Consciousness as Integrated Information: Unifying Phi, Dynamics, and Algorithmic Measures — E8 Intelligence Research

FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi), measuring irreducible causal integration in a system; Tegmark's analysis links Φ to physical dynamics, while algorithmic-information critiques propose lossless integration measures. | MATH: Core IIT quantity: Φ = min over partitions of (effective information), where effective information = H(Xₚₐₛₜ | Xₚᵣₑₛₑₙₜ) - Σ H(X_iᵖᵃˢᵗ | X_iᵖʳᵉˢᵉⁿᵗ) for system X partitioned into subsystems i. Tegmark's framework: Φ as a function of the system's state transition matrix, with bounds related to spectral gap and Markov chain mixing time. Algorithmic alternative: Φ_AIT = K(X) - Σ K(X_i) (Kolmogorov complexity difference), avoiding lossy integration. | CONNECTION: No direct geometric ratio (0.382, 0.618, etc.) appears in the cited sources. However, the partition-minimization structure of Φ is analogous to finding the minimal cut in a weighted graph — a lattice-theoretic operation. The spectral gap in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com