Two mathematically defined expressive language structures in humans and chimpanzees

Two expressive language structures have been identified mathematically in humans and chimpanzees. The first was found by measuring the waiting times between the invocation of new words or symbols, which consistently yielded individually characteristic rate constants and descending exponential curves that reflect a stochastically lawful Poisson process. The second was discovered by calculating the cumulative informational complexity (entropy) of word usage, which in all cases was a deterministically lawful logarithmic function of the number of words used to a given point in a communicative sequence. Individual and species differences in how this law is obeyed also characterized the sample. The results from the apes resembled those from the works of human poets like Shakespeare. The findings speak for deep, natural, unlearned expressive language structures in apes that are comparable to those seen in humans.