Page 65 of Katabasis

Peter sat hunched over an array of papers, still scribbling. He’d filled out eight sheets at least since she’d drifted off—all covered in crossed-out, circled, and shaded-in algorithms.

“Our way out,” he said. “I’ve got it.”

Reluctantly she sat up. “What?”

“It should have been obvious.” He spoke at a quick, robotic clip, a voice Alice knew quite well.

It was the voice he always took on in lab when he’d figured something out; when he needed to get it all out at once but couldn’t get his mouth to keep up with his thoughts.

“Something I know from introductory logic. A silly game, really. It’s got to do with types of knowledge and probabilities.

But perhaps I shouldn’t tell you, it’ll weaken the paradox—”

“Murdoch.”

“Okay. Listen.” He drew a neat circle between them, just large enough for two to stand side by side. “Would you say that when the Kripkes come, it will be a surprise?”

Alice couldn’t determine the significance of this statement, but neither could she find a problem with it. “Ah, sure.”

“And would you say that they must come sometime between now and when we starve to death five days from now, otherwise our blood will go bad?”

“I suppose that’s what I would do.”

“Excellent.” He pressed his palms together. “Then the conditions are set.”

Her head hurt. “I still don’t understand.”

“Just listen,” said Peter. “Now, suppose a prisoner is awaiting his moment at the gallows. The hangman tells him he’ll be hanged sometime in the week, but otherwise he is not to know the date of his execution. Which day of the week can we rule out, then?”

Alice pondered this, and then ventured, “Sunday?”

“Good. Why?”

“Because it’s the last day of the week. So if he hasn’t been hung on any of the previous days, then he’ll know it’s happening Sunday. Only then it won’t be a surprise.”

“Very good,” said Peter. “So Sunday’s out. What happens, then, if he still hasn’t been hung by Saturday?”

“I suppose Saturday’s out too.” Alice’s thoughts churned sluggishly.

“Because Sunday’s out, which makes Saturday the last day it could happen, but if it hasn’t happened by Friday, then Saturday isn’t a surprise either.

.. Oh.” Something clicked in her mind. “But then Friday is the last day it could happen...”

“You see,” Peter said gleefully. “It’s recursive.”

Alice saw now. “So then the prisoner can never be hung, because none of the days will be a surprise. And they have to let him go.”

“Precisely!” Peter beamed. “And are not the conditions perfect for this paradox? We know we will expire in five days. We know the Kripkes always come when least expected. But if we map you onto the Hangman’s Paradox, then you are invincible—they can never get you at all.

So my hypothesis is if we write this into an algorithm, it releases you from the trap—that, or constructs some shroud of invulnerability, so that even if they come they can’t hurt you—”

“Fine,” Alice sighed. Stupid, ineradicable hope crept back into her chest; stupid, exhausting feeling . Things had been so much better when she’d only been numb. “Give that here.”

Peter slid her notebook across the sand.

She traced her finger down the lines, willing herself to focus. Slowly she made sense of his scrawls. “You’ve messed it up.”

“How do you mean?”

“You’ve written it for only one.” She tossed the pages back into his lap. “It’s no good. You have to do the whole thing over for two.”

“Oh,” said Peter. “No, I’d noticed that. That was intentional.”

It took her a moment to register what he meant by this. “Murdoch...”

“It’s not a very strong paradox,” said Peter. “It’s not like Sorites. There’s a couple of obvious solutions, and I know them far too well. I can’t suspend my disbelief long enough for it to work.”

“All paradoxes have solutions.” Alice fought a rising swell of panic. “That’s why they’re temporary.”

“ Very temporary,” said Peter. “I’m afraid this one is particularly flimsy. And against something like an Escher trap, there’s really no room for doubt.”

“Then how do you know it’ll work on me?”

He cast her a soft smile. “Because you’re not a very good logician.”

“Fuck you, Murdoch.”

“Get in.” He gestured. “Let’s send you out.”

“I am not leaving you.”

“And I’m not letting you die,” said Peter. “We can’t have come all this way for nothing. You said it yourself. This all has to be worth something.”

“Then we go in together.”

“Not sure that’ll work.”

“Well, we’ve got to try.” She smacked the notebook. “Rewrite it. Set it for two.”

“It won’t work for me,” Peter insisted. “And when it doesn’t work, you’ll be a corrupted subject as well, and then you won’t get out either—you’ll die —”

“I’d rather die.” She meant it. She’d never meant anything so much in her life.

A week ago she hadn’t been able to say she’d save Peter’s life with certainty—but now, she knew.

She didn’t want to live. Didn’t want the future, this stupid goal they’d been chasing.

“We both live, or we both die, there’s no third option. ”

“The third option is you live . You deserve to live—”

“I don’t deserve anything.” Alice meant this, too.

What had she done since they’d come to Hell?

Lied, betrayed Peter, betrayed Elspeth, landed them all in this sorry mess.

It was about time she closed the book on this pathetic story.

She was so very tired—she only wanted now to expire quietly in the dark, but Peter wouldn’t even let her do that.

“I don’t, I really don’t—oh, gods, Peter, just let me die. ”

“Can’t. Won’t.”

“Why are you being so noble?” She would have beat him with her fists, if she could muster the strength. “Stop being so noble.”

“You’re the only one with an algorithm to bring him back. Mine doesn’t work. I get out, and the only person we send back up top is Grimes. You get out, and at least you get home alive.”

Violently she shook her head. “I don’t know if the Erichtho spell even works—”

“Well, there’s a chance it does. You’re the only one with a positive outcome here, Law. It’s just how the numbers fall.”

“I don’t care about the numbers!”

“Anyhow, you’re the only one who didn’t try to kill him—”

“You didn’t kill him. I did. I remember I didn’t close the loop. I remember, I don’t forget —”

“I double-checked the submission after. You didn’t close the loop because there was no closure. I never put it in.”

“But still I should have known.” Alice did not make mistakes; she couldn’t. She saw everything; every detail was seared in her brain. And the only way she could overlook a thing like the Ant Test was if some part of her intended it. “I’ve been over this a thousand times. I saw the gap, I knew —”

“Stop it.” Peter flung up his hands. “Just stop. We are not fighting over who gets credit for his murder . Who cares about the details—”

“The details matter,” Alice insisted. “They matter because you think you deserve to die when you don’t , when it’s not your fault at all, and you did nothing wrong, and you shouldn’t even be down here—”

“The fact remains.” Peter raised his voice, spoke right over her. “I can get this paradox to work on you. I am absolutely certain I can make it work. I have almost no certainty about the two of us. So that’s just basic decision theory, Law. Maximum expected outcome.”

“Shut up.”

“It’s just maths. I’m sorry if you don’t like it.”

“But you can’t die here.” She swallowed. “Not when—not when I’ve just—”

There was something wild, desperate in Peter’s eyes. “When you’ve just what?”

What did she want to say? Alice didn’t know.

She didn’t have the words for this pit of feeling, dark and gnawing and delirious.

She wanted to hurl herself into his unknown; wanted an intimacy she couldn’t describe.

She wanted him alive; near; beside her. The words that came to mind were clumsy and insufficient, but they were all she had.

“When we’ve just learned not to hate each other. ”

Something closed in Peter’s face.

They stared at each other, a chasm yawning between them.

Oh, why was this so hard? Alice wondered desperately.

Why couldn’t she ever tell Peter what she thought ?

Always they had been bodies hurtling just out of one another’s orbit, when all it would have ever taken was an honest word.

But that was precisely what magicians lacked; there were no honest words, only puns and illusions and constructions of reality so convoluted that you couldn’t keep track anymore of what was real and what wasn’t.

Everyone was always trying so hard to pretend they were somebody else.

If only they had caught one another, looked at each other, forced their ways across the gap.

But it was too late now, too late for everything.

Peter drew out a blade.

“What are you doing?”

“I’m deciding for both of us.”

“You can’t.”

“It’s the only rational solution,” he said. “Please, Alice. Don’t be an idiot.”

She lunged for the blade. He raised it up out of her reach.

She tried to shove him over—she tried with all the strength she had, but Peter could not be budged from the pentagram.

She smacked his arms, scratched and pulled.

But he was taller, heavier, and stronger; all he had to do was wave her aside.

“I hate you,” she cried. “You’re so—you’re such a—”

“Logician.” He gave her a sad smile. “I know.”

He drew the blade across his arm. Blood flowed thick and fast across his skin, dripped down his fingers and onto the chalk, suffused the pentagram like spreading ink until the whole thing glowed crimson.

Peter began to chant. Alice wailed. She hit him, she flailed, she railed against his grip—but he was so strong, and nothing she did could break his rhythm.

On and on he went, sonorous as ever, confident until the last.

“The rucksack, Alice.” He patted her shoulder. “Don’t forget the rucksack.”

Then, with a flick of chalk, he closed the circle.

Alice screamed, but he didn’t hear. In an instant the sand rose up around her, threw her out and blocked Peter in. The Escher trap vanished before her, cuckoo bird, boulders, and all. Then all she saw was silt, an endless flat plane, under a constant, dying sun .

“Lines that are parallel

meet at Infinity!”

Euclid repeatedly,

heatedly,

urged

Until he died.

and so reached that vicinity:

in it he

found that the damned things

diverged.

—PIET HEIN, “PARALLELISM”