Title: Geometrical morphology,
Abstract: 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 $\mu$ is
the morpheme (or set of morphemes) that maximizes the inner product of $\mu$
and M.