02.05.1996

Counting the cost

John Bayliss reviews The nature of numbers by Ian Stewart (Weidenfeld & Nicolson, London, pp150, £9.99)

Though I am a mathematician by profession I found plenty to interest me in this book. It reviews the current state of mathematical work in the spheres of greatest theoretical development at the moment.

The book’s main concerns are number, pattern, change and chaos. It deals with these in terms of their relationship with the development of science and technology.

Obviously no book of 150 pages can cover even a small part of mathematics, but this is a worthwhile introduction. Much more important for Marxists is that it treats mathematics from a materialist point of view.

By contrast, professor Penrose, based at Oxford University, is attempting to restore an idealist position in mathematics. Penrose argues that some things are unknowable, and that mathematics has no real connection with the material world. In his opinion the productive forces do not direct the development of mathematics; nor can maths describe certain patterns or processes that occur within production, the most important of these being consciousness.

There have been a number of important developments in mathematics of great social and economic importance over the last few decades. The discovery of chaos was primarily the product of attempts to predict the weather using computers. The theoretical development of chaos theory would not have been possible without computers. The development of statistics has been lacking, which has led to a situation where, for example, there is no real possibility of quantifying the risks involved in ‘mad cow’ disease. This book does not deal with these areas directly, but makes it very clear that without such developments many social and economic advances cannot take place.

The final irony is that the very narrow-minded restrictions on the development of mathematics imposed by the capitalist class stop many useful developments. The reason is that no immediate profit is foreseen.

John Bayliss