Towards an Irreducible Theory of Complex Systems

Victor Korotkikh, Faculty of Business and Informatics, Mackay Campus, Central Queensland University, Australia

To be confident in practice of complex systems, it would be ideal to have an irreducible theory not requiring a deeper explanatory base in principal. But, where could such a theory come from, if even the concept of spacetime is questioned as a fundamental entity. Suggesting that the concept of integers may take the responsibility we show that complex systems can be described in terms of self-organization processes of prime integer relations. Based on the integers as the basic building blocks and controlled by arithmetic only the self-organization processes can characterize complex systems through principles not allowing further simplification. This offers the possibility to develop an irreducible theory of complex systems.