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boundary that encloses a space is, seen as a whole, always
concave, and its sparest form is an angle (> angle and cor-
ner). Accordingly, the concave side of a curve is regarded as
an interior, and hence as a favoured > gestalt; the concave as
an exterior. When facing a concave curvature, the beholder
is equidistant from all points, is enclosed by it, and the gaze
finds a terminus in a containing concavity. This relationship
is observable in particular from a central position, but is also
evident from other points and during circulation. A shape
that is equidistant from us at all points is the easiest to grasp
visually. Because the eye need make no depth adjustments,
an impression of tranquillity and uniformity emerges. Corre-
sponding to the concentric form of a concave curvature is the
radial structure of the direction of the gaze in the form of ra-
dii that converge towards the beholder or emanate from him
or her. A tunnel vault thus appears as a space that rises above
us, and in which the radii extend centrifugally (Schmitz 1966,
47). In notions of the celestial canopy or heavenly vault, the
sky above us also forms a concavity, one that is supported by
the overhanging roofs of houses.
The formal expression and > form character of concavi-
ties is that of an enveloping and opening receptiveness. We
feel ourselves contained by concave spaces. Concave walls,
masses, or structural elements not only stand opposite us as
counterparts, but also surround us, even when we turn and
allow the gaze to wander. As the built concretization and for-
mal correspondence to the > personal sphere, they make it
possible for our bodily > extension to nestle into a containing
form. Think, for example, of caves with rounded interiors.
Gaston Bachelard (1964/1994) speaks of a ‘round existence’,
and recalls the way in which birds press and rotate their bod-
ies in order to shape the concavities of their nests.
While concavity represents the closing, enveloping prin-
ciple, convexity represents the repelling principle of a bulging
curvature that opposes us. The beholder is separated from a
convex curvature at heterogeneous distances, and its percep-