John Allen Paulos in The New York Times:
The essayist Alain de Botton has been writing a great deal lately about crushes, those sudden infatuations aroused by the merest of stimuli — the way she subtly rolls her eyes at a blowhard’s pronouncements, her intentional dropping of a glass to attract a waiter’s attention, the way he casually uses his iPhone as a bookmark. In beautiful prose laden with examples, Mr. de Botton describes how attraction can cascade into exultation but, alas, gradually dissolve into disillusionment and a slow vanishing of the mirage. A crush is undeniable, he writes, but barely explicable. That assertion appealed to my own sometimes reductionist mind-set, and I realized that the bare bones of the thesis could be expressed in statistical terms. Let’s begin by imagining a person to be an assemblage of traits. Many are personal — our looks, habits, backgrounds, attitudes and so on. Many more are situational: how we behave in the myriad contexts in which we find ourselves. The first relevant statistical notion is sampling bias. If we want to gauge public feelings about more stringent gun control, for instance, we won’t get a random sample by asking only people at a shooting range. Likewise, a fleeting glimpse of someone, or a brief exchange with him or her, yields just a tiny sample of that person’s traits. But if we find that sample appealing, it can lead to a crush, even if it is based on nothing more than an idealized caricature: We see what we want to see. In the throes of incipient romantic fog, we use what the psychologist Daniel Kahneman, in his book “Thinking, Fast and Slow,” calls System 1 thinking — “fast, automatic, frequent, emotional, stereotypic and subconscious.”
The second relevant statistical notion is Bayes’s theorem, a mathematical proposition that tells us how to update our estimates of people, events and situations in the light of new evidence. A mathematical example: Three coins are before you. They look identical, but one is weighted so it lands on heads just one-fourth of the time; the second is a normal coin, so heads come up half the time; and the third has heads on both sides. Pick one of the coins at random. Since there are three coins, the probability that you chose the two-headed one is one-third. Now flip that coin three times. If it comes up heads all three times, you’ll very likely want to change your estimate of the probability that you chose the two-headed coin. Bayes’s theorem tells you how to calculate the new odds; in this case it says the probability that you chose the two-headed coin is now 87.7 percent, up from the initial 33.3 percent.
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