If all Alan Turing had done was answer, in the negative, a vexing question in the arcane realm of mathematical logic, few nonspecialists today would have any reason to remember him. But the method Turing used to show that certain propositions in a closed logical system cannot be proved within that system--a corollary to the proof that made Kurt Godel famous--had enormous consequences in the world at large. For what this eccentric young Cambridge don did was to dream up an imaginary machine--a fairly simple typewriter-like contraption capable somehow of scanning, or reading, instructions encoded on a tape of theoretically infinite...

