Title: The Roots of the Quadratic (1/8)
Author: nancybrown
Fandoms: Torchwood, Doctor Who
Characters: Ianto, Jack, Alice, Jenny, John Hart, OCs
Rating: R
Beta/Britpick: queenfanfiction, wynkat1313, temporal_witch, and fide_et_spe had a hand in fixing this. All remaining mistakes are mine alone.
Spoilers: up through CoE, one spoiler for "End of Time," one spoiler for Bay of the Dead
Warnings: character death, angst, child endangerment, mentions of sexual coercion, violence, timey-wimey temporal physics, and of course, Captain Bad Touch rides again
Words: 46,000 (4,000 this part)
Summary: Jack and Ianto discover they can only outrun old sins for so long.
Notes: This story is the direct sequel to "Intersecting Geodesics," and also the sequel to a much shorter story called "In My Unique Position." Familiarity with both stories is suggested but not required. Written for Tardis Bigbang Round Three.

Prologue

"A woman alone might run into trouble. Two women can cause plenty of it." - Mary, "Avalon, pt 1" Gargoyles

"Every death is a holocaust to those left behind." - unknown

"Living with someone is like running a marathon. Along the way, there will be times you're gonna ask why you're doing this to yourself. Some aspects will make you want to puke. The best times will leave you hot and sweaty and accomplished. People on the sidelines will be shouting advice all the time about how to get to the finish line faster. But the point of the marathon is the run itself. Finish lines are just a way of keeping score." - from "Me: An Autobiography"

From the point of view of the entire lifetime of the planet, an eruption of this magnitude happened every several thousand years, so it was hardly remarkable when one of the world's largest volcanoes exploded. That same volcano was situated far enough away not to incinerate the human inhabitants (population: two) but instead merely change the planet's climate. For a certain immortal, it meant the difference between frying fast, and choking and freezing to death repeatedly in the aftermath. For his companion, who had already walked out alive from not one but two major catastrophes, it was just another damn nuisance.

The rambling red house, the self-sufficient gardens and lands, the rivers with their fish and the woods with their game, everything lay covered under soot and snow from the unexpected winter. The generator would hold out until the air filters finally gasped their last, and then it was just a matter of time.

They didn't talk about it. There was nothing to say.

One bitterly cold morning, the transceiver beeped. Jack was outside, bundled up from head to toe and over his face, checking on the stores in the outer building. Ianto tuned into the frequency of the passing ship. Some spiteful deity continued to look out for him, and it always showed an utter, utter bastard approach to timing.

"There's a freighter headed into the system," he said, when Jack came back inside. "It'll pick us up in an hour. I've started packing and putting everything into lockdown. In theory, when the climate restabilises, we'll be able to return."

Jack set down the load he'd brought in and began peeling off his outer layers of clothing. "How long did we think that'll be, again?"

"Ten years or more."

"I really shouldn't be out and about yet. People who know me are still alive out there." Jack had first come to this planet to stay out of his own way while he did his second go-round through the fifty-first century. The appendices to his memoirs included a handy chart showing how many times he'd passed through various eras, partially so he could remember where and when to avoid himself if he happened to loop back.

"Fair enough. See you in a decade." Ianto turned back to his packing. Jack laughed and wrapped sooty arms around him.

"If we go, will you stop whinging that I never take you anywhere?"

"Yes. If we flee certain death together aboard a space freighter, huddling in the cargo hold with nothing but a duffle bag holding all our worldly possessions, I promise that I will not complain about never going anywhere exciting with you."

"Deal."

Chapter One

"Goddamned motherfucking piece of shit machine!"

Jenny's lips twitched, specifically not laughing at her as Alice kicked the console angrily. "Did you decide sweet talk wasn't working?"

"She's doing it on purpose." Alice scowled and kicked it again. Ever since they'd accidentally reactivated the AI on this bloody Chula cargo ship, it'd given them nothing but trouble. The time travel circuit, which already only functioned under protest and with what Alice found to be a bizarre sense of humour, now refused to operate at all without an hour of coddling.

The hour hadn't worked this time. Nor had two hours. Fed up with the niceness, Alice was ready to beat in the thing's electronic brain with the nearest spanner or lead pipe. And yes, she'd noticed Jenny quietly and efficiently removing both from her reach. Jenny was good at rescuing Alice from her own worse nature. When they'd first met, she'd coaxed Alice out of the shell of her fresh grief, luring her into the stars with promises of a purpose, a reason to live. Alice had come to recognise the gift for what it was, and tried to live up to the duty implied, and when she failed, Jenny was there with a smile and a suggestion that she owed herself another go.

"Hilda," said Jenny in her sweetest voice. "You need to stop taunting Alice. It's not nice." She paused, waiting for an answer. "Hilda?"

"She yelled at me," said the ship's computer in what could best be described as a sulk.

"Of course I … "

"Alice, please."

"Fine." Alice flung herself into a seat by the console, arms wrapped around her own shoulders.

Jenny said, "Hilda, would you please let us reset the time travel circuit?"

"No."

"Why not?"

"Because Alice is angry with me."

"Alice is angry with you because you aren't being cooperative."

"So?"

Jenny sighed. Alice growled. She'd never had a daughter, certainly never a teenaged daughter (she let the twinge come, as it always did, and let it fade into the dull pain that was the background of her life) but Hilda came close to what she thought it'd be like.

Jenny said, "Do you need me to sing to you?"

There was a long pause. "Maybe."

"Would you like the lullaby again?"

"Yes."

"If I sing, will you cooperate?"

"Yes."

"All right." Jenny started to sing something they'd picked up twelve worlds ago, with an odd melody and words that made no more sense than any other lullaby. Alice had been trying to sing it for two hours. Her throat was sore, she was tired, and she was more than a bit jealous that the ship seemed to enjoy Jenny's singing much more than her own. If she'd just told them at the beginning, they'd be at their destination already.

"There," Jenny said when she was done. "Now will you let us navigate?"

"Yes."

Alice got up from her seat and approached the controls. They'd been frozen the last dozen times she'd tried them, so it was with trepidation that she grabbed the handle and went to turn the temporal dial. It moved under her fingers like it had been greased. She held back swearing at the computer again in case it heard her, but in her mind, she was showing it two fingers.

Jenny came up beside her and made the final adjustment. Time Lord thing. Alice never would, never could understand exactly what that meant, except that Jenny was sensitive to the subtle currents and eddies of space-time. That was enough for Alice.

"Ready?"

"Let's go," Alice said, and braced herself for when the ship leapt into the Time Vortex like a fish. Immediately, the ship began to shudder and shiver violently. Uh oh.

"Hilda!" Jenny shouted. "What's going on!"

"Rerouting," came the ship's voice in a monotone.

Alice and Jenny exchanged looks. Sometimes, the ship not only had a mind of its own, it also operated under its own willpower. Or someone's. Long before Hilda had come online properly, the time circuit seemed geared towards sending them places where they could have a large impact, for good or ill. Usually good, thought Alice, and she was proud of that.

Still …

"Get the guns," she said to Jenny.

"Get the packs."

Alice was ready for anything. Almost anything. Okay, landing in a clearing on what turned out to be a tropical paradise wasn't her first guess. Warm, humid air caressed her skin and lifted her hair. She scented heavily-perfumed flowers, heard the cries of sea birds, could taste the salt in the air. It was like the holiday she'd taken with Joe to Havana, the one good holiday they'd had together after their honeymoon.

Jenny breathed in deeply beside her and laughed. "Oh, this is delightful!"

"Where are we? Hawaii?"

"I've never been to that planet."

"Never mind." Alice took point. They'd seen a settlement not far from their landing site, and had surely attracted attention with their arrival. Their weapons were stowed out of sight, but where they could be reached.

Sure enough, within about fifteen minutes, they came into contact with the locals. Three human-looking men dressed in loose, simple clothing held particle guns their way, though with a nervousness that told Alice they weren't used to guns. She was glad theirs were hidden, for now. Weapon to weapon only led to faster violence, and they always tried to see what was going on first.

"Hello," said Jenny, with one of her biggest, friendliest smiles. Alice found it comforting to know that Jenny could be utterly sweet and utterly deadly, depending on her need.

"Greetings," said the tallest of the men. "Who are you and what is your business here?" Alice's right ear heard the tinny sound of the miniature translator; her left was open and heard the cadence of his true voice, heard the worry in his tone even without the words. She always wondered what her own sounded like, translated in reverse.

"I'm Jenny. This is Alice. We're travellers."

This took the men aback, and the tall one conferred with his friends for a moment.

"Please come with us."

They were led through the thick forest out past tended fields to the village. As they walked through the rough streets, villagers gathered to either side, watching them suspiciously. Jenny flashed her disarming grin, while Alice managed her own careful curl of lips. We're all friends here, the smile said, so let's keep it that way, yeah?

"Why are you here?" A man stood before them, dressed like the others but exuding a particular level of authority. The same worry that had filled the other's voice filled his.

Alice said, "We are travellers."

Jenny stepped forward. "We've come to help." The change in his expression told them both what they needed. "What's happened?"

"Forgive us, we are not trustful of strangers," he said. "Two strangers came to our village four days ago, speaking pleasantly and offering trade. The following evening, they abducted my grandchildren and fled. We have sent out search parties, asked our neighbours, but we cannot find them anywhere."

The grief written on his face hit Alice hard enough to draw a gasp. It shouldn't, she knew impassively. By her own reckoning, she'd lived almost ten years since … Since. But sure enough, every time one of their adventures involved children, the hurt came back like a hammerblow to her chest.

The woman beside him said, "The strangers may be working with them. They could be here to meet with them." Anger, such anger. That would be the children's mother. Alice felt a sudden sympathy with her.

Jenny held her hands spread wide. "We came alone. You may search inside our ship."

"We will."

Jenny looked at Alice. "Would you prefer to stay here and find out what happened, or would you rather introduce them to Hilda?"

"Hilda," she said too quickly. Jenny nodded. Jenny understood.

"Come on, then," Alice said. "You can inspect our ship. We've got no one else with us." With a last look to Jenny, Alice turned and led the three guards back towards the ship. Jenny could deal with the grieving family.

Back at the ship, the men were startled by Hilda's pleasant voice. "Welcome," she said, all smiles and sugarplums after her earlier sulk. Alice made herself not grumble.

"Please have a good look around. Our technology may be unfamiliar to you."

The shortest of the three men, the one with the darkest hair, examined the ship's control panel. "You are still using sublight? I thought most vessels were equipped with hyperdrive."

Alice's jaw opened, and then closed. "We have an alternate propulsion system," she said after a moment. "The sublight is just for intrasystem travel." She'd spent years learning how to repair it.

"Ah."

When they were satisfied with the contents of the vessel, certain that she wasn't hiding anyone's children anywhere, she let them lead her back to the village proper. Now that she knew they weren't as primitive as she'd let herself believe, she found signs of technology seamlessly woven into the village's buildings.

Jenny emerged from one of the houses, her pretty face drawn into a frown. "I have good news. And then again, I have bad news." Alice folded her arms to listen, a cold chill already creeping down her neck. "The good news is that we have a lead in the disappearances. I can positively identify one of the abductors."

"The Master? Dorin? Don't tell me it was John Bloody Hart."

"No, but you're getting warmer." Jenny's eyes were sympathetic, and that's how she knew.

"I'm going to kill him."

She waited. Somehow, she waited. Until Jenny explained to the mayor that they needed to go back to their ship. Until she said they had to research records of the man she had seen in their recording, the one with the bright smile who juggled and made all the children laugh, the bastard.

The second Hilda's door closed tight behind them, Alice let out a wordless scream of rage and frustration, punching the bulkhead so hard she bruised her knuckles.

Hilda said, "Alice?"

"Do not even start with me."

"It's all right, dear," Jenny said to Hilda. "Alice isn't angry at you. Why don't you run diagnostics for a bit?"

"Okay." The computer's hum changed tones. They weren't alone, but Hilda wasn't paying attention, either.

"I hate him."

"I know."

"I keep thinking, he'll get better. I keep thinking, he's not a monster, he's just been put into terrible situations. And then … "

"I know."

Jenny let her talk. While keeping her eyes completely on Alice, listening closely and gently, her hands made tea in the cramped kitchen space.

Alice said, "Five billion years for the son of a bitch to finally die, and I thought that could make up for what he did." She wanted to punch more, to scream more, and settled for throwing her pack against the wall. "He takes children from their families. God only knows what he did to these two. Give them to aliens for drugs? Burn up their brains?" Fresh tears were on her cheeks and she didn't care. "Damn him." She had a time machine at her disposal, but having traced every painful minute of the worst day of her life, there was no way to step back into time and pull her son out alive, not without causing a world-shattering paradox, and there was only one person in the universe to blame.

Jenny wrapped her hands around the mug of tea.

"I want to kill him. And the worst thing is, it would probably make him feel better."

"Probably." Jenny encouraged her to drink her tea, and Alice let it scald down her throat. Jenny found her a handkerchief, too, and Alice thanked her quietly.

"What are we going to do?" she asked, when the tears had passed and the anger was drained and she was left shaking with an empty mug.

"Well, I am going to do some research, like I told these nice people I would. Hilda's been getting some very good results tapping into the Vortex for information." Jenny spent hours at a time communing with Hilda that way, teaching the computer to read history books that hadn't been written yet.

When they'd met Jenny's dad the first time, Alice had learned that once upon a time, there had been an Academy, and young Time Lords had learned how to access and control the vast depth and breadth of information at their fingertips. All of that was gone now, and Jenny was a child by the old standards, teaching herself how to crawl and walk and fly. Her brain buzzed with information, so loudly sometimes Alice could almost hear her thoughts, but catching them and taming those thoughts into something useful was a skill she learned every day.

"Can I help?"

Jenny kissed her on the forehead. "You can sleep. It's late, and I'll be talking gibberish to the computer all night."

"Wake me if you need anything."

"I will."

Alice went back to her bunk, but sleep evaded her for hours.

A hand on her shoulder and lips in her hair woke her. "Alice."

"I'm up." A decade spent running into and out of danger meant she'd learned to sleep light. She sat up and threw her legs over the edge of the bed. "What is it?"

"I've been looking for traces of Jack in the current timeline. The last positive hit was from almost five hundred years ago."

Alice shook her head. "He must have gone into non-linear time again. Or went underground."

"I can't sense him in the here and now." That was settled, then.

Jenny gasps, clutching her head like she's been struck with a migraine. "What the hell is that thing?"

Alice sighs, looking at the familiar face across the street. He hasn't noticed them yet, but he will.

"That's my father."

"We'll have to go back," said Alice. The frown on Jenny's face hadn't lifted. "What is it?"

"I also looked at this history of this world. I know why we're here."

One of the rules Alice learned about time travel was that there are Places everyone went eventually. If you lived long enough, if you travelled far enough, if you pissed off the non-existent gods watching over you enough, you'd find your time-travelling self at particular foci in the space-time continuum. On Earth, the Titanic was the most over-booked ship ever built, and Pompeii the most crowded pre-volcano city.

Sometimes, they were able to help. Their transmat beam plucked a handful of survivors from the freezing waters, even as Alice choked down lungfuls of the stuff. Daff had been with them at Pompeii, and fortunately so: while they'd been dismissed as hysterical women, Daff's voice had ordered the two dozen people they'd rounded up in the chaos onto the ship and off to safety. Jenny had kept her head tilted oddly the entire time, and told her later that the Doctor had been there but that she didn't dare encounter him, not yet. Daff was gone again before they went to Hiroshima, and if they had managed only to shelter one family from the horror, it was still enough, had to be enough.

Sometimes, Alice fell asleep at night with the sense that the balances were tilting in favour of justice, of kindness, of other imaginary things she knew she used like a blanket against the darkness of the universe. Sometimes they simply stood in mute witness, the sole survivors to walk away from disaster.

More than once, they'd come upon Time Agents busy at their tasks, collecting their own bounties of human lives for the Agency's mysterious ends at disaster after disaster. Only one had turned, joining them in transporting the would-be victims of a shipwreck to someplace new, someplace safe from the Agency as well as the roiling waves. Lega's masters had taken her life for her disobedience. Alice had no love for the Time Agency, and with her friend's loss, for any of its Agents.

Convincing people to leave was always the hardest part before catastrophe struck. After, they were lucky if there were even survivors to gather.

"The asteroid will collide with this world tomorrow," Jenny said, the full knowledge of the disaster radiating off her. "If we make multiple trips, we can evacuate the entire village, but we must start now."

Lomas - the mayor, or minister, or whatever passed for leadership in the village - sat back, playing with his own fingers. He looked lost and very tired. Alice placed a hand on his arm. "You must believe us."

"No," he said at last. "We must not. The last strangers lied. What if you are taking away our people to leave us defenceless? What if you are actually here to raid our crops and take our possessions?"

Jenny offered him one of her innocent smiles. "We wouldn't."

A grim smile touched Lomas' face. "Two women, travelling alone. I can imagine that on many planets, the people assume you are harmless. We've seen your weapons, even though you've kept them hidden from us."

"We haven't used them," Alice said. They'd have noticed. Jenny never missed a shot.

"I cannot justify emptying the village on your word alone."

"Then do a scan!" Jenny said irritably, slapping her hands on the table and standing. "You have the equipment. Look into the sky. I can give you the coordinates. I can't stop the asteroid. All I can do is offer you safety. But we are running out of time."

Lomas wrote down the coordinates as Alice felt the seconds ticking away, and he left them there to wait. They weren't under arrest, and even if they were, she was sure they could fight their way out and get to the ship. They could save themselves, if nothing else, but surely Lomas would see reason?

"Mother says he thinks you are lying to us," said a small voice. A girl in her early adolescence, long dark hair swept back from her frowning face, watched them from the doorway.

"We're not," said Jenny.

Alice said, "What's your name, dear?"

"Klay."

"It's nice to meet you, Klay." Alice prodded Jenny, who merely said, "Hello." Jenny had trouble with human customs when she was agitated.

"Lomas is my grandfather, Kamb is my mother. My brothers, they were taken by Jix and his shadow." Her frown deepened.

"I'm sorry," Alice said. Against her better judgment, she added, "He took someone from me as well. My son." And it hurt, again, always.

"So you do know him. Mother said she thought you did. Did he come to your world the same way?"

"Not exactly the same."

"Did you get your son back from him?"

So much blood. "No."

Klay bowed her head. "Then I am also sorry."

Hilda cooperated with the evacuation better than was her usual wont, running back and forth between the doomed world and the new planet Jenny had found in a search. The ship could only hold so many people, and with the time constraint, the only possessions the villagers could take was what they could carry. Almost fifty chose to stay behind and take awkward shelter rather than abandon all.

History said they died.

Alice stood with Kamb outside the ship, after the last group unloaded to safe ground, as the first group was already busy constructing rude shelter.

"I'll find him," said Alice. "I'll find your children."

Kamb's eyes held disbelief, but she nodded, and without a word, went to join the others in trying to build a new home.

When Alice boarded the ship, she asked Jenny, "Five hundred years?"

"He was arrested."

"What a surprise."

The game was called kalaya, and as far as Ianto could tell, it was a cross between chess and liar's dice. Jack had tried teaching it to him over the years, but while Ianto could grasp the basic structure of the moves, the real point of the game was cheating as boldly and as often as both players could, and Jack was a much better cheater.

Or would have been were his skills not quite so rusty.

The sentence was six months, automatically enforced upon arrest. The good news about being stuck on this out of the way space station where the freighter had dumped them was that the only record the local authorities could pull on Jack was his Time Agency ID, and not any of his outstanding criminal charges. The bad news was what had got them into this mess in the first place: no access here to the various accounts Jack had squirreled away over the years. In theory, thanks to the blessings of compound interest, Jack was extremely wealthy, but theory wouldn't buy them lodging, food, or even passage off this bloody wreck of a station to someplace with a better connection to the interstellar banking system. Apparently, neither would gambling their last dozen credits on a rigged game.

"I thought I had him," Jack said, from the other side of the partition. "The whole point of the game is to cheat!" That last was shouted at one of his impassive gaolers, a twenty-stone behemoth who may well have been made of actual rock under its tough grey skin. The gaoler did not bother responding.

"Perhaps the rules changed," Ianto said, because he didn't want another argument.

"You don't change rules like that."

"And yet here we are."

Jack folded his arms. "Here I am. You could still go."

He smirked. "Hitchhike across the galaxy? Without a towel?"

"What?"

"Nothing." He should have known better. Jack had forgotten vast swathes of twentieth and twenty-first century pop culture, not that Ianto could blame him. If he could purge his memory of Oasis lyrics and exchange them for more vivid memories of his family, he'd take that trade, too. "I start work this evening." Jack's eyebrows raised suggestively, and Ianto bit back his sigh. "I told you about it already."

"The bar, right. I paid attention."

The job was nothing glamorous, although not even the Top Secret Organisation What Hunts Aliens job had been glamorous, and involved the same general cleanup and maintenance duties. The pub owner needed a new warm body to wash dishes since the last person in the position accidentally ascended to a higher plane of existence - a process which, the owner was quick to assure Ianto, hardly ever happened to the staff.

"By the time you're released, we should have enough money to leave if we're not choosy about transport."

"So no five star luxury liners?"

"Not this time."

The guard cleared its throat in a fashion that would not have been out of place in a Cardiff gaol. Ianto tried to remember the name of that one copper, Gwen's friend, but it had been over twenty years by his reckoning, and those memories were gone.

"I'll see you tomorrow," Ianto said, with a nod to the guard, who nodded back. Spouses were permitted to visit the prisoners every day, if just through an impenetrable sheet of clear polymer, and the station rules weren't picky about formal versus informal marital arrangements. Ianto came as often as possible, and cursed the partition in his thoughts, and kept up his politest demeanour for the guards so he could do it again the next day.

"See ya." Jack glanced away. Hardly off the planet, and he'd exchanged one prison for another. Ianto wouldn't blame him for being jealous of Ianto's relative freedom, even if that freedom was, not for the first time, to work a low-end and thankless job among strangers for the benefit of someone else.

With that cheerful thought, and one last look at Jack who was already being escorted back to his cell, he hurried back to the small quarters he shared with three other workers at the pub. He could stick to the plan: be quiet and helpful, keep his head down, wait for better days.

The mass jailbreak during Jack's second month was not part of the plan.