ABOUT THE SPEAKER
Benoit Mandelbrot - Mathematician
Benoit Mandelbrot's work led the world to a deeper understanding of fractals, a broad and powerful tool in the study of roughness, both in nature and in humanity's works.

Why you should listen

Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they'd been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets -- which make up, let's face it, quite a lot of the world. Mandelbrot coined the term "fractal" to describe these objects, and set about sharing his insight with the world.

The Mandelbrot set (expressed as z² + c) was named in Mandelbrot's honor by Adrien Douady and John H. Hubbard. Its boundary can be magnified infinitely and yet remain magnificently complicated, and its elegant shape made it a poster child for the popular understanding of fractals. Led by Mandelbrot's enthusiastic work, fractal math has brought new insight to the study of pretty much everything, from the behavior of stocks to the distribution of stars in the universe.

Benoit Mandelbrot appeared at the first TED in 1984, and returned in 2010 to give an overview of the study of fractals and the paradigm-flipping insights they've brought to many fields. He died in October 2010 at age 85. Read more about his life on NYBooks.com >>

More profile about the speaker
Benoit Mandelbrot | Speaker | TED.com
TED2010

Benoit Mandelbrot: Fractals and the art of roughness

伯努瓦.曼德勃罗: 分形和粗糙的艺术

Filmed:
1,448,555 views

在TED2010上,数学奇才伯努瓦.曼德勃罗开展了一个早在1984年的TED上他所讨论过的主题——粗糙的极端复杂性,以及分形数学可以从看起来无法认识的复杂图形中找到秩序。
- Mathematician
Benoit Mandelbrot's work led the world to a deeper understanding of fractals, a broad and powerful tool in the study of roughness, both in nature and in humanity's works. Full bio

Double-click the English transcript below to play the video.

00:15
Thank you very much.
0
0
2000
非常感谢。
00:17
Please excuse借口 me for sitting坐在; I'm very old.
1
2000
3000
请原谅我坐着讲; 我很老了。
00:20
(Laughter笑声)
2
5000
2000
(笑声)
00:22
Well, the topic话题 I'm going to discuss讨论
3
7000
2000
我要讨论的主题
00:24
is one which哪一个 is, in a certain某些 sense, very peculiar奇特
4
9000
3000
在某种意义上很古怪,
00:27
because it's very old.
5
12000
2000
因为它很古老。
00:29
Roughness粗糙度 is part部分 of human人的 life
6
14000
3000
粗糙永永远远是
00:32
forever永远 and forever永远,
7
17000
2000
人类生活的一部分。
00:34
and ancient authors作者 have written书面 about it.
8
19000
3000
古代的作者描写过它。
00:37
It was very much uncontrollable不可控,
9
22000
2000
它很不受控制。
00:39
and in a certain某些 sense,
10
24000
2000
在某种意义上,
00:41
it seemed似乎 to be the extreme极端 of complexity复杂,
11
26000
3000
它似乎是极度的复杂,
00:44
just a mess食堂, a mess食堂 and a mess食堂.
12
29000
2000
一片混乱、 乱七八糟。
00:46
There are many许多 different不同 kinds of mess食堂.
13
31000
2000
有许多不同类型的混乱。
00:48
Now, in fact事实,
14
33000
2000
那么,实际上
00:50
by a complete完成 fluke吸虫,
15
35000
2000
完全是出于偶然,
00:52
I got involved参与 many许多 years年份 ago
16
37000
3000
我在许多年前
00:55
in a study研究 of this form形成 of complexity复杂,
17
40000
3000
涉足于这种复杂性的研究。
00:58
and to my utter说出 amazement惊愕,
18
43000
2000
让我非常惊讶的是,
01:00
I found发现 traces痕迹 --
19
45000
2000
我发现了——
01:02
very strong强大 traces痕迹, I must必须 say --
20
47000
2000
很清晰的踪迹,我必须说——
01:04
of order订购 in that roughness粗糙度.
21
49000
3000
粗糙中秩序的踪迹
01:07
And so today今天, I would like to present当下 to you
22
52000
2000
今天,我想向你们展示
01:09
a few少数 examples例子
23
54000
2000
几个
01:11
of what this represents代表.
24
56000
2000
有代表性的例子
01:13
I prefer比较喜欢 the word roughness粗糙度
25
58000
2000
我喜欢“粗糙”这个词
01:15
to the word irregularity不规则
26
60000
2000
而不是“不规则”
01:17
because irregularity不规则 --
27
62000
2000
因为“不规则”——
01:19
to someone有人 who had Latin拉丁
28
64000
2000
对于象我这样
01:21
in my long-past长期以往 youth青年 --
29
66000
2000
年轻时学过拉丁文的人来讲——
01:23
means手段 the contrary相反 of regularity规律性.
30
68000
2000
是“规则”的反义词
01:25
But it is not so.
31
70000
2000
其实并非如此。
01:27
Regularity规律 is the contrary相反 of roughness粗糙度
32
72000
3000
“规则”是“粗糙”的反义词
01:30
because the basic基本 aspect方面 of the world世界
33
75000
2000
因为世界的基本面
01:32
is very rough.
34
77000
2000
是很粗糙的。
01:34
So let me show显示 you a few少数 objects对象.
35
79000
3000
那么让我给你们展示几个东西。
01:37
Some of them are artificial人造.
36
82000
2000
有些是人造的
01:39
Others其他 of them are very real真实, in a certain某些 sense.
37
84000
3000
另外一些在某种意义上讲是非常真实的。
01:42
Now this is the real真实. It's a cauliflower菜花.
38
87000
3000
这个是真实的,这是一个菜花。
01:45
Now why do I show显示 a cauliflower菜花,
39
90000
3000
我为什么展示一个菜花,
01:48
a very ordinary普通 and ancient vegetable蔬菜?
40
93000
3000
一种非常普通和古老的蔬菜?
01:51
Because old and ancient as it may可能 be,
41
96000
3000
因为尽管它很古老,
01:54
it's very complicated复杂 and it's very simple简单,
42
99000
3000
它却是非常复杂的,同时也是
01:57
both at the same相同 time.
43
102000
2000
非常简单的。
01:59
If you try to weigh称重 it -- of course课程 it's very easy简单 to weigh称重 it,
44
104000
3000
如果您想称它的重量,当然称它是非常容易的。
02:02
and when you eat it, the weight重量 matters事项 --
45
107000
3000
当你吃它时,你关心的是重量。
02:05
but suppose假设 you try to
46
110000
3000
但是假设您想
02:08
measure测量 its surface表面.
47
113000
2000
测量它的表面积。
02:10
Well, it's very interesting有趣.
48
115000
2000
那么,非常有意思。
02:12
If you cut, with a sharp尖锐 knife,
49
117000
3000
如果您用一把锋利的刀,
02:15
one of the florets小花 of a cauliflower菜花
50
120000
2000
切下其中一朵花,
02:17
and look at it separately分别,
51
122000
2000
分别观察它,
02:19
you think of a whole整个 cauliflower菜花, but smaller.
52
124000
3000
您会看到一棵整菜花,只是小点儿。
02:22
And then you cut again,
53
127000
2000
您然后再切,
02:24
again, again, again, again, again, again, again, again,
54
129000
3000
再切,再切,再切,….
02:27
and you still get small cauliflowers花椰菜.
55
132000
2000
您得到仍然是小菜花。
02:29
So the experience经验 of humanity人性
56
134000
2000
在人类的经验中
02:31
has always been that there are some shapes形状
57
136000
3000
总是有一些形状
02:34
which哪一个 have this peculiar奇特 property属性,
58
139000
2000
具有奇怪的特性
02:36
that each part部分 is like the whole整个,
59
141000
3000
每个部分就象整体一样
02:39
but smaller.
60
144000
2000
只是更小
02:41
Now, what did humanity人性 do with that?
61
146000
3000
现在人类是否对此做了些什么呢?
02:44
Very, very little.
62
149000
3000
非常非常少。
02:47
(Laughter笑声)
63
152000
3000
(笑声)
02:50
So what I did actually其实 is to
64
155000
3000
我实际上做的就是
02:53
study研究 this problem问题,
65
158000
3000
研究这个问题,
02:56
and I found发现 something quite相当 surprising奇怪.
66
161000
3000
我发现了相当惊奇的事情。
02:59
That one can measure测量 roughness粗糙度
67
164000
3000
我们可以用数字来度量粗糙度
03:02
by a number, a number,
68
167000
3000
用一个数字
03:05
2.3, 1.2 and sometimes有时 much more.
69
170000
3000
2.3,1.2. 有时需要多个数字
03:08
One day, a friend朋友 of mine,
70
173000
2000
一天,我一个朋友
03:10
to bug窃听器 me,
71
175000
2000
来烦我,
03:12
brought a picture图片 and said,
72
177000
2000
他带来了一张图片,说:
03:14
"What is the roughness粗糙度 of this curve曲线?"
73
179000
2000
“这条曲线的粗糙度是多少?”
03:16
I said, "Well, just short of 1.5."
74
181000
3000
我说,“好的,小与1.5。”
03:19
It was 1.48.
75
184000
2000
是1.48。
03:21
Now, it didn't take me any time.
76
186000
2000
这一点也不费事。
03:23
I've been looking at these things for so long.
77
188000
2000
我观察这些事物很长时间了。
03:25
So these numbers数字 are the numbers数字
78
190000
2000
这些数字表示
03:27
which哪一个 denote表示 the roughness粗糙度 of these surfaces.
79
192000
3000
这些表面的粗糙度。
03:30
I hasten to say that these surfaces
80
195000
2000
我急切地说这些表面
03:32
are completely全然 artificial人造.
81
197000
2000
完全是人造的,
03:34
They were doneDONE on a computer电脑,
82
199000
2000
是用计算机产生的。
03:36
and the only input输入 is a number,
83
201000
2000
唯一的输入是一个数字.
03:38
and that number is roughness粗糙度.
84
203000
3000
那个数字就是粗糙度.
03:41
So on the left,
85
206000
2000
在左边
03:43
I took the roughness粗糙度 copied复制 from many许多 landscapes景观.
86
208000
3000
我取的是从许多风景中复制的粗糙度
03:46
To the right, I took a higher更高 roughness粗糙度.
87
211000
3000
在右边,我采取了更高的粗糙度
03:49
So the eye, after a while,
88
214000
2000
过一会儿
03:51
can distinguish区分 these two very well.
89
216000
3000
眼睛就可以很好地区分这两个.
03:54
Humanity人性 had to learn学习 about measuring测量 roughness粗糙度.
90
219000
2000
人类必须了解粗糙度的测量.
03:56
This is very rough, and this is sort分类 of smooth光滑, and this perfectly完美 smooth光滑.
91
221000
3000
这个非常粗糙,这个有点光滑,这个非常光滑。
03:59
Very few少数 things are very smooth光滑.
92
224000
3000
很少东西是很光滑的。
04:03
So then if you try to ask questions问题:
93
228000
3000
所以你如果要问:
04:06
"What's the surface表面 of a cauliflower菜花?"
94
231000
2000
一个菜花的表面积是多少?
04:08
Well, you measure测量 and measure测量 and measure测量.
95
233000
3000
那么,你反复地测量。
04:11
Each time you're closer接近, it gets得到 bigger,
96
236000
3000
测量得越精确,得到的数值就会越大,
04:14
down to very, very small distances距离.
97
239000
2000
直到非常、 非常小的差距。
04:16
What's the length长度 of the coastline海岸线
98
241000
2000
这些湖泊的湖岸线
04:18
of these lakes湖泊?
99
243000
2000
长度是多少?
04:20
The closer接近 you measure测量, the longer it is.
100
245000
3000
你测量得越精确,结果越长。
04:23
The concept概念 of length长度 of coastline海岸线,
101
248000
2000
海岸线长度的概念
04:25
which哪一个 seems似乎 to be so natural自然
102
250000
2000
似乎是那么自然,
04:27
because it's given特定 in many许多 cases,
103
252000
2000
在许多情况下都会用到它,
04:29
is, in fact事实, complete完成 fallacy谬论; there's no such这样 thing.
104
254000
3000
但实际上,是完全错误的。根本没有这种东西。
04:32
You must必须 do it differently不同.
105
257000
3000
你必须换种方式对待它。
04:35
What good is that, to know these things?
106
260000
2000
知道这些事情有什么好处呢?
04:37
Well, surprisingly出奇 enough足够,
107
262000
2000
足以让人吃惊的是,
04:39
it's good in many许多 ways方法.
108
264000
2000
它的好处是多方面的。
04:41
To begin开始 with, artificial人造 landscapes景观,
109
266000
2000
首先,人工景观——
04:43
which哪一个 I invented发明 sort分类 of,
110
268000
2000
我发明的名词——
04:45
are used in cinema电影 all the time.
111
270000
3000
在电影中经常使用。
04:48
We see mountains in the distance距离.
112
273000
2000
我们看远处的群山。
04:50
They may可能 be mountains, but they may可能 be just formulae公式, just cranked手摇 on.
113
275000
3000
他们可能是山,也可能只是个公式,是手摇出来的。
04:53
Now it's very easy简单 to do.
114
278000
2000
现在很容易做。
04:55
It used to be very time-consuming耗时的, but now it's nothing.
115
280000
3000
它曾经是非常耗时的,但现在没有什么。
04:58
Now look at that. That's a real真实 lung.
116
283000
3000
现在看看这个,这是一个真正的肺。
05:01
Now a lung is something very strange奇怪.
117
286000
2000
肺是很奇怪的东西。
05:03
If you take this thing,
118
288000
2000
如果你把它拿在手里,
05:05
you know very well it weighs very little.
119
290000
3000
你就会知道它的重量很小。
05:08
The volume of a lung is very small,
120
293000
2000
肺的体积也很小。
05:10
but what about the area of the lung?
121
295000
3000
但肺的面积呢?
05:13
Anatomists解剖学家 were arguing争论 very much about that.
122
298000
3000
解剖学家们对此争论很大。
05:16
Some say that a normal正常 male's男的 lung
123
301000
3000
有人说一个正常男性的肺
05:19
has an area of the inside
124
304000
2000
其面积相当于一个篮球
05:21
of a basketball篮球 [court法庭].
125
306000
2000
内部的面积。
05:23
And the others其他 say, no, five basketball篮球 [courts法院].
126
308000
3000
有人说,不对,是五个篮球。
05:27
Enormous巨大 disagreements分歧.
127
312000
2000
分歧很大。
05:29
Why so? Because, in fact事实, the area of the lung
128
314000
3000
为何如此?因为实际上肺的面积的定义
05:32
is something very ill-defined不明确.
129
317000
2000
非常含糊不清。
05:35
The bronchi支气管 branch, branch, branch
130
320000
3000
支气管分枝,分枝,分枝。
05:38
and they stop branching分枝,
131
323000
3000
它们停止产生分枝
05:41
not because of any matter of principle原理,
132
326000
3000
不是因为规则的缘故,
05:44
but because of physical物理 considerations注意事项:
133
329000
3000
而是因为物理的考虑——
05:47
the mucus粘液, which哪一个 is in the lung.
134
332000
3000
肺内的粘液。
05:50
So what happens发生 is that in a way
135
335000
2000
假如您有一个很大的肺
05:52
you have a much bigger lung,
136
337000
2000
它的分支产生分支,
05:54
but it branches分支机构 and branches分支机构
137
339000
2000
那将会怎样呢?
05:56
down to distances距离 about the same相同 for a whale, for a man
138
341000
3000
对于鲸鱼、人和小的啮齿目动物来说
05:59
and for a little rodent啮齿动物.
139
344000
2000
没有两个距离大致相同。
06:02
Now, what good is it to have that?
140
347000
3000
那么,这有什么好处呢?
06:05
Well, surprisingly出奇 enough足够, amazingly令人惊讶 enough足够,
141
350000
2000
足以令人吃惊、足以让人称奇的是,
06:07
the anatomists解剖学家 had a very poor较差的 idea理念
142
352000
3000
解剖学家直到最近才对肺的结构
06:10
of the structure结构体 of the lung until直到 very recently最近.
143
355000
3000
有了一些正确的认识
06:13
And I think that my mathematics数学,
144
358000
2000
我认为我的数学,
06:15
surprisingly出奇 enough足够,
145
360000
2000
令人吃惊地
06:17
has been of great help
146
362000
2000
为研究肺病
06:19
to the surgeons外科医生
147
364000
2000
的外科医生
06:21
studying研究 lung illnesses疾病
148
366000
2000
帮了大忙。
06:23
and also kidney illnesses疾病,
149
368000
2000
还有肾病.
06:25
all these branching分枝 systems系统,
150
370000
2000
这些器官都具有分枝系统,
06:27
for which哪一个 there was no geometry几何.
151
372000
3000
但没有几何结构。
06:30
So I found发现 myself, in other words,
152
375000
2000
因此我发现我自己,换句话说,
06:32
constructing建设 a geometry几何,
153
377000
2000
为这种没有几何结构的事物
06:34
a geometry几何 of things which哪一个 had no geometry几何.
154
379000
3000
构造了几何规则。
06:37
And a surprising奇怪 aspect方面 of it
155
382000
2000
并且,一个惊奇的方面是,
06:39
is that very often经常, the rules规则 of this geometry几何
156
384000
3000
这几何规则经常是
06:42
are extremely非常 short.
157
387000
2000
极其简练的。
06:44
You have formulas公式 that long.
158
389000
2000
你的公式只有这么长。
06:46
And you crank曲柄 it several一些 times.
159
391000
2000
你把它迭代多次。
06:48
Sometimes有时 repeatedly反复: again, again, again,
160
393000
2000
有时需要一次一次地重复,
06:50
the same相同 repetition重复.
161
395000
2000
重复同样的运算。
06:52
And at the end结束, you get things like that.
162
397000
2000
最后,你将得到这样的东西。
06:54
This cloud is completely全然,
163
399000
2000
这朵云彩是完全地,
06:56
100 percent百分 artificial人造.
164
401000
3000
100%地人造的。
06:59
Well, 99.9.
165
404000
2000
好吧,99.9%。
07:01
And the only part部分 which哪一个 is natural自然
166
406000
2000
其中唯一自然的部分
07:03
is a number, the roughness粗糙度 of the cloud,
167
408000
2000
是一个数字,云的粗糙度,
07:05
which哪一个 is taken采取 from nature性质.
168
410000
2000
这是取自于自然的。
07:07
Something so complicated复杂 like a cloud,
169
412000
2000
象云这种团状的复杂东西,
07:09
so unstable不稳定, so varying不同,
170
414000
2000
如此不稳定,如此易变,
07:11
should have a simple简单 rule规则 behind背后 it.
171
416000
3000
背后应该有一个简单规则。
07:14
Now this simple简单 rule规则
172
419000
3000
这个简单规则
07:17
is not an explanation说明 of clouds.
173
422000
3000
不是对云的一个解释。
07:20
The seer先见者 of clouds had to
174
425000
2000
云的观察者必须
07:22
take account帐户 of it.
175
427000
2000
把它考虑在内。
07:24
I don't know how much advanced高级
176
429000
3000
我不知道这些图片有多先进,
07:27
these pictures图片 are. They're old.
177
432000
2000
他们是旧的。
07:29
I was very much involved参与 in it,
178
434000
2000
我曾经很投入地研究它们,
07:31
but then turned转身 my attention注意 to other phenomena现象.
179
436000
3000
但后来我的注意力转向了其他现象。
07:34
Now, here is another另一个 thing
180
439000
2000
这是另一件
07:36
which哪一个 is rather interesting有趣.
181
441000
3000
相当有趣的事情
07:39
One of the shattering惊天动地 events事件
182
444000
2000
数学史上的
07:41
in the history历史 of mathematics数学,
183
446000
2000
一次粉碎性事件,
07:43
which哪一个 is not appreciated赞赏 by many许多 people,
184
448000
3000
没有多少人赞赏它,
07:46
occurred发生 about 130 years年份 ago,
185
451000
2000
发生于大约130年前,
07:48
145 years年份 ago.
186
453000
2000
145年前。
07:50
Mathematicians数学家 began开始 to create创建
187
455000
2000
数学家开始创造
07:52
shapes形状 that didn't exist存在.
188
457000
2000
不存在的形状
07:54
Mathematicians数学家 got into self-praise自我表扬
189
459000
3000
数学家们有点沾沾自喜,
07:57
to an extent程度 which哪一个 was absolutely绝对 amazing惊人,
190
462000
2000
甚至在某种程度上喜不自胜,
07:59
that man can invent发明 things
191
464000
2000
因为人类能发明出
08:01
that nature性质 did not know.
192
466000
2000
大自然不知道的事物。
08:03
In particular特定, it could invent发明
193
468000
2000
具体来说,人类可以发明
08:05
things like a curve曲线 which哪一个 fills填充 the plane平面.
194
470000
3000
填装飞机的曲线。
08:08
A curve's曲线的 a curve曲线, a plane's飞机的 a plane平面,
195
473000
2000
曲线是曲线,飞机是飞机,
08:10
and the two won't惯于 mix混合.
196
475000
2000
二者不会混淆
08:12
Well, they do mix混合.
197
477000
2000
哦,他们还真混淆了。
08:14
A man named命名 Peano皮亚诺
198
479000
2000
一个名叫皮诺的人
08:16
did define确定 such这样 curves曲线,
199
481000
2000
定义了这种曲线
08:18
and it became成为 an object目的 of extraordinary非凡 interest利益.
200
483000
3000
它成为了非常有意思的对象。
08:21
It was very important重要, but mostly大多 interesting有趣
201
486000
3000
它非常重要,但更有趣的是
08:24
because a kind of break打破,
202
489000
2000
因为它导致了数学的分裂,
08:26
a separation分割 between之间
203
491000
2000
来自现实的数学
08:28
the mathematics数学 coming未来 from reality现实, on the one hand,
204
493000
3000
和纯粹来自人的头脑的新数学
08:31
and new mathematics数学 coming未来 from pure man's男人的 mind心神.
205
496000
3000
之间的分离。
08:34
Well, I was very sorry to point out
206
499000
3000
那么,我非常抱歉地指出,
08:37
that the pure man's男人的 mind心神
207
502000
2000
纯粹的人脑
08:39
has, in fact事实,
208
504000
2000
实际上
08:41
seen看到 at long last
209
506000
2000
终于看见了
08:43
what had been seen看到 for a long time.
210
508000
2000
一直是随处可见的东西
08:45
And so here I introduce介绍 something,
211
510000
2000
那么在这里我要介绍一下
08:47
the set of rivers河流 of a plane-filling平面填充 curve曲线.
212
512000
3000
一套飞机填装曲线。
08:50
And well,
213
515000
2000
那么,
08:52
it's a story故事 unto itself本身.
214
517000
2000
它本身就是一个故事。
08:54
So it was in 1875 to 1925,
215
519000
3000
那是在1875年至1925年,
08:57
an extraordinary非凡 period
216
522000
2000
一个数学本身
08:59
in which哪一个 mathematics数学 prepared准备 itself本身 to break打破 out from the world世界.
217
524000
3000
准备在世界上爆发的非凡时期。
09:02
And the objects对象 which哪一个 were used
218
527000
2000
那些在数学与
09:04
as examples例子, when I was
219
529000
2000
可见现实分裂时,
09:06
a child儿童 and a student学生, as examples例子
220
531000
2000
那时我还是个孩子和学生,
09:08
of the break打破 between之间 mathematics数学
221
533000
3000
被用作例子
09:11
and visible可见 reality现实 --
222
536000
2000
的事物-
09:13
those objects对象,
223
538000
2000
那些对象,
09:15
I turned转身 them completely全然 around.
224
540000
2000
我完全地拿它们另作他用。
09:17
I used them for describing说明
225
542000
2000
我用它们来描述
09:19
some of the aspects方面 of the complexity复杂 of nature性质.
226
544000
3000
自然复杂性的某些方面。
09:22
Well, a man named命名 Hausdorff豪斯多夫 in 1919
227
547000
3000
那么,1919年,一个名叫豪斯多夫的人
09:25
introduced介绍 a number which哪一个 was just a mathematical数学的 joke玩笑,
228
550000
3000
介绍了一个数字,这个数字简直是一个数学笑话。
09:28
and I found发现 that this number
229
553000
2000
我发现这个数字
09:30
was a good measurement测量 of roughness粗糙度.
230
555000
2000
是一个很好的测量粗糙度的值。
09:32
When I first told it to my friends朋友 in mathematics数学
231
557000
2000
当我首先把它告诉我的数学朋友时
09:34
they said, "Don't be silly愚蠢. It's just something [silly愚蠢]."
232
559000
3000
他们说: “别傻了。 那只是一个数。”
09:37
Well actually其实, I was not silly愚蠢.
233
562000
3000
事实上我不傻。
09:40
The great painter画家 Hokusai北斋 knew知道 it very well.
234
565000
3000
大画家葛饰北斋很了解它。
09:43
The things on the ground地面 are algae藻类.
235
568000
2000
地面上长的是海藻。
09:45
He did not know the mathematics数学; it didn't yet然而 exist存在.
236
570000
3000
他不懂数学;那时还没有数学。
09:48
And he was Japanese日本 who had no contact联系 with the West西.
237
573000
3000
他是日本人,没有接触过西方文化。
09:51
But painting绘画 for a long time had a fractal分形 side.
238
576000
3000
但是他的绘画长期以来就有分数维的一面。
09:54
I could speak说话 of that for a long time.
239
579000
2000
我讲这个可以将很长时间。
09:56
The Eiffel艾菲尔 Tower has a fractal分形 aspect方面.
240
581000
3000
埃佛尔铁塔也有分数维的方面。
09:59
I read the book that Mr先生. Eiffel艾菲尔 wrote about his tower,
241
584000
3000
我读了埃菲尔先生写的关于他这座塔的书。
10:02
and indeed确实 it was astonishing惊人 how much he understood了解.
242
587000
3000
他了解的程度的确使我吃惊。
10:05
This is a mess食堂, mess食堂, mess食堂, Brownian布朗 loop循环.
243
590000
3000
这是一个乱糟糟的布朗环。
10:08
One day I decided决定 --
244
593000
2000
一天,我决定
10:10
halfway through通过 my career事业,
245
595000
2000
在我职业生涯的半途中,
10:12
I was held保持 by so many许多 things in my work --
246
597000
3000
我被工作中太多的事情所缠绕,
10:15
I decided决定 to test测试 myself.
247
600000
3000
我决定考验一下自己。
10:18
Could I just look at something
248
603000
2000
我能否在
10:20
which哪一个 everybody每个人 had been looking at for a long time
249
605000
3000
每个人都很熟悉的事物中
10:23
and find something dramatically显着 new?
250
608000
3000
找到一些戏剧性的新发现呢?
10:26
Well, so I looked看着 at these
251
611000
3000
于是我观察这些
10:29
things called Brownian布朗 motion运动 -- just goes around.
252
614000
3000
被称作布朗运动的现象——只是来回转圈.
10:32
I played发挥 with it for a while,
253
617000
2000
我玩了一会儿之后,
10:34
and I made制作 it return返回 to the origin起源.
254
619000
3000
又把它放回到原处。
10:37
Then I was telling告诉 my assistant助理,
255
622000
2000
然后我对我的助手说:
10:39
"I don't see anything. Can you paint涂料 it?"
256
624000
2000
“我没有看到任何东西。你能画出它来吗?”
10:41
So he painted it, which哪一个 means手段
257
626000
2000
于是他画将它画了出来,这意味着
10:43
he put inside everything. He said:
258
628000
2000
他把一切都装进心里了。他说:
10:45
"Well, this thing came来了 out ..." And I said, "Stop! Stop! Stop!
259
630000
3000
“那么,事情是...” 我说:“停!停!停!
10:48
I see; it's an island."
260
633000
3000
我看到了,这是一个岛。”
10:51
And amazing惊人.
261
636000
2000
太神奇了。
10:53
So Brownian布朗 motion运动, which哪一个 happens发生 to have
262
638000
2000
所以布朗运动,
10:55
a roughness粗糙度 number of two, goes around.
263
640000
3000
碰巧粗糙度为2,就是转圈圈。
10:58
I measured测量 it, 1.33.
264
643000
2000
我测量了它,1.33
11:00
Again, again, again.
265
645000
2000
一次又一次
11:02
Long measurements测量, big Brownian布朗 motions运动,
266
647000
2000
长的测量,大型的布朗运动
11:04
1.33.
267
649000
2000
1.33。
11:06
Mathematical数学的 problem问题: how to prove证明 it?
268
651000
3000
数学问题:怎样证明它?
11:09
It took my friends朋友 20 years年份.
269
654000
3000
这花了我朋友20年的时间。
11:12
Three of them were having incomplete残缺 proofs样张.
270
657000
3000
其中三个人得到了一个不完整的证明。
11:15
They got together一起, and together一起 they had the proof证明.
271
660000
3000
他们不断地聚在一起研究,得到了这个证明。
11:19
So they got the big [Fields字段] medal勋章 in mathematics数学,
272
664000
3000
所以他们获得到了一个数学大奖(菲尔茨奖),
11:22
one of the three medals奖牌 that people have received收到
273
667000
2000
是三大数学奖项之一,
11:24
for proving证明 things which哪一个 I've seen看到
274
669000
3000
用来奖励那些证明了
11:27
without being存在 able能够 to prove证明 them.
275
672000
3000
别人看到了但无法证明的事情的人们。
11:30
Now everybody每个人 asks me at one point or another另一个,
276
675000
3000
大家经常问我,
11:33
"How did it all start开始?
277
678000
2000
“这一切是怎么开始的?
11:35
What got you in that strange奇怪 business商业?"
278
680000
3000
是什么让你做起了这个奇怪的行当?”
11:38
What got you to be,
279
683000
2000
是什么使我
11:40
at the same相同 time, a mechanical机械 engineer工程师,
280
685000
2000
同时成为一名机械工程师、
11:42
a geographer地理学
281
687000
2000
一名地理学家
11:44
and a mathematician数学家 and so on, a physicist物理学家?
282
689000
2000
和一名数学家,等等,还有物理学家?
11:46
Well actually其实 I started开始, oddly奇怪 enough足够,
283
691000
3000
那么,很奇怪的是,我实际上是从
11:49
studying研究 stock股票 market市场 prices价格.
284
694000
2000
研究股市价格开始的
11:51
And so here
285
696000
2000
于是
11:53
I had this theory理论,
286
698000
3000
我提出了这个理论
11:56
and I wrote books图书 about it --
287
701000
2000
并且写了关于它的书,
11:58
financial金融 prices价格 increments增量.
288
703000
2000
金融价格增量。
12:00
To the left you see data数据 over a long period.
289
705000
2000
在左边您看到的是长期数据。
12:02
To the right, on top最佳,
290
707000
2000
在右上角,
12:04
you see a theory理论 which哪一个 is very, very fashionable时髦.
291
709000
3000
您看到是一个非常非常时髦的理论。
12:07
It was very easy简单, and you can write many许多 books图书 very fast快速 about it.
292
712000
3000
它非常容易,您可以很快地写出许多关于它的书。
12:10
(Laughter笑声)
293
715000
2000
(笑声)
12:12
There are thousands数千 of books图书 on that.
294
717000
3000
有数以千计的写它的书。
12:15
Now compare比较 that with real真实 price价钱 increments增量.
295
720000
3000
现在把它与真实的价格增量比较一下。
12:18
Where are real真实 price价钱 increments增量?
296
723000
2000
真实的价格增量在哪里呢?
12:20
Well, these other lines线
297
725000
2000
这些曲线包括了
12:22
include包括 some real真实 price价钱 increments增量
298
727000
2000
真实的价格增量
12:24
and some forgery伪造品 which哪一个 I did.
299
729000
2000
和我的伪造。
12:26
So the idea理念 there was
300
731000
2000
这里的想法是
12:28
that one must必须 be able能够 to -- how do you say? --
301
733000
2000
人必须能 --怎么说呢? –
12:30
model模型 price价钱 variation变异.
302
735000
3000
模拟价格变化。
12:33
And it went really well 50 years年份 ago.
303
738000
3000
50年前这方法运行的很好。
12:36
For 50 years年份, people were sort分类 of pooh-poohing维尼poohing me
304
741000
3000
50年来,人们有点儿看不起我,
12:39
because they could do it much, much easier更轻松.
305
744000
2000
因为他们可以很容易地做到它。
12:41
But I tell you, at this point, people listened听了 to me.
306
746000
3000
但是我告诉您,此时此刻,人们听我的。
12:44
(Laughter笑声)
307
749000
2000
(笑声)
12:46
These two curves曲线 are averages均线:
308
751000
2000
这两条曲线是均线。
12:48
Standard标准 & Poor较差的, the blue蓝色 one;
309
753000
2000
标准普尔,蓝色的那个
12:50
and the red one is Standard标准 & Poor's
310
755000
2000
而红色的一个是
12:52
from which哪一个 the five biggest最大 discontinuities间断
311
757000
3000
去掉不连续性最大的五个股票后的
12:55
are taken采取 out.
312
760000
2000
标准普尔。
12:57
Now discontinuities间断 are a nuisance滋扰,
313
762000
2000
不连续性是有害的。
12:59
so in many许多 studies学习 of prices价格,
314
764000
3000
因此所有价格研究,
13:02
one puts看跌期权 them aside在旁边.
315
767000
2000
人们总是把它们放到一边。
13:04
"Well, acts行为 of God.
316
769000
2000
“哦,不可抗力
13:06
And you have the little nonsense废话 which哪一个 is left.
317
771000
3000
您就没有什么好胡搅蛮缠的了。
13:09
Acts行为 of God." In this picture图片,
318
774000
3000
不可抗力。”在这张图片中,
13:12
five acts行为 of God are as important重要 as everything else其他.
319
777000
3000
五个不可抗力同其它因素是同样重要的。
13:15
In other words,
320
780000
2000
换句话说,
13:17
it is not acts行为 of God that we should put aside在旁边.
321
782000
2000
不可抗力是不应该被放到一边的。
13:19
That is the meat, the problem问题.
322
784000
3000
那才是肉,是问题的所在。
13:22
If you master these, you master price价钱,
323
787000
3000
如果您掌握了这些,您就掌握了价格。
13:25
and if you don't master these, you can master
324
790000
2000
如果您掌握不了这些,
13:27
the little noise噪声 as well as you can,
325
792000
2000
您可以尽量掌握小噪音。
13:29
but it's not important重要.
326
794000
2000
但是这不重要。
13:31
Well, here are the curves曲线 for it.
327
796000
2000
那么,这是它的曲线。
13:33
Now, I get to the final最后 thing, which哪一个 is the set
328
798000
2000
现在,我讲最后一个事情,
13:35
of which哪一个 my name名称 is attached.
329
800000
2000
用我名字命名的一个集合。
13:37
In a way, it's the story故事 of my life.
330
802000
2000
在某种意义上它是我生命的故事。
13:39
My adolescence青春期 was spent花费
331
804000
2000
我的青春期是在
13:41
during the German德语 occupation占用 of France法国.
332
806000
2000
德军占领下的法国度过的。
13:43
Since以来 I thought that I might威力
333
808000
3000
因为我认为我也许会
13:46
vanish消失 within a day or a week,
334
811000
3000
在一天或一个星期之内消失
13:49
I had very big dreams.
335
814000
3000
我过有大的梦想。
13:52
And after the war战争,
336
817000
2000
战争过后,
13:54
I saw an uncle叔叔 again.
337
819000
2000
我又见到我的叔叔。
13:56
My uncle叔叔 was a very prominent突出 mathematician数学家, and he told me,
338
821000
2000
我的叔叔是一位非常著名数学家,他告诉我,
13:58
"Look, there's a problem问题
339
823000
2000
“你看,有一道难题,
14:00
which哪一个 I could not solve解决 25 years年份 ago,
340
825000
2000
我花了25年也没有解决,
14:02
and which哪一个 nobody没有人 can solve解决.
341
827000
2000
别人也没有解决。
14:04
This is a construction施工 of a man named命名 [Gaston加斯顿] Julia朱莉娅
342
829000
2000
这是一个名叫(加斯顿)朱丽叶和
14:06
and [Pierre皮埃尔] Fatou法图.
343
831000
2000
一个名叫(皮埃尔)费托的人提出来的。
14:08
If you could
344
833000
2000
如果你能够
14:10
find something new, anything,
345
835000
2000
有任何新发现
14:12
you will get your career事业 made制作."
346
837000
2000
你将成就你的事业。”
14:14
Very simple简单.
347
839000
2000
非常简单。
14:16
So I looked看着,
348
841000
2000
于是我就看这道题,
14:18
and like the thousands数千 of people that had tried试着 before,
349
843000
2000
象之前做过尝试的成千上万的人一样,
14:20
I found发现 nothing.
350
845000
3000
我什么也没有发现。
14:23
But then the computer电脑 came来了,
351
848000
2000
然后出现了计算机。
14:25
and I decided决定 to apply应用 the computer电脑,
352
850000
2000
我决定研究计算机,
14:27
not to new problems问题 in mathematics数学 --
353
852000
3000
而不是新的数学问题-
14:30
like this wiggle摆动 wiggle摆动, that's a new problem问题 --
354
855000
2000
例如这个“摆动”的问题,这是新问题-
14:32
but to old problems问题.
355
857000
2000
而是建立在旧问题上。
14:34
And I went from what's called
356
859000
2000
我由所谓“实数”开始,
14:36
real真实 numbers数字, which哪一个 are points on a line线,
357
861000
2000
也就是数轴上的点,
14:38
to imaginary假想, complex复杂 numbers数字,
358
863000
2000
到虚的“复数”,
14:40
which哪一个 are points on a plane平面,
359
865000
2000
也就是平面上的点,
14:42
which哪一个 is what one should do there,
360
867000
2000
人们应该在平面上研究。
14:44
and this shape形状 came来了 out.
361
869000
2000
这个形状出来了。
14:46
This shape形状 is of an extraordinary非凡 complication并发症.
362
871000
3000
这个形状异常复杂。
14:49
The equation方程 is hidden there,
363
874000
2000
公式就隐藏在那里,
14:51
z goes into z squared平方, plus c.
364
876000
3000
z等于 z的 平方加c。
14:54
It's so simple简单, so dry.
365
879000
2000
它是那么简单,相当简单。
14:56
It's so uninteresting枯燥.
366
881000
2000
一点意思也没有
14:58
Now you turn the crank曲柄 once一旦, twice两次:
367
883000
3000
现在你把它重复一次、 两次,
15:01
twice两次,
368
886000
3000
两次
15:04
marvels奇迹 come out.
369
889000
2000
奇迹出现了
15:06
I mean this comes out.
370
891000
2000
我是说这个出现了
15:08
I don't want to explain说明 these things.
371
893000
2000
我不想解释这些东西。
15:10
This comes out. This comes out.
372
895000
2000
这个出来了。这个出来了。
15:12
Shapes形状 which哪一个 are of such这样 complication并发症,
373
897000
2000
多么复杂、多么和谐、
15:14
such这样 harmony和谐 and such这样 beauty美女.
374
899000
3000
多么美丽的形状啊。
15:17
This comes out
375
902000
2000
这个出来了,
15:19
repeatedly反复, again, again, again.
376
904000
2000
不断地,一而再,再而三地出来,
15:21
And that was one of my major重大的 discoveries发现,
377
906000
2000
这就是我的一个主要发现
15:23
to find that these islands岛屿 were the same相同
378
908000
2000
我发现这些小岛的形状
15:25
as the whole整个 big thing, more or less.
379
910000
2000
与整体的大形状相同,或多或少
15:27
And then you get these
380
912000
2000
于是你得到这些
15:29
extraordinary非凡 baroque巴洛克 decorations all over the place地点.
381
914000
3000
随处可见的非凡的巴洛克式装饰。
15:32
All that from this little formula,
382
917000
3000
所有这些来自这个
15:35
which哪一个 has whatever随你, five symbols符号 in it.
383
920000
3000
只有五个符号的小小的公式
15:38
And then this one.
384
923000
2000
然后这一个
15:40
The color颜色 was added添加 for two reasons原因.
385
925000
2000
加颜色是由于两个原因
15:42
First of all, because these shapes形状
386
927000
2000
首先,因为这些形状
15:44
are so complicated复杂
387
929000
3000
是如此的复杂,
15:47
that one couldn't不能 make any sense of the numbers数字.
388
932000
3000
以至于人根本意识不到这些数字。
15:50
And if you plot情节 them, you must必须 choose选择 some system系统.
389
935000
3000
如果你想突出它们,您必须选择一些系统
15:53
And so my principle原理 has been
390
938000
2000
所以我的原则是
15:55
to always present当下 the shapes形状
391
940000
3000
总是在展示不同的形状时
15:58
with different不同 colorings色素
392
943000
2000
涂上不同的颜色
16:00
because some colorings色素 emphasize注重 that,
393
945000
2000
因为有些颜色突出这个,
16:02
and others其他 it is that or that.
394
947000
2000
有些颜色突出那个。
16:04
It's so complicated复杂.
395
949000
2000
非常复杂。
16:06
(Laughter笑声)
396
951000
2000
(笑声)
16:08
In 1990, I was in Cambridge剑桥, U.K.
397
953000
2000
1990 年,我在英国的剑桥大学
16:10
to receive接收 a prize from the university大学,
398
955000
3000
接受了一个奖项。
16:13
and three days later后来,
399
958000
2000
三天后,
16:15
a pilot飞行员 was flying飞行 over the landscape景观 and found发现 this thing.
400
960000
3000
一个飞行员在飞行时发现了这个。
16:18
So where did this come from?
401
963000
2000
这是从哪里来的?
16:20
Obviously明显, from extraterrestrials外星人.
402
965000
2000
显然,从外星人那里来的。
16:22
(Laughter笑声)
403
967000
3000
(笑声)
16:25
Well, so the newspaper报纸 in Cambridge剑桥
404
970000
2000
于是剑桥的校报上
16:27
published发表 an article文章 about that "discovery发现"
405
972000
2000
发表一篇有关这一“发现”的文章。
16:29
and received收到 the next下一个 day
406
974000
2000
第二天,
16:31
5,000 letters from people saying,
407
976000
2000
收到了5000封来信,人们说:
16:33
"But that's simply只是 a Mandelbrot曼德尔布罗 set very big."
408
978000
3000
“那只是一个放得很大的曼德尔布罗特图形。”
16:37
Well, let me finish.
409
982000
2000
好吧,让我结束演讲。
16:39
This shape形状 here just came来了
410
984000
2000
这个形状仅仅出自
16:41
out of an exercise行使 in pure mathematics数学.
411
986000
2000
纯数学的一个练习
16:43
Bottomless万丈 wonders奇迹 spring弹簧 from simple简单 rules规则,
412
988000
3000
无边的奇迹源自简单规则的
16:46
which哪一个 are repeated重复 without end结束.
413
991000
3000
无限重复。
16:49
Thank you very much.
414
994000
2000
非常感谢。
16:51
(Applause掌声)
415
996000
11000
(掌声)
Translated by James Dang
Reviewed by Xu (Jessica) Jiang

▲Back to top

ABOUT THE SPEAKER
Benoit Mandelbrot - Mathematician
Benoit Mandelbrot's work led the world to a deeper understanding of fractals, a broad and powerful tool in the study of roughness, both in nature and in humanity's works.

Why you should listen

Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they'd been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets -- which make up, let's face it, quite a lot of the world. Mandelbrot coined the term "fractal" to describe these objects, and set about sharing his insight with the world.

The Mandelbrot set (expressed as z² + c) was named in Mandelbrot's honor by Adrien Douady and John H. Hubbard. Its boundary can be magnified infinitely and yet remain magnificently complicated, and its elegant shape made it a poster child for the popular understanding of fractals. Led by Mandelbrot's enthusiastic work, fractal math has brought new insight to the study of pretty much everything, from the behavior of stocks to the distribution of stars in the universe.

Benoit Mandelbrot appeared at the first TED in 1984, and returned in 2010 to give an overview of the study of fractals and the paradigm-flipping insights they've brought to many fields. He died in October 2010 at age 85. Read more about his life on NYBooks.com >>

More profile about the speaker
Benoit Mandelbrot | Speaker | TED.com