IIT's Phi: Consciousness as Irreducible Cause-Effect Without Closed-Form Constant — E8 Intelligence Research

Abstract

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system, but current formulations depend on lossy integration and lack a closed-form mathematical constant. MATH: - Φ = integrated information, defined via effective information across a minimum information partition (MIP). - For a system of n elements with probability distribution p, effective information: φ(X; MIP) = min over partitions of [H(X) - Σ H(Xⁱ | MIP)] where H is Shannon entropy. - Algorithmic information theory variant: Φ_alg = K(X) - Σ K(Xⁱ) where K is Kolmogorov complexity. - No universal constant or ratio emerges; Φ is system-specific and partition-dependent. CONNECTION: - No direct geometric harmony (0.382, 0.618, 1.618, etc.) found in current IIT formulations. - The MIP search involves combinatorial optimization over partitions, which can be mapped to lattice structures (e.g., Boolean lattice of subsets), but Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com