Miracles and Probability

PartiallyExaminedLife.com has posted a question about the refutation of Hume's argument against miracles - that people are easily mistaken and events can be very surprising just within the range of nature. This is a fine approach for rejecting any particular miracle, and having rejected enough Hume may feel justified rejecting the rest without as close an examination - this is the balance of probabilities he talks about. But common sense is pretty much the mindset of reporters of miracles - they know virgins don't get pregnant by themselves; they know people can't walk on water. That's why events were perceived as miracles in the first place.

I think this 'balance of probabilities' question needs to refer to the statistical measure of 'confidence.' Confidence measures how sufficient the evidence base is. In engineering (my area) we use confidence math to derive a safe life from a few very accurate but hideously expensive tests. We know fatigue is cumulative damage following a log-normal distribution (or certain weibull distributions), but we can only afford a handful of test articles. If we use the test result directly, it might turn out that the test article was unexpectedly at the high-strength end of the distribution, just from the normal variation of materials and machining. This would be a problem.

Confidence calculations come to the rescue by asking what the probability is that the test cases are at odds with the real population. The more test cases, the more likely it is that the sample statistics are representative of the population statistics... A common practice is to assume that by bad luck, we selected a sample that is better. How unlucky? 20:1 are reasonable odds - 95% confidence means your evidence set was a one in twenty oddball. 50% confidence means it could have been higher or lower - 50% is the best guess. 95% is a conservative judgement.

There is a nice example at the very end of Contact by Carl Sagan. A scientist seeks evidence that the universe is a product of mind, and finds that billions of billions of places into pi is a sequence of bits that plots a circle. Is that a miracle, in the sense of evidence for a particular hypothesis? Pi is transcendental, so anything might be in there somewhere - the evidence is what it is; the interpretation requires you to make a judgment of the acceptable confidence level. How likely is it that the evidence before you is badly skewed away from the reality you are going to judge from it? The empiricist answer is 'my life is the life by which to judge reality, and i think it is probably a pretty good aim point' - which we might call 50% confidence.

Pascal's wager argues that this is more of an engineering decision, that some conservatism is required. My experience* is a kind of reverse of the wager - in a sense, I ruined my life irreparably, but somehow lived on, and unless there is something in this talk of resurrection, i find the universe is a total loss at which I had best sneer. I played the first 95% and found it (myself) absolutely empty of meaning and hope, but able to universalise it. Pandora's box opens and hope comes out last because it is the last evil, the one that gets you up in the morning to suffer all the others.

So now, I'm playing the 5% probability - that the evidence is actually worse than the reality and 'it is better to give than to receive' actually, miraculously, works.

* My friends will laugh at this description, and point out that my experience is actually of pretty great health, excellent fortune in my friends, good upbringing, incredible cost-benefit ratios on my work commitments, and a good upper middle class life in a place more orderly than Switzerland and with better weather, with not a moral or physical effort to be seen from me from January to December. Fair enough.

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