Shape

39 Trying to Be Clear
on corresponding points in figure 2. Even Birkhoff’s aesthetic measure distinguishes
the figures—without really looking! In particular, Peirce’s figure 1 taken as a square in
this orientation
has a higher value than figure 2 as the rotation
The score is 1.50 to 1.25. Does this miss the mark? What are the objects (parts) in
Peirce’s two figures anyway? Are they so obviously individual points, permanently
fixed before I have a chance to look? Maybe they’re different in each figure and vary
unpredictably. Suppose they’re horizontals or likewise verticals. Things don’t have
to touch to hang together. Stars don’t in constellations. How does this change the
arrangements the figures show? What happens to the identity between them now,
when they aren’t even numerically the same? Is any relationship ever going to be guaranteed?
What if figure 1 is something else, perhaps the sum of four squares that touch
at their corners
and figure 2 is five squares with common sides
Is this really a false distinction? Perhaps it misses what’s actually there—both of my
figures contain sixteen lines