In Chapter 1, when Alice first goes through the looking glass, she realizes that the living chess pieces cannot see or hear her. This leads to a sense of dramatic irony as Alice picks up the White King with an "invisible hand":
She said afterwards that she had never seen in all her life such a face as the King made, when he found himself held in the air by an invisible hand, and being dusted: he was far too much astonished to cry out, but his eyes and his mouth went on getting larger and larger, and rounder and rounder, till her hand shook so with laughing that she nearly let him drop upon the floor.
Whereas Alice and the reader both know exactly what is going on, the King does not understand how he is being held in the air and dusted off. His astonishment distorts his face into such an outlandish expression that Alice is moved to shaking laughter. This shaking must be somewhat horrifying to the King, which makes it all the more funny to Alice.
Alice's laughter at the idea that she is an "invisible hand" manipulating the world the chess pieces inhabit suggests that she finds it delightfully silly that she, a little girl, can have such a dramatic effect on the King. Alice goes through her life largely being ignored by adults, so to suddenly be this powerful is new and a bit absurd to her.
In Chapter 5, Alice finds herself rowing through water with the Sheep. The Sheep uses a sarcastic idiom, "complimenting" Alice on "catching a crab," which leads to dramatic irony:
“That was a nice crab you caught!” she remarked, as Alice got back into her place, very much relieved to find herself still in the boat.
“Was it? I didn’t see it,” said Alice, peeping cautiously over the side of the boat into the dark water. “I wish it hadn’t let go—I should so like a little crab to take home with me!” But the Sheep only laughed scornfully, and went on with her knitting.
What Alice doesn't realize is that "catching a crab" is a rowing term that refers to messing up a stroke of the oar by keeping it underwater too long. This is exactly what Alice has just done: she lost control of the oar and could not pull it out of the water. It ended up hitting her in the chin and knocking her over in the boat. Alice believes that the Sheep is telling her she caught a literal crustacean. Because she does not understand the rowing idiom, she fails to understand that the Sheep is making fun of her bad rowing form.
On the one hand, Alice appears naive because of her misunderstanding. A more savvy and socially graceful person would understand that they were the butt of the Sheep's joke. At the same time, Alice has been thrown into a ridiculous situation without any preparation. The Sheep's expectation that she know how to row and that she be familiar with the idiomatic language of rowing is just as laughable as Alice's naivety. This entire situation represents the process of growing up and making one's way in the adult world. Life, Carroll suggests, is a series of ridiculous and unexpected situations in which the world has ridiculous expectations of our competence and know-how.
In Chapter 6, Humpty Dumpty claims to be very good with words. As he describes the way he manages them, he personifies them. This personification draws out the situational irony of his claim that he is a wordsmith:
Alice was too much puzzled to say anything; so after a minute Humpty Dumpty began again. “They’ve a temper, some of them—particularly verbs: they’re the proudest—adjectives you can do anything with, but not verbs—however, I can manage the whole lot of them! Impenetrability! That’s what I say!”
Humpty Dumpty claims that verbs, especially, have a "temper" and are the "proudest" of all parts of speech. Adjectives, by contrast, are more docile. Words don't really possess human traits, but Humpty Dumpty imagines that they do because he feels that he can wrestle with them, interpreting any poem and making any meaning he wants to out of words.
The idea that Humpty Dumpty can "manage" words and make meaning out of them is ironic because he himself is the creation of words. Humpty Dumpty comes from a riddle, or word game, to which the answer is "an egg." The fact that he is posturing about his way with words comes through at the end of the passage above: instead of continuing to explain to Alice how he can make words mean what he wants them to mean, he simply cuts the conversation short by shouting, "Impenetrability! That's what I say!" When it gets too difficult to make words make sense, he can simply call them "impenetrable" and move on.
Carroll is making light fun of literary criticism that tries too seriously to wrestle meaning out of everything. Some literary critics stop analyzing as soon as words stop making sense, claiming "impenetrability." Carroll, as a pioneer of "nonsense literature," is always playing with the idea of "impenetrability." His work challenges the idea that "logical" words and ideas always make sense when we look at them closely. It also challenges the idea that we can't mine any meaning out of things that look like they make no sense at all. Humpty Dumpty is a silly caricature of literary critics who refuse to approach their work lightheartedly enough or to let words take them into playful new terrain.
In Chapter 7, Alice meets a Unicorn who is surprised to meet a real-life human child. The Unicorn uses a twist on an idiom that helps convey a sense of situational irony:
“This is a child!” Haigha replied eagerly, coming in front of Alice to introduce her, and spreading out both his hands towards her in an Anglo-Saxon attitude. “We only found it to-day. It’s as large as life, and twice as natural!”
“I always thought they were fabulous monsters!” said the Unicorn.
The phrase "as large as life, and quite as natural" often refers to renderings of the real world in art. Realism was a major art movement in the mid-19th century: artists tried to paint the real world just as they saw it. The idea of a painting as "large as life, and quite as natural" is complimentary, meaning that the painting is a faithful, successful reproduction. Here, the Unicorn calls Alice "as large as life, and twice as natural." This phrase, which became something of an idiom in its own right after Carroll published Through the Looking-Glass, suggests that the unicorn sees Alice as a work of art that has come to life. She is almost supernatural, eerily giving movement to the images of human children the Unicorn has only seen in art.
It is ironic that the Unicorn sees Alice as a work of art come to life because, to Alice, the Unicorn itself is a living manifestation of a mythical creature she has only seen in paintings and in her imagination. The idea that Alice is the strange, fantastical creature in this situation is an example of the many inversions of the Looking-Glass World. Not only is this a strange and fantastical world for Alice to explore, but it also reflects the "real" world and makes it look just as bizarre. This exchange raises the question of what "reality" really is. Does each one of us have our own version of reality?
