Shape

79 What Makes Calculating Visual?
when I look at embedding for lines. My new rule in whatever form finds twenty-eight
different triangles in the shape
including the sixteen from Evans’s example. But there are forty-eight other triangles in
the shape in five different constellations
These are readily defined in additional rules. (Of course, it’s easy to define all triangles
using a single rule in the way Evans does, or as effortlessly, using a schema for rules in
my way. This is also something I’ll come back to again.) I can’t find any other triangles.
My grammar is seeing what I do.
Now what happens when I erase points or look for Y’s? In the first case, my rule
is just like it was before, but for points
Point fi
Or equivalently, the erasing rule
When I apply the rule to erase the vertices of Evans’s small triangles, the shape disappears
the way it should. And if I do the same for medium triangles and for large
ones, then I get the shapes
Everything looks fine, even if the cross appears in alternative ways. In fact, this may be
a boon. I can decide whether I’ve erased the vertices of medium triangles or large ones
simply by looking at the result. There’s nothing to see that I can’t understand. Points
aren’t like lines. They don’t fill in for the loss of others because they don’t combine to
make other points and don’t contain them. The grammar I’ve got for points is doing
far better than Evans’s grammar for lines. Perhaps visual calculating is really a possibility
after all.