IIT's Phi: Consciousness as Irreducible Causal Integration — 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 linking it to algorithmic information theory and lossless integration. | MATH: Φ = effective information across the minimum information partition (MIP); for a system S with states, Φ(S) = min over partitions P of EI(S,P), where EI = H(X_0|X_1) - Σ H(X_0^i|X_1^i) (mutual information minus summed parts); algorithmic variant: Φ_A = K(S) - K(S|parts) using Kolmogorov complexity K; Tegmark's work suggests Φ scales with system dimensionality and causal density, not raw size. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear in the provided sources. However, IIT's core structure — irreducible wholes vs. parts — mirrors the mathematical notion of *indecomposable modules* and *simple Lie algebras* (e.g., A_n root systems), where the whole cannot be factored into independent components. The Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com