Geometrical morphology

We explore inflectional morphology as an example of the relationship of the discrete and the continuous in linguistics. The grammar requests a form of a lexeme by specifying a set of feature values, which corresponds to a corner M of a hypercube in feature value space. The morphology responds to that request by providing a morpheme, or a set of morphemes, whose vector sum is geometrically closest to the corner M. In short, the chosen morpheme $μ$ is the morpheme (or set of morphemes) that maximizes the inner product of $μ$ and M.