Shape

11 Answer Number Two—Three More Ways to Look at It That Tell a Story
The measure—M—was perfect. You could use it to calculate with numbers to find the
aesthetic value of polygonal shapes like these
and other things such as ornaments, tilings, vases, music, and poems. So I calculated in
earnest. But there were problems when I tried to see in the way Miss H—— implied I
should. Shapes that looked different to me had the same aesthetic value. And the value
of a shape didn’t change when I saw it in a new way. One description didn’t seem to be
enough. You could just as well try Birkhoff’s measure with your eyes closed. It was mechanical
and misleading. There wasn’t anything to see.
My question was still there, waiting to be answered. But my time hadn’t been
wasted—now I had Birkhoff’s marvelous idea: that I could calculate to find an answer.
Of course, this didn’t seem to square with what Miss H—— had shown about counting.
But I was young and didn’t mind the inconsistency. Calculating was something I
could do. And maybe it was too soon to tell if it worked. Only what could I use to calculate?
Birkhoff’s measure didn’t work. Was there another formula that would—a kind
of design equation that captured the right variables? No, that was out, too—it was still
a single description. Seeing was the key. Maybe there was another way to paint by
number that went beyond connecting dots. Suppose I could calculate with shapes.
Was this calculating the way I learned in school? Was it just counting out? What did
it mean to calculate anyway? There was more to find out.
Growing Up—How I Learned to Calculate
There are at least two ways to calculate that furnish practical answers to my original
question about where lines go on a blank sheet of paper. There’s the right mathematics
for design, and the special mathematics of design. It’s easy to see that my prepositions
are opposites. They’re almost mirror images—fo’ and of. And if I concatenate them—
the r is for reflection—they form the palindrome
forof
This is probably not what you expected. But it does use symbols to anticipate what I
want to do with shapes. There are two sides to it. First, it suggests a way of calculating.
I’m combining symbols in a deliberate way according to rules that define palindromes.