User blog comment:PsiCubed2/Counting with Ordinals/@comment-25337554-20171206093611/@comment-30754445-20171206101043

The Box Visualization for ε0 is actually supposed to be something like a vase/cup/goblet with fancy handles. It's just the limitations of ascii that makes it look like it does here.

(similarly, the [...] notation is supposed to an actual closed box)

As for the "contradiction sign", my inspiration actually came from geometry (where "a⊥b" means "a is perpendicular to b"). Seems like an apt symbol to use for signifying a brand new kind of post-tetrational "dimension".