From Phi to Intrinsic Structure: The Evolution of Integrated Information Theory — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system's state — measured via the minimum information partition (MIP), with recent work (IIT 4.0) shifting to a purely intrinsic, unconstrained maximization over possible states. | MATH: Φ = min over partitions of (effective information), where effective information = H(X⁰|MIP) − H(X⁰|full system); IIT 4.0 replaces the MIP with an intrinsic cause-effect structure (CES) whose "existence" is measured by Φ^max = ∑ over mechanisms of (unidirectional cause-effect power). Tegmark's approach uses a linear-algebraic "integrated information" Φ_T = ‖ρ − ∑ᵢ ρᵢ⊗ρ_{rest}‖₁ (trace norm of the difference between the full density matrix and the product of marginals), yielding a computable, non-negative scalar. Algorithmic information theory variant (arXiv:1405.0126) defines Φ_AIT = K(ρ) − ∑ᵢ K(ρᵢ) (Kolmogorov complexity difference), avoiding lossy integration. | CONNECT Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com