On religion and language evolutions seen through mathematical and agent based models

Religions and languages are social variables, like age, sex, wealth or political opinions, to be studied like any other organizational parameter. In fact, religiosity is one of the most important sociological aspects of populations. Languages are also obvious characteristics of the human species. Religions, languages appear though also disappear. All religions and languages evolve and survive when they adapt to the society developments. On the other hand, the number of adherents of a given religion, or the number of persons speaking a language is not fixed in time, nor space. Several questions can be raised. E.g. from a macroscopic point of view : How many religions/languages exist at a given time? What is their distribution? What is their life time? How do they evolve? From a ”microscopic” view point: can one invent agent based models to describe macroscopic aspects? Does it exist simple evolution equations? How complicated must be a model? These aspects are considered in the present note. Basic evolution equations are outlined and critically, though briefly, discussed. Similarities and differences between religions and languages are summarized. Cases can be illustrated with historical facts and data. It is stressed that characteristic time scales are different. It is emphasized that ”external fields” are historically very relevant in the case of religions, rending the study more ”interesting” within a mechanistic approach based on parity and symmetry of clusters concepts. Yet the modern description of human societies through networks in reported simulations is still lacking some mandatory ingredients, i.e. the non scalar nature of the nodes, and the non binary aspects of nodes and links, though for the latter this is already often taken into account, including directions. From an analytical point of view one can consider a population independently of the others. It is intuitively accepted, but also found from the statistical analysis of the frequency distribution that an attachment process is the primary cause of the distribution evolution in the number of adepts: usually the initial religion/language is that of the mother. However later on, changes can occur either due to ”heterogeneous agent interaction” processes or due to ”external field” constraints, or both. In so doing one has to consider competition-like processes, in a general environment with different rates of reproduction. More general equations are thus proposed for future work.