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Kaj_Sotala comments on Stuff That Makes Stuff Happen - Less Wrong
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The only trouble I see is that "koan" makes it totally okay to think about it for a while without finding the answer, while "puzzle" might cause people to propose solutions.
Given that most people seem likely to look at the koan and think "yeah, I could solve that if I thought about it for a while" and then move on without actually thinking about it, anything that actually gets people to think about it seems like a good thing.
The only trouble is if people then have to unthink things, which humans are notoriously bad at :P