Shape

372 III Using It to Design
These were the exercises I tried for shapes and rules in ‘‘Two Exercises in Formal Composition.’’
They set everything up for design synthesis and stylistic analysis. Spatial
relations were enumerated in terms of a given vocabulary of shapes, but calculating
with shapes wasn’t restricted in this way. And once more, inverses are defined in the
additional schemas
divðxÞ fi x
A þ B fi x
I used polygons in divðxÞ fi x for rules like this one
to complete Klee’s palm-leaf umbrella. Of interest, too, I can recast the schema
x fi x þ bðxÞ in terms of the schema x fi A þ B, so that x in the left side of
x fi x þ bðxÞ is a variable over A and B, and in the right side, x is A and bðxÞ is B.
This isn’t exactly normal mathematics—it’s more like Ludwig Wittgenstein’s kind of
calculating where ‘‘the figures on paper alter erratically’’—but it does let me add the
‘‘usable’’ schema
x þ bðxÞ fi bðxÞ
to my list of inverses for rules like this one
when x fi bðxÞ, that is to say
applies too broadly—perhaps to the shape
to produce