Turing's Cathedral: The Origins of the Digital Universe

by George Dyson

“Mathematics is singularly well suited to our beginning,” he explained to the trustees. “Mathematicians deal with intellectual concepts which they follow out for their own sake, but they stimulate scientists, philosophers, economists, poets, musicians, though without being at all conscious of any need or responsibility to do so.” There were practical advantages to the field as well: “It requires little—a few men, a few students, a few rooms, books, blackboard, chalk, paper, and pencils.”

“mathematicians, like cows in the dark, all look alike to me.”

Princeton, despite its role in the American Revolution, had become one of the more conservative enclaves in the United States, “a quaint and ceremonious little village of puny demigods on stilts,” as Einstein described it to the Queen of Belgium in 1933.36

A lot going on in that sentence!

According to Oppenheimer, “tea is where we explain to each other what we do not understand.”

Mathematicians produce their best work at about the same time that they produce their children, and the nursery school helped keep the two apart.

Aydelotte replied, explaining that during Gödel’s convalescence in Austria he “had the idea that all the sanitarium food was poisoned and he would eat only things that were prepared and brought to him by a young woman friend of the family (whom he later married) and then only on condition that she eat with him from the same plate and with the same spoon,” and that his mother “was so frightened concerning his condition that she slept always in a locked room at night.”31 With this statement, Gödel’s Selective Service file comes to an end.

“There should be some means by which the computer can signal to the operator when a computation has been concluded, or when the computation has reached a previously determined point. Hence an order is needed which will tell the computer to stop and to flash a light or ring a bell.”

Anticipating Gödel and Turing, Leibniz promised that through digital computing “the human race will have a new kind of instrument which will increase the power of the mind much more than optical lenses strengthen the eyes.…

The purpose of computing is insight

Absence of a signal should never be used as a signal. —Julian Bigelow, 1947

We owe the existence of high-speed digital computers to pilots who preferred to be shot down intentionally by their enemies rather than accidentally by their friends.

“One of the reasons our group was successful, and got a big jump on others, was that we set up certain limited objectives, namely that we would not produce any new elementary components,” adds Bigelow. “We would try and use the ones which were available for standard communications purposes. We chose vacuum tubes which were in mass production, and very common types, so that we could hope to get reliable components, and not have to go into component research.”

“A binary counter is simply a pair of bistable cells communicating by gates having the connectivity of a Möbius strip.”

“The bombs had saved our lives,” says Rosenberg, and however difficult von Neumann (and Oppenheimer) proved to be as his employers, he never forgot that.

Rosenberg interviewed with Bigelow and von Neumann, and started work in July. “There was a lot of anti-Semitism in the army. But there wasn’t anti-Semitism with Johnny,” he says.

“There is a lot of very nasty calculation,” he says. “For a typical structure like the one I did, there are about four thousand reflections … and you have to calculate the sum over all of the wretched atoms in your structure to calculate this wretched phase angle. It takes a hell of a long time by hand. I had a boy and one girl who were helping me with the calculations. It took us three years.”

The gloom was occasionally dispelled. Somewhere in Nevada, “a man with a nice long beard, wearing well-used denims, tied his pack-mule to the hitching-post, then rode the other one, his mount, into the bar where we were consoling ourselves,” Klári writes. “Nobody blinked an eye, the bartender handed the man a glass of beer and a bucket of the same brew was placed in front of the mule. The whole scene was a mute play; it seemed completely routine, the man paid, he and his beast drank up and quietly left the place.”

The Ulams were too impoverished in Cambridge to afford restaurants, and had been too wealthy in Poland to have learned to cook for themselves.

As to military consequences, Ulam argued that if one started to question the possible misuse of scientific research, then the infinitesimal calculus should have been abandoned, to preclude destructive effects.

“If, instead of using living organisms, one could experiment with entities which, without any doubt could evolve exclusively by ‘mutations’ and selection,” Barricelli argued, “then and only then would a successful evolution experiment give conclusive evidence; the better if the environmental factors also are under control.”15 To attempt this in 5 kilobytes was wildly ambitious, but this was 1953. Jetliners were carrying their first commercial passengers, the space age was beginning, and tail fins were beginning to appear on cars. New elementary particles were being discovered faster than Oppenheimer’s group of young theoretical physicists was able to keep up.

Von Neumann was less interested in building computers, and more interested in what computers could do.

It is easier to write a new code than to understand an old one. —John von Neumann to Marston Morse, 1952