Statistics

Bayes to Being: A Semantic Field Theory of Recursive Symmetry, Homeostasis, and CPT Invariance

Authors: Stephen P. Smith
Comments: 14 Pages.

This paper proposes a unified framework that reinterprets probabilistic inference, information theory, and semantic flow through the lens of recursive symmetry and homeostatic balance. Beginning with the foundational structure of Bayes’ theorem and its role in defining semantic boundaries given by Roy Frieden’s extreme physical information, we explore the duality between Fisher information I and the semantic bound J as a dynamic tension that governs coherence. We show that the interaction between I and J is not merely algebraic but semantically directional, invoking a Janus-faced duality reminiscent of Arthur Koestler’s holons that reveal a sematic duality. This duality necessitates a symmetry-preserving operator that we identify with CPT invariance, leading to a recursive sublation mechanism that maintains semantic homeostasis. We formalize these insights into a semantic field theory using a Lagrangian formalism, curvature tensors that adjust flat space, bijection plains in flat space, and a recursive action principle that governs the evolution of mirrored manifolds. The result is a metaphysical geometry of meaning—where probability, inference, and coherence are unified under a recursive, symmetry-informed framework. Moreover, it is argued that symmetry breaking, often seen as irreversible loss, can instead be understood as sublation—a transformation preserving a deeper bilateral symmetry beneath visible asymmetry. Drawing on Hegel’s dialectics, CPT symmetry, and Karl Friston’s free energy principle, it proposes a universal homeostat that balances two mirrored space-time manifolds. This "extrinsic gravitation" maintains ontological symmetry while allowing epistemic differences, making physical laws the product of recursive balancing. Perception mirrors this process, aligning inner and outer realities. Broken symmetries are thus appearances, not destructions, revealing a cosmos where coherence is preserved beyond what is visible, uniting physics, cosmology, and epistemology.
Category: Statistics