The material (as sheer undifferentiated causal space) is to the physical (or, corporeal) as the physical is to the sensible.
The sensible is to the mental (i.e., as the realm of percepts) as the mental is to the intellectual (i.e., as the realm of concepts).
The intellectual is to the mental as the divine is to the intellectual.
If any of these ontological “planes” or “spheres” can and do interact, then the forms of interaction we (think we) understand better (e.g., the neural basis of mentation, the physical basis of motion, etc.) can illuminate the other forms of interaction in appropriately analogous ways. If, for example, intellectual thought can somehow meaningfully depend on and causally relate to mental operations, without however being sufficiently produced by or causally “subjugated” to them, then perhaps divine action becomes more lucid as depending on and being causally connected to human existence, without being caused or limited by it.
Does intellectual action, on the whole, have any meaning apart from mental operations? Likewise, I ask, does divine “action” have any meaning apart from human operations? I suspect both human intellectual power and divine power have a real vitality ad intra, which is free from any powers activated ad extra, the former as a supra-mental contemplation of God, the latter as a supra-economical contemplation of the divine Persons.
P.S. It may be more illuminating (or perhaps just as bemusingly unilluminating, in a different way) to read the chain of analogy backwards: the divine is to the intellectual as the intellectual is to the mental; the mental is to the sensible as the sensible is to the physical; and the sensible is to the physical as the physical is to the material. Perhaps, then, the physical is to the material, in a strangely analogous way, as the God is to the world: as Pure Form-Act to pure material-potency.