Self-organization processes of prime integer relations

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[edit] Introduction

Self-organization processes of prime integer relations constitute a new type of processes. Based on the integers and controlled by arithmetic only self-organization processes of prime integer relations can describe a complex system by information not requiring further explanation. The description can be realized through the unity of its two equivalent forms, i.e., arithmetical and geometrical.

In the arithmetical form a complex system can be simultaneously characterized by a number of nonlocal correlation structures determined by self-organization processes of prime integer relations. The arithmetical form reveals a new type of nonlocal correlations with no reference to signals as well as the distances and local times of the parts. In the geometrical form the nonlocal correlation structures of a complex system become equivalently represented by the two-dimensional geometrical pattern of the complex system. To preserve a complex system as a whole the curved spacetime structures of the parts are determined to fit precisely into the geometrical pattern of the complex system. The curvature of the geometrical pattern can characterize the force moving the parts to make from their spacetime structures the geometrical pattern of the system.

[edit] References

1. V. Korotkikh, A Mathematical Structure for Emergent Computation, Kluwer Academic Publishers, Dordrecht/Boston/London,1999;

2. V. Korotkikh and G. Korotkikh, Description of Complex Systems in terms of Self-Organization Processes of Prime Integer Relations, arXiv:nlin.AO/0509008;

3. V. Korotkikh and G. Korotkikh, On an Irreducible Theory of Complex Systems, arXiv:nlin.AO/0606023.

4. V. Korotkikh, On the Potential of a Description of Complex Systems for the Unification of Quantum Mechanics and General Relativity

Self-organization processes of prime integer relations