On the Obidi Curvature Invariant (OCI) ln 2 of the Theory of Entropicity (ToE): How a Single Simple Insight Leads to Radical Implications and a New Understanding of Nature in Modern Theoretical Physics

Why a Familiar Constant Conceals a Foundational Structure of Reality

Part I — Introduction, Context, and the Central Paradox

Abstract

The natural logarithm of two, ln 2, is among the most ubiquitous numerical constants in physics, information theory, thermodynamics, and geometry. It appears in Shannon entropy, Boltzmann entropy, Landauer’s principle, black-hole thermodynamics, holography, relative entropy, Fisher–Rao information geometry, and quantum state distinguishability. Despite this ubiquity, ln 2 has historically been interpreted as a unit conversion factor, a counting artifact, or a statistical normalization, never as a fundamental structural invariant of physical reality.

The Theory of Entropicity (ToE), developed by John Onimisi Obidi, proposes a radical but internally consistent reinterpretation: ln 2 is not merely a numerical coincidence across disciplines but the minimum curvature gap required for physical distinguishability to exist at all. In ToE, entropy is elevated from a derived statistical quantity to a universal physical field, information becomes curvature in that field, and ln 2 emerges as a geometric and dynamical threshold rather than a bookkeeping constant.

This paper explains why this insight did not emerge earlier despite ln 2’s omnipresence, what ToE adds that no previous framework supplied, and why the Obidi Curvature Invariant (OCI) ln 2 represents a genuine conceptual advance rather than a rebranding of existing physics.

Note: Within the Theory of Entropicity, ln 2 is not treated as a symbolic artifact but as a physically meaningful curvature invariant. This distinction is central to ToE’s unification program, where entropy, information, geometry, and distinguishability are all manifestations of a single entropic field.

Refer to the ToE Canonical Archives for more details and resources.