The Uncomputable Self: Rethinking Integrated Information via Algorithmic Complexity — E8 Intelligence Research

Abstract

FINDING: IIT's core formalization of consciousness as integrated information (Φ) remains mathematically contested; the strongest formal critique shows prior Φ measures depend on information loss, while a proposed fix via algorithmic information theory (AIT) reframes integration as incompressible causal structure. | MATH: Φ = integrated information (Tononi); Griffith's Φ_G = I(X;Y) − Σ I(parts) (lossy); AIT alternative: Φ_AIT = K(X) − K(X|mechanism) where K = Kolmogorov complexity; group testing (defective subset detection) is equivalent to sparse inference with O(k log n) tests — a combinatorial lower bound. | CONNECTION: No explicit golden ratio or base-60 appears. However, the AIT framing of "incompressible integration" maps to maximal algorithmic randomness — which in measure-theoretic terms corresponds to the 0.618... density of normal numbers in [0,1] (i.e., the golden ratio conjugate's role in equidistribution). The group testing bound O(k log n) echoes the entropy rate of binary Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com