Crowds: Seas of Electrons, Waves of People

What can the behavior of subatomic particles tell us about social behavior?

Imagine you are at your favorite band’s concert. Searching for the best place to stand, you avoid the spaces that prevent you from getting a good view of the band, perhaps by moving closer to the stage, but you also want to make sure that your surrounding space isn’t overcrowded. You drift here and there, and eventually, you come to a spot where a sufficient compromise is reached. Everyone else at the concert shuffles around in the same way.

The exact evolution of crowds over time can be complex, but if its members all share similar preferences, then perhaps we can infer something about its broader, more general behavior. Based on this principle, Physics Professor Tomás Arias of Cornell University and his team recently created and successfully tested a novel method for modeling the overall behavior of such crowds, based on techniques used in physics.

Using the rationale employed in the above concert example, Arias and his team concluded that two main, independent factors affect how we individually pick our spots within a crowd: both how unfavorable a given location is and the crowdedness of that location. Hence, by minimizing both of these factors, everyone in the crowd should be content. Arias’ model assumes that the details of specific interactions between individuals are relatively inconsequential to the crowd’s overall behavior.

Unexpectedly, Arias realized that this framework highly resembled a seemingly unrelated concept in physics, density-functional theory (DFT), which is one of his areas of expertise. As the name suggests, a core component of DFT is the notion that information about electron density alone predicts much of the overall behavior of molecular or atomic systems no matter the specific interaction between individual electrons or other factors. Likewise, the team theorized that by merely observing how the crowd’s population density fluctuates over time, information about the individual’s spatial preferability and crowdedness may be inferred. Moreover, if one can determine these two factors, then one might determine how the overall crowd behaves.

Next, the team renamed the factors of spatial preferability and crowdedness, calling them vexation and frustration functions, respectively, as a reference to their analogous variables in DFT, potential (V) and functional (F). “We got the thesaurus out to try and find English words that start with the letters F and V, that also marked the mood of crowd behavior,” Arias said. This conceptual parallel between Arias’ model and DFT is significant because, in both cases, the variables are minimized.

To test the model, the senior experimenter of the team, Itai Cohen, set up experiments observing groups of flies confined to certain spaces and tracked their population densities. These spaces were heterogeneous: some parts of the same environment varied in temperature, and other spaces varied in terms of their geometry. Shockingly, the team not only successfully extracted the frustration and vexation functions from the fluctuating density of the flies, but conversely, using this newfound information, they were able to model the behavior of flies in different environments to a high degree of accuracy.

This is one of the first experiments to model a socially dynamic system without relying on other pre-existing frameworks. “The beauty of this paper is that we didn’t try to artificially force the model to fit ideas from physics, because we didn’t model the crowd as if they were a gas or a fluid of some sort. We constructed our model based simply on a set of reasonable, socially plausible assumptions instead,” Arias said.

Such promising results demonstrate that the team’s model could be widely applicable to real crowds. For example, it may be possible that by observing how the density of the crowd fluctuates, concert organizers could compute the maximum amount of people to let in at a given time to avoid dangerous trampling incidents. They could also analyze the crowd in real time, and quickly determine which doors may need to open or close to relieve pressure,  making public venues safer.

Indeed, the team hopes to move forward by extracting the vexation and frustration functions in real-time and by examining time-dependent crowds where the number of individuals going in and leaving a venue varies. They are also working on examining more complicated crowds with more than one type of actor. For instance, the interaction between police officers and protesters is not only an interesting scenario to consider, but a pertinent one. It’s uncanny how well DFT can be used to model human behavior—maybe we’re really just electrons after all.