A koan is a (very) short story, dialogue, statement or riddle written to encourage thought and self-reflection. This is a tradition appropriated from Zen Buddhism, but they probably don't mind. A typical koan might be a nonsensical question such as:

What is the sound of one hand clapping?
This is one of the most widely known koans, for good reason: it's brief, it sounds metaphysical while making no real sense, and it has no right answer (although Saint Terry Pratchett has attempted to answer it "cl".) In this form, however, it is unpolished. The koan can be made to sound wiser by framing it as a dialogue between some feudal-era Chinese monks, especially a novice making a supplication to a master:
Yiqing asked Yuanjian, "What is the sound of one hand clapping?"
The dialogue may go on for several more lines or it may end there. Ideally it ends with either the novice becoming enlightened, or the master hitting the novice with a stick. Occasionally one of them will do something like put his shoes on his head, empty a bottle of perfectly good wine onto the ground, or murder a cat.

For even more wisdom and philosophical depth, the koan should be curated by a later (but still many centuries old) Zen monk, who adds his own commentary in the form of footnotes. These should be convoluted, full of weird metaphors, and hard to understand – but clearly derisory:

Yiqing asked Yuanjian, "What is the sound of one hand clapping?"1
Yuanjian put a shoe on his head and hit Yiqing with a stick.2
Yiqing was enlightened.3
1. A stupid question. The radish cannot comprehend the turnip, but they are both fools!
2.Oho! Like a dog trying to bite its own mouth, Yuanjian's response conveys no understanding of Zen.
3. Was he bollocks.
Occasionally this is capped off with a short verse:
One hand that claps
Makes such a din
I had to put
One earplug in
Try creating your own!

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