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Alice’s adventures in algebra: Wonderland solved

By Melanie Bayley, New Scientist, 16 December 2009

New Scientist allows me to reproduce a 200 word excerpt of the full article online. Read the full article.

[…] The madness of Wonderland, I believe, reflects Dodgson’s views on the dangers of [the] new symbolic algebra.

The Caterpillar’s warning […] is perhaps one of the most telling clues to Dodgson’s conservative mathematics. “Keep your temper,” he announces. Alice presumes he’s telling her not to get angry, but although he has been abrupt he has not been particularly irritable at this point, so it’s a somewhat puzzling thing to announce.
To intellectuals at the time, though, the word “temper” also retained its original sense of “the proportion in which qualities are mingled”, a meaning that lives on today in phrases such as “justice tempered with mercy”. So the Caterpillar could well be telling Alice to keep her body in proportion – no matter what her size.

This may […] reflect Dodgson’s love of Euclidean geometry, where absolute magnitude doesn’t matter: what’s important is the ratio of one length to another […]. To survive in Wonderland, Alice must act like a Euclidean geometer, keeping her ratios constant, even if her size changes.

Of course, she doesn’t. She swallows a piece of mushroom and her neck grows like a serpent […].

It’s an important precursor to the next chapter […], where Dodgson parodies another type of geometry.