June 15, 2011 - 15:05 — Anonymous

Publisher:

Princeton University Press

Year:

2008

ISBN:

978-0-691-13131-3

Price (tentative):

USD 27.95

MSC main category:

00 General

Review:

The second popular-mathematics book of the author is in some sense a free sequel to the first one Nonplussed. This book, just like its predecessor, contains a collection of baffling paradoxes and mathematical occurrences that are in sharp conflict with a common, or even scientific, intuition. The book shows how deceiving the intuition can occur and where it can lead us. The author illustrates this unsettling thought on several examples of truly mind-boggling and delightfully amusing paradoxes. After a warm-up of “common-knowledge” classical puzzles and paradoxes based on elementary logic, the serious business starts. The reader will find, among many other topics, Simpson’s famous paradox, a nightmare of statisticians and a destructive weapon of demagogues, Braess’ paradox, disguised in a less common form with a rather surprising positive effect of a temporary closure of a road on the smoothness of traffic in a big city, and finally, at the end of the book, the king of all paradoxes, the Banach-Tarski theorem. This paradox, for instance, is a deep and serious result that lies on the crossroads of measure theory, the theory of sets and mathematical logic, a consequence of the existence of sets that have no volume at all, combined with the highly disputed axiom of choice. It states that a three-dimensional ball can be cut into just five pieces from which one can assemble two such balls. This result, whilst true, is so highly counterintuitive that the author himself comments on it: ‘If nothing else in this book was considered Impossible by the reader, it is hoped that this result might just have saved the author’s day.’

Reviewer:

lp