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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Replying to @ESYudkowsky @Meaningness and
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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OK, another attempt at finding a crux. For you, decision theory is THE TRUE framework, according to which any practical method must be judged. For me, it’s just one bit of math among many, with no special value.
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I'm not sure what you mean by "THE TRUE" here. I'm tempted to reply with https://arbital.com/p/expected_utility_formalism/?l=7hh … to explain what makes this math so specially relevant to decision-making and belief, but I have a dark presentiment that's not what you mean.
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I’ve just now read the first bit of that, which is the Dutch Book Argument, so we’re back to where we started… maybe twitter needs a circular thread mechanism :)
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I didn't think DBA appeared there until later? Anyway, from the end: "We have multiple spotlights all shining on the same core mathematical structure, saying dozens of different variants on, 'If you aren't running around in circles or stepping on your own feet or...
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Replying to @ESYudkowsky @Meaningness and
...wantonly giving up things you say you want, we can see your behavior as corresponding to this shape. Conversely, if we can't see your behavior as corresponding to this shape, you must be visibly shooting yourself in the foot.'"
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So, my rephrasing would be something like: if a situation behaves in a way such that probability/decision theory works well when you apply it to that situation, then you should definitely do so. Which I agree with! It’s great when it works! In most situations, it doesn’t apply.
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But when is it that you can't apply it?(By applying it I mean approximating it). What heuristics or methods are there that are superior to DT sometimes that are not approximations of it?
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Oh! After brushing my teeth and before I forget :) maybe this is helpful: When designing an airplane wing, use finite element analysis, not DT. Implementing a network protocol, use a parser, not DT. In hydrology, use percolation theory, not DT.
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