The Time Lords had known about the Discworld longer than anyone else (as is traditional, the people who lived there knowing about it simply didn't count). They had spent a few dutiful centuries studying from a distance before sensibly deciding that it was far too ridiculous to exist, and proceeding to ignore it. All that magic just wasn't on, not in a universe that otherwise managed to be more or less rational if you pretended to understand all the quantum bits.
The records of Gallifreyan exploration of the Discworld were duly locked away in case anyone asked why Discworld Library Space seemed so much like the technology used to make TARDISes bigger on the inside, or anything awkward like that. (Though informed observers might note that this is why the library of a TARDIS is substantially bigger than it really ought to be even given that the wonders of being dimensionally transcendental.)
The Secret Books of the Discworld were hidden so well that they didn't even get to be legendary. Of course, one or two people stumbled upon them while looking for book-stacks behind which they could explore their youthful sexual urges...
“Scumble,” said the Doctor, as he stepped from the TARDIS, “is supposedly one of the few drinks that can get a Time Lord drunk.”
Amy looked around at the village of Lancre. It was quite pointy. “We've come here so you can get pissed?”
“Pleasantly intoxicated,” he corrected. “Think of it as your Hen Night.”
The Doctor hadn't mentioned the whole “elephants on the back of a turtle” thing in case Amy correctly judged this to be a thing even more impressive and fascinating than the Doctor himself, and in case — this was rather more in the way of an excuse — the departed High Council of the departed race of Time Lords found out that he'd been there. Anything was possible, after all.
“I was thinking more along the lines of a dozen women in feather boas throwing up in a gutter in Blackpool,” said Amy, unaware of the important facts that she wasn't aware of. “You're not even a woman.”
“No need to be sexist about it,” said the Doctor. “I can't help having a -”
“Doctor!” came a cry from across what was probably trying to be a village green. A large old woman was hurrying towards them, waving a handkerchief.
The Doctor ran through the possibilities. Clearly this woman knew him, and since the Discworld didn't have anything remotely akin to space-flight, that meant he'd been here before later on in his life. He really had to stop crossing his own continuity. It was getting embarrassing.
He nudged Amy. “If that woman is called Iris Wildthyme, I want you to kill me.”
“Why, is she your ex-wife?”
“I don't know,” he said, worried about how accurate Amy tended to be at reading such situations.
The woman stopped in front of the TARDIS and grinned disturbingly.
“Iris?” asked the Doctor, with a look of terror.
The woman pushed the Doctor in the chest. “Don't be so rude, my love.”
“Someone's got a girlfriend,” sang Amy happily.
“It's me, Gytha Ogg, the love of your considerable life.” She looked at Amy. “Oh, have you brought us a maiden? Esme's always saying we need a new maiden, and how hard it is to get them to stay maidenly long enough to learn anything.” She prodded Amy a few times. “Are you a maiden, dear?”
“Pardon?” said Amy, stepping away from all the prodding.
“Have you known the sensual touch of a man?” Nanny Ogg clarified.
“Yes, I bloody well have!”
Nanny Ogg looked at the Doctor with some suspicion. “Was that your doing?” Before he could answer she continued, “It's a shame, we could have done with a nice young maiden.”
Amy put her hands on her hips. “Look, I'm not a sack of potatoes. I'm not for sale or rent or whatever you had in mind for me.”
“Do you have any scumble?” asked the Doctor hastily. “Only we've come quite a long way.”
Nanny Ogg winked. “You only have to ask, lovey!”
“The hedgehog can never... what is you can't do to them again?” asked the Doctor.
“If you think about it, it's quite obvious,” said Nanny Ogg, who was by far the less drink-worn of the pair.
The Doctor concentrated, his forehead creasing in that way women seemed to think of as quite attractive. “I suppose you couldn't play chess with one.”
Nanny Ogg leaned against the Doctor and grinned. “He's lovely, isn't he?” she asked Amy.
Amy had, quite sensibly, stuck to water. “Are you two... is there something going on here that I should know about?”
“Oh, I should think you're much too young to hear about such things, maiden or not.”
“Were you... young at the time?”
“I'm young now,” said Nanny Ogg patiently. “At least compared to him.”
Amy didn't like to think about old people having sex, unless they were old people who looked young enough for her to find them attractive. Like the Doctor, for instance. Amy was quite willing to let the Doctor have as much sex as he wanted. She was even willing to help him out in case he couldn't quite remember what bits went where.
“That's different,” said Amy, “because... because it just is.” There, she'd made her argument as convincingly as she could.
“I like scumble,” said the Doctor. “Scumble is...” he waved a hand, “it's whatever those other things I like are. It's slipped my mind at the moment. I'm sure it's not important.”
Nanny Ogg smiled indulgently. “Cold. You're always saying things are cold.”
“Your Death's a man,” said the Doctor suddenly. “Mine's a woman. Do you think we could match them up?”
Nanny Ogg pondered this question with the gravity it deserved. “Does she like skinny blokes? So skinny that they don't have any actual skin?”
“Ooh, she's a bad, bad girl,” said the Doctor with a far-away look and a wide smile.
“Death's not a person,” said Amy.
Nanny Ogg patted her hand. “Shouldn't you be off? It must be past your bedtime by now.”
“I can't leave,” said Amy, “you might ravish the Doctor while I'm not looking.”
The Doctor giggled. “A Time Lord can never be ravished at all,” he sang.
“This is awful,” said Amy.
“This is awful,” said the Doctor.
“It's called a hangover,” said Amy. “It's what happens when you get drunk with witchy old ladies.”
“Not that,” said the Doctor irritably. “She turned me down, that's what's awful. Can you imagine someone not wanting to travel with me? She said it wouldn't be exciting enough for her!”
Amy nudged him. “Are you trying to replace me with an older woman?”
The Doctor sniffed. “I wish you wouldn't call her old. She's sprightly.”
“Oh my God, did you... did she... what happened when I went back to the TARDIS?”
“It was magical,” he said. “Literally magical.”
“You turned me down and you got it on with an old woman?”
“A sprightly woman!”
“She's not a maiden then, I take it,” said Amy bitterly.
“She's got a number of children, some of them by her late husband.” said the Doctor, defending his latest love-interest.
“So are you going to come back and seduce her when she's young?”
“Oh, I shouldn't think so,” said the Doctor, opening the TARDIS a bit unsteadily.
“Good,” said Amy with relief.
“She's so much more interesting with a few years on her.”
Two women watched the TARDIS leave, one of them smiling and the other scowling.
“You know I can't be having with all that nonsense, Gytha,” said Granny Weatherwax.
“You and your fancy-men. We've got more important things to be getting on with.”
“It was only a fling, Esme.”
Granny Weatherwax sniffed her disapproval. “He's too old for you anyway.”
“Age ain't nothing but a number.”
“Number ain't supposed to get that big,” said Granny Weatherwax with certainty. “They should stop at about a hundred, something decent like that.”
“Did you know,” said Nanny Ogg dreamily, “there are worlds out there that are round? Round all over, like a ball.”
“Well, I for one am glad we live somewhere sensible.”
And with that comment, the story of the Doctor and Nanny Ogg came to a temporary stop. Not an ending, because the Doctor didn't quite believe in those and the Discworld had certain rules about when star-crossed lovers should be allowed to get to their happy ending.
Beside which, the Time Lords had never been able to get rid of that annoying affinity that older TARDISes had for giant elephants that stood on the backs of turtles.