Turing's Cathedral Page 7
Although it was Veblen who “conceived the whole project,” in the assessment of physicist P. A. M. Dirac, he remained in the background, as he had at the Proving Ground. In 1959, Oppenheimer wrote to Veblen asking permission to change the name of one of the Institute’s private roads, a small cul-de-sac that overlooked the Battlefield, from Portico to Veblen Lane. Oppenheimer’s notes record Veblen’s response: “Said no. Would rather wait until dead.”51 The road is named Veblen Circle today.
At the time of the founding of the IAS, mathematics was divided into two kingdoms: pure mathematics, and applied. With the arrival of von Neumann, the distinctions began to fall. “The School of Mathematics has a permanent establishment which is divided into three groups, one consisting of pure mathematics, one consisting of theoretical physicists, and one consisting of Professor von Neumann,” Freeman Dyson explained to a review committee in 1954.52
A third kingdom of mathematics was taking form. The first kingdom was the realm of mathematical abstractions alone. The second kingdom was the domain of numbers applied, under the guidance of mathematicians, to the real world. In the third kingdom, the digital universe, numbers would assume a life of their own.
FOUR
Neumann János
We are Martians who have come to Earth to change everything—and we are afraid we will not be so well received. So we try to keep it a secret, try to appear as Americans … but that we could not do, because of our accent. So we settled in a country nobody ever has heard about and now we are claiming to be Hungarians.
—Edward Teller, 1999
JOHN-LOUIS VON NEUMANN (Margittai Neumann János Lajos to his fellow Hungarians), the first child of Max Neumann and Margit (Gitta) Kann, was born in Budapest on December 28, 1903, the year that Oswald Veblen received his PhD. The nation of Hungary, the city of Budapest, and the von Neumann family were all on the ascent.
The establishment of the dual Austro-Hungarian monarchy in 1867 had brought an interlude of peace and prosperity, and a lifting of restrictions against Jews, to a country best known, according to Klári von Neumann, “for the gallantry of its men, the beauty of its women, and last, but not least, for its hopelessly unhappy and unlucky history.”1 When the towns of Buda and Pest, on opposite sides of the Danube, were amalgamated in 1873, the new Hungarian capital, now rivaling Vienna as the cultural and economic center of the Austro-Hungarian Empire, became the fastest-growing city in Europe. There were more than six hundred coffeehouses, three of the world’s most rigorous high schools, and the first subway system on the European continent in young Neumann János’s Budapest.
Max Neumann, born Neumann Miksa in 1873, grew up in Pécs, south of Budapest, and became a lawyer and investment banker specializing in the mix of technical knowledge and financial resources that drove Hungary’s modernization in the years before World War I. He married into the Jacob Kann family, whose Kann-Heller agricultural machinery supply business (originally a supplier of millstones and later a pioneer, similar to the American Sears-Roebuck, in direct sales) occupied the ground floor of a prominent building at 62 Váczi Ut in Budapest. Max and Margit moved into an eighteen-room apartment on the top floor, surrounded by Margit’s three sisters and their families, who occupied the remainder of the two upper floors, with a branch of the Heller family on the second floor below. Max commissioned a stained-glass window to commemorate his children, with John (born in 1903) symbolized by a rooster, Michael (born in 1907) symbolized by a cat, and Nicholas (born in 1911) symbolized by a hare. “When we visited Budapest for the first time in about 1983, it was still a Communist regime,” says Nicholas, “but the janitors happily and courteously received us, and the window was still there.”2
In 1913, Max was awarded a hereditary title by Emperor Franz Joseph, for “meritorious service in the financial field.” The family name was changed to Margittai Neumann, or von Neumann in Germanized form. After the death of Max in 1928, all three of his sons converted to Catholicism (“for sake of convenience, not conviction,” says Nicholas) and immigrated to the United States. Michael reverted to Neumann, while Nicholas adopted Vonneumann. John preserved von Neumann, while remaining simply “Jancsi” to his Hungarian, and “Johnny” to his American, friends.3
“There is no question that nobility, in 1913, was not the same kind of nobility which existed in the feudal ages,” explains Nicholas, who enlisted in the U.S. Army in 1942, followed by several years in the Office of Strategic Services (OSS) before settling down to a career in patent law. “Whether [my father] purchased it or not was also somewhat beside the point. It was a reward for achievements in the economic life of Hungary. It wasn’t the feudal age.” What was important, emphasizes Nicholas, is that “Father believed in the life of the mind.”4
Max installed a private library where John read voraciously while growing up, consuming Wilhelm Oncken’s forty-four-volume Allgemeine Geschichte in Einzeldarstellungen (General History) in its entirety, and citing it in detail, from memory, when asked. He studied the thousand-year span of the Byzantine Empire, a subject that remained with him even as his mathematical abilities evaporated at the end of his life. “Its power and organization fascinated him,” Stan Ulam recalls. According to Herman Goldstine, he “was able on once reading a book or article to quote it back verbatim,” even after a period of years. “On one occasion I tested his ability by asking him to tell me how the Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop.”5
Von Neumann’s happy childhood stands in sharp contrast to the global conflicts that would dominate his adult life. Children wandered freely between the adjacent households, while the clouds of war gathered outside. “One of the games played by the children, this one under John’s leadership,” remembers Nicholas, “consisted of ‘battles’ drawn symbolically or abstractly on graph paper, with castles, highways, fortifications, etc., represented by filling in or connecting the squares of the graph paper. The aim was to demonstrate and practice ancient strategies. There was no emotional content in assigning the roles of the participants in the confrontation, or of the victors and the vanquished.”6 In both World War I and World War II, Hungary ended up on the losing side.
Preparation for the Hungarian gymnasium (or high school) began at home. The von Neumann children (and cousins) were attended by both French and German governesses, with private tutors for subjects including Italian, fencing, and chess. John became fluent in Latin, Greek, German, English, and French. During World War I the children learned English from two British nationals, Mr. Thompson and Mr. Blythe, who had been held as enemy aliens in Vienna, but who, with Max’s assistance, “had no difficulties in having their place of ‘internment’ officially moved to Budapest.”7
After the war, Hungary was governed for 133 days by the Communist regime of Béla Kun. “I am violently anti-communist,” von Neumann declared on his nomination to membership in the U.S. Atomic Energy Commission in 1955, “in particular since I had about a three-months taste of it in Hungary in 1919.”8 Thanks to Max’s influence, the family retained occupancy of their house, after escaping to the safety of a summer home on the Adriatic near Venice during the worst of the upheavals in Budapest. “Under the guiding principle of equal facilities to all, the big apartments were broken up,” remembers Nicholas, who was seven years old when a committee including a Communist Party official, a soldier of the regular army, and the janitor of the house arrived to administer the reallocation. “And on the piano under a weight, my father put a bundle of British pound notes, I don’t know how much,” says Nicholas. “The Communist official with the red armband promptly went there, took it, and the committee left and we remained in the apartment.”9
At mealtimes children were treated as adults. “It was still customary at that time for the entire family to gather for a relatively full and lengthy lunch, after which we returned to our respective job, work, or studies until dinner time,” Nicholas explains. Max entertained fre
quently at home, and according to Nicholas, “we got introduced to the ‘secrets’ of making business contacts and of management with executive powers in father’s banking house.”10 Max was shrewd but kind. Nicholas remembers when their chauffeur—who had been using their expensive French Renault on his own for unauthorized purposes—wrecked the car and expected to lose his job. Max said nothing, and arranged with the Renault dealer for a replacement and repairs.
Max believed in demonstrating practical examples of the industrial applications of finance. “If these activities involved financing of a newspaper enterprise, the discussion was about the printing press and he brought home and demonstrated samples of type,” says Nicholas. “Or if it was a textile enterprise, e.g., the ‘Hungaria Jacquard Textile Weaving Factory,’ the discussion centered around the Jacquard automatic loom. It probably does not take much imagination to trace this experience to John’s later interest in punched cards!”11
For a wealthy middle-class Jewish youth from Pécs to join the Hungarian nobility was unusual, but not unprecedented, in fin de siècle Budapest. A window of liberalization had opened following the 1867 Compromise with Austria, and closed with the rise of Béla Kun and the late-1919 counterrevolution, under Admiral Horthy, that brought in the “Numerus Clausus,” requiring that university enrollment reflect the composition of the general population, effectively returning to a quota against Jews entering academic and professional life. By that time, families such as the Kanns and Neumanns had been assimilated into the Hungarian upper class.
Unscathed by both the Red Terror of Béla Kun and the White Terror that followed, Max regained his position as a banker, joining the investment bank of Adolf Kohner and Sons. He opened doors to high and otherwise inaccessible places with the same ease and charm with which his son would later open the doors to power in the United States. “The essence of his philosophical, scientific, and humanitarian heritage was to do the impossible, that which was never done before,” says Nicholas of what John learned from their father Max. “His approach was doing not just what was never done before but what was considered as impossible to be done.”12
Hungarians had been facing the impossible for eleven hundred years, with few resources except a strategic location that had been occupied by the Roman, Ottoman, Russian, Holy Roman, Habsburg, Napoleonic French, Nazi German, and Soviet empires in turn. Von Neumann, according to Stan Ulam, credited Hungarian intellectual achievements to “a subconscious feeling of extreme insecurity in individuals, and the necessity of producing the unusual or facing extinction.”13 The Hungarian language, a branch of the Finno-Ugrian family incomprehensible to outsiders and closely related only to Finnish and Estonian, fortified Hungary against encroachment by its neighbors, while prompting Hungarian intellectuals to adopt German as a medium of exchange. To survive in a non-Hungarian-speaking world, Hungarians turned to the universal languages of music, mathematics, and the visual arts. Budapest, the city of bridges, produced a string of geniuses who bridged artistic and scientific gaps. In both mathematics and cinema it was said, “You don’t have to be Hungarian, but it helps.”
Von Neumann’s talents stood out, even in Budapest. “Johnny’s most characteristic trait was his boundless curiosity about everything and anything, his compulsive ambition to know, to understand any problem, no matter on what level,” Klári recalls. “Anything that would tickle his curiosity with a question mark, he could not leave alone; he would sulk, pout and be generally impossible until, at least to his own satisfaction, he had found the right answer.” He was able to disassemble any problem and then reassemble it in a way that rendered the answer obvious as a result. He had an ability, “perhaps somewhat rare among mathematicians,” explains Stan Ulam, “to commune with the physicists, understand their language, and to transform it almost instantly into a mathematician’s schemes and expressions. Then, after following the problems as such, he could translate them back into expressions in common use among physicists.”14
Any subject was fair game. “I refuse to accept however, the stupidity of the Stock Exchange boys, as an explanation of the trend of stocks,” he remarked to Ulam in 1939. “Those boys are stupid alright, but there must be an explanation of what happens, which makes no use of this fact.” This question led to his Theory of Games and Economic Behavior, written with Oskar Morgenstern during the war years, with von Neumann giving the project his diminishing spare time and Morgenstern contributing “the period of the most intensive work I’ve ever known.”15
“Johnny would get home in the evening after having zig-zagged through a number of meetings up and down the Coast,” Klári recalls. “As soon as he got in, he called Oskar and then they would spend the better half of the night writing the book.… This went on for nearly two years, with continuous interruptions of one kind or another. Sometimes they could not get together for a couple of weeks, but the moment Johnny got back, he was ready to pick up right where they stopped, as if nothing had happened since the last session.”16
After threats of cancellation by Princeton University Press over the manuscript’s escalating length, Theory of Games and Economic Behavior was finally published in 1944. Taking 673 pages to make their case, von Neumann and Morgenstern detailed how a reliable economy can be constructed out of unreliable parts, placing the foundations of economics, evolution, and intelligence on common mathematical ground. “Unifications of fields which were formerly divided and far apart,” they counseled in their introduction, “are rare and happen only after each field has been thoroughly explored.” Game theory was adopted first by military strategists, and the economists followed. Von Neumann “darted briefly into our domain,” commented mathematical economist Paul Samuelson, looking back after fifty years, “and it has never been the same since.”17
Klári remembers John being “as inept with his hands as he was adroit with his mind,” and as a chemistry student he was considered a danger to glassware in the lab. He was drawn to “impossible” questions—predicting the weather, understanding the brain, explaining the economy, constructing reliable computers from unreliable parts. “It was a matter of pride with him to consider the weightiest questions in the spirit of a simple puzzle,” says Klári, “as if he was challenging the world to give him any puzzle, any question, and then, with the stop-watch counting time, see how fast, how quickly and easily he could solve it.”18
Edward Teller believed that “if a mentally superhuman race ever develops, its members will resemble Johnny von Neumann,” crediting an inexplicable “neural superconductivity,” and adding that “if you enjoy thinking, your brain develops. And that is what von Neumann did. He enjoyed the functioning of his brain.”19 If there wasn’t anything to puzzle over, his attention wandered off. According to Herman Goldstine, “nothing was ever so complete as the indifference with which Johnny could listen to a topic or paper that he did not want to hear.”20
As a child, von Neumann was at the head of his class in mathematics, history, languages, and science—everything except music and sports. Even in his youth, Klári remembers, “he already gave the impression of someone roly-poly, not middle-aged flabby, but babyishly plump and round like a child’s drawing of the man on the moon.” He was nonathletic, but enjoyed walking. “We had to hike a long way in order to see the ‘Bear’s Bathtub,’ the ‘Bridal Veil’ in Yosemite, the ‘Devil’s Cauldron’ in Yellowstone, the ‘Devil’s Tower’ somewhere in the Dakotas,” reported Klári. “These and others with similar names were the spots that triggered his curiosity to the point where, on several occasions, we made detours of hundreds of miles by car and sometimes even walked several miles just because his curiosity was aroused by these fancy names.” He was attracted to stairs, and although “awkward at it … he liked to run upstairs two at a time,” remembers Cuthbert Hurd, who met von Neumann while at Oak Ridge during the Manhattan Project and later became director of computing at IBM.21
Klári tried to interest John in skiing, but after two or three attempts, “He very simply and wit
hout any rancor offered divorce.… If being married to a woman, no matter who she was, would mean that he had to slide around on two pieces of wood on some slick mountainside, he would definitely prefer to live alone and take his daily exercise, as he put it, ‘by getting in and out of a pleasantly warm bathtub.’ ”22
He rarely appeared without a suit and tie, a habit he attributed to being mistaken for a student when he arrived to teach at Princeton at the age of twenty-six, but otherwise relished the informalities of American life. “In addition to being a hard worker, Johnny seemed to be a bon vivant par excellence, always ready, for instance, for a wild drive to neighboring Spanish cafés in search of the peppery enchiladas he loved,” Françoise Ulam recalls, adding that “Stan thought they probably reminded him of Hungarian goulash!” According to Klári, he was intensely superstitious. “A drawer could not be opened unless it was pushed in and out seven times, the same with a light-switch, which also had to be flipped seven times before you could let it stay.”23