Shape

223 ‘‘Nor Do Lineaments Have Anything to Do with Material’’
algebras of weights where physical properties and mathematical ideas interact on equal
footing to get a nice result.
Weights are already familiar in architecture, graphics, and the visual arts, where
lines of different thickness are used in drawing
It’s no big deal to extend this idea in a variety of ways—to points, for example, when
they have area
and to planes and solids when they’re filled with tones
as I’ve already shown. Such properties have a neat algebra with a relation and operations
that correspond to parts and to sum and difference in an algebra of shapes.
Suppose that two lines of different thickness defined by numerical values—pen
size will do—are drawn at the same time, either one overlapping the other
The thicker line appears at full length, while the thinner one is shortened. And if the
two lines have equal thickness, then a single line is formed
In both of these experiments, the weight of the embedded segment common to the
lines is the maximum of the combined weights. So for the weights u and v, it’s just
the case that
u þ v ¼ maxfu; vg
And for parts, it’s easy to see that u a v when
u þ v ¼ v
The way weights combine in differences, however, isn’t as clear as it is for sums, and
there’s little in drawing that offers genuine guidance. But algebraic considerations