Shape

10 Introduction: Tell Me All About It
blindly to get them all without looking at what I was doing. Everything seemed to be
the same—it was numbing. Something had to change. Dots weren’t numbered to make
surprise pictures
like the ones in my game books. (I learned later that computers handled shapes in this
way with lists of points, here, segmenting two squares with ten lines—they’re units—
end to end.) And where did the colors go? At least Paul Klee got it right in his Pedagogical
Sketchbook: boundary elements—points and ‘‘medial’’ lines
—formed meaningful planes. But I didn’t know this. My results just didn’t add up. Was
this kind of counting a reductio ad absurdum? Miss H—— didn’t say—it seemed to me,
though, that it was what she wanted to show. It was something to discover on your
own. My eyes were closed from the start—seeing and doing weren’t tied. Figuring out
the possibilities one by one in a mechanical process didn’t go anywhere. It wasn’t art
unless you stopped to look, and then everything could change. Miss H——’s answer
was the same, and now I knew why. There was a lesson to teach, and there was a lesson
to learn—counting in this way wasn’t seeing. That’s why there were artists.
I was barely ten years old when I asked Miss H—— about lines, so I didn’t know
that my question was the private kind you kept to yourself. I looked around and asked
again. And every time I did, I got the same kind of brusque answer I’d heard from Miss
H——, or one of its mute derivatives. But I did get lucky. A year or so later, I found
George Birkhoff’s Aesthetic Measure. This was a real surprise! I turned the pages in
awe—Birkhoff had a similar question and an articulate answer. Who was this guy, and
how did it work?
Birkhoff was a famous mathematician at Harvard, and he knew that numbers
could be used to describe how things change. He had great definitions of order—O—
and complexity—C—and the guts to put them together in a wonderful formula
M ¼ O C