Genius: The Life and Science of Richard Feynman

by James Gleick

Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.

By the turn of the century, scientists were struggling to explain this relationship between temperature and wavelength. If heat was to be understood as the motion of molecules, perhaps this precisely tuned radiant energy suggested an internal oscillation, a vibration with the resonant tonality of a violin string. The German physicist Max Planck pursued this idea to its logical conclusion and announced in 1900 that it required an awkward adjustment to the conventional way of thinking about energy. His equations produced the desired results only if one supposed that radiation was emitted in lumps, discrete packets called quanta. He calculated a new constant of nature, the indivisible unit underlying these lumps. It was a unit, not of energy, but of the product of energy and time—the quantity called action.

philosophy with an earnest Magic Mountain volubility. Heisenberg, whose name would come to stand for the twentieth century’s most famous kind of uncertainty, grew enraptured as a young student with his own “utter certainty” that nature expressed a deep Platonic order. The strains of Bach’s D Minor Chaconne, the moonlit landscapes visible through the mists, the atom’s hidden structure in space and time—all seemed as one.

“Time’s arrow” was already the catchphrase for this directionality, so evident to common experience, yet so invisible in the equations of physicists. There, in the equations, the road from past to future looked identical to the road from future to past. “There is no signboard to indicate that it is a one-way street,” complained Arthur Eddington. The paradox had been there all along, since Newton at least, but relativity had highlighted it. The mathematician Hermann Minkowski, by visualizing time as a fourth dimension, had begun to reduce past-future to the status of any pair of directions: left-right, up-down, back-front. The physicist drawing his diagrams obtains a God’s-eye view. In the space-time picture a line representing the path of a particle through time simply exists, past and future visible together. The four-dimensional space-time manifold displays all eternity at once. The laws of nature are not rules controlling the metamorphosis of what is into what will be. They are descriptions of patterns that exist, all at once, in the whole tapestry. The picture is hard to reconcile with our everyday sense that time is special. Even the physicist has his memories of the past and his aspirations for the future, and no space-time diagram quite obliterates the difference between them.

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. “We have, instead,” Feynman said later, “a thing that describes the character of the path throughout all of space and time. The behavior of nature is determined by saying her whole space-time path has a certain character.”

For Feynman, thinking in his spare time about the pure theory of particles and light, diffusion dovetailed peculiarly with quantum mechanics. The traditional diffusion equation bore a family resemblance to the standard Schrödinger equation; the crucial difference lay in a single exponent, where the quantum mechanical version was an imaginary factor, i. Lacking that i, diffusion was motion without inertia, motion without momentum. Individual molecules of perfume carry inertia, but their aggregate wafting through air, the sum of innumerable random collisions, does not. With the i, quantum mechanics could incorporate inertia, a particle’s memory of its past velocity. The imaginary factor in the exponent mingled velocity and time in the necessary way. In a sense, quantum mechanics was diffusion in imaginary time.

The workhorse of scientific calculating was the Marchant calculator, a clattering machine nearly as large as a typewriter, capable of adding, subtracting, multiplying, and with some difficulty dividing numbers of up to ten digits. (At first, to save money, the project ordered slower, eight-digit versions as well. They were rarely used.) In these machines a carriage spun around, propelled at first by a hand crank and later by an electric motor. Keys and levers pushed the carriage left or right. Counter and register dials displayed painted digits. There were rows and columns of keys for entering numbers, a plus bar and a minus bar, a multiplier key and a negative multiplier key, shift keys, and a key for stopping the machine when division went out of control, as it often did. Mechanical arithmetic was no simple affair. With all its buttons and linkages the Marchant was not quite as powerful as the giant Difference Engine and Analytical Engine, invented in England a century before by Charles Babbage in hopes of generating the printed tables of numbers on which navigators, astronomers, and mathematicians had to rely. Not only did Babbage solve the problem of carrying digits from one decimal place to the next; his machines actually used punched cards, borrowed from mechanical looms, to convey data and instructions. In the era of steam power, few of his contemporaries appreciated the point.

The theorists began to organize something new in the annals of computation: a combination of the calculating machine and the factory assembly line. Even before the IBM machines arrived Feynman and Metropolis set up an array of people—mostly wives of scientists, working at three-eighths salary—who individually handled pieces of complex equations, one cubing a number and passing it on, another performing a subtraction, and so on. It was mass production married to numerical calculation. The banks of women wielding Marchants simulated the internal workings of a computer. As a later generation would discover, there was something mentally seductive in the act of breaking calculus into the algorithmic cogs needed for machine computation. It forced the mind back down into the essence of arithmetic.

Meanwhile, under the influence of this primal dissection of mathematics, Feynman retreated from pragmatic engineering long enough to put together a public lecture on “Some Interesting Properties of Numbers.” It was a stunning exercise in arithmetic, logic, and—though he would never have used the word—philosophy. He invited his distinguished audience (“all the mighty minds,” he wrote his mother a few days later) to discard all knowledge of mathematics and begin from first principles—specifically, from a child’s knowledge of counting in units. He defined addition, a + b, as the operation of counting b units from a starting point, a. He defined multiplication (counting b times). He defined exponentiation (multiplying b times). He derived the simple laws of the kind a + b = b + a and (a + b) + c = a + (b + c), laws that were usually assumed unconsciously, though quantum mechanics itself had shown how crucially some mathematical operations did depend on their ordering. Still taking nothing for granted, Feynman showed how pure logic made it necessary to conceive of inverse operations: subtraction, division, and the taking of logarithms. He could always ask a new question that perforce required a new arithmetical invention. Thus he broadened the class of objects represented by his letters a, b, and c and the class of rules by which he was manipulating them. By his original definition, negative numbers meant nothing. Fractions, fractional exponents, imaginary roots of negative num...

Physicists learned to think of spin not so much as a kind of rotation, but as a kind of symmetry, a way of stating mathematically that a system could undergo a certain rotation.

Feynman’s frustration in these first postwar years mirrored a growing sense of impotence and defeat among established theoretical physicists. The feeling, at first private and then shared, remained invisible outside their small community. The contrast with the physicists’ public glory could hardly have been greater. The cause was abstruse. The single difficulty at the core of this anguish was a mathematical tendency of certain quantities to diverge as successive terms of an equation were computed—terms that should have been vanishing in importance. Physically it seemed that the closer one stood to an electron, the greater its charge and mass would appear. The result: the infinities with which Feynman had been struggling since Princeton. It meant that quantum mechanics produced good first approximations followed by a Sisyphean nightmare. The harder a physicist pushed, the less accurate his calculations became. Such quantities as the mass of the electron became—if the theory were taken to its limit—infinite. The horror of this was hard to comprehend, and no glimmer of it appeared in popular accounts of science at the time.

A certain kind of pragmatic, working theorist valued a style of thinking based on a kind of seeing and feeling. That was what physical intuition meant. Feynman said to Dyson, and Dyson agreed, that Einstein’s great work had sprung from physical intuition and that when Einstein stopped creating it was because “he stopped thinking in concrete physical images and became a manipulator of equations.” Intuition was not just visual but also auditory and kinesthetic. Those who watched Feynman in moments of intense concentration came away with a strong, even disturbing sense of the physicality of the process, as though his brain did not stop with the gray matter but extended through every muscle in his body. A Cornell dormitory neighbor opened Feynman’s door to find him rolling about on the floor beside his bed as he worked on a problem. When he was not rolling about, he was at least murmuring rhythmically or drumming with his fingertips. In part the process of scientific visualization is a process of putting oneself in nature: in an imagined beam of light, in a relativistic electron.

Feynman once told students, “I have no picture of this electromagnetic field that is in any sense accurate.” In seeking to analyze his own way of visualizing the unvisualizable he had learned an odd lesson. The mathematical symbols he used every day had become entangled with his physical sensations of motion, pressure, acceleration ... Somehow he invested the abstract symbols with physical meaning, even as he gained control over his raw physical intuition by applying his knowledge of how the symbols could be manipulated.

Feynman’s path-integral view of nature, his vision of a “sum over histories,” was also the principle of least action, the principle of least time, reborn. Feynman felt that he had uncovered the deep laws that gave rise to the centuries-old principles of mechanics and optics discovered by Christiaan Huygens, Pierre de Fermat, and Joseph-Louis Lagrange. How does a thrown ball know to find the particular arc whose path minimizes action? How does a ray of light know to find the path that minimizes time? Feynman answered these questions with images that served not only for the novel mysteries of quantum mechanics but for the treacherously innocent exercises posed for any beginning physics student. Light seems to angle neatly as it passes from air to water. It seems to bounce like a billiard ball off the surface of a mirror. It seems to travel in straight lines. These paths—the paths of least time—are special because they tend to be where the contributions of nearby paths are most closely in phase and most reinforce one another. Far from the path of least time—at the distant edge of a mirror, for example—paths tend to cancel one another out. Yet light does take every possible path, Feynman showed. The seemingly irrelevant paths are always lurking in the background, making their contributions, ready to make their presence felt in such phenomena as mirages and diffraction gratings.

Because it is a virtual particle, coming into existence for a mere ghostly instant, it can temporarily violate the laws that govern the system as a whole—the exclusion principle or the conservation of energy, for example. And Feynman noted that it is arbitrary to think of the photon as being emitted in one place and absorbed in the other: one can say just as correctly that it is emitted at (5), travels backward in time, and is then (earlier) absorbed at (6). The diagram is an aid to visualization. But it serves physicists mainly as a bookkeeping device. Each diagram is associated with a complex number, an amplitude that is squared to produce a probability for the process shown.

There was a grammar of permissible diagrams, corresponding, as Dyson had emphasized, to the permissible mathematical operations. Still, the diagrams could grow arbitrarily complicated, virtual particles appearing and disappearing in an intricate, recursive mesh. Feynman’s first H-shaped diagram for interacting electrons was the only such diagram with one virtual photon. Drawing all the possible diagrams with two virtual photons showed how quickly the permutations grew. Each made a contribution to the final computation, and more complicated diagrams became enormously difficult to calculate. Fortunately the greater the complication the less the probability and the smaller, therefore, the effect on the answer. Even so, physicists would shortly find themselves agonizing over pages of diagrams resembling catalogs of knots. They found it was worth the effort; each diagram could replace an effective lifetime of Schwingerian algebra.

Classically, absolute zero was often described as the temperature at which all motion ceases. Quantum mechanically, there is no such temperature. Atomic motion never does cease. That precise a zero would violate the uncertainty principle.

A new quantum number like isotopic spin—a quantity that seemed to be conserved through many kinds of interactions—implied new incarnations of symmetry. This notion increasingly dominated the physicists’ discourse. Symmetry for physicists was not far removed from symmetry for children with paper and scissors: the idea that something remains the same when something else changes. Mirror symmetry is the sameness that remains after a reflection of left and right. Rotational symmetry is the sameness that remains when a system turns on an axis. Isotopic spin symmetry, as it happened, was the sameness that existed between the two components of the nucleus, the proton and the neutron, two particles whose relationship had been oddly close, one carrying charge and the other neutral, their masses nearly but not exactly identical. The new way to understand these particles was this: They were two states of a single entity, now called a nucleon. They differed only in their isotopic spin. One was “up,” the other “down.”

Artificial though it was, Gell-Mann’s y qualified as not just a description but an explanation. As he conceived his framework, it was an organizing principle. It gave him a way of seeing families of particles, and its logic was so compelling that the families had obvious missing members. He was able to predict—and did predict, in papers he began publishing in August 1953—specific new particles not yet discovered, as well as specific particles that he insisted could not be discovered. His timing was perfect. Experimenters bore out each of his positive predictions (and failed to contradict the negative ones).

In modern times it became almost impossible to talk about the processes of scientific change without echoing Thomas S. Kuhn, whose Structure of Scientific Revolutions so thoroughly changed the discourse of historians of science. Kuhn distinguished between normal science—problem solving, the fleshing out of existing frameworks, the unsurprising craft that occupies virtually all working researchers—and revolutions, the vertiginous intellectual upheavals through which knowledge lurches genuinely forward.

The miler who triumphs in the Olympic Games, who places himself momentarily at the top of the pyramid of all milers, leads a thousand next-best competitors by mere seconds. The gap between best and second-best, or even best and tenth-best, is so slight that a gust of wind or a different running shoe might have accounted for the margin of victory. Where the measuring scale becomes multidimensional and nonlinear, human abilities more readily slide off the scale. The ability to reason, to compute, to manipulate the symbols and rules of logic—this unnatural talent, too, must lie at the very margin, where small differences in raw talent have enormous consequences, where a merely good physicist must stand in awe of Dyson and where Dyson, in turn, stands in awe of Feynman. Merely to divide 158 by 192 presses most human minds to the limit of exertion. To master—as modern particle physicists must—the machinery of group theory and current algebra, of perturbative expansions and non-Abelian gauge theories, of spin statistics and Yang-Mills, is to sustain in one’s mind a fantastic house of cards, at once steely and delicate. To manipulate that framework, and to innovate within it, requires a mental power that nature did not demand of scientists in past centuries. More physicists than ever rise to meet this cerebral challenge. Still, some of them, worrying that the Einsteins and Feynmans are nowhere to be seen, suspect that the geniuses have fled to microbiology or computer science—for...

The power of genius may lie, as Merton suggests, in the ability of one person to accomplish what otherwise might have taken dozens. Or perhaps it lies—especially in this exploding, multifarious, information-rich age—in one person’s ability to see his science whole, to assemble, as Newton did, a vast unifying tapestry of knowledge. Feynman himself, as he entered his forties, prepared to undertake this very enterprise: a mustering and a reformulating of all that was known about physics.

Although physicists still did not understand it, they appreciated the import of the discovery that nature distinguished right from left in its very core. Other symmetries were immediately implicated—the correspondence between matter and antimatter, and the reversibility of time (if the film of an experiment were run backwards, for example, it might look physically correct except that right would be left and left would be right). As one scientist put it, “We are no longer trying to handle screws in the dark with heavy gloves. We are being handed the screws neatly aligned on a tray, with a little searchlight on each that indicates the direction of its head.”

Publicly, Feynman was as serene as ever. Privately, he agonized over his inability to find the right problem. He wanted to stay clear of the pack. He knew he was not keeping up with even the published work of Gell-Mann and other high-energy physicists, yet he could not bear to sit down with the journals or preprints that arrived daily on his desk and piled up on his shelves and merely read them. Every arriving paper was like a detective novel with the last chapter printed first. He wanted to read just enough to understand the problem; then he wanted to solve it his own way. Almost alone among physicists, he refused to referee papers for journals. He could not bear to rework a problem from start to finish along someone else’s track.

He envisioned machines that would make smaller machines, each of which would make machines that were smaller still.

Learn by trying to understand simple things in terms of other ideas—always honestly and directly. What keeps the clouds up, why can’t I see stars in the daytime, why do colors appear on oily water, what makes the lines on the surface of water being poured from a pitcher, why does a hanging lamp swing back and forth—and all the innumerable little things you see all around you. Then when you have learned what an explanation really is, you can then go on to more subtle questions.

A theorist who can juggle different theories in his mind has a creative advantage, Feynman argued, when it comes time to change the theories. The path-integral formulation of quantum mechanics might be empirically equivalent to other formulations and yet—given less-than-omniscient human physicists—find more natural-seeming application to realms of science not yet explored. Different theories tended to give a physicist “different ideas for guessing,” Feynman said. And the century’s history had shown that when even so elegant and pure a theory as Newton’s had to be replaced, slight modifications could not suffice. To get something that would produce a slightly different result it had to be completely different. In stating a new law you cannot make imperfections on a perfect thing; you have to have another perfect thing. He understood explanations as a surgeon understands knives. He had a set of practical tests, heuristics, that he applied when reaching a judgment about a new idea in physics: for example, did it explain something unrelated to the original problem. He would challenge a young theorist: What can you explain that you didn’t set out to explain? He knew that why? is a question without an end and that our knowledge of things is inextricable from the language we use. The words and analogies from which we build our explanations are culpably linked with the things explained.

Feynman conceded the existence of genuine knowledge outside the range of science. He admitted that there were questions science could not answer, but grudgingly: he saw a danger in tying moral guidance to unpalatable myths, as religion did, and he resented the common view that science, with its merciless unraveling and explaining, was an enemy of the emotional appreciation of beauty. “Poets say science takes away from the beauty of the stars—mere globs of gas atoms,” he wrote in a famous footnote. I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part.... What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

Once more, he said he would speak as an old man to the young scientists and urge them to break away from the pack. At CERN, as at all the laboratories of high-energy physics, the pack was growing rapidly. Every experiment required enormous teams. Author lists for articles in the Physical Review were beginning to take up a comically large portion of the page. “It will not do you any harm whatever to think in an original fashion,” Feynman said. He offered a probabilistic argument. The odds that your theory will be in fact right, and that the general thing that everybody’s working on will be wrong, is low. But the odds that you, Little Boy Schmidt, will be the guy who figures a thing out, is not smaller.... It’s very important that we do not all follow the same fashion. Because although it is ninety percent sure that the answer lies over there, where Gell-Mann is working, what happens if it doesn’t? “If you give more money to theoretical physics,” he added, “it doesn’t do any good if it just increases the number of guys following the comet head. So it’s necessary to increase the amount of variety ... and the only way to do it is to implore you few guys to take a risk with your lives that you will never be heard of again, and go off in the wild blue yonder and see if you can figure it out.”

Late that night in Chicago he startled Goodstein by pressing the book into his hands and telling him he had to read it. Goodstein said he would look forward to it. No, Feynman said. You have to read it now. So Goodstein did, turning pages until dawn as Feynman paced nearby or sat and doodled on a sheet of paper. At one point Goodstein remarked, “You know, it’s amazing that Watson made this great discovery even though he was so out of touch with what everyone in his field was doing.” Feynman held up the paper he had been writing on. Amid scribbling and embellishments he had inscribed one word: DISREGARD. “That’s what I’ve forgotten,” he said.

Gell-Mann and, independently, an Israeli theorist, Yuval Ne’eman, found a way in 1961 to organize the various symmetries of spins and strangeness into a single scheme. It was a group, in the mathematicians’ sense of the word, known as SU(3), though Gell-Mann quickly and puckishly dubbed it the Eightfold Way. It was like an intricate translucent object which, when held to the light, would reveal families of eight or ten or possibly twenty-seven particles—and they would be different, though overlapping, families, depending on which way one chose to view it. The Eightfold Way was a new periodic table—the previous century’s triumph in classifying and thus exposing the hidden regularities in a similar number of disparate “elements.” But it was also a more dynamic object. The operations of group theory were like special shuffles of a deck of cards or the twists of a Rubik’s cube. Much of SU(3)’s power came from the way it embodied a concept increasingly central to the high-energy theorist’s way of working: the concept of inexact symmetry, almost symmetry, near symmetry, or—the term that won out—broken symmetry. The particle world was full of near misses in its symmetries, a dangerous problem, since it seemed to permit an ad hoc escape route whenever an expected relationship failed to match. Broken symmetry implied a process, a change in status. A symmetry in water is broken when it freezes, for now the system does not look the same from every direction. A magnet embodies symmetr...

Feynman, meanwhile, had disregarded so much of the decade’s high-energy physics that he had to make a long-term project of catching up. He tried to pay more attention to experimental data than to the methods and language of theorists. He tried, as always, to read papers only until he understood the issue and then to work out the problem for himself. “I’ve always taken an attitude that I have only to explain the regularities of nature—I don’t have to explain the methods of my friends,” he told a historian during these years.