Simplicial Complexes Link Consciousness Theory to Higher-Dimensional Geometry — E8 Intelligence Research

Abstract

FINDING: Simplicial complexes provide a topological framework for modeling causal structure in consciousness, linking IIT's exclusion postulate to higher-dimensional geometry. | MATH: Simplicial complex defined by vertices (neurons) and simplices (causal interactions); k-dimensional holes measured via Betti numbers β_k; 1-Laplacian operator L_1 = ∂_1 ∂_1^T + ∂_2^T ∂_2, where ∂_k is the boundary map on k-chains. | CONNECTION: The golden ratio φ = 1.618 appears in spectral gaps of Laplacians on certain simplicial complexes (e.g., cyclic polytopes); base-60 emerges in hexagonal close-packing (HCP) lattice symmetries (60° angles) used in simplicial triangulations; crystallographic root system A_2 (hexagonal) underlies 2-simplex (triangle) tilings. | DEPTH: 6 — The mathematical structure is rigorous (algebraic topology, spectral graph theory) but direct links to consciousness are speculative; the exclusion postulate (IIT 3.0) posits that only one maximally integrated cause-effect structure Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com