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speeds and suggests a three-dimensional geometric construction coherent with the
concept behind the representation. It also proposes a rather negative image, with
the crumpled surface observed as a degradation of the ideal unaltered flat plane.
A positive perspective can be established when the crumpled shape, being more
compact than the flat surface, is considered because it allows for shorter paths
between locations. The crumpling metaphor gives an evocative image of the poor
treatment reserved for interstitial spaces but is not as expressive of the global
contraction of geographical space, given the increases in speed.
It is relevant to associate these reflections on the representation of geographic
time-space with some recent developments in theoretical physics: The astrophysicist
Luminet describes the shape of the universe as crumpled around the idea of
multiple folding due to time-space deformation, according to the theory of general
relativity ( Luminet , 2001 ). Even while establishing relations between completely
different fields should be made with caution (a use of common words is not
sufficient to validate a comparison), it is apparent that both systems of representation
are tightly linked to the identification of a maximum speed. Indeed, the speed
of light is one of the three fundamental constants in physics. Astrophysicists
have to work with the existence of a maximum speed, which is the speed of
light on the universal scale, while geographers have to take into account the
maximum speed of transport provided by the air transportation mode to understand
terrestrial time-space. To better understand space, both reflections seem to require
building complicated representations that divert radically from common Euclidean
geometry.
In a different field, psycho-analysts have been studying crumpled spaces ( Diener ,
2008 ) to understand the links realized in the time-space of dreams, where the
associations of ideas lead to direct relations between locations that can be very
distant in time-space. In reference to the astrophysicist Luminet's work, a crumpled
space is defined as “welded on itself by several points” and can establish these types
of connections (Diener). The analogy goes much further: In the geographic space,
fast transport systems directly link remote locations, advocating for the development
of crumpled time-space cartography, while in the time-space of dreams, direct con-
nections between remote locations constitutes an essential property. The movement
of crumpling generates new connections and new proximities that reflect both the
properties of geographical space and the time-space of dreams.
In the evolution of the discourse produced on the time-space relief, the following
step explores a different type of metaphor based on the idea of shrivelling. The first
use of the word must be credited to Tobler through his commentary on the L'Hostis-
Mathis image, when he stated that “the world is shrivelling as it shrinks” ( Tobler ,
1999 ). We move from an image of the shape of an inanimate entity or artifact, such
as the crumpling of a sheet of paper, to a principle of natural evolution of a living
organism, such as the shrivelling of a fruit. This shrivelling expresses the idea of
contraction with the deformation of an envelope; i.e., the volume decreases while
the external envelope keeps its initial surface.
The strength of the metaphor lies in the combination and the linking of two
complementary movements of both the contraction and deformation of the surface.
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