A 59-year-old, right-hand-dominant man presented to the emergency department complaining that he could not move his right foot. Over the past month his right leg had become progressively weaker. He had difficulty climbing stairs and was frequently tripping over his right foot, which had resulted in more than one serious fall. During this period he felt a sensation of muscle tightness and frequent cramps in his right posterior thigh and lower leg.

While investigating a group of languages, one is interested in formulating an insightful picture of their internal structure as well as of the relations between the different languages in the group, reflecting the bit complexity and the social complexity aspects discussed briefly in the previous chapter. In order to proceed to a comparison and analysis of the languages, one needs to know how to define the differences between languages and group different languages together in a way that best suits the observed differences. From a more general viewpoint, the picture thus obtained cannot be disentangled from the processes underlying the origin and evolution of languages, possibly from a common ancestor. These and other related topics will be discussed in this part of the book.

Unless one is specifically interested in the comparison between different scripts, language comparison methods are not applied to written texts but to the actual spoken languages, by analyzing their phonetic transcriptions into the IPA, the International Phonetic Alphabet

The transcription of a language into IPA is difficult work, requiring the field linguists to make a faithful transcription of the spoken language even up to its smallest phonetic details. In the case of unwritten languages, that is, languages that do not have a standard written form used by the native speakers, their IPA transcription represents the only existing written source.

One of the relevant goals of an analysis of a linguistic database is to provide a reliable picture of related languages. Some prototypical linguistic scenarios used to describe language groups are the following:

• • Linkage. A linkage of languages is a group of languages deriving from a protolanguage that has gradually branched into a number of (still) interacting languages. However, despite the continuous interactions, such languages keep differentiating more and more into separate languages. The term ‘linkage’ was introduced by Ross in his study of Western Oceanic languages (see Ross [1988]). A typical example of linkage is a group of languages born within a dialect continuum. The linkage formation process resembles parapatric speciation in ecology, where species differentiate while remaining in contact with each other.

Introduction to Complexity

Complexity theory is a major interdisciplinary paradigm which unifies natural and social sciences through a combination of quantitative and qualitative methods applied at various phases of the research, from observations and data analysis to modeling, simulation, and interpretation of complex phenomena (Anderson, 1972; Ross and Arkin, 2009). In this framework, cognitive and nonlinear stochastic models and effective representation methods such as complex networks and fractal geometry, represent a part of the standard toolbox. In fact, in complexity theory, phenomena emerge dynamically from hierarchical, multi-modular systems, produced by bundles of possibly stochastic interactions and causalities rather than from correlative determinism.

As far as language and linguistic analysis are concerned, complexity itself can be understood from at least two different perspectives. On the one hand, there is ‘constitutional complexity’, or ‘bit complexity’, that is, complexity due to inventories of functional units or structural features, such as phonemes, morphemes, and lexical stems. On the other hand, there is ‘(socio-)interactional complexity’, or, in other words, ‘communal complexity’, involving intricate modules of units and features, or networks of interactive individuals and aggregates. These different aspects all find their natural description in the multiplex paradigm, that is, through a model system composed of a set of interacting, overlapping networks. The unification of the two aforementioned dimensions of complexity represents a major challenge and is a focus point of this book.

For more than a decade, a growing interdisciplinary community has applied the tools of complex systems theory and statistical mechanics to the study of problems that traditionally belong to the field of linguistics. Nowadays, language dynamics represents a relevant branch of complexity theory. The modeling of language dynamics has mainly addressed three fundamental dimensions of language complexity.

(i) Language spread and competition (the dynamics of language use in multilingual communities).

(ii) Language evolution (how the structure of language evolves).

(iii) Language cognition (the way the human brain processes linguistic knowledge).

While these three dimensions of language complexity closely interact with each other and should all be taken into account for an exhaustive description of language complexity, it is useful, for clarity, to consider them as separate aspects. In the present book, we mainly address the first two dimensions, discussing language spread and competition models and considering language evolution models. However, we will also use socio-cognitive models of linguistic and cultural change.

Background

The family tree model (Stammbaumtheorie) is a major approach to the interpretation and visualization of the (historical) relationships among languages. It provides a simple and clear picture of the emergence of a language family, starting from the single original community speaking the protolanguage, then gradually splitting up into more and more subcommunities, finally turning into the observed group of languages.

One of the main limitations of the tree model of language evolution is the underlying assumption that the protolanguage develops independently in each branched subcommunity. Such an idealized situation rarely occurs; usually, innovations are born in one community and spread to other adjacent communities. The diffusion of innovations across a dialect continuum can result in a patchwork of intersecting innovations, a scenario that does not fit into the simple pattern of a tree model and a cladistic approach. To overcome the difficulties of the tree model, the wave theory was proposed and developed in the framework of historical linguistics (see de Saussure [1915] and Bloomfield [1926]). The wave theory allows the description of languages as entities continuously evolving while interacting with each other. To distinguish between these very different situations described by a tree model on one hand and wave theory on the other hand, the term language family was proposed in a sense similar to the genetic family, that is, as isolated subgroups (Ross, 1988). The term linkage was also introduced to represent a language inside an interactive language network (Schmidt, 1872), in which, in principle, all languages interact with each other.

Wave Theory

In this section, we focus on historical glottometry, which was inspired by the wave theory and introduced in the works of Siva Kalyan and Alexandre François on the languages of Vanuatu, an island nation in the Australian continent (François, 2012). The basic idea of the wave model is the evolution and spreading of innovations, which François defined as changes shared by all the languages of modern speakers (François, 2014). The presence or absence of innovations creates geographical borders known as isoglosses which define the areas corresponding to languages, which, in the spirit of wave theory, usually overlap with each other.

All language dynamics models try to describe language change in one way or another. There is no model that provides an exhaustive description of the dynamics of language, but each model tries to capture some relevant aspects. Any particular partitioning of language dynamics models into various categories is mainly a matter of convenience, as will become clear in the following sections. Language change can concern very different features, from morphological and phonological to semiotic and cognitive ones; or it can be observed as a language shift, a drastic form of language change in which a speaker adopts a new language in place of the former language; the two languages may not change appreciably during the shift.

Semiotic Dynamics models

Semiotic dynamics models (Castellano et al., 2009) owe their name to the fact that these models study the change of (the semiotic side of) a language, which is modeled as a set of couplings between words and objects (Chandler, 1994, 2007). During the interactions among agents, some word–object couplings can be turned on or removed, leading to the appearance of new languages. Semiotic dynamics models study how a unique language can emerge within a group of interacting individuals initially speaking different languages (Hurford, 1989; Oliphant and Batali, 1996; Castellano et al., 2009); the focus is on the mechanisms underlying the appearance of a consensus (Baronchelli, 2018). These models study neither the morphological changes nor the general cognitive changes, both names and objects being considered as fixed entities, but how the links between them can change in time.

The Nowak model

As the first example of a semiotic model, we consider the basic version of the Nowak model, which is an individual-based evolutionary language game similar to Hurford's model (not described here, see see Hurford [1989]), which has been used to tackle different questions. The mechanism leading to consensus about a certain language used by a whole group of speakers is based on the reproductive success assigned to an individual who has used a more successful communication strategy; eventually, only good communicators remain in the population; in the long time limit, the best communication strategy in the system is selected.

This book provides a short and selective overview of some quantitative methods of complexity theory and statistical mechanics used in the analysis of linguistic databases and in the study of language dynamics, meaning foremost the quantitative study of language spread and evolution in terms of mathematical models. A number of applications have been included in the book to introduce, illustrate, and explain the theoretical methods considered. Most of the methods discussed are imported from various disciplines, in particular, the hard sciences, where they are standard tools, or have been developed into their current state from new fields, as in the paradigmatic example of the theory of complex networks developed within the field of complex systems theory.

The general aim of the book is to show the possible advantages in predicting and understanding language processes obtained by integrating the knowledge provided by classical linguistic methods, on one hand, with the information extracted by applying mathematical tools of complexity theory, on the other hand. The general message that we intend to communicate is not new: the interdisciplinary interactions described here have already begun at different times and in many ways. These interactions are due in part to the truly interdisciplinary nature of linguistics and, in particular, to its logical framework, representing a fertile terrain for the introduction of new quantitative methods. We are still in the first stages of a real integration between linguistics and complex systems and there is still a long way ahead, full of challenges and problems to be studied, before we reach our ideal.

The exposition of material from the technical point of view is gradual, starting from basic concepts and models and moving toward more complex features of mathematical modeling and data analysis methods. The structure of the book is designed around some general topics, such as the nature of language groups and some linguistic processes, such as language competition and language evolution. We have tried to keep theory linked with applications to real linguistic problems and have avoided technical details, in order to maintain the book at a general or introductory level, suitable both to researchers and advanced students interested in the interdisciplinary field of language dynamics.

In this chapter, some mathematical models of language dynamics (Wichmann, 2008a,b; Schulze et al., 2008; Vogt, 2009; Castellano et al., 2009; Solé et al., 2010) are discussed and illustrated with some applications. Many language dynamics models have been developed to describe, for example, the evolution of languages, the competition processes between different linguistic features (considered as fixed entities), or the cognitive dimension of language. Due to limited space, it is not possible to provide here an exhaustive discussion of language dynamics models and many important pieces of the complete picture of the field are missing. In the following sections, we will discuss a selection of examples with the goal of providing at least a general idea of the field and why it represents a framework for further possible developments.

The ultimate goal of mathematical language dynamics models is to provide a quantitative description of language change, that is, of the combined dynamics of evolution, competition, and spreading processes of languages in space and time and of the consequent diversity and correlations of the linguistic landscapes, discussed in the first part of the book. For convenience, models are classified into different types. Fully evolutionary models, in which languages themselves undergo changes, while possibly competing with each other, are discussed in Chapter 6. Competition and natural selection models, which consider the processes taking place on a shorter time scale, and on which language features can be considered fixed, are discussed in Chapter 7; they can in turn be classified into models studying the time scale of language shifts and those focusing on the shorter time scale of language use. We explore the important and interesting cognitive dimension of language only partially, by reviewing a few semiotic dynamics models, which are discussed in Section 6.1.

Motivations behind Language Dynamics Modeling

There are different motivations that drive the study of language dynamics, ranging from scientific to social ones. These diverse motivations reveal the interdisciplinary nature and wide applicability range of language dynamics.

• • Language represents one of the most complex known phenomena. This fuels the interest of scientists who are keen to solve life's every problem, be it complex or simple.

In the present monograph, we have illustrated a set of tools and concepts related to complex systems that are employed in language dynamics. In order to see how they work and how they relate to linguistics, such tools and concepts have been applied to specific case studies as well as to more general and abstract simplified models. This application follows the general point of view of complex systems theory, that there are some universal frameworks that can be applied through different fields to describe very different types of complex systems.

Language dynamics is a young field looking for an actual integration among the various tools and methods from complex systems, on the one hand, and linguistics, on the other hand, resulting in a unified and consistent picture of language change and use. Such a picture is multifold, in that it concerns (a) the study of the reconstruction of a consistent history of languages, (b) the investigations interpreting the complexity of the currently observed linguistic landscape, and (c) the forecast of the future evolution of language groups. The latter point has recently become of interest due to the fact that cultural and linguistic diversity are now recognized as an invaluable heritage. In fact, the tools of language dynamics have already been used by various authors to suggest language policies and evaluate the ability of a language to find or create the conditions and a suitable niche, in which to be successful.

The structure and contents of this book reflect the current situation: an integration of the main methods of investigation has began, but it is still underway. The path toward the goals of language dynamics is long and necessarily passes through a series of applications to real life situations and historical tests, which are represented by the many linguistic databases now available, containing data about the history of languages and the current sociolinguistic structures. We have not mentioned, for reasons of space, all the databases coming from social networks or from online contents, which offer ‘big data’ with an unprecedented amount of information and a unique level of fine-grained detail, which are by now a relevant element in linguistic analysis—see for example, Gonçalves and Sánchez (2014); Donoso and Sánchez (2017); Paradowski (2010); Paradowski et al. (2012).