Shape

104 I What Makes It Visual?
to the triangle
using a reflection, then I get the result I want. My eyes show me how to do something
I never had in mind. My representation of the initial shape as a pair of independent
polygons—a triangle that moves around and a chevron that stays put—doesn’t tell
me what to see, and in fact it keeps me from seeing what I need. It’s hard to believe,
but there’s actual proof. Calculating is creative. It conjures up a triangle and a chevron
out of thin air. But the alchemy is real—it’s all in the pentacle.
The rule
produces the star
from a triangle and chevron, and I can see both in the star. But when I apply the
rule
to the star, it changes what I see in a surprising way. Lines fuse whenever they combine,
so that all prior divisions disappear. Then new divisions are possible—anywhere.
I can find triangles, and chevrons along with them, to reconfigure the star. I don’t have
to foresee anything before I begin or have any idea of what’s going to happen. And I