Get the flock out of there

Most people act locally, even if their behavior has a global appearance. Like birds. Starlings are a case in point. In many locales they can be seen swarming to roosting sites, huge clouds of them wheeling an gyrating at dusk before settling into trees or on buildings. If attacked, the swarm splits, merges and splits again, then comes back together. They don't just scatter, literally to the four winds. This kind of emergent behavior -- where local interactions produce global patterns -- has attracted scientists. Statistical physicists have been particularly interested, as this behavior mirrors what goes on when liquids boil or ice melts. Well, maybe not actually mirrors it. But the same techniques can be used to study it. Starlings and other flocking birds also have public health importance. We don't have to tell you that, though. Back to statistical physics.

Using techniques of statistical physics you can make a variety of computer models that to the eye seem to mimic flocking behavior. The key word here is "variety." There are lots of different models that encode local behavior like regulating the distance of a point (representing a bird) to other other points, to nearest points, to the average distance of a certain number of points, etc. When you run them they look like birds flocking. But what do flocking birds really look like, quantitatively? That's a pretty hard question to answer because if you have thousands or even tens of thousands of starlings whipping around in the twilight, they are performing a complicated dance in three dimensions. One camera won't do it. You need stereo, i.e., two cameras, precisely registered. Then the problem becomes figuring out in each camera's pictures, which are the same birds. A team of statistical physicists in Italy (StarFlag) have been trying to do that for several years and finally seemed to have solved this problem. Now they have a rough idea of what a 3D swarm really looks like. With data, they are starting to figure out some of the local rules (the etiquette of each bird in relation to the others) which produce the global swarm:

"We looked at our three-dimensional data and considered a given bird, and then we measured the angular positions of its nearest neighbors," [physicist Irene Giardina] continues. The distribution of angular positions turns out to be anisotropic [not uniform in all directions], a result that StarFlag scientists presented at a couple of conferences over the summer. "There is much more probability of finding its nearest neighbor on the side, rather than in front or back along the direction of motion," says Giardina. "We measured this probability also for the second and third neighbors, and so on. And we found that birds interact with six or seven neighbors. After that, the anisotropy decays. That's the point where the spatial structure becomes isotropic."

It turns out, Giardina says, that these "topological interactions are much more robust to perturbations" than a model in which a bird interacts with other birds within a fixed distance. The anisotropy, she adds, makes sense biologically: "It's related to vision, since the physiology of the eye is not isotropic." (Physics Today)

I became interested in these kinds of applications of statistical physics because they pertain to more than phase changes (condensation, melting, etc.) or bird flocking. And epidemiologists have noticed that the sudden change from endemic to epidemic of diseases in populations bears a resemblance to other physical processes where local behavior have global significance, such as percolation of liquids through rocks or the appearance of ferromagnetism or paramagnetism. Then there's human behavior:

One [project] involves how others' choices affect what music people download. The other?topical to France's summer elections?is how people are influenced by others when they vote. Along the same lines, a group of economists in Pisa, Italy, is studying the collective behavior of banks as indicated by where they open branches. Starling flocking is more complex, says [StarFlag's Jean-Philippe] Bouchaud, "because it's a three-dimensional organization of birds in space. But the idea is to work up from the behavior of individual birds to the behavior of the flock." The connection to studies of people is indirect, he adds. "Behind these projects is the same fascination with collective effects that glues the whole project together.

We all like to think of ourselves as unique, free agents. But we are also subject to various rules regulating our behavior with other free agents. Out of those interactions come higher order regularities. So while I may not be that attractive, I (and you) have at least something in common with a magnet.