Feature4 - ChancesAre
After the stunning success of The Art of the Infinite (2003), the dynamic math duo of Michael and Ellen Kaplan have produced another thriller of the arithmetic kind. But Chances Are: Adventures in Probability (2006) is a very different kettle of fish. It is much deeper, less integrated, more uneven and (aptly) chaotic than the earlier volume.
The Art of the Infinite tracks how we stumbled on the infinitely divisible and infinitely great. It lays careful foundations and moves us steadily but cheerily forward, explaining in detail but without condescension. For example, we advance from triangular numbers to Gauss and Dedekind in the first 39 pages. But the thread of the story weaves like a mystery back and forth, following with a sure hand now an intellectual argument, now anecdotal events. The method alternates between history and rational exposition, and the latter changes from visual to algebraic modes. In short there’s something for everyone, and the brightest will leave with new insight. Moreover, the authors’ excitement transfers easily to the reader.
Chances, like Infinite, has quirky chapter titles and quotations from the literary classics, but there the resemblance ends. The book could use an editor’s sharp red pencil. Instead of exploration of a math topic, the Kaplans have produced a wandering monologue. True they start with dice and cards and what we may call issues of pure chance. We meet the heroes of the early probability screen, Pascal, de Moivre, Laplace and Poisson. We encounter the enchanting Bertrand’s paradox, Saint Petersburg paradox and Monty Hall problem. But soon we are deep in the throes of legal decision-making. How, the authors explore at length, might evidence be rationally evaluated. The trouble is that the Kaplans aren’t lawyers and don’t understand that rules of court habitually and regularly work. The question is not how to find the truth, but why we nearly always do. Sliced another way, they allow that the exceptional is normal in the context of the bell-shaped curve, but not in the curve’s legal equivalents, embodied in aphorisms that lawyers understand with every fibre of their being: hard cases make bad law, and cross-examination is the great engine of truth.
The book is larded with key concepts that aren’t adequately explained for the layman. An example is the p-number. If correlation X is purely a matter of chance, what is the likelihood of a correlation the same or greater than X? We first encounter the expression in the context of the null hypothesis. Fair enough, you say. One derives from the other or they are the same thing differently expressed. But the implications aren’t recast in any mathematical detail. This then isn’t really a math book. Nor are they unfolded slowly and carefully, turned upside down and sideways verbally, for the mathematically challenged. We desperately want the keys to the kingdom of chance. That’s after all why we buy the book. But the keys are held continuously out of our reach.
What then are the Kaplan’s trying to impart? We learn that drugs and medical procedures aren’t as useful as they appear to be, that doctors don’t understand the data upon which they make decisions about our care, that politicians are out for glory, that most generals are fools. It’s too easy to criticize a book which tries to cover such broad terrain. Rather the question is why the exercise was necessary. The Kaplans repeatedly point out that truths in probability are counter-intuitive. The exploration of why this should be so has barely begun. We are at the alchemy stage in our understanding of probability.
Let us reverse the perspective of this review and see if the result is the same. Chances contains brilliant nuggets of insight. Time flows one way, not because of a physical law of direction, but because of probability. Interference of a single photon passing apparently through two slits disappears when we measure where the photon is, because the wavelike probability has been eliminated. We are left with two circles of light. For insights and nuggets this is a great book. For comprehensive exegesis of its topic, rather disappointing. Or is this the result of having written the wonderful Art of the Infinite? Comparing the two, the earlier is much stronger, clearer, better organized. But the importance of the probable in real life is so much greater than the infinite that the Kaplans can be forgiven. I’d like to see their second attempt at this topic. I expect it would be superb.
And for publishers, there’s no comparison. Oxford University Press (The Art of the Infinite) gets an A plus, Penguin Books (Chances Are: Adventures in Probability) a C.
(by bb)
