Thursday, March 1, 2012
Chances Are...: Adventures in Probability
Michael Kaplan and Ellen Kaplan (2006, Viking.)
The dedication of Chances Are... gives a marvelously concise precis of what it’s about: “To Jane, who likes probability, Bob, who likes chance, and Felix, who likes risk.” What might that mean, exactly? What does it tell us about Jane, Bob, and Felix? Probability, chance, and risk are constant conditions of human life, but we haven’t always understood very much about them. Ellen and Michael Kaplan, mother and son, have written an elegant book both on what we need to know, and why we should care.
Though the ancient Romans had games of chance, it was not till the seventeenth century that Blaise Pascal set forth proofs of some fundamental issues in probability. Pascal, with his Wager and his triangle, is a relatively familiar figure; I didn’t know about Isaac Newton’s contemporary Abraham de Moivre, whom the Kaplans bring to life with superb economy. Of de Moivre’s parlous circumstances as a Huguenot refugee in England, they write, “This shabby man, ensconced at the window end of a greasy table in Slaughter’s Tavern, had, through the clever manipulation of abstract terms, discovered–or created–a way to describe how things happen the way they ‘ought’: how Chance scatters itself around the central pillar of Design in the shape of a bell.”
With economical clarity, we are introduced to the Marquis de Laplace, his student Poisson, Henri Lebesque, and Richard von Mises. And who could forget Andrei Nikolaevich Kolmogorov, born in 1903 on a train crossing Russia: “He remained interested in everything, from metallurgy to Pushkin, from the papacy to nude skiing.” His interests included mathematical logic, algorithmic complexity, and, “with characteristic verve, he hoicked up the tottery edifice of probability and slipped new foundations underneath.” As they’ve done with all those other singular minds, the Kaplans let us stand at the door of Kolmogorov’s work and look in.
Of course, the mathematics are only part of the story. Chances Are... is equally concerned with the human element. What’s the difference between the apparently pure hand of fate at the roulette table and the swagger and bluff of poker? Which kind of game is the stock market? In any case, it helps to start with a pile of money; even in a perfectly fair game, deeper pockets win.
Insurance is another complicated game of numbers and the human factor. Lloyds of London still operates as a series of face to face encounters between the buyers and sellers of risk. As the Kaplans say, “...each time probability leaves its cozy study full of urns and dice and descends to the marketplace of human affairs, it reveals its dependence on human capabilities–on judgement and definition. As powerful a device as it is, it remains a hand tool, not a machine.”
Medical science calls for judgement, too, complicated by ethics, and by the fact that bodies, and diseases, are often more different than they are alike. Science is based on repeatable events, and statistics on aggregated events, but we get sick as individuals. Doctors are pretty poor at guessing where in a range of outcomes our case will fall, which is, of course, the only thing we really want to know. Our peculiar psychology complicates the case further: “Red sugar pills stimulate; blue ones depress–brand name placebos work better than generic. And higher dosages are usually more effective.” It’s a wonder that clinical trials give any useful information; indeed, the truly informative trial often comes only after a new treatment is released for general use.
Often, in medicine, we’d benefit from an understanding of the likelihood of false positive results, as in tests for rare conditions. Courts of law suffer under the same deficiency, because crimes are such rare acts that we don’t have a strong intuitive background. Unfortunately, we’re not usually offered a strong statistical background to compensate for that lack; judges may be suspicious of statistical reasoning because they aren’t equipped to tell good reasoning from rhetorical hokum, but that doesn’t mean it wouldn’t be helpful.
Chances Are... combines such utility with great pleasure. It’s very clear on the math, but also on a vast swath of biography, history, and science. At heart, it’s a deeply humanist endeavor: the philosophical strands lightly flavor the whole. Like this gem: “The formal calculation of probabilities will always feel artificial to us because it slows and makes conscious our leap from perception to conclusion. It forces us to acknowledge the gulf of uncertainty and randomness that gapes below--and leaps are never easy if you look down.”
Factual certainty is elusive and contingent; if that’s the case, we are wise, and brave, to acknowledge it. Here’s to the courage for the leap.