Carroll, Lewis (1832–1898)
Lewis Carroll was the pen name of Charles Lutwidge Dodgson (obtained by anglicizing the Latin
translation, "Carolus Lodovicus," of his first two names), an English mathematician,
logician, and writer. Carroll was born at the Old Parsonage, Newton-by-Daresbury,
Cheshire, his father being the vicar of All Saints Church, Daresbury; there
is a commemorative window in the church, and a "Wonderland" weather vane,
showing the Mad Hatter, the White Rabbit, and Alice, on the local primary
school. Carroll was educated at Rugby School (the student mathematics society
there is still called the Dodgson Society in his honor) and then at Christ
Church, Oxford, at which college he was to spend the rest of his life, employed
mainly as a lecturer.
His most famous book, Alice's Adventures in Wonderland (1865), grew
out of a story he told on the hot summer afternoon of July 4, 1862, when
out rowing with the three young daughters of the Greek scholar H. G. Liddell,
dean of Christ Church. Alice, named after Alice Liddell (later Hargreaves,
1852-1934), continued her adventures in Through the Looking-Glass (1871). Carroll wrote other books for children, including a long poem "The
Hunting of the Snark," (1876) and published several mathematical works,
but was not distinguished academically. He stammered badly, never married,
and seemed to find greatest pleasure in the company of little girls, with
whom he lost his shyness. He was also an inventor of puzzles, games, ciphers,
and mnemonics, and an amateur pioneer in photography. Carroll was a master
of fantasy and his stories have their own logic. Carroll used the pun and
coined neologisms, including what he called "portmanteau words" like chortle
(combining chuckle and snort). He played games with idioms, using such expressions
as "beating time" (to music) in a literal sense. He reshaped such animals
of fable or rhetoric as the Gryphon, the March Hare (said to have been inspired
by a carved hare carrying a satchel located at St. Mary's Church, Beverly,
Humberside, where Carroll visited), and the Cheshire Cat, and invented new
ones, including the Bandersnatch and the Boojum.
Here are a few examples of puzzles invented by Carroll:
See solutions are 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?
Some Carrollian quotes
From Alice's Adventures in Wonderland:
- "The different branches of Arithmetic – Ambition, Distraction,
Uglification, and Derision."
- "Alice laughed: "There's no use trying," she said; "one can't believe
"I daresay you haven't had much practice," said the Queen. "When I was
younger, I always did it for half an hour a day. Why, sometimes I've
believed as many as six impossible things before breakfast."
- "Then you should say what you mean," the March Hare went on.
"I do, " Alice hastily replied; "at least I mean what I say, that's
the same thing, you know."
"Not the same thing a bit!" said the Hatter. "Why, you might just as
well say that "I see what I eat" is the same thing as "I eat what I
- "Take some more tea," the March Hare said to Alice, very earnestly.
"I've had nothing yet," Alice replied in an offended tone, "so I can't
"You mean you can't take less," said the Hatter. "It's very easy to
take more than nothing."
From The Hunting of the Snark:
- "What I tell you three times is true."
From Alice Through the Looking Glass:
- "Can you do addition?" the White Queen asked. "What's one and one
and one and one and one and one and one and one and one and one?" "I
don't know," said Alice. "I lost count."
- "It's very good jam," said the Queen.
"Well, I don't want any to-day, at any rate."
"You couldn't have it if you did want it," the Queen said. "The rule
is jam tomorrow and jam yesterday but never jam to-day."
"It must come sometimes to "jam to-day,""Alice objected.
"No it can't," said the Queen. "It's jam every other day; to-day isn't
any other day, you know."
"I don't understand you," said Alice. "It's dreadfully confusing."
- "When I use a word," Humpty Dumpty said, in a rather scornful tone,
"it means just what I choose it to mean – neither more nor less."
"The question is," said Alice, "whether you can make words mean so many
"The question is," said Humpty Dumpty, "which is to be master –
Solutions to puzzles
- There is as much water in the milk/water mixture as milk in the water/milk
- 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"
- Carroll, Lewis. Mathematical Recreations of Lewis Carroll.
Mineola, NY: Dover, 1958. 2 Vols.
- Carroll, Lewis. Symbolic Logic and the Game of Logic. Mineola,
NY: Dover, 1958. 2 Vols.
- Carroll, Lewis. Pillow Problems and A Tangles Tale. New York:
- Fisher, John (ed). The Magic of Lewis Carroll. New York:
Simon and Schuster, 1973.