Genius: The Life and Science of Richard Feynman - James Gleick (1993)
LOS ALAMOS
Feynman tinkered with radios again at the century’s big event. Someone passed around dark welding glass for the eyes. Edward Teller put on sun lotion and gloves. The bomb makers were ordered to lie face down, their feet toward ground zero, twenty miles away, where their gadget sat atop a hundred-foot steel tower. The air was dense. On the way down from the hill three busloads of scientists had pulled over to wait while one man went into the bushes to be sick. A moist lightning storm had wracked the New Mexican desert. Feynman, the youngest of the group leaders, now grappled more and more urgently with a complicated ten-dial radio package mounted on an army weapons carrier. The radio was the only link to the observation plane, and it was not working.
He sweated. He turned the dials with nervous fingers. He knew what frequency he needed to find, but he asked again anyway. He had almost missed the bus after having flown back from New York when he received the urgent coded telegram, and he had not had time to learn what all those dials did. In frustration he tried rearranging the antenna. Still nothing—static and silence. Then, suddenly, music, the eerie, sweet sound of a Tchaikovsky waltz floating irrelevantly from the ether. It was a shortwave transmission on a nearby frequency, all the way from San Francisco. The signal gave Feynman a bench mark for his calibrations. He worked the dials again until he thought he had them right. He reset them to the airplane’s wavelength one last time. Still nothing. He decided to trust his calibrations and walk away. Just then a raspy voice broke through the darkness. The radio had been working all along; the airplane had not been transmitting. Now Feynman’s radio announced, “Minus thirty minutes.”
Distant searchlights cut the sky, flashing back and forth between the clouds and the place Feynman knew the tower must be. He tried to see his flashlight through his welder’s glass and decided, to hell with it, the glass was too dim. He looked at the people scattered about Campania Hill, like a movie audience wearing 3-D glasses. A bunch of crazy optimists, he thought. What made them so sure there would be any light to filter? He went to the weapons carrier and sat in the front seat; he decided that the windshield would cut out enough of the dangerous ultraviolet. In the command center twenty-five miles away, Robert Oppenheimer, thin as a specter, wearing his tired hat, leaned against a wooden post and said aloud, “Lord, these affairs are hard on the heart,” as though there had ever been such an affair.
At 5:29:45 A.M., July 16, 1945, just before dawn would have lighted the place called (already) the Jornada del Muerto, Journey of Death, instead came the flash of the atomic bomb. In the next instant Feynman realized that he was looking at a purple blotch on the floor of the weapons carrier. His scientific brain told his civilian brain to look up again. The earth was paper white, and everything on it seemed featureless and two-dimensional. The sky began to fade from silver to yellow to orange, the light bouncing off new-formed clouds in the lee of the shock wave. Something creates clouds! he thought. An experiment was in progress. He saw an unexpected glow from ionized air, the molecules stripped of electrons in the great heat. Around him witnesses were forming memories to last a lifetime. “And then, without a sound, the sun was shining; or so it looked,” Otto Frisch recalled afterward. It was not the kind of light that could be assessed by human sense organs or scientific instruments. I. I. Rabi was not thinking in foot-candles when he wrote, “It blasted; it pounced; it bored its way into you. It was a vision which was seen with more than the eye.” The light rose and fell across the bowl of desert in silence, no sound heard until the expanding shell of shocked air finally arrived one hundred seconds after the detonation.
Then came a crack like a rifle shot, startling a New York Times correspondent at Feynman’s left. “What was that?” the correspondent cried, to the amusement of the physicists who heard him.
“That’s the thing,” Feynman yelled back. He looked like a boy, lanky and grinning, though he was now twenty-seven. A solid thunder echoed in the hills. It was felt as much as heard. The sound made it suddenly more real for Feynman; he registered the physics acoustically. Enrico Fermi, closer to the blast, barely heard it as he tore up a sheet of paper and calculated the explosive pressure by dropping the pieces, one by one, through the sudden wind.
The jubilation, the shouting, the dancing, the triumph of that day have been duly recorded. On the road back, another physicist thought Feynman was going to float through the roof of the bus. The bomb makers rejoiced and got drunk. They celebrated the thing, the device, the gadget. They were smart, can-do fellows. After two years in this brown desert they had converted some matter into energy. The theorists, especially, had now tested an abstract blackboard science against the ultimate. First an idea—now fire. It was alchemy at last, an alchemy that changed metals rarer than gold into elements more baneful than lead.
Accustomed to spending their days in a mostly mental world, the theorists had sweated over messy problems that they could touch and smell. Almost everyone was working in a new field, the theory of explosions, for example, or the theory of matter at extremely high temperatures. The practicality both sobered and thrilled them. 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. There was no choosing issues for their elegance or simplicity. These problems chose themselves—ticklish chemicals and exploding pipes. Feynman himself interrupted diffusion calculations to repair typewriters, interrupted typewriter repair to check the safety of accumulating masses of uranium, and invented new kinds of computing systems, part machine and part human, to solve equations that theoretically could not be solved at all. A pragmatic spirit had taken over the mesas of Los Alamos; no wonder the theorists were exhilarated.
Later they remembered having had doubts. Oppenheimer, urbane and self-torturing aficionado of Eastern mysticism, said that as the fireball stretched across three miles of sky (while Feynman was thinking, “Clouds!”) he had thought of a passage from the Bhagavad-Gita, “Now I am become Death, the destroyer of worlds.” The test director, Kenneth Bainbridge, supposedly told him, “We are all sons of bitches now.” Rabi, when the hot clouds dissipated, said he felt “a chill, which was not the morning cold; it was a chill that came to one when one thought, as for instance when I thought of my wooden house in Cambridge …” In the actuality of the event, relief and excitement drowned out most such thoughts. Feynman remembered only one man “moping”—his own recruiter to the Manhattan Project, Robert Wilson. Wilson surprised Feynman by saying, “It’s a terrible thing that we made.” For most the second thoughts did not come until later. On the scene the scientists, polyglot and unregulation though they seemed to the military staff, shared a patriotic intensity that faded from later accounts. Three weeks after the test, and three days after Hiroshima—on the day, as it happened, of Nagasaki—Feynman used a typewriter to set down his thoughts in a letter to his mother.
We jumped up and down, we screamed, we ran around slapping each other on the backs, shaking hands, congratulating each other… . Everything was perfect but the aim—the next one would be aimed for Japan not New Mexico… . The fellows working for me all gathered in the hall with open mouths, while I told them. They were all proud as hell of what they had done. Maybe we can end the war soon.
The experiment code-named Trinity was the threshold event of an age. It permanently altered the psychology of our species. Its prelude was a proud mastery of science over nature—irreversible. Its sequel was violence and death on a horrible scale. In the minute that the new light spread across that sky, humans became fantastically powerful and fantastically vulnerable. A story told many times becomes a myth, and Trinity became the myth that illuminated the postwar world’s anxiety about the human future and its reckless, short-term approach to life. The images of Trinity—the spindly hundred-foot tower waiting to be vaporized, the jackrabbits found shredded a half-mile from the blast, the desert sand fused to a bright jade-green glaze—came to presage the central horror of an age. We have hindsight. We know what followed: the blooding of the scientists, the loss of innocence—Hiroshima, Dr. Strangelove, throw weights, radwaste, Mutual Assured Destruction. The irony is built in. At first, though, ground zero stood for nothing but what it was, a mirrored surface, mildly radioactive, where earlier had stood a tower of steel. Richard Feynman, still not much more than a boy, wrote, “It is a wonderful sight from the air to see the green area with the crater at the center in the brown desert.”
The Man Comes In with His Briefcase
Thirty months had passed since the closing of the isotron project at Princeton. Feynman and the rest of Wilson’s team had been left in a tense limbo—not knowing. Wilson thought they were like professional soldiers awaiting their next orders. “We became then what I suppose is the worst of all possible things,” he said later, “a research team without a problem, a group with lots of spirit and technique, but nothing to do.” To pass the time he decided to invent some neutron-measuring equipment, sure to be needed before long. He meanwhile felt a dearth of hard information from Chicago, the project’s temporary center, domain of Enrico Fermi and his atomic “pile” (the leather-jacketed physicist from Rome was using his freshly acquired Anglo-Saxon vocabulary to coin a blunt nuclear jargon). The pile—graphite bricks and uranium balls assembled into a lattice on a university squash court—was chain-reacting. Wilson sent Feynman as his emissary.
First came a briefing on the art of information gathering. He told Feynman to approach each department in turn and offer to lend expertise. “Have them describe to you in every detail the problem to such a point that you really could sit down and work on it without asking any more questions.”
“That’s not fair!” Feynman recalled saying.
“That’s all right, that’s what we’re going to do, and that way you’ll know everything.”
Feynman took the train to Chicago early in 1943. It was his first trip west since the Century of Progress fair a decade before. He did gather information as efficiently as a spy. He got to know Teller and they talked often. He went from office to office learning about neutron cross sections and yields. He also left behind an impressed group of theorists. At one meeting he handed them a solution to an awkward class of integrals that had long stymied them. “We all came to meet this brash champion of analysis,” recalled Philip Morrison. “He did not disappoint us; he explained on the spot how to gain a quick result that had evaded one of our clever calculators for a month.” Feynman saw that the problem could be broken into two parts, such that part B could be looked up in a table of Bessel functions and part A could be derived using a clever trick, differentiation with respect to parameter on the integral side—something he had practiced as a teenager. Now the audience was new and the stakes were higher.
He was not the last prodigy to plant the kernel of a legend at the Metallurgical Laboratory. Five months after he passed through, Julian Schwinger arrived from Columbia, by way of Berkeley, where he had already collaborated with Oppenheimer, and the MIT Radiation Laboratory. Schwinger was Feynman’s exact contemporary, and the contrast between these two New Yorkers was striking. Their paths had not yet crossed. Schwinger impressed the Chicago scientists with his pristine black Cadillac sedan and his meticulous attire. His tie never seemed to loosen through that hot summer. A colleague trying to take notes while he worked at the blackboard through the night found the process hectic. Schwinger, who was ambidextrous, seemed to have fashioned a two-handed blackboard technique that let him solve two equations at once.
Strange days for physicists reaching what should have been the intense prime of their creative careers. The war disrupted young scientists’ lives with infinite gentleness compared with the disruption suffered by most draft-age men; still, Feynman could only wait uneasily for the course change war would entail. Almost as a lark he had accepted a long-distance job offer from the University of Wisconsin, as a visiting assistant professor on leave without pay. It gave him some feeling of security, though he hardly expected to become more than a professor on leave. Now, in Chicago, he decided at the last moment to take a side trip to Madison and spent a day walking about the campus almost incognito. In the end he introduced himself to a department secretary and met a few of his nominal colleagues before heading back.
He returned to Princeton with a little briefcase full of data. He briefed Wilson and the others: telling them how the bomb looked as of the winter of early 1943, how much uranium would be needed, how much energy would be produced. He was a twenty-four-year-old standing in shirtsleeves in a college classroom. Wisecracks and laughter echoed from the corridor. Feynman was not thinking about history, but Paul Olum was. “Someday when they make a moving picture of the dramatic moment at which the men of Princeton learn about the bomb, and the representative comes back from Chicago and presents the information, it will be a very serious situation, with everybody sitting in their suit coats and the man comes in with his briefcase,” he told Feynman. “Real life is different than one imagines.”
The army had made its unlikely choice of a civilian chief: a Jew, an aesthete, a mannered, acerbic, left-flirting, ultimately self-destructive scientist whose administrative experience had not extended beyond a California physics group. J. Robert Oppenheimer—Oppy, Oppie, Opje—held the respect of colleagues more for his quicksilver brilliance than for the depth of his work. He had no feeling for experimentation, and his style was unphysical; so, when he made mistakes, they were notoriously silly ones: “Oppenheimer’s formula … is remarkably correct for him, apparently only the numerical factor is wrong,” a theoretician once wrote acidly. In later physicist lingo a calculation’s Oppenheimer factors were the missing π’s, i’s, and minus signs. His physics was, as the historian Richard Rhodes commented, “a physics of bank shots”—“It works the sides and the corners … but prefers not to drive relentlessly for the goal.” No one understood the core problems of quantum electrodynamics and elementary particle physics better than he, but his personal work tended toward esoterica. As a result, though he became the single most influential behind-the-scenes voice in the awarding of Nobel Prizes in physics, he never received one himself. In science as in all things he had the kind of taste called exquisite. His suits were tailored with exaggerated shoulders and broad lapels. He cared about his martinis and black coffee and pipe tobacco. Presiding over a committee dinner at a steak house, he expected his companions to follow his lead in specifying rare meat; when one man tried to order well-done, Oppenheimer turned and said considerately, “Why don’t you have fish?” His New York background was what Feynman’s mother’s family had striven toward and fallen back from; like Lucille Feynman he had grown up in comfortable circumstances in Manhattan and attended the Ethical Culture School. Then, where Feynman assimilated the new, pragmatic, American spirit in physics, Oppenheimer had gone abroad to Cambridge and Göttingen. He embraced the intellectual European style. He was not content to master only the modern languages. To physicists Oppenheimer’s command of Sanskrit seemed a curiosity; to General Groves it was another sign of genius. And genius was what the general sought. Solid administrator that he was, he saw no value in a merely solid chief scientist. Much to the surprise of some, Groves’s instincts proved correct. Oppenheimer’s genius was in leadership after all. He bound Feynman to him in the winter of early 1943, as he bound so many junior colleagues, taking an intimate interest in their problems. He called long-distance from Chicago—Feynman had never had a long-distance telephone call from so far—to say that he had found a sanatorium for Arline in Albuquerque.
In the choice of a site for the atomic bomb project, the army’s taste and Oppenheimer’s coincided. Implausible though it may have seemed afterward, military planning favored desert isolation for security against enemy attack as well as more reasonably for the quarantine of a talkative and unpredictable scientific community. Oppenheimer had long before fallen in love with New Mexico’s unreal edges, the air clear as truth, the stunted pines cleaving to canyon walls. He had made Western work shirts and belt buckles part of his casual wear, and now he led Groves up the winding trail to the high mesa where the Los Alamos Ranch School for boys looked back across the wide desert to the Sangre de Cristo Mountains. Not everyone shared their immediate sympathy with the landscape. Leo Szilard, the Budapest native who first understood the energy-liberating chain reaction—at other times so prescient about the bomb project—declared: “Nobody could think straight in a place like that. Everybody who goes there will go crazy.”
The impatient Princeton group signed up en masse. Wilson rushed out to see the site and rushed back to report on the mud and confusion, a theater being built instead of a laboratory, water lines being mislaid. The state of secrecy was such that Feynman already knew that Groves and Oppenheimer were arguing over the state of secrecy. Cyclotron parts and neutron-counting gear started heading out by rail in wooden crates from the Princeton station. Princeton’s carloads provided the new laboratory’s core equipment, followed eventually by a painstakingly dismantled cyclotron from Harvard and other generators and accelerators. Soon Los Alamos was the best-equipped physics center in the world. The Princeton team began leaving soon after the crates of gear. Richard and Arline went with the first wave, on Sunday, March 28. Instructions were to buy tickets for any destination but New Mexico. Feynman’s contrariety warred for a moment with his common sense, and contrariety won out. He decided that, if no one else was buying a New Mexico ticket, he would. The ticket seller said, Aha—all these crates are for you?
The railroad provided a wheelchair and a private room for Arline. She had begged Richard tearfully to pay the extra price for the room and hinted that at last she might have a chance to be all that a wife should be to the husband she loves. For both of them the move out West portended an open-skied, open-ended future. It cut them off finally from their protective institutions and their childhoods. Arline cried night after night from worry and filled Richard with her dreams: curtains in their home, teas with his students, chess before the fireplace, the Sunday comics in bed, camping out in a tent, raising a son named Donald.
Chain Reactions
Fermi’s pile of uranium and graphite, sawed and assembled by professional cabinetmakers in a University of Chicago racquets court, became the world’s first critical mass of radioactive material on December 2, 1942. Amid the black graphite bricks, the world’s first artificial chain reaction sustained itself for half an hour. It was a slow reaction, where a bomb would have to be a fast reaction—less than a millionth of a second. From the two-story-high ellipsoid of Chicago pile number one to the baseball-size sphere of plutonium that exploded at Trinity, there could be no smooth evolutionary path. To go from the big, slow pile to a small, fast bomb would require a leap. There were few plausible intermediate stages.
Yet one possibility was playing itself out in Feynman’s mind the next April, as he sat in a car just outside the makeshift security gate on the Los Alamos mesa. Hydrogen atoms slowed neutrons, as Fermi had discovered ages ago. Water was cheaply bound hydrogen. Uranium dissolved in water could make a powerful compact reactor. Feynman waited while the military guards tried to straighten out a mistake about his pass. Left and right from the security gate stretched the beginnings of a barbed-wire fence. Behind it lay no laboratory, but a few ranch buildings and a handful of partially complete structures rose from the late-winter mud in what the army called modified mobilization style, namely fast-setting concrete foundations, wood frame, plain siding, asphalt roofs. The thirty-five-mile ride from Santa Fe had ended in a harrowing dirt road cut bluntly into the mesa walls. Feynman was not the only physicist who had never been farther west than Chicago. The recruiters had warned scientists that the army wanted isolation, but no one quite realized what isolation would mean. At first the only telephone link was a single line laid down by the Forest Service. To make a call one had to turn a crank on the side of the box.
As he sat waiting for the military police to approve his pass, Feynman was running through some calculations for the hypothetical in-between reactor that would be called a water boiler. Instead of blocks of uranium interspersed with graphite, this unit would use a uranium solution in water, uranium enriched with a high concentration of the 235 isotope. The hydrogen in the water would increase the effectiveness many times over. He was trying to figure out how much uranium would be needed. He worked on the water-boiler problem, picking it up and putting it down again over the next weeks, thinking about the detailed geometry of neutrons colliding in hydrogen. Then he tried something quirky. Perhaps the ideal arrangement of uranium, the one that would require the least material, would be different from the obvious uniform arrangement. He converted the equations into a form that would allow a shortcut solution in terms of a minimum principle, now his favorite technique. He worked out a theorem for the spatial distribution of fissionable material—and discovered that the difference would not matter in a reactor as small as this. When enriched uranium finally began to arrive, the water boiler took form as a one-foot sphere inside a three-foot cube of black beryllium oxide, sitting on a table behind a heavy concrete wall at the pine-shaded bottom of Omega Canyon, miles away from the main site. It served as the project’s first large-scale experimental source of neutrons and the first real explosion hazard. For all the theorists, the elements of this first problem became leitmotivs of their time working on the bomb: the paths of neutrons, the mixing of esoteric metals, the radiation, the heat, the probabilities.
In the muddy weeks of April the population of scientists reached about thirty. They came and went through a temporary office in Santa Fe and disappeared from there into a void in the landscape. If they had seen their destination from the air, they would have understood that they were to be situated in a compound atop a flat finger of ancient lava, one of many radiating from the giant crater of a long-quiet volcano. Instead, their imagining of the place began with mysterious addresses: P. O. Box 1663 for mail, Special List B for driver’s licenses. Not all the procedures devised in the name of security helped allay the suspicions of the local population. Any local policeman who pulled over Richard Feynman on the road north of Santa Fe would see the driver’s license of a nameless Engineer identified only as Number 185, residing at Special List B, whose signature was, for some reason, Not required. The name Los Alamos meant hardly anything. A canyon? A boys’ school? When scientists reached the site they would see, as likely as not, a former professor standing outdoors and peppering a military construction crew with unwanted instructions. If Oppenheimer happened to be there to greet them, he would say from beneath the already famous hat, “Welcome to Los Alamos and who the devil are you?” The first familiar face that Feynman saw belonged to his Princeton friend Olum—Olum was standing in the road with a clipboard, checking off each truckload of lumber as it arrived. At first Feynman slept in one of a row of beds lined up on the balcony of a school building. Food was still coming up from Santa Fe in the form of box lunches.
Amid the turmoil of construction, the concrete hardening in the open air, the noise of hand-held buzz saws everywhere, only the theorists had the equipment they needed to start work immediately—one blackboard on rollers. Their true ground-breaking ceremony came on April 15. Oppenheimer gathered them together, along with the first few experimentalists and chemists, to learn officially what they had been told in hushed tones. They were to build a bomb, a weapon, a working device that would concentrate the neutron-spraying phenomenon of radioactivity into a speck of space and time concentrated enough to force an explosion. As the lecture began, Feynman opened a notebook and wrote the cautionary words, “Talks are not necessarily on things we should discuss but things we have worked out.” Much was known to the teams from Berkeley and Chicago, or so it seemed. The splitting of an ordinary uranium atom required a blow from a fast, high-energy neutron. Every atom was its own tiny bomb: it split with a jolt of energy and released more neutrons to trigger its neighbors. The neutrons tended to slow, however, dropping below the necessary threshold for further fission. The chain reaction would not sustain itself. However, the rarer isotope, uranium 235, would fission when struck by a slow neutron. If a mass of uranium were enriched with these more volatile atoms, neutrons would find more targets and chain reactions would live longer. Pure uranium 235—though it would not be available in any but microscopic quantities for months—would make an explosive reaction possible. Another way to encourage a chain reaction was to surround the radioactive mass with a shell of metal, a tamper, that would reflect neutrons back toward the center, intensifying their effects as the glass of a greenhouse intensifies its infrared warming. A lanky Oppenheimer aide, Robert Serber, described the different tamper possibilities to his audience of thirty-odd men radiating an almost palpable energy of nerves. Feynman wrote quickly. “… reflect neutrons … keep bomb in … critical mass … Non absorbing equiscattering factor 3 in mass … a good explosion …” He sketched some hasty diagrams. From nuclear physics the discussion was forced to turn to the older but messier subject of hydrodynamics. While the neutrons were doing their work, the bomb would heat and expand. In a crucial millisecond would come shock waves, pressure gradients, edge effects. These would be hard to calculate, and for a long time the theorists would be calculating blind.
Making a bomb was not like making a theory of quantum electrodynamics, where the ground had already been mined by the greatest scientists. Here the problems were fresh, close to the surface, and therefore—this surprised Feynman at first—easy. Beginning with the issues raised by the first indoctrination lectures, he produced a string of small triumphs, gratifying by contrast with the long periods of wandering in the dark of pure theory. There were compensating difficulties, however.
“Most of what was to be done was to be done for the first time,” an anonymous ghostwriter of the bomb’s official history wrote afterward. (The ghostwriter was Feynman, called to this unaccustomed service by his former department head, Harry Smyth.) Struggling to sum up the problems of theoretical science at Los Alamos, he added “untried,” and then “with materials which were for a long time practically unavailable.” Materials—he could not bring himself to write uranium or plutonium after the euphemistic years of tubealloy and 49. The wait for tubealloy had been agonizing, for the theorists no less than the experimenters. More mundane materials could be requisitioned—at the laboratory’s request Fort Knox delivered two hemispheres of pure gold, each the size of half a basketball. Feynman, giving Smyth a tour one day, pointed out that he was absently kicking one of them, now in use as a doorstop. A request for osmium, a dense nonradioactive metal, had to be denied when it became clear that the metallurgists had asked for more than the world’s total supply. In the cases of uranium 235 and plutonium, the laboratory had to wait for the world’s supply to be multiplied a millionfold.
For now the only knowledge of these materials came from experiments on quantities so tiny as to be invisible. The experiments were expensive and painstaking. Even getting an early measurement of plutonium’s density challenged the team at Chicago. The first dot of plutonium did not arrive at Los Alamos until October 1943. Trials with more comfortable quantities would have to wait; in the event, just one full-size experiment would be possible. Most questions would have to be answered with pencil and paper. It soon became clear that theory at Los Alamos would be performed on a high wire without a net. The theoretical division was small, just thirty-five physicists and a computing staff, charged with providing analysis and prediction for all the much larger practical divisions: experimental, ordnance, weapons, and chemical and metallurgical. Analysis and prediction—what would happen if… ? Theorists at Los Alamos had dispensed with the luxury of contemplating simple mysteries—the way a single atom of hydrogen emits a single packet of light in such and such a color, or the way an idealized wave might travel through an idealized gas. The materials at hand were not idealized, and the theorists, no less than the experimenters, had to poke about in the rubble-strewn territory of nonlinear mathematics. Crucial decisions had to be made before the experimenters could conduct trials. Feynman, in his anonymous account, listed the main questions:
How big must the bombs be (the imploding sphere of plutonium or the gun device in the case of uranium)? What would be the critical mass and the critical radius for each material, the dimensions beyond which a chain reaction would sustain itself?
What materials would best serve as tamper, a surrounding liner that would reflect neutrons back into the bomb? The metallurgists had to begin the work of fabricating tamper long before a true test was possible.
How pure would the uranium have to be? On this calculation rested a decision to build or not build an enormous third stage in the isotope-separation complex at Oak Ridge.
How much heat, how much light, how much shock would a nuclear explosion create in the atmosphere?
The Battleship and the Mosquito Boat
They occupied a two-story green-painted box called T building (T for theoretical), which Oppenheimer made his headquarters and the laboratory’s spiritual center. He placed Hans Bethe, Cornell’s famous nuclear physicist, in charge. The corridors were narrow, the walls thin. As the scientists worked, they would hear from time to time Bethe’s booming laughter. When they heard that laugh they suspected that Feynman was nearby.
Bethe and Feynman—strange pair, some of their colleagues thought, a pedantic-seeming German professor and a budding quicksilver genius. Someone coined the nicknames “Battleship” and “Mosquito Boat.” Their collaborative method was for Bethe to plow solidly ahead, a determined giant, while Feynman buzzed back and forth across his bow, gesticulating, yelling in his scabrous New York accent, “You’re crazy” and “That’s nuts.” Bethe would respond calmly in his slow professorial way, working his way through the problem analytically and explaining that he was not crazy, Feynman was crazy. Feynman would consider and pace back and forth, and finally through the partitions the other scientists would hear him shout back, “No, no, you’re wrong.” He was reckless where Bethe was careful, and he was just what Bethe was looking for, someone who would perform the severest and most imaginative criticism, who would find flaws before an idea went too far. Challenges and fresh insights came easily from Feynman. He did not wait, as Bethe did, to double-check every intuitive leap. His first idea did not always work. His cannier colleagues developed a rule of thumb: If Feynman says it three times, it’s right.
Bethe was a natural choice as leader of the theoretical division. His sweeping three-article review of the state of nuclear physics in the thirties had established him as the authoritative theorist in that field. As Oppenheimer well knew, Bethe had not just organized the existing knowledge of the subject but had calculated or recalculated every line of theory himself. He had worked on probability theory, on the theory of shock waves, on the penetration of armor by artillery shells (this last paper, born of his eagerness in 1940 to make some contribution to the looming war, was immediately classified by the army so that Bethe himself, not yet an American citizen, could not see it again). His explanation in 1938 of the thermonuclear fires that light the sun would win him the Nobel Prize. Since arriving at Cornell in 1935 he had made it one of the new world centers in physics, as Oppenheimer and Ernest O. Lawrence had done for Berkeley.
Oppenheimer wanted him badly and strained to persuade him that the atomic bomb was practical enough to draw him from the MIT Radiation Laboratory, where he had begun to make a contribution in 1942. (When Bethe agreed, the news was sent to Oppenheimer by a prearranged code: a Western Union kiddiegram.) Bethe’s friend Edward Teller had pressed hard for his participation. No one but Teller was now surprised when Oppenheimer appointed Bethe, the sturdy pragmatist, to head the theoretical division, to nurse the egos and the prodigies, to run the most eccentric, temperamental, insecure, volatile assortment of thinkers and calculators ever squeezed together in one place.
Bethe had learned his physics all across Europe: first at Munich, where he studied with Arnold Sommerfeld, a prodigious producer of future Nobel Prize winners, and then at Cambridge and Rome. At Cambridge, Dirac’s lectures on the new quantum mechanics held center stage, but Bethe quit attending after discovering that Dirac, having perfected his formulation of the subject, was simply reading his book aloud. At Rome, where he was the first foreign student of physics in the university’s history, the attraction was Fermi. For a short time they worked together closely, and Bethe acquired from him a style that he called “lightness of approach.” His first great teacher, Sommerfeld, had always begun work on a problem by writing down a formalism selected from a heavy arsenal of mathematical equipment. He would work out the equations and only then translate the results into an understanding of the physics. By contrast, Fermi would begin by gently turning a problem over in his mind, by thinking about the forces at work, and only later sketching out the necessary equations. “Lightness” was a difficult attitude to sustain in a time of abstract, unvisualizable quantum mechanics. Bethe combined the physicality of Fermi’s attitude with an almost compulsive interest in computing the actual numbers that an equation entailed. That was far from typical. Most physicists could happily string equations down a page, working out the algebra without keeping in mind a sense of real quantities, or ranges of quantities, that a symbol might represent. For Bethe a theory only mattered when he could get actual numbers out.
From Fermi’s Rome, Bethe returned to a Germany whose scientific establishment was nearing the precipice. In his classroom at the ancient university of Tübingen, where he took an assistant professorship, he saw students wearing swastikas on arm bands. It was the autumn of 1932. That winter Hitler took power. In February the Reichstag burned. By spring the first of the Nazis’ anti-Jewish ordinances entailed the immediate dismissal of one-fourth of the country’s university physicists—non-Aryan civil servants. Bethe, his father a Prussian Protestant, did not consider himself a Jew, but because his mother was Jewish his status in Nazi Germany was clear. He was immediately shed from the faculty he had just entered. Across Europe the greatest intellectual migration in history was already beginning, and Bethe had little choice but to join it. Scientists in general had the advantage of working in a polyglot community, where international study and temporary overseas lectureships eased their emotional transition—from citizen to refugee. He reached the New World in 1935.
Feynman had known Bethe’s name since he was an undergraduate—the Bethe Bible, the three famous review articles on nuclear physics, had provided the entire content of MIT’s course. He had seen Bethe once from a distance at a scientific meeting. An ugly man, he had thought at first glance, awkward, with slightly squashed features on a strong frame, light brown hair bristling skyward above a broad brow. Feynman’s first impression dissolved when they met up close in Santa Fe before heading up to Los Alamos for the first time. Bethe, thirty-seven years old, had the body of a mountain climber, and he spent as much time as possible hiking in the canyons or up to the peaks behind the laboratory. He radiated solidity and warmth. Soon after their arrival on the mesa, a statistical fluctuation in the comings and goings of the theorists left Bethe stripped of the people he needed to consult. Victor Weisskopf, his deputy, was away. Teller was away—but Teller, anyway, had immediately grown more aloof than useful; not only had Oppenheimer passed him over in favor of Bethe, but Bethe had passed him over in favor of Weisskopf. So Bethe drifted into Feynman’s office one day, and soon people down the corridor could hear his booming laugh.
Bethe left the initial lectures trying to work out a way of calculating the efficiency of a nuclear explosion. Serber had presented a formula for the simplest case, when the mass of uranium or plutonium was just above critical. For bombs, which would require masses substantially over critical, the problem was far more difficult. He and Feynman developed a method of classic elegance that became known as the Bethe-Feynman formula. The dangerous practicalities of nuclear physics brought other questions. A lump of uranium or plutonium, even smaller than critical mass, raised the possibility of a runaway chain reaction—predetonation. Chemical explosives were far more stable. Bethe assigned this problem to Feynman in the project’s first months. Stray neutrons were always a presence, at some low level of probability—from cosmic rays, from spontaneous individual fissions, and from nuclear reactions caused by impurities. Cosmic rays alone sparked enough fission to make uranium 235 noticeably hotter in the high altitudes of Los Alamos than in sea-level laboratories. Without understanding predetonation, the scientists could not understand detonation itself, because they would not know how the bomb would behave during the split-second transition from subcritical to supercritical. 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.
Mathematics, in the form of probability theory, had barely begun to provide tools for handling such complex patterns; he discussed the problem with the Polish mathematician Stanislaw Ulam, and Ulam’s approach to it helped midwife a new field of probability called branching-processes theory. Feynman himself worked out a theory of fluctuations building upward from the easier-to-calculate probabilities of short chain reactions: a neutron splits one atom; a newly liberated neutron finds another target; but then the chain breaks. Some measurable fluctuations—audible bursts of noise on a Geiger counter—could be traced back to an origin in a single fission event. Others were combinations of chains. As with so many other problems, Feynman took a geometrical approach, considering the probability that a burst in a certain unit volume would lead to a burst in another unit volume at a given time later. He arrived at a practical method that reliably computed the chances of any premature reaction taking hold. It was suitable even for the odd-shaped segments of uranium that would be blasted into one another in the Hiroshima bomb.
Bethe found in Feynman the perfect foil and goad. This young man was quick, fearless, and ambitious. He was not satisfied to take away one problem and work on it; he wanted to work on everything at once. Bethe decided to make him a group leader, a position otherwise reserved for prominent physicists like Teller, Weisskopf, Serber, and the head of the British contingent at Los Alamos, Rudolf Peierls. 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.
Diffusion
Feynman did some recruiting for the project. He had invited one of his MIT fraternity friends to join the secret work. He even tried to recruit his father. Melville’s health had turned poor—his chronic high blood pressure affected him more and more—and Lucille wished he could afford to travel less. Richard wrote his mother that there might be a job available as a purchasing clerk. He wished, too, that Melville could see at close range the heady intellectual world toward which he had so long aimed his son. “He would be partly out of the rush, etc. of the business work, & would be among academic men to a great extent, which I’m sure he would enjoy … Purchasing these days is quite difficult, & everyone here is in a hell of a hurry for their stuff … it will be a damn important position in our project and scientific venture.”
Nothing came of that suggestion. In the spring of 1944 Feynman came across a familiar name on a list of available physicists: T. A. Welton. He filled out a requisition. His college friend, working as an instructor at the University of Illinois, had been trying to remain a civilian by teaching military-related courses and had watched unhappily as the more distinguished members of his department disappeared to mysterious locales. Feynman’s requisition rescued him. Welton, like so many physicists by then, had pieced together more than the army security officials liked to think possible. When he was invited to meet a stranger in a hotel room in Chicago, and then invited by the stranger to drop everything and move to New Mexico, he understood that this was, as he said later, the classic impossible-to-refuse offer. The day he arrived, Feynman took him on a long hike down into a gorge that had lately been named Omega Canyon. He was able to startle Feynman with an affirmative answer to his first question, “Do you know what we’re doing here?”
“Yes,” Welton said. “You’re making an atomic bomb.” Feynman recovered quickly. “Well,” he asked, “did you know we’re going to make it with a new element?” His friend admitted that the news of plutonium had not drifted as far as Illinois. While they walked—Welton’s lungs desperately drawing in the underpressurized air of 7,000 feet above sea level—Feynman intoxicated him with a briefing. They talked about the bomb. There were now two designs. A uranium bomb would take the form of a gun, creating a critical mass by firing a uranium bullet at a uranium target. A plutonium bomb would use another audacious method. A hollow sphere would be blown inward on itself by the shock from explosives packed all around it. The hot plutonium atoms would be compressed not through one dimension, as in the gun, but through three dimensions. The implosion method, as it was accurately named, was starting to look better and better—in part because so many problems had plagued the alternatives. (Feynman did not mention his own initial reaction when implosion’s inventor, Seth Neddermeyer, first reported experiments on explosives wrapped around steel pipes. He had raised his hand in the back row and announced, “It stinks.”)
As Welton listened, trying to keep up along the narrow canyon walls, he understood that Feynman was also saying that he had worked hard to establish himself as a smart kid to be reckoned with—that a young researcher had to impress the senior people with his usefulness, that he, Feynman, had been through that process, and that he had succeeded. They talked only briefly about Arline. She was not well, spending most of her days in a wooden bed in the Presbyterian Sanatorium, a small, poorly staffed facility by the side of a highway in Albuquerque. Feynman, visiting her almost every weekend, hitchhiked or borrowed a car to head down the unpaved road toward Santa Fe on Friday afternoon or Saturday. Away from the laboratory he would turn his thoughts back to the pure theory of quantum mechanics. He used the long trip, and the hours when Arline slept, to push his thesis work further. Welton remembered how obstinately his friend had resisted the Lagrangian simplification of dynamical problems when they were a pair of precocious sophomores in MIT’s theory course. He was amused and impressed to hear how far Feynman had taken the Lagrangian method in reformulating the most basic quantum mechanics. Feynman sketched out his idea of expressing quantum behavior as a sum of all the possible space-time trajectories a particle could take, and he told Welton frankly that he did not know how to apply it. He had a wonderful recipe that had not gelled.
Welton became the fourth physicist in the group Feynman headed, now formally known as T-4, Diffusion Problems. As a group leader Feynman was ebullient and original. He drove his team hard in pursuit of his latest unorthodox idea for solving whatever problem was at hand. Sometimes one of the scientists would object that a Feynman proposal was too complex or too bizarre. Feynman would insist that they try it out, computing in groups with their mechanical calculators, and he had enough unexpected successes this way to win their loyalty to the cause of wide-ranging experimentation. They all tried to innovate in his fashion—no idea too wild to be considered. He could be ruthless with work that did not meet his high standards. Even Welton experienced the humiliation of a Feynman rebuke—“definitely ungentle humor” to which “only a fool would have subjected himself twice.” Still Feynman managed to build esprit. He had taught himself to flip a pencil in one motion from a table into his hand, and he taught the same trick to his group. One day, amid a typical swirl of rumors that military uniforms were going to be issued to scientists working in the technical area, Bethe walked in to talk about a calculation. Feynman said he thought they should integrate it by hand, and Bethe agreed. Feynman swiveled around and barked, “All right, pencils, calculate!”
A roomful of pencils flipped into the air in unison. “Present pencils!” Feynman shouted. “Integrate!” And Bethe laughed.
Diffusion, that faintly obscure and faintly pedestrian holdover from freshman physics, lay near the heart of the problems facing all the groups. Open a perfume bottle in a still room. How long before the scent reaches a set of nostrils six feet away, eight feet away, ten feet away? Does the temperature of the air matter? The density? The mass of the scent-bearing molecules? The shape of the room? The ordinary theory of molecular diffusion gave a means of answering most of these questions in the form of a standard differential equation (but not the last question—the geometry of the containing walls caused mathematical complications). The progress of a molecule dependedon a herky-jerky sequence of accidents, collisions with other molecules. It was progress by wandering, each molecule’s path the sum of many paths, of all possible directions and lengths. The same problem arose in different form as the flow of heat througha metal. And the central issues of Los Alamos, too, were problems of diffusion in a newguise.
The calculation of critical mass quickly became nothing more or less than a calculation of diffusion—the diffusion of neutrons through a strange, radioactive minefield, where now a collision might mean more than a glancing, billiard-ball change of direction. A neutron might be captured, absorbed. And it might trigger a fission event that would give birth to new neutrons. By definition, at critical mass the creation of neutrons would exactly balance the loss of neutrons through absorption or through leakage beyond the container boundaries. This was not a problem of arithmetic. It was a problem of understanding the macroscopic spreading of neutrons as built up from the microscopic individual wanderings.
For a spherical bomb the mathematics resembled another strange and beautiful diffusion problem, the problem of the sun’s limb darkening. Why does the sun have a crisp edge? Not because it has a solid or liquid surface. On the contrary, the gaseous ball of the sun thins gradually; no boundary marks a division between sun and empty space. Yet we see a boundary. Energy diffuses outward from the roiling solar core toward the surface, particles scattering one another in tangled paths, until finally, as the hot gas thins, the likelihood of one more collision disappears. That creates the apparent edge, its sharpness more an artifact of the light than a physical reality. In the language of statistical mechanics, the mean free path—the average distance a particle travels between one collision and the next—becomes roughly as large as the radius of the sun. At that point photons have freed themselves from the pinball game of diffusion and can fly in a straight line until they scatter again, in the earth’s atmosphere or in the sensitive retina of one’s eye. The difference in brightness between the sun’s center and its edge gave an indirect means of calculating the nature of the internal diffusion. Or should have—but the mechanics proved difficult until a brilliant young mathematician at MIT, Norbert Wiener, devised a useful method.
If the sun were a coolly radioactive metal ball a few inches across, with neutrons rattling about inside, it would start to look like a miniaturized version of the same problem. For a while this approach proved useful. Past a certain point, however, it broke down. Too many idealizing assumptions had to be made. In a real bomb, cobbled together from mostly purified uranium, surrounded by a shell of neutron-reflecting metal, the messy realities would defy the most advanced mathematics available. Neutrons would strike other neutrons with a wide range of possible energies. They might not scatter in every direction with equal probability. The bomb might not be a perfect sphere. The difference between these realities and the traditional oversimplifications arose in the first major problem assigned to Feynman’s group. Bethe had told them to evaluate an idea of Teller’s, the possibility of replacing pure uranium metal with uranium hydride, a compound of uranium and hydrogen. The hydride seemed to have advantages. For one, the neutron-slowing hydrogen would be built into the bomb material; less uranium would be needed. On the other hand, the substance was pyrophoric—it tended to burst spontaneously into flame. When the Los Alamos metallurgists got down to the work of making hydride chunks for testing, they set off as many as half a dozen small uranium fires a week. The hydride problem had one virtue. It pushed the theorists past the limits of their methods of calculating critical masses. To make a sound judgment of Teller’s idea they would have to invent new techniques. Before they considered the hydride, they had got by with methods based on an approximation of Fermi’s. They been able to assume, among other things, that neutrons would travel at a single characteristic velocity. In pure metal, or in the slow reaction of the water boiler, that assumption seemed to work out well enough. But in the odd atomic landscape of the hydride, with its molecules of giant uranium atoms bonded to two or three tiny hydrogen atoms, neutrons would fly about at every conceivable velocity, from very fast to very slow. No one had yet invented a way of computing critical mass when the velocities spread over such a wide range. Feynman solved that problem with a pair of approximations that worked like pincers. The method produced outer bounds for the answer: one estimate known to be too large and another known to be too small. The experience of actual computation showed that this would suffice: the pair of approximations were so close together that they gave an answer as accurate as was needed. As he drove the men in his group toward a new understanding of criticality (poaching sneakily, it seemed to them, on the territory of Serber’s group, T-2), he delivered up a series of insights that struck even Welton, who understood him best, as mystical. One day he declared that the whole problem would be solved if they could produce a table of so-called eigenvalues, characteristic values of energies, for the simplified model that T-2 had been using. That seemed an impossible leap, and the group said so, but they soon found that he was right again. For Teller’s scheme, the new model was fatal. The hydride was a dead end. Pure uranium and plutonium proved far more efficient in propagating a chain reaction.
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, especially, an accommodation with uncertainty became a running theme. Few other scientists filled 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 all 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 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 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 numerically, in small increments of time. The focus of attention was pushed back down to the microscopic level of individual neutrons following 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 all 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 small 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 collisions 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 fill half a juice glass and correct with an extra splash. Anyone who calculated logarithms by mentally 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 colleagues 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 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: Suppose we treat some quantity as infinitesimal. He would allow an error and then measure the bounds of the error precisely.
It seemed to colleagues 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: “Well, four hours and twenty minutes ago it was twelve before noon,” or “In three hours and forty-nine minutes it will be two seventeen.” Few caught on. He was doing no arithmetic at all. 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? Well, 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 reached across his desk for the Marchant mechanical calculator.
Bethe said, “It’s twenty-three hundred.”
Feynman started to punch the keys anyway. “You want to know exactly?” Bethe said. “It’s twenty-three hundred and four. Don’t you know how to take squares of numbers near fifty?” He explained the trick. Fifty squared is 2,500 (no thinking needed). For numbers a few more or less than 50, the approximate square is that many hundreds more or less than 2,500. Because 48 is 2 less than 50, 48 squared is 200 less than 2,500—thus 2,300. To make a final tiny correction to the precise answer, just take that difference again—2—and square it. Thus 2,304.
Feynman had internalized an apparatus for handling far more difficult calculations. But Bethe impressed him with a mastery of mental arithmetic that showed he had built up a huge repertoire of these easy tricks, enough to cover the whole landscape of small numbers. An intricate web of knowledge underlay the techniques. Bethe knew instinctively, as did Feynman, that the difference between two successive squares is always an odd number, the sum of the numbers being squared. That fact, and the fact that 50 is half of 100, gave rise to the squares-near-fifty trick. A few minutes later they needed the cube root of 2½. The mechanical calculators could not handle cube roots directly, but there was a look-up chart to help. Feynman barely had time to open the drawer and reach for the chart before he heard Bethe say, “That’s 1.35.” Like an alcoholic who plants bottles within arm’s reach of every chair in the house, Bethe had stored away a device for anywhere he landed in the realm of numbers. He knew tables of logarithms and he could interpolate with unerring accuracy. Feynman’s own mastery of calculating had taken a different path. He knew how to compute series and derive trigonometric functions, and how to visualize the relationships between them. He had mastered mental tricks covering the deeper landscape of algebraic analysis—differentiating and integrating equations of the kind that lurk dragonlike in the last chapters of calculus texts. He was continually put to the test. The theoretical division sometimes seemed like the information desk at a slightly exotic library. The phone would ring and a voice would ask, “What is the sum of the series 1 + (½)4 + (⅓)4 + (¼)4 + … ?”
“How accurate do you want it?” Feynman replied.
“One percent will be fine.”
“Okay,” Feynman said. “One point oh eight.” He had simply added the first four terms in his head—that was enough for two decimal places.
Now the voice asked for an exact answer. “You don’t need the exact answer,” Feynman said.
“Yeah, but I know it can be done.”
So Feynman told him. “All right. It’s pi to the fourth over ninety.”
He and Bethe both saw their talents as labor-saving devices. It was also a form of jousting. At lunch one day, feeling even more ebullient than usual, he challenged the table to a competition. He bet that he could solve any problem within sixty seconds, to within ten percent accuracy, that could be stated in ten seconds. Ten percent was a broad margin, and choosing a suitable problem was hard. Under pressure, his friends found themselves unable to stump him. The most challenging problem anyone could produce was: Find the tenth binomial coefficient in the expansion of (1 + x)20. Feynman solved that just before the clock ran out. Then Paul Olum spoke up. He had jousted with Feynman before, and this time he was ready. He demanded the tangent of ten to the hundredth. The competition was over. Feynman would essentially have had to divide one by ? and throw out the first one hundred digits of the result—which would mean knowing the one-hundredth decimal digit of ?. Even Feynman could not produce that on short notice.
He integrated. He solved equations taking the spirit of infinite summation into more difficult realms. Some of these perilous, nontextbook, nonlinear equations could be integrated through just the right combination of mental gimmicks. Others could not be integrated exactly. One could plug in numbers, make estimates, calculate a little, make new estimates, extrapolate a little. One might visualize a polynomial expression to approximate the desired curve. Then one might try to see whether the leftover error could be managed. One day, making his rounds, Feynman found a man struggling with an especially complicated varietal, a nonlinear three-and-a-half-order equation. There was a business of integrating three times and figuring out a one-half derivative—and in the end Feynman invented a shortcut, a numerical method for taking three integrals at once and a half integral besides, all more accurately than had been thought possible. Similarly, working with Bethe, he invented a new and general method of solving third-order differential equations. Second order had been manageable for several centuries. Feynman’s invention was precise and practical. It was also doomed to a quick obsolescence in an age of machine computation, as was, for that matter, the skill of mental arithmetic that did so much to establish Feynman’s legend.
Computing by Machine
Not only the atomic era but also the computer era had its start in those years. Scattered about the nation’s military and civilian laboratories, a few researchers focused exclusively on the means of calculating instead of the calculations themselves. At Los Alamos, in particular, the demand for numerical computation grew more intense than anywhere else on earth. The means were mechanical and now partly electronic, though the crucial technological key, the transistor, remained to be invented at the decade’s end. Calculating technology became a hybrid with machine parts and human parts: people carrying cards from place to place served as the memories and logical-branching units of near computers that stretched across rows and columns of desks.
The bomb project could draw on the best technology available anywhere, but the best technology offered little to the working scientist. The manufacturers of such equipment—the International Business Machines Corporation already preeminent among them—considered the scientific market to be negligible. It could not imagine the vast clientele that would soon consume as much calculating capacity as could be created: for forecasting weather, designing engines, analyzing proteins, scheduling airplanes, and simulating everything from ecosystems to heart valves. Business was thought to be the sole potential consumer for business machines, and business meant accounting, which meant addition and subtraction. Multiplication seemed a luxury, although it might be necessary to multiply monthly sales by twelve. Division by machine was esoteric. Computation of mortgage payments and bond yields could be managed by humans with standard tables.
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 Marchants took a hard pounding at Los Alamos. Metal parts wore thin and came out of alignment. The officially nonexistent laboratory was poorly suited to field-service visits by the manufacturer’s repair crews, so standard procedure required the shipping of broken machines back to California. Eventually three or four machines were in the pipeline at any one time. 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.
Escalation of the computation effort came in the fall of 1943 with an order to IBM for business machines to be delivered to an unknown location: three 601 multipliers, one 402 tabulator, one reproducer-summary punch, one verifier, one keypunch, one sorter, and one collator. Astronomers at Columbia had been experimenting with punch-card computing before the war. A multiplier, an appliance the size of a restaurant stove, could process calculations in large batches. Electrical probes found the holes in the cards, and operations could be configured by plugging groups of wires into a patchboard. Among the computation-minded at Los Alamos, the prospect of such machines caused excitement. Even before they arrived, one of the theorists, Stanley Frankel, set about devising improvements: for example, tripling the output by rearranging the plugs so that three sets of three- or four-digit numbers could be multiplied in a single pass. Having requisitioned the machines, the scientists now also requisitioned a maintenance man—an IBM employee who had been drafted into the army. They were gaining adroitness at military procurement. The crates arrived two days before the repairman; in those two days Feynman and his colleagues managed to get the machines unpacked and assembled, after a fashion, with the help of nothing but a set of wiring blueprints. So much more powerful were they that Feynman—sensitive to rhythms as always—rapidly discovered that he could program them to clatter out the cadence of well-known songs. 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. It also began a long transformation in the understanding of what kinds of equations were solvable. Stacks of punch cards could solve equations for a ball of fire rising through a suddenly turbulent atmosphere, by stepping through successive approximations for time 0:01, time 0:02, time 0:03 … though by the lights of traditional analysis those sharply nonlinear equations were unsolvable.
Of the many problems put to the Los Alamos computers, none better anticipated the coming age of massive scientific simulation than implosion itself: how to calculate the motion of an inward-flowing shock wave. An explosive charge wrapped around the bomb was to set the shock wave in motion, and the pressure would crush a nugget of plutonium into criticality. How should the bomb assembly be configured to assure a stable detonation? What kind of fireball would ensue? Such questions required a workable formula for the propagation of a spherical detonation wave in a compressible fluid, the “compressible fluid” in this case being the shotput-size piece of plutonium liquefied in the microseconds before it became a nuclear blast. The pressure would be more intense than at the earth’s center. The temperature would reach 50 million degrees Centigrade. The theorists were on their own here; experimentalists could offer little more than good wishes. All during 1944 the computation effort grew. John von Neumann served as a traveling consultant with an eye on the postwar future. Von Neumann—mathematician, logician, game theorist (he was more and more a fixture in the extraordinary Los Alamos poker game), and one of the fathers of modern computing—talked with Feynman while they worked on the IBM machines or walked though the canyons. He left Feynman with two enduring memories. One was the notion that a scientist need not be responsible for the entire world, that social irresponsibility might be a reasonable stance. The other was a faint, early recognition of the mathematical phenomena that would later be called chaos: a persistent, repeatable irregularity in certain equations as they prepared to run them through their primitive computers. As a shock wave, for example, passed though a material, it left oscillations in its wake. Feynman thought at first that the irregular wiggles must be numerical errors. Von Neumann told him that the wiggles were actually features of interest.
Von Neumann also kept these new computer specialists up to date with the other sites he visited. He brought news of an electromechanical Mark I under construction at Harvard, a relay calculator at Bell Laboratories, human neuronal research at the University of Illinois, and at the Aberdeen Proving Ground in Maryland, where problems of ballistic trajectories motivated the calculators, a more radical device with a new kind of acronym: ENIAC, for Electronic Numerical Integrator and Computer, a machine composed of eighteen thousand vacuum tubes. The tubes controlled binary on-off flip-flops; in a bow to the past, the flip-flops were arranged in rings of ten, to simulate the mechanical wheels used in decimal calculating machines. The ENIAC had too many tubes to survive. Von Neumann estimated: “Each time it is turned on, it blows two tubes.” The army stationed soldiers carrying spare tubes in grocery baskets. The operators borrowed mean free path terminology from the ricocheting particles of diffusion theory; the computer’s mean free path was its average time between failures.
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 numbers—these had no immediate connection to counting, but Feynman continued pulling 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 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 ? 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.”
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 all odds the most brilliant young physicist here, and everyone knows this. He is a man of thoroughly engaging character and personality, extremely clear, extremely normal in all respects, and an excellent teacher with a warm feeling for physics in all 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 grilling steak outdoors at the Presbyterian Sanatorium in a small 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 all, 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 still had not gotten used to the raw force of storms in the open West.
His near-weekly trips through the valley 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 all. 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 officially: not a village 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 hill. 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 ballet, 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.
Los Alamos built its wall against theoutside world and thrived within. Separately and privately Richard and Arline, too, sought what refuge they could. They made their secret lives. They built a fence of their own. None of his scientific friends knew that he called her Putzie and she called him Coach; that she noticed the muscles hardening in his legs from all his hiking; that the days of respite from her illness were growing rarer. She wrote him in code, playing to his love of unraveling puzzles; his father did this, too. Their letters caught the eye of the military censors at the laboratory’s Intelligence Office. The censors alerted Feynman to regulation 4(e): Codes, ciphers or any form of secret writing will not be used. Crosses, X’s or other markings of a similar nature are equally objectionable. Censorship had been designed delicately to accommodate a nonmilitary clientele, university people who still liked to imagine that they were volunteers in a project of scientific research in a nation where the privacy of the mail was sacred. The censors trod carefully. They tried to turn mail around the day they received it, and they agreed to allow correspondence in French, German, Italian, and Spanish. They felt entitled at least to ask Feynman for the key to the codes.
He said he did not have a key or want a key. Finally they agreed that if Arline would enclose a key for their benefit they would remove it before the envelope got to Feynman.
Inevitably, he then ran afoul of regulation 8(l), a delightfully (to Feynman) self-referential law requiring the censorship of any information concerning these censorship regulations or any discourse on the subject of censorship. He got the message to Arline nonetheless, and her acid sense of fun took over. She started sending letters with holes cut in them or blotches of ink covering words: “It’s very difficult writing because I feel that the —— is looking over my shoulder.” He would respond with numerical fancies, pointing out how peculiarly the decimal expansion of 1/243 repeats itself: .004 115 226 337 448 … and his increasingly frustrated official audience would have to ensure that the string of digits was neither a cipher nor a technical secret. Feynman explained with subtle glee that this fact had the empty, tautological, zero-information-content quality of all mathematical truths. In one of her mail-order catalogs Arline found a kit for do-it-yourself jigsaw puzzles; the next letter from the Albuquerque sanatorium to Box 1663 came disassembled in a little sack. From another the censors deleted a suspicious-sounding shopping list. Richard and Arline talked about a booby-trapped letter that would begin, “I hope you remembered to open this letter carefully because I have included the Pepto Bismol powder …” Their letters were a lifeline. No wonder, under watchful eyes, the lovers found ways to make them private.
The censorship, like the high barbed-wire fence, reminded the mesa’s more sensitive residents of their special status: watched, enclosed, restricted, isolated, surrounded, guarded. They understood that no other civilian post office box had all its mail opened and read. The fence was a double-edged symbol. Few scientists were so important as to merit armed soldiers patrolling their laboratory perimeters. They could not help feeling some pride. Feynman admonished his parents to maintain secrecy: “There are Captains in the Army who live up here who don’t know what we’re doing. (Even Majors.)” Much later, in a post-Catch-22 world, the military trappings were remembered as irritants and targets of mockery. At the time it was not so simple. The men and women of Los Alamos resented the fence and respected the fence. Feynman explored most of its length. When he discovered holes, with well-beaten paths leading through, he pointed them out in a spirit of good citizenship, annoyed only that the guards responded so lackadaisically. (“I explained it to him & the officer in charge,” he wrote Arline, “but I bet they don’t do anything.”) He never realized that the holes had semiofficial sanction. The security staff tolerated them—with Oppenheimer’s connivance, it seemed—so that people from the local tribes could come to the laboratory’s twelve-cent movies.
Feynman’s exploring drew him to every secret and private place. He had a fidgety way of prying into things—the laboratory’s new Coca-Cola dispenser, for example, a contraption that secured the bottles with a locked steel collar around their necks. This device replaced an older container, the most ancient prototype of the soda machine: customers would open the lid, take a bottle, and honorably drop their coin in a box. The new dispenser struck Feynman as a withdrawal of trust; thus he felt entitled to accept the technological challenge and finesse the mechanism. Was that right or wrong? He debated the moral principles with his friends. Meanwhile he found himself abstaining from liquor. He had got so drunk one night that he could tell it was ruining his drum playing and joke telling, although it did not stop him from running all over the base singing and beating pots and pans; finally he passed out, and Klaus Fuchs took him home. He decided to give up alcohol, along with tobacco, and wondered whether it was a sign of encroaching conventionality. Was he getting “moraller and moraller” as he got older? (“That’s bad.”)
His reputation as a skilled prier spread. One scientist left some belongings in a storeroom at Fuller Lodge and borrowed Feynman’s fingers to pick the Yale lock. Paper clips, screwdriver, two minutes. Two men arrived, breathless from running up the stairs, and begged Feynman to crack a file cabinet holding a crucial document about a ski tow. Combination locks still seemed too hard. As a group leader he had been issued a special steel safe for sensitive material of his own, and he had not yet managed a way to break in. He would spin the dial from time to time. Occasionally it occurred to him that his interest in locks was turning into an obsession. Why? “Probably,” he told Arline,
because I like puzzles so much. Each lock is just like a puzzle you have to open without forcing it. But combination locks have me buffaloed.
You do too, sometimes, but eventually I figure out you.
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.
An American folklore had developed about safes and the yeggs who cracked them. Through the cowboy era and the gangster era safes grew thicker and more elaborate—double walls of cast iron and manganese, triple side bolts and bottom bolts, curb tumblers and pressure handles—and the legend, too, grew thicker and more elaborate. The consummate safeman was thought to need sandpapered fingers and hypersensitive ears. His essential skill: a feeling for the vibrations of tumblers lining up or falling into place. This was pure myth. It was true that once in a long while someone would open a safe by feel, but, the lore notwithstanding, the chief tools of successful safecrackers were crowbars and drills. Safes were cracked; holes were torn in their sides; handles and dials were torn off. When all else failed, safes were burned. The safeman used “soup”—nitroglycerin. The Los Alamos physicists had been conditioned by the myth, and when word started spreading that the laboratory had a skilled safecracker on its staff, most of them believed—and never stopped believing—that Feynman had mastered the art of listening to the tiny clicks.
To learn how to crack safes he had to find his way past the same myth. He read pulp memoirs of safemen to look for their secrets. They inspired him to dreams of glory: these authors boasted about opening bullion-filled safes underwater; he would write the book that would top them all. In its preface he would intone, I opened the safes which contained behind them the entire secret of the atomic bomb: the schedules for the production of plutonium, the purification procedures, how much was going to be needed, how the atomic bomb worked, how the neutrons are generated … the whole schmeer. Only gradually, as he looked for the nuggets of useful information, did he realize how mundane the business was. Because his repertoire would have to omit drills and nitroglycerin, it would have to make the most of such practical rules as he could find. Some he read; others he learned as he went along. Most were variations on a theme: People are predictable.
They tend to leave safes unlocked.
They tend to leave their combinations at factory settings such as 25-0-25.
They tend to write down the combinations, often on the edge of their desk drawers.
They tend to choose birthdays and other easily remembered numbers.
This last insight alone made an enormous difference. Of the 8,000 effective possible combinations, Feynman figured that only 162 worked as dates. The first number was a month from 1 to 12—given the margin of error, that meant he need try just three possibilities, 0, 5, and 10. For a day from 1 to 31 he needed six; for a year from 1900 to the present, just nine. He could try 3 × 6 × 9 combinations in minutes. He also discovered that it took just a few inexplicable successes to make a safecracker’s reputation.
By fiddling with his own safe he learned that when a door was open he could find the last number of a combination by turning the dial and feeling when the bolt came down. Given some time, he could find the second number that way, too. He made a habit of absently leaning against his colleagues’ safes when he visited their offices, twirling the dials like the perpetual fidgeter he was, and thus he built up a master list of partial combinations. 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.
The Last Springtime
Friday afternoon again. Gravel switchbacks wound perilously down the mesa. Across a desert spotted with pale green bristles, the Sangre de Cristo Mountains rose like luminous cutouts thirty miles to the east, as bright as if they were a few city blocks away. The air was clearer than any Feynman had seen. The scenery left emotional fingerprints on many of the Easterners and Europeans who lived in its spell for two years. When it snowed, the shades of whiteness seemed impossibly rich. Feynman reveled in the clouds skimming low across the valley, the mountains visible above and below the clouds at once, the velvet glow of cloud-diffused moonlight. The sight stirred something within the most rational of minds. He mocked himself for feeling it: See, I’m getting an aesthetic sense. The days blurred, especially now—no more banker’s hours, not much theory to divert the mind. The pace of computation was hectic. Feynman’s day began at 8:30 and ended fifteen hours later. Sometimes he could not leave the computing center at all. He worked through for thirty-one hours once and the next day found that an error minutes after he went to bed had stalled the whole team. The routine allowed just a few breaks: a hasty ride across the mesa to help put out a chemical fire; or one of those Los Alamos seminar-briefing-colloquium-town-meetings, where, slouching as far as his frame would permit, he would sit in the second row next to a detached-looking Oppenheimer; or a drive with his friend Fuchs to some Indian caves, where they could explore on hands and knees until dusk.
Still, each Friday or Saturday, if he could, Feynman left this place behind, making his way down the rutted road in Paul Olum’s little Chevrolet coupe or sometimes now in Fuchs’s blue Buick. He turned over and over in his mind some nagging puzzle and let his thoughts drift back to the hard quantum problems he had left behind at Princeton. He made a difficult mental transition to his weekend. The trips down from those heights marked off full weeks for him, empty ones for Arline. He was like a spy invented by a novelist: “not certain whether this time spent traveling between his two secret worlds was when he was truly himself, when he was able to hold the two in balance and know them to be separate from himself; or whether this was the one time he was nothing at all, a void traveling between two points.” Later, when Fuchs, shockingly, turned out to have been a spy for the Soviet Union, Feynman thought it might not have been so strange after all that his friend had been able to hide his inner thoughts so well. He, too, had felt he was leading a double life. His anguish over Arline, so dominating his mind, stayed invisible to the colleagues who saw his aggressively carefree self. He would sit in a group and look at someone—even at Fuchs—and think, how easy it is to hide my thoughts from others. A third springtime was coming to Los Alamos, and Feynman knew it would be the last. For a moment he thought he felt a break in the tension. He found a way to get the computation group running smoothly enough to allow him a few hours more sleep. He took a shower. For a half hour he read a book before falling asleep. It seemed, just for a moment, that the worst might be over. He wrote Arline:
You are a strong and beautiful woman. You are not always as strong as other times but it rises & falls like the flow of a mountain stream. I feel I am a resevoir for your strength—without you I would be empty and weak … I find it much harder these days to write these things to you.
He never wrote without saying I love you or I’m still loving you or I have a serious affliction: loving you forever. The pace quickened again, and Feynman sometimes thought about long days he had worked for twenty dollars a week waiting on tables and helping in the kitchen of his aunt’s summer hotel, the Arnold, on the beach at Far Rockaway. Wherever he went, his drumming could be heard through the walls, nervous or jaunty, a rapping that his staff had to enjoy or endure. It was not music. Feynman himself could barely endure the more standard tunes of his friend Julius Ashkin’s recorder, “an infernally popular wooden tube,” he called it, “for making noises bearing a one-one correspondence to black dots on a piece of paper—in imitation to music.”
Stresses were tightening, too, between the security staff and the scientists, and Feynman had lost his eager spirit of cooperation. A colleague had been interrogated for more than an hour in a smoky room, questions fired by men sitting in the dark, as in a melodramatic movie. “Don’t get scared tho,” Feynman wrote Arline, “they haven’t found out that I am a relativist yet.” Fear sometimes clutched Feynman now. His intestines suffered chronically. He had a chest X ray: clear. Names rushed through his head: maybe Donald; if a girl, maybe Matilda. Putzie wasn’t drinking enough milk—how could he help her build her strength at this distance? They were spending $200 a month on the room and oxygen and $300 more on nurses, and $300 was the shortfall between income and expenditures. His salary as a Manhattan Project group leader: $380 a month. If they spent Arline’s savings, $3,300 plus a piano and a ring, they could cover ten more months. Arline seemed to be wasting away.
Letters went back and forth almost daily. They wrote like a boy and a girl without experience at the art of love letters. They catalogued the everyday—how much sleep, how much money. Macy’s sent Arline an unexpected mail-order refund of forty-four cents: I feel like a millionaire … I.O.U. 22¢. His sporadic bad digestion or swollen eyelid; her waning or waxing strength, her coughed-up blood and her access to oxygen. They used matching stationery. It was a mail-order project of Arline’s—soon most of her relatives and many of Richard’s friends on the hill had the same green or brown block letterhead from the Dollar Stationery Company. For herself she ordered both formal (Mrs. Richard P. Feynman) and informal, with the same legend she had once caught Richard slicing from her pencils:
RICHARD DARLING,
I LOVE YOU
PUTZIE
She decorated the envelopes with red hearts and silver stars. The army decorated them with tape: OPENED BY U. S. ARMY EXAMINER.
They called each other “Dope” and then worried about whether they had given offense. You’re never that—just silly & cute & lots of fun—you know what I mean, don’t you coach? Alone in her cramped sanatorium room, decorated with a few pictures and knickknacks received as wedding gifts, Arline worried about Richard and other women. He was a popular dancer at Los Alamos parties; he flirted intently with nurses, wives, and a secretary of Oppenheimer’s. All it took to set Arline’s mind racing was an offhand mention of the wife of a colleague. Or worse: the scientists were in an uproar over the appearance of M.P.’s around a women’s dormitory (the army had discovered an active prostitution trade there), and for some reason Richard had been chosen to lead the protest. He reassured her continually. Everything is under control—& I love you only. She explained and reexplained the facts of their love like an incantation: he is tall, gentle, kind, strong; he supports her, but once in a while can lean on her, too; he must confide everything in her, as she has slowly learned to confide in him; we have to think in terms of us, always; she loves the way he stretches casually to open a high window beyond her reach, and she loves the way he talks babytalk with her.
Not until the beginning of this grim year did they make love. Their gingerly discussions had led nowhere. He was afraid of taking advantage, or afraid of harming her, or just afraid. Arline grasped ever more tightly her sense of romantic love. She read Lady Chatterley’s Lover (“No!” she said. “Love me! Love me, and say you’ll keep me. Say you’ll keep me! Say you’ll never let me go, to the world nor to anybody!”) and a popular 1943 book, Love in America. “I do not know—although there are those who profess to know with mathematical accuracy—whether sex is all-important in the life of a man or a woman,” the author wrote provocatively. Americans lag Europeans in such matters. “We have developed no concepts of love as an art or a rite… . We do not seem to realize that woman’s love is not prompted by good deeds on a man’s part or by Boy Scout conduct; that neither gratitude nor pity are love; that loving lies in demanding as well as in giving; that the woman who loves yearns to give and give again.”
Arline herself finally made the decision and set aside a Sunday when she would allow no other visitors. She missed him spiritually and physically, she told him.
Darling I’m beginning to think that perhaps this restlessness I feel within myself is due to pent up emotions—I really think we’d both feel happier and better dear if we released our desires.
She wrote Richard a few days before to tell him it was time. She could not sleep. She clipped a phrase from a newspaper advertisement: “OUR MARRIAGE COMES FIRST.” She reminded him of the future that waited for them: just a few more years in bed for her; then he would be a renowned professor (physicist still did not denote a profession with stature) and she a mother. She apologized, as she so often did, for being moody, for being difficult, for saying hurtful things, and for having to lean on him without respite. Her thoughts rambled.
… We have to fight hard—every inch of the way—we can’t slip ever—a slip costs too much… . I’ll be all a women would be to you—I’ll always be your sweetheart & first love—besides a devoted wife—we’ll be proud parents too—we’ll fight to make Donald real—I want him to be like you… . I am proud of you always Richard—your a good husband, and lover, & well, coach, I’ll show you what I mean Sunday.
Your Putzie
False Hopes
Her health continued to fail. “Drink some milk!” Richard wrote in May. Her weight had fallen to eighty-four pounds. She looked like a woman starving.
You are a nice girl. Every time I think about you, I feel good. It must be love. It sounds like a definition of love. It is love. I love you.
I’ll see you in two days.
R. P. F.
More and more they talked of medical tests. They needed optimism. He was near despair. Time passes fast. Maybe we should start looking for another doctor… . Why don’t you drink an extra bottle of milk right now while you are thinking of it.
The scientific knowledge that empowered the physicists seemed to mean nothing on the soft soil of medicine. With the final desperation of the dying, Richard and Arline reached out for slender possibilities. He had heard about a new drug, sulf-something—he was not sure—and had written to researchers in the East, who told him apologetically that studies of sulfabenamide were in the most preliminary stage. The discovery that substances of the sulfonamide family retarded bacterial growth was not yet a decade old. They were destined to prove poor substitutes for true antibiotics.
Now Richard was writing to faraway doctors again. It seemed that Arline was pregnant. After ending the celibacy of their marriage, she had immediately missed her menstrual period. Was it possible? They were frightened and jubilant at once. Richard did not tell his parents, but he told his sister, now a college student. Joan was dazzled at the prospect of becoming an aunt. They talked about names and began making new plans. Yet to Richard it still seemed that Arline was wasting away. He thought he saw symptoms of starvation. Perhaps no rational observer could have construed the cessation of menses at this stage of the disease as a sign of pregnancy, but that was how they construed it. The alternative was so grim. Their doctors saw little reason for hopefulness. The chief physician from the sanatorium in Browns Mills, New Jersey, advised urgently that any pregnancy must be “interrupted”—“have it done by a specialist.” Then a pregnancy test gave a negative result after all. They did not know what to think. A doctor at Los Alamos told Richard that the tests were notoriously unreliable but that they could try again at an Albuquerque laboratory. He thought the laboratory had the necessary rabbits for the Friedman test.
The same doctor said he had heard of a new substance made from mold growths—“streptomicin”?—that seemed to cure tuberculosis in guinea pigs. If it worked, the doctor thought it might soon become widely available. Arline refused to believe the negative pregnancy result. She wrote cryptic remarks about “P.S. 59-to-be.” The same day a nurse wrote Feynman from the sanatorium to say that Arline had been spitting blood. He opened his encyclopedia yet again. Nothing. He drifted through the pages: tuberculosis, tuff, tularemia … Tuff was a kind of volcanic rock; Tunicata an animal group. He wrote Arline another letter. “Tumors you know about & Turkey, the country, also.” Some days she was now too weak even to write back. He grasped his uncertainty. Not knowing was frustration, anguish, and finally his only solace.
“Keep hanging on,” he wrote. “Nothing is certain. We lead a charmed life.”
In the midst of their private turmoil came V-E day and then Richard’s twenty-seventh birthday. Arline had prepared another mail-order surprise: the laboratory was flooded with newspapers—handed about and tacked to walls—proclaiming with banner headlines, “Entire Nation Celebrates Birth of R. P. Feynman!” The war in Europe, having provided so many of the scientists with their moral purpose, had now ended. The bloody circle was closing in the Pacific. They needed no threat of a German or Japanese bomb to urge them onward. Uranium was arriving. There would be one test—one last experiment.
At the Mayo Clinic in Minnesota another kind of experiment was under way, the first clinical trial of streptomycin, a substance that had been discovered nearly two years before, in August 1943. The population participating in the trial: two patients. Both had been near death from tuberculosis when the experiment began in the fall of 1944; both were improving rapidly. Even so, it was not until the next August that the Mayo trial had expanded to as many as thirty patients. The doctors could see lesions healing and lungs clearing. A year after that, the study of streptomycin as an antitubercular agent had become the most extensive research project ever devoted to a drug and a disease. Researchers were treating more than one thousand patients. In 1947 streptomycin was released to the public.
Streptomycin’s discovery, like penicillin’s a few years earlier, had been delayed by medicine’s slow embrace of the scientific method. Physicians had just begun to comprehend the power of controlled experiments repeated thousands of times. The use of statistics to uncover any but the grossest phenomena remained alien. The doctor who first isolated the culture he named Streptomyces griseus, by cultivating some organisms swabbed from the throat of a chicken, had seen the same microbes in a soil sample in 1915 and had recognized even then that they had a tendency to kill disease-causing bacteria. A generation had to pass before medicine systematized its study of such microbes, by screening them, culturing them, and measuring their antibiotic strengths in carefully labeled rows of test tubes.
Nuclear Fear
In its infancy, too, was the branch of science that would have to devote itself to the safety, short-term and long-term, of humans in the presence of nuclear radiation. The sense of miasmic dread that would become part of the cultural response to radioactivity lay in the future. The Manhattan Project’s researchers handled their heavy new substances with a breeziness that bordered on the cavalier. Workers handling plutonium were supposed to wear coveralls, gloves, and a respirator. Even so, some were overexposed. The prototype reactors leaked radioactive material. Scientists occasionally ignored or misread their radiation badges. Critical-mass experiments always flirted with danger, and by later standards the safety precautions were flimsy. Experimentalists assembled perfect shining cubes of uranium into near-critical masses by hand. One man, Harry Daghlian, working alone at night, let slip one cube too many, frantically grabbed at the mound to halt the chain reaction, saw the shimmering blue aura of ionization in the air, and died two weeks later of radiation poisoning. Later Louis Slotin used a screwdriver to prop up a radioactive block and lost his life when the screwdriver slipped. Like so many of these worldly scientists he had performed a faulty kind of risk assessment, unconsciously mis-multiplying a low probability of accident (one in a hundred? one in twenty?) by a high cost (nearly infinite).
To make measurements of a fast reaction, the experimenters designed a test nicknamed the dragon experiment after a coolly ominous comment of Feynman’s that they would be “tickling the tail of a sleeping dragon.” It required someone to drop a slug of uranium hydride through a closely machined ring of the same substance. Gravity would be the agent in achieving supercriticality, and gravity, it was hoped, would carry the slug on through to a safe ending. Feynman himself proposed a safer experiment that would have used an absorber made of boron to turn a supercritical material into a subcritical one. By measuring how rapidly the neutron multiplication died out, it would have been possible to calculate the multiplication rate that would have existed without boron. The arithmetical inference would have served as a shield. It was dubbed the Feynman experiment, and it was not carried out. Time was too short.
Los Alamos hardly posed the most serious new safety challenges, for all its subsequent visibility. These belonged to the vast new factory cities—Oak Ridge, Tennessee, and Hanford, Washington—where plants thrown up across thousands of acres now manufactured uranium and plutonium in bulk. Compounds and solutions of these substances were accumulating in metal barrels, glass bottles, and cardboard boxes piled on the cement floors of storerooms. Uranium was combined with oxygen or chlorine and either dissolved in water or kept dry. Workers moved these substances from centrifuges or drying furnaces into cans and hoppers. Much later, large epidemiological studies would overcome obstacles posed by government secrecy and disinformation to show that low-level radiation caused more harm than anyone had imagined. Yet the authorities at the processing plants were overlooking not only this possibility but also a more immediate and calculable threat: the possibility of a runaway, explosive chain reaction.
Feynman had seemed to be everywhere at once as the pace of work accelerated in 1944 and 1945. At Teller’s request he gave a series of lectures on the central issues of bomb design and assembly: the critical-mass calculations for both metal and hydride; the differences between reactions in pile, water boiler, and gadget; how to compute the effects of various tamper materials in reflecting neutrons back into the reactions; how to convert the pure theoretical calculations into the practical realities of the gun method and the implosion method. He became responsible for calculating the way the efficiency of a uranium bomb would depend on the concentration of uranium 235 and for estimating safe amounts of radioactive materials under a variety of conditions. When Bethe had to assign theorists to G Division (Weapon Physics Division—G for gadget) he assigned Feynman to four different groups. Furthermore, he let Oppenheimer know that, as far as the implosion itself was concerned, “It is expected that a considerable fraction of the new work coming in will be carried out by group T-4 (Feynman).” Meanwhile, though Feynman was officially only a consultant to the group handling computation by IBM machines, Bethe decreed that Feynman would now have “complete authority.”
At Oak Ridge, where the first batches of enriched uranium were accumulating, a few officials began to consider some of the problems that might arise. One letter that made its way to Los Alamos from Oak Ridge opened, “Dear Sir, At the present time no provisions have been made in the 9207 Area for stopping reactions resulting from the bringing together by accident of an unsafe quantity of material… .” Would it make sense, asked the writer—a plant superintendent with the Tennessee Eastman Corporation—to install some kind of advanced fire-extinguishing equipment, possibly using special chemicals? Oppenheimer recognized the peril waiting in such questions. He brought in Teller and Emilio Segrè, head of the experimental division’s radioactivity group. Segrè paid an inspection visit, other theorists were assigned, and finally the problem was turned over to Feynman, with his expertise in critical-mass calculations.
As Segrè had discovered, the army’s compartmentalization of information created a perilous combination of circumstances at Oak Ridge. Workers there did not know that the substance they were wheeling about in large bottles of greenish liquid was grist for a bomb. A few officials did know but assumed that they could ensure safety by never assembling any amount close to the critical mass estimated by the physicists. They lacked knowledge that had become second nature to the experts at Los Alamos: that the presence of hydrogen, as in water, slowed neutrons to dangerously effective speeds and so reduced the amount of uranium 235 needed to sustain a reaction. Segrè astounded his Oak Ridge hosts by telling them that their accumulating stores of wet uranium, edging closer to bomb-grade purity, were likely to explode.
Feynman began by retracing Segrè’s steps and found that the problem was even worse than reported. In one place Segrè had been led into the same storeroom twice and had inadvertently noted two batches as though they were accumulating in separate rooms. Through dozens of rooms in a series of buildings Feynman saw drums with 300 gallons, 600 gallons, 3,000 gallons. He made drawings of their precise arrangements on floors of brick or wood; calculated the mutual influence of solid pieces of uranium metal stored in the same room; tracked the layouts of agitators, evaporators, and centrifuges; and met with engineers to study blueprints for plants under construction. He realized that the plant was headed toward a catastrophe. At some point the buildup of uranium would cause a nuclear reaction that would release heat and radioactivity at near-explosive speed. In answer to the Eastman superintendent’s question about extinguishing a reaction, he wrote that dumping cadmium salts or boron into the uranium might help, but that a supercritical reaction could run away too quickly to be halted by chemicals. 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.
Wielding the authority of Los Alamos was an instructive experience. Feynman’s first visit to Oak Ridge was his first ride on an airplane, and the thrill was heightened by his special-priority military status on the flight, with a satchel of secret documents actually strapped to his back under his shirt. Oppenheimer had briefed his young protégé with care. Feynman decided that the plant could not be operated safely by people kept ignorant of the nature of their work, and he insisted that the army allow briefings on basic nuclear physics. Oppenheimer had armed him with a means of handling difficult negotiations:
“You should say: Los Alamos cannot accept the responsibility for the safety of the Oak Ridge plant unless——”
“… You mean me, little Richard, is going to go in there and say——”
“… Yes, little Richard, you go in there and do that.”
John von Neumann may have advised him during their thin-air walks that there could be honor in irresponsibility, but amid the barrels and carboys of the world’s first nuclear hoards, responsibility caught up with him. Lives depended on his methods and judgments. What if his estimates were not conservative enough? The plant designers had taken his calculations as fact. He hovered outside himself, a young man watching, unsure and giddy, while someone carried off an impersonation of an older, more powerful man. As he said, recalling the feeling many years later, he had to grow up fast.
The possibility of death at Oak Ridge tormented him more urgently than the mass slaughter to come. Sometime that spring it struck him that the seedy El Fidel hotel, where he had nonchalantly roomed on his trips to Albuquerque, was a firetrap. He could not stay there any more.
I Will Bide My Time
Hitchhiking back one Sunday night, nearing the unpaved turnoff to Los Alamos, he saw the lights of a carnival shining from a few miles north in Espanola. Years had passed since he and Arline last went to a carnival, and he could not resist. He rode a rickety Ferris wheel and spun about in a machine that whirled metal chairs hanging on chains. He decided not to play the hoop-toss game, with unappealing Christ figures as prizes. He saw some children staring at an airplane device and bought them a ride. It all made him think sadly about Arline. Later he got a lift home with three women. “But they were kind of ugly,” he wrote Arline, “so I remained faithful without even having the fun of exerting will power to do it.”
A week later he rebuked her for some act of weakness and then, miserable, wrote the last letter she would read.
My Wife:
I am always too slow… . I understand at last how sick you are. I understand that this is not the time to ask you to make any effort to be less of a bother to others… . It is a time to comfort you as you wish to be comforted, not as I think you should wish to be comforted. It is a time to love you in any way that you wish. Whether it be by not seeing you or by holding your hand or whatever.
This time will pass—you will get better. You don’t believe it, but I do. So I will bide my time & yell at you later and now I am your lover devoted to serving you in your hardest moments… .
I am sorry to have failed you, not to have provided the pillar you need to lean upon. Now, I am a man upon whom you can rely, have trust, faith, that I will not make you unhappy any longer when you are so sick. Use me as you will. I am your husband.
I adore a great and patient woman. Forgive me for my slowness to understand.
I am your husband. I love you.
He also wrote to his mother, breaking a long silence. One night he awoke at 3:45 A.M. and could not get back to sleep—he did not know why—so he washed socks until dawn.
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. The cards circled the room in a multicolored sequence, small batches occasionally having to pass other batches like impatient golfers playing through. He also invented an efficient technique for correcting errors without halting a run. Because a mistake only propagated a certain distance in each cycle, when an error was found it would have tainted only certain cards. Thus he was able to substitute small new card decks that eventually caught up with the main computation.
He was at work in the computing room when the call came from Albuquerque that Arline was dying. He had arranged to borrow Klaus Fuchs’s car. When he reached her room she was still. Her eyes barely followed him as he moved. He sat with her for hours, aware of the minutes passing on her clock, aware of something momentous that he could not quite feel. He heard her breaths stop and start, heard her efforts to swallow, and tried to think about the science of it, the individual cells starved of air, the heart unable to pump. Finally he heard a last small breath, and a nurse came and said that Arline was dead. He leaned over to kiss her and made a mental note of the surprising scent of her hair, surprising because it was the same as always.
The nurse recorded the time of death, 9:21 P.M. He discovered, oddly, that the clock had halted at that moment—just the sort of mystical phenomenon that appealed to unscientific people. Then an explanation occurred to him. He knew the clock was fragile, because he had repaired it several times, and he decided that the nurse must have stopped it by picking it up to check the time in the dim light.
The next day he arranged an immediate cremation and collected her few possessions. He returned to Los Alamos late at night. A party was under way at the dormitory. He came in and sat down, looking shattered. His computing team, he found the next day, was deep in a computing run, not needing his help. He let his friends know that he wanted no special attention. In her papers he found a small spiral notebook she had used to log her medical condition. He carefully penned a final entry: “June 16—Death.”
He returned to work, but soon Bethe ordered him home to Far Rockaway for a rest. (His family did not know he was coming until the telephone rang and a foreign-accented voice asked for him. Joan replied that her brother had not been home for years. The voice said, When he comes in, tell him Johnny von Neumann called.) There Richard stayed for several weeks, until a coded telegram arrived. He flew from New York Saturday night and reached Albuquerque at noon the next day, July 15. An army car met him and drove him directly to Bethe’s house. Rose Bethe had made sandwiches. Feynman was barely in time to catch the bus to the observation site, a ridge overlooking the patch of New Mexican desert, the Jornada del Muerto, already called by its more modern name, ground zero.
We Scientists Are Clever
The test seared images into all their memories: for Bethe the perfect shade of ionized violet; for Weisskopf the eerie Tchaikovsky waltz and the unbidden memory of the halo in a medieval painting of Christ’s ascension; for Otto Frisch the cloud rising on its tornado stem of dust; for Feynman the awareness of his “scientific brain” trying to calm his “befuddled one,” and then the sound he felt in his bones; for so many of them the erect figure of Fermi, letting his bits of paper slip through the wind. Fermi measured the displacement, consulted a table he had prepared in his notebook, and estimated that the first atomic bomb had released the energy of 10,000 tons of TNT, somewhat more than the theorists had predicted and somewhat less than later measurements would suggest. Two days later, calculating that the ground radiation should have decayed sufficiently, he drove with Bethe and Weisskopf to inspect the glazed area that Feynman saw from an observation plane. The molten sand, the absent tower. Later a small monument marked the spot.
The aftermath changed them all. Everyone had played a part. If a man had merely calculated a numerical table of corrections for the effect of wind on the aerodynamically clumsy Nagasaki bomb, the memory would never leave him. No matter how innocent they remained through the days of Trinity and Hiroshima, those who had worked on the hill had knowledge that they could not keep from themselves. They knew they had been complicit in the final bringing of fire; Oppenheimer gave public lectures explaining that the legend of Prometheus had been fulfilled. They knew, despite their labors and ingenuity, how easy it had all been.
The official report on its development stated later that year that the bomb was a weapon “created not by the devilish inspiration of some warped genius but by the arduous labor of thousands of normal men and women working for the safety of their country.” Yet they were not normal men and women. They were scientists, and some already sensed that a dark association like a smoke cloud would attach itself to the hitherto-innocent word physicist. (A draft of the same report had said, “The general attitude of Americans toward their scientists is a curious mixture of exaggerated admiration and amused contempt”—never again was it quite so amused.) Not long after writing his triumphant letter home, Feynman wrote some arithmetic on a yellow pad. He estimated that a Hiroshima bomb in mass production would cost as much as one B-29 superfortress bomber. Its destructive force surpassed the power of one thousand airplanes carrying ten-ton loads of conventional bombs. He understood the implications. “No monopoly,” he wrote. “No defense.” “No security until we have control on a world level.”
Under the heading “SKILL & KNOWLEDGE” he concluded:
Most was known… . Other peoples are not being hindered in the development of the bomb by any secrets we are keeping. They might be helped a little by our mentioning which of two processes is found to be more efficient, & by our telling them what size parts to plan for—but soon they will be able to do to Columbus, Ohio, and hundreds of cities like it what we did to Hiroshima.
And we scientists are clever—too clever—are you not satisfied? Is four square miles in one bomb not enough? Men are still thinking. Just tell us how big you want it!
Many of the scientists found their magic mountain hard to leave. Lingering for months, they continued minor research that had acquired its own momentum, or skied near the Valle Grande, where they were intermittently aware that their tow rope had previously served to hoist the bomb up the tower at ground zero. Some joined the hydrogen bomb project that Teller would lead, and some remained at Los Alamos permanently, as the compound behind the fence grew into a major national laboratory and a central fixture of the American weapons-research establishment. The scientists who slowly dispersed began to realize how unlikely they were to work ever again in such a purposeful, collegial, and passionate scientific enterprise.
Nothing held Feynman to Los Alamos. He was joining Bethe’s faculty at Cornell. Raymond Birge at Berkeley had angered Oppenheimer by delaying the job offer he had recommended. Oppenheimer wrote again: “It would seem to me that under these circumstances too much of courage was not required in making a commitment to a young scientist… . I perhaps presumed too much on the excellence of his reputation among those to whom he is known… . He is not only an extremely brilliant theorist, but a man of the greatest robustness, responsibility and warmth, a brilliant and lucid teacher … one of the most responsible men I have ever met… . We regard him as invaluable here; he has been given a responsibility and his work carries a weight far beyond his years… .” Birge finally came through with an offer to Feynman that summer, but too late. When Arline was alive they had talked about moving to California for her health. Now Bethe easily swayed him.
Feynman became the first of the group leaders to leave, in October 1945. There were only a few reports to write up and some final safety tours of Oak Ridge and Hanford. It was on his last trip to Oak Ridge, as he walked past a shop window, that he happened to see a pretty dress. Before he could prevent it, a thought came. Arline would like that. For the first time since her death, he wept.