6
E = mc², ⊃ / ≡ / v + C₇H₃₈O₄₃

Pragmatism was an American philosophy, but it was grounded in empiricism, a much older notion, spawned in Europe. Although figures such as Nietzsche, Bergson, and Husserl became famous in the early years of the century, with their wide-ranging monistic and dogmatic theories of explanation (as William James would have put it), there were many scientists who simply ignored what they had to say and went their own way. It is a mark of the division of thought throughout the century that even as philosophers tried to adapt to science, science ploughed on, hardly looking over its shoulder, scarcely bothered by what the philosophers had to offer, indifferent alike to criticism and praise. Nowhere was this more apparent than in the last half of the first decade, when the difficult groundwork was completed in several hard sciences. (‘Hard’ here has two senses: first, intellectually difficult; second, concerning hard matters, the material basis of phenomena.) In stark contrast to Nietzsche and the like, these men concentrated their experimentation, and resulting theories, on very restricted aspects of the observable universe. That did not prevent their results having a much wider relevance, once they were accepted, which they soon were.

The best example of this more restricted approach took place in Manchester, England, on the evening of 7 March 1911. We know about the event thanks to James Chadwick, who was a student then but later became a famous physicist. A meeting was held at the Manchester Literary and Philosophical Society, where the audience was made up mainly of municipal worthies – intelligent people but scarcely specialists. These evenings usually consisted of two or three talks on diverse subjects, and that of 7 March was no exception. A local fruit importer spoke first, giving an account of how he had been surprised to discover a rare snake mixed in with a load of Jamaican bananas. The next talk was delivered by Ernest Rutherford, professor of physics at Manchester University, who introduced those present to what is certainly one of the most influential ideas of the entire century – the basic structure of the atom. How many of the group understood Rutherford is hard to say. He told his audience that the atom was made up of ‘a central electrical charge concentrated at a point and surrounded by a uniform spherical distribution of opposite electricity equal in amount.’ It sounds dry, but to Rutherford’s colleagues and students present, it was the most exciting news they had ever heard. James Chadwick later said that he remembered the meeting all his life. It was, he wrote, ‘a most shattering performance to us, young boys that we were…. We realised that this was obviously the truth, this was it.¹

Such confidence in Rutherford’s revolutionary ideas had not always been so evident. In the late 1890s Rutherford had developed the ideas of the French physicist Henri Becquerel. In turn, Becquerel had built on Wilhelm Conrad Röntgen’s discovery of X rays, which we encountered in chapter three. Intrigued by these mysterious rays that were given off from fluorescing glass, Becquerel, who, like his father and grandfather, was professor of physics at the Musée d’Histoire Naturelle in Paris, decided to investigate other substances that ‘fluoresced.’ Becquerel’s classic experiment occurred by accident, when he sprinkled some uranyl potassium sulphate on a sheet of photographic paper and left it locked in a drawer for a few days. When he looked, he found the image of the salt on the paper. There had been no naturally occurring light to activate the paper, so the change must have been wrought by the uranium salt. Becquerel had discovered naturally occurring radioactivity.²

It was this result that attracted the attention of Ernest Rutherford. Raised in New Zealand, Rutherford was a stocky character with a weatherbeaten face who loved to bellow the words to hymns whenever he got the chance, a cigarette hanging from his lips. ‘Onward Christian Soldiers’ was a particular favourite. After he arrived in Cambridge in October 1895, he quickly began work on a series of experiments designed to elaborate Becquerel’s results.³ There were three naturally radioactive substances – uranium, radium, and thorium – and Rutherford and his assistant Frederick Soddy pinned their attentions on thorium, which gave off a radioactive gas. When they analysed the gas, however, Rutherford and Soddy were shocked to discover that it was completely inert – in other words, it wasn’t thorium. How could that be? Soddy later described the excitement of those times in a memoir. He and Rutherford gradually realised that their results ‘conveyed the tremendous and inevitable conclusion that the element thorium was spontaneously transmuting itself into [the chemically inert] argon gas!’ This was the first of Rutherford’s many important experiments: what he and Soddy had discovered was the spontaneous decomposition of the radioactive elements, a modern form of alchemy. The implications were momentous.⁴

This wasn’t all. Rutherford also observed that when uranium or thorium decayed, they gave off two types of radiation. The weaker of the two he called ‘alpha’ radiation, later experiments showing that ‘alpha particles’ were in fact helium atoms and therefore positively charged. The stronger ‘beta radiation’, on the other hand, consisted of electrons with a negative charge. The electrons, Rutherford said, were ‘similar in all respects to cathode rays.’ So exciting were these results that in 1908 Rutherford was awarded the Nobel Prize at age thirty seven, by which time he had moved from Cambridge, first to Canada and then back to Britain, to Manchester, as professor of physics.⁵ By now he was devoting all his energies to the alpha particle. He reasoned that because it was so much larger than the beta electron (the electron had almost no mass), it was far more likely to interact with matter, and that interaction would obviously be crucial to further understanding. If only he could think up the right experiments, the alpha might even tell him something about the structure of the atom. ‘I was brought up to look at the atom as a nice hard fellow, red or grey in colour, according to taste,’ he said.⁶ That view had begun to change while he was in Canada, where he had shown that alpha particles sprayed through a narrow slit and projected in a beam could be deflected by a magnetic field. All these experiments were carried out with very basic equipment – that was the beauty of Rutherford’s approach. But it was a refinement of this equipment that produced the next major breakthrough. In one of the many experiments he tried, he covered the slit with a very thin sheet of mica, a mineral that splits fairly naturally into slivers. The piece Rutherford placed over the slit in his experiment was so thin – about three-thousandths of an inch – that in theory at least alpha particles should have passed through it. They did, but not in quite the way Rutherford had expected. When the results of the spraying were ‘collected’ on photographic paper, the edges of the image appeared fuzzy. Rutherford could think of only one explanation for that: some of the particles were being deflected. That much was clear, but it was the size of the deflection that excited Rutherford. From his experiments with magnetic fields, he knew that powerful forces were needed to induce even small deflections. Yet his photographic paper showed that some alpha particles were being knocked off course by as much as two degrees. Only one thing could explain that. As Rutherford himself was to put it, ‘the atoms of matter must be the seat of very intense electrical forces.’⁷

Science is not always quite the straight line it likes to think it is, and this result of Rutherford’s, though surprising, did not automatically lead to further insights. Instead, for a time Rutherford and his new assistant, Ernest Marsden, went doggedly on, studying the behaviour of alpha particles, spraying them on to foils of different material – gold, silver, or aluminium.⁸ Nothing notable was observed. But then Rutherford had an idea. He arrived at the laboratory one morning and ‘wondered aloud’ to Marsden whether (with the deflection result still in his mind) it might be an idea to bombard the metal foils with particles sprayed at an angle. The most obvious angle to start with was 45 degrees, which is what Marsden did, using foil made of gold. This simple experiment ‘shook physics to its foundations.’ It was ‘a new view of nature … the discovery of a new layer of reality, a new dimension of the universe.’⁹ Sprayed at an angle of 45 degrees, the alpha particles did not pass through the gold foil – instead they were bounced back by 90 degrees onto the zinc sulphide screen. ‘I remember well reporting the result to Rutherford,’ Marsden wrote in a memoir, ‘when I met him on the steps leading to his private room, and the joy with which I told him.’¹⁰ Rutherford was quick to grasp what Marsden had already worked out: for such a deflection to occur, a massive amount of energy must be locked up somewhere in the equipment used in their simple experiment.

But for a while Rutherford remained mystified. ‘It was quite the most incredible event that has ever happened to me in my life,’ he wrote in his autobiography. ‘It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration I realised that this scattering backwards must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greatest part of the mass of the atom was concentrated in a minute nucleus.’¹¹ In fact, he brooded for months before feeling confident he was right. One reason was because he was slowly coming to terms with the fact that the idea of the atom he had grown up with – J. J. Thomson’s notion that it was a miniature plum pudding, with electrons dotted about like raisins – would no longer do.¹² Gradually he became convinced that another model entirely was far more likely. He made an analogy with the heavens: the nucleus of the atom was orbited by electrons just as planets went round the stars.

As a theory, the planetary model was elegant, much more so than the ‘plum pudding’ version. But was it correct? To test his theory, Rutherford suspended a large magnet from the ceiling of his laboratory. Directly underneath, on a table, he fixed another magnet. When the pendulum magnet was swung over the table at a 45-degree angle and when the magnets were matched in polarity, the swinging magnet bounced through 90 degrees just as the alpha particles did when they hit the gold foil. His theory had passed the first test, and atomic physics had now become nuclear physics.¹³

For many people, particle physics has been the greatest intellectual adventure of the century. But in some respects there have been two sides to it. One side is exemplified by Rutherford, who was brilliantly adept at thinking up often very simple experiments to prove or disprove the latest advance in theory. The other project has been theoretical physics, which involved the imaginative use of already existing information to be reorganised so as to advance knowledge. Of course, experimental physics and theoretical physics are intimately related; sooner or later, theories have to be tested. Nonetheless, within the discipline of physics overall, theoretical physics is recognised as an activity in its own right, and for many perfectly respectable physicists theoretical work is all they do. Often the experimental verification of theories in physics cannot be tested for years, because the technology to do so doesn’t exist.

The most famous theoretical physicist in history, indeed one of the most famous figures of the century, was developing his theories at more or less the same time that Rutherford was conducting his experiments. Albert Einstein arrived on the intellectual stage with a bang. Of all the scientific journals in the world, the single most sought-after collector’s item by far is the Annalen der Physik, volume XVII, for 1905, for in that year Einstein published not one but three papers in the journal, causing 1905 to be dubbed the annus mirabilis of science. These three papers were: the first experimental verification of Max Planck’s quantum theory; Einstein’s examination of Brownian motion, which proved the existence of molecules; and the special theory of relativity with its famous equation, E=mc².

Einstein was born in Ulm, between Stuttgart and Munich, on 14 March 1879, in the valley of the Danube near the slopes that lead to the Swabian Alps. Hermann, his father, was an electrical engineer. Though the birth was straightforward, Einstein’s mother Pauline received a shock when she first saw her son: his head was large and so oddly shaped, she was convinced he was deformed.¹⁴ In fact there was nothing wrong with the infant, though he did have an unusually large head. According to family legend, Einstein was not especially happy at elementary school, nor was he particularly clever.¹⁵ He later said that he was slow in learning to talk because he was ‘waiting’ until he could deliver fully formed sentences. In fact, the family legend was exaggerated. Research into Einstein’s early life shows that at school he always came top, or next to top, in both mathematics and Latin. But he did find enjoyment in his own company and developed a particular fascination with his building blocks. When he was five, his father gave him a compass. This so excited him, he said, that he ‘trembled and grew cold.’¹⁶

Though Einstein was not an only child, he was fairly solitary by nature and independent, a trait that was encouraged by his parents’ habit of encouraging self-reliance in their children at a very early age. Albert, for instance, was only three or four when he was given the responsibility of running errands, alone in the busy streets of Munich.¹⁷ The Einsteins encouraged their children to develop their own reading, and while studying math at school, Albert was discovering Kant and Darwin for himself at home – very advanced for a child.¹⁸ This did, however, help transform him from being a quiet child into a much more ‘difficult’ and rebellious adolescent. His character was only part of the problem here. He hated the autocratic approach used in his school, as he hated the autocratic side of Germany in general. This showed itself politically, in Germany as in Vienna, in a crude nationalism and a vicious anti-Semitism. Uncomfortable in such a psychological climate, Einstein argued incessantly with his fellow pupils and teachers, to the point where he was expelled, though he was thinking of leaving anyway. Aged sixteen he moved with his parents to Milan, attended university in Zurich at nineteen, though later he found a job as a patent officer in Bern. And so, half educated and half-in and half-out of academic life, he began in 1901 to publish scientific papers. His first, on the nature of liquid surfaces, was, in the words of one expert, ‘just plain wrong.’ More papers followed in 1903 and 1904. They were interesting but still lacked something – Einstein did not, after all, have access to the latest scientific literature and either repeated or misunderstood other people’s work. However, one of his specialities was statistical techniques, which stood him in good stead later on. More important, the fact that he was out of the mainstream of science may have helped his originality, which flourished unexpectedly in 1905. One says unexpectedly, so far as Einstein was concerned, but in fact, at the end of the nineteenth century many other mathematicians and physicists – Ludwig Boltzmann, Ernst Mach, and Jules-Henri Poincaré among them – were inclining towards something similar. Relativity, when it came, both was and was not a total surprise.¹⁹

Einstein’s three great papers of that marvellous year were published in March, on quantum theory, in May, on Brownian motion, and in June, on the special theory of relativity. Quantum physics, as we have seen, was itself new, the brainchild of the German physicist Max Planck. Planck argued that light is a form of electromagnetic radiation, made up of small packets or bundles – what he called quanta. Though his original paper caused little stir when it was read to the Berlin Physics Society in December 1900, other scientists soon realised that Planck must be right: his idea explained so much, including the observation that the chemical world is made up of discrete units – the elements. Discrete elements implied fundamental units of matter that were themselves discrete. Einstein paid Planck the compliment of thinking through other implications of his theory, and came to agree that light really does exist in discrete units – photons. One of the reasons why scientists other than Einstein had difficulty accepting this idea of quanta was that for years experiments had shown that light possesses the qualities of a wave. In the first of his papers Einstein, showing early the openness of mind for which physics would become celebrated as the decades passed, therefore made the hitherto unthinkable suggestion that light was both, a wave at some times and a particle at others. This idea took some time to be accepted, or even understood, except among physicists, who realised that Einstein’s insight fitted the available facts. In time the wave-particle duality, as it became known, formed the basis of quantum mechanics in the 1920s. (If you are confused by this, and have difficulty visualising something that is both a particle and a wave, you are in good company. We are dealing here with qualities that are essentially mathematical, and all visual analogies will be inadequate. Niels Bohr, arguably one of the century’s top two physicists, said that anyone who wasn’t made ‘dizzy’ by the very idea of what later physicists called ‘quantum weirdness’ had lost the plot.)

Two months after his paper on quantum theory, Einstein published his second great work, on Brownian motion.²⁰ Most people are familiar with this phenomenon from their school days: when suspended in water and inspected under the microscope, small grains of pollen, no more than a hundredth of a millimetre in size, jerk or zigzag backward and forward. Einstein’s idea was that this ‘dance’ was due to the pollen being bombarded by molecules of water hitting them at random. If he was right, Einstein said, and molecules were bombarding the pollen at random, then some of the grains should not remain stationary, their movement cancelled out by being bombarded from all sides, but should move at a certain pace through the water. Here his knowledge of statistics paid off, for his complex calculations were borne out by experiment. This was generally regarded as the first proof that molecules exist.

But it was Einstein’s third paper that year, the one on the special theory of relativity, published in June, that would make him famous. It was this theory which led to his conclusion that E=mc². It is not easy to explain the special theory of relativity (the general theory came later) because it deals with extreme – but fundamental – circumstances in the universe, where common sense breaks down. However, a thought experiment might help.²¹ Imagine you are standing at a railway station when a train hurtles through from left to right. At the precise moment that someone else on the train passes you, a light on the train, in the middle of a carriage, is switched on. Now, assuming the train is transparent, so you can see inside, you, as the observer on the platform, will see that by the time the light beam reaches the back of the carriage, the carriage will have moved forward. In other words, that light beam has travelled slightly less than half the length of the carriage. However, the person inside the train will see the light beam hitting the back of the carriage at the same time as it hits the front of the carriage, because to that person it has travelled exactly half the length of the carriage. Thus the time the light beam takes to reach the back of the carriage is different for the two observers. But it is the same light beam in each case, travelling at the same speed. The discrepancy, Einstein said, can only be explained by assuming that the perception is relative to the observer and that, because the speed of light is constant, time must change according to circumstance.

The idea that time can slow down or speed up is very strange, but that is exactly what Einstein was suggesting. A second thought experiment, suggested by Michael White and John Gribbin, Einstein’s biographers, may help. Imagine a pencil with a light upon it, casting a shallow on a tabletop. The pencil, which exists in three dimensions, casts a shallow, which exists in two, on the tabletop. As the pencil is twisted in the light, or if the light is moved around the pencil, the shallow grows or shrinks. Einstein said in effect that objects essentially have four dimensions in addition to the three we are all familiar with – they occupy space-time, as it is now called, in that the same object lasts over time.²² And so if you play with a four-dimensional object the way we played with the pencil, then you can shrink and extend time, the way the pencil’s shallow was shortened and extended. When we say ‘play’ here, we are talking about some hefty tinkering; in Einstein’s theory, objects are required to move at or near the speed of light before his effects are shown. But when they do, Einstein said, time really does change. His most famous prediction was that clocks would move more slowly when travelling at high speeds. This anti-commonsense notion was actually borne out by experiment many years later. Although there might be no immediate practical benefit from his ideas, physics was transformed.²³

Chemistry was transformed, too, at much the same time, and arguably with much more benefit for mankind, though the man who effected that transformation did not achieve anything like the fame of Einstein. In fact, when the scientist concerned revealed his breakthrough to the press, his name was left off the headlines. Instead, the New York Times ran what must count as one of the strangest headlines ever: ‘HERE’S TO C₇H₃₈O₄₃.’²⁴ That formula gave the chemical composition for plastic, probably the most widely used substance in the world today. Modern life – from airplanes to telephones to television to computers – would be unthinkable without it. The man behind the discovery was Leo Hendrik Baekeland.

Baekeland was Belgian, but by 1907, when he announced his breakthrough, he had lived in America for nearly twenty years. He was an individualistic and self-confident man, and plastic was by no means the first of his inventions, which included a photosensitive paper called Velox, which he sold to the Eastman Company for $750,000 (about $40 million now) and the Townsend Cell, which successfully electrolysed brine to produce caustic soda, crucial for the manufacture of soap and other products.²⁵

The search for a synthetic plastic was hardly new. Natural plastics had been used for centuries: along the Nile, the Egyptians varnished their sarcophagi with resin; jewellery of amber was a favourite of the Greeks; bone, shell, ivory, and rubber were all used. In the nineteenth century shellac was developed and found many applications, such as with phonograph records and electrical insulation. In 1865 Alexander Parkes introduced the Royal Society of Arts in London to Parkesine, the first of a series of plastics produced by trying to modify nitrocellulose.²⁶ More successful was celluloid, camphor gum mixed with pyroxyline pulp and made solvent by heating, especially as the basis for false teeth. In fact, the invention of celluloid brought combs, cuffs, and collars within reach of social groups that had hitherto been unable to afford such luxuries. There were, however, some disturbing problems with celluloid, notably its flammability. In 1875 a New York Times editorial summed up the problem with the alarming headline ‘Explosive Teeth.’²⁷

The most popular avenue of research in the 1890s and 1900s was the admixture of phenol and formaldehyde. Chemists had tried heating every combination imaginable to a variety of temperatures, throwing in all manner of other compounds. The result was always the same: a gummy mixture that was never quite good enough to produce commercially. These gums earned the dubious honour of being labelled by chemists as the ‘awkward resins.’²⁸ It was the very awkwardness of these substances that piqued Baekeland’s interest.²⁹ In 1904 he hired an assistant, Nathaniel Thurlow, who was familiar with the chemistry of phenol, and they began to look for a pattern among the disarray of results. Thurlow made some headway, but the breakthrough didn’t come until 18 June 1907. On that day, while his assistant was away, Baekeland took over, starting a new laboratory notebook. Four days later he applied for a patent for a substance he at first called ‘Bakalite.’³⁰ It was a remarkably swift discovery.

Reconstructions made from the meticulous notebooks Baekeland kept show that he had soaked pieces of wood in a solution of phenol and formaldehyde in equal parts, and heated it subsequently to 140–150°C. What he found was that after a day, although the surface of the wood was not hard, a small amount of gum had oozed out that was very hard. He asked himself whether this might have been caused by the formaldehyde evaporating before it could react with the phenol.³¹ To confirm this he repeated the process but varied the mixtures, the temperature, the pressure, and the drying procedure. In doing so, he found no fewer than four substances, which he designated A, B, C, and D. Some were more rubbery than others; some were softened by heating, others by boiling in phenol. But it was mixture D that excited him.³² This variant, he found, was ‘insoluble in all solvents, does not soften. I call it Bakalite and it is obtained by heating A or B or C in closed vessels.’³³ Over the next four days Baekeland hardly slept, and he scribbled more than thirty-three pages of notes. During that time he confirmed that in order to get D, products A, B, and C needed to be heated well above 100°C, and that the heating had to be carried out in sealed vessels, so that the reaction could take place under pressure. Wherever it appeared, however, substance D was described as ‘a nice smooth ivory-like mass.’³⁴ The Bakalite patents were filed on 13 July 1907. Baekeland immediately conceived all sorts of uses for his new product – insulation, moulding materials, a new linoleum, tiles that would keep warm in winter. In fact, the first objects to be made out of Bakalite were billiard balls, which were on sale by the end of that year. They were not a great success, though, as the balls were too heavy and not elastic enough. Then, in January 1908, a representative of the Loando Company from Boonton, New Jersey, visited Baekeland, interested in using Bakelite, as it was now called, to make precision bobbin ends that could not be made satisfactorily from rubber asbestos compounds.³⁵ From then on, the account book, kept by Baekeland’s wife to begin with (although they were already millionaires), shows a slow increase in sales of Bakelite in the course of 1908, with two more firms listed as customers. In 1909, however, sales rose dramatically. One event that helps explain this is a lecture Baekeland gave on the first Friday in February that year to the New York section of the American Chemical Society at its building on the corner of Fourteenth Street and Fifth Avenue.³⁶ It was a little bit like a rerun of the Manchester meeting where Rutherford outlined the structure of the atom, for the meeting didn’t begin until after dinner, and Baekeland’s talk was the third item on the agenda. He told the meeting that substance D was a polymerised oxy-benzyl-methylene-glycol-anhydride, or n(C₇H₃₈O₄₃). It was past 10:00 P.M. by the time he had finished showing his various samples, demonstrating the qualities of Bakelite, but even so the assembled chemists gave him a standing ovation. Like James Chadwick attending Rutherford’s talk, they realised they had been present at something important. For his part, Baekeland was so excited he couldn’t sleep afterward and stayed up in his study at home, writing a ten-page account of the meeting. Next day three New York papers carried reports of the meeting, which is when the famous headline appeared.³⁷

The first plastic (in the sense in which the word is normally used) arrived exactly on cue to benefit several other changes then taking place in the world. The electrical industry was growing fast, as was the automotive industry.³⁸ Both urgently needed insulating materials. The use of electric lighting and telephone services was also spreading, and the phonograph had proved more popular than anticipated. In the spring of 1910 a prospectus was drafted for the establishment of a Bakelite company, which opened its offices in New York six months later on 5 October.³⁹ Unlike the Wright brothers’ airplane, in commercial terms Bakelite was an immediate success.

Bakelite evolved into plastic, without which computers, as we know them today, would probably not exist. At the same time that this ‘hardware’ aspect of the modern world was in the process of formation, important elements of the ‘software’ were also gestating, in particular the exploration of the logical basis for mathematics. The pioneers here were Bertrand Russell and Alfred North Whitehead.

Russell – slight and precise, a finely boned man, ‘an aristocratic sparrow’ – is shown in Augustus John’s portrait to have had piercingly sceptical eyes, quizzical eyebrows, and a fastidious mouth. The godson of the philosopher John Stuart Mill, he was born halfway through the reign of Queen Victoria, in 1872, and died nearly a century later, by which time, for him as for many others, nuclear weapons were the greatest threat to mankind. He once wrote that ‘the search for knowledge, unbearable pity for suffering and a longing for love’ were the three passions that had governed his life. ‘I have found it worth living,’ he concluded, ‘and would gladly live it again if the chance were offered me.’⁴⁰

One can see why. John Stuart Mill was not his only famous connection – T. S. Eliot, Lytton Strachey, G. E. Moore, Joseph Conrad, D. H. Lawrence, Ludwig Wittgenstein, and Katherine Mansfield were just some of his circle. Russell stood several times for Parliament (but was never elected), championed Soviet Russia, won the Nobel Prize for Literature in 1950, and appeared (sometimes to his irritation) as a character in at least six works of fiction, including books by Roy Campbell, T. S. Eliot, Aldous Huxley, D. H. Lawrence, and Siegfried Sassoon. When Russell died in 1970 at the age of ninety-seven there were more than sixty of his books still in print.⁴¹

But of all his books the most original was the massive tome that appeared first in 1910, entitled, after a similar work by Isaac Newton, Principia Mathematica. This book is one of the least-read works of the century. In the first place it is about mathematics, not everyone’s favourite reading. Second, it is inordinately long – three volumes, running to more than 2,000 pages. But it was the third reason which ensured that this book – which indirectly led to the birth of the computer – was read by only a very few people: it consists mostly of a tightly knit argument conducted not in everyday language but by means of a specially invented set of symbols. Thus ‘not’ is represented by a curved bar; a boldface B stands for ‘or’; a square dot means ‘and,’ while other logical relationships are shown by devices such as a U on its side (⊃) for ‘implies,’ and a three-barred equals sign (≡) for ‘is equivalent to.’ The book was ten years in the making, and its aim was nothing less than to explain the logical foundations of mathematics.

Such a feat clearly required an extraordinary author. Russell’s education was unusual from the start. He was given a private tutor who had the distinction of being agnostic; as if that were not adventurous enough, this tutor also introduced his charge first to Euclid, then, in his early teens, to Marx. In December 1889, at the age of seventeen, Russell went to Cambridge. It was an obvious choice, for the only passion that had been observed in the young man was for mathematics, and Cambridge excelled in that discipline. Russell loved the certainty and clarity of math. He found it as ‘moving’ as poetry, romantic love, or the glories of nature. He liked the fact that the subject was totally uncontaminated by human feelings. ‘I like mathematics,’ he wrote, ‘because it is not human & has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza’s God, it won’t love us in return.’ He called Leibniz and Spinoza his ‘ancestors.’⁴²

At Cambridge, Russell attended Trinity College, where he sat for a scholarship. Here he enjoyed good fortune, for his examiner was Alfred North Whitehead. Just twenty-nine, Whitehead was a kindly man (he was known in Cambridge as ‘cherub’), already showing signs of the forgetfulness for which he later became notorious. No less passionate about mathematics than Russell, he displayed his emotion in a somewhat irregular way. In the scholarship examination, Russell came second; a young man named Bushell gained higher marks. Despite this, Whitehead convinced himself that Russell was the abler man – and so burned all of the examination answers, and his own marks, before meeting the other examiners. Then he recommended Russell.⁴³ Whitehead was pleased to act as mentor for the young freshman, but Russell also fell under the spell of G. E. Moore, the philosopher. Moore, regarded as ‘very beautiful’ by his contemporaries, was not as witty as Russell but instead a patient and highly impressive debater, a mixture, as Russell once described him, of ‘Newton and Satan rolled into one.’ The meeting between these two men was hailed by one scholar as a ‘landmark in the development of modern ethical philosophy.’⁴⁴

Russell graduated as a ‘wrangler,’ as first-class mathematics degrees are known at Cambridge, but if this makes his success sound effortless, that is misleading. Russell’s finals so exhausted him (as had happened with Einstein) that afterward he sold all his mathematical books and turned with relief to philosophy.⁴⁵ He said later he saw philosophy as a sort of no-man’s-land between science and theology. In Cambridge he developed wide interests (one reason he found his finals tiring was because he left his revision so late, doing other things). Politics was one of those interests, the socialism of Karl Marx in particular. That interest, plus a visit to Germany, led to his first book, German Social Democracy. This was followed by a book on his ‘ancestor’ Leibniz, after which he returned to his degree subject and began to write The Principles of Mathematics.

Russell’s aim in Principles was to advance the view, relatively unfashionable for the time, that mathematics was based on logic and ‘derivable from a number of fundamental principles which were themselves logical.’⁴⁶ He planned to set out his own philosophy of logic in the first volume and then in the second explain in detail the mathematical consequences. The first volume was well received, but Russell had hit a snag, or as it came to be called, a paradox of logic. In Principles he was particularly concerned with ‘classes.’ To use his own example, all teaspoons belong to the class of teaspoons. However, the class of teaspoons is not itself a teaspoon and therefore does not belong to the class. That much is straightforward. But then Russell took the argument one step further: take the class of all classes that do not belong to themselves – this might include the class of elephants, which is not an elephant, or the class of doors, which is not a door. Does the class of all classes that do not belong to themselves belong to itself? Whether you answer yes or no, you encounter a contradiction.⁴⁷ Neither Russell nor Whitehead, his mentor, could see a way around this, and Russell let publication of Principles go ahead without tackling the paradox. ‘Then, and only then,’ writes one of his biographers, ‘did there take place an event which gives the story of mathematics one of its moments of high drama.’ In the 1890s Russell had read Begriffsschrift (‘Concept-Script’), by the German mathematician Gottlob Frege, but had failed to understand it. Late in 1900 he bought the first volume of the same author’s Grundgesetze der Arithmetik (Fundamental Laws of Arithmetic) and realised to his shame and horror that Frege had anticipated the paradox, and also failed to find a solution. Despite these problems, when Principles appeared in 1903 – all 500 pages of it – the book was the first comprehensive treatise on the logical foundation of mathematics to be written in English.⁴⁸

The manuscript for Principles was finished on the last day of 1900. In the final weeks, as Russell began to think about the second volume, he became aware that Whitehead, his former examiner and now his close friend and colleague, was working on the second volume of his book Universal Algebra. In conversation, it soon became clear that they were both interested in the same problems, so they decided to collaborate. No one knows exactly when this began, because Russell’s memory later in his life was a good deal less than perfect, and Whitehead’s papers were destroyed by his widow, Evelyn. Her behaviour was not as unthinking or shocking as it may appear. There are strong grounds for believing that Russell had fallen in love with the wife of his collaborator, after his marriage to Alys Pearsall Smith collapsed in 1900.⁴⁹

The collaboration between Russell and Whitehead was a monumental affair. As well as tackling the very foundations of mathematics, they were building on the work of Giuseppe Peano, professor of mathematics at Turin University, who had recently composed a new set of symbols designed to extend existing algebra and explore a greater range of logical relationships than had hitherto been specifiable. In 1900 Whitehead thought the project with Russell would take a year.⁵⁰ In fact, it took ten. Whitehead, by general consent, was the cleverer mathematician; he thought up the structure of the book and designed most of the symbols. But it was Russell who spent between seven and ten hours a day, six days a week, working on it.⁵¹ Indeed, the mental wear and tear was on occasions dangerous. ‘At the time,’ Russell wrote later, ‘I often wondered whether I should ever come out at the other end of the tunnel in which I seemed to be…. I used to stand on the footbridge at Kennington, near Oxford, watching the trains go by, and determining that tomorrow I would place myself under one of them. But when the morrow came I always found myself hoping that perhaps “Principia Mathematica” would be finished some day.’⁵² Even on Christmas Day 1907, he worked seven and a half hours on the book. Throughout the decade, the work dominated both men’s lives, with the Russells and the Whiteheads visiting each other so the men could discuss progress, each staying as a paying guest in the other’s house. Along the way, in 1906, Russell finally solved the paradox with his theory of types. This was in fact a logico-philosophical rather than a purely logical solution. There are two ways of knowing the world, Russell said: acquaintance (spoons) and description (the class of spoons), a sort of secondhand knowledge. From this, it follows that a description about a description is of a higher order than the description it is about. On this analysis, the paradox simply disappears.⁵³

Slowly the manuscript was compiled. By May 1908 it had grown to ‘about 6,000 or 8,000 pages.’⁵⁴ In October, Russell wrote to a friend that he expected it to be ready for publication in another year. ‘It will be a very big book,’ he said, and ‘no one will read it.’⁵⁵ On another occasion he wrote, ‘Every time I went for a walk I used to be afraid that the house would catch fire and the manuscript get burnt up.’⁵⁶ By the summer of 1909 they were on the last lap, and in the autumn Whitehead began negotiations for publication. ‘Land in sight at last,’ he wrote, announcing that he was seeing the Syndics of the Cambridge University Press (the authors carried the manuscript to the printers on a four-wheeled cart). The optimism was premature. Not only was the book very long (the final manuscript was 4,500 pages, almost the same size as Newton’s book of the same title), but the alphabet of symbolic logic in which it was half written was unavailable in any existing printing font. Worse, when the Syndics considered the market for the book, they came to the conclusion that it would lose money – around £600. The press agreed to meet 50 percent of the loss, but said they could publish the book only if the Royal Society put up the other £300. In the event, the Royal Society agreed to only £200, and so Russell and Whitehead between them provided the balance. ‘We thus earned minus £50 each by ten years’ work,’ Russell commented. ‘This beats “Paradise Lost.” ’⁵⁷

Volume I of Principia Mathematica appeared in December 1910, volume 2 in 1912, volume 3 in 1913. General reviews were flattering, the Spectator concluding that the book marked ‘an epoch in the history of speculative thought’ in the attempt to make mathematics ‘more solid’ than the universe itself.⁵⁸ However, only 320 copies had been sold by the end of 1911. The reaction of colleagues both at home and abroad was awe rather than enthusiasm. The theory of logic explored in volume I is still a live issue among philosophers, but the rest of the book, with its hundreds of pages of formal proofs (page 86 proves that 1 + 1=2), is rarely consulted. ‘I used to know of only six people who had read the later parts of the book,’ Russell wrote in the 1950s. ‘Three of these were Poles, subsequently (I believe) liquidated by Hitler. The other three were Texans, subsequently successfully assimilated.’⁵⁹

Nevertheless, Russell and Whitehead had discovered something important: that most mathematics – if not all of it – could be derived from a number of axioms logically related to each other. This boost for mathematical logic may have been their most important legacy, inspiring such figures as Alan Turing and John von Neumann, mathematicians who in the 1930s and 1940s conceived the early computers. It is in this sense that Russell and Whitehead are the grandfathers of software.⁶⁰

In 1905 in the British medical periodical the Lancet, E. H. Starling, professor of physiology at University College, London, introduced a new word into the medical vocabulary, one that would completely change the way we think about our bodies. That word was hormone. Professor Starling was only one of many doctors then interested in a new branch of medicine concerned with ‘messenger substances.’ Doctors had been observing these substances for decades, and countless experiments had confirmed that although the body’s ductless glands – the thyroid in the front of the neck, the pituitary at the base of the brain, and the adrenals in the lower back – manufactured their own juices, they had no apparent means to transport these substances to other parts of the body. Only gradually did the physiology become clear. For example, at Guy’s Hospital in London in 1855, Thomas Addison observed that patients who died of a wasting illness now known as Addison’s Disease had adrenal glands that were diseased or had been destroyed.⁶¹ Later Daniel Vulpian, a Frenchman, discovered that the central section of the adrenal gland stained a particular colour when iodine or ferric chloride was injected into it; and he also showed that a substance that produced the same colour reaction was present in blood that drained away from the gland. Later still, in 1890, two doctors from Lisbon had the ostensibly brutal idea of placing half of a sheep’s thyroid gland under the skin of a woman whose own gland was deficient. They found that her condition improved rapidly. Reading the Lisbon report, a British physician in Newcastle-upon-Tyne, George Murray, noticed that the woman began her improvement as early as the day after the operation and concluded that this was too soon for blood vessels to have grown, connecting the transplanted gland. Murray therefore concluded that the substance secreted by the gland must have been absorbed directly into the patient’s bloodstream. Preparing a solution by crushing the gland, he found that it worked almost as well as the sheep’s thyroid for people suffering from thyroid deficiency.⁶²

The evidence suggested that messenger substances were being secreted by the body’s ductless glands. Various laboratories, including the Pasteur Institute in New York and the medical school of University College in London, began experimenting with extracts from glands. The most important of these trials was conducted by George Oliver and E. A. Sharpy-Shafer at University College, London, in 1895, during which they found that the ‘juice’ obtained by crushing adrenal glands made blood pressure go up. Since patients suffering from Addison’s disease were prone to have low blood pressure, this confirmed a link between the gland and the heart. This messenger substance was named adrenaline. John Abel, at Johns Hopkins University in Baltimore, was the first person to identify its chemical structure. He announced his breakthrough in June 1903 in a two-page article in the American Journal of Physiology. The chemistry of adrenaline was surprisingly straightforward; hence the brevity of the article. It comprised only a small number of molecules, each consisting of just twenty-two atoms.⁶³ It took a while for the way adrenaline worked to be fully understood and for the correct dosages for patients to be worked out. But adrenaline’s discovery came not a moment too soon. As the century wore on, and thanks to the stresses of modern life, more and more people became prone to heart disease and blood pressure problems.

At the beginning of the twentieth century people’s health was still dominated by a ‘savage trinity’ of diseases that disfigured the developed world: tuberculosis, alcoholism, and syphilis, all of which proved intractable to treatment for many years. TB lent itself to drama and fiction. It afflicted the young as well as the old, the well-off and the poor, and it was for the most part a slow, lingering death – as consumption it features in La Bohème, Death in Venice, and The Magic Mountain. Anton Chekhov, Katherine Mansfield, and Franz Kafka all died of the disease. Alcoholism and syphilis posed acute problems because they were not simply constellations of symptoms to be treated but the charged centre of conflicting beliefs, attitudes, and myths that had as much to do with morals as medicine. Syphilis, in particular, was caught in this moral maze.⁶⁴

The fear and moral disapproval surrounding syphilis a century ago mingled so much that despite the extent of the problem, it was scarcely talked about. Writing in the Journal of the American Medical Association in October 1906, for example, one author expressed the view that ‘it is a greater violation of the proprieties of public life publicly to mention venereal disease than privately to contract it.’⁶⁵ In the same year, when Edward Bok, editor of the Ladies’ Journal, published a series of articles on venereal diseases, the magazine’s circulation slumped overnight by 75,000. Dentists were sometimes blamed for spreading the disease, as was the barber’s razor and wet nurses. Some argued it had been brought back from the newly discovered Americas in the sixteenth century; in France a strong strand of anticlericalism blamed ‘holy water.’⁶⁶ Prostitution didn’t help keep track of the disease either, nor Victorian medical ethics that prevented doctors from telling one fiancée anything about the other’s infections unless the sufferer allowed it. On top of it all, no one knew whether syphilis was hereditary or congenital. Warnings about syphilis sometimes verged on the hysterical. Vénus, a ‘physiological novel,’ appeared in 1901, the same year as a play called Les Avariés (The Rotting or Damaged Ones), by Eugène Brieux, a well-known playwright.⁶⁷ Each night, before the curtain went up at the Théâtre Antoine in Paris, the stage manager addressed the audience: ‘Ladies and Gentlemen, the author and director are pleased to inform you that this play is a study of the relationship between syphilis and marriage. It contains no cause for scandal, no unpleasant scenes, not a single obscene word, and it can be understood by all, if we acknowledge that women need have absolutely no need to be foolish and ignorant in order to be virtuous.’⁶⁸ Nonetheless, Les Avariés was quickly banned by the censor, causing dismay and amazement in the editorials of medical journals, which complained that blatantly licentious plays were being shown in café concerts all across Paris with ‘complete impunity’.⁶⁹

Following the first international conference for the prevention of syphilis and venereal diseases in Brussels in 1899, Dr Alfred Fournier established the medical speciality of syphilology, using epidemiological and statistical techniques to underline the fact that the disease affected not just the demimonde but all levels of society, that women caught it earlier than men, and that it was ‘overwhelming’ among girls whose poor background had forced them into prostitution. As a result of Fournier’s work, journals were established that specialised in syphilis, and this paved the way for clinical research, which before long produced results. On 3 March 1905 in Berlin, Fritz Schaudinn, a zoologist, noticed under the microscope ‘a very small spirochaete, mobile and very difficult to study’ in a blood sample taken from a syphilitic. A week later Schaudinn and Eric Achille Hoffmann, a bacteriologist, observed the same spirochaete in samples taken from different parts of the body of a patient who only later developed roseolae, the purple patches that disfigure the skin of syphilitics.⁷⁰ Difficult as it was to study, because it was so small, the spirochaete was clearly the syphilis microbe, and it was labelled Treponema (it resembled a twisted thread) pallidum (a reference to its pale colour). The invention of the ultramicroscope in 1906 meant that the spirochaete was now easier to experiment on than Schaudinn had predicted, and before the year was out a diagnostic staining test had been identified by August Wassermann. This meant that syphilis could now be identified early, which helped prevent its spread. But a cure was still needed.⁷¹

The man who found it was Paul Ehrlich (1854–1915). Born in Strehlen, Upper Silesia, he had an intimate experience of infectious diseases: while studying tuberculosis as a young doctor, he had contracted the illness and been forced to convalesce in Egypt.⁷² As so often happens in science, Ehrlich’s initial contribution was to make deductions from observations available to everyone. He observed that, as one bacillus after another was discovered, associated with different diseases, the cells that had been infected also varied in their response to staining techniques. Clearly, the biochemistry of these cells was affected according to the bacillus that had been introduced. It was this deduction that gave Ehrlich the idea of the antitoxin – what he called the ‘magic bullet’ – a special substance secreted by the body to counteract invasions. Ehrlich had in effect discovered the principle of both antibiotics and the human immune response.⁷³ He went on to identify what antitoxins he could, manufacture them, and employ them in patients via the principle of inoculation. Besides syphilis he continued to work on tuberculosis and diphtheria, and in 1908 he was awarded the Nobel Prize for his work on immunity.⁷⁴

By 1907 Ehrlich had produced no fewer than 606 different substances or ‘magic bullets’ designed to counteract a variety of diseases. Most of them worked no magic at all, but ‘Preparation 606,’ as it was known in Ehrlich’s laboratory, was eventually found to be effective in the treatment of syphilis. This was the hydrochloride of dioxydiaminoarsenobenzene, in other words an arsenic-based salt. Though it had severe toxic side effects, arsenic was a traditional remedy for syphilis, and doctors had for some time been experimenting with different compounds with an arsenic base. Ehrlich’s assistant was given the job of assessing the efficacy of 606, and reported that it had no effect whatsoever on syphilis-infected animals. Preparation 606 therefore was discarded. Shortly afterward the assistant who had worked on 606, a relatively junior but fully trained doctor, was dismissed from the laboratory, and in the spring of 1909 a Japanese colleague of Ehrlich, Professor Kitasato of Tokyo, sent a pupil to Europe to study with him. Dr Sachachiro Hata was interested in syphilis and familiar with Ehrlich’s concept of ‘magic bullets.’⁷⁵ Although Ehrlich had by this stage moved on from experimenting with Preparation 606, he gave Hata the salt to try out again. Why? Was the verdict of his former (dismissed) assistant still rankling two years later? Whatever the reason, Hata was given a substance that had been already studied and discarded. A few weeks later he presented Ehrlich with his laboratory book, saying, ‘Only first trials – only preliminary general view.’⁷⁶

Ehrlich leafed through the pages and nodded. ‘Very nice … very nice.’ Then he came across the final experiment Hata had conducted only a few days before. With a touch of surprise in his voice he read out loud from what Hata had written: ‘Believe 606 very effacious.’ Ehrlich frowned and looked up. ‘No, surely not? Wieso denn … wieso denn? It was all minutely tested by Dr R. and he found nothing – nothing!’

Hata didn’t even blink. ‘I found that.’

Ehrlich thought for a moment. As a pupil of Professor Kitasato, Hata wouldn’t come all the way from Japan and then lie about his results. Then Ehrlich remembered that Dr R had been dismissed for not adhering to strict scientific practice. Could it be that, thanks to Dr R, they had missed something? Ehrlich turned to Hata and urged him to repeat the experiments. Over the next few weeks Ehrlich’s study, always untidy, became clogged with files and other documents showing the results of Hata’s experiments. There were bar charts, tables of figures, diagrams, but most convincing were the photographs of chickens, mice, and rabbits, all of which had been deliberately infected with syphilis to begin with and, after being given Preparation 606, showed progressive healing. The photographs didn’t lie but, to be on the safe side, Ehrlich and Hata sent Preparation 606 to several other labs later in the year to see if different researchers would get the same results. Boxes of this particular magic bullet were sent to colleagues in Saint Petersburg, Sicily, and Magdeburg. At the Congress for Internal Medicine held at Wiesbaden on 19 April 1910, Ehrlich delivered the first public paper on his research, but by then it had evolved one crucial stage further. He told the congress that in October 1909 twenty-four human syphilitics had been successfully treated with Preparation 606. Ehrlich called his magic bullet Salvarsen, which had the chemical name of asphen-amine.⁷⁷

The discovery of Salvarsen was not only a hugely significant medical breakthrough but also produced a social change that would in years to come influence the way we think in more ways than one. For example, one aspect of the intellectual history of the century that has been inadequately explored is the link between syphilis and psychoanalysis. As a result of syphilis, as we have seen, the fear and guilt surrounding illicit sex was much greater at the beginning of the century than it is now, and helped account for the climate in which Freudianism could grow and thrive. Freud himself acknowledged this. In his Three Essays on the Theory of Sexuality, published in 1905, he wrote, ‘In more than half of the severe cases of hysteria, obsessional neurosis, etc., which I have treated, I have observed that the patient’s father suffered from syphilis which had been recognised and treated before marriage…. I should like to make it perfectly clear that the children who later became neurotic bore no physical signs of hereditary syphilis…. Though I am far from wishing to assert that descent from syphilitic parents is an invariable or necessary etiological condition of a neuropathic constitution, I believe that the coincidences which I have observed are neither accidental nor unimportant.’⁷⁸

This paragraph appears to have been forgotten in later years, but it is crucial. The chronic fear of syphilis in those who didn’t have it, and the chronic guilt in those who did, created in the turn-of-the-century Western world a psychological landscape ready to spawn what came to be called depth psychology. The notion of germs, spirochaetes, and bacilli was not all that dissimilar from the idea of electrons and atoms, which were not pathogenic but couldn’t be seen either. Together, this hidden side of nature made the psychoanalytic concept of the unconscious acceptable. The advances made by the sciences in the nineteenth century, together with the decline in support for organised religion, helped to produce a climate where ‘a scientific mysticism’ met the needs of many people. This was scientism reaching its apogee. Syphilis played its part.

One should not try too hard to fit all these scientists and their theories into one mould. It is, however, noticeable that one characteristic does link most of these figures: with the possible exception of Russell, each was fairly solitary. Einstein, Rutherford, Ehrlich, and Baekeland, early in their careers, ploughed their own furrow – not for them the Café Griensteidl or the Moulin de la Galette. Getting their work across to people, whether at conferences or in professional journals, was what counted. This was – and would remain – a significant difference between scientific ‘culture’ and the arts, and may well have contributed to the animosity toward science felt by many people as the decades went by. The self-sufficiency of science, the self-absorption of scientists, the sheer difficulty of so much science, made it inaccessible in a way that the arts weren’t. In the arts, the concept of the avant-garde, though controversial, became familiar and stabilised: what the avant-garde liked one year, the bourgeoisie would buy the next. But new ideas in science were different; very few of the bourgeoisie would ever fully comprehend the minutiae of science. Hard science and, later, weird science, were hard and/or weird in a way that the arts were not.

For non-specialists, the inaccessibility of science didn’t matter, or it didn’t matter very much, for the technology that was the product of difficult science worked, conferring a continuing authority on physics, medicine, and even mathematics. As will be seen, the main effect of the developments in hard science were to reinforce two distinct streams in the intellectual life of the century. Scientists ploughed on, in search of more and more fundamental answers to the empirical problems around them. The arts and the humanities responded to these fundamental discoveries where they could, but the raw and awkward truth is that the traffic was almost entirely one-way. Science informed art, not the other way round. By the end of the first decade, this was already clear. In later decades, the issue of whether science constitutes a special kind of knowledge, more firmly based than other kinds, would become a major preoccupation of philosophy.