Replication of Results - Spatial Mathematics: Theory and Practice through Mapping - page 86

the twentieth century, aided by the capability of contemporary computing
equipment to examine large numbers of cases, when the age-old “four color
problem” became the “four color theorem.” Appel and Haken (1976) showed
that four colors are always enough to color any map in the plane. This dis-
covery prompted the University of Illinois to issue a postage meter stamp of
“four colors suffice” announcing this result of the solution of one of the world
of mathematics' great unsolved problems.
The world of creating paper maps and publishing them has traditionally been
one that is black and white: Color processing is expensive and often has
been prohibitive. Nonetheless, cartographers, photographers, and others have
developed a number of strategies for considering color, independent of how
many colors suffice to color a map in the plane. Indeed, Arthur Robinson
noted (Robinson, 1960, p. 228):
Color is without a doubt the most complex single medium with which
the cartographer works. The complications arise from a number of cir-
cumstances, the major one being that even yet we do not know precisely
what color is. The complexity is due to the fact that, so far as the use of
color is concerned, it exists only in the eye of the observer.
Like the mathematician, the cartographer, too, has significant unsolved prob-
lems associated with the concept of color.
Thus, color choice and use is typically tailored to “standard” reactions, by a
typical observer, to color. The effect of color on an observer is often captured
using the following terms as primitive terms: Hue, saturation, and luminosity.
• Hue is the term used to describe basic color. Blue, red, and green are
all hues. White light passing through a prism is broken up into the
spectrum of the rainbow composed of a variety of hues. The basic
hues evident in this process are often referred to as spectral hues and
these can be used to generate a progression of interstitial hues to fill
in between the evident hues.
• Saturation is a measure of the amount of hue in a color; it is also
referred to as intensity. Thus brilliant colors are more intense than
are light pastels.
• Luminosity is a measure of relative lightness or darkness of a color.
Color can be matched against a gray scale to make this measurement.
One would expect, for example, that most shades of yellow are lighter
or more luminous than most shades of red.
The contemporary computing environment of today, with its high-resolution
color screens on the desktop computer and on hand-held devices including
smartphones and data loggers, has fostered a whole new world of communi-
cating data with color. Yet, an understanding of color theory is still essential.
One could argue that the digital environment makes it more important than