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Algebra In Wonderland 184

Posted by kdawson
from the you-are-sad-said-the-knight dept.
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."'"
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Algebra In Wonderland

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  • Yeah Not Really (Score:3, Insightful)

    by poopdeville (841677) on Sunday March 07, 2010 @04:45PM (#31393454)

    Sure, Dodgson was a mathematician and logician. But he was writing a mind bending kids story, not "satirizing" his trade.

    • Yeah, but that duality is possible: In the same way Animal Farm is both a political critique/swipe and also works as a children's story

    • Re:Yeah Not Really (Score:5, Informative)

      by slim (1652) <john@ha[ ]up.net ['rtn' in gap]> on Sunday March 07, 2010 @04:51PM (#31393526) Homepage

      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.

      • Re:Yeah Not Really (Score:4, Insightful)

        by Anonymous Coward on Sunday March 07, 2010 @05:39PM (#31393926)
        So do Saturday morning cartoons; hence the dual audience.
      • by Hatta (162192)

        I have a copy of the Annotated Alice, by Martin Garnder (who wrote Mathematical Games in Scientific American for many years). There's probably as much annotation in that thing as actual text. There's several pages that are nothing but annotations. Great reading.

    • by plover (150551) *

      he was writing a mind bending kids story, not "satirizing" his trade.

      Why not? Did you even RTFA? The arguments are sound, the evidence is there.

      It isn't an unusual literary device to write allegorically about other topics. For example, the Wizard of Oz was a play on the politics of a silver based economy and westward expansion.

      If I had such a gifted imagination, perhaps I could write a children's story based on floppy discs and CDs, of filesharers and industry groups, but all dressed up like trading kittens and bunnies eating cabbages and milk. (If that sounds awful, wel

      • Re: (Score:3, Insightful)

        by zappepcs (820751)

        If you read xkcd, I'm sure you'll understand why it's possible to think allegorically about math. Theorems and proofs and magic!

      • Re:Yeah Not Really (Score:5, Insightful)

        by Cabriel (803429) on Sunday March 07, 2010 @05:45PM (#31393986)
        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.)
        • Re:Yeah Not Really (Score:5, Informative)

          by node 3 (115640) on Sunday March 07, 2010 @07:30PM (#31394966)

          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.

          • by Moraelin (679338) on Monday March 08, 2010 @07:06AM (#31399078) Journal

            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.

            • by node 3 (115640)

              I'm not sure that it's _all_ satirizing

              Neither am I, which is why I wrote: "the two Alice books abound with satire"

              Is the concept of deciding badly based on incomplete data satirized there, or is it just illustrated in a humorous way?

              Um, that's a pretty close approximation to the definition of satire. The difference between satire and mere humor (such as in your sig) is that satire generally exposes some negative characteristic in a humorous way. It's similar to the difference between sarcasm and irony. Sarcasm is just irony that is meant to be biting or insulting.

              In the case of the Walrus and the Carpenter, (and many of the events in those books) the thing is b

          • by acroyear (5882)

            Even if they tell you to your face exactly what their intentions are, you can only ever speculate if they are telling the truth.

            Agreed, and this is ever more true in (classical) music than in literature. Stravinsky's commentary on musical aesthetics and his own works are full of contradictions, both to the popular view of his works and to his own past commentary.

        • by plover (150551) *

          The original poster stated the fixed position that he was not satirizing his trade, offering no rationale or reasoning. Like you, I thought that was a very black and white position to take, and I saw plenty of room to question it. Whether it was intentional or subconscious, at one level the tale seems to parallel his antipathy towards his contemporaries.

          Is that speculative on my part? Sure. Was that his original intent? Based on the evidence of multiple chapters appearing to parody the ridiculousness o

      • by cayenne8 (626475)
        "For example, the Wizard of Oz was a play on the politics of a silver based economy and westward expansion."

        Really?

        I always thought it was a movie created to sync up with The Dark Side of the Moon [wikipedia.org] ...

    • Re: (Score:2, Funny)

      by toastar (573882)

      I always thought Alice was more about pedophilia then mathematics.

      • Re: (Score:2, Informative)

        by Ricwot (632038)

        Odd that this is marked as a troll when a widely held belief is that Lewis Carol wrote it about a small girl of his acquaintance with whom he was reputedly on intimate terms.

    • Re: (Score:3, Informative)

      by b4dc0d3r (1268512)

      As it is, the article was substantially more convincing. Had you included references to his other works such as

      Moreover, Dodgson was a rather exceptional student of Aristotelian logic, and he delighted his friends with games, puzzles and riddles. Dodgson's mock-heroic poem, The Hunting of the Snark (1876), ending with the line "For the Snark was a Bojuum, you see", received mixed reviews when it appeared. The meaning of the poem, which tells of the journey to capture the mythical Snark, has puzzled generat

      • Re: (Score:3, Funny)

        Also, if you accounted for your method of understanding the intentions of someone who is now deceased, and has been for a while, we might have been able to independently confirm your theory, or properly and with all authority label you a quack.

        Yes, but don't you see? Ducks have everything to do with it!

        Hit any key to continue.

    • Sounds like somebody found a copy.
      There is so much stuff alluded to in Alice that the annotations seem to go on for ever.
      It is an interesting read, but slow.

  • by pbjones (315127) on Sunday March 07, 2010 @04:48PM (#31393478)

    sometimes a cigar is just a cigar...

  • by slim (1652) <john@ha[ ]up.net ['rtn' in gap]> on Sunday March 07, 2010 @04:50PM (#31393502) Homepage

    Surely a mammal is a torus.

    • Re: (Score:3, Funny)

      by maxume (22995)

      It all hinges on the topological properties of a sphincter.

      • by digitig (1056110) on Sunday March 07, 2010 @09:02PM (#31395748)
        In Linderholm's "Mathematics made difficult" he speculated that there were two sorts of people, loud and quiet ones. Loud ones keep their mouths and anuses open and are isomorphic to tori (genus 2 because of the nose, but I think Linderholm missed that), whereas quiet people keep them shut and are isomorphic to spheres.
      • by fractoid (1076465)

        It all hinges on the topological properties of a sphincter.

        That's disturbingly informative considering the visual it gives.

    • Following the developmental path of mammals back in evolutionary time, back past chordates, the basic design behind mammals and similar animals is a hypothetical creature that is simply a mouth and a digestive system, expelling waste at the other end. Essentially, a torus. When mammal embryos are developing, one of the stages is essentially just that. It's the basic core of mammalian structure.

      Ryan Fenton

  • How is that possible...?

    • by bane2571 (1024309)
      Funniest thing I always take away from all the highest grossing movie bragging that the studios always do is that if they are grossing more each time, doesn't that mean the sales are going up? Or is the "highest grossing" concept complete BS they use simply to sell their movies. I lean more toward the latter.
      • Both can be true, since gross isn't adjusted for inflation [boxofficemojo.com].

        So even though the number of dollars is higher than ever, blockbusters are selling fewer tickets than they used to. Of course, whether this is due to P2P, people waiting for DVD releases or simply because Avatar was just Pocahontas performed by tall thin Smurfs is a matter of debate.

  • Uh huh (Score:3, Funny)

    by davidbrit2 (775091) on Sunday March 07, 2010 @04:55PM (#31393556) Homepage
    It was my understanding that there would be no math.
  • by sammyF70 (1154563) on Sunday March 07, 2010 @04:55PM (#31393560) Homepage Journal
    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).
    • by bane2571 (1024309)
      Unfortunately as far as I'm concerned you basically discribed high school english lit. I remember always sitting there thinking, "Yeah, sure it could be a metaphor for his penis, but how did you know the author didn't just really like bannannas?" Well, ok maybe not that exactly but it's close enough.
    • and possibly perspective-stretching mushrooms

      Let's do the Mario!

    • by gardyloo (512791)

      In one of my high school English classes, we were tasked with delving into the real meaning of various poems. I chose Dodgson's Hunting of the Snark, since it had been one of my favorites for a while, and the ending, after all the build-up and so on, is brilliant.

      After doing some rather extensive phil-awful-sizing into the "meaning" of Snark, I finally had to rely on a series of letters that Dodgson wrote to several acquaintances. In those letters he was explicitly asked "What is the meaning?

    • Dodgson wrote a lot more than just Alice, and there is plenty of data.

      I wish I'd seen the thread earlier because there is an error: Dodgson was not a tutor in mathematics. He was a Student of Christ Church Oxford(The House), which means he was a top level research mathematician. He was a pioneer of photography (in a day when that mean also being a cutting-edge chemist) whose social circle included people like Tennyson. He wrote seriously not only on mathematics but also theology. It's clear from his writing

  • by lennier (44736) on Sunday March 07, 2010 @05:16PM (#31393728) Homepage

    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 [wiktionary.org]

    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 [typepad.com]), 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/ [online-literature.com]

    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.

  • To understand infinitesimal calculus, you must first understand the easy half of infinitesimal calculus.

  • ... for each analysis part.

  • by ClosedSource (238333) on Sunday March 07, 2010 @06:14PM (#31394310)

    you'd already know that "Alice" was a satire.

  • Full Version (Score:5, Informative)

    by Tirhakah (1223100) on Sunday March 07, 2010 @06:14PM (#31394314)
    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 [newscientist.com]
  • Thats interesting news to me, that Alice was a statire on maths, and i'm not sure i believe it. But at least one scientific hypothesis, that of the red queen, has been named after Alice in wonderland. The red queen hypothesis, is

    "For an evolutionary system, continuing development is needed just in order to maintain its fitness relative to the systems it is co-evolving with."

    Named of course after, alice's meets with the red queen, where she has to run as fast as she can, just to stand still

    ---

    Mathe [feeddistiller.com]

    • Those who work on quantum mechanics feel a greater affinity for the White Queen; she is quite capable of believing six impossible things before breakfast.
  • I think they use it to calculate the box office numbers too.

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