The Improbability Principle: Rare events and coincidences happen all the time.

Five Reasons Why Absurdly Improbable Things Happen All the Time

Five Reasons Why Absurdly Improbable Things Happen All the Time

The state of the universe.
Feb. 12 2014 12:59 PM

It’s Not Actually a Miracle

Five reasons why absurdly improbable things happen all the time.

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That strand of the principle that I call the law of near enough says that events that are sufficiently similar may be regarded as identical. So how does that increase my chances of meeting other people with my name? After all, however you cut it, surely I don’t have many opportunities to meet other David Hands?

Well, actually, I didn’t meet someone else with my name. It was the hotel receptionist who spotted the identical names. So it wasn’t quite me meeting them, but it was near enough to be identified as a coincidence. The difference between me meeting him, and the hotel receptionist spotting the names, is dramatic. Suppose I check into hotels 20 times a year, and that over the course of a week 400 people check into each hotel. That’s 8,000 opportunities for a receptionist to spot the match. That’s far more than the relatively few new people I meet personally each year.

What if we combine this with the law of truly large numbers? This says that, given enough opportunities, the probabilities of even very unlikely events can mount up to be almost certain. I’ve been attending conferences for several decades now. The number of opportunities for such an encounter is starting to build up.


The law of truly large numbers is amplified by a subsidiary law, the law of combinations. I’ve been talking about the chance that another guest would have the same name as me. But what’s the chance that some two or more guests in the hotel will have the same name as each other? The answer depends on how many people there are with each name. In the United States, for example, there are some 50,000 John Smiths, about 1,000 James Bonds, and approximately 100 Harry Potters. And, for the record, about 300 with the name David Hand. Just to show how the law of combinations can have a huge effect, I’ll simplify and suppose there are 50,000 names in the population, and that the same number of people have each name. Calculation shows that if just 263 check into a hotel, then it’s more likely than not that at least two of them will have the same name. No wonder highly improbable events are commonplace!

Things are further amplified by another manifestation of the law of near enough. Sure, I knew of two other people who had been named “David Hand,” but were they David J. Hand? In fact, the Disney animator was David D. Hand, and the former bishop of Papua New Guinea was G. David Hand. Not an exact match, but near enough for me to be struck by the coincidence. Indeed, no doubt the hotel receptionist would also have noted it if the other David Hand checking into the hotel had been David Hands, not David Hand, or if he’d been Daniel Hand or Donald Hand. In each case it would have been near enough to make the receptionist sit up and take notice—to regard it as a coincidence. Every time the law of near enough comes into play, it increases the chance of a (near) match, and makes it more probable that one will see a coincidence.


So the various laws of the improbability principle work in concert to make it quite likely that encounters between two people who have the same name will occur. It’s not surprising at all: Extremely improbable events are commonplace.

That’s all very well, but it’s a bit harder to explain the coincidence of the two Dennis the Menaces.

On March 12, 1951, issue No. 452 of the British comic The Beano appeared on the streets. Inside it was the first appearance of Dennis the Menace.

A few hours later on the same day, but on the other side of the Atlantic, a syndicated comic strip was launched in American newspapers—you may see it even today. The character was called Dennis the Menace.

Fair enough, you may say: a simultaneous (allowing for time differences) launch of the same cartoon character—except that the British Dennis the Menace was drawn by David Law, and the American one by Hank Ketcham, and they’d never heard of each other’s creation before.

The two Dennis the Menaces could hardly be more different. The British one has spikey black hair, an evil grin on his face, wears short trousers, and causes all sort of mayhem. You will get the picture when I tell you his dog (who joined Dennis in 1968) is called Gnasher. The American one has smooth blond hair, wears long trousers, and often embarrasses adults by virtue of his innocent honesty. His dog is called Ruff.

The simultaneous but unconnected appearance of these two characters, with the same name on the same date on opposite sides of the Atlantic, seems to be just one of those extraordinary coincidences. Except ... when such coincidences occur, out of the countless billions and billions of things going on around us every moment, we notice them. We abstract them from the boiling noise of random events and say, “Hey, look! What an extraordinary coincidence!” Coincidences are as much a feature of the human mind as of the external world.

All this talk of matching names reminds me of the old joke about the controversy of who actually wrote Shakespeare’s works. It’s been suggested that it wasn’t William Shakespeare at all, but another person with the same name …