Preface 

What images come to mind when
you think about "space"? Threedimensional space?

Outer space? The space
between these l e t t e r s ? A parking space? All of these
images 
connote the idea that space is
empty and devoid of any form of its own. Its existence is 
defined by its boundaries,
whether these are abstract dimensions, cosmological limits, or 
the surfaces of objects.
This also implies that space can assume any shape defined by 
those boundaries, which it can
of course. 
. 
Since the shape of space
appears to be completely dependent on those things that define 
it, you might assume that
space itself has no effect on the shape of the things that reside in 
it. After all, we
commonly speak of things occupying or taking up space. We speak of
it 
as though space is just a
passive recipient of the thing's form, like an empty hole that is 
filled with something.
Like it's nowhere. 
. 
However, space is not only
shaped by those things that bound it. It also forms the
boundaries 
of those things, whether they
are abstract geometrical constructions or concrete objects. 
Just as space is bounded by
dimensions, so too are the things that space surrounds. In fact, 
their dimensions are only
discernable in reference to the surrounding space. They have a 
front and a back, a top and a
bottom, a beginning and an end, an inside and an outside, a 
perimeter, a surface, and a
volume. They have a size and are separated from others by a 
specific distance. All
of these attributes are defined by the space within and without them. 
. 
However, space does more than
just form the boundaries of objects. It has a structure of its 
own that limits the structural
forms that things can exhibit. For example, each line can only 
have two end points.
Each plane has two surfaces and one perimeter. All polygons have a 
constant proportion of edges
to vertices. The ratio of the circumference to the radius of a 
circle
is an irrational constant. The sum of the interior or dihedral
angles of polygons and 
polyhedra must be constant. All polyhedra must have constant
proportions of edges, faces, 
and
vertices. Each regular and semiregular polyhedron has a constant set
of rotational axes 
and
mirror planes ... These are just a few of the ordering
principles that spatial limitations 
impose
on the structure of objects, regardless of their size or shape. 
. 
In the following lesson,
Geometry rules,
you will see how spatial constraints determine the 
structure of abstract objects
such as polygons and polyhedra. And how those ordering 
principles account for the
striking symmetry and transformability of these objects. Next, 
Structure matters
demonstrates how
this influences the way that atoms pack together to 
form elements,
and how elements are
combined together into minerals.
Building stability 
illustrates how these same
governing principles can be used to build stable manmade 
structures. And,
finally, in
Gizmoneering,
you will learn how stable and unstable structural 
elements can be combined
together to build simple machines. 
. 
Hopefully, you will see
that space is not nothing. It's something else! 
. 
Back
to Knowhere 
. 

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