MAP: A MEANS OF RESEARCH

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The author assumes that to draw a map is to transform a base map (R2) into a new map (M2). Suppose there is a special map transformation; f: R2→M2, where M2 is a mental map. It is clear that both R2 and M2 are at least topologized. But, f is not always a homeomorphism.1) In the case of Gould's (1966; 1974) mental map, f is a homeomorphism. People are asked to provide rank order of their space preferences for various areas. Basic data of the mental map consist of this rank order matrix, whose rows represent places. It is important to understand that these places mean the points in R2. Therefore, the topological relations in R2 are mapped into M2, although R2 is merely used descriptively as a statistical device for summary. Then, f is a homeomorphism. Generally, however, f is not always a homeomorphism. For example, a person may have a imaginary place sequence: A-C-B, while there is A-B-C in R2. In this case, it must be recongized that the gap between geographical images and realities is not ascribed to our failure to perceive the geograhical realities correctly. The reason why the gap occurs is not based on the fact that our mental images are the imperfect copies of the geographical reali-ties, but is due to the fact that our geographical images can be constructed according to their own principles (Takahashi, 1973). Therefore, the topological relations in R2 cannot be mapped into M2. We must draw M2 without reference to R2. Yamamoto (1976) has developed an interesting discussion. He is concerned with "the division of rural space in Japan through the analysis of people's imaginary perceptions". At first, the whole land of Japan was divided into the 8 traditional districts. Then, he visited the Agricultural Bureaus in the districts, and asked the experts to subdivide their own districts into 6 Ideal types space. These ideal types are provided deliberately through his previous analysis of the employment structure of farm households. The experts could provide the regional divisions within their own districts, relying upon their imaginary thinking. Suppose the regionalzations in neighbouring districts R and R' are given in Fig. 3. Then, Yamamoto posed an intereting question: Are the boundaries of 11, 12 in R continuous with the boundaries of 11', 12', in R' respectively? In Fig. 3, 12 and 1'2 seem to be continuous, but 11 and 1'1 do not. According to his previous analysis, each pair of boundaries is known (or may be expected) to be continuous. But, as mentioned above, the knowledge cannot be drawn into the mental maps. Yamamoto does not seem to find the ultimate answer to his own question. An approach to solve the problem is to ask the experts to produce "predicted maps". If the results are shown in Fig. 4, we can perhaps tell that each pair of boundaries is continuous. There are many situations, however, in which we cannot identify how much degree of confidence the experts have for their predicted maps. In order to avoid this difficulty, it would be useful to introduce the concept of "neigh-bourhood"2). Draw a circle with the center at a place p within R and with a radius of ε. Then, we ask a third expert to divide the area within the circle using the same instructions. We can conclude that the boundaries of 11 and 11' are continuous, if he has drawn such a boundary of 1 shown in Fig. 5. If we extend this procedure, we can connect boundaries continuously (Fig. 6).
The Association of Japanese Geographersの論文

MAP: A MEANS OF RESEARCH

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The Association of Japanese Geographers | 論文

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