---
slug: convergence-encyclopedia-c05
title: Convergence Encyclopedia: C05 — Criticality / Edge Of Chaos / Power Laws
canonical: https://miscsubjects.com/a/convergence-encyclopedia-c05
---

**F1 — Tier.** T1 (core SOC mechanism); T2 (ubiquity claim — contested). Uncertainty flag: The extent of SOC’s applicability remains actively debated. Both critics cited below.

**F2 — Sources.** 
- Bak, P., Tang, C. & Wiesenfeld, K. (1987). “Self-organized criticality: An explanation of the 1/f noise.” Physical Review Letters, 59(4), 381–384.
- Bak, P., Tang, C. & Wiesenfeld, K. (1988). “Self-organized criticality.” Physical Review A, 38(1), 364–374.
- Kauffman, S.A. (1993). The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press.
- Kauffman, S.A. & Johnsen, S. (1991). “Coevolution to the edge of chaos.” Journal of Theoretical Biology, 149(3), 467–506.
- Langton, C.G. (1990). “Computation at the edge of chaos: Phase transitions and emergent computation.” Physica D, 42(1–3), 12–37.
- Wilson, K.G. (1971). “Renormalization group and critical phenomena. I.” Physical Review B, 4(9), 3174–3183.
- Mandelbrot, B.B. (1963). “The variation of certain speculative prices.” Journal of Business, 36(4), 394–419.

**F3 — Domains.** Sandpile dynamics, earthquakes (Gutenberg-Richter), neural avalanches, financial markets, city sizes (Zipf), river geomorphology, forest fires, solar flares.

**F4 — Scale.** Grain of sand (~10⁻⁴ m) → tectonic plates (~10⁶ m); single neuron (~10⁻⁵ m) → cortical networks (~10⁻² m).

**F5 — Falsifier.** An adaptive system operating far from criticality with no power-law signatures in its event distribution, yet performing robustly. If such systems are common, the “edge of chaos” claim fails.

**F6 — Rival 1 (observation bias).** Power laws appear because we look for them. Clauset, Shalizi & Newman (2009) “Power-law distributions in empirical data” SIAM Review 51(4):661–703 showed that many claimed power-law distributions do not survive rigorous statistical fitting; alternative distributions (log-normal, stretched exponential) often fit as well or better. The ubiquity of criticality is an artifact of methodological preference. CITED.
Rival 2 (replication failure): Mitchell, Crutchfield & Hraber (1993) “Revisiting the edge of chaos: Evolving cellular automata to perform computations.” Complex Systems 7:89–130 showed that Langton’s headline result — that computation peaks at intermediate lambda values — did not robustly replicate. The “edge of chaos” as a privileged zone for computation is less clean than advertised. CITED.

**F7 — Independence.** HIGH. Bak (theoretical physics, Brookhaven), Kauffman (theoretical biology, Santa Fe Institute/U. Chicago), Mandelbrot (mathematics, IBM/ Yale) — three independent research programs, no shared institutional lineage until post-discovery convergence at Santa Fe. Wilson (Nobel 1982, Cornell) developed renormalization group independently.

**F8 — Pattern type.** Mathematical.

**F9 — Maps.** A2 (thermodynamic/computational), A7 (pattern geometry).

---

## Corpus map
- Previous: [Convergence Encyclopedia: C04](/a/convergence-encyclopedia-c04)
- Next: [Convergence Encyclopedia: C06](/a/convergence-encyclopedia-c06)
- Encyclopedia start: [The Schema](/a/convergence-encyclopedia-schema)
- Same node, other planes: [Catalogue node C05](/a/oip-node-c05-criticality-edge-of-chaos-power-laws) · [Catalogue hub](/a/oip-convergence-public-article)
- Edges touching C05: [convergence edge 4](/a/oip-convergence-edge-4) · [disconfirming edge 2](/a/oip-disconfirming-edge-2)
- Kin corpora: [Total Structure](/a/oip-total-structure) · [Signature of the Grain](/a/oip-sog-preamble-axioms)
