Infinity Symbol

The infinity symbol is the horizontal figure-of-eight, the lemniscate, a single continuous loop that crosses itself and returns without beginning or end. As a mathematical sign it is precisely dated: the English mathematician John Wallis introduced it in 1655, in De Sectionibus Conicis, to denote the infinite, a quantity greater than any assignable number. Its inspiration is uncertain; proposed derivations include a variant Roman numeral for a great number, and the Greek final letter omega, the last and so the endless, but both are conjecture, since Wallis gave no explanation. The symbol is often conflated with the lemniscate curve proper, but the two have separate histories: the curve was described mathematically by Jacob Bernoulli in a 1694 paper in Acta Eruditorum, where he named it lemniscus, Latin for a hanging ribbon, for its resemblance to a looped ribbon lying on its side, some forty years after Wallis had already put a similar-looking mark to an unrelated use.

Bernoulli's curve has its own defining equation; Wallis's mark is typographic notation with no equation behind it, so treating them as one symbol collapses two distinct inventions into a single myth. The sign has no ancient religious pedigree, and is not the ouroboros nor an Egyptian device, though it is regularly presented as both. Its esoteric career begins in the nineteenth century, when the French occultist Eliphas Levi set it above the head of the Magician as a sign of unlimited spiritual force; that reading passed into the Rider-Waite tarot of 1909, illustrated by Pamela Colman Smith, hovering over the Magician and again over the woman in Strength, and from there into modern occultism and the jewellery trade, circulating today detached from both its mathematical origin and its occult borrowing.

Beyond mathematics the endless loop has been read as an emblem of eternity and of the limitless divine, of that which is without beginning, end or measure. The idea it pictures has deep religious roots: the mystical theology of the Kabbalah names the ultimate Godhead Ein Sof, the Without-End, the infinite beyond all limit and name, and many traditions figure the eternal by the circle, the endless knot or the serpent that swallows its tail, kindred images of a whole that has no edge.

In the modern esoteric tradition the lemniscate was set explicitly over the head of the Magician, and again with the tamer of the lion in the Strength card, of the influential Waite-Smith tarot of 1909, as a sign of unlimited spiritual power and of the eternal life-force channelled through the adept. The figure's wide decorative use today, on jewellery and as a token of endless love, is a recent and popular extension of this old meaning of the boundless.