Algebra In Wonderland 184
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."'"
Yeah Not Really (Score:3, Insightful)
Sure, Dodgson was a mathematician and logician. But he was writing a mind bending kids story, not "satirizing" his trade.
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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, Funny)
How can math be unrigorous? Either something adds up, or it doesnt, or both.
Re:Yeah Not Really (Score:5, Informative)
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)
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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.
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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
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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)
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)
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.
TBH, I'm not sure about satirizing (Score:4, Insightful)
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.
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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
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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.
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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
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And is their similar symbolism in "The Hunting of the Snark"? I am thinking specifically of the poem "Jabberwocky".....
Travelling knot theorem in text. If you take a piece of string, connect it to a piece of fishing line, connect that to a piece of rope, then make an overhand knot in the string and work the knot along until it reaches the rope, what, then is a "knot"?
Es Brillig war. Die schlichte Toven warten und wibbleten in Waben. Alle mumsige war die Borgegoven, und die Momeraths ausgraben.
Travelling knot becomes travelling meme.
There is a mathematical structure to the common meme, too. Think about it.
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Really?
I always thought it was a movie created to sync up with The Dark Side of the Moon [wikipedia.org] ...
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I always thought Alice was more about pedophilia then mathematics.
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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.
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While the phrasing may not have been the best, I don't know that it's necessarily a troll to mention pedophilia wrt Lewis Carroll.
You don't know? OK, let me help you out there, it is.
He *did* spend a lot of time around young children ...
What proportion of his time was that?
one of his hobbies was photography, his favorite subject young children.
Quick! Let's run out and lynch Anne Geddes! (Well that might not be such a bad idea ;)
And he named the main character of and dedicated "Alice" to a certain y
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It certainly is NOT a troll to mention paedophilia with regard to Lewis Carroll. There's a subsection about his purported paedophilia in his Wikipedia entry:
http://en.wikipedia.org/wiki/Lewis_Carroll#Suggestions_of_paedophilia [wikipedia.org]
Moreover, most of his 20th century biographers have at least hinted at the possibility, and many discussed it outright--any biography of the man would be sorely incomplete without mentioning that the theory of Carroll as repressed paedophile permeated much 20th century analysis of the
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It certainly is NOT a troll to mention paedophilia with regard to Lewis Carroll.
I won't pretend to expertise as regards the jurisprudence appropriate to trolls. However, I doubt that notion of prior art constitutes a defence here. ;)
The fact that ... all play into that notion. That isn't to say it's true.
IAAL and where I'm from, before we accuse people of serious wrongdoing such as sexually interfering with children, we make sure we have the EVIDENCE to back up such a charge. Moreover we would hope su
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IAAL and where I'm from, before we accuse people of serious wrongdoing such as sexually interfering with children, we make sure we have the EVIDENCE to back up such a charge. Moreover we would hope such evidence is more than merely circumstantial.
Paedophilia is an attraction to children, it doesn't necessarily imply any actual physical acts, or any criminal behaviour. Safest to keep this one in proportion.
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by your standards (Score:2)
anyone who spends a lot of time around children is a pedophile, like kindergarten teachers or nannies
unless you can point to a situation in which SEXUAL interest is suggested, to suggest he is a pedophile is completely spurious
for example, his pictures: is there anything even remotely erotic about them? innocence is another thing adults are fascinated about children, and "innocence" does not directly connote sexual innocence. being genuinely unaware of and unspoilt by adult concerns: economic innocence, soc
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As it is, the article was substantially more convincing. Had you included references to his other works such as
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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.
The Annotated Alice (Score:2)
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.
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Is Sulphur 1548251's 'between' meant chronologically or philosophically?
you're kidding (Score:4, Funny)
sometimes a cigar is just a cigar...
Re:you're kidding (Score:5, Funny)
And sometimes a caterpillar sitting on a giant mushroom smoking a hookah is just a caterpillar sitting on a giant mushroom smoking a hookah.
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Personally i think the person that wrote the article was smoking the hookah a little much.
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Actually, it was a perfectly ordinary mushroom of the normal sort of size. It only seemed like a giant mushroom because Alice, at the time, was extremely small.
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And sometimes its a simply connected, three dimensional topological space isomorphic to a spherical ball.
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And sometimes, a cow is spheric symmetric... at least in the eyes of a physicist.
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sometimes a cigar is just a cigar...
What is it at the other times?
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According to George Carlin, it's a big brown dick.
A baby is not a sphere (Score:5, Funny)
Surely a mammal is a torus.
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It all hinges on the topological properties of a sphincter.
Re:A baby is not a sphere (Score:4, Insightful)
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It all hinges on the topological properties of a sphincter.
That's disturbingly informative considering the visual it gives.
Actually, mammals are tori... (Score:2)
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
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So, I guess the answer might be: mammals have varying numbers of holes. A mammal is a 3-torus or 5-torus or maybe even 7.
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I was going to argue that the nose terminates at the lung, but you're right -- there is a hole starting at the nose and ending at the mouth.
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I was going to argue that the nose terminates at the lung, but you're right -- there is a hole starting at the nose and ending at the mouth.
Actually it's a Y-section, which adds to the manifold. A cow is actually a rather topologically interesting beast.
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people have 4 entry and exit points, all linked. Each nostril connects to each other, and that connects to the mouth, and that connects to the sphincter. A person is more like a 4 way tube intersection with asymmetrical tubes. I have no idea what to call that geometric configuration though.
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Re:a mammal is a torus (Score:5, Funny)
I am sure there is some German porn on the Internet that refutes that statement.
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Nostrils go through to the sinuses, which are also connected to the throat, but the latter doesn't matter much; with the proper stretches and contortions, it can be shown that topologically, that makes 3 "holes".
And then there are the tear ducts, which also go throu
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I don't think I follow.
2 nostrils.
2 tear ducts.
1 mouth.
1 sphincter.
I count 6 orifice if you count the tear-ducts (i didn't consider them earlier).
But to state that the mouth-> sphincter is one hole? Then wouldn't it be one hole with 6 openings for the whole thing and not 5 holes?
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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
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In that case, my point stands. There is only 1 hole and not 5 because all the orifices eventually lead to the same place.
Left nostril drains to throat, right nostril drains to throat, left tear duct drains to throat, right tearduct drains to throat, mouth drains to throat, throat drains to sphincter.
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By way of an example of stretching and twisting: an inner tube (a hollow torus with a "hole" through to the "inside" at the air valve) can be twisted and stretched in such a way that you can actually turn it inside out. So topologically an inner tube (which is not really a true torus because of the hollowness and the sort-of hole at the air valve) has no insid
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So, topologically speaking, I should not end up in court for slander when I see someone drink a coffee and ask whether he enjoys his enema?
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Oh, I don't know. The oopie-cow sounds like it could be, um, udderly hilarious. :-P
Cheers
You mean P2P isn't killing cinema?? (Score:2)
How is that possible...?
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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.
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Same thing.
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Correction: Pocahontas and Avatar were both animated. Kevin Costner is anything but animated.
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Correction: Pocahontas and Avatar were both animated. Kevin Costner is anything but animated.
Darn - and I spent all my mod points on a state change.
Uh huh (Score:3, Funny)
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All of the above and Cowboy Neal (Score:5, Insightful)
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Must be where Nintendo got the idea (Score:2)
and possibly perspective-stretching mushrooms
Let's do the Mario!
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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?
Well, you can ask Dodgson directly in a sense (Score:2)
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
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Not sure about the specifics (Score:5, Interesting)
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.
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I searched in vain for a reference to The Annotated Alice in your post but didn't find one. Pardon me if I just overlooked it. Anyway, here's a link: http://www.amazon.com/Annotated-Alice-Definitive-Lewis-Carroll/dp/0393048470/ref=sr_1_1?ie=UTF8&s=books&qid=1267996987&sr=8-1 [amazon.com]
Re:Not sure about the specifics (Score:5, Informative)
There's an annotated edition that is much more than "decent".
http://search.barnesandnoble.com/Annotated-Alice/Lewis-Carroll/e/9780393048476/?itm=1&USRI=annotated+alice [barnesandnoble.com]
The scariest part about it is ... (Score:5, Funny)
http://search.barnesandnoble.com/Annotated-Alice/Lewis-Carroll/e/9780393048476/?itm=1&USRI=annotated+alice [barnesandnoble.com]
..."Customers who bought this also bought"
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Ooh! Shiny! and Martin Gardner too!
See, this is why I post on Slashdot, to learn things like this. Thank you.
To understand infinitesimal calculus (Score:2)
To understand infinitesimal calculus, you must first understand the easy half of infinitesimal calculus.
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But what is the ... oh... oh! Ohhhkay....
Should had included images... (Score:2)
... for each analysis part.
If you had read the cliff notes thirty years ago (Score:5, Informative)
you'd already know that "Alice" was a satire.
Full Version (Score:5, Informative)
Just sayin'
http://www.newscientist.com/article/mg20427391.600-alices-adventures-in-algebra-wonderland-solved.html?full=true [newscientist.com]
Alice and Science (Score:2)
"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]
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New Math (Score:2)
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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
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If you plan to see the 3D IMAX version (seems worth it for this movie), make sure you know whether or not you're getting the huge 72-foot version or the "just a slightly bigger than normal" version (called "IMAX Digital"). Both versions cost extra, but many unwitting customers have been feeling ripped off by the smaller "IMAX Digital" version.
A local (to me) example: the Metreon in San Francisco [amcentertainment.com] is showing Avatar: An IMAX 3D Experience on its hug
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Maybe the article isn't all about 3D and Johnny Depp?
Re:-1, Don't Care? (Score:4, Insightful)
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.
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Yes, it's yet another Alice movie. And I'm quite sure it's different from any that have been made so far.
Its Alice 'Nightmare Before Christmas' style!
Funny really. I HATE Tim Burton movies but I could tell, looking at the poster from a distance, that this was a Tim Burton movie. It was just so obvious *just* from the poster.
It may as well have singing, dancing skeletons in it...
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In projective space a "parabola" has a point at infinity and thus is homeomorphic to a circle.
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They went a bit overboard there, but a pig and a baby are probably homeomorphic.
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It was to amuse little children (Score:3, Interesting)
Dodgson also carefully distinguished his writing
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Lysergic-diethylamide wasn't synthesized until the late 1930's. Through the Looking Glass was published almost 70 years before.
There are certainly a handful of drug references in the two books. The 60's counter-culture adopted the Alice adventures as their drug metaphor, not the other way around. It is a pretty shallow interpretation of the books, in my opinion. If all someone takes away from the story is, "whoa, this story is trippy dude", then maybe its time for them to lay off the hookah.