Shape

382 III Using It to Design
x fi x
is a good example. I first erase the shape assigned to x and then draw it again exactly as
it was. This is copying according to the formula
ðx
xÞþx
But there’s more to rules than identities that keep shapes the same—even if this
changes the way shapes look. Rules in the schema
x fi tðxÞ
copy a shape or any part of one, erasing it and drawing it someplace else. The schema
shows again why embedding—fusing shapes and then dividing to pick out parts—is so
important. What you copy depends on reciprocal tests—what you can see with your
eyes or trace out with your hands. And there’s nothing rote about the results when
there aren’t any units to keep you from going on in your own way. Copying triangles
with the rule
to turn the shape
upside down
proves it beyond doubt. Copying three triangles gives two new ones to copy, and then
this goes in reverse from two triangles to three. There’s magic in the scribe’s hand
when there’s always something new to see. (This may not be scholarship, but it does
seem to be art.) Or perhaps boundaries are better as copies to delineate regions and
mark endpoints. This is one way drawing works to copy what’s there. Then the rules
in the schema
x fi bðxÞ
are perfect. The schema shows even more how copying changes according to what you
see and what you draw, as boundaries are decided in different ways—here in a collage
of points, lines, and planes