Let Us Calculate

This is the most illuminating book that has yet come my way on the topic of artificial intelligence. One of its great merits is that it does not confine itself to the sterile question whether machines can properly be said to think but provides, as its title indicates, a succinct account of the ways in which modern computers work and of the social implications of their use. Mr. Bolter is an offspring of the marriage of C.P. Snow’s “Two Cultures.” A professor of classics, he also holds a master’s degree in computer science. The greater part of the book is devoted to matters of technological detail, but its originality and principal interest lie in the way in which it embeds the developments of technology in their cultural setting.

Alan Mathison Turing, to whom this book owes its title, was an English mathematician who was born in 1912 and died in 1954, most probably by his own hand. He was harried by his homosexuality, the practice of which, even between consenting adults, was still illegal in England at that date. During the war he had rendered great service to his country as a cryptographer. The paper that made him famous, “On Computable Numbers, with an Application to the Entscheidungsproblem (problem of decidability),” was published in the Proceedings of the London Mathematics Society as early as 1936. The paper was a contribution to symbolic logic but Turing was led to speak of machines by his concern with the question how far the exercise of logic resembles a mechanical procedure, and accordingly supplied computer scientists with what has become the standard concept of a Turing machine.

The definition of a Turing machine, as set out in the Collins English Dictionary, is that it is “a hypothetical universal computing machine able to modify its original instructions by reading, erasing, or writing a new symbol on a moving tape of fixed length that acts as its program.” This is misleading only insofar as it suggests that the tape is required to be of some specific length. Clearly the length of any actual tape must be finite, but no limit is set to the length of the tape in the concept of the machine.

In explaining the nature of the Turing machine, Mr. Bolter hits upon the useful analogy of a game. Like a good game, a Turing machine is self-contained. The point of the game is to reach an end result by performing a series of operations upon an initial set of data by the successive application of a finite number of rules. There is a rule that determines when the end has been achieved. Both the data and the rules are encoded in the machine. The information is stored on a tape on which the machine also writes its output. In a simple example, supplied by Mr. Bolter, the tape is divided into cells, each of which contains just one symbol, either “0,” “1,” or a blank, with a marker to show which…

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