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Location refers to the relationship of a place to other places in a space. The space can be absolute or relative. Imagine absolute space as a container, or an array of containers, in which elements are found. To move an element means to change its position among the locations available. Locations remain ﬁxed; elements repositioned have changed location. In contrast, relative location is deﬁned by the positions of the places relative to each other. Places are nearest their neighbors where they share a boundary. An intervening nearest neighbor separates a place from its second nearest neighbors. Places are remote from one another where connecting them requires crossing many boundaries. Some boundaries and territories are more easily crossed than others, which means that the intervening places aﬀect the extent of separation or relative location.
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The distinction between absolute and relative location has both philosophical and practical importance (Couclelis 1992). At the philosophical level, there are two prevalent views of geographic space: space as a plenum, ﬁxed, and continuous with elements contained within it (absolute); and space as neighborhood, deﬁned by the interaction and exchange between places (relative). The issue will not be resolved in favor of one or the other view, because each is valid and useful in diﬀerent applications—not unlike the wave and particle views of electromagnetic energy.
In practice, the diﬀerence arises in the way geographic space is depicted as either a ﬁxed array of pixels (smallest distinguishable grains) in a raster database, in which spatial elements are distinguished by diﬀerences in values of individual pixels, or as topological relationships between spatial objects in a vector database. Satellite images, aerial photographs, newspaper pictures, and art portfolio prints are all raster images, in which spatial elements are distinguishable by diﬀerences in value, intensity, or color of individual pixels. The size of the pixels deﬁnes the resolution of the images. By contrast, objects in vector models are deﬁned by their edges or end points, and by adjacency and containment relationships with other objects. A road network may be modeled as a set of points (intersections and end points) and lines (road segments). You can travel through the network by moving through a sequence of lines connected by points of intersection. Attributes of the street segments and intersections, such as number of lanes, direction of travel, posted speed limits, signal lights, and turn restrictions, aﬀect the measure of separation between locations. Changes in any of these attributes change the relative location of places. The reference above to spatial resolution is germane, because space has other attributes that aﬀect the notion of location, including scale, distance, and dimension.
1. Place or Location: Scale Dependent
A place is a fundamental spatial element, spatially undiﬀerentiated within and positioned relative to other places beyond. The dichotomy site and situation establishes this level of spatial abstraction and is scale dependent. It distinguishes what is within a site from what is exterior. The site or place may be any size, such as that of a nation, a city, or a residential neighborhood. Situation or location refers to the external relations of places. Ullman (1956) noted that linkages beyond the borders of a place require exchange or movement between locations. Consequently, as transportation and communication technologies evolve, the relative locations of places change. The familiar expression that the world is shrinking alludes to this trend.
A sense of place is evocative of an emotional attachment to a locale. Normally this requires repeated and deep experience in a place, be it home or wilderness. In the writings of structuralists, exempliﬁed by works of Sack (1986) and Curry (1998) and by humanists such as Yi-Fu Tuan (1977) and J. B. Jackson (1994), place trumps location in the processes in which society attaches sentiment, value, and power to socially constructed places. Unlike in Ullman’s works, maps do not play a prominent role in these traditions, because consideration of place takes president.
Gatrell (1983) deﬁnes space as a relation deﬁned on a set of objects. Keeping in mind that places are spatial entities, the set theory view of locations allows consideration of topological relations between places, such as nesting, clustering, and adjacency, without reference to distance (Worboys 1995).
2. Metric Space and Dimensions
Distance is the deﬁning relationship between places in a metric space. The concept of distance in a metric space has very speciﬁc characteristics, including: that the distance from a place to itself is zero; that distance to any other place is a positive real number; that distance between places is the same in each direction (symmetry); and that the shortest distance between two places is the direct path between them (triangular inequality). Being able to use a metric space in an analysis is useful because familiar geometry and algebra hold. However, spaces often do not possess all the properties of metric distance. In city street networks with overpasses and one-way streets, neither symmetry nor triangular inequality holds. A ﬁnite network of points and lines is an appropriate model for city street space.
Location in a metric space can be speciﬁed by a Euclidean coordinate system, in which the number of axes deﬁnes the dimensions of the space. In a ﬂat, twodimensional surface, ordered pairs of real numbers (x, y) specify locations. An ordered triplet of numbers is required to specify location in a three-dimensional space. To complicate matters further, although imbedded in a three-dimensional space, the earth’s surface is itself two dimensional, and two numbers (latitude and longitude) are suﬃcient to locate a place on it. It is also a closed space, which means there is a ﬁnite maximum distance separating places.
Location is a central theme in a class of practical location–allocation problems in which the best location for sources and volumes of ﬂows are investigated. Specifying the locations of warehouses, so minimizing the total cost of delivering food to supply a chain of supermarkets, is an example of an application of location–allocation models. Determining the arrangement of emergency vehicle stations in an urban area, such that no place is more than a certain number of minutes from help, is another example (Ghosh and Rushton 1987).
The notion that space can be deﬁned by an ordered n-tuple of real numbers leads to many interpretations. The spatial properties of a place may be deﬁned by the triplet (x, y, a), where x and y are spatial coordinates and a is a vector of attributes of the place. When a is elevation, displaying a at all locations creates a terrain model. If a is a collection of attributes, a (a₁ , a₂ , a … an), displaying each separately creates a series of overlays that show spatial juxtaposition of the variables. In Design with Nature, an early well-known application of this method, Ian McHarg used multiple attributes of places, including physical, social, economic, and historical conditions, to assess the suitability of territories for land use development (McHarg 1967). Alternatively, each element in the vector a could be considered a dimension. For example, an n-dimensional ecological space might include soil moisture, temperature, slope, and direction of exposure as dimensions of the space. Places could be located in a moisture temperature space or in an n-dimensional space that includes all the site variables. Clusters in this space represent multidimensional similarity of places. Studies of spatial behavior—that is, studies of how people perceive, move about, and use space— have employed this type of multivariate analysis.
4. Locational Referencing
There are many practical ways of specifying location. Street addresses and zip code zones are used to locate homes and businesses. Cadastral surveys establish ownership of land parcels for tax purposes. The Census Bureau uses a nested hierarchy of areal units to report demographic data. Police use road intersections and mileposts to locate emergency incidences along roadways. State plane coordinate systems and global referencing systems are used to specify locations referenced to the earth’s surface— in particular, the familiar latitude and longitude reference system. When locational referencing systems are based on diﬀerent models of space, problems arise in the process of comparing or converting locational information between systems, because not all the attributes of spaces are likely to be preserved in the transformation. Providing a Rosetta stone for transferring locational information between locational referencing systems involves using standardized symbols and proper map projections, but semantics and purpose also dictate what is needed.
More broadly, whenever location of places enters into consideration, the nature of the spatial–temporal context rises to importance. The issue is more than a technical and semantic matter. The user’s purposes and fundamental views of space as absolute or relative, whether realized or not, will underlie understanding and actions.
- Couclelis H 1992 People manipulate objects (but cultivate ﬁelds): beyond the raster–vector debate. In: Frank A, Campari I, Formentini U (eds.) Theories and Methods of Spatial–temporal Reasoning in Geographic Space. Springer-Verlag, Berlin, pp. 65–77
- Curry M R 1998 Digital Places: Li ing with Geographic Information Systems. Routledge, New York
- Gatrell A 1983 Distance and Space: A Geographical Perspective. Clarendon Press, Oxford, UK
- Ghosh A, Rushton G 1987 Spatial Analysis and Location– Allocation Models. Van Nostrand Reinhold, New York
- Jackson J B 1994 A Sense of Place, a Sense of Time. Yale University Press, New Haven, CT
- McHarg I L 1967 Design with Nature. Wiley, New York
- Sack R D 1986 Human Territoriality: Its Theory and History. Cambridge University Press, Cambridge, UK
- Tuan Y-F 1977 Space and Place: The Perspective of Experience. University of Minnesota Press, Minneapolis, MN
- Ullman E 1956 The role of transportation and the bases for interaction. In: Thomas W, Jr (eds.) Man’s Role in Changing the Face of the Earth. University of Chicago Press, Chicago, pp. 862–80
- Worboys M 1995 GIS: A Computing Perspective. Taylor & Francis, London