Are knots technology? Knots were never invented: like fires, knots happen naturally. But unlike fire they cannot not be made useful by propagation: they have to be translated. Like language, knots are immaterial, passed on by example and subject to regional variation. Unlike language, knots are finite – there are only so many – and eternal – the same knots recur worlds and ages apart.

Like tools, knots are useful and increase our power over nature; but unlike tools, we carry them in our heads, not our hands. When they parallel tools, it is on a different level of abstraction. The trucker’s hitch is an image in cord of a block and tackle. It is no more a tool than a picture of a tool is – and yet it has the power of a tool.

Knots are a form of mathematics, but math with a difference. Arithmetic has a history of progress: but before history began, knots already embodied the highest level of mathematical abstraction. Knot theory is a twentieth century invention. Only in the twentieth century, only after thousands of years of development, did exoteric mathematics finally equal the mathematics esoteric in knots.

Knots are magic. With a piece of cord and a sequence of gestures we produce direct results in matter. “The rabbit jumps out of the hole, runs around the tree, and jumps back down the hole”: what is this but an incantation? Reasoning from knots, we get magic; reasoning from tools, we get technology. Technology works, magic doesn’t; nonetheless, the existence of knots violates the order of nature that technology presumes.