This post is part of a series of posts originally written for my blog at Forbes.com that I’m copying to my personal site, so I have a (more) stable (-ish) archive of them. This is just the text of the original post, from October2016, without the images that appeared with it, which were from the publicity materials sent out by the Nobel Foundation.

Most years, when I write about the Nobel Prize in Physics, I can feel free to pitch it a little on the high side, because there are large numbers of media reports giving a more basic version of the story. This year, as I grumbled on Twitter a while ago, that hasn’t been a great assumption. Between the U.S. Presidential election sucking up media attention and the kind of esoteric nature of the prize, the coverage has been… sparse. Even outlets that are generally really good, like the New York Times, offer only brief and sketchy descriptions. (Philip Ball’s piece for Prospect in the UK is a rare exception.) And some of the less-good outlets offer, well, lazy and dismissive pieces that devote more words to jokes about baked goods than explaining the physics. As a result, my piece from last Tuesday is standing more alone than I expected it to, and as a result is less illuminating than it ought to be.

This is genuinely important physics, though, and deserves better than the duck-and-run treatment it’s mostly gotten, so I’ll circle back and try to explain the general nature of the Nobel-winning work in a broader context, without so much specific and detailed physics content. The work that Haldane, Kosterlitz and Thouless won for has genuinely transformed the way people think about condensed matter physics, and as such is richly deserving of the wider recognition that’s supposed to come with the Nobel. Explaining how and why goes all the way back to the question of mindsets and approaches that I’ve blogged about before.

The fundamental reason why Haldane, Kosterlitz and Thouless needed to do what they did is that they’re working in a subfield where the simple and straightforwardly reductionist approach that characterizes physics seems to run into trouble. As I’ve said before, physics largely works by abstracting away messy details to get down to simple universal behavior. In the introductory mechanics course I’m teaching this term, for example, we start by treating complicated macroscopic objects — baseballs, people, cars — as featureless points, and ignore things like air resistance and friction when considering simple motion. Later on, we’ll add those complicating factors back in, but taking them away lets us explore the basic underlying laws.

This works great for a wide range of physics subfields — from huge astrophysical objects down to subatomic particles — but there are areas that are unavoidably complex. One of the biggest of these is the subfield of “condensed matter,” which tries to study the properties of vast assemblages of atoms making up solid or liquid systems. In condensed-matter systems you’re worried about the collective behavior of many more particles than you have any hope of counting. As Phillip Anderson pointed out in a famous paper from 1972, these collective behaviors aren’t necessarily obvious, even when the underlying rules governing the interactions between particles are simple and well-understood. More is different, in Anderson’s phrase, but more importantly, more is difficult.

There are still reductionist things you can do to try to understand these systems, and strip out some of the complexity– you imagine perfect crystals free of dirt and defects, extending infinitely far in all directions, and weak interactions between individual particles. And you can talk about condensed-matter systems in terms of collective properties that are a little more abstract than the individual motions of the particles making the system up. These methods get you a handful of problems you can solve with pencil and paper, and give a conceptual framework for thinking about this stuff, that you can use to draw some very general conclusions about what sort of collective states are possible.

As with most of physics, though, you exhaust the pencil-and-paper problems pretty quickly. Once you start adding complicating factors back in — defects in the lattice, strong inter-particle interactions, boundaries to the system — things get very messy, very quickly. And unlike basic classical mechanics where you can think about the motion of just a few objects, it’s extraordinarily difficult to simulate these systems in a direct way, because the collective behavior you’re after demands many more particles than you can readily keep track of.

This leads to a situation where the very simplified models physicists can usefully work with in a fairly direct way — in the case of Kosterlitz and Thouless a two-dimensional fluid, or in the case of Haldane, a one-dimensional string of quantum magnets — don’t obviously capture the complete reality. In particular, the Berezinskii-Kosterlitz-Thouless system I wrote about the other day is one where the simplest theoretical models say that superfluid behavior — where particles flow without resistance — shouldn’t be possible in a two-dimensional system, while some experiments seemed to show a low-temperature transition to exactly that sort of behavior. So there must be more going on than can be captured with the tools that were readily available in the late 1960’s and early 1970’s.

What Kosterlitz and Thouless (and Berezinskii independently) did was to bring in another high-level way of looking at collective behavior that simplifies the problems, namely looking at the topology of the system. You can sort of see how this works in the two-dimensional superfluid problem: if you imagine looking down on a sheet of fluid, a superfluid flow just looks like all the particles moving in the same direction at the same speed, say, from left to right across the screen of whatever you’re using to read this. Breaking that up requires particles to move in other directions — toward the top or bottom of the screen, and even back from right to left — otherwise, they’d still be part of the superfluid flow. This diversion necessarily introduces some circular motion, little eddies in the flow where it looks like the fluid is spinning clockwise or counter-clockwise. And the amount and rate of flow possible in these “vortices” is governed by straightforward quantum-mechanical rules, meaning that each has an energy and an entropy associated with it.

The Nobel-worthy realization here is that these “vortices” in the flow change the topology of the system — each individual vortex looks a bit like a whirlpool with a hole punched through the center. And topology is all about classifying sheets by the numbers of holes punched through them. When you bring the math of topology to bear on the problem of vortices in a two-dimensional fluid, you find that there are conditions where these vortices tend to pair up — loosely, one spinning clockwise and the other counter-clockwise — in a way that cancels out their disruption of the flow so you still basically have a superfluid. Put a bit more energy into the system, though — by raising the temperature — and these vortices split up, destroying the superfluid flow. There’s a sharp transition between the basically-superfluid phase and the not-superfluid phase, and that behavior emerges very naturally from the topological picture (you’re basically going from a sheet with no holes in it to a sheet with holes in, which is necessarily a sudden jump), while it’s extremely difficult to understand from trying to look at the microscopic motion of individual particles.

That’s the transformative aspect of this work: describing systems containing enormous numbers of atoms in terms of their topology offers a whole new way of looking at problems that can’t readily be solved using a lower-level description. In a sense, it’s re-enabling reductionism: you can’t easily understand what’s going on in condensed matter by breaking things down to the level of individual particles, but if you think about a higher-level description, you can classify systems very simply in terms of topology, and this lets you solve problems that you couldn’t hope to work out with other methods.

So, this is one of those Nobel Prizes where the achievement is not so much the specific technical problem that was solved — like the prize for blue LED’s in 2014 — but the introduction of a new tool that broadens the scope of problems that physicists can attack. To attempt an analogy for non-scientists, bringing topology into condensed matter is a bit like introducing the “Intentional Fallacy” to the study of literature — it allows you to ask and answer questions that you couldn’t even consider asking under previous methods. It’s not just an excuse to bring baked goods to a press conference, it’s a game-changing innovation in physics, and for that richly deserves the acclaim that comes with a Nobel Prize.