Page 47 of Katabasis
Curious, she tugged them out. She’d always enjoyed reading Peter’s work; it was fun to see where his thoughts matched with or diverged from hers.
The first two pages were sketches of pentagrams—four failed ways to get to Hell, and one that succeeded. She recognized those theorems; she’d spent weeks puzzling through them herself. She felt the thrill of the familiar as she traced his work, as she glimpsed at what stage and how he’d solved the same riddles she had. Peter’s process was, of course, brilliant. Several of his solutions were far more elegant than hers, and at one stage he’d bypassed a thorny formula she’d struggled with by apparently intuiting the solution. In the end, he’d settled on the same method she had—Ramanujan’s Summation, with Setiya’s Modifications. No wonder he’d realized immediately what she was up to. All their work was the same.
The last several pages were pure logic. She almost flipped past them—she hated logic and was only passingly fluent because taking Fundamentals of Logic had been a degree requirement—but something about the final page made her stop.
He’d circled and underlined the last formulas several times over. It was so unlike the rest of his handwriting—hurried, scrawled, most of it barely legible—that these conclusions must have been of great importance.
She flipped back up to the previous page and read the derivations again, taking care this time to decipher it all as best she could. The endeavor hurt her head—she’d taken logic before her tattoo, and she barely remembered what half the symbols were—but at last the scribblings solidified into a certain shape.
It was a spell for organic exchange.
Her hands went sticky with a sudden, cold sweat. She rubbed them hastily against her shirt, glancing backward at Peter. He hadn’t stirred—which shocked her, for her heart seemed then to beat so loudly it was deafening.
When had he come up with this?
She’d seen these proofs before. She’d herself chased down equations for living exchange into the most obscure corners of the library, from alchemical scribblings of Samarkand to Wittgenstein’s lost notebooks (not lost, it turned out, only hidden in a special room in the faculty library and under constant lock and key). She’d given up on exchange after a week of searching because it seemed so clearly like a dead end, and all the references kept turning up lost, destroyed, or misplaced. She should have realized someone else had gotten to them first.
Here, right before her, was the final piece of the puzzle that she’d never been able to solve.
Professor Grimes’s name on the left. And at the bottom of the page, under the right side of the equation, the thing that had first caught her eye: her own name, written in clear, bold letters. Then underlined twice. Then punctuated with three question marks.
That was undoubtedly Peter’s handwriting. She’d seen him etch her name so many times before. On labels. On stacks of papers meant for her to grade.In the corner of the chalkboard, on little jokes meant for her.Dear Alice. Ha ha.Always the same spidery letters, always fully capitalized; always theclooping into thee.
You could not perform organic exchange on yourself. This was an inviolable axiom of magick. The pentagram required the sustained consciousness of its user to take effect. You needed a human mind present, willing to believe in the logical contradiction. No pentagram that deliberately destroyed the magician would take effect. You could only rend yourself apart by accident.
You could not, in effect, use magick to kill yourself. Alice knew this to be true. She had looked into the matter, as it were. You could use pentagrams to eviscerate a soul, but you had to do it to someone else.
If Alice.
She clamped a palm over her mouth, so Peter would not hear her panicked whine.
There was only one possible interpretation for what she was looking at.
Peter intended to trade her soul for Professor Grimes’s.
Peter was going to trap her here in Hell.
Chapter Eleven
Two principles ground the whole of classical logic. They are the Law of Noncontradiction and the Law of the Excluded Middle. The Law of Noncontradictionholds, quite simply, that two contradictory propositions cannot both be true at once. You cannot have both P and not-P. It cannot be true both that it is snowing and that it is not snowing. It cannot be true that Alice and Peter are friends and not friends. Schrödinger’s cat is dead, or it is not.
TheLaw of the Excluded Middle holds that either a proposition is true, or it is false. There is no hazy middle ground. As Aristotle put it, sentences can be ambiguous in their meaning but not in their truth. So either the statement that Alice and Peter are friends is true, or it is false. This statement cannot be some mysterious third thing.
Many problems threaten to break classical logic. The Sorites Paradox and the Liar Paradox, for instance, are difficult puzzles that force classical logic to reexamine what it means by truth. classical logic also has yet to come up with an answer to Russell’s Paradox, which is too complicated to explain here but has to do with a contradiction of set theory. And classical logic especially falls apart as a language applied to human relationships, which are messy and complicated and often situated in that excluded middle; that space where no one is right and no one is wrong and things are neither true nor false. The upshot here is that classical logic does not know what to do with the statement:
S:Peter and Alice are friends.
Alice would always remember the momentshe first laid eyes on Peter Murdoch. Michaelmas Term, two years prior. Cambridge was gorgeous in golden autumn sun. The wind was pleasantly cool, the leaves reddening ever so slightly in a way that had always excited Alice, for the end of summer meant the start of a new semester; new classes, new instructors, and new classmates. A chance to reinvent herself, and become the person she wanted to be.
Six students had been admitted to their cohort but that afternoon only five were present at the tea in the courtyard behind the department, clutching cups and saucers close to their chests as they cautiously made introductions. There was Belinda Wilcox, an English rose whose red-gold hair and pert nose made Alice hopelessly jealous; a Frenchman and an Italian whose names she could not make out over the clamor of voices; and Calvin Bailey, a fellow American transplant from Michigan, who shared Alice’s ineptitude with all the little spoons, saucers, and tongs that went into constructing a cup of tea.
The small talk was polite and meaningless. Alice was too focused on keeping her hands from shaking to say much. She felt badly out of place—American colleges were grand, but they didn’t havehistory, didn’t havetradition, and her advisor at Cornell had actually invited her to a sit-down dinner in which he taught her how to use cutlery before she flew out to London—and the easy shine and polish of her new cohort-mates made her feel doubly inadequate. Even the Europeans seemed more fluent in British English than she was; she could barely keep up with what they were saying. She didn’t know what a tripos was; she was still saying “math” in the singular; she didn’t understand what anyone meant by Mill or Peterhouse. That morning she’d put on her best summer dress, a frilly yellow thing with a lace collar that normally made her feel sharp, but now, among her sleek, darkly dressed colleagues, she felt like a cheap and gaudy daffodil.
She tried to squash her anxieties and focus on Belinda, though up close Belinda was so dazzling it was hard to get any words out. The sun kept catching her eyelashes in a manner that was truly unfair, for how could lashes be so dark and shimmering both at once? Belinda was telling some story about a Chinese undergraduate she’d mentored over the summer—“Her English was fine, and she was very sweet and polite and all that, but myGod, she never talked. It was only everYes, Belinda, orI’m great, Belindain these little simpering tones—and I was getting really angry at her for it, that is, the fact that she was so uninteresting, because being boring is a trait I findunforgivable. And then halfway through the summer she revealed that her father is one of the richest men in Taiwan, one of those real estate millionaires, and he didn’t approve of women in the sciences, and she’d told him she’d come to an art history program and was learning magick on the sly! Can you imagine!”
Something in this story disposed Alice to not like Belinda but she couldn’t immediately articulate why, especially as the punch line to this story indicated that Belinda wasnotracist, and everyone else was laughing so hard. Anyhow Belinda had pulled all the attention into her orbit; there was no other conversation to escape to.
“Did you do your undergraduate studies here as well?” Alice managed.
