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Trying to add some precision to its meaning, Mathematician J.E. Littlewood defined it as "an event that has special significance when it occurs, but occurs with a probability of one in a million."; what word is it?

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Answer: miracle

According to physicist Freeman Dyson:

"The paradoxical feature of the laws of probability is that they make unlikely events happen unexpectedly often.

A simple way to state the paradox is 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."

[Note: The above passage was taken from The New York Review of Books (Freeman Dyson reviewing Debunked! ESP, Telekinesis, Other Pseudoscience by Georges Charpak and Henri Broch)

You can read the review at:


I get up at 6 am and go to bed at 12 am, I am awake for 18 hours not 8. Should I have miracles more often? The calculation is all wrong, and I think that the whole law makes no sense at all.

I find Littlewood's endeavour unsatisfactory, because it amounts to begging the question. Miracles are often associated with divine providence - the notion that god or gods interceded in human life to make something unnatural occur.

Since god is but a metaphysical postulate, a miracle cannot be the result of a rational action. it therefore is little more than a synonym for an unexplainable random occurrence.

Consequently, the attempt to "prove" anything about a miracle is fruitless.

A miracle is an event contrary to the laws of nature. A god could perform several miracles a day, and they would all be miracles. The frequency shouldn't matter. Any rare event will eventually occur, but it is not necessarily a miracle. It is even possible, although extremely unlikely, to be dealt two royal flushes in a row, but it is not a miracle. I think Littlewood is confusing probability with transgressions of the laws of nature.

The description of "miracle" is tidy, but insufficient. One connotation for "miracle" demands the presence of religion or faith-based associations.

For this to be true, one would have to "recognize" the event as having special significance ... what if an event was specially significant to some but not to others, does that mean it was not a miracle? Or, what if the event was a commonplace event but you deem it to be specially significant to you on any given it still a miracle? Using this definition miracles are subjective to that really the "common-sense" understanding of the word?

If you are a believer, this doesn't hold water. Miracles happen without a mathematical significance and happen as those who believe trust in a higher being decides that a miracle needs to happen.

Aside from the religious notion of a miracle - which I personally believe in - and have received. One miracle a month - is based on the assumption that events only take a second.

Actually, events could on average take say 10 minutes, and under the same mathematical law - that means one miracle every 10 years - which altogether seems more realistic. Does this mean that you could lotto once every 10 years - no way - this that miracle is 1:100 million chance, so that would be once in a thousand years, which means no hope, really.

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