Asked by: Robin Liddle, Manchester
The ability of flex, rope, cord or anything stringy to become hopelessly tangled is one of life’s familiar frustrations. Now some headphone makers have started fitting their products with flat, ribbon-like flex that they claim combats the menace.
The explanation lies in a branch of mathematics known as self-avoiding random walk theory. This focuses on the properties of random paths in three dimensions. These are what headphone flex follows when you shove it in your pocket. In 1988, mathematicians discovered that flex following such random paths is virtually certain to form a knot. The remedy is to stop the flex performing such contortions. Like ordinary flex, ribbon-like flex can bend easily – but only in two dimensions; its thickness makes it less able to bend in the third dimension. As knots require free movement in all three dimensions, this makes ribbon flex less prone to knotting.
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