Philip Martin McCaulay

Alice in Wonderland - from a mathematical and philosophical point of view
Lewis Carroll is the author of Alice’s Adventures in Wonderland and Through the Looking Glass - timeless classics.
Alice in Wonderland is a masterpiece example of reading that caters to a two-tiered audience.
There is the audience that reads his work as an entertaining, if bizarre fairy tale, never suspecting the darkly mysterious dimension of his work. Those who are able to comprehend Lewis Carroll’s hidden intentions, however, are in for a delicious treat that stretches the mathematical imagination as much as it makes one laugh at its implications.
Lewis Carroll plays with the limits of Euclidian Geometry, the Principle of Continuity, Proportion and Absolute Length, Symbolic Logic, even the maddeningly confusing world of Quaternions.
The Cheshire cat, the Mad Hatter, the March Hare, the Dormouse, the Caterpillar and first and foremost the Red Queen are the mouthpieces and experimental outlets of various mathematical laws, some more bizarre then the other.
Need any examples? Clearly, tea-party alludes to t-party, t being the mathematical notation for time. The Red Queens’s inclinations to execute everyone with axes ought to be seen as her infatuation with axis. More intriguing even an effect paying homage to her character, The Red Queen Effect, as it is used in the science of evolution and philosophy in general, when describing the relationship of the rate of change of evolving species to each other. As Darwin observed not all animals evolve at the same rate as others as some species are more responsive to change.
There are periods in many species, yes even humans, where we push hard to gain an advantage. Yet, as species around us coevolve, we seem not make any progress as our environment speeds up too. As we push ahead even harder, the environment adapts to us even quicker. This, essentially makes us feel like treading water, or running on a treadmill. Another example is how trees grow in height so that other trees will not be able to block their light. Naturally, according to the principle of evolution, the surrounding trees need to grow taller as well. When this eventually becomes a race to reach the sky, they are captured by the Red Queen Effect for all the while as the trees put all their energy to sustain the growth of the stem, the fruit becomes smaller and smaller.
Needless to say, as another example could serve the Cold War with its proliferation of nuclear weapons and its subsequent devastating effect it had on world economy and overall survival of the human race.
Pertaining Excerpt: Alice never could quite make out, in thinking it over afterwards, how it was that they began: all she remembers is, that they were running hand in hand, and the Queen went so fast that it was all she could do to keep up with her: and still the Queen kept crying ‘Faster! Faster!’ but Alice felt she could not go faster, though she had not breath left to say so.
The most curious part of the thing was, that the trees and the other things round them never changed their places at all: however fast they went, they never seemed to pass anything. ‘I wonder if all the things move along with us?’ thought poor puzzled Alice. And the Queen seemed to guess her thoughts, for she cried, ‘Faster! Don’t try to talk!’
Eventually, the Queen stops running and props Alice up against a tree, telling her to rest.
Alice looked round her in great surprise. ‘Why, I do believe we’ve been under this tree the whole time! Everything’s just as it was!’
‘Of course it is,’ said the Queen, ‘what would you have it?’
‘Well, in our country,’ said Alice, still panting a little, ‘you’d generally get to somewhere else — if you ran very fast for a long time, as we’ve been doing.’
‘A slow sort of country!’ said the Queen. ‘Now, here, you see, it takes all the running you can do, to keep in the same place.
If you want to get somewhere else, you must run at least twice as fast as that!’
“Bees have to move very fast to stay still.” — David Foster Wallace
This quote shows us the dangers of unexamined behavioral patterns. If Lewis Carroll’s ought to teach us anything besides not taking all mathematical theories that seriously, it teaches us that the survival of the human race lies within cooperation. There is no need to ever grow taller, larger, grander but lifeless and “calcified” edifices in fear of not getting our share of “light”. Instead, if we could just trust each other and agree that all of us, yes that includes the animal species and plant species, must get their share of resources then the “fruit” of our labors shall be rewarding indeed.… (mehr)