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ments that can be used for measurement' (Rykiel, 1998, p. 488). A scale is used to
ascertain some attribute of an object or phenomenon - such as length, mass, volume,
velocity, and so forth; in geographical contexts, scale in this sense generally refers
to
size
.
Cartographic scale
is the oldest kind of geographical scale, having emerged
with the science of cartography during the eighteenth century. It refers to the math-
ematical relationship between a map and what it represents: the 'representative
fraction' or ratio of a unit space on a map to space in the world, such as 1 : 62,500
for maps in which one inch represents one mile. Expressed in this way, smaller scale
maps depict larger areas than do maps of larger scales, resulting in the peculiarity
that cartographers employ 'large scale' and 'small scale' in the opposite way from
scholars in other fi elds. Choice of scale has obvious implications for cartographic
generalisation: Smaller scale maps (depicting larger areas) necessarily sacrifi ce details
that can readily be included on maps of larger scales (depicting smaller areas).
(Hereinafter, I will use 'small' and 'large' scale the way non-cartographers do, to
avoid confusion.) Scale is a central conceptual and representational issue in carto-
graphy because it strongly determines selection, simplifi cation, classifi cation, and
symbolisation. Different tasks - depicting a neighborhood, a city, a region or a
continent, for instance - call for the use of different cartographic scales.
Developments in Geographical Information Science (GISc) raise the possibility of
overcoming constraints of cartographic scale, at least in theory. Digitised data can
be assembled and analysed across multiple scales, such that details visible at small
scales are not lost (to the computer, at least) when one 'zooms out' to much larger
scales. As Sheppard and McMaster (2004, p. 4) note, however, this does not mean
that 'there is no scale' in GISc, because the underlying data are themselves typically
derived from scaled sources. (Think of what happens when one zooms in on Google
Earth, for example: the image becomes blurry at certain scales, then regains focus
when the programme shifts to an image taken at another scale.) The technical details
and particularities of GISc cannot be adequately reviewed here, but the issues of
scale discussed below are nonetheless relevant to that fi eld.
Cartographic scale is principally a representational issue, but in the second half
of the twentieth century other fi elds in geography identifi ed empirical corollaries:
situations in which spatial analysis resulted in different (or even opposite) conclu-
sions depending on the scale employed. The distribution and intensity of poverty,
for example, might look very different if the smallest unit of analysis were city
blocks rather than census tracts, cities, or entire states. Openshaw (1977; 1984)
famously demonstrated that the boundaries and size of units for spatial aggregation
could determine whether two variables correlated positively, negatively, or not at
all: a form of ecological fallacy known as the modifi able areal unit problem.
Obser-
vational scale
refers to this methodological issue, which at face value resembles
cartographic scale: At what spatial dimensions can one best perceive and analyse
particular phenomena? Even when the question is not posed as such, scientists
cannot avoid this issue: 'Because science is about the search for and explanation of
patterns, all scientifi c inquiry explicitly or implicitly incorporates scale into the
process of identifying research objects: the very act of identifying a particular pattern
means that scale, extent, and resolution have been employed' (Gibson et al., 2000,
p. 221).
Observational scale has two components.
Resolution
, or
grain
, is the smallest
unit of measurement: it determines the precision or detail captured by a certain
method.
Extent
is the overall dimensions of a study: the area (and time period) over
