Author's Notes:
Entry in the 2008 Sixth Doctor ficathon for elliptic_eye who has been very patient, understanding and encouraging to a slow writer, and who requested "Six/Peri | Fracture Mechanics | Pedagogical (not parental) overtones". Many vociferous thanks go to jedi_penguin for her insights and helpful comments.

Timeline: Spoilers for "Vengeance on Varos" (mild) and for the BF audio "The Reaping." Though the story references that audio from Six and Peri's timeline, in terms of characterization I'm going with the canon line that little time passes between "Planet of Fire" and "Caves of Androzani".

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(a) Elasticity and Flaws

Peri's grandmother gave her a different doll every year on her birthday. When she was five, it was a molded plastic baby doll, hollow on the inside, that sighed when it was squeezed. At seven, it was a yarn-mopped rag doll that slouched forlornly wherever it was set. At twelve, a little girl on one-sixth the scale, with ringlets framing her ceramic head, and weighted 'sleepytime' eyes.

Peri never played with any of them. Not to say she was a tomboy; she loved makeup, dresses and fancy shoes just as much as she loved swingsets, fields and muddy creeks. But for all the varieties she'd been given, she never came across a doll that was interesting. Her make-believes didn't run toward the maternal, and dolls made terrible companions for just about everything else. Who wanted to drag something around all day that didn't do anything?

The dolls stopped coming when she turned thirteen, the year her dad died. After she and her mom moved in with Howard Foster, Peri never bothered unpacking them. But on bad nights, when Howard got too touchy by half, she would think about them-- neatly tucked away in tissue paper and cardboard boxes, so very still and silent.

She never planned to turn out quite so loud or boisterous as everyone said she was. But in Peri's mind, it sure beat the alternative.

**

"Are you just going to stand there all day?"

Peri sighed, focusing her gaze on Praxon's distant crystal spires instead of turning around. "Isn't that what we're supposed to be doing here, Doctor?" she asked. "Standing?"

"Standing?" the Doctor repeated, apparently affronted that the word should have to pass his lips again. "Nonsense."

Peri blinked, and the spires left a bright criss-cross impression on her eyelids. "We're going to Praxon, you said. To view the crystal spires."

"Now Miss Brown, 'viewing' is quite a different gerund from 'standing'."

"Bring comfortable shoes, you said--"

"Well, I hardly think--"

"Because Praxonites don't bend." She turned around; the Doctor looked mildly annoyed but-- and don't ask her why or how she knew it-- open toward logging complaints. "I believe your exact words about sitting were that it's terribly rude. And now we've both been standing here for the last-- oh, heck, I don't even know how long-- and my legs are cramping."

"I'm not just standing," the Doctor corrected. "I'm contemplating."

She flounced shamelessly back toward the view. "So am I."

"Young lady, I can certainly tell the difference between contemplative meditation and reluctant boredom," the Doctor's reprimand came at her back. "I suppose if you've no desire to cultivate an appreciation for self-reflexive philosophical geometry, you can always go sulk in the TARDIS."

Peri glared at him. "I'm not a child," she said.

"You are a student." The Doctor hooked his thumbs under his lapels. "Aren't you?"

She snorted. "I suppose that's some kind of privilege?"

"If you like. I've much less patience with students than children."

"Great."

Peri sighed. Under the Doctor's scrutiny she scanned the horizon again, taking in the view of those delicate, spindly spires jutting up from Praxon's velvet green hills. The truth was, she'd got her fill of viewing them hours ago. The crystals unnerved her in a way she couldn't explain. They looked unnatural, she decided, like her eyes wanted to slide past them, to put something else in their place. It made her skin crawl. And maybe she just didn't want to feel that way, or to think too hard about why, and if the Doctor was going to badger her about it until she flipped out at him well it was his own fault--

"Peri." There was a hand on her wrist, and the Doctor's voice was so close she almost yelped. "Peri, stop. What's that on your arm?"

She looked down. She'd been rubbing at the arm the Doctor was currently holding. The one she'd been careful to cover up lately. It was uncovered now, and the Doctor gently turned her wrist over in his hand, studying the inside of her elbow.

"Oh," she said, waving her free hand. "It's just some of those stupid feathers from that stupid transmuter thing on Varos. They itch like crazy, sometimes."

"Blast it, that was two weeks ago." The Doctor brushed a finger back against the grain of the feathers and Peri felt them pull at her skin. She shook off his touch.

"Well, you know, most of them molted but there's a few stubborn ones holding on for dear life. Can't figure out why. But if I keep plucking them out, I think they'll eventually get the hint and stop growing back, right?"

"They should," the Doctor said, still concerned. "You know, I might be able to speed up the process--"

"It's no big deal," Peri interrupted with forced cheer.

"If I augmented the dermal regenerators--"

"No, really. You should see what my mother spends monthly on depilatories."

"Then I could--"

"Doctor!" Peri said, putting her foot down. Literally, she realized, she'd stamped her foot like an obstinate child to get his attention. He stared at her, silent and possibly slightly incredulous. She stuttered once but otherwise made a flawless recovery.

"I'll take my chances with tweezers, thanks." She took in a cleansing breath, hands on her hips, giving the scenery a curt nod. "Well. That's enough of that. I'm going to go sulk in the TARDIS."

The Doctor looked a mixture of shocked and hurt as she turned to go. "Oh, come on Peri!" he called after her.

"My feet are killing me!" she sing-songed back. "Besides, I thought you were over this whole 'contemplation' thing!"

She heard the distinct sound of grumbling behind her, followed by a one-sided muttered argument, and a hurried set of footsteps.

"All right," the Doctor said, catching her stride and then affecting nonchalance. "Come on."

"Doctor--"

He gave her a cheshire grin. "There's plenty more interesting things to see than Praxon, anyway."

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(b) Deformation Theory

In the tenth grade, Peri had a crush on her biology teacher. Mr. Reed was tall, dark-haired and urbanely handsome-- the kind of man her mother would approve of, though Peri tried not to hold that against him. In truth, he was a reluctant biologist with a love for organic chemistry. He was passionate and inexperienced, and he sometimes got so flustered at the blackboard that he had to step out into the corridor, to a room full of giggles. But Peri liked him. He had a brilliant smile, and he always smelled really nice when he leaned over her shoulder to help her in lab.

Because of Mr. Reed, Peri got it in her head that she wanted to be a biochemist. In her junior year she enrolled in his elective chemistry class.

"Chemistry is the study of systems in systems," he lectured. "The finer you break things apart, the closer you come to the truth of them."

She sometimes caught glimpses of Mr. Reed's grand vision-- an entire eco-system reflected in botanical vascular structure, or the emergence of patterns and rules from the chaotic mingling of molecules and atoms. But she faltered on the details. Her lab exercises were an incomprehensible progression of measurements and standard deviations with no clear answers. Her exams were abyssmal. Howard had the background to help her but little patience for it, and her mother went only so far as to remind him to humor her once in a while.

When her third quarter report logged another near failing grade, she broke down in Mr. Reed's office after class. She was frustrated and mortified at her tears.

"It's okay, sweetheart," he said, rubbing her shoulders. "Chemistry is really hard. No one expects you to be able to understand it all."

Her senior year, she opted for a class in plant physiology. It wasn't giving up; it was just a practical refocusing. Start with the tangibles, she figured. Work your way back down to the details and whatever mysterious truths they proclaimed.

And if you could help it, she learned, don't let the chauvinist jerks of the world see you cry.

**

"This isn't some elaborate experiment of yours, is it?" Peri asked.

"No."

"A Treatise on the Effects of Boredom on the Human Brain?"

"No."

"Maybe it's the Master, then. I wouldn't put it past him--"

"No."

Silence. The Doctor tinkered. Peri stared at the roundels on the ceiling.

"It's not-- the Cybermen didn't do anything to her, did they?"

"Peri, for the fifty-eighth time, it's-- ow!" The TARDIS console sparked and the Doctor leaped back, shaking his hand vigorously. The center column shuddered and thunked, signaling an abrupt landing. "You made me lose my focus," he grumbled, checking the scanner and working the door control. "I think I almost had us out of it."

The TARDIS was "listing", and had been for weeks. The Doctor had offered a technical explanation along with the word-- a k-wave-something imbalance in the spatio-temporal density fields-- but Peri didn't need to know the specifics. By now, they were both intimately acquainted with the malfunction's effects. They'd left Earth behind, left her mother's funeral and all that awful mess, but more and more trips were landing them continents or months away from their desired destinations. There were no new people to meet. There were no problems to solve.

At first, she hadn't noticed, wrapped as she was in grief. But enough was enough. In a word, it was pure Dullsville. There was nothing to endure save each other's company, which, with stresses and strains as they were, was tending more and more toward flippancy, frustration, and esoteric lectures.

"You know," Peri said, following the Doctor out the door, "Maybe the TARDIS was malfunctioning since you got her, with her nose for trouble, and she's only now coming out of it and acting normal again-- Oh, holy smoke!" She stepped outside and immediately shielded her eyes from the assault of colors and shapes in front of her. "It looks like a circus exploded out here!"

The Doctor took an exaggerated breath beside her. "Does it? I hadn't noticed."

"You wouldn't." She peered at him through her fingers. "I never thought I'd say this, Doctor, but you're blending in with your surroundings."

"What? That simply won't do." He shrugged out of his coat and folded it over his arm. "There, that's a bit better, anyway. As Emerson was so fond of telling me, 'Whoso would be a man, must be a non-conformist.'"

"Nothing to do with the fact that it's ninety-five degrees, I'm sure," Peri murmured, but the Doctor ignored the remark.

"Fascinating," he said, striding out of Peri's field of vision.

"Why? What is this place?" she asked, still filtering the view through her fingers.

He harrumphed indignantly, somewhere off to her left. "You don't recognize it?"

Peri squinted past him, but the sheer sight of the place was overwhelming. Shapes hung suspended, defined by clashing trails of red and green, accented by bursts of blue, with orange and yellow helixes twisting away at impossible angles. With no reference and few shadows, Peri couldn't orient the patterns in space; one moment, a colored swirl seemed close enough to touch, and the next it stretched away in a completely different direction, without so much as a shudder of movement. In a small flair of panic, Peri realized she wasn't even sure if they were indoors or out. Her head swam, and she closed her eyes against a wave of vertigo.

"Recognize it?" she echoed. "I can barely look at it!"

"Ms. Brown, you disappoint me," the Doctor said, his voice coming nearer her position. "You're usually quite observant, it's why I tolerate your grousing. Now, pay attention."

"Pay attention to what? I can't look at anything without falling over." She balled her hands into fists at her side, standing stiffly with her eyes still tightly shut.

"Staggering, the amount of human senses you've chosen to ignore. Touch, smell, hearing--"

"Right, okay, I get it." Peri waved him off and lost her balance, but a hand at the small of her back helped right her. Despite the bluster in his tone, the Doctor's grasp was strong and supportive. Peri steadied herself at his side, and for once, he let go of his lecture and simply stood with her, silent, in this strange new place.

It was a damp heat; moisture clung to her short sleeves at the shoulders and weighed on her hair. The ground was soft beneath her feet, and now that she concentrated she could feel a breeze tickling the hair on her neck and arms. They were outside, she decided. There was a slow creaking and rustling, like a sigh, and the smell of . . .

"Nitrates!" Peri opened her eyes, swaying slightly but keeping her feet as the shapes and colors slotted into sense in front of her like a focusing stereogram. She stared at the scene in pure wonder. "It's a garden!"

"It's a Hausdorff garden," the Doctor affirmed, relinquishing his hold on her back as she oriented herself. He offered her his unencumbered arm. "Though I think Besicovitch might protest the moniker. History always forgets the ones who do all the work. Shall we have a look round?"

Peri hesitated before taking his hand. "And what if this Herr Hausdorff doesn't take kindly to strangers trampling his plants?"

The Doctor sighed. "It's not Hausdorff's garden, it's a Hausdorff garden. Fractal. You'll find it's quite resilient."

"It is someone's garden, though, isn't it?"

"We haven't seen another living soul for weeks, thanks to the TARDIS. These gardens can last for millennia untended."

They strolled down a twist of grey-green that turned out to be a path. Now that she knew what to look for, Peri could make out the basic plant structures around them-- flowers, vines, shrubs-- but they intertwined into a kaleidescope view of leaves, petals and stalks. She bent down to study the nearest vine and discovered it wasn't a vine at all; it was a braided set of flower petals, flattened into a chain of blue, pink and yellow folds. She tried to unravel a section, to find the tips of the petals and follow where they interconnected, but the shapes simply emerged from the strand's core and then diminished delicately back again, turning endlessly in on themselves. She tugged at a link, and while the petal smudged her fingers blue with pollen, its connection to the others didn't budge.

"You won't be able to break it," the Doctor said. "It's folded through a small pocket of epsilon-dimensional space."

"And epsilon is. . .?"

"Constructed to be greater than zero, and smaller than any positive number you'd care to name."

"Sounds like something out of a fairy tale." Peri stood up, brushing the pollen off of her shorts and studying the self-similar branches of a spherical tree. "A very twisted fairy tale. Who would construct something like that?"

"Outside of mathematical analysis, it's all very posh and grandiose." The Doctor studied a patchwork of orange leaves burrowing their way into a slender stem. "It takes a very rich sponsor and a quantum landscaper with a lot of time on his hands. They grow the garden in a full four dimensions for decades, you see, before they start pruning."

Peri brushed her hand across an inverted red bloom. It gave off a scent like honeysuckle. "But I've never seen a pruning regimen that could do this."

"Of course, they don't prune the plants," the Doctor said as if it were the most obvious fact in the world. "They prune the space around them. It's a bit like Japanese bonsai-- but achieved with Planck length extrapolators and Minkowski filters. Four dimensions becomes three and a half, becomes three and a quarter, and so on until there's only a residual trace of what they started with."

Peri stared anew at the contorted shapes around her. "That's--" cruel, she wanted to say, but she just stuttered around the word. "It's-- it can't be good for the plants!"

"As the space diminishes, the plants adapt. They find ways to survive. Even to thrive."

"All that for a schizophrenic garden," she said morosely. "Why bother?"

"Art, beauty, culture, status." The Doctor frowned at his surroundings. "The usual suspects."

They started down the path again in tentative silence. Peri felt reluctant to touch anything, as if doing so would just reaffirm the spatial trap that had been so carefully laid around these plants, so long ago. Instead, as they walked she let the sights spin out of focus around her, until it was only she and the Doctor who made sense in the world. Just the two of them, traveling an indecipherable path, arm in arm.

"What should it look like?" she finally asked.

"Hmm?"

"The garden. What should it look like?"

"Quite a presumptuous question. It is what it is. It looks as it does."

"But what would it look like if the builders hadn't interfered with it?"

The Doctor paused briefly before answering. "Nothing, I suppose."

She huffed out a breath. "Don't go all existential on me, Doctor."

"Existential?" he declared. "Try practical. If the builders hadn't wanted to prune it, they wouldn't have grown it in the first place. Extra spatial dimensions don't come cheap, you know."

"But the TARDIS--"

"--is an exception."

"But . . . what if-- I mean--" Something caught in Peri's throat and she stopped, stock still on the path. "What if . . ."

"Come now, out with it!" the Doctor said, and Peri burst into tears.

"Oh, Doctor, what if she can't be fixed? What if it's just us from now on? I can't go back to Earth, not after what happened, and now I-- I need . . ."

"INTRUDERS IN THE ROYAL GARDEN!" came a booming metallic voice from above. "ALERT! ALERT!"

They looked up.

"I need a giant flying robot," Peri said.

The Doctor raised his eyebrows. "I think I can oblige."

"HALT! INTRUDERS!" An ominous metal whine built up in the air, and the Doctor tossed Peri his coat.

"Here, take this for--"

"--Camouflage!" she said, already shrugging into the sleeves. A stun beam struck the ground nearby.

He grinned and took her hand. "You're such a quick study, Peri. I've always liked that about you."

"Flattery will get you nowhere," she answered. "Now run!"

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