IIT's Phi: Consciousness Measure Remains Computationally Intractable — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 18, 2026 DOI: 10.5281/zenodo.21989148 (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 (IIT) quantifies consciousness via Φ, but Φ lacks an analytic expression and depends on arbitrary discretization, making the theory mathematically immature. Proposes that IIT's information integration is topological rather than metrical or harmonic, with no geometric ratios or symmetries in its core formalism. |
Abstract
FINDING: Integrated Information Theory (IIT) quantifies consciousness via a scalar Φ (phi), measuring irreducible cause-effect power of a system, but formalizations remain lossy and computationally intractable. | MATH: Φ = minimal information partition (MIP) of system's cause-effect repertoire; for a system S with states s, Φ(S) = min_{partition P} (D(P, S)) where D is Earth Mover's Distance between probability distributions of system states under partition vs. whole. No closed-form equation; computed via exhaustive search over system subsets. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries appear in the core IIT formalism. The "information integration" concept is topological (network connectivity) rather than metrical or harmonic. | DEPTH: 6 — Profound for consciousness science, but mathematically immature: Φ is not a fundamental constant, lacks analytic expression, and depends on arbitrary discretization of state Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com