Approximate is a verb in this context and not an adjective. The idea under discussion goes roughly like this: the classical ("earthly") Turing Machine has an infinite tape, but each square can only be marked with a selection from a finite number of symbols; let us suppose angels —being more perfect than humans— can discriminate among a (countably) infinite number of symbols, so their ("celestial") turing machines could then have a finite number of squares, potentially even only 1. However, this additional power of discrimination doesn't buy them much, because (per Scott) in order for their function spaces (D->D) to have a small enough cardinality to be only part of their data space (D), they still must only use continuous functions, meaning that while they'd arguably be able to compute quantitatively more ideally than we do, they'd still be restricted to computing qualitatively in the same manner, approaching infinite objects via finite approximations. Slogan: "As below, so above"