cbh_complexity

cbh_complexity — a computational instantiation of the Complex Brain Hypothesis

A constructive engagement with Mago, Lopez-Sola, Vohryzek, Lifshitz, Carhart-Harris, Friston & Chandaria (2026), The Complex Brain Hypothesis: Resolving the Entropy–Content Conundrum in Minimal Phenomenal Experience (arXiv:2605.16146).

The CBH argues that the richness of conscious experience is indexed by complexity, not entropy: both high-content psychedelic states and contentless meditative states show elevated brain entropy, so entropy cannot distinguish them, but complexity — shaped by the grain of inference — can. The paper is conceptual and explicitly calls for a computational measure and model. We supply one, on the authors' own example systems (the Ising model; a small system where IIT-4.0 Φ is exact).

Result

The CBH's central dissociation holds on exactly-computable systems (see FINDINGS.md):

• Exact 4×4 Ising: entropy H is monotone in temperature (1.0 → 15.3 bits), but TSE neural complexity Cₙ is non-monotone — peaks at 8.26 near Tc and collapses to 1.84 at the highest entropy. High entropy ≠ high complexity.
• Parity ring (exact IIT-4.0 Φ): as a system goes order → disorder, entropy rises monotonically (0 → 4 bits) while Cₙ peaks at intermediate disorder and exact Φ falls to 0 — the maximal-entropy state is maximally diverse yet has zero complexity and zero integration ("contentless").
• Matched-entropy dissociation: two systems at H = 3.17 bits, separated by complexity and Φ (Cₙ=0, Φ=0 vs Cₙ=0.25, Φ=0.39).
• Grain-dependence: the high-entropy disordered state has the lowest apparent complexity under coarse-graining.

Which measure realises the claim: exact Φ and coarse-grained apparent complexity cleanly; raw TSE Cₙ resolves the high-entropy end but conflates order with complexity at the low-entropy end. We report this honestly.

→ Full paper: paper_draft.md.

Contents

complexity.py (measures + controls), ising.py (exact 2D Ising + Metropolis), run.py (the three experiments), dissociation.py (matched-entropy cases), analyze.py (summary), figures.py, concepts.md, research_question.md, methods.md, FINDINGS.md, literature/ (notes + references).

Reproduce

python -m foundations.cbh_complexity.complexity → python -m foundations.cbh_complexity.run → python -m foundations.cbh_complexity.dissociation → python -m foundations.cbh_complexity.analyze → python -m foundations.cbh_complexity.figures. Built on the exact IIT-4.0 Φ oracle in proxy_audit/.