Alice's Wonderland Is a World of Absurd Mathematics

December 22, 2009

Lewis Carroll was a pseudonym. The man behind the classic tale was a mathematician at Christ Church College, Oxford. In a recent article for New Scientist, Melanie Bayley, a doctor of Philosophy candidate at Oxford, explores the story and how Carroll used some of the most popular characters as vehicles to criticize 19^th century mathematicians.

The 19th century was a turbulent time for mathematics, with many new and controversial concepts, like imaginary numbers, becoming widely accepted in the mathematical community. While seemingly nonsensical, these concepts gave mathematicians the freedom to explore new ideas. According to Bayley, “some [mathematicians] were prepared to go along with these strange concepts as long as they were manipulated using a consistent framework of operations.”

Unfortunately Charles Dogson, Carroll’s real name, was a stubbornly conservative mathematician and found the new mathematics absurd.

“Even Dodgson's keenest admirers would admit he was a cautious mathematician who produced little original work,” said Bayley. “He was, however, a conscientious tutor, and, above everything, he valued the ancient Greek textbook Euclid's Elements as the epitome of mathematical thinking.” Unfortunately contemporary mathematicians were not always as rigorous as Euclid and their work departed from the physical reality that had grounded his works. 

“Outgunned in the specialist press, Dodgson took his mathematics to his fiction,” said Bayley. Using reducto ad absurdum, he picked apart the new abstract mathematics, taking its premises to their logical conclusions. The results were several scenes and characters in Alice’s Adventures in Wonderland. Specifically the Cheshire Cat, the trial, the Duchess’s baby, the Mad Hatter’s tea party, and the caterpillar.

In the chapter titled "Advice from a caterpillar," Alice a caterpillar smoking a hookah pipe. At this point in the story she has eaten a cake that has shrunk her to a height of just three inches. The caterpillar points out a mushroom that can restore her to proper size. The problem Alice then has to solve is how to consume this mushroom. Eating one side of it stretches her neck, while eating the other side shrinks her torso. She must eat exactly the right proportions 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,” said Bayley.

"The madness of Wonderland," said Bayley, "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."

Read the rest of Bayley’s analysis here.

Source: The New Scientist (December 16, 2009).

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