Related to: Truly Part of You, A Technical Explanation of Technical Explanation

Partly because of LessWrong discussions about what really counts as understanding (some typical examples), I came up with a scheme to classify different levels of understanding so that posters can be more precise about what they mean when they claim to understand -- or fail to understand -- a particular phenomenon or domain.

Each level has a description so that you know if you meet it, and tells you what to watch out for when you're at or close to that level. I have taken the liberty of naming them after the LW articles that describe what such a level is like.

Level 0: The "Guessing the Teacher's Password" Stage

Summary: You have no understanding, because you don't see how any outcome is more or less likely than any other.

Description: This level is only included for comparison -- to show something that is not understanding. At this point, you have, a best, labels that other people use when describing the phenomenon. Maybe you can even generate the appearance of understanding on the topic. However, you actually have a maximum entropy probability distribution. In other words, nothing would surprise you, no event is more or less likely to happen, and everything is consistent with what you "know" about it. No rationalist should count this as an understanding, though it may involve knowledge of the labels that a domain uses.

Things to watch out for: Scientific-sounding terms in your vocabulary that don't correspond to an actual predictive model; your inability to say what you expect to see, and what you would be surprised by.

Level 1: The "Shut up and Calculate" Stage

Summary: You can successfully predict the phenomenon, but see it as an independent, compartmentalized domain.

Description: This is where you can predict the phenomenon, using a generative model that tells you what to expect. You are capable of being surprised, as certain observations are assigned low probability. It may even be tremendously complicated, but it works.

Though low on the hierarchy, it's actually a big accomplishment in itself. However, when you are at this stage, you see its dynamics as being unrelated to anything else, belonging to its own domain, following its own rules. While it might have parallels to things you do understand, you see no reason why the p...

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