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ALAN MATHISON TURING (1912-1954)
'On Computable Numbers, with an Application to the Entscheidungsproblem', in: Proceedings of the London Mathematical Society, series 2, vol. 42, pt. 3, pp. 230-40 and pt. 4, pp. 241-65. London: C.F. Hodgson & Son, Ltd. for The London Mathematical Society, 30 November 1936-23 December 1936. 2 issues, 4° (260 x 174mm). Original grey printed wrappers (spines and outer edges browned, chipped causing small losses on spines and one lower wrapper); later cloth box.
FIRST EDITION. A FOUNDATION OF THE THEORY OF COMPUTING. Whilst at King's College, Cambridge, Turing learned from the Cambridge topologist Max H. A. Newman, that David Hilbert's Entscheidungsproblem remained an open question, and drafted this paper in April 1936, learning at nearly the same time of Alonzo Church's totally different solution of the problem in 'An Unsolvable Problem of Elementary Number Theory'. The need to add an appendix to his paper, showing that both writers had reached the same conclusion through different routes, delayed the submission of Turing's paper for publication until August. 'On Computable Numbers' introduced the concept of a 'universal machine', an imaginary computing device designed to replicate the mathematical 'states of mind' and symbol-manipulating abilities of a human computer. Turing conceived of the universal machine as a means of answering the last of Hilbert's three questions about mathematics: 'is mathematics decidable'. This question -- the Entscheidungsproblem -- concerns whether there exists a definite method that can be applied to any mathematical assertion, which is guaranteed to produce a correct decision as to whether that assertion is true. The Czech logician Kurt Gödel had already shown that arithmetic (and by extension mathematics) was both inconsistent and incomplete (thus answering Hilbert's first two questions), and Turing showed, by means of his universal machine, that mathematics was also undecidable. To demonstrate this, Turing came up with the concept of 'computable numbers', which are numbers defined by some definite rule, and thus calculable on a universal machine (named 'Turing machine' by Church), and then showed that these computable numbers could give rise to uncomputable ones (which could not be calculated using a definite rule), and that therefore there could be no 'mechanical process' for solving all mathematical questions, since an uncomputable number was an example of an unsolvable problem. A few months later Emil Post, working independently of Turing, published his 'Finite combinatory processes -- formulation 1', which described an automaton almost exactly like a Turing machine. In showing that a universal machine was possible, Turing's paper was highly influential in the theory of computation, and it remained a powerful expression of the virtually unlimited adaptability of electronic digital computers. Origins of Cyberspace 394. (2)
'On Computable Numbers, with an Application to the Entscheidungsproblem', in: Proceedings of the London Mathematical Society, series 2, vol. 42, pt. 3, pp. 230-40 and pt. 4, pp. 241-65. London: C.F. Hodgson & Son, Ltd. for The London Mathematical Society, 30 November 1936-23 December 1936. 2 issues, 4° (260 x 174mm). Original grey printed wrappers (spines and outer edges browned, chipped causing small losses on spines and one lower wrapper); later cloth box.
FIRST EDITION. A FOUNDATION OF THE THEORY OF COMPUTING. Whilst at King's College, Cambridge, Turing learned from the Cambridge topologist Max H. A. Newman, that David Hilbert's Entscheidungsproblem remained an open question, and drafted this paper in April 1936, learning at nearly the same time of Alonzo Church's totally different solution of the problem in 'An Unsolvable Problem of Elementary Number Theory'. The need to add an appendix to his paper, showing that both writers had reached the same conclusion through different routes, delayed the submission of Turing's paper for publication until August. 'On Computable Numbers' introduced the concept of a 'universal machine', an imaginary computing device designed to replicate the mathematical 'states of mind' and symbol-manipulating abilities of a human computer. Turing conceived of the universal machine as a means of answering the last of Hilbert's three questions about mathematics: 'is mathematics decidable'. This question -- the Entscheidungsproblem -- concerns whether there exists a definite method that can be applied to any mathematical assertion, which is guaranteed to produce a correct decision as to whether that assertion is true. The Czech logician Kurt Gödel had already shown that arithmetic (and by extension mathematics) was both inconsistent and incomplete (thus answering Hilbert's first two questions), and Turing showed, by means of his universal machine, that mathematics was also undecidable. To demonstrate this, Turing came up with the concept of 'computable numbers', which are numbers defined by some definite rule, and thus calculable on a universal machine (named 'Turing machine' by Church), and then showed that these computable numbers could give rise to uncomputable ones (which could not be calculated using a definite rule), and that therefore there could be no 'mechanical process' for solving all mathematical questions, since an uncomputable number was an example of an unsolvable problem. A few months later Emil Post, working independently of Turing, published his 'Finite combinatory processes -- formulation 1', which described an automaton almost exactly like a Turing machine. In showing that a universal machine was possible, Turing's paper was highly influential in the theory of computation, and it remained a powerful expression of the virtually unlimited adaptability of electronic digital computers. Origins of Cyberspace 394. (2)
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