One of the most powerful themes of Sun Tzu’s The Art of War is that of form and formlessness in warfare (and, more generally, in situations of poorly constrained conflict where winning matters).

I will be equating form with specialization. By assuming a specific form, an army sacrifices the ability to do some things in order to do other things well. For example, an infantry unit can form a square in order to better ward off cavalry attacks, and in the process sacrifices its ability to move. On the margin, if one wants to do better at A, one must accept worse performance at B. Or, as I said in one of my earlier posts, optimization equals specialization.

Therefore any form will have strengths and weaknesses. There cannot be any universally dominant form. In war, if a general always uses a certain form, it will be recognized by his enemies and they will adapt themselves to flow to its weakness.

…when you induce others to construct a formation while you yourself are formless, then you are concentrated while the opponent is divided.

Of course an intelligent general will adapt to this adaptation, and seek to exploit the weaknesses that arose from his adversary taking form to attack his weakness. With two intelligent adversaries, the conflict becomes a race for adaptation to the other’s changing form. As the rate of change approaches infinity (i.e. each side is constantly changing form), the army approaches formlessness. At any given moment it could assume any form; therefore it has no form.

Be extremely subtle, even to the point of formlessness. Be extremely mysterious, even to the point of soundlessness. Thereby you can be the director of the opponent’s fate.

Throughout The Art of War, Sun Tzu uses water as a metaphor for the adaptive manner in which a formless army can flow towards an opponent’s weaknesses.

When the victorious get their people to go to battle as if they were directing a massive flood of water into a deep canyon, this is a matter of formation.

A particularly powerful metaphor, since it reflects both the power and the vulnerabilities of water. A mass of water flowing downhill is a powerful force indeed. Scattered droplets of water, however, have little force. The danger in rapidly shifting forms is that friction increases, fracturing one’s force, until what could have been a rushing torrent has been so divided that it is now hardly a trickle. Boyd’s answer to this challenge was that the force needed a robust internal orientation to resist this friction. Sun Tzu’s answer was that the general needed the way (or mandate of heaven, or the tao) on his side, meaning that the motivation of the soldiers are aligned with the goals of their leaders. This leads, among other things, to greater combat efficiency:

…when people are skillfully led into battle, the momentum is like that of round rocks rolling down a high mountain - this is force.

This potential energy metaphor also comes through in Sun Tzu’s descriptions of the attack:

Those skilled in defense hide in the deepest depths of the earth, those killed in attack maneuver in the highest heights of the sky. Therefore they can preserve themselves and achieve complete victory.

Attack, and you wield the power of turning that potential energy into kinetic energy. Aimed accurately against a vulnerability of the defense’s form, this cataclysmic power will crush the defender. Aimed poorly, however, the force of the attacker will scatter like rain on a mountain ridge flowing to different watersheds. And of course, as the attack flows downhill, the defense has the opportunity to adapt to that attack and adapt their form.

The more that one adheres to a form, the more predictable one becomes, opening the opportunity to manipulate those patterns:

Therefore there are five traits that are dangerous in generals: Those who are ready to die can be killed; those who are intent on living can be captured; those who are quick to anger can be shamed; those who are puritanical can be disgraced; those who love people can be troubled.

Ultimately, this play between form and formlessness, leading to patterns and rhythm, is what creates the environment for the game of cheng and ch’i:

There are only five notes in the musical scale, but their variations are so many that they cannot all be heard. There are only five basic colors, but their variations are so many that they cannot all be seen. There are only five basic flavors, but their variations are so many that they cannot all be tasted. There are only kinds of charge in battle, the unorthodox surprise attack and the orthodox direct attack, but variations of the unorthodox and the orthodox are endless. The unorthodox and the orthodox give rise to each other, like a beginningless circle - who could exhaust them?

Infinite variation springs from the dynamic interaction between opposed forces. Any equilibrium creates a new orthodoxy, creating the opportunity for an unorthodox approach.