# Simanaitis Says

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# IT SEEMS LIKE AN INFINITY… AND SO IT IS: ∞

IN MY CONTINUING exploration of math symbols, what better one to examine these days than ∞, the symbol for infinity. Here are tidbits on its definition, origin, and modern uses.

A Dictionary’s View. Merriam-Webster defines “infinity” as “the quality of being infinite; unlimited extent of time, space, or quantity: boundlessness.” It adds “an indefinitely great number or amount,” and then gets positively mathematical about it with infinite sums, functions, variables, parallel lines, and other stuff like aleph-null. To get more of these, check out “You Can Count on Me—or Maybe Not.

Infinity’s etymology is straightforward: “borrowed from Latin infinitāt-, infinitās.” These employ the Latin in- (as in “inaccessible”) with its finis, (as in “final”). Loosely, “no finality.”

M-W cites the word’s earliest use was in the 14th century, in the sense of “no finality.” The symbol ∞ came some 300 years later.

The symbol ∞. English mathematician John Wallis is credited with introducing ∞ to represent the concept of infinity.

John Wallis, 1616–1703, English clergyman, mathematician, chief cryptographer for Parliament and, later, for the royal court.

Wallis also took part in the development of calculus. This mathematical study of continuous change was invented dually, but not jointly by Sir Isaac Newton, 1643–1727, and Gottfried Wilhelm von Leibnitz, 1646–1716. Calculus was originally called “the calculus of infinitesimals,” calculation of little stuff. Having introduced ∞ for infinity, Wallis also employed 1/∞ to represent an infinitesimal.

The Lemniscate. In algebraic geometry, there’s a related curve called the lemniscate, sort of an ∞-shape curve looking like a ribbon bow. Indeed, lemniscates have been studied since ancient Greek mathematics. According to Wikipedia, they get their name from the Greek λημνίσκος, lemniskos, “ribbons.”

The Lemniscate of Bernoulli, showing its two foci. Image by Zorgit from Wikipedia.

With its foci included, it reminds me of someone wearing cool glasses.

On Tarot Cards. I hadn’t realized there was more than one kind of Tarot Cards, but research indicates otherwise: The Rider-Waite-Smith tarot deck, a relative newcomer in 1910, is only one of many. It gets its name from illustrator Pamela Colman Smith, who gained her tarot lore from academic and mystic A.E. Waite, the resulting deck being published by the Rider Company.

It seems to me that the Smith-Waite-Rider would be a more appropriate name, but this combination isn’t listed among others at Rider-Waite tarot deck.

“The infinity symbol appears on several cards of the Rider-Waite tarot deck,” writes Wikipedia.

My exhaustive examination of the 78 cards in the Rider-Waite tarot deck yielded a total of three. In addition to Strength shown here, The Magician and the Two of Pentacles each has an ∞.

I did find a reasonable sketch of my cat πwacket accompanying the Queen of Wands.

Vladimir Nabokov’s Lemniscate. Russian-American poet/novelist Vladimir Nabokov used the lemniscate in his novel/poem Pale Fire and in his final novel The Gift as symbolic representations of the Möbius strip and the infinite, “descriptions of the shapes of bicycle tire tracks and of the outlines of half-remembered people,” or so says Wikipedia.

I didn’t understand Lolita either, but maybe it’s just me. I’m fine with ∞. ds