Turing, More, Analogies

Michael L. Johnson
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Michael L. Johnson: University of Kansas

Chapter 14 in Mind, Language, Machine, 1988, pp 73-79 from Palgrave Macmillan

Abstract: Abstract Alan M. Turing several decades ago proved that ‘all computers (save a few special-purpose types…) are equivalent to one another, i. e., are all universal’.1 That is, all computers, regardless of the stuff of which they are made (they exist, in a functional sense, apart from it), are also abstract machines of a certain kind: they are universal Turing machines. Or, to put it another way, a computer language is, in effect, a set of instructions for building such a machine. (The Turing machine is a theoretical device formulated by Turing in the 1930s as a way of discussing algorithms or procedures for solving problems, a preoccupation that grew from logicians’ interest in a methodology whereby ‘the proofs of mathematical theorems could be generated automatically by a mechanical process’. The device consists of three parts: an infinitely long paper tape that is divided into an infinite number of squares, a mechanism that moves the tape and prints or erases marks [symbols from a finite alphabet] on individual squares, and a scanning head that senses whether or not a given square contains a mark. It ‘can be programmed to find the solution to a problem by executing a finite number of scanning and printing actions’, and ‘in spite of its simplicity it is not exceeded in problem-solving ability by any other known computing device.’)2

Keywords: Turing Machine; External Memory; Abstract Machine; Paper Tape; Finite Alphabet (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-1-349-19404-9_14

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