Another instalment of our serialisation of The Titan Kiss, by Clark Nida (2014, 2016). A further 3,000 words (or so) will appear tomorrow.
Jack is joined in the ornithopter by Shval, and they descend to Platform Two. En-route, Jack asks her to explain the ominous Last Verse of the Book of Titan.

But Jack did know the answer to that one.  He had been trained as a mathematician, not as a physicist.

“That’s why you have to specify  {An}0  as  n.”

Then he too began to write hurriedly with his point-of-gaze on the slate.  “Take a case where it doesn’t.  Where  An=1  for all n.  Then:

Σ(A + B) = 11+11+11+1…

“…and so on, and so on.  Now the right-hand side of the equation is zero—or is it?  Let’s bracket it, like this…”

1 + (1+11+11+1…)

“Now, inside the parentheses, swap around successive pairs of plus and minus terms…”

1 + (11+11+11…)

“Hey presto!  Inside the parentheses it’s the original series once more.  Which we said was zero.  So we get 1+0, which is 1.”  He waved the slate in triumph.  “You can do it again and again to get 1+1+0, then 1+1+1+0…”

“So you can make it add up to any integer you like?”

“Yes…” Jack’s voice faded as if he’d been telling a joke that had fallen flat.

Shval transfixed him with her cuttlefish eyes.  “And you don’t see the significance of that?”

Jack looked blank.

“Every groubian child was made to learn it by heart.  It’s what impelled us to reach out from Titan and colonise Mars.  And from Mars we reached out towards Gaia and Selene.  And from Selene we hoped to reach for the stars.”

“I still don’t see…”

“Look up.  Look up at the sky.  Can you see the stars?”

“There’s too much haze…”

“Then it’s no good asking you to count them, is it?”  She took the slate and brandished it.  “Now look at this…”  She began to write.

Jack did as she said, eyes growing wide with dawning awareness.

“The series Σ(AnAn) stands for the activity of the species.  It’s folded-in on itself, like a snake eating its tail.  For every buyer there’s a seller.  For every lover there’s someone who is loved.  For every killer, someone has to die.”

Jack’s voice was dreamlike.  The lover who strikes you dead.  For ‘lover’ read ‘double’.  Read ‘partner’.  Read ‘complementary part.’  For every element An there exists a minus-An.  The sigma of the combined series is its valuta:  its net worth.  To someone brought up to think of the universe as finite, the net value is always zero.”

“Precisely.  You gaians insist the universe is finite.  But to a groubian that’s just a play on words.  Try counting the stars.  And when you get to the last one, then tell me that their number is finite.”

Jack sat with his mouth in his hands.  “But of course I never will…”

“So gaian mathematics is nothing but a silly game with symbols that cannot possibly bear the meaning placed on them.”

“That’s what Turing said.  Most mathematicians don’t believe him…”

“Words… words.  We groubians do not think in words.  Our mathematics is not couched in discrete symbols.  The Book of Titan bridges the gap between the finite and the infinite, the integers and the continuum.  Gaians can have no awareness of it.  When the Book of Titan imparts it, the gaian brain explodes.”

“So that’s why it’s so dangerous to gaians!”

“Yes.”

“But you’re saying groubians naturally grasp the concept of infinity?”

“To a groubian, infinity is not a concept to be grasped.  It is a decision to be taken—for life.”

Jack sank in his seat like a deflated balloon.  Now I see what you’re driving at.  Groubians can’t reproduce.  So the series no longer diverges, not even notionally.  If you stop believing in infinity, the answer’s nothing—and whichever way you add it up you’re never going to make it any different.”

They lapsed into silence.  Jack stared out of the window.  Drops of lifeless spray hurtled into the beam of the landing light and out again into oblivion.  Lightning flickered in the distance on frozen sierras jutting from cryonic seas.  Flickered and vanished.

“Are you a pious man?” said Shval at length.  “A man of faith?”

Jack winced.  “I used to be.  But what they call faith is nothing but a state of denial, a refusal to hear the evidence because it’s too painful to contemplate.  Well, in my book that’s not piety—that’s moral cowardice.”

“You speak for me too.  Fifty thousand years of moral cowardice, as regards us groubians.  An extinct species, going nowhere… but in a state of denial over it.  A state of denial bolstered by an ancient book.  Hollow footsteps… in an empty valley… leading nowhere but a dead end.  That’s the meaning of your precious Last Verse.”

All around the horizon lightning flared and glittered, an incessant feature of Titan’s surface.  Soon, through the brown murk of a titanic storm, Jack saw a flicker of greenish fire:  oxygenated gas being flared-off from the tall central stack on Platform Two.  A flame danced from the pipe-laced stack like a ribbon in a breeze.  It was their main source of light as they touched down on the landing pad, coating every strut and girder in a gruesome glimmer.

“Clip your belt to the guard-rail and hold on tight,” Shval shouted.  “The wind here is phenomenal.”

The first person they met off the ornithopter was someone calling himself the adjutant.  From behind him, rig-personnel thrust past to fetch the cargo.  The first of the baggage-handlers pushing past the other way were carrying the ectoplasts.  Jack, recalled Agent Zero’s instructions to “Metapelet” to distribute them around the place and it gave him a queer feeling.  Might one of those ectoplasts be it?

The adjutant conducted Jack and Shval through a narrow passage to the guardroom, one of four superstructure buildings which rose on stilts out of the main body of the rig.  Each building had a commanding view of one of the four orni-pads jutting out over the ocean from the rig’s corners.

In the guardroom they met the commander, a smouldering presence who introduced himself by the single word “Sprenger”.  It took a moment for Jack to recognise the bear-like man on the VIP hover-platform at Voronka Cosmodrome.

“Nimrod, eh?”  He didn’t hold out a hand or make any other welcoming sign.  “Here’s Metapelet.  She’s been waiting for you.”  He pointed to a figure sitting by the doorway of a side-office.

“Nimrod…”  The figure stood up in amazement.  Jack felt his SP unit rattle.  It was Gabrielle.

Jack glanced aside at Shval.  Just in time to catch a purple flash of consternation, before her face settled down to a neutral pattern.  She had recognised Gabrielle but was determined to give nothing away.  Among groubians only Shval could control her skin like that—and she was only managing to do so now by emulating a groubian ectoplast.

Gabrielle led them into a side-office, twisting the handle savagely to shut the door.  They sat around the desk in heavy silence before Jack spoke, his eyes boring into Gabrielle’s.  But it wasn’t to her he addressed his question.

Agent Zero… were you aware of this?”  There was a jagged edge to his voice.  He suddenly got the impression they were all just pawns in the hands of a universally-acknowledged grand master of deceit, namely Shval.  But Shval herself was giving an excellent impression of having been taken right off-guard.

“I ought to have worked it out,” Shval confessed.  “But I didn’t.  Not even TMG, I thought to myself, would have the nerve to do this to you… Metapelet.”

Jack stared at her, wondering how far she was telling the truth.   Groubians, like gaians, have difficulty telling apart members of the other human species.  But after months of close proximity on Oberon, Shval could hardly fail to recognise her erstwhile courier.

Jack stared even harder at Gabrielle.  Had she in her turn recognised Shval Meteor, or hadn’t she?  He knew how misleading he himself had found groubians’ resemblance to each other—and blushed to recall the shameful consequence of that.  Gabrielle had been anticipating the arrival of Agent Zero.  With luck she was under the illusion that this was what sat facing her, not Shval.  What she said next served to reassure Jack that this was so—but not for long.

“I thought,” said Gabrielle addressing Shval, “you knew perfectly well it was me you were speaking to over the t-unit.  And by the way… tak for sidst to you too.”

As a Selenean denizen, Shval knew enough Selensk to know what tak for sidst meant.  But she completely missed the drift of Gabrielle’s shibboleth—which Agent Zero had given her for a watchword.  She couldn’t do otherwise.  She had not been party to the voice messages shuttling between TMG and Platform Two that fateful day.  And for all her hacking prowess, she had not managed to intercept them, nor become aware of them in any way.  Neither had it occurred to Jack to mention them.

Gabrielle followed-up her breakthrough, tightening the snare around her adversary’s neck.  “Now that you’re here with the supplies you had me order, we’ve got everything we need.  Or should I say… you need?”

But Jack remembered what Agent Zero had said to Metapelet.  He knew that Gabrielle was referring to the ectoplasts—something to which Shval hadn’t cottoned-on.  How could he warn her?

“You’re very welcome,” Shval replied, taking a guess at what was meant.  “As it happens we’ve brought along our own hibernator.  It’s out in the flopper.  We’ll send out for it when it’s needed.”

Gabrielle bit her lip, giving no sign that her bait had been taken.  Will it be needed?”

“Everyone on the Prometheus has to go in one sooner or later.”

“Yes, but why do you suppose my charge won’t accompany you voluntarily back to Mars?”

“Well, we hope so too,” interjected Jack.  He smiled, hoping vainly to soften the steel he knew had slipped into his voice.

Gabrielle was frowning now.  “Anyway, you didn’t need to bring a hibernator all the way from Prometheus.  We have hibernators here, in the sick bay.  When we get a case we can’t handle, we freeze the patient down until the next supply visit.  But my charge can walk, you know…”

“Well, that’s great,” said Shval, garnishing her voice with a brittle cheeriness.  She sensed something was wrong.  Somehow she’d made a slip-up.  Had it blown her cover?  Having to continue masquerading as her own estranged imperson in front of somebody who might or might not know who she really was, was taxing even her resourcefulness.

“I wasn’t talking of hibernators…” said Gabrielle, a hint of menace in her voice.

Desperately Jack tried to help Shval out.  “You mean the ectoplasts…?”

Gabrielle glanced towards the door as if they might be overheard.  It was a solid one however and there were no windows.  “Don’t say the e-word out aloud,” she hissed.  “Commander Sprenger was suspicious when he saw them all arrive.  What was I planning to do up there, he said—put on a pantomime?”

Jack sniggered and caught Shval’s eye, but the latter saw nothing to be amused at.  After her phantom-hunt in Bay 33, ectoplasts had exhausted their entertainment value.  In a dry voice she said “Do you think we can see Tvoul now?”

“Code-names only,” reminded Gabrielle.

“We mean the groubian you’ve got here,” grumbled Jack.

At that, the reins of self-restraint slipped from Gabrielle’s grasp and she exploded.  “We don’t have any groubians in the Special Unit,” she screamed.  “That’s what I keep trying to tell you people!”  Her fury instantly gave way to icy calm.  Fixing her eyes on Shval she carefully articulated “Right at this moment, there’s precisely one real groubian on board!”

Shval must now have sensed the only thing to do was call her bluff.  “Miss Metapelet,” she said in an electrified voice.  “You compel me to speak with the authority of the Strana of Olympia.  Tvoul Williams happens to be wanted on Mars for crimes against the transgenic laws.  I am here, with the explicit consent of your superiors, as her replacement.”

Gabrielle flushed crimson.  “There are no transgenic laws on Titan,” she retorted.  “No denizen of this mir is guilty of any sort of wrongdoing.”

Jack put his palm on the desk in front of Gabrielle.  “Hush now, hinny.”  His voice was patronising, though he’d intended it to be soothing.  “Can we just see Tvoul… please?  You said she was ready to come quietly.  And I am her father-in-law… Treaty of Moscow, like.”

Gabrielle hesitated, but only for a moment.  She knew that in the end she had no power to deny Jack access to his own close relative.  His spooky companion was another matter.  She picked up the handset of the t-unit.  “Mama-duck,” she said baldly, “how do you feel about it?”

Mama-duck, said Jack to himself.  If it wasn’t all such a serious matter he’d have burst out laughing.

“My patient consents to see just one of you.”  Gabrielle rose to her feet.  “Mr… Nimrod—would you come with me, please?”

Shval rose to her feet too.  Z-niks, even robot ones, don’t take kindly to being sidelined—and Shval meant to play her part to the finale.  But Jack patted the air, meaning she was to stay put for now.

“You can leave your uzi here, with Agent Zero,” said Gabrielle, with ironic emphasis on Shval’s cover name.  “It won’t be necessary.”

Glancing at Shval, Jack said “I’ll take it with me, all the same.  I’m covered by this warrant too, y’know, like.”

Gabrielle didn’t budge.  No doubt she was wondering how to alert Sprenger secretly to Shval’s presence on the rig.

“I have no Zasta six-shooter, as you’ll observe,” said Shval, in a move she knew was checkmate.  “It’s part of the protocol allowing the police of another mir on board.  Nimrod cannot leave his weapon here with me without violating the Treaty and provoking an intermondial incident.”

Gabrielle eyed her adversary up and down.  Out of her top pocket came the probe Jens had given her to take on board the Oberon.  She pointed it at Shval, who didn’t flinch, knowing just what it was.  It would confirm she wasn’t armed—not even with the regulation TP.  Gabrielle could see there was no immediate hope of parting Jack from his weapon.  Acknowledging defeat with a slight shrug, she turned and led the way for Jack.  But not before she’d made him detach the uzi’s magazine and place it on the desk in front of Shval.

“Ammunition is no use without a weapon, Agent Zero,” she said.  “So this won’t violate the Treaty.”

It was the best Gabrielle could manage in the circumstances.  Jack nodded in silent admiration—he’d always known how quick-witted she was.  But how could she have known about the two spare magazines he had in his calf-pockets?  They had been there ever since the day of his fateful rendezvous with the wrong Tvoul.  On Prometheus they had relieved him of his uzi—it was the one Shval had recovered from the first mate.  But nobody at any stage had thought to subject Jack to a proper search.

On her own at last, Shval got out the midget interception kit she always carried on her person.  Prying open the handset of the t-unit, she poked around inside, doing what she was supremely good at.  She was determined to miss nothing of what transpired anywhere on the rig.

…to be continued.