How can a shoelace knot hold and still come undone?

A shoelace can stay tied through many steps and then suddenly trail behind a shoe. Nothing has been cut or broken. A bow holds because of its shape and the friction between its strands, and those same strands can slide free when the arrangement loosens.

Inside the tightened knot, the lace bends around itself. Touching strands press against one another, and friction resists their sliding. The contact pattern matters: knots that look almost alike can distribute forces differently and hold differently. The bow is a small structure made from a flexible line.

The loops are folded lengths of lace. Pulling a free end can draw one of those folds back through the knot, allowing the bow to open without cutting it. A loop lets the same knot be both a fastening and something that can be released.

Walking repeatedly changes the forces. Impacts disturb the knot, while the moving free ends tug on it. If enough slipping begins, a loop can shrink rapidly and disappear. That explains the surprise of a suddenly loose lace: small disturbances have changed the arrangement until the grip no longer holds. The material remains the same; its path and contacts have changed.