Phases in Signature Space

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his monograph develops a general theory of phase as a fundamental category for describing the organization of systems in the natural sciences, social sciences, and in the theory of cognition. The point of departure is the Greek concept φάσις (phásis), understood as “appearance” or “manifestation” whose meaning is reconstructed from semantic, historical, and scientific perspectives. This analysis reveals the evolution of the concept of phase - from aphenomenological intuition to a formal and geometric structure for describing systems. The central thesis of the work is that phase is neither a single state nor merely a temporal stage, but a qualitative class of organization that determines how a system manifests itself, evolves, andresponds to perturbations. In classical frameworks, phase appears in two complementary forms: asa relational coordinate (e.g., in wave theory and quantum mechanics) and as a class of states (e.g. in thermodynamics and dynamical systems theory). This duality, however, proves insufficient fordescribing complex systems.

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