We know from experience that we understand an idea much better after we have succeeded in teaching it to someone else; and the advent of computers has brought the realization that even more is true: The best way to understand something is to know it so well that you can teach it to a computer. Machines provide the ultimate test, since they do not tolerate “hand-waving” and they have no “common sense” to fill the gaps and vagaries in what we do almost unconsciously....
People often find that the knowledge gained while writing computer programs is far more valuable than the computer's eventual output.
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