We’re probably a little off-topic here, but with the renewed interest in Alice’s Adventures in Wonderland (the proper title), due to the Tim Burton film, people are starting to pick up Lewis Carroll’s books again, which I can only see as a good thing (being an Alice fan myself and all). The New York Times is running an interesting article about an aspect of the Alice books you won’t see in most adaptations: the mathematical one.
Alice is the creation of writer Charles Dodgson, who used the pen name Lewis Carroll to publish the Alice books. Contrary to popular belief, there are two Alice books, and neither of them are named “Alice in Wonderland”. The first book, published in 1865, is called “Alice’s Adventures in Wonderland”, and has a decidedly card deck theme to it all. The second book, titled “Through the Looking-Glass, and What Alice Found There”, was published in 1872, and shifts to a chess theme. In other words, no, the Red Queen (chess theme) and the Queen of Hearts (card theme) are not one and the same.
Most films based on the two Alice books mix and match themes, characters, and locations from the two books, completely disregarding the fact that the two books are quite different from one another. The feeling I get watching any modern interpretation of the Alice books can more or less be described as the feeling people will have if someone were to mix and match various locations and characters from the Lord of the Rings trilogy, mangling them together at random into some sort of storyline that doesn’t align itself at all with the three books. It just doesn’t feel right.
Even something as basic as forcing an actual storyline atop the Alice books is something that appears wholly alien to me. The beauty – and power – of the Alice books is exactly that it doesn’t have much of what you would traditionally call a storyline, with basic elements like goals, motivations, and the likes. Wonderland, and the events that take place there, as well as Alice’s role in those events are entirely the construct of Alice’s own mind.
This is crucial.
Alice is a young girl, round and about seven years old, which means her mind isn’t the same as that of adults. It makes less sense, has less structure, and tends to jump from here to there without much logic. Anyone who has ever seen a young child play with a whole bunch of toys can attest to this; multiple different types of toys are played with interchangeably, seemingly without much structure or logic behind it all.
Since Wonderland is a construct of Alice’s own mind, it reflects this chaotic nature. Events in the books seem quaintly disjointed, and there’s no real reason why one event follows the other. This is the beauty of it all; it doesn’t have to make sense. It doesn’t have to have a point. It doesn’t have to have a moral. This is what created the books’ lasting appeal.
I know I’m a bit off the topic I wanted to talk about here, but hey, Alice is a passion of mine. I love the books, the ideas behind them, the dark undercurrent, the absurdity of it all. In a way, Lewis Carroll is the 19th century version of Pixar; they, too, have that uncanny ability to thoroughly entertain both children and adults within one and the same work of art.
Anyway – to get back on topic. Another important and oft-neglected aspect of the Alice books is math. Charles Dodgson was a mathematics tutor at the University of Oxford, and his love for math can most surely be seen in the Alice books in countless ways. In lieu of the Tim Burton film, The New York Times decided to run a piece on this particular aspect of the books, which contains some interesting examples (although there’s one oft-made error in there too; contrary to what the article states, Alice was not based on Alice Liddell specifically).
Melanie Bayley, the author of the piece, explains that Dodgson’s work contains a lot of satire about then-modern ideas in the world of mathematics. “Dodgson found the radical new math illogical and lacking in intellectual rigor,” Bayley writes, “In ‘Alice’, he attacked some of the new ideas as nonsense – using a technique familiar from Euclid’s proofs, reductio ad absurdum, where the validity of an idea is tested by taking its premises to their logical extreme.”
Dodgson was able to achieve this because Wonderland, being a construct of Alice’s mind, did not have to adhere to the laws of physics and science as would the real world; this gave him the freedom to explore what the world would look like if the logical extremes of the mathematical ideas he disagreed with were truth. I especially like the example of chapter 6, “Pig and Pepper”.
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.”
The article contains many more interesting examples that seem to make a lot of sense – but do remember that it is impossible to know exactly what Dodgson meant with all the symbolism in his books. He never explained himself, so all we can do is look back and place his work in the proper context, and go from there.
And this is yet another important aspect of the books: the mystery. You can read just about anything into the strange things that happen to Alice and her Wonderland companions, meaning that child and adult alike can lose themselves in the experience.
Tim Burton
I was really looking forward to the Tim Burton film, by the way, but I have this sneaking suspicion that it won’t be a good film. You see, both Burton and Dodgson are incredibly good artists, with their own unique styles, and while Wonderland itself might present Burton with a wonderful canvas for his creative genius, I’m afraid that the actual Alice stories do not.
Tim Burton makes Hollywood films. He does this incredibly well – I’m a huge fan – but being a Hollywood director, working for Disney (of all places), means the film must adhere to basic story telling, with goals, motivations, and most likely, a love interest of some sort squeezed in somewhere. This kind of thinking just doesn’t become Alice. I saw some previews that showed Alice running around with swords and armor, fighting in some Helm’s Deep-esque battle.
With Wonderland being a construct of Alice’s mind, I wonder just how mentally messed up Burton’s “real” Alice has to be in order to have her running around like that. American McGee got it right; his “real” Alice was in a psychotic and catatonic state in an old-world insane asylum, rendering McGee’s twisted Wonderland rendition totally believable.
For some reason, I doubt Disney would allow the film to start with a psychotic and mentally deranged Alice – leading me to the scary conclusion that Burton had to violate the most important aspect of the Alice mythos: Wonderland is Alice.
If you severe the two, it’s no longer Alice, now, is it?
Ok, first, let me tell you that I have a PhD in math (algebraic topology), really.
I had to register just to comment on this stupid (imo) article.
From the mathematical point of view, it is extremely poor (more on that later), and apparently, from a english scholar point of view, it is not great (well, according to the comment about the real Alice).
The example about “projective geometry and continuity” does not make any sense. Historically, continuity has always been quite well understood (at least intuitively) and never was strange. Also, continuity stems from real analysis and has nothing to do with projective geometry. The concept he seems to talk about is ‘continuous deformation’ (or perhaps homeomorphism, hard to tell from the text). It is a perfectly simple definition which is about studying common properties of spaces which ‘look alike’. However, it has nothing to do whatsoever with projective geometry.
And pretty much every other examples in the article is flawed.
My opinion is that the author uses random technical words to try to look interesting, but it seems that he doesn’t know what he is talking about. I really dislike that kind of scholarship. It is lazy, sloppy thinking.
Well, this is the internet and not some science journal. A good site has a comment section for brighter people (there are always brighter people) to give _constructive_ criticism and point out what is wrong. So would you elaborate on all the flaws you found in the examples?
If you provide that kind of feedback then your negativity will be received a lot better.
PS: I know comments are mostly abused by trolls and flamers, but there are often nuggets of wisdom in the big pile of crap that are internet comments.
++ (since I can’t actually vote your post up anymore)
Maybe completely inaccurate articles shouldnt be posted in the first place. A novel thought on the Interwebs, I know, but think about it.
Despite the headline, the OSnews article is mostly about Wonderland taking place inside Alice’s head. I think it’s a valid point that its erratic nature can hardly be preserved in a Disney film.
The math examples are taken from the linked New York Times article. Before you comment on them, you should read the entire text. I admit that I did not catch it when I read the book, but the example of the Mad Hatter’s tea party being about quaternions seems plausible and too elaborate to be an over-interpretation.
The author of the NYT article provides further justification for his interpretation by comparing Alice to Dodgson’s other works.
You registered an account just to say you’re a PhD and there are mistakes in the article? Wow
Many people here register their accounts for a lot less…
I think you totally missed the point of the article. I admit this NYT article is not really that great, but I’ve read an article on the same topic (by the same author) in New Scientist a couple of months ago. You’re arguing from today’s standpoint all these mathematical concepts are well understood. However in the 19th century when modern (abstract) Algebra came about a lot of these concepts met quite strong opposition from “traditionalists” who thought that it was all to abstract. Essentially they believed mathematics could only describe “real” things.
Charles Dodgson was such a “traditionalist” (you supposedly can find historical evidence for it). And the author wrote her PhD thesis about Alice possibly being a satire for about abstract algebra. I suggest reading the New Scientist article, which I found quite informative.
This Article?
http://www.newscientist.com/article/mg20427391.600-alices-adventure…
Mirror
http://74.125.155.132/search?q=cache:7E_OTAPdaM0J:www.newscientist….
Is some of the mathematics wrong or misunderstood? Sure. However, some of the interpretations made by the grad student (don’t remember the name) are pretty novel and your complaints don’t take away from the thesis – Alice in Wonderland is, at least in part, inspired by Carrol’s intreptation of the mathematics of his day.
In regards to your specific complaint regarding projective geometry, the article is wrong, or, at best, confused. I believe the point they are trying to make is this:
In the ordinary real plane, a conic (curve given by the zeros of a degree two polynomal) can either be a circle, ellipse, parabola, or hypberola. We can do a coordinate change (think of changing the perspective at which you’re looking at the object) to transform any circle to any ellipse, but the circle/ellipse group is certainly different from the parabola or the hyperbola groups. The first two groups are connected (the hyperbola has two pieces) while the parabola never “closes up” like the cirlce/ellipse. In fancier language, up to topological equivalence (or algebraic, linear, analytic, choose your category…), there are three distinct conics.
However, if we add points at inifity to produce the projective plane (think of adding points so that parallel lines meet in the horizon – like train tracks), the circle/ellipses don’t change (they never make it to inifinty, the parabolas close up at the top, and hyperbolas close up into one piece (here, the parallel sections meet in a twisted fashion so we’re adding two points to the original).
It is here in the projective plane where all three of these groups become the same. Once you’ve added these points at inifity, you can change perspective (linearly, not just any topological deformation) to bring any one group into the other.
In other words, they all look the same, if viewed from the right perspective, but only when you add points at inifinty. It is this latter point that I don’t think the author understands.
They got the Arabic phrase incorrect (or maybe De Morgan got it incorrect). The phrase is actually: al jebr w al mokabala (or an equivalent transliteration thereof). The original is الجبر والمقابلة.
…in our Bible Study/Small group last night.
Don’t get anyone started on scientific inaccuracies in the bible
American McGee’s Alice was awesome.
Sorry, not the most useful comment to make, but hey :p
I was also a bit disappointed to hear that Tim Burton will be directing it. He does certain types of films really well and it will probably be visually-interesting, but Terry Gilliam would have been a much better choice given the source material – just look at Time Bandits (a film he described as “intelligent enough for kids to enjoy, but with enough action to keep adults entertained”).
That, and Tim Burton’s track record the last few years has been pretty shaky (especially the Willy Wonka and Planet of the Apes remakes, blech).
I don’t think Burton should be doing remakes, period. He used to be creative enough to his own original stuff.
American McGee’s Alice would have been better IMO. Supposedly they’re making a sequel to the game, hopefully it hasn’t become vaporware.
Yeah, and there does seem to be a general epidemic of unnecessary remake-itis lately. Remakes should be illegal unless they improve on (or add something interesting to) the original.
Alice is not a remake. The only remake Burton has done is the Apes and, maybe, Sweeny Todd.
While I like Gilliam I have nothing against Burton. Wodnerlans was good. Plus, Wonka was awesome and Apes wasn’t that bad.
I consider both of them one of the few actually visionary directors today although visionary does not always translate into great movies. Always interesting though.
I don’t think either film was unilaterally horrid – but where they were bad, they were really REALLY bad (E.g. the CGI Oompa Loompas, the Twilight Zone cliche ending for Apes – Ape-braham Lincoln, haw haw haw – etc).
Yeah, in context a bad Burton film is probably still better than 90% of its competition. The main reason I find Burton’s recent work disappointing is that he’s shown he can make much better films.
I found out yesterday that Burton was responsible for arguably one of the worst films I’ve ever endured: Mars Attacks
Hey Tom,
if you make a claim that some article is wrong, like here by saying Alice is not based on Alice Liddell you really should back that up. I’ve just looked at the Wikipedia article about Dodgson and that also states Alice is based on A.L.. Also the person who wrote the NYT article is writing her PhD about Alice in Wonderland, so I’d assume she knows what she’s talking about. There might be some controversy about if Alice is really based on A.L. but it’s definitely not clear that she’s not.
Straight form the horse’s mouth… Dodgson himself has stated repeatedly that Alice was not based on the Liddell Alice. She was an influence for sure, but just one of many (hence why I say “Alice was not based on Alice Liddell specifically“).
http://en.wikipedia.org/wiki/Lewis_Carroll#Alice
Edited 2010-03-08 23:22 UTC
My bad I totally missed that sentence in the Wikipedia article. Sorry Thom, you were correct.
Edited 2010-03-09 03:47 UTC
“Since Wonderland is a construct of Alice’s own mind, it reflects this chaotic nature. Events in the books seem quaintly disjointed, and there’s no real reason why one event follows the other. This is the beauty of it all; it doesn’t have to make sense. It doesn’t have to have a point. It doesn’t have to have a moral. This is what created the books’ lasting appeal.”
It all makes sense now!!1 I am not referring to the Alice books, but to Thom’s posting and writing style.
You see, most of Thom’s posted comments and original stories are, how would he say, “quaintly disjointed.”
You see, using this rule set, Thom has allowed his creative mind to venture off negating need for things to, “make sense” or “have a point.” This allows for endless “lasting appeal” for the community and ensures that we will have something to comment about even if it is commenting on Thom’s posts and ignoring the information in the article, simply due to the readers need to comment on what he says. It’s brilliant! It’s creating both supply AND demand, even in a slow news day.
See the key to popularity is not if you are right or wrong, its how loud you are when you say something. In fact, being wrong often generates more hype and spurs a longer conversations with more user interaction. This is an inherent characteristic for most people, if the correct answer has not been suplied and the wrong answer has been pushed forward, the need to correct it makes us computer people to speak to it (or obsess. example here: http://xkcd.com/386/).
So just remember, next time Thom posts something, no matter what it is, it makes for a good OS News discussion.
This post is entirely intended to be read in a joking fashion. It is not actually intended to discredit Thom, but it presented an opportunity I couldn’t resist
. Also, Thom is right, Alice is not based on Alice Liddell, though she was one of many things that did inspire Lewis Carrol’s Alice.
The movie is not a good ‘Alice’ movie, simply because the focus is not on the allegories of the original but on the battle between good and evil, which has nothing to do with the question Alice asks herself.
Not only that, but good is absolutely good and evil is absolutely evil, just like every other movie out there in the last decade.
After I saw the movie, I had to watch the 1999 BBC TV production in order to reintroduce myself to the wonderful world of Alice. If anyone cares about a good Alice film, then the BBC production is very good, unlike Burton’s film.
If this premise is true (and it appears to me it most certainly is), then Dodgson’s works are analogous to “hard” science fiction, where the author is exploring scientific concepts, perhaps even promoting their own as a scientist.
But there aren’t many other works of fiction I can think of that address mathematics specifically. The Phantom Tollbooth by Norton Juster might come close (incidentally, it’s been compared to the Alice books – http://www.sparknotes.com/lit/tollbooth/context.html – sorry I don’t have a better reference) but as it’s considered primarily a children’s book with grade school math references (mostly arithmetic as I recall) I’m not sure it holds up as well by comparison.
Hi,
It is wrong to refer to Mathematics.
The continuity Law comes from Cognitive Sciences.
The principle is known by “Gestalt Laws/Principles”
There are many principles, just search and you’ll find them. And from them you’ll find the Continuity Law.
(The Law you have put is called the “Simple Geometry Law”)
That only strengthens my theory that it is mostly scientific concepts that are explored in literary fiction, and rarely mathematical ones.