“exactly what are vertical and horizontal forces?”

War has been defined by many descriptions, but it simply is the displacement of energy, from one orientation into another. This is the main reason the power-law distribution applies to war. There are two forms of energy inside every displacement, kinetic and potential. Kinetic energy has mostly a component of Vertical force, while potential energy has mostly a component of horizontal force. Together the vertical and horizontal forces move the displacement from potential to kinetic and back again. It works in a loop and that loop, to some, is called an OODA loop.

Vertical forces are the forces that the horizontal forces of a country are able to support. The horizontal force is the amount of force between you and I, which is growing. Actually, the horizontal force is the amount of force a society has between its past and future, but it is not always (never) figured in that way.

Force at a distance is the definition of energy. When the vertical force moves, the distance from one country to another, it is called kinetic energy. The amount of power, energy per second, a country can throw at another country depends on how much vertical force the horizontal force can support, @ the distance and over time.

My guess why the power-law distribution “works” in Iraq or any war is that Alpha describes the structure of the insurgency and that structure, in Iraq, represents the orientation on the other side of the power curve of the US, and to a degree the Iraqi Security Forces. The Data is not for a particular orientation (religious, warlords, tribes, or thugs) only that orientation opposing the new Orientation. I capitalized the last Orientation because it represents the second "O" in the OODA loop (Orientation is what a vertical force does after it Penetrates the Observed environment of another displacement; it Isolates the displacement into Orientations, isolation does not always mean: to kill).