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Alexei comments on Tendencies in reflective equilibrium - Less Wrong
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I don't think it really matters at that point. I would not treat the situation differently if the mugger said "3^^^3" or if he explicitly stated some number "34084549...843".
I don't think you are appreciating the complexity penalty of the (presumably not very compressible) data hidden behind that ellipses, if the number is meant to be on the order fo 3^^^3.
Well, see, I would disagree with your presumption. The data might look random to you, but I could just point out that all the digits are actually taken from PI, starting with 3^^3rd digit. That simplifies the complexity tremendously. Or I could say I got those digits randomly. That again simplifies the complexity, because generating that number was simple.
If my presumption that the digits are not very compressible is wrong, then you have not really responded to Daniel's point about the ridiculous roundness of the number (where roundness is one way a number can be compressible).
No. Getting "random" digits is not simple, or even an available action, for a deterministic generator. Saying to get "random" data can feel simple because you are just pointing at some source of data that you are ignorant about, but really, you have to account for the complexity of that source of data.
I would pay $5 to not have to listen to the mugger explicitly state a number that long.
I once offered a similar deal to a tuba player on a subway platform.