Evolutionary paths of language

Abstract

We introduce a stochastic model of language change in a population of speakers who are divided into social or geographical groups. We assume that sequences of language changes are driven by the inference of grammatical rules from memorised linguistic patterns. These paths of inference are controlled by an inferability matrix which can be structured to model a wide range of linguistic change processes. The extent to which speakers are able to determine the dominant linguistic patterns in their speech community is captured by a temperature-like parameter. This can induce symmetry breaking phase transitions, where communities select one of two or more possible branches in the evolutionary tree of language. We use the model to investigate a grammatical change (the rise of the phrasal possessive) which took place in English and Continental North Germanic languages during the Middle Ages. Competing hypotheses regarding the sequences of precursor changes which allowed this to occur each generate a different structure of inference matrix. We show that the inference matrix of a "Norway hypothesis" is consistent with Norwegian historical data, and because of the close relationships between these languages, we suggest that this hypothesis might explain similar changes in all of them.

Using spatial patterns of English folk speech to infer the universality class of linguistic copying

“…Hopfield networks represent a particularly simple model of agents who learn or copy from the previous behavior of others. Similar systems of dynamical equations, in which the rate of change of state is equal to the difference of the output of some learning or selection process, and the current state, form the basis of a number of language models [10,11,13,[39][40][41]. The discrete stochastic Hopfield network may also be viewed as a generalized dynamical version of the Ising model [42].…”

“…In this context, the activation function modelled the pulse required to trigger the neuron to fire. Equations of the form (4)-the difference of the output (generally construed) of a learning process, and its input-appear in a number of different language models [10,11,13,39,40]. In the linguistic context, the activation function may also be referred to as the learning function or copying rule.…”

“…Nevertheless, every language is generated and maintained by a large number of interacting speakers with similar properties (vocal apparatus, a need to communicate, to display status and cooperate). It is therefore natural for statistical physicists to construct models which capture how languages arise and evolve, based on the interactions of such agents [7][8][9][10][11][12][13][14][15]. We provide a glossary of important linguistic terms in Appendix F.…”

Replicator–mutator dynamics of linguistic convergence and divergence

“…Although previous studies have modelled accommodation to community behaviour by way of various mechanisms of frequency matching [6,18,19,22,50], extrinsic fitness has rarely, if ever, been included as an explicit macro-level term in mathematical models of language dynamics. The proposal here is to consider, initially, two population substrata, which could be thought to correspond to two socioeconomic classes, two subgroups of an age cohort, two age cohorts in a single community, or in general any two subpopulations of a speech community whose members are inclined to converge toward the speech patterns of those in their own subpopulation but diverge from the usage of those in the other subpopulation.…”

“…Most mathematical models of linguistic variation and change fall into one of two classes: (1) those that study homogeneous populations of speakers in frameworks that admit an analytical exploration of the model's dynamics [1][2][3], and (2) those that aim to elucidate complex interactions of language learning and use in social networks through agent-based simulations [4][5][6]. The former class is usually characterized by the use of continuoustime dynamics in infinite populations; such significant idealizing assumptions often limit the range of empirical application of these models.…”