Mathematical mockery in Wonderland

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:
 2008 08 Alice-And-The-Caterpillar 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.

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.

"Alice's adventures in algebra: Wonderland solved"



  1. Wasn’t this already covered in Godel, Escher, Bach? Then again, most people never get through the first few chapters.

    1. Surely you mean they don’t get through the last few chapters.
      But then, actually warning you that the book stops making sense near the end, was by my reckoning a callous and dirty trick to have been played by the tortoise.

  2. This makes me a little sad, actually.

    I don’t really like to think of the guy who wrote Alice in Wonderland as a sad, spiteful, little man resorting to mockery because he doesn’t have the technical chops to go beyond a fairly narrow and reactionary circle of accepted mathematics.

  3. The full article seems to smack of the logic frequently employed by numerologists. On the other hand, my dismissal of the article’s logic could be a gut reaction similar to Phisrow’s reasoning.

  4. I’m not so sure that it has to be either mathematics or drugs. It could be both.

    Stoned Mathematician A: “Dude, what would happen if you found the square root…of negative one?!”

    Stoned Mathematician B: “Man, you are blowing my mind…we gotta write this shit down!”

    1. heh. i was a math major at berkeley, and was a weed fiend.

      another of the better students once mocked pot-head mathematicians within my earshot, for my benefit. guess my predilection was pretty obvious. “Dude, what IS a number? Can you put a number in a box?”

      after the final (abstract algebra, indecently), which i rocked vengefully, he asked me about one of the problems. after explaining my solution, i offered up the parting shot, “Later on man. Gotta go put some numbers in boxes.”

      Also: what’s the deal with older folks calling joints “numbers?” As in, “I hit my last number, I walked to the road. Last dance with Mary Jane….”

  5. @Daedalus: Heh, I am almost through reading “An Imaginary Tale: The Story of sqrt(-1)” by Paul Nahin, which is exactly what it says on the tin.

    Yay for Euler! I’m an EE (signal processing) and use imaginary numbers day in, day out.

  6. I’ve heard it said that the bit about the difference between a song, and the song’s name, and what the song is called, and what the song’s name is called, works as an introduction to the idea of references and dereferencing in programming languages.

  7. I agree with daedalus.

    Why can’t it be about both?

    I like multiple meanings and layers in my fiction.

  8. Being picky here but could you not have used one of the fantastic original illustrations for this story rather than a still from the Disney film?

  9. Imaginary numbers might have been controversial in the 16th century, but Euler was 18th century, and Gauss early 19th. It is extremely unlikely that Dodgson had any issues with imaginary numbers. Maybe the author is confusing them with quarternions, which are mid-19th century?

  10. This makes me think of a very old friend of mine (he’s now 79), who wrote his monograph on Dodgson’s incorporation of mathematics and logic way back in 1963. “Charles Dodgson, Semeiotician” by Daniel F. Kirk (University of Florida Press). Good luck finding a copy to read…

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