Shape

314 III Using It to Design
does more when I apply it in another way
Then what I’m doing can repeat with plenty of surprises—here are four of them
It’s a lot easier to follow this with your eyes than to be consistent about it in
words. Certainly, I haven’t succeeded, fooling around with the squares I add and
the squares I see and moving chevrons that pop up in unexpected ways. It’s all a little
crazy when I can change what I see and do this freely. It’s hard to know what to say
that isn’t misleading or wrong. And really, that’s the whole story. I can use rules to
change shapes without being consistent about what I see. This doesn’t sound like calculating,
but it is. And it’s what you need to design, so that you can change your mind
about what you see and do as you go on. What it shows is that statement 4 isn’t that
far-fetched—
design is calculating when you don’t know what you’re going to see and do next
What a shape is depends on what rules are used, and when and how. This can vary for
different rules, and, in actual fact, it changes every time any rule is tried. Yet there are
some other things to consider that open up calculating even more.
As an example of what I want to see and do, the rule A fi B may be too narrow.
This was the problem in part II for squares and quadrilaterals. But there was a straightforward
solution I could try. Instead of drawing rules or pointing to specific shapes, I
could use schemas. This made calculating easier in some nice ways without compromising
the embedding relation.
The new setup is pretty much the same as the one I have for rules, with the addition
of variables, assignments, and predicates. There’s a shape
C
and now a schema
x fi y
where x and y are variables that take shapes as values. These are given in an assignment
g that may be restricted in some way by a predicate. The assignment defines the
rule