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Birds' turns match math of quantum matter

Equations of superfluidity may explain spread of information in a starling flock

10:00am, July 31, 2014

CHANGING DIRECTION  Flocks of starlings turn in less than a second. The math that explains those turns may be similar to the equations used to describe superfluid helium’s quantum behavior.

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Starlings seem to have nothing in common with quantum matter. But the equations explaining some of the quantum dynamics of superfluid helium may describe what happens when a flock of starlings makes a sharp turn.

Hundreds or thousands of starlings can flock together and appear to move through the sky as a single organism, shifting directions as though of one mind. “The moment the decision to turn is sweeping through the flock is a moment of weakness in the group,” says physicist Andrea Cavagna of the Sapienza University of Rome. He explains that during starlings’ turns, predators such as peregrine falcons can strike because the flock isn’t flying as cohesively as possible.

Since sticking together during turns is so important, Cavagna and his colleagues wondered how information about which way and when to turn spreads through a flock. Previous computer simulations suggested that each bird’s behavior changes to match its neighbor’s in a manner that resembles the game of telephone: The cue to turn diffuses from one bird to the next but may fade out as it reaches the outer birds in a flock.

But when Cavagna and his colleagues filmed 12 flocks, each with up to 500 starlings, and tracked the three-dimensional trajectory of each bird, the footage suggested something different. The birds turn as a nearly cohesive group, almost like synchronized swimmers. The decision to turn begins with a few birds and then travels through the flock at a fixed speed, spreading across 400 birds in a little more than half a second, Cavagna and his colleagues report July 27 in Nature Physics. That’s too fast for the diffusion scenario to work.

To develop a mathematical explanation of how flocks turn, researchers recorded groups of starlings flying above Rome. The team then simulated each bird’s three-dimensional trajectory (axes shown in meters). A few birds lead the turn, the researchers found, and the information about changing direction reaches all birds in a little more than half a second

A. Attanasi et al/Nature Physics 2014

This is a “really extraordinary experimental observation,” says physicist William Bialek of Princeton University, who was not involved in the study. Another problem with diffusion, he says, is that it assumes that if a bird suddenly found itself surrounded by neighbors flying in the opposite direction, the wayward bird could reverse its direction almost instantaneously. That seems wrong, he says. The bird should have some inertia, or resistance to change its direction.

Cavagna and his colleagues account for inertia in their own mathematical description of flock turns. They conclude that variations in how the birds orient themselves with each other are the cues that pass through a turning flock. Those variations have to be maintained throughout the flock for the birds to fly cohesively, which could be why the cue to change direction moves in a fixed amount of time from bird to bird. If a misalignment between birds arises somewhere in the flock, the kink cannot be resolved among a few birds. Instead, the misalignment has to travel through the entire flock, and the group collectively changes its direction.

The equations that explain this behavior match the mathematics used to describe some of the quantum dynamics of superfluid helium. A superfluid acts like a fluid but can flow freely without resistance. In this state, all particles orient in the same way, as if they were clocks with hands pointed to the same time. The similarities between the way the birds and quantum particles orient themselves leads to an identical mathematical structure in two very different systems, Cavagna and his colleagues write. 

Not everyone is convinced. Physicist John Toner of the University of Oregon in Eugene argues that the new mathematical description isn’t necessary to understand the birds’ behavior. He also suggests that even if the new equations do hold up, they may not apply to all bird flocks, especially extremely large ones such as flamingo flocks in Africa and India, which each have hundreds of thousands of birds.


A. Attanasi et al. Information transfer and behavioural inertia in starling flocks. Nature Physics. Published online July 27, 2014. doi: 10.1038/NPHYS3035.

Further Reading

D. Castelvecchi. Birds network too. Science News. Vol. 173, February 23, 2008, p. 125.

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