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Therefore we shall now try to clarify the nature of these things that we call buildings by the following brief consideration.

For one thing, what is the relation
between location and space? For another, what is the relation between man and
space? The bridge is a location. As such a thing, it allows a space into which
earth and heaven, divinities and mortals are admitted. The space allowed by the
bridge contains many places variously near or far from the bridge. These
places, however, may be treated as mere positions between which there lies a
measurable distance; a distance, in Greek στάδιον, always has room made
for it, and indeed by bare positions. The space that is thus made by positions
is space of a peculiar sort. As distance or Stadion, it is what the
same word, Stadion, means in Latin, a *spatium*, an intervening
space or interval. Thus nearness and remoteness between men and things can
become mere intervals of intervening space. In a space that is represented
purely as spatium, the bridge now appears as a mere something at some position,
which can be occupied at any time by something else or replaced by a mere
marker. What is more, the mere dimensions of height, breadth, and depth can be
abstracted from space as intervals. What is so abstracted we represent as the
pure manifold of the three dimensions. Yet the room made by this manifold is
also no longer determined by distances; it is no longer a *spatium, *but
now no more than *extensio*—extension. But* *from a space as *extensio*
a further abstraction can be made, to analytic-algebraic
relations. What these relations make room for is the possibility of the
construction of manifolds with an arbitrary number of dimensions. The space
provided for in this mathematical manner may be called "space," the
"one" space as such. But in this sense "the" space ,
"space," contains no spaces and no places. We never find in it any
locations, that is, things of the kind the bridge is. As against that, however,
in the spaces provided
for by locations there is always space as interval, and
in this interval in turn there is space as pure extension.