Quantifying Consciousness: Phi, Cause-Effect Power, and Geometric State-Space Partitions — E8 Intelligence Research

Abstract

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system's state, with recent work linking it to algorithmic information theory and geometric state-space partitions. | MATH: Core IIT quantity Φ = minimum information partition (MIP) distance: Φ = min_P [D(mechanism's cause-effect repertoire || product of partitioned repertoires)], where D is Earth Mover's Distance (Wasserstein metric). IIT 4.0 refines this via intrinsic cause-effect power: Φ = ∑_i p_i · d(CE_i, CE_i^∅) over all system elements. Algorithmic variant (arXiv:1405.0126): Φ_AIT = K(mechanism state) − K(mechanism state | system partition), using Kolmogorov complexity K. Tegmark's contribution: derives Φ-like measures from quantum decoherence and spectral properties of the system's Hamiltonian, yielding Φ ∝ −Tr(ρ ln ρ) (von Neumann entropy) for integrated subsystems. | CONNECTION: The Wasserstein metric used in Φ is the optimal transport di Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com