Is our climate headed for a mathematical tipping point? - Victor J. Donnay

我们的气候正在走向数学意义的混沌么？ -维克多 J. 唐奈

翻译人员: Kevin Lau 校对人员: Xinze Jiang

For most of us, two degrees Celsius is a tiny difference in temperature,

对于我们大多数人来说，2摄氏度的温度变化并没有多大区别

not even enough to make you crack a window.

还不足以让你开关窗户

但是科学家警告由于大气中二氧化碳浓度的升高

But scientists have warned that as CO2 levels in the atmosphere rise,

an increase in the Earth's temperature by even this amount

地球上即便升高这一点点温度

can lead to catastrophic effects all over the world.

将会在全球导致一个灾难性的影响

这样单个可测因素的微小变化

How can such a small measurable change in one factor

lead to massive and unpredictable changes in other factors?

是怎样导致其他因素发生大量不可预测的变化的呢？

The answer lies in the concept of a mathematical tipping point,

答案就是数学上的一个临界点的概念

which we can understand through the familiar game of billiards.

我们可以从熟悉的桌球游戏中理解

The basic rule of billiard motion is

桌球的基本运动规律

that a ball will go straight until it hits a wall,

就是它会沿着直线运动，直到撞到壁上

then bounce off at an angle equal to its incoming angle.

会有一个与进入角度相等的反弹角

为了简化，我们假设没有摩擦

For simplicity's sake, we'll assume that there is no friction,

so balls can keep moving indefinitely.

所以球的运动就有很不确定性

And to simplify the situation further,

为了使情况更加简单

let's look at what happens with only one ball on a perfectly circular table.

让我们看看只让一个球在一个绝对圆的桌上运动会发生什么

当球被击中并开始按规律运动的时候

As the ball is struck and begins to move according to the rules,

it follows a neat star-shaped pattern.

会形成一个平滑的星形图案

If we start the ball at different locations,

如果我们在不同的位置或角度开球

or strike it at different angles, some details of the pattern change,

图案上的一些细节就会受到影响

but its overall form remains the same.

但是整体情况是一样的

With a few test runs, and some basic mathematical modeling,

经过一些测试和一些基本的数学模型分析后

we can even predict a ball's path before it starts moving,

仅仅简单依靠开球的条件

simply based on its starting conditions.

我们能在球运动之前就预测它的路线

But what would happen if we made a minor change

但是如果我们对桌子的形状做一小点改变

会发生什么呢？

in the table's shape by pulling it apart a bit,

我们将桌子分成两半

and inserting two small straight edges along the top and bottom?

在顶部和底部插入两条直边

We can see that as the ball bounces off the flat sides,

我们会看到，随着球从平整的边弹出

it begins to move all over the table.

它开始在整个桌上运动

The ball is still obeying the same rules of billiard motion,

它同样遵循着桌球的运动规律

but the resulting movement no longer follows any recognizable pattern.

但是运动的结果就不再是我们认识的模型了

With only a small change to the constraints

在这个系统运行的过程中

under which the system operates,

我们只改变了一小点约束条件

我们就改变了这个桌球的运动模式

we have shifted the billiard motion

from behaving in a stable and predictable fashion,

从可以预测的、稳定的运动

to fluctuating wildly,

到混乱的、不受控制的运动模式

thus creating what mathematicians call chaotic motion.

因此创造了一个数学家数学家称作无序运动模型的东西

在（圆形）桌子上放置两条直边作为临界点

Inserting the straight edges into the table acts as a tipping point,

switching the systems behavior from one type of behavior (regular),

将这个系统的规律运动

to another type of behavior (chaotic).

变成了无序运动

So what implications does this simple example have for the much more complicated

对于复杂的地球气候问题

我们能从这个简单的例子中得到什么启发呢？

reality of the Earth's climate?

We can think of the shape of the table as being analogous to the CO2 level

我们可以把桌子的形状比作大气中二氧化碳的水平

and Earth's average temperature:

或是地球的平均温度

Constraints that impact the system's performance

在这个桌球运动或说是气候变化的模型中

in the form of the ball's motion or the climate's behavior.

这两者是影响这个系统表现的条件

During the past 10,000 years,

在过去的一万年里

the fairly constant CO2 atmospheric concentration of

二氧化碳在大气中的当量集中在百万分之二百七十左右

270 parts per million kept the climate within a self-stabilizing pattern,

以此保证整体系统保持稳定

fairly regular and hospitable to human life.

这对于人类的生活相当规律和适宜

But with CO2 levels now at 400 parts per million,

但现在二氧化碳水平达到了百万分之四百左右的水平

而且在下个世纪可能达到五百至八百

and predicted to rise to between 500 and 800 parts per million

over the coming century, we may reach a tipping point where

我们就可能到了“临界点”了

even a small additional change in the global average temperature

那时，在全球平均温度范围内一个小的附加变化

would have the same effect as changing the shape of the table,

可能与桌球实验中的变化有同样的影响

导致非常危险的气候变化

leading to a dangerous shift in the climate's behavior,

with more extreme and intense weather events,

出现更多难以预测的极端的、激烈的天气事件

less predictability, and most importantly, less hospitably to human life.

更重要的是，越发不适宜人类生活

The hypothetical models that mathematicians study in detail

数学家们仔细研究的这些假想模型

may not always look like actual situations,

可能与我们的实际情况有所不同

but they can provide a framework and a way of thinking

但是它提供给我们一个思考的框架和方法

that can be applied to help understand the more complex problems of the real world.

能被用于理解更多真实生活中更复杂的问题

In this case, understanding how slight changes

在这种情况下

理解在系统中一个微小的条件变化的影响怎样导致一个更大的影响

in the constraints impacting a system can have massive impacts

gives us a greater appreciation for predicting the dangers

给我们更多对目前凭我们的感官不能鉴别的

that we cannot immediately percieve with our own senses.

预测危险的能力

Because once the results do become visible, it may already be too late.

因为一旦我们看到这个结果，那时已经太迟了