The Cup, the Donut, and the Thing You're Not Allowed to Do

Soren was holding a donut up to the light when Maya said the thing that started it.

"That's the same as your mug," she said.

"It's a donut."

"It's the same shape as your mug. One hole. The hole in the donut, the hole in the mug handle. Same."

Soren put the donut down very slowly, like it might be a trick. "The mug holds coffee. The donut holds nothing."

"Doesn't matter. Pretend they're made of clay." Maya picked up the empty mug and turned it so the handle faced him. "You could squish the mug. Push the bowl part flat. Keep the handle. You'd end up with a ring. A donut. Without ever poking a new hole or closing the old one."

"You can't squish a real mug."

"I said pretend it's clay."

Soren got out his notebook and drew a mug. Then he drew an arrow. Then he drew a fat ring. He stared at it. "Okay. Yeah. The handle is the hole and the bowl is just stretched material around it." He tapped the page. "So they're the same to a mathematician. The number of holes is what counts."

"One hole, one shape," Maya said. "A bowl has zero holes. A bowl is the same as a plate. Same as a spoon. Same as a banana."

"The banana is the same as a spoon." Soren said it like he was tasting it.

"Smush, smush, no holes. Yeah."

They went around the kitchen doing it. The colander was a maniac, holes everywhere. The two-handled pot made Soren laugh because it was the same as a pair of pants. They were almost finished when Maya picked up an orange off the counter and went quiet.

Then she said, "Can you turn it inside out?"

"The orange?"

"The skin. Pretend the skin is the whole thing. A ball. A sphere. Can you turn a sphere inside out?"

"Sure. Like a sock." Soren reached for the orange.

"No. A sock has a hole, that's how you reach in. The sphere has no hole. It's sealed. The orange skin is sealed if you don't break it. Can you get the inside to the outside without ripping it?"

Soren held the orange and thought. "No," he said. "No way. There's no opening. To flip it you'd have to tear it."

"That's what I think too," Maya said. "But I read it's a famous thing. Turning a sphere inside out. Mathematicians have a name for it. Eversion."

"Then they tear it."

"No. That's the whole point. No tearing. No holes. No creases."

Soren put the orange down. "Maya. That's the same as the mug-donut thing in reverse. The mug works because you never make a new hole. If you can't make a hole, and you can't tear, then the inside stays in. It has to."

"That's what makes sense," Maya agreed. "So either the math people are lying or we're missing something."

They both looked at the orange.

"Read me exactly what it said," Soren said.

Maya found it on the tablet and read slow. "You can turn a sphere inside out without tearing it, if you allow the surface to pass through itself."

The kitchen got very quiet. "Pass through itself," Soren repeated.

"Like a ghost," Maya said. "The orange skin would be allowed to slide through the orange skin. Two layers in the same spot at the same time."

"You can't do that with an orange."

"No. You can't do it with anything real. That's why it's only a math thing." Maya was up on her knees on the chair now. "But here's what gets me. With the mug, the rule was no new holes. And that rule held. The mug stayed a donut forever. Solid rule."

"And with the sphere there's a different rule," Soren said slowly. He picked his pen back up but didn't write yet. "No tearing, no creasing. But it turns out the surface is allowed to overlap itself. That's a thing you're allowed to do that I didn't even know was a category of allowed."

"You thought there were two boxes," Maya said. "Allowed and not allowed. Stretch, allowed. Tear, not allowed."

"And there's a third box." Soren's voice went up. "Pass through yourself. Which is impossible for an orange and completely fine for the math."

Maya grabbed two clear plastic bags from the drawer, the kind for sandwiches. She pushed one inside the other so they nested.

"Watch. This is the inside one." She wiggled it. "To turn it inside out I want the inside one to become the outside one. And if I'm allowed to let the plastic go through the plastic, like they're both ghosts, I can sort of, ugh, I can't actually do it with my hands. But I can see the move. The inside layer balloons out, passes right through the outside layer, and ends up wrapping it. No rip. They just shared space for a second."

Soren took the bags. He pushed. The plastic crinkled and bunched and refused, because it was plastic and not a ghost. But his eyes were going somewhere the bags couldn't.

"So the orange can't," he said. "And the bag can't. And nothing I can hold can. But the sphere itself, the pure one, the one that's only a sphere and not made of anything, that one can. Because the only thing stopping it is being made of stuff."

"Being made of stuff," Maya said, "is the only reason no."

They sat with that. The orange on the counter. The mug that was a donut. The two bags that wanted to be a ghost and weren't allowed, here, in a kitchen, with hands.

Soren turned the orange over once. Then he set it down exactly where it had been, very gently, like it might decide on its own to begin.