Vivid guesses

This passage from Polya's How to Solve It makes a nice companion to the earlier quote from Dwight Eisenhower on planning.

I do, however, have one criterion that I think Polya needed to add. In addition to attentiveness, understanding and interest, to get guesses of real value, the guesser needs independence. If your thinking simply follows the tracks laid down by other, you're probably wasting everyone's time.