The enso (“circle”) is the emblem of Zen Buddhism. A simple circle drawn with a single, broad brushstroke, it is a symbol of infinity, and represents the infinite void, the ‘no-thing,’ the perfect meditative state, and Satori (enlightenment.)
Ouroboros is a greek word, and means “tail swallower.” The ouroboros is usually depicted in the form of a snake swallowing its tail, and is usually circular, although it is sometimes depicted in a lemniscate shape. It originated in Egypt as a symbol of the sun, and represented the travels of the sun disk. In Gnosticism, it was related to the solar God Abraxas, and signified eternity and the soul of the world.
In alchemy, the ouroboros represents the spirit of Mercury (the substance that permeates all matter), and symbolizes continuous renewal (a snake is often a symbol of resurrection, as it appears to be continually reborn as it sheds its skin.), the cycle of life and death, and harmony of opposites. A double ouroboros (two creatures swallowing one another) in alchemy signifies volatility. Spiritually, it signifies the balance of the upper and lower natures.
The Ouroboros appears in many other cultures and settings as well…the Serpent Jormungandr of Norse legend, who encircled the world, and guarded Yggdrasil, the Tree of Life, is often depicted as an ouroboros. The Aztec serpent God Queztacoatl was depicted similarly, and Chinese alchemical dragons have both similar shapes and meaning.
The mathematical symbol for infinity is known as the lemniscate. It was devised in 1655 by mathematician John Wallis, and named lemniscus, ribbon, by Bernoulli about forty years later. The symbol is patterned after the device known as a mobius (named after a nineteenth century mathematician) strip. A mobius strip is a strip of paper which is twisted and attached at the ends, forming a two dimensional surface.
The religious aspect of the infinity symbol predates its mathematical origins. It has been found in Tibetan rock carvings; the ouroboros, or infinity snake, is often depicted in this shape. In the tarot, the lemniscate represents the balance of forces and is often associated with the magician card.