All these similarities seem to point to a grand unified theory of the swarm—a fundamental ultra-calculus that unites the various strands of group behavior. In one paper, Vicsek and a colleague wondered whether there might be “some simple underlying laws of nature (such as, e.g., the principles of thermodynamics) that produce the whole variety of the observed phenomena.”
Couzin has considered the same thing. “Why are we seeing this again and again?” he says. “There’s got to be something deeper and more fundamental.” Biologists are used to convergent evolution, like the streamlining of dolphins and sharks or echolocation in bats and whales—animals from separate lineages have similar adaptations. But convergent evolution of algorithms? Either all these collectives came up with different behaviors that produce the same outcomes—head-butting bees, neighbor-watching starlings, light-dodging golden shiners—or some basic rules underlie everything and the behaviors are the bridge from the rules to the collective.
Stephen Wolfram would probably say it’s the underlying rules. The British mathematician and inventor of the indispensable software Mathematica published a backbreaking 1,200-page book in 2002, A New Kind of Science, positing that emergent properties embodied by collectives came from simple programs that drove the complexity of snowflakes, shells, the brain, even the universe itself. Wolfram promised that his book would lead the way to uncovering those algorithms, but he never quite got there.
Couzin, on the other hand, is wary of claims that his field has hit upon the secret to life, the universe, and everything. “I’m very cautious about suggesting that there’ll be an underlying theory that’ll explain the stock market and neural systems and fish schools,” he says. “That’s relatively naive. There’s a danger in thinking that one equation fits all.” Physics predicts the interactions of his locusts, but the mechanism manifests through cannibalism. Math didn’t produce the biology; biology generated the math.
Still, just about any system of individual units pumped with energy—kinetic, thermal, whatever—produces patterns. Metal rods organize into vortices when bounced around on a vibrating platform. In a petri dish, muscle proteins migrate unidirectionally when pushed by molecular motors. Tumors spawn populations of rogue, mobile cells that align with and migrate into surrounding tissues, following a subset of trailblazing leader cells. That looks like a migrating swarm; figure out its algorithms and maybe you could divert it from vital organs or stop its progress.
The same kind of rules apply when you step up the complexity. The retina, that sheet of light-sensing tissue at the back of the eye, connects to the optic nerve and brain. Michael Berry, a Princeton neuroscientist, mounts patches of retinas on electrodes and shows them videos, watching their electrophysiological responses. In this context, the videos are like the moving spotlights Couzin uses with his shiners—and just as with the fish, Berry finds emergent behaviors with the addition of more neurons. “Whether the variable is direction, heading, or how you vote, you can map the mathematics from system to system,” Couzin says.