Model of World: Her Cities, Languages and Countries

Abstract

The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise [1] and the fragmentationprocesses, where the related families, size distributions, lifetimes, bilinguals, etc. are studied. Earlier we treated the cities and the languages differently (and as connected; languages split since cities split, etc.). Hence, two distributions are obtained in the same computation at the same time. The same approach is followed here and Pareto-Zipf law for the distribution of the cities, log-normal for the languages, decreasing exponential for the city families (countries) in the rank order over population, and power law -2 for the language families over the number of languages in rank order are obtained theoretically in this combination for the first time (up to our knowledge) in the literature; all of which are in good agreement with the present empirical data.

A Theoretical Approach for Pareto–zipf Law

“…( 13)-(17) imply. [2] The important points are: 1) The initial parameters (P max and M 0 ) in Eqs. (4) and (7), respectively are not important for the results and changing them amounts to shifting (back or forth) the origin for the time axis (for example in Eqs.…”

Meaning and Form in a Language Computer Simulation

“…We start with one language and one form, where all meanings have the central form S i = Q/2; thus both the initial evolution of languages and their later competition are simulated. Then we apply three processes: Change ("mutation") and diffusion ("transfer") of single features S i as in the Schulze model [8], plus splitting [12] and merging of whole languages. In this last (new?)…”

“…The real-world parallel to merging would be cases where incipient differences disappear shortly after they arise, something that happens when children change "wrong" forms popular among their peers to grown-up "correct" forms, when slang forms are invented and later forgotten again, when ingroup varieties emerge and disappear, or when speakers of dialects shift to the standard variety. Different from the Schulze model and more similar to the Viviane und Tuncay models [13,12], we no longer simulate each individual but only the language as a whole. Thus the "population" for one language no longer is part of this model, and therefore, in contrast to the Schulze model, we have no shift from languages spoken by few people to more widespread languages, only merging of similar variants, as mentioned above.…”

Competition and fragmentation: a simple model generating lognormal-like distributions

“…Two works focused on the apparently lognormal shape of the DPL. Tuncay [20] described language differentiation by means of a process of successive fragmentations, in combination with a multiplicative growth process. In a recent paper by Zanette [21], the dynamics of language evolution is considered as a direct consequence of the demographic increase of the speaker populations, which is modeled by means of a simple multiplicative process.…”