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Thread: Mathematics of War

  1. #21
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    Quote Originally Posted by Ken White View Post
    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.
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    Council Member MikeF's Avatar
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    Quote Originally Posted by jmm99 View Post
    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

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    Quote Originally Posted by Larry Dunbar View Post
    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.
    This I find very confusing, for one it attempts to be analogous with conservation of energy (T + V = c in a system), but its descriptive components (vertical, horizontal force) are aliens. I guess those components could be analogous to heat and work, but then "force" is a misnomer and orientation has little if anything to do with it (energy and energy flux are useless quantities if not represented as scalars). None of this really has anything to do with why Gourney et. al. divined a power law out of their data.

    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.
    Whether or not alpha represents the structure of the insurgency in any way remains to be seen (and I can't even find the results of this research online, so it may be premature to say the least). It's possible this "theory" why alpha is stable around some point (2.5) may be no more than one working hypothesis amongst many. Gourley is coupling another unstated assumption, group dynamics, to this model in order to explain alpha and his talk completely skimped over that point.

    The power law "works" because we intuit the probability of destructive events occurring decreasing with their destructiveness (nuclear terrorism on a Western target is harder and costlier than setting an IED in your own backyard). Everything else is a question of how it behaves in a scaling limit. The fact that it behaves like a power law at all means that it can only not be a power law asymptotically--some other term overwhelms the scaling exponent and breaks invariance--or the function is piece wise with the addition of more data.
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    Default Hmm...

    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
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    you are pulling my leg - right ?

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    Council Member MikeF's Avatar
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    Default Kidding myself

    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

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    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.
    Last edited by Presley Cannady; 05-11-2009 at 08:13 PM.
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    Quote Originally Posted by Presley Cannady View Post
    Whether or not alpha represents the structure of the insurgency in any way remains to be seen (and I can't even find the results of this research online, so it may be premature to say the least). It's possible this "theory" why alpha is stable around some point (2.5) may be no more than one working hypothesis amongst many. Gourley is coupling another unstated assumption, group dynamics, to this model in order to explain alpha and his talk completely skimped over that point.

    The power law "works" because we intuit the probability of destructive events occurring decreasing with their destructiveness (nuclear terrorism on a Western target is harder and costlier than setting an IED in your own backyard). Everything else is a question of how it behaves in a scaling limit. The fact that it behaves like a power law at all means that it can only not be a power law asymptotically--some other term overwhelms the scaling exponent and breaks invariance--or the function is piece wise with the addition of more data.
    From what I googled on Gourley, apparently he is working out in San Fran right now. I may contact him to see if he can share some more of his findings; however, if his team is analyzing a working hypothesis, then they might not want to share.

    I was suprised that he submitted it to Ted, and even more suprised that they accepted it without any analysis.

    IMO, Dr. Gordon McCormick (NPS Defense Analysis) could probably have presented a more thorough briefing.

    Regardless, his presentation is sparking discussion amoungst practisioners and academics. That is a good thing.

    v/r

    Mike

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    Quote Originally Posted by MikeF View Post
    From what I googled on Gourley, apparently he is working out in San Fran right now. I may contact him to see if he can share some more of his findings; however, if his team is analyzing a working hypothesis, then they might not want to share.

    I was suprised that he submitted it to Ted, and even more suprised that they accepted it without any analysis.
    SWJ isn't set up to peer review work like this, I think, at least not on its own. Gourley's not the only one publicizing these results piecemeal. His team member Michael Spagat is also giving talks on the matter (hopefulyl in advance of something). I'm not surprised. I don't expect the weight of the material to be such that it would be challenging for review, so far the results don't contradict what has come out before, and to be honest I expect the end result to be what most interdisciplinary "research" teams put out: a huge TO-DO list ready made for a brand spanking new, regularly funded academic chair at some big league university.

    NOTE: Gourley's not only all over youtube, but his Younoodle page is higher ranked than his faculty one *and* he's all over Facebook and LinkedIn. This ain't a bad thing, but just an indicator of how early this research probably is.

    IMO, Dr. Gordon McCormick (NPS Defense Analysis) could probably have presented a more thorough briefing.

    Regardless, his presentation is sparking discussion amoungst practisioners and academics. That is a good thing.
    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?
    Last edited by Presley Cannady; 05-11-2009 at 08:24 PM.
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    Default Describing war mathematically is worthy goal, but it is not an easy one...

    Quote Originally Posted by Larry Dunbar View Post
    “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.
    From an irrigation standpoint it can be beneficial to think of the potential energy of water in terms of hydraulic head or elevation...using this baseline analogy potential energy is seen as due to position in a gravitational field (E=mgh, SI units) while kinetic energy is a form of mechanical energy associated with movement or rotation (E =1/2mv2, E rotational= 1/2Iw2, SI units).
    Last edited by Surferbeetle; 05-11-2009 at 08:33 PM.
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    "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).

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    Default Math & Social Science

    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

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    Default I am not saying that you can't or shouldn't...

    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.
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    Last edited by jmm99; 05-12-2009 at 02:08 AM. Reason: add text and links

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    Thumbs up Nice

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    Cogitationis poenam nemo patitur

  14. #34
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    Quote Originally Posted by Larry Dunbar View Post
    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.
    PH Cannady
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    Council Member MikeF's Avatar
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    Default Things I learned today

    - 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

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    Council Member Ron Humphrey's Avatar
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    Wink With ya on three of those

    Quote Originally Posted by MikeF View Post
    - 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
    As to COL Gentile from what I remember I'm not sure many here ever said he wasn't right.

    What's been cloudy has alway's been that in the end not only does the enemy get a vote but the HN does to and there's limits to what any counter-insurgent can do about that.

    All you can do is set condition's the rest is up to them.
    Gotta hand it to the man, solid as a rock when it comes to what he feels is right
    Any man can destroy that which is around him, The rare man is he who can find beauty even in the darkest hours

    Cogitationis poenam nemo patitur

  17. #37
    Council Member Ken White's Avatar
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    Default Be careful...

    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...

  18. #38
    Council Member Ken White's Avatar
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    Default Then I got to this page...

    Quote Originally Posted by Presley Cannady View Post
    ...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...

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    Quote Originally Posted by Ken White View Post
    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.
    PH Cannady
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    Council Member William F. Owen's Avatar
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    Quote Originally Posted by Presley Cannady View Post
    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.
    The idea that War or conflict might conform to an elegant model is pretty much a nail in the coffin of the concept. War simply does not work that way. What if he included data from WW1, or the Crimea? The data he uses is from 21st century insurgencies and civil wars - which are characterised by single murders and shootings. The whole thing fails the "so what" test.

    I bet you'll find that the number of people killed per domestic hand-gun attacks is 0.75 world wide and has been for 100 years. - so what?

    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.
    - see my signature.
    Infinity Journal "I don't care if this works in practice. I want to see it work in theory!"

    - The job of the British Army out here is to kill or capture Communist Terrorists in Malaya.
    - If we can double the ratio of kills per contact, we will soon put an end to the shooting in Malaya.
    Sir Gerald Templer, foreword to the "Conduct of Anti-Terrorist Operations in Malaya," 1958 Edition

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