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Algebra In Wonderland
theodp writes "As Tim Burton's 'Alice in Wonderland' shatters 3-D and IMAX records en route to a $116.3 million opening, the NY Times offers a rather cerebral op-ed arguing that Alice's search for a beautiful garden can be neatly interpreted as a mishmash of satire directed at the advances taking place in mid-19th century math. Charles Dodgson, who penned 'Alice' under the name Lewis Carroll, was a tutor in mathematics at Christ Church in Oxford who found the radical new math illogical and lacking in intellectual rigor. Op-ed writer Melanie Bayley explains: 'Chapter 6, "Pig and Pepper," parodies the principle of continuity, a bizarre concept from projective geometry, which was introduced in the mid-19th century from France. This principle (now an important aspect of modern topology) involves the idea that one shape can bend and stretch into another, provided it retains the same basic properties — a circle is the same as an ellipse or a parabola (the curve of the Cheshire cat's grin). Taking the notion to its extreme, what works for a circle should also work for a baby. So, when Alice takes the Duchess's baby outside, it turns into a pig. The Cheshire Cat says, "I thought it would."'"
Surely a mammal is a torus.
It's pretty well established that the Alice books contained all kinds of references and allusions that would have gone straight over a child's head.
The nice (frustrating) thing about both Alice stories is that they can stand for pretty much everything. From the obvious ( one pill makes you larger ... dumdidum) to the less obvious ( Alice is supposed to be Queen Victoria?). Unless you can ask Dodgson directly, my guess is that it's just a tale he concocted on the fly, using whatever was on his mind at the time (so, yeah, probably mathematics, queen Victoria and possibly perspective-stretching mushrooms).
"DRM is like the Ford Pinto: it's a smooth ride, right up the point at which it explodes and ruins your day."-C.Doctorow
The weirdness of logic and maths certainly is a large part of Alice, though I doubt it's all of it. But it's fairly obvious to me, just as a geek with a bit of general knowledge, that the Alice books parody a number of things from late-Victorian era politics and education. It's also about puns, wordplay, and the strict application of logic beyond the domains where it applies; and just general nerdy amusement.
* The organising principle of 'Wonderland' is the card game
* The 'Caucus-race' obviously a satire on politics: the members run in a circle, accomplishing nothing except a lot of hot air. http://en.wiktionary.org/wiki/caucus_race
I couldn't speak for certain about whether the Mad Hatter's party and the stuckness of Time really is a reference to Hamilton's quaternions, but quaternions are fascinating and they did introduce the idea of a 4D space-time continuum (and therefore time travel) half a century before Einstein/Minkowski, and scandalised and baffled the maths world, so it wouldn't surprise me if that was in the background.
* The organising principle of 'Looking Glass' is the chess game
* Anglo-Saxon literature (possibly Beowulf?) appears in Looking Glass - 'Jabberwocky' is a parody of the Beowulfian sort of epic, with the hero slaying the monster and lots of untranslated words
* The March Hare and Mad Hatter reappear as 'Anglo-Saxons' Haigha and Hatta. Again, this is the sort of stuff that educated children would have been expected to know as a matter of course, along with Latin and Greek and art ('Laughing and Grief; reeling, writhing and fainting in coils')
* The White Knight's speech ('the name of the song is called...') parses out the fine but very important distinction between objects and names, which becomes a major issue in logic (and more so in computer programming):
The name of the song is called 'Haddocks' Eyes.'"
"Oh, that's the name of the song, is it?" Alice said, trying to feel interested.
"No, you don't understand," the Knight said, looking a little vexed. "That's what the name
is called. The name really is 'The Aged, Aged Man.'"
"Then I ought to have said 'That's what the song is called'?" Alice corrected herself.
"No you oughtn't: that's another thing. The song is called 'Ways and Means' but that's only
what it's called, you know!"
"Well, what is the song then?" said Alice, who was by this time completely bewildered.
"I was coming to that," the Knight said. "The song really is 'A-sitting On a Gate': and the
tune's my own invention."
Like Terry Pratchett (and Bram Stoker - see Dracula Blogged), Alice really needs a decent annotated edition to explain the obvious cultural and scientific references, since it is densely packed with references which might now be misunderstood, and so many weird conspiracy theories have arisen around the books.
The classic example of Dodgson's geeky humour is from 'Four Riddles':
http://www.online-literature.com/carroll/2826/
Yet what are all such gaieties to me
Whose thoughts are full of indices and surds?
x*x + 7x + 53 = 11/3
It doesn't just rhyme and form part of an overall story - it's an equation to be solved, which gives you a word, from which you can take the first and last letters and which give you a crossword/acrostic clue. Beat THAT for geek cred.
You are not a brain: http://books.google.com/books?id=2oV61CeDx-YC
So do Saturday morning cartoons; hence the dual audience.
Judging intent is a phenomenally difficult task. To say Charles Dodgson was satirizing his trade can only be speculative, and it's just as easy to speculate that he wasn't. If an author writes a modern-day story involving a corrupt god, is he satirizing religion or is it merely just a story device he decided to use because he's religious and familiar with the concepts deity and good/bad?
Ultimately, and I think you know this already, authors write what they know about. Dodgson knew math, so is it really so odd to think he included mathematical concepts in his story because he thought it would be cool?
(Yes, I read the full article, and I see a whole lot of room for uncertainty.)
How can math be unrigorous? Either something adds up, or it doesnt, or both.
A bullet may have your name on it but splash damage is addressed "To whom it may concern."
And sometimes a caterpillar sitting on a giant mushroom smoking a hookah is just a caterpillar sitting on a giant mushroom smoking a hookah.
xkcd is not in the sudoers file. This incident will be reported.
I am sure there is some German porn on the Internet that refutes that statement.
you'd already know that "Alice" was a satire.
For those interested, the full version of this article originally comes from the New Scientist, just before Christmas. The NYTimes version is shortened and split onto two pages.
Just sayin'
http://www.newscientist.com/article/mg20427391.600-alices-adventures-in-algebra-wonderland-solved.html?full=true
http://search.barnesandnoble.com/Annotated-Alice/Lewis-Carroll/e/9780393048476/?itm=1&USRI=annotated+alice
..."Customers who bought this also bought"
Judging intent is a phenomenally difficult task.
Sort of. If you look at it in an absolutist, objective sense, then yes. If you look at it in a subjective, probability sense, it's not that difficult at all. In fact, most people successfully do this many times a day.
To say Charles Dodgson was satirizing his trade can only be speculative
Of course. But that's true of anything done by anyone. Even if they tell you to your face exactly what their intentions are, you can only ever speculate if they are telling the truth. At the end of the day, it always comes down to speculation.
and it's just as easy to speculate that he wasn't.
This is the part you get exactly wrong. It's *not* just as easy, because given that he was a mathematician, and that the two Alice books abound with satire, it's difficult to believe that he wasn't satirizing mathematics when his books have so many examples of such.
Ultimately, and I think you know this already, authors write what they know about. Dodgson knew math, so is it really so odd to think he included mathematical concepts in his story because he thought it would be cool?
Here's a simple litmus test. Does the math seem bolted-on? Or does it integrate with the work as a whole? If it feels bolted-on, then perhaps it's just something he thought would be cool. If it fits the work as a whole, then it's most likely meant to be taken in the same way the rest of the work is, which is very much to be satire.
Like you said, though, you can never be absolutely certain, but you can be certain enough to make a personal judgement.