Universal Symmetry of Complexity and Its Manifestations at Different Levels of World Dynamics

TL;DR

This paper introduces a universal symmetry of complexity that unifies various properties of real systems through a nonperturbative, dynamically multivalued analysis, offering new insights into the structure and behavior of complex systems across different levels.

Contribution

It presents a universal law of conservation of complexity that unifies and extends traditional symmetries, providing a complete, dynamically derived framework for understanding complex systems.

Findings

Universal symmetry of complexity is always exact, uniting different patterns.

Provides a rigorous expression of the arrow of time applicable to all complex systems.

Offers solutions to longstanding mysteries in physics, biology, and consciousness.

Abstract

The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived, universal definitions of randomness, probability, chaoticity, complexity, fractality, self-organisation, and other properties, extending their axiomatic introduction in the conventional, dynamically single-valued (unitary) theory (physics/9806002, physics/0211071). Any real system emergence, structure, and behaviour can be expressed now by the universal law of conservation, or symmetry, of complexity that unifies extended versions of any (correct) symmetry, law, or "principle". Both the observed world structure and its unreduced dynamics result from that universal, unique symmetry, instead of formal imposition of separated, broken and simplified symmetries upon the existing, postulated structures in the unitary world "model". Whereas any unitary "symmetry" is regular and therefore practically always "spontaneously broken" (violated) in the real world dynamics, the universal symmetry of complexity remains always exact, but unites different, irregular, dynamically nonlinear, and intrinsically unstable patterns of unreduced world structure. It also provides the rigorous, dynamically derived expression of the ``arrow of time" (generalised entropy growth law) applicable to any real, necessarily complex system, from elementary particle to the universe. Particular applications of the universal symmetry of complexity, from fundamental physics to biology and theory of consciousness, provide old mysteries solutions and new research perspectives.