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.
- Log in to post comments
"This kind of emergent behavior -- where local interactions produce global patterns -- has attracted scientists."
Gawd, Revere. I love it when you talk dirty. Early in my indtrodution to H5N1 I began entertaining the notion that the emergence of a pandemic strain of H5N1 would be an emergent property of a system that includes the virus, the individual human host, and the collective of human behavior.
The phylogenic tree for H5N1 continues to expand and provide more possibilities for interaction between the elements of the system. As pointed out, it is in the interactions between elements that the new behavior emerges. As such, the behavior cannot be reduced to the behavior of any individual element, and it is, therefor, unpredictable.
It's also possible the next pandemic could emerge in several spatial locations at nearly the same time. In other words, there may be many index cases instead of one.
Fascinating and scary.
Snickel: "As such, the behavior cannot be reduced to the behavior of any individual element, and it is, therefore, unpredictable."
This doesn't necessarily make it unpredictable, but it might require new ways of predicting. Even sensitive dependence on initial conditions doesn't make something unpredictable in the short run, just in the "long run." Think weather systems; we're OK out a few days, maybe a week, but after that even small imprecisions in our initial conditions might swamp our predictions, might, that is, if the Navier-Stokes equations (or their equivalent for the weather system) were chaotic in the relevant parameter regimes. If you can prove they are, you can win yourself a million dollars from the Clay Institute.
The behavior of the Solar System is not reducible to the behavior of any individual planet, yet we can still predict well enough to send probes to Neptune, rovers to Mars and men to the Moon.