I think of knowledge as familiarity with facts or formulae; and understanding as the ability to apply the principles of knowledge to new conditions and circumstances. Creativity (I would never limit this term to the arts only) involves understanding and, paradoxically and simultaneously, not knowing; entering a process where ready answers are inadequate to the task, and where the resolution is at first uncertain. You can know a lot about something and be thought to be good at it, yet not know for sure where things are going to come out.
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