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Turing, Alan Mathison

TURING, ALAN MATHISON

(b. London, England, 23 June 1912;

d. Wilmslow, England, 7 June 1954), mathematics, mathematical logic, computer technology. For the original article on Turing see DSB, vol. 13.

It is perhaps not surprising that so many discussions of Turing’s work have been confined to the esoteric realms of mathematics, logic, and philosophy given that his name is most often associated with a class of abstract machines within computability theory or in connection to a deliberately provocative test he proposed to determine whether a machine could think. However, as the significance of the computer looms ever larger, so too has general interest grown in Turing’s work. In the time since van Rootselaar’s original DSB entry, Turing scholarship has advanced to uncover the full extent of Turing’s influence across a wide range of disciplines, including, mathematics, logic, cryptology, computer engineering (both hardware and software), artificial intelligence, cognitive science, philosophy, and biology. In addition, several biographies have since been published that bring to light many of the idiosyncratic qualities that defined Turing’s life and research. While none of this scholarship alters the basic biographic contours presented by van Rootselaar, it does provide a richer context in which Turing’s contributions can be seen to extend beyond mathematical logic or bold comments about thinking machines.

Entscheidungsproblem. One area where the scholarship has deepened concerns the publication date and significance of Turing’s “On Computable Numbers, with an Application to the Entscheidungsproblem.” Whereas the original DSB entry gives a publication date of 1937 and implies that the work was undertaken while Turing was at Princeton, more recent scholarship gives a date of 1936 (or sometimes as 1936–1937) and very clearly establishes that Turing had worked out his solution to the Entscheidungsproblem independently. Although the Entscheidungsproblem was at the time the outstanding problem of mathematical logic, the significance of Turing’s independent solution lies not so much with any claim to priority (which is due to Alonzo Church), but, rather, the formal characterization Turing gave to intuitions about effective computation. Indeed, the fact that the unsolvability of the Entscheidungsproblem had a decapitating impact on David Hilbert’s quest for a purely formal mathematics almost seems incidental as scholars have instead celebrated Turing’s analysis of effective computation as the most influential among his contemporaries. Inspired by the human computer (i.e., the human engaged in computation), Turing described a notional machine that could read and write symbols along a segmented tape. The machine itself would be capable of assuming various internal states that, together with the input of a single symbol along the tape, could lead to a few primitive atomic actions. Based on the current state and the current symbol, each configuration specifies a change (or not) of symbol, a move right or left, and a next state. Working under some straightforward assumptions about the finite and discrete nature of the machine, Turing was able to demonstrate the wide range of numbers (equivalently, the wide class of functions) that could be computed and, moreover, able to specify a single machine, the universal machine, that would be capable of simulating the computations of any such machine. Turing’s characterization has come to be seen as a more compelling account of what it means to be effective, mechanical, or algorithmic than any of the various extensionally equivalent formulations offered by his contemporaries.

Practical Computing. Scholarship has also deepened with respect to the contributions Turing made to the development of working electronic computers. Again, in terms of priority Turing misses out, as credit is most often given to John von Neumann for the first specification of the electronic stored-program computer. Nevertheless, scholars have continued to uncover Turing’s contributions not just to developments in England but also to von Neumann’s thinking. Scholars also point out that Turing’s understanding of the significance of software was probably deeper than that of his contemporaries. While Turing’s observations about computing might seem pedestrian by twenty-first-century standards, they are remarkable considering that Turing was anticipating practice which had yet to be fully realized in his time. In a similar spirit, some scholars have attributed to Turing the anticipation of so-called hypercomputers, machines capable of outstripping the bounds of computing as they are traditionally conceived. Although such attributions depend on a controversial reading of Turing’s work, they have precipitated a lively debate

that touches on issues of mechanism, the limits of computation, and the proper interpretation of the Church-Turing thesis (roughly, the claim that the intuitive notion of effective computation can be identified with the class of functions computed by a Turing machine).

Turing scholarship has also broadened in several respects. First, some of Turing’s less known works and other unpublished sources are receiving attention as possible antecedents to contemporary discussions of theoretical biology, “artificial life,” machine learning, and connectionism. Second, as computers have become more powerful and the possibility of artificial intelligence becomes less remote in the popular imagination, Turing’s once seemingly bold comments about machine intelligence have found a new audience. Of course, not all of the popular interest in machine intelligence and the mind’s workings mentions, much less centers on, Turing, but enough of it does to breathe new life into the secondary literature. Finally, it is worth noting the great extent to which cognitive science in general has been shaped either directly by computational views of mind or in reaction to them. As the computational view of mind has come under increasing scrutiny, so too have more foundational questions about the nature of computing itself and the role it plays in our understanding of mind. Although these questions do not illuminate the historical Turing, they often invite the reexamination of the Turing machine and its role and significance in cognitive science.

Biographies of Turing emphasize his solitary tendencies and his unwillingness to conform to convention. It is often suggested that these are exactly the qualities that allowed Turing to bring such fresh perspective to difficult problems. It is also often suggested that these same qualities might have compounded the difficulties that ensued after Turing’s arrest and “treatment” for homosexual behavior, then illegal in England. Considered a security risk, and subject to surveillance, Turing eventually committed suicide.

SUPPLEMENTARY BIBLIOGRAPHY

Several Web sites maintain Turing bibliographies along with online access to many primary and secondary sources. A good place to start is the Alan Turing Home Page (http://www.turing.org.uk/), maintained by the Turing biographer Andrew Hodges. Slightly less user friendly but containing digital facsimiles of many of Turing’s unpublished works is the Turing Digital Archive (http://www.turingarchive.org/). Digital facsimiles of Turing’s work are also available from the Turing Archive for the History of Computing (http://www.alanturing.net/).

WORKS BY TURING

The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions. Edited by Martin Davis. New York: Raven Press, 1965. Reprint, Mineola, NY: Dover, 2004. A collection of classic works of computability theory by Turing and his contemporaries.

Collected Works of A. M. Turing. Vol. 1, Mechanical Intelligence, edited by D. C. Ince. Vol. 2, Pure Mathematics, edited by J. L. Britton. Vol. 3, Morphogenesis, edited by P. T. Saunders. Vol. 4, Mathematical Logic, edited by R. O. Gandy and C. E. M. Yates. Amsterdam; New York: Elsevier Science, 1992, 2001.

The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life, plus the Secrets of Enigma. Edited by B. Jack Copeland. New York: Oxford University Press, 2004. A single volume that contains Turing’s most influential work.

OTHER SOURCES

Herken, Rolf, ed. The Universal Turing Machine: A Half-Century Survey. Oxford: Oxford University Press, 1988. An excellent collection of commentaries on Turing’s influence from the perspectives of leading mathematicians and logicians.

Hodges, Andrew. Alan Turing: The Enigma. New York: Simon & Schuster, 1983. Reprint, New York: Walker 2000. The authoritative biography of Turing.

———. Turing: A Natural Philosopher. London: Phoenix, 1997.A very concise, very accessible biography.

Leavitt, David. The Man Who Knew Too Much: Alan Turing and the Invention of the Computer. New York: Atlas Books, 2006. A good read, but occasionally misleading in its technical detail and presents some strained speculation about motives.

Scheutz, Matthias, ed. Computationalism: New Directions. Cambridge, MA: MIT Press, 2002. A book more about Turing’s ideas than about Turing himself. A useful starting point into the vast secondary literature concerning computation, the philosophy of mind, and cognitive science.

Teuscher, Christof, ed. Alan Turing: Life and Legacy of a Great Thinker. Berlin: Springer, 2004. A wide-ranging collection of commentary on Turing.

Walter Warwick

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Turing, Alan Mathison

TURING, ALAN MATHISON

(b. London, England, 23 June 1912; d. Wilmslow, England, 7 June 1954)

mathematics, mathematical logic, computer technology.

Turing was the son of Julius Mathias Turing and Ethel Sara Stoney. After attending Sherborne School he entered King’s College, Cambridge, in 1931. He was elected a fellow of the college in 1935 for his dissertation “On the Gaussian Error Function,” which won a Smith’s prize in the following year. From 1936 until 1938 Turing worked at Princeton University with Alonzo Church.

While at Princeton Turing published one of his most important contributions to mathematical logic, his 1937 paper “On Computable Numbers, With an Application to the Entscheidungsproblem,” which immediately attracted general attention. In it he analyzed the processes that can be carried out in computing a number to arrive at a concept of a theoretical “universal” computing machine (the “Turing machine”), capable of operating upon any “computable” sequence–that is, any sequence of zeros and ones. The paper included Turing’s proof that Hilbert’s Entscheidungsproblem is not solvable by these means. Church had, somewhat earlier, solved Hilbert’s problem by employing a λ -definable function as a precise form of the intuitive notion of effectively calculable function, while in 1936, S. C. Kleene had proved the equivalence of λ -definability and the Herbrand-Gödel theory of general recursiveness. In his “Computability and λ-Definability” of 1937, Turing demonstrated that his and Church’s of 1937, Turing demonstrated that his and Church’s ides were equivalent.

In 1939 Turing published “Systems of Logic Based on Ordinals,” in which he examined the question of constructing to any ordinal number α a logic Lα, such that any problem could be solved within some Lα. This paper had a far-reaching influence; in 1942 E. L. Post drew upon it for one of his theories for classifying unsolvable problems, while in 1958 G. Kreisel suggested the use of ordinal logics in characterizing informal methods of proof. In the latter year S. Feferman also adapted Turing’s ideas to use ordinal logics in predicative mathematics.

In 1939 Turing returned to King’s College, where his fellowship was renewed. His research was interrupted by World War II, however, and from the latter part of 1939 until 1948 he was employed in the communications department of the Foreign Office; he was awarded the O.B.E. for his work there. After the war, he declined the offer of a lectureship at Cambridge and, in autumn of 1945, joined the staff of the National Physical Laboratory to work on the design of an automatic computing engine (ACE).

In 1948 Turing became a reader in the University of Manchester and assistant director of the Manchester automatic digital machine (MADAM). He also continued to work in mathematical theory, and improved E. L. Post’s demonstration of the existence of a semigroup with unsolvable word problem by exhibiting a semigroup with cancellation for which the word problem is (recursively) unsolvable. He made further contributions to group theory and performed calculations on the Riemann zeta-function in which he incorporated his practical work on computing machines.

In 1950 Turing took up the question of the ability of a machine to think, a subject that had gained general interest with the increasing application of mechanical computing devices to more and more complex tasks. His “Computing Machinery and Intelligence“was addressed to a broad audience and marked by a lively style. The Programmer’s Handbook for the Manchester Electronic Computer, Produced under his direction, was published in the same year.

Throughout his life Turing was also interested in applying mathematical and mechanical theory to the biological problem of life forms. He made a promising approach to this question in his 1952 publication “The Chemical Basis of Morphogenesis.” In this work he exploited the mathematical demonstration that small variations in the initial conditions of first-order systems of differential equations may result in appreciable deviations in the asymptotic behavior of their solutions to posit that unknown functions might function biologically as form-producers; he was thus able to account for asymmetry in both mathematical and biological form. He was at work on a general theory when he died of perhaps accidental poisoning.

BIBLIOGRAPHY

I. Original Works. An edition of Turing’s collected works is in preparation by Professor Dr. R. O. Gandy. See especially Turing’s “On Computable Numbers, With an Application to the Entscheidungsproblem,“in Proceedings of the London Mathematical Society, 42 (1937), 230–265; “On Computable Numbers, With an Application to the Entscheidungsproblem. A Correction,“ibid43 (1937), 544–547; “Computability and λ-Definability,“in Journal of Symbolic Logic, 2 (1937), 153–163; “Systems of Logic Based on Ordinals,“in Proceedings of the London Mathematical Society, 45 (1939), 161–228; “The Word Problem in Semigroups With Cancellation,“in Annals of Mathematics, 52 (1950), 491-505; “Computing Machinery and Intelligence,“in Mind, 59 (1950), 433–460, repr. as “Can a Machine Think?“in J. R. Newman, The World of Mathematics, IV (New York, 1956), 2099–2133; and “The Chemical Basis of Morphogenesis,“in Philosophical Transactions of the Royal Society237 (1952), 37–72.

II. Secondary Literature. S. Turing, Alan M. Turing (Cambridge 1959), includes a bibliography of works by and about Turing. See also M. Davis, Computability and Unsolvability (New York, 1958); S. Feferman, “Ordinal Logics Re-examined,” in Journal of Symbolic Logic, 23 (1958), 105; “On the Strength of Oridinal Logics,” ibid., 105–106: “Transfinite Recursive Progressions of Axiomatic Theories,“ibid., 27 (1962), 259-316; and “Autonomous Transfinite Transfinite Progressions and the Extent of Predicative Mathematics,” in B. van Rootselaar and J. F. Staal, eds., Logic, Methodology and Philosophy of Science, III (Amsterdam, 1968), 121–135; S. C. Kleene, Introduction to Metamathematics (Amsterdam–Groningen, 1952); and Mathematical Logic (New York, 1967); G. Kreisel, “Ordinal Logics and the Characterization of Informal Concepts of Proof,” in Proceedigns of the International Congress of Mathematicians, 1958 (Cambridge, 1960), 289–299; and M. H. A. Newman, “Alan Mathison Turing,” in Biographical Memoris of Fellows of the Royal Society 1955, I (London, 1955), 253–263, which also has a bibliography.

B. van Rootselaar

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Alan Mathison Turing

Alan Mathison Turing

The British mathematician Alan Mathison Turing (1912-1954) was noted for his contributions to mathematical logic and to the early theory, construction, and use of computers.

Alan Turing was born in London, England, on June 23, 1912. Both his parents had upper middle class origins, and his father continued that tradition as an administrator in the Indian civil service. With his father off in India, Turing was sent away to private boarding schools. After some early problems with social adjustment, he distinguished himself in mathematics and science.

Turing's exceptional mathematical abilities were first generally recognized in his college years (1931-1936) at King's College of Cambridge University. His most important mathematical work, "On Computable Numbers, " was written in Cambridge in 1936. In this paper Turing answered a question of great significance to mathematical logic— namely, which functions in mathematics can be computed by an entirely mechanical procedure. His answer was phrased in terms of a theoretical machine (today known as the "Turing machine") which could mechanically carry out these computations. Embodied in the Turing machine idea is the concept of the stored program computer.

In 1936 Turing was awarded a Proctor fellowship to visit Princeton University for a year. There he came in contact with Alonzo Church, a professor of mathematics working on problems in logic related to those addressed by Turing in his 1936 paper. He decided to remain at Princeton an additional two years to write a doctoral dissertation under Church's direction on ordinal logics.

Soon after Turing's return to England Britain was drawn into World War II. He joined the Government Code and Cypher School in Bletchley Park, located between Oxford and London, where a massive effort was underway to break German codes which had been encyphered by machine. Turing played an important role (still partly classified) in the design of equipment and development of techniques to break these codes.

Work at Bletchley provided Turing with valuable experience in electronics and with special-purpose calculating equipment which served him well after the war. In 1945 he moved to the National Physical Laboratory (NPL) in Teddington, England, to assume responsibilities for designing an electronic computer to be used in government work. Turing drew up plans for the ACE computer, an ambitious stored program computer utilizing vacuum tubes for switching and mercury delay lines for storage. A scaled down version completed in 1950, known as Pilot ACE, was one of the earliest operating stored program computers. Pilot ACE served many important functions, including aircraft design, for many years.

Meanwhile, dissatisfied with progress on his project at NPL, Turing accepted a position at Manchester University where a large computer, the Mark I, was being built. His position as chief programmer of the Mark I allowed him the opportunity to program the computer to do mathematics, play chess and other games, investigate automatic language translation, and do cryptanalysis. This was probably the first major attempt to use a stored program computer for non-computational activities.

Turing's work on computers influenced the design of early computers built by the English Electric and Bendix companies. However, of more enduring significance were his theoretical contributions to automata theory and artificial intelligence. The 1936 paper and the concept of the Turing machine is the starting point of the modern theory of automata, and Turing anticipated many of the fundamental questions. During and after the war Turing began to investigate and champion the field of artificial intelligence. To his credit are the Turing Test (a test for determining whether a machine can be claimed to be thinking), a series of papers arguing against the most common objections to the possibil-ity of intelligent machinery, and the recognition that scientists should approach the problem of artificial intelligence through the programming of stored program computers rather than through the construction of robots that mimic human actions. Turing also made a number of other contributions to mathematical logic, algebra, statistics, and morphogenesis (the study of biological forms).

Turing died in his home in Manchester, England, of cyanide poisoning. His death, ruled to be suicide by the coroner, may have been the result of a depression caused by chemotherapy. The courts had mandated this treatment as a result of his conviction for public practice of homosexuality, then a criminal offense in Britain.

Further Reading

Two biographies of Turing have been written: a short study by his mother, Sara Turing, Alan M. Turing (1959), and a longer study by Andrew Hodges, Alan Turing: The Enigma (1983). Hodges cites references to Turing's published paper and other secondary literature about him.

Additional Sources

Hodges, Andrew, Alan Turing: the enigma, New York: Simon and Schuster, 1983. □

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Turing, Alan

Turing, Alan


British Mathematician and Cryptanalyst 19121954

In the October 1950 issue of Mind, the brilliant thinker Alan Turing wrote, "We may hope that machines will eventually compete with men in all purely intellectual fields." Turing believed that machines could mimic the processes of the human brain but acknowledged that people would have difficulty accepting such a machinea problem that still plagues artificial intelligence today.

Turing also proposed a test to measure whether a machine could be considered "intelligent." The widely acclaimed "Turing test" involved a connecting a human by teletype (later a computer keyboard) to either another human or a machine. The first human would then ask questions that are translated through these mechanical links. If the respondent on the other end was indeed a machine, but the human asking questions could not tell whether the responses came from a human or machine, then the machine should be regarded as intelligent.

While attending graduate school in mathematics, Turing wrote On Computable Numbers (1936), in which he described hypothetical devices (later dubbed "Turing machines") that presaged today's computers. A Turing machine could perform logical operations and systematically read, write, or erase symbols written on paper tape.

Upon completing his doctorate at Princeton University in 1938, Turing was invited to the Institute of Advanced Studies (also at Princeton) to become assistant to John von Neumann, the brilliant mathematician, synthesizer, and promoter of the stored program concept. Turing declined and instead returned to Cambridge, England. Turing began to work for the wartime cryptanalytic headquarters at Bletchley Park, halfway between Oxford and Cambridge, after the British declared war with Germany on September 3, 1939.

At Bletchley Park, Turing and his colleagues utilized electric and mechanical forms of decryption to break the code of the Enigma cipher machines, on which almost all German communications were enciphered (computed arithmetically). Turing helped construct decoders (called Bombes) that could more rapidly test key codes until correct combinations were found, cutting the time it took to decipher German codes from weeks to hours. As a result, many Allied convoys were saved, and it has been estimated that World War II might have lasted 2 more years if not for the work at Bletchley Park.

Turing's life was not without tumult or a sad conclusion. In 1952, Turing was tried and convicted of "gross indecency" for being homosexual. He was sentenced to probation and hormone treatments. In June 1954, he died from cyanide poisoning. Although he possessed the cyanide in connection with chemical experiments he was performing, it is widely believed he committed suicide.

Turing's life has inspired writers, artists, and sculptors. Breaking the Code, a play based on his life, opened in London in 1986. Although the dialogue and scenes are mostly invented, the play ably conveys the remarkable life of this extraordinary man.

see also Computers, Evolution of Electronic; Cryptology.

Marilyn K. Simon

Bibliography

Hinsley, F. H., and Alan Stripp. Codebreakers. New York: Oxford University Press, 1993.

Hodges, Andrew. Alan Turing: The Enigma. New York: Simon & Schuster, 1983.

Turing, Alan. "Computing Machinery and Intelligence." Mind 59, no. 236 (1950):433460.

Williams, Michael R. A History of Computing Technology. Englewood Cliffs, NJ: Prentice Hall, 1985.

Internet Resources

The Alan Turing Home Page. Ed Andrew Hodges. <http://www.turing.org.uk/turing/index.html>.

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Turing, Alan Mathison

Alan Mathison Turing, 1912–54, British mathematician and computer theorist. While studying at Cambridge he began work in predicate logic that led to a proof (1937) that some mathematical problems are not susceptible to solution by automated computation; in arriving at this, he postulated a universal machine, now called a Turing machine, that was the theoretical prototype of the electronic digital computer. After completing a Ph.D. at Princeton (1938), he returned home to England, where, during World War II, he was instrumental in deciphering German messages encrypted by the Enigma cipher machine. After the war, he helped design computers, first for the British government (1945–48) and then for the Univ. of Manchester (1948–54). During this period, he produced a body of work that helped form the basis of the newly emerging field of artificial intelligence; among his contributions was the Turing test, a procedure to test whether a computer is capable of humanlike thought. Two years after being arrested for a homosexual offense (and then undergoing chemical castration as a "treatment" ), he died of cyanide poisoning. His death was ruled a suicide at the time, but the exact circumstances of his death are unclear, and it has been argued that it could have been accidental. In 2013 Turing was posthumously pardoned for his 1952 conviction for homosexuality.

See biographies by S. Turing (his mother, 1959, rev. ed. 2012) and A. Hodges (1983, repr. 2012)); G. Dyson, Turing's Cathedral: The Origins of the Digital Universe (2012).

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Turing, Alan Mathison

Turing, Alan Mathison (1912–54) English mathematician. In 1937, he invented the Turing machine, a hypothetical machine that could modify a set of input instructions. It was the forerunner of the modern computer. During World War 2, Turing played a major role in deciphering the German ‘Enigma’ code. In 1950, he devised the Turing test, which paved the way for the foundation of artificial intelligence (AI). He committed suicide after being prosecuted for homosexuality.

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