It is a small world, isn’t it? You are on holiday in the Pyrenees. You write a postcard to a friend at home and set off to post it. Then who should you meet but that same friend coming up the street. This not only saves you the cost of a stamp but it also provides a great holiday story – enough to make you think that something spooky is going on.
Similar coincidences happen all the time to someone, somewhere, making the plot-driving inventions of Charles Dickens seem almost plausible. Normally we statisticians deal with the dark underbelly of risk – accidents, deaths, disasters, general gloom and doom – but coincidences show the bright, fun side of the way chance plays out in our lives.
We should perhaps begin by exploring what exactly is a coincidence. It has been defined as a “surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection”. Earlier this year, I invited people to submit examples of surprising concurrences to my website, and looking at over 3,000 of these extraordinary stories, it seems that they tend to fall into certain categories.
A chance event may be two things that happen at exactly the same time, for example, a parent and child whose letters to each other crossed after 37 years without contact. Or it could be meeting a familiar figure in some unexpected place, or finding some unexpected extra connection, such as the engaged couple who found they had been born in the same bed. Or it could feature objects: such as buying a second-hand picture frame in Zurich, and finding in its lining a 30-year-old newspaper cutting containing your own photograph as a child, or being on holiday in Portugal and finding a coat-hanger that belonged to your brother 40 years previously.
Forces at work
Why do these extraordinary events happen? Various strange forces have been put forward. Austrian biologist Paul Kammerer proposed that coincidences arise from a basic physical force, called “seriality”, though he dismissed as superstition any supernatural ideas that could, for example, link dreams to future events. In contrast, psychoanalyst Carl Jung revelled in paranormal ideas such as telepathy, collective unconscious and extra sensory perception, and coined the term “synchronicity” as a kind of mystical “acausal connecting principle” that not only explains physical coincidences but also` premonitions.
More mundane explanations are possible, though. First, some kind of hidden cause or common factor could be present – maybe you and a friend have both heard that the Pyrenees is a good place to go on holiday? Psychological studies have identified our unconscious capacity for heightened perception to a recently heard word or phrase, so that we notice when something on our mind immediately comes up in a song on the radio. And of course we only hear about the matches that do occur, not all the people you have spoken to with whom you had nothing in common, and indeed were pleased to get away from.
Simple chance can be a strange and unintuitive thing that throws up surprising concurrences more often than we might think, since truly random events tend to cluster – if you throw a bucket of balls on the floor they do not arrange themselves in a nice regular pattern. This produces some fairly brain-mangling results. For example, it only takes 23 people in a room to make it more likely than not that two have the same birthday.
Calculating coincidences
Don’t believe me? There is some nice, fairly simple maths that allows you to work out how many people you need to have a good chance of a match for any characteristic. Suppose that any two people have a 1 in C chance of matching – for example, for an exact birthday match, C = 365. Then to have a 50% chance of a match in a group of N people, it turns out that N needs to be around 1.2 √C. For a birthday match, this means that we need around 1.2 √365 = 23 people.
