Knot Theory

Rain struck the skylights in hard, separate taps. The loft held the sound and gave it back off the clean wooden floor. Tamsin sat cross-legged in the middle of it, a panel of canvas across her knees, needle going in and out at the same pace as the weather. A coil of soft line lay by her hip. Another waited nearer the bench, pale against the boards.

Mei had the old couch and a stack of papers that kept trying to slide. She pinned them with one elbow and read as if the room were a lecture hall that had forgotten its chairs.

“A knot,” she said, “is an embedding of a circle in three-dimensional space. A closed loop. No ends.”

“Mm.” Tamsin drew the thread through and didn’t look up.

“Which means what you do all week is not knotting. You make hitches. You make bends. You leave a tail and call it finished.” Mei turned a page with a snap. “Sailors’ knots are fake.”

Tamsin bit the thread and smiled at the canvas. “There it is.”

“There what is?”

“Sunday.” She set the needle in the hem and finally looked over. Mei’s socks were mismatched. One had a hole at the toe. The papers had a ring on the top sheet where a mug had sat too long. “You start it the same way every time. Closed loop, no ends, sailors are frauds.”

“Because it’s true.” Mei swung her feet to the floor. The couch complained. “Your bowline has two ends. A mathematical knot cannot be undone without cutting. Yours come apart if you sneeze at them. That’s not a knot. That’s a suggestion.”

“A suggestion that holds a sail in a gale.”

“A gale is not a proof.”

Tamsin stood, stretched the ache out of her shoulders, and crossed to the kettle on the side bench. Steam had already fogged the little window above it. She poured two mugs of tea, strong and plain, and carried one over.

Mei took it with both hands. “Thank you. I’m still right.”

“Drink that before you declare war.” Tamsin sat on the arm of the couch, close enough that Mei’s shoulder brushed her thigh. “A loop with no ends is a picture. Pretty. Useless in weather. You can’t tie a circle to a cleat.”

“You can prove things about it that you will never prove about a bowline. Invariants. Crossings. Whether two tangles are the same tangle wearing a different coat.” Mei sipped and made a face at the heat. “Your knots are costumes. Take the costume off and there’s just rope.”

“Take the costume off a closed loop and there’s nothing to hold the boat.” Tamsin nodded at the coils. “Soft line. Cotton. I use it for teaching and for hands that aren’t mine. It holds. Then it doesn’t, when I say so.”

Mei studied the nearest coil. The rain thickened. Water ran in sheets over the glass overhead, and the light in the loft went grey and even.

“Show me,” she said.

“You’ve seen a bowline.”

“Not as an argument.” Mei set the mug on the floor, careful of the papers. “On me. Sleeve. So I can watch the lie you tell with your hands.”

Tamsin went quiet in the way she did when a job got interesting. She slid off the arm of the couch, picked up a short length of the soft line, and crouched in front of Mei. The floor was cool under her. Mei’s sleeve was pushed to the middle of her forearm already, as if she had been waiting to write.

“Wrist,” Tamsin said.

Mei offered it. Not the bare skin. The cuff.

Tamsin’s hands moved without hurry and without waste. A small loop, the end through, around, back. She snugged it against the fabric until the bowline sat neat as a stitch, the tail short, one strand left long on purpose. She didn’t pull it tight against the arm. The sleeve took the hold. The wrist under it could still turn.

“There,” she said. “Working knot. Two ends. One of them is the trick.”

Mei didn’t answer.

She had gone very still. Her tea sat forgotten. Her eyes stayed on the loop where the cotton crossed itself, on the way it bit the cloth and not the skin. Color rose in her face and stayed. She didn’t joke. She didn’t reach for the definition. She just looked, and looked, and didn’t take her eyes off it.

Tamsin felt the change before she named it. Mei’s breath had shortened. Her free hand had closed on the couch cushion. The argument, which usually filled the loft from skylight to floor, had stopped in her mouth.

“Mei.”

“I’m looking.”

“I know.” Tamsin kept her voice even. She didn’t tug the line. She didn’t smile yet. “You’ve looked at a bowline a hundred times and called it a party trick. You’re not doing that.”

Mei swallowed. The red reached her ears. “Don’t undo it.”

“I wasn’t going to.” Tamsin sat back on her heels. Rain tapped. Somewhere in the harbor a halyard knocked, faint through the wall. “Talk to me.”

Mei glanced at the door, though no one came up here on Sundays, then back at the knot. Her mouth worked. When she spoke, the words came fast, the way her proofs did when she had already lost the fight with herself.

“I’ve been reading. Not papers. Not for work.” She shut her eyes, opened them, faced Tamsin properly. “Months. Rope. On a person. How it’s supposed to feel when someone you trust puts it there and can take it off. I didn’t know how to say it. I thought if I asked you to demonstrate, the rest would be obvious, and then it was obvious, and I still couldn’t say it.”

Tamsin waited.

“I want to try it,” Mei said. “Not with anyone. With you. Here. That line, the soft one. I want you to tie me, and I want to be able to get out, and I want—” She stopped. The flush was fierce now. “I want you to be the one holding the end.”

The loft seemed to draw in around the two of them and the small bowline.

Tamsin laughed.

Not the sharp laugh she used on a bad measurement. This one came out low and surprised, almost glad. Mei flinched anyway.

“I’m not laughing at you,” Tamsin said at once. She put her hand over Mei’s free one, on the cushion. “I’m laughing because I’ve been walking around this for months with the same sentence in my mouth and no nerve to spend it. I make rope behave all day. I kept thinking if I asked my mathematician to let me put it on her, she’d decide I’d lost the plot.”

Mei stared. “You wanted to ask.”

“Since before the winter gales. Maybe since you spent an hour explaining why a trefoil can’t be the unknot and then stole my good gloves.” Tamsin’s thumb moved once across Mei’s knuckles. “I thought you’d find it strange.”

“I find your bowline strange. I find this—” Mei looked down at her sleeved wrist, at Tamsin’s hand on hers. “I find this not strange. I find it late.”

“Bossy.”

“Accurate.” Mei’s voice had gone thin and bright. “So you aren’t going to tell me a closed loop is the only real knot and send me back to my papers.”

“I’m going to tell you a closed loop can’t save you if you change your mind.” Tamsin lifted Mei’s tied wrist, careful, the cotton easy in her palm. The long end hung between them. “This can. One pull. That’s the whole point of the ones I trust.”

Mei leaned in.

The kiss landed before either of them had arranged a face for it. Mei’s mouth was warm from the tea and a little unsteady. Tamsin answered by staying, by tipping her head so the angle worked, by letting Mei set the pace for the first few seconds and then meeting her properly. Mei’s free hand came up into Tamsin’s hair and held. Tamsin’s hand stayed around the tied wrist, not squeezing, the bowline pressed between her fingers and the cuff.

They kissed like people who had done it for a year and had still managed to surprise each other. Mei made a small sound and chased it, closer, the papers sliding off the couch onto the boards. Tamsin felt the smile start against her own mouth and didn’t let the kiss break for it. Rain ran over the skylights. The canvas on the floor lifted at one corner in a draft and settled again.

When they eased apart, Mei’s forehead rested against Tamsin’s. Her eyes were open. Her breath touched Tamsin’s cheek.

“Still fake?” Tamsin asked.

“Don’t gloat while you’re kissing me.”

“I’m between kisses.”

Mei kissed her again, shorter, sure. Her fingers stayed in Tamsin’s hair. Tamsin’s other hand came up and fit along Mei’s jaw, thumb at the hinge, learning the heat in the skin there. The tied wrist turned in her grip. Mei felt it and went quiet in that new way, attention dropping to the cotton as if the argument had moved into her arm.

Tamsin found the long end without looking down. She drew it once, smooth, the way she drew a thread clear of a seam.

The bowline collapsed. The loop opened. The line fell away from the sleeve and pooled in her hand, ordinary cotton, nothing left of the knot but the memory of the crossings.

Mei watched it go. Her lips were parted. She didn’t pull her arm back.

“That’s the difference,” Tamsin said. “Mine come undone the second you want them to.”

The rain kept on. The tea was cooling on the floor beside a spilled page about circles with no ends. Tamsin held the soft line and waited, because waiting was part of what Mei had asked for, and because she could see the want arrive before the words did.

Mei lifted her chin. She looked at Tamsin’s hands, then at her face, then held both wrists out between them, sleeves and skin, steady.

“Then do it again,” she said. “Both. And don’t let go until I say.”