Shape

216 II Seeing How It Works
where points have area, lines have thickness, and planes have tones. Among other
things, weights include different graphical properties such as color and surface texture,
but any material property will do, and more abstract things like sets of labels, numerical
values that vary in some way, or combinations of sets and values are fine, too.
Labels and weights let me put shapes together in alternative ways. I can place a
triangle on top of a square to make the shape
in the algebra U 12 , and then take away the triangle I’ve added. But the result isn’t the
square
that you expect from listening to the words—‘‘take away the triangle after you add it to
a square.’’ The piece that the triangle and square have in common is erased from the
top of the square in the way this happens in drawing to produce the shape
It’s a mistake to assume that the things words pick out are always independent in
combination. The intuition is common yet misguided, just another semantic fallacy.
Language doesn’t structure shapes permanently. You can always be surprised when
descriptions don’t count. But this is familiar territory—I experimented erasing squares
in the shape