Geoscience Reference
In-Depth Information
3.1.2.2. “
Unfolded” time and “folded” time
When Berry adds time to its “spatial information matrix”, this involves three
dimensions. It is then interesting to recall the analogy between spatial dimension and
temporal dimension discussed at length in Chapter 1. According to the terminology
used by [GAL 04], the temporal dimension can be regarded as a field where each
point can be informed by the state of the studied system: these are for instance the
dates of the population census to describe the population dynamics of cities; the
dates of school start to describe the social composition of high schools; the dates of
the satellite images to describe land use in a region. Galton qualifies this time
conceptualization as “history”, as opposed to “chronicles” where the temporal
dimension is made explicit in terms of events. Two cases can thus be differentiated:
- “histories”: the X variable being studied is measurable
for all statistical
individuals
, on each of the dates. The variable X is thus stamped (dated) and
replicated in time, (X
t
…X
tk
). It should be noted that in a table hence formed (just as
for space) order exists only through the indices. Some specialized statistical analyses
will take this order into account (methods of time series analysis) but in most
applications, the user will interpret this order
a posteriori
. Berry's table corresponds
to this situation in the case of a description of the places by several variables.
(X
1,t1
….X
1,tk
, X
2,t1
….X
2,tk, …
). Each temporal plan therefore describes a “history” that
characterizes the state of the system at this date;
- “chronicles”: the sequence of events
differs from one statistical individual to
the other
(Ms. H gets married, divorces, remarries and then becomes widowed,
while Ms. S remains single; the municipality X merges with another, joins an inter-
municipal union, and then is integrated into an urban unit). Some specialized
methods allow such trajectories (
event-history analysis
) to be analyzed directly. In
the other cases, in order to integrate these different temporalities in a classic
statistical table, it will be necessary to build indicators summarizing the chronicle.
For example, it will be possible to calculate the number of events in the period, the
date or the duration of an event or the average duration between two events. In this
case, the indicator is not stamped but it “contains” time.
It is possible to go from a “history” formalization to a “chronicle” formalization by
defining events (for example, the date at which the population exceeds a certain
threshold), and vice versa for a “chronicle” formalization to a “history” formalization.
This can be achieved by associating, for example, a state with each event: the state of
“existence” is, for example, related to the “emergence” event (of a shop for example)
and the state of “absence” with the “disappearance” event. These states may then be
projected over the time line over the considered period.
These different time formalizations suggest an analogy with the differentiation
that we have introduced between a “support” space and an “active” space. Here we
