Shape

68 I What Makes It Visual?
And my rules find all of these figures wherever they are in the shape. There are five
squares, four rectangles, six bow ties, and two crosses of each type. This is great. But
already there are signs of trouble. I can’t tell the crosses apart just by looking at them,
even if I can by the rule I apply. Calculating and seeing are beginning to look different.
Now suppose I go on to define an additional rule
Line fi
that erases lines—the lowest-level constituents—in Evans’s shape. What do I get if I
apply my new rule to erase the lines in all small triangles, or in all medium or large
ones? Whatever happens, I don’t expect to see the lines I’ve removed in my result. If
I do the erasing by hand to remove the lines I see in small triangles, the shape disappears.
And for medium or large triangles—erasing what I see by hand without thinking
about it—I get a cross that looks like this
But in all three cases when I calculate with the rule, my results look like this
Some parts are hard to delete when I use my eyes, even after I’ve applied the rule.
The shape is visually intact whichever lines I erase. You can check me if you like. I
haven’t made any careless mistakes, yet I don’t get what I expect. I must be seeing
things. And, actually, I am. I always knew it would be this way. Seeing is believing,
but not always. The lines I’ve erased with the rule aren’t there. No two of the resulting
shapes are the same. They’re numerically distinct—what better way to tell things
apart—with eight, sixteen, and eighteen constituents apiece, and they’re all different
from the shape
I started with.
Be careful, though. The problem is not that I can’t trace eight or more distinct
lines in Evans’s shape—that’s easy—but that for Evans there are four numerically distinct
versions either with eight lines, sixteen, eighteen, or twenty-four. And these versions
are hard to keep straight. How can I tell which is which by looking? What