The Mathematics and Neurology of Wonderland

Tim Burton's highly stylized Alice in Wonderland brings to life Lewis Carroll's imagination, one inspired by mathematics and neurobiology. Historical evidence and conjecture paint Carroll's Alice's Adventures in Wonderland (1865) as less of a mere children's tale and more of a symbolic depiction of Carroll's views on novel algebraic concepts and his mental milieu. Carroll (1832–1898) was a 19th-century mathematician who likely suffered from epilepsy and/or migraines.

Researchers often cite Alice's growing and shrinking as support for the idea that the novel is saturated with symbolism. In Wonderland, Alice spends a good amount of time consuming things that alternately cause her to shrink and grow.

One interpretation of Alice's transformations takes into account Carroll's conservative mathematical views. Living and writing in a period that saw the emergence of controversial algebraic concepts, Carroll was apparently skeptical of these novel principles. In an article in New Scientist, Melanie Bayley argues that Wonderland represents in part symbolic geometry, which Carroll believed to be an absurd slight against Euclidean geometry. The latter, Bayley says, is more concerned with maintaining ratios than absolute magnitudes. In Wonderland, of course, Alice struggles to keep her size and proportions straight but finds that the bizarre world around her prevents her from doing either very easily.

Casting the mathematics hypothesis aside, there is another hypothesis which stipulates that Carroll may have experienced physical sensations of bodily distortion, possibly stemming from migraine-induced hallucination. In one analysis of the story, Podell and Robinson hypothesize that Carroll suffered from visual aura migraine symptoms that may have inspired some of the author's fanciful narratives. They report finding a Carroll drawing featuring a man with part of his right side missing, similar to what a migraine sufferer with a negative scotoma (or missing spot on the visual field) would see. Carroll's diary entries reveal that he consulted an oculist in the years before writing Wonderland, and that later, after publication of the Alice series, he explicitly experienced migraine hallucinations. Podell and Robinson thus believe that Carroll suffered from migraine variants early, which can manifest without head pain.

Carroll is not the only writer who has been documented as having a neurological condition. A score of eminent authors and artists, including Vincent van Gogh (1853–1890) and Fyodor Dostoevsky (1821–1881), likely had hypergraphia (an overwhelming urge to paint or write) and other symptoms of mania and temporal lobe epilepsy.

Though the debilitating nature of these neurological disorders cannot be denied, one wonders whether they contributed to the genius and innovation behind some of the most influential and most loved works of art throughout history. Or perhaps Alice's Adventures in Wonderland was just a big joke to mock the emerging mathematical concepts of the time. Then again, Alice may be a mixture of both.

But judging by the buzz caused by Tim Burton's adaptation, Alice's Adventures in Wonderland looks as though it is still a classic indeed.

--Denise Xu

Image Credit: http://www.wikimedia.org