DOWN THE RABBIT-HOLE

Alice's Adventures in Wonderland

by

Lewis Carroll

CHAPTER I

DOWN THE RABBIT-HOLE

ALICE was beginning to get very tired of sitting by her sister on the bank and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, "and what is the use of a book," thought Alice, "without pictures or conversations?'

References to mathematics

Since Carroll was a mathematician at Christ Church, it has been suggested^[5] that there are many references and mathematical concepts in both this story and also in Through the Looking-Glass; examples include:

• In chapter 1, "Down the Rabbit-Hole," in the midst of shrinking, Alice waxes philosophic concerning what final size she will end up as, perhaps "going out altogether, like a candle."; this pondering reflects the concept of a limit.
• In chapter 2, "The Pool of Tears," Alice tries to perform multiplication but produces some odd results: "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate!" This explores the representation of numbers using different bases and positional numeral systems (4 x 5 = 12 in base 18 notation; 4 x 6 = 13 in base 21 notation. 4 x 7 could be 14 in base 24 notation, following the sequence).
• In chapter 5, "Advice from a Caterpillar," the Pigeon asserts that little girls are some kind of serpent, for both little girls and serpents eat eggs. This general concept of abstraction occurs widely in many fields of science; an example in mathematics of employing this reasoning would be in the substitution of variables.
• In chapter 7, "A Mad Tea-Party," the March Hare, the Mad Hatter, and the Dormouse give several examples in which the semantic value of a sentence A is not the same value of the converse of A (for example, "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"); in logic and mathematics, this is discussing an inverse relationship.
• Also in chapter 7, Alice ponders what it means when the changing of seats around the circular table places them back at the beginning. This is an observation of addition on a ring of the integers modulo N.
• The Cheshire cat fades until it disappears entirely, leaving only its wide grin, suspended in the air, leading Alice to marvel and note that she has seen a cat without a grin, but never a grin without a cat. This is usually seen as either a reference to the deep abstraction of concepts (non-Euclidean geometry, abstract algebra, the beginnings of mathematical logic...) that was taking over mathematics at the time. Even more pertinently, it can be taken to represent the very concept of mathematics and number itself. For example, instead of considering two or three apples, one may easily consider the concept of 'apple,' upon which the concepts of 'two' and 'three' may seem to depend. However, a far more sophisticated jump is to consider the concepts of 'two' and 'three' by themselves, just like a grin, originally seemingly dependent on the cat, separated conceptually from its physical object.

References to classical languages

In chapter 2, Alice initially addresses the mouse as "O Mouse," based on her vague memory of the noun declensions in her brother's textbook: "A mouse (nominative)— of a mouse (genitive)— to a mouse (dative)— a mouse (accusative)— O mouse! (vocative)." This corresponds to the traditional order that was established by Byzantine grammarians (and is still in standard use, except in the United Kingdom and some countries in Western Europe) for the five cases of Classical Greek; because of the absence of the ablative case, which Greek does not have but is found in Latin, the reference is apparently not to the latter as some have supposed.

Historical references

In chapter 8, three cards are painting the roses on a rose tree red, for they accidentally planted a white-rose tree which theQueen of Hearts hates. Red roses symbolized the English House of Lancaster, while white roses were the symbol for their rival House of York. Therefore, this scene may contain a hidden allusion to the Wars of the Roses.^[6]

Ablative Absolute: In Latin grammar. an adverbial phrase syntactically independent from the rest of the sentence and containing two main elements in the ablative case. Regibus expulsis, leges respublica condit (The kings having been expelled, the republic sets up laws)