The essay appears to mix two different meanings of "hole".

Holes are a topological property of the slice of cheese. It's not scale invariant, as we're talking about holes on a human visible scale, not microscopic holes. The actual number is not fixed and may depend on the person doing the measuring.

I therefore don't see the need for "perforated", much less shape-predicates like "singly-perforated", "doubly-perforated" and "triply-perforated."

> For ‘hole’ read ‘bottle;’ for ‘hole-lining’ also read ‘bottle.’

Topologically speaking, a bottle doesn't have a hole, so this uses a different definition.