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If you analyze enemy military forces under the operational factor force and the civilian population under the operational factor space, where should you analyze insurgents? Why?

The distinction between force and space is a false dichotemy, which is exacerbated in this question by simplified ontologies. The fundamental conceits of operational art are still very much applicable, but require a more elemental framing.

Clausewitz's peculiar wording has so thoroughly pervaded modern theories of strategy that even his oversimplifications are inescable terminological shibboleths. That his metaphores consistently stand up to this rough treatment is testament to their aptness. However, like the ballistics he drew upon to describe his contest of wills, not every problem can be usefully reduced to a single pointmass and the forces acting upon it. So it is with insurgencies.

Employing force in a traditional conflict is metaphorically similar to hitting a baseball. While in theory the baseball is made up of many different parts, in practice it acts as a unified whole, and hitting it will make it fly off on a single trajectory. The only question is what /force/ to apply and where in /space/ to apply it, to achieve the desired trajectory. This is because, in the specific case of a baseball, the center of mass is at the center of the largest object (the baseball), and the center of gravity's trajectory /defines/ the baseball's trajectory.

In the case of insurgency, a thrown handful of gravel would be a more apt metaphor. Any set of masses has a center of gravity (by definition), but a pointcloud is not completely described by the path of its center. Further, even to the extent that the state of the center of gravity is a sufficient descriptor of an end state, any individual rock's trajectory change has minimal effect on the trajectory of the center.

In reality though, any conflict will have elements of the baseball and of the gravel. Seizing or destroying a center of gravity does not magically cause complete capitulation, but will have significant effects (by definition) to that center's side.

Fortunately, Clausewitz and modern taxonomy each provide ways of talking about individual actors in the broader theoretical construct of war as a contest of wills. Clausewitz describes this through his discussion of war as a sustained effort, by introducing the concept of “friction.” modern terminology implicitly incorporates friction through the concept of “culmination.”

so what

Ultimately though, how Clausewitz might have described any given situation is no more than a interesting aside. Far more relevant is what action that description might prompt. Presumably, the original question here is not idle speculation, but instead is meant to inform decisions on which set of tools will best achieve the desired end state. It is for that reason that the above discussion is crucial, vice mere mindless pedantry: binning popular insurrections with either terrain or forces is a mistake; they have elements of each and will best be addressed with a three-pronged approach: first, increase relative friction on individual efforts. Second, apply force to individual elements. Third, coalesce and link the opposition, then apply conventional strategy. Throughout, recognize that force protection will consist more in reducing friction and forestalling culmination than In directly opposing enemy action.

Increasing friction is the most straightforward.