On the physical origin of linguistic laws and lognormality in speech

Physical manifestations of linguistic units include sources of variability due to factors of speech production which are by definition excluded from counts of linguistic symbols. In this work we examine whether linguistic laws hold with respect to the physical manifestations of linguistic units in spoken English. The data we analyze comes from a phonetically transcribed database of acoustic recordings of spontaneous speech known as the Buckeye Speech corpus. First, we verify with unprecedented accuracy that acoustically transcribed durations of linguistic units at several scales comply with a lognormal distribution, and we quantitatively justify this ‘lognormality law’ using a stochastic generative model. Second, we explore the four classical linguistic laws (Zipf’s law, Herdan’s law, Brevity law, and Menzerath-Altmann’s law) in oral communication, both in physical units and in symbolic units measured in the speech transcriptions, and find that the validity of these laws is typically st...