> If you instead envision a FA as being a flying head that moves back and forward across a tape that is fixed in space, the ideas behind modern CPUs become much more clear: the tape is memory, the FA is a CPU being stepped through successive states, and the 'location' of the FA is the PC register.

It would seem an apt analogy for the (basic) Von Neumann architecture, but "modern" CPUs have a hierarchy of "cache lines" that quite neatly -- at least in my mind -- map to a FA "fixed in space" [the cache line], with a "magical tape" [virtual memory and cache coherence].