Oh, I was thinking about multiplying just two numbers. I guess I don’t follow your question about shadows and so on. If you’re talking about products of any number of numbers, this rule is useless. Maybe we can think of a better example of a roughly-right heuristic.
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Some things we agree about strongly: There are situations in which probability/decision theory works well, and there it can be extraordinarily valuable. In those situations, empirically, people who don’t know the theory often make bad decisions. They should learn the theory!
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Or rather, it's a theory that *implies* all manner of useful imperfect prescriptions, the same way that Arithmetic tells us about the counting-digits trick and also tells us that the counting-digits trick won't always work exactly.
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