Джеймс Глик - Genius - The Life and Science of Richard Feynman

In this way, amid these clusters of scientists, the theory of diffusion underwent a kind of scrutiny with few precedents in the annals of science. Elegant textbook formulations

were examined, improved, and then discarded altogether.

In their place came pragmatic methodologies, gimmicks with patches. The textbook equations had exact solutions, at least for special cases. In the reality of Los Alamos, the special cases were useless. In Feynman’s Los Alamos work, especial y, an accommodation with uncertainty became a running theme. Few other scientists fil ed the foreground

of

their

papers

with

such

blunt

acknowledgments of what was not known: “unfortunately cannot be expected to be as accurate”; “Unfortunately the figures contained herein cannot be considered as

‘correct’”; “These methods are not exact.” Every practical scientist learned early to include error ranges in their calculations; they learned to internalize the knowledge that three miles times 1.852 kilometers per mile equals five and a half kilometers, not 5.556 kilometers. Precision only dissipates, like energy in an engine governed by the second law of thermodynamics. Feynman often found himself not just accepting the process of approximation but manipulating it as a tool, employing it in the creation of theorems. Always he stressed ease of use: “… an interesting theorem was found to be extremely useful in obtaining approximate expressions … it does permit, in many cases, a simpler derivation or understanding …”; “…

in al cases of interest thus far investigated … accuracy has been found ample … extremely simple for computation and, once mastered, quite simple to use in thinking about a wide variety of neutron problems.” Theorems as theorems, or objects of mathematical beauty, had never been so

unappealing as at Los Alamos. Theorems as tools had never been so valued. Again and again the theorists had to devise equations with no hope of exact solution, equations that sentenced them to countless hours of laborious computation with nothing at the end but an approximation.

When they were done, the body of diffusion theory had become a hodgepodge. The state of knowledge was written in no one place, but it was more practical than ever before.

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 col isions, 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 difficulties of calculating practical diffusion problems forced the Los Alamos theorists into an untraditional approach. Instead of solving neat differential equations, they had to break the physics into steps and solve the problem numerical y, in smal increments of time. The focus

of attention was pushed back down to the microscopic level of individual neutrons fol owing individual paths. Feynman’s quantum mechanics was evolving along strikingly similar lines. His private work, like the diffusion work, embodied an abandonment of a too simple, too special differential approach; the emphasis on step-by-step computation; and above al the summing of paths and probabilities.

Computing by Brain

Walking around the hastily built wooden barracks that housed the soul of the atomic bomb project in 1943 and 1944, a scientist would see dozens of men laboring over computation.

Everyone

calculated.

The

theoretical

department was home to some of the world’s masters of mental arithmetic, a martial art shortly to go the way of jiujitsu. Any morning might find men such as Bethe, Fermi, and John von Neumann together in a single smal room where they would spit out numbers in a rapid-fire calculation of pressure waves. Bethe’s deputy, Weisskopf, specialized in a particularly oracular sort of guesswork; his office became known as the Cave of the Hot Winds, producing, on demand, unjustifiably accurate cross sections (shorthand for the characteristic probabilities of particle

col isions

in

various

substances

and

circumstances). The scientists computed everything from the shapes of explosions to the potency of Oppenheimer’s cocktails, first with rough guesses and then, when

necessary, with a precision that might take weeks. They estimated by seat of the pants, as a cook who wants one-third cup of wine might fil half a juice glass and correct with an extra splash. Anyone who calculated logarithms by mental y interpolating between the entries in a standard table—a technique that began to vanish thirty years later, when inexpensive electronic calculators made it obsolete—

learned to estimate this way, using some unconscious feeling for the right curve. Feynman had a toolbox of such curves in his head, precalibrated. His Los Alamos col eagues were sometimes amused to hear him, when thinking out loud, howl a sort of whooping glissando when he meant, this rises exponentially ; a different sound signified arithmetically . 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 real y 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: Suppose we treat some quantity as infinitesimal. He would al ow an error and then measure the

bounds of the error precisely.

It seemed to col eagues that some of his computation was a matter of conscious reputation building. One day Feynman, who had made a point of considering watches to be affectations, received a pocket watch from his father. He wore it proudly, and his friends began to needle him; they asked the time at every opportunity, until he began responding, with a glance at the watch: “Wel , four hours and twenty minutes ago it was twelve before noon,” or “In three hours and forty-nine minutes it wil be two seventeen.”

Few caught on. He was doing no arithmetic at al . Rather, he had designed a simple parlor trick in the spirit of gauge theories to come. Each morning he would turn his watch to a fixed offset from the true time—three hours and forty-nine minutes fast one day; the next day four hours and twenty minutes slow. He had only to remember one number and read the other directly from the watch. (This was the same Feynman who, years later, trying to describe to a layman the intricate shiftings of time and orientation on which theoretical physics depended, said, “You know how it is with daylight saving time? Wel , physics has a dozen kinds of daylight saving.”)

When Bethe and Feynman went up against each other in games of calculating, they competed with special pleasure.

Onlookers were often surprised, and not because the upstart Feynman bested his famous elder. On the contrary, more often the slow-speaking Bethe tended to outcompute Feynman. Early in the project they were working together on a formula that required the square of 48. Feynman