Quantifying Consciousness: Phi and Higher-Order Causality in IIT 4.0 — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a scalar quantity Φ (phi) measuring irreducible cause-effect power of a system, with recent IIT 4.0 revisions focusing on higher-arity causal structures. | MATH: Φ = minimum information partition (MIP) distance — formally, Φ = min over partitions P of (effect repertoire distance + cause repertoire distance), using Earth Mover's Distance (Wasserstein metric) on probability distributions over system states. IIT 4.0 replaces the "big alpha" (α) with a "big phi" (Φ) computed via *intrinsic* cause-effect power, using a *difference* measure (not ratio) between actual and counterfactual repertoires. Key constants: none intrinsic; Φ is a real number ≥ 0, with Φ=0 for reducible systems. | CONNECTION: Weak direct link — but the *partition* structure of IIT (MIP) relates to *lattice* of partitions of a set (a Boolean lattice), and the Wasserstein metric on state-space has *geodesic* structure. No golden-ratio or base-60 cons Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com