Shape

357 Seeing Won’t Do—Design Needs Words
calculate—but it shows that knowing how to count means first knowing how to see.
This is where meaning starts and how it grows, and the process is far from dry. ‘‘To [observe]
well,’’ notes J. S. Mill, ‘‘is a rare talent.’’ Shapes are filled with meaning as rules
are tried. And it seems to me that this is the only kind of meaning that matters for
shapes, whether in words, numbers, or topologies. Perhaps it’s the only kind of meaning,
period. It depends on what I see and do, and on what I make of it as I go on to
see and do more. Rules apply to shapes and bring in words and numbers to make
this possible. It’s a process in which everything can interact and connect, and it’s all
calculating.
Let’s try something that appears to be a little harder, although meaning doesn’t
have to be when it’s a question of seeing. Suppose I’m looking at the rooms in a Palladian
villa plan, and that I want to count them. Once again, there are numbers, and this
involves distinguishing spaces and naming them in terms of what they’re for. And, in
fact, both naming and counting depend mainly on the rules I apply to pick out parts
and change them as I calculate to produce the plan.
Let L and R be the number of polygons in the left side and the right side of a rule,
and let k be defined as follows
k ¼ L
R
This seems to be OK, but there’s really a lot more to it than I’ve said. Rules are made
with shapes that aren’t divided in advance, and not with distinct symbols that are
ready to count. This isn’t generative grammar or syntax and words, so I have to figure
out a way to count polygons. But remember what I did to define squares and triangles
with identities from the schema x fi x. In much the same way, I can use erasing rules
from another schema
poly fi
to count what I want. These rules pick out polygons—there are rectangles, crosses, T’s,
and I’s—so that I add plus one every time a rule is tried with no chance of doublecounting.
There’s an example of this kind in part II for squares and triangles in the
shape
only it gives multiple answers between four and eight, and there’s another example in
part I for triangles in the shape