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"Computers themselves are an unanticipated consequence of the search for a systematization of abstraction. Mathematician Alan Turing famously used the thought experiment that has become known as the Turing machine as part of a proof that mathematics could never be completely described by any logical system.50 When John von Neumann and others connected Turing's imaginary machine with George Boole's algebra of logic and hitched them up to mechanical calculators, machines that could perform aspects of thought became possible.51 When the physical tokens used for manipulating abstractions were first used to represent logical functions, and the logical functions were instantiated as an electrical circuit, the abstraction of abstraction became increasingly a human-machine process. The use of computers to solve human problems through the mediation of symbolic languages became a "fifth language," according to Logan, together with speech, the alphabet, mathematics, science, and printing. The use of Internet-based media, in Logan's view, is the sixth language.52"

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