The Compass Rose - Map of China: Decoding the Secrets of a Vanished Cartographer - page 105

explained. But in the course of explaining it, Shen describes how to use a compass
to draw a map.
Select any point on the landscape, Shen explains, and draw straight lines from
thatcentral pointinthefourcardinal directions (N,W,S,E).Next,doubletheseby
addingthefourordinaldirections(NE,SE,SW,NW)foratotalofeight.Uptothis
point, the Chinese and Persian/European compasses are the same. Both traditions
refer to the four cardinal and four ordinal directions - and both call them the eight
winds. (To judge from the journal Will Adams kept when he sailed from Japan
to Tonkin in 1617, the Chinese names for the eight winds were among the first
wordsaEuropeanmarinerwantedtolearn.)Beyondthoseeightwinds,thesystems
diverge. The Western compass bisects: you divide the angles of the eight winds
into sixteen points (half-winds) and then subdivide them into thirty-two (quarter-
winds). Each of these thirty-two winds has a distinctive name in Italian, and every
student of navigation had to be able to recite all of them in sequence, an exercise
known as 'boxing the compass'.
TheChineseboxedadifferentcompass.Tomakesenseoftheirsystem,wehave
to go back to the eight cardinal and ordinal directions and start again. These eight
winds divide the circle into 45° wedges. The logic of bisection for the European
compass produces half-winds every 22½° around the circle, and quarter-winds at
every 11¼°. The Chinese system trisects rather than bisects. It does this by adding
two lines on either side of each of the eight lines, producing a central point from
whichradiatetwenty-fourlinesratherthansixteen,eachpointinginadirectionthat
has a unique name. Instead of producing four wedges of 11¼°, trisection creates
three wedges measuring 15°. The Chinese compass then trisects again, producing
points at every 5°, unlike the Western compass, which bisects 11¼° into wedges
of 5 ⅝ °. The European system is geometrically clean but arithmetically messy, the
Chinese system elegant and simple. To go back to the metaphors of direct flight,
why trouble yourself with figuring out how crows fly at 5 ⅝ ° when you could have
birds do it at 5°?
The naming system for the basic set of twenty-four compass points is not
simple, even for Chinese. This is because it combines names taken from three dif-
ferent Chinese counting systems: base 8(the eight Trigrams ofthe I Ching or Book
of Changes ), base 10 (a sequence known as the Heavenly Stems) and base 12 (a
complementary sequence known as the Earthly Branches). The compass does not
use all the names in all three counting systems, which would be too many for the
twenty-four points that needed to be named. Instead, it takes four of the trigrams