Littlewood's law

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Littlewood, c. 1960
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Littlewood's law (or Littlewood's law of miracles) is a mathematical conjecture by John LittlewoodWikipedia (1885–1977) of Cambridge University that relates to the frequency of a "miracle" occurring. It argues that events viewed as miraculous are actually commonplace if considered in the context of how much occurs in a person's life.

Physicist and mathematician Freeman Dyson explains it in his review of the book Debunked! ESP, Telekinesis, Other Pseudoscience:[1]:327

Littlewood's law of miracles states that in the course of any normal person's life, miracles happen at the 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 one per second. So the total number of events that happen to us is about 30,000 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.

Mathematically this is dependent on the arbitrary definition of "discrete events" and the arbitrary assignment of a probability for a miracle — although "one in a million" is a common sense estimate for something spectacularly unlikely. So, this is a heuristic, or rule-of-thumb approach. Furthermore, if one calculates the actual probability, it is approximately 0.632, meaning that there is 63.2% chance that some miracle(s) occurs, not close to 100%.[note 1]

Of course, altering these arbitrary factors alters the frequency of a "miracle" happening. But that isn't really the point. The purpose of the law is to show if you define a miracle as any unlikely event, then miracles are bound to happen frequently, just by chance. To claim a genuine "hit" you have to define your expected event in advance.

See also[edit]


  1. The probability of no miracle occurring is (999,999/1,000,000)1,000,000, and hence the probability of at least one miracle occurring is 1-(999,999/1,000,000)1,000,000. This comes out to be 0.632.


  1. The Scientist as Rebel: A New York Review Collection by Freeman Dyson (2008) Random House. ISBN 1590172949.