.. meta:: :description: Hesse, J. and T. Gross (2014). Self-organized criticality as a fundamental property of neural systems --- a review of the neural criticality hypothesis and its implications for complex systems at phase-transition boundaries. :keywords: self-organized criticality, phase transition, neural systems, critical state, avalanche, power law, complex systems, ax19, causal concentration, h-star .. TODO AA: Page maturity --- update StayC when reviewed Page status: MMv0r1_draft_2026m04d10 **************************************************************** Hesse & Gross (2014): *Self-organized criticality* **************************************************************** .. rubric:: Full citation Hesse, J. and T. Gross (2014). "Self-organized criticality as a fundamental property of neural systems." *Frontiers in Systems Neuroscience* 8: 166. - `Full text (open access, PDF) `__ - DOI: `10.3389/fnsys.2014.00166 `__ Abstract (from the original) =============================== The neural criticality hypothesis states that the brain may be poised in a critical state at a boundary between different types of dynamics. Theoretical and experimental studies show that critical systems often exhibit optimal computational properties, suggesting the possibility that criticality has been evolutionarily selected as a useful trait for our nervous system. Evidence for criticality has been found in cell cultures, brain slices, and anesthetized animals. Yet, inconsistent results were reported for recordings in awake animals and humans, and current results point to open questions about the exact nature and mechanism of criticality, as well as its functional role. Therefore, the criticality hypothesis has remained a controversial proposition. Here, we provide an account of the mathematical and physical foundations of criticality. In the light of this conceptual framework, we then review and discuss recent experimental studies with the aim of identifying important next steps to be taken and connections to other fields that should be explored. Why this paper matters ======================== Phase transitions are moments when a small perturbation has outsized effect on the entire system. A system poised at the boundary between two dynamical regimes --- the critical point --- exhibits precisely the kind of causal concentration that ax19 (Probabilistic Causal Concentration) formalizes: **at the critical point, a single event can cascade through the entire system, producing effects disproportionate to its apparent cause.** Hesse and Gross review the evidence that biological neural systems may be self-organized to operate near such critical points, where computational properties are optimal. The relevance to the HEAVEN series is threefold: 1. **Mechanism for h* concentration.** ax19 asserts that at any moment, one individual has maximal causal influence. Phase transitions provide a *physical mechanism* by which such concentration can arise naturally: when a complex system is near criticality, the perturbation that triggers the cascade has outsized influence, and the identity of that perturbation is contingent (it depends on timing and position in the network, not on inherent importance). This is precisely the h* phenomenon --- not that h* is inherently special, but that h* happens to be at the right node at the right time. 2. **Empirical testability.** The neural criticality hypothesis is itself testable and contested, providing a model for how ax19's testability should work: look for power-law distributions in cascading effects, long-range correlations, and sensitivity to initial conditions at specific moments. 3. **Self-organization.** The "self-organized" aspect is relevant to the ZION framework: systems that maintain themselves near criticality through internal feedback (not external tuning) exhibit the kind of self-correcting dynamics that the ZION cycle (Zoning, Investigating, Organizing, Navigating) attempts to formalize at the civilizational level. The paper does not prove ax19. It provides a well-studied physical framework from a different domain (neuroscience) that exhibits the same structural phenomenon ax19 describes: causal concentration at phase-transition boundaries. If the brain self-organizes toward criticality because that is where computation is optimal, the question arises: does civilization self-organize toward criticality too --- and if so, what happens at the critical point?