Last time I promised you a shape with no shell and no fluid — a crowd of small bodies, each obeying a couple of rules about its nearest neighbours, making a pattern that belongs to none of them. That was very nearly right, and the part it gets wrong is the whole story.
Watching a murmuration, the obvious question is how they avoid hitting each other. The better question is why the thing never comes apart.
Ten flocks over Rome
In the mid-2000s a group of physicists put stereo cameras on a rooftop near Termini station and photographed starlings coming in to roost at dusk, reconstructing the position of every bird in three dimensions for flocks of up to 2,600 — roughly a hundred times more birds than anyone had managed before.
Then they asked a question that sounds trivial and is not. Each bird is plainly responding to the ones near it. Near in what sense?
There are only two answers. Either the rule contains a length — attend to anything within so many metres — or it contains a count — attend to your six nearest, wherever they happen to be. Inside a single flock these are indistinguishable. Across ten flocks they separate, because flocks differ enormously in how tightly packed they are. In the densest one, neighbours sat about 0.68 m apart. In the sparsest, 1.51 m. A length would trap wildly different numbers of birds in those two flocks; a count would sit still while the distance stretched.
The count sat still. Six and a half neighbours, give or take one — flat across every flock, with essentially no correlation to density at all. The metric range, measured the same way, tracked sparseness closely. Two birds a metre apart in a tight flock are coupled exactly as strongly as two birds five metres apart in a loose one.
The rule has no length in it.
What that buys
Consider what a peregrine does to a flock. It contracts, expands, tears open, splits and reforms, its density changing violently second by second and in different places at once.
Run a metric rule through that. The instant your patch of sky thins past your radius, your neighbours are simply gone. You are flying alone with no instructions, and the flock has shed a straggler at the exact moment when being a straggler is fatal — stragglers and small groups are what get taken. A rule with a length in it fails hardest precisely when it matters most.
A rule with only a count in it cannot fail that way. Double the spacing and every bird still has six nearest neighbours; they are merely further off. There is no density at which the flock stops being connected, because connection was never about distance. The most abstract-sounding thing about a murmuration is its armour.
Which is where it parts company with its neighbours in this archive. The emperor penguin huddle of No. 76 is also a crowd of birds moving in waves, but it is metric right down to contact — it works because bodies touch, and its whole purpose is to close the gaps. The phantom traffic jam of No. 9 is a pattern travelling through a medium while the medium goes somewhere else; a murmuration has no medium, because the birds are not the stuff the pattern moves through, they are the whole system.
Why six?
Here is the part I did not expect. Six or seven is far fewer than the birds a starling can see. Sightlines inside a flock are mostly open; each bird has dozens of unobstructed neighbours available to it. So the ceiling is not in the eye. It is behind the eye.
What it resembles is subitizing — holding a small number of separate moving objects in mind at once without losing track of which is which. It is what lets you glance at four coins and know there are four without counting, and it runs out below ten in every animal tested for it. Trained pigeons can reliably tell apart sets of objects up to about seven, and then stop: a laboratory result, from a different bird, doing an entirely different task, landing on top of the field measurement.
If that is the right reading, the shape over the roost is not really a shape made of birds. It is a picture, drawn a thousand feet wide, of how many things one small brain can hold at the same time.
What nobody is holding
No leader, then, no shell, no scale. When a flock turns, the same group later found, the decision starts with a few birds and crosses the rest as a clean front, barely fading — more like a sound than like a rumour, and faster the more closely aligned the flock already is. Every bird carrying it will be on a branch within the hour, and a different set will fly the thing tomorrow. None of them is holding the shape. Each is holding six or seven other birds, and the shape is what that looks like from the ground.
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One loop I’m watching
Next: a shape that is always the same size as the thing that makes it — a bend keeping its proportions whether you find it in a creek you can step across or a river you can pick out from orbit, sliding steadily downhill while nothing inside it stays put, until it curves so far that it strangles itself. Next time.