Shape

378 III Using It to Design
I said I could augment my catalogue of schemas and rules, and indeed, it’s never
set once and for all. I can add to it as I please, and I have no reason to be parsimonious.
Actually, I enjoy being messy and prodigal. There are many ways to frame schemas
that are useful, even if the new ones I get are included in the ones I already have or
are derived from them in some way. For example, six of the schemas I’ve given are
ordered in terms of inclusion in the lattice
with a new schema at the top—
x fi X xA
—that extends the second schema x fi xA þ xAA I gave for ice-rays. And building from
scratch, the schema x fi A þ B þ C and larger sums are defined when the schema
x fi A þ B is applied recursively. But why should I bother with relationships like this?
Trying to decide whether one schema is included in another or whether to reduce
everything to a few ‘‘primitive’’ schemas seldom repays the effort. In general, each is
difficult to do, and either way there’s an inevitable loss of immediacy—all of a sudden,
things are harder than they look. It’s better to define schemas, so that they capture
what I want to see and do now—whatever that is. Schemas should be easy to use.
Some organization may help to remember what I have in my catalogue, although it
doesn’t go much farther than that. There’s little to gain—the descriptions schemas
contain don’t carry over to shapes as I calculate. Seeing more to get new designs is
what’s important, not elegant schemas in a formal catalogue. Nonetheless, my catalogue
is a database, and I’m told that’s vital for cognition and thought. But more rigor
and formality seems unnecessary, and even what there is may be too much. Adding to
my catalogue, so that there are always schemas to use, is all that counts.
Where do I find schemas to add? Well, I’ve already given some hints. I can combine
the sides of the ones I’ve got in sums, or switch sides to define inverses. Or I can
combine schemas in various ways—as above in x fi P xA, or by incorporating transfor-