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Pentashagon comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong
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What is Magic besides some form of superintelligence, or at least the remnants of superintelligence? The strongest evidence is that magic-users and even creators don't really have to understand how the spells actually work in order to use them. There is information entering the system from somewhere, and it's enough information to accurately interpret the vague wand movements and sounds of humans and do sufficiently amazing things without too many chaotic side-effects. Even the chaotic side-effects are usually improbably harmless. It's like an almost-Friendly, or perhaps a broken previously-Friendly, AI. Possibly the result of some ancient Singularity that is no longer explicitly remembered.
You don't need to know how muscles work in order to use them to move.
You also don't need to know how algorithms work in order to use them, or even to write them. I don't know how Ukkonen's algorithm works, but I've implemented it. You haven't seen magic until you've seen the suffixes of a string sorted in linear time.
Here's another, roughly isomorphic statement:
Never mind, I see your point, although I still disagree with your conclusion on the grounds of narrative plausibility and good writing.