by James Gleick
Knowledge was rarer then. A secondhand magazine was an occasion. For a Far Rockaway teenager merely to find a mathematics textbook took will and enterprise. Each radio program, each telephone call, each lecture in a local synagogue, each movie at the new Gem theater on Mott Avenue carried the weight of something special. Each book Richard possessed burned itself into his memory. When a primer on mathematical methods baffled him, he worked through it formula by formula, filling a notebook with self-imposed exercises. He and his friends traded mathematical tidbits like baseball cards. If a boy named Morrie Jacobs told him that the cosine of 20 degrees multiplied by the cosine of 40 degrees multiplied by the cosine of 80 degrees equaled exactly one-eighth, he would remember that curiosity for the rest of his life, and he would remember that he was standing in Morrie’s father’s leather shop when he learned it.
Even with the radio era in full swing, one’s senses encountered nothing like the bombardment of images and sounds that television would bring—accelerated, flash-cut, disposable knowledge. For now, knowledge was scarce and therefore dear. It was the same for scientists. The currency of scientific information had not yet been devalued by excess. For a young student, that meant that the most timely questions were surprisingly close to hand. Feynman recognized early the special, distinctive feeling of being close to the edge of knowledge, where people do not know the answers. Even in grade school, when he would haunt the laboratory late in the afternoon, playing with magnets and helping a teacher clean up, he recognized the pleasure of asking questions that the teacher could not handle. Now, graduating from high school, he could not tell how near or how far he was from science’s active frontier, where scientists pulled fresh problems like potatoes from the earth, and in fact he was not far. The upheaval caused by quantum mechanics had laid the fundamental issues bare. Physics was still a young science, more obscure than any human knowledge to date, yet still something of a family business. Its written record remained small, even as whole new scientific frameworks—nuclear physics, quantum field theory—were being born. The literature sustained just a handful of journals, still mostly in Europe. Richard knew nothing of these.
Across town, another precocious teenager, named Julian Schwinger, had quietly inserted himself into the world of the new physics. He was already as much a creature of the city as Feynman was of the city’s outskirts: the younger son of a well-to-do garment maker, growing up in Jewish Harlem and then on Riverside Drive, where dark, stately apartment buildings and stone town houses followed the curve of the Hudson River. The drive was built for motor traffic, but truck horses still pulled loads of boxes to the merchants of Broadway, a few blocks east. Schwinger knew how to find books; he often prowled the used-book stores of lower Fourth and Fifth Avenues for advanced texts on mathematics and physics. He attended Townsend Harris High School, a nationally famous institution associated with the City College of New York, and even before he entered City College, in 1934, when he was sixteen, he found out what physics was—the modern physics. With his long, serious face and slightly stooped shoulders he would sit in the college’s library and read papers by Dirac in the Proceedings of the Royal Society of London or the Physikalische Zeitschrift der Sowjetunion. He also read the Physical Review, now forty years past its founding; it had advanced from monthly to biweekly publication in hopes of competing more nimbly with the European journals. Schwinger struck his teachers as intensely shy. He carried himself with a premature elegant dignity.
That year he carefully typed out on six legal-size sheets his first real physics paper, “On the Interaction of Several Electrons,” and the same elegance was evident. It assumed for a starting point the central new tenet of field theory: “that two particles do not interact directly but, rather the interaction is explained as being caused by one of the particles influencing the field in its vicinity, which influence spreads until it reaches the second particle.” Electrons do not simply bounce off one another, that is. They plow through that magnificent ether substitute, the field; the waves they make then swish up against other electrons. Schwinger did not pretend to break ground in this paper. He showed his erudition by adopting “the quantum electrodynamics of Dirac, Fock, and Podolsky,” the “Heisenberg representation” of potentials in empty space, the “Lorentz-Heaviside units” for expressing such potentials in relatively compact equations. This was heavy machinery in soft terrain. The field of Maxwell, which brought electricity and magnetism together so effectively, now had to be quantized, built up from finite-size packets that could be reduced no further. Its waves were simultaneously smooth and choppy. Schwinger, in his first effort at professional physics, looked beyond even this difficult electromagnetic field to a more abstract field still, a field twice removed from tangible substance, buoying not particles but mathematical operators. He pursued this conception through a sequence of twenty-eight equations. Once, at equation 20, he was forced to pause. A fragment of the equation had grown unmanageable—infinite, in fact. To the extent that this fragment corresponded to something physical, it was the tendency of an electron to act on itself. Having shaken its field, the electron is shaken back, with (so the mathematics insisted) infinite energy. Dirac and the others had grudgingly settled on a response to this difficulty, and Schwinger handled it in the prescribed manner: he simply discarded the offending term and moved on to equation 21.
Julian Schwinger and Richard Feynman, exact contemporaries, obsessed as sixteen-year-olds with the abstract mental world of a scientist, had already set out on different paths. Schwinger studying the newest of the new physics, Feynman filling schoolboy notebooks with standard mathematical formulas, Schwinger entering the arena of his elders, Feynman still trying to impress his peers with practical jokes, Schwinger striving inward toward the city’s intellectual center, Feynman haunting the beaches and sidewalks of its periphery—they would hardly have known what to say to each other. They would not meet for another decade; not until Los Alamos. Long afterward, when they were old men, after they had shared a Nobel Prize for work done as rivals, they amazed a dinner party by competing to see who could most quickly recite from memory the alphabetical headings on the spines of their half-century-old edition of the Encyclopaedia Britannica.
As his childhood ended, Richard worked at odd jobs, for a neighborhood printer or for his aunt, who managed one of the smaller Far Rockaway resort hotels. He applied to colleges. His grades were perfect or near perfect in mathematics and science but less than perfect in other subjects, and colleges in the thirties enforced quotas in the admission of Jews. Richard spent fifteen dollars on a special entrance examination for Columbia University, and after he was turned down he long resented the loss of the fifteen dollars. MIT accepted him.
MIT
A seventeen-year-old freshman, Theodore Welton, helped some of the older students operate the wind-tunnel display at the Massachusetts Institute of Technology’s Spring Open House in 1936. Like so many of his classmates he had arrived at the Tech knowing all about airplanes, electricity, and chemicals and revering Albert Einstein. He was from a small town, Saratoga Springs, New York. With most of his first year behind him, he had lost none of his confidence. When his duties ended, he walked around and looked at the other exhibits. A miniature science fair of current projects made the open house a showcase for parents and visitors from Boston. He wandered over to the mathematics exhibit, and there, amid a crowd, his ears sticking out noticeably from a very fresh face, was what looked like another first-year boy, inappropriately taking charge of a complex, suitcase-size mechanical-mathematical device called a harmonic analyzer. This boy was pouring out explanations in a charged-up voice and fielding questions like a congressman at a press conference. The machine could take any arbitrary wave and break it down into a sum of simple sine and cosine waves. Welton, his own ears burning, listened while Dick Feynman rapidly explained the workings of the Fourier transform, the advanced mathematical technique for analyzing complicated wave forms, a piece of privileged knowledge that Welton until
that moment had felt sure no other freshman possessed.
Welton (who liked to be called by his initials, T. A.) already knew he was a physics major. Feynman had vacillated twice. He began in mathematics. He passed an examination that let him jump ahead to the second-year calculus course, covering differential equations and integration in three-dimensional space. This still came easily, and Feynman thought he should have taken the second-year examination as well. But he also began to wonder whether this was the career he wanted. American professional mathematics of the thirties was enforcing its rigor and abstraction as never before, disdaining what outsiders would call “applications.” To Feynman—having finally reached a place where he was surrounded by fellow tinkerers and radio buffs—mathematics began to seem too abstract and too far removed.
In the stories modern physicists have made of their own lives, a fateful moment is often the one in which they realize that their interest no longer lies in mathematics. Mathematics is always where they begin, for no other school course shows off their gifts so clearly. Yet a crisis comes: they experience an epiphany, or endure a slowly building disgruntlement, and plunge or drift into this other, hybrid field. Werner Heisenberg, seventeen years older than Feynman, experienced his moment of crisis at the University of Munich, in the office of the local statesman of mathematics, Ferdinand von Lindemann. For some reason Heisenberg could never forget Lindemann’s horrid yapping black dog. It reminded him of the poodle in Faust and made it impossible for him to think clearly when the professor, learning that Heisenberg was reading Weyl’s new book about relativity theory, told him, “In that case you are completely lost to mathematics.” Feynman himself, halfway through his freshman year, reading Eddington’s book about relativity theory, confronted his own department chairman with the classic question about mathematics: What is it good for? He got the classic answer: If you have to ask, you are in the wrong field. Mathematics seemed suited only for teaching mathematics. His department chairman suggested calculating actuarial probabilities for insurance companies. This was not a joke. The vocational landscape had just been surveyed by one Edward J. v. K. Menge, Ph.D., Sc.D., who published his findings in a monograph titled Jobs for the College Graduate in Science. “The American mind is taken up largely with applications rather than with fundamental principles,” Menge noticed. “It is what is known as ‘practical.’” This left little room for would-be mathematicians: “The mathematician has little opportunity of employment except in the universities in some professorial capacity. He may become a practitioner of his profession, it is true, if he acts as an actuary for some large insurance company… .” Feynman changed to electrical engineering. Then he changed again, to physics.
Not that physics promised much more as a vocation. The membership of the American Physical Society still fell shy of two thousand, though it had doubled in a decade. Teaching at a college or working for the government in, most likely, the Bureau of Standards or the Weather Bureau, a physicist might expect to earn a good wage of from three thousand to six thousand dollars a year. But the Depression had forced the government and the leading corporate laboratories to lay off nearly half of their staff scientists. A Harvard physics professor, Edwin C. Kemble, reported that finding jobs for graduating physicists had become a “nightmare.” Not many arguments could be made for physics as a vocation.
Menge, putting his pragmatism aside for a moment, offered perhaps the only one: Does the student, he asked, “feel the craving of adding to the sum total of human knowledge? Or does he want to see his work go on and on and his influence spread like the ripples on a placid lake into which a stone has been cast? In other words, is he so fascinated with simply knowing the subject that he cannot rest until he learns all he can about it?”
Of the leading men in American physics MIT had three of the best, John C. Slater, Philip M. Morse, and Julius A. Stratton. They came from a more standard mold—gentlemanly, homebred, Christian—than some of the physicists who would soon eclipse them, foreigners like Hans Bethe and Eugene Wigner, who had just arrived at Cornell University and Princeton University, respectively, and Jews like I. I. Rabi and J. Robert Oppenheimer, who had been hired at Columbia University and the University of California at Berkeley, despite anti-Semitic misgivings at both places. Stratton later became president of MIT, and Morse became the first director of the Brookhaven National Laboratory for Nuclear Research. The department head was Slater. He had been one of the young Americans studying overseas, though he was not as deeply immersed in the flood tides of European physics as, for example, Rabi, who made the full circuit: Zurich, Munich, Copenhagen, Hamburg, Leipzig, and Zurich again. Slater had studied briefly at Cambridge University in 1923, and somehow he missed the chance to meet Dirac, though they attended at least one course together.
Slater and Dirac crossed paths intellectually again and again during the decade that followed. Slater kept making minor discoveries that Dirac had made a few months earlier. He found this disturbing. It seemed to Slater furthermore that Dirac enshrouded his discoveries in an unnecessary and somewhat baffling web of mathematical formalism. Slater tended to mistrust them. In fact he mistrusted the whole imponderable miasma of philosophy now flowing from the European schools of quantum mechanics: assertions about the duality or complementarity or “Jekyll-Hyde” nature of things; doubts about time and chance; the speculation about the interfering role of the human observer. “I do not like mystiques; I like to be definite,” Slater said. Most of the European physicists were reveling in such issues. Some felt an obligation to face the consequences of their equations. They recoiled from the possibility of simply putting their formidable new technology to work without developing a physical picture to go along with it. As they manipulated their matrices or shuffled their differential equations, questions kept creeping in. Where is that particle when no one is looking? At the ancient stone-built universities philosophy remained the coin of the realm. A theory about the spontaneous, whimsical birth of photons in the energy decay of excited atoms—an effect without a cause—gave scientists a sledgehammer to wield in late-evening debates about Kantian causality. Not so in America. “A theoretical physicist in these days asks just one thing of his theories,” Slater said defiantly soon after Feynman arrived at MIT. The theories must make reasonably good predictions about experiments. That is all.
He does not ordinarily argue about philosophical implications… . Questions about a theory which do not affect its ability to predict experimental results correctly seem to me quibbles about words, … and I am quite content to leave such questions to those who derive some satisfaction from them.
When Slater spoke for common sense, for practicality, for a theory that would be experiment’s handmaid, he spoke for most of his American colleagues. The spirit of Edison, not Einstein, still governed their image of the scientist. Perspiration, not inspiration. Mathematics was unfathomable and unreliable. Another physicist, Edward Condon, said everyone knew what mathematical physicists did: “they study carefully the results obtained by experimentalists and rewrite that work in papers which are so mathematical that they find them hard to read themselves.” Physics could really only justify itself, he said, when its theories offered people a means of predicting the outcome of experiments—and at that, only if the predicting took less time than actually carrying out the experiments.
Unlike their European counterparts, American theorists did not have their own academic departments. They shared quarters with the experimenters, heard their problems, and tried to answer their questions pragmatically. Still, the days of Edisonian science were over and Slater knew it. With a mandate from MIT’s president, Karl Compton, he was assembling a physics department meant to bring the school into the forefront of American science and meanwhile to help American science toward a less humble world standing. He and his colleagues knew how unprepared the United States had been to train physicists in his own generation. Leaders of the nation’s rapidly growing technical industries knew it, too. When Slater arrived, th
e MIT department sustained barely a dozen graduate students. Six years later, the number had increased to sixty. Despite the Depression the institute had completed a new physics and chemistry laboratory with money from the industrialist George Eastman. Major research programs had begun in the laboratory fields devoted to using electromagnetic radiation as a probe into the structure of matter: especially spectroscopy, analyzing the signature frequencies of light shining from different substances, but also X-ray crystallography. (Each time physicists found a new kind of “ray” or particle, they put it to work illuminating the interstices of molecules.) New vacuum equipment and finely etched mirrors gave a high precision to the spectroscopic work. And a monstrous new electromagnet created fields more powerful than any on the planet.
Julius Stratton and Philip Morse taught the essential advanced theory course for seniors and graduate students, Introduction to Theoretical Physics, using Slater’s own text of the same name. Slater and his colleagues had created the course just a few years before. It was the capstone of their new thinking about the teaching of physics at MIT. They meant to bring back together, as a unified subject, the discipline that had been subdivided for undergraduates into mechanics, electromagnetism, thermodynamics, hydrodynamics, and optics. Undergraduates had been acquiring their theory piecemeal, in ad hoc codas to laboratory courses mainly devoted to experiment. Slater now brought the pieces back together and led students toward a new topic, the “modern atomic theory.” No course yet existed in quantum mechanics, but Slater’s students headed inward toward the atom with a grounding not just in classical mechanics, treating the motion of solid objects, but also in wave mechanics—vibrating strings, sound waves bouncing around in hollow boxes. The instructors told the students at the outset that the essence of theoretical physics lay not in learning to work out the mathematics, but in learning how to apply the mathematics to the real phenomena that could take so many chameleon forms: moving bodies, fluids, magnetic fields and forces, currents of electricity and water, and waves of water and light. Feynman, as a freshman, roomed with two seniors who took the course. As the year went on he attuned himself to their chatter and surprised them sometimes by joining in on the problem solving. “Why don’t you try Bernoulli’s equation?” he would say—mispronouncing Bernoulli because, like so much of his knowledge, this came from reading the encyclopedia or the odd textbooks he had found in Far Rockaway. By sophomore year he decided he was ready to take the course himself.
