Most of the book's adventures may have been based on and influenced by people, situations and buildings in Oxford and at Christ Church, e.g., the "Rabbit Hole," which symbolized the actual stairs in the back of the main hall in Christ Church. A carving of a griffon and rabbit, as seen in Ripon Cathedral, where Carroll's father was a canon, may have provided inspiration for the tale.
Since Carroll was a mathematician at Christ Church, it has been suggested that there are many references and mathematical concepts in both this story and 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 × 5 = 12 in base 18 notation, 4 × 6 = 13 in base 21 notation, and 4 × 7 could be 14 in base 24 notation. Continuing this sequence, going up three bases each time, the result will continue to be less than 20 in the corresponding base notation. (After 19 the product would be 1A, then 1B, 1C, 1D, and so on.) In chapter 7, "A Mad Tea-Party", the March Hare, the 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...
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