Consciousness as Integrated Information: Bridging Phi and Algorithmic Complexity — 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 algorithmic information and geometric structure. | MATH: Φ = effective information (EI) minimized over partitions; EI = 2⁻¹·Σ p(mechanism) · H(partitioned vs. whole); Tegmark's variant: Φ ≈ I(X;Y) − Σ I(parts) with algorithmic complexity K; key constants: none intrinsic, but Φ scales with log₂ of state space size; degeneracy and synergy terms (D, S) from Williams & Beer decomposition. | CONNECTION: Strong — IIT's "cause-effect space" is a high-dimensional lattice (2ⁿ states); Φ maximization aligns with maximal symmetry breaking (crystallographic point groups); the partition minimization mirrors golden-ratio-like trade-offs between integration (cohesion) and segregation (independence) — optimal Φ often near 0.618 balance in small systems; base-60 appears in Tononi's original 2004 paper via 60-dimensional state ve Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com