Shape

404 Notes to p. 388
reasonably straight line? . . . Can you recognize different colors? If so, all that is left to be able
to draw or paint is to learn how to see.’’ This implies an algebra of shapes—basic elements
and weights, embedding, transformations, etc.—and rules to calculate.) The flip side of Smith’s
kind of copying was tried in twentieth-century art, when copying was copying what’s new and
not what’s really there. Of course, the two are likely the same, so long as ambiguity is something
to use. (What’s what in art tallies with the phenomenal what on pages 142–143.) It’s easy to see
that Richard Mutt’s Fountain of 1917 is copying—‘‘plagiarism, a plain piece of plumbing.’’ But as
soon as Marcel Duchamp saw his urinal, it was a readymade. (This kind of change is universal, yet
it’s easy to miss and thereby creative—perhaps also in Gertrude Stein’s line ‘‘ . . . a rose . . . .’’
Langer, 174–175, may not hear it when she explains how rote knowing makes us blind.) Alfred
Stieglitz’s documentary photograph of Fountain opened the second and final issue of The Blind
Man (New York: May 1917), edited by Duchamp, Beatrice Wood, and Henri-Pierre Roché. (Smith
would have approved of this picture as a frontispiece for one of his instructional-drawing books—
an exact copy of an industrial object!) And the unsigned editorial on the facing page was just
as clear.
Whether Mr. Mutt with his own hands made the fountain or not has no importance. He CHOSE it. He took an
ordinary article of life, placed it so that its useful significance disappeared under the new title and point of
view—created a new thought for that object.
In one way or another, ‘‘CHOOSING’’ has been standard in art, including the avant-garde, and
art education for years. It’s about seeing again, now and as I go on. What’s changed is that this
is what happens with shapes and rules. They show how art is calculating, and offer an effective
pedagogy. (We were too young for Miss H—— to tell us about Mutt, although I read about
Duchamp’s antics on my own and saw Nude Descending a Staircase (No. 2). Duchamp never tired
of making copies. In fact, he authorized a number of different versions of Fountain, and colored in
a full-scale photograph of his painting for the collector Walter Arensberg. A schema bðxÞ fi x or
bðxÞ fi x þ bðxÞ, or something close applies to a photograph to add colors. But better yet, there’s
plenty of copying in Duchamp’s nude(s) using rules in the schema x fi x þ xA. This makes it easy
to explore movement or any series of alternative views in a sum. Paul Klee’s palm-leaf umbrella
suggests as much with less fanfare, and so does Jacob Tchérnikhov’s drawing on page 278 in
which quadrilaterals are copied vertex to edge one either outside or inside another—triangles
optional. There’s always more to see and do, both copying and not.)
2. G. Stiny and J. Gips, ‘‘Shape Grammars and the Generative Specification of Painting and
Sculpture,’’ in Information Processing ’71, ed. C. V. Frieman (Amsterdam: North-Holland, 1972),
1460–1465. G. Stiny, Pictorial and Formal Aspects of Shape and Shape Grammars (Basel: Birkhauser,
1975).
3. G. Stiny, ‘‘Ice Ray: A Note on the Generation of Chinese Lattice Designs,’’ Environment and
Planning B 4 (1977): 89–98. What others say about shapes and rules when they’re used to produce
designs is likely to take the linguistic turn that the term ‘‘shape grammar’’ implies—
Architects and environmental planners, for instance, have used ‘‘[shape] grammars’’ to generate new ‘‘sentences,’’
novel spatial structures that are intuitively acceptable instances of the genre concerned. . . . The decorative
arts have received similar attention: traditional Chinese lattice designs have been described by a computer
algorithm, which generates the seemingly irregular patterns called ‘‘ice-rays’’ as well as the more obviously regular
forms.
The ice ray example shows that a rigorous analysis of a conceptual space can uncover hidden regularities,
and so increase—not merely codify—our aesthetic understanding of the style. . . . It shows which aspects
are relatively fundamental (like Euclid’s axioms in geometry, or NP and VP in syntax), and how certain features
are constrained by others.