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ArisKatsaris comments on The self-fooling problem. - Less Wrong Discussion
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All those are complications that needn't arise with a slightly different formulation. Just imagine that we're talking about someone who for fun decides to put such a challenge to their future self.
Anyway, we can postulate a person who hides something as best as they can, then they erase their own memory, then they decide to locate what they previously hid. Both hider version and searcher version try to do the best they can, because that's the maximum amount of fun for both of them. (The searcher will reintegrate the hider portion of their memories afterwards)
I recall something like this coming up a few times in fiction - someone erases their memory of something because they need not to know it for a time; then, later, must re-discover it.
Memory Gambit.
Thank you.