Shape

72 I What Makes It Visual?
Table 1
Census of Triangles in Evans’s Shape
Number of lines 3 4 5 6 7 8 9 3–9
Number of triangles 16 48 124 180 120 36 4 528
So there are five versions of each medium triangle, and a hundred twenty-five of each
large one. The census is given in table 1. More is happening in Evans’s shape than I can
possibly see. What use are my eyes when nearly everything is hidden? I’ve no doubt
that Evans’s shape contains sixteen triangles that meet his definition and mine. I simply
have to look to find them. I can trace them out. But this is only a half—actually 3
percent—truth.)
Constituents are made to calculate, and they’re supposed to work. Surely, I can
debug what I’ve done. That’s an important part of defining rules and understanding
what they do. If I erase a long line, I can also remove its halves at the same time. This
takes another rule
Three collinear lines fi
but gives some interesting results. I get a cross (two lines) and another one (four
halves)—at least this looks right—erasing the sides of large triangles
three crosses (either two lines or four halves)—for the sides of medium triangles
and Evans’s shape—evidently, the version with eight lines—for the sides of small
triangles
This is a marked improvement, plus it shows what’s left to do. If I add the conjugate
rule for halves
Two collinear lines fi