The Geometry and Dynamics of Intelligence: A Finite Reference Structure Model of Ideational Space

This paper develops a geometric and dynamic theory of intelligence as a finite reference structure. Building on the thermodynamic structural conditions for emergence and maintenance derived in the author's previous work, the present study reformulates intelligence as a convex polytope defined by a finite set of value axes. Part I establishes the general high-dimensional theory, introducing reality space, ideational space, and optimization target space, together with cost asymmetries between degeneration and expansion. Part II presents a triangular projection model (n=3) structured around past, present, and future, enabling visualization of structural ignorance, phase transitions, and inter-agent friction. Part III returns to the high-dimensional formulation and derives stepwise degeneration sequences, a minimal attraction–repulsion force model, and the dynamics of irreversibilization. The theory proposes that civilization emerges as a dynamic overlap of finite ideational polytopes, sustained by an antagonistic balance between attraction and repulsion. The framework provides a minimal structural skeleton for re-describing intelligence and civilizational stability.