Narrow Results

It is argued that the present log-normal distribution of language sizes is, to a large extent, a consequence of demographic dynamics within the population of speakers of each language. A two-parameter stochastic multiplicative process is proposed as a model for the population dynamics of individual languages, and applied over a period spanning the last ten centuries. The model disregards language birth and death. A straightforward fitting of the two parameters, which statistically characterize the population growth rate, predicts a distribution of language sizes in excellent agreement with empirical data. Numerical simulations, and the study of the size distribution within language families, validate the assumptions at the basis of the model.

A formulation of bit-string models of language evolution, based on differential equations for the population speaking each language, is introduced and preliminarily studied. Connections with replicator dynamics and diffusion processes are pointed out. The stability of the dominance state, where most of the population speaks a single language, is analyzed within a mean-field-like approximation, while the homogeneous state, where the population is evenly distributed among languages, can be studied. This analysis discloses the existence of a bistability region, where dominance coexists with homogeneity as possible asymptotic states. Numerical resolution of the differential system validates these findings.

Understanding how knowledge emerges and propagates within groups is crucial to explain the evolution of human populations. In this work, we introduce a mathematically oriented model that draws on individual-based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in [F. Cucker and S. Smale, On the mathematical foundations of learning, Bull. Amer. Math. Soc. 39 (2002) 1–49; F. Cucker, S. Smale and D. X. Zhou, Modeling language evolution, Found. Comput. Math. 4 (2004) 315–343]. After deriving the model, we study some of its mathematical properties, and establish theoretical and quantitative results in a simplified case. Finally, we run numerical simulations to illustrate some properties of the model. Our main result is that, as time goes to infinity, individuals’ knowledge can converge to a common shared knowledge that was not present in the convex combination of initial individuals’ knowledge.

Language development in children provides a window to understand the transition from protolanguage to language. Here we present the first analysis of the emergence of syntax in terms of complex networks. A previously unreported, sharp transition is shown to occur around two years of age from a (pre-syntactic) tree-like structure to a scale-free, small world syntax network. The development of these networks thus reveals a nonlinear dynamical pattern where the global topology of syntax graphs shifts from a hierarchical, tree-like pattern, to a scale-free organization. Such change seems difficult to be explained under a self-organization framework. Instead, it actually supports the presence of some underlying innate component, as early suggested by some authors.

Here, we test Neutral models against the evolution of English word frequency and vocabulary at the corpus scale, as recorded in annual word frequencies from three centuries of English language books. Against these data, we test both static and dynamic predictions of two neutral models, including the relation between corpus size and vocabulary size, frequency distributions, and turnover within those frequency distributions. Although a commonly used Neutral model fails to replicate all these emergent properties at once, we find that modified two-stage Neutral model does replicate the static and dynamic properties of the corpus data. This two-stage model is meant to represent a relatively small corpus of English books, analogous to a ‘canon’, sampled by an exponentially increasing corpus of books among the wider population of authors. More broadly, this model — a smaller neutral model within a larger neutral model — could represent more broadly those situations where mass attention is focused on a small subset of the cultural variants.