69 22 March 2010 10:33PM

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Comment author: 23 March 2010 05:18:56PM 4 points [-]

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.

Comment author: 09 June 2010 08:52:14PM *  1 point [-]

This would suggest a typology of understanding: type N* understanding knows the passwords, type I understanding knows the equations (edit: or can otherwise find the answer - thanks, SilasBarta), type II understanding knows the connections to other fields of knowledge, and type III understanding generates type I and II knowledge within the domain and connections to other fields of knowledge (type II knowledge in other domains).

* Zero in roman numerals. Which is appropriate, of course, because the passwords are just names and can be wrong in a number of ways.

Comment author: 09 June 2010 08:57:48PM *  0 points [-]

Very good, but I just want to emphasize that Level 1, as I've defined it, doesn't necessary involve equations; it just means that you get the right answers somehow, as long as it's not cheating. (So I think the "calculate" part in its name is a bit misleading and I should probably pick a different one.)

To put it another way: for purposes of determining whether you have type I understanding, ad hoc is okay, but post hoc is not.

Comment author: 09 June 2010 09:07:44PM 0 points [-]

I see - yes, that's a good point. I'll edit in a note.

(By the way, I switched from Arabic to Roman numerals to distinguish the typology from the hierarchy - it's level 1 and type I because the two are related, not perfectly identical.)

Comment author: 09 June 2010 09:33:31PM 0 points [-]

Oops, I had thought to correct my first reference (which should have been "Level 1"), but only corrected it halfway! Fixed now.

Comment author: 23 March 2010 05:44:05PM 1 point [-]

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.

Comment author: 23 March 2010 05:37:25PM 0 points [-]

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.

Comment author: 23 March 2010 05:48:10PM *  1 point [-]

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.]