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Cry havoc! And let slip the maths of war

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  • Cry havoc! And let slip the maths of war

    Cry havoc! And let slip the maths of war
    Warfare seems to obey mathematical rules. Whether soldiers can make use of that fact remains to be seen

    Mar 31st 2011 | from the print edition

    Military strategy: Cry havoc! And let slip the maths of war | The Economist

    IN 1948 Lewis Fry Richardson, a British scientist, published what was probably the first rigorous analysis of the statistics of war. Richardson had spent seven years gathering data on the wars waged in the century or so prior to his study. There were almost 300 of them. The list runs from conflicts that claimed a thousand or so lives to the devastation of the two world wars. But when he plotted his results, he found that these diverse events fell into a regular pattern. It was as if the chaos of war seemed to comply with some hitherto unknown law of nature.

    At first glance the pattern seems obvious. Richardson found that wars with low death tolls far outnumber high-fatality conflicts. But that obvious observation conceals a precise mathematical description: the link between the severity and frequency of conflicts follows a smooth curve, known as a power law. One consequence is that extreme events such as the world wars do not appear to be anomalies. They are simply what should be expected to occur occasionally, given the frequency with which conflicts take place.

    The results have fascinated mathematicians and military strategists ever since. They have also been replicated many times. But they have not had much impact on the conduct of actual wars. As a result, there is a certain “so what” quality to Richardson’s results. It is one thing to show that a pattern exists, another to do something useful with it.

    In a paper currently under review at Science, however, Neil Johnson of the University of Miami in Coral Gables, Florida, and his colleagues hint at what that something useful might be. Dr Johnson’s team is one of several groups who, in previous papers, have shown that Richardson’s power law also applies to attacks by terrorists and insurgents. They and others have broadened Richardson’s scope of inquiry to include the timing of attacks, as well as the severity. This prepared the ground for the new paper, which outlines a method for forecasting the evolution of conflicts.

    Progress, of a sort

    Dr Johnson’s proposal rests on a pattern he and his team found in data on insurgent attacks against American forces in Afghanistan and Iraq. After the initial attacks in any given province, subsequent fatal incidents become more and more frequent. The intriguing point is that it is possible, using a formula Dr Johnson has derived, to predict the details of this pattern from the interval between the first two attacks.

    The formula in question (Tn = T1n-b) is one of a familiar type, known as a progress curve, that describes how productivity improves in a range of human activities from manufacturing to cancer surgery. Tn is the number of days between the nth attack and its successor. (T1 is therefore the number of days between the first and second attacks.) The other element of the equation, b, turns out to be directly related to T1. It is calculated from the relationship between the logarithms of the attack number, n, and the attack interval, Tn. The upshot is that knowing T1 should be enough to predict the future course of a local insurgency. Conversely, changing b would change both T1 and Tn, and thus change that future course.

    Though the fit between the data and the prediction is not perfect (an example is illustrated right), the match is close enough that Dr Johnson thinks he is onto something. Progress curves are a consequence of people adapting to circumstances and learning to do things better. And warfare is just as capable of productivity improvements as any other activity.

    The twist in warfare is that two antagonistic groups of people are doing the adapting. Borrowing a term used by evolutionary biologists (who, in turn, stole it from Lewis Carroll’s book, “Through the Looking-Glass”), Dr Johnson likens what is going on to the mad dash made by Alice and the Red Queen, after which they find themselves exactly where they started.

    In biology, the Red Queen hypothesis is that predators and prey (or, more often, parasites and hosts) are in a constant competition that leads to stasis, as each adaptation by one is countered by an adaptation by the other. In the case Dr Johnson is examining the co-evolution is between the insurgents and the occupiers, each constantly adjusting to each other’s tactics. The data come from 23 different provinces, each of which is, in effect, a separate theatre of war. In each case, the gap between fatal attacks shrinks, more or less according to Dr Johnson’s model. Eventually, an equilibrium is reached, and the intervals become fairly regular.

    The mathematics do not reveal anything about what the adaptations made by each side actually are, beyond the obvious observation that practice makes perfect. Nor do they illuminate why the value of b varies so much from place to place. Dr Johnson has already ruled out geography, density of displaced people, the identity of local warlords and even poppy production. If he does find the crucial link, though, military strategists will be all over him. But then such knowledge might perhaps be countered by the other side, in yet another lap of the Red Queen race.
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    “the misery of being exploited by capitalists is nothing compared to the misery of not being exploited at all” -- Joan Robinson

  • #2
    It would take a lot of information to make meaningful predictions. But in today's information rich environment - that might not be so hard to accumulate anymore. I wonder if statistics is the best tool, I was thinking more in terms of tensor analysis. With accurate broad spectrum intel, functions and dimensional relations might be developed to allow battlefield tensors to be formulated - perhaps integrated into software they could help a commander evaluate to the outcome of potential tactics options?
    sigpic"If your plan is for one year, plant rice. If your plan is for ten years, plant trees.
    If your plan is for one hundred years, educate children."

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    • #3
      war is a matter of life and death.... another way to look at it, do we really want to reduce that to a statistics exercise?
      “the misery of being exploited by capitalists is nothing compared to the misery of not being exploited at all” -- Joan Robinson

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      • #4
        Originally posted by xinhui View Post
        war is a matter of life and death.... another way to look at it, do we really want to reduce that to a statistics exercise?
        Good point, I was thinking that anything that helps us win, and shorten the war could ultimately reduce the death toll. But it is a cold and cruel business.
        sigpic"If your plan is for one year, plant rice. If your plan is for ten years, plant trees.
        If your plan is for one hundred years, educate children."

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        • #5
          War itself is a cold and cruel business, and I guarantee you that every single army in the world has reduced it to a statistics exercise. How many will die in each attack, how many soldiers die per square km of ground gained, how many officers die per minute, etc...
          Meddle not in the affairs of dragons, for you are crunchy and taste good with ketchup.

          Abusing Yellow is meant to be a labor of love, not something you sell to the highest bidder.

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          • #6
            Originally posted by Shamus
            In the words of Uncle Joe..."One death is a tragedy,a million is a statistic...." or words to that effect .....reducing the numbers involved in a war to pure statistics may be useful for predictive theories but it reduces the impact in human terms to a soulless calculation on a graph.
            Yes, but that souless calculation may save lives in the mid-long term. A breif war at the first provocation might have prevented both world wars by allowing a natural readjustment. Instead the alliance system acted as a cork and let the pressure build on the warriors while letting the wizards of armament proceed full steam.

            In Britain had moved in and sank the kaiser's fleet in 1910 and made a demonstration of the power of blockade maybe Willie would not have acted so agressively. Likewise, an earlier use of mining and subs might have ended the war in the Pacific sooner. A demosntration of power seems to be much more effective than the threat of it without dmeosntration. Also the bombing of Warsaw and its shock affect demosntration kept the Warsaw seige to a single month. The US tried to duplicate that in effect if not in means with shock and awe but it largely failed in part becuase of the delay in 91 allowed Iraq to adapt and partly becuase PGM's limited the impact of the war on the civilian population.

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            • #7
              Originally posted by zraver View Post
              Yes, but that souless calculation may save lives in the mid-long term. A breif war at the first provocation might have prevented both world wars by allowing a natural readjustment. Instead the alliance system acted as a cork and let the pressure build on the warriors while letting the wizards of armament proceed full steam.

              In Britain had moved in and sank the kaiser's fleet in 1910 and made a demonstration of the power of blockade maybe Willie would not have acted so agressively. Likewise, an earlier use of mining and subs might have ended the war in the Pacific sooner. A demosntration of power seems to be much more effective than the threat of it without dmeosntration. Also the bombing of Warsaw and its shock affect demosntration kept the Warsaw seige to a single month. The US tried to duplicate that in effect if not in means with shock and awe but it largely failed in part becuase of the delay in 91 allowed Iraq to adapt and partly becuase PGM's limited the impact of the war on the civilian population.
              I wouldn't disagree with any of this Z,all valid examples of major mis-calculations.

              I was expressing a personal animus towards the impersonal nature of statistics when used to describe the death of a human being.Spur of the moment post on my part and probably shouldn't be up here.Mea' culpa
              "Every government degenerates when trusted to the rulers of the people alone. The people themselves, therefore, are its only safe depositories." Thomas Jefferson

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              • #8
                Originally posted by Shamus View Post
                I wouldn't disagree with any of this Z,all valid examples of major mis-calculations.

                I was expressing a personal animus towards the impersonal nature of statistics when used to describe the death of a human being.Spur of the moment post on my part and probably shouldn't be up here.Mea' culpa
                If was wasn't personalized for us and depersonalized for them, could we fight one?

                Likewise if wonks could develop a theory/law that had a high degree of reliability in predicting the course of a war the impersonal nature might save lives. For example, lets say a refined version of Dr. Johnson's law could not only predict attack patterns, but the arena where an over matched opponent is likely to try and seek a redress of balances then the side with the conventional over match could plan for it, even if that planning consists of nothing more than money and R&D teams set aside to tackle the problem as soon the laws prediction of event sequences pops up.

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                • #9
                  Originally posted by zraver View Post
                  If was wasn't personalized for us and depersonalized for them, could we fight one?

                  Likewise if wonks could develop a theory/law that had a high degree of reliability in predicting the course of a war the impersonal nature might save lives. For example, lets say a refined version of Dr. Johnson's law could not only predict attack patterns, but the arena where an over matched opponent is likely to try and seek a redress of balances then the side with the conventional over match could plan for it, even if that planning consists of nothing more than money and R&D teams set aside to tackle the problem as soon the laws prediction of event sequences pops up.
                  Highly advanced, actual force matched, real time wargaming?
                  sigpic"If your plan is for one year, plant rice. If your plan is for ten years, plant trees.
                  If your plan is for one hundred years, educate children."

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                  • #10
                    Originally posted by zraver View Post
                    Likewise if wonks could develop a theory/law that had a high degree of reliability in predicting the course of a war the impersonal nature might save lives. For example, lets say a refined version of Dr. Johnson's law could not only predict attack patterns, but the arena where an over matched opponent is likely to try and seek a redress of balances then the side with the conventional over match could plan for it, even if that planning consists of nothing more than money and R&D teams set aside to tackle the problem as soon the laws prediction of event sequences pops up.
                    Hmm, have doubts about this.

                    Imagine both armies that have access to this same theory/law.

                    Each can in some way predict what the other will do.

                    What happens then ?

                    Do they try to game so that each time they have the advantage. So they have a few rallies.

                    OTOH it might lead to a massive accumulation of arms and spark an arms race. Well thats not good going at all in that case.

                    What effect did the law have then.
                    Last edited by Double Edge; 06 Apr 11,, 21:16.

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                    • #11
                      Before we scoff too much the systems analyst approach war was vital to US success in World War 2. Led by a young ORSA named Robert S. McNamara the War Department and other government agencies used ORSA techniques to manage the resourcing of the war. It was the only way to manage the resouces of an undertaking that large in the pre-information.

                      War at the pointy end is the cold calculus of blood and courage...but at the strategic level where economic pressure points can be exploited it makes more sense.

                      Case in point...the US Pacific reaction post Pearl Harbor. Unrestricted submarine warfare against the Japanese merchant marine. The IJN main force was a secondary target.
                      “Loyalty to country ALWAYS. Loyalty to government, when it deserves it.”
                      Mark Twain

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                      • #12
                        the issue is that you can't use either approach all the time. the difficulty is discerning when it makes sense...and when it doesn't.
                        There is a cult of ignorance in the United States, and there has always been. The strain of anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that "My ignorance is just as good as your knowledge."- Isaac Asimov

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                        • #13
                          Originally posted by Albany Rifles View Post
                          Before we scoff too much the systems analyst approach war was vital to US success in World War 2. Led by a young ORSA named Robert S. McNamara the War Department and other government agencies used ORSA techniques to manage the resourcing of the war. It was the only way to manage the resouces of an undertaking that large in the pre-information.

                          War at the pointy end is the cold calculus of blood and courage...but at the strategic level where economic pressure points can be exploited it makes more sense.

                          Case in point...the US Pacific reaction post Pearl Harbor. Unrestricted submarine warfare against the Japanese merchant marine. The IJN main force was a secondary target.
                          You say systems analysis but am wondering if rather you mean operations research.

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