General Science and Philosophy

Toward a Pre-Spacetime Ontology of Two-Sidedness: Lie Algebra, Semiosis, and Homeostatic Order

Authors: Stephen P. Smith
Comments: 11 Pages.

The search for a unified ontology has long been divided between mathematical descriptions of external structure and phenomenological accounts of lived experience. This paper argues that an unexpected bridge between these domains may already exist within the elementary axioms of Lie algebra. The antisymmetry of the Lie bracket expresses a fundamental principle of two-sidedness, while the Jacobi identity introduces an irreducible triadic relation that stabilizes this polarity through algebraic closure. Together these axioms suggest a primitive logic of reciprocity and homeostasis that precedes geometric realization and therefore exists conceptually prior to spacetime structure. Building upon this observation, the paper explores structural correspondences between Lie algebra, Peircean semiotics, Friston's free energy principle, Hegelian dialectics, and CPT-symmetric cosmological models. In each case, a common pattern emerges: an initial unity gives rise to a dyadic tension whose persistence requires mediation by a third term capable of restoring coherence without eliminating difference. The resulting triadic structure functions as a homeostat, regulating relations across scales while preserving the integrity of the participating elements. The paper proposes that this recurring pattern may represent a scale-invariant principle of organization. While not offered as a physical theory, the framework provides a conceptual ontology in which meaning, symmetry, homeostasis, and semiosis emerge from a common relational architecture. The central thesis is that two-sidedness and triadic homeostasis are not late products of biological or cognitive evolution but may instead constitute primordial conditions for the existence of stable relational order.
Category: General Science and Philosophy