Word: tapes
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Happily, in those days before tape recorders, some of Wittgenstein's disciples took verbatim notes, so we can catch a rare glimpse of two great minds addressing a central problem from opposite points of view: the problem of contradiction in a formal system. For Turing, the problem is a practical one: if you design a bridge using a system that contains a contradiction, "the bridge may fall down." For Wittgenstein, the problem was about the social context in which human beings can be said to "follow the rules" of a mathematical system. What Turing saw, and Wittgenstein...
...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 length. As the scanner moved from one square of the tape to the next--responding to the sequential commands and modifying its mechanical response if so ordered--the output of such a process, Turing demonstrated, could replicate logical human thought...
...device in this inspired mind-experiment quickly acquired a name: the Turing machine. And so did another of Turing's insights. Since the instructions on the tape governed the behavior of the machine, by changing those instructions, one could induce the machine to perform the functions of all such machines. In other words, depending on the tape it scanned, the same machine could calculate numbers or play chess or do anything else of a comparable nature. Hence his device acquired a new and even grander name: the Universal Turing Machine...
...British National Physical Laboratory offered him the opportunity to create an actual Turing machine, the ACE or Automatic Computing Engine, and Turing accepted. What he discovered, unfortunately, was that the emergency spirit that had short-circuited so many problems at Bletchley Park during the war had dissipated. Bureaucracy, red tape and interminable delays once again were the order of the day. Finding most of his suggestions dismissed, ignored or overruled, Turing eventually left the NPL for another stay at Cambridge and then accepted an offer from the University of Manchester where another computer was being constructed along the lines...
...while working on the Ferranti Mark I, the first computer sold commercially. They taught him to think unconventionally; he'd play games over the breakfast table with imaginary numbers (what's the square root of minus 4?). He made pretend computers out of cardboard boxes and five-hole paper tape and fell in love with electronics. Later, at Oxford, he built his own working electronic computer out of spare parts and a TV set. He also studied physics, which he thought would be a lovely compromise between math and electronics. "Physics was fun," he recalls. "And in fact a good...