Shape

156 I What Makes It Visual?
(TRI(XYZ) ((PT X) (PT Y) (PT Z) (ELS XY) (ELS XZ) (ELS YZ) (NONCOLL XYZ)) NIL)
which says a triangle consists of three points XYZ such that the predicate ‘exists a line segment
between’ (ELS) holds, pairwise, between them, and that the 3 points are noncollinear
(NONCOLL). When this grammar was supplied along with the input, the program found the 16
triangles.’’ 8
But where does the input pattern come from without prior analysis? How is this done
today? To find out, I asked one of the stars in my shape grammar class how he would
represent Evans’s shape, so that it contained everything he could see. ‘‘I’d drag a point
to make a square, insert the diagonals, and then rotate [and trim] them to make the
horizontal and vertical.’’ It works, but triangles may or may not be defined, depending
on how squares are handled. If there are triangles, then there are four. No one questions
the inevitability of this kind of structure when you calculate—well, almost no
one. I do a seminar in design and computation. One of the participants knows exactly
what it’s about—‘‘We only talk about it here.’’ Her peers aren’t so sure. They say, ‘‘It’s
theory—it can’t be used to make things. What can you do without structure?’’ For a
start, you might try and see. Picture languages, etc., encourage Evans’s kind of thought,
and have implications elsewhere. Christopher Alexander’s ‘‘pattern language’’ is worth
looking at, especially with its intended applications in design. 9
I start with a quotation from Ivan Sutherland that’s remarkably forthright about
the importance of structure in computer drawing. 10 I like it a lot because it describes
the crucial difference between pencil and paper—structureless stuff—and computer
drawings so accurately. Herbert Simon’s The Sciences of the Artificial is a classic. Every
time I pick it up, I find something more of immediate interest in design. The quotes I
use are from the second edition that includes the new chapter ‘‘Social Planning’’ in
which Simon links painting and calculating. 11 John McCarthy discusses the missionaries
and cannibals puzzle in a short paper in Artificial Intelligence. 12 The circumscriptive
inference in McCarthy’s example 1 shows how objects are limited from the
start. 13 The material from Marvin Minsky is from two places. His thoughts on creativity
and the Body-Support concept are found in The Society of Mind. 14 And the rest on paradigms,
heuristic search, and structure is in his chapter in Patrick Winston’s book The
Psychology of Computer Vision. 15
Terry Winograd and Fernando Flores show the limits of calculating with fixed
representations. 16 But their conclusions seem much too pessimistic once embedding
in its robust sense is taken into account. I quote from Hans-Georg Gadamer’s Truth
and Method, 17 Robert Sokolowski’s Husserlian Meditations 18 —the few lines on spatial
profiles—Gian-Carlo Rota’s Indiscrete Thoughts, 19 and, finally, Maurice Merleau-Ponty’s
Phenomenology of Perception 20 to show that you may really be calculating even when