"He's an old softy really," said Nanny.

Greebo turned upon Granny Weatherwax a yellow-eyed stare of self-satisfied malevolence, such as cats always reserve for people who don't like them, and purred. Greebo was possibly the only cat who could snigger in purr.

"Anyway," said Nanny, "witches are supposed to like cats."

"Not cats like him, they're not."

"You're just not a cat person, Esme," said Nanny, cuddling Greebo tightly.

Jason Ogg pulled Magrat aside.

"Our Gran read to me in the almanac where there's all these fearsome wild beasts in foreign parts," he whispered. "Huge hairy things that leap out on travellers, it said. I'd hate to think what'd happen if they leapt out on mum and Granny."

Magrat looked up into his big red face.

"You will see no harm comes to them, won't you," said Jason.

"Don't you worry," she said, hoping that he needn't. "I'll do my best."

Jason nodded. "Only it said in the almanac that some of them were nearly extinct anyway," he said.

The sun was well up when the three witches spiralled into the sky. They had been delayed for a while because of the intractability of Granny Weatherwax's broomstick, the starting of which always required a great deal of galloping up and down. It never seemed to get the message until it was being shoved through the air at a frantic running speed. Dwarf engineers everywhere had confessed themselves totally mystified by it. They had replaced the stick and the bristles dozens of times.

When it rose, eventually, it was to a chorus of cheers.

The tiny kingdom of Lancre occupied little more than a wide ledge cut into the side of the Ramtop mountains. Behind it, knife-edge peaks and dark winding valleys climbed into the massive backbone of the central ranges.

In front, the land dropped abruptly to the Sto plains, a blue haze of woodlands, a broader expanse of ocean and, somewhere in the middle of it all, a brown smudge known as Ankh-Morpork.

A skylark sang, or at least started to sing. The rising point of Granny Weatherwax's hat right underneath it completely put it off the rhythm.

"I ain't going any higher," she said.

"If we go high enough we might be able to see where we're going," said Magrat.

"You said you looked at Desiderata's maps," said Granny.

"It looks different from up here, though," said Magrat. "More... sticking up. But I think we go... that way."

"You sure?"

Which was the wrong question to ask a witch. Especially if the person doing the asking was Granny Weatherwax.

"Positive," said Magrat.

Nanny Ogg looked up at the high peaks.

"There's a lot of big mountains that way," she said.

They rose tier on tier, speckled with snow, trailing endless pennants of ice crystals high overhead. No-one ski'd in the high Ramtops, at least for more than a few feet and a disappearing scream. No-one ran up them wearing dirndls and singing. They were not nice mountains. They were the kind of mountains where winters went for their summer holidays.

"There's passes and things through them," said Magrat uncertainly.

"Bound to be," said Nanny.

You can use two mirrors like this, if you know the way of it: you set them so that they reflect each other. For if images can steal a bit of you, then images of images can amplify you, feeding you back on yourself, giving you power...

And your image extends forever, in reflections of reflections of reflections, and every image is the same, all the way around the curve of light.

Except that it isn't.

Mirrors contain infinity.

Infinity contains more things than you think.

Everything, for a start.

Including hunger.

Because there's a million billion images and only one soul to go around.

Mirrors give plenty, but they take away lots.

Mountains unfolded to reveal more mountains. Clouds gathered, heavy and grey.

"I'm sure we're going the right way," said Magrat. Freezing rock stretched away. The witches flew along a maze of twisty little canyons, all alike.

"Yeah," said Granny.

"Well, you won't let me fly high enough," said Magrat.

"It's going to snow like blazes in a minute," said Nanny Ogg.

It was early evening. Light was draining out of the high valleys like custard.

"I thought... there'd be villages and things," said Magrat, "where we could buy interesting native produce and seek shelter in rude huts."

"You wouldn't even get trolls up here," said Granny.

The three broomsticks glided down into a bare valley, a mere notch in the mountain side.

"And it's bloody cold," said Nanny Ogg. She grinned. "Why're they called rude huts, anyway?"

Granny Weatherwax climbed off her broomstick and looked at the rocks around her. She picked up a stone and sniffed it. She wandered over to a heap of scree that looked like any other heap of scree to Magrat, and prodded it.

"Hmm," she said.

A few snow crystals landed on her hat.

"Well, well," she said.

"What're you doing, Granny?" said Magrat.

"Cogitatin'."

Granny walked to the valley's steep side and strolled along it, peering at the rock. Nanny Ogg joined her.

"Up here?" said Nanny.

"I reckon."

" ‘S a bit high for ‘em, ain't it?"

"Little devils get everywhere. Had one come up in my kitchen once," said Granny." "Following a seam", he said."

"They're buggers for that," said Nanny.

"Would you mind telling me," said Magrat, "what you're doing? What's so interesting about heaps of stones?"

The snow was falling faster now.

"They ain't stones, they're spoil," said Granny. She reached a flat wall of ice-covered rock, no different in Magrat's eyes from the rock available in a range of easy-to-die-on sizes everywhere in the mountains, and paused as if listening.

Then she stood back, hit the rock sharply with her broomstick, and spake thusly:

"Open up, you little sods!"

Nanny Ogg kicked the rock. It made a hollow boom.

"There's people catching their death of cold out here!" she added.

Nothing happened for a while. Then a section of rock swung in a few inches. Magrat saw the glint of a suspicious eye.

"Yes?"

"Dwarfs?" said Magrat.

Granny Weatherwax leaned down until her nose was level with the eye.

"My name," she said, "is Granny Weatherwax."

She straightened up again, her face glowing with self-satisfaction.

"Who's that, then?" said a voice from somewhere below the eye. Granny's expression froze.

Nanny Ogg nudged her partner.

"We must be more'n fifty miles away from home," she said. "They might not have heard of you in these parts."

Granny leaned down again. Accumulated snowflakes cascaded off her hat.

"I ain't blaming you," she said, "but I know you'll have a King in there, so just you go and tell him Granny Weatherwax is here, will you?"

"He's very busy," said the voice. "We've just had a bit of trouble."

"Then I'm sure he don't want any more," said Granny.

The invisible speaker appeared to give this some consideration.

"We put writing on the door," it said sulkily. "In invisible runes. It's really expensive, getting proper invisible runes done."

"I don't go around readin' doors," said Granny.

The speaker hesitated.

"Weatherwax, did you say?"

"Yes. With a W. As in "witch"."

The door slammed. When it was shut, there was barely a visible crack in the rock.

The snow was falling fast now. Granny Weatherwax jiggled up and down a bit to keep warm.

"That's foreigners for you," she said, to the frozen world in general.

"I don't think you can call dwarfs foreigners," said Nanny Ogg.

"Don't see why not," said Granny. "A dwarf who lives a long way off has got to be foreign. That's what foreign means."