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Manfred 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
People have already been proposing solutions to the "koans", and I don't understand why that's a bad thing.
The goal is to apply those algorithms we call "rationality" towards solving the koan, one of which involves withholding even just mentally formulating solutions as much as possible, and instead just thinking about the elements and properties of the problem properly without subjecting oneself to hack heuristics.
The word puzzle is, for most people, loaded with a trained impulse to shoot the first solution-sounding thing that pops to mind so that you can see whether you get a hedon / tribal status coin for a good answer or not.
Alright. I see where you're coming from, though I doubt that "puzzle" and "koan" have as many deep connotations as you claim.
Maybe the right thing to do is to actually write something to the effect of "Here is how you should be approaching these puzzles/koans"?