules. But those detailed motions of molecules, if we were more sophisticated observers, we would say, look, in that detailed motion of molecules is the whole sort of, is the whole trace of that great civilization that existed, you know, a billion years earlier, so to speak. So in other words, the fact that we think, oh, everything has been lost, it's just random heat, is a consequence of being observers of the kind we are looking only in the aggregate of those molecules and not being able to untangle the sort of computational details of their motions. So I think the heat death of the universe, which was very strongly believed and talked about by Kelvin and talked about his kind of theological significance and so on, and Kelvin had a lot of sort of issues with that because he was kind of a Presbyterian who had definite beliefs about the role of God and so on. And so it was a complicated kind of tangle of what this meant, but it was still it became kind of a for a hundred years, more than 100 years. It was just one of these things that people just assume the universe is doomed, it's going to eventually just be a bunch of heat with no structure in it. And it's just not really right because it's only no structure to observers like us. But by the time we are sort of part of that heat, so to speak, and we might be observers different from the way we are observers with, for example, more Computational capabilities, then it's no longer sort of this seemingly structuralist thing. Let's see. RBS asked, are there ways to measure the efficiency of stochastic systems using principles derived from Carnot's work on heat engines? I'm not sure. I have to say that the efficiency of heat engines arguments strangely tangle up what will later become the kind of notion of entropy. And this idea of kind of the states of a system consistent with certain constraints, with the particular details of the number of degrees of freedom in the system carrying a certain amount of energy, it kind of tangles up as much later thermodynamics does, kind of the notions, the informational notions of entropy, which is really an informational concept with the energetic notions of heat and so on. Because we're sort of attaching to every degree of freedom that's being described by the entropy, we're attaching some energy. That attachment of energy to this sort of informational counting of states in entropy is quite unnecessary. But it's been very confusing to people that the second law has to do with things like temperature and so on. It does not. The second law is a much more general computational principle that is true of any computationally irreducible system observed by a computationally bounded observer. It has nothing to do with actual molecules, the conservation of energy, existence of temperature, things like this. Harry comments. Heat engines were the AI of their times. Absolutely. They were the, they were the thing that was sort of launching new industries and, and, and making sort of changing the way one thought about things. Are people commenting? Carnot's quotes will be good as tweets. Yeah. Pity didn't have Twitter in the 18th in 1830. Let's see. Well, gosh, a couple more comments here and then probably wrap up here. But left is commenting. How did scientists deem dark matter to be a real thing? Well, I mean, I think Fitzwick was the person who first started talking about it in the 1930s from observation of galaxies. And for a while it was like, oh, I don't really know whether it works that way and it must just be dead stars and so on and so on and so on. And then it kind of, I would say in the 1980s, probably it started to be more of a, a thing where, you know, it's always suspicious when, when any area of science says 90% of, of what's there, we don't, we can't account for. I mean, that's true of when people say 90% of the brain is unused, 90% of the genome is unused, 90% of the of the content of the universe is unseen. These kinds of things. It's always a bit suspicious, but I think there have been a succession of pieces of evidence about how dark matter behaves. I mean, what became the lambda CDM model, the cosmological constant, together with cold dark matter, became sort of the standard model of cosmology by certainly around the year 2000. And there have been more detailed measurements. There's this particular pair of galaxies that pass through each other and they kind of left behind something which seems like it has gravitational effect, seems like it's dark matter matter. It's something different that seems like it must be matter. And there are discussion from features of the cosmic microwave background, particularly the so called baryon acoustic oscillations, which are again sort of a thing that behaves like cold matter, cold matter that has low temperature so that it doesn't have a pressure, it's pressureless matter. But that doesn't mean it has to be matter. But it's just that people have attempted to change the laws of gravity to essentially make deviations from Einstein's equations, which in turn give you things like the inverse square law of gravity. They've attempted to modify those things. And the obvious modifications that people have done haven't worked. They produce other effects that are not seen. Now. People have not looked at the thing that comes out in our models, which is dimension fluctuations, the fluctuations of the dimension of space away from three. And my guess is that one can reformulate general relativity not in terms of curvature change, but in terms of dimension change. And that may reveal some kinds of effects that would be only visible on the scale of galaxies and things like this. Not visible. And which could account for these sort of anomalies in gravity. But we don't really know how that works yet. Let's see. Memes asks, has anyone ever done further investigation into the paper that I wrote long ago with my friend Jan Ambjorn on the thermodynamics of the vacuum? Yeah, well, so, so that was in, oh, 1981 I think it was, when I was still a card carrying particle physicist, sort of wrote a couple of papers called Properties of the Vacuum. And there's one called mechanical one called electrodynamic. And we promised a part three, which was the gravitational, which was about gravitational properties of the vacuum. We never wrote part three. We got many, many requests over the years for part three. And I think I finally figured out a year or two ago what part three should talk about. But at the time, back in the beginning of the 1980s. And there's a time when properties, gravitational properties of the vacuum were definitely things that were sort of emerging through studies of Hawking radiation, black holes, other kinds of things like this. But we didn't sort of know how that worked. I think we now more do know how that works. And I keep on telling Jan Ambjorn that we should. I keep on saying, let's spend a weekend and try and write part three. And I don't think he takes me seriously because, you know, he's an academic and academics don't write papers, you know, substantial papers on a weekend. It's only crazy people like me who, well, who've spent decades building tools and so on that it becomes even conceivable to actually do significant scientific work in a weekend. But in any case, if you ask what became of those papers, the most interesting thing that became of them, they were studying what happens to a little piece of vacuum that's put in a box. Actually a chap called Robert Forward pointed out quite a few years after we'd written those papers, said, you know what, the way that you've set this up there's been, as you change the shape of this box, by the way, the big effect is the thing called the Casimir effect, which is that if you have two metal plates, two big metal plates, and they're very close together and it's all in the vacuum, there's a small force of attraction between those metal plates. The origin of that is that in quantum field theory there are always vacuum fluctuations, there are always zero point fluctuations of the field of, for example, the electromagnetic field. There's always little electron positron pairs that are coming up and disappearing in short amounts of time. There are always these fluctuations in electromagnetic field. But it turns out between the plates, the presence of those plates is cutting out certain low frequency long wavelength fluctuations of the field. So there are fewer fluctuations of the field between the plates than there are outside the plates. And that's sort of why there's a force of attraction even in the vacuum between those plates. Because sort of the vacuum isn't quite the same between the plates because you've cut out these low frequency modes by the fact that the plates are there. Well, that argument about, you know, that sort of intuitive argument doesn't quite work because if you have a metal box, so to speak, that's a whole three dimensional box. Actually the force, the Casimir effect goes to pressure outwards rather than a pressure inwards. People for a little while thought that maybe the Casimir effect could account for Kind of a mechanical model of the electron where the electron will be sort of held together by Casimir forces, even though electromastatic forces would tend to make it fall apart. But it doesn't work because the intuitive argument I gave isn't quite right. When you analyze the three dimensional modes of the electromagnetic field, which is what Jan and I did back in 1981, and we kind of analyzed it for arbitrary shapes of boxes. And what Robert Ford then pointed out was if you take our results on these shapes of boxes, you kind of squidge them around, you will discover that there's a closed cycle very much like Carnot's cycle, a closed cycle of action to this machine in the vacuum, so to speak. If you change the shape of this box in the vacuum, you can go through a closed cycle and extract energy from the vacuum. And so he wrote some papers. He was also a science fiction writer, and I think he put this in his science fiction books as well. But he wrote papers about kind of extracting energy from zero point energy of the vacuum. And it even became. There were some studies of kind of spacecraft propulsion based on zero point energy. I think the main place where that's landed is in dialogue in various science fiction movies about sort of zero point energy as a source of action of various kinds. But in any case, that was. So it seemed at first when this came up, it was like, did I get the calculations wrong? Well, no, I didn't. But the thing that happens. So does this work? Can you extract energy from the vacuum? Can you make a perpetual motion machine basically by using this closed cycle of these Casimir forces and so on? Well, the answer, I think is no, because basically what happens is when you make these sort of borders and you're trying to sort of prevent vacuum, you're trying to constrain the vacuum, turns out you can only do that to some extent. It turns out that it's only opaque to some modes. But in order to make this work, it has to be the case that this material is sort of perfectly opaque. And by the time it starts to be affected by the fact that you have to make the material out of atoms and so on, and you can't make something which sort of has that perfect opacity. You might wonder, could you make a configuration of a field just like when you do plasma confinement to get fusion? You're not trying to constrain that 10 million degree plasma in a. You know, no material substance can have its atoms hang together at 10 million degrees. But a magnetic field doesn't care about temperature. In that sense. And so you can have a magnetic field that can withstand that. And it makes me wonder as I'm thinking about this now, whether you can imagine kind of a field that is constructed to make sort of this box that will constrain the vacuum. It's worth looking at, actually. Worth looking at. That would be the ultimate irony if on the 200th anniversary of Carnot's argument, where he used the argument that there can be no perpetual motion machine. If in fact one figures out how to construct a perpetual motion machine that continually extracts energy from the vacuum. It's not an impossible thing. Because the vacuum, if one extracted energy from the vacuum, if one was able to, kind of what one would be doing is essentially exactly what Carnot was talking about. Namely going from the heat, not really heat, but the randomness of the zero point fluctuations of quantum fields, and taking that randomness and turning into mechanical work. Actually, it's an interesting idea to see to what extent one can make kind of inequalities of the same kind that Carnot did, to see to what extent you can extract energy from the structure of the vacuum. Now, I mean, there are things that one can do with event horizons and black holes where one can make arguments that are sort of Carnot like arguments that end up being about the thermodynamics of black holes. They don't really have thermodynamics in the same sense, but there are kind of Carnot like arguments that could be made there. So this makes one wonder whether if one thinks about sort of this changing the shape of the, of the vacuum, of the box in the vacuum, to what extent a closed cycle there is able to extract energy from the vacuum. If it did extract energy from the vacuum, what that would be saying is essentially one is trading off some features of, for example, the cosmological expansion of the universe from things that are happening locally. We'd be in terms of the. Is it a renewable energy source? Well, ultimately no. If we took all the energy of expansion of the universe and provided it to run our cars or whatever, no, it wouldn't be. We'd have to have an awful lot of cars to make any dent on the cosmological expansion of the universe. But in principle it would do that. Now, one thing that's also tricky in thinking about what's going on there is that the idea of energy conservation is only a local idea. When you look at the whole structure of the universe at a cosmological level, energy conservation is a much more complicated issue, and it's much Less clear what it means to say, quotes, energy is conserved. That's something that's absolutely true locally. But when you look at the energy associated with the expansion of the universe and how that has effects at cosmological scales, it's not so clear. Let's see, last couple of things here. Links between Carnot's findings. Let's see. Prab asks, is there any link between Carnot's finding a modern information theory? Not really. That was a pretty circuitous route. I mean, that really went from Carnot and the sort of original intuition about the second law to Kelvin and Clausius kind of sort of nailing down the second law. And Maxwell was involved in that as well, to really Boltzmann talking about sort of the second law as interpreted in terms of molecules. And that led to actually, Clausius invented the term entropy, but invented it as kind of a bulk property of matter. Boltzmann kind of understood the microscopic character of entropy, which is why he had on his tombstone, S equals K log omega, K log W, I think, which was kind of the representation of entropy is the log of the number of states of the system. But that was. And then only much later, you know, when Shannon started talking about kind of the. The number of configurations in a communications channel, that became kind of. Well, I think. Was it. I think it was. Was it von Neumann who. No, I forget who. Who told Shannon that if he. If he calls the thing he's talking about, you know, if he relates it to entropy, everybody's confused about entropy. So nobody will kind of question what Shannon is doing. But eventually Shannon kind of makes this connection to entropy, as was described by Boltzmann as a configuration of molecules. Shannon is talking about it as a sort of a configuration of bits. In the end, the second law is not what's talked about in terms of information theory. There hasn't been a second law, an analog of the thermodynamics second law. In information theory, people have sort of assumed that the second law is a thing that involves molecules and temperature and energy and so on, which is just not true. There is, as I've kind of, I think shown, sort of a computational analog of the second law that's all wound up with computational irreducibility. So in a sense, there could have been a merger of kind of information theory with thermodynamics, with entropy and so on, but that didn't really happen. I suppose it's, you know, my little efforts, as captured in the. Has to show the book thing, you know, is my attempt to do that and I think that's we finally have that, but it's sort of long after the fact through a very circuitous route. The. All right, well. Well, thanks. Thanks for joining me. And. I wanted to celebrate this particular anniversary. I've been meaning to do this for a few years, so I'm glad we had a chance to be here today to talk about the 200th anniversary of Sadi Kano's publication of Sadi Kano's book. So thanks very much and bye for now.