Algebra With Alice

The first time I read “Alice’s Adventures in Wonderland,” by Lewis Carroll, I’d read an abridged, version, meant for toddlers. It went by in a whir.

When I read it for the second time, as an adult, I read the unabridged version, but with an inattentive mind.

It’s when I picked the book up for the third time, recently, that I read it very slowly and closely, even keeping track of the number of times Alice see-sawed between the sizes, XXL and XS.

When Alice scurries down the rabbit hole, she enters an absurd land where she can’t hold her height steady.

She swings between the extremes of either shrinking into an itty-bitty, doll, no taller than a thimble, or blowing up into a giantess, towering over treetops.

Every creature she encounters there has a strangeness about it: a Cheshire Cat that grins; a baby that morphs into a pig; a tea party, forever frozen at six o’clock; a curious croquet ground where the balls are live hedgehogs and the mallets, live flamingoes.

They speak in a peculiar English, infused with a twisted logic.

The Duchess, who has a habit of punctuating her every story with the word “moral,” tells Alice, “There’s a large mustard-mine near here. And the moral of that is—“The more there is of mine, the less there is of yours.”

When Alice asks the Mock Turtle, “Why did you call him Tortoise if he wasn’t one?

“We called him Tortoise because he taught us,” he replies.

The Cat, apparently only affirming Alice’s belief, declares, “We’re all mad here.”

If they all sound a tad crazy, well, then, they ought to.

The author, whose real name was Charles Dodgson, was a math instructor at Oxford, and he used the tale as an allegory to attack the emergent concepts in mathematics that were gaining ground in his day as hokum, writes Melanie Bayley, in an op-ed in the New York Times.

Dodgson found the radical new math illogical and lacking in intellectual rigor.

Alice has slid down from a world governed by the logic of universal arithmetic to one where her size can vary from nine feet to three inches.

When Alice tells the Caterpillar, “Being so many different sizes in a day is very confusing,” he says, “No, it isn’t.” He advises her to “keep [her] temper.”

The Caterpillar, writes Bayley, represents Augustus De Morgan, a London math professor, who’d proposed in the mid-19th century, “a more modern approach to algebra, which held that any procedure was valid as long as it followed an internal logic.”

In Dodgson’s day, intellectuals still understood “temper” to mean the proportions in which qualities were mixed — as in “tempered steel” — so the Caterpillar is telling Alice not to avoid getting angry but to stay in proportion, even if she can’t “keep the same size for 10 minutes together!” Proportion, rather than absolute length, was what mattered in Alice’s above-ground world of Euclidean geometry.

The chapter “Pig and Pepper,” spoofs the principle of continuity, a bizarre concept from projective geometry, introduced in the mid-19th century France, which suggests that one shape can bend and stretch into another.

In a case of a notion stretched to its extreme, the Duchess’ baby turns into a pig.

We should read the “Tea-Party” as “t-party,” where “t” is the mathematical symbol for time.

At the mad tea party, time is the absent fourth presence at the table. The Hatter tells Alice that he quarreled with Time last March, and now “he won’t do a thing I ask.” So the Hatter, the Hare and the Dormouse (the third “term”) are forced to rotate forever in a plane around the tea table.

The Queen of Hearts probably represents an irrational number. “(Her keenness to execute everyone comes from a ghastly pun on axes — the plural of axis on a graph.)”

h/t: NYT


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