---
slug: oip-node-c05-criticality-edge-of-chaos-power-laws
title: Node C05: Criticality / Edge of Chaos / Power Laws
canonical: https://miscsubjects.com/a/oip-node-c05-criticality-edge-of-chaos-power-laws
---

# Node C05: Criticality / Edge of Chaos / Power Laws

C05 — Criticality / Edge of Chaos / Power Laws
{
  "id": "C05",
  "claim": "The most adaptive, information-rich behavior occurs at the boundary between frozen order and noise; many natural systems self-organize to this critical point, producing power-law statistics.",
  "domain": ["condensed matter physics", "seismology", "neuroscience", "economics", "urban science", "linguistics", "ecology"],
  "pattern": ["self_organized_criticality", "power_law", "edge_of_chaos", "scale_invariance", "1/f_noise"],
  "mechanism": "In self-organized criticality (SOC), slowly driven dissipative systems with threshold dynamics naturally evolve to a critical state where events of all sizes occur (sandpile model). Power laws: P(X>x) ~ x^(-α) with no characteristic scale. Renormalization group explains universality — same exponents across different microscopic details.",
  "scale": "molecular → civilization",
  "claim_tier": "T1 (core physics) / T2 (ubiquity claims)",
  "sources": [
    "Bak, P., Tang, C. & Wiesenfeld, K. (1987). 'Self-Organized Criticality.' Phys. Rev. A, 38(1), 364-374.",
    "Kauffman, S.A. (1993). The Origins of Order: Self-Organization and Selection in Evolution. Oxford.",
    "Langton, C.G. (1990). 'Computation at the Edge of Chaos.' Physica D, 42(1-3), 12-37.",
    "Wilson, K.G. (1971). 'Renormalization Group and Critical Phenomena.' Phys. Rev. B, 4(9), 3174-3183.",
    "Beggs, J.M. & Plenz, D. (2003). 'Neuronal Avalanches in Neocortical Circuits.' J. Neurosci., 23(35), 11167-11177."
  ],
  "dual": "Rigid lattice (too ordered, no information processing) vs. pure randomness (too noisy, no structure to propagate).",
  "falsifier": "A living or adaptive system provably tuned far from criticality (deeply subcritical or supercritical) with no power-law signatures in its event statistics, yet performing as well as or better than critical systems.",
  "rival_frame": "Criticality is an artifact of observation. Power laws appear because we look for them (using log-log plots) and because they are mathematically easy to fit. Most claimed SOC systems are actually tuned to criticality by external parameters, not self-organized. The 'edge of chaos' is a slogan, not a mechanism.",
  "independence_check": "HIGH. Bak (physics, Brookhaven) derived SOC from sandpile models. Kauffman (theoretical biology, Santa Fe) derived the edge of chaos from Boolean network dynamics. Wilson (physics, Cornell) derived universality from renormalization group. Beggs (neuroscience, Indiana) found neuronal avalanches empirically. Four fields, four methods, convergent finding: maximum complexity at intermediate disorder.",
  "pattern_type": "structural",
  "maps_to_axiom": ["A2", "A7"]
}

---

## Corpus map
- Same node, other planes: [Encyclopedia C05](/a/convergence-encyclopedia-c05) · [Inventory invariant](/a/oip-invariant-5-35-criticality-edge-of-chaos-power-laws)
- Edges touching C05: [convergence edge 4](/a/oip-convergence-edge-4) · [disconfirming edge 2](/a/oip-disconfirming-edge-2)
- Catalogue hub: [Public Article](/a/oip-convergence-public-article) · [Schema](/a/oip-convergence-schema)
