Shape

227 Solids, Fractals, and Other Zero-Dimensional Things
culate, and I can measure their complexity as a result of the rules I use to pick out parts.
In this sense, shapes may be just as complex as anything else. There is, however, a telling
difference. The complexity of shapes is retrospective. It’s an artifact of the rules I try
that depends on how they’re actually applied. Without rules, there’s no complexity.
And with rules, complexity varies—up and down—as I calculate. There aren’t any
units before I start, and I have to finish to get an accurate and final count. I may not
know what’s going to happen until it does.
I’ve already shown that units in combination needn’t correspond with experience.
What a computer knows and what I see may be entirely different. The shape
is sixteen lines that describe two squares with four sides apiece and four triangles with
three sides apiece. This explains how it works. But there are too many lines, and too
few. Some parts are hard to delete—the outside square won’t go away. And some parts
are impossible to find—lowercase k’s aren’t there. But even if I’m willing to accept this
because the definitions of squares and triangles are exactly what they should be—and
for the time being, they’re more important than k’s—there’s still a problem. I may not
know how the shape is described before I start to use it. Does it include only squares, or
some combination of squares and triangles? I can see the shape easily enough—there
it is
—but I can’t see its decomposition. I need to find this hidden structure. Experiments
are useful, only they take time and may fail. I’m stuck without help and the occult
(personal) knowledge of experts. Shapes aren’t anything like this. What you see is
what you get. This is a good reason to use shapes in design. There are times when I
don’t know what I’m doing and I look at shapes to find out. That’s why drawing makes
a difference. It’s a little like listening to what you say to learn what you think. But
there’s nothing to gain if I have to ask somebody else what shapes are. Then I don’t
need to draw because I can see what they say.
Decompositions don’t work. There are many reasons for this as just described,
and maybe a few more to prove my point. First, there’s the problem of the original
analysis. How can I possibly know how to divide a shape into parts that suit my present
interests and goals and that anticipate whatever I might do next? Nothing keeps
me from seeing triangles and K’s after I draw squares—even if I’m sure that squares
are all I’ll ever need and I’m blind to triangles and K’s right now. It’s much easier to