THE FIRST STEAMSHIP TO CROSS the Atlantic arrived in New York on April 23, 1838, having left Cork, in Ireland, 19 days earlier. This vessel, the Sirius, was hardly the model of a transoceanic liner. A typical packet boat of the sort that had been crossing the English Channel routinely for some decades, it had been hastily modified to make the transatlantic voyage in order to beat the new liner Great Western, built by the celebrated English engineer Isambard Kingdom Brunel. To complete its trip to New York, Sirius had to burn some of its cargo during the last couple of days. Great Western, delayed by various mishaps, arrived a few days later, but after a speedier 15-day journey and with fuel to spare. It had been thought by many engineers that no ship could carry enough fuel to make it all the way to the New World, a point that Sirius’s adventure reinforced. Brunel, however, had made the scientific observation that resistance to a ship’s motion through the sea increases in approximate proportion to its surface area, while its coal-carrying capacity depends on the ship’s volume. A larger ship, therefore, could take on proportionately more fuel, and complete the voyage comfortably.
Even so, the success of Great Western hardly made transatlantic travel routine. This ship used sea water in its steam engines, which as a result clogged and corroded quickly. The pistons had to be dismantled and cleaned regularly, which meant they could only be of an inefficient, low-pressure design. In 1856 came the innovation of a new condenser for such engines, which allowed them to recycle a limited quantity of fresh water. The engines could be sealed tight and operated at higher pressure. The new marine steam engine, as much as any innovation, began to make ocean-crossing steamships commonplace, and by the 1860s, travel from Europe to America was becoming more frequent and relatively cheap.
The man who invented the new condenser was the Scottish physicist William Thomson, later Lord Kelvin. If physicists in Vienna were inclined to debate philosophy in their spare time, those in Britain and Germany were more likely to tinker with steam engines or the telegraph. Boltzmann was something of an exception. Before his eyesight became altogether too poor for laboratory work, he had been a talented experimenter, and something of a domestic tinkerer too. He had once rigged up an electric motor to run his wife’s sewing machine. In 1879, he presented a short note to the Viennese Academy of Science on some aspects of electrical theory relevant to telephone communications (Alexander Graham Bell had taken out his first telephone patent just three years earlier). Late in life, stimulated by the interest his surviving son, Arthur, showed in ballooning, Boltzmann became fascinated by the possibility of powered flight, to the extent of arranging some small experiments on suitable engines and giving lectures on his observations. He joined the newly founded Electrical Engineering Society of Vienna and even served as its president for a time. On one occasion he organized a little party at his house in Vienna to demonstrate a new light bulb invented by his friend the chemist Walter Nernst. He and his wife ordered 50 liters of beer, a cold buffet, and sent out 55 invitations. Seven of his colleagues showed up to see the new technological marvel.
Boltzmann was also quicker than most of his Viennese contemporaries to take advantage of the burgeoning steamship industry. Always a great traveler, he had before the end of his life been to America three times. His first Atlantic crossing came in 1899, when he was 55 years old. He had been awarded an honorary doctorate by Clark University in Worcester, Massachusetts, then celebrating its centenary, and he went there to pick up his degree and deliver a series of lectures on mechanics. The trip would be, he observed, a break from “the monotonous working life of Vienna,” but when he reached Worcester he professed to find it “rather boring.” After receiving the invitation, he had written to G. Stanley Hall, the president of Clark University, to explain that his health had become much poorer after he left Munich for Vienna and that because of his nervous state, it was essential for his wife to come with him—so that he would need a little more financial support for the expedition.
In June 1899, he and Henriette made the lengthy voyage to New York, which they found impressive but dangerous because of the speeding trams. From there they traveled to Boston (“the dust is terrible,” Henriette wrote on a postcard) and thence to Worcester. They also took trains up and down the East Coast, going as far north as Buffalo and Montreal (taking in the Niagara Falls) and south to Baltimore and Washington. The travels were a combination of tourism and academic visiting. There were a few American physicists, mostly experimentalists, whose reputations were known in Europe.
Boltzmann did not, however, meet the single American scientist whose endeavors were most closely aligned with his own. In New Haven, Connecticut, resided Josiah Willard Gibbs, who like his Austrian counterpart was a pioneer of statistical thinking in physics. Boltzmann was certainly aware of Gibbs and his work. But Gibbs was something of a shadowy figure, and there were reasons Boltzmann may have thought him more an intellectual adversary than an ally.
Gibbs was an enigmatic and little-appreciated figure even among his own countrymen, in part because of the seeming abstruseness of his work, in part because of his personality. Born in 1839 in New Haven to a professor of sacred languages in the Yale School of Divinity, he spent his entire life from the age of about seven in the house his father had built, close to the university. In death, he progressed no farther than a cemetery two blocks away. After a three-year excursion to France and Germany to round off his education, Gibbs never left America again, and indeed rarely left New Haven. Five years older than Boltzmann, he had spent a year in Berlin and then a year in Heidelberg shortly before Boltzmann’s first visits to those places, but he occupied his time there in studious invisibility. The professors whose classes he attended recalled no anecdotes about him, and he came under the influence of no particular teacher. He never married, and on returning to New Haven settled in his now-deceased father’s house with an older sister, who also never married.
But he was not a hermit. Another sister had married, and the nieces and nephews were fond of their Uncle Willie, as he was of them. He enjoyed walking and riding vacations in the New England countryside and would drive the horse and cart to take the children on picnics and adventures. Students found him a patient and encouraging teacher, thoughtful and occasionally amusing. He had little time for scientific societies and organizations, but he corresponded warmly with a number of individual scientists, including many in Europe. His work was known and respected by those who knew about such things, but he expended no extra effort to explain himself beyond the confines of his scientific papers, which even his admirers found clear but terse to the point of indigestibility. He was a profoundly self-contained man, in both his work and his life, and seems to have been perfectly happy in that condition. “Effusiveness was foreign to his nature,” one colleague recalled, rather understating the matter.
Gibbs was, in a sense, self-taught. As an undergraduate, he had learned mathematics and classics, with only a rudimentary selection of science, because that was all that Yale had to offer at the time. Physics was covered in a single course, completed in one year under the rubric “natural philosophy” and encompassing a little chemistry, astronomy, mineralogy, and so on. After his degree he enrolled as a student of engineering, which included the novelty of laboratory work—something his previous science studies had not covered. His first small thesis was on the design of gears. Shortly afterward, he obtained a patent for an improved design for a railway car brake. In 1863, he was awarded a Ph.D., only the second scientific doctorate to be given in the United States and the third overall.
In 1866, with his two sisters, he went to Europe, visiting France and then Germany. They supported themselves modestly but adequately with family money. Gibbs worked hard to acquire a more sophisticated knowledge of mathematics and physics, which no American university could then provide. All that survives is a selection of his characteristically succinct lecture notes, with no real indication of whether any subject particularly excited or repelled him. On his return, he minded his own business for a couple of years, but then Yale decided it needed to modernize its teaching, particularly in science. Gibbs was taken on as a professor of mathematical physics, for no pay. At that time he had published nothing besides a few small ventures in engineering design, but he became known as an effective and diligent teacher. He seemed destined for a quiet and uneventful life, in keeping with his character.
But just a few years later, Gibbs burst out of his anonymity with three redoubtable scientific works. The first two shorter items appeared in the Transactions of the Connecticut Academy of Sciences in 1873. The third and much longer work was published in the same journal in two sections, in 1876 and 1878. With these publications, Gibbs transformed the state of classical thermodynamics.
The first two papers consisted, in essence, of a variety of novel graphs and diagrams. Scientists by this time had accustomed themselves to describing the states or phases of materials—gases, liquids, and solids—in terms of pressure, volume, temperature, energy, entropy, and so on. In his characteristically thorough and systematic way, Gibbs went through all possible combinations of these properties and showed that the resulting graphs (pressure versus temperature for a fixed volume, for example) could answer all kinds of questions. Some of the graphs turned out not to be especially useful, but one in particular—a graph of entropy versus volume—proved ideal for studying the conditions under which a gas would transform into a liquid, or a liquid into a solid. The second paper went on to show the utility of three-dimensional graphs whose axes represented three thermodynamics properties. Specifically, he described a graph plotting entropy, energy, and volume against each other. For any substance, this three-dimensional space divides into regions corresponding to the gaseous, liquid, and solid states; the boundaries between those regions form surfaces that, Gibbs showed, contain further information. For example, the gradient of the surface separating the liquid and the solid regions is related to the temperature and pressure at which solid and liquid transform into each other.
This may sound a little simple-minded, as if a great scientific discovery emerged just by drawing a lot of graphs and pictures, but it took great insight, in the 1870s, to see how such diagrams combined a wealth of formerly disparate notions about stability, equilibrium, heats of evaporation and condensation, and a host of other physical attributes of materials. Gibbs’ achievement was to see how these deceptively straightforward devices could be exploited to yield a wealth of information. Maxwell, for one, was delighted. In 1875, he delivered in a lecture to the Chemical Society in London to alert British scientists to “a most important American contribution to . . . thermodynamics.” By the use of Gibbs’ methods, he went on, “problems which had long resisted the efforts of myself and others may be solved at once.” So enchanted indeed was Maxwell that out of plaster of Paris he constructed a three-dimensional “thermodynamic surface” for water, according to Gibbs’ design, and sent it off to Yale, where it resided proudly on Gibbs’ bookshelf.
But the third installment of Gibbs’ work was by far the greatest. In two papers amounting to more than 300 pages, Gibbs tackled as completely and comprehensively as he could the question of thermodynamic stability. Previously Gibbs, like everyone else, had been mainly thinking about the thermodynamics of single substances, and how the transitions from solid to liquid to gas depended on physical conditions. The element of genius in his 1878 work was to perceive that essentially the same analysis could be applied to mixtures of more than one substance, and to changes other than transformations of physical state. A simple example would be moisture in air: Under what conditions does it remain suspended, and when does it condense out into droplets? A more complex case would be a solution containing several chemicals that react with each other in a variety of ways: When is one reaction preferred over another? When will a solid product drop out of the solution, and when will it dissolve back again? These are all, Gibbs realized, questions that can be answered thermodynamically.
Moreover, he recognized that it is only a matter of practical complication to add as many substances and as many phases and as many interactions as one cared to. Most notably, he could include chemical changes, in which components of a system reacted to form a new component, perhaps giving out energy in the process. He could include decompositions, in which one component broke apart into two others when the temperature reached a certain value. All such changes came down to questions of stability: in some circumstances, it was preferable for two components to remain separate; in other circumstances they might react or dissolve. Any mixture of interacting components could be treated in the same way. It was, Gibbs demonstrated, merely a matter of keeping track of all the possible states each component could be in, and all the interactions they could participate in.
So complex was this analysis that the drawing of graphs was inadequate to the task. Nevertheless, the principle was the same, and Gibbs patiently set out a comprehensive system of algebraic equations that embodied any physical system he wanted to understand. The key to his technique was both simple and versatile. Imagine, Gibbs instructed, what would happen if some tiny element of a large and complex system were to change in some way. A little volume of gas might become a liquid; a dissolved component might separate out; a chemical compound might break up into its constituents. Any such change has thermodynamic consequences, producing corresponding changes in energy, pressure, temperature, entropy, and so on.
Taking all this into account, Gibbs asked, when such a change occurs, does the system as a whole turn into an energetically more favored or less favored state? If a small change leads to an overall lowering of energy, then the system as a whole will spontaneously undergo the change and transform into a different state. If, on the other hand, the imagined change costs energy, then the system will stay where it is.
By this method, Gibbs established a universal and completely general way to analyze the stability of any system. The same technique made it possible to understand how the system would react when external conditions were changed. It might be heated up or cooled down, expanded or compressed; what would all the internal components do? His way of answering that question was to examine (algebraically, that is) all the possible consequences of change to small units of the system as a whole, and to sort out which were energetically favorable.
The end result of this great effort was that Gibbs showed how to calculate questions of stability, mixing, and equilibrium, for any mix of ingredients, defined strictly by their physical properties. His method relied only on the thermodynamic properties of materials, making no assumptions of any kind about their fundamental composition, atomic or otherwise. This indeed was both its greatest virtue and, for some, the greatest barrier to understanding. Gibbs’ strategy was novel. His aim was to construct a perfectly logical and rational system into which the interested physicist, chemist, or engineer could plug in whatever details were appropriate to the question at hand. His method was as suitable for understanding when raindrops would condense out of moist air as it was for calculating how impurities of carbon would dissolve in molten iron.
So versatile was Gibbs’ technique that to many chemists and engineers—the audience for whom it would prove most useful—it seemed fabulously abstract. His style of exposition, which put a maximum of meaning in a minimum of words, didn’t make his work any easier to grasp. (Some years later the British physicist Lord Rayleigh wrote to Gibbs asking if he might not be able to produce an augmented and amplified version of some of his works, easier for less expert readers to comprehend. Gibbs replied that “I myself had come to the conclusion that the fault was that it was too long.”)
Nevertheless, Maxwell got the point immediately, and wrote a short notice for the Proceedings of the Cambridge Philosophical Society expressly to bring Gibbs’ ideas to the attention of British scientists. In Germany, his ideas struck Wilhelm Ostwald as a revelation. Expressing the laws of chemical and other transformations in physical terms, with matters of stability tied directly to considerations of the overall energy and entropy of the system, was exactly his goal, the essence of the subject that came to be called physical chemistry. Ostwald had been going at the problem piecemeal, and now an unknown American had written an encyclopedia on the subject all at once.
Although the Transactions of the Connecticut Academy of Sciences was not widely in evidence among the university libraries of Europe, Gibbs took care to send copies of his works to some hundred or so scientists he presumed would understand and appreciate them. Maxwell and Clausius, Helmholtz and Ostwald, were on the list; the name of Boltzmann, who was not yet well known in the early 1870s, was added for the third of the three papers. Ostwald translated the papers into German and arranged for their publication. In his autobiography he recalled: “This work had the greatest influence on my development. For, although he does not especially emphasize it, Gibbs deals almost exclusively with energy and its factors and holds himself free from all kinetic hypotheses. Because of this, his results possess a certainty and a lasting quality of the highest degree humanly attainable.”
Ostwald’s evaluation was accurate but shaded by his own prejudices. It was true that Gibbs did not indulge in any “kinetic hypotheses”—that is, Gibbs did not make any specific assumptions about the nature of atoms or their motions and interactions. But the point was not that he was against such ideas, rather that he didn’t need them for his own purposes. Ostwald takes this omission, along with Gibbs’ emphasis on the use of standard thermodynamic properties, as covert support for his own philosophy of energeticism. Gibbs’ ideas seemed to follow Mach’s prescription of basing theoretical arguments on tangible physical characteristics, not speculative abstractions, and it seemed to adhere to Ostwald’s preference for making transactions of energy the fundamental principle for deciding stability or instability of any system.
But Gibbs had no interest in Mach’s philosophy and showed no particular liking for energeticism. He dealt straightforwardly in well-defined thermodynamic properties, and eschewed any speculation as to the true nature of the world, or the correct philosophy to employ. His agnosticism was the strength of his work, but it allowed believers in any number of philosophical camps to believe he was secretly one of them.
Perhaps because of Ostwald’s enthusiasm for Gibbs’ work, Boltzmann’s attitude to the new ideas coming from Yale was ambivalent. Where Ostwald took Gibbs to be a closet energeticist, Boltzmann imagined instead that he was using atomic ideas but then concealing the fact. “In justifying his theorems, Gibbs must surely have used molecular ideas, even if he nowhere introduced molecules into the calculation,” he wrote on one occasion. Elsewhere, Boltzmann refers to a Gibbs theorem “which he had discovered by a different method though still presupposing certain basic conceptions of molecular theory.” That both Ostwald and Boltzmann could see Gibbs as a potential ally surely testifies to his philosophical neutrality.
In one important respect, however, Gibbs was not only sympathetic to Boltzmann’s views but ahead of them. Like Maxwell, he perceived the fundamental importance of probability and statistics in this kind of physics before Boltzmann somewhat reluctantly tackled the issue. He arrived at this insight, typically, in his own way. Gibbs’ general analysis relied on considering a large system as being composed of numerous small units, each with its own thermodynamic properties, and then deducing the behavior of the whole as a consequence of what all the component parts were doing. He therefore grasped early on the fundamentally statistical nature of such systems. The question came up clearly in a curious observation that has become known as Gibbs’ paradox.
Imagine a chamber divided into two halves, separated by a removable partition. Suppose first that the two halves are filled with different gases at the same temperature and pressure, and that the partition is lifted. The gases would mix and, as Gibbs demonstrated with his new style of reasoning, there would be an increase in entropy precisely because they had mixed.
Now, Gibbs went on, imagine the same thing except with two identical volumes of the same gas in the two sides of the chamber. Lifting the partition and allowing the gases to mix could not, in this case, produce an increase in entropy because, for practical purposes, nothing has happened. The two volumes of gas will certainly mix, but since they are the same gas, no perceptible physical change follows. The thermodynamicist cares only about overall properties; it doesn’t matter that elements of one gas that were formerly on one side of the partition have moved to the other, or vice versa. The details of how all the microscopic elements of the gas get themselves mixed up with each other are of no consequence. The entropy is the same regardless.
This difference—entropy goes up when different gases mix, but not when identical gases mix—has become known as Gibbs’ paradox largely because of the consternation it still causes to the average (and even above average) physics student. There’s no sign Gibbs himself found anything paradoxical in it. Rather, he saw it as a demonstration that thermodynamic properties cannot depend on microscopic details of exactly which atom is where. But he used it to make a further characteristically astute observation (and one, incidentally, in which he specifically talks of “molecules” of gas).
When identical gases mix, it doesn’t matter where all the molecules go after the partition is lifted. All motions are equal; they intermix at random and the entropy stays the same. But now imagine putting labels on all these molecules so that they correspond to two distinct gases. Their movement is unaffected, but now the entropy depends on how the labels distribute themselves. There must be some sets of molecular motion, Gibbs said, which put one kind of molecule mostly on one side of the chamber and the second kind on the other. The argument concerning identical gases says that that must be a physically allowable possibility, but applied to the case of different gases, the same possibility amounts to a spontaneous separation of the gas into distinct halves, which would correspond to violation of the second law. “In other words,” as Gibbs put it, “the impossibility of an uncompensated decrease of entropy seems to be reduced to improbability.” By “uncompensated decrease” Gibbs means a reduction in entropy without there being a concomitant increase somewhere else; this is what the classical second law is supposed to forbid.
These words come from the first installment of Gibbs’ long paper, which appeared in 1876. That was the year after Boltzmann had been faced with Loschmidt’s objection to the H-theorem, which forced him to recognize the very possibility that Gibbs has hit on, and the year before he published his famous formula, S = k log W, connecting entropy with statistics—a result that Gibbs’ own reasoning anticipates.
Uninfluenced by either the Vienna or the Cambridge way of thinking, Gibbs developed a new way to think about probability in thermodynamics, a way that depended not at all on arguable assumptions about the nature or existence of atoms.
Boltzmann understood his microscopic analysis to refer specifically to systems of atoms, and he understood the changes in them to be specifically changes in the distribution of atoms. Gibbs, by contrast, thought of a system in terms of microscopic components and changes, but those components were defined entirely by their thermodynamic qualities. As in the preceding example, he used the word molecule from time to time, but he held no fixed notion about what these molecules might be. It didn’t matter. This gave his analysis a greater power than Boltzmann’s, since he could imagine any thermodynamic property he liked, not just those for which an atomic model was at hand.
But contrary to what Ostwald wanted to believe, Gibbs was not in any strident sense an anti-atomist. He saw no reason to take one side or another. It was a practical matter: “we avoid the gravest difficulties when, giving up the attempt to frame hypotheses concerning the constitution of material bodies, we pursue statistical inquiries as a branch of rational mechanics.” As Ostwald observed, Gibbs’ methods derive their strength and universality from their independence of any assumptions about the nature of matter, but at the same time there is nothing in Gibbs’ writings to suggest that he had any fundamental antipathy to atomism, or any fondness for the strictures of energeticism.
Gibbs’ published treatise of 1876 and 1878 was, for all its power, both apparent and implicit, in some ways an obscure work. Perhaps not even the author grasped all its implications, and it was some 20 years before Gibbs himself returned to the subject in order to set out in a book a fuller and more systematic account of his methods.
Nonetheless, in the late 1870s and early 1880s, as Gibbs’ work became known in Europe, it could have been embraced by Boltzmann as a powerful complement to his own ideas. Gibbs had no need for any atomic hypothesis, but at the same time, the fruits of the atomic approach—Boltzmann’s statistical definition of entropy, for example—could have been allied to Gibbs’ methods and used to extend the versatility and range of atomic theory. Boltzmann, in other words, might have used Gibbs’ analysis as a means to systematically explore the wider implications of his own vision of the nature of heat.
Boltzmann was certainly aware of what Gibbs had done, but he seems not to have fully appreciated its scope. For one thing, Gibbs’ long papers concerned themselves in minute details with complex systems of mixed substances of a general nature, gaseous or otherwise, interacting chemically as well as physically, and this may have seemed to Boltzmann far removed from his own more specific concern of trying to understand the behavior of individual gases from the motion of their atoms. Where Boltzmann mentions Gibbs, he seems mostly at pains to suggest that Gibbs is really using atomic models and reasoning, if in a somewhat surreptitious way. In the second volume of his Lectures on Gas Theory, for example, Boltzmann says “in many places it seems evident that Gibbs has these molecular-theoretic concepts continuously in mind, even if he does not make use of the equations of molecular mechanics.” More strikingly, Boltzmann’s introduction to this volume uses as a motto Gibbs’ phrase about the “uncompensated decrease” of entropy being an improbability rather than an impossibility. This again is an instance of Gibbs seeming to be in Boltzmann’s corner, since the energeticists and assorted other followers of Mach and Ostwald took the second law to be absolute.
Mostly, though, it was Ostwald who seized on Gibbs as an ally, arguing (despite Gibbs’ own occasional use of the word molecule and his express desire to avoid fundamental assumptions as to the nature of matter) that he was really engaged on a project to free thermodynamics of any “metaphysical” assumptions. Gibbs himself, comfortable in New Haven, is not known to have expressed any views on his being co-opted in this way. Most likely he would have been quietly amused at being misinterpreted by both sides, and would have kept his amusement to himself.
DESPITE A NUMBER of chances, Gibbs and Boltzmann never met. After his one trip to Europe as a young man, before Boltzmann’s name was well known, Gibbs remained on his side of the Atlantic. In the late 19th century, physicists in Europe were not in the habit of flitting over to the United States and would have seen little reason to go there even had travel been less inconvenient. Gibbs was invited to meetings of the British Association in 1887 and 1893, but didn’t go. He was not invited, apparently, to the 1894 B.A. meeting in which kinetic theory was a prime topic and in which Boltzmann so enthusiastically took part. This omission may indicate a general belief that Gibbs’ work was not seen as directly relevant to atomism and kinetic theory. Or it may be that British scientists had figured out that Gibbs was not likely to come anyway.
Boltzmann himself invited Gibbs to a scientific meeting in Nuremberg in 1892, but the American once again declined, and when Boltzmann went to the United States in 1899, he made no effort to seek out Gibbs. A few years later, in 1901, Yale celebrated its bicentennial, and an invitation to the festivities was sent to Boltzmann. But by then Boltzmann’s health was deteriorating, and he didn’t go. In any case, it’s far from obvious that a meeting between the two would have produced any enlightenment. During the 1890s, Gibbs was mainly occupied with teaching and with a variety of less consequential researches than his earlier endeavors in thermodynamics; he was not to return to them until the early 1900s, when he was persuaded to assemble his arguments and thoughts in an influential book called simply Elementary Principles in Statistical Mechanics. Boltzmann meanwhile was embroiled in philosophical debates over what theories of physics ought to do, and his published scientific research was less momentous.
Then too there was the matter of personality. Gibbs would no doubt have got on famously with Maxwell; both were dry, ironic characters, capable of a sharp wit, affable in private but undemonstrative in general. And both, for all their prowess and insight in physics, had a capacity for not taking things too seriously. Maxwell had contributed to many areas of physics, and he looked upon each one of them as profound in its own right but not necessarily indicative of some vast underlying system to physics in general. Gibbs too, in his careful and exhaustive way, had raised thermodynamics to a new level of sophistication and logical order, but he saw it as a self-contained subject, enormously powerful within its own well-stated confines but indifferent to the underlying nature of matter. Gibbs and Maxwell shared a kind of wry detachment from even their own greatest creations, and a sense of irony is a sure antidote to any temptation toward grand philosophical systems. Indeed, Maxwell had written on one occasion to his friend Tait that “I have read some metaphysics of various kinds and find it more or less ignorant discussion of mathematical and physical principles, jumbled with a little physiology of the senses. The value of the metaphysics is equal to the mathematical and physical knowledge of the author divided by his confidence in reasoning from the names of things.” The second sentence is a characteristically sharp Maxwellian gibe: it means literally that the greater a philosopher’s confidence in his thinking, the smaller the value of the resulting cogitation.
Boltzmann, however, returning to Vienna from Munich, found himself beset on all sides by philosophers and energeticists who disputed the very essence of kinetic theory. He lacked, furthermore, a capacity for detached amusement that would have enabled him to ignore their harangues and complaints and to see that their arguments were bound to fail in the end. He took it all very seriously. He had devoted the bulk of his intellectual life to a single question—how does the behavior of atoms explain why hot things always cool down?—and in his single-mindedness he was often humorless, obstinate, and fierce. Could Gibbs and Boltzmann have even conducted a conversation? Would the laconic New Englander have reacted to the voluble and irrepressible Austrian simply by lapsing into silence, nodding occasionally to show he was listening, and hoping for the hour to be up when he could make an excuse and leave? It’s tempting to suppose that an earnest conversation between Gibbs and Boltzmann in Nuremberg in 1892 might have sorted out some puzzles that troubled Boltzmann throughout the following decade, or bolstered his confidence that the philosophical attacks were not worth the time he spent on them. But it’s equally easy to imagine such an encounter as a spectacular mismeeting of minds, leaving the austere Gibbs quietly stunned and the manic Boltzmann perplexed and frustrated.
AFTER RETURNING to Europe from his first trip to the United States and before taking up the reins of teaching once again, Boltzmann took a short break in Abbazia, a resort now known as Opatija on the Adriatic coast of Croatia but at that time an Austrian possession. He had traveled a good deal in the previous year, visiting Göttingen, London, and the Netherlands for a variety of reasons, including official duties on behalf of the Viennese Academy of Sciences. His health was increasingly troublesome. His worsening eyesight forced him to pay an assistant to read scientific papers to him, and he was incapable of any further work in the lab. Over the years he had gone from plump to fat to corpulent, and he suffered sporadically from bladder problems, asthma, and what he called catarrh, the latter being a sort of catchall term for a variety of ailments (“stomach catarrh” was a recurring nuisance, something that might today be called, with equal inaccuracy, stomach flu). Physical ill-health upset him mentally, and in the midst of a Vienna in which he had more intellectual enemies and detractors than supporters, he suffered from episodes when he felt defeated and forgotten. His triumph at the debate in Lübeck (if he even counted it as a triumph) was in the past, and the continuing attacks on the H-theorem, no matter how many times he rebutted what was essentially the same question in different guises, began to dent his confidence. In 1898, he had written to Felix Klein, his assistant at the Lübeck debate, “Just when I received your dear letter I had another neurasthenic attack, as I so often do in Vienna, although I was spared them altogether in Munich. With it came the fear that the whole H-curve was nonsense.”
In the introduction to the second volume of his great monograph Lectures on Gas Theory, published in 1898, he publicly expressed his assessment of his subject and his own position. “I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that when the theory of gases is again revived, not too much will have to be rediscovered.”
And in September of the following year, Boltzmann delivered a historical and philosophical survey entitled “On the Development of the Methods of Theoretical Physics in Recent Times,” in the course of which he observed, “I feel like a monument of ancient scientific memories. . . . I regard as my life’s task to help ensure . . . that the great portion of valuable and permanently usable material [in my work] need not be rediscovered one day.”
By the turn of the century, Boltzmann had been back in Vienna, his home town, for six years, and he was lecturing and writing in the wounded tones of a man composing an obituary notice for himself that would only be appreciated by an unborn generation.