Design Brief

Design Brief.

Design Strategy:

Using this concept of Alice in Wonderland syndrome, I would like to apply this condition to a different protagonist. Explore a new context for the protagonist and apply his perception to the world of Wonderland. Exploring new character design possibilities for Iconic Wonderland characters and re-creating the scenes in an exhibition format that will look different but feel familiar to Wonderland.

 Project Brief:

I will create a character to act as protagonist, defining key character traits, conceptualizing the context in which he exists, and communicating them via character boards and model sheets that show a range of expressions.

Choosing a series of iconic scenes from the original Alice in Wonderland texts, I will analyse the existing themes, characters, environments, mood and style. Then I will map out changes that can be made based around my protagonist.


Using primarily style and proportion, I will use the principles of character design to distil the essence of each character from these scenes and then apply them to the context of my protagonist.

Using these redesigns, I will create 6 illustrations that emphasize the mood, theme and sense of drama contained within the original Alice in Wonderland text, as perceived by my protagonist.

Alice Abstract

CP:  If the hallucinative condition of Alice in Wonderland syndrome were applied to a new protagonist how would this then affect the design of the inhabitants and the world of Wonderland?

Description:

Lewis Carroll’s Alice’s adventures in Wonderland Is the story of a young girl who falls down a rabbit hole in the fantasy world of Wonderland. Where she meets strange and interesting characters, the narrative is nonsensical and seems to follow the structure familiar to that of a dream or hallucination.

Research:

As part of my research I referred to theoretical analysis of Alice in Wonderland and things relating to it. Part of my research led me to an interesting find of a disorienting condition called Alice in Wonderland syndrome. It is a neurological condition that effects human perception.  “The patient complains of visual, auditory and tactile hallucinations and altered perceptions.” Alteration of body image, parts of their body are perceived incorrectly also distorted time perception, time moving quickly or slowly.

American McGee’s Alice somewhat uses this notion. In his re-telling, Alice suffers the loss of her family in a horrific fire and is institutionalised into Rutlidge asylum. She slowly loses touch with reality and is sucked back into Wonderland that has been twisted by her own broken mind.

Strategy:

Using this concept of Alice in Wonderland syndrome, I would like to apply this condition to a different protagonist. Explore a new context for the protagonist and apply their perception to the world of Wonderland. Exploring new character design possibilities for Iconic Wonderland characters and re-creating the scenes in an exhibition format that would visually differentiate but retain the familiarities to Wonderland.

American McGee's Alice

American McGee's Alice is a third-person action game released for PC on October 6, 2000.


Plot.
Shortly after her second adventure, Through the Looking-Glass, Alice's house is burnt down by an accidental fire, killing her family and leaving her as the only survivor. As time progresses Alice loses touch with reality. She is institutionalized in Rutledge Asylum, where she is observed and treated by Dr. Heironymous Wilson. Alice's only possession in Rutledge is a stuffed rabbit. Ten years after Alice was committed to Rutledge, she finds herself sucked back into a Wonderland that has been twisted by her own broken mind. The White Rabbit summons Alice to aid a radically altered Wonderland, which became a twisted version of itself as it came under the horrible rule of the Queen of Hearts. The Cheshire Cat serves as Alice's companion throughout the game, frequently appearing to guide her with cryptic comments.

Setting

The game's setting presents a considerably more macabre rendition of Wonderland than seen in Lewis Carroll's original portrayal. Wonderland, being a creation of Alice's mind, has been corrupted by her insanity. Alice's primary objective is to save Wonderland, and in doing so restore her own sanity.

The new Wonderland is composed of nine provinces. When Alice falls down the rabbit hole, she finds herself in the Village of the Doomed, the home of the Torch Gnomes. The Village of the Doomed is composed of a network of tunnels and caves, patrolled by the Queen of Hearts' card guards. Beyond the subterranean village is the Fortress of Doors, where the main attraction is a school of insane children. Within the school lies an ancient book of recipes for magic potions, as well as the ingredients for one concoction in particular which will be useful to Alice.

World map of Wonderland

Beyond the fortress and across a rough, uncharted landscape lies the Vale of Tears, where Alice's friends Bill McGill and the Mock Turtle reside, along with the Duchess. A giant river runs throughout the gloomy, mist-shrouded landscape, and another aquatic location is accessible through a well inside Bill McGill's house. The well is sealed until the Duchess is slain.

On the other side of the Vale of Tears lies Wonderland Woods, one of the largest regions in the game. The woods are initially filled by ponds, cliffs and jump mushrooms, but much deeper into the woods is a region of rock and magma. This section leads to several new regions including the Cave of the Oracle, the Pale Realm, the Jabberwock's Lair, and the Majestic Maze. The Cave of the Oracle is home to a wise entity that is revealed later to be the Caterpillar.

The Pale Realm makes a transition to the surface of a chessboard, as delving further into this area leads to the White Castle of Looking Glass Land, which is home to life-size chess pieces; the White pieces join Alice in the fight against the Red pieces, a deviation from her normally unhelpful "allies" from earlier portions of the game. Alice is twice transformed into a chess piece herself to pass certain obstacles.

Following this is a distorted version of Rutledge Asylum (where Alice has been incarcerated since her parents' tragic deaths). It is run by Tweedle Dee and Tweedle Dum and also houses the Mad Hatter's laboratory.

The path to the Jabberwock's Lair leads into the Land of Fire and Brimstone, a volcanic region of Wonderland and a reminder of the fire in which her family died. It is here that the terrible Jabberwock—a semi-mechanized servant of the Queen of Hearts and the incarnation of Alice's guilt—resides, in the remains of Alice's old home.

The Majestic Maze ends on the road to Queen of Hearts Land, a region heavily guarded by card guards, boojums, and other members of the Queen of Hearts' personal army.

Queensland is the final province of Wonderland. In it lies the Heart Palace from which the Queen of Hearts commands. Tentacles and other repulsive appendages are seen protruding from every organic wall in this area, and numerous areas even resemble body parts, giving the impression that Alice is travelling through her own body.

Characters

Main article: List of characters in American McGee's Alice

The game's characters are generally based on the inhabitants of Lewis Carroll's original novels, but they do not demonstrate the same identities. Many of them are warped incarnations of their conventional selves. The casebook^[3] of Q. Wilson (a supplement included with the game and written from the point of view of Alice's doctor) suggests that many of the characters Alice encounters in Wonderland are symbolic of real life people who get through to the catatonic Alice in some way. Other characters within the game are metaphors for Alice's own feelings, and because she is unhappy, they have become twisted. Some people (Cheshire Cat, White Rabbit) help her; others (Mad Hatter, Queen of Hearts) try to cause pain, first by taking away those she loves and then by taking her down with them.

source: http://en.wikipedia.org/wiki/American_McGee's_Alice

            http://alice.wikia.com/wiki/American_McGee%27s_Alice

Alice Analysis.

Interpretations and opinions

It is important to bear in mind that Alice's Adventures in Wonderland, however special it may seem and however many different interpretations one thinks one can find, is, after all, but a story written to entertain Charles Dodgson's favourite child-friends.

It is very obvious in the story that it was written for the three Liddell girls, of whom Alice was the closest to Dodgson. In the introductory poem to the tale, there are clear indications to the three, there named Prima, Secunda and Tertia — Latin for first, second and third respectively in feminized forms. The part considering rowing on happy summer days was derived directly from reality. It is said that he used to row out on picnics with the Liddell girls and tell them stories. On one of these excursions it started raining heavily and they all became soaked. This, it is said, was the inspiration to the second chapter of the book, The Pool of Tears. The ever-occurring number of three points out Dodgson always having in mind the three girls he tells the story to. It could, of course, having in mind the fact that he was a cleric, be the Christian Trinity or something completely different.

Many people have seen Alice's Adventures in Wonderland as a prime example of the limit-breaking book from the old tradition illuminating the new one. They also consider it being a tale of the "variations on the debate of gender" and that it's "continually astonishing us with its modernity". From the looks of it, the story about Alice falling through a rabbit-hole and finding herself in a silly and nonsense world, is fairly guileless as a tale. The underlying story, the one about a girl maturing away from home in what seems to be a world ruled by chaos and nonsense, is quite a frightening one. All the time, Alice finds herself confronted in different situations involving various different and curious animals being all alone. She hasn't got any help at all from home or the world outside of Wonderland. Lewis Carroll describes the fall into the rabbit-hole as very long and he mentions bookshelves on the sides of the hole. Perhaps it is an escape into literature he hints at. Carroll is an expert at puns and irony. The part with the mad tea-party is one of the best examples of this. There's a lot of humour in the first Alice book, but in the second the mood gets a bit darker and more melancholic. The theme with Alice growing and shrinking into different sizes could reflect the ups and downs of adolescence with young people sometimes feeling adult and sometimes quite the opposite. The hesitation so typical of adolescent girls is reflected in Alice's thoughts: "She generally gave herself good advice (though she very seldom followed it)." Many short comments point to teenage recklessness, restlessness and anxiety in all its different forms.

One other example of maturing is Alice getting used to the new sizes she grows. She talks to her feet and learns some of the new ways her body works in. Her feelings are very shaken from her adventures and she cries quite often when it's impossible to obey the rules of the Wonderland — or is it adulthood? "Everything is so out-of-the-way down here", as Alice often repeats to herself. Alice doesn't like the animals in Wonderland who treat her as a child, but sometimes she gets daunted by the responsibility she has to take. The quote "Everyone in Wonderland is mad, otherwise they wouldn't be down here" told by the Cheshire Cat can be given an existential meaning. Is it that everyone alive is mad being alive, or everyone dreaming him- or herself away is mad due to the escape from reality? Time is a very central theme in the story. The Hatter's watch shows days because "it's always six o' clock and tea-time". Time matters in growing up, I guess, but further interpretations are left unsaid. The poem in chapter 12 hints at forbidden love, and it is entirely possible that it is about his platonic love for children, or Mrs. Liddell, for that matter. Considering the fact, that the first manuscript was called Alice's Adventures Underground, and that some — at least the Swedish — translation of the title is a bit ambiguous, it becomes more apparent, that the world Alice enters isn't just any childrens' playground, but a somewhat frightening and dangerous place for maturing. The "underground" part of the old title undeniably suggests drawing parallells to the direction of Dante or the Holy Bible.

Continuing in this direction, the wonderful garden, into which Alice wants to get, can be a symbol of the Garden of Eden. It can be assumed that Dodgson, being a cleric and a strictly religious man, had read and was very familiar with the biblical myths aswell as Milton's Paradise Lost. It becomes more interesting when Alice finally gets into the garden and finds a pack of cards ruling it, with a very evil queen at its head. It appears to be a way of saying that even The Garden of Eden can be in chaos, or that the garden isn't really what it appears to be. Or, having in mind his Victorian irony in the tale, a way of saying that our lives on Earth are, in fact, the closest we can get to a paradise, and that it is ruled my a malignous queen with little respect for human lives. These theories are, of course, merely speculations and it would be quite rude to suggest even madder parallells, which isn't at all difficult with a childrens' story of this kind.

Some people have gone very far in their claims that Lewis Carroll wrote the stories while influenced by opium. They say the fifth chapter with the smoking Blue Caterpillar is about drugs. These claims have no real evidence or facts to point at, and it seems that they're just mad rumours made up by people who want to see more than there is in a fairy tale. It is fairly obvious that the visions of the stories derive from the genious of a man, and not from drug influence. If the worlds in the books are somewhat surreal it surely comes from Dodgson having a vivid imagination and an ability to make nonsense worlds alive. He definitely had his share of problems, but drugs don't seem to have been one of them. At a closer look, there seems to be a whole lot of anguish in the story. This becomes even more apparent in the sequel, Through the Looking Glass, and its introductory poem, where the following can be found: "I have not seen thy sunny face, / Nor heard thy silver laughter; / No thought of me shall find a place / In thy young life's hereafter—". The part surely expresses Dodgson's feelings for missing the young girl Alice used to be before growing up.

Perhaps the first story is more like a description of a young friend growing up and disappearing out of one's life by becoming an adult, and as such, out of Dodgson's reach. Dodgson lost contact with Alice Liddell in 1868, a few years before the publishing of the sequel. It seems that the first book is a tribute to a friend who, in time, will be lost to Dodgson, and that the sequel is, considering its tone, an epitaph. This is clearly seen in the last lines (actually, it's just one long sentence) of the first story when Alice's sister thinks of Alice:

"Lastly, she pictured to herself how this same little sister of hers would, in the after-time, be herself a grown woman ; and how she would keep, through all her riper years, the simple and loving heart of her childhood: and how she would gather about her other little children, and make their eyes bright and eager with many a strange tale, perhaps even with the dream of Wonderland of long-ago: and how she would feel with all their simple sorrows, and find a pleasure in all their simple joys, remembering her own child- life, and the happy summer days."

It appears to be Dodgson's own thoughts about the girl growing up expressed through one of Alice's sisters. Another quote that expresses Dodgson's feelings for getting old found in the same introduction mentioned above: "We are but older children, dear, / Who fret to find our bedtime near." This melancholy tone of Dodgson's can be found in various parts of the sequel, which expresses his grief of losing the close friend he once had before she grew up and vanished. The very last poem in the sequel begins its lines with letters that make up "Alice Pleasance Liddell" — her complete name. Charles Dodgson’s academic education shows in his books. The exotic fantasy creatures who inhabit the worlds of his imagination all have very peculiar names made up from real words in English, French and Latin. For example, the Dormouse is a sleeping mouse. Dormire in Latin means to sleep, while there's no need to explain the rest of the word.

Conclusion

It is very difficult to decide on or write a conclusion to a project concerning so intricate subjects as this. I've tried to show some different interpretations and keep the whole project as objective as possible. The subject is vast and there could probably be years spent on it without reaching a definitive answer, and therefore I suggest people use their own imagination, common sense and logic when discussing the book Alice's Adventures in Wonderland. One of the few certain things are that Charles Lutwidge Dodgson really loved children and dedicated his works for them. Whether this love of his was sexual or platonic is almost impossible to decide with the few indications he left after him.

source: http://www.alice-in-wonderland.net/explain/alice841.html

original source: http://www.privat.katedral.se/~sp95jema/alicepro.htm

AIWL and Lewis Carroll discussion.

 Few Words About Lewis Carroll

Presumably everyone in the English-speaking world knows of Alice in Wonderlandand thus of Lewis Carroll. But if you have never read the books themselves, or have not been back to them for a long time, these few notes may be useful.

With Carroll, there is a massive temptation to get sidetracked discussing the man rather than the works--for he was a thoroughly interesting person--but that is not to our purpose here, nor is a recounting of how the stories came to be (a familiar tale anyway), interesting as that too is. So I will stick to the books and, as always, will write as if you were not familiar with them.

The Alice Books

Alice is so well-known an image that it is easy to forget that she is given to us in two quite distinct books, not a single "Wonderland" book. The original, the one that established her and Carroll's fame, was Alice's Adventures in Wonderland; the successor, like and yet very unlike, was Through the Looking Glass and what Alice found there. A great number of the best-liked and best-remembered "Alice" images, which too many people vaguely associate with Wonderland, are actually from Looking-Glass Land: Humpty Dumpty, Tweedledum and Tweedledee, The Walrus and the Carpenter, plus the White Knight, the Red Queen and all the chess-piece characters.

Perhaps the single most important thing to convey about such well-established works is that there is a great deal more in them than what they are too commonly taken for, which is sheer delightful nonsense. There is no harm, and often great good, in sheer delightful nonsense, as L. Frank Baum's Oz books demonstrate in excelsis; but neither is there harm, and often even greater good, in apparent nonsense that turns out to have a wonderfully clever sense to it after all.

Much of the cleverness of the Alice books is now invisible, owing mainly to two causes: what we now call "in" jokes--for many of the references you need to be English, for a fair part of those you specifically need to be from Oxford, and for even a good part of those you need to have been in Carroll's immediate circle of friends--and the passage of time, in that so much has changed since Carroll's day that what were once obvious, commonplace references (not just words and phrases but poems and even political affairs) are now obscure or simply meaningless. There is no remedy for those problems save knowledge gleaned from relevant investigation, which is why I so strenuously recommend Martin Gardner's edition of the two books, published as The Annotated Alice, in which much that would otherwise be obscure is made clear.

Beyond that which Carroll deliberately put into the tales there is what he may have put in unknowingly. There seems an unscratchable itch in some brains to not leave well enough alone; we cannot read and enjoy Alice, we must have a psychoanalytic explanation of the meaning or meanings of all the unusual things--which is virtually everything--that Alice finds in the strange worlds she visits. Those who fancy that such stuff is interesting, or in fact anything but swill, are welcome to their opinion, which is obviously not mine.

It helps to recall that Carroll was immensely fond of logic and of witty logical problems. Much of the strange passages in Alice have beneath them a bedrock of logic. Consider, as but one example, this passage from Through the Looking Glass, as Alice is shown the sleeping Red King (a chess figure) by Tweedledee (of Tweedledum and Tweedledee--you see how much of Carroll is become a part of the heritage of all English speakers?):

"He's dreaming now," Tweedledee exclaimed, clapping his hands triumphantly. "And if he left off dreaming about you, where do you suppose you'd be?"

"Where I am now, of course," said Alice.

"Not you!" Tweedledee retorted contemptuously. "You'd be nowhere. Why, you're only a sort of thing in his dream!"

"If that there King was to wake," added Tweedledum, "you'd go out--bang!--just like a candle!"

"I shouldn't!" Alice exclaimed indignantly. "Besides, if I'm only a sort of thing in his dream, what are you, I should like to know?"

"Ditto," said Tweedledum.

"Ditto, ditto!" cried Tweedledee. He shouted this so loud that Alice couldn't help saying "Hush! You'll be waking him, I'm afraid, if you make so much noise."

"Well, it's no use your talking about waking him," said Tweedledum, "when you're only one of the things in his dream. You know very well you're not real."

"I am real," said Alice, and began to cry.

"You won't make yourself a bit realer by crying," Tweedledee remarked: "there's nothing to cry about."

"If I wasn't real," Alice said--half-laughing through her tears, it all seemed so ridiculous--"I shouldn't be able to cry."

"I hope you don't suppose those are real tears?" Tweedledum interrupted in a tone of great contempt.

Of that passage--which (as Gardner points out) parallels the famous, or notorious, position of Bishop Berkeley on reality and Sam'l Johnson's equally famous or notorious rejoinder--Bertrand Russell remarked "A very instructive discussion from a philosophical point of view, but if it were not put so humorously, we should find it too painful."

Then there is the passage in which the White Knight proposes to comfort Alice by singing her a song:

"Is it very long?" Alice asked, for she had heard a good deal of poetry that day.

"It's long," said the Knight, "but it's very, very beautiful. Everybody that hears me sing it--either it brings the tears into their eyes, or else--"

"Or else what?" said Alice, for the Knight had made a sudden pause.

"Or else it doesn't, you know. The name of the song is called 'Haddock's 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 quite 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."

Now that is formal logic served up with an apple in its mouth! Those familiar with programming computers in higher-level languages will see there a clear delineation of the difference between a datum, the symbolic name of that datum, the address at which the datum is stored, and the symbolic name of that address. Philosophers will see "meta-languages" and the self-referential problems being side-stepped with them, an effort going back to the classical Greeks. The whole thing looks to the casual reader a total nonsense, but it's not: the song is A-sitting on a Gate; the song is called 'Ways and Means', but what it is called is not what its name is (as, for example, the once-popular song named "In Other Words" is usually called "Fly Me to the Moon"); the proper name of the song is 'The Aged Aged Man'; but--and here we go beyond commonplace usage but not at all beyond logic--the name of the song has its own nickname, 'Haddock's Eyes'. Confused? Carroll wasn't.

Both the books share this quality: they are, both literally and figuratively, dream-like. Few have captured the essence of dreaming as most people really experience it--a thing very different from the usual literary presentations of it as relatively lifelike--so well as Carroll. Things and situations drift and transmute with little or no logic save that peculiar logic of the subconscious, which is (and modern neurology seems to support this on a scientific basis) more or less playing random-association games. That is true of both books, but it is markedly truer of the second (which, as you may have gathered from the references to chess pieces, is actually laid out, in concept and exactly in narrative, as a more or less playable chess game). Look, for instance, at this:

"Then I hope your finger is better now?" Alice said very politely, as she crossed the little brook after the Queen.

"Oh, much better!" cried the Queen, her voice rising into a squeak as she went on. "Much be-etter! Be-etter! Be-e-e-etter! Be-e-ehh!" The last word ended in a long bleat, so like a sheep that Alice quite started.

She looked at the Queen, who seemed to have suddenly wrapped herself up in wool. Alice rubbed her eyes, and looked again. She couldn't make out what had happened at all. Was she in a shop? And was that really--was it really a sheep that was sitting on the other side of the counter? Rub as she would, she could make nothing more of it: she was in a little dark shop, leaning with her elbows on the counter, and opposite to her was an old Sheep, sitting in an arm-chair, knitting, and every now and then leaving off to look at her through a great pair of spectacles.

It is regrettable that length prohibits full presentation of the rest of that remarkable scene, in which Alice sees things on the shop shelves but which she cannot make out when she tries to look closely, and in which eventually the shop turns into a rowboat with Alice and the Sheep in it. But that is the very stuff of dreams, and Carroll has caught it as few before or since.

Both tales are, we are led to believe, dreams from which Alice eventually wakes; but the second tale, the more "constructed" one--consider its design as a playable chess game--has more overt references, some of which I have illustrated above, to the philosophical questions of dream and reality, of epistemology generally, and is more thought-provoking for adults. The first book, the original Wonderland book, strikes me as more a series of ideas that popped into Carroll's head (which, however, was richly furnished with raw materials) as he told it, a sort of "stream of consciousness" tale; the second book, the Looking-Glass book, is also dreamlike, but the transitions more deliberate and thought-out. The two slightly differ in flavor but are equally delightful.

Carroll was also extravagantly given to puns and similar word-play, and is often, beneath a calm and sober narrative, being uproariously funny. Here is yet another famed scene (Carroll is in this respect like Shakespeare: the works appear to be made entirely of famous quotations stitched together), occurring right after Humpty Dumpty has taken his cosmically required fall--Alice and the White King are speaking:

"I've sent them all!" the King cried in a tone of delight, on seeing Alice. "Did you happen to meet any soldiers, my dear, as you came through the wood?"

"Yes, I did," said Alice: "several thousand, I should think."

"Four thousand two hundred and seven, that's the exact number," the King said, referring to his book. "I couldn't send them all the horses, you know, because two of them are wanted in the game [the steeds for the White Knights]. And I haven't sent the two Messengers, either. They're gone to the town. Just look along the road and tell me if you can see either of them."

"I see nobody on the road," said Alice.

"I only wish I had such eyes," the King remarked in a fretful tone. "To be able to see Nobody! And at that distance too! Why, it's as much as I can do to see real people, by this light!"

All this was lost on Alice, who was still looking intently along the road, shading her eyes with one hand. "I see somebody now!" she exclaimed at last. "But he's coming very slowly--and what curious attitudes he goes into!" (For the Messenger kept skipping up and down, and wriggling like an eel, as he came along, with his great hands spread out like fans on each side.)

"Not at all," said the King. "He's an Anglo-Saxon Messenger--and those are Anglo-Saxon attitudes."

(Better yet: when able readers manage to recover sufficiently to pick themselves off the floor and recover their breath and wipe enough of the tears from their eyes to carry on, we discover that the two messengers bear the quite Anglo-Saxon names Haigha and Hatta, which--when pronounced correctly, Haigha being "hayor"--make us aware that they are our old friends from the last book, the March Hare and the Mad Hatter, transmuted.)

Well, look--if this hasn't been enough to send you running for copies of those books, nothing will be. End of thesis.

source: http://www.alice-in-wonderland.net/school/alice1020.html

originally from: http://greatsfandf.com/AUTHORS/LewisCarroll.php

Alices's adventures in Algebra.

What would Lewis Carroll's Alice's Adventures in Wonderland be without the Cheshire Cat, the trial, the Duchess's baby or the Mad Hatter's tea party? Look at the original story that the author told Alice Liddell and her two sisters one day during a boat trip near Oxford, though, and you'll find that these famous characters and scenes are missing from the text.

As I embarked on my DPhil investigating Victorian literature, I wanted to know what inspired these later additions. The critical literature focused mainly on Freudian interpretations of the book as a wild descent into the dark world of the subconscious. There was no detailed analysis of the added scenes, but from the mass of literary papers, one stood out: in 1984 Helena Pycior of the University of Wisconsin-Milwaukee had linked the trial of the Knave of Hearts with a Victorian book on algebra. Given the author's day job, it was somewhat surprising to find few other reviews of his work from a mathematical perspective. Carroll was a pseudonym: his real name was Charles Dodgson, and he was a mathematician at Christ Church College, Oxford.

The 19th century was a turbulent time for mathematics, with many new and controversial concepts, like imaginary numbers, becoming widely accepted in the mathematical community. Putting Alice's Adventures in Wonderland in this context, it becomes clear that Dodgson, a stubbornly conservative mathematician, used some of the missing scenes to satirise these radical new ideas.

Even Dodgson's keenest admirers would admit he was a cautious mathematician who produced little original work. He was, however, a conscientious tutor, and, above everything, he valued the ancient Greek textbook Euclid's Elements as the epitome of mathematical thinking. Broadly speaking, it covered the geometry of circles, quadrilaterals, parallel lines and some basic trigonometry. But what's really striking about Elements is its rigorous reasoning: it starts with a few incontrovertible truths, or axioms, and builds up complex arguments through simple, logical steps. Each proposition is stated, proved and finally signed off with QED.

For centuries, this approach had been seen as the pinnacle of mathematical and logical reasoning. Yet to Dodgson's dismay, contemporary mathematicians weren't always as rigorous as Euclid. He dismissed their writing as "semi-colloquial" and even "semi-logical". Worse still for Dodgson, this new mathematics departed from the physical reality that had grounded Euclid's works.

By now, scholars had started routinely using seemingly nonsensical concepts such as imaginary numbers - the square root of a negative number - which don't represent physical quantities in the same way that whole numbers or fractions do. No Victorian embraced these new concepts wholeheartedly, and all struggled to find a philosophical framework that would accommodate them. But they gave mathematicians a freedom to explore new ideas, and some were prepared to go along with these strange concepts as long as they were manipulated using a consistent framework of operations. To Dodgson, though, the new mathematics was absurd, and while he accepted it might be interesting to an advanced mathematician, he believed it would be impossible to teach to an undergraduate.

Outgunned in the specialist press, Dodgson took his mathematics to his fiction. Using a technique familiar from Euclid's proofs, reductio ad absurdum, he picked apart the "semi-logic" of the new abstract mathematics, mocking its weakness by taking these premises to their logical conclusions, with mad results. The outcome is Alice's Adventures in Wonderland.

Algebra and hookahs

Take the chapter "Advice from a caterpillar", for example. By this point, Alice has fallen down a rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. Enter the Caterpillar, smoking a hookah pipe, who shows Alice a mushroom that can restore her to her proper size. The snag, of course, is that one side of the mushroom stretches her neck, while another shrinks her torso. She must eat exactly the right balance to regain her proper size and proportions.

While some have argued that this scene, with its hookah and "magic mushroom", is about drugs, I believe it's actually about what Dodgson saw as the absurdity of symbolic algebra, which severed the link between algebra, arithmetic and his beloved geometry. Whereas the book's later chapters contain more specific mathematical analogies, this scene is subtle and playful, setting the tone for the madness that will follow.

The first clue may be in the pipe itself: the word "hookah" is, after all, of Arabic origin, like "algebra", and it is perhaps striking that Augustus De Morgan, the first British mathematician to lay out a consistent set of rules for symbolic algebra, uses the original Arabic translation in Trigonometry and Double Algebra, which was published in 1849. He calls it "al jebr e al mokabala" or "restoration and reduction" - which almost exactly describes Alice's experience. Restoration was what brought Alice to the mushroom: she was looking for something to eat or drink to "grow to my right size again", and reduction was what actually happened when she ate some: she shrank so rapidly that her chin hit her foot.

De Morgan's work explained the departure from universal arithmetic - where algebraic symbols stand for specific numbers rooted in a physical quantity - to that of symbolic algebra, where any "absurd" operations involving negative and impossible solutions are allowed, provided they follow an internal logic. Symbolic algebra is essentially what we use today as a finely honed language for communicating the relations between mathematical objects, but Victorians viewed algebra very differently. Even the early attempts at symbolic algebra retained an indirect relation to physical quantities.

De Morgan wanted to lose even this loose association with measurement, and proposed instead that symbolic algebra should be considered as a system of grammar. "Reduce" algebra from a universal arithmetic to a series of logical but purely symbolic operations, he said, and you will eventually be able to "restore" a more profound meaning to the system - though at this point he was unable to say exactly how.

When Alice loses her temper

The madness of Wonderland, I believe, reflects Dodgson's views on the dangers of this new symbolic algebra. Alice has moved from a rational world to a land where even numbers behave erratically. In the hallway, she tried to remember her multiplication tables, but they had slipped out of the base-10 number system we are used to. In the caterpillar scene, Dodgson's qualms are reflected in the way Alice's height fluctuates between 9 feet and 3 inches. Alice, bound by conventional arithmetic where a quantity such as size should be constant, finds this troubling: "Being so many different sizes in a day is very confusing," she complains. "It isn't," replies the Caterpillar, who lives in this absurd world.

The Caterpillar's warning, at the end of this scene, is perhaps one of the most telling clues to Dodgson's conservative mathematics. "Keep your temper," he announces. Alice presumes he's telling her not to get angry, but although he has been abrupt he has not been particularly irritable at this point, so it's a somewhat puzzling thing to announce. To intellectuals at the time, though, the word "temper" also retained its original sense of "the proportion in which qualities are mingled", a meaning that lives on today in phrases such as "justice tempered with mercy". So the Caterpillar could well be telling Alice to keep her body in proportion - no matter what her size.

This may again reflect Dodgson's love of Euclidean geometry, where absolute magnitude doesn't matter: what's important is the ratio of one length to another when considering the properties of a triangle, for example. To survive in Wonderland, Alice must act like a Euclidean geometer, keeping her ratios constant, even if her size changes.

Of course, she doesn't. She swallows a piece of mushroom and her neck grows like a serpent with predictably chaotic results - until she balances her shape with a piece from the other side of the mushroom. It's an important precursor to the next chapter, "Pig and pepper", where Dodgson parodies another type of geometry.

By this point, Alice has returned to her proper size and shape, but she shrinks herself down to enter a small house. There she finds the Duchess in her kitchen nursing her baby, while her Cook adds too much pepper to the soup, making everyone sneeze except the Cheshire Cat. But when the Duchess gives the baby to Alice, it somehow turns into a pig.

The target of this scene is projective geometry, which examines the properties of figures that stay the same even when the figure is projected onto another surface - imagine shining an image onto a moving screen and then tilting the screen through different angles to give a family of shapes. The field involved various notions that Dodgson would have found ridiculous, not least of which is the "principle of continuity".

Jean-Victor Poncelet, the French mathematician who set out the principle, describes it as follows: "Let a figure be conceived to undergo a certain continuous variation, and let some general property concerning it be granted as true, so long as the variation is confined within certain limits; then the same property will belong to all the successive states of the figure."

The case of two intersecting circles is perhaps the simplest example to consider. Solve their equations, and you will find that they intersect at two distinct points. According to the principle of continuity, any continuous transformation to these circles - moving their centres away from one another, for example - will preserve the basic property that they intersect at two points. It's just that when their centres are far enough apart the solution will involve an imaginary number that can't be understood physically (see diagram).

Of course, when Poncelet talks of "figures", he means geometric figures, but Dodgson playfully subjects Poncelet's "semi-colloquial" argument to strict logical analysis and takes it to its most extreme conclusion. What works for a triangle should also work for a baby; if not, something is wrong with the principle, QED. So Dodgson turns a baby into a pig through the principle of continuity. Importantly, the baby retains most of its original features, as any object going through a continuous transformation must. His limbs are still held out like a starfish, and he has a queer shape, turned-up nose and small eyes. Alice only realises he has changed when his sneezes turn to grunts.

The baby's discomfort with the whole process, and the Duchess's unconcealed violence, signpost Dodgson's virulent mistrust of "modern" projective geometry. Everyone in the pig and pepper scene is bad at doing their job. The Duchess is a bad aristocrat and an appallingly bad mother; the Cook is a bad cook who lets the kitchen fill with smoke, over-seasons the soup and eventually throws out her fire irons, pots and plates.

Alice, angry now at the strange turn of events, leaves the Duchess's house and wanders into the Mad Hatter's tea party, which explores the work of the Irish mathematician William Rowan Hamilton. Hamilton died in 1865, just afterAlice was published, but by this time his discovery of quaternions in 1843 was being hailed as an important milestone in abstract algebra, since they allowed rotations to be calculated algebraically.

Just as complex numbers work with two terms, quaternions belong to a number system based on four terms (see "Imaginary mathematics"). Hamilton spent years working with three terms - one for each dimension of space - but could only make them rotate in a plane. When he added the fourth, he got the three-dimensional rotation he was looking for, but he had trouble conceptualising what this extra term meant. Like most Victorians, he assumed this term had to mean something, so in the preface to his Lectures on Quaternions of 1853 he added a footnote: "It seemed (and still seems) to me natural to connect this extra-spatial unit with the conception of time."

Where geometry allowed the exploration of space, Hamilton believed, algebra allowed the investigation of "pure time", a rather esoteric concept he had derived from Immanuel Kant that was meant to be a kind of Platonic ideal of time, distinct from the real time we humans experience. Other mathematicians were polite but cautious about this notion, believing pure time was a step too far.

The parallels between Hamilton's maths and the Hatter's tea party - or perhaps it should read "t-party" - are uncanny. Alice is now at a table with three strange characters: the Hatter, the March Hare and the Dormouse. The character Time, who has fallen out with the Hatter, is absent, and out of pique he won't let the Hatter move the clocks past six.

Reading this scene with Hamilton's maths in mind, the members of the Hatter's tea party represent three terms of a quaternion, in which the all-important fourth term, time, is missing. Without Time, we are told, the characters are stuck at the tea table, constantly moving round to find clean cups and saucers.

Their movement around the table is reminiscent of Hamilton's early attempts to calculate motion, which was limited to rotatations in a plane before he added time to the mix. Even when Alice joins the party, she can't stop the Hatter, the Hare and the Dormouse shuffling round the table, because she's not an extra-spatial unit like Time.

The Hatter's nonsensical riddle in this scene - "Why is a raven like a writing desk?" - may more specifically target the theory of pure time. In the realm of pure time, Hamilton claimed, cause and effect are no longer linked, and the madness of the Hatter's unanswerable question may reflect this.

Alice's ensuing attempt to solve the riddle pokes fun at another aspect of quaternions: their multiplication is non-commutative, meaning that x × y is not the same as y × x. Alice's answers are equally non-commutative. When the Hare tells her to "say what she means", she replies that she does, "at least I mean what I say - that's the same thing". "Not the same thing a bit!" says the Hatter. "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"

It's an idea that must have grated on a conservative mathematician like Dodgson, since non-commutative algebras contradicted the basic laws of arithmetic and opened up a strange new world of mathematics, even more abstract than that of the symbolic algebraists.

When the scene ends, the Hatter and the Hare are trying to put the Dormouse into the teapot. This could be their route to freedom. If they could only lose him, they could exist independently, as a complex number with two terms. Still mad, according to Dodgson, but free from an endless rotation around the table.

And there Dodgson's satire of his contemporary mathematicians seems to end. What, then, would remain of Alice's Adventures in Wonderland without these analogies? Nothing but Dodgson's original nursery tale, Alice's Adventures Under Ground, charming but short on characteristic nonsense. Dodgson was most witty when he was poking fun at something, and only then when the subject matter got him truly riled. He wrote two uproariously funny pamphlets, fashioned in the style of mathematical proofs, which ridiculed changes at the University of Oxford. In comparison, other stories he wrote besides the Alice books were dull and moralistic.

I would venture that without Dodgson's fierce satire aimed at his colleagues,Alice's Adventures in Wonderland would never have become famous, and Lewis Carroll would not be remembered as the unrivalled master of nonsense fiction.

Source: http://www.newscientist.com/article/mg20427391.600-alices-adventures-in-algebra-wonderland-solved.html?full=true

The Annotated Alice.

The Annotated Alice is a work by Martin Gardner incorporating the text of Lewis Carroll's major tales: Alice's Adventures in Wonderland and Through the Looking-Glass as well as the original illustrations by John Tenniel. It has extensive annotations explaining the contemporary references (including the Victorian poems that Carroll parodies), mathematical concepts, word play, and Victorian traditions (such as the snap-dragons) featured in the two books.


http://en.wikipedia.org/wiki/The_Annotated_Alice