Mirror symmetry is an example of a duality, which occurs when two seemingly different systems are isomorphic in a non-trivial way. The non-triviality of mirror symmetry involves quantum corrections. It's like the Fourier transform, where "local" in one domain translates to "global"--something requiring information from over the whole space--in the other domain. Under a local/global isomorphism, complicated quantities get mapped to simple ones in the dual domain. For this reason the discovery of duality symmetries has revolutionized our understanding of quantum theories and string theory.
summer school on mirror symmetry (liberally edited)
 Thinking about local-global dualities gave me another idea about my model-sketch of knowledge, ignorance & expectation.
Under physical limitations, at a fixed energy level, Fourier duality causes a complementary tradeoff between frequency and time domains--not both can be specific. Same with position & momentum, again at a fixed energy level.
Under human limitations, at a fixed commitment of effort|time|concentration, you can either dive deep into a few areas of knowledge|skill, or swim broadly over many areas of knowledge|skill.
If I could come up with a specific implementation of that duality it would impose a boundary constraint on that model-sketch. Which would be great as optimal time|effort|concentration|energy could be computed from other parts of decision theory.
