and why does it happen so quickly?

為什麼發生的速度這麼快？

Why is a financial institution too big to fail?

為什麼金融機構會大到不能倒？

How does a virus in Africa end up

非洲的病毒如何能

in the United States in a matter of hours?

在幾小時內抵達美國？

Why are Facebook and Google such powerful companies

為什麼 Facebook 和 Google 如此強大

at creating global connections?

能夠連結全世界？

Well, in a word:

答案只有兩個字：

networks.

「網絡」

But what are networks?

網絡到底是什麼？

Everyone knows about their social network,

大家都知道社群網絡

but there are all different kinds of networks

但事實上還有各式各樣的網絡

you probably haven't thought about.

你大概想都沒想過

Networks are collections of links

網絡是連結的集合

which combine by specific rules and behaviors if they are alive.

以特定規則和行為相連 好像活的一樣

We say that networks are alive

我們說網絡是活的

because they are in constant change.

因為隨時都在變化

Over time, the connections within a network

網絡中的連結會隨時間

migrate and concentrate in new places,

遷移並集中到不同地方

forming evolving structures.

形成不斷演化的結構

How the evolution and concentration

關於研究連結

of constantly changing connections occurs

如何隨時間演化和集中於

is the subject of a whole discipline called

不同位置，這種學問就是

network theory.

「網絡理論」

We can think of networks as neighborhoods.

我們可以把網絡想成社區

Neighborhoods are defined by maps.

社區的連結受地圖規範

A Google map demonstrates the relationship

跟 Google 地圖如何顯示

between locations in exactly the same fashion

地點間的關係一樣

a network connects hubs and nodes,

網絡連接樞紐和節點

using streets as links to connect neighborhoods.

好像街道連接各社區

The reason a network can expand and evolve so quickly

網絡之所以能高速成長與演化

is based upon a mathematical concept called

是因為一個數學概念

power functions.

叫做「冪函數」 (ㄇㄧˋ)

A power function is a mathematical amplification mechanism,

冪函數是一種數學放大機制

which over specific and very small ranges,

在特定的極小範圍內

accelerates changes logarithmically.

將變化以對數加速放大

That is, a very small change in one parameter

意思是，某個參數只要改變一點點

produces a huge change in another

另一個參數就會改變很多

over a very specific range of values.

但限於特定範圍內的值

An example of how network structure emerges

網絡結構如何出現的一個例子

is the algorithm used by Google.

就是 Google 使用的演算法

As the number of links around a search term, say "friends", increases,

隨著某個搜尋詞 如「朋友」相關連結的增加

connections begin to form among millions

幾百萬次「朋友」的搜尋之間

of different searches using the term "friend".

就會開始形成關連

What Google has cleverly accomplished

Google 發明了很聰明的

is a real-time mathematical model

即時演算數學模型

for how to predict the emergence of growing connections

能預測幾十億個搜尋詞之間

among billions of search terms.

逐漸成長的連結

The algorithm Google derived collects

Google 的演算法會蒐集

the number of references to any search object.

任何搜尋對象被引用的次數

As references to a search object increase,

隨著引用次數增加

the number of links also increases, creating a node.

連結的數目也會增加，形成節點

As the node increases in size,

隨著節點變大

it eventually becomes a hub,

最後會形成樞紐

which links to many nodes.

連結到許多節點

Networks will continue to emerge

網絡會持續成長

as new ways of connecting and creating neighborhoods are defined.

因為連接和建立社區的方式增加了

Perhaps you can begin to see why networks are so powerful.

也許你已開始發現網絡強大的原因

As Google continues to collect the billions of daily searches,

隨著 Google 持續收集 每天幾十億次的搜尋紀錄

new clusters of links will rapidly emerge,

新的連結群組會迅速浮現

forming additional and growing networks.

讓網絡更新與成長

Despite the logarithmic expansion of your network,

雖然網絡以對數速度成長

the laws of six degrees of separation still apply.

六度分隔理論依然適用

Therefore, if you explore a close friend or acquaintances

如果探索朋友或熟人

in you Facebook network,

使用你的 Facebook 網絡

everyone on average will be separated

任何兩個人平均只會

by six individuals or less

相隔六個人以內

and a map of your social network will create neighborhoods

而你的社交網絡將會形成

linked by common connections among friends.

由朋友相連的各個社區