Euclidean distance between syntactically linked words

We study the Euclidean distance between syntactically linked words in sentences. The average distance is significantly small and is a very slowly growing function of sentence length. We consider two nonexcluding hypotheses: (a) the average distance is minimized and (b) the average distance is constrained. Support for (a) comes from the significantly small average distance real sentences achieve. The strength of the minimization hypothesis decreases with the length of the sentence. Support for (b) comes from the very slow growth of the average distance versus sentence length. Furthermore, (b) predicts, under ideal conditions, an exponential distribution of the distance between linked words, a trend that can be identified in real sentences.