A girl named Alice chases a clothed white rabbit that that runs past her while hurriedly consulting a pocket watch. After falling down a rabbit hole, Alice is suddenly immersed in a fantastic land inhabited by a grinning cat that becomes invisible, by playing cards that speak and by a queen who demands the beheading of anyone who dares to contradict her. As this is a story for children, it is natural that Alice in Wonderland and its sequel, Through the Looking Glass, portray an imaginary world. However, there is something about these stories of Lewis Carroll that makes them a special case and a matter of debate for adults even today, 150 years after the publication of the first volume on November 26, 1865.

What distinguishes Alice from other children’s stories is its unique use of logic, sometimes taken to extremes, as when the Mad Hatter tells Alice that she can have more tea, given that she has not yet had anything to drink, but what she cannot do is “take less.” But at other times, the logic is twisted to absurdity – watches give the day but not the hour, time and memory work in both directions, several days pass at the same time, and one has to run to stay in the same place.

This peculiarity of Alice has an explanation: Charles Lutwidge Dodgson, the real name of British writer Lewis Carroll (1832-1898), was also a photographer, inventor and deacon of the Anglican Church, but above all he was a mathematician, the profession that he studied and tutored at Christ Church College, Oxford. The mathematical work of Dodgson, which he signed with his real name in nearly a dozen books, has only been explored in depth in recent decades, such as his contributions to matrices and determinants, his ciphers, or his probabilistics. However, according to what mathematician and science populariser Keith Devlin, co-founder and director of the Human-Sciences and Technologies Advanced Research Institute (H-STAR) at Stanford University (USA) explained to OpenMind, “he appears to have been very much a traditionalist, opposed to new developments in the discipline.”

This vision of Carroll as a conservative mathematician inspired the Briton Melanie Bayley, a doctor in English literature at the University of Oxford, to interpret certain passages of Alice as a mockery of the progress of his time. In the mid-nineteenth century, algebra was penetrating into an increasingly abstract area, a drift that Carroll frowned upon. The mathematician Solomon Golomb cites as an example the passage from Through the Looking Glass in which Alice converses with Humpty Dumpty, a dialog full of invented words. “I believe this was Carroll’s spoof on ‘modern abstract mathematics’, which was giving very specific technical meanings to such everyday words as ‘set’, ‘group’, ‘ring’, ‘field’, etc.” says Golomb to OpenMind. “Humpty Dumpty similarly asserted that words should mean whatever he wanted them to mean.”

Bayley’s theory about Alice as a parody of the new mathematics is exemplified in the chapter of the tea party, in which the girl meets the Mad Hatter and his two companions, the March Hare and the Dormouse. The three are eternally having tea at six because Time has abandoned them. According to Bayley, there exists a clear analogy with the concept of quaternions, proposed by the mathematician William Rowan Hamilton. Just as complex numbers consist of two terms, quaternions consist of four, corresponding to the three spatial dimensions and time. In the absence of Time, the three characters in the scene do nothing but go round and round the tea table, just as Hamilton’s quaternions only permit rotation in a plane if the fourth term is eliminated.

Some experts, such as Golomb, disagree with Bayley’s thesis. The researcher, who was a scientist before turning to literature, points out to OpenMind that the algebraic terms suggested by Golomb as being the inspiration for the dialogue of Humpty Dumpty are of continental origin and were not yet popular in Victorian math, so Carroll was probably unaware of them. On the other hand, Devlin believes that Bayley is right and that the readers of the time would have been able to recognize those references, and, “that was why the Alice books became sufficiently well known to endure. I suspect most mathematicians find them amusing, as I do.”

But Bayley adds that the hidden jokes in Alice are not limited to mathematics. Carroll wrote the story for a little girl, Alice Liddell, whose father was the dean of Christ Church and therefore the author’s boss. According to the researcher, the first version of the story, titled Alice’s Adventures Under Ground, “was handed to the Liddell family and displayed on their coffee table.” In this initial instalment some passages are still missing, such as the tea party and others that Carroll added later after holding discussions with the dean on the policies of Oxford and the new mathematics. “Bringing together Dodgson’s own mathematical writings, his tendency to criticise Oxford politics through humour, his views on contemporary mathematical education and his rift with Alice Liddell’s father, I think we can look for jibes in the inserted scenes,” summarizes Bayley.

This also reveals to us that Carroll was an innovator, and that he employed a means that nowadays is very common in children’s films. “Alice is a book for children with adult in-jokes about Dodgson’s Oxford world interspersed through its pages,” Bayley concludes. For this reason, the mathematician Charles Dodgson will always be best remembered as the author Lewis Carroll. “We don’t really have any way of knowing if he was a good mathematician,” says Devlin. “If it is indeed the case that his Alice stories were satire, they may have made him a bit of an outcast from the mathematical community of the time, though he was never really a member of that community to begin with.”

By Javier Yanes for Ventana al Conocimiento