Williams Byers
PRINCETON UNIVERSITY PRESS 2011, 224 PAGES PRICE £16.95, ISBN 978-0-691-14684-3
A fair number of authors have the ability to explain complicated ideas in simple terms, but William Byers also has the rarer gift of taking the almost banally familiar and revealing its hidden depths and complications. Mathematicians manipulate fractions on a daily basis and can quickly forget how bizarre the idea of writing one number above another may appear to a learner encountering them for the first time. While his earlier book How Mathematicians Think explored the workings of mathematical creativity, Byers now extends his thinking to cover science itself.
The central contention is that its nature as a human activity creates inherent limitations on science, the ‘blind spot’ of the title. The reader is presented with two positions: a ‘science of wonder’, which not only accepts but thrives on these limitations, and a ‘science of certainty’ which denies them. The latter view is argued to be a misunderstood version of the former, and to be responsible for a plethora of modern troubles from the economic crisis to tensions between science and religion.
Byers’ breadth of learning is impressive, appealing to chaos theory, quantum mechanics, philosophy and beyond in making his case. The majority of the individual sections are admirably clear, with a particularly convincing example being the limitations of financial mathematics: models can’t take account of other investors also using models without infinite regression. In other cases though it is not so obvious how they contribute to the book’s central arguments, such as the claim that the impossibility of absolute observational detachment ‘threatens to destabilize the entire scientific process’ as perceived by scientists (page 102).
Two other problems arise from the book’s use of terminology. The first is unavoidable: since Byers is advocating novel positions he is often obliged to provide new terms to communicate his ideas. Nevertheless, the introduction of so many unfamiliar definitions in quick succession means this is not an easy read, especially in the later chapters. The second problem is that the new terms sometimes appear misleading, such as claiming to reconcile science and religion by redefining ‘fundamentalism’ to encompass pretty much all organised religion and then dismissing it, leaving only a vague mysticism behind (page 65). In such cases the reader may feel that they haven’t been presented with a new point of view so much as a new nomenclature.
In fairness, The Blind Spot is significantly more ambitious in scope than How Mathematicians Think at less than half the length. Byers’ insight is unquestionable, and although the brevity of the book makes it challenging there’s still a lot here to repay a careful reading. His earlier book covered many of the same ideas at a gentler pace, and is a great help in getting the most out of this one. The issues will be of interest to anyone concerned with philosophical questions about the nature of science and mathematics.
Paul Taylor AMIMA
Mathematics Today April 2012
The Blind Spot: Science and the Crisis of Uncertainty can be purchased at Amazon.co.uk