Shape

21 Answer Number Two—Three More Ways to Look at It That Tell a Story
Symbols are OK, but shapes do something different. They don’t always look the
same. Shapes are subtle and devious. They combine to confuse the eye and to excite
the imagination. They fuse and then divide in surprising ways. There are endless possibilities
for change. How to deal with this novelty while you calculate—neither limiting
the alternatives nor frustrating the process—is the test. It’s a question of what calculating
would be like if Turing and Post had been painters instead of logicians, although
Turing was a photographer. Painting and calculating together—what an exotic idea.
Only the idea might not be that strange. Herbert Simon proposes as much in his speculative
account of social planning without goals in The Sciences of the Artificial. Painting
and language are creative in the same way. They rely on ‘‘combinatorial play’’ with
simple things to make complex ones. There are symbols, and rules to combine them.
(In fact, there’s more. Chomsky and Simon are both keen on describing things—
sentences and pictures—as parenthesis strings, that is to say, in ‘‘trees’’ or, identically,
in ‘‘hierarchically organized list structures.’’) But my idea is not to show that painting
is like calculating in Turing’s sense—it’s to make Turing’s kind of calculating more like
painting. This means giving up on symbols. And more, it means showing how my calculating
as painting and Simon’s painting as calculating are related. This is what my
scheme for visual expression with shapes and verbal expression with symbols is all
about.
The best way to see what’s involved here is to try to use symbols to calculate with
shapes. The trick is to segment shapes into lowest-level constituents—these are the
symbols or units that are necessary for syntax—and to combine these constituents
using rules in the same way that angle brackets are combined to define strings. Analogy
number 2 is
shapes : lowest-level constituents < sentences : words
I’ve given the unknown x a name, but the difficult task remains of defining the constituents
to use. Which way of dividing shapes into parts makes the most sense in terms
of what I want to calculate? Which analysis works best? The main difficulty may already
be obvious. In design, it may not be evident what you want to calculate before
you start. You may not know until you’re finished. The constituents may change
dynamically—is this possible?—as long as calculating goes on. That’s one reason why
the unknown x is undefined, why the vocabulary of design is so elusive. But let’s try
to find fixed constituents anyway, just to see how it comes out.
What constituents should I use to describe the shape
if I want to calculate with it? Well, it’s going to depend on the rules I use—both the
rules I apply to the shape itself and the rules I apply to the shapes produced from it in
an indefinitely distant future. Maybe rules are like this