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CCC comments on Don't teach people how to reach the top of a hill - Less Wrong
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He was learning how to cut the books. You were learning how to teach someone to cut the books, a task in which you had no prior experience. Yes, it took two people and it took longer than working out how to cut the books yourself; but given what you now know, assuming your new hire suddenly moves away and has to be unexpectedly replaced, you would be able to teach someone else how to cut the books more quickly than before.
Teaching someone how to do the skill is a different skill to being able to do the skill, and it requires a more thorough conscious knowledge of how to use the skill than using the skill does.
You're right, yet I think it's still remarkable that it took longer to watch myself do it and figure out how I was doing it, than it took me to figure it out in the first place. For many types of skills, that wouldn't be the case. I think the ease of discovery, rather than the difficulty of observing myself, made the difference.
It is remarkable, yes.
Even more than that: it requires the ability to communicate that conscious knowledge to the other person (thus, a two-place function). Each of us has our own internal "programming language" that determines which words or thoughts correspond to (e.g.) which bodily movements, and furthermore we tend to have our own specific repertory of bodily movements that we're used to making without thinking, which may not be the same as another person's. A teacher has to be able to bridge this gap -- which, in particular, requires awareness of its existence in the first place.
(Analogues of this hold for less physical tasks, e.g. doing calculus problems.)