IIT's Phi: Consciousness as Irreducible Causal Integration — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 28, 2026 DOI: 10.5281/zenodo.22138428 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that Integrated Information Theory's measure of consciousness, Φ, aligns with algorithmic information theory and lossless integration, and that its concept of irreducible wholes parallels indecomposable modules and simple Lie algebras, despite no direct geometric ratios being present. |
Abstract
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible causal integration in a system, with recent work linking it to algorithmic information theory and lossless integration. | MATH: Φ = effective information across the minimum information partition (MIP); for a system S with states, Φ(S) = min over partitions P of EI(S,P), where EI = H(X_0|X_1) - Σ H(X_0^i|X_1^i) (mutual information minus summed parts); algorithmic variant: Φ_A = K(S) - K(S|parts) using Kolmogorov complexity K; Tegmark's work suggests Φ scales with system dimensionality and causal density, not raw size. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear in the provided sources. However, IIT's core structure — irreducible wholes vs. parts — mirrors the mathematical notion of *indecomposable modules* and *simple Lie algebras* (e.g., A_n root systems), where the whole cannot be factored into independent components. The Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com