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CCC comments on Rationality Quotes September 2012 - Less Wrong
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"I wish for the result of the hypothetical nth wish I would make if I was allowed to make n wishes in the limit as n went to infinity each time believing that the next wish would be my only one and all previous wishes would be reversed, or if that limit does not exist, pick n = busy beaver function of Graham's number."
I can see a genie taking a shortcut here.
— Granny Weatherwax, A Hat Full of Sky.
In short, the genie may well conclude that every m'th wish, for some m (Granny Weatherwax suggests here that 'm' is three) your wish would be to have never met the genie in the first place. At this point, if you're lucky, the genie will use a value of n that's a multiple of m. If you're unlucky, the genie will use a value of n that's km-1 for some integer k...
Alternatively, you'll end up with a genie who can't handle the math and does not understand what you're asking for.