Placeholder Image

字幕列表 影片播放

  • On the 30th of May, 1832,

    在1832年5月30日,

  • 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。