Use Of Satire In Alice In Wonderland

Mathematical satire in “Alice’s Adventures in Wonderland”
”Alice’s Adventures in Wonderland” are probably one of the most analyzed-in-class books ever written. It does not take a lot of research to realize that there are numerous different approaches to fully understand that book. In this essay I chose to look at it through a prism of Lewis Carroll’s profession and passion – mathematics. Lewis Carroll, or rather Charles Dodgson was an oxford mathematician and was known in particular for being stubbornly conservative and unable to adapt to the changes occurring in the fields of mathematics in the nineteenth century. As a fan of pure, simple mathematics he in particular valued “Euclid’s Elements” as the epitome of mathematical thinking. “Euclid’s
Elements” cover the basics of geometry, arithmetic and trigonometry - they carry solid, testable information.
Meanwhile, nineteenth century was a turbulent time for mathematics. Many new and controversial concepts such as symbolic algebra or imaginary numbers were being proposed and widely accepted in the mathematical community. Dodgson considered all of the changes nonsense and would even refer to all the mathematicians who weren’t as rigorous as him as “semi-colloquial” or even “semi-logical”. When looking at “Alice’s Adventures in Wonderland” in this perspective one could argue that the author used some of the stories to satirize the increasing abstraction in Charles Dodgson’s favorite subject. Inspired by Martin Gardner’s book “The Annotated Alice” I believe that many of the scenes are a reflection of his skepticism of those radical new ideas. To prove my point I will be analyzing three passages from the book – the caterpillar smoking the hookah (chapter 5), the Mad Hatter’s tea party (chapter 7) and
Alice’s calculations in the beginning of the second chapter.
Let’s start with the chapter “Advice from a Caterpillar” as the reflection is very subtle and makes an opening to other, stronger allusions. For Charles Dodgson mathematics only had the right to exist in a form in which it was a direct translation of the real world while by the time he got to Oxford it became a language, or rather many languages in and of itself due to the development of, e.g. symbolic algebra. If certain rules were set up for a particular problem opposite rules could have been set up for a problem of a different nature and by that two contradicting conclusions both could have been proven right. The author decides to exemplify that particular concept with the mushroom, one side of which would make you smaller and the other would cause growth. The word “algebra” originates from Arabic and means “Restoration and Reduction”. Alice desperately looking for something to eat or drink to grow back to her prior size can be considered an act of restoration, while reduction can be seen after she eats a part of the mushroom and physically shrinks. Furthermore, during the conversation with the caterpillar Alice is told to “control her temper” which can be understood as “watch her proportions”. In Euclidean geometry size and magnitude did not matter whatsoever, it was all about proportions and ratios. Carroll is basically implying that in order to bear all the madness she has to behave like a Euclidean geometer. That just so happens to also be the phrase he used in his letters to describe himself. He felt as if all of his colleagues were blindly drowning in the nonsense, he felt as if he was the last one standing.
That gets us to the probably most iconic scene from the entire book – the Tea Party. It is the nineteenth century and an Irish physician sir William Rowan Hamilton after years of failed attempts of describing rotations in a three dimensional space introduces a new concept- quaternions. Quaternions are numbers existing in four dimensions that can be expressed in the form of ai+bj+ck+d where a, b, c and d are the real components and i, j and k are imaginary. For years he tried calculating rotations using three components only (each designated to one spatial dimension) but that only allowed him to rotate on a plane. He finally realized – he needed the fourth dimension which, he decided, was most likely time. The idea of time being an extra-spatial unit, a dimension, seemed to the author bizarre and absolutely nonsense. When Alice arrives at the tea party there are only three guests left – time used to be the fourth member of the tea club, but he got fed up and left. As mentioned before, without time you can only rotate in a plane, like the hands of a clock, like our three friends around the table, like an incomplete quaternion.
Unlike in case of other number systems quaternions are non-commutative. That means that simple arithmetic we use every day don’t apply (x*y is not equal to y*x). That can be seen when the mad hatter says: “Not the same thing a bit! ' said the Hatter. `You might just as well say that "I see what I eat" is the same thing as "I eat what I see"! ' You might just as well say, added the March Hare, that "I like what I get" is the same thing as "I get what I like"! ' You might just as well say, added the Dormouse, who seemed to be talking in his sleep that "I breathe when I sleep" is the same thing as "I sleep when I breathe!”” (Carroll, 98). In the end of that scene the March Hare and Mad Hatter are trying to drown the dormouse. If they had managed to do so they would become a complex number consisting of two components only, which would free them from the infinite rotation. That is another piece of evidence adding up to the idea of Lewis Carroll only adding some of the chapters to satirize the new rules of mathematics.
Last passage I will be discussing in this essay is taken from chapter 2 and describes Alice trying to remember her multiplication tables.
One of Dodgson’s main complains about the ongoing changes was that even a concept as stable and basic as arithmetic does not apply in all the cases, hence in Alice addition, subtraction, multiplication and division becomes ambition, distraction, uglyfication and derision. We read “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!” which is an example of uglyfication. Why can’t Alice ever get to twenty though? There seems to be logic in the way she is counting. Four times five is twelve in a base 18 system, four times six can indeed equal 13 if counting base 21, four times seven is fourteen when base we change the base to 24 etc. Following this pattern twenty would have to be expressed as four times thirteen base 42, however that is already expressed as the letter F rather than a number. Therefore, it is impossible to get to twenty when changing rules if we would want to stick to good old
arithmetic.
Charles Dodgson could not adapt to the changes occurring around him the same way Alice couldn’t adapt to a whole new world with whole new rules. As stated before I am certain that the madness of wonderland was how the author saw the mathematical community and Alice trying to find sense in all of that was supposed to reflect Carroll himself. Most of the passages I quoted from were actually added after the first version of the book (“Alice’s Adventures Under Ground”) was written and I strongly believe they were only added and written in that way to show how bizarre the author finds the new rules and how little or no application they have in the real world.
Bibliography:
Martin Gardner, “The Annotated Alice”, New York City, New York, W.W.Norton&Company, 1990
Lewis Carroll, “Alice’s Adventures in Wonderland”, Chicago, Illinois, VolumeOne Publishing, 1998