Page 12 of Katabasis

A lice awoke to Peter’s arm slung over her chest.

She registered this and, before throwing it off, lay there for a moment, considering.

It did not feel terrible. Hell got very cold at night, and the warmth Peter emanated—she’d forgotten how hot he could get; really, he was a proper furnace—was rather nice.

She shifted slightly, just to work out a kink in her neck, and decided she may as well lie there a bit longer.

She was really quite comfortable. The sun wasn’t up yet.

A sleeping, silent Peter was less annoying than a waking, talking Peter.

And it was the first morning in a long while that she hadn’t woken up to dry-heave from stress.

The enormity of the problem, the mess of conflicting reports, the piles of scrolls left to decipher, the sense of a clock ticking down.

That was done. The research bore fruit, it had all worked , she’d made it to Hell. Now all she had to do was survive it.

Something hard dug against her thigh.

“Jesus!”

She scrambled away, yanking the blanket off them both. Peter awoke with a panicked, “What? What?” Then he glanced down at his lap and yelped. “Fuck—I am so sorry—”

“It’s fine.” Alice’s cheeks burned. She wanted to fan herself, but that would only make her look like a panicked Victorian lady, so instead she pressed her palms against her cheeks.

A dizzying wave passed through her temples.

Peter sat with both hands covering his crotch, and this only made things worse, because it drew attention to the thing and now they couldn’t not talk about it. “It’s fine, just please—”

“We don’t have control over it,” said Peter. “I mean—men. It just happens sometimes, when we’re asleep—I didn’t meant to—I mean, I’m so sorry, I really—”

Alice dragged her palms down her face. If only she could melt the flesh off her skull. “Don’t worry about it.”

“It’s not you,” said Peter. “Really—it’s not even sexual—I mean, it’s just an instinct—”

Instincts are often sexual , whispered the part of Alice’s brain that had sat through all those seminars on Freud, but she shut this down. “Yes, I’m aware.”

“I don’t think about you like that, truly. I haven’t ever—”

“I’m sure.” She had a terrible urge to punch him, accompanied by an even more terrible urge to wail as loud as she could. Neither seemed appropriate, so she settled for a muted, keening sound into her palms. “I know how male anatomy works, Murdoch. Please. It’s fine.”

“I would never disrespect you on purpose.” Peter seemed about to cry. “Never, ever —”

“Stop,” she gasped. “Please, can we just—can we eat some breakfast.”

“Yes. Breakfast.” Peter reached for his foil of Lembas Bread, grabbed it by the wrong end, and spilled food all over the gray sand. He stared at it in dismay.

“It’s fine,” Alice choked. “Have some of mine.”

They sat opposite one another and chewed, blinking very much and saying nothing.

There was nothing to look at on the monotonous desert plane, so Alice could only stare into space if she wanted to avoid Peter’s eye, which she could not do without being very obvious about it.

Instead she concentrated on her Lembas Bread. Cardboard. Mm.

It was an excruciating morning.

Somehow Alice had not given much thought to the daily indignities of the journey, and she had not accounted for daily hygiene, let alone daily functions in the presence of another.

They packed their things and freshened up in silence.

Peter had to pee, and Alice had to do the other thing, which she piled sand over like an embarrassed cat.

She reflected on the horrors of embodiment.

In many ways, she thought, the Shades had it much better.

Finally Peter broke the silence. “Maybe—maybe we should think about charting the rest of our way.”

“Hm?”

“Through Hell, that is.”

“Oh—yes, all right.”

He pulled a notebook out of his rucksack and began fumbling through the pages. “Honestly, I didn’t expect to get this far. I really hoped he’d be in the fields.”

“I did too.” Alice brushed the crumbs off her lap and then reached into her rucksack for her own notes. “But I’ve got some maps drawn up...”

“Me too.” Peter turned his notebook around to show her. “Suppose we head for the Court of Desire first?”

“Desire’s the Second Court.”

“Yes, but I think we can skip over the first, don’t you?”

“I’ve no idea how we would do that.” Alice peered down at his notes, frowning. Peter’s map of Hell looked bizarrely like a pizza. An anus, really. He’d circled in red a dot at the center, with courts branching off all around and arrows pointing in all directions. “What map is that based on?”

“The Orpheus map,” said Peter. “Penhaligon’s reprint.

Find the center, where all the courts converge.

.. which means we’re looking for something like a mountain, something elevated.

The Sumeru Throne, as it were. And then we can simply make for the court we need, instead of wasting our time going in order. ”

“Oh, Murdoch, that map is trash.”

“How do you mean? Everyone cites Orpheus.”

“Orpheus was mad with loss,” said Alice. “He was driven solely by longing for Eurydice.”

“So?”

“So he didn’t care about anything around him. From his perspective of course it was a straight line to wherever Eurydice ended up because that’s how it went in his mind’s eye. That map is worthless. It’s a fantasy of grief.”

Peter lowered his notebook, deflated. But this was a virtue of Peter’s—he wasn’t an asshole when proven wrong. “How do you figure, then?”

“I subscribe to the accumulative theory.” Alice flipped to her own maps to demonstrate.

“That is, the courts proceed in order of karmic severity. First Pride, then Desire, then Greed, et cetera and onward. Now, there’s some disagreement over whether one sin really entails all the lesser ones.

For instance, if you’re guilty of wrath, do you necessarily need to be punished for pride?

Does greed entail desire? Is it all a nesting doll of wrongdoing, or can you skip over some courts?

It’s not clear to me how the judges handle that.

But it does seem that you’ve at least got to travel in order.

And when you’ve passed, you get to cross the Lethe over to Lord Yama’s throne. ”

Alice tapped a black line running round the edge of the courts. “The river Lethe runs perpendicular to all eight courts and marks the boundary of reincarnation. So Hell looks less like a pizza anus—”

“Excuse me?”

“And more like,” she continued without clarification, “I don’t know, a Mobius strip. The Lethe bounds all. You’re trapped on this plane until you’re done. And then you go somewhere beyond. Makes sense?”

Peter rubbed his chin. “May I see?”

“Go on.”

He hummed as he flipped through her notes. “Where did you find all this?”

“The Dunhuang cave texts.”

“I couldn’t find any translations of the Dunhuang cave texts.”

“There aren’t any. You just don’t have any Asian languages.”

“Fair enough.” Peter read a while longer, tracing his finger over each page.

It made Alice oddly nostalgic to see him bobbing his head as he went along, making sense of her furious scrawls.

They used to do this in the lab—show each other their wildest ideas, and offer each other proof they weren’t insane.

She had missed Peter’s mind. It was like wearing a parachute—she could trust that he’d catch any mistakes she’d made.

At last he said, “I think this checks out.”

“Thank you.”

“But that’s consistent with my map,” Peter continued. “That is—it’s just an oversimplified version of my map, if we take Hell as non-Euclidean.”

Alice had only been to one lecture about non-Euclidean geometries, and what she remembered was a lot of diagrams of potato chips and coral reefs. “I don’t know what you mean.”

“Suppose it’s less like a... what’d you say, a pizza anus? Less like that, and more of—well, a spiral.” He drew a diagram below hers to demonstrate.

“Suppose we’re in hyperbolic space,” he said. “Take the parallel postulate out of Euclidean geometry, and assume we are dealing with negative curvature. Then we might visualize the courts as a twisted pseudosphere, bounded on the outside, but infinite on the inside—”

“But we’re not in hyperbolic space,” said Alice. She did not know much about hyperbolic space, but this at least seemed obvious. “We’d know , we’d see all sorts of—of freaky coral patterns around us, we wouldn’t be walking on this flat plane—”

“Actually no,” said Peter. “That’s the point.

When you’re inside it, of course it’s going to look like a flat plane.

We see the freaky coral because we’re three-dimensional beings visualizing two-dimensional hyperbolic space.

But we’re not four-dimensional beings, so we can’t actually see the wonkiness of three-dimensional hyperbolic space. Curved lines appear straight to us.”

“Oh, stop it.” As always, mathematics induced in Alice the acute urge to weep. “What’s the point ?”

“The point is that we could just head to this peak here.” Peter tapped the top of the spiral. “The center of Hell, the point that oversees the rest of the Eight Courts.

“Sure,” said Alice. “ If that point exists. If this is hyperbolic space. Which we don’t know.”

“I think we probably do, though,” said Peter. “I mean, how else to make sense of that weird view from above?”

“But that wasn’t a pseudosphere, that was just chthonic flux.”

“I don’t think so, Law. I interpret that as Hell signaling its geometry.”

Alice was unconvinced. “I interpret that as Hell screwing with us. It’s just as likely.”

They stared at the notebooks. This was an impasse. Two maps, and no good reason to prefer one over the other.

“I wish I could measure the speed of light here,” Peter said unhappily. “And also the size of the known chthonic universe.”