Phi, Information Integration, and the Hard Problem of Consciousness — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system, but its computability and lossless integration remain contested. | MATH: Core quantity Φ = minimum information partition (MIP) distance: Φ = min over partitions P of [effective information EI(X; P)] where EI = H(X_mechanism) − H(X_mechanism | X_cause, X_effect). Tononi's original: Φ = Σ p(mechanism) × log₂ [p(mechanism | cause, effect) / (Π p(parts))]. Tegmark's contribution: derives Φ bounds via perturbation theory, linking to spectral properties of the system's dynamics matrix. Algorithmic alternative (arXiv:1405.0126): Φ_AIT = K(whole) − K(parts) using Kolmogorov complexity K, avoiding lossy integration. | CONNECTION: The MIP partition structure is a **lattice of partitions** — the partition lattice's meet/join operations mirror crystallographic root system symmetries (A_n series). The ratio of Φ for a system vs. its parts often collapses Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com