How Big is Heaven, Refined

I think I am on safe ground (for example, Porphyry's Sentences XXXII, On the Gods and the World VIII (with Murray's note), etc.) to venture that there are simply four realms of being for the Neoplatonists: the One, Mind, Soul, and Bodies (plural). (If I were to put on my Empedocles hat, these are simply fire, air, water, and earth, transposed an octave higher.)

So I'll refine my Neoplatonic cosmos as follows:

Realm	Root	Size	Virtue	Computational Model
material	bodies	finite (bounded)	civic	finite state machine
ætherial	spirits	finite (unbounded)	purificatory	Turing machine
empyrean	Soul	infinite	contemplative	oracle machine
intelligible	Mind	trans-infinite	archetypal	[all of them]
unitary	the One	[transcendant]	[transcendant]	[transcendant]

(It is perhaps folly to distinguish the material from the ætherial, as they are inextricably bound together and anyway of a similar nature. Still, perhaps it is useful to distinguish them in the same sense that the first step upon a journey, while still within one's own home, is nonetheless somehow distinct.)

I think this is a line of argument in favor of the Church-Turing Thesis: if you want to go beyond a Turing machine, you're gonna have to leave this world behind.