Introduction. Bak, Tang and Wiesenfeld proposed in 1987 that slowly driven, extended dissipative systems evolve spontaneously to a critical state with no characteristic scale, so that event sizes follow power laws and time series show 1/f noise, without any parameter being tuned. The sandpile is the canonical model: grains added slowly produce avalanches of all sizes. The idea was applied to earthquakes, extinctions, forest fires, traffic, markets and, from 2003, to the brain, where Beggs and Plenz reported neuronal avalanches with power-law size distributions and the “critical brain” hypothesis followed: systems poised at criticality maximise dynamic range, information transmission and susceptibility to input. Related but distinct is Langton’s and Kauffman’s “edge of chaos” claim that computation and evolvability are maximised at the order–chaos boundary. The criticisms are as important as the hypothesis. Power laws arise from many non-critical mechanisms, and Touboul and Destexhe showed that thresholded stochastic processes with no critical dynamics reproduce both the power laws and the scaling relations between exponents. Priesemann and colleagues found that in vivo spike avalanches deviate from the critical prediction and are better explained by a driven, slightly subcritical network. Clauset, Shalizi and Newman showed that most claimed empirical power laws do not survive proper statistical testing. Mitchell, Hraber and Crutchfield failed to reproduce the edge-of-chaos computation result.
Important authors. Per Bak (1948–2002), then at Brookhaven National Laboratory, with Chao Tang and Kurt Wiesenfeld, founded the programme. John Beggs (Indiana) and Dietmar Plenz (NIH) introduced neuronal avalanches. Viola Priesemann (Max Planck Institute for Dynamics and Self-Organization, Göttingen) leads the empirical qualification of brain criticality; Jonathan Touboul (Brandeis) and Alain Destexhe (CNRS) supplied the null-model critique. Aaron Clauset (Colorado), Cosma Shalizi (Carnegie Mellon) and Mark Newman (Michigan) wrote the standard statistical critique of power-law claims. Christopher Langton and Melanie Mitchell are the principals of the edge-of-chaos debate.
Importance for cybernetics and the VSM. If viability required operating near criticality, the VSM would be wrong at its centre: Beer’s model is homeostatic—it damps oscillation, attenuates variety and resists departure from a stable regime—and System Two’s job as usually taught would be actively harmful. The two claims cannot both be right, and the disagreement is about the thing the model claims to explain. But the criticality hypothesis is over-applied and its neuroscience version has serious critics; the correct move is to stage it as a rival, not to build on it. The episode is also a model of a field testing its own popular result with null models, which is what the paper asks of the VSM. Cybernetics has an internal version of the tension in Ashby’s ultrastability, which requires a system to leave a regime in order to find a new one.
Importance for the article. The article note locates this in §3.3, but v02 §3.3 does not mention criticality; the rival appears only in the critique, Applying new lenses §V (C5), which stages it and adds the caution that “power laws arise from many non-critical mechanisms”. The nearest v02 passages are §2.1 (the senses of viability that criticality would bear on—ecological resilience and adaptive capacity), §3.4 (the scale-free episode as a precedent for a field dismantling its own result; Broido and Clauset’s “scale-free networks are rare” is the same statistical lesson) and the §10.5 candidate on emergent versus designed exception signalling, since early-warning signals and criticality share the dynamics vocabulary. A reviewer will press on whether the “over-damping / loss of criticality” pathology that C5 proposes has any organisational operationalisation, on the difference between SOC (a specific mechanism) and criticality in general, and on the risk of citing a contested neuroscience hypothesis in a paper that has just audited the VSM’s borrowed neuroscience (§6).
Sources in the reading list.
- the original proposal and the sandpile; four pages.
- non-critical processes reproduce the power laws and scaling relations; the null-model critique.
- in vivo evidence for a driven, slightly subcritical brain; the empirical qualification.
Other important sources and authors.
- Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. Copernicus/Springer — the programme’s popular statement and the source of its over-application.
- Beggs, J. M., & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. Journal of Neuroscience, 23(35), 11167–11177 — the origin of the critical-brain hypothesis.
- Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703 — the statistical standard any power-law claim must meet.
- Stumpf, M. P. H., & Porter, M. A. (2012). Critical truths about power laws. Science, 335(6069), 665–666 — a short statement of why most power-law claims are weak.
- Beggs, J. M., & Timme, N. (2012). Being critical of criticality in the brain. Frontiers in Physiology, 3, 163 — a balanced review of the evidence from inside the hypothesis.
- Wilting, J., & Priesemann, V. (2019). 25 years of criticality in neuroscience — established results, open controversies, novel concepts. Current Opinion in Neurobiology, 58, 105–111 — the current state of the debate.
- Mitchell, M., Hraber, P. T., & Crutchfield, J. P. (1993). Revisiting the edge of chaos: evolving cellular automata to perform computations. Complex Systems, 7, 89–130 — the failed replication of the edge-of-chaos computation claim.