Very unlikely things happen all the time. In New York, a city of eight million inhabitants, you frequently run into people you know—quite often, it's the people you least want to run into. Sometimes, poker players get dealt a Royal Flush (the chance of that happening is roughly 1 in 650,000). You've probably had the experience of opening a book to the page you were looking for, as I did twice while preparing this review. Less fortunate souls get struck by lightning (1 in 300,000). The creation of life itself was an event so unlikely that it would seem impossible—and yet here we are.
Why is this? Intuitively, the very idea of probability would suggest that unlikely events ought to happen infrequently. But in The Improbability Principle: Why Coincidences, Rare Events, and Miracles Happen Everyday, David J. Hand contends that everything we know about statistics points to the exact opposite. He crystallizes his argument in a single, simple law: "extremely improbable events are commonplace." He calls it the Improbability Principle.
Statistics can't explain why things happen (a coin falls heads roughly half of the time because of its shape, not because it has a .50 probability of falling heads). But, as Hand demonstrates, statistics can explain why things that seem unlikely are more likely than you think. "With a large enough number of opportunities, any outrageous thing is likely to happen," he writes. This is the Law of Truly Large Numbers, the most important tenet of the Improbability Principle. The world is so full of objects and forces interacting in complex ways—rocks to be tripped upon, lotteries to be won, holes-in-one to be made—it would be unusual to go a day and not witness some kind of fluke.
Hand's reasoning extends from the mundane to the cosmic. In a Ted talk a few years ago, Arthur Benjamin said, "The laws of nature are written in the language of calculus." But the creation of the universe and life itself is a story about probability—a story that Hand tells courageously in one of the later chapters. Hand's work here, in particular, is a testament to the power of statistics.
For anybody in need of a primer in this important field, the book is a non-drowsy review of the fundamentals—normal distribution, selection bias, conditional probability, and so on. Hand's previous publications include a number of textbooks, and his tone can occasionally veer toward the collegiate: "With that discussion of the normal distribution under our belt." But on the whole, he shows an uncommon concern for style (especially uncommon for an author whose previous contributions include Multivariate Analysis of Variance and Repeated Measures). For those susceptible to flashbacks, certain passages are reminiscent of the SAT: "Suppose that there are 100,000 people, each throwing a ten-sided die six times…" Look beyond that, though, and the math is exquisite. It's both straightforward and complex, rational and magical.
That said, the mathematical view of unlikely events can also, at times, be a disorienting and disconcerting. As Hand puts it, "our intuitive grasp of probability isn't very good." No matter how much you try to absorb the book, you'll still catch yourself marveling at the lowliest coincidence. Accidents, miracles and coincidences interrupt the predictable, mathematical flow of existence. They give us a sense that anything is possible, that life doesn't move along determinate, numerical paths. The fact that The Improbability Principle is so counterintuitive proves that we're hardwired to think this way. We believe in coincidences not because we are ignorant; we believe in them because it's in our nature. A case in point: All good stories hinge, to some extent, on the premise of chance. When something improbable produces a negative outcome, we call it a tragedy. Irony—as Hand points out, a kind of coincidence—is a pillar of comedy. When something unlikely produces a positive result, we call it a miracle. We have developed these mechanisms because the mathematical explanation can't always satisfy our appetite for meaning. My sister ran into the same fellow three times on two different continents over the course of five years; now he's the love of her life and the father of my nephew. Hand would say that it was simply the Law of Selection at work. But where's the romance in that?
This would of course be a very bad reason not to pay attention to The Improbability Principle. Like most brave science, Hand's work directly challenges deeply held beliefs that are based on intuition rather than reason. The social, economic, and institutional benefits of thinking probabilistically are considerable. But from time to time, Hand's reasoning produces what Flinders Perry—whom Hand quotes—calls an "ugly little fact which killed the beautiful theory." While every event lies somewhere on the scale of probability, from 1 (inevitable) to 0 (impossible), sometimes, for the sake of a good story, it might just be better to say "what are the chances!" and leave it at that.
Arthur Holland Michel is the founder and Co-Director of the Center for the Study of the Drone, an interdisciplinary research, art, and education project at Bard College.