Shape

215 ‘‘Nor Do Lineaments Have Anything to Do with Material’’
is the first algebra of shapes in the series U ij in which (1) basic elements have boundaries,
and the identity relation and embedding are different, and (2) there are rules that
are determinate and rules that aren’t when I apply them to calculate with shapes. For
example, the rules I’ve already used to find and move polygons in stars and superstars
are determinate, and rules in U 11 are also indeterminate in U 12 . The algebra U 12 has
extended basic elements and the right Boolean and Euclidean properties. It’s representative
of all of the other algebras where i isn’t zero. This lets me show almost everything
I want to about these algebras and the shapes they contain in line drawings.
And that’s mostly what I’ve been using. Pencil lines on paper are a perfect way to experiment
with shapes, and to see how they work when I calculate. I rarely use anything
else—perhaps a few points and planes now and again. Then the technology is still easy
in the right way.
‘‘Nor Do Lineaments Have Anything to Do with Material’’
Alberti points out that lines—and likewise points, planes, and solids—don’t have anything
to do with material. This is a dogma in geometry, but sometimes the connection
is worth making in design. And in fact, there are a host of things that can be connected
with basic elements and shapes when I calculate. The path is clear when the algebras
U ij are elaborated and combined in different ways to define new algebras of shapes.
This provides an open-ended repertoire of expressive devices that can be used in whatever
way you please.
Shapes often come with other things besides basic elements. Labels from a given
vocabulary, for example, a, b, c ..., may be associated with basic elements to get shapes
like these
The labels may simply classify basic elements and so parts of shapes, or they may have
their own semantics to introduce other kinds of things. In a more ambitious fashion,
basic elements may also have properties associated with them that interact as basic elements
do when they’re combined. I call these weights. Weights go together with basic
elements to get shapes that look like these