https://doi.org/10.1140/epjp/s13360-023-04498-w
Regular Article
Founding a mathematical diffusion model in linguistics: the case study of German syntactic features in the North-Eastern Italian dialects
Department of Physics, University of Trento, via Sommarive, 14, 38123, Povo, TN, Italy
Received:
26
July
2023
Accepted:
16
September
2023
Published online:
23
September
2023
The initial motivation for this work was the linguistic case of the spread of Germanic syntactic features into Romance dialects of the North-Eastern Italy, which occurred after the immigration of German people in the Tyrol during the High Middle Age. To obtain a representation of the data over the territory suitable for a mathematical formulation, an interactive map is produced as a first step, using tools of what is called Geographic Data Science. A smooth two-dimensional surface 
is introduced, expressing locally which fraction of territory uses a given German language feature: it is obtained by a piece-wise cubic curvature-minimizing interpolant of the discrete function that says if at any surveyed locality that feature is used or not. This surface is thought of as the value at the present time of a function describing a diffusion–convection phenomenon in two dimensions (here said tidal mode), which is subjected in a very natural way to the same equation used in physics, introducing a contextual diffusivity concept: it is shown that with two different assumptions about diffusivity, solutions of this equation, evaluated at the present time, fit well with the data interpolated by , thus providing two convincing different pictures of diffusion–convection in the case under study, albeit simplifications and approximations. Very importantly, it is shown that the linguistic diffusion model known to linguists as Schmidt ‘waves’ can be counted among the solutions of the diffusion equation: to look also at more general then the present study case, superimposing Schmidt ‘waves’ generated at different due times and localities and with a ‘tidal linguistic flooding’ just around the main region of linguistic diffusion can reproduce complexities of real events, thus probing diffusivity assumptions based on historical, local cultural, social and geographical grounds. The present work is motivating a long term research plan, seeking answers to fundamental questions of linguistics as a science, which are recalled in the article.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
