Well, to get decision theory to apply, you have to characterize the situation in terms of a set of well-defined actions, well-defined outcomes, well-defined goodnesses, and you need some meaningful way of estimating probabilities. None of those are objectively given.
It'll actually end up being an overestimate. 20 * 20 * 20 ~ 10000 not 100000.
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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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It's in fact useful for eye-checking many sets of numbers we multiply in practice. It tells us ordering 37 of a $16 product should not cost $100,000 like the computer says, even if you can't do the arithmetic in your head.
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You need to understand the right context in which to use this tool, and its limits, and not take the recipe as an absolute, and check the results against common sense and reality.
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OK, this is great—that’s exactly what I’m calling “meta-rational judgement”! My thesis is that you always need to do that when applying rational methods, and there’s skillsets for doing that, and those tend to be neglected, and it would be good to help people learn them.
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Threading is a nightmare here. See my continuing reply. "Decision theory" isn't the adding-digits recipe, it's the more abstract idea of Peano arithmetic that helps us understand when the recipe might fail or succeed, even though applying the Peano axioms is way too laborious.
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Yes, boo to twitter threading!
End of conversation
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