Page 42 of Katabasis

Alice was doing much better. A fog was clearing from her head. It was the first home-cooked meal she’d had in ages—at the department, it was all Lembas Bread and cold tea—and she ate with such enthusiasm that soon all that was left was a neat pile of bones sucked clean.

She set her plate down. A wet burp escaped her mouth. “Sorry.”

“Excuse yourself.” Elspeth looked very pleased. “I’m glad you liked it.”

“So, Elspeth.” Peter set his fork down. He had not looked once at Alice since Elspeth’s return; now he spoke as if she were not there. “I’ve been wondering. How are you and the Kripkes using magick?”

“How do you mean?”

“We thought—perhaps it doesn’t work down here. The sand eats it up.”

“Oh.” Elspeth laughed. “You haven’t figured that out?”

She drew out a knife from her belt. Alice and Peter both instinctively shrank back, but Elspeth held the point to her own wrist and pressed. What bubbled out was not blood, precisely, but a thick, black-blue sludge.

Elspeth extended her other hand. “Chalk?”

Peter fished about in his pocket and handed her a stick.

“Anything you need patched up?”

“Cuts and bruises,” said Peter.

“Of course. Will Curry’s Paradox do?”

“Probably, yeah.”

They both watched in awed silence as Elspeth dipped the chalk in her not-blood like it was an inkwell and drew a perfect circle on the deck around her ankles. The pentagram was not a pristine white but a phosphorescent green that cast a pallid light around her ankles. But it did not sink away.

Curry’s Paradox. Commonly taught in Introduction to Analytic Magick classes, this was a silly play on conditional statements and self-reference that could, just for an instant, make true any arbitrary claim.

Consider: If this statement is true, then pigs can fly .

Call this statement S. Statement S has the structure “If S, then P.” If you write it out as a logic proof, you will discover you do end up proving S true, for you do end up writing “If S, then P.” So the statement S is true, and pigs can fly.

The statement is S true, and Peter has no wound.

“There you go,” said Elspeth.

Peter withdrew his arm, running fingers over soothed skin. “Thanks.”

“I figured that out long ago,” said Elspeth.

“It’s the only thing that makes the chalk take effect—some kind of life force.

It congeals with the living-dead force of the chalk.

Adds some sort of... insulation, I suppose, against the silt.

Though it doesn’t work so well with my blood.

Whatever this is”—she patted her pale, not-bleeding arm—“seems a pale approximation of the real thing. It’s vital force that’s the key, it seems. Not much force one can draw from a Shade.

But your blood... it’s warm, it’s bursting. ”

She blinked at the knife, then blinked at Peter and Alice with an uncomfortably hungry look. Alice slid her sleeve over her wrist.

“Just a little dip, then?” Peter asked. “That’s all you need?”

“The more, the better. The effect seems proportional to—well, the sacrifice.” Elspeth blinked again, then set the knife down. “Curry is easy. Doesn’t take much.”

“How much would a harder spell take?”

“Depends on your blood,” said Elspeth. “With Shade’s blood, quite a lot. Living blood, I don’t know.”

“Should we try it?”

“Do Banach-Tarski.” Alice spoke up. “Do Banach-Tarski on your flask.”

The Banach-Tarski Paradox proved you could cut apart a ball into a finite number of subsets of points and reassemble them into two balls equal in volume to the first. Alice could not perform it herself; she understood only that it involved heavy maths, and had something to do with set theory and little infinities.

But she knew Peter knew it, and that was good enough.

The thought had been lurking at the back of her mind. She needed a working flask. Hers was soiled. Peter’s was fine. Alone she would quickly die of thirst, but with a copied flask she would be all right, independent—free to go her own way.

If Peter had considered the same implications, he did not show it. He reached for his rucksack and pulled out his flask.

“Now the blood,” said Elspeth. “Knuckles are best, you won’t hit a tendon.”

Peter hesitated.

Alice drew her knife. “Here.” She dug the sharp end into the knuckle of her thumb, harder and harder, until blood beaded around the metal. “Is that enough?”

“Might be,” said Elspeth.

Alice held her hand out to Peter. He paused just a moment, then pressed his chalk against her thumb. The chalk soaked it up like a sponge; in seconds the entire stick was red.

Quickly Peter drew a circle around the flask, inscribed the paradox, and chanted it out loud.

The Perpetual Flask shimmered. Peter reached in and drew it out.

When he lifted it from the center its double remained, still in place.

Alice, watching, could not help a little sigh.

For no matter how many spells she had seen, no matter how long she’d studied magic, the act itself still astonished her.

That you could fool the conservation of mass.

That a thing could be one, and then two.

“Try it,” said Peter.

He was right to check. Banach-Tarski copies didn’t always work.

For one thing they always seemed flimsier.

If it was food, it never tasted as good; if wine, it lacked depth—as if it knew it owed its existence to a mathematical loophole.

They had a bad habit of randomly vanishing on you—two decided to reunite as one—but Alice couldn’t do anything about that.

She untwisted the flask and tipped some water in. She drank. It tasted clean, fresh. “It worked.”

“Good.” Peter would not look at her. “Keep it.”

“Thank you.” Alice slid the doubled flask into her own rucksack. Her thumb was still bleeding. She twisted it into a corner of her shirt and held it tight.

“So the Kripkes.” Peter turned to Elspeth. “Whose blood...”

“Come on,” said Elspeth. “Why do you think they’ve got all those patrols?”

Peter blinked, speechless. Alice shuddered. Elspeth appraised them with grim satisfaction. “Think hard,” she said. “In all your research in Tartarology, have you found a shred of documentation from the last decade? Tell me. I’m really curious.”

Peter tilted his head. “Huh.”

“None.” Alice was certain about this. “Not even gossip.”

“And why do you think that is?”

“Don’t tell me the Kripkes got to them all,” said Peter.

“The Kripkes ensure there are no survivors.” Elspeth nodded.

“Any magician comes down here, the Kripkes hunt them. No one’s going to make their way back from Hell before the Kripkes do, you see.

No one’s going to beat them to the scoop.

They steal their chalk, steal their notes and textbooks.

Sometimes they interrogate their prey for the latest in research developments—I’ve seen poor souls stretched out over the racks for days and days.

And always, always, it ends with draining their blood.

They fill up their bladder sacks, they drench their chalk sticks, and off they go. ”

“That’s sick,” said Peter.

“That’s research,” said Elspeth. “Nothing matters to anyone in Hell, I told you. Dogs, squirrels, the stray lost child...” Her throat pulsed. “They’re all just fuel for them. Materials for the Great Quest.”

“You keep saying the Great Quest,” said Alice. “What’s that mean?”

“They’re not calling it the Great Quest anymore? Why are you here, then?”

Alice glanced quickly to Peter. It seemed obvious the last thing they should tell Elspeth was who they were here for. “I suppose we...”

“Might be an outdated term by now.” Elspeth rubbed her chin.

“That’s what we were all calling it my year, anyways.

To Hell and back was the goal. That was all the rage.

It started with the Kripkes, and then everyone wanted to do it.

Nothing like a spectacular failure to inspire a thousand followers.

Houdini only ever freed himself from death’s jaws; he never came back from the other side. ”

“But you weren’t going on the quest,” said Peter. “You—I mean, I thought—”

“Right, just a normal suicide,” Elspeth said sharply. “But then I discovered pretty quick I don’t want to stay here, do I?”

Peter bobbed his head. “No, that’s very reasonable.”

“So now I’m on the Great Quest, same as the Kripkes. And we’re all looking for the same thing to get out.”

“And what’s that?” asked Peter.

“Why, the True Contradiction,” said Elspeth. “The Dialetheia.”

Alice nearly dropped her plate with excitement.

The power of a true contradiction—Contradiction Explosion—was the first thing anyone learned in logic class.

Ex contradictione quodlibet —from a contradiction, anything follows.

If you had a True Contradiction, then you could prove anything.

Indeed, it exploded your boundaries of proof.

She had been taught the silly, informal version: if you could accept the simple contradiction that one and two were the same, you could prove you were the Pope.

You and the Pope are two. Therefore you and the Pope are one.

More rigorously, once you had a logical contradiction in hand, you could inject any statement into a proof using disjunction.

You could prove the sky was green. That rocks were bread, and water wine.

For a long time Alice had pursued the Contradiction Explosion as a way to get Professor Grimes out of Hell.

But the trail kept running cold, and eventually she’d given up.

The only basis anyone had for believing there existed a True Contradiction was the unlikelihood of Persephone’s persimmon seeds, but those seeds might never have existed at all.

“I thought the Dialetheia was a myth.” Peter echoed her thoughts. “There’s just no literature—I mean, it’s all just conjectures—”

“Only because no one in the modern era’s found one.” Elspeth huffed. “But we’re overdue for a discovery, and mark my words, it’s going to be me.”

“Wait.” Alice leaned forward. “You know where to find one?”

“I have some leads,” said Elspeth. “I’ve been at this for a decade. One does make some modest progress.”

Peter asked, “So where is it?”

But Elspeth’s face closed up. She looked between the two of them, fingers tapping against the floor. “Well,” she said after a pause. “Don’t suppose I’m about to just tell you.”

“Oh,” said Peter. “Sorry—”

“Don’t get me wrong. You seem like very nice kids. It’s only I barely know you, and all that. And it’s not like there’s dozens of True Contradictions to go around.”

There was an awkward silence—not unlike that which descended on a room of scholars who realized they were all interviewing for the same job.

Alice felt a bit wounded, for she had thought they were getting along quite well. But then she supposed, from Elspeth’s perspective, they were no different than the Kripkes. They’d both only come to Hell for research purposes. And they were both Cantabrigians.

“You’re welcome to stay on the boat, though.” Elspeth gathered up their plates, tipping the bones carefully into a tin can. “I’m not like Nick and Magnolia. I won’t drain your blood in your sleep. Only I hope you’re not offended if I don’t share everything I know.”

“No, of course.” Peter’s voice was curiously flat. Alice could not read his face. She thought she saw something dark in his expression, but what to make of it, she didn’t know. “You’ve been very generous. We couldn’t ask for more.”

“Anytime,” said Elspeth. “We’ve got to look out for each other, we magicians. It’s a sad world when we don’t.”