Hard, but not impossible. In a study published last week in Physical Review Letters, physicists say they have found a principle at work in crowd motion. Rather than behaving like particles, people appear to move in a uniquely human but roughly predictable way—driven by precise but unconscious calculations that help us avoid collisions.

For two decades, researchers have been trying to pin down just what those laws are. Why do people in crowds move the way they do? The effort has been complicated by a simple fact: Unlike physical particles, which respond blindly to forces, people are capable of making their own decisions, and it’s hard to find a consistent rule to describe them.

Walking down the street , we feel like agents of our own destiny. But perhaps we shouldn’t be so sure. Behavioral scientists like to point out that often we move in a patterned way, as though conforming to natural laws we’re not even aware of. When you look at big groups in places like train stations and shopping malls, crowds sometimes mirror the behavior of liquids—clogging, forming channels, or assembling into vortexes.


“People, as they move through crowds, are always extrapolating into the future and deciding how far they are from colliding,” says Brian Skinner, a condensed matter physicist at the Argonne National Laboratory in Illinois and one of the authors of the paper.

Skinner and his coauthors, a pair of computer scientists at the University of Minnesota, looked at six data sets that capture individual movements in crowded places: four from natural settings, like video footage of pedestrians on a college campus, and two from laboratory experiments, in which participants were tracked with cameras as they navigated a corridor that narrowed into a bottleneck. Such data sets have become available only in the last five years, as improvements in camera technology and the field of computer vision have made large-scale pedestrian tracking possible.

Initially the researchers assumed they would find a “repulsive force” between people, like the one that pushes charged particles apart. As they looked closer, they realized it wasn’t that simple: There was a repulsive force between individuals, but it only operated sometimes. “Two people walking head first into each other have a strong interaction,” Skinner says, “but people walking side-by-side have almost no interaction.”


So the researchers went looking for a new rule. They found it in a variable they called “time to collision,” which explained many of the course adjustments they observed. The closer two people get to colliding, the more energy they expend getting out of each other’s way. To be technical, they found that the interaction between individuals in a crowd could be described as 1 over the square of the time to collision: As a collision becomes more imminent, the energy you apply to avoiding it goes up drastically.

Unlike with particles, the mechanism that produces these adjustments is an instinctive mental calculation rather than any kind of physical force. There’s also a limit to how far out we can—or need—to account for other people’s movement. When the time to collision was more than three seconds, the researchers found that the interaction energy between two pedestrians fell to zero, meaning people weren’t taking each other into account at all.

“If you’re close to somebody and they’re walking away from you, you automatically account for [that] fact,” says Stephen Guy, a computer scientist and coauthor of the study. “On the other side, if somebody is far away from you, but walking at you quickly...you’re likely to make a large adjustment to your velocity.”

The research describes the underlying dynamic present in every kind of crowd situation, be it a jumble of fans exiting a stadium or a loose constellation of pedestrians strolling through the park. “All these different kinds of flows follow this same kind of energy law, even though each has a different visual outcome,” says Guy. “There’s some aspect that’s the same in all of them, this aspect of anticipation.”


Research on crowd behavior has a lot of immediate applications. Rules of movement can help architects design buildings to better handle the way people really flow through them. Dinesh Manocha, a computer scientist at the University of North Carolina, is currently working with Boeing to model the movement of passengers onto and off of airplanes; he calls the recent paper “a wonderful explanation of humans in nature.”

Crowd modeling is also useful for creating training environments, in which event managers or soldiers can practice crowd control, and for making movie and video game animations more convincing. (“Artists can’t simulate every person in a crowd,” says Guy.) Eventually this kind of research could allow site managers to create real-time models of crowd behavior, allowing them to forecast and maybe prevent events like stampedes.

These types of applications suggest that even if people don’t behave in crowds like masses of electrons, that doesn’t mean we’re not our own flavor of elementary particle. Call it the person particle: It may have a mind of its own, but it turns out to be fairly predictable all the same.

Kevin Hartnett writes the Brainiac blog for Ideas. He can be reached at kshartnett18@gmail.com.

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