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Pinker, S. (1997). How the Mind Works, New York: Norton.

Turing, A. (1950). ‘Computing Machinery and Intelligence’, Mind 59, pp. 433–460.

Turing, A. (1936). ‘On computable numbers’, Proc. Lond. Math. Soc. 2nd Series, 42, pp. 230–265.

YORICK WILKS

Department of Computer Science

University of Shefﬁeld

Shefﬁeld, S11 4DP, UK

E-mail: yorick@dcs.shef.ac.uk

John von Neumann, The Computer and the Brain, 2nd edition, Mrs. Hepsa Ely

Silliman Memorial Lectures, New Haven: Yale University Press, 2000, xxviii + 82 pp., $9.95 (paper), ISBN 0-300-084373-0.

When John von Neumann turned his interest to computers, he was one of the leading mathematicians of his time. In the 1940s, he helped design two of the ﬁrst stored-program digital electronic computers. He authored reports explaining the functional organization of modern computers for the ﬁrst time, thereby inﬂuencing their construction worldwide (von Neumann, 1945; Burks et al., 1946). In the ﬁrst of these reports, von Neumann described the computer as analogous to a brain, with an input “organ” (analogous to sensory neurons), a memory, an arithmetical and a logical “organ” (analogous to associative neurons), and an output “organ”

(analogous to motor neurons).

His experience with computers convinced him that brains and computers, both having to do with the processing of information, should be studied by a new discipline–automata theory. In fact, according to von Neumann, automata theory would cover not only computers and brains, but also any biological or artiﬁcial systems that dealt with information and control, including robots and genes. Von Neumann never formulated a full-blown mathematical theory of automata, but he wrote several important exploratory papers (von Neumann, 1951, 1956, 1966). Meanwhile, besides designing hardware, he developed some of the ﬁrst programs, programming languages, programming techniques, and numerical methods for solving mathematical problems using computers. (Much of his work on computing is reprinted in Aspray and Burks, 1987.) Shortly before his death in 1956, he wrote an informal synthesis of his views about brains. Though von Neumann left his manuscript sketchy and unﬁnished, Yale University Press published it as The Computer and the Brain in 1958. The 2000 reprint of this small but informative book is an opportunity to learn, or be reminded of, von Neumann’s thoughts on the computational organization of the mind-brain.

Von Neumann began by explaining computers, which for him were essentially number crunchers: to compute was “to operate on . . . numbers according to a predetermined plan” (p. 3; all page references are to von Neumann’s book). In any

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computer, some components (input “organs”) received numerical data from the environment while other components (output “organs”) delivered the calculations’ results. The most important components, which he called “active organs,” were those that performed operations inside the machine. Each active organ performed a particular operation, which could be arithmetical (e.g., addition, subtraction, multiplication, or division), logical (e.g., conjunction, disjunction, or negation), or physical (e.g., restoring voltage levels in the machine or amplifying signals). Numbers could be “represented” in the machine, and arithmetical operations could be carried out, in two ways. The ﬁrst was analog: numbers were represented by continuous physical quantities (for example, an angle of rotation or a voltage level), and operations on numbers were performed by physically manipulating those quantities.

Machines that represented and manipulated numbers in this way were called analog computers. The second was digital: numbers were represented by discrete “markers” (typically, the presence or absence of an electric pulse), and operations on numbers were performed by combining markers according to logical rules (that is, when an active