I was the shadow of the waxwing slain

By feigned remoteness in the windowpane.

I had a brain, five senses (one unique),

But otherwise I was a cloutish freak.

In sleeping dreams I played with other chaps

But really envied nothing — save perhaps

The miracle of a lemniscate left

Upon wet sand by nonchalantly deft

Bicycle tires.

-Vladimir Nabokov, Pale Fire

The lemniscate is the symbol of infinity, an endlessly traceable sideways figure eight, a twisted ouroboros engaged in an eternal process of renewal.


First called a “horse fetter” by Proclus, 5th century AD Greek philosopher and mathematician, who studied cross sections of tori. Analytically described by Bernoulli as the set of solutions to (x^2 + y^2)^2 - 2a^2(x^2-y^2) = 0, where a is a fixed real number. First used as a symbol for infinity by John Wallis, a 17th century English mathematician who pioneered the use of infinitesimals and helped prepare the ground for the calculus of Newton and Leibniz; he did not explain his choice. Euler later used an open variant, which has since fallen into disuse.

Euler’s open lemniscate. By Sapphorain, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=28853336

The lemniscate is source material for writers and artists. Beloved by mystics. Ubiquitous in tarot decks, particularly on the Juggler (Magician), who links Heaven and Earth, and on the Two of Pentacles.

The Juggler (or Magician) with a lemniscate in his hat. Note also the aleph on the right card. It signifies that, in the Tarot deck, the Juggler is the first of the Major Arcana and also calls to mind Cantor’s choice of notation for the infinite cardinals.
The Two of Pentacles

It is the figure idly traced on a tabletop while the mind is wandering elsewhere.


(1) to molder lazily on the couch. (2) to be sloth-like. (3) to lounge purposelessly, often associated with procrastination.

-Urban Dictionary

Victor Brauner, “The Surrealist”

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