Fireflies

Some fireflies do this in the wild. Whole riverbanks of them in Southeast Asia, and a species in the Great Smoky Mountains, end up flashing in unison — thousands of insects keeping one beat with no conductor, no signal to start, and nobody counting. For a long time it was easier to believe the observers were imagining it than to explain how it could happen.

The explanation turned out to be almost embarrassingly small. Give every firefly its own clock, running a little fast or a little slow. Let each one, when it sees others flash slightly ahead of it, hurry a touch; slightly behind, wait a touch. That's the whole rule. In 1975 the physicist Yoshiki Kuramoto wrote down the cleanest version of it, and showed something surprising: the meadow does not drift gradually toward order. It stays a random twinkle until the pull between the insects passes a critical strength set by how much their clocks disagree — and then order switches on, like water freezing.

The slider is that pull, in units of the critical value, so the threshold is always at 1. Below it, the phase dial underneath shows a ring of scattered dots and the arrow at its centre stays short. Above it, a clump forms on the dial, pulls in its neighbours, and the arrow swings out toward the rim. At the default setting this meadow pulls itself together in about ten seconds. The chart beside the dial was measured on sixteen copies of this exact meadow, one per setting, so you can see the cliff it falls off.

Then play with it. Hold a lantern in the grass and flash your own steady beat: the fireflies near you lock to it even with the dial at zero, because to the model a lamp is just one more firefly that refuses to be persuaded. Switch sight to neighbours only and the meadow synchronises in patches that compete before one wins. Startle a patch and watch the rest of the meadow drag it back into step. The same arithmetic describes pacemaker cells in a heart, generators on a power grid and crowds that fall into rhythmic applause — order nobody ordered.