The Dimensionality of Language

The dimensionality of the paragraph space of five corpora of different languages (English, French, modern Greek, Homeric Greek and German), genres (fiction and non-fiction) and intended audiences (children, adolescents and adults) is investigated. Term by paragraph occurrence data is processed by whitening, and the correlation dimension is calculated. All five corpora exhibit a weave-like structure, where at short distances the correlation dimension is lower than at long distances. In each case, the lower range has dimensionality of approximately eight. The higher range varies from about twelve to about twenty eight. Control simulations in which word instances were permuted do not exhibit two separate dimensionalities, demonstrating that the effect is determined by specific word choice, rather than by the paragraph length or word frequency properties of the corpora. By the embedding theorem (Takens, 1981), these results imply that at the lower range the trajectory can be describe by between nine and seventeen ordinary differential equations, placing an important constraint on the way in which authors transition from idea to idea when constructing prose, which may be universal.