Written: March 24, 1998
What is the difference between a good Bar-Mitzvah chanter and a bad one? Neither of them understands a word of what they are saying, since in the typical American Hebrew School you don't learn the meaning of Hebrew words, only how to pronounce and chant them. The good chanter is just a better parrot, he memorized it better.
The same is true about the difference between an A student and an F student in calculus. Neither of them has any clue of what it all means, or what it is a good for (except for getting into medical school). The A-student just knows how to repeat faithfully what the teacher did on the blackboard.
But, wait a minute. If we go one, or perhaps two notches up, to the meta or meta-meta level, then we, professors, (with the possible exception of such giants as Godel, Chomsky, and Turing), are also like Bar-Mitzvah kids. We are just proving yet another theorem, or designing yet another algorithm, or even creating yet another theory, but we have no clue about the BIG picture, if you make BIG big enough.
To get a glimpse of what IT all means, try to teach it to your computer. Even if you fail, at least you have transcended one level up: from letters to words, or from words to phrases, or from phrases to sentences....