Document (#27073)

Author

Davis, M.

Title

¬The universal computer : the road from Leibniz to Turing

Imprint

New York : W.W. Norton

Year

2000

Pages

257 S

Isbn

0-393-04785-7

Footnote

Rez. in: JASIST 55(2004) no.1, S.89-90. (J. Warner): "This book is a review of the work of logicians, particularly mathematical logicians, who developed concepts crucial to modern computers. Leibniz, Boole, Frege, Cantor, Hilbert, Gödel, and Turing are covered, with some attention to their personal biographies. The prose style is lucid, with clear and potentially widely intelligible exposition of technical issues. The author, Martin Davis, has had a long and distinguished career, occupying a crucial locus between mathematical logic and engineering design and construction and accepting a responsibility to make the theory of computability accessible to non-technical readers. The clarity of presentation and themes developed are continuous with his previous publications, without repetition. The broad relevante of the work to information science is through the gestalt of the computer. More specifically relevant issues lie in the connections between mathematical and ordinary discourse concerns and in the intersection between logic and engineering. The idea of the computer as a universal machine, developed in mathematical logic in the 1930s and obscured in ordinary discourse by an emphasis an the stored-program concept as the revolutionary element, is discussed (pp. xi and 186). From the perspective of economics, the context of conceptualization (mathematical logic) is different from that of invention (wartime cryptography). Innovation and diffusion have brought the computer into further arenas: as Time (1999) noted: "every one who taps at a keyboard, opening a spreadsheet or a word-processing program, is working an an incarnation of a Turing machine" (p.192). The formal logic of the context of conceptualization may not be applicable to human and ordinary language concerns of the context of diffusion and more could have been made of this contrast. The received position, noted by Davis, has been that conceptualization and invention of the computer occurred largely separately, in mathematical logic and engineering. The position was questioned by Minsky, as long ago as 1967: "While it is often said that the 1936 paper [by Turingl did not really muck affect the practical development of the computer, 1 could not agree to this in advance of a careful study of the intellectual history of the matter." (Minsky, 1967, p. 104). Davis refers to the emerging evidente, whose release had been complicated and delayed by security considerations, indicating greater personal continuity and interaction, specifically between Turing and von Neumann, than had previously been allowed for (p. 192). A deeper cultural conflict between engineering and logic could also be detected, between a concern with robustness and developing and preserving robustness by incremental innovation and an interest in radical reconceptualization (curiously, Wittgenstein, who produced a robust account of formal logic, had trained as an engineer and designed a house). The image of the machine and its relation to mathematical reasoning is also considered and Poincare quoted: We might imagine a machine where we should put in axioms at one end and take out theorems at the other, like that legendary machine in Chicago where pigs go in alive and come out transformed into hams and sausages. It is no more necessary for the mathematician than it is for these machines to know what he is doing. (p.93) A stronger distinction between the process and product of mathematical reasoning, analogous to the distinction between the context of discovery and of justification in the philosophy of science and consistent with the Marxist view of the congealing of human labor in the product, might have reduced the need to identify the human process of mathematical reasoning with its mechanical analogue. A more radical move would to acknowledge both mathematics and technology as human constructions.
The stability of logie over time, from Aristotle to Boole, and the continual change since Boole is noted. For information science, the relative stability of forms of writing over the same period and the intensive developments in writing and message transmission (shorthand, the telegraph, codes for telegraphic transmission, the telephone, and the Internet) since the mid-nineteenth century represent parallel developments. Communication models, from the Aristotelian view of writing as a secondary symbolism for oral speech to Shannon's information theory, have characteristically developed after the technologies they can be used to describe. Information theory developed from wartime cryptography, played a part in the creation of information science, and remained influential in its early development, with some indications of revival. A theme explored by Davis in the logicians' biographies given is of discordance between the qualities required for intellectual eminence and social adjustment. An insistence an questioning practices and seeking fundamental issues can be socially disruptive: Gödel, for instance, famously questioned the consistency of the United States Constitution during his citizenship examination (p. 137). In some instances, the logical contradictions explored reflect or project the logician's biography: most obviously, Russell was both a member of a class and not a member of a dass; themes of exile can be detected in Gödel's work. The intensity with which these paradoxes are pursued may indicate the extent to which their possible biographical source was not fully known to the pursuer (Freud, 1990). A crucial issue might revolve around the idea of acceptance: the potential productivity of questioning and possibly rejecting the current state of affairs in intellectual activities; and the destructiveness of continual questioning in social life. In conclusion, the book is to be recommended for its lucidity and intelligibility and for the interest of its personalization. It could be used as supplementary reading for historical awareness in information science programs."

Field

Informatik

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