Turing's Cathedral

by George Dyson

  By 1958, numerical forecasts were running neck and neck with manual ones, and by 1960 they had pulled ahead. Starting with twenty-four-hour forecasts, there was an improvement of about twenty-four hours per decade in extending the forecast range. The question for von Neumann and Charney was: What next? “Von Neumann seemed to feel that the problem of short range forecasting was pretty well in hand,” remembers Thompson. “Well, I think he had a somewhat naive view of how far we had come and how far we still had to go, but he was looking ahead.” Von Neumann divided the problem into three regimes. In the first, short-range regime, what happens depends more on the initial conditions than on the subsequent energy inputs and dissipation. With sufficient observations, and enough computing, short-range predictions, on the order of a few days to one week, can be made. In the second, medium-range regime, beyond a week, the influences become increasingly divided between those produced by the initial conditions and those introduced by the energy inputs and dissipation, and the behavior becomes very difficult, perhaps impossible, to predict. In the third, long-range regime, “the atmosphere very quickly forgets what it looked like in the beginning,” as Thompson put it, “and its behavior is dominated almost entirely by the integrated day-to-day effects of the energy inputs and by the dissipation.”50 With sufficient knowledge of those inputs and dissipations, the task of predicting not weather but climate should be computationally tractable, and von Neumann and Charney, now joined by Norman Phillips and Joseph Smagorinsky, decided to tackle this next.

  In September 1954, Norman Phillips began running a primitive general circulation model (the ancestor of all climate models in use today) that remained stable for up to forty days of simulated time. As Smagorinsky described it, “despite the simplicity of the formulation of energy sources and sinks, the results were remarkable in their ability to reproduce the salient features of the general circulation.” Although the results became irregular and nonlinear when run beyond forty days, Phillips and Charney felt this was due to numerical instabilities, not the underlying model, and that with better coding and a more powerful computer, a true prediction of climate might be reached. “The code almost completely exhausts the resources of the present machine,” they reported, “there being only about a dozen ‘words’ in the combined Williams-Drum memory of 3072 words which are not used.” In February and March 1954, the model was run to thirty-one days and appeared “surprisingly realistic.” Even “features similar to the cold and warm fronts of the classical Norwegian wave cyclone” were produced.51

  “Our object was to establish a purely physical theory of climate, that is to say, to make the infinite forecast,” Charney later explained to Stan Ulam. “Johnny foresaw that this would be a simpler problem than the problem of long-range prediction, since the statistical properties of the motion were likely to be more correct than the individual motions.” We now know this is not as easy as it seemed at the time. “He always had, in the back of his mind, of course, large-scale weather modification,” Charney adds. “We spent many pleasant Sunday afternoons together inventing theories of climate, and it became clear that nothing could be done to explain past climates or to lay the groundwork for climatic modification until we were able to understand our own climate in purely physical terms.”52

  To launch the new project, von Neumann and Charney hosted a conference on the dynamics of climate at the Institute on October 26–28, 1955. Oppenheimer gave the opening address, drawing “a parallel between the present conference dealing with problems of the general circulation of the earth’s atmosphere and the conference held at Los Alamos, New Mexico, in preparation for work on the atomic bomb,” and noting that “the problem which faces the participants of the present conference—a problem dealing with the complicated dynamics of atmospheric motions—is a much more difficult one.”53

  Von Neumann, while a master of simplifying assumptions, was realistic about the obstacles. “Even if we were adequately informed, the inclusion of turbulence and radiation in the prediction equations would be quite involved,” he announced. Nearly all the phenomena under consideration were unstable, and minute differences could be amplified into large effects. “For example, only about 1/100,000 of all the water on earth occurs in vapour form in the atmosphere; yet the presence of water vapour makes a difference of 40°C in the average temperature of the earth,” he observed. “This is more than twice the difference between the temperature at the time of maximum glaciation and that at the time of total deglaciation of the earth.”54

  The twenty-nine attendees, although hopeful about modeling the climate, acknowledged the problem to be highly complex. “Consideration was given to the theory that the carbon dioxide content of the atmosphere has been increasing since the beginning of the industrial revolution, and that this increase has resulted in a warming of the atmosphere since that time,” the proceedings report. “Von Neumann questioned the validity of this theory, stating that there is reason to believe that most of the industrial carbon dioxide introduced into the atmosphere must already have been absorbed by the ocean.” The debate was on.55

  Sigmund Fritz, of the U.S. Weather Bureau, added that “the effects of plant life must also be taken into consideration.” William von Arx, from Woods Hole Oceanographic Institution, stressed that “the balance depends on the buffer capacity of the seawater,” and noted that “there is a significant amount of carbon dioxide locked up in the plankton cycle.” Charney asked about “the statistical significance of Wexler’s result that substantially more blocking activity takes place in Januaries which occur during periods of sunspot maxima than in those which occur during minima of the sunspot cycle.” Von Neumann “felt that there must be a minimum size of the ice field that would be self perpetuating” and “called attention to the fact that the processes which led to periods of glaciation and deglaciation must have been relatively constant over many centuries.” He asked “whether there is any evidence to suggest that high volcanic activity had been sustained over such long periods of time.”56

  “It is not necessary,” von Neumann and Charney argued, “to resort to explanations of climatic change which require external mechanisms such as solar and volcanic activity.” Richard Pfeffer, of Columbia University, noting that “the radiation absorbed by a unit mass of air is measured as the small difference between two large fluxes,” asked “whether present-day measurements of the distribution of water vapour and temperature (the chief variables which determine the radiational characteristics of the atmosphere) are sufficiently accurate to determine this difference.” Edward Lorenz, of MIT, noted, concerning the effects of clouds, that “it would be necessary to specify, in addition to the mean cloud cover, the diurnal range … whether the clouds appear at night or during the day.” Von Neumann, in conclusion, advised that they should “first attempt to determine the extent to which climate can be changed by internal mechanisms through non-linear feedback processes,” and “stressed that the problem is a complicated one.”57

  Weather prediction remains divided into the three regimes established in 1955. The first, short-term regime is predictable. The second, medium-term regime is now known to be unpredictable, much as many suspected, despite von Neumann’s hopes. The third regime is still under debate. “I think in those days we were very optimistic,” says Charney. “I remember at that time receiving reports that Norbert Wiener had regarded von Neumann and [me] as practically gonifs—thieves. That we were trying to mislead the whole world in thinking that one could make weather predictions as a deterministic problem. And I think in some fundamental way Wiener was probably right.”58

  It was Edward Lorenz, a consultant to the IAS meteorology project, who would establish the unpredictability of the atmosphere—shortly after von Neumann’s death. Approaching the question from another direction, Charney asks, “if Laplace’s mathematical intelligence were replaced by a computing machine of unlimited speed and capacity, and if the atmosphere below 100 km were spanned by a computational lattice whose mesh size were less th
an the scale of the smallest turbulent eddy, say one millimeter … would the problems of meteorology then have been solved?”59 He answers that all predictability would vanish in less than one month, “not because of quantum indeterminacy, or even because of macroscopic errors of observation, but because the errors introduced into the smallest turbulent eddies by random fluctuations on the scale of the mean free path (ca 10–5 mm at sea level), although very small initially, would grow exponentially .… The error progresses from 1 mm to 10 km in less than one day, and from 100 km to the planetary scales in a week or two.”60

  As to whether climate—the “infinite forecast”—is predictable, the jury is still out. Von Neumann expected that not only would climate become predictable, but it would also be controlled. The balance points, once identified, would be too easy to tip. The real climate change crisis, according to von Neumann, was not whether we can control climate, but how to decide who sits at the controls. “After global climate control becomes possible,” he warned in 1955, “this will merge each nation’s affairs with those of every other, more thoroughly than the threat of a nuclear or any other war may already have done.”61

  Von Neumann and Wiener could both be right. Wiener may well be as correct about climate as he was about medium-term weather prediction: that the atmosphere can no longer be treated as a deterministic system beyond thirty days or so. Von Neumann could be right in the sense that even if climate cannot be predicted, that does not mean it cannot be controlled.

  Imagine a future, combining the visions of Lewis Fry Richardson with those of von Neumann, where the Earth (including much of its oceans) is covered by wind turbines immersed in the momentum flux of the atmosphere, and photovoltaics immersed in the radiation flux from the sun. Eventually enough of these energy-absorbing and energy-dissipating surfaces will be connected to the integrated global computing and power grid, to form, in effect, the great Laplacian lattice of which Charney and Richardson dreamed. Every cell in this system would account for its relations with its neighbors, keeping track of whether it was dark, or sunny, or windy, or calm, and how those conditions may be expected to change. Coupled directly to the real, physical energy flux would be a computational network that was no longer a model—or rather, was a model, in Charney and Richardson’s sense of the atmosphere constituting a model of itself.

  Any such distributed planetary system, however, once it is sufficiently fine-grained, will itself become unpredictable—just like the atmosphere in which it is immersed. Whether the photovoltaic landscape is absorbing or reflecting, and whether the wind farms are under full load, freewheeling, or nudging the atmosphere here and there, may, in the course of time, indeed control the climate, but the workings of the model, and how it is going to behave a week from Thursday, will remain as mysterious as a partly cloudy day still is to us.

  “Sometime in the early 1950s, von Neumann, I, and several others were standing outside of the Electronic Computer Project Building in Princeton,” remembers Joseph Smagorinsky, “and Johnny looked up at a partially cloudy sky and said, ‘Do you think we will ever be able to predict that?’ ”62

  TEN

  Monte Carlo

  Between 1946 and 1955 we crossed the country twenty-eight times by car.

  —Klári von Neumann, 1963

  “WE WERE on the Riviera, in Monte Carlo, at the center of gravity for incurable gamblers,” remembers Klári von Neumann, of a gambling expedition with Francis, her first husband, midway between World War I and World War II. “When we walked into the Casino, the first person we saw was Johnny; he was seated at one of the more modestly priced roulette tables with a large piece of paper and a not-too-large mound of chips before him. He had a ‘system’ and was delighted to explain it to us: this ‘system’ was, of course, not foolproof, but it did involve lengthy and complicated probability calculations which even made allowance for the wheel not being ‘true’ (which means in simple terms that it might be rigged).”1

  “Francis went on to another table,” Klári continues. “For a while I wandered around watching the lunatic pleasure of people destroying themselves, then I went to the bar and sat down, wishing I had company with my drink. As I was sipping my cocktail, Johnny appeared.” The game theorist had run out of luck at the roulette table, and Klári, who was running out of luck with her first marriage—“an absolute disaster”—had to pay for his drink. “I was a rich girl, my father was very wealthy and Francis was an incurable gambler—this just about sums up my sex-appeal to him. After four years of all kinds of troubles, we divorced—my father bought it for me.”2

  Klára Dán was born on August 18, 1911, into a wealthy Jewish family in Budapest. “The most pampered, spoiled brat in a very large closely knit clan,” she remembers herself as “a beautiful and absolutely obnoxious child, who squealed, yelled and howled her way through the first formative years of life.” Her father, Charles Dán, an industrialist and financier, served as an officer in the Austro-Hungarian Army during World War I, surviving the war in relative comfort, but with the end of the war, “there was terrible confusion and we fled, partly on foot, across the border to Vienna, escaping from the communist terror of Béla Kun.” After escorting the family to safety, her father returned to join the counterrevolutionary underground. “The strongest and most lasting memory of my childhood,” says Klári, “is standing across the bridge and watching him walking back into what, I had by then realized, could be grave personal danger.”3

  With the overthrow of the Béla Kun regime, Budapest entered the golden years between World War I and World War II. “The counterrevolution led by Admiral Horthy succeeded,” writes Klári. “We could all go home again and then the Hungarian version of the ‘Roaring Twenties’ was on its way.”4 Klári became a national figure-skating champion at age fourteen, before being sent to England to boarding school. Like the von Neumanns, her family occupied a large house divided into three apartments, presided over by her maternal grandfather, and featuring “a huge terrace which could, and very often did, seat over a hundred people for dinner or other festivities.” The garden was divided into a formal section, off-limits to children, and an overgrown, wild area, off-limits to adults. “This line of demarcation,” Klári adds, “was the only separation between children and adults in that happy house, which gradually became the center of the ‘Roaring Twenties’ Budapest.”5

  The entire household gathered regularly at Klári’s grandfather’s table for dinner, often followed by celebration well into the night. “Soon after dinner we all drifted down, my uncle and aunt and their two children (second floor), my parents, my sister and I (third floor),” Klári explains. “There was a bottle of wine and the confab started. As often as not, another bottle was passed around; pretty soon a gypsy-band was summoned, perhaps some close friends cajoled out of bed, and a full-fledged ‘mulatsag’ was on its way.

  “It is absolutely impossible to translate ‘mulatsag’ in one simple word,” Klári notes. “It is not a party, it is not a feast, it is not even an orgy; it is simply the spontaneous combustion of a bunch of people having a good time. At six o’clock in the morning, the band was dismissed, we went back upstairs, had a quick shower, the men went to work, the children to school, and the ladies with their cooks to the market.”6

  Klári’s father and grandfather also founded a series of “Thursday Night” parties, held, once a month, in an all-male club called The Nest, with, in Klári’s words, “the laudable aim of having men from the business, financial and political world meet with artists, writers and other members of the literary and intellectual community.” When it was decided to open this gathering, with its “fertilious effect on that handkerchief-sized country’s extraordinary production of creative minds,” to women, Klári’s grandfather announced “that the first party to include the ladies unquestionably had to be held at our house.”

  “It was simply wonderful,” Klári remembers. “All three households were turned inside-out; pianos were moved, furniture rearranged.… On one
floor was the dinner; on the other, quarters for those who wanted to talk or play cards; the third was for music and dancing—all three kitchens in continuous uproar for at least three days.” No attempt was made to put children to bed. “Thus, at about the age of thirteen and for many years after, I got to know the most interesting and exciting people of our town.”7

  Klári acquired a social appetite that remained with her for life. “I met people, people and more people,” begins a memoir left unfinished at her death, “some of them world-famous, others no one ever heard about; family patriarchs, cardsharps, ex and future queens, charwomen and call-girls, statesmen and politicians at the height of their power, nightshift workers and bar philosophers, certified geniuses and frustrated total failures—all these and many more.” Klári suffered from depression, yet lived life to the full. “It was the spirit of a warmhearted conspiracy with the friends around her against what—if I sensed it right—was felt as the indifference and perhaps even the malevolence of fate,” wrote physicist John Wheeler, two weeks after her death. “The spirit to work against what might have looked to be black fate but what could nevertheless be defeated.”8

  After her divorce from Francis, Klári married a respectable, non-gambling banker. “We did the right things at the right time, we had a smoothly running household where we gave the appropriate parties at the correct intervals,” Klári writes. “He was a kind, gentle, attentive husband—he was also eighteen years older than I—and I was bored to tears.” Then, in August of 1937, Johnny, nearing the end of his first marriage, made contact during his customary summer visit to Budapest.

  “We struck up a telephone acquaintance which soon turned into sitting in cafes and talking for hours, just talking and talking,” Klári recalls. “We both were keenly interested in politics and indulged in detailed prediction of the gloomy future (Johnny’s assessment of the shape of things to come were amazingly close … and I shudder at the accuracy of some of his prognoses). We talked about this, and ancient history, and the probability to win against the roulette wheel. We told each other not-too-clean stories and little ditties that we made up between our marathon talk sessions; we talked about the difference between America and Europe, the advantage of having a small Pekinese or a Great Dane.”9