propinquitine: John, looking up while in a cell, from the lovely blue-lit episode Aurora. (Default)
[personal profile] propinquitine
Title: An Eighth of a Mile Isn't That Far Away (but an Eighth of a Kilometer's Even Closer)
Rating: PG-13
Pairing: John/Rodney
Word count: 3,617
Spoilers: vaguely for 5x14 - The Prodigal
Summary: Rodney discovers the joys of the collaborative process.
A/N: This is for [livejournal.com profile] newkidfan, to thank her for her amazing work running the [livejournal.com profile] artword Round Robin challenge. Originally posted in the [livejournal.com profile] newkidtastic comm, now somewhat revised and betaed by [livejournal.com profile] winkingstar and M.


The thing was, life on Atlantis wasn't always exciting -- there were far more days of quiet lab time, stultifying staff meetings, and boring milk-run missions that actually didn't go bad than there were days of running/shooting/speed-science problem-solving/getting abducted/trying to prevent John from haring off on suicide mission #57. (He knew the number. Of course he knew the number. He also knew the Guy Code well enough to know that he wasn't supposed to let on that he knew the number, and he knew John well enough to know that he knew that Rodney knew, anyway. At least, he thought so.)

Point being, there was actual downtime on Atlantis, time when nothing critical was going on, and nothing was going critical (or the naquadah equivalent). When he was off-duty, Rodney had no problem filling this time -- side projects, team movie nights, race cars, baby sitting (which was definitely a team sport), computer games with varying degrees of influence on the real world (contrary to John's frequent complaint, Rodney's abysmally high scores at video golf were not making Tiger Woods cry), that ridiculous ping-pong game Ronon had invented that involved switching sides, three color-coded paddles per player, and entirely too much running -- all of this made for a much fuller social calendar than Rodney'd anticipated having on the far side of forty.

But while he was on-duty, the calm periods could be mind-numbing, a potentially dangerous effect when he had to be able to snap back to complete attention as soon as the next inevitable crisis came along. Rodney had learned early on that his brain worked best when it had multiple questions to tackle at once; sometimes he needed to distract himself with an easy problem while the rest of his brain worked through some other issue. ("Easy" being a relative term -- he hadn't stooped to such an intellectual low as to work on problems that had already been solved, of course. Except when he disproved or improved proofs, but he made that kind of exercise more challenging by trying not to rely on the highly classified information he worked with every day that rendered many of these fields of study functionally irrelevant. Give the others some glimmer of a chance, at least.)

To this end, he'd set up a small whiteboard in a mostly-concealed corner of his lab. He didn't exactly want to broadcast the fact that he was working on cake-level problems, especially since they sat untouched and unsolved for the not-inconsiderable spans of time that he was saving the city/imprisoned off-world/recovering in the infirmary. He'd snapped at the first few nosy subordinates to poke around in that nook, so everyone kept a respectful distance from it now. (Well, semi-respectful. He'd overheard some sniggers about it being "McKay's alone-time place", but since that was basically true, he'd let it slide.)

So it was a surprise when he checked the board one it's-never-boring-because-we're-in-a-10,000-year-old-city-that-flies-but-it's-still-kind-of-slow day to find that someone had completed another step in his proof of the Lonely Runner conjecture for k = 8.

He'd picked the Lonely Runner conjecture (which posits that for any number of runners k running around a unit length track at distinct speeds, for each individual there will be a time when s/he is 1/k distance from the other k - 1 runners, i.e., the runner will be far away from them and "lonely") where k = 8 because mathematicians back on Earth had just proved it for 6 and 7 in the past year. Rodney was curious to see whether he could, in his free time, do something the best minds on Earth were devoting their entire careers toward accomplishing. For Earth's sake, and in an example of just how much the past few years had changed him, he actually hoped not.

(His interest in the Lonely Runner problem had absolutely nothing to do with the image it conjured of a lean, lanky, spiky-haired guy who ran for fun and always seemed to keep his distance from everyone else.) (Or with Ronon. It honestly had nothing at all to do with Ronon.)

The new line of math that had appeared on the board didn't lead in the same direction that Rodney had been headed with his proof. It followed from the previous lines, certainly, but it had clearly been added by someone who hadn't read Barajas & Serra's proof for k = 7. Still, as Rodney frowned at it, the unexpected symbols sparked a few lines of thought, and he quickly scribbled out the beginnings of several possible paths the proof could take.

Before he could work much further on the problem, his radio pinged in his ear, Simpson reporting that the desalination tanks had broken, again, and he ran off to a semi-crisis period that lasted through one tank recalibration, two anomalous readings on the power grid, one trade mission gone slightly awry (a beans/bees translation glitch with the Amalkians that lead Rodney to sit out that mission in the jumper, epi-pen at the ready), and a temporary shortage of pudding cups in the mess.

By the time things had calmed down, it was weeks later, and Rodney had forgotten all about the mysterious additional math. It was thus a strange experience of déjà-suprise when he discovered that someone had worked on each of the potential branches of the proof in his absence. One route had been quickly discarded: his mystery colleague had gotten about four lines into an expansion of it before ending with a "???", and Rodney had to agree -- that line didn't work toward proving the conjecture at all, though it might have some application toward other view-obstruction problems.

One of the branches, though, had been significantly advanced, though it left off in a strange place. Anyone remotely familiar with the study of chromatic numbers in circulant graph theory would have seen the obvious next step. Filling in this line, Rodney called over his shoulder to the lab at large, "Hey, who's been messing with my board?"

"That is your special place, Rodney," Radek answered. "We all know better than to try to enter there. Or to want to."

"Oh, ha, ha. No, seriously," he said, coming out from behind the larger whiteboard that served as a privacy screen. "Who's been working on this?" Still no response; most of the scientists wouldn't meet his eyes, though whether that was due to fear or them not bothering to look away from their work, he couldn't tell. "Really, I'm not actually angry, here. This is interesting work, at least; creative defacement, which is better than some of you ever manage." At this, he got a few scowls, but no one volunteered to take credit.

"Perhaps it is a dědek. A, uh, a brownie?" Radek offered. Off of Rodney's glare, he added, "A helper spirit, to do the chores that you neglect? Though why it would still leave your paperwork for me to do, I do not know."

"Yes, Radek, that must be it. A brownie." Rodney didn't try to mask his scorn. Of course, he never really did.

Radek shrugged. "You should be careful, the dědek, they do not like it when the house is full of profanity and strife, and sometimes they retaliate."

"Is that a threat?"

"Merely advice, that if you want to keep your helpful mathematician happy, you should consider leaving him gifts." Radek tilted his head to one side. "I believe, milk, biscuits, an old boot -- these are traditional, but you must make do with what is available."

"What? Are you asking for bribes, now? Weird bribes?"

Radek snorted. "My friend, I am not your dědek. I have too much of my own work to waste time doing your math for you. Please do not give me your boot."

Rodney went back to his own projects after that, the important ones that kept the city afloat and significantly advanced the sum of human knowledge in the universe, but his mind kept wandering back to his dědek problem. He added a few lines to the proof over the course of the day, erasing the other tangents and concentrating on the most intriguing branch. It was a strange experience, not to know exactly where he was headed with the math he was doing. It certainly looked like it could solve the Lonely Runner for 8, but it also might work its way back around to prove the conjecture for any number of runners, with a few tweaks to the beginning of the proof. But the math seemed to want to pull in an entirely new direction, too, and that was very tempting. This dědek (or whoever it was, because Rodney emphatically did not believe that some helpful spirit was lurking around the labs at night. Knowing the Ancients, it was probably some robot and/or monster that would soon try to kill them all) was approaching the problem in an unorthodox way, and as much as it frustrated Rodney not to know the origin of these ideas, it was exhilarating (in a novel way, that did not at all involve running for his life) to work with them and see where they led.

(If he briefly entertained the thought that maybe this dědek -- who kept appearing in his mind's eye with hazel eyes and a smirk -- would be interested in a long and happy life of co-authorship and hot sex, well, that just showed what mischief his idle mind could get up to, and why it was best to keep it occupied.)

Later that night, having inadvertently worked through dinner (and that was the downside of downtime -- there was the luxury of getting immersed in a project, but the danger of spending all of your not-imperiled time on work), Rodney left the lab, no closer to discovering the identity of his math sprite. He headed to the mess to pick up some sandwiches before tracking down John; Rodney vaguely remembered making plans to watch the new Batman movie together, though even if they hadn't, John was usually pretty easily strong-armed into hanging out.

But John wasn't in the mess, or the gym, or his quarters, or even Rodney's own quarters (the man could certainly let himself in easily enough, and Rodney was just waiting for the day he walked in to find that John had made himself at home). Disposing of his sandwich wrappers in the incinerator near his quarters (all of this tromping around the city was hungry work), Rodney decided to return to his lab and take another look at the Lonely Runner problem. If he hadn't run into John yet, it was likely that John didn't want to be found.

Feeling somewhat deflated, Rodney walked into his lab, only to be surprised for the third time at the state of his secret whiteboard. But this time, it wasn't just the additional math that caught him off-guard, it was the person standing there, frowning at the integral symbol he'd just scrawled on the board: his very own lean, lanky, spiky-haired quasi-inspiration for the problem.

"Dědek!" Rodney shouted, for lack of a more coherent response. John dropped his whiteboard marker as he whirled around, leaving a smear across the short length of unfilled space at the bottom of the board. They'd need another board, soon.

"Jeez, Rodney! When'd you learn how to sneak up on people?" John ran a hand through his hair, looking off-balance (though his whirl had actually been fairly graceful). "And what the hell did you call me?"

Rodney waved a hand dismissively. "Dědek, it's a sprite, brownie, elf-thing, whatever. Radek is . . . strange," he said. "But that's not -- the point is, what are you doing?"

"Math?" John said, biting his lip. He seemed torn between wanting to fight and wanting to run right out of the lab. Rodney tried to subtly position himself between John and the door, but judging by John's glare, he hadn't achieved "subtle". "I was looking for you."

"And found, what, math on my board, instead? That's my -- my special place!" And damnit, this was exactly why he never should have lapsed in berating absolutely every shred of wise-assery out of his minions, because allowed to run wild, they'd fill his head with inane comments that his brain would regurgitate at the most inopportune times, much to the obvious amusement of sneaky math bandits masquerading as Air Force colonels. "And you didn't just do this tonight. Some of that's been there for weeks."

"I kinda come looking for you a lot, Rodney." John looked down, rubbing at the back of his neck. "But if you'd prefer," he said, turning back to the board and raising his right hand, "I can always just erase--"

"No!" Rodney shouted, lunging forward to grab John's wrist. This had the corollary effect of plastering Rodney against John's back, which caused both of them to stumble slightly, and John's still-outstretched fingers to dip perilously close to the surface of the board. So, when Rodney brought his left hand up to clutch at John's hip, it was really only a prudent reaction to stabilize them and ensure the continued safety of the proof.

"No?" John asked, bending his elbow a bit but otherwise making no effort to extricate himself. "I shouldn't erase this?"

"Are you insane?" Rodney asked, shaking John's wrist for emphasis. "This is -- this is interesting, what's going on here." Rodney leaned closer, pressing in, just to get a better view of the board, of course. "This first part that you added." He gestured with the hand still holding onto John's wrist; John helpfully pointed with his index finger. "Yes, that bit. That came out of nowhere! What were you trying to do? Where did you come up with that?"

John shrugged, and seemed to relax. He wasn't exactly melting back into Rodney, but he was at least leaning with some interest. "I . . . don't really know what I'm doing here."

"Right," Rodney snorted, "Yes, you just happened to wander by and write an equation that followed logically from the preceding argument. You don't even know what all of those squiggly lines mean, you're practically illiterate!" he said, flopping John's hand around sarcastically.

"Rodney," John said, in his I'm-more-entertained-than-exasperated voice. "Okay, I do remember some math from college, I did a bunch of calculus for pilot training, but I don't even know what we're trying to prove, here." He turned to direct this last comment at Rodney, who had to duck his head a bit to the right to avoid an unsightly nose collision. Still, their faces were very, wow, very close. Rodney heard someone inhale sharply, but he wasn't sure who.

"Lonely," Rodney started, but then he had to swallow; his throat had gotten really dry all of a sudden. John was frowning slightly, looking concerned, and Rodney felt a weirdly insistent urge to reassure him. He flexed the hand that was still resting on John's hip, and tried to smile. "Lonely Runner," he clarified. "If, ah, in this case, eight people run around a unit track at distinct speeds, will an individual runner--"

"Be at least an eighth of a mile from every other runner at some point?" John looked back at the board, eyes making a quick scan of the entire proof.

"I'm pretty sure these runners have the good sense to be running around a metric track, but otherwise, yes, that's the question we're answering. Well," Rodney considered, drumming his fingers against John's hip, "that's the question I was focusing on, until you came along and, and -- disrupted things."

"Sorry." John sounded anything but. He leaned more of his weight back against Rodney.

"No, don't be, this is a much more interesting direction than the one I'd had planned. It'll probably still complete the proof in some form or another, but, more importantly, it opens up many more possibilities than I-- than it would have, otherwise."

"And this?" John turned to face him, and Rodney, in what he thought was a pretty brilliant job of reading body language and social cues, let his left hand drag softly across John's lower back. As he resettled his hand on John's right hip, he thought he felt John shiver. John twisted his wrist gently within the circle of Rodney's hand, so that his knuckles came to rest against Rodney's sternum. The jump of John's pulse under Rodney's thumb, the dark hair over the golden skin of his fingers, the pale nail beds that he'd never had occasion to really look at before -- these were all fascinating to him, now, and highly distracting. John rapped his knuckles lightly against Rodney's chest, reminding him that John had just asked a fairly important question. "This?" he repeated.

"This is a, uh, new and exciting tangent to our previous work?" He looked up at John, who was, oh, who was smiling, and that sent a warm flush through Rodney that felt damn good and left him a little unsteady on his feet. It wasn't even a full smile, he could really only see it around John's eyes, but it was there, and sincere and content and Rodney thought he'd probably better be sitting down (lying down) if (when) John ever really beamed at him.

"But why?" The question popped out before Rodney knew he'd intended to ask it. It was a good question, though. "Why did you start this? Now? I'm really not complaining, but . . . ."

John dropped his eyes, raising his free hand to tug at the sleeve of Rodney's uniform shirt. "I've always liked . . . math, even if I haven't done much with it recently, and I found your board and saw, I don't know, something that made sense?" He flattened his palm against Rodney's bicep, dragging it slowly up to rest on Rodney's shoulder. "I figured I'd give it a try, and maybe you wouldn't notice, wouldn't know it was me, or you would, but maybe at the worst, you'd yell at me for screwing things up."

"Well, you'll notice a distinct lack of yelling on my part."

John laughed. "Yeah, except for when you swore at me in Czech."

"I called you a helper-spirit, not an osoba provádějící felaci." Though, Rodney reflected, he hoped he was that, too. Judging from the gleam in John's eye, they were of one mind on that particular issue.

"Still," John said, running his thumb lightly along Rodney's shoulder and up his neck. "No yelling? When I tampered with your important work? Are you sure you're feeling okay?"

Rodney let his eyes drift shut, savoring the drag of skin against skin at his neck and inching his own thumb under the hem of John's shirt. The weight of John's other hand rested solidly against his chest. "I've been a bit distracted." He opened his eyes again, and all he could seem to focus on were John's lips, pink and soft and right there.

"Yeah," John breathed, sliding his hand up the back of Rodney's neck, fingers curling in the hair at the nape of his neck. And then they were kissing, gently, just a press of lips to lips, until Rodney groaned and pulled, his whole hand under John's shirt now, pulled John in with an easy pressure against his lower back, and then they were really kissing, tongues licking into mouths, clasped hands untangling to roam over chests, sides, backs, up into hair, and Rodney couldn't really tell who was doing what (though he was pretty sure the hand that slid immediately to his ass belonged to John), but it all felt fantastic.

The squawk of his radio in his ear was one of the most unwelcome sounds Rodney had ever heard. "Oh, goddamnit, what now?" he demanded, lifting his head slightly away from John's, but otherwise not disengaging.

On the other end, Frobischer was nattering on about some power converter situation out on the west pier, but Rodney was more focused on the way John leaned forward to rest his forehead on Rodney's shoulder, hand still settled comfortably on Rodney's ass. "There's the yelling," John muttered into Rodney's t-shirt.

"And for good cause, I should say," Rodney whispered back, nosing along John's ridiculously pointy ear. He could feel John grin into the skin of his neck. "No, not you, Frobischer, there's no good cause for those kinds of readings from the generators. Give me a minute, I'll be there."

John dragged himself to a standing position, stepping back a few paces and bringing his hands down to his sides. He looked a little bit mussed, though with that hair it was difficult to tell. "So," he said. "Back to work as usual?"

Rodney straightened his shirt and rubbed at his jaw. Definitely some stubble burn, there. "Don't think you're getting off so easily, Sheppard," he said, ignoring John's smirk. "This is a collaborative process we've started, here." He threw his hand out to encompass the two of them, the whiteboard with their proof of who-knows-what, everything. "It's going to require diligent, consistent effort to see this thing through. No backing out," he finished, pointing a stern finger at John who was, oh, wow, beaming. Where was a stool when he needed one?

"I didn't think you were one for much collaboration with your colleagues, Rodney." John bumped shoulders with him companionably as they left the lab and headed off to avert certain doom.

Rodney looked at him, lips still red, hair, yeah, a little wilder than usual, eyes bright with ideas that Rodney couldn't wait to learn. "Mmm, yes, well: it's really all a matter of finding the right person to work with."


------------
A/N 2: In the real Lonely Runner conjecture, the problem for 8 runners would have k = 7, as the total number of runners in these problems = k + 1. I'm sure that the way I've simplified it totally ruins the math, and I apologize to any cringing mathematicians in the audience. If you'd like to see the real math in action, check out Barajas & Serra's proof for 7 runners (remember, k = 6, now --- tricky!).


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propinquitine: John, looking up while in a cell, from the lovely blue-lit episode Aurora. (Default)
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