My Life as a Quant (7 page)

At Columbia and far beyond, T. D. was renowned and celebrated. At the weekly research seminars I attended on the eighth floor of Pupin, every speaker felt compelled to focus on him; as they spoke, their eyes fixated only on him, and he let no statement he did not fully agree with pass him by. No matter who lectured at the seminar, T. D. concentrated intensely on their argument, and interrupted at the first instant something was not satisfactory. At times he broke in on the initial sentence of the talk, refusing to let a speaker proceed until the point was clarified. Sometimes clarification never came; I once witnessed the humiliation of a visiting postdoc who was forced to defend the first sentence he uttered for the entire hour and a half allowed for his seminar. No one dared restrain T. D.

With his Moses-by-Michelangelo persona, beams of light emerging from his forehead, T. D. radiated an intense purity. At first I imagined that his rigorous questioning was the by product of a pure search for knowledge and truth. Later I began to detect a latent glee with which he savaged the imperfections in other people's talks. He enjoyed disorienting them. The only person I ever saw shake loose of his dogged grasp was the late Bram Pais, a small but feisty Dutch-born professor at Rockefeller University, who was able to half-playfully, half-ironically kid T. D. into loosening his jaws.

Brilliance seemed paramount in the Columbia physics department. T. D. was willing to supervise only the stellar
wunderkinder
who often went on to become inordinately young Columbia physics professors. The department developed an incestuous air; the pressure of his presence on his students-turned-faculty, like sons in their father's house, must have been fierce. Over time they seemed to gravitate towards research problems a little removed from the mainstream, as though searching for clear air to breathe. Unlike Rabi or Schwinger, who took on many more students and generated schools of disciples who propagated out into the world, T.D. never gave birth to anyone of his caliber.

Over time I noticed a darker side to Lee and Yang's genius. At an American Physical Society meeting I attended in the late 1960s, I observed that although they were both on the same panel, they avoided acknowledging each other's presence. In class at Columbia, I noticed that T. D.'s recounting of the insights central to their jointly published discoveries seemed to focus on his own feats. Finally, someone told me what most people in the field knew, that Lee and Yang had stopped working together several years earlier, and now no longer spoke to each other. Years later, after I left physics, I saw a copy of an angry reminiscence that T. D. had circulated in response to a published reminiscence of Yang's. It contained his vengeful version of how he and Yang had argued and then separated, and described how Yang had wept in his office.

I have no idea on whose side justice lay. I focus on T. D. here only because he was most visible to me, because he had made such enviable discoveries, and because he had such a powerful influence on the atmosphere we inhaled in Pupin Hall. It was disappointing to learn that even the Nobel Prize and almost eternal fame were not enough to overcome vanity and competition.

History takes strange turns. To Columbia students in the 1960s, Lee seemed to have the inside track in what we foolishly thought of as his race with Yang; I say “foolishly” because both of them had done outstanding work we could never realistically hope to emulate. Then in the 1970s, Yang's reputation accelerated. Two decades earlier, in what is now a classic paper, he had observed that Maxwell's theory of electromagnetism was the consequence of a subtle but powerful symmetry called
local gauge invariance
. Going out on a limb, Yang extended this symmetry to the strong and weak forces, too. The idea lay fallow for a decade or more. Then, suddenly, it provided the foundation for both the Glashow-Weinberg-Salam unified theory of weak and electromagnetic interactions and Gell-Mann's quantum chromodynamics theory of strong forces. Recently, some practicing physicists with an interest in finance have even begun to apply the same principle to the “trading force” between market participants that determines financial values. On this matter the jury has not even been assembled.

For current physics students, Lee and Yang are a part of history. For those of us who witnessed them, it was hard to resist the unfair urge to rank. The truth is that any one of us would be happy to have written just one the several remarkable papers they authored or coauthored. Yet when fellow Columbia physics students from those days meet up, they still argue about whether Lee or Yang was a better physicist, discussing the ancient epic feats of bygone heroes the way that the animals in the final chapter of
The Wind in the Willows
reminisce about the fabled exploits of Mr. Toad and his friends.

I worked studiously throughout that first American academic year of 1966–67 and then, after a short trip home to South Africa, began my preparations for the September PhD qualifying exams.

The quals were extremely broad. They aimed to test one's general understanding of all of physics—classical mechanics, electromagnetic theory, optics, thermodynamics, solid-state, atomic and nuclear physics, and quantum mechanics—and probed your ability to explain all sorts of observed phenomena. One question, set by the constantly inventive Friedberg, described the denizens of a planet in a distant galaxy who recorded the risings, settings, and eclipses of their several suns and moons, and then demanded that you deduce their orbits from Kepler's seventeenth-century laws of planetary motion. For a brief but heady period after I finished studying, I felt that I had a good grasp of the whole of physics and would be able to come up with a reasoned answer to any question about the universe tossed at me.

I also took the theory section of the exam, in which an essay question asked for a description of some independent theoretical work. I wrote about the unified field theories of electromagnetism and gravitation that I had studied for my senior thesis two years earlier in Cape Town. I had been particularly attracted to a paper by Theodor Kaluza and Oskar Klein, two European physicists of the 1920s. Their paper had postulated that the universe we lived in was five- rather than four-dimensional, but that the extent of the fifth dimension was so small that we were unaware of it. They had then shown that if Einstein's general theory of relativity held in this larger five-dimensional world, with one dimension unobserved, we would experience the theory's forces as those of ordinary (four-dimensional) electromagnetic theory and gravitation. It was a platonically beautiful theory that seemed quaintly irrelevant to the pragmatic particle-hunting theorists and experimentalists at Columbia in the 1960s, but its day was to come again later in the 1980s and 1990s when string theories of particles and their interactions became fashionable.

I passed my qualifying exams easily and well enough to be admitted to the privileged class of people who were “allowed to do theoretical physics” at Columbia. But there was a caveat—I was required to complete two extra years of coursework before beginning my research. I was in for a long haul.

Although it was premature, I soon began to strategize about seeking a PhD advisor who would take me on as a student. I quickly but regretfully discarded any idea of working for T. D. Even the thought of approaching him was too daunting; he accepted only one exceptional student every few years.

Then I hit on the idea of working for Gerald Feinberg, the earliest of T. D.'s
wunderkinder
. Feinberg was a tall, skinny, stiff-looking man with a flattop haircut that always reminded me of someone I had once seen in an
Archie
comic book. Every day he wore a very small conservative bow tie and a belt whose gold buckle proclaimed “GF.” The whole effect was very Fifties.

Feinberg was renowned as one of the earliest people to propose that the muon particle, to all initial appearances simply a sort of heavy electron, carried a special sort of quantum-mechanical flavor, a sort of “mu-ness” that differentiated it from the electron. He had attended the Bronx High School of Science, where he had been a classmate and friend of both Glashow and Weinberg, the physicists who later won the Nobel Prize for their unification of weak and electromagnetic interactions. Perhaps in order to avoid competing on T. D.'s turf, he had drifted out of the center field of particle physics and was then developing his own esoteric theories of hypothetical faster-than-light particles that he named
tachyons
. Physicists usually conjecture the existence of new particles in order to make a flawed or incomplete theory consistent, but Feinberg seemed to have had no really good reason for suggesting the existence of tachyons. Gell-Mann had once wittily suggested that Nature operated on the Totalitarian Principle that states, “Everything not forbidden is compulsory.” So, perhaps, Feinberg's logic wasn't as frivolous as it seemed. In any event, it was a risky wager; if tachyons were found it would be staggering, but if they were not, nothing would change and no one would care. Anyone can speculate.

I wanted to be Feinberg's student, but I didn't know how to go about it. Since it was premature for formal arrangements and since I was naturally reticent and shy, I simply began to greet him very politely whenever our paths crossed.

Graduate school was a small community. In corridors and elevators and on campus, I was soon running into Feinberg several times a day, always giving him a polite hello and a nice smile. He would reciprocate similarly with a sort of nervous curling of the lips. As time passed, this limbo of flirtatious foreplay continued unabated. I could never find the courage to broach the question of being his student; I suppose I must have hoped it would just happen wordlessly. Every time I saw him I smiled; every time I smiled he bared his lips back at me with greater awkwardness. Our facial manipulations bore increasingly less resemblance to anything like a real smile; each of our reciprocated gestures was a caricature, a Greek theatrical mask signaling friendliness. One day, on about the fifth intersection of our paths on that particular day, I could stand it no longer. I saw him heading towards me down one of the long dark, old-fashioned, Pupin corridors, and immediately turned towards the nearest stairwell and went up one floor to avoid him. Having succeeded at this once, I was compelled to do it repeatedly. Soon I was moving upstairs or downstairs to another floor as soon as I saw him approaching, like the protagonist in some ghastly version of the video game
Lode Runner
.

My courtship of Feinberg, now badly out of control, ended abruptly one discomforting morning when we both entered the same elevator and rode up eight floors without looking at each other, pretending to be absorbed in reading the elevator inspection certificate. The end was a great relief.

I watched Feinberg from a distance afterwards. At the weekly coffee hour in Pupin, I noticed his vaguely Strangelovian bent for carrying logic to extremes, a weakness I later came to associate with many graduates of the University of Chicago business school. He had created an organization called the Prometheus Project, which aimed to plan for humanity's future. I observed long discussions between Feinberg and Milton Friedman's son David, then a physics postdoc at Columbia, about the application of hard-nosed rationality to society. I once heard Feinberg suggest that many of Manhattan's 1970s social problems could be solved by forbidding anyone who earned less than, say, $10,000 per year to live there. It had not occurred to him, apparently, that this excluded many of the people who worked at the university. Several years later we heard that he intended to be cryogenically frozen when he died, in anticipation of being reheated and resuscitated at a later time when whatever would cause his death would be curable. Sadly, he died of cancer in 1992. I recently found hundreds of Internet references to both Feinberg and the New York Cryonics Society, lamenting the fact that despite his advocacy of the Society, he ultimately left no instructions for his own bodily preservation.

Late in 1968, still searching for a thesis advisor, I ran into one last temptation to avoid becoming a particle theorist. My American cousin in Manhattan introduced me to Robert Herman, his old City College student friend from the 1930s. Herman, a physicist, had abandoned academia for family reasons and was now working at General Motors, analyzing vehicular traffic flow. Academic particle physicists looked down on this kind of applied physics as pedestrian work, so to speak, but Herman had done outstanding fundamental research before that. In the 1940s he had coauthored the first paper to suggest that the Big Bang that created our universe would have filled all of space with microwave radiation. Arno Penzias and Robert Wilson at Bell Laboratories later fortuitously detected this background radiation and won the Nobel Prize. Then in the 1950s, Herman and Robert Hofstadter, another City College friend of my cousin's, became the first physicists to probe the internal structure of the proton by shooting fast electrons at it and then watching them bounce off. If the proton were a hard, small object—like a miniature billiard ball—one would expect to see the electron occasionally recoil at a very large angle to the line of fire; if, however, the proton were spongy, there would be very few sharp collisions. Surprisingly, Hofstadter and Herman observed very few dramatic recoils; they concluded that the proton was a cotton-candy sphere with a soft interior rather than the small, hard, elementary object everyone had imagined. Hofstadter alone won the Nobel Prize for this work. My cousin claimed that Herman was deprived of his share of the Prize because of the selection committee's prejudice against scientists outside academia.

When we spoke, Herman suggested that I work in applied physics and sent me some papers on traffic flow he had written, but I was still a stranger to compromise and I declined. Coincidentally, though, my future PhD thesis would turn out to be closely related to the Hofstadter-Herman electron-proton scattering experiment.