Miracles Follow the Law of Large Numbers

Both religious and paranormal beliefs are consistently defended by references to so-called "miracles" - events which are so improbable that they simply must have been causes by supernatural or paranormal forces. The problem is, these "miracles" are often not so improbable after all. To understand why, we just need to know a little math and statistics.

In Scientific American Michael Shermer writes:

[A] principle of probability called the Law of Large Numbers shows that an event with a low probability of occurrence in a small number of trials has a high probability of occurrence in a large number of trials. ... In the case of death premonitions, suppose that you know of 10 people a year who die and that you think about each of those people once a year. One year contains 105,120 five-minute intervals during which you might think about each of the 10 people, a probability of one out of 10,512--certainly an improbable event.

Yet there are 295 million Americans. Assume, for the sake of our calculation, that they think like you. That makes 1/10,512 X 295,000,000 = 28,063 people a year, or 77 people a day for whom this improbable premonition becomes probable. With the well-known cognitive phenomenon of confirmation bias firmly in force (where we notice the hits and ignore the misses in support of our favorite beliefs), if just a couple of these people recount their miraculous tales in a public forum (next on Oprah!), the paranormal seems vindicated. In fact, they are merely demonstrating the laws of probability writ large.

In a review of Debunked! [physicist Freeman Dyson of the Institute for Advanced Study in Princeton] invoked "Littlewood's Law of Miracles" (John Littlewood was a University of Cambridge mathematician): "In the course of any normal person's life, miracles happen at a rate of roughly one per month." Dyson explains that "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."

It almost goes without saying that most bad, poorly reasoned, and unfounded beliefs would not exist if it were not for widespread ignorance — in particular ignorance of science and math. If people were more knowledgeable and better thinkers, they wouldn’t fall for every hokey idea that comes along. Maybe if the above information is spread around a bit, some people will be spared from perpetuating bad beliefs.

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