Polymorf - Knowhere

Preface

What images come to mind when you think about "space"? Three-dimensional 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 semi-regular 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 man-made

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!

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