One theme of Book III is the contrast between strategy, a world of uncertainty, and tactics, a world of mechanistic certainty. This contrast is most striking in the contrast between the moral and the material. Military theorists like von Bulow and Jomini, the immediate predecessors of Clausewitz, attempted to take the deterministic approach that met with some success in tactics and use it to reduce strategy to a “war by algebra”, amputating that inconvenient and unquantifiable moral dimension:
It is even more ridiculous when we consider that these very critics usually exclude all moral qualities from strategic theory, and only examine material factors. They reduce everything to a few mathematical formulas of equilibrium and superiority, of time and space, limited by a few angles and lines. If that were really all, it would hardly provide a scientific problems for a schoolboy.
But we should admit that scientific formulas and problems are not under discussion. The relations between material factors are all very simple; what is more difficult to grasp are the intellectual factors involved. Even so, it is only in the highest realms of strategy that intellectual complications and extreme diversity of factors and relationships occur. At that level there is little or no difference between strategy, policy, and statesmanship, and there, as we have already said, their influence is greater in question of quantity and scale than in forms of execution. While execution is dominant, as it is in the individual events of a war whether great or small, than intellectual factors are reduced to a minimum.
One part of Clausewitz’s pedagogical approach throughout On War is first to propose something and then immediately to hedge his proposal. This creates a gap between the proposed tenet and its caveat that can only be filled by the imagination. Clausewitz seems intent on luring the mind of the aspiring strategist into this gap. He may be attempting to stimulate the deep brain activity necessary for strategy-think, a much harder state of mind to reach than tactical reductionism. On War is filled with flashes of lightening that illuminate scattered sections of an otherwise dark landscape. Strategy is like Zen koans, inaccessible to normal reductionism but possibly accessible to a developed intuition:
Principles and opinions can seldom reduce the path of reason to a simple line. As in all practical matters, a certain latitude always remains. Beauty cannot be defined by abscissas and ordinates; neither are circles and ellipses created by their algebraic formulas. The man of action must at times trust in the sensitive instinct of judgment, derived from his native intelligence and developed through reflection, which almost unconsciously hits on the right course.
The path of reductionism is quicker, easier, more seductive. It’s easy to strain for certainty. But this quest is in vain:
In minor engagements it is not too difficult to judge approximately how much force is required to achieve substantial success, and what would be superfluous. In strategy, this is practically impossible, because strategic success cannot be defined and delineated with the same precision. What may be regarded as surplus strength in a tactical situation must be considered in strategy as a means of exploiting success if the opportunity arises. Since the margin of profit increases with the scale of victory, superiority of force can quickly reach a level which the most careful calculation of strength could never have determined.
Strategy will never be reduced to simple equations:
[W]e do not consider it an established truth that in strategy the number and scale of the engagements won are more meaningful than the pattern of the major lines connecting them.
The very opposite view was a favorite of recent theorists, who believed that in this way [by applying geometry to war] they would increase the importance of strategy. Strategy, they thought, expressed the higher functions of the intellect; they thought that war would be ennobled by its study, and according to a modern substitution of concepts, be made more scientific. We believe that it is one of the chief functions of a comprehensive theory of war to expose such vagaries, and it is because the geometrical element usually provides the point of departure for these fantasies that we have drawn special attention to it.