Classic but not classical

Bach and the Patterns of Convention

January 23, 1998

The Harvard biologist and popular-science writer Stephen Jay Gould once remarked: "Misunderstanding of probability may be the greatest of all impediments to scientific literacy". To the average person on the street, odds of 10,000 to 1 or 1 million to 1 sound exactly the same, although the occurrence of the first event is a hundred times more likely than the last. In this first-rate account of the logic and fallacies of probability theory, John Haigh has gone a very long way towards rectifying this deplorable state of affairs.

In just a bit more than 300 pages, Haigh introduces literally hundreds of everyday situations ranging from football pools to Monopoly to TV games and poker to illustrate how evolution simply did not prepare our brains for assessing the true likelihood of things. For instance, suppose you toss three coins and ask for the likelihood that all three show the same face, either heads or tails. One argument says that at least two of the three coins must be alike, both heads or both tails. Then since the third coin is equally likely to fall heads or tails, half the time it is the same as the other two. Thus, the probability that all three are alike is one-half. By just enumerating the eight possible ways the coins can fall, we see that this answer is definitely wrong; the true answer is one-fourth, not one-half.

Where is the logical flaw in the argument? It lies in the vague statement "the third coin", since if we do not distinguish the coins from one another, how do we know which one is the third?

Probability theory is littered with pitfalls of this sort for the unwary, and Haigh's book illustrates many of them. Fortunately for the reader, Haigh is a master at exposition, conducting this tour of the world of chance without ever using any mathematics beyond what one would find in a secondary-school course in elementary algebra. So the volume is ideally suited for readers with virtually no training in mathematics, but who are curious about how actually to assess the odds of things like winning a single game at lawn tennis or on which hands in poker one should raise.

For the more mathematically inclined, Haigh offers several technical appendices, a reasonably varied bibliography and even a short examination for the reader to test himself on what he has learned from the book.

All in all I can recommend this book highly to anyone who has ever wondered why it takes only 23 people in a room for the chances to be 50-50 that two (or more) of them will share a birthday. This is a book to ponder, savour, study - and give to your mathematically illiterate friends.

John L. Casti is resident member, Santa Fe Institute, New Mexico, United States.


Bach and the Patterns of Convention

Author - John Haigh
ISBN - 0 674 06005 9
Publisher - Harvard University Press
Price - £29.95
Pages - 0

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