by Peter Watson
Einstein was born in Ulm, between Stuttgart and Munich, on March 14, 1879.25 Hermann, his father, was an electrical engineer. Unhappy at school, Albert hated the autocratic atmosphere just as he hated the crude nationalism and vicious anti-Semitism. He argued incessantly with his fellow pupils and teachers, to the point where he was expelled. When he was sixteen, he moved with his parents to Milan, attended the University of Zurich at nineteen, and later found a job as a patent officer in Bern. Half educated and half-in and half-out of academic life, he began in 1901 to publish scientific papers.26
The first were unremarkable. 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—Ludwig Boltzmann’s methods—and this stood him in good stead. More important still perhaps, the fact that he was outside the mainstream of science may have helped his originality, which flourished suddenly in 1905. Einstein’s three great papers were published in March, on quantum theory, in May, on Brownian motion, and in June, on the special theory of relativity.27 Though Planck’s original paper had caused little stir when it was read to the Berlin Physics Society in December 1900, other scientists soon realized 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. But at the same time, for years experiments had shown that light behaved as a wave.28
In the first part of his paper Einstein, showing early the openness of mind for which physics would become celebrated, 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 realized that Einstein’s insight fit the available facts. In time the wave-particle duality, as it became known, formed the basis of quantum mechanics in the 1920s.*
Two months after this paper, Einstein published his second great work, on Brownian motion. When suspended in water and inspected under the microscope, small grains of pollen, no more than a hundredth of a millimeter in size, jerk or zigzag backward and forward. Einstein’s idea was that this “dance” was owing to the pollen being bombarded by molecules of water hitting them at random. Here his knowledge of statistics paid off, for his complex calculations were borne out by experiment. This is generally regarded as the first proof that molecules exist.
It was Einstein’s third paper, on the special theory of relativity, that would make him famous.29 It was this theory that 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—yet fundamental—circumstances in the universe, where common sense breaks down. But a thought experiment might help. 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 the carriage, is switched on. Now, if you assume that 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, the light beam has traveled slightly less than half 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. Thus the time the light beam takes to reach the back of the carriage is different for the two observers. 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. His most famous prediction was that clocks would move more slowly when traveling at high speeds. This anti-commonsense notion was actually borne out by experiment many years later. Physics was transformed.30
THE SECRET OF CONTINUITY AND THE MEANING OF “BETWEEN”
In the late nineteenth century, Germany bred an extraordinary generation of “pure” mathematicians who were very concerned with ideas that, though extremely theoretical to begin with, would eventually prove fundamental and practical in equal measure.31 Together with Planck, but operating from a very different starting point, they conceived the basis of what would, in the future, become the digital revolution.
As we have seen, Carl Friedrich Gauss, Bernhard Riemann, and Felix Klein had helped established Göttingen as the world capital of mathematics, though other German university towns—Heidelberg, Halle, and Jena—were close seconds. In these small, remote, and self-contained worlds, away from the teeming metropolises, mathematicians’ minds were free and cleared to explore basic issues. And for many, number theory was the ultimate abstraction.
Richard Dedekind, born in 1831, was one of Gauss’s last students at Göttingen and a pallbearer at his funeral.32 Dedekind was a dedicated academic who never married and spent much of his time editing for publication one or two contributions by Gauss and the bulk of the papers by his other great teacher, Peter Lejeune Dirichlet, on differentiable functions and trigonometric series (Dirichlet, he liked to say, had made “a new man” of him).33 This exercise had given Dedekind some ideas of his own, and though it was no more than a pamphlet when it was published in 1872, Continuity and Irrational Numbers soon became a classic, the best description to date of what mathematicians call the “numerical continuum” or the secret of continuity.
The “secret” of continuity is one of those issues that troubles mathematicians if no one else (though of course it was theoretically linked to quantum theory, which advocated that energy was not continuously emitted, as Newton had said). The problem of continuity becomes apparent once you try to grasp what it means to be “between.” As early as the sixth century B.C., Pythagoras knew that fractions lay “between” whole numbers. Then irrational numbers quashed this thinking, their decimal representation just went on and on and on. The problem of “between” now had to be restated. If irrational numbers lay between whole numbers and rational fractions, how many numbers were there between, say, 0 and 1? More perplexing still, there seemed to be just as many numbers between 0 and 1 as there were between 1 and 1,000. How could that be?34
Dedekind’s solution was as simple as it was elegant. In mathematical terms, he wrote, “if one could choose one and only one number, a, which divided all the others in the interval into two classes, A and B, such that all numbers in A were less than a, all in B were greater than a, while a itself could be assigned to either class, then the interval was continuous by definition.” Dedekind had defined (the numerical meaning of) continuity by removing the concept of “between.”
The concept of “between” borders on the philosophical, and brings to mind such concepts as “before” and “beyond,” which had troubled Kant. This, in a sense, is what interested Dedekind’s colleague, Georg Cantor. Just as Dedekind had studied with Gauss, so Cantor had been a pupil of Karl Weierstrass in Berlin at least until 1866. Born in 1845 into a devout Lutheran family, Cantor was very interested in metaphysics and believed that when he made his major discovery—infinite cardinal numbers—they had been revealed to him by God.35 A manic-depressive, he ended his days in an asylum, but between 1872 and 1897 he created the theory of sets and the arithmetic of infinite numbers.36
The paper that started it was entitled “On the Consequences of a Theorem in the Theory of Trigonometric Series.” In this paper, with its jaw-breaking title, Cantor made the concept of “set” one of the most interesting terms in both mathematics and philosophy (he is generally regarded as the founder of set theory).37 But it was his next step that took mathematicians by surprise (though in truth it was also a surprise that no one had noticed this before). The series, 1, 2, 3…n, was an infinite set and so was 2, 4, 6…n. But it followed from this that some infinite sets were larger than others—there are more integers in the infinite series, 1, 2, 3…n than in 2, 4, 6…n. Nex
t came Cantor’s proof that the infinite number of points on a line segment is equal to the infinite number of points in a plane figure. “I see it, but I don’t believe it!” he wrote to Dedekind on June 29. It is as well to remember this sentence.
Not everyone thought that the revolution was anything of the kind. From Berlin, Cantor’s former professor, Leopold Kronecker, attacked the new ideas, as did Hermann von Helmholtz and even Friedrich Nietzsche, who agreed that numbers, though necessary, were “fiction.” By now both Gottlob Frege at Jena, upriver from Cantor at Halle, and the Italian Giuseppe Peano, were also grappling with the nature of number. Frege’s answer was less complicated than Peano’s (and Dedekind’s) but used a special notation he had himself devised.38
Born in 1848, Frege is now known for two fundamental works, the Begriffsschrift of 1879 and Die Grundlagen der Arithmetik (Foundations of Arithmetic) of 1884, in which his basic idea was that language described logic much as mathematics does and that by comparing them, the essential elements of logic would become clear. This was an approach that interested another of Weierstrass’s students, Edmund Husserl, of Halle, whose doctoral dissertation, Über den Begriff der Zahl (On the Concept of Number), was followed in 1891 with his ambitiously titled Philosophie der Arithmetik (Philosophy of Arithmetic). Having used Frege’s Foundations of Arithmetic in his own work, Husserl sent the Philosophy to Frege as a mark of respect.39 Instead of trying to define a set mathematically, Husserl asked how the mind forms generalities—to convert multiplications into units in the first place. In other words, it was a philosophical or epistemological problem before it was a mathematical one. And he gave a Kantian answer. The continuum of real numbers, Husserl said, could never be made present to consciousness. Continuity was like space or time, or infinity, a creation of our minds. This was too much for Frege, who dismissed Philosophy of Arithmetic as a “devastation.”40
The youngest of the second great generation of German mathematicians, David Hilbert (1862–1943), was in the Frege/Husserl mold in that he viewed mathematics philosophically. But he was also in the Cantor/ Dedekind mold, being equally interested in the mathematics of sets.
Born in Königsberg, East Prussia, now Kaliningrad, he attended the Collegium Friedrichianum, the school Kant had himself attended 140 years before. Hilbert was a professor at Königsberg until 1895, when Felix Klein lured him to Göttingen. There he became a mentor to many other subsequently famous mathematicians, including Hermann Weyl, Richard Courant, and John von Neumann. 41
Hilbert was interested in number and in the difference between intuition and logic. He thought that certain aspects of number (for example, order and some sets) were intuitive, and he wanted to define where logic took over from intuition. He became best known for his “exceptional” identification of twenty-three unsolved problems of mathematics, which he presented at the International Congress of Mathematicians in Paris in 1900, although these were, he said, just a sample of problems that remained to be discovered.42 Later he became interested in what he called “infinite dimensional Euclidean space,” later called a “Hilbert space,” and he worked with Einstein on the final form of General Relativity, the so-called Einstein-Hilbert action.
Physics and mathematics had, in a sense, a conceptual overlap, both being concerned with the nature of continuity and particularity. That concern would help produce dividends in the digital revolution—but decades in the future.
26.
Sensibility and Sensuality in Vienna
In early September 1887, Arthur Schnitzler—physician, writer, amateur pianist—was out for one of his regular strolls in Vienna (he was such a familiar figure, says Clive James, that he was “practically part of the Ringstrasse”), when he encountered an attractive young woman who called herself “Jeanette.” Socially they were poles apart. He was from the well-educated bourgeoisie, she was an embroiderer. Nonetheless, two days later she visited his rooms and they became lovers. Over the next months Schnitzler recorded in his diary every sexual encounter that took place. When the affair ended, acrimoniously, at the end of 1889, he was able to calculate that in the intervening two years they had made love 583 times. The exactitude was remarkable, but so was Schnitzler’s potency: he had been away from the city many times and on occasions, to keep up his tally, he and Jeanette had performed five times a night.1
This admixture of scientific certitude, bravado, experimentation, and sexual license (in a pre-Salvarsan world) illustrates as well as anything the miasma of ideas swirling around in Vienna at the close of the nineteenth century. And in 1900, among German-speaking cities, Vienna certainly took precedence. If one place could be said to represent the mentality of continental Europe as the twentieth century began, it was the capital of the Austro-Hungarian Empire.
THE ORIGINAL CAFÉ SOCIETY
The architecture of Vienna played a crucial role in determining the unique character of the city. The Ringstrasse, a circle of monumental buildings that included the university, the opera house, and the parliament building, had been erected in the second half of the nineteenth century around the central area of the old town, in effect enclosing the intellectual and cultural life of the city inside a relatively small and accessible area. There had emerged the city’s distinctive coffeehouses, an informal institution that helped make Vienna different from London, Paris, or Berlin.2 The marble-topped tables were just as much a platform for new ideas as the newspapers, academic journals, and books of the day. These cafés were reputed to have had their origins in the discovery of vast stocks of coffee in the camps abandoned by the Turks after their siege of Vienna in 1683. Whatever the truth of that, by 1900 Viennese cafés had evolved into informal clubs where the purchase of a small cup of coffee carried with it the right to remain there for the rest of the day and to have delivered, every half hour, a glass of water on a silver tray. Newspapers, magazines, billiard tables, and chess sets were provided free of charge, as were pen, ink, and (headed) writing paper. Regulars could have their mail sent to them at their favorite coffeehouse; at some establishments, such as the Café Griensteidl, large encyclopedias and other reference books were kept on hand for writers who worked at their tables.3
LEADERSHIP AS AN ART FORM
A group of bohemians who gathered at the Café Griensteidl was known as Jung Wien (Young Vienna). This group included Schnitzler; Hugo von Hofmannsthal; Theodor Herzl, a brilliant reporter, an essayist, and later a leader of the Zionist movement; Stefan Zweig, a writer; and their leader, the newspaper editor Hermann Bahr. His paper, Die Zeit, was the forum for many of these talents, as was Die Fackel (The Torch), edited no less brilliantly by Karl Kraus, more famous for his play Die letzten Tage der Menschheit (The Last Days of Mankind).4
The career of Arthur Schnitzler (1862–1931) shared a number of intriguing parallels with that of Freud. He too trained as a doctor and neurologist and studied neurasthenia. But Schnitzler turned away from medicine to literature, though his writings reflected many psychoanalytic concepts (he thought love affairs provided an education). His early work explored the emptiness of café society, but it was with the story “Lieutenant Gustl” (1901) and the novel Der Weg ins Freie (The Road into the Open; 1908) that Schnitzler really made his mark. “Lieutenant Gustl,” a sustained interior monologue, takes as its starting point an episode when a “vulgar civilian” dares to touch the lieutenant’s sword in the busy cloakroom of the opera. This gesture provokes in the lieutenant confused and involuntary “stream-of-consciousness ramblings” that in some ways prefigure Proust. In The Road into the Open, the dramatic structure of the book takes its power from an examination of the way the careers of several Jewish characters have been blocked or frustrated. Schnitzler indicts anti-Semitism, not simply for being wrong, but as the symbol of a new, illiberal culture brought about by a decadent aestheticism and by the arrival of mass society which, together with a parliament “[that] has become a mere theatre through which the masses are manipulated,” gives full rein to the instincts, and which in the novel over
whelms the “purposive, moral and scientific” culture represented by many of the Jewish characters. Schnitzler was a committed realist who thought, for example, that “the battle between imagination and fidelity” was “a fact of life.”5
Hugo von Hofmannsthal (1874–1929) went further. Born into an aristocratic family, his father introduced his son to the Café Griensteidl set when Hugo was quite young, so that the group around Bahr acted as a forcing house for the youth’s precocious talents. In the early part of his career, Hofmannsthal produced what has been described as “the most polished achievement in the history of German poetry,” but he was never totally comfortable with the aesthetic attitude and, noting the encroachment of science on the old aesthetic culture of Vienna, he wrote in 1905, “The nature of our epoch is multiplicity and indeterminacy. It can rest only on das Gleitende [the slipping, the sliding].” Could there be a better description about the way the Newtonian world was slipping after Boltzmann’s and Planck’s discoveries? “Everything fell into parts,” Hofmannsthal wrote, “the parts again into more parts, and nothing allowed itself to be embraced by concepts any more.”6 Like Schnitzler, Hofmannsthal was disturbed by political developments in the dual monarchy and in particular the growth of anti-Semitism. For him, this rise in irrationalism owed some of its force to science-induced changes in the understanding of reality; the new ideas were so disturbing as to promote a large-scale reactionary irrationalism. He therefore abandoned poetry at the grand age of twenty-six, feeling that the theater offered a better chance of meeting current challenges. Hofmannsthal came to believe that (in the Greek manner) theater could help to counteract political developments. His works, from the plays Fortunatus and His Sons (1900–01) and King Candaules (1903) to his librettos for Richard Strauss, are all about political leadership as an art form, the point of kings being to preserve order and control irrationality. Yet the irrational must be given an outlet, Hofmannsthal says, and his solution is “the ceremony of the whole,” a ritual form of politics in which no one feels excluded.7 His plays are attempts to create ceremonies of the whole, marrying individual psychology to group psychology in dramas that anticipate Freud’s theories. As he put it, the arts had become “the spiritual space of the nation.” Hofmannsthal always hoped that his writings about kings would help Vienna throw up a great leader, someone who would offer moral guidance and show the way ahead. The words he used were uncannily close to what eventually came to pass. What he hoped for was a “genius…marked with the stigma of the usurper,” “a true German and absolute man,” a “prophet,” “poet,” “teacher,” “seducer,” an “erotic dreamer.”8
