Benjamin Goodman

Benjamin Goodman, Paul Tupper

In spoken languages, speakers divide up the space of phonetic possibilities into different regions, corresponding to different phonemes. We consider a simple exemplar model of how this division of phonetic space varies over time among a population of language users. In the particular model we consider, we show that, once the system is initialized with a given set of phonemes, that phonemes do not become extinct: all phonemes will be maintained in the system for all time. This is in contrast to what is observed in more complex models. Furthermore, we show that the boundaries between phonemes fluctuate and we quantitatively study the fluctuations in a simple instance of our model. These results prepare the ground for more sophisticated models in which some phonemes go extinct or new phonemes emerge through other processes.

B. Goodman, P. F. Tupper

Exemplar models are a popular class of models used to describe language change. Here we study how limiting the memory capacity of an individual in these models affects the system's behaviour. In particular we demonstrate the effect this change has on the extinction of categories. Previous work in exemplar dynamics has not addressed this question. In order to investigate this, we will inspect a simplified exemplar model. We will prove for the simplified model that all the sound categories but one will always become extinct, whether memory storage is limited or not. However, computer simulations show that changing the number of stored memories alters how fast categories become extinct.