Stardate 20030520.1642

(On Screen): In response to my post on the use of induction in religion, Jonathon writes:

Suppose a signal from a star 100 light years away contained the message, in English, (at some obvious frequency) "Steven Den Beste, believe in me." After thoroughly investigating all possibilities of a hoax, you convince yourself the message is not faked. It seems to me there are two possibilities:

1) With enough signals coming from enough stars and treated as English, there is some probability that one of them will contain this message. Call this the "monkeys at typewriters" hypothesis.

2) Your firmly held atheistic belief is wrong. (So is your belief is relativity, but isn't that secondary?)

By the way, by "thoroughly convince yourself," I mean with roughly the same level of investigation you have used to convince yourself of atheism. If you accept "monkeys at a typewriter.." assume that the same signal comes the next day from a different star, and from a sufficient number of stars on consecutive days (and with minor variations in text, "Mr. Den Beste...", "Steverino....", "... "believe or don't believe, your pick" until finally the probability of these messages according to hypothesis 1 becomes untenable.

By the means of this thought experiment, I mean to explore two issues. When you say, that you are convinced of atheism, do you really mean it despite any conceivable evidence? Second, while you are free to not waste your time searching for further confirmatory evidence of your induction, how, given Pascal's wager, do you justify not investing time on disconfirmatory evidence?

While this thought experiment can easily be used to justify agnosticism... I do not see how it (even inductively) can justify atheism.

My conviction about atheism is not dogma, and it is not the case that I would ignore actual evidence which contradicted it. However, I would be highly skeptical and would be far more likely to conclude deception; it would take a lot at this point to convince me were something like this to happen that it wasn't a fake. Being open minded doesn't require you to be gullible.

On the other hand, there's a difference between being presented with disconfirming evidence and merely discussing things which could be considered disconfirming evidence were they to show up. If some sort of "miracle" did actually occur, and if serious examination of it showed that it was genuine, it would then require me to seriously reconsider my atheism. But the mere fact that someone brings the possibility up is less interesting (to the point of outright irrelevance).

If it were somehow shown that someone had traveled faster than light, or that there had been instantaneous communications over a significant distance, we'd have to seriously reevaluate the Special Theory. But merely talking about them doesn't force us to do so. Speculation isn't evidence.

"You should doubt Special Relativity because it would be disproved if someone proved instantaneous communications!" To which the only answer is, get back to me when you've actually done it. In the mean time, I've got more important things to worry about.

Equally, Jonathon's thought experiment does not in fact justify agnosticism. The things he describes would be disconfirming cases if they arose, but based on my current evaluation of the situation they're also so unlikely as to be unimportant, and it is not worth my time to actively work to seek them out. If they come along, I'll pay attention. Until then, I'm not going to worry about the possibility.

But he raises a larger question: when using induction, when should you act? When do you feel as if your conclusions are sufficiently reliable to actually begin to base policy on them?

Oddly enough, induction also deals with that for most of us, and what we derive about various conclusions isn't an actual likelihood that they're true as much as a conviction about whether we should use them in our concrete plans.

The process of evaluating the reliability of uncertain conclusions is not easily subject to methodical analysis, but it turns out that game theory has heavily analyzed the latter problem. One of the interesting results of that is that the metadecision to base decisions on a given conclusion is not based on whether the certainty of that conclusion exceeds a single fixed threshold. Rather, it's based on an analysis of costs and benefits, and there will be cases where you may act on a 10% chance and not on a 90% chance.

The original process was created as part of analysis of how one decides whether a given form of wager in gambling was a "good bet". Any single wager in a game, or a short sequence of them, will have results which are impossible to predict. But there's a phenomenon known as "regression to the mean" which says that the overall cumulative result becomes more and more predictable as the number of wagers involved increases. You may not be able to predict whether you'll win money or lose money if you spend ten minutes playing Craps, but over the course of a week the casino itself can make a very good guess as to how much money it will make as a function of how much gambling is going on and what stakes are involved.

The basic calculation determines the average payoff one would expect over a very long sequence of wagers, and compares that to how much each wager would cost you. For instance, if you have a 10% chan