# The Mathematical Satire Hidden in Alice’s Adventures in Wonderland

Over the last 150 years, many readers and literary critics have pondered sources of inspiration for *Alice’s Adventures in Wonderland* and *Alice Through the Looking Glass. * There have been many diverse theories about the characters, the plot, and world created by Lewis Carroll. Few, though, would have guessed that underneath the madness of Wonderland lies a world of mathematics.

In *The New Scientist*, Melanie Bayley (2009) analyzed *Alice’s Adventures in Wonderland* to find the mathematical inspiration hidden in the novel. According to her article “Alice’s Adventures in Algebra: Wonderland Solved,” Lewis Carroll, whose real name was Charles Dodgson, wanted to satirize the new abstract mathematics that were beginning to championed in Oxford University during the 1860s.

Dodgson was a teacher of mathematics at Oxford during a turbulent period for mathematicians. The discovery of non-Euclidean geometry, the development of symbolic algebra, and the use of imaginary numbers were not acceptable to those who held very traditional views of mathematics; Dodgson was one of their numbers, a traditional mathematician who heartily disliked “the new abstract math” being taught at the university. Bayley describes him as a “stubbornly conservative” intellectual who was disheartened by what he saw as the deteriorating standards of rigor in the field of mathematics. He did not like the changes some of his fellow mathematicians were bringing to the discipline and he found those changes ripe for satire.

When the first version of *Alice’s Adventures in Wonderland*, titled *Alice’s Adventures Under Ground*, had been presented to the “real Alice,” a young lady named Alice Liddell, it did not contain any of the scenes that Bayley identifies as mathematical satire. Dodgson added the new material for publication and it is in this material that the mathematical allusions are found. One example of an added scene rife with Dodgson’s wit is The Mad Hatter’s Tea Party.

Bayley believes that the Tea Party scene was written to poke fun at William Hamilton, who introduced the concept of quaternion algebra in 1843. Working with the idea that complex numbers could be interpreted as points in a plane, Hamilton searched for a way to do the same for points in three-dimensional space. He worked with three terms for years—one for each dimension in space—but could only make them rotate in a plane. Only by adding a forth term—which he conceptualized as time—was he able to get the three-dimensional rotation he needed.

“It’s an idea that must have grated on a conservative mathematician like Dodgson,” Bayley explains. Hamilton’s work was hailed as an important milestone in abstract algebra, but not by Dodgson who satirized it in his novel. Bayley argues that the three characters of the Hatter, the March Hare, and the Dormouse represent three terms of a quaternion. The forth term, time, is missing.

The character of Time in the novel has fallen out with the Hatter and won’t let the Hatter move the clocks past six. Without Time the characters are trapped at the tea table (a plane) simply moving to find clean cups and saucers. As Bayley notes, this movement parallels Hamilton’s early attempts to calculate motion, which was limited to rotations in a plane before he added time to the mix. Without time, the numbers keep rotating and do not go anywhere—just like the Hatter, the March Hare, and the Dormouse keep going around the table without the character of Time. The madness in the scene parallels the idiocy Dodgson believed inherent in Hamilton’s concept.

Bayley discusses many more scenes from *Alice’s Adventures in Wonderland* that were added simply to poke fun at colleagues who championed “the new abstract math” or to ridicule changes at the University of Oxford. “I would venture that without Dodgson’s fierce satire aimed at his colleagues,” Bayley claims, “*Alice’s Adventures in Wonderland* would never have become famous, and Lewis Carroll would not be remembered as the unrivalled master of nonsense fiction.”

Reference

Bayley, M. (2009). Alice’s adventures in algebra: Wonderland solved. *New Scientist*. Retrieved from http://bit.ly/1HJG2jH

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