The Starship and the Canoe. Kenneth Brower
however. He was a wunderkind.
“It is said,” Sir George wrote, “that the mental processes of a mathematical prodigy differ in no essential respect from those of ordinary folks who can handle more modest problems. The prodigy’s gift is the power of incessant concentration on more and more complicated mental calculations, until his brain can instantly recall the end products of the thousands of factors with which his mind has been busy.” Sir George was writing here about genius in music, and he was going to math for analogy. It is not hard to guess which mathematical prodigy had aroused his wonder.
“In Mozart you hear this fantastic intricacy,” says Brian Dunne, one of Freeman Dyson’s colleagues on Project Orion. “You know he has to hold a whole series of things in balance, in order to make it come out right. Freeman has this. He has a wonderful ability to carry his train of thought through fantastic numbers of logical steps.”
If Freeman’s synapses sparked more electric than his father’s, his personality was somewhat less forceful. This is, at any rate, Freeman’s own view of things. Others who know the Dyson history seem to share it. Sir George was the country boy who made good by determination. Freeman, because of the social advantage provided by his father’s success, and because of his own dazzling, force-of-nature gift, never had to develop that determination. Freeman will admit that as a boy he was competitive. He enjoyed doing anything he could do well. He excelled at Latin and history, as well as at math, but he avoided sports, except for distance running—the steeplechase—for which his slender frame was suited. He was mostly an indoorsman. He lived in books.
English schools advanced students according to ability, not age, and Freeman was usually three years or so ahead of his contemporaries. His older classmates did not mind this precociousness, but his age-mates did, and Freeman suffered black eyes from small fists.
“Why?” I asked, when I learned this. “Why did they resent you?”
For a time the physicist was lost for an answer. “Well,” he said at last. “Well, I suppose I was quite unbearable.” He insisted that he likes the English system, in spite of the black eyes. They were a small price for the freedom to grow at his own speed.
“I was lucky,” he has written, “to go through high school and college in England during World War II when there was an acute shortage of paper. In England, oral examinations are not part of the system. No paper, no examinations. So the regular examination routine was disrupted and we were free to get ourselves an education. In my last year of high school I sat in class for a total of seven hours a week. We made good use of our freedom. I learned higher mathematics (and French) from three fat and dusty volumes of Jordan’s Cours d’Analyse which I found in the school library. I often wondered who had had the vision to put these marvelous books into our library. Nobody on the teaching staff ever looked at them. The famous mathematician Hardy had been a boy at the same school forty years earlier, so perhaps he had had something to do with it. He wrote in his book, A Mathematician’s Apology, that his eyes were opened to the beauty of mathematics by reading Jordan’s Cours d’Analyse. How many American high-school libraries have a copy? And how many American high schools would give the children enough time to read it if they had it?
“When I came to Cambridge University in the middle of the war I was again lucky, because the war had swept away all the graduate students. The mathematicians Hardy, Littlewood, Besicovitch gave courses of advanced lectures in a small room with three or four undergraduates sitting around a table. The geophysicist Harold Jeffreys gave his course to an audience of one. Mondays, Wednesdays, and Fridays at nine, I was always there punctually so that he would not begin talking to an empty room. It was a great time to be a student.”
6
Fire Storm
Then the war caught up with Freeman. At the end of his second year at Cambridge, he was interviewed by C. P. Snow, whose wartime job was finding appropriate military uses for technical people. Freeman became, at the age of nineteen, a mathematician with the Royal Air Force Bomber Command.
This was irony, though an irony fairly common at the time. Freeman had been a “fierce pacifist” for most of his youth. He had grown up in the grim years after the First World War. “The older generation,” he has written of that time, “were determined that we should be constantly reminded of their tragedy. And, indeed, our whole lives were overshadowed by it. Every year, on November 11, there was the official day of mourning. But much heavier on our souls weighed the daily reminders that the best and brightest of a whole generation had fallen.
“We of the class of 1941 were no fools. We saw clearly in 1937 that another bloodbath was approaching. We knew how to figure the odds. We saw no reason to expect that the next round would be less bloody than the one before. We expected that the fighting would start in 1939 or 1940, and we observed that our chances of coming through it alive were about the same as if we had belonged to the class of 1915 or 1916. We calculated the odds to be about ten to one that we would be dead in five years.”
To Freeman and his small circle of fellow pacifists, the world was insane. Hitler was just a symptom. The German people were not enemies, but fellow victims; it was the times that were sick. The old men in power in Britain had no answers to any of the nation’s problems. Chamberlain was a hypocrite. Hitler was no hypocrite, but he was insane. Churchill was a warmonger “planning the campaigns in which we were to die.” The only world leader that Freeman’s friends admired was Gandhi. They subscribed to Peace News. They boycotted OTC, the British equivalent of ROTC. “We raged against the hypocrisy and stupidity of our elders in the same way the young rebels are raging today, and for very similar reasons.”
But the holocaust that Freeman’s circle expected did not materialize. The war came, but proved not so bloody as they had calculated. Churchill won their grudging admiration. The nonviolent, Hitler-accommodating Pétain-Laval government ended their Gandhism. “Pacifism was destroyed as a moral force as soon as Laval touched it,” Freeman has written. He was no longer a fierce pacifist when he reported for duty with the RAF.
“I arrived at the headquarters of the Royal Air Force Bomber Command in July 1943, just in time for the big raids against Hamburg. On July 27, we killed forty thousand people and lost only seventeen bombers. For the first time in history, we had created a fire storm.”
Fire storms were devastatingly effective accidents. No one understood, or understands today, what makes them. They seem to depend on a climatic instability with which the bombs interact. The storms travel very fast, generate enormous heat, and burn up the oxygen in large areas of a city. They kill people even inside bomb shelters.
“In every big raid, we tried to raise a fire storm, but we succeeded just twice—once in Hamburg and once, two years later, in Dresden.” American forces had a similar success in bombing Japan, twice triggering fire storms, Freeman notes. A fire storm in Tokyo killed as many people as the Hiroshima bomb—a hundred thousand. It was more devastating than the atomic bomb that fell on Nagasaki.
Freeman did not work directly on the mathematics of the fire storm. He became the Bomber Command expert on collisions. British bombers flew at night, and occasionally in the darkness they ran into one another. The bomber crews resented dying by accident; they felt slightly better about dying by enemy fire. The problem was that loosely bunched formations, though they suffered fewer collisions, lost more planes to enemy fighters. Freeman’s chore was to find the grim median.
“The ratio of lethal to nonlethal collisions over England proved to be about three to one. In this ratio, I had already allowed for the fact that some nonlethal collisions over England would have been lethal if they had occurred over Germany. So in the end I told the Command that our best guess at the number of lethal collisions over Germany was to multiply the number of nonlethal collisions by three. That was all the mathematics I had to do. In practical terms my information meant that we were losing only about one bomber to collisions in a thousand sorties. I told the Command that this was not nearly enough. I told them to increase the density of the bomber force five-fold, so that the collision losses would come up one-half percent. I told them that they would save much more