Shape

12 Introduction: Tell Me All About It
The mechanics of this is sketched a little later. And then, there’s a trick that relies on a
sudden switch in perspective. This is fairly common in puns, sight gags, and other
practical things—for example, the word bed that children make with their hands
to distinguish the small letters b and d. There’s just one way to do this—try a rotation.
Well, I guess you can cross your arms to confuse b and d with deb. But maybe
there’s more to put this right. ‘‘Bed’’ is an especially nice mnemonic—the word
bed looks like a bed, so the compound noun ‘‘word bed’’ contains what it means. The
word
bed
is a word bed, and so, it appears, is forof. I’m going to play tricks like this as I calculate
with shapes—in fact, every time I try a rule.
Ambiguity lets me change what I see as I talk about it:
—The shape
is a square and two diagonals. And it also shows triangular planes.
—Are you positive about that? Which planes are they?
—There are only four. They’re easy to see. Sure, it’s perfectly clear. Use your eyes.
—OK, let’s see. You said it’s a square and its diagonals. Sides and diagonals are single lines, aren’t
they? So you must be looking at the planes
with boundaries from these lines. What other choice is there?
—Don’t be silly—use your eyes. What I said isn’t what I see. Diagonals divide in four other triangles.
My planes are obviously these
How can I do this with rules? And what does it mean for calculating? Let’s get back to
my distinction between the mathematics for and the mathematics of design, and see
how this works out in the normal way.
(Seeing words for what they mean instead of as strings of letters for sounds is
nothing new. I know a poet / visual artist who designed a wonderful word door