Shape

389 Background
and his current followers. They relish hard problems where things stay the same, yet
sometimes problems are hard only because of the way they’re set up to start. It’s easier
not to worry about this and to let things alter freely, as they do calculating with shapes
or copying Wittgenstein’s ‘‘figures on paper.’’ An account of George Birkhoff’s aesthetic
measure and its information-theoretic counterpart E Z is in Algorithmic Aesthetics. 17 For
an incisive discussion of value in design, see March’s classic essay ‘‘The Logic of Design
and the Question of Value.’’ 18 March goes on to consider C. S. Peirce’s famous trio of
inferential categories in design—these are deduction and induction, as expected, and
then, in addition, abduction. Roughly speaking, going from shapes to their descriptions
corresponds to deduction, going from descriptions to shapes to abduction, and
figuring out schemas and rules in the first place to induction. March puts this together
in a cyclic model of design that applies in some telling ways. Peirce is keen on clarity,
albeit each kind of inference holds alternative choices with a combinatorial (syntactic)
uncertainty or ambiguity of its own. The lines I’ve quoted form Søren Kierkegaard
are copied from my introduction. Mine Ozkar chronicles the artistic adventures of
Denman Ross and Arthur Dow, and the incidental interactions of the former with
William James at Harvard and the noteworthy relationship of the latter with John
Dewey at Columbia. 19 More important, though, shapes and rules are compatible with
open-ended experiment in the design studio.
All this prevails in the distinctive pedagogical standpoint shared by Ross and Dow. . . . Individuals
are encouraged in their unique ways, which can only be represented in temporary and discardable
conceptual structures. 20
Better still, every rule—even an identity—implies a new (original) conceptual structure
every time it’s applied to a shape. The way topologies are redefined on the fly is a good
example of how this works, but there are many other examples throughout this book.
Ordinarily, design and calculating are worlds apart. Sometimes, a brief alliance is
formed when calculating produces things designers want to use and can’t make on
their own. Then it’s one way calculating and another way when design works its magic—there’s
a discrepancy between what the computer does and what the designer sees.
This exposes shortcomings in both calculating and design, and the divide between
them. Yet now, the ‘‘two cultures’’ fuse. My initial metaphor is equality—
design ¼ calculating
—not because design is calculating in the usual way, but because calculating is more
than it’s supposed to be. Design is calculating with shapes and rules. It’s seeing and
doing, and all that follows as I go on.
Today, there are far too many examples of shape grammars in design—including
architecture and engineering—to be cited item by item. Most of this material is in
Environment and Planning B: Planning and Design from 1976. Nonetheless, there are
two pioneers of the subject whose work has been widely influential—Ulrich Flemming
and Terry Knight. 21