Turing's Cathedral Read online

  Johnny and Mariette (followed by Johnny and Klári in 1938) sought to reconstruct a fragment of the life they had left behind in Budapest. They entertained lavishly and frequently—in old Princeton style, with domestic servants to help. The household established with Klári on Westcott Road became “an oasis in otherwise somewhat stuffy Princeton,” according to Robert Richtmyer, with parties that “were a mixture of intense scientific discussion and then complete irrelevance,” according to Oskar Morgenstern. “You went there with a light feeling every time, because there was a spirit of freedom in that house.” Adds Richtmyer: “and always something to drink.”45

  Von Neumann did his best to undermine the Institute for Advanced Study’s reputation as a refuge where great minds retreated into quiet seclusion to think. “He could not work without some noise or at least the possibility of noise,” explains Klári. “Some of his best work was done in crowded railroad stations and airports, trains, planes, ships, hotel lobbies, lively cocktail parties or even among a bunch of shrieking very minor minors whooping it up.” At Fine Hall, his office door was always open. “Weyl is happier in a room smaller than yours, and Johnny is productive in a room smaller than Weyl’s,” Abraham Flexner wrote to Oswald Veblen, arguing against a request for even more luxurious offices in Fuld Hall.46

  Although happy in small, nondescript offices, von Neumann liked large, fast cars. He bought a new one at least once a year, whether he had wrecked the previous one or not. Asked why he always purchased Cadillacs, he answered, “Because no one would sell me a tank.” In 1946 the Diracs were visiting in Princeton, and Mrs. Dirac asked for help in finding an inexpensive used car. “How can I tell her without wounding her feelings,” von Neumann wrote to Klári, “that her chances to getting a used car in US ’46 are as good as getting a second hand snowball in Hell!”47

  “I always tried to arrange it so that I could drive,” remembers Cuthbert Hurd, who had brought von Neumann in as a consultant, two days a month, for IBM, and often shared the drive up the West Side Elevated Highway to IBM’s headquarters in Poughkeepsie, New York. “When the conversation lagged he would sing. The tune was indistinguishable, so he would sway from side to side like this and the car wouldn’t go very straight.” Von Neumann was regularly ticketed for speeding. “I’d take that ticket and give it to the downtown manager in New York, where the Police court was, and he would go around and pay the fine,” says Hurd.48

  “He drove like mad and only needed to sleep for three or four hours a night,” says Marina, recalling an early drive across the United States. “Remember, those were 1930s motels in 1946; nothing had been built during the war. Many of them had no indoor plumbing. I had led a sheltered life, and I had never seen an outhouse, except once at camp.” Herman Goldstine, with whom von Neumann occasionally shared hotel rooms while on government assignments, remembers that “he would waken in the night, at two or three in the morning, and would have thought through what he had been working on. He would then write [it] down.”49

  Von Neumann could deliver publishable text, and even mathematical proofs, on the first draft. “I write rather freely and fast if a subject is ‘mature’ in my mind,” he explained in 1945, apologizing for an undelivered manuscript, “but develop the worst traits of pedantism and inefficiency if I attempt to give a preliminary account of a subject which I do not have yet in what I can believe to be in its final form.” His handwritten letters sometimes end with an informal “P.S.” that continues, for several pages, to explain some new result. “Each day he would start writing before breakfast,” says Ulam. “Even at parties in his house, he would occasionally leave the guests to go to his study for half an hour or so to record something that was on his mind.” In speech or on paper, every idea expressed was precise. “Von Neumann was one of the greatest of all mathematical artists,” says Goldstine. “It was never enough for him merely to establish a result; he had to do it with elegance and grace.”50

  After obtaining U.S. citizenship on January 8, 1937, von Neumann applied for a commission in the army but was rejected for being too old, despite perfect written examination scores. Oswald Veblen arranged for the army to enlist von Neumann as a consultant instead. The U.S. Army Ordnance Department’s Proving Ground at Aberdeen had been left in suspended animation at the end of World War I, subsisting on an annual budget of about $6 million until 1937, when funding tripled to $17 million, before jumping to $177 million on the eve of World War II. Von Neumann’s involvement with the military increased over the next twenty years. “He seemed to admire generals and admirals and got along well with them,” explains Ulam, adding that this “fascination with the military … was due more generally to his admiration for people who had power. He admired people who could influence events. In addition, being softhearted, I think he had a hidden admiration for people or organizations that could be tough.”51

  All three military services regarded von Neumann as one of their own. “I think that we have a chance to do some work which is useful, both to the Army and to the mathematical community,” von Neumann answered mathematician Saunders Mac Lane, who questioned whether academic mathematicians should take on military work. “We can do this in one particular sector of the Army where the authorities have ‘seen the light.’ I don’t think that we should be influenced too much by the inadequacies in other sectors.” According to Ulam, von Neumann was especially favored for his role as chairman of committees, “this peculiar contemporary activity,” essential to getting anything done in the United States. “He would press strongly his technical views, but defer rather easily on personal or organizational matters.” According to Rear Admiral Lewis Strauss, von Neumann was “able to take the most difficult problem, separate it into its components, whereupon everything looked brilliantly simple, and all of us wondered why we had not been able to see through to the answer as clearly as it was possible for him to do.”52

  While World War I had been a battle for bigger guns, World War II (and the cold war that followed) became a battle for bigger bombs. In 1937, with war looming, it was time to remobilize the scientists, and Veblen was brought back as the army’s chief mathematician at the Proving Ground. Von Neumann was appointed, in quick succession, to the Scientific Advisory Committee of the Ballistic Research Laboratory, the War Preparedness Committee of the American Mathematical Society and Mathematical Association of America, and the National Defense Research Committee. “The functions of all these sets and sets of sets are not very well defined as yet, but I suppose they will be, when ‘The Day’ comes around,” he wrote to Ulam in 1940. “So far I have chiefly worried about spherical and Gaussian measures of various functions.”53 This was shorthand for calculating the behavior of high explosives—the surprising thing about large explosions being not how much energy was released, but how unpredictable was the damage produced as a result.

  Von Neumann, who believed that mathematics grew best when nourished by “a certain contact with the strivings and problems of the world,” became a great friend of the weaponeers. “Physicists—particularly experimental physicists—are more in demand for defense work,” he explained to a fellow mathematician once war had been declared, “while we must, so to say, create the demand for our services.”54 Wherever new weaponry went, von Neumann followed—or got there first. The behavior of both high-explosive detonations and supersonic projectiles depended on the effects of shock waves whose behavior was nonlinear and poorly understood. What happens when a discontinuity is propagated faster than the local speed of information ahead of the disturbance (for pressure waves, this being the speed of sound)? What happens when two (or more) shock waves collide?

  Shock waves are sudden discontinuities propagated in compressible media—usually air. “Under the conditions in and around an explosion all known substances must be regarded as compressible,” von Neumann pointed out.55 Drawing upon his training in chemical engineering as well as mathematical physics, he took a broad view of weapons design: starting with the chemical energy released by
high explosives, through the detonation wave that propagates the explosion, to the blast wave that causes the destructive effects. The resulting insights into shock waves (especially reflected shock waves) contributed to the development of the shaped charges used in antitank weapons, torpedoes, and armor-piercing shells, as well as more effective depth charges against submarines and more effective targeting of conventional bombs. His novel mathematical technique for treating shocks led to the success of the implosion method of initiating a nuclear explosion, and his theory of blast waves helped determine the height at which to explode the resulting weapon for maximum effect. He was one of a handful of scientists who were present at both the conception and the delivery of the atomic bomb.

  The amount of fissile material needed to support a self-sustaining chain reaction is a function not only of mass but of density. Squeeze a subcritical mass of plutonium to a high enough density and it becomes critical, and if confined by a surrounding shell of dense, neutron-reflecting material (the “tamper”), it will violently explode. Von Neumann suggested how the requisite high explosive could be formed into implosive lenses that, if arranged like the panels on a soccer ball, and detonated in precise synchronization, would focus the resulting shock wave into a converging front. A far smaller quantity of fissionable material can thereby be made to explode.

  Von Neumann’s theory of reflected shock waves could then be used to maximize a bomb’s effects. “If you had an explosion a little above the ground and you wanted to know how the original wave would hit the ground, form a reflected wave, then combine near the ground with the original wave, and have an extra strong blast wave go out near the ground, that was a problem involving highly non-linear hydrodynamics,” recalls Martin Schwarzschild. “At that time it was only just understood descriptively. And that became a problem that I think von Neumann became very much interested in. He wanted a real problem that you really needed computers for.”56

  The results were surprising. In a report to the Navy Bureau of Ordnance in 1943, von Neumann, who normally limited his use of exclamation marks in his mathematical writings to the symbol for factorial (4! = 1 × 2 × 3 × 4 = 24), used two exclamation marks, as punctuation, in a row. “Even for a weak shock the reflected shock can be twice as strong as it is head-on, if the angle of incidence is properly chosen!” he reported. “And this happens at a nearly glancing angle, where a weaker reflection would have seemed plausible!”57

  By the time the United States entered the war (against Japan on December 8 and Germany on December 11, 1941), “Johnny had started on his travels,” Klári reported. “Almost continuous: from Princeton to Boston, from Boston to Washington, from Washington to New York—a short stop in Princeton, then to Aberdeen, Maryland, the Army Proving Grounds—back to Washington, maybe one night at home, then starting on the rounds again, not necessarily in the same order, but up and down the Eastern seaboard with occasional forays further inland—not the West yet—that came later.”58

  In February 1943, after a series of false starts, he received orders on behalf of the navy to report to England, the official assignment being to assist with a statistical approach to the problem of mines, submarines, and related countermeasures and counter-countermeasures. Loss of Allied shipping was threatening to turn the tide of the war. What von Neumann actually did during his stay in England remains a mystery, particularly the extent to which he consulted with the British groups who were working, secretly, on code breaking and the feasibility of atomic bombs. We do know that he made a visit in late April of 1943, with John Todd, to Her Majesty’s Nautical Almanac Office, one of the largest non-secret computing operations at the time. The office had been evacuated to Bath from Greenwich for safety from German air raids, and on the train ride back to London, having witnessed the capabilities of a six-register National Cash Register Accounting Machine, von Neumann developed a short interpolation routine. He later wrote to Todd that “I received in that period a decisive impulse which determined my interest in computing machines.”59

  Upon his return from England in July of 1943 he was enlisted for “Project Y,” as the Manhattan Project was code-named. As a mathematical consultant to the project, he was allowed to travel freely outside Los Alamos, a privilege denied most participants, who were required to bring their families and remain sequestered for the duration of the war. “Progress elsewhere in computing was carried to Los Alamos by von Neumann,” says Nicholas Metropolis, “who consulted for several government projects at such a pace that he seemed to be in many places at the same time.”60

  Von Neumann arrived at Los Alamos on September 21, 1943, traveling from Chicago with Isidor Rabi on the Atchison, Topeka and Santa Fe Railway’s flagship diesel-electric streamliner Super Chief. From the railroad depot at Lamy, New Mexico, they were driven “across a number of good class canyons and mesas” to the new laboratory, which von Neumann described, in a letter to Klári the next day, as “an odd combination of an Army Post, a Western National Park with Lodge, and a few assorted other things.” He concluded that the project “is worth meditating about, although one should probably not sell one’s soul to it,” and added, in a postscript, that “computers are, as you suspected, quite in demand here, too.” Two days later he added that “the whole place is queerer than I can describe. And … believe me, if I begin to develop a craving for normality and reality, then it’s pretty bad.”61

  By “computers” von Neumann meant human computers, the kind that Oswald Veblen had assembled at the Proving Ground during World War I. At the time of von Neumann’s arrival at Los Alamos there were about twenty human computers (initially recruited among the wives of physicists, soon aided by reinforcements from the army’s Special Engineering Detachment, or SED) equipped with Marchant 10-digit electromechanical desk calculators. The Marchant “Silent Speed” machines, built on San Pablo Avenue in Oakland, California, and requisitioned for the war effort, weighed almost 40 pounds, incorporated 4,000 moving parts, and cycled at 1,300 rpm.

  As Nicholas Metropolis, who became director of computing at Los Alamos, put it, “the very nature of the Laboratory’s objective—an atomic bomb—precluded extensive field testing.”62 At a time when even one shock wave at a time was poorly understood, predicting the behavior of an implosion weapon accurately enough to build one that stood a reasonable chance of working on the first try was out of reach of the small computing group. To follow the process from start to finish required modeling the initial propagation of a detonation wave through the high explosive, the transmission of the resulting shock wave through the tamper and into the fissile material (including the reflection of that shock wave as it reached the center), the propagation of another shock wave as the core exploded, the passage of that shock wave (followed by an equally violent rarefaction wave) outward through the remnants of the previous explosion and into the atmosphere, and finally the resulting blast wave’s reflection if the bomb was at or near the ground. Von Neumann had arrived just in time.

  A set of punched-card accounting and tabulating machines were requisitioned from IBM, which could not be told where the machines were going, or why. The machines—three 601 multipliers, a 402 tabulator, a reproducer, a verifier, a sorter, and a collator—arrived, in huge wooden crates, without documentation or an installation crew. IBM was asked for the name of their best technician who had been drafted into the army, who was immediately given a security clearance and reassigned to Los Alamos, but this took time. In the interim, Stanley Frankel, a Berkeley graduate student of Oppenheimer’s who had been put in charge of the hand computing group, and Richard Feynman, a graduate student (and amateur safecracker) from Princeton who was game for any unauthorized challenge, managed to uncrate the machines and get them to work.

  Feynman and Frankel were hooked. “Mr. Frankel, who started this program, began to suffer from the computer disease that anybody who works with computers now knows about,” Feynman later explained. “The trouble with computers is you play with them.” Feynman and Frankel, joined by Nich
olas Metropolis, adapted the IBM machines to accelerate the work of the hand computing group. “If we got enough of these machines in a room, we could take the cards and put them through a cycle,” explained Feynman. “Everybody who does numerical calculations now knows exactly what I’m talking about, but this was kind of a new thing then—mass production with machines.”63

  The strategy was to start from a prescribed initial state and model the progress of the explosion from point to point in space and from step to step in time. A single, initial punched card was established for each point in space, with a deck of these cards representing the state of the explosion at a given instant in time. “Processing a deck of cards through one cycle in the calculation effectively integrated the differential equations ahead one step in the time dimension,” explains Metropolis. “This one cycle required processing the cards through about a dozen separate machines with each card spending 1 to 5 seconds at each machine.”64 The result was a new deck of cards used as the input for the next time step. The process was tedious, repetitive, intolerant of error, and quickly bogged down.

  “The real trouble was that no one had ever told these fellows anything,” explains Feynman. “The Army had selected them from all over the country for a thing called Special Engineer Detachment—clever boys from high school who had engineering ability. They sent them up to Los Alamos. They put them in barracks. And they would tell them nothing.” Feynman secured permission from Oppenheimer to give a lecture to the recruits. “They were all excited: ‘We’re fighting a war! We see what it is!’ They knew what the numbers meant. If the pressure came out higher, that meant there was more energy released. Complete transformation! They began to invent ways of doing it better. They improved the scheme. They worked at night.”65 Productivity went up by a factor of ten.