Shape

58 Introduction: Tell Me All About It
can you measure the ability to see in your own way if it’s known in advance? Answers
on a test are right and wrong without results to check seeing. At least energy and sensitivity
are related to hand and eye. Shapes and rules bypass standards, tests, and the
trivial idea that accountability makes a difference. Final answers are out of reach when
there’s more to see and do.)
My own field strives to be a full-fledged science. And there are many who work
tremendously hard to make sure that this happens. Michael Batty is one of the most
energetic. He’s the long-standing editor of Environment and Planning B. This is the leading
scholarly journal in which serious papers on shape grammars appear. Listen to
what he says about shape grammars, urban morphology, and science. There are clear
echoes of Quine.
With the exception of research at the architectural level involving shape grammars which do unpack
the rule-based dynamics of how form is created, most conventional approaches to urban
morphology such as those based on fractal geometry and space syntax are limited in their explanatory
power. . . . There is no consensus in urban morphological research as to the fundamental [basic
or atomic] unit of description. . . . What is required is research into what constitutes the most
basic unit, but until there is consensus, little progress can be made. Only when there is agreement
about the nature of the data can science begin. Only then can classifications and comparisons be
made, alternative theories conjectured and falsified, and consistent methods of analysis meeting
basic mathematical standards developed. 50
I’m almost positive that shape grammars are mathematics—and not just as a
method of analysis. I’m equally confident that Batty’s fractal geometry (cellular automata)
and Bill Hillier’s space syntax are mathematics, too. 51 In fact, they’re calculating
with shapes when embedding is identity—in the special case where shapes behave
like symbols. But shape grammars, cellular automata, and space syntax also differ
according to Batty’s measure of explanatory power. This highlights the split between
shapes and symbols, even if standards and measures are likely to suppress novelty and
exclude a lot that may be useful. The truth is I really don’t like permanent standards
and measures whatever they show, and try to work without them. So why am I sure
that shape grammars are mathematics? I have some circumstantial evidence to support
my claim. First, shape grammars let me calculate in algebras of shapes, and this sounds
like mathematics to nearly everyone. It’s the same whether you like shape grammars or
not, and it may be the reason why. Words make a difference. More notably, though,
math majors—graduate and undergraduate students—take my classes on shape grammars.
And they do so voluntarily, without any kind of curricular coercion. Are there
better judges of mathematics than students who want to do it? Our free choices let
standards grow up and change within experience as part of it, whether they’re haphazard
everyday standards, rigorous mathematical ones, or something in between.
Shape grammars let me calculate with shapes—they let me use my eyes to decide
what to do next. In this way, they ‘‘unpack the rule-based dynamics of how form is
created.’’ No one has complained yet that there’s a loss of explanatory power because
there aren’t any units. In fact, shape grammars show it’s possible to go on rigorously