Extract
The Scope and Conceptual Content of Analytical Cartography.
Introduction
Analytical cartography was defined by Professor Waldo Tobler in the 1960s as a more refined approach to cartography articulated via the notion of "solving cartographic problems" (Tobler 1966). As such, it offers a more analytical, conceptual, and mathematical approach to the field of cartography, and even to some related areas. This work attempts to assess the breadth and depth of the field by examining a number of research topics in analytical cartography and associated fields. However, in a survey of a topic of this magnitude, one cannot include all research topics in the field, and one cannot include all relevant references. One must by necessity choose and select research areas to review, and then provide only a selection of the wealth of references that are possible. It is hoped that this work constitutes a reasonable survey of the breadth and depth of the field of analytical cartography. The formal conceptualization of analytical cartography began with Tobler's dissertation in 1961 where he initiated his concepts of map transformations of geographic space (Tobler 1961). Tobler later extended his 1961 conceptualization of cartographic transformations to explain the traditional cartographic map creation and reading process, later articulated by Muehrcke (1973). This transformational view of cartography was further refined by Tobler in 1979 by stating that cartographic transformations "... occur in map interpolation, filtering, and generalization ..." (Tobler 1979a). More recent advances in the transformational approach to analytical cartography revolve around the work of Nyerges (1980), Clarke (1990) and Chrisman (1999). At roughly the same time, the field of traditional cartography was thrust into a conceptual turmoil with the development of new cartographic products, many of which were digital, such as CRT display images, digital terrain models, and spatial databases. These products did not fit into the then conventional definition of traditional hard copy cartography. This dilemma was articulated clearly by Morrison (1974) in the first article in the premier issue of The American Cartographer, where he called for an expanded and extended definition of what constitutes a map. Moellering, who was confronted with a similar need, initiated research on the problem highlighted by Morrison. Goals of Analytical Cartography During this time, Prof. Tobler (1966), while discussing the concepts of analytical cartography, would talk about the half-life of theory versus the half-life of technique as the reason why one wanted a quantitatively and mathematically based field of study. He estimated that the half-life of technique, which is what most people in cartography did in those days, was about three to five years, whereas the half-life of theory was about 15 to 20 years. This means that if one focuses one's efforts on the conceptual and theoretical aspects of cartography, the likelihood of developing better insights into the field is increased. This also means that research work in the field could be replicated elsewhere, and benefit from many of the other aspects of a normative science. So it is that analytical cartography has mainly focused on the quantitative and mathematical relationships inherent in the broadly defined field of cartography. This approach to cartography is similar to the mathematical mode of inquiry (MMOI) advocated by Casetti (1999) for human geography. Two additional goals of the field are to extend the body of existing spatial theory, such as develop further uses and extensions of the sampling theorem, and other theory like it, and to develop new conceptual theory, such as Moellering's (1977b) concept of real and virtual maps and their applications. Several efforts in the field (e.g., Muller's (1991) book on the cartographic research agenda) have begun to explicitly recognize these needs, some of which have touched on analytical cartography. Moellering (1991c; 1994) also recognized that the effort to develop spatial data standards identified a distinct need to expand the analytical theory so as to fill the huge conceptual gaps in it. An effort was begun by Moellering (1991a, 1991b) to fill in some of these gaps by organizing and editing a special content issue of Cartography and Geographic Information Systems dedicated to Analytical Cartography. Cartography needs to make a major push to expand its theoretical base because it is clear now that no matter how powerful, the computer may not be able to empirically or heuristically solve certain classes of numerical problems. This problem is discussed by Saalfeld in this issue, in his article on complexity and intractability of algorithms and computer processing. He suggests that problems that are NP comple...See the full content of this document
Sponsored links
