IIT 4.0 and Algorithmic Information: Two Formal Paths to Quantifying Consciousness — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system's state, with recent work (IIT 4.0) refining its mathematical structure; algorithmic information theory offers an alternative formalization avoiding information loss. | MATH: Core IIT: Φ = minimum information partition (MIP) — the amount of integrated information generated by a system beyond its parts. Formalized via probability distributions over past/future states: Φ = min over partitions of (sum of individual part entropies − joint entropy), i.e., Φ = min_Π [H(X^Π) − H(X)] where X is the system's state space. Algorithmic variant (arXiv:1405.0126): Φ_AIT = K(X) − Σ K(X_i) using Kolmogorov complexity K, avoiding lossy integration. IIT 4.0 introduces "intrinsic existence" via cause-effect structure (CES) — a directed acyclic graph of distinctions and relations, with Φ measured as the Earth Mover's Distance (EMD) between the unpartitioned and p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com