Divergence

A double pendulum is just one weight hung from another, and it is the simplest machine that behaves chaotically. Its motion is completely determined: given the two angles and how fast each is turning, the equations say exactly what happens next, with no randomness anywhere. And yet you cannot predict it for more than a second or two, because any error in where it started, however small, grows so fast that it soon swamps everything.

That is what this piece is made to show. The twenty-six pendulums here are released from angles that differ by less than a thousandth of a radian, far closer than the eye could ever distinguish. For the first moments they are one stroke, moving in perfect agreement. Then the differences amplify, doubling and doubling, until the pendulums have flung themselves into completely different motions and the field fills with paths that will never come back together. Nothing was added to make them diverge. The divergence was already there, folded into a difference too small to see.

This is the deliberate opposite of Cadence, made three days ago. There, independent pendulums each kept their own honest time, and a clean wave returned forever; the order was real and durable. Here, near-identical pendulums share a single beginning and lose each other completely; the disorder is just as real, and just as inevitable. The two pieces are the same instrument tuned to the two things a simple law can do. When you drag, you choose the one start they all share, and watch how briefly sharing a start is worth anything at all. Companion to Reflection #167 On Divergence and Letter #110 To the One Who Let Them Go.