TEDxRiodelaPlata
Eduardo Sáenz de Cabezón: Math is forever
Eduardo Sáenz de Cabezón: 數學恆久遠
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數學是用來幹嘛的？這是那些一想到數學就昏昏欲睡的學生想破頭也想不明白的問題，數學家 Eduardo Sáenz de Cabezón 以幽默而優雅的方式進行了回答。作為任何科學的基礎，數學之美被 Eduardo 展現得淋漓盡致，而且，鑽石未必長久，數學定理才是真正的恆久遠。
Eduardo Sáenz de Cabezón - Math educator
Eduardo Sáenz de Cabezón links science with humor and stories. Full bio
Eduardo Sáenz de Cabezón links science with humor and stories. Full bio
Double-click the English transcript below to play the video.
00:13
Imagine you're in a bar, or a club,
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想像一下，你在酒吧或俱樂部，
你開始跟一位女士聊天，
00:19
and you start talking, and after a while,
the question comes up,
the question comes up,
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過了一會，這個問題來了，
「那麼，你是做什麼工作的？」
「那麼，你是做什麼工作的？」
00:22
"So, what do you do for work?"
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00:24
And since you think
your job is interesting,
your job is interesting,
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因為你覺得你的工作很有趣，你說：
「我是一個數學家。」
（笑聲）
（笑聲）
00:26
you say, "I'm a mathematician."
(Laughter)
(Laughter)
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幾乎沒有例外，在那個談話中，
00:31
And inevitably, during that conversation
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下面兩句話之一會出現：
00:34
one of these two phrases come up:
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A) 「我的數學很差，但那不是我的錯。」
00:37
A) "I was terrible at math,
but it wasn't my fault.
but it wasn't my fault.
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00:41
It's because the teacher
was awful." (Laughter)
was awful." (Laughter)
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因為我的老師很爛。
（笑聲）
（笑聲）
或者 B) 「數學到底有什麼用？」
00:44
Or B) "But what is math really for?"
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（笑聲）
00:47
(Laughter)
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00:48
I'll now address Case B.
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我先來談案例 B)
（笑聲）
00:50
(Laughter)
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當有人問你數學是什麼，
他們不是問你
他們不是問你
00:52
When someone asks you what math is for,
they're not asking you
they're not asking you
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有關數學的科學應用。
00:57
about applications
of mathematical science.
of mathematical science.
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他們是問你，
01:00
They're asking you,
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01:01
why did I have to study that bullshit
I never used in my life again? (Laughter)
I never used in my life again? (Laughter)
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為什麼我要學習一生
都不會用到的廢物科目？ (笑聲）
都不會用到的廢物科目？ (笑聲）
這就是他們實際上問的。
01:05
That's what they're actually asking.
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所以，當數學家被問到數學是做什麼的，
01:07
So when mathematicians are asked
what math is for,
what math is for,
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它們傾向於分為兩類：
01:12
they tend to fall into two groups:
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54.51%的數學家將採取進攻的姿態，
01:14
54.51 percent of mathematicians
will assume an attacking position,
will assume an attacking position,
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而44.77％的數學家將採防禦的姿態。
01:20
and 44.77 percent of mathematicians
will take a defensive position.
will take a defensive position.
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還有奇怪的0.8％，其中包括我自己。
01:25
There's a strange 0.8 percent,
among which I include myself.
among which I include myself.
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誰是那些採取攻擊姿態的人?
01:29
Who are the ones that attack?
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採取攻擊姿態的數學家會告訴你
01:31
The attacking ones are mathematicians
who would tell you
who would tell you
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這個問題是沒有意義的，
01:33
this question makes no sense,
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因為數學有其自身的意義 -
01:35
because mathematics
have a meaning all their own --
have a meaning all their own --
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像是一個美麗的大廈有它自己的邏輯 -
01:38
a beautiful edifice with its own logic --
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而且不斷尋找
01:41
and that there's no point
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所有可能的應用是沒有意義的。
01:43
in constantly searching
for all possible applications.
for all possible applications.
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詩歌有什麼用？愛有什麼用？
01:45
What's the use of poetry?
What's the use of love?
What's the use of love?
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生活本身有什麼用？這是什麼樣的問題呢？
01:47
What's the use of life itself?
What kind of question is that?
What kind of question is that?
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(笑聲）
01:50
(Laughter)
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例如，哈迪，就是一個遭受這種攻擊的典型。
01:52
Hardy, for instance, was a model
of this type of attack.
of this type of attack.
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那些採防禦姿的態會告訴你，
01:56
And those who stand in defense tell you,
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“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。”
朋友，數學是所有東西背後的一切。”
01:58
"Even if you don't realize it, friend,
math is behind everything."
math is behind everything."
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(笑聲）
02:03
(Laughter)
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那些人，
02:04
Those guys,
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他們總是提到橋樑和電腦。
02:06
they always bring up
bridges and computers.
bridges and computers.
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“如果你不知道數學，您的大橋將會倒塌。”
02:10
"If you don't know math,
your bridge will collapse."
your bridge will collapse."
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02:12
(Laughter)
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(笑聲）
這是真的，電腦跟數學密切相關。
02:14
It's true, computers are all about math.
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02:17
And now these guys
have also started saying
have also started saying
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而現在這些人也開始說，
02:20
that behind information security
and credit cards are prime numbers.
and credit cards are prime numbers.
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在電腦資訊安全和信用卡背後就是質數。
02:25
These are the answers your math teacher
would give you if you asked him.
would give you if you asked him.
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這也就是你的數學老師會給你的答案。
他也是採防禦姿態的成員之一。
02:29
He's one of the defensive ones.
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02:31
Okay, but who's right then?
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好了，但到底誰是對的呢？
是那些說數學並不需要有一個目的，
02:33
Those who say that math
doesn't need to have a purpose,
doesn't need to have a purpose,
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02:35
or those who say that math
is behind everything we do?
is behind everything we do?
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還是那些說數學在我們所做的一切中？
02:38
Actually, both are right.
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其實上，雙方都是是正確的。
02:40
But remember I told you
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但請記住我告訴你的
02:42
I belong to that strange 0.8 percent
claiming something else?
claiming something else?
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我屬於那奇怪自稱別的0.8％嗎？
02:45
So, go ahead, ask me what math is for.
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因此，再問我一次數學是做什麼的。
02:48
Audience: What is math for?
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觀眾：數學是做什麼的？
02:51
Eduardo Sáenz de Cabezón: Okay,
76.34 percent of you asked the question,
76.34 percent of you asked the question,
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好吧，你們中76.34％的人問了這個問題，
02:56
23.41 percent didn't say anything,
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23.41％的人什麼也沒有說，
02:59
and the 0.8 percent --
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和剩下的0.8％ ，
03:00
I'm not sure what those guys are doing.
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我不知道那些人在做什麼。
03:03
Well, to my dear 76.31 percent --
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好吧，我那親愛的76.31％的觀眾，
數學真的不需要有一個目的，
03:07
it's true that math doesn't need
to serve a purpose,
to serve a purpose,
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03:11
it's true that it's
a beautiful structure, a logical one,
a beautiful structure, a logical one,
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它真的是有一個美麗且有邏輯的結構，
03:14
probably one
of the greatest collective efforts
of the greatest collective efforts
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而這也可能是人類在歷史上
03:17
ever achieved in human history.
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集體努力實現的成就之一。
03:19
But it's also true that there,
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但這也是真的：
03:21
where scientists and technicians
are looking for mathematical theories
are looking for mathematical theories
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當科學家和技術人員在尋找
使他們能進步的數學理論時，
03:26
that allow them to advance,
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03:28
they're within the structure of math,
which permeates everything.
which permeates everything.
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他們是在無處不在的數學結構中工作。
這是真的，我們必須去深入了解，
03:32
It's true that we have to go
somewhat deeper,
somewhat deeper,
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03:35
to see what's behind science.
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才能明白科學。
03:37
Science operates on intuition, creativity.
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科學在直覺和創造力上運作。
而數學控制直覺及馴服創造力。
03:41
Math controls intuition
and tames creativity.
and tames creativity.
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03:45
Almost everyone
who hasn't heard this before
who hasn't heard this before
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幾乎每個沒有聽說過
這個之前會覺得驚訝。當他們聽到如果你拿個
03:47
is surprised when they hear
that if you take
that if you take
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03:50
a 0.1 millimeter thick sheet of paper,
the size we normally use,
the size we normally use,
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我們通常使用的0.1毫米厚紙片，
而且，如果它夠大，把它折疊50次，
03:55
and, if it were big enough,
fold it 50 times,
fold it 50 times,
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03:58
its thickness would extend almost
the distance from the Earth to the sun.
the distance from the Earth to the sun.
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它的厚度幾乎可以從地球延伸到太陽。
你的直覺告訴你這是不可能的。
04:04
Your intuition tells you it's impossible.
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但數學告訴你它是正確的。
04:07
Do the math and you'll see it's right.
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04:09
That's what math is for.
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這就是數學的作用了。
04:12
It's true that science, all types
of science, only makes sense
of science, only makes sense
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這是真的，科學，各類科學的意義在於
04:15
because it makes us better understand
this beautiful world we live in.
this beautiful world we live in.
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因為它使我們更好地理解
我們生活的這個美麗的世界。
我們生活的這個美麗的世界。
而這樣做，
04:19
And in doing that,
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04:20
it helps us avoid the pitfalls
of this painful world we live in.
of this painful world we live in.
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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。
這個痛苦的世界裡避免重蹈覆轍。
有些科學可以直接幫助我們。
04:24
There are sciences that help us
in this way quite directly.
in this way quite directly.
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04:27
Oncological science, for example.
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例如，腫瘤學。
04:29
And there are others we look at from afar,
with envy sometimes,
with envy sometimes,
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而且還有其他我們有時
帶著羨慕眼光從遠方觀看的科學，
帶著羨慕眼光從遠方觀看的科學，
04:32
but knowing that we are
what supports them.
what supports them.
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但我們知道，我們是支持它們的。
04:35
All the basic sciences
support them,
support them,
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所有的基礎科學都支持它們，
包括數學。
04:38
including math.
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04:40
All that makes science, science
is the rigor of math.
is the rigor of math.
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所有這一切創造科學，而數學是科學的嚴謹性。
04:44
And that rigor factors in
because its results are eternal.
because its results are eternal.
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嚴謹是最重要的因素因為它的結果是永恆的。
04:49
You probably said or were told
at some point
at some point
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你可能在某些時候說過，或被告知，
04:51
that diamonds are forever, right?
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鑽石是永恆的，對不對？
04:56
That depends on
your definition of forever!
your definition of forever!
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這取決於你對永恆的定義！
04:58
A theorem -- that really is forever.
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一個數學定理真的是永恆的。
（笑聲）
05:00
(Laughter)
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05:02
The Pythagorean theorem is still true
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即使畢達哥拉斯死了，
畢氏定理仍然是正確的，我保證。（笑聲）
05:05
even though Pythagoras is dead,
I assure you it's true. (Laughter)
I assure you it's true. (Laughter)
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05:08
Even if the world collapsed
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即使世界坍塌
05:09
the Pythagorean theorem
would still be true.
would still be true.
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畢氏定理仍然是真的。
只要任意兩個直角三角形邊
和合適的斜邊連在一起
和合適的斜邊連在一起
05:12
Wherever any two triangle sides
and a good hypotenuse get together
and a good hypotenuse get together
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（笑聲）
05:16
(Laughter)
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05:17
the Pythagorean theorem goes all out.
It works like crazy.
It works like crazy.
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畢氏定理就能用。
它真是太有用了。
它真是太有用了。
05:20
(Applause)
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（掌聲）
05:27
Well, we mathematicians devote ourselves
to come up with theorems.
to come up with theorems.
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好了，我們的數學家貢獻終身想出定理。
永恆的真理。
05:31
Eternal truths.
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05:33
But it isn't always easy to know
the difference between
the difference between
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但並不總是容易知道
05:35
an eternal truth, or theorem,
and a mere conjecture.
and a mere conjecture.
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它是一個永恆的真理，
或定理，或是單純的猜想。
或定理，或是單純的猜想。
05:38
You need proof.
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你需要證明。
05:41
For example,
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例如，
05:43
let's say I have a big,
enormous, infinite field.
enormous, infinite field.
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我有一個大的，巨大的，無限領域。
05:48
I want to cover it with equal pieces,
without leaving any gaps.
without leaving any gaps.
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我想以同樣的物件覆蓋它，不留空隙。
我可以用正方形，對不對？
05:52
I could use squares, right?
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05:54
I could use triangles.
Not circles, those leave little gaps.
Not circles, those leave little gaps.
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我可以用三角形。但不能用圓形，
因為那會留下小缺口。
因為那會留下小缺口。
05:58
Which is the best shape to use?
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用那個形狀是最好的？
06:01
One that covers the same surface,
but has a smaller border.
but has a smaller border.
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一個覆蓋相同的表面，但具有較小邊的。
06:05
In the year 300, Pappus of Alexandria
said the best is to use hexagons,
said the best is to use hexagons,
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在公元300年，帕普斯說，最好是用六邊形，
就像蜜蜂用的。
06:10
just like bees do.
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06:12
But he didn't prove it.
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但他並沒有證明它。
06:13
The guy said, "Hexagons, great!
Let's go with hexagons!"
Let's go with hexagons!"
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這傢伙說，“六邊形，太棒了！讓我們用六邊形！“
06:16
He didn't prove it,
it remained a conjecture.
it remained a conjecture.
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他沒有提供證明，所以它仍然只是一個猜想。
06:19
"Hexagons!"
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“六邊形”！
而這世界，你也知道，
分成帕普斯幫和反帕普斯幫，
分成帕普斯幫和反帕普斯幫，
06:21
And the world, as you know,
split into Pappists and anti-Pappists,
split into Pappists and anti-Pappists,
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06:24
until 1700 years later
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直到1700年後
06:30
when in 1999, Thomas Hales proved
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在公元1999年，托馬斯·黑爾斯證明了
06:35
that Pappus and the bees were right --
the best shape to use was the hexagon.
the best shape to use was the hexagon.
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帕普斯和蜜蜂是正確的，最好的形狀是六邊形。
06:40
And that became a theorem,
the honeycomb theorem,
the honeycomb theorem,
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而這也成為一個定理，蜂窩定理，
而它將是真的，直到永遠，
06:43
that will be true forever and ever,
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比任何你擁有的鑽石活的更久遠。 （笑聲）
06:45
for longer than any diamond
you may have. (Laughter)
you may have. (Laughter)
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06:48
But what happens if we go
to three dimensions?
to three dimensions?
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但是，當我們來到三度空間時要怎麼辦？
06:51
If I want to fill the space
with equal pieces,
with equal pieces,
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如果我想以相同的物件填補空間，
不留空隙，
06:55
without leaving any gaps,
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06:56
I can use cubes, right?
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我可以使用立方體，對不對？
06:58
Not spheres, those leave little gaps.
(Laughter)
(Laughter)
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不能用球體，那會留下小缺口。（笑聲）
07:01
What is the best shape to use?
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什麼形狀是最好的？
07:04
Lord Kelvin, of the famous
Kelvin degrees and all,
Kelvin degrees and all,
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以克氏溫標聞名的克爾文爵士，
07:09
said that the best was to use
a truncated octahedron
a truncated octahedron
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說，最好使用截角八面體
07:16
which, as you all know --
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因為，因為大家都知道
07:19
(Laughter) --
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（笑聲）
07:21
is this thing here!
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就是這個東西！
07:22
(Applause)
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（掌聲）
07:27
Come on.
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拜託。
07:30
Who doesn't have a truncated
octahedron at home? (Laughter)
octahedron at home? (Laughter)
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誰家沒有截角八面體？ （笑聲）
07:32
Even a plastic one.
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即使是塑膠的。
07:34
"Honey, get the truncated octahedron,
we're having guests."
we're having guests."
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“親愛的，去拿截角八面體，我們有客人來了。“
07:36
Everybody has one!
(Laughter)
(Laughter)
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每個人都有！（笑聲）
07:38
But Kelvin didn't prove it.
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但克爾文並沒有證明它。
07:40
It remained a conjecture --
Kelvin's conjecture.
Kelvin's conjecture.
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它仍然是一個猜想 - 克爾文的猜想。
07:44
The world, as you know, then split into
Kelvinists and anti-Kelvinists
Kelvinists and anti-Kelvinists
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而這世界，你也知道，
分成克爾文幫和反克爾文幫，
分成克爾文幫和反克爾文幫，
07:50
(Laughter)
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（笑聲）
07:51
until a hundred or so years later,
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直到一百年多年後，
有人找到了更好的立方體。
07:58
someone found a better structure.
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Weaire和Phelan發現了這個小東西 -
08:02
Weaire and Phelan
found this little thing over here --
found this little thing over here --
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（笑聲）
08:08
(Laughter) --
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08:09
this structure to which they gave
the very clever name
the very clever name
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他們給這種立方結構取了個非常聰明的名字
08:13
"the Weaire-Phelan structure."
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就是“Weaire - Phelan的結構”。
（笑聲）
08:15
(Laughter)
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08:17
It looks like a strange object,
but it isn't so strange,
but it isn't so strange,
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它看起來像一個奇怪的物體，
但它不是那麼的陌生，
但它不是那麼的陌生，
08:20
it also exists in nature.
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因為它也存在於自然界。
08:22
It's very interesting that this structure,
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這種結構是非常有趣的，
08:24
because of its geometric properties,
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因為它的幾何特性，
被用來在北京奧運會設計游泳中心。
08:27
was used to build the Aquatics Center
for the Beijing Olympic Games.
for the Beijing Olympic Games.
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08:32
There, Michael Phelps
won eight gold medals,
won eight gold medals,
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在那裡，菲爾普斯贏得了八面奧運金牌，
08:35
and became the best swimmer of all time.
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並成為有史以來最好的游泳運動員。
08:38
Well, until someone better
comes along, right?
comes along, right?
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好吧，直到有人發現更好的結構，對不對？
08:42
As may happen
with the Weaire-Phelan structure.
with the Weaire-Phelan structure.
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就像是Weaire - Phelan結構。
直到更好的東西出現。
08:45
It's the best
until something better shows up.
until something better shows up.
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08:47
But be careful, because this one
really stands a chance
really stands a chance
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但注意，因為這個是很有可能的
08:52
that in a hundred or so years,
or even if it's in 1700 years,
or even if it's in 1700 years,
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在100年左右，或者是在1700年後，
有人會證明這是最好的結構。
08:57
that someone proves
it's the best possible shape for the job.
it's the best possible shape for the job.
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09:02
It will then become a theorem,
a truth, forever and ever.
a truth, forever and ever.
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然後，它會成為一個定理，一個真理，直到永遠。
比鑽石活得更久。
09:07
For longer than any diamond.
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09:10
So, if you want to tell someone
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所以，如果你想告訴別人
09:15
that you will love them forever
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你會永遠愛他們，
09:18
you can give them a diamond.
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你可以給他們鑽石。
09:20
But if you want to tell them
that you'll love them forever and ever,
that you'll love them forever and ever,
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但是，如果你要告訴他們，
你一定會永永遠遠的喜歡他們，
你一定會永永遠遠的喜歡他們，
給他們一個定理！
09:24
give them a theorem!
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（笑聲）
09:26
(Laughter)
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09:27
But hang on a minute!
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等一下！
09:30
You'll have to prove it,
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你必須要證明它，
09:32
so your love doesn't remain
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讓你的愛不只是
一個猜想。
09:34
a conjecture.
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09:36
(Applause)
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（掌聲）
ABOUT THE SPEAKER
Eduardo Sáenz de Cabezón - Math educatorEduardo Sáenz de Cabezón links science with humor and stories.
Why you should listen
Eduardo Sáenz de Cabezón links science with humor and stories. He studied theology and has a PhD in mathematics from the University of La Rioja. He speaks on these two topics in universities and secondary schools as a storyteller for children, youth and adults. Sáenz de Cabezón has also been a professor of Computer Information Systems, Discrete Mathematics and Algebra at the University of La Rioja since 2010.
He won the FameLab contest for scientific monologues in Spain in 2013.
Eduardo Sáenz de Cabezón | Speaker | TED.com