IIT's Phi Faces Information-Loss Problem in Formalizing Consciousness — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible cause-effect power of a system, but current formalizations face a fundamental information-loss problem. | MATH: Φ = minimum information partition (MIP) — the amount of integrated information generated by a system beyond its parts; IIT 4.0 uses *intrinsic existence* via cause-effect structures (CES), with Φ computed from the Earth mover's distance (Wasserstein metric) between probability distributions of system states; alternative: algorithmic information theory (AIT) formulation where Φ ≈ K(system) − ΣK(parts) (Kolmogorov complexity difference). | CONNECTION: The MIP partition problem is structurally analogous to finding minimal cuts in graph theory — which connects to lattice structures and root systems (e.g., the partition lattice of a system's state space). The Wasserstein metric used in IIT 4.0 is a distance on probability manifolds, which in 2D reduces to Euclidean di Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com