Geoscience Reference
In-Depth Information
practitioners to be able to repeat experiments so that the outcome is consis-
tent. That goal is particularly difficult to achieve when the dynamic Earth is
the laboratory. Establishing controlled experiments is hard. Imagination can
help; visualization can help; and, art can help.
As we have seen in previous chapters, one way to ensure the replication of
results is to have a clear system for organizing information. In the case of cre-
ating a replicable coordinate system, standard circular measure coordinates
were used to transform the relative locational system of counting parallels and
meridians to the absolute, and replicable, system of latitude and longitude.
We have also seen, particularly in the “practice” sections, that organization
of information in tabular form, as an attribute table in a GIS map, is a helpful
and natural scheme. Clear thinking, coupled with clear organization, enables
replication of results.
Beyond two organizational tools, one visual (a table, or a spreadsheet), and
one numerical (the latitude/longitude system), there are tools that are more
subtle that can be used for organizing geographic and mathematical informa-
tion. In this chapter, we explore two of these subtle tools. Again, one is visual,
color; and the other is numerical, prime factorization. We interpret both these
concepts in terms of maps and conclude, in the practice section, with an exer-
cise involving color and number.
4.2 Background—Color
Background is important not only in color visualization but also in fostering a
deep understanding of a variety of abstract concepts. One place to begin any
background study of color is with the four-color problem (now, “theorem”;
Appel and Haken, 1976). For centuries, mathematicians have concerned them-
selves with how many colors are necessary and sufficient to portray maps of a
variety of regions and themes. For example, two regions were said to be adja-
cent, and therefore required different colors, if and only if they share a com-
mon edge; a common vertex, alone, was not enough to force a new color. The
answer of how many colors to use depends on the topological structure of
the surface onto which the map is projected. When the map is on the surface
of a torus (doughnut), seven colors are always enough (the reader interested
in discovering the reasons why seven is considered “enough” is referred to
the section on extra readings at the end of this topic). Surprisingly, perhaps,
the result was known on the torus well in advance of the result for the plane
(then again, the plane is unbounded and the torus is not). The same number
of colors that work for the plane will also work for the surface of a sphere
(viewing the plane as the surface of the sphere with one point removed).
How is the plane a spherical surface with one point removed? Through ste-
reographic projection, everything on the spherical surface but the North Pole
maps into a plane tangent to the sphere at the South Pole (more detail to
come later in Chapters 9 and 10). It was not, however, until the last half of
Search WWH ::
Custom Search