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In his book, The Tao of Physics,
Fritjof Capra (one of Erich's heroes) offers the definition,
"Koans are carefully devised nonsensical
riddles which are meant to make the student of Zen realize the limitations
of logic and reasoning in the most dramatic way. The irrational wording
of these riddles makes it impossible to solve them by thinking."
(Fritjof should know!)