Shape

56 Introduction: Tell Me All About It
I mentioned William James on page 41. He links reasoning and novelty in The
Principles of Psychology. 39 This relationship yields yet another telling way to characterize
rules when I calculate with shapes. Rather than seeing and doing, the behaviorist’s
stimulus and response, or Peirce’s when and how, it’s sagacity and learning. These
terms may sound quaint today—sagacity fails when learning ends with standardized
tests—but they’re valuable nonetheless. I’ll return to both in part I. Meanwhile, it’s
the inverse of James’s relationship between reasoning and novelty that explains why
education is worth having. For James, ‘‘An ‘uneducated’ person is one who is nonplussed
by all but the most habitual situations.’’ 40 Learning how to behave in everyday
situations whether at home or on the job is a vital goal in education. You know what
to see and what to do as habits are fixed—when ‘‘the enormous fly-wheel of society’’ is
put in motion—so that life goes by with relaxed certainty, and it pays to be on time
and work hard. But in parallel, education acts against conservative inertia. This radical
impulse resists final results. Even the humdrum is more than it seems and always
merits another look. Seeing never stops. Blake saw a world in a grain of sand 41 —so
much for units—and found ‘‘Republican Art’’ in this hackneyed line
James has it going east and west not heeding the inconsistency. 42 Ambiguity is intrinsic
in what there is to see, and has many uses. At its best, education makes it possible to
experiment and learn how ambiguity works. You’re encouraged to play around freely
with whatever you see in an open-ended way. Novelty isn’t routinely dismissed as confusion
or noise, or as our Republicans imprudently demand, suppressed as a threat to
high test scores, big business, civic pride, and homeland security. Order, predictable
results, and steady plans aren’t the goals. What’s needed is creativity—the freedom to
see and do. Education isn’t all about standards and authority. It’s to instill habits that
bypass habit, too, to nurture the ability to go on seeing and doing when things are
new. It’s the same using rules to calculate with shapes.
Also on page 41, there’s a quotation from Mel Levine’s book A Mind at a Time. 43
The absence of a visual approach to education in schools is something that I hope calculating
with shapes will help to address. At least it shows that it’s possible to be formal
with your eyes—as formal as mathematics—without losing anything that’s creative in
the process. With shapes and rules, novelty, seeing things in new ways, and experience
that’s ongoing and variable are emphasized. The social psychologist Ellen Langer calls
this ‘‘sideways learning’’ and ‘‘mindfulness.’’ 44 Means and methods of teaching make a
difference in education—to learn by counting and more by seeing.
The triangle
on page 45 is in Mary Warnock’s Imagination in a quotation from Wittgenstein’s Investigations.
45 Transformations of shapes are easy to mix up. Sometimes it’s good to keep