When I lecture I like to improvise. I prepare notes, of course, the more detailed the more precise I need to be, but my performing instincts are most satisfied when I just go in front of the class with some key points to hit and maybe a few key lines worked out ahead of time. But I did recently make an iconic mistake, repeating the mathematics instructor’s equivalent of the lawyer asking in court a question without already knowing what the answer will be. Improvisation has to be carefully prepared.

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