Shape

392 Notes to pp. 47–48
1994), 221–235. Of additional interest, see L. March, ‘‘Architectonics of Proportion: A Shape
Grammatical Depiction of Classical Theory,’’ Environment and Planning B: Planning and Design 26
(1999): 91–100, L. March, ‘‘Architectonics of Proportion: Historical and Mathematical Grounds,’’
Environment and Planning B: Planning and Design 26 (1999): 447–454, and L. March, ‘‘Proportional
Design in L. B. Alberti’s Tempio Malatestiano, Rimini,’’ arq 3 (1999): 259–269. March argues for
geometry in design and against making it digital in computer models, echoing Fowler that Greek
geometry wasn’t arithmetized. This fits nicely with shapes and rules.
3. Christopher Alexander’s ‘‘pattern language’’ is meant for a Platonic world that’s divided once
and for all. C. Alexander, The Timeless Way of Building (New York: Oxford University Press,
1979), and see also note 6 below. Still, change is a staple of studio teaching in architecture, especially
for digital architects who use parametric models and other computer tools in nonstandard
praxis. This is about being poetic—
[The] poetic act has no past, at least no recent past, in which its preparation and appearance [can] be followed.
. . . [The] poetic image is essentially variational, and not, as in the case of the concept, constitutive.
G. Bachelard, The Poetics of Space, trans. M. Jolas (Boston: Beacon Press, 1969), xi, xv. It’s hard to
imagine a respectable design instructor who doesn’t know Bachelard’s phenomenology and rely
on it in some way. But is the poetic image something to calculate? Variation is the business of
parametric models. Nonetheless, they’re constitutive and imply a Platonic world—finite elements,
etc. (constituents) are set in advance, that is to say, entirely in the past. This gives objective
(combinatorial) results that block subjective experience. A lot is left out. I’m free to see and do
more than my prior decisions allow. Constituents change—once shapes fuse, their immediate
past is lost and I can divide them in any way I choose. The whole reason for shapes and rules is
to make this kind of variation possible, so that calculating and seeing coincide. When I calculate
with shapes, what happens now isn’t decided by the rules I’ve used (preparation), but depends on
the rules I try (appearance). I can keep track of how shapes change in this process to define retrospective
links between what I draw and what I see, but these relationships are never fixed. They’re
reestablished afresh every time I apply a rule. There’s no concept for what I see and do, or anything
permanent. What comes next doesn’t follow a definite sequence. The poetic act has no
past—it’s always in the present. The poetic image is always something new.
4. 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. An early description of grammars for shapes (triangles) is in R. A. Kirsch, ‘‘Computer
Implementation of English Text and Picture Patterns,’’ IEEE Transactions on Electronic Computers
EC-13, 4 (1964): 363–376. Kirsch’s approach is unabashedly syntactic.
5. J. Gips, Shape Grammars and Their Uses (Basel: Birkhauser, 1975).
6. G. Stiny, Pictorial and Formal Aspects of Shape and Shape Grammars (Basel: Birkhauser, 1975).
Here and also in G. Stiny, ‘‘Kindergarten Grammars: Designing with Froebel’s Building Gifts,’’
Environment and Planning B 7 (1980): 409–462, I rely on vocabularies (alphabets) of shapes to
define shape grammars and spatial relations, but not without showing that vocabularies fail
when you calculate with what you see. The use of vocabularies of constituents or units to link calculating
and design may seem contrived. Yet history proves otherwise, for example, for logic and
architecture—‘‘Both enterprises sought to instantiate a modernism emphasizing what I will call
‘transparent construction,’ a manifest building up from simple elements to all higher forms,’’
P. Galison, ‘‘Aufbau/Bauhaus: Logical Positivism and Architectural Modernism,’’ Critical Inquiry 16
(1990): 709–752. Ludwig Wittgenstein’s Tractatus is crucial to this, and it’s the model for Susanne