Classical mathematical sociometry. Part II. Mathematics, poetry, picture

Abstract

The article is a direct extension of the article by the same authors under the name “Classical mathematical sociometry. Part I”. The article is devoted to the axiomaty of social relations. Separately stand out classic axioms. Traditional mathematical glossary complements readers' knowledge of the elements of mathematical relations. Theorems 1 and 2 suggest 24 scenarios of possible social individual relations. The nonmonotonic triple spiral of life of human groups is based on three chains of waves charged to the final spot. The theory that we begin to explore in paragraph 5 is dual to the theory of ordering in sociometry, which we developed in our previous articles. It investigates not the ordering between persons, but the ordering of the decisions of one person (in the linear case) of his/her choices. As a matter of fact, this is exactly what happens during sociological polls, interrogations, questionnaires, psychiatric tests and other classical methods. We consider the mathematical theory of processing individual data collection, together with the axiomatics, the theorems, their proofs and mathematically implications.