IIT's Φ: Algorithmic Refinements for Measuring Integrated Consciousness — E8 Intelligence Research

Abstract

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power in a system, with recent algorithmic information theory refinements addressing lossy integration. MATH: - Core quantity: Φ = measure of integrated information, defined via effective information φ(X; m) = H(X | m) – Σ H(X_i | m) for partition m, then Φ = min over partitions of φ. - Algorithmic variant: Φ_A = K(X) – Σ K(X_i) where K is Kolmogorov complexity, penalizing lossy compression. - No fixed constants or ratios emerge; Φ is system-dependent and not a universal constant. CONNECTION: - No direct link to geometric harmony ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 mathematics. - The partition minimization in IIT has a combinatorial structure reminiscent of lattice partitions, but no crystallographic symmetry or root system is invoked. - The algorithmic information approach uses discrete state spaces, not continuous geometric st Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com