Genius: The Life and Science of Richard Feynman

by James Gleick

The field grew so dominant in physicists’ thinking that even matter itself sometimes withdrew to the status of mere appendage: a “knot” of the field, or a “blemish,” or as Einstein himself said, merely a place where the field was especially intense.

Thus Feynman, looking for a new eyepiece himself, began drifting back to a classical notion of unfieldlike particle interaction. The wavelike transmission of energy and the hocus-pocus of action at a distance were issues that he would have to address.

Pure mathematics had swerved away from the fields of direct use to contemporary physicists and toward such seeming esoterica as topology, the study of shapes in two, three, or many dimensions without regard to rigid lengths or angles. An effective divorce had occurred between mathematics and physics. By the time practitioners reached the graduate level, they shared no courses and had nothing practical to say to one another. Feynman listened to the mathematicians standing in groups or sitting on the couch at tea, talking about their proofs. Rightly or wrongly he felt he had an intuition for what theorems could be derived from what lemmas, even without quite understanding the subject.

He enjoyed the strange rhetoric. He enjoyed trying to guess the counterintuitive answers to their nearly unvisualizable questions, and he enjoyed applying the physicist’s favorite needle, the claim that mathematicians spent their time proving the obvious. Although he teased them, he thought they were an exciting group—happy and interested in a kind of science that was getting beyond him.

Stone had brought with him English-standard loose-leaf notebooks. The American-standard paper he bought at Woolworth’s overhung the notebooks by an inch, so he presently found himself with a supply of inch-wide paper ribbons, suitable for folding and twisting in different configurations. He tried diagonal folds at the 60-degree angle that produced rows of equilateral triangles. Then, following these folds, he wrapped a strip into a perfect hexagon.

Feynman’s best contribution was the invention of a diagram, called in retrospect the Feynman diagram, that showed all the possible paths through a hexaflexagon. Seventeen

One neighbor barged in on Feynman sitting by the window, open, on a wintry day, madly stirring a pot of Jell-O with a spoon and shouting “Don’t bother me!” He was trying to see how the Jell-O would coagulate while in motion.

They discovered that Feynman could read to himself silently and still keep track of time but that if he spoke he would lose his place. Tukey, on the other hand, could keep track of the time while reciting poetry aloud but not while reading. They decided that their brains were applying different functions to the task of counting: Feynman was using an aural rhythm, hearing the numbers, while Tukey visualized a sort of tape with numbers passing behind his eyes.

Once in a while a small piece of knowledge from the world outside science would float Feynman’s way and stick like a bur from a chestnut. One of the graduate students had developed a passion for the poetry of Edith Sitwell, then considered modern and eccentric because of her flamboyant diction and cacophonous, jazzy rhythms. He read some poems aloud, and suddenly Feynman seemed to catch on; he took the book and started reciting gleefully. “Rhythm is one of the principal translators between dream and reality,” the poet said of her own work. “Rhythm might be described as, to the world of sound, what light is to the world of sight.” To Feynman rhythm was a drug and a lubricant. His thoughts sometimes seemed to slip and flow with a variegated drumbeat that his friends noticed spilling out into his fingertips, restlessly tapping on desks and notebooks.

A development in twentieth-century entertainment technology—the motion picture—incidentally provided an advance in the technology of thought experiments. It was now natural for a scientist, in his mind’s laboratory, to play the film backward

Centuries of speculation and debate had left them unprepared for the physicists’ sudden demolition of the notion of simultaneity (in the relativistic universe it meant nothing to say that two events took place at the same time). With simultaneity gone, sequentiality was foundering, causality was under pressure, and scientists generally felt themselves free to consider temporal possibilities that would have seemed farfetched a generation before.

In the fall of 1940 Feynman returned to the fundamental problem with which he had flirted since his undergraduate days. Could the ugly infinities of quantum theory be eliminated by forbidding the possibility that an electron acts on itself—by eliminating, in effect, the field? Unfortunately he had meanwhile learned what was wrong with his idea. The problem was a phenomenon that could only be explained, it seemed, in terms of the action of an electron on itself. When real electrons are pushed, they push back: an accelerating electron drains energy by radiating it away. In effect the electron feels a resistance, called radiation resistance, and extra force has to be applied to overcome it. A broadcasting antenna, radiating energy in the form of radio waves, encounters radiation resistance—extra current has to be sent through the antenna to make up for it. Radiation resistance is at work when a hot, glowing object cools off. Because of radiation resistance, an electron in an atom, alone in empty space, loses energy and dies out; the lost energy has been radiated away in the form of light. To explain why this damping takes place, physicists assumed they had no choice but to imagine a force exerted by the electron on itself. By what else, in empty space?

One day, however, Feynman walked into Wheeler’s office with a new idea. He was “pie-eyed,” he confessed, from struggling with an obscure problem Wheeler had given him. Instead he had turned back to self-action. What if (he thought) an electron isolated in empty space does not emit radiation at all, any more than a tree makes a sound in an empty forest. Suppose radiation were to be permitted only when there is both a source and a receiver. Feynman imagined a universe with just two electrons. The first shakes. It exerts a force on the second. The second shakes and generates a force that acts back on the first. He computed the force by a familiar field equation of Maxwell’s, but in this two-particle universe there was to be no field, if the field meant a medium in which wav...

And there was another problem: Feynman had not properly accounted for the delay in the transmission of the force to and fro. Whatever force was exerted back on the first particle would come at the wrong time, too late to match the known effect of radiation resistance. In fact Feynman suddenly realized that he had been describing a different phenomenon altogether, a painfully simple one: ordinary reflected light. He felt foolish.

An imaginative leap was needed to see that the earth swerves in its orbit not because the sun is there but because it was there eight minutes before, the time needed for gravity’s influence to cross nearly a hundred million miles of space—to see that if the sun were plucked away, the earth would continue to orbit for eight minutes. To accommodate the insights of relativity, the field equations had to be amended. The waves were now retarded waves, held back by the finite speed of light.

What if the apparent time-symmetry of the equations were taken seriously? One would have to imagine a shaken electron sending its radiation outward symmetrically in time. Like a lighthouse sending its beam both north and south, an electron might shine both forward and backward to the future and the past. It seemed to Wheeler that a combination of advanced and retarded waves might cancel each other in a way that would overcome the lack of any time delay in the phenomenon of radiation resistance.

The new notion turned paradoxical as soon as it was expressed in words: Shake a charge here—then another charge shakes a little earlier. It explicitly required an action backward in time. Where was the cause and where was the effect? If Feynman ever felt that this was a deep thicket to enter merely for the sake of eliminating the electron’s self-action, he suppressed the thought. After all, self-action created an undeniable contradiction within quantum mechanics, and the entire profession was finding it insoluble. At any rate, in the era of Einstein and Bohr, what was one more paradox? Feynman already believed that it was the mark of a good physicist never to say, “Oh, whaddyamean, how could that be?” The

Thus, given that one cosmological assumption—that the universe has enough matter in every direction to soak up outgoing radiation—Feynman found that a system of equations in which advanced and retarded waves were combined half and half seemed to withstand every objection.

If they were going to make grand theories, Wheeler would make sure they publicized the work properly. Early in 1941 he told Feynman to prepare a presentation for the departmental seminar, usually a forum for distinguished visiting physicists, in February. It would be Feynman’s first professional talk. He was nervous about it.

As the day approached, Wigner, who ran the colloquiums, stopped Feynman in the hall. Wigner said he had heard enough from Wheeler about the absorber theory to think it was important. Because of its implications for cosmology he had invited the great astrophysicist Henry Norris Russell. John von Neumann, the mathematician, was also going to come. The formidable Wolfgang Pauli happened to be visiting from Zurich; he would be there. And though Albert Einstein rarely bestirred himself to the colloquiums, he had expressed interest in attending this one.

Feynman prepared carefully. He collected his notes and put them into a brown envelope. He entered the seminar room early and covered the blackboard with equations. While he was writing, he heard a soft voice behind him. It was Einstein. He was coming to the lecture and first he wondered whether the young man might direct him to the tea.

Then, politely, Pauli said, “Don’t you agree, Professor Einstein?” Feynman heard that soft Germanic voice again—so pleasant, it seemed—saying no, the theory seemed possible, perhaps there was a conflict with the theory of gravitation, but after all the theory of gravitation was not so well established ...

During one occurrence he wrote out an hourly schedule of his activities, both scholarly and recreational, “so as to efficiently distribute my time,” he wrote home. When he finished, he recognized that no matter how careful he was, he would have to leave some indeterminate gaps—“hours when I haven’t marked down just what to do but I do what I feel is most necessary then—or what I am most interested in—whether it be W.’s problem or reading Kinetic Theory of Gases, etc.” If there is a disease whose symptom is the belief in the ability of logic to control vagarious life, it afflicted Feynman, along with his chronic digestive troubles.

Arline was visiting more and more often. They would have dinner with the Wheelers and go for long walks in the rain. She had the rare ability to embarrass him: she knew where his small vanities were, and she teased him mercilessly whenever she caught him worrying about other people’s opinions—how things might seem.

Einstein received this pair of ambitious young physicists sympathetically, as he did most scientists who visited in his last years. They were led into his study. He sat facing them behind his desk. Feynman was struck by how well the reality matched the legend: a soft, nice man wearing shoes without socks and a sweater without a shirt. Einstein was well known to be unhappy with the acausal paradoxes of quantum mechanics. He now spent much of his time writing screeds on world government which, from a less revered figure, would have been thought crackpot.

A tendency toward disorder is the most universal manifestation of time’s arrow. A movie showing a drop of ink diffusing in a glass of water looks wrong when run backward. Yet a movie showing the microscopic motion of any one ink molecule would look the same backward or forward. The random motions of each ink molecule can be reversed, but the overall diffusion cannot be. The system is microscopically reversible, macroscopically irreversible. It is a matter of chaos and probability. It is not impossible for the ink molecules, randomly drifting about, someday to reorganize themselves into a droplet. It is just hopelessly improbable.

Feynman and Wheeler pushed on their theory. They tried to see how far they could broaden its implications. Many of their attempts led nowhere. They worked on the problem of gravity in hopes of reducing it to a similar interaction. They tried to construct a model in which space itself was eliminated: no coordinates and distances, no geometry or dimension; only the interactions themselves would matter. These were dead ends. As the theory developed, however, one feature gained paramount importance. It proved possible to compute particle interactions according to a principle of least action.

The approach was precisely the shortcut that Feynman had gone out of his way to disdain in his first theory course at MIT. For a ball arcing through the air, the principle of least action made it possible to sidestep the computation of a trajectory at successive instants of time. Instead one made use of the knowledge that the final path would be the one that minimized action, the difference between the ball’s kinetic and potential energy. In the absorber theory, because the field was no longer an independent entity, the action of a particle suddenly became a quantity that made sense. It could be calculated directly from the particle’s motion. And once again, as though by magic, particles chose the paths for which the action was smallest. The more Feynman worked with the least-action approach, the more he felt how different was the physical point of view. Traditionally one always thought in terms of the flow of time, represented by differential equations, which captured a change from instant to instant. Using the principle of least action instead, one developed a bird’s-eye perspective, envisioning a particle’s path as a whole, all time seen at once.

The point about positrons, however, reverberated. In his first published paper two years before, on the scattering of cosmic radiation by stars, he had already made this connection, treating antiparticles as ordinary particles following reversed paths. In a Minkowskian universe, why shouldn’t the reversal apply to time as well as to space?

He decided to approach the quantizing of his theory just as he had approached complicated problems at MIT, by working out cases that were stripped to their bare essentials. He tried calculating the interaction of a pair of harmonic oscillators, coupled, with a time delay—just a pair of idealized springs. One spring would shake, sending out a pure sine wave. The other would bounce back, and out of their interaction new wave forms would evolve. Feynman made some progress but could not understand the quantum version. He had gone too far in the direction of simplicity.

At twenty-three he was a few years shy of the time when his vision would sweep hawklike across the breadth of physics, but there may now have been no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear to the senior physicists at Princeton that the mathematical machinery emerging in the Wheeler-Feynman collaboration was beyond Wheeler’s own ability). Feynman seemed to possess a frightening ease with the substance behind the equations, like Einstein at the same age, like the Soviet physicist Lev Landau—but few others.

In preparing for his oral qualifying examination, a rite of passage for every graduate student, he chose not to study the outlines of known physics. Instead he went up to MIT, where he could be alone, and opened a fresh notebook. On the title page he wrote: Notebook Of Things I Don’t Know About. For the first but not the last time he reorganized his knowledge. He worked for weeks at disassembling each branch of physics, oiling the parts, and putting them back together, looking all the while for the raw edges and inconsistencies. He tried to find the essential kernels of each subject. When he was done he had a notebook of which he was especially proud. It was not much use in preparing for the examination, as it turned out.

In writing up course notes on nuclear physics, Feynman had been frustrated by a complicated formula of Wigner’s for particles in the nucleus. He did not understand it. So he worked the problem out for himself, inventing a diagram—a harbinger of things to come—that enabled him to keep a tally of particle interactions, counting the neutrons and protons and arranging them in a group-theoretical way according to pairs that were or were not symmetrical. The diagram bore an odd resemblance to the diagrams he invented for understanding the pathways of folded-paper flexagons. He did not really understand why his scheme worked, but he was certain that it did, and it proved to be a considerable simplification of Wigner’s own approach.

Less glamorously, Feynman spent his summer at the Frankford Arsenal working on a primitive sort of analog computer, a combination of gears and cams designed to aim artillery pieces. It all seemed mechanical and archaic—later he thought Bell Laboratories would have been a better choice after all. Still, even in his college workshops, he had never confronted such an urgent blending of mathematics and metal. To aim a gun turret meant converting sines and tangents into steel gears. Suddenly trigonometry had engineering consequences: long before the tangent of a near-vertical turret diverged to infinity, the torque applied to the teeth of the gears would snap them off. Feynman found himself drawn to a mathematical approach he had never considered, the manipulation of functional roots.

The number-two man, Paul Olum, threw away the paper. Olum had considered himself the best undergraduate mathematician at Harvard. He arrived at Princeton in 1940 to be Wheeler’s second research assistant. Wheeler introduced him to Feynman, and within a few weeks he was devastated. What’s happening here? he thought. Is this the way physicists are, and I missed it? No physicist at Harvard was like this. Feynman, a cheerful, boyish presence spinning across the campus on his bicycle, scornful of the formalisms of modern advanced mathematics, was running mental circles around him. It wasn’t that he was a brilliant calculator; Olum knew the tricks of that game. It was as if he were a man from Mars. Olum could not track his thinking. He had never known anyone so intuitively at ease with nature—and with nature’s seemingly least accessible manifestations. He suspected that when Feynman wanted to know what an electron would do under given circumstances he merely asked himself, “If I were an electron, what would I do?”

The purest mathematicians had to soil their hands. Stanislaw Ulam lamented that until now he had always worked exclusively with symbols. Now he had been driven so low as to use actual numbers, and, even more humbling, they were numbers with decimal points.

Feynman spent a long time thinking about the properties of a chunk of matter in the peculiar condition of near-criticality, a form of matter that science had not had occasion to ponder before. He recognized that the essence of the problem was not its average behavior but its fluctuations: bursts of neutron activity here and there, spreading in chains before dying out.

For his part Feynman, who had lived through twenty-five years and a full formal education without ever falling under the spell of a mentor, began to love Hans Bethe.

When he started managing groups of people who handled laborious computation, he developed a reputation for glancing over people’s shoulders and stabbing his finger at each error: “That’s wrong.” His staff would ask why he was putting them to such labor if he already knew the answers. He told them he could spot wrong results even when he had no idea what was right—something about the smoothness of the numbers or the relationships between them. Yet unconscious estimating was not really his style. He liked to know what he was doing. He would rummage through his toolbox for an analytical gimmick, the right key or lock pick to slip open a complicated integral. Or he would try various simplifying assumptions:

Feynman, frustrated, turned to Nicholas Metropolis, a mustached Greek mathematician who later became an authority on computation and numerical methods, and said, “Let’s learn about these damned things and not have to send them to Burbank.” (Feynman grew a temporary mustache, too.) They spent hours taking apart new and old machines for comparative diagnosis; learned where the jams and slippages began; and hung out a shingle advertising, “Computers Repaired.” Bethe was not amused at this waste of his theoreticians’ time. He finally ordered a halt to the tinkering. Feynman complied, knowing that within weeks the shortage of machines would change Bethe’s mind.

He was recapitulating centuries of mathematical history—yet not quite recapitulating, because only a modern shift of perspective made it possible to see the fabric whole. Having conceived of complex powers, he began to compute complex powers. He made a table of his results and showed how they oscillated, swinging from one to zero to negative one and back again in a wave that he drew for his audience, though they knew perfectly well what a sine wave looked like. He had arrived at trigonometric functions. Now he posed one more question, as fundamental as all the others, yet encompassing them all in the round recursive net he had been spinning for a mere hour: To what power must e be raised to reach i? (They already knew the answer, that e and i and π were conjoined as if by an invisible membrane, but as he told his mother, “I went pretty fast & didn’t give them a hell of a lot of time to work out the reason for one fact before I was showing them another still more amazing.”) He now repeated the assertion he had written elatedly in his notebook at the age of fourteen, that the oddly polyglot statement eπi + 1 = 0 was the most remarkable formula in mathematics. Algebra and geometry, their distinct languages notwithstanding, were one and the same, a bit of child’s arithmetic abstracted and generalized by a few minutes of the purest logic. “Well,” he wrote, “all the mighty minds were mightily impressed by my little feats of arithmetic.”

“He is a second Dirac,” Wigner said, “only this time human.”

Locks mixed human logic and mechanical logic. The designer’s strategy was constrained by the manufacturer’s convenience or the limits of the metal, as it was in so many of the bomb project’s puzzles. The official logic of a Los Alamos safe, as displayed in the dial’s numbers and hatch marks, indicated a million different combinations—three numbers from 0 to 99. Some experimentation, though, showed Feynman that the markings disguised a considerable margin of error, plus or minus two, attributable to plain mechanical slackness; if the correct number was 23, anything from 21 to 25 would work as well. When he was searching combinations systematically, therefore, he needed only to try one number in every five—0, 5, 10, 15 ... —to be sure of hitting the target. By thinking in terms of error ranges, instead of accepting the authority of the numerals on the dial, he brought a pragmatic physicist’s intuition to bear. That one insight effectively reduced the total combinations from one million to a mere eight thousand, almost few enough to try, given a few hours.

The remaining trial and error was so trivial that he found himself—for the sake of cultivating his legend—carrying tools as red herrings and pretending that safe jobs took longer than they really did.

He considered seemingly remote contingencies: “During centrifuging some peculiar motion of the centrifuge might possibly gather metal together in one lump, possibly near the center.” The nightmare was that two batches, individually safe, might accidentally be combined. He asked what each possible stuck valve or missing supervisor might mean. In a few places he found that the procedures were too conservative. He noted minute details of the operations. “Is CT-1 empty when we drop from WK-1... ? Is P-2 empty when solt’n is transfered ... ? Supervisor OK’s solution of P-2’s ppt. Under what circumstances?” Eventually, meeting with senior army officers and company managers, he laid out a detailed program for ensuring safety. He also invented a practical method—using, once again, a variational method to solve an otherwise unsolvable integral equation—that would let engineers make a conservative approximation, on the spot, of the safe levels of bomb material stored in various geometrical layouts. A few people, long afterward, thought he had saved their lives.

His computing team had put everything aside to concentrate on one final problem: the likely energy of the device to be exploded a few weeks hence at Alamogordo in the first and only trial of the atomic bomb. The group’s productivity had risen many times since he took over. He had invented a system for sending three problems through the machine simultaneously. In the annals of computing this was an ancestor to what would later be called parallel processing or pipelining. He made sure that the component operations of an ongoing computation were standardized, so that they could be used with only slight variations in different computations, and he had his team use color-coded cards, with a different color for each problem.

Feynman thought he knew what was useful and what was mere textbook knowledge taught because it had always been taught. He intended to emphasize nonlinearity more than was customary and to teach students the patchwork of gimmicks and tricks that he used himself to solve equations. Beginning with his jottings on the night train that brought him to Ithaca, he designed a new course from the bottom up.

On the first page of a cardboard notebook like the ones he had used in high school he began with first principles: Phenomena complex—laws simple— connection is math-phys—the solution of equ obtained from laws.

Nevertheless, during the few years that he taught the course, it drew some of the younger members of the physics and mathematics faculty along with the captive graduate students. The coolest among them had to feel the jolt of an examination problem that began, “In an atom bomb in the form of a cylinder radius a, height 2π, the density of neutrons n ...” The students found themselves in the grip of a theorist whose obsession with mathematical methods concerned the uneasy first principles of quantum mechanics. Again and again he showed his affinity with the purest core issues of the propagation of sound and light.

On October 7 he collapsed from a stroke. He died the next day. Richard signed his second death certificate in two years. Melville Feynman had written him: “The dreams I have often had in my youth for my own development, I see coming true in your career.... I envy the life of culture you will have being constantly with so many other big men of equal culture.”