This year marks the centenary of British mathematician Alan Turing, whose researches in the unlikely and very abstruse field of mathematical logic did much to create the world in which we now live. In 1936, Turing published a paper titled “On Computable Numbers” in the Proceedings of the London Mathematical Society. The paper received almost no attention. “Only two requests for reprints came in,” George Dyson tells us. The reason for this is interesting — is, in fact, one of the main themes in Dyson’s book.
It is an odd thing that, in 1936, digital technologies were old hat. The coming age looked to be entirely analog. (Digital phenomena are staccato, stepping from one value direct to another; analog is legato, gliding smoothly through all intermediate points.) If you had asked a well-informed person of that date to point to some digital technologies, he would have cited the Western Union man with his green eyeshade and sleeve garters, tapping out Morse code on the telegraph key, or perhaps the Asian shopkeeper working his abacus. The spiffiest new devices were all analog: radio, movies, vinyl discs, and soon TV and radar.
So were the latest grand scientific theories. The spacetime of general relativity flexed analogically to accommodate mass and charge. Quantum mechanics contained some irritatingly digital elements — you can’t have half a quantum — but the underlying equations were written in the comfortingly analogic language of traditional calculus. Only biology had been through a modest digital revolution. The notion of “blending inheritance” (the trait of the offspring falls halfway between the corresponding trait in the parents) had caused much vexation to 19th-century biologists, including Darwin, as it led logically to a population of clones; but no one could come up with an alternative. The 1900 rediscovery of Mendel’s more digital theory resolved the issue.
Genetics aside, the late 1930s was thus a time of analog triumphalism. Across the following decades, everything changed. We now live in a thoroughly digital world. Digital gadgets twitter and beep all around us. At the deepest level, there are serious speculations that spacetime itself may be digital: Scientific American magazine recently did a cover story on the topic. Analog principles and gadgets survive only in a few pockets of the deepest reaction. My own house, for example, contains an analog TV set and a slide rule.
George Dyson tells the story of this great conceptual and technological transformation in Turing’s Cathedral, concentrating on the key years from 1936 to 1958. It was in the latter year that the computer at the Institute for Advanced Study in Princeton was decommissioned after seven years of operation. The IAS computer, which had no formal name (MANIAC, with which it is confused, was a clone machine at Los Alamos), was the brainchild of John von Neumann, one of the most tremendous geniuses who ever lived. He had been one of the first to notice Turing’s 1936 paper — the two shared office space in Princeton. Turing studied for his Ph.D. at the university, from 1936 to 1938; von Neumann had come to the university in 1930, then been given a professorship at the new IAS in 1933.
They shared much else. Though both were brilliant pure mathematicians, neither disdained physical gadgetry. When researching a book on a famous conjecture in pure mathematics, I was surprised to learn that Turing had conceived the idea of a mechanical computing device to disprove the conjecture, and had even cut some of the gear wheels himself in his college’s engineering workshop.
There lay the reason for the lack of interest in Turing’s 1936 paper. In it he had conceived the idea of a universal computing machine: an imaginary device that could duplicate the behavior of any other you might think up. The paper was founded in the purest of pure mathematics, drawing from work by the previous generation of mathematical logicians, who themselves had built on work by David Hilbert, Whitehead and Russell, and earlier enquirers all the way back to Leibniz. The centerpiece of it, though, was that machine. Dyson: “Engineers avoided Turing’s paper because it appeared entirely theoretical,” while “theoreticians avoided it because of the references to paper tape and machines.”
John von Neumann’s career at the Institute for Advanced Study hit the same fault line. The IAS had been conceived as a place where the greatest minds might think their lofty thoughts without the distraction of students, publication schedules, or academic politics — the purest of pure-research institutes. Though not a tinkerer like Turing (“He would have made a lousy engineer,” testified his colleague Herman Goldstine), von Neumann was free of intellectual snobbery. He was in fact a worldly man, a bon vivant even — he never drove anything but Cadillacs — and thus quite opposite to the popular image of a math professor. He believed, he told J. Robert Oppenheimer, that mathematics grew best when nourished by “a certain contact with the strivings and problems of the world.”