BEYOND SCIENCE

New Zealand Listener, Volume 32, Issue 819, 7 April 1955, Page 13

BEYOND SCIENCE

MATHEMATICS IN WESTERN CULTURE, by Morris Kline; Allen and Unwin, English price 30/-. ‘THE apparent movement of science away from reality bewilders many. Kline offers little comfort to the disturbed, but he does show how it is happening. It is a necessary consequence of the advance of mathematics. He demonstrates how mathematics, in passing and without conscious intent, not only made modern science possible, but also reversed its direction not once but many times. All this as a subsidiary to the main stream of mathematical thought! The book is not an introduction to mathematics as is Hogben’s Mathematics for the Million. It is historical and philosophical in the manner of Dantzig’s Nurnber. No prior knowledge of mathematics is assumed. As the title indicates, (continued on next page)

BOOKS

(continued from previous page) Kline confines himself to Western culture. This weakens the historical approach as Arab and Indian contributions"must be omitted. All the illustrations, grouped at the beginning, are of art. This serves to em--phasise the author’s thesis that mathematics is the greatest of all fields for creative endeayour. Like art, mathematics and its derived sciences are shown as limited by the habit of thought in the society in which they arise. This accounts convincingly for the "baffled point" at which Greek mathematics came to the limit set by habit of thought of their times. It is interesting to see Newton and the 17th Century mathematicians in the same boat. And, subsequently, those of the 18th and 19th, future will note the same of us. The breaking of these habits falls to original minds. Kline points out that Euclid was very doubtful of two of his own axioms. The questioning of them in modern times has led, not only to Einstein’s space-time universe, but to a broadening of the whole cf our thought Peo philosophy and science. How men, living on a sphere, could have avoided for thousands of years the discovery that a line is finite in length but endless is one measure of how convincing Euclid | could be. The author summarises adequately the impact of relativity on science, philosophy and religion. He examines how it bears on causality and proclaims the end of determinism. He does not see the alternative view by which determinism could be. strengthened, nor has he heard of the new determinism which the geneticists, most unwillingly, are being forced to espouse. Kline can be delightfully amusing when he so chooses. One could gain something of a reputation by quoting

him. Yet on occasion he too narrowly acdresses himself to his native American , audience. Your true mathematician is a

citizen of the world,

J.D.

McD.