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© Copyright 2002, Jim Loy
Coincidences happen often, as probability theory says they must. If you flip a coin many times, you must get several heads in a row every once in a while, and several tails in a row every once in a while. If you flip ten times, you should not get ten heads. But, if you flip millions of times, you should almost certainly get ten or more heads in a row, more than once. And, when it happens, it seems amazing, and makes people believe in miracles or psychic phenomena.
Let's say that I was thinking of my mother, and then she called me on the phone. Amazing? Telepathy? Probably not. It is very difficult to calculate just how rare such an occurance is. How often do I think of my mother, when she didn't call? I may not remember such occurances. I probably will remember the coincidences, and forget (or not notice) the more mundane times, and so my memory of the coincidences makes a biased sample. How often does she call, when I didn't think of her? How long was it between when I thought of her, and when she called? If several days or weeks have gone by, will I still be amazed at the coincidence. Also, just how close does my preconception have to match the event? Maybe I am amazed that I was thinking of my mother when my brother called, or when someone else called and we talked about my mother. All of these factors complicate the possible study of coincidences.
A teacher has his students generate some random data, and then hand it in. The teacher can then tell who cheated, who pretended to generate random data by making it up. People are not good judges of random events. Their made-up data in no way resembles random data. This teacher is familiar enough with random data, that he can usually tell the bad data at a glance.
Let's say that you go to a party, and you find that two of the people there have the same birthday. Is that amazing or what? Well, if there are 367 people at the party, then there are certainly at least two people there with the same birthday. I suppose that some people would still be amazed at this sure thing. What if there are only 25 people there? Should you be amazed to find that two people have the same birthday? Doesn't it seem that this would be an amazing coincidence? No, if there are only 23 people there, the odds are better than even (.5) that two people have the same birthday. It is difficult to judge coincidences.
And people convert to belief in ESP, or astrology, or whatever pseudoscience or fraud that they happen to encounter, by some seemingly miraculous coincidence. And they are not competent to judge if it is miraculous or not.