Optimal hipster theory

I think people are trying to send me a message. For the last few days, I’ve been getting a steady stream of emails letting me know about a new paper posted on the arXiv – The hipster effect: When anticonformists all look the same (for the record, I have never had an ironic mustache.) It’s definitely because of the math involved. Yeah, that’s it.

Just as I started to write this up, though, I see that someone else has already done a fantastic job at a lay introduction to the paper:

Touboul begins by envisioning a world where people choose between just two styles: Call them punk or normcore. There are two kinds of people in this world: those who like to go with the flow, and those who do the opposite — hipsters, in other words. Over time, people perceive what the mainstream trend is, and either align themselves with it or oppose it.

Here are some examples with 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. Take white to be normcore, and black to be punk (obviously).

What if this world contained equal numbers of conformists and hipsters? No matter how the population starts out, it will 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.

Essentially, the model assumes that individuals have two states (styles) and they flip between them. The switching rate is determined by the mean-field trend such that mainstream individuals will flip to the mainstream (mean-field) style at a high rate; hipsters will flip at a much lower rate. This can be modeled as a spin-glass system where many analytical results are already known.

Now, spin-glass systems are known from magnetism: they help describe how whole systems can suddenly switch from one macro state to another. For instance, from disorder to sudden order. In the hipster system, near the critical point you get sudden transient alignments of hipsters before switching randomly:

hipster critical point

A lot of flop flop flopping from the nonconformists (hipsters).

A more interesting result is that a time-delay induces a Hopf bifurcation in the system causing systematic hipster alignment:

hipster hopf bifurcations

This immediately suggests that decreased time delays should reduce the coherence of anticonformist trends. Luckily we have a natural experiment – the Internet. I’m not aware enough of fashion to comment on that but I am a pretty big music junky. Thanks to the internet, music genres have split into subgenres which split into microgenres and oh god it’s so hard to even keep track of what is what any more.

Similarly, the paper shows that if you there is a spatial extent to the model, then at low delays you only get hipster synchronization when the spatial extent is not too large or too small (in the figure below, the x-axis a is spatial extent, y-axis tau_0 is temporal delay).

hipster time and area delays

Despite the simplifications in the model – fashion is one-dimensional and everyone exists at unit distance etc – there is insight to be gained.

Additionally, while hipster-hunting is an Internet past-time, distinctiveness is a serious matter in ecology and sociology. This is useful!

Reference

Jonathan Touboul (2014). The hipster effect: When anticonformists all look the same arXiv arXiv: 1410.8001v1

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