In _On War_ Clausewitz repeatedly attacks reducing war to algebra. Yet his dialectical way of analyzing war demands of him a certain reductionism, if only to progress his argument on the other hand. In an attempt to explore this reductive side of the dialectic, I have tried to capture the variables of war introduced by Clausewitz in Book 1 Chapter 1 of _On War_.
I know my mathematical notation skills are not up to scratch, and if any mathematicians in the audience should offer their services, it would be greatly appreciated. Consider the following:
Description:
(P) *Policy* is a superset of (W) *War* which is equal to the maximum (F) *Force* of opponent (A) A divided by the maximum (F) *Force* of opponent (B) B plus (f) “blind natural *force*” multiplied by (c) *chance*.
_where_
(F) *Force* is equal to (A) *Attack* minus (D) *Defense* minus (E) *Emotion* or kindness, all multiplied by (h) *human factors* and divided by the (p) *political objective*.
_and_
(f) “blind natural *force*” is equal to violence multiplied by hatred multiplied by enmity
A foolhardy venture I know, and not nearly accurate. However, one must be ready to undertake unorthodox approaches when considering our dear Prussian. I look forward to your commentary and insight.
If you don’t figure distance it cannot be right
Hehe, god point Oliver. I guess you could put it in with (F) Force, as getting your gear to the front is vital. Clausy does talk about mobilizing forces a bit in the first chapter.
But distance also affects logistics and you have to assume the relationship is not linear. In addition your second equation implies that the relationship between attack and defense is linear. That is not the case. And in both uses of force you’ll have exponential effects. A force twice as big is more than twice as strong, if properly supplied.
Then you’d have to consider the exponential effect of morale in war, a la Ardent du Pique.
Another interesting idea, if you want to try to reduce foreign policy to an equation, is Bruce Bueno de Mesquita’s work on expected utility.
For example:
E(U) of war = Probability (success) * Utility (success) + (1-P(success))*(Utility(failure))…..
Or you might try (F) Force is equal to (A) Attack minus (D) Defense plus (O) Orneriness…
(f) Blind natural force should surely be (R) for Rage as in
“Sing, Goddess, sing of the rage of Achilles, son of Peleus—
that murderous anger which condemned Achaeans
to countless agonies and threw many warrior souls
deep into Hades, leaving their dead bodies
carrion food for dogs and birds—
all in fulfilment of the will of Zeus.”
But seriously, if you’re going that way, then would not (W) – if you are measuring effects – be (Fa) multiplied by (Fb) – for surely it was an effect of (F)-USA times (F)-Japan that led to the need to drop the Bomb?
And how does your equation factor in technology? The longbow at Crecy, the stirrup during the Mongol invasions, the gatling gun, the Bomb again?
Where do clever tactics come in?
And I don’t get how (h) and (p) factor into the equation at all.
I’m not convinced this is a useful exercise since the premise looks shaky, but if you sure it will help are I can’t fault you for trying. I would say try again, then.
“Oliver said”:http://cominganarchy.com/2009/01/13/solving-for-war/#comment-387332 “your second equation implies that the relationship between attack and defense is linear. That is not the case.” Glad you noticed that. I will be posting on Clausewitz’s dualism later.
“@vKT”:http://cominganarchy.com/2009/01/13/solving-for-war/#comment-387334 One of the things Clausewitz is often criticized over is his neglect of technology. I think “clever tactics” comes in with (h) human factors. See CvC’s discussion of “military genius” in 1/3.
I admit this is a shaky premise. Clausewitz tries to define war from a bunch of different angles in nearly 30 pages. I have tried to collect all those individual factors together in one glance, and express the relationships between each that Clausewitz discusses in his book. But one must remember that there are _another 600 pages_ in which CvC challenges and refines his definition. This equation is simply a Coles Notes of the first book, first chapter for those reading along with the Clausewitz Roundtable.
I have no experience with the mathematics of war, but I can’t fathom how some of those factors can be represented by numbers at all. How are enmity, hate, violence, and political objective expressed numerically?
By giving them the numerical value of the number of soldiers they substitute for
@YH – You’re right – I should have stuck closer to the text of the first chapter. Indeed CvC does use mathematical imagery. Here are some points to think about, and I hope they fit into the exercise you are undertaking. I get W as a subset of P. How would the aim or war (to disarm the enemy) fit in this notation? He also mentions the product of sum of available means (technology?) and strength of will (rage of Achilles?) He talks about will being related to motive – an existential fight? A just cause? So that will need to be figured in somehow, I would think.
“…I can’t fathom how some of those factors can be represented by numbers…”
.
Then leave the factors as letters. I say that without any flippancy. The formula allows you to see the relationships, even if you do not agree that they can ever be (meaningfully, accurately) quantified.
The problem with these exercises (and they can be useful) as Psudo points out and I am afraid Oliver passes over too quickly is MEAUSUREMENT. It is not simply a question of developing a formula or model that identifies the correct variables and expresses their relationships, it is also a matter of devising reliable and accurate measures for the variables so that the formula can bet tested and falsified. If you do as Oliver suggests and measure the variables ‘enmity,’ ‘hate,’ ‘political objective’ with the ‘number of soldiers’ you have either devised a measure that is unreliable or inaccurate or you have replaced the variable itself.
I think the literature on National Power would be useful here (particularly David Baldwin’s article, the “Paradox of Unrealized Power” or more recently Ashley Tellis’s “Comprehensive National Power an Analysts Guidebook”). The point is that National Power is a relative and contingent concept, is based on context and thus cannot be easily measured, quantified and compared. In particular theories or formulas of warfare and national power change over time as technology and tactics evolve. When Clausewitz was writing, the era of industrial warfare was fast approaching and strategy was basically one of attrition. It was like the game Risk: how many soldiers do you have lined up on the battlefield? How many oppose you? Roll the dice, they shoot at each other and probability says the guy with more troops to lose will emerge victorious over enough iterations.
Modern warfare includes so many more variables that developing models is immeasurably more complicated. Nor does the task of devising accurate measures for those variables become any easier. It can still be a useful exercise, but it is always important to recognize the elements of chance etc. that prevents those with superior forces from obtaining their objectives (i.e. the U.S. in Vietnam).
Some aspect of national power can be more easily quantified than others, but the history has enough instances where measurement and prediction have failed so abysmally that we ought to use the empirical approach towards war with extreme caution.
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I hereby dub thee “Jomini”! :-)
I’m sure the Airmen in the audience are reveling in joy that linearity and reductionism have been brought to that most complex of human activities.
Seriously, though, you can’t claim this shows “relationships” without adding the oh-comma-so-useful independent variable to account for “everything else” not already accounted for (akin to the factor “gamma” in Einstein’s Special Theory of Relativity).
BTW: Wouldn’t you agree that Clausewitz describes the factor of Chance (c) as applicable not only to “bnf” but also to F(max)a and F(max)b? So maybe you should add some parentheses so the (c) factor commutes across both (bfc) and your F(max).
Also, do you really think Force goes up as Emotion goes down? Or that the smallest political objectives (e.g., (p) -> 0) would cause Force to approach infinity?
Nonetheless, a fun diversion from the prose! BZ!
There is no measurement. The equasion is run in the heads of the rulers of the affected countries. Their decision rests on estimates. If these quantities could be measured, rational people wouldn’t go to war, as the outcome would be clear.
So the relevant variable becomes the individuals with the authority to wage war and their acumen and judgement? On that I think we agree.
However, I would suggest that the quantities can be measured–albeit with varying degrees of accuracy–but wars continue to occur becuase the rationallity of the rulers is bounded.
” … wars continue to occur becuase the rationallity of the rulers is bounded.”
Wars continue to occur, also, because the interests of the “deciders” and the interest of the people who pay for the wars and the people who die and get maimed in them are not aligned.
There is an agency issue here,not just a bounded rationality issue.
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