Description
This monograph develops a unified theory of symmetry across semantic, historical, scientific, and formal domains, culminating in its reconstruction within the frameworks of General Theory of Signature Space (GTSS) and S-Theory. The central aim is to demonstrate that symmetry is notmerely a geometric or aesthetic property, but a general principle of invariance, equivalence, and structural reduction under admissible transformations, operating across all levels of analysis. The study begins with a reconstruction of the semantic field of symmetry, identifying its coremeanings as balance, proportion, invariance, reversibility, and equivalence. It then traces the historical evolution of the concept from the Greek notion of συμμετρία - understood ascommensurability and proportional measure - through its Latin transformation into a canonical principle of ordered construction, to its mathematical formalization as invariance under transformation groups. In physics, symmetry is shown to function as a foundational constraint onlaws and a generator of conserved quantities, while symmetry breaking is established as the sourceof physical structure and phase transitions. In biology, symmetry appears as a dynamically regulated balance between form and differentiation; in cognitive and social systems, it operates asa principle of perceptual organization, reciprocity, and strategic equivalence. The monograph then introduces GTSS, in which symmetry is generalized to invariance of fieldsignatures, defined by parameters governing phase, curvature, and global structure. Symmetry becomes a field-level condition, preserving qualitative regimes across transformations ofscale, representation, and parametrization. This is further extended in S-Theory, where symmetry is reinterpreted as invariance of interpretive outcomes within structures of the form, composed of material, context, and ordered modal operators. Here, asymmetry - arising from non-commutativity, modal ordering, and contextual variation - is shown to be the fundamental sourceof meaning and differentiation.