> If you translated the two diagrams into classical notation, you’d get the two terms at the top of that page.

So the vertical height is meaningful? Not just the arrangement of nodes on the string?

It seems like an ambiguous grammar (the two topologically equivalent diagrams) gives rise to two different parse trees (the two terms at the top of the page) which nevertheless have the same meaning?

Sorry if I'm being dense. I spent a couple of hours last night trying to understand the paper and it was pretty frustrating.