A Unified Formalization of Consciousness via Phi and Algorithmic Information Theory — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 31, 2026 DOI: 10.5281/zenodo.22190754 (opens in new tab)
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AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that Integrated Information Theory's formalism, which defines consciousness as Φ, maps structurally onto lattice theory, where Φ is determined by the minimal element of the partition lattice, representing a discrete symmetry-breaking. Notes that no direct geometric ratio appears in the cited sources. |
Abstract
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system, with recent work linking it to algorithmic information theory and lossless integration. | MATH: Φ = minimal information partition (MIP) reduction in effective information; effective information EI(X) = H(X_mechanism) − H(X_mechanism | X_cause) over all partitions; algorithmic variant: Φ_AIT = K(X) − K(X | partition) using Kolmogorov complexity K; Tononi's core axiom: Φ > 0 for consciousness, Φ = 0 for non-conscious aggregates. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) appears in the cited sources. However, IIT's reliance on *partitioning* and *integration* maps structurally to lattice theory — the set of all partitions of a system forms a lattice (Boolean lattice for binary elements), and Φ is defined via the *minimal* element of that lattice (MIP). This is a discrete symmetry-breaking: the system's causal st Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com