Conclusion |
|
In your
trek through Knowhere you have seen how the structure of space
orders things |
around.
It facilitates individual expression of form on the local level while
maintaining |
overall
uniformity of composition on the extended level. |
. |
On the
one hand, as you saw in Geometry rules, spatial ordering principles permit
things |
to have
complementary mirror planes and axes of symmetry, similar surface and |
volumetric relationships, congruent structural elements, and dual
frameworks, to name |
a few.
This allows structures to be transformed into each other via truncation,
sectioning |
and
rearrangement, compounding, and stellation operations. Also
structures can be |
inscribed in each other and they can be packed together to fill space.
All of these |
attributes are conducive to creating a rich mix of diverse forms that can
inhabit space. |
. |
On the
other hand, the structure of space limits diversity of form by invoking
certain other |
ordering
principles that things must abide. As you probably already
know from geometry, |
two-dimensional polygons and three-dimensional polyhedra must maintain a
topological |
balance
between their vertices, edges, and faces. And, as you saw in
Building stability, |
for
polygons, polyhedra, lattices, and plate structures to be inherently
stable they must |
adhere
to additional topological constraints. Another purely geometrical
limitation is that |
the sum
of the interior or dihedral angles of polygons and polyhedra must be
constant. |
And the
sum of the angles about a point must equal 360o, for example.
In structural terms, |
the
bearing capacity of beams and columns is limited by spatial considerations
such as |
their
moment of inertia and their length. And the strength of trusses and
spaceframes |
depends
significantly on the ratio of their height, or depth, to their span.
All of these |
factors limit the possible forms that things can take. |
. |
Taken as a whole, these abstract ordering principles provide the
structural matrix within |
which the dynamic interaction of physical forces are played out in the
real world. In |
Structure matters, you saw how the crystal lattice structure accommodates
the attractive |
and repulsive forces of atoms of different size, ligancy, and charge so
that they can pack |
together uniformly into elements and minerals. Building stability
demonstrated that the |
omni-triangulated two-dimensional truss structure permits the internal
forces induced by |
external loads to be exactly and intimately balanced by aligning them
axially. Likewise, |
the three-dimensional spaceframe framework can bear a load perpendicular
to its plane by |
dissipating the resulting forces axially among its members by means of
lattice action. The |
stability of a plate structure is due to the fact that its plates can
dissipate internal forces |
across the entire surface of the plate, and concentrate them at its
edges, as counter acting |
shear stresses. A lattice tower can dissipate its load throughout
its omni-triangulated |
framework. And, Gizmoneering showed that machines can be engineered
with different |
combinations of rigid and moving parts to efficiently convert and transmit
externally |
applied forces into mechanical motion that can do work. |
. |
All of these structural systems owe their strength, stability, and
efficiency in large part to |
the structural properties of space. Without these ordering
principles existence might well |
be relegated to either a diverse sand pile of non-uniform particles at one
extreme, or a |
single, uniform entity at the other. Instead, because of these
principles, we enjoy a great |
diversity of materials and structures that contribute substantially to our
welfare and |
security. Indeed space is something else! |
. |