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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.
Well death of the author and all that, and it's an interesting idea, but I can't really see how this holds weight. It just seems as though the paper is reading far too much into this, and I'm saying this after just writing a paper on psychoanalysis..
i know not what weapons the next world war will be fought with, but world war IV will be fought with sticks and stones.
i dont even
Surely a mammal is a torus.
Can I haz one?
while it lasts cause this fad is like time travel right back to whenit was created 3d heh
what a twitty attempt at some wonder of tech ya know what i just saw
a p2p release you can download and YOU guessed it watch in 3d
now its gonna fade quick as the money goes ALL cause a p2p im sure
How is that possible...?
No sig today...
I heard the movie infringed upon some readers ownership of the idea of Alice In Wonderland. Not everyone was happy
'
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
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
Comment removed based on user account deletion
says so in the
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
To understand infinitesimal calculus, you must first understand the easy half of infinitesimal calculus.
Actually, no. I don't have any piercing and I believe I represent an average mammal in all its glory.
Counting my own orifices, it's more like 3-torus.
Ears, while having Eustachian tubes, are still closed by ear drums and urinary tract is a dead end.
I also believe the above applies not to mammals only but to all tetrapods.
Maybe to all vertebrae too but I am not sure how many open orifices fishes have.
I mean, it's 3D, and has Johnny Depp playing another cookie-cutter role, but why the fuss over the Nth retelling of Alice ?
I want to delete my account but Slashdot doesn't allow it.
"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."
It's been a while since I studied topology, but as I recall, a circle is homeomorphic to (topologically the same as) an ellipse, but not a parabola or a baby.
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.
The default state of a sphincter is, arguably, not 'orifice'.
(It is also fairly unlikely that all of the various constrictions between the mouth and anus would be open simultaneously)
Nerd rage is the funniest rage.
and possibly perspective-stretching mushrooms
Let's do the Mario!
Just call it; talking out your ass and you'll be fine.
My karma is not a Chameleon.
... for each analysis part.
Ant(Dude) @ Quality Foraged Links (AQFL.net) & The Ant Farm (antfarm.ma.cx / antfarm.home.dhs.org).
I am sure there is some German porn on the Internet that refutes that statement.
No, there are 5: topologically, mouth and anus constitute one "hole", going through the entire body, albeit in a labyrinthine way. But topology does not care about the twists and turns, it is still just one "hole" going all the way through.
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 through to the sinuses. So: 5 holes total. All other apparent "holes" are dead ends.
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
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?
For topology it does not matter. An opening is an opening even if it is tightly squeezed to a point.
I am not sure that all mammals have tear ducts.
Do all mammals have tear ducts? I'm not sure.
http://search.barnesandnoble.com/Annotated-Alice/Lewis-Carroll/e/9780393048476/?itm=1&USRI=annotated+alice
..."Customers who bought this also bought"
what about sweat glands? sure they are small but you can't dismiss them.
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?
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
Try "The Annotated Alice" by Martin Gardner. While Carroll's works have redeeming entertainment value, the truth is they contain considerable social and academic references which are undeniably obvious when placed in appropriate historical context. There is a fair amount of philosophical musings and, yes, mathematical concepts; some of which are mocked, others advanced, others simply mentioned in passing. I can't see how his intent could be misjudged here; it was not to entertain drug-influenced hippies, or amuse little children. His intent was to broadcast a host of sophisticated views on some rather advanced subject matters. Carroll is not the only person to take this route to deliver philosophical ideas or social critiques under obscurity of allegory and metaphor. Dante did it. Parmenides did it. Well, a hell of a lot of people have done it. *shrugs* There is really no point in arguing about it.
not to be that guy, but i thought this was common knowledge.
guess not!
Thanks for saving us the trouble of having to read through the Cliff's Notes. I hate long waits.
- youll be telling me "Puff the Magic Dragon" was about cannabis next.
"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
---
Mathematics Feed @ Feed Distiller
Hmmm. Good point. I was just thinking "human".
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.
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.
They are "dead ends", no connections to other holes.
Anthropological chauvinism? :)
Seals do not have tear ducts.
Non sequitur: Your facts are uncoordinated.
Otters are mustelids like ferrets. I don't know if ferrets have tear ducts (though their eyes gum up like humans' eyes when they have the flu, so maybe). But a ferret's external ear holes connect to the throat, making 2 more holes.
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.
Are you trying to say the guy wasn't an acid head?
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.
No, it does not :(
In this kind of topology you can bend, stretch, distort and thin out but you can't merge holes or make new ones or glue loose ends or tear a connection.
The case of 6 holes:
Imagine a hollow sphere with 6 holes on it surface.
This sphere is equivalent to a wire cube or better a pyramid with 5 sides (and a pentagon at the base, to make it easier to imagine).
Now flatten this pyramid and its sides will form 5 holes.
This 2D shape is equivalent to 3D 5-torus (yes, one can go easily from N-D to 2D in topology).
By stretching and twisting the shape (I realize it is not intuitive), it is still possible to show that those are 5 different holes, topologically.
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 inside and no outside. They are merely continuations of the same surface.
It would be nice if there were an easy way to draw you diagrams of how these things work. That is much easier than trying to describe it.
I think they use it to calculate the box office numbers too.
or anthropomorphic topology?
This is why you should be wary of topologists asking you out on a date.
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 writings that what he really wanted was a family, but owing to the weird setup of the day only the Master of a college could be married - and Dodgson makes it clear frequently that he felt much better qualified for that job than the incumbent. The Alice of the stories is Alice Liddell, daughter of the head of The House, and there is at least one sarcastic reference (regarding its banality) to Liddell's book in Alice.
Dodgson wrote a number of stories for children that were designed to exemplify mathematical ideas, but which today are almost unreadably sentimental. But his intentions with the Alice books were perfectly clear. He wanted to write the very best children's books he could, and he paid obsessive (and expensive) attention to detail in getting them illustrated and published. He was writing for an extremely intelligent little girl and her friends, all from academic backgrounds. I am sure all the other stuff simply sprang from his extremely well stocked mind.
The relevance of this to the film is obvious - Burton is a highly intelligent (if slightly eccentric) film maker. Had Dodgson been around today, it's all too easy to believe that Burton would have been his automatic first choice for director.
From scarped cliff or quarried stone she cries "A thousand types are gone, I care for nothing, no not one."
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.
It's been a while but I don't think a circle and a parabola are topologically equivalent. If you remove a point from a circle it remains path connected, where removing a point from a parabola cuts it in two. I'm pretty sure a proof by contradiction can be sussed up wherein we assume a homeomorphism between the circle and the parabola and then look at that homeomorphism acting on the subset "circle - point" and "h(circle - point)" and find that those are clearly not homeomorphic.
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."
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, social convention innocence, racist and ethnocentric innocence, knowledge of mortality innocence, moral innocence, etc
and for dedicating a book to a child: in what way is that indication of sexuality? people can be captivated by other people, including children, for all sorts of reasons. maybe this alice was just hilariously precocious and a wise ass and sort of a savant of the absurdist commentary. i've met kids who not only say the most hilariously captivating and incongruent things, but they do so in a way no adult mind could construct, and they do it consistently. for a man of dodgson's interests, such plasticity of childlike mind probably was completely enthralling and absorbing, and for completely nonsexual reasons, yet very magnetic reasons. so maybe he dedicated "alice" to her because it fit her personality, or perhaps she actually is a coauthor, if not overtly, but in subtle ways like planting the seeds in dodgson's minds of the various situations in the story
believe it or not, there are genuinely nonsexual reasons that some adults spend a lot of time around children and become captivated by them. and its normal, and its way more common: its the majority of life experience. ask any parent who befriends his own child, or any older relative, or caretaker. or even scattered situational settings, say a boarder who winds up being stuck at home with a child of another boarder or house's owner over an extended period of time: a completely innocent and normal friendship can develop, without any sexual overtones
of course, pedophiles do exist, and they are the scum of the earth. they deserve severe punishment, because of the threat they represent to children's well-begin. but exactly because of that, you need to be extremely careful with the charge of "pedophile!", it is not a charge to level lightly
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
Contrary to what your mom told you, people on the internet care a lot about your opinions. Even more so when you don't even bother explaining them. CAPS are an excellent way to grab people's attention.
Ears don't count? They do connect to the lungs indirectly.. Ever seen someone blow smoke out of them? freaky.