How Long Is the Beach

"Two hundred and six," said Soren. He dropped the last loop of rope onto the wet sand and stood up straight, hands on his knees. "Two hundred and six rope-lengths. So the beach is two hundred and six times ten meters. That's two thousand and sixty meters."

"No it isn't," said Maya.

"I just measured it."

"You measured a straighter beach than the one that's here."

Soren looked at his rope. It ran from the black rocks at the north end all the way down to the creek mouth, laid out in long clean segments, each one exactly ten meters, each one skipping over the little bays and bumps like a bridge over a river.

"The bet was who gets the real length," Maya said. "Your rope jumps across all the wiggly bits. Look." She crouched by one of the segments. Under the taut rope the sand curved in and out, a little bay the size of a bathtub, a little cape the size of her shoe. The rope had cut straight across the mouth of it. "You didn't measure that. You went over the top of it."

"It's a rounding error," said Soren. But he was already frowning at the sand, which meant he was taking it seriously.

"It's a lot of rounding errors." Maya pulled the string out of her jacket pocket, the kind you tie parcels with. She started laying it along the same stretch of beach, but hers went into the little bay and around the little cape and into the next dip, hugging every curve. When she reached Soren's next knot she straightened up.

"Okay," she said. "How long was that bit with your rope?"

"Ten meters. One segment."

Maya measured her string against the rope. Her string, for the same stretch, was longer. A good arm's length longer.

"So the real beach is longer than yours," she said. "Everywhere. All the way down. You went over the wiggles. I went into them."

Soren knelt beside her string and looked at where it hugged the sand. And then he stopped looking pleased that she was right, because he had noticed something.

"Your string does the same thing," he said.

"What?"

"It cuts across." He put his finger on a spot where her string curved around the little cape. "Look at the edge of the sand there. Right where your string is."

Maya looked. The edge of the sand was not a line. Up close it was crumbs. Around every grain the water had left a tiny scallop, a bay smaller than her fingernail, a cape smaller than a match head. Her string went over the top of all of them, exactly the way Soren's rope had gone over the top of hers.

"Oh," she said.

"Your string's a rounding error too," said Soren. He said it quietly. He wasn't winning. He was somewhere past winning.

Maya put her face right down close to the sand. "If I had a smaller string," she said. "Like a thread. It would go around all these little ones. And it would be longer than mine."

"And then a smaller thread than that."

"Around the bumps on each grain."

"And the bumps on the bumps." Soren had his notebook out. He drew a straight line. Then under it he drew the same line with wiggles. Then under that the same wiggles with smaller wiggles on them. His pencil started to slow because he could see there was no bottom to the drawing. Every line he drew could have smaller wiggles put on it, and each time the line got longer.

"Wait," said Maya. "Wait. So which one is the real length?"

"The smaller you measure with, the longer it gets."

"But when does it stop?"

Soren looked at his three lines. Then he looked at the beach, all two thousand meters of it, or two thousand three hundred, or however much more it was with the bays put back in, and the bays inside the bays, and the scallops on the grains.

"I don't think it stops," he said.

Maya sat down on the wet sand without caring that it was wet.

"That can't be right," she said. But she was smiling "The beach is right there. You can see both ends. It's not that big. You can't have a not-that-big thing that's infinitely long."

"You can if it's crinkled all the way down," said Soren. "The ends stay where they are. The line between them just keeps folding in." He wrote a number in his notebook, then crossed it out, because any number he wrote was too small.

"So there's no answer to the bet," said Maya.

"There's no answer to the bet."

"The question was wrong."

"The question was wrong," Soren agreed. He looked almost happy about it, which was a strange thing to be about losing a question. "How long is the beach isn't a real question. You have to say how long is the beach measured with a ten-meter rope. Or a one-meter string. Or a thread. The answer's only real if you say the ruler."

Maya was quiet. She was thinking about maps. She was thinking about every map she had ever seen with a coast drawn on it, a nice firm blue-and-yellow edge, one single confident line, and how not one of them was telling the truth, and how they couldn't, because there wasn't a truth to tell, there was only whichever ruler the mapmaker had happened to hold.

"Everybody who ever measured a coastline," she said slowly, "got a different number. And none of them was wrong."

"And none of them was right," said Soren.

A small wave came up the sand and touched the tail of Maya's string and lifted it and set it down again in a new shape, a little longer than before, with new bays in it that had not been there a second ago.

Maya reached out and picked up the wet end of the string, and did not measure it.