Under The Microscope

PI IN THE SKY: COUNTING, THINKING AND BEING, by John D. Barrow; Penguin, 1994; 317 pp; $24.95

Reviewed by Russell Dear

This is the fifth book on popular science written by astronomer John Barrow. It follows on from his very successful Theories Of Everything, indeed the final chapter of the earlier work, called "Is pi really in the sky?", lays the foundation and may have even provided the inspiration for the follow-up.

In Pi In The Sky, Barrow sets out to solve the mystery of why mathematics is such a powerful tool for describing the universe and through this to explore the meaning of mathematics itself. What lifts the book from being just another thematic history of mathematics is the author's ability to draw from pertinent characters of history just those points which both capture the reader's interest and the ideas he wishes to discuss.

Early in the book Barrow looks at how numbers originated in the hope that it will tell us something about the nature of mathematics. The result is 80 pages of some of the best history of the development of number systems that I have read. A conclusion that the Indian system of counting, which we all use today, has been the most successful intellectual innovation ever made might be debatable but is exceedingly well argued.

In his discussion of whether mathematics is discovered or invented he examines the scenario of an alien species developing mathematics through experiment, with computers testing results to the nth degree. He looks, for example, at how Fermat's "Last" theorem (not proven at the date of publication) might be proved by extensive computer searches for exceptions. He suggests that the advancement of technology would not have suffered from this lack of consideration of rigorous proof.

Pi In The Sky is no light Sunday afternoon browse. The concepts are deep but the numerous anecdotal asides span the main historical arguments giving us an entertaining and accessible read.

Russell Dear is a Mathematician living in Invercargill