Jonathan Touboul is a French mathematician and neuroscientist who typically publishes papers with titles like “Pulsatile localized dynamics in delayed neural-field equations in arbitrary dimension” and “Propagation of chaos in neural fields.”
Lately, though, Touboul has been thinking about hipsters. Specifically, why hipsters seem to dress alike, even though they’re supposed to be all about nonconformity. In a working paper titled “The Hipster Effect” and posted to the arXiv website, he argues that people don’t instantly perceive what trends are mainstream. There’s a delay. And when the delay is long enough, the contrarians may inadvertently synchronize with one another. “In wanting to oppose the trends, there actually emerges some sort of hipster loop,” Touboul said.
The paper has been catnip, of course, for the hipster blogosphere, which loves all objets highbrow/lowbrow, the more meta the better. But this is a whimsical analogy for a serious topic. In Touboul’s line of work, there are neurons that behave like hipsters. They fire when every other neuron around them is quiet, or they fall silent when every other neuron around them is chattering. Widespread synchronicity in the brain is considered harmful, Touboul noted. It’s a feature of epileptic seizures, which can occur when groups of neurons fire together in abnormal ways.
To help lay readers better understand his mathematical argument, Touboul walked me through his paper, which he is submitting to a physics journal. He begins by envisioning a world where people choose between just two styles: Call them punk and normcore (typified by relaxed-fit jeans, white sneakers and other bland suburban attire). There are just two kinds of people in this world: those who like to go with the flow, conformists, and those who do the opposite, hipsters. Over time, people perceive what the mainstream trend is, and either align themselves with it or oppose it.
To the right are examples involving a population of three conformists and one hipster. How the world evolves over time depends on who starts off in the majority and who starts off in the minority.
In example A1, the three conformists start off with the same style; the nonconformist is different. This world is stable. The conformists are happy because they are the majority. The hipster is happy because she’s the minority. They all stick with their current styles.
In example A2, two of the conformists start off normcore; the other conformist is punk; the hipster is also punk. From the perspective of each normcore conformist, the consensus seems to be punk (they don’t count themselves). They both decide to be punk. Eventually, after a few switches, the system settles into stability: three punk conformists and one normcore hipster.
What if this world contained equal numbers of conformists and hipsters? No matter how the population starts out, it would end up in some kind of cycle, as the conformists try to catch up to the hipsters and the hipsters try to differentiate themselves from the conformists.
Now let’s consider a world with just hipsters and a larger population — Touboul examined a simulation with 5,000 of them. When each is randomly assigned to be either punk or normcore, the result is a field of noise. The hipsters cannot reach a consensus; they try vigorously to be in the minority, but collectively, they act like a dog chasing its tail. (Touboul’s model, by the way, includes a bit of randomness at each turn — a dash of realism.)
Here comes the crucial twist. All the examples so far assumed that everyone had instant knowledge of what everyone else was wearing. People knew exactly what the mainstream trend was. But in reality, there are always delays. It takes time for a signal to propagate across a brain; likewise, it takes time for hipsters to read publications like Complex or Pitchfork to figure out how to be contrarian.
So Touboul included a delay in the model, as shown in example B: People base their decisions not on the current state of affairs but on the state of affairs some number of turns prior. And if the delay is increased past a certain point, a pattern emerges out of what had appeared to be random noise. All the hipsters start to synchronize and oscillate in unison.
As Touboul described it in his paper: “A random imbalance will be detected after some time and all anticonformist individuals will tend to disalign to this trend, regardless of the fact that an increasing proportion of them do and therefore yield a clear bias towards the opposite trend. This will be detected at later times, leading to a reciprocal switch, and these oscillations will periodically repeat. Despite their efforts, at all times, anticonformists fail being disaligned with the majority.”
Translation: The hipsters are recoiling from the mainstream, but each holds an outdated concept of what the mainstream is. Because they are slow to react, all of them end up looking alike and switching fashions at the same time. (Irony of ironies!)
You might object that Touboul’s model oversimplifies. In real life, there are a million ways to be nonconformist: You can be goth, you can be preppy, you can be grunge. Touboul’s model doesn’t quite explain the current hipster obsession with scraggly beards and undercuts. He admits as much. “The brain is more complex than the model I looked at, and of course hipsters are more complex,” he said.
But the beauty of his model, which he sketches out in just four pages, lies in its succinctness. He doesn’t aim to explain everything. His goal is to express a single idea about how nonconformists might synchronize. He belongs to a breed of theoreticians who see themselves as storytellers working in numbers. They value tight pacing, a plot that’s boiled down to its essence.
“That’s the real role of mathematics,” Touboul said. “To abstract things. To see what is really important.”
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