Shape

355 Seeing Won’t Do—Design Needs Words
x fi
that help to count, and identities and other rules in the schema
x fi tðxÞ
Topologies are simply descriptions that show how I’m calculating and how shapes
and their parts change continuously as I go on. But I may want to name parts and
give them meaning in alternative ways. So, on the other hand, I sketched a general
approach in which different algebras are combined in sums and products to define
compound shapes. It includes both what I did in algebras like U 12 þ W 22 with lines,
planes, and colors (weights) to produce paintings and what I did originally when I
handled shapes and colors separately. Now I’m going to give a couple of examples to
illustrate some of the things I proposed, strictly with shapes and words—actually numbers,
but these are words as well, and are largely equivalent in practice. Using words
and using numbers both require looking at what’s there. Words and numbers divide
shapes, naming their parts, although numbers do it sequentially in order to count
them up. The two work together to describe visual experience. They’re there to give
shapes meaning and they tend to keep it constant. The consistency seems right, yet it
isn’t necessary. Ordinarily, it’s expected, and it lets us anticipate the future and plan for
it without having to worry that everything might change without rhyme or reason.
Perhaps this explains why creative activity, drawing and playing around with shapes
when their parts alter erratically, is apt to seem ineffable. Yes, there are always topologies,
although they aren’t exactly everyday descriptions in words. But words and
descriptions don’t have to be used in design all the time, only if they’re useful. And
they are in my two examples. The second is the more elaborate. It uses schemas and
rules for Palladian villa plans to explain how shapes and words (numbers) work and
what this shows.
The main idea is easy enough—I’m going to associate description rules with the
rules I apply to shapes, and use both kinds of rules to calculate in parallel. Every time I
give a rule for shapes, for example, this one
there are description rules for something else:
(1) If the new shape is not the previous one, then the total number of squares I’ve
inscribed increases by one, where squares are defined in the identity