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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."'"
Sure, Dodgson was a mathematician and logician. But he was writing a mind bending kids story, not "satirizing" his trade.
After all, I am strangely colored.
sometimes a cigar is just a cigar...
There was an unknown error in the submission.
Surely a mammal is a torus.
It was my understanding that there would be no math.
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
It's in 3D, which much like "...on a computer" and patents, completely changes everything. And yes, I'm planning on seeing it tomorrow with my wife, ;^P
Just call it; talking out your ass and you'll be fine.
My karma is not a Chameleon.
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
In projective space a "parabola" has a point at infinity and thus is homeomorphic to a circle.
http://search.barnesandnoble.com/Annotated-Alice/Lewis-Carroll/e/9780393048476/?itm=1&USRI=annotated+alice
..."Customers who bought this also bought"
Alice in Wonderland is one of the few books that you can make a billion movies of and still manage to show a different angle of. The book gives you the material to tell pretty much anything, from a Disney-esque fairy tale with fluffy animals and a song every other minute to a gothic-horror splatter movie that makes you lift your feet every other minute to let the blood flood past.
I'm fairly sure that it's also the book that has been reviewed and discussed in more different classes and subjects than any other book. It contains material for sociology, politics, psychology and as we can see now, math. And I'm fairly sure a few more that I can't think of right now. It has a lot of angles you can look at it.
Yes, it's yet another Alice movie. And I'm quite sure it's different from any that have been made so far.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
It's not about "orificies". It's about "holes". Topology is a little bit strange to wrap one's head around.
Example: a typical coffee cup. It has one hole: the handle. The part where the coffee goes is an orifice, but it is not a hole. So a coffee cup is a 1-torus. (Called a "torus" because if you stretched the coffee cup around, like rubber or clay, you can get a torus-shape. Topologically they are the same.)
So, the mouth and anus constitute opposite sides of one "hole", that goes all the way through a human being. If you straighted out the hole, and squashed the human down, you can get something like a torus.
Except that there are more holes. Do some more stretching, and the nostrils become two more holes, just like the first one. The idea is that you can stretch and squash and move stuff around, but you can't open or close any holes. So stretch out the tear ducts and you get two more holes, for a total of 5.
So, take a piece of modeling clay and flatten it out to a big pancake. Then take a cookie cutter or some such and cut 5 holes in it. Topologically, that's what a human being looks like.
To answer some others: I don't know if all mammals have tear ducts. I know that cats and dogs do.
Correction: Pocahontas and Avatar were both animated. Kevin Costner is anything but animated.
Blank until
TBH, having read both Alice novels and The Hunting Of The Snark, I'm not sure that it's _all_ satirizing. There are some pretty important concepts illustrated in some places. In a humorous way, sure. But I don't think the concept itself is being satirized most of the time.
E.g., the Walrus and the Carpenter part of Through The Looking Glass illustrates the problems inherent in deciding something rashly based on incomplete data, and without exploring it any further. Alice flip-flops between liking the walrus or the carpenter more, as new information is provided. And eventually comes to the realization that _both_ are repulsive characters, regardless of which one of them may be slightly less so. That's a lesson which is still lost even on many adults who seem to think that when taking sides between two parties, they must go all the way and make one the knight in shiny armour if that's the side they chose. (Heck, fanboy wars or armchair political debates are a prime example of that in action.)
Is the concept of deciding badly based on incomplete data satirized there, or is it just illustrated in a humorous way?
In a sense, see my sig below this message. Sure, it's intended to be a funny way to go about it (though if it's actually funny to anyone else, that's another question), and I particularly like the utter nerdiness of it. But by spreading that quote, I'm _not_ satirizing the concept of polar coordinates. I don't find anything silly or invalid about them, and have used them before. The joke is merely in the equivocation fallacy around "polar", nothing else.
A polar bear is a cartesian bear after a coordinate transform.
Dodgson also carefully distinguished his writings on mathematics and his children's books, hence the assumed name. After meeting Queen Victoria, and mistakenly assuming he was being honoured for his work in mathematics, he sent her a copy of his next book - "A treatise on Fluxions" - which must have baffled the Palace. It is very clear indeed that he did not regard the Alice books as aimed at adults.
The fact that he joked about things the Victorians took seriously - including taking the piss out of "moral" writing for children - was because he wanted to protect them from being treated as moral adults. But he was writing for children - so the idea was that they would see the funny side of the stuff adults were trying to impose on them. When he wanted to do that kind of thing for adults he wrote a serious essay or a sermon. As part of the Victorian Establishment, he knew how careful he had to be in employing ridicule.
From scarped cliff or quarried stone she cries "A thousand types are gone, I care for nothing, no not one."