Geometry of Language

Abstract: In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal grammar or a mechanism which explains significant aspects of the human faculty of language, which in turn can be considered a natural disposition for the evolution and deployment of the diverse human languages. We describe such a mechanism, which differs from existing logical and grammatical approaches by its geometric nature. Our main contribution is to explore the assumption that sentence recognition takes place by forming chains of tokens representing words, followed by matching these chains with pre-existing chains representing grammatical word orders. The aligned chains of tokens give rise to two- and three-dimensional complexes. The resulting model gives an alternative presentation for subtle rules, traditionally formalized using categorial grammar.