Thinking along the lines of the in-progress Math Ability sequence, I think some people (including myself) are so reliant on being able to quickly derive and compute things in our heads that we have allowed our facility of memorization and memory-recall to atrophy. The prospect of learning, for example, all the individual notes on a guitar fretboard feels so agonizing to me that I still just "derive" the notes when I need them, even though this is terribly slow, after many years of playing the instrument.

I have a horrible problem with foreign language vocabulary for a reason very similar to this: there's no way to derive the word for "green" from a list of every other color word except "green"...