13 January 2010

Alice's Adventures in Algebra


There was an fascinating article at New Scientist last month about the influence of Charles Dodgson's mathematics interests on his writing of Alice in Wonderland.
What would Lewis Carroll's Alice's Adventures in Wonderland be without the Cheshire Cat, the trial, the Duchess's baby or the Mad Hatter's tea party? Look at the original story that the author told Alice Liddell and her two sisters one day during a boat trip near Oxford, though, and you'll find that these famous characters and scenes are missing from the text...

...in 1984 Helena Pycior of the University of Wisconsin-Milwaukee had linked the trial of the Knave of Hearts with a Victorian book on algebra... [Victorian] scholars had started routinely using seemingly nonsensical concepts such as imaginary numbers - the square root of a negative number... To Dodgson, though, the new mathematics was absurd, and while he accepted it might be interesting to an advanced mathematician, he believed it would be impossible to teach to an undergraduate.
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
The article then goes on to discuss the relationship of the Cheshire cat scene, the tea party, and the other non-original scenes to Dodgson's conservative view of mathematics.
What, then, would remain of Alice's Adventures in Wonderland without these analogies? Nothing but Dodgson's original nursery tale, Alice's Adventures Under Ground, charming but short on characteristic nonsense.
Full details at the link, via NAACAL.  The embedded photos are selections from a wonderful gallery of film stills from Alice in Wonderland ( Clyde Geronomi and Wilfred Jackson, 1951)

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