Book number 61 of 2024!
Charles Dodgson, a.k.a. Lewis Carroll, will forever be known as the author of Alice In Wonderland and Through The Looking Glass, but he was also a very accomplished mathematician at Oxford University as well as a pioneering and talented photographer. Robin Wilson’s biography of Dodgson, Lewis Carroll in Numberland, His Fantastical Mathematical Logical Life documents this lesser-known aspect of him.
If you enjoy reading about mathematical topics, then this book is for you. If you’re more interested in the fantasies Carroll wrote, you may be disappointed. I found Lewis Carroll in Numberland to be very enjoyable and insightful, but I’m a high school math teacher, so I’m probably not the best judge!
One thing that comes across clearly is how playful and humorous Dodgson was from an early age. Beginning when he was thirteen, he put together family magazines that featured poetry, stories, games, puns, and jokes.
Dodgson also showed great promise in mathematics from his first days as a student. His math instructor, Robert Mayor, wrote to Dodgson’s father,
I have not had a more promising boy at his age since I came to Rugby. (page 33)
Dodgson eventually was accepted at Oxford, where he planned to be ordained an Anglican priest. He was such a good mathematician, though, that he instead became a deacon so that he could continue lecturing at Oxford. Throughout his career there, he published books and pamphlets on various mathematical topics designed to help undergraduates pass their exams. He also wrote lots of satirical essays on politics, Oxford professors and campus gossip, and church matters. At the same time, he devoted himself to mastering the relatively new technology of photography, becoming one of the most sought-after artists in Victorian England.
Charles Dodgson polishing his camera lens
One of my favorite insights into Dodgson’s personality was his use of puns when writing about math. Here’s an exchange from Sylvie and Bruno regarding Euclidean geometry:
Professor: (drawing a long line on the blackboard, and marking the letters “A”, “B”, at the two ends, and “C” in the middle) If AB were to be divided into two parts at C…
Bruno: It would be drownded.
Professor: What would be drownded?
Bruno: Why the bumble-bee, of course! And the two bits would sink down in the sea!
Wilson also includes the background to Dodgson’s composition of Alice In Wonderland. He and a friend, the Rev. Robinson Duckworth, took Alice Liddell and her two sisters, Edith and Lorina on a boating excursion in Oxford. As Dodgson and Duckworth were rowing the boat, Dodgson began telling the story of Alice in Wonderland extemporaneously. When they returned, Alice asked him to write the story down, which he did. Later, his manuscript was published in book form, and the rest is literary history.
In the Alice books, there are all kinds of references to real people and events, such as this passage:
the pool was getting quite crowded with the birds and animals that had fallen into it: there was a Duck and a Dodo, a Lory, and an Eaglet, and several other curious creatures.
The Duck was Robinson Duckworth, the Dodo was Dodgson, the Lory was Lorina, and the Eaglet was Edith.
In mathematics, Dodgson came up with an efficient way to evaluate determinants, which can be used to solve systems of equations. Before computers, solving large systems was very tedious and cumbersome. Dodgson’s method of “condensation” was an original and useful advance in matrix mathematics.
He was also interested in developing fair and equitable ways of seeding sports tournaments and conducting elections. He lobbied for more representatives to be elected to Parliament so that the populace would be better represented. And many of his suggestions for seeding tournament participants were put in place in the 20th century.
Dodgson loved devising mathematical puzzles and numerical “tricks” such as this one:
Carroll asked a little boy to write down the number 12,345,679. He surveyed it in silence, then said, “You don’t form your figures very clearly, do you? Which of these figures do you think you have made the worst?” The boy thought his 5 was poorest. Lewis Carroll suggested he should multiply the line by 45. The child laboriously worked it out and to his surprise found the result was 555555555. “Supposing I should have said four, what then?” the boy queried. “In that case we would have made the answer all fours,” Carroll replied. He would have told the boy to multiply by 36, another multiple of 9. But he did not attempt to explain ‘mystic nines’ to us.
The trick works because 9 x 12,345,679 = 111,111,111. (Page 158)
The final topic Wilson covers is Dodgson’s love of symbolic logic. He developed a game that taught it to adolescents, and he wrote an accompanying book. Here’s an example of a two-premise syllogism he posed:
No bald creature needs a hairbrush.
No lizards have hair.
Conclusion: No lizard needs a hairbrush.
In his game and book, Dodgson increased the number of premises to as many as ten, and by using the provided game board, players could reach the correct conclusion.
Lewis Carroll in Numberland is a fun book for aficionados of mathematical games and puzzles, and it illustrates a side of Carroll that not many people are aware of. He was much more than the author of Alice In Wonderland, even though that was an extraordinary achievement in and of itself.
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