Shape

75 A First Look at Calculating
things are the same; for example, Lego blocks and Tinkertoys—only the disparity between
identity for points and embedding for lines has some bewildering consequences.
Take two.
First, the shape
has no obvious constituents to serve as points. It’s easy to see that lines come undivided.
How can I cut these
into meaningful segments without knowing beforehand what rules there are and how
I’m going to use them? Internally, both of the lines are homogeneous. And externally,
their relationship is arbitrary. This is how it is for the lines in any shape. I can never be
sure how many segments there are. Lines aren’t numerically distinct like points. They
fuse and divide freely. I can draw two lines to make a cross
and then see alternating pairs of L’s
or I can turn this around and draw L’s, and see a cross. Nonetheless, I’ve decided to calculate.
So I have to define points explicitly in whatever way I can cook up according to
my immediate interests and goals. Right now I’m looking for triangles. There’s a kind
of funny circularity here that’s almost hermeneutic. I’ve got to find triangles in order to
define a rule that lets me find triangles, or something of the sort. Seeing and calculating
are linked. That’s for sure. But perhaps their relationship isn’t what I want. Seeing