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  • Translator: Tomás Guarna Reviewer: Sebastian Betti

    譯者: xueling Sun 審譯者: Karen SONG

  • Imagine you're in a bar, or a club,

    想像一下,你在酒吧或俱樂部,

  • and you start talking, and after a while, the question comes up,

    你開始跟一位女士聊天,

  • "So, what do you do for work?"

    過了一會,這個問題來了, 「那麼,你是做什麼工作的?」

  • And since you think your job is interesting,

    因為你覺得你的工作很有趣,你說:

  • you say, "I'm a mathematician." (Laughter)

    「我是一個數學家。」 (笑聲)

  • And inevitably, during that conversation

    幾乎沒有例外,在那個談話中,

  • one of these two phrases come up:

    下面兩句話之一會出現:

  • A) "I was terrible at math, but it wasn't my fault.

    A) 「我的數學很差,但那不是我的錯。」

  • It's because the teacher was awful." (Laughter)

    因為我的老師很爛。 (笑聲)

  • Or B) "But what is math really for?"

    或者 B) 「數學到底有什麼用?」

  • (Laughter)

    (笑聲)

  • I'll now address Case B.

    我先來談案例 B)

  • (Laughter)

    (笑聲)

  • When someone asks you what math is for, they're not asking you

    當有人問你數學是什麼, 他們不是問你

  • about applications of mathematical science.

    有關數學的科學應用。

  • They're asking you,

    他們是問你,

  • why did I have to study that bullshit I never used in my life again? (Laughter)

    為什麼我要學習一生 都不會用到的廢物科目? (笑聲)

  • That's what they're actually asking.

    這就是他們實際上問的。

  • So when mathematicians are asked what math is for,

    所以,當數學家被問到數學是做什麼的,

  • they tend to fall into two groups:

    它們傾向於分為兩類:

  • 54.51 percent of mathematicians will assume an attacking position,

    54.51%的數學家將採取進攻的姿態,

  • and 44.77 percent of mathematicians will take a defensive position.

    而44.77%的數學家將採防禦的姿態。

  • There's a strange 0.8 percent, among which I include myself.

    還有奇怪的0.8%,其中包括我自己。

  • Who are the ones that attack?

    誰是那些採取攻擊姿態的人?

  • The attacking ones are mathematicians who would tell you

    採取攻擊姿態的數學家會告訴你

  • this question makes no sense,

    這個問題是沒有意義的,

  • because mathematics have a meaning all their own --

    因為數學有其自身的意義 -

  • a beautiful edifice with its own logic --

    像是一個美麗的大廈有它自己的邏輯 -

  • and that there's no point

    而且不斷尋找

  • in constantly searching for all possible applications.

    所有可能的應用是沒有意義的。

  • What's the use of poetry? What's the use of love?

    詩歌有什麼用?愛有什麼用?

  • What's the use of life itself? What kind of question is that?

    生活本身有什麼用?這是什麼樣的問題呢?

  • (Laughter)

    (笑聲)

  • Hardy, for instance, was a model of this type of attack.

    例如,哈迪,就是一個遭受這種攻擊的典型。

  • And those who stand in defense tell you,

    那些採防禦姿的態會告訴你,

  • "Even if you don't realize it, friend, math is behind everything."

    “即使你沒有意識到這一點, 朋友,數學是所有東西背後的一切。”

  • (Laughter)

    (笑聲)

  • Those guys,

    那些人,

  • they always bring up bridges and computers.

    他們總是提到橋樑和電腦。

  • "If you don't know math, your bridge will collapse."

    “如果你不知道數學,您的大橋將會倒塌。”

  • (Laughter)

    (笑聲)

  • It's true, computers are all about math.

    這是真的,電腦跟數學密切相關。

  • And now these guys have also started saying

    而現在這些人也開始說,

  • that behind information security and credit cards are prime numbers.

    在電腦資訊安全和信用卡背後就是質數。

  • These are the answers your math teacher would give you if you asked him.

    這也就是你的數學老師會給你的答案。

  • He's one of the defensive ones.

    他也是採防禦姿態的成員之一。

  • Okay, but who's right then?

    好了,但到底誰是對的呢?

  • Those who say that math doesn't need to have a purpose,

    是那些說數學並不需要有一個目的,

  • or those who say that math is behind everything we do?

    還是那些說數學在我們所做的一切中?

  • Actually, both are right.

    其實上,雙方都是是正確的。

  • But remember I told you

    但請記住我告訴你的

  • I belong to that strange 0.8 percent claiming something else?

    我屬於那奇怪自稱別的0.8%嗎?

  • So, go ahead, ask me what math is for.

    因此,再問我一次數學是做什麼的。

  • Audience: What is math for?

    觀眾:數學是做什麼的?

  • Eduardoenz de Cabezón: Okay, 76.34 percent of you asked the question,

    好吧,你們中76.34%的人問了這個問題,

  • 23.41 percent didn't say anything,

    23.41%的人什麼也沒有說,

  • and the 0.8 percent --

    和剩下的0.8% ,

  • I'm not sure what those guys are doing.

    我不知道那些人在做什麼。

  • Well, to my dear 76.31 percent --

    好吧,我那親愛的76.31%的觀眾,

  • it's true that math doesn't need to serve a purpose,

    數學真的不需要有一個目的,

  • it's true that it's a beautiful structure, a logical one,

    它真的是有一個美麗且有邏輯的結構,

  • probably one of the greatest collective efforts

    而這也可能是人類在歷史上

  • ever achieved in human history.

    集體努力實現的成就之一。

  • But it's also true that there,

    但這也是真的:

  • where scientists and technicians are looking for mathematical theories

    當科學家和技術人員在尋找

  • that allow them to advance,

    使他們能進步的數學理論時,

  • they're within the structure of math, which permeates everything.

    他們是在無處不在的數學結構中工作。

  • It's true that we have to go somewhat deeper,

    這是真的,我們必須去深入了解,

  • to see what's behind science.

    才能明白科學。

  • Science operates on intuition, creativity.

    科學在直覺和創造力上運作。

  • Math controls intuition and tames creativity.

    而數學控制直覺及馴服創造力。

  • Almost everyone who hasn't heard this before

    幾乎每個沒有聽說過

  • is surprised when they hear that if you take

    這個之前會覺得驚訝。當他們聽到如果你拿個

  • a 0.1 millimeter thick sheet of paper, the size we normally use,

    我們通常使用的0.1毫米厚紙片,

  • and, if it were big enough, fold it 50 times,

    而且,如果它夠大,把它折疊50次,

  • its thickness would extend almost the distance from the Earth to the sun.

    它的厚度幾乎可以從地球延伸到太陽。

  • Your intuition tells you it's impossible.

    你的直覺告訴你這是不可能的。

  • Do the math and you'll see it's right.

    但數學告訴你它是正確的。

  • That's what math is for.

    這就是數學的作用了。

  • It's true that science, all types of science, only makes sense

    這是真的,科學,各類科學的意義在於

  • because it makes us better understand this beautiful world we live in.

    因為它使我們更好地理解 我們生活的這個美麗的世界。

  • And in doing that,

    而這樣做,

  • it helps us avoid the pitfalls of this painful world we live in.

    它可以幫助我們在我們居住的 這個痛苦的世界裡避免重蹈覆轍。

  • There are sciences that help us in this way quite directly.

    有些科學可以直接幫助我們。

  • Oncological science, for example.

    例如,腫瘤學。

  • And there are others we look at from afar, with envy sometimes,

    而且還有其他我們有時 帶著羨慕眼光從遠方觀看的科學,

  • but knowing that we are what supports them.

    但我們知道,我們是支持它們的。

  • All the basic sciences support them,

    所有的基礎科學都支持它們,

  • including math.

    包括數學。

  • All that makes science, science is the rigor of math.

    所有這一切創造科學,而數學是科學的嚴謹性。

  • And that rigor factors in because its results are eternal.

    嚴謹是最重要的因素因為它的結果是永恆的。

  • You probably said or were told at some point

    你可能在某些時候說過,或被告知,

  • that diamonds are forever, right?

    鑽石是永恆的,對不對?

  • That depends on your definition of forever!

    這取決於你對永恆的定義!

  • A theorem -- that really is forever.

    一個數學定理真的是永恆的。

  • (Laughter)

    (笑聲)

  • The Pythagorean theorem is still true

    即使畢達哥拉斯死了,

  • even though Pythagoras is dead, I assure you it's true. (Laughter)

    畢氏定理仍然是正確的,我保證。(笑聲)

  • Even if the world collapsed

    即使世界坍塌

  • the Pythagorean theorem would still be true.

    畢氏定理仍然是真的。

  • Wherever any two triangle sides and a good hypotenuse get together

    只要任意兩個直角三角形邊 和合適的斜邊連在一起

  • (Laughter)

    (笑聲)

  • the Pythagorean theorem goes all out. It works like crazy.

    畢氏定理就能用。 它真是太有用了。

  • (Applause)

    (掌聲)

  • Well, we mathematicians devote ourselves to come up with theorems.

    好了,我們的數學家貢獻終身想出定理。

  • Eternal truths.

    永恆的真理。

  • But it isn't always easy to know the difference between

    但並不總是容易知道

  • an eternal truth, or theorem, and a mere conjecture.

    它是一個永恆的真理, 或定理,或是單純的猜想。

  • You need proof.

    你需要證明。

  • For example,

    例如,

  • let's say I have a big, enormous, infinite field.

    我有一個大的,巨大的,無限領域。

  • I want to cover it with equal pieces, without leaving any gaps.

    我想以同樣的物件覆蓋它,不留空隙。

  • I could use squares, right?

    我可以用正方形,對不對?

  • I could use triangles. Not circles, those leave little gaps.

    我可以用三角形。但不能用圓形, 因為那會留下小缺口。

  • Which is the best shape to use?

    用那個形狀是最好的?

  • One that covers the same surface, but has a smaller border.

    一個覆蓋相同的表面,但具有較小邊的。

  • In the year 300, Pappus of Alexandria said the best is to use hexagons,

    在公元300年,帕普斯說,最好是用六邊形,

  • just like bees do.

    就像蜜蜂用的。

  • But he didn't prove it.

    但他並沒有證明它。

  • The guy said, "Hexagons, great! Let's go with hexagons!"

    這傢伙說,“六邊形,太棒了!讓我們用六邊形!“

  • He didn't prove it, it remained a conjecture.

    他沒有提供證明,所以它仍然只是一個猜想。

  • "Hexagons!"

    “六邊形”!

  • And the world, as you know, split into Pappists and anti-Pappists,

    而這世界,你也知道, 分成帕普斯幫和反帕普斯幫,

  • until 1700 years later

    直到1700年後

  • when in 1999, Thomas Hales proved

    在公元1999年,托馬斯·黑爾斯證明了

  • that Pappus and the bees were right -- the best shape to use was the hexagon.

    帕普斯和蜜蜂是正確的,最好的形狀是六邊形。

  • And that became a theorem, the honeycomb theorem,

    而這也成為一個定理,蜂窩定理,

  • that will be true forever and ever,

    而它將是真的,直到永遠,

  • for longer than any diamond you may have. (Laughter)

    比任何你擁有的鑽石活的更久遠。 (笑聲)

  • But what happens if we go to three dimensions?

    但是,當我們來到三度空間時要怎麼辦?

  • If I want to fill the space with equal pieces,

    如果我想以相同的物件填補空間,

  • without leaving any gaps,

    不留空隙,

  • I can use cubes, right?

    我可以使用立方體,對不對?

  • Not spheres, those leave little gaps. (Laughter)

    不能用球體,那會留下小缺口。(笑聲)

  • What is the best shape to use?

    什麼形狀是最好的?

  • Lord Kelvin, of the famous Kelvin degrees and all,

    以克氏溫標聞名的克爾文爵士,

  • said that the best was to use a truncated octahedron

    說,最好使用截角八面體

  • which, as you all know --

    因為,因為大家都知道

  • (Laughter) --

    (笑聲)

  • is this thing here!

    就是這個東西!

  • (Applause)

    (掌聲)

  • Come on.

    拜託。

  • Who doesn't have a truncated octahedron at home? (Laughter)

    誰家沒有截角八面體? (笑聲)

  • Even a plastic one.

    即使是塑膠的。

  • "Honey, get the truncated octahedron, we're having guests."

    “親愛的,去拿截角八面體,我們有客人來了。“

  • Everybody has one! (Laughter)

    每個人都有!(笑聲)

  • But Kelvin didn't prove it.

    但克爾文並沒有證明它。

  • It remained a conjecture -- Kelvin's conjecture.

    它仍然是一個猜想 - 克爾文的猜想。

  • The world, as you know, then split into Kelvinists and anti-Kelvinists

    而這世界,你也知道, 分成克爾文幫和反克爾文幫,

  • (Laughter)

    (笑聲)

  • until a hundred or so years later,

    直到一百年多年後,

  • someone found a better structure.

    有人找到了更好的立方體。

  • Weaire and Phelan found this little thing over here --

    Weaire和Phelan發現了這個小東西 -

  • (Laughter) --

    (笑聲)

  • this structure to which they gave the very clever name

    他們給這種立方結構取了個非常聰明的名字

  • "the Weaire-€“Phelan structure."

    就是“Weaire - Phelan的結構”。

  • (Laughter)

    (笑聲)

  • It looks like a strange object, but it isn't so strange,

    它看起來像一個奇怪的物體, 但它不是那麼的陌生,

  • it also exists in nature.

    因為它也存在於自然界。

  • It's very interesting that this structure,

    這種結構是非常有趣的,

  • because of its geometric properties,

    因為它的幾何特性,

  • was used to build the Aquatics Center for the Beijing Olympic Games.

    被用來在北京奧運會設計游泳中心。

  • There, Michael Phelps won eight gold medals,

    在那裡,菲爾普斯贏得了八面奧運金牌,

  • and became the best swimmer of all time.

    並成為有史以來最好的游泳運動員。

  • Well, until someone better comes along, right?

    好吧,直到有人發現更好的結構,對不對?

  • As may happen with the Weaire-€“Phelan structure.

    就像是Weaire - Phelan結構。

  • It's the best until something better shows up.

    直到更好的東西出現。

  • But be careful, because this one really stands a chance

    但注意,因為這個是很有可能的

  • that in a hundred or so years, or even if it's in 1700 years,

    在100年左右,或者是在1700年後,

  • that someone proves it's the best possible shape for the job.

    有人會證明這是最好的結構。

  • It will then become a theorem, a truth, forever and ever.

    然後,它會成為一個定理,一個真理,直到永遠。

  • For longer than any diamond.

    比鑽石活得更久。

  • So, if you want to tell someone

    所以,如果你想告訴別人

  • that you will love them forever

    你會永遠愛他們,

  • you can give them a diamond.

    你可以給他們鑽石。

  • But if you want to tell them that you'll love them forever and ever,

    但是,如果你要告訴他們, 你一定會永永遠遠的喜歡他們,

  • give them a theorem!

    給他們一個定理!

  • (Laughter)

    (笑聲)

  • But hang on a minute!

    等一下!

  • You'll have to prove it,

    你必須要證明它,

  • so your love doesn't remain

    讓你的愛不只是

  • a conjecture.

    一個猜想。

  • (Applause)

    (掌聲)

Translator: Tomás Guarna Reviewer: Sebastian Betti

譯者: xueling Sun 審譯者: Karen SONG

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B1 中級 中文 美國腔 TED 數學 定理 笑聲 數學家 姿態

【TED】愛德華多-薩恩斯-德-卡貝松:數學是永遠的(數學是永遠的(英文字幕)|愛德華多-薩恩斯-德-卡貝松)。 (【TED】Eduardo Sáenz de Cabezón: Math is forever (Math is forever (with English subtitles) | Eduardo Sáenz de Cabezón))

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