Eduardo Sáenz de Cabezón: Math is forever (with English subtitles) | TED
190,450 views ・ 2015-04-07
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00:00
Translator: Tomás Guarna
Reviewer: Sebastian Betti
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翻译人员: Yumeng Guo
校对人员: Xiaoya Song
00:13
Imagine you're in a bar, or a club,
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设想这样一个场景,在酒吧,或是俱乐部里,
你跟一位女士搭讪,
00:19
and you start talking, and after a while,
the question comes up,
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不久聊到了这个问题,「你做什么工作的?」
00:22
"So, what do you do for work?"
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00:24
And since you think
your job is interesting,
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00:26
you say, "I'm a mathematician."
(Laughter)
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你觉得你的工作蛮有趣的,因此你说,
「我是一位数学家。」
00:31
And inevitably, during that conversation
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(笑声)
00:34
one of these two phrases come up:
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有33.51%的女士,
00:37
A) "I was terrible at math,
but it wasn't my fault.
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听到这句话之后,
会假装接到了紧急电话而离开。
00:41
It's because the teacher
was awful." (Laughter)
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(笑声)
00:44
Or B) "But what is math really for?"
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有64.69%的女士会感到绝望,
00:47
(Laughter)
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00:48
I'll now address Case B.
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赶紧转换话题,然后离开。
00:50
(Laughter)
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00:52
When someone asks you what math is for,
they're not asking you
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(笑声)
还有0.8%的人,即你的姐妹、女朋友和母亲,
00:57
about applications
of mathematical science.
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她们知道你做的是一份奇怪的工作,
但却想不起来具体是什么了。(笑声)
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)
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还有1%的人仍然想继续这段对话。
不可避免地是,后面的对话中
01:05
That's what they're actually asking.
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01:07
So when mathematicians are asked
what math is for,
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会出现这两句之一:
A) 「我数学很差,但不是我的错,
01:12
they tend to fall into two groups:
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01:14
54.51 percent of mathematicians
will assume an attacking position,
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我老师教得太差了。」(笑声)
或B) 「数学到底是干什么用的呢?」
01:20
and 44.77 percent of mathematicians
will take a defensive position.
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(笑声)
下面我就谈谈B这种情况
(笑声)
01:25
There's a strange 0.8 percent,
among which I include myself.
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当有人问你数学是用来干什么的,
他们并不是在问你
01:29
Who are the ones that attack?
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数学科学的应用。
01:31
The attacking ones are mathematicians
who would tell you
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01:33
this question makes no sense,
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他们是在问你,
为什么我不得不学这些
一辈子都不会再用到的垃圾?(笑声)
01:35
because mathematics
have a meaning all their own --
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01:38
a beautiful edifice with its own logic --
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这才是他们真正想知道的。
当数学家被问起来这个问题,
01:41
and that there's no point
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01:43
in constantly searching
for all possible applications.
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01:45
What's the use of poetry?
What's the use of love?
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他们的回应可分为两类:
01:47
What's the use of life itself?
What kind of question is that?
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54.51%的数学家会为之争辩,
01:50
(Laughter)
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01:52
Hardy, for instance, was a model
of this type of attack.
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44.77%的数学家会为自己辩护。
01:56
And those who stand in defense tell you,
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01:58
"Even if you don't realize it, friend,
math is behind everything."
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还有0.8%奇怪的数学家,我也属于这一类。
这些为之争辩的数学家是谁?
02:03
(Laughter)
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02:04
Those guys,
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他们会告诉你这个问题
02:06
they always bring up
bridges and computers.
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没有意义,
因为数学自身就是全部意义所在——
02:10
"If you don't know math,
your bridge will collapse."
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由逻辑搭建起的美丽的建筑——
02:12
(Laughter)
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02:14
It's true, computers are all about math.
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一直寻找其用处
是没有意义的。
02:17
And now these guys
have also started saying
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诗歌有什么用处?爱有什么用处?
02:20
that behind information security
and credit cards are prime numbers.
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生命本身的用处是什么?这是个什么问题?
(笑声)
02:25
These are the answers your math teacher
would give you if you asked him.
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Hardy,举个例子,就是这类人。
02:29
He's one of the defensive ones.
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那些回护自己的数学家会告诉你,
02:31
Okay, but who's right then?
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「即便你没有意识到,
朋友,数学无处不在。」
02:33
Those who say that math
doesn't need to have a purpose,
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02:35
or those who say that math
is behind everything we do?
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(笑声)
那些人,
02:38
Actually, both are right.
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就是用数学来建造桥梁和发明计算机的。
02:40
But remember I told you
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02:42
I belong to that strange 0.8 percent
claiming something else?
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「如果你不懂数学,你造的桥就会塌。」
02:45
So, go ahead, ask me what math is for.
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(笑声)
没错,计算机要应用到数学。
02:48
Audience: What is math for?
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那些人还会说
02:51
Eduardo Sáenz de Cabezón: Okay,
76.34 percent of you asked the question,
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信息安全和信用卡背后是质数。
02:56
23.41 percent didn't say anything,
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如果你问你的数学老师,他会给你这些答案。
02:59
and the 0.8 percent --
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03:00
I'm not sure what those guys are doing.
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他属于回护这一类的。
03:03
Well, to my dear 76.31 percent --
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哪种说法是对的呢?
是那些说数学没必要有意义的人,
03:07
it's true that math doesn't need
to serve a purpose,
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还是那些说数学无处不在的人?
03:11
it's true that it's
a beautiful structure, a logical one,
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事实上,两种说法都对。
但你们应该还记得,
03:14
probably one
of the greatest collective efforts
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我告诉过你们我属于那有其他观点的奇怪的0.8%。
03:17
ever achieved in human history.
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来吧,问我数学是干什么用的。
03:19
But it's also true that there,
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03:21
where scientists and technicians
are looking for mathematical theories
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观众:数学是干什么用的?
Eduardo: 好,76.34%的人问了这个问题,
03:26
that allow them to advance,
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03:28
they're within the structure of math,
which permeates everything.
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23.41%什么都没说,
03:32
It's true that we have to go
somewhat deeper,
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还有0.8%——
我不知道这些家伙在干什么。
03:35
to see what's behind science.
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好,至亲爱的这76.34%的人——
03:37
Science operates on intuition, creativity.
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诚然,数学不需要为某个目的而存在,
03:41
Math controls intuition
and tames creativity.
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数学的确是有一个逻辑的、美丽的构造,
03:45
Almost everyone
who hasn't heard this before
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03:47
is surprised when they hear
that if you take
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数学很可能是人类历史上最伟大的
03:50
a 0.1 millimeter thick sheet of paper,
the size we normally use,
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集众人之力的成就之一。
但这种说法也是无可厚非的:
科学家和工程师不断利用数学理论
03:55
and, if it were big enough,
fold it 50 times,
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03:58
its thickness would extend almost
the distance from the Earth to the sun.
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来进行研究,
这些理论是属于数学架构的,而数学无处不在;
04:04
Your intuition tells you it's impossible.
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我们需要深入思考,
04:07
Do the math and you'll see it's right.
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去探索科学背后的奇妙。
04:09
That's what math is for.
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科学需要直觉和创造力,
04:12
It's true that science, all types
of science, only makes sense
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而数学会将直觉和创造力转变为非对即错的事实。
04:15
because it makes us better understand
this beautiful world we live in.
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下面这个事实,当第一次听到时,
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.
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几乎所有人都会觉得不可思议:
如果你拿一张0.1毫米厚的纸张,
平常用的纸就这么厚,
04:24
There are sciences that help us
in this way quite directly.
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04:27
Oncological science, for example.
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如果它足够大,对折50次,
04:29
And there are others we look at from afar,
with envy sometimes,
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纸的厚度几乎相当于地球到太阳的距离。
04:32
but knowing that we are
what supports them.
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04:35
All the basic sciences
support them,
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你的直觉告诉你这不可能。
04:38
including math.
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04:40
All that makes science, science
is the rigor of math.
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但用数学算一下,你就知道这是事实。
这就是数学的用处。
04:44
And that rigor factors in
because its results are eternal.
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科学,所有科学,
让我们更好地理解世界——
我们生活的这个美丽的世界。
正因此,科学才有意义。
04:49
You probably said or were told
at some point
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04:51
that diamonds are forever, right?
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在赋予我们对这个世界的理解时,
科学帮助我们避免在这个世界里受苦受难。
04:56
That depends on
your definition of forever!
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有诸多科学是以非常直接地方式帮助我们,
04:58
A theorem -- that really is forever.
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05:00
(Laughter)
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如肿瘤学;
05:02
The Pythagorean theorem is still true
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还有一些科学我们只能遥看,
有时心怀嫉妒,
05:05
even though Pythagoras is dead,
I assure you it's true. (Laughter)
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但知道是我们在推动科学的进步。
05:08
Even if the world collapsed
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所有的基础科学都在推动它们,
05:09
the Pythagorean theorem
would still be true.
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包括数学。
05:12
Wherever any two triangle sides
and a good hypotenuse get together
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所有的都是科学,科学是严谨的数学表达。
05:16
(Laughter)
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05:17
the Pythagorean theorem goes all out.
It works like crazy.
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把严谨考虑在内是因为其结果是永恒的。
05:20
(Applause)
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你或许说过,也可能听过这样的说法,
即钻石恒久远,是吧?
05:27
Well, we mathematicians devote ourselves
to come up with theorems.
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这取决于你对永恒的定义!
05:31
Eternal truths.
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定理——才是真正的永恒。
05:33
But it isn't always easy to know
the difference between
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(笑声)
05:35
an eternal truth, or theorem,
and a mere conjecture.
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虽然毕达哥拉斯已经死了,
05:38
You need proof.
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但勾股定律依然是正确的,
我可以向你保证。(笑声)
05:41
For example,
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即便世界消亡了,
勾股定律还是正确的。
05:43
let's say I have a big,
enormous, infinite field.
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每当两个直角边和一个合适的斜边聚在一起,
05:48
I want to cover it with equal pieces,
without leaving any gaps.
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(笑声)
勾股定律就能适用。简直太好用了。
05:52
I could use squares, right?
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(掌声)
05:54
I could use triangles.
Not circles, those leave little gaps.
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05:58
Which is the best shape to use?
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我们数学家为定理投入了大量精力,
06:01
One that covers the same surface,
but has a smaller border.
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这永恒的事实。
06:05
In the year 300, Pappus of Alexandria
said the best is to use hexagons,
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但弄清永恒的真理,或定理,
与猜想之间的差别不总是容易的。
06:10
just like bees do.
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需要证明。
06:12
But he didn't prove it.
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06:13
The guy said, "Hexagons, great!
Let's go with hexagons!"
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比如说,
06:16
He didn't prove it,
it remained a conjecture.
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有一个巨大的,无限大的二维平面,
06:19
"Hexagons!"
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06:21
And the world, as you know,
split into Pappists and anti-Pappists,
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我想用相同的片状物覆盖住它,
不留任何空隙。
06:24
until 1700 years later
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我可以用正方形,对吧?
我可以用三角形。
圆不行,会留下空隙。
06:30
when in 1999, Thomas Hales proved
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最好的形状是什么呢?
覆盖住最大的面积,而边长最小。
06:35
that Pappus and the bees were right --
the best shape to use was the hexagon.
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在公元300年,亚历山大的帕普斯
说六边形最好,
06:40
And that became a theorem,
the honeycomb theorem,
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06:43
that will be true forever and ever,
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就像蜜蜂那样。
06:45
for longer than any diamond
you may have. (Laughter)
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但他没有证明这个说法。
他说,「六边形,伟大!
让我们用六边形吧!」
06:48
But what happens if we go
to three dimensions?
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他没有证明它,这只是一个猜想。
06:51
If I want to fill the space
with equal pieces,
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「六边形!」
你们也知道,这个世界分成了
帕普斯和反帕普斯两派,
06:55
without leaving any gaps,
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06:56
I can use cubes, right?
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直到1700年后的1999年,
06:58
Not spheres, those leave little gaps.
(Laughter)
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07:01
What is the best shape to use?
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Thomas Hales证明
07:04
Lord Kelvin, of the famous
Kelvin degrees and all,
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帕普斯和蜜蜂是正确的——
最佳的形状是六边形。
07:09
said that the best was to use
a truncated octahedron
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这变成了一个定理,
即蜂窝定理,
07:16
which, as you all know --
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永恒的真理,
要比任何钻石都长久远。(笑声)
07:19
(Laughter) --
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07:21
is this thing here!
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如果是三维空间呢?
07:22
(Applause)
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如果我们想用相同的结构填满空间,
07:27
Come on.
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不留任何空隙,
我可以用立方体,对吧?
07:30
Who doesn't have a truncated
octahedron at home? (Laughter)
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不能用曲面体,会留下空隙。(笑声)
07:32
Even a plastic one.
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07:34
"Honey, get the truncated octahedron,
we're having guests."
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最佳的结构是什么呢?
07:36
Everybody has one!
(Laughter)
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开尔文爵士,就是开氏温度的开氏,
07:38
But Kelvin didn't prove it.
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07:40
It remained a conjecture --
Kelvin's conjecture.
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说最佳的是结构是截角八面体,
07:44
The world, as you know, then split into
Kelvinists and anti-Kelvinists
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你们都知道的——
07:50
(Laughter)
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07:51
until a hundred or so years later,
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(笑声)——
就是这个东西!
(掌声)
07:58
someone found a better structure.
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拜托,
08:02
Weaire and Phelan
found this little thing over here --
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谁家没有截角八面体?(笑声)
塑料的更别提了。
「亲爱的,把截角八面体拿来,
客人要来了。」
08:08
(Laughter) --
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08:09
this structure to which they gave
the very clever name
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每个人都有!(笑声)
但开尔文没有证实这个理论。
08:13
"the Weaire-€“Phelan structure."
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这是一个猜想——开尔文猜想。
08:15
(Laughter)
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08:17
It looks like a strange object,
but it isn't so strange,
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你们都知道的,世界分成了
开尔文派和反开尔文派,
08:20
it also exists in nature.
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08:22
It's very interesting that this structure,
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(笑声)
08:24
because of its geometric properties,
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直到大约一百年后,
08:27
was used to build the Aquatics Center
for the Beijing Olympic Games.
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有人发现了更好的结构。
08:32
There, Michael Phelps
won eight gold medals,
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08:35
and became the best swimmer of all time.
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威尔勒和菲兰发现这个小东西——
08:38
Well, until someone better
comes along, right?
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(笑声)——
08:42
As may happen
with the Weaire-€“Phelan structure.
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他们很聪明地将其称之为
08:45
It's the best
until something better shows up.
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「威尔勒-菲兰多面体」。
08:47
But be careful, because this one
really stands a chance
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(笑声)
它看起来很奇怪,但其实并没那么奇怪,
08:52
that in a hundred or so years,
or even if it's in 1700 years,
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自然中可以见到它的身影。
其结构非常有趣,
08:57
that someone proves
it's the best possible shape for the job.
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鉴于它的几何特性,
北京奥运会的水立方场馆的设计
就是采用的该结构。
09:02
It will then become a theorem,
a truth, forever and ever.
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在这个场馆中,
迈克尔•菲利普斯赢得了8枚金牌,
09:07
For longer than any diamond.
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成为史上最佳游泳健将。
09:10
So, if you want to tell someone
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直到有人发现更好的结构,没错吧?
09:15
that you will love them forever
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威尔勒-菲兰多面体可能也无出其右。
09:18
you can give them a diamond.
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在有人发现更好的之前,
它一直会是最佳的结构。
09:20
But if you want to tell them
that you'll love them forever and ever,
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但要注意,很有可能
09:24
give them a theorem!
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在100年左右的时间之内,
甚至是1700年后,
09:26
(Laughter)
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09:27
But hang on a minute!
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09:30
You'll have to prove it,
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有人证明它是最佳的填满空间的结构,
09:32
so your love doesn't remain
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09:34
a conjecture.
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它就会成为定理,永远正确,
09:36
(Applause)
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比钻石还要久远。
所以,如果你想告诉另一位
你会永远爱Ta,
你可以给Ta一颗钻石。
但如果你想告诉Ta你对Ta的爱真正永永远远,
就给他一个定理!
(笑声)
但稍等片刻!
你要证明这个定理,
这样你的爱才不是一个猜想。
(掌声)
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