Quantifying Consciousness: Phi, Minimal Partitions, and IIT 4.0 — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible causal integration in a system, with recent work (IIT 4.0) extending to higher-arity causal analysis and algorithmic information theory critiques. | MATH: Φ = integrated information, defined via the minimal information partition (MIP) — the partition that causes the least information loss. IIT 4.0 uses the "intrinsic cause-effect power" of a mechanism: φ = min over partitions of the Earth Mover's Distance (EMD) between the actual and partitioned probability distributions. Algorithmic critique (arXiv:1405.0126) replaces Shannon entropy with Kolmogorov complexity: Φ_alg = K(mechanism) − K(mechanism | partition), arguing lossless integration requires algorithmic irreducibility. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618) appears in the formal definitions. However, the EMD metric in IIT 4.0 operates on a probability simplex — a lattice structure whose Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com