Integrated Information Theory: Φ as Algorithmic Irreducible Complexity — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 28, 2026 DOI: 10.5281/zenodo.22138507 (opens in new tab)
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AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
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| Key points | Argues that Integrated Information Theory's partition-minimization structure, particularly the minimum information partition, mirrors lattice and root-system symmetries by resembling a minimal cut in a weighted graph. The author also notes that no direct geometric ratios or base-60 appear in the cited sources. |
Abstract
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ, measuring irreducible causal integration in a system, with recent work linking it to algorithmic information theory to avoid information loss. | MATH: Φ = effective information (EI) minimized over partition; EI = 2^-H(mechanism) — Tononi's 2008 formulation; algorithmic variant: Φ_A = K(whole) − Σ K(parts) where K is Kolmogorov complexity (Grasso/arXiv:1405.0126); Tegmark's approach uses perturbation-based Φ with matrix norms (||M||_1 or spectral radius) on state transition matrices. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appears in the cited sources. However, Φ's partition-minimization structure mirrors lattice/root-system symmetries — the "minimum information partition" (MIP) is a discrete optimization over partitions, analogous to finding the minimal cut in a weighted graph, which in crystallographic terms corresponds to identifying the weakest cleava Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com