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Francis Bacon on root of superstition

(If you spot any errors (in my maths, for example) let me know)

Francis Bacon (1561-1626)

The general root of superstition is that men observe when things hit, and not when they miss; and commit to memory the one, and forget and pass over the other.

Bacon is a pivotal figure in the development of the modern scientific method. Here he puts his finger on a common error, an example of selection bias.

Consider these anecdotes:

“Joan was thinking about Mary, whom she only thinks about rarely, and whom she had not heard from for a year. Later that same day, Joan’s phone rang, and it was Mary! Joan is clearly psychic!”

“It looked as if John would die, but I prayed he would get better, and he did. God answered my prayer!”

Such anecdotes can appear to provide compelling evidence of psychic abilities and supernatural events, particularly when many are collected together in a book or article. But do they supply good evidence of such supernatural phenomena?

Let’s focus on the first anecdote for a moment. Let’s focus on the first anecdote for a moment.

Suppose each of us knows five people we think about rarely – only five times a year, say - and from whom we hear only, say, once a year. Suppose each of us also knows 10 people very well. These aren’t implausible averages, I’d suggest. And they entail that, on average, within roughly any 7 and a bit year period, one such coincidence will happen to one person you know very well, and to ten of the people whom you know very well know very well.

Because such coincidences are dramatic, they make memorable stories. It is hardly surprising, then, that we should hear such stories told and retold even by people whom we know very well and whom we have every reason to suppose are being accurate and honest. But then the fact you have heard a handful of such stories does not provide you with any evidence of psychic powers.

Our mistake is to focus on the few “hits”, the coincidences, and forget about the many “misses” – all those occasions on which people thought about someone they rarely think about whom they haven’t heard from in years, who didn’t then immediately get in touch with them.

We should be similarly wary about the second anecdote. Given the huge numbers of sick people prayed for daily, it’s hardly surprising if a few make astonishing recoveries. We should expect this by chance. If we ignore the “misses” – all those occasions on which sick people were prayed for but they experienced no astonishing recovery, and focus only on the “hits”, the small proportion of occasions the person recovered, we can, again, easily convince ourselves that that we have evidence of the miraculous efficacy of prayer.

Of course, none of this proves that people don’t have psychic powers, or that miracles don’t happen. But it does explain away much of the evidence on which people base their belief in such phenomena.


I'm still waiting for a car accident victim to grow a new leg

and to 55 of the people you know quite well know quite well.
jeremy said…
My impression:

I'm not sure the math's is right for the rare friends, and I don't think we have enough information for the people we know quite well.

By my reckoning, the average time you'll wait for the coincidence of (a) thinking about someone and (b) hearing from them the same day, is given by the formula:

(Likelihood of thinking about them on any particular day) x (Likelihood of hearing from them on any particular day)

So for one "rare" friend this would be (5/365) x (1/[3*365]).

This means that you would achieve this coincidence, on average, once every 219 years! Of course if you have five such friends, you would divide this waiting time by 5 to get to the average waiting time for this coincidence to occur with ANY of them (=43.8 years).

For the second instance, the friends you know quite well, I don't think you've given us the value for how often you'll (a) think of them or (b) hear from them.

If you use the SAME ratios (which would be odd, since you'd expect the ratios to be much higher for the latter cases), then one such coincidence would occur every 3.65 years, by my calculations.

(I think?)
jeremy said…
Also, I'm not a stastician, but wouldn't what Bacon was talking about be more an example of "recall bias" (and/or "confirmation bias") than "selection bias"?
Stephen Law said…
Jeremy - I have fixed it up a bit. The maths was done v quick on back of an envelope (literally). I THINK this is right now.

It doesn't matter how often I think of or hear from friends I know quite well, does it?

I will cut "selection bias" as it is not explained. It is a variety of, depending how you define "selection bias".
Steven Law said…
I was in a motorcycle wreck and sustained a Grade 3 Open Fracture with complete dislocation of my ankle 10 yrs. ago. My surgeon told me one patient in ten thousand with this injury walks again. I am that one. Refuse to lose was and is my mantra. Salvation, as does Damnation, lies within.
Steven Law said…
In my opinion, to pray is simply directing the Will to an end. I think John got better because he willed himself so. If you give up on yourself you truly have no place left to go. People who succumb to illness have given up the struggle. Medical history has numerous "miraculous" recoveries that can not be physically explained. They can only be attributed to triumphs of the will.
Anonymous said…
There's another kind of superstition which is based on attributing magical powers to amulets, through the LACK of contrary evidence. For example, "I've always carried the picture of Virgin Mary with me, and nothing bad has happened to me, therefore it has special power."

When I formulate it like this, it seems absurd, but this is just a rephrasal of the classic induction mechanism employed by science. "All ever performed experiments have shown this result, therefore this result is scientifically valid."

David Hume was first to point out this logical fallacy but scientists have not listened. To this day they are talking about "laws of nature" and "physical constants" even though technically this is just a form of superstition that the future will be like the past.
jeremy said…
"And they entail that, on average, within roughly any 7 and a bit year period, one such coincidence will happen to one person you know very well, and to ten of the people whom you know very well know very well."

Oh, sorry, I now see where you were going with the "friends you know very well" - I misunderstood you.

Running the numbers really does blow your intuition out the water, doesn't it? In reality, the net is made even wider by the looseness with which we judge such 'hits'. I'd bet it doesn't have to be the same day, does it? Dreaming of them the night before would probably be included, as would receiving an email about
them, rather than from them, etc. All this would make such coincidences almost highly probable!

(I think you need to delete the last phrase though?)
Steven Law said…
Does not perception override fact? Is not selection bias the same as that which one wishes? Selective memory chooses the reality one wishes was so. Don't we all rationalize our own reality? Don't we disregard the distasteful and yearn to believe the beautiful? To stare at the grotesque is to tremble at the possibility it exists within ourselves, a thought which unnerves us.
Stephen Law said…
oh sod it. there is a flaw. the people whom those you know well know well will include no doubt, a significant number of those you know well. So 10 is too high.
Steven Law said…
The thought of selective bias is not flawed. I beleive it exists. Every human thought is 100% subjective, created by our personal frame of reference and colored by our personal experiences,prejudices,and wishes.Bacon and Newton and other thinking men back then were seeking an understanding of their worlds, a scientific search for rational explanation. The search could go anywhere and everywhere. At that time superstition must have been prevelant. They looked at superstition as a possible truth, but of course cannot disprove it exists. Who can say for sure?
Andrew Louis said…
this follows the multiplicative law of probability, i.e. we want to know the pobablity of two independent events, taking place at the same time is.

if you have one friend that you think about 5 times a year (365/5) that means the probablity of thinking about that person is 1.37%.

If that particular friend calls you once per year (365/1), the probability of that person calling you is .27%.

The probablity of those two events taking place at the same time is 1.37% * .27%, which equals .00375%, or once every 26645 days.

For 5 people, you simply multiply 1.37% by 5 to get 6.85%, and 5 by .27% to get 1.37%. From there the odds of thinking about one of these 5 friends and them calling is .094%, or once every 1065 days.
Andrew Louis said…
Now, if you know 10 people who fit this bill, you follow the addative law of probability (two events are not mutually exclusive).

i.e. if you know 10 people whom the probability of this event happening to them is .094%, what is the probability of this happening to at leat one of them at any given moment.

For this you do the following.
You sum the probabilities, .095+.095+.095.... (or .095% * 10) and subtract from that the probability of them happening together, which is, .095*.095*.095.....

.095% * 10 = .95%
.095*.095*.095..... = essentially 0

You are essentially looking at this happening once every 105 days, or 3 times a year within the 10 people you know.
Andrew Louis said…
I'm realizing that I put 365 over 5 and 356 over 1. Sorry for the confusion on that one.... Nonetheless, the math should be correct
Anonymous said…
'facts are the idlest of superstitions'

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