Thanks for the reviews. Sorry for the belated update -- I didn't get the chance to finish it on Tuesday, and then on Wednesday the site wouldn't let me post it. (The whole "Oceanic Six" thing also threw a spanner in the works of my plans, and I had to decide whether or not to incorporate it!) Everything in this chapter is canon, but I'm deviating from the show's mythology in favour of what was revealed in The Lost Experience, so some people might not be familiar with it.

Now that the site's back online, I'm going to try to update "Hide And Seek" some time later in the day, or tomorrow... ;)

Chapter 13. The Valenzetti Equation

"Is it just me, or is there something weird about Elsa?" Kate asked Jack as they returned to the rental. They'd just spent an hour making small talk with her and Sayid over coffee, and yet, in spite of her best efforts, she still couldn't understand what he saw in her. Or rather, she could, and that was what worried her.

"Weird as in how?" he checked, frowning as he slid back behind the wheel.

"Weird as in… fake," she explained, climbing in to the passenger's seat, self-conscious as she realised that he didn't share her suspicions. As far as she could tell, Elsa had failed to leave a favourable impression on him too, but he didn't dislike her. Not as much as she did.

"A lot of women are fake, Kate," he reminded her, slotting the key into the ignition, but he didn't start the engine, turning to her instead. "Shannon was fake."

"Shannon – you noticed that too?" she asked him, seizing on this, surprised that the resemblance didn't seem to bother him as much as it bothered her.

"Yeah. It was pretty obvious," he agreed, giving her a look as if to say, So?

"So, what if she's one of them, and he's just to close to see it?" she filled in for him, withdrawing her cell as panic clutched at her heart. "What if they chose her, Jack?"

This seemed to strike a nerve with him; he shifted his gaze to the windshield, staring straight ahead. "It's always possible, I guess, but Sayid's the best judge of character of anyone we know. He's never given us any reason not to trust him – he was right about Ben when everyone else, even I, believed him."

"What about Juliet?" she pointed out, still not convinced that she was being paranoid; years on the run had taught her to treat strangers' intentions with a healthy amount of cynicism. "He was wrong about her."

"That's different," he complained with a sigh, running a hand over his eyes. "There's nothing wrong with being overly cautious."

It was exactly the response she'd been hoping for. "That's all I'm saying," she told him, and he put his hand down as he realised that he'd fallen into her trap.

"You heard what your dad said this morning – he's fine, Kate," he said, softening as he reached across the console to stroke her jaw with his thumb. He moved in as if to kiss her, stopping when their faces were inches apart.

"We made it this far, so let's hear what Sayid has to say tonight," he told her, his voice low and intimate, comforting, and, as she looked into his eyes, she found herself relaxing, "Then, if you're still worried, I'll drive you to the train station as soon as we're done."

He closed the distance between them, finishing the kiss, before pulling back with a reassuring smile. "I promise."

Under the guise of walking them to the lift at the end of their visit, Sayid had slipped Jack the address of a quiet pub on the inner city limits, where it was unlikely that the three of them would be seen together. He had already staked out a corner table when they arrived, catching each of their eyes in turn as he glanced up to check the clock over the bar.

"I must admit," he confessed, sounding apologetic, once they'd dispensed with the handshakes and hugs, and they were all seated, Jack and Kate on one side, him on the other, "I was surprised to see the two of you together, under the circumstances. Tell me, what brings you to Berlin?"

Following his example, and cutting to the chase, Jack's voice took on the same determined tone it had at the hospital. "We wanna know about D.H.A.R.M.A. Everything you've found out since you started working for them."

Sayid stared back at him, holding his gaze, as if he were trying to see inside his mind, to figure out what he was missing. "It's been almost three years, Jack," he said in his careful, even tone. "Why now?"

Clearly, this wasn't how Jack had imagined the conversation playing out. "Why now?" he repeated, struggling to control his temper as he was forced to remember what had brought them there. "Because one of them threatened Kate."

"Really?" A light went on in Sayid's eyes as he shifted his attention to her, regarding her with interest. "What did he say?"

Until that moment, she had been careful not to mention J.J., just in case he or Elsa couldn't be trusted, but remembering Jack's words, she admitted, her disgust and outrage returning, "He told me they were gonna kidnap my son – use him in some kind of experiment."

Sayid raised an eyebrow in surprise. "Your son?" he repeated.

Pulling her wallet from the back pocket of her jeans, she slid out a more recent picture than the one she'd given Jack; his eyes were open this time, leaving little doubt about who his father was. "This is J.J.," she told him as he took it from her. "He's six months old, and he met his father for the first time this week."

He studied it carefully, glancing from her, to Jack, without comment, before handing it back. "D.H.A.R.M.A. is only the tip of the iceberg," he began, lowering his voice, and Kate smiled.

"It stands for the Department of Heuristics and Research on Material Applications. It's a research initiative, financed by the Hanso Foundation – a non-profit organisation set up by Alvar Hanso, a Danish weapons supplier – and two other corporations—" he gave them each a meaningful look "—The Widmore Corporation and Paik Heavy Industries."

It took Kate a moment to realise where she'd heard the names before, and then her mouth fell open in surprise. "Is that…?"

Sayid nodded. "The companies owned by Sun's father, and Charles Widmore, father of Penelope Widmore, Desmond's girlfriend – the one Naomi told us employed her."

Jack let out a low whistle. "It's all connected."

"It is," Sayid agreed, "which is why we need to approach this with caution."

"Any idea what they might be hiding?" Jack pressed.

"There're rumours within the foundation of an equation – the Valenzetti Equation – commissioned by the U.N. to predict the exact date of humanity's extinction. It's a sequence of numbers, totalling 108 – 4, 8, 15, 16, 23, 42…"

"The numbers," Kate supplied, thinking back to all the times she'd punched them into the computer while on shift in the Hatch. "They were an equation?"

"According to Gary Troup, the author of the only known book on the subject," Sayid agreed.

Again, Kate was struck by a strange sense of deja vu. "Why does that name sound familiar?" she asked, trying to place it.

"He was one of the people killed in the crash – Hurley found one of his other manuscripts in the wreckage," he explained, and something inside her brain clicked as she remembered Jack throwing the last pages into the fire to convince Sawyer to give back the guns. "Conspiracy theorists have speculated that it was orchestrated to cover his murder, since Hanso bought up all the copies of The Valenzetti Equation shortly after publication."

"Why would anyone plan something like that?" Kate couldn't help insisting, sickened by the thought. She couldn't believe that all of those deaths were a means to an end, not when they couldn't even be sure that they'd succeeded. "Sun was on that plane – why would her father want her dead?"

"Either Hanso was acting alone, or Desmond was right, and it was an accident," Sayid agreed. "It's more likely that Troup's death was a fortunate coincidence."

Jack had fallen silent, processing this, but he jumped back into the conversation then. "So then what does all this have to do with us?"

"According to the rest of the book, the D.H.A.R.M.A Initiative was designed to alter the course of human history by using scientific research to manipulate the environment, in hopes of changing these core factors," he explained, and Kate found she had to replay it in her head a couple of times before she was sure that she understood it.

"That's what they were doing on the island? Manipulating the environment?" Jack repeated.

"Apparently."

"So if they're trying to help, why don't they want this getting out?" she asked, confused. If they were the good guys, why was secrecy so important to them? And why were they threatening her and Jack to ensure it?

"The island has properties not seen anywhere else on earth," Sayid told them, and Jack nodded, his expression a combination of enlightenment and disgust as he seemed to guess what was coming. "They don't want to share that with the rest of the scientific community, any more than they want to create mass hysteria by publishing their findings."

"I guess the question now is, how do we stop them?" he asked.

This time, it was Kate who arrived there first. "We find the books," she said, before the thought had even finished forming in her mind.

Jack looked to Sayid for confirmation, and he nodded. "She's right. Once we have the books, we have evidence, which leaves them with two choices – they can go public with their findings before we have the chance to do so, in which case, we will no longer be liabilities to them, or they can agree to meet a list of demands."

What he was saying made sense, but Jack didn't look convinced. "That sounds good in theory," he agreed, and Kate could feel the but coming, "but what's to stop everything from going back to the way it is now once they have them back?"

Sayid smiled, the broad smile that always told them he'd already factored this into his plan. "We make a copy for each of the survivors before we return them. If anything happens to one of us, we agree to alert media."

A slow smile crept over Jack's face, and Kate found that she was grinning to, until it occurred to them that this might not be possible. Did they really think that Hanso was going to leave all those books in a warehouse somewhere, where anyone could find them? It was extortion waiting to happen. "What if he destroyed them all?"

"It's possible," Sayid allowed, sobering as he considered this, "but if the book is as important as everyone says, I'm willing to bet that Troup had a back up plan."

Next chapter: More conspiring... and Coming Up: Scotland! ;)