The Butterfly Effect

Beyond two or three days, the world's best weather forecasts are speculative, and beyond six or seven they are worthless. The Butterfly Effect is the reason. For small pieces of weather -- and to a global forecaster, small can mean thunderstorms and blizzards -- any prediction deteriorates rapidly. Errors and uncertainties multiply, cascading upward through a chain of turbulent features, from dust devils and squalls up to continent - size eddies that only satellites can see. The modern weather models work with a grid of points of the order of sixty miles apart, and even so, some starting data has to be guessed, since ground stations and satellites cannot see everywhere. But suppose the earth could be covered with sensors spaced one foot apart, rising at one - foot intervals all the way to the top of the atmosphere. Suppose every sensor gives perfectly accurate readings of temperature, pressure, humidity, and any other quantity a meteorologist would want. Precisely at noon an infinitely powerful computer takes all the data and calculates what will happen at each point at 12.01, then 12.02, then 12.03... The computer will still be unable to predict whether Princeton, New Jersey, will have sun or rain on a day one month away. At noon the spaces between the sensors will hide fluctuations that the computer will not know about, tiny variations in the flow of the atmosphere that will interact with other fluctuations and create a turbulence that will spread rapidly and unpredictably. In a very short time, the computer will lose track of where the turbulence is going, and even more important, it will not know if a new disturbance has occurred somewhere else. Even with the most powerful computers, there will always be a degree of uncertainty about whether the weather will change or not, and by how much. This is the essence of the Butterfly Effect. The name comes from an example by the mathematician Edward Lorenz. He was thinking about how small changes in initial conditions can lead to large - scale effects. He imagined a butterfly flapping its wings in Brazil and then considered what would happen. "Could it be," he wondered, "that a single flap of a butterfly's wings could cause a hurricane in Texas?" His answer was yes, in principle. A butterfly flaps its wings and it causes a tiny change in the air pressure. That change in air pressure causes a slightly different pattern of air movement. That slightly different pattern of air movement causes another slightly different pattern, and so on. By the time the air movement has spread across the Atlantic Ocean, the change has become large enough to cause a hurricane in Texas. The Butterfly Effect is not just a theoretical concept. It has practical implications for weather forecasting, climate modelling, and many other fields. For example, in climate modelling, we need to understand how small changes in the Earth's climate system can lead to large - scale changes in the global climate. If we do not understand the Butterfly Effect, we may make incorrect predictions about the future of the Earth's climate. In addition to weather forecasting and climate modelling, the Butterfly Effect has implications for many other fields. For example, in economics, small changes in interest rates or exchange rates can lead to large - scale changes in the economy. In ecology, small changes in the environment can lead to large - scale changes in the ecosystem. In social science, small changes in public opinion or social behavior can lead to large - scale changes in society. The Butterfly Effect is a reminder that the world is a complex and interconnected place, and that small changes can have large - scale effects.

世界上最好的两三天以上的天气预报具有很强的猜测性，超过六七天的天气预报就没有什么价值了。这是由蝴蝶效应造成的。对于小片的天气状况——对一个全球性的气象预报员来说，“小”可以指雷暴和暴风雪——任何预测都会迅速变得不准确。误差和不确定性会成倍增加，通过一连串的不稳定因素向上级联放大，从尘卷风、飑一直到只有卫星才能观测到的大陆大小的涡旋。现代气象模型以间距约为60英里的格点网络来运作，即便如此，有些初始数据还是不得不依靠推测，因为地面观测站和卫星不可能监测到每个地方。

但假设地球上可以布满间距为一英尺的传感器，每个传感器都垂直间隔一英尺一直排列到大气层的顶端。假设每个传感器都能极为精确地读出温度、气压、湿度以及气象学家需要的任何其他数据。在正午时分，一台性能无限强大的计算机采集所有数据并计算出12点01分、12点02分、12点03分……各个格点将发生的情况。计算机仍然无法预测一个月后的某一天新泽西州的普林斯顿是晴天还是雨天。在正午时分，传感器之间的间距将会隐藏计算机无法得知的波动，大气流动中微小的变化将会与其他波动相互作用，从而产生一种气流扰动，这种扰动会迅速且不可预测地扩散开来。在很短的时间内，计算机就会失去对气流扰动去向的跟踪，更重要的是，它将不知道在其他地方是否已经发生了新的扰动。即使有最强大的计算机，天气是否会变化以及变化多少总是存在一定程度的不确定性。这就是蝴蝶效应的本质。

这个名称来源于数学家爱德华·洛伦兹举的一个例子。他在思考初始条件的微小变化是如何导致大规模影响的。他想象一只蝴蝶在巴西扇动翅膀，然后考虑会发生什么情况。他寻思：“一只蝴蝶扇动一下翅膀有没有可能在得克萨斯州引发一场飓风呢？”原则上，他的答案是肯定的。一只蝴蝶扇动翅膀会引起气压的微小变化。这种气压变化会导致空气流动模式稍有不同。这种稍有不同的空气流动模式又会导致另一种稍有不同的模式，如此等等。当空气流动扩散到大西洋彼岸时，这种变化已经大到足以在得克萨斯州引发一场飓风了。

蝴蝶效应不仅仅是一个理论概念。它对天气预报、气候模拟以及许多其他领域都有实际意义。例如，在气候模拟方面，我们需要了解地球气候系统的微小变化是如何导致全球气候大规模变化的。如果我们不理解蝴蝶效应，我们可能会对地球气候的未来做出错误的预测。

除天气预报和气候模拟之外，蝴蝶效应对许多其他领域也有影响。例如，在经济学中，利率或汇率的微小变化会导致经济的大规模变化。在生态学中，环境的微小变化会导致生态系统的大规模变化。在社会科学中，公众舆论或社会行为的微小变化会导致社会的大规模变化。蝴蝶效应提醒我们，世界是一个复杂且相互关联的地方，微小的变化可能会产生大规模的影响。