Shape

305 Background
in everyday design practice, and with taxonomic prescience defines types of emergence,
anticipated and not, and ambiguity before rules are tried), 18 Ramesh Krishnamurti
(the first computer implementation of shapes and rules—around 1980—and
many improvements since in terms of shapes and their boundaries), 19 Djordje Krstic
(algebras of shapes and decompositions), 20 Lionel March (miracles and what they
mean), 21 and Mark Tapia (computer implementations). 22 There are other authors,
though, of equal interest. More references are in part III.
George A. Miller’s speculative comments at the beginning of this part are in ‘‘Information
Theory in Psychology.’’ 23 His extension of the engineer’s idea of noise to
define ambiguity in a theory of semantic information is captured in the neat formula
ambiguity ¼ noise
Perhaps Miller is looking for a way to handle ambiguity to help with meaning, so that
semantic errors can be usefully detected and corrected. This seems to be a goal today
for advanced research in computer science. I recently saw the sign
AMBIGUITY
in an office for PhD students in artificial intelligence (AI) who were working on ‘‘design
rationale’’—in particular, on a sketch-recognition language complete with a vocabulary
of predefined shapes and a syntax for combining them. 24 It seems that ambiguity
is something to stop in AI. But this seldom if ever happens with signs, and can’t be
expected for designs. In fact, it misses what drawing and sketching are for. Meaning is
closed off in advance to anything new. There’s no reason for reason. My retrospective
account of meaning in terms of topologies provides a workable alternative in an openended
process. 25
I refer to Alfred North Whitehead and extensive connection in several places. 26
In particular, there are his diagrams from Process and Reality showing how regions are
related, first on page 174 and then on page 211. Shapes connect both to Whitehead’s
regions and to Henry Leonard and Nelson Goodman’s more comprehensive individuals.
27 These are also the focus of Stanislaw Lesneiwski’s earlier mereology (the theory of
parts and wholes). Alfred Tarski describes it nicely. 28 Peter Simons provides an omnibus
survey of the whole field—his discussion of extensional mereology is useful to
compare shapes and individuals. 29 Goodman and W. V. Quine use ‘‘shape-predicates’’
to calculate with ink marks (individuals) in a ‘‘nominalistic syntax’’—after discussing
this with Tarski and Rudolf Carnap. 30 The brainpower is simply staggering. It seems
almost comical, along with the results that suppress what marks can do. It’s amazing
how hard it is to make the world—even a small part of it—behave syntactically, and
then everything is lost. Luckily, syntax isn’t necessary to calculate. Leonard and Goodman,
and Lesneiwski, establish the Boolean standard for individuals, too, all with
qualms about the zero. 31 Shapes are like ‘‘regularized’’ point sets, as well. 32