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Francis Bacon on Chance and Superstition

Probability, Coincidence, and the Paranormal

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Humans seem to be a rather superstitious lot — whatever the subject, people are able to develop superstitions around it. People wear lucky clothing, carry lucky objects, and think that they have lucky numbers or days. How do such superstitious beliefs develop and what causes them to be reinforced?

    The general root of superstition is that men observe when things hit, and not when they miss, and commit to memory the one, and pass over the other.
    - Francis Bacon, quoted in 2000 Years of Disbelief, by James A. Haught.

Here we have one of the most important and insightful observations about superstition and superstitious beliefs that can probably be made. What's amazing is that it was made several hundred years ago yet, despite that, most people today are completely unaware of it. Even worse is the fact that rather than be aware of this problem, most people simply succumb to it.

Quite a lot of people report "psychic" or "paranormal" experiences based upon quirky and unusual coincidences that they cannot otherwise explain. They are thinking of an old friend just before getting a phone call from that same friend. They dream about something happening just a few days before something similar does, in reality, occur. Proof of the paranormal?

Not at all — far from it, in fact. The mistake that people make here is that they readily remember such incidents but fail to remember all of the other times where nothing unusual occurs: all the instances when they though of an old friend without receiving any phone calls and all the times they had dreams without anything similar occurring later. If you think of old friends a thousand times over the course of a year and only receive a call from one once a year, that's not a very remarkable occurrence, is it?

Even more interesting is the fact that the unusual coincidences occur far more often than we realize. Not long ago I quoted from a Scientific American article written by Michael Shermer:

    A principle of probability called the Law of Large Numbers shows that an event with a low probability of occurrence in a small number of trials has a high probability of occurrence in a large number of trials. ... In the case of death premonitions, suppose that you know of 10 people a year who die and that you think about each of those people once a year. One year contains 105,120 five-minute intervals during which you might think about each of the 10 people, a probability of one out of 10,512--certainly an improbable event.
    Yet there are 295 million Americans. Assume, for the sake of our calculation, that they think like you. That makes 1/10,512 X 295,000,000 = 28,063 people a year, or 77 people a day for whom this improbable premonition becomes probable. With the well-known cognitive phenomenon of confirmation bias firmly in force (where we notice the hits and ignore the misses in support of our favorite beliefs), if just a couple of these people recount their miraculous tales in a public forum (next on Oprah!), the paranormal seems vindicated. In fact, they are merely demonstrating the laws of probability writ large.
    In a review of Debunked! [physicist Freeman Dyson of the Institute for Advanced Study in Princeton] invoked "Littlewood's Law of Miracles" (John Littlewood was a University of Cambridge mathematician): "In the course of any normal person's life, miracles happen at a rate of roughly one per month." Dyson explains that "during the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month."

These are figures about the statistical occurrence of strange coincidences, the ones we readily remember. Just how much more common are the events that aren't so strange — all of the events that we don't remember because there simply isn't anything remarkable about them? It's unfortunate that Francis Bacon's insight into the development of superstition remains unknown and unrecognized for so long.

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