The Information - James Gleick [98]
With that subject off the table, Turing showed Shannon a paper he had written seven years earlier, called “On Computable Numbers,” about the powers and limitations of an idealized computing machine. They talked about another topic that turned out to be close to their hearts, the possibility of machines learning to think. Shannon proposed feeding “cultural things,” such as music, to an electronic brain, and they outdid each other in brashness, Turing exclaiming once, “No, I’m not interested in developing a powerful brain. All I’m after is just a mundane brain, something like the president of the American Telephone & Telegraph Company.”♦ It bordered on impudence to talk about thinking machines in 1943, when both the transistor and the electronic computer had yet to be born. The vision Shannon and Turing shared had nothing to do with electronics; it was about logic.
Can machines think? was a question with a relatively brief and slightly odd tradition—odd because machines were so adamantly physical in themselves. Charles Babbage and Ada Lovelace lay near the beginning of this tradition, though they were all but forgotten, and now the trail led to Alan Turing, who did something really outlandish: thought up a machine with ideal powers in the mental realm and showed what it could not do. His machine never existed (except that now it exists everywhere). It was only a thought experiment.
Running alongside the issue of what a machine could do was a parallel issue: what tasks were mechanical (an old word with new significance). Now that machines could play music, capture images, aim antiaircraft guns, connect telephone calls, control assembly lines, and perform mathematical calculations, the word did not seem quite so pejorative. But only the fearful and superstitious imagined that machines could be creative or original or spontaneous; those qualities were opposite to mechanical, which meant automatic, determined, and routine. This concept now came in handy for philosophers. An example of an intellectual object that could be called mechanical was the algorithm: another new term for something that had always existed (a recipe, a set of instructions, a step-by-step procedure) but now demanded formal recognition. Babbage and Lovelace trafficked in algorithms without naming them. The twentieth century gave algorithms a central role—beginning here.
Turing was a fellow and a recent graduate at King’s College, Cambridge, when he presented his computable-numbers paper to his professor in 1936. The full title finished with a flourish in fancy German: it was “On Computable Numbers, with an Application to the Entscheidungsproblem.” The “decision problem” was a challenge that had been posed by David Hilbert at the 1928 International Congress of Mathematicians. As perhaps the most influential mathematician of his time, Hilbert, like Russell and Whitehead, believed fervently in the mission of rooting all mathematics in a solid logical foundation—“In der Mathematik gibt es kein Ignorabimus,” he declared. (“In mathematics there is no we will not know.”) Of course mathematics had many unsolved problems, some quite famous, such as Fermat’s Last Theorem and the Goldbach conjecture—statements that seemed true but had not been proved. Had not yet been proved, most people thought. There was an assumption, even a faith, that any mathematical truth would be provable, someday.
The Entscheidungsproblem was to find a rigorous step-by-step procedure by which, given a formal language of deductive reasoning, one could perform a proof automatically. This was Leibniz’s dream revived once again: the expression of all valid reasoning in