ABSTRACT

Keywords: Data (95), map (51), resolution (39), points (32), spatial (30)

They cannot look out far, They cannot look in deep;

But when was that ever a bar, To any watch they keep.

Robert Frost Neither Out Far, Nor In Deep

Mathematics, like musical composition and other fine arts, is purely a human creation. Without us, does it exist? This sort of “meta” question has long interested scholars with multidisciplinary interests. Indeed, does the societal culture and historical epoch in which the predominant mathematics is developed and embedded influence the kind of mathematics that is developed? Again, this question might be studied in many ways: We consider one case here-that of the mathematical relation and selected real-world interpretations. These are displayed in a number of visual formats not merely as curiosities but more significantly for the suggestion they might offer as to why or why not certain types of formal structures get created. It is important to attempt to understand deeper processes such as these: The mathematics we use in the real-world often influences the decisions we make (and vice versa). All data that we use are created, modeled, and maintained based on mathematics. This includes how data are classified, how they are symbolized, what map projection the data are cast in, and even, as we will consider in this chapter, the transformations that are used on the data and the model that is used to represent them on maps and in spatial databases.