Shape

71 A First Look at Calculating
with triangles, pyramids, and tetrahedrons, and the pair of figures
from C. S. Peirce. In fact, what I’m trying to show in this book is how the embedding
relation makes statement 1 practicable for shapes like these when rules are used to calculate.
Rules let me see in alternative ways. And then Evans’s shape gives four examples
of statement 2. This is solid evidence that’s right to heed. Nonetheless, I’m
uncomfortable with my taxonomy. I’m going to affirm 1 and deny 2—it’s just not the
way shapes work. I can vary how shapes look any time there’s something else to do.
Their parts change freely, so they can be anything they need to be. There’s plenty of
ambiguity to go on. That’s why drawing is useful in design. But constitutive distinctions
that are permanent and fixed—‘‘eternal and unchangeable’’—and lost out of
sight get in the way. They have to be remembered and honored to go on. Seeing begins
and ends with my eyes. There’s nothing more than they can find. If shapes look the
same, then they are the same. What you see is what you get. Really, it’s simply a question
of logic. Deny statement 2 yourself and see if I’m right.
(The best way to explore the occult properties of Evans’s shape is to count the
different kinds of triangles it contains. This is what descriptions—representations like
lists, strings, graphs, networks, trees, schemas, sets, structures, etc.—that are given in
terms of constituents are for. Small triangles all have three lines apiece, but medium
ones can have three to five lines and large ones three to nine. Lines are taken from
these schemes
There are five distinct configurations for each grouping of three collinear lines