Poisson evolution in word selection

This paper presents the finding that the invocation of new words in human language samples is governed by a slowly changing Poisson process. The time dependent rate constant for this process has the form

λ(t) = λ₁(1−λ₂t)e^-λ₂t+λ₃(1−λ₄t)e^-λ₄t+λ₅

, where

λ_i > 0, I=1,…,5

.

This form implies that there are opening, middle and final phases to the introduction of new words, each distinguished by a dominant rate constant, or equivalently, rate of decay. With the occasional exception of the phase transition from beginning to middle, the rate λ(t) decays monotonically. Thus, λ(t) quantifies how the penchant of humans to introduce new words declines with the progression of their narratives, written or spoken.