Cry havoc! And let slip the maths of war

Military strategy军事策略

Cry havoc! And let slip the maths of war
悲剧呀，没注意战争数学

Warfare seems to obey mathematical rules. Whether soldiers can make use of that fact remains to be seen
战争看起来符合数学规则。军方能否充分利用这个事实还拭目以待。
Mar 31st 2011 | from the print edition

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.
1948年，英国科学家刘易斯•弗赖伊•理查森（Lewis Fry Richardson）公布了当时也许是第一份精确分析战争数据的报道。理查森曾花费了七年时间研究了本世纪发生的以及在他做研究时间之前的战争数据。总共约有300组数据。数据所涉及的范围从伤亡一千人左右的战争到两次世界大战。但是，在他公布了结果后，他发现，这些不同的事件有一个规律。在这些看似繁杂无序的战争背后都体现了一个迄今都不清楚的自然规律。

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.
猛一看，这些规律似乎都比较明显。理查森发现，那些伤亡人数比较小的战争次数远远多于那些死亡人数多的战争。不过，看似明显的结论背后实则是精确的数学描述：在战争的严重程度和频率间遵循一个光滑的曲线，这就是幂法则。因此一些极端的事件例如世界大战这种结果的出现并不是异常现象。这些曲线仅表示那些偶然发生的事件是可以预料的，曲线可以给出战争发生的频繁。

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.
从那以后，数学家和军事战略家就沉迷于这些结果。这样的结果已经上演了无数次。不过它们还没有在实际的战争中产生重要的作用。结果就是，大家都认为理查森的结果也就那样。规律存在与实际应用是两码事。

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.
不过，目前在《科学》的一个评论文章中，佛罗里达州迈阿密大学珊瑚岛校区的尼尔•约翰逊（Neil Johnson）和他的同事暗示那里面也许会有某些有用的东西。约翰逊博士的团队在以前的论文中已经表明，理查森的幂法则可以用于分析恐怖分子和叛乱分子的袭击。他们和其他的一些团队已经扩展了理查森看问题思路的广度，包括对付一些预谋好的严重袭击事件。这就为新的论文准备了思路：分析恐怖袭击的时间和规模大小。

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.
约翰逊博士建立的模型基础是在阿富汗和伊拉克的美军受到武装分子袭击的次数。在考虑到任何省份发生第一次袭击后，接下来的严重事件会越来越频繁的情况。有意思的是，由最初两次的袭击事件的间隔时间，再加上约翰逊博士列的一个公式，这样就可以预测出这种规律的细节部分。

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.
这个还在讨论中的公式(Tn = T1n-b)是一种比较熟悉的公式类型，经常作为一个进度曲线，它主要用来描述人类在各种活动中生产力提高的现象，涉及范围从制造业到癌症手术。Tn表示在第N次与第N+1次袭击之间的天数(T1 因此就是第1次和第2次袭击的间隔天数)。这个公式的其他因子b是一个直接与T1有关的量。它是用来估计袭击次数n和袭击间隔时间Tn的一个对数。这样的话，知道T1的值就足以预测未来当地武装袭击事件了。相反，如果改变b的话，就会改变T1和Tn，这样就会改变未来的事情发展。


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.
虽然在数据和预测的匹配还不是非常精确（下边的一个例子就可以说明），不过约翰逊博士认为这对于某些事件来说已经足够用了。进度曲线是人们适应环境并学习如何做得更好的一个总结。战争和其他的人类活动一样，也是一种生产力提高现象。

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.
战争中的胶结是两个对立集团的彼此之间的调整。通过借用一个生物进化学家的术语（这个术语实际上是从刘易斯•卡罗尔[1]的书《爱丽丝穿镜奇幻记》借用的），约翰逊就将其比作在明确知道爱丽斯和红皇后在哪里开始狂奔后，对于接下来的情况就可以很清楚地知道。

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[3] 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.
在生物学中，红皇后假说[2]指的捕食者和猎物（或者说更多的时候指的是寄生虫和宿主）之间存在一个长期的竞争关系，双方的适应和调整相互抵消从而达到一个静态平衡。在这个案例中，约翰逊博士研究了袭击者和占领者之间的协同进化[3]，双方都在不断地适应对方的战术。这些数据来自23个不同的省份，实际上，它们中间的每一个数据都来自于一个独立的战区。根据约翰逊的模型来看，在每一个省份的数据中，严重袭击的间隔逐渐缩短。最终，这会达到一种平衡，这样每起袭击事件的间隔就看起来比较有规律了。

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[4].
不过数学并没有从这些显而易见预测规律中更深一步，并没有从本质上揭示双方是如何去适应的。他们并不能阐明为什么b值从一个地点到另一点变化如此之大。约翰逊博士已经排除了地理，流民密度，当地的军阀甚至是罂粟的产量这些因素的影响。尽管如此，一旦约翰逊真的找出了关键规律，军事家们必将会竞相追捧。但到那时，约翰逊的理论一样会被敌方利用到战略调整上，这就像红皇后假说所设想的那样，双方兜兜转转还是又回到原点。

注：
[1] 刘易斯•卡罗尔（Lewis Carroll），原名查尔斯•路德维希•道奇逊，与安徒生、格林兄弟齐名的世界顶尖儿童文学大师。原名查尔斯•路德维希•道奇逊。曾在牛津大学基督堂学院任教达30年之久，业余爱好非常广泛，尤其喜爱儿童肖像摄影。他的第一本童书《爱丽丝奇境历险记》于1865年出版，当时就引起了巨大轰动，1871年又推出了续篇《爱丽丝穿镜奇幻记》，更是好评如潮。两部童书旋即风靡了整个世界，成为一代又一代孩子们乃至成人最喜爱的读物。

[2]红皇后假说：生态上密切相关的物种的相互关联地进化叫做协进化或协同进化（coevolution）。协同进化的结果是相互适应（coadaptation）。物种之间形成非常复杂的相互作用、相互依存的关系。这种关系是除了物理的环境条件之外的另一种重要的外环境。在物理环境条件相对稳定的情况下，物种之间的关系构成驱动进化的选择压。一个物种的任何进化改进可能构成对其他相关物种的竞争压力，所以，即使物理环境不变，种间关系也可能推动进化。在通常的环境下，物种之间保持着一种动态的平衡。物种间的生态关系的牵制作用使得物种在其生存期间绝灭的风险相对恒定：后代与祖先，新种与老种绝灭的机会几乎是相同的。这就是红皇后假说所要解释的现象。

[3]协同进化（coevolution）：两个相互作用的物种在进化过程中发展的相互适应的共同进化。一个物种由于另一物种影响而发生遗传进化的进化类型。例如一种植物由于食草昆虫所施加的压力而发生遗传变化，这种变化又导致昆虫发生遗传性变化。这是用来说明袭击者和占领者两者的博弈。

[4]这个应该是《爱丽丝穿镜奇幻记》中的内容，我没看过，不知道什么意思，希望看过的高手帮忙译一下