Despite the surface tension between their positions, Prof. Harper’s description of the “computational trinity” and Prof. Wand’s reply that “the map is not the territory” are both accurate. Indeed, taken together, they reveal an important fact about knowing which is that, when discussing complicated things, we tend to “say what things are” by sketching sequences of descriptions that (hopefully!) converge on the boundaries of the thing in question.

compact vs. “effectively computable” concepts…

One of my favorite mathematical concepts is the concept of a *compact set*.

A compact set is a set for which *every* open cover \(U\) has a finite sub-cover.