Showing posts with label Chaos theory. Show all posts
Showing posts with label Chaos theory. Show all posts

Sunday, October 6, 2013

Notes to Clausewitz's On War, Book 3, Part I


Notes to Carl von Clausewitz, On War.  Ed. and Trans. by Michael Howard and Peter Paret.  Princeton University Press, 1976

On War Book 3:  On Strategy In General


It’s important to note that only Book One of On War is the only book that Clausewitz considered as complete.  Books Three (On Strategy in General) and Eight (On War Plans): Peter Paret considers the most beneficial and integrated with respect to Book One.

“The Enduring legacy of Clausewitz is that he ignored question of “how” “posed by modern science since the 17th century and returned to earlier questions, the Platonic “what is” and the Aristotelian “what for,” which are more valid ones for investigating social phenomena like strategy and war.”  (Creveld, pp. 42-43)

3.1    Chapter One: Strategy


Strategy is the use of the engagement for the purpose of the war. (Book Three, Chapter One, p. 177)  Strategic theory must therefore study the engagement in terms of its possible results and of the moral and psychological forces that largely determine its course.  (Id.) 

The strategist… will draft the plan of the war, and the aim will determine the series of actions intended to achieve it:  he will, in fact, shape the individual campaigns and, within these, decide on the individual engagements… The strategist, in short, must maintain control throughout.  (Book Three, Chapter One, p. 177)

Strategic theory, therefore, deals with planning; or rather, it attempts to shed light on the components of war and their interrelationships, stressing those few principles or rules that can be demonstrated. (Book Three, Chapter One, p. 177)

A prince or general can best demonstrate his genius by managing a campaign exactly to suit his objectives and his resources, doing neither too much nor too little.  But the effects of genius show not so much in novel forms of action as in the ultimate success of the whole.  What we should admire is the accurate fulfillment of the unspoken assumptions, the smooth harmony of the whole activity, which only becomes evident in final success.  (Book Three, Chapter One, pp. 177-178)

In fact, the means and forms that the strategist employs are so very simple, so familiar from constant repetition, that it seems ridiculous in the light of common sense when critics discuss them, as they do so often, with pompous solemnity.  (Book Three, Chapter One, p. 178)

 
In other words, in was as in politics results count.  Clausewitz states that strategy cannot be reduced to examining only material factors as it cannot exist outside the moral realm.  Contrary to the beliefs of some operations analysts [number crunchers] and academic theorists [who usually have no military experience other than reading books] it cannot just be reduced to “a few mathematical formulas of equilibrium and superiority, of time and space, limited by a few angles and lines.”  (Book Three, Chapter One, p. 178)

The relations between the 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 … there their influence is greater in questions of quantity and scale that in forms of execution.  Where execution is dominant, as it is in the individual events of a war whether great or small, then intellectual factors are reduced to a minimum.  (Book Three, Chapter One, p. 178)

The Charge of the Light Brigade

Alfred, Lord Tennyson


1.

Half a league, half a league,
Half a league onward,
All in the valley of Death
Rode the six hundred.
"Forward, the Light Brigade!
"Charge for the guns!" he said:
Into the valley of Death
Rode the six hundred.

2.

"Forward, the Light Brigade!"
Was there a man dismay'd?
Not tho' the soldier knew
Someone had blunder'd:
Theirs not to make reply,
Theirs not to reason why,
Theirs but to do and die:
Into the valley of Death
Rode the six hundred.

Clausewitz observes that “Everything in strategy is simple, but that does not mean that everything is easy.”  (Book Three, Chapter One, p. 178) This is the equivalent of the modern observation that it is easy to start a war but it is not so easy to complete it successfully.  Why?

Once is has  been determined, from the political conditions, what a war is meant to achieve and what it can achieve, it is easy to chart the course.  But great strength of character, as well as great lucidity and firmness of mind, is required in order to follow through steadily, to carry out the plan, and not to be thrown off course by thousands of diversions.  (Book Three, Chapter One, p. 178)

Clausewitz states that it takes “more strength of will to make an important decision in strategy than in tactics.”  (Book Three, Chapter One, p. 178)  The reason for this is that there is more time for deliberation and “ample room for apprehensions, one’s own and those of others; for objections and remonstrations and, in consequence, for premature regrets.”  (Book Three, Chapter One, p. 178)   It takes a person of strong will to make strategic decisions which will affect the course of the war.  However, strong will is not enough.  It has to be combined with knowledge of what you are doing.  Saddam Hussein had a strong will and made disastrous strategic decisions because he didn’t know what he was doing. 

The other aspect to be admired concerns the difficulties of execution.  Maneuvers designed to turn a flank are easily planned.  It is equally easy to conceive a plan for keeping a small force concentrated so that it can meet a scattered enemy on equal terms at any point, and to multiply its strength by rapid movement.  There is nothing admirable about the ideas themselves.  Faced with such simple concepts, we have to admit that they are simple.

            But let a general try to imitate Frederick! [the Great] (Book Three, Chapter One, p. 179)

This is the part of strategy that most would-be generals fail to understand.  The concepts of strategy are in of themselves simple. Their execution is what separates a Frederick the Great or a Napoleon from a Saddam Hussein.

Another difficult of execution involves exertions and great hardships imposed on the armed forces.  Clausewitz states that during Frederick the Great’s Campaign of 1760 against the Austrians and the Russians, his army was constantly on the move and had to be ready to fight on a moment’s notice.  Under these conditions, he decisively defeated the Austrians at Leignitz and at Torgau.  (McCleod, p. 322)

Could this be done without subjecting the military machine to serious friction?  Is a general, by sheer force of intellect, able to produce such mobility with the ease of a surveyor manipulating an astrolabe?  Are the generals and supreme commander not moved by the sight of the misery suffered by their pitiful, hungry, and thirsty comrades in arms?  Are complaint and misgivings about such conditions not reported to the high command?  Would an ordinary made date to ask for such sacrifices, and would these not automatically lower the morale of the troops, corrupt their discipline, in short undermine their fighting spirit unless an overwhelming belief in the greatness and infallibility of their commander outweighed all other considerations?  It is this which commands our respect; it is these miracles of execution that we have to admire.  (Book Three, Chapter One, p. 180)

Clausewitz own experience is in the Napoleonic Wars.  Napoleon made the same point in his maxims:  “XV.  The first consideration with a general who offers battle should be the glory and honour [sic] of his arms; the safety and preservation of his men is only the second; but it is in the enterprise and courage resulting from the former that the latter will most assuredly be found.” (Chandler, p. 60)

In strategy:

We are constantly brought back to the question:  what, at any given stage of the war or campaign, will be the likely outcome of all major and minor engagements that the two sides can offer one another?  In the planning of a campaign or a war, this alone will decide the measures that have to be taken from the outset.  (Book Three, Chapter One, p. 182)

If we do not learn to regard a war, and the separate campaigns of which it is composed, as a chain of linked engagements each leading to the next, but instead succumb to the idea that the capture of certain geographical points or the seizure of undefended provinces are of value in themselves,  we are liable to regard them as windfall profits … [W]e also ignore the possibility that their possession may later lead to definite disadvantages… [J]ust as a businessman cannot take the profit from a single transaction and put it into a separate account, so an isolated advantage gained in war cannot be assessed separately from the over result…
By looking on each engagement as part of a series, at least insofar as events are predictable, the commander is always on the high road to his goal.  (Book Three, Chapter One, p. 182)

Thus war is a continuum both in time and space and breadth as well.  The strategist must be able to link these engagements into one whole sequence in order to succeed. 

Bibliography


Chandler, D. G. (1988). The Military Maxims of Napoleon. New York: Macmillan Publishing Complany.

Creveld, M. v. (1986). Eternal Clausewitz. In M. I. Handel (Ed.), Clausewtiz and Modern Strategy. London: Frank Cass.

McCleod, T. (2001). Fredrick II 'the Great', King of Prussia. In R. Holmes (Ed.), The Oxford Companion to Military History (pp. 321-323). London: Oxford University Press.

 

 

 

Sunday, August 4, 2013

Chaos Theory and War

Preface:  I was reviewing some old materials and found this paper I wrote while in a service school.  I stand by it.
1) Chaos Theory

a) "A chaotic system is one in which nearly nearly identical initial conditions can lead after a while to entirely different outcomes."[1]

The presence of chaos in a system means that for any given accuracy with which we specify the intitial conditions, there will eventually come a time at which we lose all ability to predict how the system will behave, but it is still true that however we want to be able to predict the behavior of a physical system governed by Newton's laws, there is some degree of accuracy with which a measurement of the initial conditions would allow us to make this prediction."[2]

i) What this means is that a chaotic system is dependent upon the initial conditions[3]

b) According to Nicholls and Tagarev, there is evidence that warfare is chaotic.

First, strategic decision making, an integral part of war, has been found to be chaotic. Second, nonline- arity, which is a requirement for chaotic behavior, appears to be a natural result of Clausewitzian friction. Third, some computer war games and arms race simulations have been found to exhibit chaotic behavior. Fourth, previous work ... applied several tests for chaos to historical data related to war. Those tests demonsrated that warfare is chaotic at the grand strategic, strategic, and operational levels.[4]

What this means for us is that is warfare is chaotic at the strategic level, it is very difficult for statesmen to control what they have begun. More importantly, the initial period of the war is critical. Chaotic systems are extremely dependent on their initial conditions.

Chaotic systems never repeat exactly because their future behavior is extremely sensitive to initial conditions. Thus, infinitesimal differences in initial conditions eventually cause large changes in system behavior.[5]

c) What this means for warfare is that while it cannot be reduced to a set of equations, chaos theory can at least provide bounds.

i) Problem is that equations which govern chaotic systems are nolinear equations and therefore not analytically soluble.

ii) A theory of warfare must be based on obsertvations, hypothesis and testing. A model of warfare would require a structure of the model, the determination of the number and type of variables, and the determination of the form of the equations. Chaos theory can be used to define the minimum number of variables required in our computer model.

The rate of information loss can be calculated for a chaotic system. This quantity is related to how far into the future predictions can be reasonably be made.[6] For example if we found ourselves in conditions of great unpredictability, we could determine what conditions could bring us to a new position where the outcome is predictable and desirable (i.e., controllable). Additionally, a warfare model can be used to determine the initial conditions and whcih variables have the most effect on the predictions. This would aid in identifying the center of gravity of the enemy.

All chaotic systems are nonlinear. Among other things, nonlinearity means that a small effort can have a disproportionate effect. If warfare is chaotic, then chaos theory suggests COGs may be found where there is a nonlinear process in the enemy's system ... Because you can't predict future behavior of a chaotic system based on initial conditions, chaos theory suggests that the campaign planner should concentrate on process in an emeny system rather than data on its current condition.[7]

iii) Sources of nonlinearity in warfare:

(1) Feedback - Col Warden suggested massing for a few blows rather than many minor blows as a result of attrition analysis.

(2) Psychology associated with interpreting enemy actions. Clausewitz stated that in strategy everything is very simple, but not on that account very easy. Maneuvers, such as flanking movements are simple in concept, they are difficult to accomplish because there is always the danger of what the enemy might be doing. "In this environment, small actions on the part of the enemy often assume larger significance in a commander's mind than they deserve."[8]

(3) There are a number of processes within warfare that appear to be inherently nonlinear. Mass for example being one. Warden showed that airpower losses vary disproportionately with the ratio of forces involved.

(4) Clausewitzian friction demonstrates that there are events in war which, whether through chance or not, have a disproportionate effect out of their apparent importance. Though difficult to predict, it can be taken advantage of once it happens. German doctrine of Auftragstaktik, allowing initiative on part of junior commanders, was designed to do precisely this.[9]

(5) The process of decision making is itself nonlinear. Sometimes decision clear-cut, but other times the decision can depend upon relatively minor circumstances at the time.

iv) If warfare is chaotic, then aspects of it must be fractal

(1) The attracto of a chaotic system is fractal and therefore infinitely complex. Efforts to analyze every aspect of an enemy's system are bound to be in vain as there will always be some finer level to analyze.

(2) Behaviors at the tactical, operational, and strategic level are linked. One thing that succeeds at the tactical level can succeed at higher levels. Sun Tzu implied fractal nature of war "Generally, management of many is the same as management of few." This means that the principles and processes in war are essentially the same regardless of the scale of the fight.[10]

d) Multiple attractors are possible in war. That is the difficlty that we encounter, because chaotic systems can have multiple quasi-stable states.
In war, this means that the enemy can change the organization and means of fighting a war. Example, North Vietnamese and Viet Cong actions. As warfare is chaotic, enemy systems can exist in different states. We must be capable of changing our own state in response. [11]

e) Some terms associated with Chaos Theory

i) Strange attractor - paths around which chaotic trajectories occur. The space paths never coincide and indeed the longer one looks at a chaotic system the more paths are taken and the more messier the phase space plot of the attractor appears.[12]

ii) Poincaré Map - Two-dimensional slice through attractor, makes its structure more obvious.

iii) Fractals - Objects with fractional dimensions. Ex. object wtih 1.5 dimensions is more than a line but less than a plane. An example of such a figure is the Koch snowflake (and equilateral triangle with one-third scale triangle added to each side of the resulting figure, ad-infinitum). Benoit Mandelbrot calculated the dimension of the perimeter of the Koch Snowflake to be 1.26 (between a line and a plane). These geometries are central to chaos theory because strange attractors are fractal. Strange attractors are infinite curves that never intersect within a finite area or volume.[13] If system is chaotic it will have a strange attractor and the Poincaré map will show fractal characteristics.

[1] Steven Weinberg, Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of the Universe, (New York: Vintage Books edition, 1994), p. 36.
[2] Ibid.
[3] Maj David Nicholls, USAF and Maj Todor D. Tagarev, Bulgarian AF, "What does Chaos Theory Mean for Warfare?" Airpower Journal, Vol. VIII, No. 3, Fall 1994, p. 49.
[4] Ibid.
[5] Ibid.
[6] Ibid., p. 53.
[7] Ibid., p. 55.
[8] Ibid., p. 55.
[9] Ibid., p. 56.
[10] Ibid.
[11] Ibid., p. 57.
[12] Ibid., p. 51.
[13] Ibid., p. 52.1)