Friday, August 3, 2007

The physics of crowds

In thinking of "social" behavior, we usually think of interactions with friends and community, social norms and so on. But these are fairly complicated human phenomena. In simplest terms, "social" merely implies some interaction between people, and maybe the simplest example is just walking around. You can walk on your own, as a lonely social atom wandering through empty space, or you can walk in the presence of others -- in which case interesting things start to happen.

In a post a while back I explored the curious phenomenon of lane formation in a street or hallway, whereby people walking with their own independent aims nevertheless segregate into well-defined lanes moving in either direction. There's a fascinating simulation of the process on the (old) website of the German physicist Dirk Helbing. Yesterday, in the course of some other research, I came upon some more recent work of Helbing's on human stampedes, in which people in the collective seem to follow physics that is eerily similar to that of the molecules in a fluid.

At least once a year, human stampedes seem to cause several hundred deaths. Most prominently are the almost routine problems during the Hajj (pilgrimage to Mecca) in Saudi Arabia. On 12 January, 2006, about 350 people died, while back in 1990 a similar crush killed almost 1500. Obviously, you can't do experiments with real people to see what causes these catastrophes.

Helbing, working with several Saudi scientists, has instead undertaken the analysis of video, where they can follow the motions of thousands of people in great detail, and then study the mathematics of their movements -- both in relatively normal flow conditions, and in times of crisis -- to clarify the differences. What they've already found is that the crowd at times undergoes a spontaneous transformation from regular ordered flow, akin to that of a fluid moving steadily within a pipe, to a turbulent flow characterized by enormous fluctuations -- irregular and chaotic motions within the crowd with the power to injure people.

Here's a fairly disturbing description of what happens, which they quote from earlier observations of other researchers:

At occupancies (crowd densities) of about 7 persons per square meter, the crowd becomes almost a fluid mass. Shock waves can be propeled through the mass, sufficient to... propel them distances of 3 meters or more... People may be literally lifted out of their shoes, and have clothing torn off. Intense crowd pressures, exacerbated by anxiety, make it difficult to breathe, which may finally cause compressive asphyxia. The heat and thermal insulation of surrounding bodies cause some to be weakened and faint. Access to those who fall is impossible.


The frightening thing is how utterly inhuman this description is; the people here simply do not have free will, but act as mechanical parts in a system, in this case in extreme conditions, which pushes them about according to its own collective forces.

Interestingly, and hopefully, the research of Helbing and colleagues shows that more mathematical scrutiny of such events may indeed help us understand these collective forces and learn to manage them. As they note, critical crowd conditions -- those that lead to real danger -- aren't obvious. Monitoring the average crowd density isn't enough, because there are often local fluctuations that produce much higher densities. Moreover, the most important quantity emerging from the video analysis isn't the density, but a slightly more abstract quantity -- the variance of people's moving speeds (how much they differ in a region) multiplied by the density, which plays the role of a pressure. Monitoring this pressure, which is what really leads to human damage, can help identify the places and moments when real trouble threatens. As they note, for example,

The crowd accident on January 12, 2006 started about 10 minutes after turbulent crowd motion set in, i.e. after the pressure exceeded a [critical] value...


They suggests that this pressure could be monitored (and rapidly calculated) from automatic video recordings.

As grisly and frightening as this example is, I think it illustrates with remarkable clarity how we can lose control over our own lives to stronger collective forces, even in this simplest of all social settings.

73 comments:

Len said...

And people have always thought I was crazy for not liking crowds.

Partha said...

I hesitate to bring this up because of the obvious macabre implications. Two-phase fluid flow (involving the flow of water together with various fractions of entrained vapor or gas) has been studied quite extensively (though mostly empirically), and might have applicability for the behavior of "heterogeneous" crowds.

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Social psychologists have studied the power of the situation from day 1. I practically laughed out loud to discover that physicists can use fluid mechanics to describe crowd behavior and the phenomena of stampedes! Fluid mechanics!!! Just imagine! Now if they could just look at authoritarism...

A crowd density of 7 persons per square meter is very, very dense --each person in a space ~15" x 15." It is hard to imagine too much variance in moving speed under such conditions unless some idiot yells "fire".

Earlier this summer, in Rome, I estimated the crowd density in the Vatican Museum at 1 person per 30" square, quadruple the space per person estimated by Helsing. That was unpleasantly crowded. Though, as I think about it now, it was rather like a river. Most people flowed along in the fast current in the middle, but some people formed little eddies on the sides. Those human particles thought they were stopping to admire a particular piece of art, but, heh. we know better. Plus at the end there was the Sistine Lake caused by the Michaelangelo Dam.

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