I think that the "teaching" benchmark you claim here is actually a bit weaker than a Level 2 understanding. To successfully teach a topic, you don't need to know lots of connections between your topic and everything else; you only need to know enough such connections to convey the idea. I really think this lies somewhere between Level 1 and Level 2.
I'll claim to have Level 2 understanding on the core topics of my graduate research, some mathematics, and some core algorithmic reasoning. I'm sure I don't have all of the connections between these things and the rest of my world model, but I do have many, and they pervade my understanding.
I think that the "teaching" benchmark you claim here is actually a bit weaker than a Level 2 understanding. To successfully teach a topic, you don't need to know lots of connections between your topic and everything else; you only need to know enough such connections to convey the idea. I really think this lies somewhere between Level 1 and Level 2.
I agree in the sense that full completion of Level 2 isn't necessary to do what I've described, as that implies a very deeply-connected set of models, truly pervading everything you know about.
But a...
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.