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pwno 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.
The original draft of this made sure to note that a) the levels aren't really discrete in that you can be e.g. partway/ halfway/ mostly toward completing Level 2; and that b) it's conceivably possible to complete them out of order, but that should be extremely unusual. I decided that explaining all of that would be a distracting "caveat overload"
Also, I don't think your situation counts as bypassing levels. Level 1, by design, doesn't say that you must have the standard equation in your model, or that you could provide it right this second. It just requires that you have a model that works. So if you know enough to generate a predictive, successful model, then you're at least at Level 1, even if you need some time to flesh out the specific predictions.