Posted by: sclee09 | November 8, 2008

Math 152 in Alice in Wonderland

Alice’s Adventures in Wonderland is a childhood classic and one of my favorite books. Written by Charles Lutwidge Dodgson (under the pseudonym Lewis Carroll), it tells the story of Alice falling down the rabbit hole into a world of fantasy with strange and peculiar creatures. As many know, Dodgson was a mathematician, so the work contains many references to mathematics. Just for fun, I thought I’d use this post to enumerate on some of the mathematical references in Alice’s Adventures in Wonderland, especially those relevant to coursework in Math 152:

In chapter two, “The Pool of Tears,” Alice says, “Let me see: four times five is twelve, and four times six is thirteen, and four times seven is–oh dear! I shall never get to twenty at that rate!” Seems like nonsense, but Alice could be multiplying in base notation (four times five is twelve in base 18, four times six is thirteen in base 21, four times seven can be fourteen in base 24…)

Alice then goes on to say, “However, the Multiplication Table doesn’t signify: let’s try Geography. London is the capital of Paris, and Paris is the capital of Rome, and Rome–no, that’s all wrong, I’m certain!” Sounds a lot like the cyclic notation of permutations…

In chapter seven, “A Mad Tea-Party,” there are many references to logic. The Mad Hatter, the March Hare, and the Dormouse discuss converses:

“Not the same thing one bit!” said the Hatter. “Why, you might as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see!'”

“You might just as well say,” added the March Hare, that ‘I like what I get’ is the same thing as ‘I get what I like’!”

“You might just as well say,” added the Dormouse, which seemed to be talking in his sleep, “that ‘I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!”

Also in chapter seven, Alice wonders about movement around a circular table, which is similar to the addition on a ring of integers modulo n. Here’s the quote:

“Then you keep moving around, I suppose?” said Alice.

“Exactly so,” said the Hatter: “as the things get used up.”

“But what happens when you come to the beginning again?” Alice ventured to ask.

And just for good measure, I’ll include my favorite quote (from chapter five in Through the Looking Glass):

Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things.”

“I daresay you haven’t had much practice,” said The Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes sometimes I’ve believed as many as six impossible things before breakfast.”

There are plenty more fun references to mathematics, including some to geometry, calculus, and arithmetic. I highly recommend reading The Annotated Alice–lots of cool stuff in there. Have a great weekend!



  1. What a romantic post! I remember the movie (Disney’s) Alice in Wonderland scaring the socks off of me when I first saw it as a kid, but now I find the entire story ever so elegant and lovely.

    It reminds me of my favorite work of mathematical fiction (which I’m sure some of you have read): Flatland by Edwin Abbott. If you haven’t read it, it’s great: short, easy, and fun–with hilarious social commentary.

    Of that genre, I also highly recommend Ian Stewart’s “sequel,” Flatterland–much thicker, more wordy, also marvelous. However, an search may then point you in the direction of Spaceland by Rudy Rucker. Don’t buy it! It doesn’t share the same philosophy at all; it reads like a bad novel, and I threw it out halfway through.

    Wow, math fiction reviews: I’m such a stereotype.

  2. Yes, Alice is delightful. Thanks for the enjoyable reminiscence. As for Flatland, by the way, I second the vote for reading that. Justpeachie, have you seen the new movie of it? I haven’t seen it yet, but I’m curious if the tone is faithful to the original. The trailer looks kind of hollywood:

    Flatland: The Movie

  3. The trailer looks a little over the top, but from what I’ve seen of the movie (mainly grainy uploaded clips), it looks pretty good. Well animated, nice color scheme, and not too cheesy or fancy. Hex sounds cute.

  4. I wish you had completed the observation when you correctly noted concerning Alice doing her multiplication tables in chapter 2, that “Alice could be multiplying in base notation”. Yes, indeed! This, in fact, explains her final remark “oh dear! I’ll never get to twenty [i.e., 20] at that rate!” for her efforts work up through 4 x 12 = “19” in base 39, and break at the very next calculation, for in base 42, 4 x 13 = “1*” [using whatever character is chosen to represent ten] rather than “20”. Carroll’s fascination with the number 42, and frequent uses of it in his writings explain why this mathematician gave this mathematical joke the specific form he did.

    (Incidentally, this also belies Douglas Adams’s evasive claim that he didn’t write jokes in base 13. In fact, 6 x 9 in base 13 = 42, suggesting he is ‘reversing’ Carroll’s joke in Alice. Adams’s borrowing from Carroll, despite all his claims, is quite easy to establish. It is already transparent in his naming the episodes of the radio plays which comprises the first form of his “Hitchhiker’s Guide to the Galaxy” the odd, archaic title of “fits”, the very term Carroll chose for the chapters of “The Hunting of the Snark”.)

  5. “… Oh dear, how puzzling it all is! I’ll try if I know all the things I used to know. Let me see; four times five is twelve, and for times sever is oh dear! I shall never get to twenty at that rate!” Why couldn’t Alice get to twenty at that rate?

  6. […] 4. Lewis Carroll was a brilliant mathematician, and when Alice says, “4 X 5 = 12” it’s not nonsense but multiplication in base 18. – Source […]

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