Shape

29 Answer Number Two—Three More Ways to Look at It That Tell a Story
(1) A line can be divided in half
(1A) Two halves can be combined.
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(2) A line can be divided at ð2 2 Þ=2
(2A)
The two pieces in rule 2 can be combined.
It’s worth being explicit here about what I’ve been doing from the start, and to emphasize
that arrangements of constituents and rules to define them are given symbolically
(schematically) with words and diagrams. I can’t draw constituents in shapes—lines
fuse whenever they’re combined. With shapes, the four rules I have all look alike. Visually,
they’re the same identity
—a line is a line. And certainly, these aren’t the only rules I need for constituents.
There are rotations of squares, as well, and many details to avoid unwanted results.
These are mostly artifacts—products of abstraction that block my way unless I plan
for them in advance. But the details aren’t automatic—filling them in takes more
than your eyes. Shapes aren’t the same when constituents are defined. Structure
intrudes. Logic becomes a necessary distraction.
The successors of the shape
show that finite limits on what I can see and do needn’t make a difference. Words and
syntax may not work even when I can draw everything. Just turning a handful of
squares defies analysis, at least for exact constituents permanently arranged from the
start. But perhaps it’s worth seeing again how easy it is for analysis to fail when there’s
more to draw. I can use my original rule
to rotate squares 45 degrees with other rules like this one