Cartographic Projection
every map is wrong, and by exactly how much
Figure

Four cities left out, one at a time

Drawn here at the parameters it defaults to, with every essay that calls it.
Four cities left out, one at a time. The least worst-case error of a flat picture as cities are left out one at a time, each time the one whose absence helps most. Without Sydney it is 25.5%; without Singapore it is 20.4%; without Honolulu it is 16.9%; without Los Angeles it is 13.3%. The dashed line is the best projection in the library on all sixteen, 57.6%; the best flat picture beats it by 8%, and leaving out the first city beats the best picture by a factor of 2.09. Greedy rather than exhaustive: the best four to omit together need 1,820 searches and these took fifty-eight.

The least worst-case error of a flat picture as cities are left out one at a time, each time the one whose absence helps most. Without Sydney it is 25.5%; without Singapore it is 20.4%; without Honolulu it is 16.9%; without Los Angeles it is 13.3%. The dashed line is the best projection in the library on all sixteen, 57.6%; the best flat picture beats it by 8%, and leaving out the first city beats the best picture by a factor of 2.09. Greedy rather than exhaustive: the best four to omit together need 1,820 searches and these took fifty-eight.

It is one of 44 figures drawn by the same construction, and the drawing above is this one with nothing changed.

1 essay calls it. Every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this changes every one of these figures.

Sixteen cities, each left out in turn. The least worst-case distance error any flat picture of these sixteen cities can have is 53.3%; the best projection in the library, Azimuthal equidistant, manages 57.6%. Each bar is that least error with one city left out. Leaving out Sydney brings it to 25.5%; leaving out Cape Town, the next most costly, to 46.7%; and leaving out any of five — New York, Tokyo, Anchorage, Singapore, Los Angeles — changes it not at all. The note on a row counts the pairs holding the picture at its worst that the city belongs to. The impossibility

The error belongs to a few of the places

The least error of any flat picture of sixteen cities is 53.3 per cent, and it is not spread over the sixteen. Six pairs hold it there and Sydney is in three of them: leave Sydney out and it falls to 25.5, while leaving out any of five other cities changes it not at all. Choosing which places to draw is worth more than any choice of how to draw them.

The whole library