Mathematics and Literature

G1ASOC/G1A2SP-Mathematics and Society

* Mathematics and Literature

Lewis Carroll: Mathematics in Literature

"\'Can you do Addition?\' the White Queen asked. \'What\'s one and one and one and one and one and one and one and one and one?\'

\'I don\'t know,\' said Alice. \'I lost count.\'

\'She can\'t do Addition.\' The Red Queen interrupted."

--Lewis Carroll, Through the Looking Glass.

The literary works of Lewis Carroll are littered with references to mathematics, the vast majority more subtle and involved than the above. Although unquestionably written for a young audience, his renowned Alice books and his less well known novels all include references and allusions to sophisticated mathematical concepts and problems. This essay will introduce Carroll as a man and author, and attempt to identify examples of these references, analyzing their purpose and effect.

Charles Lutwidge Dodgson was born on January 271832 in rural Cheshire, the third of eleven children. He was apparently of colourful ancestry, Bakewell (1996) claiming he can, with "a certain amount of ingenuity" claim to have been related to Lady Godiva, the Earls of Mercia and Northumbria and even Queen Victoria. Yet the man himself seems to have led a far from colourful life. In 1851 he entered Christ Church, Oxford where he distinguished himself in mathematics, and remained there as librarian, mathematics lecturer, and curator for the next forty-seven years. As a mathematician his texts are widely considered as conservative and never significant, and are read now only because of historical interest. As a man he has been traditionally regarded as eccentric and at home only in the company of little girls. In fact, only the recent work of Karoline Leach (1996) in destroying the reliability of Dodgson\'s early biographers has begun to alter the long held view that his love for young girls was a suppressed sexual passion. Under the pen name of Lewis Carroll, Dodgson produced in Alice\'s Adventures in Wonderland, and the follow up Through the Looking Glass and what Alice Found There, two of the best loved children\'s books of all.

It is widely known that the Alice tales were born during what Dodgson described in his diary as "that golden afternoon" of the 4th of July 1862 when he entertained the children of the Dean at Christ Church with his stories, whilst on a rowing trip in Oxford. One of these children was of course the six-year-old Alice Liddell, the inspiration for the main character. Some months later Dodgson was encouraged to write the first draft of Alice\'s Adventures Under Ground, which by 1865 had developed into Alice\'s Adventures in Wonderland. This being well received, he followed up with the equally successful Through the Looking Glass in 1871. His first publication of humorous and other verses was Phantasmagoria and Other Poems in 1869. The acclaimed nonsense poem The Hunting of the Snark: an Agony in Eight Fits was published in March 1876. Sylvie and Bruno in 1889 and Sylvie and Bruno Concluded four years later represented the biggest effort by Carroll in literature, a mixture of fairy-tale, social novel and collection of ethical discussions, but they never came close to matching the success of his Alice books.

His other works are generally not well known, although were often quite interesting. A Tangled Tale published in 1885 was a series of puzzles and paradoxes and according to Fisher (1972) represented "...Carroll at his playful best in combining tantalising whimsy with straightforward mathematics". Similar puzzles appeared in Pillow-Problems in 1893. An attempt to introduce formal deductive logic to a kindergarten audience, was The Game of Logic which Carroll published in 1886. Although unsuccessful in so far as it was too challenging for such a young audience, it did introduce some interesting methods and the examples were as quaint as the contents of Wonderland. In developing the theme for a more adult audience his last book was Symbolic Logic: Part 1, Elementary, interestingly under the authorship of Lewis Carroll rather his real name that he still used for his mathematical publications. Of these none were of great impact, Euclid and his modern rivals is usually pointed to as a work of historical interest if not great mathematical incision.

To consider first Alice\'s Adventure in Wonderland, mathematical references and hints are present right from the very beginning. Alice\'s fall down the rabbit hole at the start