When? Academic learning isn't at all bad, but those two examples are a very poor choice. Measuring computational complexity at all well requires far more than order notation (and perhaps more than graduate level computational complexity theory). Performance modeling remains a poorly understood and active field of research, and the gains are being made quite slowly.
So in practice, the concept of "P vs NP", and order notation are largely useless. "Polynomial space/time" explodes quadradically for a polynomial as low as two! The choice of P vs NP boils down to "too slow to be workable" versus "really too slow to be workable". The exception, of course, if the constants are nice, and N is small enough to be workable: but that's exactly what order notation and most computational complexity theory ignores in the first place!
Personally, I found that while academic learning is interesting, it's rarely useful. It's nice that you can write your own compiler, but your job will involve producing graphs and reports, not writing compilers. And when and if some of that deep, complex academic learning is required, your company will just hire a PhD: so unless you're willing to give your life to CS theory, there's no great benefit to a mere undergrad degree. Perhaps that's why there's so many open source languages: people desperate to find an excuse to write their own compiler, now that they've wasted thousands of dollars learning how!
One guy I worked with was so desperate to do something "academic" with his job that he wrote his own recursive descent parser ... for a configuration language that he invented himself ... for an EBICDIC to ASCII translator ... which only needed a very limited set of options ... and which never actually changed. But hey, he got to be all "academic"; and now I've got a tonne of painfully useless code to untangle if I ever have to maintain his over-engineered monstrosity.
Back in school, I took a lot of courses in things like multidimensional calculus, vector algebra, and group theory. None of it is terribly useful for producing billing reports and the other assorted drudge work that actually pays the bills. In some sense, I understand why my co-worker decided to waste company funds on his wierd design; but I certainly can't condone it.
In any case, I've been left with a distaste for breathless undergrads, and people who think that "more complicated is better", or people who think "new is better": most of the time, the boring, obvious encoding is the most maintainable encoding, and when it's not, you can at least understand what was done, and slot in your clever little algorithm where it's needed.
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Re^5: Worst blog post ever on teaching programming
by adrianh (Chancellor) on Apr 06, 2006 at 08:30 UTC