As a minor contribution to the good advice above -- It's my impression that this phenomenon comes, mechanically speaking, from the right cerebral hemisphere. Or something like that - never mind if that's an oversimplification, unless you're going into neurosurgery the exact details aren't so important, but there's a substantial mental faculty that allows us to act rapidly on things that would take long, troublesome thought if they had to be calculated the way a computer would do it. In a ball sport, for example, you might be able to gauge the approach of a very fast moving small object, and strike it accurately enough, with something that isn't even in your field of view, that it will go off in a somewhat predictable direction.
Stuff that if you think about it, seems a bit miraculous. It is, but it isn't. There aren't any miracles, outside of the fact that we're all here. Hence all the practice, in which we build this machine that can do these marvelous things. The additional problem I have, is to keep that machine on the job and not let it get pushed aside by other kinds of mental processes that are accustomed to getting my attention. Learning, very late in the game unfortunately, to focus better on the music when playing, and not think about my fingers or whatever.
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