Something that the author seems to be missing is that traditional complexity analysis (with mathematical proofs etc) is done for Turing Machines which have one-dimensional memory (an abstract tape), and reachable memory is linear with time. Current microchips are two-dimensional, so reachable memory increases square with time. If we had three dimensional memory (stacked chips?), then reachable memory would increase cube with time.

It all depends on what kind of machine you are talking about...