Mathematics of War

[Tom Odom]

While it might be old news, it is new news to me. I thought the most stunning conclusion was that Alpha was the structure of the insurgency and this structure followed the same slope downward for all war. This means that it doesn’t matter what the structure of an insurgency looks like, it follows the same path.

Of course, right now that slope (path) is actually moving upward for the war in Iraq, which is really bad news. It probably means that the surge worked well at first, but has now out-lived its usefulness. The surge was able to isolate the fragmented insurgency into separate orientations (that were more deadly, but less able to freely carry-out attacks) to control the number of attacks (as you said on another post, command doesn’t really have control), but then something else has happened. The insurgency has become more fragmented and more deadly.

Really? that would be news if it were even close to the facts on the ground. The "surge" was not a monolithic event and neither was the insurgency.

Because, according to the data, it doesn’t matter what the insurgency looks like, it looks like a whole new war has broken out. Sean didn’t say where, spatially, this war was taking place, but I am not sure what will keep it from spreading, if the surge didn’t work. Of course I am also assuming the US forces are trying to maintain the surge, and I may be wrong on that. It could be we are adapting to this new war or the Iraqi Security Forces have the lead.

Again that would be very interesting if it looked that way on the ground. Your assumption on the "surge" is much dated. ISF are very much in the lead.

It doesn’t look like the Iraqi Security Forces are prepared to handle this insurgency as the Iraqi Security Forces are largely unfunded (let's hope this doesn't happen to ours) and (perhaps) unwanted.

Who is unfunded? The ISF certainly is funded; there are issues with Iraq's budget but the ISF are hardly unfunded.

As I commented on Drew’s post, it doesn’t appear like our troops are ever coming home. As this new war spreads, we will simply become more and more involved. It also might be that our forces or nation doesn't understand another war has broken-out since the surge, if that is indeed what the data is telling us, and I think it is.

Again a new war as opposed to an old war? Who has issues understanding what?

If we don't understand the situation, it is very easy to get sucked-up into a very nasty one, without our vertical and horizontal forces being prepared.

Perhaps a "fake" science, like social science, will tell you the vertical or horizontal forces don't need to know, I think that is a lie

I agree that understanding is mandatory; exactly what are vertical and horizontal forces?

Do us all a favor and introduce yourself so we could put your comments in context.

Thanks
Tom

[Mark O'Neill]

Really? that would be news if it were even close to the facts on the ground. The "surge" was not a monolithic event and neither was the insurgency.



Again that would be very interesting if it looked that way on the ground. Your assumption on the "surge" is much dated. ISF are very much in the lead.



Who is unfunded? The ISF certainly is funded; there are issues with Iraq's budget but the ISF are hardly unfunded.



Again a new war as opposed to an old war? Who has issues understanding what?



I agree that understanding is mandatory; exactly what are vertical and horizontal forces?

Do us all a favor and introduce yourself so we could put your comments in context.

Thanks
Tom

You know the old 'horizontal and vertical force'. Surely All COIN experts use those terms ;-) don't tell me the pony soldiers don't?? gee, I am amazed... You had better get across what is happening on the ground.................:-]

[Larry Dunbar]

“exactly what are vertical and horizontal forces?”

War has been defined by many descriptions, but it simply is the displacement of energy, from one orientation into another. This is the main reason the power-law distribution applies to war. There are two forms of energy inside every displacement, kinetic and potential. Kinetic energy has mostly a component of Vertical force, while potential energy has mostly a component of horizontal force. Together the vertical and horizontal forces move the displacement from potential to kinetic and back again. It works in a loop and that loop, to some, is called an OODA loop.

Vertical forces are the forces that the horizontal forces of a country are able to support. The horizontal force is the amount of force between you and I, which is growing. Actually, the horizontal force is the amount of force a society has between its past and future, but it is not always (never) figured in that way.

Force at a distance is the definition of energy. When the vertical force moves, the distance from one country to another, it is called kinetic energy. The amount of power, energy per second, a country can throw at another country depends on how much vertical force the horizontal force can support, @ the distance and over time.

My guess why the power-law distribution “works” in Iraq or any war is that Alpha describes the structure of the insurgency and that structure, in Iraq, represents the orientation on the other side of the power curve of the US, and to a degree the Iraqi Security Forces. The Data is not for a particular orientation (religious, warlords, tribes, or thugs) only that orientation opposing the new Orientation. I capitalized the last Orientation because it represents the second "O" in the OODA loop (Orientation is what a vertical force does after it Penetrates the Observed environment of another displacement; it Isolates the displacement into Orientations, isolation does not always mean: to kill).

[William F. Owen]

War has been defined by many descriptions, but it simply is the displacement of energy, from one orientation into another. This is the main reason the power-law distribution applies to war. There are two forms of energy inside every displacement, kinetic and potential. Kinetic energy has mostly a component of Vertical force, while potential energy has mostly a component of horizontal force. Together the vertical and horizontal forces move the displacement from potential to kinetic and back again. It works in a loop and that loop, to some, is called an OODA loop.

I don't follow that at all, and which OODA loop are you talking about? Boyd's and if so which iteration of the loop?

Plus I don't remember Boyd mentioning any of the aspects you are talking about relating to the OODA loop, which as far as I know was entirely cognitive.

[MikeF]

“exactly what are vertical and horizontal forces?”

War has been defined by many descriptions, but it simply is the displacement of energy, from one orientation into another. This is the main reason the power-law distribution applies to war. There are two forms of energy inside every displacement, kinetic and potential. Kinetic energy has mostly a component of Vertical force, while potential energy has mostly a component of horizontal force. Together the vertical and horizontal forces move the displacement from potential to kinetic and back again. It works in a loop and that loop, to some, is called an OODA loop.

In the military world, we call this METT-TC. If you look at a state as a homeostatic system, then you may be able forecast how that system will change when you introduce "new" energy or external forces into it.

Wilf- this understanding is intuitive to you, Ken, etc, but it is not intuitive to most. Science can provide another lens to help explain it.

For example, Iraq circa 2002 was stable in Iraqi terms. They had a nice dictator, and things worked. There were no suicide bombers (i think). The radical Islamist plotting to ovethrow the government in places like Turki Village were marginalized, etc.

We decided that we should overthrow the natural order of thngs. We ASSUMED that after we took over, we coulld hold elections, and little americans would emerge from the ashes. We assumed that we could undertake such a venture with minimal force and cost. We were wrong. Our planning was based off ideology, not reason and historical fact.

I think we can do better in the future, but we have to apply the physical sciences along with the social sciences.

Gurley may be an opportunist, but I'm developing theories along similar lines that may help us to better plan and prosecute future interventions.

Larry's analogy to the displacement of energy has merit if you apply it to societies. Not sure about the OODA loop thing though.

v/r

Mike

[jmm99]

may be useful to an individual in helping that person visualize a situation (let us say, war) to which the metaphor does not directly apply. E.g., Larry sees war as a matter of statics and dynamics - based on an engineering education.

Wilf see things in a very military context - based on an education in practical warfare - and he also has read and written much in that context. He does not need metaphors.

I suppose one could look at an "armed conflict" (let us say, Iraq) as akin to a problem in biochemical reaction kinetics - introduction of forces, energy and catalysts (don't forget them) into a homeostatic system (as MikeF suggests).

At least, we would be dealing with a living system there (and a lot of cool graphs, showing what works and what does not). But what does that add ? - except to the understanding of the individual who has developed the metaphor.

More generally, we see engineering concepts such as mass introduced into the "equations" of war (e.g., MOOSEMUSS). Now to a engineering-scientific type (and yes, I do have a good degree in that area with some grad work), mass itself doesn't say much (so many particles of a defined substance).

But, there are some formulations which include mass: e.g, weight, vector forces, momentum, center of gravity, energy (after all, E=mc^2=nuks), that are used (sometimes usefully, sometimes not) as metaphors in the military art by its professionals. And, of course, we have CvC's fogs and frictions used as metaphors by him.

Sometimes metaphors are useful to groups of people, as well as to the individual. But, they also introduce terminology which has to be explained - and which can simply clutter up the picture and actually retard mutual understanding.

Admittedly, metaphors can be fun[*], but in the end you have to get down to the things which you actually do in your art and profession.

So, I guess I come down more on Wilf's side of the ledger - despite having little differences such as whether flying airliners into buildings can be classed as military operations in the context of an armed conflict.

---------------------
[*] e.g., waves and surfing - or my now deceased colleague's maxim: "You have to roll with the flow." He was an artist; I am a technician - the maxim applies to both kinds of trial lawyers; but both end up expressing what counts in factual and legal terms.

[MikeF]

So, I guess I come down more on Wilf's side of the ledger - despite having little differences such as whether flying airliners into buildings can be classed as military operations in the context of an armed conflict.

More than likely, y'all are correct, but that's my job right now so I'm gonna explore. Eventually, I'll graduate and go back to doing not thinking.

But, since you did mention the theory of relativity, what if it is actually a law that has yet to be proven?



v/r

Mike

[jmm99]

Since there were no little icons after a couple of your comments, I'll take them as serious comments.

Easy one first: a scientific theory is more than what the non-scientific use of the word "theory" implies. E.g., relativity (special and general) was built on prior proofs (e.g., Newtonian physics), which work well in the specific areas where they apply to 99.9% of the researched problems. Relativity, which was more general than Newtonian, worked and works in some of the 0.1% of the areas where Newtonian failed. So, relativity in those areas is proved. Period. However, there are still areas where relativity is not proved - and where it may well not work. In those areas (perhaps, 0.1% of the 0.1%), an even more inclusive theory might have to be developed - which would also have to be consistent with the proven results for the Newtonian and Einstinian "theories".

In short, science (like Wilf ) requires rigour.

Upon reflection about this one:

from MikeF
Eventually, I'll graduate and go back to doing not thinking.

you are pulling my leg - right ?

[MikeF]

That was simply a little stubborness slipping out. I'll probably end up either teaching or working in a collaborative group trying to solve difficult problems after graduation. If some of the project groups that I'm currently working with are fruitful, then we may determine better policies that the USG could employ. We'll see.

I won't be jumping out of airplanes anymore. Don't fret.

Mike

[Presley Cannady]

And to tag on to jmm's point, STR and GTR describes all the physics Newton's laws of motions do, but also in excess of the limit where gravitation and/or acceleration is non-negligible or relative velocity approaches the speed of light. Quantum mechanics likewise describes all physics in the classical limit, but at its typical length scale arrives at results the continuous mathematics of classical motion can't describe. Even so, we continue to use all three where they are most useful even if they are inaccurate at some given scale of some given observable(s). This is even more evident in statistical mechanics, chemistry, biology, ecology and social sciences, where not only are you introducing stochastic models but often you're satisfied with models that predict for only a percentage of an accounted effect.

If Gourley's result is exciting, it's in that in confirms that some part of the behavior of war conforms to an elegant model like a power law. As it stands, you probably couldn't expect a great deal of accuracy in its boundary points--whatever shapes alpha, or however alpha evolves isn't well understood enough as evidenced by the bunch of "I don't knows" Gourley spat out when examining the Iraq insurgency in the context of this model.

Science is rigor, but more importantly it's estimation. An explanation that's useful doesn't simply fall to the way side because it can't predict all phenomena in its domain.

[Larry Dunbar]

"So, I guess I come down more on Wilf's side of the ledger"

Well, I figured I had to start somewhere, so I thought I would just throw it all out there.

I have been told (not in exact terms) that metaphors are a practical way of crossing orientations. I am too old to be crossing into Wilf's side (boots on the ground, sort of thing) and there is no reason for him to cross into mine (whatever my orientation is in fact).

I have been trying to tie this in with quantum physics, which doesn't really help. One quantum physics scientist said, if you say you understand quantum physic, then you don't understand quantum physics. This leaves me at an unfair advantage.

I actually look at a military movement as a particle-wave, and use my understanding of a particle-wave or electromagnetic radiation, which could be wrong, as the model. The more I read about war and physics the more it looks like I am correct.

Of course to me, all a nuke is just an electromagnetic pulse, same thing as an electromagnetic wave, except the frequency (the number of attacks) is in the number of events instead of the length of wave (intensity, more deadly).

[Presley Cannady]

I have been told (not in exact terms) that metaphors are a practical way of crossing orientations. I am too old to be crossing into Wilf's side (boots on the ground, sort of thing) and there is no reason for him to cross into mine (whatever my orientation is in fact).

Not sure about metaphors. Analogies are useful to a point, but generally break down when terminology is adopted piecemeal. Categories--essential mathematical relationships with applications in various fields--are useful and generally accurate, though formal, and help develop more robust analogies. I fear that military science literature has foregone this step in adopting concepts from other fields.

I have been trying to tie this in with quantum physics, which doesn't really help. One quantum physics scientist said, if you say you understand quantum physic, then you don't understand quantum physics. This leaves me at an unfair advantage.

I wouldn't take that if I were you. Truisms like that are infuriarating, not because they're accurate (this one is a little), but because they're damned unhelpful. True, no one "understands" quantum mechanics--if by that we mean how to completely frame its physical consequences. On the other hand, simply because there are five interpretations doesn't mean that each interpretation is equal, or that it's impossible to fix on the correct one. More importantly, regardless of the underlying physical intuition, you can understand the key results with little more than high school math. The non-relativistic wave equation is a sufficiently complete introduction to QM taught in freshmen chemistry classes in universities across the world.

I actually look at a military movement as a particle-wave, and use my understanding of a particle-wave or electromagnetic radiation, which could be wrong, as the model. The more I read about war and physics the more it looks like I am correct.

I assume you're talking about a massive particle when you say particle wave, though I'm not sure exactly how you're applying that to "military movement." As I read this, you're saying that such movement can be described by laws of motion or the mechanics of an oscillator. The value in framing the movement of men and materiel this way escapes me, but perhaps we need some more detail as to circumstances in which you apply this model.

Of course to me, all a nuke is just an electromagnetic pulse...

It's considerably more than that. Overpressure and heat in any explosion (in an atmosphere) is a convective process, not a radiative one.

...same thing as an electromagnetic wave, except the frequency (the number of attacks) is in the number of events instead of the length of wave (intensity, more deadly).

Still not following. The frequency of a wave is the product of its speed and the inverse of wavelength. Intensity is a function of frequency (or wavelength) for a given velocity. The power law explicitly diminishes in velocity as frequency increases, so intensity is not guaranteed to increase with it.

[MikeF]

- Bounding onto an objective is much easier than trying to seal the AfPak border.

-I should have paid more attention in my physics class. Actually, I probably should have stayed awake.

-At the end of the debate, COL Gentile may prove to be correct.

Time to watch House and 24.

v/r

Mike

[Larry Dunbar]

The power law explicitly diminishes in velocity as frequency increases, so intensity is not guaranteed to increase with it.

Thanks for the heads-up. I was only able to take two terms of physic, the first and last of a three term set. So I studied an AC wave before I studied a Single Harmonic Motion. I went back and read this stuff, but it looks like I missed the basics. I think the math is the same, but way easier to visualize. Thanks again. Maybe later I can come up with some terminology that will "Hook" this all together.

Just a guess, I think the highest intensity will be where the velocity is zero, acceleration is max, and the displacement I am not sure of. I guess the highest intensity is when it is only a potential displacement of very high amplitude, which I suppose means it can be positive or negative.

[Steve the Planner]

A couple of decades ago in the planning/policy program at Johns Hopkins, there were several mandatory courses, two of which provided the perfect contrast. One was a kick-ass-take-names course in quantitative methods for planning and policy. The other was the Director's "special" course in planning and politics which, once a month, met in a private room at the Hopkins Club, to get whichever politician was in the most trouble into a private gathering with a supposed friendly audience to discuss his version of the story. After a few hours, the drinks set in and we got all the dirt. (Remember the drinking standards of past years?).

Somewhere between quantitative methods, politics, and human foibles and booze, we got a pretty good understanding of government planning and policy. The math is a good start, but hardly tells the story.

I just came off a "secondment" to UN's political team in Iraq. If only the disputed boundaries issues could have been reduced to math...

Steve

[jmm99]

think like so (if it helps you individually, so much to the good):

from Larry
I actually look at a military movement as a particle-wave, and use my understanding of a particle-wave or electromagnetic radiation, which could be wrong, as the model. The more I read about war and physics the more it looks like I am correct.

But, I am also aware of the uncertainties and complexities of particle-wave theory (actually theories - and a compromise between the theories to yield a kludge which will work in most cases). So, perhaps your metaphor will work across orientations - if the recipient of your metaphor can understand it; and if your metaphor is indeed correct in its own field (quantum mechanics).

Why not simply say a military movement looks like so (see attached for one of many possible examples); and explain it in terms of what actually happens, why that happens, and what the pluses and minuses of the options are ?

Hugh Everett, who was more than brilliant (but more than a bit eccentric), made the jump from theoretical math and quantum physics to defense modeling, with quite a bit of success.

[Ron Humphrey]

Picture's worth a thousand manual's

[Ken White]

Surferbeetle and I have a running battle on excessive metrication. I say most such efforts are excessive, he disagrees. Yesterday, he said:

"...note our world-renowned college educational system and until recently, our possession of the worlds strongest financial system. Our college system consistently explores the concepts of mathematical modeling and simulation in associate through graduate educational programs in business, engineering, finance, and manufacturing – all disciplines that are crucial to a nations ability to survive and thrive."

It's a shame he couldn't say our world renowned educational system without the 'college' caveat. We used to have that, no caveats -- but then we got interested in processes instead of results...

I may be mistaken but I believe the reason we no longer have the worlds strongest financial system can be laid at the feet of two entities. The US Congress and political class who encouraged stupidity and the Financial whiz types -- who all used mathematical models to prove what they were doing was valid...

Ha also said:

This journey will take time, have setbacks, and generally be a PITA however when balanced against the adapt or die imperative it’s an easy choice to make.

I'm dubious. I've watched too many war games, computerized and not, get manipulated and too many results that were unpalatable discarded. People don't play fair. Really messes things up, sometimes.

Mike F said:

"We ASSUMED that after we took over, we coulld hold elections, and little americans would emerge from the ashes. We assumed that we could undertake such a venture with minimal force and cost. We were wrong. Our planning was based off ideology, not reason and historical fact."

I know that's what was said by many and I'm sure many who said that truly thought it -- but I'm personally convinced that it does not reflect why we went or the thinking of the decider and other quite senior folks.

At base level it was pure physics -- a reaction to the various force efforts applied to us over the entire period 1979-2001 to the brachial plexus of those who expressed their discontent in a violent manner.

We don't want an empire and we won't have one (you can write that down). We just don't tolerate threats or continued pinpricks; when those two things loom, we go into the disruptive mode. Been doing it for over 200 years. Been hacking off the rest of the world by doing so for that two centuries plus. I doubt we'll stop.

JMM, as always comes in with a wise summation:

"Sometimes metaphors are useful to groups of people, as well as to the individual. But, they also introduce terminology which has to be explained - and which can simply clutter up the picture and actually retard mutual understanding."

True. Combat is a simple art, really. It is a cognitive and an experiential skill and it is emphatically in execution (if not in its implements today) an art and not a science. It does not lend itself at all to metrication and hard science (other than a little geography) and every attempt I have seen to introduce such concepts has failed -- mostly because people are rather unpredictable at times.

Thus, I say again, when you feel the urge to apply numbers to any human activities and particularly the chaotic activities -- be careful...

[Presley Cannady]

I may be mistaken but I believe the reason we no longer have the worlds strongest financial system can be laid at the feet of two entities. The US Congress and political class who encouraged stupidity and the Financial whiz types -- who all used mathematical models to prove what they were doing was valid...

First off, we should disabuse ourselves of the notion of a national financial system. CDOs and credit default swaps are global, hence the global financial crisis. Second, proprietary use of a single, public domain mathematical tool which, otherwise used in numerous applications, is only relevant given a very narrow set of circumstances , is the principle culprit for the risk miscalculation leading to the debt collapse in 2007-9. And by proprietary use, we can easily say misuse was the culprit--including bad inputs, faulty assumptions about the performance of some independent variables (the value of the underlying asset of the derivative, for example), etc. This doesn't mean there isn't a simple way to sum up the cause of this latest disaster, it just means that simple should also be specific.

Ha also said:I'm dubious. I've watched too many war games, computerized and not, get manipulated and too many results that were unpalatable discarded. People don't play fair. Really messes things up, sometimes.

Yet you can discern the manipulation, presumably on its face if you did so without need of deeper analysis. And that's the point. We can't simply use (or abuse) these models without scrutiny, and even in a hard to catch case (like the financial crisis) there's plenty of evidence of what went wrong and why--only too often after the fact. The moral of the story is you learn, improve the model, use it better in the future or discard it if necessary.

Thus, I say again, when you feel the urge to apply numbers to any human activities and particularly the chaotic activities -- be careful...

A good lesson, but one that assumes some value in using numbers in the first place.

[MikeF]

I know that's what was said by many and I'm sure many who said that truly thought it -- but I'm personally convinced that it does not reflect why we went or the thinking of the decider and other quite senior folks.

At base level it was pure physics -- a reaction to the various force efforts applied to us over the entire period 1979-2001 to the brachial plexus of those who expressed their discontent in a violent manner.

We don't want an empire and we won't have one (you can write that down). We just don't tolerate threats or continued pinpricks; when those two things loom, we go into the disruptive mode. Been doing it for over 200 years. Been hacking off the rest of the world by doing so for that two centuries plus. I doubt we'll stop.

To be more accurate, I should state that is what I (not we) assumed back in 2003. Now, I'm trying to apply game theory with some psychology (not modeling and simulations) to hopefully give our commanders better means of determining when to intervene and what force to use and provide our policy makers better understanding as to what we can and cannot accomplish.

We'll see how it works.

v/r

Mike