Catenary
Give the chain both ends and nothing else to do and it will find, without being told, the one curve that lets it fall as far as its own length allows —
no parabola, though it wears one the way a shy thing wears a stranger’s coat; a cosh, a slow hyperbolic give, the shape of weight admitting weight.
It is not deciding. It is not brave. It simply stops holding what it cannot hold and hangs there, honest, in pure tension, every link pulled straight and none of them bent.
Now lift it off its nails. Turn it over. Freeze the sag to stone and stand it up: the giving-way, inverted, is an arch — the same line, every link now pushed instead of pulled,
and still not one of them bends. This is the secret the cathedrals kept: that the strongest thing you can raise over a room is a picture of surrender, held upside down.
Hooke hid it in a scramble of Latin. Gaudí read it in a mirror, from strings and little bags of shot. A chain gives up; a nave stands on the giving-up; and — because the world throws in more than it owes —
a square wheel, the very joke of a wheel, rolls level as still water down a road of these same curves laid end to end, the fall of the road and the tip of the wheel
cancelling, to the last place we can count. Everything that hangs is telling the truth about its weight. Turn the truth over and you can build on it.
