IIT Formalizes Consciousness as Non-Computable Integrated Information (Φ) — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system, with algorithmic information theory suggesting non-computable aspects. MATH: - Φ = integrated information, defined via effective information φ(X) = H(X|MIP) – H(X|MIP, mechanism), where MIP = minimum information partition. - For a system S with partition P = {M1, M2, ...}, φ(S) = min over partitions of Kullback-Leibler divergence between whole and partitioned probability distributions: φ = D_KL( p(S) || ∏ p(Mi) ). - Algorithmic approach: Φ_AIT = K(S) – K(S|mechanism), where K is Kolmogorov complexity, avoiding lossy integration. - No fundamental constants or ratios emerge from these sources; Φ is system-dependent. CONNECTION: - No explicit geometric ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries appear in these findings. - However, the concept of irreducible cause-effect structure implies a lattice of possi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com