Shape

143 What’s That or How Many?
The way rules handle ambiguity adds to Rota’s examples. The whats of shapes depend
on their parts, and these are resolved anew every time a rule is tried. For parts, ‘‘the
only kind of ‘existence’ that makes any sense—if any—is the evanescent existence of
the trump card.’’ Parts are necessary now, and then go away as I go on calculating. The
changing results contribute to the flow of meaning. Perception trumps logic to guarantee
that there’s something new to see that makes a difference. Wandering around is
really wandering around. Is this existential? Maurice Merleau-Ponty suggests as much
in an apt description of rationality.
Rationality is precisely measured by the experiences in which it is disclosed. To say that there
exists rationality is to say that perspectives blend, perceptions confirm each other, a meaning
emerges.
Like views are found elsewhere. James and Dewey both rely on the same kind of dynamic
rationality in reasoning. Jacques Barzun admires the ‘‘artist mind’’ below. And
my topologies keep a record of what I do as I calculate with shapes. So what’s next? Is
computational phenomenology in the cards? Don’t be silly. This isn’t what calculating
is supposed to do, but there’s no denying it—rules restructure shapes every time
they’re used. (Rota treats phenomenology and combinatorics as separate worlds—
what’s that and how many?—and has a cavalier answer when he’s asked how he
inhabits both—‘‘I am that way.’’ But it seems to me that there’s an important relationship.
It’s combinatorics if shapes are made up of points, and phenomenology if they’re
not. The elements of thought either have dimension zero or greater. There’s more than
identity in embedding.)
Calculating and reasoning—visual or not—common sense, missionaries and cannibals,
and other whats are no better off than shapes. But isn’t this how it should be?
The ambiguity is something to use, even with computers. Minsky is clever about this—
he thinks that calculating and reasoning are the same without excluding my kind of
rules that rely on embedding, the way McCarthy does, or impling that they’re very difficult
if not impossible to define, as Winograd and Flores do. Once you see the ambiguity,
it’s easy to make it work for you in many ways. In fact, what Minsky says about
creativity is telling.
What is creativity? How do people get new ideas? Most thinkers would agree that some of the secret
lies in finding ‘‘new ways to look at things.’’ We’ve just seen how to use the Body-Support
concept to reformulate descriptions of some spatial forms. . . . let’s look more carefully at how we
made those four different arches seem the same, by making each of them seem to match ‘‘a thing
supported by two legs.’’ In the case of Single-Arch, we did this by imagining some boundaries that
weren’t really there: this served to break a single object into three.
However, we dealt with Tower-Arch by doing quite the opposite: we treated some real boundaries
as though they did not exist: