Eduardo Sáenz de Cabezón: Math is forever (with English subtitles) | TED

191,233 views ・ 2015-04-07

TED


請雙擊下方英文字幕播放視頻。

00:00
Translator: Tomás Guarna Reviewer: Sebastian Betti
0
0
7000
譯者: xueling Sun 審譯者: Karen SONG
00:13
Imagine you're in a bar, or a club,
1
13370
5750
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,
2
19120
3010
過了一會,這個問題來了, 「那麼,你是做什麼工作的?」
00:22
"So, what do you do for work?"
3
22130
1870
00:24
And since you think your job is interesting,
4
24015
2935
因為你覺得你的工作很有趣,你說:
00:26
you say, "I'm a mathematician." (Laughter)
5
26950
4280
「我是一個數學家。」 (笑聲)
00:31
And inevitably, during that conversation
6
31690
2390
幾乎沒有例外,在那個談話中,
00:34
one of these two phrases come up:
7
34080
3670
下面兩句話之一會出現:
00:37
A) "I was terrible at math, but it wasn't my fault.
8
37750
3445
A) 「我的數學很差,但那不是我的錯。」
00:41
It's because the teacher was awful." (Laughter)
9
41195
3418
因為我的老師很爛。 (笑聲)
00:44
Or B) "But what is math really for?"
10
44613
2969
或者 B) 「數學到底有什麼用?」
00:47
(Laughter)
11
47582
1028
(笑聲)
00:48
I'll now address Case B.
12
48610
2345
我先來談案例 B)
00:50
(Laughter)
13
50955
1555
(笑聲)
00:52
When someone asks you what math is for, they're not asking you
14
52510
4844
當有人問你數學是什麼, 他們不是問你
有關數學的科學應用。
00:57
about applications of mathematical science.
15
57354
2849
他們是問你,
01:00
They're asking you,
16
60203
1351
01:01
why did I have to study that bullshit I never used in my life again? (Laughter)
17
61554
3931
為什麼我要學習一生 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.
18
65485
2439
01:07
So when mathematicians are asked what math is for,
19
67924
4200
所以,當數學家被問到數學是做什麼的,
它們傾向於分為兩類:
01:12
they tend to fall into two groups:
20
72124
2280
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,
21
74404
5335
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.
22
80609
4950
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.
23
85559
3509
誰是那些採取攻擊姿態的人?
01:29
Who are the ones that attack?
24
89068
2087
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
25
91155
2747
這個問題是沒有意義的,
01:33
this question makes no sense,
26
93902
1947
因為數學有其自身的意義 -
01:35
because mathematics have a meaning all their own --
27
95849
2748
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 --
28
98597
2547
而且不斷尋找
01:41
and that there's no point
29
101144
1867
所有可能的應用是沒有意義的。
01:43
in constantly searching for all possible applications.
30
103011
2547
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?
31
105558
2289
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?
32
107847
3061
01:50
(Laughter)
33
110908
1621
(笑聲)
01:52
Hardy, for instance, was a model of this type of attack.
34
112529
3767
例如,哈迪,就是一個遭受這種攻擊的典型。
那些採防禦姿的態會告訴你,
01:56
And those who stand in defense tell you,
35
116296
1946
“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。”
01:58
"Even if you don't realize it, friend, math is behind everything."
36
118242
4840
(笑聲)
02:03
(Laughter)
37
123082
1258
02:04
Those guys,
38
124340
1878
那些人,
他們總是提到橋樑和電腦。
02:06
they always bring up bridges and computers.
39
126218
4028
“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."
40
130246
2595
02:12
(Laughter)
41
132841
1445
(笑聲)
02:14
It's true, computers are all about math.
42
134286
3237
這是真的,電腦跟數學密切相關。
02:17
And now these guys have also started saying
43
137523
2485
而現在這些人也開始說,
02:20
that behind information security and credit cards are prime numbers.
44
140013
5037
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.
45
145710
3669
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.
46
149379
2165
02:31
Okay, but who's right then?
47
151544
1840
好了,但到底誰是對的呢?
02:33
Those who say that math doesn't need to have a purpose,
48
153384
2606
是那些說數學並不需要有一個目的,
02:35
or those who say that math is behind everything we do?
49
155990
2859
還是那些說數學在我們所做的一切中?
02:38
Actually, both are right.
50
158849
1671
其實上,雙方都是是正確的。
02:40
But remember I told you
51
160520
1663
但請記住我告訴你的
02:42
I belong to that strange 0.8 percent claiming something else?
52
162183
3543
我屬於那奇怪自稱別的0.8%嗎?
02:45
So, go ahead, ask me what math is for.
53
165726
3203
因此,再問我一次數學是做什麼的。
02:48
Audience: What is math for?
54
168929
2929
觀眾:數學是做什麼的?
02:51
Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question,
55
171858
4815
好吧,你們中76.34%的人問了這個問題,
02:56
23.41 percent didn't say anything,
56
176673
2927
23.41%的人什麼也沒有說,
02:59
and the 0.8 percent --
57
179600
1227
03:00
I'm not sure what those guys are doing.
58
180827
2848
和剩下的0.8% ,
我不知道那些人在做什麼。
03:03
Well, to my dear 76.31 percent --
59
183675
3500
好吧,我那親愛的76.31%的觀眾,
03:07
it's true that math doesn't need to serve a purpose,
60
187175
4640
數學真的不需要有一個目的,
03:11
it's true that it's a beautiful structure, a logical one,
61
191815
2870
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
62
194685
2852
而這也可能是人類在歷史上
03:17
ever achieved in human history.
63
197537
2096
集體努力實現的成就之一。
03:19
But it's also true that there,
64
199633
2099
但這也是真的:
03:21
where scientists and technicians are looking for mathematical theories
65
201732
4599
當科學家和技術人員在尋找
03:26
that allow them to advance,
66
206331
2310
使他們能進步的數學理論時,
03:28
they're within the structure of math, which permeates everything.
67
208641
3797
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,
68
212438
3147
03:35
to see what's behind science.
69
215585
1723
才能明白科學。
03:37
Science operates on intuition, creativity.
70
217308
3550
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.
71
221348
3424
03:45
Almost everyone who hasn't heard this before
72
225747
2190
幾乎每個沒有聽說過
03:47
is surprised when they hear that if you take
73
227937
2710
這個之前會覺得驚訝。當他們聽到如果你拿個
03:50
a 0.1 millimeter thick sheet of paper, the size we normally use,
74
230647
4540
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,
75
235187
3318
03:58
its thickness would extend almost the distance from the Earth to the sun.
76
238505
5700
它的厚度幾乎可以從地球延伸到太陽。
04:04
Your intuition tells you it's impossible.
77
244600
2601
你的直覺告訴你這是不可能的。
04:07
Do the math and you'll see it's right.
78
247201
2421
但數學告訴你它是正確的。
04:09
That's what math is for.
79
249622
2513
這就是數學的作用了。
04:12
It's true that science, all types of science, only makes sense
80
252135
3782
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.
81
255917
3371
因為它使我們更好地理解 我們生活的這個美麗的世界。
04:19
And in doing that,
82
259288
1381
而這樣做,
04:20
it helps us avoid the pitfalls of this painful world we live in.
83
260669
3510
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。
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.
84
264179
3478
04:27
Oncological science, for example.
85
267657
1756
例如,腫瘤學。
04:29
And there are others we look at from afar, with envy sometimes,
86
269413
3491
而且還有其他我們有時 帶著羨慕眼光從遠方觀看的科學,
04:32
but knowing that we are what supports them.
87
272904
2560
但我們知道,我們是支持它們的。
04:35
All the basic sciences support them,
88
275464
2749
所有的基礎科學都支持它們,
04:38
including math.
89
278213
2436
包括數學。
04:40
All that makes science, science is the rigor of math.
90
280649
3717
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.
91
284366
4876
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
92
289242
2515
你可能在某些時候說過,或被告知,
04:51
that diamonds are forever, right?
93
291757
2951
鑽石是永恆的,對不對?
04:56
That depends on your definition of forever!
94
296178
2214
這取決於你對永恆的定義!
04:58
A theorem -- that really is forever.
95
298392
2491
一個數學定理真的是永恆的。
05:00
(Laughter)
96
300883
1251
(笑聲)
05:02
The Pythagorean theorem is still true
97
302134
3352
即使畢達哥拉斯死了,
05:05
even though Pythagoras is dead, I assure you it's true. (Laughter)
98
305486
3115
畢氏定理仍然是正確的,我保證。(笑聲)
05:08
Even if the world collapsed
99
308601
1345
05:09
the Pythagorean theorem would still be true.
100
309946
2445
即使世界坍塌
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
05:12
Wherever any two triangle sides and a good hypotenuse get together
101
312391
4061
05:16
(Laughter)
102
316452
1221
(笑聲)
05:17
the Pythagorean theorem goes all out. It works like crazy.
103
317673
2861
畢氏定理就能用。 它真是太有用了。
05:20
(Applause)
104
320534
2821
(掌聲)
05:27
Well, we mathematicians devote ourselves to come up with theorems.
105
327535
3872
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.
106
331407
1736
05:33
But it isn't always easy to know the difference between
107
333143
2766
但並不總是容易知道
05:35
an eternal truth, or theorem, and a mere conjecture.
108
335909
2906
它是一個永恆的真理, 或定理,或是單純的猜想。
05:38
You need proof.
109
338815
3014
你需要證明。
05:41
For example,
110
341829
1767
例如,
05:43
let's say I have a big, enormous, infinite field.
111
343596
4827
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.
112
348423
3709
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?
113
352132
2124
05:54
I could use triangles. Not circles, those leave little gaps.
114
354256
3966
我可以用三角形。但不能用圓形, 因為那會留下小缺口。
05:58
Which is the best shape to use?
115
358777
2357
用那個形狀是最好的?
06:01
One that covers the same surface, but has a smaller border.
116
361134
4553
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,
117
365687
4709
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.
118
370396
1847
06:12
But he didn't prove it.
119
372243
1747
但他並沒有證明它。
06:13
The guy said, "Hexagons, great! Let's go with hexagons!"
120
373990
2698
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.
121
376688
2968
他沒有提供證明,所以它仍然只是一個猜想。
06:19
"Hexagons!"
122
379656
1678
“六邊形”!
06:21
And the world, as you know, split into Pappists and anti-Pappists,
123
381334
3630
而這世界,你也知道, 分成帕普斯幫和反帕普斯幫,
06:24
until 1700 years later
124
384964
5289
直到1700年後
06:30
when in 1999, Thomas Hales proved
125
390253
5454
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.
126
395707
4934
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,
127
400641
2482
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,
128
403123
2060
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)
129
405183
3041
06:48
But what happens if we go to three dimensions?
130
408229
2804
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,
131
411033
3911
如果我想以相同的物件填補空間,
不留空隙,
06:55
without leaving any gaps,
132
415464
1341
06:56
I can use cubes, right?
133
416805
1833
我可以使用立方體,對不對?
06:58
Not spheres, those leave little gaps. (Laughter)
134
418638
3356
不能用球體,那會留下小缺口。(笑聲)
07:01
What is the best shape to use?
135
421994
2963
什麼形狀是最好的?
07:04
Lord Kelvin, of the famous Kelvin degrees and all,
136
424957
4060
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
137
429607
5514
說,最好使用截角八面體
07:16
which, as you all know --
138
436791
2716
因為,因為大家都知道
07:19
(Laughter) --
139
439507
1528
(笑聲)
07:21
is this thing here!
140
441035
1779
就是這個東西!
07:22
(Applause)
141
442814
2939
(掌聲)
07:27
Come on.
142
447778
1447
拜託。
07:30
Who doesn't have a truncated octahedron at home? (Laughter)
143
450025
2837
誰家沒有截角八面體? (笑聲)
07:32
Even a plastic one.
144
452862
1227
即使是塑膠的。
07:34
"Honey, get the truncated octahedron, we're having guests."
145
454089
2757
“親愛的,去拿截角八面體,我們有客人來了。“
07:36
Everybody has one! (Laughter)
146
456846
1394
每個人都有!(笑聲)
07:38
But Kelvin didn't prove it.
147
458240
2374
但克爾文並沒有證明它。
07:40
It remained a conjecture -- Kelvin's conjecture.
148
460614
4041
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
149
464655
5522
而這世界,你也知道, 分成克爾文幫和反克爾文幫,
07:50
(Laughter)
150
470177
1422
(笑聲)
07:51
until a hundred or so years later,
151
471599
3897
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.
152
478203
3869
08:02
Weaire and Phelan found this little thing over here --
153
482917
5109
Weaire和Phelan發現了這個小東西 -
(笑聲)
08:08
(Laughter) --
154
488026
1639
08:09
this structure to which they gave the very clever name
155
489665
3544
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."
156
493209
2166
就是“Weaire - Phelan的結構”。
(笑聲)
08:15
(Laughter)
157
495375
2536
08:17
It looks like a strange object, but it isn't so strange,
158
497911
2657
它看起來像一個奇怪的物體, 但它不是那麼的陌生,
08:20
it also exists in nature.
159
500568
1671
因為它也存在於自然界。
08:22
It's very interesting that this structure,
160
502239
2605
這種結構是非常有趣的,
08:24
because of its geometric properties,
161
504844
2193
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.
162
507037
5192
08:32
There, Michael Phelps won eight gold medals,
163
512969
2745
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.
164
515714
3161
並成為有史以來最好的游泳運動員。
08:38
Well, until someone better comes along, right?
165
518875
3741
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.
166
522616
2399
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.
167
525015
2618
08:47
But be careful, because this one really stands a chance
168
527633
4592
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,
169
532225
4980
在100年左右,或者是在1700年後,
08:57
that someone proves it's the best possible shape for the job.
170
537205
5398
有人會證明這是最好的結構。
09:02
It will then become a theorem, a truth, forever and ever.
171
542978
4370
然後,它會成為一個定理,一個真理,直到永遠。
09:07
For longer than any diamond.
172
547348
2954
比鑽石活得更久。
09:10
So, if you want to tell someone
173
550837
3730
所以,如果你想告訴別人
09:15
that you will love them forever
174
555777
3046
你會永遠愛他們,
09:18
you can give them a diamond.
175
558823
2067
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,
176
560890
3531
但是,如果你要告訴他們, 你一定會永永遠遠的喜歡他們,
09:24
give them a theorem!
177
564421
1751
給他們一個定理!
09:26
(Laughter)
178
566172
1091
(笑聲)
09:27
But hang on a minute!
179
567263
2590
等一下!
09:30
You'll have to prove it,
180
570783
1400
你必須要證明它,
09:32
so your love doesn't remain
181
572183
2283
讓你的愛不只是
09:34
a conjecture.
182
574466
1833
一個猜想。
09:36
(Applause)
183
576299
3244
(掌聲)
關於本網站

本網站將向您介紹對學習英語有用的 YouTube 視頻。 您將看到來自世界各地的一流教師教授的英語課程。 雙擊每個視頻頁面上顯示的英文字幕,從那裡播放視頻。 字幕與視頻播放同步滾動。 如果您有任何意見或要求,請使用此聯繫表與我們聯繫。

https://forms.gle/WvT1wiN1qDtmnspy7