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The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine by Charles Petzold

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10  Computers and Computability

By imagining a computing machine that does almost nothing, Turing was actually conceiving a very versatile “general purpose” computer. This was a revolutionary concept. The common assumption at the time was that computers would be designed specifically for particular types of jobs. The early analog computer known as the Differential Analyzer (designed and built by M.I.T. professor Vannevar Bush and his students in the 1920s) exemplified this approach. The Differential Analyzer did something very important — solve ordinary differential equations — but that was all it did.

Even people deeply involved in building digital computers often didn't grasp the generality of digital logic. Howard Aiken, for example, was one of the computer's true pioneers and had been working with digital computers since 1937. Yet, in 1956 Aiken said:

[I]f it should turn out that the basic logics of a machine designed for the numerical solution of differential equations coincide with the logics of a machine intended to make bills for a department store, I would regard this as the most amazing coincidence I have ever encountered.1

Turing, who visualized the computer as a logic machine, knew better. While most early computer builders thought in terms of hardware, Turing had been writing software since 1936. To Turing, even basic arithmetical operations like addition could be achieved in software. Compare Aiken's 1956 statement with what Turing wrote in 1950:

This special property ...

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