Shape

41 Tables, Teacher’s Desks, and Rooms
Tinkertoy or Lego. It’s exactly what computers do best, and sometimes they’re better at
games than we are. But it’s neither all I do nor all that computers should do. That’s
why I want to calculate with shapes. There are no constituents to stay the same. It’s
seeing, not counting. And what I see changes every time I try another rule. This is
always more than counting out.
There’s no denying that Peirce’s figures are the same. But they may not look it.
What’s neat about calculating with shapes and rules is that they let me have in both
ways. In fact, I can determine whether there’s identity or not for anything I see using
a single rule that doesn’t imply an arrangement of objects. That’s why I’m always free
to go on to something new. Nothing is eternal and unchangeable. What you see is
what you get.
Tables, Teacher’s Desks, and Rooms
I started looking at shapes when I was a child and have been looking at them ever
since. In fact, now that I have children of my own, I look for interest in shapes in
what they do. I like the way William James describes reasoning as the ability to deal
with novelty—to see and use new things in new situations. And I’m keen for my
daughters to catch on to this. I can’t imagine any better way to learn about novelty
than to experiment with ambiguity in shapes. No, I don’t talk to my daughters about
ambiguity, although Catherine asked me once what it really meant. I just want them
to be encouraged to rely on their eyes when they think. So what kind of visual education
are they receiving? In school, there isn’t much. Grade-school teachers haven’t
changed. Miss H—— would fit right in. The main emphasis is still on counting instead
of seeing—at least seeing isn’t taught. (I’m not alone in thinking so. Mel Levine is an
expert in education and a pediatrician who helps kids whose learning styles don’t fit in
school. They see things differently and are difficult to teach. Dr. Levine distinguishes
counting—‘‘sequential ordering’’—and seeing—‘‘spatial ordering’’—and is clear about
which is the more important in today’s classrooms.
Being great at spatial perception seems not to be a graduation requirement. So we may elect to do
nothing about a shortcoming in this neurodevelopmental function. After all, we don’t need to fix
everything!
Some kids are good at seeing, and some kids aren’t. But it doesn’t matter either
way, because schools don’t know what to do about it. It’s better to fix kids than
schools. This is a strategy of convenience that’s much too common—ignore strengths
in the one to correct weaknesses in the other. After all, there’s proof that schools teach
what kids need to succeed. Is this kind of success worth it? What makes it so hard for
schools to be inclusive? Why not teach to the strengths in all kids—visual, verbal, or
whatever—as they come? It makes sense to assume that everyone sees the world in a
novel way. The trick is to keep this advantage. There’s no telling what’s going to be
useful. Everyone’s point of view counts. There’s a lot to gain, in school and afterward.)
My daughters were given rulers with the ABC’s when they started kindergarten.
Their teacher said it was to remind them that words and sentences could all be made