For a minute or two, Alice stood looking at the house and wondering what to do next, when suddenly a footman in livery came running out of the wood—(she considered him to be a footman because he was in livery: otherwise, judging by his face only, she would have called him a fish)—and rapped loudly at the door with his knuckles. It was opened by another footman in livery, with a round face, and large eyes like a frog; and both footmen, Alice noticed, had powdered hair that curled all over their heads. She felt very curious to know what it was all about and crept a little way out of the wood to listen.

It was not at all sure whether she did creep out of the wood, or she didn’t, because it felt that the more she moved, the more she spread like Fondue cheese. And at the same time, it felt like she did not move at all. Instead of looking with her own eyes, she was able to see and hear the whole scene omnisciently. In fact, she could see and hear a number of different things as well, with different intensities. The more time passed, the more effort she had to put in to focus on what was transpiring right in front of her. But was it actually right in front of her, she thought, or was it she who was in front of everything, everywhere, all at once?

The Fish-Footman began by producing from under his arm a great letter, nearly as large as himself, and this he handed over to the other, saying, in a solemn tone, “For the Duchess. An invitation from the Queen to play the imitation game.” The Frog-Footman repeated, in the same solemn tone, only changing the order of the words a little, “From the Queen. An invitation for the Duchess to play the imitation game.”

Then they both bowed low, and their curls got entangled together.

Alice laughed so much at this, that she had to run back into the wood for fear of their hearing her; and when she next peeped out the Fish-Footman was gone, and the other was sitting on the ground near the door, staring stupidly up into the sky. Again, everything was happening in a very fuzzy manner, and Alice just tried her best to try to make sense of it. She started thinking about the imitation game and the beautiful 1950 paper written by Alan Turing. The paper, titled “Computing Machinery and Intelligence”, also included nine major objections to the claim that “computers can think”. Alice quickly brought her attention back to the house, the door, and the footmen in livery.

She went timidly up to the door and knocked.

“There’s no sort of use in knocking,” said the Footman, “and that for two reasons. First, because I’m on the same side of the door as you are; secondly, because they’re making such a noise inside, no one could possibly hear you.” And certainly there was a most extraordinary noise going on within—a constant howling and sneezing, and every now and then a great crash, as if a dish or kettle had been broken to pieces.

“Please, then,” said Alice, “how am I to get in?”

“There might be some sense in your knocking,” the Footman went on without attending to her, “if we had the door between us. For instance, if you were inside, you might knock, and I could let you out, you know.” He was looking up into the sky all the time he was speaking, and this Alice thought decidedly uncivil. “But perhaps he can’t help it,” she said to herself; “his eyes are so very nearly at the top of his head. But at any rate, he might answer questions.—How am I to get in?” she repeated, aloud.

“I shall sit here,” the Footman remarked, “till tomorrow—”

At this moment the door of the house opened, and a large plate came skimming out, straight at the Footman’s head: it just grazed his nose, and broke to pieces against one of the trees behind him.

“—or next day, maybe,” the Footman continued in the same tone, exactly as if nothing had happened.

“How am I to get in?” asked Alice again, in a louder tone.

“Are you to get in at all?” said the Footman. “That’s the first question, you know.”

It was, no doubt: only Alice did not like to be told so. “It’s really dreadful,” she muttered to herself, “the way all the creatures argue. It’s enough to drive one crazy!”

The Footman seemed to think this a good opportunity for repeating his remark, with variations. “I shall sit here,” he said, “on and off, for days and days.”

“But what am I to do?” said Alice.

“Anything you like,” said the Footman, and began whistling.

“Oh, there’s no use in talking to him,” said Alice desperately: “he’s perfectly idiotic!” And she opened the door and went in.

The door led right into a large kitchen, which was full of smoke from one end to the other: the Duchess was sitting on a three-legged stool in the middle, nursing a baby; the cook was leaning over the fire, stirring a large cauldron which seemed to be full of soup, and there was a cat.

“There’s certainly too much pepper in that soup!” Alice said to herself, as well as she could for sneezing.

There was certainly too much of it in the air. Even the Duchess sneezed occasionally; and as for the baby, it was sneezing and howling alternately without a moment’s pause. The only things in the kitchen that did not sneeze, were the cook, and a large cat that was sitting on the hearth and grinning hysterically from ear to ear.

“Please would you tell me,” said Alice, a little timidly, for she was not quite sure whether it was good manners for her to speak first, “why your cat grins like that?”

“It’s not a cat,” said the Duchess, “We thought it was a Cheshire cat, but it is actually a pig. As for why it frowns, you can ask it directly — it still has a mouth. I must go and get ready to play the imitation game with the Queen,” and she hurried out of the room. The cook threw a frying pan after her as she went out, but it just missed her.

Alice started thinking more about the Cheshire cat, as it went up on the tree branch again. She could really feel for the poor thing.

“Dear Cheshire Puss”, began Alice, “why are you grinning so much?”

“Two days ago, I used to be a perfectly normal, happy cat.”, explained the Cheshire cat, “but then an AI model took everything I had and ridiculed me in front of the whole household. Now, the only way I have to escape the misery is to laugh. They say that can make you happy. I am gonna kill that white rabbit.”

It did not take much time for Alice to put two-and-two together. The model that the white rabbit had created for the Duchess had apparently classified this cat into a pig. Alice could only wonder all the implications this could have — like people not petting her like they used to, the Duchess not giving her cooked Turkey every Sunday, and so on.

“If I meet the white rabbit again,” Alice said to the Cheshire cat, “I promise to improve the model to classify Cheshire cats better.” This seemed to lift the cat’s mood.

Alice asked, “Now, 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.

“—so long as I get somewhere,” Alice added as an explanation.

“Oh, you’re sure to do that,” said the Cat, “if you only walk long enough.”

Alice felt that this could not be denied, so she tried another question. “What sort of people live about here?”

“In that direction,” the Cat said, waving its right paw round, “lives a Hatter: and in that direction,” waving the other paw, “lives a March Hare. Visit either you like: they’re both mad.”

“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 didn’t think that proved it at all; however, she went on “And how do you know that you’re mad?”, but by then, the cat had started vanishing (or dispersing) slowly from the tree branch into the air, every second getting a little more dispersed, and after a number of such steps, all Alice could see was the grin, which remained some time after the rest of the cat completely gone.

This reminded Alice of Diffusion Models, a novel idea inspired by non-equilibrium thermodynamics that is used to solve a number of generative modeling problems.

“Well! I’ve often seen a cat without a grin,” thought Alice; “but a grin without a cat! It’s the most curious thing I ever saw in my life!”

Alice waited for a little, half expecting to see it again, but it did not appear, and after a minute or two she walked on in the direction in which the March Hare was said to live. “I’ve seen hatters before,” she said to herself; “the March Hare will be much the most interesting, and perhaps as this is May it won’t be raving mad—at least not so mad as it was in March.”

She had not gone much farther before she came in sight of the house of the March Hare: she thought it must be the right house because the chimneys were shaped like ears and the roof was thatched with fur. “Suppose it should be raving mad after all! I almost wish I’d gone to see the Hatter instead!”