Shape

50 Introduction: Tell Me All About It
Shapes are indeterminate—ambiguous—before I calculate, and have constituent
distinctions—parts—only as a result of using rules in this ongoing process. At least
that’s what I thought, and that’s why I thought calculating with shapes had a lot to
do with design. Schon didn’t say one way or the other. Maybe he enjoyed the ambiguity.
It’s always there to use, and there’s no reason to make up your mind when you can
go on talking.
There’s an illustration on page 10 from Paul Klee’s Pedagogical Sketchbook that
shows ‘‘medial’’ lines. 12 Points are connected to make lines that form planes in the
way Miss H—— said. I like to think that Klee and Wassily Kandinsky, too—now it’s
explicitly Point and Line to Plane—might enjoy the idea of calculating with shapes.
The first lessons in Klee’s Sketchbook are wonderfully suggestive in this regard. I return
to them in part II. And certainly, Kandinsky was trying something similar, although, at
root, combinatorial. 13
George Birkhoff’s Aesthetic Measure is well worth looking at today. 14 It’s one
of the few books on aesthetics I know that actually contains pictures and worked
examples. This alone is a major breakthrough. A technical account of Birkhoff’s formula
and new examples are in a later book by Gips and myself. 15 We also offer
our own measure E Z , with much else of independent interest. Like Birkhoff’s formula
M ¼ O=C, E Z involves generic ideas of unity and variety—richness of ends and economy
of means—that apply to a broad range of things from paintings to music to scientific
theories. But the definition of E Z depends on algorithms and information theory.
There’s counting, and a ratio for relative entropy. As I said earlier, I’m not keen on it.
But Gips is still very enthusiastic, and who knows, he may be right.
Elizabeth Goldring did the nifty word door I’m inviting you to enter—it’s on
page 13. This is a standard narrative device to begin stories and tales. Lewis Carroll’s
Alice pops to mind whenever things change like shapes without rhyme or reason. But
there’s also a rabbit-hole to start—or is it
—and then a little door. What’s at stake here is not how good you are at this—
Alexandra’s l’s, i’s, and fish are better—but how to do it not knowing in advance that
you’re going to. (For more with an eye to children and calculating, and in particular,
on counting things like tables and desks, see part I, note 14.) Otto Neurath talks about
visual language in ‘‘Visual Education’’—
Visual statements and verbal statements are different and not translatable element by element. An
example: a boy walks through a door