Clausewitz’s idea of culminating points of attack and of victory are important but abstract theories in military science. This is also called the “tipping point.”

Every offensive operation will reach a point where there attacker’s strength no longer outweighs the defender. After this point, the attacker’s strength declines and they become more vulnerable to over-extension and defeat. Commanders must recognize this critical point and change strategies accordingly.

A Critical Point is the point where the graph of the function changes from increasing to decreasing. The “Culminating Point” is a form of a critical point. It’s the maximum point in the offense. The tip of a bell curve would be the culminating point.

As commanders attack the enemy, they increase in power as they bring all their units to bear on the defenders. As time passes and attrition increases, the attacks will lose steam and unit cohesion. The Attackers have a set limit on time to capitalize on their success before the situation is restored to equilibrium.

A number of elements cause this decline in power. As units move deeper into enemy territory, their logistical tail grows, they must post guards and garrisons, they suffer attrition, encounter unknown terrain, face an unpredictable enemy, and manage friction. This is inevitable.

The problem for commanders is that the Culminating Point cannot be determined in advance. There are a number of “false” culminating points, where the situation becomes erratic. Sudden reinforcements can give the offensive a second wind. The defenders may break suddenly. A good commander knows the limitations of his men. He can sense the change and know when to push for victory and when to stop and defend his gains.

Defenders have the advantages of time and space. Space gives them room to retreat to more favorable ground and to allow the enemy to overextend themselves. Patient defenders can wait until the attacker’s strategy is clear and precisely react to counter them. Then the defenders counterattack.

The Counterattack shifts the momentum of the battle or war. The defender becomes the attacker and rises in power until it too reaches a culminating point. This back and forth struggle continues until one side achieves a decisive victory.

The concept of a culminating point is an abstraction. It helps us imagine a highly complex situation by reducing it to its core elements. It is similar to using two-dimensional Geometry to describe the world. It has limitations, but it is a useful way to generate ideas.

We can trace the culminating points of historical battles and wars. Yet due to change and probability, we cannot foresee culminating points in the future. Social sciences are “historical sciences” where prediction is imperfect. This is also true of biological evolution – we understand how evolution occurred in the past but biologists cannot predict what current animals will evolve into.

The theory cautions us not to believe that a current trend will continue indefinitely into the future. The rise in power and fortunes of an attacker does not mean his power will rise in a straight infinite line. It will reach the critical point and then decline.