Alice In Wonderland And Math.

Alice in Wonderland, a book that has been made into multiple movies over the generations.  This famous book, written in 1865 by Lewis Carroll aka The Reverend Charles Lutwidge Dodgson.  Dodgson taught mathematics at Christ Church College in Oxford, England.

Apparently in 1862 Dodgson and the Reverend Robinson Duckworth were rowing three girls up the Thames.  During the five mile trip, Dodgson made up a story about a girl named Alice who wanted adventure because she was bored.  The girls loved the story.

One of the girls, Alice Liddell, asked him to write the story down.  Two years later, he presented her with a handwritten copy titled "Alice's Adventures Under Ground". It was complete with drawings done by him.

He'd based much of the story on actual places in Oxford and in Christ Church such as the stairs in the back of the college's main hall where she began her adventures.  A year later, a greatly expanded version, now titled "Alice's Adventures in Wonder Land", was published by Dodgson under the name "Lewis Carroll". Within a short time, it was a best seller.  This book has never been out of print and has been translated into over 100 languages.  In fact, a sequel "Alice Through the Looking Glass".

Dodgson, being a mathematics professor, included references to math in the story.  In fact, he is the one who is given credit for creating logic puzzles with his Knights and Knaves, the first always tells the truth and the second always tells lies. 

It is said that many of the mathematical references contained in Alice provide a satirical commentary on what was happening to the field at that time.  Dodgson is classified as a conservative mathematician who did not agree with the changes.  To him x times y should equal y times x but others of the time expanded the known number system.

There was an Irish mathematician of the time, William Hamilton, who put forth the idea of "quaternions" which are used to extend the complex plane and used to describe mechanics in a three dimensional space.  He stated one of the four terms in quaternions is time so time had to be involved in these numbers.

Lewis Carroll addresses this topic at the tea party with The Mad Hatter, The March Rabbit, and The Dormouse when he purposely leaves out Time.  He indicated he thinks people should get rid of the complexities and go back to the old fashioned math.  Dodgson actually eleven books on mathematics but very little of it was new. He was considered an excellent mathematics tutor.  He felt that Euclid's "Elements" was the pinnacle of mathematical thought.

He felt that many of the mathematicians of his time did not produce works as rigorous as done by Euclid and strayed from reality into areas such as the complex value for the square root of -1.  To him, i and other imaginary numbers did not represent real quantities. Although he found these new ideas to be absurd, he allowed that they would be of interest to advanced mathematicians they could not be taught to undergraduates. 

 He used his fiction to pull apart the logic of the new ideas, taking the weaknesses to the absurd end so as to show the ideas really were not great. 

The local English teacher told the kids that Dodgson used Hashish as he wrote the book.  She supported this by pointing out the Hookah smoking Caterpillar and demonstrated Dodgson's smoking and writing but I pointed out that  he was not known to use the drug.  She didn't even know about the trip down the river.  It has been said that particular scene along with the mushrooms that shrunk her are actually represent the way the connection between algebra and geometry was cut by Symbolic Algebra.

The whole book "Alice in Wonderland" is filled with all sorts of things like that both warnings and actual mathematics but like most of us, I grew up thinking it was nothing more than a children's story.  I had no idea Lewis Carroll was a mathematician in his everyday life. 

Let me know what you think, I'd love to hear.  Have a great day.