Automata Networks for Memory Loss Effects in the Formation of Linguistic Conventions

This work attempts to give new theoretical insights into the absence of intermediate stages in the evolution of language. In particular, a mathematical model, based on automata networks, is proposed with the purpose to answer a crucial question: How a population of language users can reach agreement on linguistic conventions? To describe the appearance of drastic transitions in the development of language, an extremely simple model of working memory is adopted: at each time step, language users simply lose part of their word memories according to a forgetfulness parameter. Through computer simulations on low-dimensional lattices, sharp transitions at critical values of the parameter are described.