My Life as a Quant (6 page)

The first year at Columbia consisted of four courses per semester followed by “the quals,” the general PhD qualifying examination one had to pass in order to be allowed to continue with the doctoral program. To be a theorist, you also had to pass a special theory section on the quals. Without this formal admittance, no advisor would take you on.

I knew little modern physics so that, even if I were to pass the quals and be admitted to the rarified world of theory, I would have to spend another two years taking a host of preparatory courses. If I had gone to graduate school in Cambridge, England, where there was less required coursework, I might have finished my PhD in three or four years. Now I would have to wait that long before even beginning research! I had taken one step forward, but now faced two disappointing steps back.

Given that I wanted to be a theorist, there was little choice. Without the proper education, it is impossible to do theoretical research. I half-envied my budding experimentalist friends who were able to contribute something useful as soon as they started their apprenticeship—they could build particle detectors, write computer programs, and analyze data. Despite their worm's eye view, they had something constructively rewarding to tackle. We theorists seemed to be dishearteningly useless and alone.

Years later, when I moved to Wall Street, I especially liked the ways in which one could be usefully busy in quantitative finance. There was always a program to write, a trading interface to design, a calculation to do. It was nice to be able to contribute without having to be extraordinary.

Meanwhile, as I settled down into New York in 1966, life gradually improved. Every morning I rose to WNEW AM's Klavan and Finch, who pretended to be the men in the traffic helicopter that WNEW did not possess; one of them read printed traffic reports over the rotor noise simulated by the other. I still meet people who recall their endless pitches for “Dennison's, a men's clothier, Route 22, Union, New Jersey, open 10 A.M. to 5 the next morning. Money talks, nobody walks!” The Route 22 I imagined as I heard this was some exotic Kerouac cross-country highway, with a touch of the tawdry charm of Nabokov's
Lolita
motels. In 1980, when I finally decided to leave physics, I found myself driving down the same Route 22 en route to my interview at Bell Laboratories in Murray Hill, New Jersey. It didn't totally disappoint.

I liked New York's Upper West Side, its almost Caribbean atmosphere and vibrant street life. Manhattan was a marvelous place in which to be lonely. You could walk all the way down Broadway from Columbia to Times Square, watching people, stopping for a solitary coffee at soon-to-be-extinct Automats or Hopperesque Chock-Full-of-Nuts diners, and never feel isolated. Hope lurked on every block. The Puerto Ricans around I. House sat on the steps of their brownstones until late on hot summer nights. My friend and fellow student Eté Szüts, a 1956 refugee from Hungary, taught me the ropes. After an evening of doing homework problems, we would walk down to 123rd Street and Broadway for a midnight slice of pizza made by a small dapper Italian man in a white apron and T-shirt who combed his elegant grey hair while he looked at himself admiringly in the mirror as his enormously fat wife observed him resentfully from a thin metal folding chair that somehow supported her. The jukebox, I remember, played “There's a Kind of Hush (All Over The World).”

Some aspects of life in New York took getting used to. I was surprised by the easy and familiar kidding around between whites, blacks, and Asians in I. House. Twenty-one years of seeing blacks regarded as the invisible backdrop to white life in South Africa had left its mark on me, which only then began to fade.

I was also struck by the discrepancy in styles of cursing. I had never actually heard the word “motherfucker” uttered until a few weeks after I arrived in Manhattan, when two ten-year-old boys imperturbably called each other just that on the 104 bus that ran up and down Broadway. Heard for the first time, it sounded shockingly literal.

Finally, I was impressed by the exceptional independence of American graduate students. At the University of Cape Town, textbooks were regarded as auxiliary material. We took careful lecture notes and studied them thoroughly, and that was usually enough. In my second week at Columbia, I was shocked to discover that one assigned homework problem was totally unrelated to any material covered in class. Thinking that the professor had erred, I walked down the I. House corridor to query Eté, who told me that the relevant material could be found in the last section of the second chapter of our textbook. I was momentarily dismayed at the notion that someone might set problems on topics that were never discussed in class. From then on, I focused as much on textbook reading as I did on note-taking.

At Columbia, the classes I liked best were taught by people who gave you a feel for what it was like to discover something new, as well as a sense of how it had been done.

In my first year, I took a course in advanced electromagnetic theory from Richard Friedberg, a dishevelled-looking
wunderkind
who, as an undergraduate, we heard, had cracked a famous unsolved problem in logic and number theory. The method he used to solve it is still called Friedberg numbering. Now a young professor, he was one of a stable of young whizkids who had studied under T. D. Lee and then joined the department as faculty.

Friedberg was unkempt, distracted, and pale. He often closed his eyes for long periods in class as he tried to concentrate. Eté delighted in telling me that Friedberg was a true genius. In keeping with his persona, he quickly put his own stamp on the course he taught. Instead of taking the standard didactic approach to electricity and magnetism, Friedberg plunged us into thrilling intellectual history. We were each told to buy a Dover reprint of the Dutch physicist Lorentz's early-twentieth-century classic
The Theory of Electrons
. The book, based on Lorentz's lectures at Columbia in 1906, was an account of his heroic pre-Einsteinian intellectual struggles to resolve the contradictions between the laws of Newton and the laws of Maxwell on which all of physics was then based.

Maxwell's late-nineteenth-century theory of electromagnetism described the propagation of light waves through a stationary material fluid, the ether, that supposedly filled all of space. Newton's seventeenth-century laws of mechanics described the motion of all matter, and hence the motion of the ether itself. Step by painful step, Lorentz explained how to combine the two theories so as to predict how light would propagate in moving fluids or how it would change its appearance to moving observers. There were paradoxes in Lorentz's stitched-together theory that he could eliminate only by making modifications to the assumed structure of matter itself. He deduced that moving objects would have to contract in size as they moved through the ether. These painstaking conclusions brought him closer and closer to the formulas of Einstein's 1905 theory of special relativity, but without the insight about space and time to match it.

Lorentz's theories were relegated to the footnotes of history, and he never fully grasped Einstein's radical insights. Friedberg's lectures brought Lorentz's struggles to life; they gave me an immense appreciation for how Einstein's cerebral and yet intuitive analysis eliminated or sidestepped the confusion that came before. Ever since, I have been curious about
how
breakthroughs occur. No discovery, in physics or finance, is as obvious as it seems to the people who read the textbooks written even a few years later.

It amazed me that, using Einstein's formalism, I could so easily solve problems about the motion of light in moving fluids that had once been too complex for anyone to tackle. Somehow, Einstein had transformed almost inconceivable mysteries into mere formalism and rules. Now, after a little education, any first-year graduate student could, like an organ-grinder making music, calculate the correct answers to questions that couldn't have been posed a few decades earlier. I became ever more constantly aware of the gap between creator and disciple. Everything looks simple once you have been taught it. However, it is only when you have struggled amidst the chaos of the sensible world on your own that you can understand how difficult it is to impose or discern an order that eventually, in retrospect, looks deceptively obvious.

I still have a copy of my 1967 blue examination book for Friedberg's course, filled with my handwritten essay on Lorentz's attempts to explain the propagation of light through the ether. Once every few years I like to take a look at the complimentary comment Friedberg wrote in the margin, saying that my answer had gone beyond the question asked, but that it dealt “with the required points as well as the superfluous material in a completely clear and intelligent way, correct in every detail.”

The best single lecture I have ever attended was a seminar by Mark Kaç given at Columbia sometime in the early 1970s. Kaç, a Polish-born expert in probability theory, is well known to both physicists and finance theorists for the eponymous Feynman-Kaç method of solving the differential equations that occur both in quantum mechanics and in options theory. His seminar had the catchy title “Can you hear the shape of a drum?” In it he described the conditions under which an imaginary blind listener, endowed with a perfect ear capable of hearing all the frequencies of the sound waves emitted from a drum, would be able to mathematically determine the shape of the drum itself. This problem is part of the more general field of inverse scattering; years later at Goldman Sachs, Iraj Kani and I used a similar approach to show how an imaginary options market observer who, having recorded the prices of all options on a stock, could then mathematically determine the shape of the surface that described all future stock volatilities.

What was so impressive about Kaç's presentation was his painstaking explanation of how he used his intuition to find his way out of the blind alleys he drifted into as he searched for a solution. He was also amusing. He recounted that in Amsterdam the same talk had mistakenly been advertised on campus with the title “Can you hear the shape of a dream?” and had consequently drawn a large and very different late-1960s audience. It reminded me of a similar story at Columbia about the curious crowd of medical students who showed up for an astrophysics seminar on stellar structure entitled “White Dwarfs and Red Giants.”

To be one of T. D. Lee's graduate students was everyone's dream. The 1950s and '60s were the dawn of the age of symmetry in particle physics. Lee's theories and Columbia's experimenters—Lederman, Schwartz, Steinberger, and the one female professor in the department, Chien-Shiung Wu, whom everyone referred to as Madame Wu—were at the center of the search for symmetry and the discovery of its subtle violations.

Symmetry is the pattern that tells you how to generate one part of an object from another. It condenses information. Saying that a human face is symmetrical is another way of telling you that you do not need to draw both sides of it; instead, you can generate the left side from the right. Said differently, a truly symmetric human face is indistinguishable from its mirror image, which flips the left and right sides.

Before Lee and Yang, every physicist believed it to be obvious beyond question that the forces of nature are reflection-invariant, so that the mirror image of every natural event is itself an equally probable natural event. This assumed property of nature was called the law of parity conservation, because of the equality or parity between the mirror image and the actual event itself.

Physicists are familiar with four forces, the strong, the electromagnetic, the weak, and the gravitational force. The strong force binds together the protons and neutrons that make up the nucleus at the center of every atom. The electromagnetic force causes the electrons in atoms to orbit their nucleus and emit light. The weak force is responsible for “beta decay,” the radioactive disintegration of nuclei by electron emission. Gravity, the oldest and most familiar force, governs the motions of falling apples, the earth and the moon, the planets, stars, and galaxies.

In the 1950s physicists knew that the strong and electromagnetic forces conserved parity. They unquestionably assumed that the weak force conserved parity, too. It seemed inconceivable that it shouldn't. No one could imagine that looking at nature in a mirror might yield a world that couldn't exist.

Then, two strange new and unstable particles, the
tau
and the
theta
, were discovered in cosmic rays. In most respects the two particles seemed almost identical; they had the same mass and electric charge, but they decayed differently. What could make two almost indistinguishable particles decay into two different final states? That was the famous
tau-theta puzzle
of the 1950s.

In 1956 Lee and his collaborator Chen-Ning Yang pointed out that the two particles might in fact be one and the same particle, which then, subject to the weak force, decayed in two different ways, but that this could only happen if the weak force responsible for its decay was
not
reflection-invariant. It was a preposterous suggestion that Lee and Yang took seriously and systematically. They analyzed all previous experiments that had studied the weak force in atoms and nuclei and found that, contrary to everyone's unquestioned belief, no previous experiment had ever truly tested the assumed symmetry between an event and its reflection. With further study, Lee and Yang suggested specific experiments to check for parity violation in nuclear weak decays.

Most physicists were skeptical. How, they wondered, could any of nature's laws not be symmetric under reflection? But within a few months, by early 1957, Madame Wu and her collaborators carried out the experiment Lee and Yang proposed, and showed that they were vindicated. Lee and Yang received their Nobel Prize that same year.

Lee and Yang's discovery that Nature was slightly asymmetric sparked a revolution. Slowly but inexorably, further experiments in the 1950s and 1960s revealed further subtle asymmetries of the weak interaction. T. D. was at the center of these investigations.