Tuesday, October 20, 2009


Sometimes things happen together. An act of seemingly miraculous coincidences. And to the casual observer, it seems almost as if there must be some reason, some hidden cause, something special about the individual to whom the coincidences are happening.
Having just had a day rather like that, I want to remind you all that coincidences happen! And in fact, the biggest coincidence would be if there were no coincidences at all.

In mathematics this sort of thing abounds. For a start, randomness often surprises us with how structured it seems. For example, the classic "birthday paradox": if you have at least 23 people in a room (chosen randomly, say) then the odds are slightly better than even that two of them will share the same birthday. This result is easy to prove, but surprising to most people when they first see it --- 23 seems like a remarkably small number of people, given that there are 365 days in the year.

To take another example: you can never destroy all structure, no matter how hard you try: if you list the numbers from 0 to 100 in any order you like, you will always find either a subsequence of at least 11 of them in increasing order, or a subsequence of at least 11 of them in decreasing order. Not necessarily together, but... Why 11? It turns out that that is the best that you can do.

So, next time life hits you with a series of coincidences, don't assume that it is because you are somehow favoured, and don't go out and play the lottery because "good things come in threes". Far more often they come in twos or ones, and it's just that you notice the threes....

Yours, as it happens,


awareness said...

Oh, Ok..... but some things out there aren't explainable. Or maybe I'm just a Pollyanna who wants to believe in Jungian Synchronicity.

did you ever read The World According to Garp? In the story, Garp and his wife are out looking for a house to buy. While they are checking one out, a plane crashes into the side of it. Right then and there, Garp decides to buy that house because he figures the odds are that a plane will never hit it again. That scene cracked me up, and obviously stayed with me for YEARS.

BreadBox said...

I scored a free copy of Garp when they decided to give away thousands of copies in the UK as a promo deal. I loved, and still do love, the book.
The equivalent joke, by the way, is of the nervous flier who always carried a bomb on a plane, on the grounds that the odds that a plane would have two bombs on were miniscule.

Of course, the correct perspective is that the odds of a plane crashing into any particular house are miniscule. The odds of a house being hit for a second time, given that it's already been hit, are the same as the odds that a house in another town will be hit (not really --- a house that has been hit has been exhibited to be on a flight path, in a slightly riskier area, etc.... -- but the truth is still reasonably close to what I said)