Is it only nostalgia that makes genius seem to belong to the past? Giants did walk the earth—Shakespeare, Newton, Michelangelo, DiMaggio—and in their shadows the poets, scientists, artists, and baseball players of today crouch like pygmies. No one will ever again create a King Lear or hit safely in fifty-six consecutive games, it seems. Yet the raw material of genius—whatever combination of native talent and cultural opportunity that might be—can scarcely have disappeared. On a planet of five billion people, parcels of genes with Einsteinian potential must appear from time to time, and presumably more often than ever before. Some of those parcels must be as well nurtured as Einstein’s, in a world richer and better educated than ever before. Of course genius is exceptional and statistics-defying. Still, the modern would-be Mozart must contend with certain statistics: that the entire educated population of eighteenth-century Vienna would fit into a large New York apartment block; that in a given year the United States Copyright Office registers close to two hundred thousand “works of the performing arts,” from advertising jingles to epic tone poems. Composers and painters now awake into a universe with a nearly infinite range of genres to choose from and rebel against. Mozart did not have to choose an audience or a style. His community was in place. Are the latter-day Mozarts not being born, or are they all around, bumping shoulders with one another, scrabbling for cultural scraps, struggling to be newer than new, their stature inevitably shrinking all the while?
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—forgetting momentarily that the individual microbiologists and computer scientists they meet seem no brainier, on the whole, than physicists and mathematicians.
Geniuses change history. That is part of their mythology, and it is the final test, presumably more reliable than the trail of anecdote and peer admiration that brilliant scientists leave behind. Yet the history of science is a history not of individual discovery but of multiple, overlapping, coincidental discovery. All researchers know this in their hearts. It is why they rush to publish any new finding, aware that competitors cannot be far behind. As the sociologist Robert K. Merton has found, the literature of science is strewn with might-have-been genius derailed or forestalled—“those countless footnotes … that announce with chagrin: ‘Since completing this experiment, I find that Woodworth (or Bell or Minot, as the case may be) had arrived at this same conclusion last year, and that Jones did so fully sixty years ago.’” 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.
Scientists still ask the what if questions. What if Edison had not invented the electric light—how much longer would it have taken? What if Heisenberg had not invented the S matrix? What if Fleming had not discovered penicillin? Or (the king of such questions) what if Einstein had not invented general relativity? “I always find questions like that … odd,” Feynman wrote to a correspondent who posed one. Science tends to be created as it is needed.
“We are not that much smarter than each other,” he said.
Weak Interactions
By the late 1950s and early 1960s, as the discovery of new particles became more commonplace, physicists found it harder to guess what might and might not be possible. The word zoo entered their vocabulary, and their scientific intuition sometimes seemed colored by a kind of aesthetic queasiness. Weisskopf declared at one meeting that it would be a shame if anyone found a particle with double charge. Oppenheimer added that he personally would hate to see a strongly interacting particle with spin greater than one-half. Both men were quickly disappointed. Nature was not so fastidious.
The methods assembled under the label of field theory just a few years before—direct computation of particle interactions, in the face of those still-troubling infinities—fell out of favor with many. The success of quantum electrodynamics did not extend easily to other particle realms. Of the four fundamental forces—electromagnetism; gravity; the strong force binding the atomic nucleus; and the weak force at work in radioactive beta decay and in strange-particle decays—renormalization seemed to work only for electromagnetism. With electromagnetism, the first, simplest Feynman diagrams told most of the story. Mathematically the relative weakness of the force expressed itself in the diminishing importance of more complicated diagrams (for the same reason that the later terms in a series like 1 + n + n2 + … vanish if n is 1/100). With the strong force, the forest of Feynman diagrams made an unendingly large contribution to any calculation. That made real calculations impossible. So where the more esoteric forces were concerned, it seemed impossible to match the success of quantum electrodynamics in making amazingly precise dynamical predictions. Instead, symmetries, conservation laws, and quantum numbers provided abstract principles by which physicists could at least organize the experimentalists’ data. They looked for patterns, organized taxonomies, filled in holes. A diverging branch of mathematical physicists continued to pursue field theory, but most theorists now found it profitable to sift through particle data—the data now arriving in huge volume—looking for general principles. Searching for symmetries meant not tying oneself to the microscopic dynamics of particle behavior. It came to seem almost immoral, or at least silly, for a theorist to write down a specific dynamic or scale.
The understanding of symmetry also became an understanding of symmetry’s imperfections, for, as symmetry laws came to dominate, they also began to break down. One of the most obvious of all symmetries led the way: the symmetry of left and right. Humans seem mostly symmetrical, but not perfectly so. The symmetry is “broken,” as a modern physicist would say, by an off-center heart and liver and by more subtle or superficial differences. We learn to break the symmetry ourselves by internalizing an awareness of the difference between left and right, although sometimes this is not so easy. Feynman himself confessed to a group gathered around the coffee pot in a Caltech laboratory that even now he had to look for the mole on the back of his left hand when he wanted to be sure. As early as his MIT fraternity days he had puzzled over the classic teaser of mirror symmetry: why does a mirror seem to invert left and right but not top and bottom? That is, why are the letters of a book backward but not upside down, and why would Feynman’s double behind the mirror appear to have a mole on his right hand? Was it possible, he liked to ask, to give a symmetrical explanation of what a mirror does—an explanation that treats up-and-down no differ
ently from left-and-right? Many logicians and scientists had debated this conundrum. There were many explanations, some of them correct. Feynman’s was a model of clarity.
Imagine yourself standing before the mirror, he suggested, with one hand pointing east and the other west. Wave the east hand. The mirror image waves its east hand. Its head is up. Its west hand lies to the west. Its feet are down. “Everything’s really all right,” Feynman said. The problem is on the axis running through the mirror. Your nose and the back of your head are reversed: if your nose points north, your double’s nose points south. The problem now is psychological. We think of our image as another person. We cannot imagine ourselves “squashed” back to front, so we imagine ourselves turned left and right, as if we had walked around a pane of glass to face the other way. It is in this psychological turnabout that left and right are switched. It is the same with a book. If the letters are reversed left and right, it is because we turned the book about a vertical axis to face the mirror. We could just as easily turn the book from bottom to top instead, in which case the letters will appear upside down.
Our own asymmetries—our blemishes, hearts, handednesses—arise from contingent choices nature made in the process of building up complicated organisms. A preference for right or left appears in biology all the way down to the level of organic molecules, which can be right- or left-handed. Sugar molecules have this intrinsic corkscrew property. Chemists can make them with either handedness, but bacteria digest only “right-handed” sugar, and that is the kind that sugar beets produce. Earthly sugar beets, that is—for evolution might just as well have chosen a left-handed pathway, just as the industrial revolution might have settled on left-threaded rather than right-threaded screws.
On still smaller scales, at the level of elementary particle interactions, physicists assumed that nature would not distinguish between right and left. It seemed inconceivable that the laws of physics would change with mirror reflection, any more than they change when an experiment is conducted at a different place or a different time. How could anything so featureless as a particle embody the handedness of a corkscrew or a golf club? Right-left symmetry had been built into quantum mechanics in the form of a quantity called parity. If a given event conserved parity, as most physicists consciously or unconsciously assumed it must, then its outcome did not depend on any left-right orientation. Conversely, if nature did have some kind of handedness built into its guts, then an experimenter might be able to find events that did not conserve parity. When Murray Gell-Mann was a graduate student at MIT, a standard problem in one course was to derive the conservation of parity by mathematical logic, transforming coordinates from left-handed to right-handed. Gell-Mann spent a long weekend transforming coordinates back and forth without proving anything. He recalled telling the instructor that the problem was wrong: that the conservation of parity was a physical fact that depended on the structure of a particular theory, not on any inescapable mathematical truth.
Parity became an issue in theorists’ unease about the liveliest experimental problem coming out of the accelerators in 1956: the problem of the theta and the tau, two strange particles (strange in Gell-Mann’s sense). It was typical of the difficulties physicists were having in making taxonomical sense of the jumble of accelerator data. When the theta decayed, a pair of pions appeared. When the tau decayed, it turned into three pions. In other ways, however, the tau and the theta were beginning to look suspiciously similar. Data from cosmic rays and then accelerators made their masses and lifetimes seem indistinguishable. One experimenter had plotted thirteen data points in 1953. By the time the 1956 Rochester conference convened, he had more than six hundred data points, and the theorists were trying to face the obvious: perhaps the tau and the theta were one and the same. The problem was parity. A pair of pions had even parity. A trio of pions had odd parity. Assuming that a particle’s decay conserved parity, a physicist had to believe that the tau and the theta were different. Intuitions were severely tested. Sometime after the Rochester conference ended, Abraham Pais wrote a note to himself: “Be it recorded here that on the train back from Rochester to New York, Professor Yang and the writer each bet Professor Wheeler one dollar that the theta- and tau-meson are distinct particles; and that Professor Wheeler has since collected two dollars.”
Everyone was making bets. An experimenter asked Feynman what odds he would give against an experiment testing for the unthinkable, parity violation, and Feynman was proud later that he had offered a mere fifty to one. He actually raised the question at Rochester, saying that his roommate there, an experimenter named Martin Block, had wondered why parity could not be violated. (Afterward Gell-Mann teased him mercilessly for not having asked the question in his own name.) Someone had joked nervously about considering even wild possibilities with open minds, and the official note taker recorded:
Pursuing the open mind approach, Feynman brought up a question of Block’s: Could it be that the [theta] and [tau] are different parity states of the same particle which has no definite parity, i.e., that parity is not conserved. That is, does nature have a way of defining right- or left-handedness uniquely?
Two young physicists, Chen Ning Yang and Tsung Dao Lee, said they had begun looking into this question without reaching any firm conclusions. So desperately did the participants dislike the idea of parity violation that one scientist proposed yet another unknown particle, this time one that departed the scene with no mass, no charge, and no momentum—just carrying off “some strange space-time transformation properties” like a sanitation worker carting away trash. Gell-Mann rose to suggest that they keep their minds open to the possibility of other, less radical solutions. Discussion continued until, as the note taker put it, “The chairman”—Oppenheimer—“felt that the moment had come to close our minds.”
But in Feynman’s tentative question the answer had emerged. Lee and Yang undertook an investigation of the evidence. For electromagnetic interactions and strong interactions, the rule of parity conservation had a real experimental and theoretical foundation. Without parity conservation, a well-entrenched framework would be torn apart. But that did not seem to be true for weak interactions. They went through an authoritative text on beta decay, recomputing formulas. They examined the recent experimental literature of strange particles. By the summer of 1956 they realized that, as far as the weak force was concerned, parity conservation was a free-floating assumption, bound neither to any experimental result nor to any theoretical rationale. Furthermore, it occurred to them that Gell-Mann’s conception of strangeness offered a precedent: a symmetry that held for the strong force and broke down for the weak. They quickly published a paper formally raising the possibility that parity might not be conserved by weak interactions and proposing experiments to test the question. By the end of the year, a team led by their Columbia colleague Chien Shiung Wu had set one of them up, a delicate matter of monitoring the decay of a radioactive isotope of cobalt in a magnetic field at a temperature close to absolute zero. Given an up and down defined by the alignment of the magnetic coil, the decaying cobalt would either spit out electrons symmetrically to the left and right or would reveal a preference. In Europe, awaiting the results, Pauli joined the wagerers: he wrote Weisskopf, “I do not believe that the Lord is a weak left-hander, and I am ready to bet a very large sum that the experiments will give symmetric results.” Within ten days he knew he was wrong, and within a year Yang and Lee had received one of the quickest Nobel Prizes ever awarded. 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.”
Feynman made an odd presence at the high-energy physicists’ meetings. He was older than the bright young scientists of Gell-Mann’s generation, younger than the Nobel-wielding senators of Oppenheimer’s. He neither withdrew from the discussions nor dominated them. He showed a piercing interest in the topical issues—as with his initial prodding on the question of parity—but struck younger physicists as detached from the newest ideas, particularly in contrast to Gell-Mann. At the 1957 Rochester conference it occurred to at least one participant that Feynman himself should have applied his theoretical talents to the question he had raised a year earlier, instead of leaving the plum to Yang and Lee. (The same participant noticed a revisionists’ purgatory in the making: theorists from Dirac to Gell-Mann “busy explaining that they personally had never thought parity was anything special,” and experimenters recalling that they had always meant to get around to an experiment like Wu’s.) 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 also knew that when he broke his own rule he could be devastatingly cruel. He summarized one text by writing, “Mr. Beard is very courageous when he gives freely so many references to other books, because if a student ever did look at another book, I am sure he would not return again to continue reading Beard,” and then urged the editor to keep his review confidential—“for Mr. Beard and I are good personal friends.”) His persistently iconoclastic approach to other people’s work offended even theorists whom he meant to compliment. He would admire what they considered a peripheral finding, or insist on what struck them as a cockeyed or baroque alternative viewpoint. Some theorists strived to collaborate with colleagues and to set a tone and an agenda for whole groups. Gell-Mann was one. Feynman seemed to lack that ambition—though a generation of physicists now breathed Feynman diagrams. Still, he was frustrated.