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simplicio comments on Understanding your understanding - Less Wrong
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Actually, this is a good example of why I don't think this is really a linear hierarchy.
My understanding is like your description in level 2, but I don't know the equation. I could probably derive it if I had enough time, knew the speed of sound in air, had a way to check that I could properly relate wavelength to frequency, and I could use a computer to check my results by programming it to simulate the sound of a constant-pitch siren as an ambulance passes by.
Is that level 2, or level 3? 2.8? I find the whole idea of levels rather confusing here.
So maybe there should be level 2a: conceptual understanding, and level 2b: quantitative + conceptual understanding.
The fact that nobody quite falls perfectly into a discrete level doesn't mean it isn't a useful heuristic though. Even in your case you could say that you're "on your way" to level 2.
Right - but that's what I think is wrong with the definition of levels 2 and 3. Since I could get to the equation, if I had to, shouldn't that also be a valid description of level 3? Requiring me to know the equation in order to be level 2, yet not requiring it at level 3, kind of makes the point that this is not really a linear progression.
[Edit to add: I don't necessarily mean that understanding itself isn't linear, just that this particular set of definitions does not seem to be.]