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The story’s protagonist, Alice is a young girl from wealthy English family. Despite her privileged existence, Alice is unhappy with her environment because she deems it ordinary and uninspiring. Instead, she longs to explore another world that challenges her thoughts and attitude toward life. Alice demonstrates above-average intellect through her precocious understanding of her environment and curiosity for the unknown.

Because of her elevated social class and Victorian-era education, Alice appears a decent girl with good manners. In both a literal and figurative sense, Alice stands tall among others. In addition to her decency, though, Alice proves herself to be a go-getter with a sufficient supply of patience and wherewithal to get what she wants. However, Alice is not perfect. She retains an exaggerated sense of entitlement. For example, Alice describes a girl she knows as a “poky little hose” in comparison to herself. Alice’s condescension to less-privileged individuals impairs her ability to develop positive relationships with Wonderland’s inhabitants.

The story’s action revolves around the contrast between Alice’s sense of order and structure and the madness and nonsense of Wonderland. In Wonderland, Alice’s existence turns upside down as everything she believes to be true becomes different or altogether untrue. For example, the White Rabbit confuses Alice for a servant, something that would never happen to her life outside of Wonderland. In another instance, the Mad Hatter and March Hare ridicule Alice for her misunderstanding of the underworld. The Cheshire Cat humbles Alice by telling her that, in Wonderland, all creatures — including her — are insane.

Alice’s experiences in Wonderland give her exactly what she wanted: a challenge to her understanding of the world and a new conception of life for her to explore. However, Alice struggles because Wonderland presents her with values and ideas that are inconsistent with her own. Alice sees that life cannot always go her way and that events within it are sometimes shaped by forces beyond her understanding. In many ways, Wonderland threatens Alice’s comfortable existence, causing her to feel isolated and sometimes despondent. In short, Alice’s exposure to all sides of adventure — the good, the bad, and the ugly — tests her maturity and ability to handle unpredictability.

Although the King of Hearts might be expected to rule Wonderland, the Queen of Hearts is its undisputed leader. One of Alice’s challenges in adapting to life in Wonderland is finding ways to appease the Queen. However, the Queen is difficult to please. She demands unquestioned obedience from her subjects and orders for their execution when they upset her. Whereas Alice frets over Wonderland’s nonsense and illogical nature, the Queen enforces it. The Queen has made Wonderland hers and retains power over everyone within it, including the King. Although the Queen frequently threatens execution upon dissidents, she rarely carries out her orders. The Gryphon’s conversation with Alice reveals the tactics the Queen employs to indulge her whims and desires in Wonderland. Ultimately, the Queen’s authoritarian style acts as the glue that holds Wonderland together. In a place in which reason and logic do not apply, the Queen’s chaotic regime thrives.

The Cheshire Cat retains a prominent position in the story because he helps Alice comprehend the madness of Wonderland. Upon meeting Alice, the Cheshire Cat explains to her that nonsense controls Wonderland, and any attempt of her to create normality within it will be met with disorder. He notes that everyone in Wonderland — including Alice — is mad, perhaps because she attempts to bring order and reason to a disordered and unreasonable place. The Cheshire Cat’s wisdom is a critical factor in helping Alice cope with life in Wonderland.

Unlike many other creatures in Wonderland, the Cheshire Cat displays bravery and composure in the fact of difficulty. The Cheshire Cat’s deep understanding of Wonderland has equipped him with strategies to survive and thrive in challenging, threatening, and unpredictable circumstances. In fact, the Cheshire Cat is one of the most respected figures in Wonderland. Moreover, nothing epitomizes the Cheshire Cat’s understanding of and harmony with Wonderland more than his enigmatic grin.

Alice in Wonderland’s Hidden Satire: Math Slips Down the Rabbit Hole

Alice’s Adventures in Wonderland is universally admired for its ability to speak to readers both young and adult through its fanciful language and expansive narrative tableaux of colorful, eccentric characters. Would you be surprised to learn that its author, Charles Dodgson, aka Lewis Carroll, undergirded Alice with a hidden world? Several scholars have “cracked the code” to reveal that Dodgson, an Oxford math professor, augmented several of his best-known scenes with theoretical math. Let’s crack open some of these “Easter eggs” the author planted for our astonishment and delight.

«Alice had begun to think that very few things indeed were really impossible.»

We all think we know the story of Alice in Wonderland. But what if we’re missing something really interesting about this beloved – and often bizarre – story?

For example, soon after tumbling down the rabbit hole, Alice begins trying to reconcile what she was experiencing with what she thought she knew:

“[O]h dear, how puzzling it all is! I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate!”

What fun to laugh along with Alice’s obvious confusion – but wait. What if she’s correct and just doesn’t know it? To some specialized readers, her mathematics, strange though it seems, is accurate. But not if you limit yourself to the traditional “base-10” form of math – the one we use every day.

What Alice’ s author, Lewis Carroll, was doing was having a little fun at the expense of “abstract” mathematics, the leading edge of math in his day. If you switch out of base-10 calculations and into, say, base-18, where digits switch at 18, then four times five is 12; in base 19, four times six is 13; and so on, never getting to 20, just as Alice inadvertently foresaw.

Lewis Carroll’s Invention of Alice, with Help from Charles Dodgson

«Alice thought the whole thing very absurd.»

Carroll’s real name was Charles Dodgson, a professor of mathematics at Oxford University. He did his best to keep these mathematical incursions into the narrative hidden, secreted away, only to be discovered by practitioners of advanced math.

Alice encounters numerous “impossible” situations (and handles them with remarkable grace, all things considered). As she attempts to fit in with her increasingly “curiouser” surroundings, we are likely to feel amused, if not slightly discomfited, by the depths of nonsense, absurdity, and downright surrealism in which she finds herself immersed.

Dodgson/Carroll wrote Alice for young people’s entertainment. He reportedly had children “focus-test” an early version to ensure it was child-friendly. And it certainly has a large contingent of fans who would put it in the pantheon of children’s fantasy/nonsense literature, perhaps the first and best example.

Lewis Carroll’s Mathematical Rationale

“No wise fish would go anywhere without a porpoise.”

While Charles Dodson’s alter ego, Lewis Carroll, wrote beloved tales for children’s entertainment, Dodgson himself had a rather more mundane life. As an Oxford professor, he was close with the dean of the college where he taught, who was the father of the real-life Alice who inspired the tale that bore her name.

Dodgson was known in mathematics circles as an educator who revered the Classical beginnings of his field of study, and he saw the ancient Greek Euclid as the paragon of heuristic elegance and eloquence. The great mathematician, who lived in Alexandria, Egypt, in the 4th century BCE, gave his name to Euclidean geometry. His Elements was a model of logic and mathematical rigor, as well as clarity.

Euclid is known for what are called “mathematical proofs,” step-by-step accumulations of agreed-upon facts that combine to demonstrate, or “prove,” a mathematical theorem. His proofs were often completed with a flourish, the rhetorical statement quod erat faciendum (literally, “which had to be done”), or QEF, a close cousin to the better known argument-ender QED (“which had to be shown”).

Dodgson taught Euclid’s “logical” geometry to Oxford undergrads in the mid-19 th century, an era that was (among other things) a hot cauldron of burning issues for mathematicians like Dodgson. It was during this time that Euclid’s point of reference for math was being challenged on numerous fronts.

Mathematical thinking of Dodgson’s time was rapidly evolving with the introduction of “abstract” math concepts, including such ideas as “imaginary” integers (for example, the square root of a negative number) and non-Euclidean geometry, which was pointedly not based on a correspondence with nature.

Frankly, Dodgson the educator and traditionalist was horrified by abstract math. He railed against its “unteachability” to undergrads, and found the development of non-Euclidean anything to be anathema to his philosophy of mathematical education.

Alice Mocks New-Fangled Forms of Logic

Carroll, Dodson’s literary persona, presents a “critique of illogic” in the Alice stories that produced a rich world of symbolic takes on narrative realism that generations of writers found liberating. It can even be said that his work was the progenitor of a genre of fiction where rules of logic are altered or suspended, from The Wizard of Oz to The Hobbit and beyond.

When viewed this way, many well-known scenes from Alice take on a special significance, including the Mad Hatter’s Tea Party, the Duchess and her baby, and the mysterious and quite absurd Cheshire Cat.

The Cheshire Cat Purrs at the Borders of Logic

“We’re all mad here. I’m mad. You’re mad.”

Alice’s series of encounters with the Cheshire Cat is a prime example of Dodgson’s hidden interventions. The Cheshire Cat appears to Alice numerous times in the course of the novel, and its commentary on the course of the plot is at once knowing and completely bonkers. First sighted outside the Duchess’s window, the Cat gives its assessment of the situation quite frankly. Alice asks:

“Would you tell me, please, which way I ought to go from here?”

“That depends a good deal on where you want to get to,” said the Cat.

“I don’t much care where—” said Alice.

“Then it doesn’t matter which way you go,” said the Cat.

The Cat seems unbound by the rigors of illogic in the absurd kingdom into which Alice has fallen, and speaks so plainly that even its internal logic appears absurd. We can see, then, that the Cheshire Cat takes the point of view of pure, traditional logic, which in this environment seems just as mad as any other point of view.

It would seem that the only logical response to the lunacy is to declare oneself a lunatic as well. When Alice demands that the Cat explain itself, it offers this nugget: “[A] dog growls when it’s angry, and wags its tail when it’s pleased. Now I growl when I’m pleased, and wag my tail when I’m angry. Therefore I’m mad.”

While the Cat may represent the point of view of its author, other characters in Wonderland display quirks of another stripe indeed. Let’s take the Duchess, whom we meet in her kitchen with her suckling baby while the cook is preparing a soup with copious amounts of pepper.

The Duchess (it’s OK if you don’t remember her, as this scene was left out of the Disney version) is feeding her baby, and when the baby sneezes while being held by Alice it promptly turns into a pig. All other things being equal, the pig does still bear somewhat of a resemblance to the baby. But when Alice lets it go outside the Duchess’s residence, it ambles off contentedly into the forest. Ergo, the baby is an equivalent of a pig, with porcine tendencies.

The Mad Hatter’s Tea Party and the Use (and Abuse) of Time

“[T]he stupidest tea-party I ever was at.”

He later added a term to his calculations that allowed the rotation to take place in three-dimensional space, and the term he added was – note this – Time. This makes the March Hare’s repeated references to a lack of time, or a loss of time, fall right into place in Carroll’s takedown of Hamilton’s “absurd” conjecturing on quaternions.

A Traditionalist’s Take on a Complex New Reality

“I’ve had such a curious dream!”

In a sense, Carroll was tilting at windmills à la Don Quixote; it was quixotic at best to try to defeat advances in math, and particularly in abstract mathematics, with satiric symbols and metaphors hidden within a tale ostensibly for children.

But how crafty, then, to construct a web of veiled references to people and issues he knew all too well. They certainly knew they were receiving a reductive ribbing, to the point of absurdity, and that must have given satisfaction to Dodgson. Mathematics gave Alice a covert, second level of meaning, and made it the kind of puzzle that could continue providing surprises to its readers, even a century-and-a-half later.

Kevin Martin is Senior Writer for MagellanTV. He writes on a wide variety of topics, including outer space, the fine arts, and modern history. He has had a long career as a journalist and communications specialist with both nonprofit and for-profit organizations. He resides in Glendale, California.

‘Off with their heads!’ – the 10 greatest quotes from Alice in Wonderland

Celebrate Alice’s 150th birthday by reading our top 10 quotes from the nonsensical and magical world of Wonderland!

Alice in Wonderland tea party. Photograph: Print Collector/Getty Images

Alice in Wonderland tea party. Photograph: Print Collector/Getty Images

Lewis Carroll’s children’s classic, Alice in Wonderland, turns 150 this year.

For a century and a half it has delighted and puzzled us in equal measure. We have fallen down the rabbit hole with Alice, taken tea with her and the Mad Hatter, been maddened by the Cheshire Cat and had to convince the Queen of Hearts that we didn’t steal her tarts!

Alice in Wonderland was first published in 1865 and was inspired by a boat trip that author Lewis Carroll took with some family friends, the Liddell children, down the River Thames in Oxford. He told the youngest daughter, Alice, a story as they rowed along and she begged him to write it down. When he got home that evening he began straight away.

The book, and its sequel Through The Looking Glass and What Alice Found There, have been translated into at least 65 languages, including Cornish and Latin, and countless film and theatre adaptations have been made.

Alice in Wonderland is a book that remains as enchanting as ever, no matter how many times we reread it. Here, to celebrate its birthday, we share our top 10 favourite quotes!

The White Rabbit

“Who in the world am I? Ah, that’s the great puzzle.”

“Oh, you can’t help that,” said the cat. “We’re all mad here.”

“Why, sometimes I’ve believed as many as six impossible things before breakfast.”

“First, however, she waited for a few minutes to see if she was going to shrink any further: she felt a little nervous about this; ‘for it might end, you know,’ said Alice to herself; ‘in my going out altogether, like a candle. I wonder what I should be like then?’ And she tried to fancy what the flame of a candle looks like after the candle is blown out, for she could not remember ever having seen such a thing.

“I can’t go back to yesterday because I was a different person then.”

“No wise fish would go anywhere without a porpoise.”

“And what is the use of a book,” thought Alice, “without pictures or conversation?”

“Off with their heads!”

“You used to be much more. muchier. You’ve lost your muchness.”

“Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!”

We want to add your favourite Alice in Wonderland quotes to this blog. So you can either email them to childrens.books@theguardian.com or share on Twitter, @GdnChildrensBks – use #alicequotes and you’ll see other quotes and thoughts as well!

Noel, via email

“If only they would ‘purr for ‘yes’, and mew for ‘no’, or any rule of that sort,” Alice had said, “so that one could keep up a conversation!”
(This is the basis of the binary number system from which the Internet, and everything in it, was created.)
“When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means what I choose it to mean – neither more nor less.”
“The question is,” said Alice, “whether you can make words mean different things.”
So many out-of-the-way things had happened lately, that Alice began to think that very few things indeed were really impossible

Sue, via email

One of my favorite quotes from Alice in Wonderland that certainly rings true in my life is, “I give myself good advice, but I seldom follow it.”

Caroline, on email

“It would have made a dreadfully ugly child; but it makes rather a handsome pig, I think.”

“Open your mouth a little wider when you speak.”

Jamin, on email

(The Cheshire Cat’s head is floating above the King, Queen, & executioner)
“The executioner’s argument was, that you couldn’t cut off a head unless there was a body to cut it off from: that he had never had to do such a thing before, and that he wasn’t going to begin at his time of life. The King’s argument was, that anything that had a head could be beheaded, and that you weren’t to talk nonsense. The Queen’s argument was, that if something wasn’t done about it in less than no time, she’d have everyone executed, all around.”

Kamlesh, on email

From the Dutchess:
“Be what you would seem to be – or, if you’d like it put more simply – never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.”

Princess, on email

“If I had a world of my own everything would be nonsense nothing would be what it is because everything would be what it isn’t.”

Georgina, on email

‘Begin at the beginning,’ the King said gravely, ‘and go on till you come to the end: then stop.’

Angela, on email

‘What a curious helmet you’ve got!’ said Alice cheerfully. ‘Is that your invention too?’

It is said to the White Knight in Through the Looking Glass.

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