Probability

We all know co-incidences happen. At what point should the person, who discovers one after another, such as numbers/names/colours, which all link together, turn and say: There must be more behind these co-incidences and I shall find out, what it is all about?

Comments

There's no simple answer to this question, but there is a caution: both common experience and a good deal of psychological work suggest that we have a strong tendency to project patterns onto random events. We also tend to notice things that interest us and ignore things that don't. And remember that it is overwhelming probable that some improbable events or other will occur. A single run of ten heads in a row on flipping a fair coin has a chance of 1 in 1,024. But if lots of people perform the same experiment, it becomes nearly certain that someone will get 10 heads.

Still, some apparent coincidences do seem to call out for explanation. Without offering a full-blown story of how this should work, here are some thoughts. First, do you have a hypothesis in mind? Casting around blindly for an "explanation" may not get you very far. Second, would your hypothesis really make what you noticed that much less surprising? Or is what you noticed the sort of thing that might well have happened by chance anyway? Third, has your hypothesis been gerry-rigged to fit the data? If so, it's no surprise that the data "confirms" it. Fourth, would your hypothesis really explain the data? Saying that the "explanation" for the facts is magic or ESP doesn't really give us much insight. Finally, how wild is the hypothesis? A low "prior probability" for the hypothesis means that it has to make the data quite a bit more likely than the alternative before the data do much to confirm it. That's why conspiracy theories are usually not credible. Ordinary human screw-ups call for far fewer moving parts.

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