The Notices quote which started this is particularly annoying because it seems both to take the myopic view of category theory as a "language" and then to claim that category theory doesn't do any better in that role than the "debauch of indices". The discussion reminds me, however, of the incident involving Moshe Flato, Nicholai Reshetikhin and myself, which I related in the introduction to my book: at a Joint-Summer Research Conference in the early 1990's Reshetikhin and I had a long discussion about Shum's coherence theorem and the role of monoidal categories in "quantum knot invariants", Flato was persistently dismissive of category theory as "mere language". I retired for the evening, leaving the discussion to the others. In the morning before the first session, as he was going to his seat, Flato tapped me on the shoulder, and whispered with a thumbs up sign, "Hey, viva les categories. These new ones, the braided monoidal ones." Of course, I suppose it would only muddy the waters further to try to explain both old fashioned commutative diagrams and new fashioned "string diagrams".