Aristotle distinguished “moved movers” from “unmoved movers”. The most famous examples of unmoved movers come from his accounts of astronomical phenomena. I’ve previously noted that in a lesser-known text, he also reached the perhaps surprising conclusion that there is an unmoved mover involved in the movements of an animal’s leg joint. This additional case suggests a vast generalization of the concept of an unmoved mover.
In both the biological and the astronomical case, an unmoved mover is associated with the geometrical form of an axis of rotation. Putting to one side considerations of the special perfection of circular motions, I’d like to focus on the characterization of a mathematical description of a motion as an “unmoved mover”. In this same sense, modern mathematical-physical laws arguably qualify as Aristotelian unmoved movers.
On a yet broader level, I would propose that Aristotelian form and ends are kinds of things that can function as unmoved movers, and means of realization can also contextually do so, whereas material conditions function exclusively as moved movers. (Something can be effectively operative in a process without itself being moved or changed, or it may also itself be moved or changed. In functional programming, for instance, it is actually possible to completely define all computational work to be done using static constructs, pushing any use of non-static constructs down to a purely instrumental compiled-execution level.)
In a more “metaphysical” way, Plotinus anticipated such a generalization, e.g., in his essay on “The Impassivity of the Unembodied”. Going in a very different overall direction from Aristotle, he effectively made unmoved-moving into a kind of paradigm for all causality. On a poetic level, perhaps the ultimate guide to thinking in terms of unmoved moving is the work of Lao Tzu.