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Euclidean Motion

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"I should have liked to meet this Waterhouse friend of yours. It is strange that he could not join us." Rudy says, watching Alan Turing's reaction from the corner of his eye. The front wheel of Alan's bicycle quivers and he fights, momentarily, to regain control.

The two are biking slowly down an old mine road that runs parallel to the Delaware river, having ridden nearly half the day to get from Princeton to their current location.

"Yes, it is." Alan replies, "He has always been eager to join me on my trips, but declined this time, due to an unexpected engagement."

Alan is telling the truth, albeit only one form of it: Waterhouse is currently in Iowa, attending his cousin's funeral. Although Alan knows of this, he has arranged for a camping trip anyway, inviting Rudolf von Hacklheber to join them.

The two share a common acquaintance in Alan's major professor, Alonzo Church, who had captured Rudy's interest following a lively discussion of set-theoretic paradoxes in relation to lambda calculus. Rudy had been unfamiliar with the notion, finding himself at a loss for words when Alan was present — he frequently and mysteriously lost all cognitive abilities around the Brit — and was overjoyed to find common ground when he and Alan began working together on zeta functions.

Eventually Rudy grew more secure in their relationship; he was young and fearless, prone to teasing Alan mercilessly about his obsession with artificial intelligence as exhibited by machinery. The fact that Rudy occasionally caught Alan openly staring at him did nothing to diminish this confidence.

So although Rudy would've liked to meet this Lawrence Pritchard Waterhouse — who Alan had described as a genuinely thoughtful, intelligent man who was susceptible to moments of sheer, unfettered ignorance — he was, overall, quite pleased to be alone with Alan Turing, miles from proper civilization.

They stop by the shore where the river doubles back in a sharp curve, allowing the water of the Delaware to slow to a crawl and build into a deep, inviting pool. They pitch their tent on the high, flat bank of the river, and settle down to eat their lunch. They work their way through half a bottle of schnapps, and, feeling brave, they strip naked and dive into the river, swimming back and forth across the border under the hot sun.

If Alan deliberately splashes water in Rudy's face, coyly challenging him to a ferocious session of water wrestling, and if Rudy accidentally brushes against Alan more often then necessary, and lingers — neither of them mentions it.

It is late afternoon by the time they crawl back onto the bank, speckled here and there with algae and dirt, exhausted from a day of swimming and bicycling. Alan collapses on the grass, laughing and enjoying the warmth of the afternoon sun as it glitters off the water. Rudy stretches out next to him, hands tucked behind his head, allowing him to glance over Alan's body occasionally. They pass the last of the schnapps between them, and talk about mathematics.

"Look, if you just pretend that those clouds up there—" Alan thrusts an arm toward the sky, where the clouds in question are puffy and slightly pink from the setting sun, "—are an arbitrary symbolic representation of the cells which divide an infinitely long tape into finite sections, then maybe I can get on with my explanation of computational algorithms without you interrupting me every five seconds."

Rudy grins, unable to hide his amusement. "Although you are right to simplify the problem by symbolic representation, it hurts me greatly that you feel the origin of the symbols is arbitrary and unimportant."

Alan sighs, irritated, "I'm not really saying they're arbitrary—"

"But you are!" Rudy rolls on his side and props himself up on an elbow, facing Alan. "The way you are simplifying symbolic notation is similar to what would happen if I, for example, reduced your hypothesis on artificial intelligence to a mere parody of man and machine — after all, is it not conceivable that a complex machine should produce different arrangements of words so as to give a meaningful answer, easily imitating the least thoughtful of men, and disproving your test entirely?"

Alan turns red at this statement, perturbed. He takes a moment to collect his composure; meanwhile Rudy grins at him and lets his eyes wander down Alan's lithe frame in an unsubtle fashion.

"Quoting Descartes is somewhat unoriginal, isn't it, Rudy?" Alan chides.

"Does this mean I have failed the Turing Test?" Rudy counters slyly, watching as Alan flushes, his cheeks as red as the sunset.

Alan glances at him, and then turns away. "I suppose if you demonstrated a novel form of intelligence, you might pass the test."

"Natürlich," Rudy chuckles, and, still lying on his side, he moves closer to Alan. "So if I were to refute your previous symbolic assignments and replaced them with a working arrangement, I would pass?"

Alan swallows a nervous lump in his throat and shrugs. "It would depend on the new symbolic assignments, of course."

"Shall I demonstrate?" Rudy holds up a finger, waiting until he has Alan's full attention. "Using the I Ching's symbolic assignments—"

"Oh, you and the I Ching."

"Don't interrupt, Herr Türing." Rudy wags his finger reproachfully. "As I was saying — if you pretend that a raised finger is a solid line, representing yang, and a bent finger is an open line, representing yin, then I can arrange my hand into any number of unique messages."

"I don't understand." Alan replies, looking genuinely confused.

Rudy leans closer and slowly moves his hand to rest on Alan's naked abdomen, aware of the ripple of muscle under his fingertips as Alan shivers.

"If you'll allow me..." Rudy presses an index finger to Alan's skin and traces a sequence of parallel lines, tortuously slow, down his stomach. His fingernail leaves six pale, white lines running across Alan's abdomen, with the last two being intersected by Alan's belly button. Rudy's hand comes to rest below these fading lines, his fingertips touching the dark curls of Alan's pubic hair.

"Here," Rudy whispers, his voice warm and husky in Alan's ear. "I have drawn the symbol for dà zhuàng—" Alan shudders as the word rolls effortlessly off Rudy's tongue. "—which would translate to 'a great invigorating power'."

Alan nods vaguely, breathless. "Yes," he says, absentmindedly, "it certainly is..."

Rudy slides his hand off Alan's stomach, bracing it on the other side of his body, and moves downward. Rudy can't help but notice the way Alan's eyelashes flutter against his cheeks for an instant, and that his lips are moist and parted. Alan is watching him, wide-eyed with anticipation. Rudy leans over his abdomen, locking eyes with Alan.

"But," he pauses, watching Alan fidget under him, "if I fill the gap—" Rudy dips his head, flicking his tongue into Alan's navel, eliciting a sudden gasp and a faint, breathy moan from the Englishman, "—then the new symbol becomes qián, which means to initiate an action."

"Herr von Hacklheber," Alan nearly chokes on Rudy's name in his eagerness to say it, "if you don't mind my saying — although your, ah, lecture, on the symbolic theory of the I Ching was thoroughly, er, stimulating—I suggest that, unless you should like to find yourself trapped in this unfamiliar Pennsylvanian wilderness with no way of getting back to Princeton, you initiate an action immediately."

Rudy chuckles again, and slides his body against Alan's, one of his hands moving between their bodies to wrap around Alan's hardened cock, causing him to raise his hips and moan softly.

"Are you trying to tell me, Herr Türing, that you find nothing sensual in the discussion of pure mathematics?" Rudy asks, kissing the curve of Alan's collarbone, his fingers sliding expertly over Alan's cock, "That you find no notion of eroticism in the curve—" Alan gasps and arches, keening, as Rudy moves his hand lower, running a finger across the cleft of Alan's ass, "—of integral notation? That you feel no attraction to the concept of infinitely perpetuating summation of powers that is a zeta function? That the perfection—" Rudy rubs his thumb over the head of Alan's cock and revels in the sound Alan emits, writhing and gasping for breath, "—of Euler's identity doesn't resonate with your very soul, mirroring the depth of your existence in its astounding complexity?"

Rudy leans back slightly, admiring the pink marks where he worried Alan's warm, supple skin with his tongue. Alan is gripping the German's forearms with white-knuckled hands, clinging to him for dear life.

"Rudy," Alan breathes, trying to regain his composure, "I am trying to tell you—" His voice falters and he whimpers as Rudy delicately presses a finger into his anus, "—to shut up about maths and fuck me."

Rudolf von Hacklheber needs no further encouragement; he leans back and admires Alan's nude form for an instant, before lust fogs his mind and hurries his actions.

Alan is clutching at the ground impatiently, and he flushes with anticipation when Rudy shifts his position and hooks one of Alan's legs over his shoulder. Rudy slicks his palm with spit and coaxes a few desperate moans from Alan's cracked lips when he slips his fingers into Alan's body.

"Relax, mein schatz," Rudy murmurs, leaning forward to suck at the flesh of Alan's neck. He continues whispering in German, and Alan shudders at the sound, raising his hips impatiently.

"Jesus," Alan sobs, when Rudy finally thrusts into him, trying to move delicately and failing, overcome by his eagerness and lust. They lay quietly for a moment, trying to get their bearings; Alan digs his fingers into Rudy's back and hangs on, panting.

After an eternity, Rudy moves, slowly at first, heeding Alan's pained whimpers and quiet, desperate moans; he begins to thrust faster, sweat beading on his body and muscles tightening, and before long they're moving in unison, gasping each other's names in the darkness.

"Mein Gott, Alan," Rudy grits his teeth and buries his face in the crook of Alan's neck, "so eng—"

They rock together, a tangle of sweaty limbs; Alan grips blindly at flesh and ground and whatever vegetation he can get his hands on, attempting to anchor their bodies — he tries to take control too late, and loses himself in the chaotic motion, his voice building to a crescendo as he sobs Rudy's name over and over again, like a mantra.

In a movement that's almost sinusoidal, Rudy arches away from Alan and thrusts, eyes closed, panting, his fingers leaving bruises against Alan's skin. He comes suddenly, straining against Alan's legs, his body shuddering with the effort.

Rudy pulls away from Alan and collapses next to him, mind reeling and incoherent, his hand still resting on the Englishman's hip. They lie still for several minutes, catching their breath and trying to regain a level of consciousness that's befitting of higher organisms.

After a moment Rudy stands on shaking legs and dusts himself off, before pulling Alan up to meet him. They stagger to the tent — glad, now, that they took the time to put it up earlier — and collapse inside in an exhausted heap.

Alan lights a small lantern and, after making sure it won't tip over and inadvertently set their tent ablaze, he looks to see Rudy staring at him, his lips curving into a smug grin. Blushing hotly, Alan finally clears his throat to break the silence, feeling that something is expected of him.

"Well, Rudy," he says, still flushed, "you've certainly demonstrated that you're not a machine."

At this, Rudy laughs, low and guttural, and the sound bypasses Alan's ears and goes straight to his cock. Rudy, noticing his reaction, reaches over suddenly and tugs him forward, catching Alan in an embrace and kissing the tender skin of his neck.

"I don't know, mein liebchen, I think I could perform these duties indefinitely," Rudy says, grinning at Alan's expression.

"Instructions." Alan corrects him, weakly, as Rudy extinguishes the lantern and pulls him down, whispering something about the curvature of Riemannian manifolds.