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

我們的氣候正在走向數學所提及的混亂嗎？-維克多 J. 唐尼

譯者: 葉 Yah 宇倫 審譯者: 瑞文Eleven 林Lim

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

對我們大多數人來說， 2°C的溫差是一個很小的變化

not even enough to make you crack a window.

還不足以讓你開或關閉窗戶

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

但科學家警告 隨着大氣中二氧化碳濃度升高

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

即使地球僅升高一點點溫度

can lead to catastrophic effects all over the world.

也可能導致全球災難性的影響

How can such a small measurable change in one factor

這樣一個可測因素的微小變化

lead to massive and unpredictable changes in other factors?

是如何導致其他因素大規模 和不可預測的變化呢?

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

答案出現在數學裡 臨界點這個概念上

which we can understand through the familiar game of billiards.

我們可以透過熟悉的 桌球中理解

The basic rule of billiard motion is

桌球運動的基本運動規律是

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

球會沿著直線運動， 直到它碰壁

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

接着它以與入射角相同的角度彈開

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

爲了簡化，我們假設沒有摩擦

so balls can keep moving indefinitely.

所以球運動的規則 就有很多不確定性

And to simplify the situation further,

為了使情況更加簡單

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

我們來看看 一張圓桌上的球會怎樣運動

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

當球被擊中並開始按規律運動

it follows a neat star-shaped pattern.

會形成平滑的星型圖案

If we start the ball at different locations,

如果我們在不同的位置或者角度擊球

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

圖案的一些細節會有所變化

but its overall form remains the same.

但整體的形狀保持一致

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

經過幾次測試和一些基本的 數學模型分析後

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

僅僅依靠簡單的擊球條件

simply based on its starting conditions.

我們就能在球運動前 便預知它的軌跡

But what would happen if we made a minor change

但如果我們對桌子做一點微小的變動

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

會發生什麼事呢?

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

我們將桌子向左右拉長

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

會看到球由較平整的邊彈出

it begins to move all over the table.

並開始在整張桌子上運動

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

球仍遵循桌球運動的規律

but the resulting movement no longer follows any recognizable pattern.

但最終的運動軌跡 不再是我們認識的圖形

With only a small change to the constraints

在整個系統運行的過程中

under which the system operates,

我們只改變一點點的約束條件

we have shifted the billiard motion

我們就能改變桌球的運動

from behaving in a stable and predictable fashion,

從可以預測的，穩定的運動

to fluctuating wildly,

到混亂的、不受控制的運動模式

thus creating what mathematicians call chaotic motion.

產生了數學家所說的混沌運動

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

在(圓形)桌子上放置兩條直邊作為臨界點

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

將這個系統的規律運動

to another type of behavior (chaotic).

變成混沌運動

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

而對於複雜的地球環境氣候問題

reality of the Earth's climate?

我們能在這簡單的例子 得到甚麼想法呢?

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

我們可以把桌子的形狀 類比成二氧化碳的濃度

and Earth's average temperature:

或是地球的平均溫度

Constraints that impact the system's performance

在這桌球運動或說是 氣候變化的模型中

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

這兩者都是影響 這個系統表現的條件

During the past 10,000 years,

在過去的一萬年裡

the fairly constant CO2 atmospheric concentration of

為了確保整個系統保持穩定

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

二氧化碳在大氣中的含量維持在 百萬分之兩百七十左右

fairly regular and hospitable to human life.

這對於人類的生活相當規律和適宜

But with CO2 levels now at 400 parts per million,

但現在二氧化碳含量已達到了 百萬分之四百左右

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

下個世紀甚至可能達到五百至八百

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

我們可能就達到"臨界點"了

even a small additional change in the global average temperature

那時，在全球平均溫度範圍中一個 小小的額外變化

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

與改變桌子的形狀有同樣的影響

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

會導致危險的氣候變遷

with more extreme and intense weather events,

出現更難預測、極端且劇烈的氣候問題

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

更重要的是，不再適合人類生活

The hypothetical models that mathematicians study in detail

數學家詳細地研究這些假設模型

may not always look like actual situations,

可能與實際的情況有所不同

but they can provide a framework and a way of thinking

但它們可以提供我們 思考的框架和方式

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

這些模型可以幫助理解真實世界中 更複雜的問題

In this case, understanding how slight changes

在這個例子中， 理解在系統中微小的變化

in the constraints impacting a system can have massive impacts

是如何導致一個龐大的問題

gives us a greater appreciation for predicting the dangers

使我們具有更多無法憑感官

that we cannot immediately percieve with our own senses.

而預測危險的能力

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

因爲當我們看見結果時， 為時已晚