Mathematical modeling of results of borrowing foreign words of the Russian language a reflection of the process of historical interaction between Russians and foreigners

As was mentioned by known sociologist Kenneth Ewart Boulding, the human community, divided into various social organizations, is the most complex class of biological systems. This article is dedicated for mathematical modeling of the process of historical interaction between Russians and foreigners, which are reflected in the formation of a living Russian language. The difficulty lies not only in the large number of relationships, but also in the complexity experienced by the researcher who is inside the system under study. The natural desire to abstract in this study from the system itself can be realized using a strictly scientific approach and computational programming. Namely, by using formal objects and the same formal methods of comparing them, as is customary in mathematics, physics, and other sciences that study the laws of nature in areas that are not directly related to human being and society. To form an objective knowledge base about the interaction of social groups of people, you can use the analysis of traces of this interaction, one of which is their language. It is in the language of a people that the main factors of influence of other peoples - native speakers of another language-remain. These traces, in particular, are borrowed words and expressions. To work with such words and expressions, you must first discard those matches that can be attributed to random. Only in this case can the nature of our research be objective. This article uses statistical analysis methods to identify the fact of accidental coincidence of phonetic and semantic images of words from different languages. The basic tool we have chosen is the birthday paradox theorem. As a result, a method for identifying borrowed words that appeared in the language as a result of the interaction of native speakers of different languages, excluding the random nature of their coincidence, is obtained. The application of software definition of matching words in digitized dictionaries is justified. The method is applied to the Russian language. Conclusions are made about the history of the development of the Russian people and its language. These conclusions are that the main significant influence on the Russian population and its language was exerted by Europeans, primarily the French. At the same time, no traces of the influence of Mongolian or other Eastern languages were found. The influence of the Turkic language group and the Greek language occupy a middle position. At the same time, if the semantic load of Turkic and Greek borrowings is of a general scientific or economic nature, then European borrowings are primarily associated with trade, administration, war, and luxuries. The authors concludes that the family character of interaction between native English speakers and language groups close to the English geographically with the Russian population, since the names of the main family members are borrowed mainly from the English language, while the corresponding names was already exist in the old Slavonic language.