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jscn comments on Saturation, Distillation, Improvisation: A Story About Procedural Knowledge And Cookies - Less Wrong
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Procedural knowledge is often initially constructed out of propositional knowledge. But once procedural knowledge is had, it also incorporates things like body memory and pure automatic habit, which, when observed in oneself, are just as likely to be rationalized after the fact as they are to be antecedently planned for sound reasons. It's also easy to forget the initial propositions about a mastered procedure. I am likely to forget why I separate eggs with spoons at some point, until and unless I decide to go back to doing it by hand and get the corresponding poor results: I will just reach for the silverware drawer and set about separating eggs. (This is probably a bad example, since by mentioning in the post above my reasons for changing methods, I've cemented those reasons in my mind. However, I'm sure there are a dozen things I do automatically in the kitchen that have no cognitively occurrent relationship to the reasons I started doing them in the first place.)
I've also noticed this kind of thing in my martial arts training.
For instance, often times high level black belts will be incredibly successful at a particular technique but unable to explain the procedure they use (or at least, they'll be able to explain the basic procedure but not the specific detail that makes the difference). These details are often things the practitioner has learned unconsciously, and so are not propositional knowledge for them at all. Or they may be propositions taught long ago but forgotten (except in muscle memory).
The difference between a great practitioner and a great teacher is usually the ability to spot the difference that makes a difference.