Lewis Carroll: The Mad Mathematician?
Lewis Carroll is best known as the author of Alice's adventures in wonderland
(1865) and Through the looking glass
(1872), children's books that are among the most popular of all time. They are distinguished as satire and as examples of verbal wit. Carroll is credited with liberating juvenile literature from its history of didacticism and overt moralizing. With the Alice
books, he ushered in the Golden Age of children's literature, a period characterized by its imaginative and purely entertaining works for the young. The stories about Alice are often praised as the first children's books that could be read with equal pleasure by both children and adults; in fact, appeal to the latter group is so strong that the tales have transcended their status as books for children to become classics of the English language.
However, Lewis Carroll is a pseudonym for his real name Charles Lutwidge Dodgson. For his children's books he invented the pen name "Lewis Carroll" by translating his first two names "Charles Lutwidge" into Latin as "Carolus Lodovicus", then anglicising and reversing their order. Dodgson was a brilliant mathematician. He was a mathematics professor at Christ Church, Oxford. Dodgson worked primarily in the fields of geometry, matrix algebra and mathematical logic, producing nearly a dozen mathematics books. There are many that argue that Dodgson's Alice books were a mishmash of satire directed at the advances taking place in Dodgson’s field of mathematics. In the mid-19th century, mathematics was rapidly blossoming into what it is today: a finely honed language for describing the conceptual relations between things. Dodgson found the radical new math illogical and lacking in intellectual rigor. People were developing all kinds of bizarre new algebras, where x times y was not equal to y times x. So why is a raven like a writing desk? Because the new mathematics didn't make sense to Carroll.
He was also an inventor of puzzles, games, ciphers, and mnemonics.
Examples of his puzzles (answers below)
- You are given two glasses. One contains 50 tablespoons of milk, the other 50 tablespoons of water. Take one tablespoon of milk and mix it with the water. Now take one tablespoon of the water/milk mixture and mix it with the pure milk to obtain a milk/water mixture. Is there more water in the milk/water mixture or more milk in the water/milk mixture?
- If you paint the faces of a cube with six different colors, how many ways are there to do this if each face is painted a different color and two colorings of the cube are considered equivalent if you can rotate one to get the other? What if we drop the restriction that the faces be painted different colors?
- Make a word-ladder from FOUR to FIVE. (Every step in a word ladder differs from the previous step in exactly one letter and each step in the ladder is an English word.)
- Why is a raven like a writing desk?
Solutions to puzzles
- There is as much water in the milk/water mixture as milk in the water/milk mixture.
- There are 30 ways of painting the cube. If the restriction that each face be painted a different color is dropped, there are 2226 ways of painting the cube.
- FOUR → FOUL → FOOL → FOOT → FORT → FORE → FIRE → FIVE
- Carroll didn't have an answer in mind when he wrote the riddle, though he later came up with: "Because it can produce a few notes, though they are very flat; and it is nevar put wrong end in front!" (Note the variant spelling of "never".) Other authors have come up with: "Because Poe wrote on both" (Sam Loyd); "Because it slopes with a flap" (Cyril Pearson) ; and "Because both have quills dipped in ink"
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