The Uncomputable Mind: Algorithmic Complexity and the Limits of Consciousness — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Consciousness may be fundamentally non-computable if integrated information (Φ) is measured via algorithmic information theory rather than Shannon entropy, linking formal proof limits to causal structure. | MATH: IIT defines Φ as effective information across a system's minimum information partition (MIP): Φ = min over partitions of (H(X) − Σ H(parts)); algorithmic variant replaces Shannon entropy H with Kolmogorov complexity K, yielding Φ_AIT = K(system) − Σ K(parts), which is uncomputable in general (due to K's non-computability). Wolpert's "Monotheism theorem" shows no physical theory can infer all causal structure without circularity — formalized via conditional independence and algorithmic randomness (K(x|y) vs K(x)). | CONNECTION: The MIP partition structure mirrors lattice-theoretic cuts in root systems (e.g., A_n, D_n) — the minimal partition corresponds to a Coxeter-Dynkin diagram's minimal cut, and Φ's value scales with the ratio of integrated to segregated informatio
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026uncomputable,
title = {{The Uncomputable Mind: Algorithmic Complexity and the Limits of Consciousness — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526376},
url = {https://zenodo.org/records/23526376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Uncomputable Mind: Algorithmic Complexity and the Limits of Consciousness — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526376
UR - https://zenodo.org/records/23526376
AB - FINDING: Consciousness may be fundamentally non-computable if integrated information (Φ) is measured via algorithmic information theory rather than Shannon entropy, linking formal proof limits to causal structure. | MATH: IIT defines Φ as effective information across a system's minimum information partition (MIP): Φ = min over partitions of (H(X) − Σ H(parts)); algorithmic variant replaces Shannon entropy H with Kolmogorov complexity K, yielding Φ_AIT = K(system) − Σ K(parts), which is uncomputable in general (due to K's non-computability). Wolpert's "Monotheism theorem" shows no physical theory can infer all causal structure without circularity — formalized via conditional independence and algorithmic randomness (K(x|y) vs K(x)). | CONNECTION: The MIP partition structure mirrors lattice-theoretic cuts in root systems (e.g., A_n, D_n) — the minimal partition corresponds to a Coxeter-Dynkin diagram's minimal cut, and Φ's value scales with the ratio of integrated to segregated informatio Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -