Page 103 of Katabasis
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”
On Paradoxes
The reason why paradoxes trouble us is not because their conclusions are true. The donkey does not starve. The world does not consist of unending staircases. Of course Achilles could outrun a turtle, of course the arrow hits its mark, of course the heap runs out. The principle we must accept if we want to go on with our lives is that no paradox makes the world stop functioning as it should. The laws of the universe get their say. Things always snap back to how they should be, and a paradox always eventually runs out its charge. The only reasons why paradoxes perpetuate for as long as they do is because we let them.
No—the reason paradoxes trouble us is because their absurd conclusions make us rethink all of our premises. A paradox is like a staircase, in which each step leads inexorably to the destination. But you get to the top, and the destination is impossible; you’ve stepped off into empty air. So one of the steps must be folly. Because the conclusion must necessarily be false, because we cannot live in a world where logic does not work, one of our premises must necessarily be flawed. This is the source of our unease. A paradox means that somewhere along the path, we have gotten something deeply, terribly wrong.
Chapter Twenty-Four
Late summer in Cambridge, two weeks to Michaelmas. The town was birdsong and rippling water and the barest hint of red peeking around the edges of the leaves, and the sun still shone warm enough to make you forget, year after year, the winter rains around the corner. Everything was new and shiny and full of promise.
Alice Law tripped up to the department in a brand-new pencil skirt and stiff white oxford shirt. She had ironed both herself that morning in a panic; she thought she’d seen a crease in the mirror on her way out the door. She could still feel the heat of the iron as she paused before the main entrance, one hand on the door handle, bracing herself for her first meeting with her new advisor.
The night before she had flown her first transcontinental journey, then ridden the late train from King’s Cross to Cambridge station, then dragged her trunk the two miles north to her little room in Audley Cottage. Everything was new and exciting—the taste of digestives, the bright red telephone boxes, the cars zooming down the road on the right. When she stepped outside that morning she felt she had traveled across both space and time, down the rabbit hole and into a fantasy of her own making, into a more genteel and colorful world. She felt that she had jumped through the last hoop. They had finally let her into the club.
She had not yet met Jacob Grimes in person. She’d watched him present at a few conferences in America but never summoned the nerve to go up and say hello. Every conversation they’d had since her acceptance had been through the post—Professor Grimes seemed to hate the telephone—through which she’d tried to glean clues about his personality. He struck her as blunt, casual, and a bit scattered—he’d asked her the same question about her arrival date thrice over two months. But what else could you expect from the greatest magician in the world?
She steadied herself with a breath, opened the door, and stepped through. The building was silent. Term would not start until next month; the campus was empty. Professor Grimes’s office was at the end of the hall. The door hung slightly ajar. Alice saw, with relief, that someone was sitting behind it. She knocked.
“Come in.”
“Good morning,” she said, and her voice cracked only a little. “I’m—I’m your new advisee. Alice Law.”
“Hello, Alice. Have a seat.” He came around the front of his desk and stood leaning against it, hands clasped before him as he stared down at her. Afterward, she couldn’t say what he looked like. It would take several weeks of blinking out of the corner of her eye, registering his profile, his height, the faint beginnings of a stoop. Professor Grimes was like the sun. She couldn’t look directly at him, she could only sense his presence from the edges. “It’s lovely to meet you.”
“I’m so excited to be here.” She’d rehearsed this statement many times over but could never make the words come out in a way that didn’t seem fawning or stilted. Now they tumbled out her mouth all out of order, breathless and silly. “It’s such an honor to be working in your laboratory—I’m so grateful to be here, I can’t wait to get started—”
“You sound nervous, Alice.”
“I—I am.” She swallowed. “Well, of course I am.”
“Don’t be.” He smiled, and for the first time Alice understood what it meant for someone’s eyes to literally twinkle. “You deserve to be here. Yours was the strongest application I’ve read in a long while.”
“Oh.” Alice’s eyelashes fluttered, actuallyfluttered, and her fingers twisted frantically in her lap. She had prepared for a litany of questions. She was waiting for Professor Grimes to realize he’d made a mistake in accepting her; she still felt she had to pass a test. She had no idea how to react to such a compliment. “I don’t know what to say.”
