I see computing at the intersection of language and the desire for rationality and certainty. Perhaps the most explicit expression of this intersection was Leibniz' Characteristica universalis and Calculus ratiocinator. As a modern descendant of this line of thought, there's for example Lojban.
Recommended reading: "In search of the perfect language", by Umberto Eco.
As for "Computation has the ability to provide a uniquely unifying framework, exerting a massive centripetal force on ideas and fields of knowledge. We must nurture its connective power", this is very close to my personal interest in computation. What's frustrating about it is the very much opposite, centrifugal, force of actual computing technologies. If you want to bring together ideas from different fields that have all been formalized as computations, you spend long unpleasant hours sorting out low-level interfacing issues.