The German Genius

by Peter Watson

  The next year, 1925, the center of activity moved for a time to Göttingen. Before World War I, British and American students regularly went to Germany to complete their studies, and Göttingen was a frequent stopping-off place. Bohr gave a lecture there in 1922 and was taken to task by a young student who corrected a point in his argument. Bohr, being Bohr, hadn’t minded. “At the end of the discussion,” said Werner Heisenberg later, “he came over to me and asked me to join him that afternoon on a walk over the Hain Mountain.”4 It was more than a stroll, for Bohr invited the young Bavarian to Copenhagen where they set about tackling yet another problem of quantum theory. According to this theory, energy—like light—was emitted in tiny packets, but according to classical physics it was emitted continuously. How could that be? Heisenberg returned to Göttingen enthused by his time in Copenhagen but also confused. And so, toward the end of May 1925, when he suffered one of his many attacks of hay fever, he took two weeks’ holiday in Helgoland, a narrow strip of land off the German coast on the North Sea, where there was next to no pollen, and he cleared his head with long walks and bracing dips in the sea. The idea that came to Heisenberg in that cold, fresh environment was the first example of what came to be called quantum weirdness. Heisenberg formed the view that if something is measured as continuous at one point, and discrete at another, that is the way of reality. If the two measurements exist, it makes no sense to say that they disagree: they are just measurements.

  This was Heisenberg’s central insight, but in a hectic three weeks he went further, developing a method of mathematics known as matrix math, originating from an idea by David Hilbert, in which the measurements obtained are grouped in a two-dimensional table of numbers where two matrices can be multiplied together to give another matrix.5 In Heisenberg’s scheme, each atom would be represented by one matrix, each “rule” by another. If one multiplied the “sodium matrix” by the “spectral line matrix,” the result should give the matrix of wavelengths of sodium’s spectral lines. To Heisenberg’s, and Bohr’s, great satisfaction, it did: “For the first time, atomic structure had a genuine, though very surprising, mathematical base.” Heisenberg called his creation/discovery quantum mechanics, though Nancy Thorndike Greenspan’s recent biography of Max Born confirms how his role in the conception of the probabilistic nature of quantum waves, and of matrices themselves, was underacknowledged in the past by the likes of Heisenberg. Born won the Nobel Prize in 1954, but his contribution has now been properly positioned.6

  The acceptance of Heisenberg’s idea was made easier by a new theory of Louis de Broglie in Paris, also published in 1925. Both Planck and Einstein had argued that light, hitherto regarded as a wave, could sometimes behave as a particle. Broglie reversed this idea, arguing that particles could sometimes behave like waves. No sooner had he broached this theory than experimentation proved him right. The wave-particle duality of matter was the second weird notion of physics, but it caught on quickly and one reason was the work of the Austrian Erwin Schrödinger, who was disturbed by Heisenberg’s idea and fascinated by Broglie’s. Schrödinger added the notion that the electron, in its orbit around the nucleus, is not like a planet but like a wave. Moreover, this wave pattern determines the size of the orbit, because to form a complete circle the wave must conform to a whole number, not fractions (otherwise the wave would descend into chaos). In turn this determined the distance of the orbit from the nucleus.

  The final layer of weirdness came in 1927, again from Heisenberg. It was late February, and Bohr had gone skiing in Norway. In his room high up in Bohr’s institute, Heisenberg decided he needed some air, so he trudged across the muddy soccer fields nearby. As he walked, an idea began to germinate in his brain. Could it be, Heisenberg asked himself, that at the level of the atom there was a limit to what could be known? To identify the position of a particle, it must impact on a zinc-sulphide screen. This alters its velocity, meaning it cannot be measured at the crucial moment. Conversely, when the velocity of a particle is measured—by scattering gamma rays from it, say—it is knocked into a different path, and its exact position at the point of measurement is changed. Heisenberg’s uncertainty principle, as it came to be called, posited that the exact position and precise velocity of an electron could not be determined at the same time (Heisenberg said: “To measure is to disturb,” “messen ist stören”). This was certainly disturbing both practically and philosophically, because it implied that in the subatomic world cause and effect could never be measured. The only way to understand electron behavior was statistical, using the rules of probability. “Even in principle,” Heisenberg was affirming, “we cannot know the present in all detail.” Einstein was never happy with the basic notion of quantum theory, that the subatomic world could be understood only statistically. It remained a bone of contention between him and Bohr until the end of his life.7

  Several physicists were not very happy with Einstein himself. These were the “anti-relativists,” notably Philipp Lenard and Johannes Stark. Both Lenard and Stark were good scientists but, as the 1920s passed, they convinced themselves that relativity was a bogus Jewish science. Lenard, memorably described as having an “angry beard,” was Hungarian but had studied in Germany under Heinrich Hertz and became his assistant.8 He himself won the Nobel Prize (in 1905) for showing that cathode rays could pass through atoms, confirming how much atoms were made of empty space. Despite his experimental brilliance, however, Lenard was a great hater—he delivered a series of lectures in 1920 attacking relativity, although by then some of its predictions had been confirmed experimentally. And in 1929 he published a book of scientific biographies, designed to show that “Aryan-Germans” were a leading creative/innovative force and attributing other discoveries, by Jews and foreigners, to little-known, but always German, individuals.

  Stark was another Nobel Prize winner, in 1919 for “the Stark effect,” the influence of electrical fields on spectral lines. Surrounded by “Einstein lovers” at the University of Würzburg, he resigned his chair and was not to get another until the Nazis came to power.9 But he wrote a book, Die gegenwärtige Krise der deutschen Physik (The Contemporary Crisis in German Physics), which argued that relativity was part of the cultural malaise then afflicting the Weimar Republic, followed by an article, “Hitlergeist und Wissenschaft” (The Hitler Spirit and Science), written jointly with Lenard, in the Grossdeutsche Zeitung in May 1924, in which they compared Hitler with the giants of science. This marked the emergence of “Deutsche Physik” (German physics), which eschewed relativity and quantum theory, arguing that they were too theoretical, too abstract, and “threatened to undermine intuitive, mechanical models of the world.”10

  Yet 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 moved into the home in the 1920s; television was first demonstrated in August 1928. Another invention using physics revolutionized life in a completely different way: this was the jet engine, developed almost simultaneously by the Englishman Frank Whittle and the German Hans von Ohain.

  In the early 1930s, Ohain, a student of physics and aerodynamics at the University of Göttingen, had had much the same idea as Whittle. But whereas Whittle tried to enlist the aid of the British government, Ohain took his idea to the private plane-maker, Ernst Heinkel.11 Heinkel, who realized that high-speed air transport was much needed, took von Ohain seriously from the very start. A meeting was called at Heinkel’s country residence, at Warnemünde on the Baltic coast, where the twenty-five-yearold Ohain was faced by some of the plane-maker’s leading aeronautical brains. Despite his youth, Ohain was offered a contract, which featured a royalty on all engines that might be sold.12 This contract, which had nothing to do with the air ministry, or the Luftwaffe, was signed in April 1936, one month after Whittle concluded a deal for Power Jets, the company eventually formed in Britain between a firm of city bankers, t
he Air Ministry, and Whittle himself. Between the British company being formed, and Ohain’s agreement, Britain’s defense budget was increased from £122 million to £158 million, partly to pay for 250 more aircraft for the Fleet Air Arm. Four days later, German troops occupied the demilitarized zone of the Rhineland, thus violating the Treaty of Versailles. War suddenly became much more likely, a war in which air superiority might well (and did) prove crucial.

  The intellectual overlap between physics and mathematics has always been considerable. In the case of Heisenberg’s matrices and Schrödinger’s calculations, the advances made in physics in the golden age involved the development of new forms of mathematics. By the end of the 1920s, the twenty-three outstanding mathematical problems identified by David Hilbert at the Paris conference in 1900 (see Chapter 25) 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 mathematics was complete, and internally consistent, as it appeared to be, that said something fundamental about the world.13

  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 twenty-five-year-old mathematician from Brno (Brünn) whose revolutionary arguments were later published in a German scientific journal in an article titled “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme” (On the Formally Undecidable Propositions of Principia Mathematica and Related Systems). The author was Kurt Gödel, 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 Frege’s, Russell’s, and 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. As John Dawson Jr. has written, Gödel’s work raises “the spectre of unsolvability.”14

  His theorem is difficult. The simplest way to explain his idea is by analogy and makes use of the so-called Richard paradox, first put forward by the French mathematician Jules Richard in 1905. 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: 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 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 it is Richardian if, and only if, n is not Richardian.”

  No analogy can do full justice to Gödel’s theorem, but this at least conveys the paradox. It was, for some mathematicians, a profoundly depressing conclusion, for Gödel had effectively established that there were limits to mathematics and to logic—and it changed mathematics for all time.15

  One place where such questions were frequently discussed was among a group in Vienna who, in 1924, began to meet every Thursday. Originally organized as the Ernst Mach Society, in 1928 they changed their name to the Wiener Kreis, the Vienna Circle.16 Under this title they became what is arguably the most important philosophical movement of the last century. The guiding spirit was Moritz Schlick (1882–1936), Berlin-born who, like many members of the Kreis, had trained as a scientist, in his case as a physicist under Max Planck, from 1900 to 1904. The twenty-odd members of the circle that Schlick put together included Otto Neurath from Vienna, a remarkable Jewish polymath; Rudolf Carnap, a mathematician who had been a pupil of Gottlob Frege at Jena; Philipp Frank, another physicist; Heinz Hartmann, a psychoanalyst; Kurt Gödel, the mathematician we have just met; and at times Karl Popper, who became an influential philosopher after World War II. Schlick’s original label for the kind of philosophy that evolved in Vienna in the 1920s was Konsequenter Empirismus, or consistent empiricism. However, after he visited America in 1929 and again in 1931–32, the term “logical positivism” emerged—and stuck.

  The logical positivists made a spirited attack on metaphysics, against any suggestion that “there might be a world beyond the ordinary world of science and common sense, the world revealed to us by our senses.” For them, any statement that wasn’t empirically testable—verifiable, or a statement in logic or mathematics—was nonsensical. And so vast areas of theology, aesthetics, and politics were dismissed. There was more to it than this, of course. As the British philosopher A. J. Ayer, himself an observer of the circle for a short time (one of only two outsiders ever allowed, the other being W. V. O. Quine), described it, they were also against “what we might call the German past,” the Romantic and to them rather woolly thinking of Hegel and Nietzsche (though not Marx). 17 Otto Neurath would hum “metaphysics” every time the circle strayed from the logical positivist path.18 The American philosopher Sidney Hook, who also traveled in Germany at the time, confirmed the split, saying that the more traditional German philosophers were hostile to science and saw it as their duty “to advance the cause of religion, morality, freedom of the will, the Volk and the organic nation state.” Ayer observed that there were more philosophical books published in Germany than in all other places put together.19 The aim of the circle was to clarify philosophy, using techniques of logic and science.20

  THINKING WITH THE BLOOD

  Much opposed to the Vienna Circle was a man ill at ease with the whole of Weimar culture, with modernity in general and Berlin in particular. Martin Heidegger was arguably the most influential and certainly the most controversial philosopher of the twentieth century. Born in southern Germany in 1889, he studied under Edmund Husserl before becoming himself a professional teacher of philosophy. His deliberate provincialism, his traditional mode of dress—knickerbockers—and his hatred of city life all confirmed his philosophy for his impressionable students. In 1927, at the age of thirty-eight, he published his most important book, Sein und Zeit (Being and Time). Despite the fame of Jean-Paul Sartre in the 1940s and 1950s, Heidegger was—besides being earlier—a more profound existentialist.

  Being and Time is an impenetrable book, “barely decipherable,” in the words of one critic. Yet it became immensely popular.21 For Heidegger the central fact of life is man’s existence in the world, and we can only confront this central fact by describing it as exactly as possible. Western science and philosophy have all developed in the last three or four centuries so that “the primary business of Western man has been the conquest of nature.” Heidegger saw science and technology as an expression of the will, a reflection of this determination to control nature. He thought, however, that there was a different side to man, which he aimed to describe better than anyone else and which, he said, is revealed above all in poetry. The central aspect of a poem, said Heidegger, was that “it eludes the demands of our will…The poet cannot will to write a poem, it just comes.” This links him directly with Rilke. Furthermore, the same argument applies to read
ers: they must allow the poem to work its magic on them. This is a central factor in Heidegger’s ideas—the split between the will and those aspects of life, the interior life, that are beyond, outside, the will, where the appropriate way to understanding is not so much thinking as submission. This sounds not unlike Eastern philosophies, and Heidegger certainly believed that the Western approach needed skeptical scrutiny (he had a famous exchange with a Buddhist monk), that science was becoming intent on mastery rather than understanding. He argued—as the philosopher William Barren has said, summing up Heidegger—that there may come a time “when we should stop asserting ourselves and just submit, let be.”22