A flexible thread, coiled into a loop, was locked in a tiny box with liquid. It can either absorb water and swell like a sponge, or expel the moisture and shrink into a tight ball. The choice between these states depends on whether the thread has a knot – and which one.

The reason lies in entropy, a measure of disorder. A knot limits the possible bends of the thread, shifting the balance between order and chaos. Even a simple trefoil knot markedly shifts the critical point where the sponge turns into a ball.

Surprisingly, this molecular geometry isn't just for artificial carbon-based polymers. Inside cells, DNA and proteins constantly get tangled into knots, and their shape regulates biological processes. By controlling knots, you could create nanomachines that change shape on command.