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fractalman comments on Truly Part Of You - Less Wrong
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I don't think you've understood the article. The idea of the article is that if you're able to derive it, then yes, you can regenerate it. That's what 'regenerate' means.
I think nominul does understand it, and at one level higher than you do. he understands the principle so well he goes and makes a tradeoff in terms of memory used vs execution time.
Take a symetric matrix with a conveniently zero'd out diagonal... you could go and memorize every element on the matrix....(no understanding, pure rote memorization).... you could go and memorize every element AND noticing it happens to be symmetric...(understanding, what you seem to be thinking of...) Or noticing it happens to be symmetric and then only memorizing half the entries in the first place(nominull's approach).
I go with nominull's approach myself...I'm just a lot sloppier about selecting what info to rote memorize.