1 I was re-reading some old universality papers. You know, universality in the stat-mech sense—the critical exponents that characterize phase transitions are insensitive to details of your model or crystal structure of your material. This insight, allegedly flowing around in the stat-mech community in the 1960s, was first articulated by Robert Griffiths in 1970. It got a more solid theoretical ground with Kenneth Wilson’s development of the renormalization group a few years later. The renormalization group is a theoretical method to calculate critical exponents that also explain why some features (like if you have a square or hexagonal grid in your spin model) don’t affect the exponents. Leo Kadanoff—who many think should have shared Wilson’s Nobel prize for providing one of the key insights behind the renormalization group (the block-spin argument)—wrote in 1976:
In its simplest terms, the universality hypothesis is the statement that all critical problems may be divided into classes differentiated by:
LP Kadanoff, “Scaling, universality and operator algebras”, in Domb & Green, Phase Transitions and Critical Phenomena, vol. 5a (1976).
(a) The dimensionality of the system;
(b) The symmetry group of the order parameter; and
(c) Perhaps other criteria.
Within each class, the critical properties are supposed to be identical or, at worst, to be a continuous function of a very few parameters.
Before I continue, let me confess that I am a big fan of Per Bak. The way he was brazenly going for the big questions and the audacity of his ideas . . during the heydays of self-organized criticality, it must have felt (to everyone around him) like they had the key to the secrets of the universe in their hands. If I relived my life, I wish I could hang out with his crowd back then . . it must have been an experience on par with assembling computers in Steve Jobs’ garage or rapping with The Sugar Hill Gang.
Anyhow, reading about universality in Per Bak’s How Nature Works, it is remarkable how the tone changed from the physics literature 20 years earlier. The 2nd chapter now calls it “the universality principle” and is a “theorist’s dream” because it justifies studying simple models in general. There is no explicit mention of critical phenomena, and the examples (like optimizing milk production) are most certainly not critical (i.e., universality somehow (by virtue of its name?) extended itself beyond critical phenomena).
I don’t think any radically new evidence elevated the universality hypothesis to a principle. Did it just become a convenient truism and battle call for physicists wanting to invade other disciplines (tacitly assuming readers wouldn’t question physical “principles”)? I don’t know, but it’s nevertheless bizarre.
It’s also worth recalling that the quest to validate Bak, Tang, and Wiesenfeld’s sandpile model, inadvertently led to a beautiful illustration that sometimes details do matter. When a research team at Oslo University set out to measure avalanches in sandpiles, they discovered that sand didn’t really produce power-law avalanches, but unboiled rice could. Well, not any rice, though, but a particular type from a specific Asian import store in Oslo’s suburbia.
One thing that happened between 1976 and 1996 is that emergence became a hot topic in interdisciplinary physics. Critical phenomena are one class of physical emergent phenomena, but there are much more mundane examples—like how different forms of matter get their physical properties away from the critical points—and for such phenomena, indeed, details do matter. Still, some conflation of the phenomena of emergence and universality might have led to overhyping the latter (my hypothesis).
There are other logical glitches in how the self-organized criticality literature invokes universality. One is that discovering “universal properties” (typically power-law exponents) is a highly valued result. But if the “universality principle” is so fundamental that it can even sweepingly justify simple toy models, then wouldn’t the discovery of similar exponents be close to trivial? Another is that Bak took power-law probability distributions as proof of complexity and criticality, whereas the causality, if any, is the reverse—the distributions of some quantities turn power-law at criticality. But, as every Russian schoolboy knows,2 there are dozens of mechanisms producing power laws independently of critical phenomena. Like fellow maverick scientist Ilya Prigogine, Bak dug the grave for his theory by reversing cause and effect.
Another, slightly more subtle inconsistency is the way the world is out of balance. Bak often mentioned that reality is constantly changing, sometimes catastrophically, but scientific models are comfortably neat, predictable, and depict a world in harmonious equilibrium. But given the ambition of SOC— “Self-organized criticality is the only known mechanism to [explain how] the universe [could] start with a few types of elementary particles at the big bang, and end up with life, history, economics, and literature.” [HNW]—many of the systems it pertains to explain are not sitting neatly and harmoniously at a critical point of a single model either. From that time perspective, reality would not only push around the parameters in ways that don’t happen in the SOC model world, but also wash away the entire model on occasion.
The final and most compromising conundrum is that the “details don’t matter” mantra wasn’t only used to motivate stylized, minimal models. It was also the self-organized criticality believers’ fallback excuse when a model output didn’t fit reality. This shows the scientifically biggest issue with Bak et al.’s (ab)use of the “universality principle.” It is de facto a plea against critical thinking. How can we falsify anything if it’s OK that paintings don’t look like reality because “we are painting with broad brush strokes here.” Where are we on the science vs. religion scale, really?
Notes
- The title comes from a chess video on the Agadmator channel that stuck to my mind and seemed somewhat appropriate. ↩︎
- Just sticking to the chess jargon here. ↩︎
Petter Holme 