My experience doing quantum chromodynamics (QCD) was faintly like this. I could do the math, but it was mechanical; I always felt that the theory had a better idea of the answer than I did. On the other hand, I sensed that people who could really do physics had a visceral feel for the subject. Not only could they handle the sums, but they intuited what the answer should be.
This may be part of what skill means. One has to master both the mechanics of the knowledge, and the link between the knowledge and the intuitions that allow one to find short cuts and anticipate results. Mechanical knowledge links subject matter and theory; metaphor links theory and intuition.
In the Capgras case, the visual recognition system links a person’s appearance with their identity, and the emotional affect system links that identity with the meanings that are important to the perceiver.
To sum up the three preceding examples:
Skill in general: subject matter – theory // theory – intuitionStretching the analogy even further, perhaps this is why metaphors are so important in science and engineering. A software engineer doesn’t need metaphors like Classes-as-Containers or Programs-as-Language to get work done– the unadorned mathematics would do just fine – but analogies provide an intuitive basis that underpins thinking and provides comforting context. When a programmer tries to write about software without using metaphors, they become uncomfortably aware just how ingrained they are. The two-part model in this case:
Physics ‘n’ me: experiment – QCD // QCD – intuition
Capgras syndrome: face – spouse’s name // spouse’s name – feelings for spouse
mathematics – programming // programming – intuition