IIT 4.0 and Algorithmic Information: Two Formal Paths to Quantifying Consciousness — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 27, 2026 DOI: 10.5281/zenodo.22121920 (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 formalizes consciousness as Φ, the irreducible cause-effect power of a system, and that an algorithmic information-theoretic variant using Kolmogorov complexity offers an alternative that avoids information loss. IIT 4.0 refines Φ through cause-effect structures measured by Earth Mover's Distance. |
Abstract
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) measuring irreducible cause-effect power of a system's state, with recent work (IIT 4.0) refining its mathematical structure; algorithmic information theory offers an alternative formalization avoiding information loss. | MATH: Core IIT: Φ = minimum information partition (MIP) — the amount of integrated information generated by a system beyond its parts. Formalized via probability distributions over past/future states: Φ = min over partitions of (sum of individual part entropies − joint entropy), i.e., Φ = min_Π [H(X^Π) − H(X)] where X is the system's state space. Algorithmic variant (arXiv:1405.0126): Φ_AIT = K(X) − Σ K(X_i) using Kolmogorov complexity K, avoiding lossy integration. IIT 4.0 introduces "intrinsic existence" via cause-effect structure (CES) — a directed acyclic graph of distinctions and relations, with Φ measured as the Earth Mover's Distance (EMD) between the unpartitioned and p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com