Consciousness as Integrated Information: Unifying Phi, Dynamics, and Algorithmic Measures — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 29, 2026 DOI: 10.5281/zenodo.22154716 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
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| Key points | Argues that although no direct geometric ratio appears in the cited sources, the partition-minimization structure of Integrated Information Theory's Φ is analogous to finding a minimal cut in a weighted graph, a lattice-theoretic operation. The paper also presents Tegmark's spectral-gap framework and an algorithmic-information alternative, Φ_AIT, based on Kolmogorov complexity differences. |
Abstract
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 physical dynamics, while algorithmic-information critiques propose lossless integration measures. | MATH: Core IIT quantity: Φ = min over partitions of (effective information), where effective information = H(X_{past} | X_{present}) - Σ H(X_i^{past} | X_i^{present}) for system X partitioned into subsystems i. Tegmark's framework: Φ as a function of the system's state transition matrix, with bounds related to spectral gap and Markov chain mixing time. Algorithmic alternative: Φ_AIT = K(X) - Σ K(X_i) (Kolmogorov complexity difference), avoiding lossy integration. | CONNECTION: No direct geometric ratio (0.382, 0.618, etc.) appears in the cited sources. However, the partition-minimization structure of Φ is analogous to finding the minimal cut in a weighted graph — a lattice-theoretic operation. The spectral gap in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com