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Decius comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong Discussion
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Heat death is a problem that the builders of the game have to deal with. Every time I type out BB(BB(BB(...))) the builder of the game has to figure out how I can get a noncomputable increase to the degree of the function by which the multiple of my preference for the world increases. If there is some conceivable world with no heat death which I prefer any computable amount more than any world with a heat death (and infinity is not a utility!), then by playing this game I enter such a world.
Not if your current universe ends before you are able to finish specifying the number. Remember: you receive no utility before you complete your input.