Quantifying Consciousness: Phi as Integrated Information via Minimum Partition — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system, with recent work linking it to algorithmic information theory and lossless integration. | MATH: Tononi's IIT defines Φ via the *minimum information partition* (MIP) — the partition that causes the least loss of integrated information. Core equation: Φ = min over partitions of [H(X) − Σ H(X_i)] (mutual information across the partition), where H is Shannon entropy. Tegmark's approach uses *effective information* and spectral analysis of the connectivity matrix W: Φ_eff ≈ Σ_i λ_i² / (1 + λ_i²) for eigenvalues λ_i of the system's dynamics matrix. The algorithmic information theory variant (arXiv:1405.0126) replaces Shannon entropy with Kolmogorov complexity K: Φ_AIT = K(X) − K(X|partition), requiring *lossless* integration (no information destruction), avoiding the "lossy integration" paradox of Griffith's 2014 formulation. | CONNECTION: The eige Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com