Modeling the life and death of competing languages from a physical and mathematical perspective

Recent contributions address the problem of language coexistence as that of two species competing to aggregate speakers, thus focusing on the dynamics of linguistic traits across populations. They draw inspiration from physics and biology and share some underlying ideas -- e. g. the search for minimal schemes to explain complex situations or the notion that languages are extant entities in a societal context and, accordingly, that objective, mathematical laws emerge driving the aforementioned dynamics. Different proposals pay attention to distinct aspects of such systems: Some of them emphasize the distribution of the population in geographical space, others research exhaustively the role of bilinguals in idealized situations (e. g. isolated populations), and yet others rely extremely on equations taken unchanged from physics or biology and whose parameters bear actual geometrical meaning. Despite the sources of these models -- so unrelated to linguistics -- sound results begin to surface that establish conditions and make testable predictions regarding language survival within populations of speakers, with a decisive role reserved to bilingualism. Here we review the most recent works and their interesting outcomes stressing their physical theoretical basis, and discuss the relevance and meaning of the abstract mathematical findings for real-life situations.Comment: 22 pages, 4 figures. Fifth chapter of the book Bilingualism and Minority Languages in Europe: Current trends and developments by F. Lauchlan, M. C. Parafita Couto, ed

Coupled dynamics of node and link states in complex networks: A model for language competition

Inspired by language competition processes, we present a model of coupled evolution of node and link states. In particular, we focus on the interplay between the use of a language and the preference or attitude of the speakers towards it, which we model, respectively, as a property of the interactions between speakers (a link state) and as a property of the speakers themselves (a node state). Furthermore, we restrict our attention to the case of two socially equivalent languages and to socially inspired network topologies based on a mechanism of triadic closure. As opposed to most of the previous literature, where language extinction is an inevitable outcome of the dynamics, we find a broad range of possible asymptotic configurations, which we classify as: frozen extinction states, frozen coexistence states, and dynamically trapped coexistence states. Moreover, metastable coexistence states with very long survival times and displaying a non-trivial dynamics are found to be abundant. Interestingly, a system size scaling analysis shows, on the one hand, that the probability of language extinction vanishes exponentially for increasing system sizes and, on the other hand, that the time scale of survival of the non-trivial dynamical metastable states increases linearly with the size of the system. Thus, non-trivial dynamical coexistence is the only possible outcome for large enough systems. Finally, we show how this coexistence is characterized by one of the languages becoming clearly predominant while the other one becomes increasingly confined to "ghetto-like" structures: small groups of bilingual speakers arranged in triangles, with a strong preference for the minority language, and using it for their intra-group interactions while they switch to the predominant language for communications with the rest of the population.Comment: 21 pages, 15 figure

What is India speaking? Exploring the "Hinglish" invasion

© 2016 Elsevier B.V. All rights reserved. Language competition models help understand language shift dynamics, and have effectively captured how English has outcompeted various local languages, such as Scottish Gaelic in Scotland, and Mandarin in Singapore. India, with a 125 million English speakers boasts the second largest number of English speakers in the world, after the United States. The 1961-2001 Indian censuses report a sharp increase in Hindi/English Bilinguals, suggesting that English is on the rise in India. To the contrary, we claim supported by field evidence, that these statistics are inaccurate, ignoring an emerging class who do not have full bilingual competence and switch between Hindi and English, communicating via a code popularly known as "Hinglish". Since current language competition models oc clude hybrid practices and detailed local ecological factors, they are inappropriate to capture the current language dynamics in India. Expanding predator-prey and sociolinguistic theories, we draw on local Indian ecological factors to develop a novel three-species model of interaction between Monolingual Hindi speakers, Hindi/English Bilinguals and Hinglish speakers, and explore the long time dynamics it predicts. The model also exhibits Turing instability, which is the first pattern formation result in language dynamics. These results challenge traditional assumptions of English encroachment in India. More broadly, the three-species model introduced here is a first step towards modeling the dynamics of hybrid language scenarios in other settings across the world

Optimal language policy for the preservation of a minority language

We develop a dynamic language competition model with dynamic state intervention. Parents choose the language(s) to raise their children based on the communicational value of each language as well as on their emotional attachment to the languages at hand. Languages are thus conceptualized as tools for communication as well as carriers of cultural identity. The model includes a high and a low status language, and children can be brought up as monolinguals or bilinguals. Through investment into language policies, the status of the minority language can be increased. The aim of the intervention is to preserve the minority language in a bilingual subpopulation at low costs. We investigate the dynamic structure of the optimally controlled system as well as the optimal policy, identify stable equilibria and provide numerical case studies

The role of bilinguals in language competition

International audienceWe study the role played by bilinguals in competition between two languages and in bilingual community formation. To this aim we introduce a simple three-state model that combines the Minett-Wang model, in which bilinguals do not directly affect the probability of an individual's transition from monolingualism to bilingualism, and the Baggs-Freedman model, where perhaps only bilinguals can trigger this transition. The model used predicts the possibility of the existence of a stable bilingual community without any particular conditions being assumed for the two competing languages: the asymptotic stability of the bilinguals' community is due only to the type of dynamics regulating the transitions between different linguistic groups. The proposed model and the obtained results give some suggestions for the conditions necessary for the formation of a stable bilingual community. First, it is important that the bilinguals are valid representatives of the two languages, in the sense that they are regarded by monolinguals also as speakers of the other language. Moreover, the transition from bilinguals to monolinguals must be smaller than the reverse transition. Unless both these conditions are met, the stable equilibrium solution to the language competition is a monolingual society