Heaven is Round, Earth is Square - Map of China: Decoding the Secrets of a Vanished Cartographer - page 139

not have available to him all the steps in the logic that distorted both Chinese and
Europeanmapsinthisperiod.TherewasnotrueorobjectiveimageofChinaatthe
time, only the images that culture and experience shaped, and not always in ways
that everyone spotted.
____________________
At the heart of the matter is the geometrical challenge that drove the development
of modern cartography: the problem of how to relate the curved to the flat. For
Zhang Huang this wasn't a problem he had to solve. He saw the relationship
between circle and square as a cosmic pattern that shaped the disposition of the
landhemapped. ForEuropean cartographers inthesixteenth century,however,the
problem was the curvature not of heaven but of earth. And it was a problem they
had to solve because their navigators needed it solved.
The simplest solution to the problem of the earth's spherical shape was to draw
the world on a globe. Will Adams did this for the shogun of Japan, who at first
thought Adams was lying to him but in the end was mightily impressed. Adams
wrote to the East India Company asking that they send him a pair of globes in
order to persuade the shogun to support England's bid to open a North-East Pas-
sage over Russia that would shorten the route between them. However visually
impressive they could be, globes were utterly impractical for navigation. Mariners
neededlargerscaleandfinerdetailthananyglobecouldprovide.Theyalsoneeded
something that could be stored flat.
The solution is called a projection: that is, a method for casting an image of the
earth's curved surface onto a flat piece of paper in a way that respected curvature
while limiting the distortion as much as possible. But distortion is unavoidable.
Theshortanswertotheproblemofreducingthecurvedtotheflatisthatyoucan't.
You can only approximately square a circle. Pi is the name we give to the relation-
ship between a circle and a square. Calculating pi produces a number that never
ends. Cast the problem in three dimensions and completing the calculation only
gets harder. A globe didn't completely solve this problem, since the gores or strips
of paper that a globe-maker pasted onto the surface of a ball had to be printed first
in a flat format. Every projection is a compromise.
Mariners encountered the problem of curvature in the course of doing the
simplestthing:sailinginastraightline.Drawastraightlinefromafixedpointona
globe and then draw one from the same point on a flat map, and you will discover
that they do not end up in the same place. Map a route on the land and this is not