Importance of Mathematics in Alice's Adventures in Wonderland
In his essay "Alice's Journey to the End of Night," Donald Rackin describes Wonderland as "the chaotic land beneath the man-made groundwork of Western thought and convention" where virtually all sense of pattern is absent and chaos is consistent. Rackin claims that "there are the usual modes of thought-ordinary mathematics and logic: in Wonderland they possess absolutely no meaning." Rackin argues that our traditional view of mathematics as an existing set of facts and rules that are predictable does not hold true in Wonderland.1 However, Rackin's concept of mathematics is limited-he sees math as simply mathematical operations (multiplication, division, addition, and subtraction), which produce predictable results in our "logical" world. But mathematics also exists as abstract forms of structure, which indeed exist in Wonderland through sequence and measurement. Even though Alice's Adventures in Wonderland presents a world that appears random and full of nonsense and inconsistency, these mathematical forms are preserved in Wonderland.
Contemporary philosophies of mathematics define the subject as the study of patterns, as opposed to the traditional study of numbers. These patterns exist in many abstract forms, such as numeric patterns, spatial (visual reasoning) patterns, patterns of motion, and patterns of growth or decay. Rackin recognizes the breakdown of one specific pattern, specifically the relationship between factors and products in base ten multiplications. From this evidence, he concludes that mathematics is meaningless in Wonderland, with no defined structure. But Rackin is making this assertion based on a small piece of evidence. Operations are a small part of mathematics, and can work as patterns themselves, just like the ones mentioned above. By looking specifically at number sequences and the use of measurement in the text, Rackin's point is weakened simply by his narrow conception of mathematics.
The most obvious example in the text where mathematics as we know it is different is when Alice tries to recall basic arithmetic facts when she first falls down the well: "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!"2 We, along with Rackin, recognize that the multiplication is incorrect, but is that enough to assert that there is no mathematical structure within the facts that Alice rambles off the top of her head? Martin Gardner, in The Annotated Alice, attempts to make sense of Alice's multiplication, as quoted above from the text, if she continued forward. "The multiplication table traditionally stops with twelves, so if you continue this nonsense progression...you end with 4 times 12 (the highest she can go) is 19-just one short of twenty." 3
The placement of this scene...