Coincidences: (not particularly) funny things

The Skeptic, 9.5

For some people, coincidences are weird, spooky and far-out: windows into a deeper level of reality, a glimpse of unseen connections between apparently unrelated parts of the Universe. I say that coincidences are a pain in the bum.

If I may explain, and recount the recent incidents. There are 5.

Number 1. I am driving from Manchester to Fort William. Although I love him dearly, after four hours of Van Morrison tapes I can't stand to hear another note. I turn on the radio, and it searches for the strongest local station. After a few sconds of silence I suddenly hear a familiar voice. It is Steve Donnelly, my Skeptic co-editor. I am so surprised that I spin around, expecting to find Steve inexplicably crouched in the back seat. He isn't. But he's live here on Radio Scotland, at the moment I happen to have switched it on.

Number 2. A colleague discusses a new software system he is developing, called 'MAVERIK'; Ten minutes later I receive email from a friend in the USA reccommending a new pop group he has discovered: 'The Mavericks'; on the way home that evening I find myself behind a 4-wheel drive vehicle with a spare type labelled 'Maverick'; two minutes later the word 'Maverick' is spoken on Radio 4's 6pm news.

Number 3. I receive email from someone I have never met, a BBC radio producer. He has been searching the Internet's World Wide Web for his own name (a new Displacement Activity for the 90s). Instead of finding himself (metaphorically speaking) he has found me. He has four given names, and the first two are Toby Howard. We communicate. This other Toby is a member of the Association of British Science Writers. So am I. The other reads The Skeptic, co-edited by... myself.

Number 4. I am trying the Guardian Crossword, with the radio on in the background. I scan the clues but can solve only one. At the exact moment I start to write in the solution -- 'united' -- that same word is sung by the band on the radio.

Number 5. I sit down to write this column, with the idea to mention these recent coincidences, and say something suitable skeptical about them. I take a break to look at The Skeptic's postbag. The first letter I open is from parapsychologist Susan Blackmore of the University of the West of England. Sue sends a copy of a paper she has co-written with Robert Matthews of the Department of Applied Mathematics at the University of Aston, suggesting that The Skeptic might find it interesting. The paper's title? 'Why are coincidences so impressive?'.

My examples are, of course, puny. I'm sure you have your own, or perhaps know of some of the more famous ones: the top-secret code-words OMAHA, UTAH, MULBERRY, NEPTUNE and OVERLORD all appeared in the Daily Telegraph crossword printed in the month preceding the 1944 Normandy landing; the incidents in 'Midwife toad' faker Paul Kammerer's diary of coincidences, heartily endorsed by Arthur Koestler in his Roots of Coincidence (Hutchinson, 1972), Jung's widely-reported 'scarab beetle' experience, and so on.

The 'coincidence' is a chimera of the first order. Even a superficial analysis -- which I will omit -- of the five experiences mentioned above -- would show that they are not very surprising at all. But many people rarely undertake such analysis, preferring instead of remember the 'coincidence', and to recount it as an event only slightly less important than a Miracle. However, I can be as skeptical as James Randi watching a spoon bend, and still stand around fulminating at these damned 'coincidences'. Their cosmic significance lies entirely in the fact that they get on our nerves.

In their paper 'Why are coincidences so impressive?', Matthews and Blackmore try to pin down why people suffer 'coincidences'. They cite the well known 'Birthday Paradox', in which one is asked to estimate how many people it would be necessary to assemble to give even odds that at least two people present share the same birthday. The answer, extremely surprising to most people who haven't heard it before, is 23 (see Chip Denman's article 'Lies, Damn Lies and Statistics', The Skeptic, 9.4 for details).

But why is it surprising? Because, suggest Matthews and Blackmore, our mental models of how likely events are to occur are, quite simply, wrong. They propose a measure of this wrongness, called the 'astonishment factor', defined as the ratio of our mental prediction of the likelihood of some event occurring, and the mathematically computed predicted likelihood. They conducted trials with 124 subjects, presenting them with a series of questions based on a generalisation of the Birthday Problem, asking them to estimate how many people (N) would need to be present to give even odds on at least two belong to the same one of a number of differnt groups (G). When the average results were compared to the correct mathematically computed values, it was found that the mental models used by the subjects were linear. For instance, if the number of groups G, doubled, so would the estimate. The correct mathematically derived prediction, however, increases as the square root of G.

The 'coincidence' is a ghost: a shadow of mismatch between our mental models of probablilities, and actual probablilities. But ghost or not, it is still a pain in the bum.