Alexander K. Cherkashin

V.B. Sochava Institute of Geography Siberian Branch of the Russian Academy of Sciences

The problem of using mathematical knowledge for modeling real processes and phenomena by comparing the features of numerical systems with the laws of the structure and development of systems of the observed world is discussed. The basis and limitations of modeling in the procedures of formalization of conceptual constructions and substantial interpretation of mathematical formulas are determined. The cognitive procedure of transition from abstract to concrete knowledge is described as the metatheoretic transformation of knowledge connected with emergence of new quality of numerical systems, new information layers on old bases of numerical point sets. Description of new specific situations requires more complex and abstract mathematical constructions.

innovative mathematical knowledge, comparison of real world phenomena with numerical sets of monas and epimonas hidden knowledge, the development of real systems according to the structure of the hyperreal numbers