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

+ c = a + ( b + c ) , laws that were usual y assumed unconsciously, though quantum mechanics itself had shown how crucial y some mathematical operations did depend on their ordering. Stil 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 numbers—these had no immediate connection to counting, but Feynman continued pul ing them from his silvery logical engine. He turned to irrational numbers and complex numbers and complex powers of complex numbers—these came inexorably as soon as one from facing up to the question: What number, i , when multiplied by itself, equals negative one? He reminded his audience how to compute a logarithm from scratch and showed how the numbers converged as he took successive square roots often and thus, as an

inevitable by-product, derived the “natural base” e , that ubiquitous fundamental constant. 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 oscil ated, swinging from one to zero to negative one and back again in a wave that he drew for his audience, though they knew perfectly wel what a sine wave looked like. He had arrived at trigonometric functions. Now he posed one more question, as fundamental as al the others, yet encompassing them al 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 ? were conjoined as if by an invisible membrane, but as he told his mother, “I went pretty fast & didn’t give them a hel of a lot of time to work out the reason for one fact before I was showing them another stil 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. “Wel ,” he wrote, “al the mighty minds were mightily impressed by my little feats of arithmetic.”

Indeed, if Feynman was, as his friend Welton thought, consciously trying to establish himself among these influential physicists, he was succeeding even more than he knew. As early as November 1943, seven months after the Los Alamos project began, Oppenheimer began trying to persuade his department at Berkeley to hire Feynman for after the war. He wrote to the department chairman, Birge: He is by al odds the most bril iant young physicist here, and everyone knows this. He is a man of thoroughly engaging character and personality, extremely clear, extremely normal in al respects, and an excel ent teacher with a warm feeling for physics in al its aspects.

Oppenheimer warned that Feynman was sure to have other job offers, because “a not inconsiderable number of ‘big shots’” had already noticed him. He quoted two of the big shots. Bethe, according to Oppenheimer, had said bluntly that he would sooner lose any two scientists than lose Feynman. And Wigner of Princeton had made what was, for a physicist’s physicist in the 1940s, perhaps the ultimate tribute.

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

Fenced In

Feynman celebrated his wedding anniversary by gril ing steak outdoors at the Presbyterian Sanatorium in a smal charcoal broiler that Arline had ordered from a catalog. She also got him a chef’s hat, apron, and gloves. He wore them self-consciously, along with his new mustache, while she reveled in the domesticity of it al , until he could no longer stand the idea of people watching him from passing cars.

She laughed, asking, as she so often did, why he cared what other people thought. Steak was an extravagance—

eighty-four cents for two pounds. With it they ate watermelon, plums, and potato chips. The hospital lawn sloped down to Route 66, the cross-country highway, where the traffic roared by. Albuquerque was sweltering, and they were happy. Arline talked to her parents by long-distance telephone for seven minutes, another extravagance. After Richard left to hitchhike back north, a late-afternoon thundershower blackened the desert. Arline worried about him in the downpour. She stil had not gotten used to the raw force of storms in the open West.

His near-weekly trips through the val ey that lay between the Jemez and Sangre de Cristo mountains made him a rarity on the mesa. Few residents of that hermetic community had occasion to leave at al . Once, in a fanciful conversation about likely candidates to be a Nazi spy, one friend, Klaus Fuchs, a German turned Briton, suggested that it could only be Dick Feynman—who else had insinuated himself into so many different parts of the laboratory’s work? Who else had a regular rendezvous in Albuquerque? In its unreal isolation, with its unusual

populace, Los Alamos was growing into a parody of a municipality. It took its place in the mental geography of its residents as it was official y: not a vil age in the lee of the Jemez Mountains, not only a fenced-in circle of houses on dirt paths by a pond, with ducks, but also a fictitious abstraction, P. O. Box 1663, Santa Fe, New Mexico. To some it carried an ersatz resonance of a certain European stereotype of America, as one resident noted—“a pioneer people starting a new town, a self-contained town with no outside contacts, isolated in vast stretches of desert, and surrounded by Indians.” Victor Weisskopf was elected mayor. Feynman was elected to a town council. The fence that marked the city line heightened a magic-mountain atmosphere—it kept the world apart. An elite society had assembled on this hil . Elite and yet polyglot—in this cauldron, as in the other wartime laboratories, a final valedictory was being written to the Protestant, gentlemanly, leisurely class structure of American science.

Los Alamos did gather an aristocracy—“the most exclusive club in the world,” one Oxonian said—yet the princely, exquisitely sensitive Oppenheimer made it into a democracy, where no invisible lines of rank or status were to impede the scientific discourse. The elected councils and committees furthered that impression. Graduate students were supposed to forget that they were talking to famous professors. Academic titles were mainly left behind with the business suits and neckties. It was a democracy by night, too, when inflamed parties brought together cuisines and cocktails of four continents, dramatic readings and

political debates, waltzes and square dances (the same Oxonian, bemused amid the clash of cultures, asked, “What exactly is square about it—the people, the room, or the music?”), a Swede singing torch songs, an Englishman playing jazz piano, and Eastern Europeans playing Viennese string trios. Feynman played brassy drum duets with Nicholas Metropolis and organized conga lines. He had never been exposed to culture as such a flamboyant stew (certainly not when he was a student learning to disdain the packaged morsels that MIT handed to its would-be engineers). One party featured an original bal et, to modernistic-sounding music by Gershwin, titled Sacre du Mesa . At the end a clattering, flashing mechanical brain noisily revealed the sacred mystery of the mesa: 2 + 2 = 5.