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Perhaps, Feynman has answered Peter's question?
Omni: Do physicists vary greatly in their ability to see the
qualitative consequences of an equation?
Feynman: Oh, yes — but nobody is very good at it. Dirac said that to
understand a physical problem means to be able to see the answer
without solving equations. Maybe he exaggerated; maybe solving
equations is experience you need to gain understanding — but until you
do understand, you’re just solving equations.
alphonsus