Shape

133 What’s That or How Many?
gone. There are no surprises—just rote results. Nothing is ever ambiguous or vague.
This is the end of anxiety and uncertainty, and it makes it unnecessary to trust others
and give them a chance to think on their own. But is it a sensible way to educate people
to recognize and exploit new opportunities? What good are my rules now? Of
course, training needn’t limit experience. It may be open-ended—for example, in
studio instruction and situated learning. In the latter, master and apprentice interact
during actual practice. They work on the same thing without having to see it in
the same way. They go on. There’s no underlying structure to control or guide the
process—‘‘structure is more the variable outcome of action than its invariant precondition.’’
This is like visual calculating. Nothing guarantees that it’s the same way twice.)
But why not try something new? Is training necessary for a successful conclusion when
I calculate?
Of course, even if we do not make the above assumption, this calculation could lead to usable
results.
Ignoring ‘‘the above assumption’’ is what visual calculating is about. Whether or not
you think it’s real calculating doesn’t actually matter. The ambiguity cuts in opposing
ways: once to explain why greater attention hasn’t been focused on visual calculating
as a useful alternative to calculating with numbers—the one isn’t calculating—and
then again to explain why it’s so easy to think that visual calculating is necessarily
the same as calculating in the ordinary way. I like to calculate by seeing. But whenever
I try, either no one believes it or they think I’m doing something else—that I’m calculating
by counting. Maybe I’m wasting my time when it comes to visual calculating.
Only what can I do? I want to see how far reasoning goes. And there’s always something
new to see that takes me somewhere else to look. My instincts aren’t conservative
when it comes to seeing shapes. There’s simply no need to remember what was
there before. I’m free to look again now to decide what to do next.
I guess my approach to shapes and rules isn’t the norm. This much is evident in
the quotation from Ivan Sutherland—one of the pioneers of computer graphics and
computer-aided design—that I started with on page 61. Here it is again—
To a large extent it has turned out that the usefulness of computer drawings is precisely their
structured nature and that this structured nature is precisely the difficulty in making them. . . . An
ordinary draftsman is unconcerned with the structure of his drawing material. Pen and ink or
pencil and paper have no inherent structure. They only make dirty marks on paper. The draftsman
is concerned principally with the drawings as a representation of the evolving design. The
behavior of the computer-produced drawing, on the other hand, is critically dependent upon the
topological and geometric structure built up in the computer memory as a result of drawing operations.
The drawing itself has properties quite independent of the properties of the object it is
describing.
The preliminary appeal to structure and memory in early efforts to draw with the
computer is unassailable today throughout practice and education. It makes the computer,
and pencil and paper appear to be irreconcilably different kinds of media. The
draftsman always has the option to draw it in one way and to see it in another—to