Take a doughnut (not a traditional British one, but an American one with a hole in the middle). Lay it on a chopping block. Take a sharp knife and hold the blade so that its edge is exactly above the inside edge of the doughnut. Cut vertically downwards to split the doughnut in two. If you examine the cut ends of the pieces, you will find the outline of the smaller one looks like a figure eight or an infinity sign. You have just created an imperfect example of a lemniscate, a type of mathematical curve.
Lemniscates were named by the Swiss mathematician Jacob Bernoulli, who published a description of them in 1694. He took their name from the Latin lēmniscātus, decorated with ribbons, for no very obvious reason we can now understand except that perhaps the curves looked like ribbons tied into a bow. He is remembered for his studies of one member of the set in particular, now called the lemniscate of Bernoulli. The one in your doughnut is the lemniscate of Booth, named after James Booth, a nineteenth-century mathematician of Irish birth who worked in the same field.
To attach Booth’s name to it is to deprive a Greek mathematician of the fifth century CE named Proclus of the credit for discovering it. He called Booth’s curve a hippopede, a horse fetter, because it looked like a device for hobbling a horse’s feet.
Outside mathematics, lemniscate frequently takes on mystical or occult undertones because of the associations of the infinity symbol with the Tarot and the teachings of the Russian spiritualist Madame Blavatsky.
The cosmic lemniscate, or sidewise figure-eight, the symbol of infinity, hovered like a halo above the Magician’s head, and about his waist was clasped a serpent devouring its own tail: the worm Ouroborus, a symbol of eternity. All things in all space and time — that was the grandeur of the concept for which this modern Magician strived.
God of Tarot, by Piers Anthony, 1989.
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