Splay and Relief

Splay went first, because the roundness is the deeper trouble.

She scored her orange into sections and pressed it toward the flat page, and — as always — it split and curled and refused. "See? A ball won't lie flat and keep everything true. Somewhere it stretches." She smoothed a torn section. "So I choose the stretch. This map keeps the shapes tidy and blows the far-north sizes up huge. That map keeps the sizes honest and lets the shapes go squashed. Neither one is cheating — as long as I write down which trade I made." She tapped the empty corner where the honest words would go. "That's my whole job. Turn the ball into a sheet, and never pretend it was free."

The traveler frowned. "But once it's flat and honest — you're done, right? The map's finished?"

"The roundness is handled," Splay said. "But look." She set the little clay hill on her flattened page, and it stood up, stubborn and three-dimensional, throwing a shadow across the paper. "The page is flat. The mountain is not. I flattened the ball. I never touched the bumps." She turned to her friend. "That's where Relief comes in. My trouble was that the world is round. Hers is that the world is tall."

Relief took the little clay hill in her paws.

"Splay flattened the world's roundness," she said. "But a real place isn't just a smooth flat ball — it's got mountains standing up off it, and a page can't grow a bump any more than it can hold a sphere." She set the clay hill in a shallow dish of water. "So I do to the height what Splay did to the roundness. I trade it into lines." She marked the waterline around the hill, then poured in a little more water and marked the new, higher line, and again. "Every waterline, traced flat, becomes a ring. Rings crowded close — steep. Rings spread wide — gentle." She lifted the clay away, and on the page lay only loops. "The mountain's height, kept safe on flat paper. I gave up the standing-up-ness. But I remembered exactly how tall and how steep — in a code any reader can stand back up in their mind."

The traveler stared at the loops. "So you flattened the mountain like Splay flattened the ball."

"Same brave trick, different dimension," Relief said. "She squashes the round. I squash the tall. And each of us leaves an honest note about what we gave up." She looked across at Splay. "But watch what happens when we finally do it together, on one map."

Then they did the thing neither could do alone, and the young traveler did it with them.

Splay took a real globe — round and mountainous, a whole world of it — and began her flattening: she peeled the roundness onto a flat sheet, writing in the corner exactly which sizes she'd stretched to do it. "There. The ball is a sheet now. But feel it —" she ran a claw over a mountain range still standing proud off the paper "— it's flat where the world was round, and it's still bumpy where the land is tall. Half-flattened."

Then Relief moved in over the same sheet, over Splay's stretched-flat continents, and began to ring every mountain — waterline by waterline, loop by loop — until the standing bumps lay down into crowded and spreading rings. "And there," she breathed. "The tall is flattened too. Now the whole round, bumpy world lies on one page."

"But look what it cost," Splay said, laying a claw beside Relief's paw on the finished map. "Two trades, not one. My flattening stretched the far-north sizes — see, this frozen cap looks too big. Her flattening turned every mountain into a ring you have to know how to read. This single honest map gave up a true size and a standing mountain — and it says so, in two little notes in the corner, one from each of us."

The traveler ran a hand over the map — flat under her palm, yet round and mountainous in her mind, because she now knew both trades. "It's the whole world," she said, amazed. "Round and tall, on a flat page. But only because you both gave something up. And told me."

"That's the secret of every flat map ever made," said Splay and Relief together. "It survived two flattenings — and stayed honest about both."