Posted in Matematikhistorie, Mathematics and Culture

Wilson and Alice: Lewis Carroll in Numberland

In his lecture on September 19, 2012, professor Robin Wilson (Pembroke College, Oxford and Open University) lectured on “Lewis Carroll in Numerland: His Fantastical Mathematical Logical LIfe” based on his book with the same title (Allen Lane, 2008). The lecture was a lively introduction to the life, time and production (both literary and mathematical) of Charles Dodgson aka Lewis Carroll.

Part of the lecture provided a balanced biography, in which Wilson clearly distanced himself from the part of the literature which has seen anything but natural innocense in Dodgson’s relations with Alice Liddle. That part of the lecture clearly embedded Dodgson in the cultural and biographical contexts of mid-nineteenth-century Britain.

Portrait of Lewis Carroll: This was first publ...
Portrait of Lewis Carroll: This was first published in Carroll’s biography by his nephew, Stuart Dodgson Collington: Collingwood, Stuart Dodgson (1898). The Life and Letters of Lewis Carroll, p. 50, London: T. Fisher Unwin. Retrieved on 2010-12-22. Collington credited no one for this photograph (he has explicitly credited his uncle for other works authored by Carroll). (Photo credit: Wikipedia)

To me, the perhaps most interesting part of the lecture consisted in the numerous and well-explained examples of Dodgson’s/Carroll’s literary writing (often whimsical) which could only be understood and appreciated when his mathematical training and knowledge was taken into account. Thus, for instance, Dodgson’s political pamphlet “The Dynamics of a Parti-cle” (1865) was formulated in definitons mimicking Euclid’s planar geometry such as

Plain anger is the inclination of two voters to one another, who meet together, but whose views are not in the same direction.

which reflects Euclid’s

A plane angle is the inclination of two straight lines to one another, which meet together, but which are not in the same direction.

From such definitions, Dodgson “deduced” political results or desires cast as geometrical theorems.

Perhaps even clearer in the connection between mathematics (and logic) and literature is Dodgson’s work on automating syllogistic reasoning using a diagrammatic appoarch and manipulations of counters. This enabled him to treat complicated syllogistic combiations which were instantiated in whimsical examples such as:

(1)  No kitten that loves fish is unteachable.
(2)  No kitten without a tail will play with a gorilla.
(3)  Kittens with whiskers always love fish.
(4)  No teachable kitten has green eyes.
(5)  No kittens have tails unless they have whiskers.
=>  No kitten with green eyes will play with a gorilla.

These and similar examples can also be found in the strange logic of Alice’s Adventures in Wonderland and Through the Looking-Glass, in particular in the characters of Tweedledum and Tweedledee which mimicks such elaborate syllogism but with nonsensical assumptions and inferences.

Through such examples from geometry, arithmetic and Dodgson’s interests in logic, professor Wilson succeeded in elucidating the strictly mathematical and logical foundation for Carroll’s whimsical style which is often seen as nonsense. Indeed, we can perhaps now say that what precisely makes Carroll’s poems and rants nonsensical is the way in which they resemble and mimick the strict and rigid structure of mathematics (in parciular Euclid’s planar geometry) and logic (in particular syllogisms).

Every schoolboy (or perhaps even -girl) educated in Victorian Britain (or anywhere else in Europe) would be familiar with the defintions from Euclid which had to be mastered by heart. A Danish satirical cartoon by Fritz Jürgensen dating from the 1860s relects the perceived view of Euclidean education:

A small boy is being examined by his teachers who ask him: “What can you say about two quantities which are equal to one and the same third quantity?” The boy fumbles and answers: “That they are neither greater nor less than one another”. For this, he is scolded by the headmaster who ask another, cleverer boy to provide the correct answer: “That they are equal to one another” for which that boy is praised. That the two answers are mathematically equivalent is the key to understanding the satirical nature of the drawing (see Sørensen 2005).

Thus, professor Wilson’s talk and his book provide excellent examples of how knowledge and understanding of contemporary mathematics enables the reader to appreciate levels of literary works that are otherwise difficult to access. And it is my claim that such levels of analysis goes beyond the “merely” biographical and contextual levels of textual analysis and are important for many other aspects of literary criticism.

Some references


Professor (m.s.o.) ved Institut for Naturfagenes Didaktik, Københavns Universitet.

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