Shape

152 I What Makes It Visual?
these hypothetic masses and velocities are the qualities for me; they will stay numbered all the
time.’’
By such elaborate inventions, and at such a cost to the imagination, do men succeed in
making for themselves a world in which real things shall be coerced per fas aut nefas under arithmetical
law.
The cost to the imagination is twofold. First the effort to think up ‘‘elaborate
inventions’’—the devices that make calculating hard, and so important—can be a lot
of fun. There’s evident wit in Evans’s shape. But then the toll these inventions take on
my future experience—limiting its scope and content—is no fun at all. My initial investment
shows negative returns. I can lose much more than I put in. My imagination
is free to work in any way I like when I calculate with shapes. Counting parts isn’t the
only way to check experience. There are many other things to see and do. There’s ambiguity
and all the novelty it brings.
When it comes to novelty, I try to take James as broadly as I possibly can.
There’s seeing new things—for example, visiting Los Angeles for the first time—and
equivalently, seeing things in different ways—going back (looking again) to find out
how the city has changed. Either way, the same question invokes novel experience.
What’s that? And of course, this leads directly to visual calculating, while the reciprocal
question—how many?—continues with calculating in the usual way. In fact, James
presents his own series of visual examples in Pragmatism: A New Name for Some Old
Ways of Thinking:
In many familiar objects everyone will recognize the human element. We conceive a given reality
in this way or in that, to suit our purpose, and the reality passively submits to the conception. . . .
You can take a chessboard as black squares on a white ground, or as white squares on a black
ground, and neither conception is a false one. You can treat [this] figure
as a star, as two big triangles crossing each other, as a hexagon with legs set up on its angles, as six
equal triangles hanging together by their tips, etc. All these treatments are true treatments—the
sensible that upon the paper resists no one of them. You can say of a line that it runs east, or you
can say that it runs west, and the line per se accepts both descriptions without rebelling at the
inconsistency.
Let’s try to define the options in the star once and for all. How would Evans do it? His
method is clear. I count twenty-four constituents—six long lines and their thirds—if
I’m going to look for triangles. Halves don’t work anymore. They were ad hoc from
the start. But will these same constituents do the job if I jiggle the two big triangles a
little to get another six small ones? What happens if I jiggle harder and harder? Or
maybe lines stay put. What about diamonds, trapezoids, and the pentagon in Wittgenstein’s
addition? And what about the A’s and X’s—big ones and little ones? Only why