Charles Lutwidge Dodgson

This display in the Museum of Natural History in Oxford is about the real Alice - the character in the books having been based on a real person.  Well, this post is about THE REAL LEWIS CARROLL.  His name was actually Charles Lutwidge Dodgson (1832-1898), and mathematics was his "day job."  He earned the Christ Church, Oxford, Mathematical Lectureship in 1855 and held it for the next 26 years.  His Fellowship at Christ Church, Oxford, gave him the privilege of living at Christ Church for the rest of his life provided he did not marry and that he prepared for holy orders, which is simply what was expected of Fellows living at the college at that time.

Museum of Natural History, Oxford

In 1856, Henry Liddell became dean at Christ Church.  Dodgson (Carroll) became very close to the Liddell family, especially Henry's wife Lorina and three of their children - the daughters Lorina, Edith and Alice.  He would sometimes take them to the Museum of Natural History (pictured above and below), and some of the characters in the Wonderland books came from creatures they saw here.  In particular it is likely that Dodgson represented himself as a Dodo because he had a stammer, so his name sometimes came out "Do-do-dodgson."

Museum of Natural History, Oxford

Dodo skeleton and taxidermy at Museum of Natural History, Oxford

Lewis Carroll enjoyed entertaining others.  This began early in life when he entertained his siblings.  He even used puzzles and riddles in his mathematics lectures at Oxford in order to engage his students.  He especially loved entertaining children.  I noticed in reading a biography of him that he used many of the same magic tricks that Mathemagician Arthur Benjamin, professor at Harvey Mudd College, uses today.

His friendship with the Liddell family involved excursions by boat, first with the son, Henry, and later with the daughters.  On July 4, 1862 Carroll invented the outline of the story we now know as Alice's Adventures in Wonderland while out rowing with a friend and the girls.  Alice pressed him to write it down, and, after a long time, he finally presented her with a manuscript of the story, originally titled Alice's Adventures Under Ground.  

Writer George MacDonald, a pioneer of fantasy writing, was a friend and mentor of Lewis Carroll (and also influenced C. S. Lewis, J. R. R. Tolkien, Madaleine L'Engle and others).  It was after the family of George MacDonald had read the manuscript and after the MacDonald children had received it especially enthusiastically that Carroll took the manuscript to a publisher.  The rest, as they say, is history!

From the Alice display in the Museum of Natural History, Oxford

Another influence on Carroll was the pre-Raphaelite circle, including the Rossetti family - Dante Gabriel and Christina.  Below is an imagine of the Rossetti family plot in Highgate Cemetery, London.  Christina is buried here, and her name is on the flat stone on the ground.  The picture below is of a fox in the cemetery, which is a haven for wildlife.

Rossetti Family Plot - Highgate Cemetery, London

Fox in Highgate Cemetery, London (west)

Had Carroll not been remembered for his writing, he would have been remembered as the second-greatest photographer of the Victorian Era and the greatest photographer of children.  He was a very gifted artist, but, sadly, his reputation (as a person) has waxed and waned over the last century.  Many photographs he took of children were nude photographs, but he always took such photographs with the permission of the parents.  Also, it was the fashion of the time to take such photographs.  His writing too has gone through the scrutiny of Freudian psychology long after the fact, and people have come up with some pretty "interesting" and not so complimentary interpretations.  I side with Carroll biographer Robin Wilson who writes, "Sadly much nonsense has been written about Dodgson's friendships with children  .  .  .  .  Subjecting him to modern 'analysis' rather than judging him in the context of his time is bad history and bad psychology and says more about the writer than it does about Carroll."  

To that I say, "Amen!"

Here are some pictures of Christ Church College, Oxford.

Christ Church Cathedral as seen from the cloisters

Organ of Christ Church Cathedral

Court of Christ Church College, Oxford

Entrance to Christ Church, Oxford as seen from the road

A view of the entrance of Christ Church College from the court

In terms of mathematics, he worked particularly in geometry, logic, linear algebra and recreational mathematics.  Dodgson discovered a method for finding determinant of matrices that significantly shortened the process, especially for matrices of order 4 or larger; it is called his method of condensation.  He did excellent mathematical work with ideas relating to electoral reform.  In general, however, he was a very conservative mathematician who did not really break new ground, so none of his books have proven to be of enduring importance.

I am going to touch on two of his books, however.  I have enjoyed looking into The Game of Logic, which seems to me to include a method that would be an improvement on Venn Diagrams in working with syllogisms.  Another book that has endured has done so for historical purposes, and that is his work Euclid and His Modern Rivals.  Then, as now, there were arguments about how mathematics (and other subjects) should be taught.  For centuries Euclid's Elements was taught as if it were the Bible - with students actually memorizing its books and propositions by number as if they were chapters and verses in scripture.  Others in his day wanted to use different geometry texts in which exploration and discovery were emphasized more than memorization; Carroll, very conservative, wanted things to remain as they had been.  This sounds quite familiar to me in what is going on today with our pendulum swing between "back-to-basics" movements and "discovery-based" learning, as we are seeing right now with the Common Core fights raging around us.  Clearly this is nothing new.

I recommend Robin Wilson's 2009 biography Lewis Carroll in Numberland: His Fantastical, Mathematical, Logical Life.  As a teacher and as a person I especially enjoyed excerpts from Carroll's (or should I say "Dodgson's") diary in which he expresses his thoughts about his teaching - his feelings when things went well and his self-doubt when things went poorly.  I found it impacting, eye-opening and touching to read about Lewis Carroll in Lewis Carroll's own words; I found that many of his feelings about his teaching echoed my own feelings about my teaching - both the ups and the downs.