Applied General Systems Research

A new approach has been developed for modelling natural systems. This approach uses ‘arithmetical relators’; systems are described within two different types of referentials: discrete and continuous. Stabilized systems are complexified by integrating their environment and their underlying structures are BCR’s. ‘Virtual Information Numbers’ give a new approach of the semantic aspects of information.

Natural Complexification of Systems by Integration of Their Environment

Arithmetical Relators and Virtual Information

The arithmetical relator is a new mathematical tool for the modelization of natural systems, mainly physical and biological ones Essentially, it expresses the adaptation of a system to its environment and may take into account many imbrication levels Several examples, especially in biology, has been obtained by a holistic approach, at different organization levels But in order to prove the physical relevance of these models and to increase the easiness for finding them, a new presentation of this tool and an attempt of connection with the integro-differential formalism have been developed We use a “building of neighbourhoods” applied to different complementary kinds of models : degenerated, linearized, multiquadratic This “building” combines the underlying dynamics, the positioning of the reference frames and the class of processing in a multi-levelled system A very simple example illustrates the “opening-closing” dynamics Some results in physics are briefly presented

Application of a “Building of Neighbourhoods” to the Modelization of Natural Systems

While technical systems are quite successfully modelized by classical analysis, the description of natural systems, like biological and sociological ones, raises many problems Godel’s theorems have shown that formal algebraic systems are always incomplete and, to modelize the inner wholeness of natural systems, new mathematical tools are needed, going beyond pure algebra The arithmetic of quadratic congruences, as using the properties of prime numbers, can provide a suitable approach in that direction

Basic Cyclic Relators as a Description of Multi-Levelled Systems

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Basic Cyclic Relators as a Description of Multi-Levelled Systems