Shape

130 I What Makes It Visual?
be described consistently to calculate? The shape gðxÞ may have indefinitely many
descriptions besides the description that defines it. And none of these is final. Embedding
works for parts of shapes—not for their descriptions—when I try the rule. My account
of how I calculate may appeal to as many different descriptions as I like that
jump from here to there haphazardly. It may sound incoherent or contradictory—
even crazy or nuts—while I’m doing it. But whether or not the conclusion is favorable
with useful results doesn’t depend on this. I can always tidy up after I’ve finished calculating
to provide a retrospective explanation that’s consistent. Trying to be rational
as I calculate may not be an effective way to go on. Rationality is simply a kind of nostalgia.
It’s a sentiment to end with, after everything has finished and a pattern can
be established. A process becomes inevitable once it’s completed and final. Then it’s
safe to say what happened in one way or another, and not worry that this could all
change.
So when is calculating visual? I have another answer that may be better than my
formula dimðelÞ ¼dimðemÞ.
Calculating is visual when descriptions don’t count.
Descriptions aren’t binding. There’s no reason to stick to any of them that’s not mere
prejudice. I’m happy with this, yet I’m not sure everyone will be happy with what it
means for everything from reasoning in its widest sense to narrow technical specialisms
like parametric design that go only as far as schemas with set variables. I use rules
to calculate, but I don’t have to play by them. I can cheat. And I can get away with it
calculating. I’m totally free to change my mind about what there is, and I’m free to act
on it. Children play games in this way, unless we intervene to make them follow the
rules. But these are limiting, grown-up rules, not the kind that children must have
already. Children’s rules are surely more like mine. There are no definitions to conform
to, and there’s no vocabulary to build from. It’s all fluid and in flux. Constituents—
atoms, units, and the rest of it—are merely occasional afterthoughts. Is this going too
far? What makes me think I’m calculating? But then, what’s reasoning all about?
What’s That or How Many?
I confess. I really don’t know what reasoning is, and I’m not totally sure about calculating.
For James, reasoning is sagacity and learning. And surely, this includes what I’ve
been saying, especially about calculating with shapes and rules. Still, others may demur
for one reason or another. Not everyone is as generous as James when he encourages
alternative points of view and welcomes the novelty they bring—reasoning is at stake.
There are standards to keep that decide exactly what’s right and what’s wrong—no
doubt about it. But where does this lead? Wandering around is the best way to see.
I’m going to look at some of the things a number of thinkers say about reasoning, calculating,
and their relationships. This lets me explore visual reasoning and calculating
in various ways. I want to reinforce the idea that shapes and rules do many things that
calculating isn’t supposed to do. (Shape grammars aren’t what you think they are.) This