Geographers depend on models to accomplish spatial analysis, and people in general form mental models through which they filter information about the world in which they live. Such perceptive models allow individuals to decide what is important and what is not, and to maintain at least a modicum of predictability about what is likely to happen in a given situation or environment. Scientific inquiry, however, is a far more precise process than simple perceptive modeling. Nevertheless, models are never as complex as the systems they represent. Instead, geographers use models to simplify spatial systems so that they can manipulate one variable at a time in order to determine the probability of a specific outcome (Willmott, Cort J. and Gary L Gaile, Modeling, in chapter 8 of Geography's Inner Worlds.
Although geographic modeling is not new, it did not become a conspicuous part of the discipline until the 1960s. Since then, models of spatial analysis have evolved to the point that they are now essential parts of the discipline. In order to be useful, geographic models must have practical applicability in spatial analysis and as predictors of human geospatial behavior.
As is true of all disciplines, geography has experienced numerous changes in emphasis over the years. Even so, space has long remained its unifying theme. During the 1960s, many believed that a "new" American geography was emerging from its many years of focus on the description of regions and cultures into the more precise world of spatial models that could be quantifiably tested and substantiated. Of course, some rejoiced at this interest in quantification, while others saw the "new" emphasis as a way to exclude geographers who were mathematically challenged. During the 1970s and 1980s, the geographic journals seemed to prefer to publish research findings that included numerous quantitative spatial models. Moreover, the long tried and tested technique of using reasonable judgment samples as part of geographic research projects was, for all practical intents and purposes, abandoned. By the 1990s, it would have difficult to argue with someone who insisted that geographic research that did not use, develop, or in some way explore, a quantitative spatial model or two, would not be funded, or considered for publication.
Currently, some geographers, such as Roger Brunet, believe the discipline has drifted into a vague intellectual milieu of "free" discourse in which solid research has been overwhelmed by focus on the individual. In other words, Brunet argues that the idiographic (the study of the individual as a unique being) is winning out over the nomothetic (the study of classes or cohorts of individuals). Even so, he also notes that models of spatial analysis are now regularly in use by people in a wide variety of professions. For example, regional planners regularly use geospatial modeling to develop plans and facilitate land-use decisions.
Despite the initial concerns about the use of models in geospatial analysis by geographers committed to a chorographic focus, almost everyone now accepts the fact that models not only make it possible to more accurately describe spatial realities, but they also help people understand why things are where they are, and why they are as they are.
Models are about spatial relationships
Geographers are interested in discovering, explaining, and understanding the nature of spatial relationships. Prior to the "quantitative revolution" in geography, such relationships were typically described in a narrative format. Such narratives were useful in establishing a basis for intuitive predictions based mostly on observation and judgment sampling. The development of quantitative models made it possible to more accurately evaluate, analyze and explain spatial patterns and relationships. A simple quantitative relationship model might look something like Y=f(X). For example, in the 1980s, a particular kind of cancer in children was discovered to be concentrated in a suburban community (called Love Canal) in New York. Childhood cancer Y was a function (f) of location X (Love Canal). Eventually this neighborhood was abandoned because it had been built on a toxic waste site that contained cancer causing residues. In the case of childhood cancer in New York, the medical data clearly pointed to the Love Canal neighborhood as a concentration point. That is the numbers of childhood cancer cases diminished as the distance from the Love Canal neighborhood increased. One could plot this on a map or present that data via a matrix (or graph) in order to demonstrate that a relationship exists between childhood cancer and Love Canal. One could also apply the formula Y (cancer) = f(X) location. A geographer could have noticed that this part of the state of New York experienced far more childhood cancer than is normal throughout the rest of the country, and by plotting the places where the children who were afflicted with cancer live; she or he could have identified the source area. With that accomplished, she or he could have done the research needed to discover why Love Canal experienced a higher rate of cancer than all of its nearby neighbors. Upon finding that Love Canal was built on an old industrial waste site, soil tests would have revealed that dangerous chemicals were leaching out of the soil upon which the subdivision rested. In fact, the scenario described above is approximately what actually happened. The result was that the people of Love Canal had to abandon their homes in order to protect their children. See chapter five in your text book for a more detailed discussion of measurements, relationships, and classifications.
All scientific inquiry seeks to discover and explain patterns and relationships in order to clarify the seemingly chaotic nature of the world. Geographers have long used their primary models (maps and globes) to visually present spatial relationships. Sometimes, they use maps to contrast and compare patterns by making overlays. In fact, GIS is a computer-driven quantitative mapping technology that builds on the manual mapping techniques that evolved over thousands of years of human endeavor to analyze, explain, and understand the world. Quantitative methods make it possible for geographers to rigorously examine theoretical and intuitive concepts about spatial relationships. If sufficient evidence is available, we can plot data on graphs (see page 120 of your textbook for an example of a scatter diagram, etc.). Also: see https://www.mathsisfun.com/data/scatter-xy-plots.html.
What if a very religious geographer believes that there is a direct relationship between violent crime and the number of churches located in communities? In other words, communities that have fewer churches experience more violent crime than do those that have many churches. She or he could approach this inquiry by first doing some background research (general statistical reviews and community profiles, etc.). After that, she or he must figure out a way to get a representative sample of communities. For example, the hypothesis could be that in Pulaski County, Arkansas, an inverse relationship exists between the number of churches and violent crime in communities with populations of less than ten thousand people. After that, the effort would require a detailed assembly of the violent crime statistics of each community involved in the study; and it would be necessary to categorize the communities relative to the number of churches operating in each of them. For example, such a categorization might be: 1. communities with 0 churches; 2. communities with 1-2 churches; 3. communities with 3-5 churches; 4. communities with 6-10 churches, and 5. communities with more than 10 churches). The crime data could then be plotted on a scatter graph relative to community category to determine whether or not a relationship exists (the X axis could be church categories, and the Y axis could be violent crime data).
Check Your Understanding
How does Roger Brunet view current trends in geographic research?
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Brunet believes that the discipline has drifted into a vague, intellectual milieu of free discourse in which solid research has been overwhelmed by focus on the individual.