by Peter Watson
So far as his own interest was concerned, the nature of the chemical bond, his visit to Zurich was the most profitable. There he came across two less famous Germans, Walter Heitler and Fritz London, who had developed an idea about how electrons and wave functions applied to chemical reactions.57 At its simplest, imagine the Following: Two hydrogen atoms are approaching one another. Each is comprised of one nucleus (a proton) and one electron. As the two atoms get closer and closer to each other, ‘the electron of one would find itself drawn to the nucleus of the other, and vice versa. At a certain point, the electron of one would jump to the new atom, and the same would happen with the electron of the other atom.’ They called this an ‘electron exchange,’ adding that this exchange would take place billions of times a second.58 In a sense, the electrons would be ‘homeless,’ the exchange forming the ‘cement’ that held the two atoms together, ‘setting up a chemical bond with a definite length.’ Their theory put together the work of Pauli, Schrödinger, and Heisenberg; they also found that the ‘exchange’ determined the architecture of the molecule.59 It was a very neat piece of work, but from Pauling’s point of view there was one drawback about this idea: it wasn’t his. If he were to make his name, he needed to push the idea forward. By the time Pauling returned to America from Europe, Caltech had made considerable progress. Negotiations were under way to build the world’s biggest telescope at Mount Wilson, where Hubble would work. A jet propulsion lab was planned, and T. H. Morgan was about to arrive, to initiate a biology lab.60 Pauling was determined to outshine them ad. Throughout the early 1930s he released report after report, all part of the same project, and all having to do with the chemical bond. He succeeded magnificently in building on Heitler and London’s work. His early experiments on carbon, the basic constituent of life, and then on silicates showed that the elements could be systematically grouped according to their electronic relationships. These became known as Pauling’s rules. He showed that some bonds were weaker than others and that this helped explain chemical properties. Mica, for example, is a silicate that, as all chemists know, splits into thin, transparent sheets. Pauling was able to show that mica’s crystals have strong bonds in two directions and a weak one in a third direction, exactly corresponding to observation. In a second instance, another silicate we all know as talc is characterised by weak bonds all around, so that it crumbles instead of splitting, and forms a powder.61
Pauling’s work was almost as satisfying for others as it was for him.62 Here at last was an atomic, electronic explanation of the observable properties of well-known substances. The century had begun with the discovery of fundamentals that applied to physics and biology. Now the same was happening in chemistry. Once more, knowledge was beginning to come together. During 1930–5, Pauling published a new paper on the bond every five weeks on average.63 He was elected to the National Academy of Sciences in America at thirty-two, the youngest scientist ever to receive that honour.64 For a time, he was so far out on his own that few other people could keep up. Einstein attended one lecture of his and admitted afterward that it was beyond him. Uniquely, Pauling’s papers sent to the Journal of the American Chemical Society were published unrefereed because the editor could think of no one qualified to venture an opinion.65 Even though Pauling was conscious of this, throughout the 1930s he was too busy producing original papers to write a book consolidating his research. Finally, in 1939 he published The Nature of the Chemical Bond. This revolutionised our understanding of chemistry and immediately became a standard text, translated into several languages.66 It proved crucial to the discoveries of the molecular biologists after World War II.
The fresh data that the new physics was producing had very practical ramifications that arguably have changed our lives far more directly than was at first envisaged by scientists mainly interested in fundamental aspects of nature. Radio, in use for some time, moved into the home in the 1920s; television was first shown in August 1928. Another invention, using physics, revolutionised life in a completely different way: this was the jet engine, developed with great difficulty by the Englishman Frank Whittle.
Whittle was the working-class son of a mechanic who lived on a Coventry housing estate. As a boy he educated himself in Leamington Public Library, where he spent all his spare time devouring popular science books about aircraft – and turbines.67 All his life Frank Whittle was obsessed with flight, but his background was hardly natural in those days for a university education, and so at the age of fifteen he applied to join the Royal Air Force as a technical apprentice. He failed. He passed the written examination but was blocked by the medical officer: Frank Whittle was only five feet tall. Rather than give up, he obtained a diet sheet and a list of exercises from a friendly PE teacher, and within a few months he had added three inches to his height and another three to his chest measurement. In some ways this was as impressive as anything else he did later in life. He was finally accepted as an apprentice in the RAE and although he found the barrack-room life irksome, in his second year as a cadet at Cranwell, the RAF college – at the age of nineteen – he wrote a thesis on future developments in aircraft design. It was in this paper that Whittle began to sketch his ideas for the jet engine. Now in the Science Museum in London, the paper is written in junior handwriting, but it is clear and forthright.68 His crucial calculation was that ‘a B oomph wind against a machine travelling at 6oomph at 120,000 feet would have less effect than a 2omph head wind against the same machine at 1,000 feet.’ He concluded, ‘Thus everything indicates that designers should aim at altitude.’ He knew that propellers and petrol engines were inefficient at great heights, but he also knew that rocket propulsion was suitable only for space travel. This is where his old interest in turbines resurfaced; he was able to show that the efficiency of turbines increased at higher altitudes. An indication of Whittle’s vision is apparent from the fact that he was contemplating an aircraft travelling at a speed of 500mph at 60,000 feet, while in 1926 the top speed of RAF fighters was 150 mph, and they couldn’t fly much above 10,000 feet.
After Cranwell, Whittle transferred to Hornchurch in Essex to a fighter squadron, and then in 1929 moved on to the Central Flying School at Wittering in Sussex as a pupil instructor. All this time he had been doggedly worrying how to create a new kind of engine, most of the time working on an amalgam of a petrol engine and a fan of the kind used in turbines. While at Wittering, he suddenly saw that the solution was alarmingly simple. In fact, his idea was so simple his superiors didn’t believe it. Whittle had grasped that a turbine would drive the compressor, ‘making the principle of the jet engine essentially circular.’69 Air sucked in by the compressor would be mixed with fuel and ignited. Ignition would expand the gas, which would flow through the blades of the turbine at such a high speed that not only would a jet stream be created, which would drive the aircraft forward, but the turning of the blades would also draw fresh air into the compressor, to begin the process all over again. If the compressor and the turbine were mounted on the same shaft, there was in effect only one moving part in a jet engine. It was not only far more powerful than a piston engine, which had many moving parts, but incomparably safer. Whittle was only twenty-two, and just as his height had done before, his age now acted against him. His idea was dismissed by the ministry in London. The rebuff hit him hard, and although he took out patents on his inventions, from 1929 to the mid-193os, nothing happened. When the patents came up for renewal, he was still so poor he let them lapse.70
In the early 1930s, Hans von Ohain, a student of physics and aerodynamics at Göttingen University, had had much the same idea as Whittle. Von Ohain could not have been more different from the Englishman. He was aristocratic, well off, and over six feet tall. He also had a different attitude to the uses of his jet.71 Spurning the government, he took his idea to the private planemaker Ernst Heinkel. Heinkel, who realised that high-speed air transport was much needed, took von Ohain seriously from the start. A meeting was called at his country residence, at Warnemünde
on the Baltic coast, where the twenty-five-year-old Ohain was faced by some of Heinkel’s leading aeronautical brains. Despite his youth, Ohain was offered a contract, which featured a royalty on all engines that might be sold. This contract, which had nothing to do with the air ministry, or the Luftwaffe, was signed in April 1936, seven years after Whittle wrote his paper.
Meanwhile in Britain Whittle’s overall brilliance was by now so self-evident that two friends, convinced of Whittle’s promise, met for dinner and decided to raise backing for a jet engine as a purely business venture. Whittle was still only twenty-eight, and many more experienced aeronautical engineers thought his engine would never fly. Nonetheless, with the aid of O. T. Falk and Partners, city bankers, a company called Power Jets was formed, and £20,000 raised.72 Whittle was given shares in the company (no royalties), and the Air Ministry agreed to a 25 percent stake.
Power Jets was incorporated in March 1936. On the third of that month Britain’s defence budget was increased from £122 million to £158 million, partly to pay for 250 more aircraft for the Fleet Air Arm for home defence. Four days later, German troops occupied the demilitarised zone of the Rhineland, thus violating the Treaty of Versailles. War suddenly became much more likely, a war in which air superiority might well prove crucial. All doubts about the theory of the jet engine were now put aside. From then on, it was simply a question of who could produce the first operational jet.
The intellectual overlap between physics and mathematics has always been considerable. As we have seen in the case of Heisenberg’s matrices and Schrödinger’s calculations, the advances made in physics in the golden age often involved the development of new forms of mathematics. By the end of the 1920s, the twenty-three outstanding math problems identified by David Hilbert at the Paris conference in 1900 (see chapter 1) had for the most part been settled, and mathematicians looked out on the world with optimism. Their confidence was more than just a technical matter; mathematics involved logic and therefore had philosophical implications. If math was complete, and internally consistent, as it appeared to be, that said something fundamental about the world.
But then, in September 1931, philosophers and mathematicians convened in Königsberg for a conference on the ‘Theory of Knowledge in the Exact Sciences,’ attended by, among others, Ludwig Wittgenstein, Rudolf Carnap, and Moritz Schlick. All were overshadowed, however, by a paper from a young mathematician from Brünn, whose revolutionary arguments were later published in a German scientific journal, in an article entitled ‘On the Formally Undecidable Propositions of Principia Mathematica and Related Systems.’73 The author was Kurt Godei, a twenty-five-year-old mathematician at the University of Vienna, and this paper is now regarded as a milestone in the history of logic and mathematics. Gödel was an intermittent member of Schlick’s Vienna Circle, which had stimulated his interest in the philosophical aspects of science. In his 1931 paper he demolished Hilbert’s aim of putting all mathematics on irrefutably sound foundations, with his theorem that tells us, no less firmly than Heisenberg’s uncertainty principle, that there are some things we cannot know. No less importantly, he demolished Bertrand Russell’s and Alfred North Whitehead’s aim of deriving all mathematics from a single system of logic.74
There is no hiding the fact that Gödel’s theorem is difficult. There are two elements that may be stated: one, that ‘within any consistent formal system, there will be a sentence that can neither be proved true nor proved false’; and two, ‘that the consistency of a formal system of arithmetic cannot be proved within that system’.75 The simplest way to explain his idea makes use of the so-called Richard paradox, first put forward by the French mathematician Jules Richard in 1905.76 In this system integers are given to a variety of definitions about mathematics. For example, the definition ‘not divisible by any number except one and itself’ (i.e., a prime number), might be given one integer, say 17. Another definition might be ‘being equal to the product of an integer multiplied by that integer’ (i.e., a perfect square), and given the integer 20. Now assume that these definitions are laid out in a list with the two above inserted as 17th and 20th. Notice two things about these definitions: 17, attached to the first statement, is itself a prime number, but 20, attached to the second statement, is not a perfect square. In Richardian mathematics, the above statement about prime numbers is not Richardian, whereas the statement about perfect squares is. Formally, the property of being Richardian involves ‘not having the property designated by the defining expression with which an integer is correlated in the serially ordered set of definitions.’ But of course this last statement is itself a mathematical definition and therefore belongs to the series and has its own integer, n. The question may now be put: Is n itself Richardian? Immediately the crucial contradiction appears. ‘For n is Richardian if, and only if, it does not possess the property designated by the definition with which n is correlated; and it is easy to see that therefore n is Richardian if, and only if, n is not Richardian.’77
No analogy like this can do full justice to Gödel’s theorem, but it at least conveys the paradox adequately. It is for some a depressing conclusion (and Godei himself battled bouts of chronic depression. After living an ascetic personal life, he died in 1978, aged seventy-two, of ‘malnutrition and inanition’ brought about by personality disturbance).78 Godei had established that there were limits to math and to logic. The aim of Gottlob Frege, David Hilbert, and Russell to create a unitary deductive system in which all mathematical (and therefore all logical) truth could be deduced from a small number of axioms could not be realised. It was, in its way and as was hinted at above, a form of mathematical uncertainty principle – and it changed math for all time. Furthermore, as Roger Penrose has pointed out, Gödel’s ‘open-ended mathematical intuition is fundamentally incompatible with the existing structure of physics.’79
In some ways Gödel’s discovery was the most fundamental and mysterious of all. He certainly had what most people would call a mystical side, and he thought we should trust [mathematical] intuition as much as other forms of experience.80 Added to the uncertainty principle, his theory described limits to knowledge. Put alongside all the other advances and new avenues of thought, which were then exploding in all directions, it injected a layer of doubt and pessimism. Why should there be limits to our knowledge? And what did it mean to know that such limits existed?
16
CIVILISATIONS AND THEIR DISCONTENTS
On 28 October 1929 the notorious stock market crash occurred on Wall Street, and U.S. loans to Europe were suspended. In the weeks and months that followed, and despite the misgivings of many, Allied troops prepared and then executed their departure from the Rhineland. In France, Georges Clemenceau died at the age of eighty-eight, while in Thuringia Wilhelm Frick was about to become the first member of the Nazi Party to be appointed minister in a state government. Benito Mussolini was clamouring for the revision of the Versailles Treaty, and in India Mohandâs Gandhi began his campaign of civil disobedience. In Britain in 1931 a National Government was formed to help balance the budget, while Japan abandoned the gold standard. There was a widespread feeling of crisis.
Sigmund Freud, then aged seventy-three, had far more personal reasons to feel pessimistic. In 1924 he had undergone two operations for cancer of the mouth. Part of his upper jaw had to be removed and replaced with a metal prosthesis, a procedure that could only be carried out using a local anaesthetic. After the operation he could chew and speak only with difficulty, but he still refused to stop smoking, which had probably been the cause of the cancer in the first place. Before he died in London in 1939, Freud underwent another two dozen operations, either to remove precancerous tissue or to have his prosthesis cleaned or renewed. During all this time he never stopped working.
In 1927 Freud had published The Future of an Illusion, which both explained away and yet amounted to an attack on organised religion. This was the second of three ‘cultural’ works by Freud (the first, Totem and Taboo, was discussed e
arlier: see above, page 141). At the end of 1929, as Wall Street was crashing, Freud delivered the third of these works, Civilisation and Its Discontents. There had been famine in Austria and attempted revolution and mega-inflation in Germany, and capitalism appeared to have collapsed in America. The devastation and moral degeneration of World War I was still a concern to many people, and Hitler was on the rise. Wherever you looked, Freud’s title fitted the facts.1
In Civilisation and Its Discontents, Freud developed some of the ideas he had explored in Totem and Taboo, in particular that society – civilisation – evolves out of the need to curb the individual’s unruly sexual and aggressive appetites. He now argued that civilisation, suppression, and neurosis are inescapably intertwined because the more civilisation there is, the more suppression is needed and, as a direct result, the more neurosis. Man, he said, cannot help but be more and more unhappy in civilisation, which explains why so many seek refuge in drink, drugs, tobacco, or religion. Given this basic predicament, it is the individual’s ‘psychical constitution’ which determines how any individual adjusts. For example, ‘The man who is predominantly erotic will give first preference to his emotional relationships with other people; the narcissistic man, who inclines to be self-sufficient, will seek his main satisfactions in his internal mental process.’2 And so on. The point of his book, he said, was not to offer easy panaceas for the ills of society but to suggest that ethics – the rules by which men agree to live together – can benefit from psychoanalytic understanding, in particular, the psychoanalytic concept of the superego, or conscience.3