So it turns out that mathematics is a very powerful language.

數學是十分強大的語言

It has generated considerable insight in physics,

可幫助人更深入探討物理學

in biology and economics,

生物學和經濟學

but not that much in the humanities and in history.

但對人文和歷史卻沒有太大幫助

I think there's a belief that it's just impossible,

我想大家都認為這是不可能的

that you cannot quantify the doings of mankind,

因為我們無法量化人類的行為

that you cannot measure history.

也無法計量歷史

But I don't think that's right.

但對此，我抱持著不同的看法

I want to show you a couple of examples why.

我想舉幾個例子跟大家解釋原因

So my collaborator Erez and I were considering the following fact:

我和合作夥伴 Erez 對於以下這件史實是這麼想的

that two kings separated by centuries

相隔幾個世紀的兩位君王

will speak a very different language.

會說截然不同的語言

That's a powerful historical force.

這就是歷史的強大力量

So the king of England, Alfred the Great,

因此古代英國國王艾佛烈大帝

will use a vocabulary and grammar

使用的字彙和文法

that is quite different from the king of hip hop, Jay-Z.

跟當代嘻哈之王 Jay-Z 非常不一樣

(Laughter)

(笑聲)

Now it's just the way it is.

事實就是這樣

Language changes over time, and it's a powerful force.

語言隨時間變化，而且還是一股強大的力量

So Erez and I wanted to know more about that.

Erez 和我想更深入了解這件事

So we paid attention to a particular grammatical rule, past-tense conjugation.

我們因而注意到一條特別的文法規則：過去式動詞變化

So you just add "ed" to a verb at the end to signify the past.

也就是在動詞後加上「ed」來代表過去

"Today I walk. Yesterday I walked."

今天我走 (walk)，昨天我走了 (walked)

But some verbs are irregular.

但是還有一些不規則動詞

"Yesterday I thought."

昨天我想 (thought)

Now what's interesting about that

而這件事的有趣之處在於

is irregular verbs between Alfred and Jay-Z have become more regular.

從艾佛列大帝到 Jay-Z 的年代 不規則動詞是否變得更加規則？

Like the verb "to wed" that you see here has become regular.

如你所見，像動詞「結婚」就變得更加規則

So Erez and I followed the fate of over 100 irregular verbs

因此 Erez 和我觀察了超過 100 個不規則動詞的演進變化

through 12 centuries of English language,

時間橫跨 12 世紀的英文

and we saw that there's actually a very simple mathematical pattern

我們發現其中存在著一個很簡單的數學模式

that captures this complex historical change,

足以描述這個複雜的歷史演變

namely, if a verb is 100 times more frequent than another,

當一動詞的常用程度比其他動詞高出 100 倍時

it regularizes 10 times slower.

其規則化的速度就比其他動詞慢 10 倍

That's a piece of history, but it comes in a mathematical wrapping.

這就是一個可以用數學概括描述的歷史片段

Now in some cases math can even help explain,

而在其他狀況下，數學也有助於解釋歷史

or propose explanations for, historical forces.

或者為其提出假說

So here Steve Pinker and I

Steve Pinker 和我

were considering the magnitude of wars during the last two centuries.

思考兩個世紀以來戰爭規模的變化

There's actually a well-known regularity to them

其中其實存在著大家都很孰悉的規則性

where the number of wars that are 100 times deadlier

死傷人數高達其它戰爭100 倍的戰爭數量

is 10 times smaller.

其實只有 10 分之 1

So there are 30 wars that are about as deadly as the Six Days War,

有 30 場戰爭其死亡人數與以阿六日戰爭相同

but there's only four wars that are 100 times deadlier --

但死傷人數是其 100 倍的戰爭只有四場

like World War I.

例如第一次世界大戰

So what kind of historical mechanism can produce that?

而這又是哪種歷史機制造成的呢？

What's the origin of this?

其起因又是什麼？

So Steve and I, through mathematical analysis,

Steve 和我透過數學分析

propose that there's actually a very simple phenomenon at the root of this,

提出了其實起因來自很簡單的現象

which lies in our brains.

這種現象就存在大腦之中

This is a very well-known feature

是種大家都熟知的特性

in which we perceive quantities in relative ways --

也就是我們對「量」的觀感是相對的

quantities like the intensity of light or the loudness of a sound.

如光線「強度」或音量「大小」

For instance, committing 10,000 soldiers to the next battle sounds like a lot.

舉例來說，派 1 萬名士兵去打下一場仗 感覺好像很多

It's relatively enormous if you've already committed 1,000 soldiers previously.

假使先前已派了 1 千名士兵的狀況下 感覺的確是如此

But it doesn't sound so much,

但是有時我們並不覺得人數有這麼多

it's not relatively enough, it won't make a difference

因為「量」的對比不大，因此無法感受差異

if you've already committed 100,000 soldiers previously.

假使先前其實已經派了 10 萬大軍

So you see that because of the way we perceive quantities,

所以大家現在可以體會我們對「量」的觀感

as the war drags on,

隨著戰爭持續下去

the number of soldiers committed to it and the casualties

派遣的士兵和死傷人數

will increase not linearly --

將不會呈線性成長

like 10,000, 11,000, 12,000 --

趨勢不是 1 萬、1萬1、1 萬2

but exponentially -- 10,000, later 20,000, later 40,000.

而會呈指數成長，從 1 萬到 2 萬到 4 萬

And so that explains this pattern that we've seen before.

這解釋了我們先前看過的模式

So here mathematics is able to link a well-known feature of the individual mind

在此數學可以連結大眾熟知的思維特性

with a long-term historical pattern

以及長期歷史模式

that unfolds over centuries and across continents.

這種模式跨越幾個世紀橫跨幾大洲慢慢成形

So these types of examples, today there are just a few of them,

這種例子即便在今日仍然屈指可數

but I think in the next decade they will become commonplace.

但我認為十年之後便將成為常態

The reason for that is that the historical record

原因是歷史記錄

is becoming digitized at a very fast pace.

以很快的速度數位化

So there's about 130 million books

有史以來

that have been written since the dawn of time.

人類已經寫了13 億本書

Companies like Google have digitized many of them --

Google 這類公司已經將其中的一大部分數位化

above 20 million actually.

實際數量超過 2 億本

And when the stuff of history is available in digital form,

因此當歷史記錄被數位化後

it makes it possible for a mathematical analysis

就能拿來做數學分析

to very quickly and very conveniently

讓我們能很快又便利的

review trends in our history and our culture.

檢視歷史和文化趨勢

So I think in the next decade,

因此我認為接下來十年

the sciences and the humanities will come closer together

科學和人文將更緊密結合

to be able to answer deep questions about mankind.

而且能夠回答一些與人類相關的深層問題

And I think that mathematics will be a very powerful language to do that.

我更認為數學這種強大語言將能做到此點

It will be able to reveal new trends in our history,

數學將能揭開歷史的新趨勢

sometimes to explain them,

有時加以解釋

and maybe even in the future to predict what's going to happen.

最後甚至也有可能可以預測未來

Thank you very much.

謝謝各位

(Applause)

(掌聲)