What Makes a Coincidence Meaningful?

There are two kinds of people in the world: People who say, “What a coincidence,” and people who say, “Just a coincidence.” Same facts, different reactions. Are you the “what a” kind or the “just a” kind? I want your emails.

I’m a “just a coincidence” person. I attended an economics conference in the World Trade Center on Sept. 10, 2001, and decided not to go back for the second day. I read nothing into it. (The conference was below ground level, so everybody who stayed for Sept. 11 got out safely, for what it’s worth.)

Coincidences are hard to define. It’s not just two things happening at once. There has to be an element of surprise. But what counts as surprising is subjective and squishy. For example, rolling a die and getting 6-6-6-6-6-6-6-6-6-6 seems more surprising than getting, say, 6-2-4-5-1-3-2-5-4-6, but the two are equally probable. If you live in Eldena, Ill., you’d be amazed to roll 6-1-3-2-4 because that’s your ZIP code. For everybody else, meh.

How many people do you think need to enter a room before there’s a 50-50 chance that two of them will have the same birthday? Just 23. Remember that it’s any two people, not necessarily you and someone else, so there are many potential pairs.

Our brains don’t “do” randomness. To prove it to yourself, try spitting out digits randomly as fast as you can. You’ll find yourself stupidly repeating 1, 2, 3 and other obvious patterns over and over. The only way to make your digits sound random is to slow way down, which only means you’re concealing your thought pattern. No wonder we see faces in clouds and portents in lottery numbers.

I interviewed Persi Diaconis, a mathematician and statistician at Stanford as well as a former professional magician. “What’s surprising to me is how easily surprised people are by coincidences,” he told me.