A lesson from the surprising frequency of disaster
I first heard the word tsunami from a colleague interested in the mathematics of extreme statistics. He was wondering why there are more catastrophes in the world than there should be.
At first sight, that seems a silly question. One disaster such as the Indian Ocean tidal waves is one too many. But those who study extreme statistics ask why there are more catastrophic events than are consistent with standard theories of how the world works.
Our expectations of events that are hard to predict earthquakes, financial crises, political upheavals are founded on classical theories of probability and statistics developed in the 18th and 19th centuries. These theories use simple mathematical models to make generalisations about the world.
At the University of Strasbourg, Professor Ladislaus Bortkiewicz, who knew nothing about horses or military training, predicted the incidence of deaths from horse kicks among Prussian officer cadets. A Guinness employee worked out the same formula to explain the fermentation of stout. And these same equations were indispensable when telephone engineers calculated how many exchange lines to install.
The sense of wonderment I felt on learning the range of these regularities has never quite left me. The distribution of household incomes has similar mathematical properties to the distribution of the length of human life. And Myron Scholes won the Nobel Prize in economics for discovering that the equations needed to value complex derivative securities also describe how bath salts disperse in the tub.
The scope and achievements of these theories are so great that it is a shock when they do not work. The stock market rarely moves by more than 1 or 2 per cent in a day. Classical statistical theory therefore tells us that Black Monday, October 19 1987, when stock markets fell by more than 20 per cent, could not have happened. In terms of probability, it was like simultaneously being struck by lightning, hit by a meteorite and felled by a stray rifle shot. Similarly, there are too many large earthquakes, given the frequency of smaller earthquakes. So different models are needed. In classical statistical distributions, compounding events are independent of each other. Professor Bortkiewicz's theory worked because undisciplined horses were rare in the Prussian army. Householders make independent decisions to pick up the phone, and individually unpredictable decisions become predictable in aggregate. But if mad horse disease had spread across Prussia, Bortkiewicz would never have secured an appointment in Berlin. Phone lines jam when everyone wants to make the same inquiry, tell the same news, or share the same greeting.
And such a cascade of events led to the Aceh earthquake and the Indian Ocean waves. Rocks are constantly in motion along the fault lines between tectonic plates. Every movement provokes a movement in every surrounding rock, which transmits the disturbance. So shocks may be amplified many times: sometimes, as on December 26, to devastating effect.
Cascade models also have uses outside physics. Many economists describe a world of rational, independent decision makers, eagerly assimilating each new piece of information so that at every moment markets reflect the distillation of all available knowledge. But business and finance is more like the fault systems in the oceans, in which vibrating rocks transmit their instability to each other: greed, fear, panic and misinformation are spread like measles, or forest fires, and the same models that describe measles, forest fires and earthquakes apply. Contagious processes give rise to the Black Monday crash and the 3G auction fiasco, the new economy boom and the dollar's rollercoaster ride.
It is perhaps easier for Indonesian villagers than for western rationalists to accept that big events have no real cause, that small slippages can become catastrophes that we can neither predict nor prevent. Still we can calculate their frequency, watch them developing and anticipate where they are most likely to happen. The lesson from the Indian Ocean disaster is that there is nothing you can do to control extreme statistics but a lot you can do to insulate yourself from the consequences. That lesson is as relevant to American companies as to Indonesian fishermen.
灾难频发的教训
“海啸”这个词，我第一次是从一位对极值统计学感兴趣的同事那里听到。当时他正纳闷，为什么世界上的灾难超过本该有的数量。
乍一看，这似乎是个愚蠢的问题。印度洋巨浪滔天这样的灾难一次已经太多。但那些研究极值统计学的人却问，为何灾难事件多过符合世界运行方式标准理论的数字。
对于地震、金融危机、政治动乱等难以预测的事件，我们的预期是基于18至19世纪发展起来的有关概率和统计的古典理论。这些理论运用简单的数学模型来概述这个世界。
斯特拉斯堡大学(University of Strasbourg)的拉迪斯劳斯?博特基威茨(Ladislaus Bortkiewicz)教授对马匹或军事训练一无所知，但他预测到普鲁士实习军官被马踢死的概率。健力士公司(Guinness)的一名员工推出了同样的公式，来解释烈性黑啤的发酵。而当电话工程师计算出需要安装多少交换线路时，同样的等式也是必不可少的。
在得知这些规律性的沿用范围时，我觉得非常不可思议，而这种感觉至今犹存。家庭收入的分配与人类寿命的分配有着类似的数学属性。而梅隆?斯科尔斯(Myron Scholes)发现，对复杂衍生证券进行估价所需的等式也能描述浴盐在浴缸中分散的方式。他还因此获得了诺贝尔经济学奖。
这些理论的应用范围如此广泛、而且成就如此大，因此当它们不管用时令人大为震惊。股市一天的波动很少超过1%或2%。因此古典统计理论告诉我们，1987年10月19日这样的黑色星期一照理不会发生。这一天股市跌幅超过了20%。从概率角度说，这就像同时被闪电、流星和步枪流弹击中倒地。同样，鉴于小地震发生的频率，大地震发生得太多了。因此需要不同的模型。根据古典统计学分布理论，一些复合事件是彼此独立的。博特基威茨教授的理论之所以管用，是因为普鲁士军队中失控的马匹很少。各家户主分别决定去拿起电话，而个别的、无法预知的决定放在一起时，就变得可预测了。但如果疯马病在整个普鲁士蔓延，博特基威茨就永远得不到在柏林的职位。如果每个人都想打同一个电话询问同样的内容、通报同样的消息，或发出同样的问候，那么电话线路就会堵塞。
而这种许多事件并发的情形导致了亚齐地震和印度洋海啸。岩石沿着地壳板块间的断层移动，每次移动都引发了周围每块岩石的移动，从而传递着震荡。这样一来，一些震动可能会被放大很多倍，有时会达到毁灭性效果，就如12月26日所发生的那样。
并发模型在物理学之外也有用处。在很多经济学家所描绘的世界中，理性、独立的决策者急切地吸收每个新的信息，这样市场就时时刻刻反映了所有可获知识的精髓。但商业和金融更像是海洋中的断层系统，其中不断振动的岩石彼此传递不稳定因素：贪婪、害怕、恐慌和错误信息像麻疹或者森林大火一样蔓延，而且描述麻疹、森林大火和地震的模型在这里同样适用。传染过程导致了黑色星期一的崩盘、3G拍卖一败涂地、新经济风潮，以及美元的大起大落。
相对西方理性主义者来说，也许印尼村民更容易接受这样的说法：这次大海啸并无真正的原因，小小的波折就可能酿成大灾难，我们既不能预测也不能阻止。不过我们可以计算大灾难发生的频率、观察它们的动向，并预测它们最有可能发生在什么地方。印度洋灾难带给我们的教训是：你无法左右极值统计数字，但你可以做很多事让自己免受事件后果的影响。这一教训与美国企业和印尼渔民同样相关。
