Have you ever felt in Algebra class that you were sliding down a rabbit hole where things didn’t make sense any more? Maybe it’s because you were?!
Melanie Bayley, in New Scientist, argues that some of the most memorable scenes in Lewis Carroll’s (or Charles Dodgson, Oxford mathematician’s) opus ‘Alice’s Adventures in Wonderland’ – from the cheshire cat, to the caterpillar, to the Mad Hatter’s tea party – were in fact a satirical analysis of the (then) newfangled ideas of algebra and abstract maths. The tea party and quaternions?
the parallels between Hamilton’s maths and the Hatter’s tea party – or perhaps it should read “t-party” – are uncanny. Alice is now at a table with three strange characters: the Hatter, the March Hare and the Dormouse. The character Time, who has fallen out with the Hatter, is absent, and out of pique he won’t let the Hatter move the clocks past six. Reading this scene with Hamilton’s maths in mind, the members of the Hatter’s tea party represent three terms of a quaternion, in which the all-important fourth term, time, is missing. Without Time, we are told, the characters are stuck at the tea table, constantly moving round to find clean cups and saucers.
…Alice’s ensuing attempt to solve the riddle pokes fun at another aspect of quaternions: their multiplication is non-commutative, meaning that x × y is not the same as y × x. Alice’s answers are equally non-commutative. When the Hare tells her to “say what she means”, she replies that she does, “at least I mean what I say – that’s the same thing”. “Not the same thing a bit!” says the Hatter. “Why, you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!”
Hmmm… Or maybe the answer is that Maths is the Wonderland where fantastic things are possible?!
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