The original story of Alice's Adventures in Wonderland is missing what have become some of the book's most iconic characters and scenes: the Cheshire Cat, the Mad Hatter's tea party, the Knave of Hearts' trial, and several other great moments. Why did Charles Dodgson (aka Lewis Carroll) add them later? According to Alice scholar Melanie Bayley, Dodgson, a mathematician by day, created the scenes to make fun of edgy math ideas floating around at the time. From New Scientist:
Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid's proofs, reductio ad absurdum, he picked apart the "semi-logic" of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice's Adventures in Wonderland.
"Alice's adventures in algebra: Wonderland solved"
Take the chapter "Advice from a caterpillar", for example. By this point, Alice has fallen down a rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. Enter the Caterpillar, smoking a hookah pipe, who shows Alice a mushroom that can restore her to her proper size. The snag, of course, is that one side of the mushroom stretches her neck, while another shrinks her torso. She must eat exactly the right balance to regain her proper size and proportions.
While some have argued that this scene, with its hookah and "magic mushroom", is about drugs, I believe it's actually about what Dodgson saw as the absurdity of symbolic algebra, which severed the link between algebra, arithmetic and his beloved geometry...
The madness of Wonderland, I believe, reflects Dodgson's views on the dangers of this new symbolic algebra. Alice has moved from a rational world to a land where even numbers behave erratically.
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