The Scientist as Rebel (21 page)

Manin’s book defies summary, because it already compresses into its small compass enough ideas to fill a dozen books of ordinary density. Each of its many topics is discussed without wastage of words. When I began trying to summarize it, I found myself willy-nilly selecting sentences and quoting them directly. The flavor of Manin’s thinking is conveyed better by quotation than by paraphrase. I abandoned the attempt to describe the book in detail. Instead, I devote the rest of this review to the pursuit of a single question suggested by Manin’s survey of contemporary science. Are we, or are we not, standing at the threshold of a new scientific revolution comparable with the historic revolutions of the past?

The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. Manin sees no causal connection between the two revolutions. He describes them as occurring independently: “Physicists were disturbed by the interrelation between thought and reality, while mathematicians were disturbed by the interrelation between thought and formulas. Both of these relations turned out to be more complicated than had previously been thought, and the models, self-portraits and self-images of the two disciplines have turned
out to be very dissimilar.” This lucid characterization emphasizes the differences between the Heisenberg and Gödel revolutions. But a study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. Seen in the perspective of history, the geographical and temporal propinquity of Heisenberg and Gödel no longer appears to be a coincidence.

The historical dimension of science is explored in another short and excellent book,
Weimar Culture, Causality, and Quantum Theory, 1918–1927: Adaptation by German Physicists and Mathematicians to a Hostile Intellectual Environment
, by Paul Forman.
²
Forman is a historian, more familiar with physics than with mathematics. His book overlaps hardly at all with Manin’s. To arrive at a balanced picture of our scientific heritage, the two books should be read together. I now turn my attention to Forman and come back to Manin later.

Forman begins with Felix Klein, sixty-nine years old and approaching the end of his long career as
grand seigneur
of German mathematics. It is June 1918, the last summer of World War I, and Klein is talking in Göttingen to an audience including leaders of German industry and of the Prussian government. He is addressing a formal session of the Göttingen Society for the Advancement of Applied Physics and Mathematics. He talks confidently of the coming victorious conclusion of the war, of the harmonious collaboration of German science with industry and the armed forces, and of the expected increase in support for mathematical education and research after the victory is won. Here in wartime Germany we see the first full flowering of the military-industrial complex in its modern style, soldiers and politicians sharing their dreams of glory with scientists and mathematicians. The Prussian minister of education responds to Klein with
a generous grant of money for the foundation of a Mathematical Institute in Göttingen. Less than five months later, the dreams of glory have collapsed, the German Empire is utterly defeated, the Mathematical Institute indefinitely postponed. In the new era of defeat and misery that begins in November 1918, the exact sciences are discredited together with the military-industrial complex that had sustained them. The Göttingen Mathematical Institute is ultimately built, after Klein’s death, not with German government funds but with American dollars supplied by the Rockefeller Foundation.

Forman uses Klein’s Göttingen speech to set the stage for a dramatic description of the intellectual crosscurrents of Weimar Germany. The dominant mood of the new era was doom and gloom. The theme song was
Untergang des Abendlandes, Decline of the West
, the title of the apocalyptic world history of Oswald Spengler. The first volume of Spengler’s prophetic work was published in Munich in July 1918, the month in which the tide of war on the western front finally turned against Germany. After the November collapse, the book took Germany by storm. It went through sixty editions in eight years. Everybody talked about it. Almost everybody read it. Forman demonstrates with ample documentation that mathematicians and physicists read it too. Even those who disagreed with Spengler were strongly influenced by his rhetoric. Spengler himself had been a student of science and mathematics before he became a historian. He had much to say about science. Not all of what he said was foolish. He said, among other things, that the decay of Western civilization must bring with it a collapse of the rigid structures of classical mathematics and physics. “Each culture has its own new possibilities of self-expression which arise, ripen, decay and never return. There is not one sculpture, one painting, one mathematics, one physics, but many, each in its deepest essence different from the other, each limited in duration and self-contained.” “Western European physics—let no-one deceive himself—has reached the limit of its possibilities. This is the origin of the
sudden and annihilating doubt that has arisen about things that even yesterday were the unchallenged foundation of physical theory, about the meaning of the energy principle, the concepts of mass, space, absolute time, and causal natural laws generally.” “Today, in the sunset of the scientific epoch, in the stage of victorious skepsis, the clouds dissolve and the quiet landscape of the morning reappears in all distinctness.… Weary after its striving, the Western science returns to its spiritual home.”

Two people who came early and strongly under the influence of Spengler’s philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. Both were writers with a deep feeling for the German language, and perhaps for that reason were easily seduced by Spengler’s literary brilliance. Both became convinced that mathematics and physics had reached a state of crisis that left no road open except radical revolution. Weyl had been, even before 1918, a proponent of the doctrine of intuitionism, which denied the validity of a large part of classical mathematics and attempted to place what was left upon a foundation of intuition rather than formal logic. After 1918 he extended his revolutionary rhetoric from mathematics to physics, solemnly proclaiming the breakdown of the established order in both disciplines. In 1922 Schrödinger joined him in calling for radical reconstruction of the laws of physics. Weyl and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics.

In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and
proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant. The victorious revolutionaries were not irrational dreamers but rational scientists. The physics of Heisenberg, once it was understood, turned out to be as mundane and practical as the physics of Newton. Chemists who never heard of Spengler could successfully use quantum mechanics to calculate molecular binding energies. And in mathematics, the discoveries of Gödel did not lead to a victory of intuitionism but rather to a general recognition that no single scheme of mathematical foundations has a unique claim to legitimacy. After the revolutions were over, the new physics and the new mathematics became less and less concerned with ideology. In the long run, the value systems of physics and mathematics emerged from the revolutions essentially unchanged. Spengler’s dream of a reborn, vitalistic, spiritualized science, “Western science returning to its spiritual home,” was forgotten. The practical achievements of Hilbert and Einstein outlasted the fashionable despair of Spengler.

Now, fifty years later, the wheel has come full circle. The physics of quantum devices and the mathematics of effective computability have become everyday tools for engineers and industrialists to exploit. The new physics and the new mathematics are as friendly to the military-industrial complex of modern America as the old physics and the old mathematics were to the military-industrial complex of Germany in the days of Felix Klein. And once again we hear voices preaching revolution, a return to holistic thinking, a spiritualization of science. “Physics of Consciousness” is a fashionable slogan today, like the
Lebensphilosophie
of the 1920s. Fritjof Capra steps tentatively into the shoes of Oswald Spengler. Capra’s
Tao of Physics
³
is selling, like
Spengler’s
Untergang
of old, in hundreds of thousands of copies. Are we heading toward a period of radical changes in science, comparable with the Heisenberg revolution of 1925 and the Gödel revolution of 1931? Who can tell? Forman’s historical analysis may illuminate the past, but it cannot predict the future.

Forman and Manin represent two contrasting styles in the historiography of science. Forman looks at science from the outside, Manin from the inside. Forman sees science responding to external social and political pressures; Manin sees science growing autonomously by the logical interplay of its own concepts. Forman takes his evidence from what scientists say, in speeches and writings directed toward the general public. Manin takes his evidence from what scientists do, as they exchange methods and ideas with one another. Forman is concerned with the rituals of science, Manin with the substance.

Looking back on the events of the 1920s with the benefit of hindsight, we can see clearly that Heisenberg and Gödel did not need Spengler to tell them what they had to do. It is true, as Forman demonstrates, that Spengler created a mood of revolutionary expectation in German-speaking Europe, and that the existence of this mood helps to explain why young people in Germany and Austria were better prepared than young people elsewhere to make revolutionary discoveries. But the discoveries of quantum mechanics and mathematical undecidability would have been made within a few years, either in German-speaking Europe or somewhere else, even if Spengler had never existed. The time was ripe for these discoveries, and the internal development of physics and mathematics made them inevitable. An external mood of revolutionary expectation is neither a necessary nor a sufficient condition for the occurrence of a scientific revolution. If we wish to assess realistically the prospects of scientific revolutions in the future, we should study science itself and not the philosophical or political ambience of science. We should leave Forman aside and go back to Manin.

The picture of present-day physics and mathematics that Manin presents to us is far removed from the intellectual turmoil of the 1920s. Manin’s picture is idyllic. He shows us physics and mathematics as two neighboring gardens, each growing luxuriantly with trees and flowers in great variety, while the busy physicists and mathematicians fly to and fro like bees carrying pollen for the cross-fertilization of one plant by another. In Manin’s gardens there is growth and decay, sunshine and showers, but no hint of gloom and doom. Looking to the future from Manin’s perspective, one sees no evidence of a coming cataclysm, no sign of that “craving for crisis” which was, according to Forman, the hallmark of a German academic in the 1920s. On the contrary, Manin’s picture of science promises us a long period of fruitful and multifarious growth, with plenty of surprises and sudden illuminations but no radical changes of objective. In Manin’s view, the present epoch is characterized by a growing willingness of physicists and mathematicians to learn from one another and to transfer tools and techniques from one branch of science to another. The increasing overlap between physics and mathematics provides opportunities for the continuing enrichment of both disciplines. The future of physics and mathematics lies in evolution rather than revolution. Manin sees Spengler’s “quiet landscape of the morning” not as an end but a beginning.

The concluding paragraph of Manin’s book gives us a glimpse of his vision of the future:

In the twenty-four years since this review was written, the development of mathematics and physics has continued as Manin predicted. The main area in which physicists and mathematicians are working together is string theory. Progress has been evolutionary rather than revolutionary. There is much talk of a radical revolution still to come, but no clear sign of its arrival.

EDWARD TELLER
’
S
Memoirs: A Twentieth-Century Journey in Science and Politics
¹
is a pleasure to read and is also a unique historical document. Teller is intensely interested in people. The story of his life is a portrait gallery of people he has known, each of them brought to life and portrayed as an individual, all of them swept along by the tides of war and revolution and political passion in which Teller’s life was lived. Teller observes and records the personal qualities of these people, their follies and their kindnesses and their often tragic fates, beginning with the friends of his childhood in Hungary eighty years ago and ending with the death of his wife, Mici, who loved and sustained him through more than seventy years of joys and sorrows.