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any point in space, which will allow studying the movements and variations of the
glacier?
These questions must be raised in a dynamic context: the main idea is to adopt
the point of view for which the change that we are interested in makes the most
sense. This choice is fundamental because the formalization of the spatio-temporal
objects of interest and the empirical information necessary for their construction
depend on it.
Depending on the point of view, the objects that ought to be built and analyzed
are, as a matter of fact, different. We will illustrate it here, in the context of the study
of the infraregional demographic dynamics of a French region, for example,
Provence, between 1960 and 2010. According to the question, it may be convenient
to represent space in the form of objects, such as the municipalities, which will be
then described by their populations in time, or in the form of a continuous field; in
such case, we will rely on a chronological series of density grids. The point of view
specifies the question and objects to build (Figure 2.1):
1) If the evolution of the spatial organization of the demography is of interest, we
could choose to work at the level of the municipality (object) or at the level of a grid
cell (field). The grid in this context is a simple tool for the localization of the
population. Only the states of the territory are of interest and not the underlying
process (such as the mobility trajectories of the inhabitants). Only the representation
of the sequence of the population's spatial organization is necessary to follow the
evolution (Figure 2.1(a)). This is typically a “snapshot” approach: the aim is, for
example, to produce a series of maps presenting the states of the density on each of
the dates. A synthetic indicator can also be calculated, characterizing the shape
of the spatial organization associated with each date (for example, a coefficient of
spatial autocorrelation). In this context, the follow-up of the whole (at the
department level) is considered important and not the follow-up of each elementary
entity (the municipalities or cells level). The elementary entities are only
apprehended in the manner in which they make up the instantaneous state of the
whole, and there is no need to reconstruct their history.
2) If the evolution of the territory is of interest, it may also be important to shed
light on local trajectories (evolution of the populations of municipalities or grid
cells). In this case, it will be necessary to build and represent the “municipal”
populations, and each municipality will have as many attributes as census years. The
municipalities or the meshes are then the only entities of interest. The states of the
municipalities are described by the importance of the population at different dates:
the change is apprehended through endurant objects whose states are followed up
during the period. The evolution of the department will be analyzed through “local
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