a gunshot was heard

人們聽到一聲槍響，

ringing out across the 13th arrondissement in Paris.

槍聲穿透了巴黎的第十三區

(Gunshot)

（槍聲）

A peasant, who was walking to market that morning,

一個那天早晨正前往市集的農民

ran towards where the gunshot had come from,

朝槍聲傳來的地方跑了過去，

and found a young man writhing in agony on the floor,

發現一名年輕男子正痛得在地上打滾，

clearly shot by a dueling wound.

顯然他在決鬥中遭到了槍擊。

The young man's name was Evariste Galois.

這個年輕人名叫 Evariste • Galois

He was a well-known revolutionary in Paris at the time.

是巴黎當時一個有有名的革命者

Galois was taken to the local hospital

Galois 被送到了當地的醫院，

where he died the next day in the arms of his brother.

第二天死在他兄弟的懷中

And the last words he said to his brother were,

他對他兄弟說的臨別遺言是

"Don't cry for me, Alfred.

“不要為我哭泣, Alfred

I need all the courage I can muster

我需要聚集我能聚集的所有勇氣

to die at the age of 20."

讓我在20歲時死去。 ”

It wasn't, in fact, revolutionary politics

實際上，革命政治並不是

for which Galois was famous.

使 Galois 著名的原因。

But a few years earlier, while still at school,

而是幾年前，當他還在上學時，

he'd actually cracked one of the big mathematical

他破解了

problems at the time.

當時重大數學問題之一

And he wrote to the academicians in Paris,

隨後他寫信給巴黎的院士

trying to explain his theory.

嘗試解釋他的理論

But the academicians couldn't understand anything that he wrote.

但院士們弄不懂他寫的任何東西。

(Laughter)

（大笑）

This is how he wrote most of his mathematics.

這就是他怎麼寫大部分數學理論的

So, the night before that duel, he realized

因此，在決鬥的前一天晚上，他意識到

this possibly is his last chance

這可能是他最後一次機會

to try and explain his great breakthrough.

來嘗試解釋他的重大突破

So he stayed up the whole night, writing away,

所以他徹夜未眠，不停地寫東西，

trying to explain his ideas.

試圖解釋他的想法

And as the dawn came up and he went to meet his destiny,

隨著黎明的到來，他準備迎接自己的命運。

he left this pile of papers on the table for the next generation.

他把桌子上的一堆文件留給了下一代。

Maybe the fact that he stayed up all night doing mathematics

也許徹夜研究數學

was the fact that he was such a bad shot that morning and got killed.

是他那天早晨受到槍擊且被殺的真正原因

But contained inside those documents

但包含在那些文件中的

was a new language, a language to understand

是一種新的語言，這種語言能讓人們理解

one of the most fundamental concepts

科學的一個最基本的概念，

of science -- namely symmetry.

即對稱性。

Now, symmetry is almost nature's language.

現今，對稱性幾乎是大自然的語言。

It helps us to understand so many

它有助於我們了解許多

different bits of the scientific world.

科學世界裡不同的小東西。

For example, molecular structure.

例如，分子結構。

What crystals are possible,

什麼晶體是能讓

we can understand through the mathematics of symmetry.

我們可以通過數學的對稱性來了解的？

In microbiology you really don't want to get a symmetrical object,

在微生物學中，你真的不想研究對稱的東西。

because they are generally rather nasty.

因為它們一般都比較令人討厭。

The swine flu virus, at the moment, is a symmetrical object.

目前的豬流感病毒就是一種結構對稱的病毒。

And it uses the efficiency of symmetry

而且它利用對稱的功效

to be able to propagate itself so well.

來增強自己繁殖的速度

But on a larger scale of biology, actually symmetry is very important,

但從大方向來說，對稱性事實上對生物學非常重要

because it actually communicates genetic information.

因為它能傳遞遺傳信息

I've taken two pictures here and I've made them artificially symmetrical.

我帶了兩張照片到這兒來，並人工的把他們做成了對稱的

And if I ask you which of these you find more beautiful,

如果我問你們覺得哪些更漂亮，

you're probably drawn to the lower two.

你們可能會被下面的兩張吸引住。

Because it is hard to make symmetry.

因為很難做到對稱，

And if you can make yourself symmetrical, you're sending out a sign

所以如果你可以使自己對稱，那麼你在傳遞一種信號

that you've got good genes, you've got a good upbringing

它意味著你得到了好的遺傳基因，你有好的教養，

and therefore you'll make a good mate.

因而你會有一個好的伴侶。

So symmetry is a language which can help to communicate

所以，對稱性是一種語言，它能有助於傳遞

genetic information.

遺傳信息。

Symmetry can also help us to explain

對稱性還可以幫助我們解釋

what's happening in the Large Hadron Collider in CERN.

歐洲粒子物理研究所大型強子對撞機正發生著什麼事情。

Or what's not happening in the Large Hadron Collider in CERN.

或者歐洲粒子物理研究所的大型強子對撞機沒有發生什麼事情。

To be able to make predictions about the fundamental particles

為了能夠對基本粒子作出預測，

we might see there,

我們可能會在那兒看到的（基本粒子），

it seems that they are all facets of some strange symmetrical shape

似乎所有的小平面都有某種奇怪的對稱形狀

in a higher dimensional space.

當它們在更高維的空間中時。

And I think Galileo summed up, very nicely,

我認為伽利略很好地概括了

the power of mathematics

數學的力量：

to understand the scientific world around us.

它讓我們得以了解周圍的科學世界

He wrote, "The universe cannot be read

他寫道：“我們無法閱讀宇宙，

until we have learnt the language

除非學會它的語言，

and become familiar with the characters in which it is written.

且熟悉其寫作特點。

It is written in mathematical language,

它是用數學語言寫的。

and the letters are triangles, circles and other geometric figures,

字母是三角形、圓和其他的幾何數字，

without which means it is humanly impossible

沒有這些字母就意味著在人力所能及的範圍內是不可能

to comprehend a single word."

理解任何一個字。 ”

But it's not just scientists who are interested in symmetry.

不只是科學家們對對稱性感興趣。

Artists too love to play around with symmetry.

藝術家也喜歡擺弄對稱性。

They also have a slightly more ambiguous relationship with it.

他們與對稱性有一些更模糊的關係。

Here is Thomas Mann talking about symmetry in "The Magic Mountain."

這是托馬斯•曼在《魔山》中談到的對稱性。

He has a character describing the snowflake,

他這樣描寫雪花

and he says he "shuddered at its perfect precision,

他說他，“因其有完美的精確度而震撼，

found it deathly, the very marrow of death."

發現它死亡的精髓讓他想到死亡。 ”

But what artists like to do is to set up expectations

但藝術家們想要做的是樹立對對稱性的期望，

of symmetry and then break them.

然後打破它們。

And a beautiful example of this

就這一點我找到了一個很好的例子，

I found, actually, when I visited a colleague of mine

其實是當我拜訪我的同事

in Japan, Professor Kurokawa.

在日本的黑川紀章教授時發現的

And he took me up to the temples in Nikko.

他帶我到日光市的寺廟去

And just after this photo was taken we walked up the stairs.

就在拍好這張照片後，我們走上樓梯，

And the gateway you see behind

你們看到的這後面的大門

has eight columns, with beautiful symmetrical designs on them.

有八根柱子，都有著漂亮的對稱性設計。

Seven of them are exactly the same,

其中七個是完全一樣的，

and the eighth one is turned upside down.

而第八個是顛倒過來的。

And I said to Professor Kurokawa,

我就對黑川紀章教授說：

"Wow, the architects must have really been kicking themselves

“哇，建築師們肯定自責的很

when they realized that they'd made a mistake and put this one upside down."

要是他麼發現犯了這麼一個錯誤，這根柱子竟然是相反的。 ”

And he said, "No, no, no. It was a very deliberate act."

他說，“不，不，不。這是故意設計成這樣的。”

And he referred me to this lovely quote from the Japanese

他還向我提到了這個可愛的出處，來自日本

"Essays in Idleness" from the 14th century,

1 4世紀的《徒然草》

in which the essayist wrote, "In everything,

其中，散文家寫道：“在一切事物中，

uniformity is undesirable.

一致性是不可取的。

Leaving something incomplete makes it interesting,

留下一些不完整的東西會更有趣，

and gives one the feeling that there is room for growth."

而且一致性給人一種沒有發展空間的感覺。 ”

Even when building the Imperial Palace,

即使是建造皇宮時，

they always leave one place unfinished.

他們也總是留下一個未完工的地方。

But if I had to choose one building in the world

但如果我必須選擇這世界上的一個建築，

to be cast out on a desert island, to live the rest of my life,

將其扔到一個荒島上，且我要在那裡度過餘生，

being an addict of symmetry, I would probably choose the Alhambra in Granada.

作為一個對對稱性痴迷的人，我可能會選擇在格拉納達的阿爾罕布拉。

This is a palace celebrating symmetry.

這是一座歌頌對稱性的宮殿。

Recently I took my family --

最近，我帶我的家人——

we do these rather kind of nerdy mathematical trips, which my family love.

我們進行這種並沒有學術氣息的數學旅行，我的家人都很喜歡。

This is my son Tamer. You can see

這是我的兒子塔梅爾。你們可以看到

he's really enjoying our mathematical trip to the Alhambra.

他真的很喜歡我們在阿爾罕布拉的數學之旅。

But I wanted to try and enrich him.

但我想嘗試使他變得充實。

I think one of the problems about school mathematics

我認為學校教的數學存在的一個問題就是

is it doesn't look at how mathematics is embedded

它沒有關注數學是如何被運用於

in the world we live in.

我們所處的這個世界。

So, I wanted to open his eyes up to

所以，我想開拓他的眼界，讓他知道

how much symmetry is running through the Alhambra.

阿爾罕布拉運用著多少對稱性。

You see it already. Immediately you go in,

你們已經看到了。你一走進去，

the reflective symmetry in the water.

水中有反映出對稱。

But it's on the walls where all the exciting things are happening.

但是，所有令人興奮的事情發生在牆壁上。

The Moorish artists were denied the possibility

人們否認摩爾藝術家能夠

to draw things with souls.

用靈魂來繪畫。

So they explored a more geometric art.

因此，他們探索出一種更加幾何化的藝術。

And so what is symmetry?

那麼什麼是對稱性？

The Alhambra somehow asks all of these questions.

阿爾罕布拉以某種方式提出了所有這些問題。

What is symmetry? When [there] are two of these walls,

什麼是對稱性？當[那兒]有兩面牆時，

do they have the same symmetries?

他們有相同的對稱性嗎？

Can we say whether they discovered

我們可以說他們是否發現了

all of the symmetries in the Alhambra?

阿爾罕布拉所有的對稱性嗎？

And it was Galois who produced a language

是 Galois 研製出了一種語言

to be able to answer some of these questions.

來回答這樣的問題

For Galois, symmetry -- unlike for Thomas Mann,

對 Galois 來說，對稱性不是托馬斯曼所說的

which was something still and deathly --

靜態的和死一般的東西

for Galois, symmetry was all about motion.

對 Galois 來說，所有的對稱性都是關於運動的

What can you do to a symmetrical object,

你能對一個對稱性的物體做些什麼？

move it in some way, so it looks the same

用某種方法移動它，讓它看起來

as before you moved it?

跟你移動它之前一樣？

I like to describe it as the magic trick moves.

我喜歡把這形容為神奇的假動作。

What can you do to something? You close your eyes.

你對一些東西可以做些什麼？閉上你的眼睛。

I do something, put it back down again.

我移動它，再把它放回到原處。

It looks like it did before it started.

它看起來和動之前一樣。

So, for example, the walls in the Alhambra --

那麼，例如，阿爾罕布拉的牆壁。

I can take all of these tiles, and fix them at the yellow place,

我可以把所有的這些瓦片拿起來，把他們放在這個黃色的地方，

rotate them by 90 degrees,

並把它們旋轉九十度，

put them all back down again and they fit perfectly down there.

再把他們都放回去，它們非常吻合。

And if you open your eyes again, you wouldn't know that they'd moved.

如果你再睜開你的眼睛，你不會知道它們被移動過。

But it's the motion that really characterizes the symmetry

但正是運動才使對稱性

inside the Alhambra.

在阿爾罕布拉具有特色。

But it's also about producing a language to describe this.

但也要創造一種語言來描繪它。

And the power of mathematics is often

數學的力量往往

to change one thing into another, to change geometry into language.

把一樣東西變成另一樣，把幾何變成語言。

So I'm going to take you through, perhaps push you a little bit mathematically --

因此，我將帶你經歷，可能強加一些數學的東西給你們，

so brace yourselves --

所以撐住自己，

push you a little bit to understand how this language works,

強加一些數學的知識讓你們了解這種語言是怎麼運作的，

which enables us to capture what is symmetry.

這讓我們能夠捕捉到什麼是對稱性。

So, let's take these two symmetrical objects here.

那讓我們把這兩個對稱物放到這兒。

Let's take the twisted six-pointed starfish.

拿這個扭曲了的六角海星來說。

What can I do to the starfish which makes it look the same?

我怎麼做能讓這個海星看起來和原來一樣呢？

Well, there I rotated it by a sixth of a turn,

嗯，我把它旋轉了六分之一圈，

and still it looks like it did before I started.

它看起來仍然跟我動過之前一樣。

I could rotate it by a third of a turn,

我可以把它旋轉三分之一圈，

or a half a turn,

或者半圈，

or put it back down on its image, or two thirds of a turn.

或將它恢復到原圖，或旋轉三分之二圈。