Rhetorical universality classes

The recent talk by Nigel Goldenfeld on "Life and Death of Turbulence" (easy enough to find in recordings) makes several connections that might seem provocative to an outsider. On one side, it is about turbulence, a phenomenon of fluid dynamics in which the flow suddenly becomes disordered and chaotic. On another side, it is about the ecology of predator-prey models (hence birth and death). On the third side, this has something to do with the optimal pressure for an espresso machine to make good coffee. On the fourth side, all the strands are tied together by statistical mechanics of rare events. Leaving aside the fact that Nigel has perfected the art of giving a physics talk, let's dig into why he has the right to draw such grand connections. This has to do with something called a universality class.

For a number of years, I worked with high school science competitions, specifically in roles that require collecting, filtering, organizing, and disseminating information about teams, problems, visas, logistics, and finances. Of course, sometimes information is missing and not easy to request. Yet my boss and mentor liked to reiterate that "Knowing certain principles frees you from needing to know certain facts." At times, this adage helps making decisions over limited information. After all, a group of people who tried to defraud our competition to get visa invites would never have admitted to defrauding us, yet it was clear from the pattern of their actions and we could turn them away appropriately. Other than the fraudsters, the typical attendees of such events formed several loose classes, and understanding those classes helped tremendously in herding the sheep without detailed information.

Assumption of universality was at the core of one of the most offensive things ever said to me (which, for the record, was promptly forgiven). It was a simple phrase by my undergrad dorm neighbor: "I know your type". The type of smart, nerdy, Russian-ish kids. Ones that know physics, go mushroom picking, flirt with girls, eat black bread, play guitar around an imaginary campfire, and read Pushkin for fun. Once you know that type, you know how to deal with me.

I belong to the generation of post-Soviet kids born in the early 90s. My generation started at the rift where everything Soviet became post-Soviet. For many Soviet scientists, especially younger ones, this meant a collapse of their source of livelihood, the state-funded science. Many of them emigrated, many emigrated to the United States. Being young, many of them had kids near that time, either before or after skipping country.

I arrived at MIT in 2012, when I was college-aged, just like the rest of my generation. At MIT I met so many Russian immigrant kids, mostly girls for whatever reason, like my neighbor two paragraphs above. It's just that, while we are in the same generation, my parents never emigrated, and I am not quite Russian, and I don't engage in the full set of those stereotypical behaviors. My belonging to the universality class (or "type") was mis-identified.

In physics, universality is the ultimate get-out-of-jail free card. It is the answer why the simplistic models we can come up with often give surprisingly accurate predictions and explanations. On one occasion, one of my professors called this the "physics license". On another occasion, universality gave rise to my favorite xkcd issue of all time. And taken out of its cradle of origin, condensed matter, universality is a nearly universal explanation of why physicists can be so insufferable, especially when encountering another discipline.

In condensed matter theory, there is actually a pretty compelling and quantitative explanation of why we are allowed to be naive. We can write some complicated model with many terms and try to predict the large-scale properties of the system close to a phase transition. This requires a coarse-graining procedure about which I wrote so much. For many models, one can show that most terms disappear under coarse-graining. So even when your human-created model and the innately-correct model of the system differ in these irrelevant details, after coarse-graining only the essential terms remain. If your model is in the same universality class as the real thing, it will give correct coarse results without necessarily capturing the fine details.

Condensed matter physics of the last half a century mapped out a large number of universality classes. Lots of physics models can now be grouped by falling into this or that universality class. Nigel has spent a large chunk of his career contributing to that literature - and most recently he showed that the laminar-turbulent phase transition falls into the same universality class as extinction in predator-prey models and percolation of hot water through a coffee puck. Not only is this a quantitatively rigorous connection, but also an utterly fascinating story to watch unfold - can't recommend his talk highly enough.

So where is the disconnect? Why is universality so powerful and accurate, yet can be so abrasive on both personal and scientific levels? Coarse-grained theories describe, dare I say, "fundamental" properties of collective behaviors. But they break down when one cares about particularities, about numerical predictions, about behavior away from the tipping points. They break down when the topological structure of the system changes with scale: while a 2D plane or a cubic lattice would look like a 2D plane or a cubic lattice at any magnification, it is not true for complex networks and finite-size systems. If you guess the universality class of the system, you have a good prior for how it will behave. But if your guess was incorrect, or if you have overwhelming evidence to describe the non-universal parts of behavior, referring to universality classes becomes much less useful. Don't tell your friends that you know their type.

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