Forget the title: read the subtitle. This book is an excellent brief account of the life of Alan Turing, examining the extraordinary contributions that he made to the intellectual culture of the 20th century.

Although it gives a frank account of his almost open homosexuality, it lacks any hint of Hitchcockian adventure.

The book's main theme is pure logic, regarded as a codification of the basic principles of rational human thought. Logic has been the province of philosophers ever since it was invented by Aristotle. The idea of a machine that could reason logically about the truths of mathematics was proposed by the German philosopher Leibnitz; in the early 20th century, logic was further developed as a foundation for mathematics, culminating in * Principia Mathematica * by A. N. Whitehead and Bertrand Russell. Mathematicians, led by David Hilbert, hoped that pure logic could prove the consistency of the whole of mathematics, offering protection from the paradoxes of set theory.

In 1936, Kurt Godel dashed these hopes by showing that a proof of the consistency of mathematics would in itself be a mathematical contradiction.

Turing made a similar discovery. As an exercise in pure thought, he postulated a mechanical realisation of the principles of pure logic, in the form of the universal Turing machine. It was the forerunner of the modern stored-program digital computer, and universal in the sense that it could execute programs written for any other similar machine. He then demonstrated the existence of a mathematical function that could never be computed by any program on any machine. The function is peculiarly self-referential, since it addresses the question of whether a computer program will ever terminate.

Undeterred by this negative result, Turing speculated that computers would one day exercise all the functions normally attributed to human intelligence - for example, playing chess or conducting cultured conversations with humans.

Computers today are universal in the other sense, that they are incorporated in countless products of our technological civilisation - cars, washing machines and even beds. They are millions of times more powerful, capacious, compact and numerous than the machines known to Turing, and many thousands of times cheaper. The logic they embody is no longer the province of philosophers and mathematicians: it is the everyday stock in trade of millions of professional software engineers. Yet it is only now that Turing's dreams of artificial intelligence are being partially realised.

This book explains how many of the basic ideas of computing we owe to the genius of Turing. It places him firmly in the context of the history of ideas, particularly those flowering in the Cambridge of the early 20th century in the time of Keynes, Forster, Russell, Hardy and Wittgenstein.

The book is particularly valuable for its selection of quotations from these writers and other great pioneers of logic and computing, as well as from Turing himself. Homosexuality is the book's secondary theme, and is put forward unconvincingly in places as a hidden inspiration or motivation for Turing's most original ideas.

The style of exposition is clear and easy, the index useful. The details of the working of a Turing machine are well explained, although its universality is glossed over. The book can be read for instruction and enjoyment by those already familiar with its story and its characters, as well as readers for whom they are new. I hope that the latter will be enticed to follow the author's excellent recommendations for further reading.

Sir Tony Hoare is principal researcher at Microsoft Research Ltd, Cambridge.

## The Man Who Knew Too Much: Alan Turing and the Invention of the Computer

Author - David Leavitt

Publisher - Weidenfeld and Nicholson

Pages - 319

Price - £16.99

ISBN - 0 297 84655 8