a bird suddenly found itself surrounded by neighbors flying in the opposite direction,
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, the wayward bird could reverse its direction almost instantaneously. That seems wrong,
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, he says. The bird should have some inertia,
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, 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,
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, 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,
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, the misalignment has to travel through the entire flock,
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, 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,
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, 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,
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. Physicist John Toner of the University of Oregon in Eugene argues that the new mathematical description isn’t necessary to understand

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