Concept

Cut length — where it appears

The length of ground, or of water, that an interrupted map's cut runs across between the equator and the pole. It prices an interruption by what a reader must jump: coastlines drawn twice on a land map, currents and sea lanes broken on an ocean map.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as homolosine — the same set of essays touches all of them, so they are one junction rather than several.

Goode's lobes and the lobes the land would choose, at his own count of two north and four south. The land in two-degree cells, Antarctica pale because it is not scored, with Goode's cuts dashed and the land's own solid; a short tick at the equator marks each lobe's central meridian. Goode's: edge at 180°, northern cut at 40°W, southern cuts at 100°W, 20°W and 80°E, meridians 100°W and 30°E north and 160°W, 60°W, 20°E, 140°E south — 16.51° of mean angular deformation on the land outside Antarctica. The land's, with no cut crossing more land than Goode's worst: edge at 20°W, northern cut at 165°E, southern cuts at 70°E, 155°E, 175°W, meridians 65°E and 100°W north and 25°E, 135°E, 175°E, 60°W south — 14.48°.

The land would move Goode's lobes before his join

Goode chose his lobes by eye: where the cuts run and where each lobe's meridian sits. Scored on the land outside Antarctica and found exactly on a five-degree grid, the land's own layout at his count of two lobes north and four south deforms it by 14.48° against his 16.51° — two degrees, more than his meridians were worth in the first place — while its cuts cross less land than his: 2,057 kilometres against 2,391, the worst of them 1,056 against the 1,946 his northern cut spends on Greenland. The land wants the map's edge in the Atlantic and its northern cut in the Pacific. His fourth southern lobe is worth four hundredths of a degree, and once the lobes are the land's the best join climbs again, to sixty degrees.

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The lobes the ocean would choose, against the lobes the land chose. The water in two-degree cells, with the land's own layout dashed and the ocean's solid; a short tick at the equator marks each lobe's central meridian. The land's, at two lobes north and four south: edge at 20°W, northern cut at 165°E, southern cuts at 70°E, 135°E, 180° — 14.40° of mean angular deformation on the land outside Antarctica and 19.75° on the water. The ocean's: edge at 40°E, northern cut at 110°W, southern cuts at 135°E, 140°W, 60°W, meridians 175°E and 40°W north and 85°E, 180°, 105°W, 10°W south — 13.31° on the water and 26.18° on the land.

The ocean centres its lobes on the land's cuts, and cannot keep its own cuts short

Run on the water instead of the land, the same exact search gives an interrupted homolosine whose lobes sit on the Pacific, the Atlantic and the Indian Ocean — five of its six central meridians within twenty degrees of a cut the land's own layout chose — and it deforms the water by 13.31° against the 19.75° the land's layout gives it. The inversion stops at the cuts. Every meridian on Earth crosses at least 7,172 kilometres of water, so the ocean's map has no layout whose cuts stay under seven thousand, where the land's went below nine hundred. And no layout serves both: none comes within 2.57° of both optima at once, though a single wide Pacific lobe buys the water 2.8° for a tenth of a degree of land.

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Named alongside it

The objects these essays reach for when they reach for this one.

Angular deformation Central meridian Equal-area Homolosine Interruption Verification Mollweide Pareto front Seam Sinusoidal Topology Trade-off

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