Mathematicians have discovered the hidden patterns that exist within ‘chaotic’ crowds
A huge throng of people may seem chaotic. Think of the pandemonium of top-bill gatherings such as Coachella’s music festival or a Comic-Con convention, or even the bedlam at high-profile political rallies and protests.
But as you’re swimming (or surfing) through the crowd, even in your deepest moments of confusion and frustration, there is order all around you. Because, just like in nearly every corner of nature, mathematics is omnipresent.
That’s according to a new analysis from the United Kingdom’s University of Bath, led by mathematical sciences professor Tim Rogers—who was struck by previous observations that even in the most cluster-jammed of crowds, people will subconsciously fall into makeshift “lanes” of movement. They do this as if compelled by some invisible force. Rogers wondered if there was more to it.
There was. As published in the journal Science, Rogers’s team of researchers discovered curious phenomena when they conducted an experiment that asked volunteers to walk within a maze of entrance and exit gates, modeled after the King’s Cross railway station in London. “At a glance, a crowd of pedestrians attempting to pass through two gates might seem disorderly,” Rogers said in a statement. “But when you look more closely, you see the hidden structure. Depending on the layout of the space, you may observe either the classic straight lanes, or more complex curved patterns, such as ellipses, parabolas, and hyperbolas.”
The team then partnered with the Academy of Physical Education in Poland, giving them access to more humans for crowd simulation. They distilled their data into a theory that, by the end, could accurately predict whether the lanes in a given situation would be straight or curved, or even how they might tilt due to wonks such as crowd-people’s sense of traffic rules—one of which instructed study participants to always pass on the right side, for example.
In their search for answers, the mathematicians drew inspiration from Albert Einstein’s theory of Brownian motion, which describes the random flow of liquid or gas molecules that collide with each other in a given area. (Brownian motion might describe, for example, the diffusion of dust particles from a cloud in the Sahara desert as they bump into air particles along the way.) It’s a series of microcalculations that let the particles coexist as efficiently as possible—and just like the laws of physics are hardwired into nature, they might be hardwired into our brains.
“Lane formation doesn’t require conscious thought,” Karol Bacik, a life sciences researcher at Bath, said in a statement. “The participants of the experiment were not aware that they had arranged themselves into well-defined mathematical curves. . . . The order emerges spontaneously when two groups with different objectives cross paths in a crowded space and try to avoid crashing into each other. [It’s the inadvertent] cumulative effect of lots of individual decisions.”
The discovery of hidden mathematical patterns—ellipses, parabolas, hyperbolas—in human movement could ripple across the interdisciplinary study of “active matter,” which examines group behavior in populations ranging from clumps of bacteria to herds of animals. Lane formation has already been observed at so-called zebra crossings—pedestrian street crosswalks marked by fat white stripes—but now, the Bath team believes mathematical shapes could be nucleated in flocks of all species, or even inanimate entities such as charged atoms or cell organelles.
It’s a “neat mathematical theory,” said Rogers. “We now know that much more structure exists than previously thought.”
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