Structural duality

Abstract

Charles L. Dodgson, the eminent Oxford mathematician, once expounded, in the form of a conversation between an egg and a seven-and-a-half-year-old girl, the interesting concept of an “unbirthday.” Conversely and perhaps complementarily, lexiphiles enjoy making lists of words like couth, plussed, ept, ebriety, peccable. Structural duality is, of course, more than whimsical playing with words, but it is concerned with such notions as contrastatus (versus status), antibalance (versus balance), and unliaison person (versus liaison person). It also involves the use of various kinds of graphs as a mathematical model, an approach whose value lies in the fact that it is not bound by physical units of measurement. The rigorous mathematical development of a duality theory may provide a source of fruitful concepts for behavioral science.

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