I can guarantee that the books have no religious teaching whatever in them – in fact they do not teach anything at all.

Lewis Carroll, Letter to “The Lowrie Children” (undated), A Selection from the Letters of Lewis Carroll to his Child-Friends (1933) p.242

“Who cares for you?” said Alice, (she had grown to her full size by this time.) “You’re nothing but a pack of cards!”

And so, it ends. The heroine vanquishes the Queen of Hearts and the cards tumble. Alice awakes on bank with her head cradled in her sister’s lap, thinking she dreamed of Wonderland.

Wonderland, of course, is no house of cards and Alice’s adventure, of course, is no dream. The Queen of Hearts, though, was a card – as were her soldiers. Alice remarks during the croquet game (live flamingos for mallets and hedgehogs for balls), “They’re dreadfully fond of beheading people here; the great wonder is, that there’s any one left alive!” But – as the Gryphon tells her later – nobody is actually executed. There is misrule in Wonderland and cruelty as well, but there is also invulnerability, whimsy, and – yes – madness.

As we plummet down the rabbit hole, what should we make of Professor Carrol’s guarantee? No religious teaching perhaps. But no teaching at all? Perhaps there is no teaching because the lessons of Alice are not learned, but remembered – Alice in Wonderland and Through the Looking Glass do not teach, so much as help us recollect divine nonsense drowned in the river Lethe of adulthood.

And yet.

The Cheshire Cat informs her that in one direction lives the Mad Hatter and in the other direction lives the equally mad March Hare.

“But I don’t want to go among mad people,” Alice remarked.
“Oh, you can’t help that,” said the Cat: “we’re all mad here. I’m mad. You’re mad.”
“How do you know I’m mad?” said Alice.
“You must be,” said the Cat, “or you wouldn’t have come here.”
(Alice’s Adventures in Wonderland, Chapter 6: Pig and Pepper)

Kyomai, the fool in Kurosawa’s Ran, tells us that in a mad world, only the mad are sane. The Mad Hatter tells us that if you wish to speak with Time, you shouldn’t beat him for he won’t stand beating. What the Mad Hatter says makes more sense.

In Through the Looking Glass, the White Queen consoles Alice, recommending that she consider things to stop crying.

“Can you keep from crying by considering things?” [Alice] asked.

“That’s the way it’s done,” the Queen said with great decision: “nobody can do two things at once, you know. Let’s consider your age to begin with—how old are you?”

“I’m seven and a half exactly.”

“You needn’t say ‘exactually,’” the Queen remarked: “I can believe it without that. Now I’ll give you something to believe. I’m just one hundred and one, five months and a day.”

“I can’t believe that!” said Alice.

“Can’t you?” the Queen said in a pitying tone. “Try again: draw a long breath, and shut your eyes.”

Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things.”

“I daresay you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”

There is something to be learned here.