Mathematics of War

[Ken White]

human interaction will always show patterns -- and different modelers will draw different patterns from the same data. You cannot put people in boxes IMO; you have to deal with the person or group as they are and as they constantly shift and change.

Well, you can put 'em in boxes and rely on trends, I suppose. Seen a lot of folks do some fascinating variations on that. None successfully, as I recall...

All things considered, though, I don't guess a Physicist playing around with the People thing is any worse than Economists trying to do that...

[Surferbeetle]

Drew,

Thanks for the link, it led to the JASS site which has some interesting papers and references a book from the Springer publishing house; I enjoy some of their financial mathematical modeling series books...quality works which require a fair amount of time, but are well worth the read.

Regards,

Steve

[Gringo Malandro]

human interaction will always show patterns -- and different modelers will draw different patterns from the same data. You cannot put people in boxes IMO; you have to deal with the person or group as they are and as they constantly shift and change.

Well, you can put 'em in boxes and rely on trends, I suppose. Seen a lot of folks do some fascinating variations on that. None successfully, as I recall...

All things considered, though, I don't guess a Physicist playing around with the People thing is any worse than Economists trying to do that...

I think the military might actually benefit from applying some principles of economics. And data analysis can make sense out of seamingly unrelated events. But it can't replace common sense. It was, after all, often physicists who built mathmatical models for pricing financial products. Oops!

[Larry Dunbar]

"But it can't replace common sense. It was, after all, often physicists who built mathmatical models for pricing financial products. Oops!"

True, common sense would have told us not to put that much power in the hands of greedy and unregulated bodies, but how was the physicist supposed to know? It doesn't seem related.

Sean pretty-much just laid it out without any conclusions, as did the physicists who put the mathmatical models for pricing financial products together. It was then on a need-to-know protocol. The financial sector picked the wrong guys.

[Presley Cannady]

human interaction will always show patterns -- and different modelers will draw different patterns from the same data. You cannot put people in boxes IMO; you have to deal with the person or group as they are and as they constantly shift and change.

Modelers will almost certainly not draw different patterns from the same data. To arrive at a different distribution, you'll need to infer that the domain (in this case the sample size) is too small to rule out piecewise or differential behavior, or that the data set is inconsequential to your object of study. Either way, the fact remains to a degree of accuracy clusters of thinking human beings can be modeled successfully and have been for decades.

Now the data itself--particularly the chosen input streams--can definitely be challenged. Though it's unlikely that three independent studies happened upon k-power polynomial relationships between different sets of variables on their own, they can differ wildly in their constants.

Well, you can put 'em in boxes and rely on trends, I suppose. Seen a lot of folks do some fascinating variations on that. None successfully, as I recall...

If that's the case, we're wasting a lot of money on pshrinks, term insurance, and advertising with absolutely zero discernible benefit.

All things considered, though, I don't guess a Physicist playing around with the People thing is any worse than Economists trying to do that...

A physicist is generally a better working mathematician and statistician than an economist. We've had too few of those in the social sciences in recent decades.

[Ken White]

...the fact remains to a degree of accuracy clusters of thinking human beings can be modeled successfully and have been for decades.

Sure have. My issue is with your "degree of accuracy." Adequate for your trade perhaps -- in my former trade that 'degree of accuracy' can easily get you killed.

If that's the case, we're wasting a lot of money on pshrinks, term insurance, and advertising with absolutely zero discernible benefit.

I'm unsure who constitutes your "we" but I do know that I'm not wasting any money on pshrinks. Or Term Insurance. As for advertising -- some success stories, some abject failures and even the success stories didn't get nearly everyone...

If one's ad campaign doesn't work out, few to no lives are likely lost -- if one's war campaign doesn't work out, many lives and perhaps more will be lost.

"This I find kind of disturbing, considering the key result was discovered almost half a century ago. What the hell have we been doing since? I mean it really feels like Gourley et. al. are shopping for new office space and maybe a graduate degree program, but why isn't there a whole field of Quantitative Conflict Studies out there?"

You are familiar with these guys? LINKThey and their founder have been at it since shortly after WW II.

They and others have tried the numerate approach to war for years. None of those attempts ever really took hold. I think perhaps there's a message in that...

[Presley Cannady]

Sure have. My issue is with your "degree of accuracy." Adequate for your trade perhaps -- in my former trade that 'degree of accuracy' can easily get you killed.

Agreed. So the question is whether or not the degree of accuracy in a quantitative model is more or less likely to get someone killed than not using it. In the medical profession--where life and death is equally, and probably more frequently, at question--the answer's obvious.

I'm unsure who constitutes your "we" but I do know that I'm not wasting any money on pshrinks. Or Term Insurance. As for advertising -- some success stories, some abject failures and even the success stories didn't get nearly everyone...

Certainly, but the outliers--or even a sizable deviation under certain circumstances (not life threatening, to be sure)--doesn't overwhelm the value gained from predicting behavior in the aggregate. Optimization doesn't guarantee perfection, only a good bet that practice that considers it is better than practice that doesn't.

If one's ad campaign doesn't work out, few to no lives are likely lost -- if one's war campaign doesn't work out, many lives and perhaps more will be lost.You are familiar with these guys? LINKThey and their founder have been at it since shortly after WW II.

They and others have tried the numerate approach to war for years. None of those attempts ever really took hold. I think perhaps there's a message in that...

Don't get me wrong. I'm the first to say that there's no evidence that the power law Gourley et. al. have rediscovered will yield any valuable prescriptions. You can say the same about any number of aphorisms about violence--war is hell, whoever gets there with the mostest the firstest wins, guns don't kill people blah blah--all accurate and probably not all that helpful when faced with a real need to plan and execute.

On the other hand, you can plainly see the value in quantitative methods in force flow planning, bridging, navigation, decision trees, acquisitions (jokes go here), etc. These methods should and do prove their worth the same way tradition does--by being tested under specific conditions time and time again and under fire. We generalize their lessons at our own risk.

[Presley Cannady]

We generalize their lessons at our own risk.

I should admit this is a weasel phrase. More often than I'd care to count, but not often enough to detract from the aggregate value gained, lessons drawn from quantitative methods applied to people are applicable only to the sample studied. You can have the most elegant model of conflicts from 1931 to 2009 and find out it has no predictive value whatsoever. I guess this is why so many evaluators will qualify their recommendations with pages long "provided that such and such is this and that..." preliminaries. Happens in every industry.

[Ken White]

"Agreed. So the question is whether or not the degree of accuracy in a quantitative model is more or less likely to get someone killed than not using it. In the medical profession--where life and death is equally, and probably more frequently, at question--the answer's obvious."

My observation has been that the success rate of good intuitive commanders is about 75%; that of their more numerately inclined peers is about 35-40%. My observation has also been that Medical Doctors are Like Economists; if you don't like what one says, ask another. Had a Grandfather who was a Doctor. He contended after over 50 years of practicing medicine that it was more art than science.

My observation of the Medicos leads me to believe that their numbers probably would roughly co8incide with my combat commanders...

"...doesn't overwhelm the value gained from predicting behavior in the aggregate. Optimization doesn't guarantee perfection, only a good bet that practice that considers it is better than practice that doesn't."

I agree with that for many actions and activites. I do not agree that it is correct when applied to warfare -- or Blackjack -- by most people.

"..blah blah--all accurate and probably not all that helpful when faced with a real need to plan and execute.

Blah blah is never helpful in anything. Aphorisms and metaphors have their place. So do numbers and models. Warfare mostly is not one of those places.

On the other hand, you can plainly see the value in quantitative methods in force flow planning, bridging, navigation, decision trees, acquisitions (jokes go here), etc. These methods should and do prove their worth the same way tradition does--by being tested under specific conditions time and time again and under fire. We generalize their lessons at our own risk.

Having undergone the pain of coping with 'force flow planning' on numerous occasions, I can tell you that it usually gets totally screwed up -- frequently but not always dues to human error -- and then a human has to unstick it. Bridging is an Engineering endeavor and obviously needs several skills to do it efficiently -- not so many are needed to do it effectively. I've seen a number of matrices and decision trees fail totally -- usually at some cost in pain and suffering. Acquisitions, as you say...

Actually, very few things are "tested under specific conditions time and time again and under fire." That's because almost every effort attempted under fire is subject to the vagaries and variances of the mission, the particular enemy at a given point and time, the terrain and the type or lack of vegetation thereon, the troops one has available (and even with the same troops exactly, time will affect their abilities and effectiveness), the time of year and of day as well as that available and in any situation, not just COIN but mid level or major war, civilian considerations (and that can include own as well as international political constraints, like Rules of Engagement, media coverage and such). Throw in human foibles and you have too many variables so you will build a model upon which you cannot rely above the 50% level -- I like my fights to have better odds and that can usually be arranged.

BTW, don't conflate tradition and experience -- or principle and application.

[jmm99]

The attached attack was sand tabled and rehearsed for a couple of weeks. In the event, tactical bombing failed to dent Siegfried - so also div & regt arty & 4.2 mortars. Charlie (my dad's company) & an attached MG platoon from Dog took most of their casualties in the first hour from pre-registered Jerry arty & mortars.

So, Charlie stalled by the RR tracks, until a few guys took out the blocking pillbox - and a couple of platoon leaders put together a composite platoon which was at least able to provide Able & Baker with supporting fires. All of C's assault squads (the guys with explosives & flamethrowers) were lost to the Jerry barrage.

A & B assaulted as planned - and all pillboxes were reduced by day's end. So, 1/117 was the can opener that opened the gap for the rest of the 30ID and 2AD.

Are there mathematical models for the tip of the spear ?

Would they predict the casualties sustained ?

[William F. Owen]

T
Are there mathematical models for the tip of the spear ?

Would they predict the casualties sustained ?

1. Very interesting example. Shake your Dad's hand for me. I mean it.

2. To answer your question, no their are not, (that I am aware of) in terms of proven reliability. There are general approximations for certain conflicts at certain times, but that doesn't tell you much. The Soviets had extensive and comprehensive sets of data used for planning, but there is no way of knowing how accurate of useful they were.
A while ago I spoke to some old US Army Colonel who told me that some work done with modern simulations shows them to be generally accurate. - who knows? Personally I think it's an area with little merit in studying.

[Presley Cannady]

My observation has been that the success rate of good intuitive commanders is about 75%; that of their more numerately inclined peers is about 35-40%. My observation has also been that Medical Doctors are Like Economists; if you don't like what one says, ask another. Had a Grandfather who was a Doctor. He contended after over 50 years of practicing medicine that it was more art than science.

At one point the medical profession was more art than science. Men generally also only lived until their late 40s and bacterial infections were considerably more fatal. And since little if any warfighting prescriptions following from quantitative modeling clearly contradict long experience, I'm not surprised to find that intuition performs so well. As for the performance of the more numerically inclined, I'd say this: the bean counter is not the model and visa versa.

My observation of the Medicos leads me to believe that their numbers probably would roughly co8incide with my combat commanders...I agree with that for many actions and activites. I do not agree that it is correct when applied to warfare -- or Blackjack -- by most people.

Most people don't understand the mathematics behind Blackjack. When they do, they make a book and a movie about it.

Blah blah is never helpful in anything. Aphorisms and metaphors have their place. So do numbers and models. Warfare mostly is not one of those places.Having undergone the pain of coping with 'force flow planning' on numerous occasions, I can tell you that it usually gets totally screwed up -- frequently but not always dues to human error -- and then a human has to unstick it. Bridging is an Engineering endeavor and obviously needs several skills to do it efficiently -- not so many are needed to do it effectively. I've seen a number of matrices and decision trees fail totally -- usually at some cost in pain and suffering. Acquisitions, as you say...

And yet for more than half a century modern warfare has embraced quantitative methods in all these fields and more. A fair assessment of the success math has in the field would compare the performance of one generation of warfighters to its predecessors.

Actually, very few things are "tested under specific conditions time and time again and under fire." That's because almost every effort attempted under fire is subject to the vagaries and variances of the mission, the particular enemy at a given point and time, the terrain and the type or lack of vegetation thereon, the troops one has available (and even with the same troops exactly, time will affect their abilities and effectiveness), the time of year and of day as well as that available and in any situation, not just COIN but mid level or major war, civilian considerations (and that can include own as well as international political constraints, like Rules of Engagement, media coverage and such). Throw in human foibles and you have too many variables so you will build a model upon which you cannot rely above the 50% level -- I like my fights to have better odds and that can usually be arranged.

Vagary and variance are terms of art in stochastic modeling. A model does not yield an analytically exact answer, it specifies a distribution of probabilities within a given domain. This tells us two things--one, models are highly conditional on their subject samples and two, any modeler risks discovering variance so wide that statistically significant relationships are impossible to identify. Readily conceded. The question is whether or not modelers are doomed to find only either statistically useless models or useful ones contrained to useless domains.

As for the number of variables, climate change models handle orders and orders of magnitude more variables than those you've listed, counted in econometric or broader military science. The number of inputs is irrelevant if techniques to crunch them exist.

BTW, don't conflate tradition and experience -- or principle and application.

I don't on the latter, but on the former I see no difference. Neither tradition nor experience as terms demand unwavering adherence, simply deference and consideration.

[Ken White]

At one point the medical profession was more art than science.

Because all the science merely provides mor information to fuel a better guess. Sometimes.

...the bean counter is not the model and visa versa.

True but he often pushes his model in spite of knowing it's flaws -- pride of author or owner ship is a terrible thing.

And yet for more than half a century modern warfare has embraced quantitative methods in all these fields and more. A fair assessment of the success math has in the field would compare the performance of one generation of warfighters to its predecessors.

I think if you give that few seconds thought and refresh your History cells, you may not really want to go there. Put another way, how well has that worked out for us?

The question is whether or not modelers are doomed to find only either statistically useless models or useful ones contrained to useless domains.

You do know that all of our disagreement really revolves around the unconstrained application of metrics, matrices and modeling -- the three 'M's (Good copy, bad practices for warfare) to war. I have no quarrel with the utility and even necessity in many fields -- to include building weapons and supporting war fighters. I do not urge they not be used in actual combat operations but do urge great caution in that use.

I don't on the latter, but on the former I see no difference. Neither tradition nor experience as terms demand unwavering adherence, simply deference and consideration.

True -- and exactly the same conditions apply to math and models.

What all you believers forget is that humans presented with a bunch of numbers that prove something tend to accept them because that means they don't have to think about the problem. That's the danger that most math centric folks do not think about much less care to mention or guard against...

I go back to what I said earlier. Nothing you've said indicates that I was incorrect:

""human interaction will always show patterns -- and different modelers will draw different patterns from the same data. You cannot put people in boxes IMO; you have to deal with the person or group as they are and as they constantly shift and change.""

You have essentially said that's correct.

""Well, you can put 'em in boxes and rely on trends, I suppose. Seen a lot of folks do some fascinating variations on that. None successfully, as I recall...""

I have watched the US Army try many numerate / modeling efforts and been the victim of attempts to apply templates, matrices and decision trees to combat -- all failed miserably. Whether the model was wrong or through human error in application, they are dangerous.

I go back to my first comment on this thread (which was not don't use them but) -- "People and numbers don't mix well."