# Miracles

on April 6, 2004 at 6:55 am in Science

Freeman Dyson introduces us to Littlewood’s Law of Miracles:

Littlewood was a famous mathematician who was teaching at Cambridge University when I was a student. Being a professional mathematician, he defined miracles precisely before stating his law about them. He defined a miracle as an event that has special significance when it occurs, but occurs with a probability of one in a million. This definition agrees with our common-sense understanding of the word “miracle.”

Littlewood’s Law of Miracles states that in the course of any normal person’s life, miracles happen at a rate of roughly one per month. The proof of the law is simple. During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month. Broch [co-author of the book Dyson is reviewing] tells stories of some amazing coincidences that happened to him and his friends, all of them easily explained as consequences of Littlewood’s Law.

The law echoes a comment I’ve seen attributed to another mathematician, Persi Diaconis. Diaconis supposedly said that if you study a large enough population over a long enough time period, then “any damn thing can happen.”

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