The Purpose of Computing
“The purpose of computing is insight, not numbers.” Richard Hamming
In order to gain insight, deep understanding of the source of the numbers is of paramount importance. Until deep understanding of the source of the numbers is attained, the numbers do not provide insight. In my opinion, deep understanding of the source of the numbers is best attained by a bottom-up approach. Merely comparing line, contour, or 3-dimensional plots of some calculated numbers does not constitute either understanding or verification/validation.
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