Turing's Cathedral

by George Dyson

  “La Jolla is a wonderful place and I feel that I do not have to travel anymore because I am there already,” she added in a penciled postscript, shortly before her death.43 Her body was found washed up on Windansea Beach, at the foot of Gravilla Street, at 6:45 a.m., on November 10, 1963, “clothed in a black dress with sleeves about wrist length with black fur cuffs, high neckline, and a zippered back.” The body of the dress, “which at first had the appearance of a padded jacket … contained approximately 15 pounds of wet sand.” Her black sedan (Johnny’s last Cadillac) was found parked less than a block away, with the engine cold. Her jewelry was found at home on a coffee table in the living room beside several tumblers “with residual alcoholic contents,” and her blood alcohol, tested at 10 a.m., was 0.18%. Upon further investigation, the coroner determined that “she was known to have been a strong surf swimmer,” and that, according to her psychiatrist, who “had been able to establish a thin line of the ‘death instinct’ in her family,” she found her husband “disinterested; absorbed in his work; didn’t want to go out and mix.” Carl Eckart indicated “that he had retired about 3:00 a.m., leaving his wife still up (separate rooms in opposite end of house).” There was no sign of trauma, and her blood chloride levels (left heart 667, right heart 660) were consistent with death by drowning in seawater. (In freshwater, the differential in concentrations would be reversed.) Sand was found in her lungs. Her heart—that appeared to be in good health but had never recovered from the suicide of her father—weighed 280 grams.44

  “I never cease to wonder about my good fortune, that led me into this exciting maze of people and events,” Klári wrote in the introduction to The Grasshopper. “I, a tiny little speck, an insignificant insect just chirruping around to see where the most fun could be had and then, swept up by the hurricane force turbulence of international events and global minds.”45 John von Neumann died at fifty-three; Klári at fifty-two. Caught between the secrecy surrounding her work on nuclear weapons and the shadow of her famous husband, her role in the beginnings of Monte Carlo and the prehistory of programming languages remains obscure. The second half of the twentieth century might have unfolded differently without the contributions of a figure skater who was born a century ago in Budapest.

  The bombs that Klári helped bring into existence were a spectacular success. By the time the United States finished testing in the Marshall Islands, there had been forty-three explosions at Enewetak and twenty-three at Bikini, for a total yield of 108 megatons. The computers did their job perfectly, but on Castle Bravo, the successor to Ivy Mike, there was a human error, perhaps the largest human error in history, in failing to account for the generation of tritium from lithium-7 as well as lithium-6. The explosion, on March 1, 1954, was expected to yield some 6 megatons, but yielded over 15 megatons instead. One person, on the Japanese fishing vessel Lucky Dragon, was killed directly, and an unknown number of others indirectly over time. The aftereffects forced the evacuation of Rongelap, Rongerik, Ailinginae, and Utirik, and parts of Bikini remain uninhabitable today. Fallout was dispersed throughout the world. The strontium 90 from Ivy Mike and Castle Bravo, taken up in place of calcium in children’s teeth, mobilized opposition to atmospheric testing over the next ten years.

  First-generation electronic computers fostered first-generation nuclear weapons, and next-generation computers fostered next-generation nuclear weapons, a cycle that culminated in the Internet, the microprocessor, and the multiple-warhead ICBM. Willis Ware, after obtaining his PhD from Princeton, left the Institute in August 1951, working briefly on missile development at North American Aviation before settling in at RAND in Santa Monica, where the JOHNNIAC, an improved copy of the MANIAC, had just been built. The JOHNNIAC (John von Neumann Numerical Integrator and Automatic Computer) was designed to be at least ten times as reliable as its Princeton progenitor, and incorporated a working memory of 40 Selectron tubes, storing 256 bits each. Instead of being used to design thermonuclear weapons, the JOHNNIAC was used to better understand their effects. An extended series of RAND Research Memoranda, with titles such as “Equilibrium Composition and Thermodynamic Properties of Air to 24,000°K,” examined what temperatures four times that of the surface of the sun would do to the surface of the earth.

  RAND began looking at how to design redundant digital communications networks for coordinating defenses both before and after nuclear attack, prompted by the game theorists’ conclusions that a survivable communications network, capable of launching even a handful of remaining missiles, was the best preventive to premeditated attack. Left unstated, but not unconsidered, was the possibility that the survivors of a nuclear attack, instead of making a final suicidal response, might want to coordinate not launching a retaliatory strike. “There was a clear but not formally stated understanding,” explained Paul Baran, a RAND colleague who helped develop the communication architecture now known as packet switching, “that a survivable communications network is needed to stop, as well as to help avoid, a war.”46

  Baran’s study “On Distributed Communications” was released in 1964, and played the same role in the development of the Internet as Preliminary Discussion of the Logical Design of an Electronic Computing Instrument had played in the development of the individual machines out of which the Internet was composed.47 A similar decision was made not to patent or classify the work. “We felt that it properly belonged in the public domain,” explained Baran. “Not only would the US be safer with a survivable command and control system, the US would be even safer if the USSR also had a survivable command and control system as well!”48

  JOHNNIAC gave rise to JOSS (JOHNNIAC Open-Shop System), one of the earliest online, time-shared, multi-user computing environments, and a RAND subdivision, the Systems Development Division, later spun off as the Systems Development Corporation, developed the first million-line codes for the SAGE air defense system, whose legacy survives in all large, real-time computing systems in use today. Many of the assumptions underlying the Internet—from its addressing architecture to its redundancy—go back to RAND’s decision to purchase eighty 256-bit Selectrons, ordered in 1951 and delivered in 1952, for $800 each. “There is another item we have been wanting to tell you about … which I believe will be a source of satisfaction to you and Julian; even though it makes us look like deviationist inventors,” John Williams, director of computing at RAND, wrote to von Neumann in October 1951. “We are placing an order with RCA for 100 Selectrons.”49 One reason RAND was able to accomplish so much, over the next decade, was the head start gained by avoiding the impediment of recalcitrant Williams tubes.

  Nicholas Metropolis died in 1999, having helped keep Los Alamos at the forefront of scientific computing since 1943. “Rather than the way the Institute in Princeton worked, where Johnny had to get the money and scramble for it, at Los Alamos Nick had everything he needed,” says Harris Mayer, “and also he had Johnny von Neumann still.”50 After von Neumann’s death, it was Los Alamos, more than anywhere else, that kept his unfinished agenda alive until its importance was recognized by other institutions in later years.

  Robert Richtmyer, who died in 2002, moved from Los Alamos to the Courant Institute at NYU in 1953, and to Boulder, Colorado, in 1964. “I get the impression that machines are now mostly being designed not by problem-solving people but by people who regard machines as an end in themselves,” he complained to Nicholas Metropolis in 1956. “John von Neumann’s idea to put numbers and instructions in the same kind of memory was a wonderful advance, but it doesn’t follow that numbers and instructions have to be interconfusible.”51 Richtmyer, like Bigelow, was surprised that computing remained largely stuck where von Neumann had left off, with machines and codes growing in power and complexity but not in the fundamental way the systems worked. “A curious phenomenon that has accompanied the development of software is a tendency for the hardware to become dependent on it,” he observed in 1965.52

  Von Neumann never returned to pure mathematics, and even his attention to com
puting was distracted by his duties at the AEC. At the International Congress of Mathematicians held in Amsterdam on September 2–9, 1954, he was invited to give the opening lecture, billed as a survey of “Unsolved Problems in Mathematics” that would update David Hilbert’s famous 1900 Paris address. The talk, instead, was largely a rehash of some of von Neumann’s own early work. “The lecture was about rings of operators, a subject that was new and fashionable in the 1930s,” remembers Freeman Dyson. “Nothing about unsolved problems. Nothing about the future. Nothing about computers, the subject that we knew was dearest to von Neumann’s heart. Somebody said in a voice loud enough to be heard all over the hall, ‘Aufgewärmte Suppe,’ which is German for ‘warmed-up soup.’ ”53

  Afterward, says Benoît Mandelbrot, “I saw von Neumann leaving the hall. He was all by himself, lost in thought. Nobody was following him, and he was rushing somewhere, by himself.” Over the next several days, Mandelbrot noticed an “old man, hanging around with us, and I asked him what he was doing.” This was Michael Fekete, with whom von Neumann had published his first paper, at age eighteen, in 1922. Fekete, who had gone on to become the first professor of mathematics at the Hebrew University of Jerusalem, answered that “von Neumann wrote his first paper in collaboration with me. And so he wanted me to write my last paper in collaboration with him.” Von Neumann was too preoccupied with his imminent appointment to the AEC, and the symmetry was never achieved.54

  Later, during the meetings, von Neumann met with Veblen alone. They spoke from 10:00 p.m. on the seventh until 2:00 a.m. on the eighth, partly to discuss the Oppenheimer hearings and partly because von Neumann was about to announce publicly that he was leaving the IAS. “Veblen started with a tirade against L.L.S. [Strauss] and E.T. [Teller] as arch enemies, E.T. being the man who brought Me’lissende [Oppenheimer] down,” von Neumann reported to Klári later that morning, using their private code name for Oppenheimer. “I said that I considered L.L.S. a tyrant but the best chairman the AEC ever had, E.T. a fool but a man with merits and who is my personal friend.”

  “We had only few residual disagreements,” von Neumann continued.

  He [Veblen] said that he felt that Me’lissende’s resignation, forced or voluntary, would be very bad for the Institute.… I was not willing to say that the latter, if properly managed, would not be the best. He also said that Me’lissende had previously told him that he disagreed with my views about a “quick” [preventive] war, but that I might well be right.… I told him that I felt that a “quick” war was academic by now, since it would now—or within a rather short time—hardly be “quick.”55

  The reconciliation with Veblen was short-lived, and von Neumann grew increasingly estranged from the mathematical community in which he had spent his youth.

  Oswald Veblen died in 1960, at his summer home on the shores of Blue Hill Bay, in Maine, living in the style more of his Norwegian grandfather than of an Institute trustee. Thanks largely to Veblen, some 589 of the Institute’s 800 acres remain designated a permanent woodland reserve, and, in 1957, he and his wife, Elizabeth, donated the 81 acres they owned on the outskirts of Princeton to Mercer County, forming the Herrontown Woods nature reserve, “a place where you can get away from cars, and just walk and sit.”56 He never reconciled his differences with von Neumann. “Johnny, even in his last days, in his last month of his life, there was really only one man, one person whom he wanted to see,” says Klári. “I wrote begging letters to Veblen to come and visit him, but he did not come.”57

  At 4:50 a.m. on May 27, 1953, during the final push to develop a deliverable hydrogen bomb, the engineers who were running a thermonuclear problem for the AEC were suddenly alarmed by an unknown noise. “Mouse climbed into blower behind regulator rack, set blower to vibrating: result no more mouse & a!!! of a racket,” records the machine log (a stronger word having been replaced). Below the logbook entry, one of the engineers drew a gravestone on which was inscribed:

  HERE

  LIES

  MOUSE

  BORN

  ?

  DIED

  4:50 AM

  5/27/53

  Another engineer inserted “Marsten,” so the tombstone read, HERE LIES MARSTEN MOUSE, a comment directed at Marston Morse, who had long opposed the invasion of the Institute by engineers. Morse, who grew up on a farm in Maine, had his reasons for opposing the computer project, and deserves his own final word.

  “In spirit we mathematicians at the Institute would cast our lot in with the humanists,” Morse wrote to Aydelotte at the beginning of World War II. He served full-time in the Office of the Chief of Ordnance of the Army for the duration of the war, but believed that, with the war over, the Institute for Advanced Study was no place for weaponeers. “Mathematicians are the freest and most fiercely individualistic of artists,” he argued, and the government contracts that supported the computer project, he believed, were in conflict with this.58

  In October 1950, when the construction of the computer was at its peak, its budget outshadowing the entire budget of the School of Mathematics by more than three to one, Morse went off to Kenyon College, in Ohio, to deliver a talk on “Mathematics and the Arts,” at a conference in honor of Robert Frost. “One hundred miles northeast of Derry, New Hampshire, lie the Belgrade Lakes, and out of the last and longest of these lakes flows the Messalonskee,” he began.

  I was born in its valley, “north of Boston” in the land of Robert Frost. The “Thawing Wind” was there, the “Snow,” the “Birches” and the “Wall” that had to be mended: I was born on a sprawling farm cut by a pattern of brooks that went nowhere—and then somewhere. A hundred acres of triangles of timothy and clover, and twisted quadrilaterals of golden wire grass, good to look at, and good riddance. At ten I combed it all with horse and rake, while watching the traffic of mice beneath the horse’s feet.

  “One cannot decide between Kronecker and Weierstrass by a calculation,” Morse continued, warming up. “There is a center and final substance in mathematics whose perfect beauty is rational, but rational ‘in retrospect.’ ” He went on to question “the science of cold newsprint, the crater-marked logical core, the page that dares not be wrong, the monstrosity of machines, grotesque deifications of men who have dropped God, the small pieces of temples whose plans have been lost and are not desired, bids for power by the bribe of power secretly held and not understood.

  “It is science without its penumbra or its radiance, science after birth, without intimations of immortality,” he concluded. “The creative scientist lives in ‘the wildness of logic’ where reason is the handmaiden and not the master. I shun all monuments that are coldly legible. It is the hour before the break of day when science turns in the womb, and, waiting, I am sorry that there is between us no sign and no language except by mirrors of necessity. I am grateful for the poets who suspect the twilight zone.”59

  The secrecy Morse so objected to is now permanently entrenched. The U.S. government now produces more classified information than unclassified information—and, since even the amount of classified information is classified, we may never know how much dark matter there is. Von Neumann’s monument, however, has turned out not to be as coldly legible as it first appeared. There will always be truth beyond the reach of proof.

  Alan Turing received the Order of the British Empire in 1946, yet, under the Official Secrets Act, he could never talk openly about his wartime work. After leaving the National Physical Laboratory in 1948, he thrived under Max Newman’s auspices at the University of Manchester, where the core of the computing group from Bletchley Park were continuing from where their work on Colossus had left off. All went well until 1952, when Turing was convicted on a charge of gross indecency (for homosexuality), forced to undergo “therapy” with estrogen injections, and had his security clearance (and ability to visit the United States) revoked. He died, evidently of cyanide poisoning, at his home in Manchester on June 7, 1954, two weeks before he would have turned forty-two. His promising new resul
ts on the chemical basis of morphogenesis were left unfinished, a jar of potassium cyanide was in his home laboratory, and a partially eaten apple was at his side, leaving the circumstances of his death as undecidable as the Entscheidungsproblem that had been such a landmark in his life.

  With the gradual lifting of secrecy came long-overdue recognition not only of the importance of Turing’s contribution to the war, but of the contributions that Colossus, as a physical embodiment of Turing’s theoretical principles, had made to the development of hardware and software in the aftermath of World War II. On September 10, 2009, “on behalf of the British government, and all those who live freely thanks to Alan’s work,” British prime minister Gordon Brown issued a formal apology for the “inhumane” treatment that Turing received. “We’re sorry, you deserved so much better,” were his closing words.

  Kurt Gödel died in Princeton on January 14, 1978, weighing only sixty-five pounds and with malnutrition listed as the cause of death. He never made it to Hanover to search the Leibniz manuscripts for the clues he believed existed as to where digital computing, logical calculus, and universal language were destined to end up. On March 20, 1956, he wrote to von Neumann about a question that “would have consequences of the greatest significance,” but never received an answer, von Neumann having given up his correspondence by that time. “It is easy to construct a Turing machine that allows us to decide, for each formula F of the restricted functional calculus and every natural number n, whether F has a proof of length n,” Gödel wrote. “The question is, how rapidly does φ(n) [the number of steps required] grow for an optimal machine?” The answer to this question, still unresolved, would determine whether “in spite of the unsolvability of the Entscheidungsproblem,” as Gödel put it, “the thinking of a mathematician in the case of yes-or-no questions could be completely replaced by machines.”60