Model of World; her cities, languages and countries

TL;DR

This paper presents a theoretical model of Earth's cities, languages, and countries evolution using multiplicative noise and fragmentation processes, deriving distributions that match empirical data.

Contribution

It introduces a unified approach to model cities, languages, and countries simultaneously, deriving multiple distribution laws within a single framework for the first time.

Findings

Pareto-Zipf law for city size distribution

Log-normal distribution for languages

Exponential decay for country families

Abstract

The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise and the fragmentation- processes, 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 dis- tributions 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.