Maverick Genius

by Phillip F. Schewe

  Freeman Dyson did not go to Japan because his services weren’t needed. His killing days were over.

  2. Life Is a Blur

  Dyson as Mathematician

  (1945–1947)

  He was alive. They wouldn’t need to chisel Freeman Dyson’s name into that memorial wall at Winchester honoring the war dead. The avoidance of early death was a fact that would powerfully shape his worldview.

  After six years the war was over. From Winchester College 2,370 men had served and 269 had perished. Of the 98 admitted to the school with Dyson in 1936, 16 died in service to the king. The Second World War had been terrible but, for Britain at least, not as bad as the First World War.

  How had the war risen in the first place? Here is a Dysonian summary based on a conversation with a man who had lived in Germany in the turbulent prewar years. This man implicated the efficiency of the German education system:

  His argument was this. The very processes of mass education, practiced in the integrated industrial communities of our time, could and did produce the soil in which these monstrous weeds of hysteria and hate could suddenly appear and grow beyond control. We made our people literate without teaching them to think. We gave them technical skills without any controlling judgment. We stimulated their ardor and energy without any commensurate ethical or emotional discipline. We thus made them into the easy victims of any plausible political theory.1

  These are the words not of Freeman Dyson but those of his father, George Dyson, in a memoir written years after the war. The father, like the son, was to have a varied career. Besides building grenades, George Dyson was a conductor of orchestras, a teacher at numerous schools, and a composer, mostly of choral music. His thick Yorkshire accent did not prevent him from hosting a radio show about music. In 1937 he became director of the Royal College of Music, one of Britain’s leading conservatories. Despite pressure to close up during the Blitz, he kept the college open. In that way he provided badly needed jobs for musicians and helped give London a musical life during its years of greatest trial. In 1941 he was knighted by King George VI, who had been a musical pupil of his many years before.2 (This is the same king depicted in the movie The King’s Speech.)

  The war was over and life had to begin again. Sir George Dyson’s recommendation for keeping such a war from happening again was to inculcate a “controlling judgment” among citizens. “Honest knowledge and creative arts: these should be the goals of education.” Three types of people, he believed, helped to keep chaos at bay: saints, who appeal to civic virtue; prophets, including scientists and philosophers, who “fearlessly proclaim truth”; and artists, who can imaginatively offer “an intuition of order and proportion.”3 All three of these idealized human callings would play a part in the life of Sir George’s son.

  THE GIFT OF MATHEMATICS

  The war was over. Reorganizing society and withdrawing armies was the task of politicians and generals. For millions of ordinary people, the survivors, the main thing was to get on with making a living. You were supposed to find a job, reunite with family members, and secure a home. For many this wasn’t easy. Rationing continued, jobs were scarce, and for some people nightmares continued to plague their thoughts.

  When we see him again Freeman Dyson is in London living with his parents near the Royal College of Music, around the corner from the Royal Albert Hall. His father had many musical duties and his mother was involved with various charitable causes. And what about Freeman? What was his career supposed to be?

  Freedom from war meant that you could worry about things other than the close spacing of bombers in the sky. You could worry about the close spacing of electrons inside atoms. During his days at Bomber Command, Dyson had read a book that set his mind on fire. He was impressionable in that way: books, especially those filled with equations, could occupy him and motivate him. In 1938 it had been Piaggio’s book on differential calculus. Now it was Walter Heitler’s volume on quantum reality. It helped get Dyson through the last months of the war and was now nourishing him in the first months of peace. The material in this book was still largely mathematics, but with a difference. The numbers and symbols on the page stood not for themselves but were instead associated with parcels of energy and particles.

  Quantum science was now Dyson’s preoccupation even if not yet an occupation. He no longer worked for the air force but he did have another year of national service to perform. Fortunately for him he was assigned to an easy teaching job at Imperial College. His nominal supervisor had nothing for him to teach, so Dyson was free to do as he liked. He often went over to Birbeck College, a short Underground ride away across London. There he befriended a professor, Harold Davenport. Not only did Davenport invite Dyson into the circle of Birbeck mathematicians, but he even served as a sort of unofficial advisor to the young man.

  Davenport sustained Dyson’s appetite for mathematics by feeding him tough problems to solve. One of these assignments would be a test case. Siegel’s conjecture was a tricky algebraic proposition that had resisted many attempts at rigorous proof. Dyson fatefully resolved that if he succeeded in proving the conjecture he would stick with pure mathematics. If he failed he would intensify his pursuit of quantum mathematics—in effect, he would become a physicist.

  He labored for three months and was able to tighten the boundaries on the conjecture. But he did not achieve a full proof; that honor fell to another man a decade later.4 Did this settle the matter? Not exactly. You don’t just announce you are going to be a physicist. You have to do research. Where do you work?

  Dyson decided to try for a fellowship at Cambridge University. And for this, mathematics would still be his passport to advancement. Davenport supervised Dyson in writing the paper that would serve as his audition piece at Cambridge. The work, in typical Dyson fashion, was an audacious bringing together of elements from several disciplines.

  One conjecture had nudged him toward physics and another, Minkowski’s conjecture, would now get him into Cambridge. In his cover letter to the university, Dyson wasn’t exactly modest in staking his claim:

  Hitherto, analysis, geometry, abstract algebra, and almost every branch of mathematics, have been brought into the service of the theory of numbers, but topology has retained its independence. It is therefore the achievement of my paper which I value most highly, to have successfully used in one branch of mathematics ideas belonging to another branch apparently so remote from it.5

  Cambridge was impressed and Dyson won his fellowship.6

  A TENSION IN SPACE

  He’d been accepted into Cambridge for his mathematical brilliance, but he came to study quantum science. What was this body of thought—part abstruse mathematics, part hard-edged predictions—that he found so irresistible?

  In the past, most big turnovers in scientific thinking, such as Copernicus’s argument that the planets go around the sun and not the Earth or Charles Darwin’s observations about the evolution and heritage of living things, were accompanied by wide skepticism and even hostility. Quantum mechanics, the name for the all-encompassing theory of the microworld, was no exception. It had successfully explained many facts—one mark of good science—but had also prompted troubling philosophical questions. Troubling and wonderful at the same time. Because this subject is going to occupy young Mr. Dyson’s attention for years to come, we’re going to peek into this strange Alice-in-Wonderland realm to have a look around.

  The trouble and wonder began in the year 1900 when scientists were puzzled by the rainbow of light emitted by objects when they were heated. The German scientist Max Planck successfully explained the puzzle by introducing an idea so strange that even he didn’t believe it. His hypothesis was that energy was not a continuous thing coming in any and all amounts, but instead was parceled out in bundles, which he called quanta. Fortunately, energy quanta were so small that one would ordinarily never notice that the universe was chunky. The world appeared reassuringly continuous at the human level.

  But quantum
energy wasn’t the end of it. Weirder hints of quantum reality started to show themselves. Only twenty-five years after Planck’s quantum hypothesis, the young German physicist Werner Heisenberg argued that the very notion of measurement was problematic. The more carefully you measured the position of an object, the less you could know about its velocity, and vice versa. This proposition became known at the Heisenberg uncertainty principle.

  Uncertainty as a principle? Not only did energy come in blocks, but also knowledge? Actually, “uncertainty” in this case is not something to do with human psychology or with the fallibility of our instruments. Instead, uncertainty arises from the fact that the particle never had a single velocity or position to begin with.7 It’s as if scientific measurement were a form of photography and the new quantum science was saying that no matter how you fiddled with your camera’s shutter speed or focus, all the photos you took will be just slightly blurred. Freeman Dyson was giving up the stately solidity of number theory in order to embrace enforced uncertainty.

  Coming out of world war, there were plenty of things for people to be unsure about. And here was a new theory—indeed, its proponents were confident that it was the theory of reality—that seemed to say that a sure sense of material existence was problematic. Was it any wonder that many scientists, even some physicists, were doubtful about the theory’s rightness?

  Freeman Dyson didn’t seem to have any doubts. He took to quantum theory with relish. If the quantum books said that a particle such as an electron was usefully described not as a hard object located at a definite place but rather as a kind of spread-out cloud, then that was fine with him. Instead of the firm knowledge of a particle that Isaac Newton’s laws provided, the new quantum laws were expressed in terms of probability and uncertainty.

  If you like having a sure sense of your reality, if you like your photographs to be sharp, then you’re not going to like what came next. The implication of Heisenberg’s proposals was that an electron does not actually exist anywhere particular until the moment you detect it with some apparatus. Only then does the electron cease being a nebulous, extended cloud of maybe and become a definite thing here. This bafflement as to the particle’s existence is known as the principle of indeterminacy. A thing is nowhere in particular until we make a measurement. Then it’s somewhere.

  At the human level we’re used to some forms of uncertainty. When it comes to choosing a career or a spouse, or remaining in good health, chance seems to play an uncomfortably large role. We expect this. It comes as a surprise, though, that such indeterminacy should also be at the heart of physics, the most exact of sciences.

  The blurrings of existence suggested by quantum science—uncertainty and indeterminacy—sound retrograde since they apparently revoke much of the steadfast knowledge of the world seemingly guaranteed by Newton’s mighty worldview of two centuries before. Dyson didn’t find the blurrings disturbing. For him they were mathematically beautiful. If this was the true nature of the world, then so be it.

  Dyson was glad to be out of London. At last in Cambridge he had a physics mentor, an instructor named Nicholas Kemmer. Kemmer had worked on the atomic bomb during the war and was the one who had proposed the names for those two new heavy elements, plutonium and neptunium, that figured so prominently in nuclear weaponry. Now, as if Kemmer were swearing him into some secret society as an apprentice, Dyson received the last of the great inspirational books that would propel him into physics. The author of this book was Gregor Wentzel and the topic was quantum field theory. Kemmer’s copy of Wentzel, in German, was one of the few in Britain and was, in Dyson’s words, a “treasure without price.”8

  Freeman Dyson has always liked drawing analogies, relating things to other things. That’s what quantum field theory does. It is a vast mathematical accounting scheme for describing not one electron but all electrons. Indeed, it says that all electrons are just manifestations of one electron entity, a universal electron field. Recall that as a teenager, amid the fatalistic lead-up to world war, Dyson had dreamed up Cosmic Unity, the idea that all people were aspects of a single human existence.

  Well, quantum field theory does for electrons and light what Dyson had hoped to do with people. The big difference, of course, is that humans can’t be reduced to equations. The idea of fields is, by contrast, another of those many intellectual efforts to describe reality in terms of numbers, arrows, unseen forces, and evolving states of being. The concept dates back to the middle of the nineteenth century, when the English scientist Michael Faraday tried to explain how magnetic and electric forces projected themselves invisibly through otherwise empty space. Why, for example, should the south end of one magnet attract the north end of a second magnet without the magnets touching each other? Faraday argued that space wasn’t empty. It was filled with an unseen but real, forcible agency, a thing that was present at every point in the surrounding area, exercising an influence over anything else that was in the vicinity. Even if there were no such object to feel the force, Faraday argued, the force field would still be on duty. It is a sort of tension in space.

  The electric, magnetic, and gravitational fields, as understood in the nineteenth century, took on a continuously variable range of strengths and possessed a definite value at each location in space and time. These fields retained the decidedness that characterized nineteenth-century science. Consequently, they are referred to as classical fields. By contrast, quantum fields designate not so much the presence of a thing as the likelihood of the presence of a thing (an electron, say, or a bit of light) at that point in space.

  Freeman Dyson found field theory satisfying. It provided a mathematical framework so consistent that it was practically a kind of philosophy—not just a body of scientific propositions. The main thrust of field theory was to reformulate the nature of existence just as radically as Plato did, two and a half millennia before, when he said that the things we see—a chair, an apple—are not “real.” The real chair, Plato argued, was elsewhere, an abstraction, in heaven. All the mundane chairs we see in normal life are but inferior copies, earthly versions, of the ideal chair.

  To illustrate his point Plato introduced a famous analogy. Suppose, he said, that you huddle in a dark cave where the only light comes from a fire behind you. By the light of this fire you see shadows of things behind you on the wall in front of you. What you see are the shadows of a chair, not a “real” chair. We are fooled by our experience, by our limited ability to “see,” into believing we are encountering real things when in fact we are seeing mere shadows.

  Quantum field theory says that there is a universal electron field—a sort of ideal electronness—from which we get, in the act of measurement, a particular electron at that place at that time. Before we measure that electron, only the wavelike field exists. In a sense the electron we observe is a kind of coagulation of the electron field at that point in space, and only comes into being by our making a measurement. The same is true for light. A parcel of light, a photon, is no more than the precipitation of the larger electromagnetic field in a particular place during an observation, such as the triggering of a light meter or a twinkling we experience in the retina of our eye.

  Modern quantum field theory is more egalitarian than Plato’s theory of existence. We don’t say that the field is better or more ideal than the particle. Electrons or photons are just as real as the electron field or the electromagnetic field. A raindrop and the cloud of water vapor from which it precipitates are both made of water. They’re equally “real.”

  WITTGENSTEIN IN A BAD MOOD

  Dyson’s two best friends at Cambridge during his fellowship year were physicists, Hermann Bondi and Thomas Gold. Bondi became famous later as an astronomer and opponent of the big bang theory of cosmology. He was also a longtime scientific advisor to the British government, just as Dyson would later be an advisor to the U.S. government. Gold would become another brilliant scientist who courted controversy. He too dissented from the big bang theory but was more famous f
or advancing the theory that petroleum is not made from biological material compressed over millions of years. Dyson admired scientists who swam upstream of prevalent thinking.

  Cambridge was intellectually rich. We’ve already met the mathematician G. H. Hardy and the quantum physicist Paul Dirac. Among the many other eminent thinkers and scholars was literary scholar F. R. Leavis, who was just then finishing his book The Great Tradition, about the English novel. Another was William L. Bragg, in effect Dyson’s boss at the Cavendish Laboratory. Bragg, at the age of twenty-five, had been the youngest person ever to win a Nobel Prize. He and his father had pioneered the use of X-rays to form images of materials. (A few years after Dyson’s time at Cambridge X-ray crystallography would reveal the structure of DNA molecules.)

  Dyson’s interests were wide, but at this moment in his life there was a need to focus on a single topic—his chosen subject of field theory. He loved literature but there wouldn’t have been time to see Leavis. Dyson, as an undergraduate, had studied with Hardy and Dirac. Hardy represented pure mathematics, which Dyson was laying aside. Dirac represented field theory, but Dyson had found Dirac hard to understand. The use of X-ray beams to understand biological molecules, an important occupation of Bragg and his lab, would be of intense interest to Dyson—but not for another forty years.

  So a lot of Dyson’s study, as it would be during much of his life, was solitary. Actually there was a scholar at hand, a man who might have been of interest to Dyson. This man was perhaps the most famous professor at Cambridge, and he lived just down the hall from Dyson in his residence hall at Trinity College.

  Like Dyson, philosopher Ludwig Wittgenstein pondered propositions about reality. Both men wondered about how our perceptions of the world are blurred. Wittgenstein wrote about how many arguments in philosophy foundered upon imprecision in our use of language, while Dyson was learning about how quantum fields encapsulated our imperfect knowledge of electrons.