Logic and Lewis Carroll

Francine F Abeles in Nature:

CatIn 1855, Charles L. Dodgson became the mathematical lecturer at Christ Church College in the University of Oxford, UK. His job was to prepare Christ Church men (for it was all men) to pass examinations in mathematics. Dodgson (1832–98) would go on to publish Alice's Adventures in Wonderland (1865) and Through the Looking-Glass (1871) under the pen name Lewis Carroll, but he also produced many pamphlets and ten books on mathematical topics. In some of these, he exhibited unusual methods — for rapid arithmetic, for example. Others featured innovative ideas that foreshadowed developments in the twentieth century, for instance in voting theory. All but two of these books were published by Macmillan (until this year, the parent company of this journal's publisher). Macmillan co-founder Alexander Macmillan was Dodgson's trusted publisher and friend for 35 years (see go.nature.com/9q8oqe).

What unifies Carroll's oeuvre is the wit and colour apparent in the manifestations of his wide-ranging mathematical interests, particularly in geometry and logic. The Alice books contain many supreme examples. The “Mad Tea-Party”, for instance, has the Hare, Hatter, Dormouse and Alice circling around static place settings like numbers on a circle, as in a modular system, rather than in a line. Carroll developed the earliest modern use of today's 'logic trees', a graphical technique for determining the validity of complex arguments that he called the 'method of trees'. This was a step towards automated approaches to solving multiple connected problems of logic. True to form, the puzzles that Carroll solves with his trees are given quirky names — “The Problem of Grocers on Bicycles”, “The Pigs and Balloons Problem”.

Picture: A love of puzzles is clear in the call to behead the bodyless Cheshire Cat: what, exactly, would you behead?

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