Convergence: The Idea at the Heart of Science

ISBN-13: 9781476754352

Media Type: Paperback

Publisher: Simon & Schuster

Publication Date: 02-27-2018

Pages: 576

Product Dimensions: 6.00(w) x 8.90(h) x 1.50(d)

Peter Watson is an intellectual historian, journalist, and the author of thirteen books, including Convergence; Ideas: A History; The Age of Atheists; The German Genius; The Medici Conspiracy; and The Great Divide. He has written for The Sunday Times, The New York Times, the Observer, and the Spectator. He lives in London.

Read an Excerpt

Convergence “THE GREATEST OF ALL GENERALIZATIONS”
One morning in late August 1847, James Prescott Joule, a wealthy Manchester brewer but also a distinguished physicist, was walking in Switzerland, near Saint-Martin, beneath the Col de la Forclaz, in the south of the country, not too far from the Italian border. On the road between Saint-Martin and Saint-Gervais he was surprised to meet a colleague, William Thomson, a fellow physicist, later even more distinguished as Lord Kelvin. Thomson noted in a letter the next day to his father—a professor of mathematics—that Joule had with him some very sensitive thermometers and asked if Thomson would assist him in an unusual experiment: he wanted to measure the temperature of the water at the top and bottom of a local waterfall. The request was particularly unusual, Thomson suggested in his letter, because Joule was then on his honeymoon.

The experiment with waterfalls came to nothing. There was so much spray and splash at the foot of the local cataract that neither Joule nor Thomson could get close enough to the main body of water to make measurements. But the idea was ingenious and it was, moreover, very much a child of its time. Joule was homing in on a notion that, it is no exaggeration to say, would prove to be one of the two most important scientific ideas of all time, and a significant new view of nature.

He was not alone. Over the previous few years as many as fifteen scientists, working in Germany, Holland, and France as well as in Britain, were all thinking about the conservation of energy. The historian of science Thomas Kuhn says that there is “no more striking instance of the phenomenon known as simultaneous discovery than conservation of energy.” Four of the men—Sadi Carnot in Paris in 1832, Marc Seguin in Lyon in 1839, Carl Holtzmann in Mannheim in 1845, and Gustave-Adolphe Hirn in Mulhouse in 1854—had all recorded their independent convictions that heat and work are quantitatively interchangeable. Between 1837 and 1844, Karl Mohr in Koblenz, William Grove and Michael Faraday in London, and Justus von Liebig in Giessen all described the world of phenomena “as manifesting but a single ‘force,’ one which could appear in electrical, thermal, dynamical, and many other forms but which could never, in all its transformations, be created or destroyed.”1 And between 1842 and 1847, the hypothesis of energy conservation was publicly announced, says Kuhn, by four “widely scattered” European scientists—Julius von Mayer in Tübingen, James Joule in Manchester, Ludwig Colding in Copenhagen, and Hermann von Helmholtz in Berlin, all but the last working in complete ignorance of the others.

Joule and his waterfalls apart, perhaps the most romantic of the different stories was that of Julius von Mayer. For the whole of 1840, starting in February, Julius Robert von Mayer served as a ship’s physician on board a Dutch merchantman to the East Indies. The son of an apothecary from Heilbronn, Württemberg, he was a saturnine, bespectacled man who, in the fashion of his time, wore his beard under—but not actually on—his chin. Mayer’s life and career interlocked in intellectually productive yet otherwise tragic ways. While a student he was arrested and briefly imprisoned for wearing the colors of a prohibited organization. He was also expelled for a year and spent the time traveling, notably to the Dutch East Indies, a lucky destination for him, as it turned out. Mayer graduated in medicine from the University of Tübingen in 1838, though physics was really his first love, and that was when he enlisted as a ship’s doctor with the Dutch East India Company. The return to the East was to have momentous consequences.

On the way there, in the South Atlantic, off South Africa, he observed that the waves that were thrown about during some of the wild storms that the three-master encountered were warmer than the calm seas. That set him thinking about heat and motion. Then, during a stopover in Jakarta in the summer of 1840, he made his most famous observation. As was then common practice, he let the blood of several European sailors who had recently arrived in Java. He was surprised at how red their blood was—he took blood from their veins (blood returning to the heart) and found it was almost as red as arterial blood. Mayer inferred that the sailors’ blood was more than usually red owing to the high temperatures in Indonesia, which meant their bodies required a lower rate of metabolic activity to maintain body heat. Their bodies had extracted less oxygen from their arterial blood, making the returning venous blood redder than it would otherwise have been.2

Mayer was struck by this observation because it seemed to him to be self-evident support for the theory of his compatriot, the chemist and agricultural specialist Justus von Liebig, who argued that animal heat is produced by combustion—oxidation—of the chemicals in the food taken in by the body. In effect, Liebig was observing that chemical “force” (as the term was then used), which is latent in food, was being converted into (body) heat. Since the only “force” that enters animals is their food (their fuel) and the only form of force they display is activity and heat, then these two forces must always—by definition—be in balance. There was nowhere else for the force in the food to go.

Mayer originally tried to publish his work in the prestigious Annalen der Physik und Chemie. Founded in 1790, the Annalen der Physik was itself a symptom of the changes taking place. By the 1840s it was the most important German journal of physics, though many new journals proliferated in that decade. The Annalen’s editor since 1824, Johann Christian Poggendorff, a “fact-obsessed experimentalist and scientific biographer,” had a very firm idea of what physics was. By the middle of the century, there had emerged “a distinctive science of physics that took quantification and the search for mathematical laws as its universal aims.” (This, it will be recalled, is what drew Mary Somerville to the subject.) Poggendorff could make or break scientific careers. All the more so because he edited the Annalen for fifty-two years, until he died in 1877.

Owing to a number of basic mistakes, however, due to his poor knowledge of physics, Mayer’s paper was rejected by Poggendorff. Disappointed but undeterred, he broached his ideas to the physics professor at Tübingen, his old university, who disagreed with him but suggested some experiments he might do to further develop his ideas. If what Mayer was proposing was true, the professor said, if heat and motion are essentially the same, water should be warmed by vibration, the same thought that had occurred to Joule.

Mayer tried the experiment, and found not only that water is warmed by vibration (as he had spotted, months before, aboard the merchantman), but that he was able to measure the different forces—vibration, kinetic energy, and heat. These results, “Remarks on the Forces of Inanimate Nature,” were therefore published in the Annalen der Chemie und Pharmacie in 1842, and it was here that he argued for a relationship between motion and heat, that “motion and heat are only different manifestations of one and the same force [which must] be able to be converted and transformed into one another.” Mayer’s ideas did not have much impact at the time, no doubt because he was not a “professional” physicist, though obviously enough the editor of the Annalen der Chemie und Pharmacie thought them worth printing. That editor was none other than Justus von Liebig.3
“Interwoven into One Great Association”
These experiments, ideas, and observations of Mayer and Joule did not come quite out of the blue. Throughout the early nineteenth century, and apart from Liebig’s observations, provocative experimental results had been obtained for some time. In 1799, Alessandro Volta, in Como, north Italy, had stunned the world with his invention of the battery, in which two different metals, laid alternately together in a weak solution of salt, like a multilayered sandwich, generated an electric current. In 1820 Hans Christian Ørsted, in Copenhagen, had noticed that a magnetized compass needle was deflected from magnetic north when an electric current from a battery was switched on and off and passed through a wire near the needle. Five months later, in September that same year, in London, Michael Faraday, working in his basement laboratory in the Royal Institution in Albemarle Street, repeated Ørsted’s experiment, and found the same result. Then he moved on to new ground. He brought together a cork, some wire, a glass jar, and a silver cup. He inserted the wire into the cork and put some water in a jar with mercury lying at the bottom. Then he floated the cork in the water, in such a way that the end of the wire in the cork made contact with the mercury. Faraday next fixed the top of the wire into an inverted silver cup with a globule of mercury held under its rim. When connected to a battery, this comprised a circuit that would allow the wire to flex without breaking the flow of electricity. Next, he brought up a magnet near the wire—and it moved. He repeated the action on the other side of the wire, with the same result.

Now came a crucial adjustment. He fixed the magnet in a glass tube and arranged the other contents so that the wire on its cork in the mercury could revolve around it when the current was switched on. Then he joined the circuit and—flick-flick-flick—the wire did a jig around the magnet. Faraday, we are told, did a jig of his own around the workbench.4

In Volta’s battery, chemical forces produced electricity, Ørsted had demonstrated a link between electricity and magnetism, and in Faraday’s experiments, electricity and magnetism together produced movement. On top of this, the new technology of photography, invented in the 1830s, used light to produce chemical reactions. Above all, there was the steam engine, a machine for producing mechanical force from heat. Steam technology would lead to the most productive transformations of all, at least for a time. During the 1830s and 1840s the demand for motive power soared. In an age of colonial expansion, the appetite for railways and steamships was insatiable, and these needed to be made more efficient, with less and less leakage of power, of energy.

But Thomas Kuhn also observed that, of these twelve pioneers in the conservation of energy, five came from Germany itself, and a further two came from Alsace and Denmark—areas of German influence. He put this preponderance of Germans down to the fact that “many of the discoverers of energy conservation were deeply predisposed to see a single indestructible force at the root of all natural phenomena.” He suggested that this root idea could be found in the literature of Naturphilosophie. “Schelling, for example [and in particular], maintained that magnetic, electrical, chemical and finally even organic phenomena would be interwoven into one great association.” Liebig studied for two years with Schelling.5

A final factor, according to science historian Crosbie Smith, was the extreme practical-mindedness of physicists and engineers in Scotland and northern England, who were fascinated by the commercial possibilities of new machines. All of this comprised the “deep background” to the ideas of Mayer, Joule, and the others. But the final element, says John Theodore Merz (1840–1922) in his four-volume History of European Thought in the Nineteenth Century (1904–12), was that the unification of thought that was brought about by all those experiments and observations “needed a more general term . . . a still higher generalisation, a more complete unification of knowledge . . . this greatest of all exact generalisations [was] the conception of energy.”6

The other men who did most, at least to begin with, to explore the conservation of energy—Joule and William Thomson in Britain, Hermann von Helmholtz and Rudolf Clausius in Germany—fared better than Mayer, though there were interminable wrangles in the mid-nineteenth century as to who had discovered what first.

Joule (1818–89), born into a brewing family from Salford, had a Victorian—one might almost say imperial—mane, hair which reached almost as far down his back as his beard did down his front: his head was awash in hair. He is known for just one thing, but it was and is an important thing and was one for which he conducted experiments over a number of years to provide an ever more accurate explanation.

As a young man he had worked in the family’s brewery, which may have ignited his interest in heat. This interest was no doubt fanned all the more when he was sent to study chemistry in Manchester with John Dalton. Dalton was famous for his atomic theory—the idea that each chemical element was made up of different kinds of atoms, and that the key difference between different atoms was their weight. Dalton thought that these “elementary elements” could be neither created nor destroyed, based on his observations which showed that different elements combined to produce substances which contained the elements in set proportions, with nothing left over.

With his commercial background, Joule was always interested in the practical end of science—in the possibility of electric motors, for instance, which might take over from steam. That didn’t materialize, not then anyway, but his interest in the relation between heat, work, and energy did eventually pay off. “Eventually,” because Joule’s early reports, on the relationship between electricity and heat, were turned down by the Royal Society—just as Mayer’s ideas had been turned down by Poggendorff—and Joule was forced to publish in the less prestigious Philosophical Magazine. But he continued his experiments, which, by stirring a container of water with a paddle wheel, sought to show that work—movement—is converted into heat. Joule wrote that “we consider heat not as substance but as a state of vibration.” (This implicit reference to movement echoes his idea about the different temperatures of water at the top and bottom of waterfalls, and Mayer’s observation that storm waves were warmer than calm seas.) Over his lifetime, Joule sought ever more accurate ways to calculate just how much work was needed to raise the temperature of a pound of water by one degree Fahrenheit (the traditional definition of “work”). Accuracy was vital if the conservation of energy was to be proved.7

And gradually people were won over. For example, Joule addressed several meetings of the British Association for the Advancement of Science, in 1842, and again in 1847. In between these meetings, Mayer published his observations, about body heat and blood color, but Joule had the momentum and, in the BAAS, the stage. The BAAS was well established then, having been founded in 1831, in York, modeled on the German Gesellschaft Deutscher Naturforscher und Ärzte. It held annual meetings in different British cities each year. But Joule needed only one individual in his BAAS audience to find what he had to say important, and that moment came in the 1847 meeting, when his ideas were picked up on by a young man of twenty-one. He was then named William Thomson but he would, in time, become better known as Lord Kelvin.

Just as Joule befriended the older Dalton, so he befriended the younger Thomson. In fact, he worked with Thomson on the theory of gases and how they cool and how all that related to Dalton’s atomic theory. Joule was in particular interested in nailing the exact average speed at which molecules of gas move (movement that was of course related to their temperature). He focused on hydrogen and treated it as being made up of tiny particles bouncing off one another and off the walls of whatever container they were held in. By manipulating the temperature and the pressure, which affected the volume in predictable ways, he was able to calculate that, at a temperature of sixty degrees Fahrenheit and a pressure of thirty inches of mercury (more or less room temperature and pressure), the particles of gas move at 6,225.54 feet per second. Similarly, with oxygen, the molecules of which weigh sixteen times those of hydrogen, and since the inverse-square lawI applies, in ordinary air the oxygen molecules move at a quarter of the speed of hydrogen molecules, or 1,556.39 feet per second. To pin down such infinitesimal activity was an amazing feat, and Joule was invited to address the Royal Society and elected a fellow, more than making up for his earlier rejection.

Joule shared a lot with Thomson, including his religious beliefs, which played an important part in the theory for some people. The principle of continual conversions or exchanges was established and maintained by God, he argued, as a basis for “nature’s currency system,” guaranteeing a dynamic stability in “nature’s economy.” “Indeed the phenomena of nature, whether mechanical, chemical, or vital, consist almost entirely in a continual conversion of attraction through space, living force, and heat into one another. Thus it is that order is maintained in the universe—nothing is deranged, nothing ever lost . . . the whole being governed by the sovereign will of God.”8

Thomson followed on where Joule left off. Born in Belfast in June 1824, he spent almost all his life in university environments. His father was professor of mathematics at the Royal Belfast Academical Institution, a forerunner of Belfast University, and William and his brother were educated at home by their father (his brother James also became a physicist). Their mother died when William was six, and in 1832 their father moved to Glasgow, where again he became professor of mathematics. As a special dispensation, both his sons were allowed to attend lectures there, matriculating in 1834, when William was ten. After Glasgow, William was due to go to Cambridge, but there were concerns that graduating in Glasgow might “disadvantage” his prospects down south, so although he passed his finals and the MA exams a year later, he did not formally graduate. At the time, he therefore signed himself as William Thomson BATAIAP (Bachelor of Arts To All Intents And Purposes).

William transferred to Cambridge in 1841, graduating four years later, having won a number of prizes and publishing several papers in the Cambridge Mathematical Journal. He then worked for a while in Paris, familiarizing himself with the work of the brilliant French physicist Sadi Carnot (who had died tragically young), and then joined his father in Glasgow, as professor of natural philosophy. James Thomson Senior, who had worked tirelessly to bring his son to Glasgow, died shortly afterwards from cholera. But William remained at Glasgow from when he was appointed professor (in his mid-twenties) until he retired at seventy-five, when, “to keep his hand in,” he enrolled as a student all over again. This, as historian John Gribbin rejoices in saying, made him “possibly both the youngest student and the oldest student ever to attend the University of Glasgow.”9

Thomson was much more than a scientist. He had a hand in the first working transatlantic telegraph, between Great Britain and the USA (after other attempts had failed), which transformed communication almost as much as, and maybe more than, the Internet of today. He made money from his scientific and industrial patents, to such an extent that he was, first, knighted in 1866 and then made Baron Kelvin of Largs in 1892 (the River Largs runs through the campus of Glasgow University).
“A Principle Pervading All Nature”
Thomson echoed Joule in his theology as well as his science. “The fact is,” he wrote, “it may I believe be demonstrated that work is lost to man irrecoverably [when conduction occurs] but not lost in the material world.” Employing the word “energy” for the first time since 1849, says Crosbie Smith, Thomson expressed his analysis in theological and cosmological terms. “Although no destruction of energy can take place in the material world without an act of power possessed only by the supreme ruler, yet transformations take place which remove irrecoverably from the control of man sources of power which, if the opportunity of turning them to his own account had been made use of, might have been rendered available.”10 God, as “supreme ruler,” had established this law of “energy conservation,” but nonetheless there were sources of energy in nature (such as waterfalls) that could be made use of—in fact, it was a mistake for Thomson if they were not made use of, because that implied waste, the Presbyterian’s abiding sin. Finally, nature’s transformations had a direction which only God could reverse: “The material world could not come back to any previous state without a violation of the laws which have been manifested to man.”

In purely scientific terms, however, Kelvin’s most important contribution was to make thermodynamics (as the conservation of energy became more formally known) a consolidated scientific discipline by the middle of the century. Together with Peter Guthrie Tait, another Scot, their joint work, Treatise on Natural Philosophy (1867), was both an attempt to rewrite Newton and to place thermodynamics and the conservation of energy at the core of a new science—nineteenth-century physics. Kelvin may even have been the first person to use the word “energy” in this new sense. In 1881 he said, “The very name energy, though first used in the present sense by Dr. Thomas Young about the beginning of this century, has only come into use practically after the doctrine which defines it had . . . been raised from a mere formula of mathematical dynamics to the position it now holds of a principle pervading all nature and guiding the investigator in every field of science.”11 Tait and Kelvin planned a second volume of their book, never written, which would have included “a great section on ‘the one law of the Universe’, the Conservation of Energy’.”

On top of all this, Kelvin established the absolute scale of temperature, which also stems from the idea that heat is equivalent to work (as Joule had spent his lifetime demonstrating) and that a particular change in temperature is equivalent to a particular amount of work. This carries the implication that there is in fact an absolute minimum possible temperature: –273° Fahrenheit, now written as 0°K (for Kelvin), when no more work can be done and no more heat can be extracted from a system.
“The Human Engine Is Little Different from the Steam Engine”
Thomson’s ideas were being more or less paralleled in Germany by the work of Hermann von Helmholtz and Rudolf Clausius. With hindsight, everything can be seen as pointing toward the theory of the conservation of energy, but it still required someone to formulate these ideas clearly, and that occurred in the seminal memoir of 1847 by von Helmholtz (1821–94). In On the Conservation of Force he provided the requisite mathematical formulation, linking heat, light, electricity, and magnetism by treating these phenomena as different manifestations of “energy.”

Like Kelvin, von Helmholtz had many fingers in many pies. He was born in Potsdam when it was “a one-class” garrison town, and von Helmholtz’s parents were part of the intellectual middle class (his father was a high school teacher) and no fewer than twenty-three godparents graced Hermann’s baptism. His early studies were funded by a Prussian Army scholarship in the course of which he studied physiology. In return for his education being paid for, von Helmholtz served as a medical officer before becoming, in 1849, associate professor of physiology at the University of Königsberg. In 1850 he invented the ophthalmoscope, which allows the far wall of the eye to be inspected, and contributed many papers on optics and the physiology of stereoscopic perception, as well as such subjects as fermentation. But von Helmholtz fits in here because of his 1847 pamphlet, “On the Conservation of Force.”12

Like Mayer, he had sent his paper to Poggendorff at the Annalen der Physik but was rebuffed, and he chose to publish his pamphlet privately. And, like Mayer, von Helmholtz approached the problem of energy from a medical perspective. His previous physiological publications had all been designed to show how the heat of animal bodies and their muscular activity could be traced to the oxidation of food—that the human engine was little different from the steam engine. He did not think there were forces entirely peculiar to living things but insisted instead that organic life was the result of forces that were “modifications” of those operating in the inorganic realm. He had parallel ideas not just with Mayer and Kelvin, but with Liebig too.

In the purely mechanical universe envisaged by von Helmholtz there was an obvious connection between human and machine work. For him, Lebenskraft, as the Germans called the life force, was no more than an expression of “organisation” among related parts which carried no implication of a vital force.13 “The idea of work is evidently transferred to machines from comparing their performances with those of men and animals, to replace which they were applied. We still reckon the work of steam engines according to horse power.” Which led him to the principle of the conservation of force: “We cannot create mechanical force, but we may help ourselves from the general storehouse of Nature. . . . The possessor of a mill claims the gravity of the descending rivulet, or the living force of the moving wind, as his possession. These portions of the store of Nature are what give his property its chief value.” His idea of the “store” of nature complemented Joule’s notion of the “currency” of nature.

In making his case without any experimental evidence (which the members of the Berlin Academy noticed, while being impressed by his presentation), von Helmholtz “first established a clear distinction between theoretical and experimental physics.”

While Mayer and von Helmholtz, being doctors, came to the science of work through physiology, von Helmholtz’s fellow Prussian Rudolf Clausius approached the phenomenon, like his British and French contemporaries, via the ubiquitous steam engine.

In later life Clausius had a rather forbidding appearance: a very high forehead, rather hard, piercing eyes, a thin, stern mouth, and a white beard fringing his cheeks and chin. In fairness to him, this sternness may have reflected nothing more than the pain he was in continuously after suffering a wound in the Franco-Prussian War of 1870–71. At the same time he was a fervent nationalist and that may also have been a factor.

He was born in January 1822, in Köslin, Prussia (now Koszalin, Poland), where his father was a pastor with his own private school. The sixth of his father’s sons, Rudolf attended the family school for a few years, before transferring to the gymnasium at Stettin (now Szczecin, Poland) and then going on to the University of Berlin in 1840. To begin with he was drawn to history and studied under the great Leopold von Ranke, which may have had something to do with his subsequent nationalism. But Clausius switched to math and physics. In 1846, two years after graduating from Berlin, he entered August Böckh’s seminar at Halle, and worked on explaining the blue color of the sky. The theory Clausius came up with about the blue of the sky, and its redness at night and morning, was based on faulty physics. He thought it was caused by reflection and refraction of light, whereas John Strutt, later Lord Rayleigh, was able to show it was due to the scattering of light.14

But Clausius’s special contribution was to apply mathematics far more deeply than any of his predecessors, and his work was an important stage in the establishment of thermodynamics and theoretical physics. His first paper on the mechanical theory of heat was published in 1850. This was his most famous work and we shall return to it in just a moment. He advanced rapidly in his career, at least to begin with, being invited to the post of professor at the Royal Artillery and Engineering School at Berlin in September 1850 on the strength of his paper, then moving on to the Polytechnikum in Zurich, where he remained for some time despite being invited back to Germany more than once. He eventually accepted a chair at Würzburg in 1869, moving on to Bonn after only a year, when the Franco-Prussian War intervened. A “burning nationalist,” as someone described him, Clausius volunteered, despite being just short of his fiftieth birthday, and was allowed to assume the leadership of an ambulance corps, which he formed from Bonn students, helping to carry the wounded at the great battles of Vionville and Gravelotte—the Germans suffered twenty thousand casualties at the latter battle. During the hostilities, Clausius was wounded in the leg, which caused him severe pain and disability for the rest of his life.15 He was awarded the Iron Cross in 1871.

Unlike Mayer and von Helmholtz, Clausius did succeed in having his first important paper, “On the Moving Force of Heat, and the Laws Regarding the Nature of Heat That Are Deducible Therefrom,” accepted by the Annalen. It appeared in 1850 and its importance was immediately recognized. In it he argued that the production of work