Turing, Alan Mathison

Alan Mathison Turing (1912-1954), British mathematician and logician, was born in London and was educated at Sherborne School and King's College Cambridge. The originality and precocity of his mathematical thinking soon became apparent -- not always to his advantage. A preference for supplementing theory with experiments (particularly of the kind that he could carry out himself) and an obsession with working everything out from first principles also developed during his school days. These traits distinguished him all his life. Thus he was elected a fellow of King's College Cambridge for a dissertation on the central limit theorem in probability theory. He had rediscovered this from scratch, being in ignorance of the previous work. His disinclination to build on the work of others sometimes slowed him down, but it preserved his forceful originality.

The contribution to LOGIC for which he is best known is his 1936-1937 paper. He set out to demonstrate rigorously what many already believed -- that Hilbert's program, requiring a decision procedure to evaluate the truth or falsehood of any mathematical statement, was a logical impossibility.

Turing's search for a precise definition of "decision procedure" led him to devise and analyze the abstract notion of a computing machine. The invitation to Princeton that followed was prompted by his teacher M. H. A. Newman in a letter to Alonzo Church. With Stephen Kleene, Church had arrived at the same result as Turing by different means (see CHURCH-TURING THESIS). In fact the mathematical functions described in Gödel and Herbrand's system as general-recursive, in Church and Kleene's as lambda-definable, and in Turing's as computable all constitute identically the same class.

Soon after Turing returned to Cambridge from his two years in Princeton, World War II broke out. He wrote two further papers in mathematical logic but was mainly occupied with his work for the Foreign Office in the British cryptographic establishment at Bletchley Park. His major contribution to the breaking of the Enigma code made it possible routinely to read this German traffic, used widely in submarine warfare. He also made one of the important contributions in the breaking of Fish, the highest-level German cipher, and indirectly to the development for this work of the Colossus high-speed electronic computers (Good 1993).

At the end of the war Turing joined the National Physical Laboratory. In early 1946 he submitted initial design ideas for the NPL's groundbreaking "Automatic Computing Engine" ACE. He spent 1947 on leave of absence at King's College, during which he wrote on semigroups (published in 1950) and on "intelligent machinery" (published posthumously). Earlier in that same year Turing delivered a lecture to the London Mathematical Society. Taking the Pilot ACE as his point of departure, he formulated the main principles and future modes of application of practical embodiments of his Universal Turing Machine. These included their use to simulate human cognition. On the latter, his proposals were:

Programming can be done in symbolic logic and will then require the construction of appropriate interpreter/translator programs.
MACHINE LEARNING is needed so that computers can discover new knowledge inductively from experience as well as deductively.
Humanized interfaces are required to enable machines to adapt to people, so as to acquire knowledge tutorially.

These three points have been substantiated during the intervening fifty years. Their integration finds its most explicit expression in modern INDUCTIVE LOGIC PROGRAMMING, particularly in its applications to computer-assisted discovery of new CONCEPTS in the applied sciences.

Turing reinforced his second point in the final and rarely cited section of his Mind paper (1950) with calculations demonstrating the infeasibility of alternative means of equipping machines with the requisite knowledge. At least two attempts in the 1980s at general intelligent systems paid a price for neglecting his arguments, notably the CYC project of the MCC Corporation and the Fifth Generation project of the MITI department of the Japanese government (see Michie 1994). Both projects used explicit programming as their only KNOWLEDGE ACQUISITION tool.

Turing's celebrated 1950 paper in Mind described what became known as the "Turing test." Through a postulated imitation game, the intelligence of a machine is tested via its ability to sustain humanlike discourse. Several simple computer programs have since been able to deceive human observers into believing that a person and not a machine is "conversing" with them. This has accordingly led some to dismiss the Turing test as invalid. Closer reading of the paper shows that Turing was concerned with a machine's ability to answer questions, not to deflect them with counterquestions, as is done by the above-mentioned programs.

In the postwar period Turing also engaged in experimentation with CHESS mechanization. In the early 1950s he turned his attention to the mathematical description of the biological phenomena of morphogenesis. He was still working in this area in 1954, when he died just eleven days short of his forty-second birthday.

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-- Donald Michie

References

Carpenter, B. E., and R. W. Doran, Eds. (1986). A. M. Turing's ACE Report of 1946 and Other Papers. Vol. 10, the Charles Babbage Institute reprint series for the History of Computing, University of Minnesota. Cambridge, MA: MIT Press.

Good, I. J. (1993). Enigma and Fish. In F. H. Hinsley and A. Stripp, Eds., Codebreakers: The Inside Story of Bletchley Park. Oxford: Oxford University Press.

Michie, D. (1994). Consciousness as an engineering issue. Part 1. J. Consc. Studies 1(2):182-195.

Turing, A. M. (1936-7). On computable numbers with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 2(42): 230 - 265.

Turing, A. M. (1946). Proposal for Development in the Mathematical Division of an Automatic Computing Engine (ACE), Report to the Executive Committee of the National Physical Laboratory. Reprinted in B. E. Carpenter and R. W. Doran, A. M. Turing's ACE Report of 1946 and Other Papers (1986). Vol. 10, the Charles Babbage Institute reprint series for the History of Computing, University of Minnesota. Cambridge, MA: MIT Press.

Turing, A. M. (1947). Lecture to the London Mathematical Society. Reprinted in B. E. Carpenter and R. W. Doran, A. M. Turing's ACE Report of 1946 and Other Papers (1986). Vol. 10, the Charles Babbage Institute reprint series for the History of Computing, University of Minnesota. Cambridge, MA: MIT Press.

Turing, A. M. (1948). Intelligent Machinery, Report to the Executive Committee of the National Physical Laboratory. Reprinted in B. Meltzer and D. Michie, Eds., Machine Intelligence 5. Edinburgh: Edinburgh University Press, pp. 3-23.

Turing, A. M. (1950a). Computing machinery and intelligence. Mind 59:433-460.

Turing, A. M. (1950b). The word problem in semi-groups with cancellation. Ann. Math 52:491-505.

Turing, Alan Mathison

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