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1、www.XiYuS锡育软件Thank you very much.非常感谢。00:12Please excuse me for sitting;Im very old.请原谅我坐着讲;我很老了。00:14(Laughter)Well,the topic Im going to discuss is one which isin a certain sense very peculiar because its very old.(笑声)我要讨论的主题 在某种意义上很古怪,因为它很古老。00:17Roughness is part of human life forever and foreve
2、r.粗糙永永远远是 人类生活的一部分。00:26And ancient authors have written about it.古代的作者描写过它。00:31It was very much uncontrollable.它很不受控制。00:34And in a certain sense,it seemed to be the extreme ofcomplexity,just a mess,a mess and a mess.在某种意义上,它似乎是极度的复杂,一片混乱、乱七八糟。00:36There are many different kinds of mess.有许多不同类型的混乱
3、。00:43Now,in fact,by a complete fluke,I got involved many yearsago in a study of this form of complexity.那么,实际上 完全是出于偶然,我在许多年前 涉足于这种复杂性的研究。00:45And to my utter amazement,I found traces-very strongtraces,I must say-of order in that roughness.让我非常惊讶的是,我发现了 很清晰的踪迹,我必须说 粗糙中秩序的踪迹00:55And so today,I would
4、 like to present to you a few examplesof what this represents.今天,我想向你们展示 几个 有代表性的例子01:04peculiar:adj.特殊的；独特的；奇怪的；罕见的/n.特权；特有财产 Roughness:n.粗糙(度);粗暴;猛烈;篷乱毛发;未加工uncontrollable:adj.无法控制的;无法管束的;难以驾驭的 fluke:n.侥幸;锚爪;意外的挫折/vt.侥幸成功;意外受挫/vi.侥幸成功amazement:n.惊异;惊愕I prefer the word roughness to the word irregul
5、arity becauseirregularity-to someone who had Latin in my long-pastyouth-means the contrary of regularity.我喜欢“粗糙”这个词 而不是“不规则”因为“不规则”对于象我这样 年轻时学过拉丁文的人来讲 是“规则”的反义词01:10But it is not so.其实并非如此。01:22Regularity is the contrary of roughness because the basicaspect of the world is very rough.“规则”是“粗糙”的反义词 因
6、为世界的基本面是很粗糙的。01:24So let me show you a few objects.那么让我给你们展示几个东西。01:31Some of them are artificial.有些是人造的01:34Others of them are very real,in a certain sense.另外一些在某种意义上讲是非常真实的。01:36Now this is the real.Its a cauliflower.这个是真实的,这是一个菜花。01:39Now why do I show a cauliflower,a very ordinary and ancientveg
7、etable?我为什么展示一个菜花,一种非常普通和古老的蔬菜？01:42Because old and ancient as it may be,its very complicatedand its very simple both at the same time.因为尽管它很古老,它却是非常复杂的,同时也是非常简单的。01:48If you try to weigh it,of course its very easy to weigh it.如果您想称它的重量,当然称它是非常容易的。01:56And when you eat it,the weight matters.当你吃它时,你关
8、心的是重量。01:59But suppose you try to measure its surface.但是假设您想 测量它的表面积。02:02irregularity:n.不规则;无规律;不整齐 regularity:n.规则性;整齐;正规;匀称 cauliflower:n.花椰菜,菜花Well,its very interesting.那么,非常有意思。02:07If you cut,with a sharp knife,one of the florets of acauliflower and look at it separately,you think of a wholeca
9、uliflower,but smaller.如果您用一把锋利的刀,切下其中一朵花,分别观察它,您会看到一棵整菜花,只是小点儿。02:09And then you cut again,again,again,again,again,again,again,again,again.您然后再切,再切,再切,再切,.02:19And you still get small cauliflowers.您得到仍然是小菜花。02:24So the experience of humanity has always been that there aresome shapes which have this
10、peculiar property,that eachpart is like the whole,but smaller.在人类的经验中 总是有一些形状 具有奇怪的特性每个部分就象整体一样 只是更小02:26Now,what did humanity do with that?现在人类是否对此做了些什么呢？02:38Very,very little.非常非常少。02:41(Laughter)So what I did actually is to study this problem,and I found something quite surprising.(笑声)我实际上做的就是 研究
11、这个问题,我发现了相当惊奇的事情。02:44That one can measure roughness by a number,a number,2.3,1.2 and sometimes much more.我们可以用数字来度量粗糙度 用一个数字 2.3,1.2.有时需要多个数字02:56TED演讲者：Benoit Mandelbrot|伯努瓦.曼德勃罗演讲标题：Benoit Mandelbrot:Fractals and the art of roughness|分形和粗糙的艺术内容概要：Benoit Mandelbrot.s work led the world to a deeper
12、 understanding of fractals,abroad and powerful tool in the study of roughness,both in nature and in humanity.s works.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。One day,a friend of mine,to bug me,brought a picture,andsaid,What is the roughness of this curve?一天,
13、我一个朋友 来烦我,他带来了一张图片,说:“这条曲线的粗糙度是多少？”03:05florets:n.小花;绢丝(等于florette);菜茎 separately:adv.分别地;分离地;个别地 cauliflowers:n.花椰菜;白菜花(cauliflower的复数形式)I said,Well,just short of 1.5.我说,“好的,小与1.5。”03:13It was 1.48.是1.48。03:16Now,it didnt take any time.这一点也不费事。03:18Ive been looking at these things for so long.我观察这些
14、事物很长时间了。03:20So these numbers are the numbers which denote theroughness of these surfaces.这些数字表示 这些表面的粗糙度。03:22I hasten to say that these surfaces are completely artificial.我急切地说这些表面 完全是人造的,03:27They were done on a computer.是用计算机产生的。03:31And the only input is a number.唯一的输入是一个数字.03:33And that number
15、 is roughness.那个数字就是粗糙度.03:35And so on the left,I took the roughness copied from manylandscapes.在左边 我取的是从许多风景中复制的粗糙度03:38To the right,I took a higher roughness.在右边,我采取了更高的粗糙度03:43So the eye,after a while,can distinguish these two very well.过一会儿 眼睛就可以很好地区分这两个.03:46Humanity had to learn about measurin
16、g roughness.人类必须了解粗糙度的测量.03:51This is very rough,and this is sort of smooth,and thisperfectly smooth.这个非常粗糙,这个有点光滑,这个非常光滑。03:53denote:vt.表示,指示 surfaces:n.表面;曲面(surface的复数)/v.使成平面(surface的第三人称单数形式)hasten:vt.加速;使赶紧;催促/vi.赶快;急忙 landscapes:n.风景;风景地貌(landscape的复数)/v.从事庭园设计;美化(landscape的三单形式)distinguish:v
17、t.区分；辨别；使杰出，使表现突出/vi.区别，区分；辨别Very few things are very smooth.很少东西是很光滑的。03:56So then if you try to ask questions:whats the surface of acauliflower?所以你如果要问:一个菜花的表面积是多少？04:00Well,you measure and measure and measure.那么,你反复地测量。04:05Each time youre closer it gets bigger,down to very,verysmall distances.测量
18、得越精确,得到的数值就会越大,直到非常、非常小的差距。04:08www.XiYuS锡育软件Whats the length of the coastline of these lakes?这些湖泊的湖岸线 长度是多少？04:13The closer you measure,the longer it is.你测量得越精确,结果越长。04:17The concept of length of coastline,which seems to be sonatural because its given in many cases,is,in fact,completely fallacy;the
19、res no such thing.海岸线长度的概念 似乎是那么自然,在许多情况下都会用到它,但实际上,是完全错误的。根本没有这种东西。04:20You must do it differently.你必须换种方式对待它。04:29What good is that,to know these things?知道这些事情有什么好处呢？04:32Well,surprisingly enough,its good in many ways.足以让人吃惊的是,它的好处是多方面的。04:34To begin with,artificial landscapes,which I invented sor
20、t of,are used in cinema all the time.首先,人工景观 我发明的名词 在电影中经常使用。04:38We see mountains in the distance.我们看远处的群山。04:45They may be mountains,but they may be just formulae,justcranked on.他们可能是山,也可能只是个公式,是手摇出来的。04:47coastline:n.海岸线 begin with:以开始;开始于 in the distance:在远处 cranked:adj.有曲柄的,弯曲的/v.转动曲柄;使成曲柄状;曲折行
21、进(crank的过去分词)Now its very easy to do.现在很容易做。04:50It used to be very time consuming,but now its nothing.它曾经是非常耗时的,但现在没有什么。04:52Now look at that.Thats a real lung.现在看看这个,这是一个真正的肺。04:55Now a lung is something very strange.肺是很奇怪的东西。04:58If you take this thing,you know very well it weighs very little.如果你
22、把它拿在手里,你就会知道它的重量很小。05:00The volume of a lung is very small.肺的体积也很小。05:05But what about the area of the lung?但肺的面积呢？05:07Anatomists were arguing very much about that.解剖学家们对此争论很大。05:10Some say that a normal males lung has an area of the insideof a basketball court.有人说一个正常男性的肺 其面积相当于一个篮球内部的面积。05:13And
23、the others say,no,five basketball courts.有人说,不对,是五个篮球。05:20Enormous disagreements.分歧很大。05:24Why so?Because,in fact,the area of the lung is somethingvery ill-defined.为何如此？因为实际上肺的面积的定义 非常含糊不清。05:26The bronchi branch,branch,branch.支气管分枝,分枝,分枝。05:32And they stop branching,not because of any matter ofpri
24、nciple,but because of physical considerations,themucus,which is in the lung.它们停止产生分枝 不是因为规则的缘故,而是因为物理的考虑 肺内的粘液。05:35consuming:adj.消费的;强烈的/v.消耗(consume的ing形式)Anatomists:n.解剖学家;剖析者 ill-defined:adj.不清楚的;不明确的 bronchi:n.细支气管(bronchus的复数)branching:adj.发枝的;分歧的/n.分支;分歧/v.分支(branch的ing形式)considerations:n.考虑;
25、注意事项(consideration的复数形式);体贴 mucus:n.粘液;黏液So what happens is that its the way you have a much biggerlung,but if it branches and branches,down to distancesabout the same for a whale,for a man and for a little rodent.假如您有一个很大的肺 它的分支产生分支,那将会怎样呢？对于鲸鱼、人和小的啮齿目动物来说 没有两个距离大致相同。05:47Now,what good is it to hav
26、e that?那么,这有什么好处呢？05:59Well,surprisingly enough,amazingly enough,the anatomistshad a very poor idea of the structure of the lung until veryrecently.足以令人吃惊、足以让人称奇的是,解剖学家直到最近才对肺的结构 有了一些正确的认识06:02And I think that my mathematics,surprisingly enough,hasbeen of great help to the surgeons studying lung ill
27、nessesand also kidney illnesses,all these branching systems,forwhich there was no geometry.我认为我的数学,令人吃惊地 为研究肺病 的外科医生 帮了大忙。还有肾病.这些器官都具有分枝系统,但没有几何结构。06:10So I found myself,in other words,constructing a geometry,ageometry of things which had no geometry.因此我发现我自己,换句话说,为这种没有几何结构的事物 构造了几何规则。06:27And a sur
28、prising aspect of it is that very often,the rules ofthis geometry are extremely short.并且,一个惊奇的方面是,这几何规则经常是 极其简练的。06:34You have formulas that long.你的公式只有这么长。06:41And you crank it several times.你把它迭代多次。06:43rodent:adj.啮齿类的;咬的,嚼的;侵蚀性的/n.脊椎啮齿动物 surgeons:外科医生 kidney:n.解剖肾脏;腰子;个性geometry:n.几何学/几何结构 constr
29、ucting:n.构造/v.构造(construct的现在分词)formulas:n.数公式;配方;规则(formula的复数)crank:n.曲柄;奇想/adj.易怒的/vt.装曲柄Sometimes repeatedly,again,again,again.有时需要一次一次地重复,06:45The same repetition.重复同样的运算。06:47And at the end you get things like that.最后,你将得到这样的东西。06:49This cloud is completely,100 percent artificial.这朵云彩是完全地,100%
30、地人造的。06:51Well,99.9.好吧,99.9%。06:56And the only part which is natural is a number,the roughnessof the cloud,which is taken from nature.其中唯一自然的部分 是一个数字,云的粗糙度,这是取自于自然的。06:58Something so complicated like a cloud,so unstable,sovarying,should have a simple rule behind it.象云这种团状的复杂东西,如此不稳定,如此易变,背后应该有一个简单规则
31、。07:04Now this simple rule is not an explanation of clouds.这个简单规则 不是对云的一个解释。07:11The seer of clouds had to take account of it.云的观察者必须 把它考虑在内。07:17I dont know how much advanced these pictures are,theyreold.我不知道这些图片有多先进,他们是旧的。07:21I was very much involved in it,but then turned my attentionto other phe
32、nomena.我曾经很投入地研究它们,但后来我的注意力转向了其他现象。07:26Now,here is another thing which is rather interesting.这是另一件 相当有趣的事情07:31One of the shattering events in the history of mathematics,which is not appreciated by many people,occurred about130 years ago,145 years ago.数学史上的 一次粉碎性事件,没有多少人赞赏它,发生于大约130年前,145年前。07:36va
33、rying:adj.不同的;变化的/v.变化,改变(vary的现在分词)seer:n.预言家;幻想家;先知者 take account of:考虑到;顾及;体谅shattering:adj.破碎的;令人震惊的;令人极度疲劳的/v.打碎;削弱;使震惊(shatter的ing形式)/n.破碎;震裂;脱落现象;粉碎理论Mathematicians began to create shapes that didnt exist.数学家开始创造 不存在的形状07:47Mathematicians got into self-praise to an extent which wasabsolutely
34、amazing that man can invent things that naturedid not know.数学家们有点沾沾自喜,甚至在某种程度上喜不自胜,因为人类能发明出 大自然不知道的事物。07:51In particular,it could invent things like a curve which fills theplane.具体来说,人类可以发明 填装飞机的曲线。08:00A curves a curve,a planes a plane,and the two wont mix.曲线是曲线,飞机是飞机,二者不会混淆08:05Well they do mix.哦,
35、他们还真混淆了。08:09A man named Peano did define such curves,and it becamean object of extraordinary interest.一个名叫皮诺的人 定义了这种曲线 它成为了非常有意思的对象。08:11It was very important,but mostly interesting because a kindof break,a separation between the mathematics comingfrom reality on the one hand and new mathematics co
36、mingfrom pure mans mind.它非常重要,但更有趣的是 因为它导致了数学的分裂,来自现实的数学 和纯粹来自人的头脑的新数学之间的分离。08:18Well,I was very sorry to point out that the pure mans mind那么,我非常抱歉地指出,纯粹的人脑 实际上 终于看见了 一直是随处可见的东西08:31Well,I was very sorry to point out that the pure mans mindhas,in fact,seen at long last what had been seen for a longt
37、ime.看见了 一直是随处可见的东西08:31And so here I introduce something,the set of rivers of aplane-filling curve.那么在这里我要介绍一下 一套飞机填装曲线。08:42Mathematicians:n.数数学家(mathematician的复数形式)In particular:尤其,特别 curves:n.数曲线;弯曲状(curve的复数形式)/v.弯曲;使弯曲(curve的第三人称单数)on the one hand:一方面 point out:指出,指明And well,its a story unto it
38、self.那么,它本身就是一个故事。08:47So it was in 1875 to 1925,an extraordinary period in whichmathematics prepared itself to break out from the world.那是在1875年至1925年,一个数学本身 准备在世界上爆发的非凡时期。08:51And the objects which were used as examples,when I was achild and a student,of the break between mathematics andvisible re
39、ality-those objects,那些在数学与 可见现实分裂时,那时我还是个孩子和学生,被用作例子 的事物-那些对象,08:59I turned them completely around.我完全地拿它们另作他用。09:12I used them for describing some of the aspects of thecomplexity of nature.我用它们来描述 自然复杂性的某些方面。09:14Well,a man named Hausdorff in 1919 introduced a numberwhich was just a mathematical jo
40、ke.那么,1919年,一个名叫豪斯多夫的人 介绍了一个数字,这个数字简直是一个数学笑话。09:19And I found that this number was a good measurement ofroughness.我发现这个数字 是一个很好的测量粗糙度的值。09:25When I first told it to my friends in mathematics they said,Dont be silly.Its just something silly.当我首先把它告诉我的数学朋友时 他们说:“别傻了。那只是一个数。”09:29Well actually,I was no
41、t silly.事实上我不傻。09:34The great painter Hokusai knew it very well.大画家葛饰北斋很了解它。09:37The things on the ground are algae.地面上长的是海藻。09:40unto:prep.到,直到;向(等于to)break out:v.爆发;突发 describing:v.描述;表示(describe的ing形式)/adj.描述的 aspects:n.方面;相位;面貌(aspect的复数)algae:n.植藻类;植海藻He did not know the mathematics;it didnt ye
42、t exist.他不懂数学;那时还没有数学。09:42And he was Japanese who had no contact with the West.他是日本人,没有接触过西方文化。09:45But painting for a long time had a fractal side.但是他的绘画长期以来就有分数维的一面。09:48I could speak of that for a long time.我讲这个可以将很长时间。09:51The Eiffel Tower has a fractal aspect.埃佛尔铁塔也有分数维的方面。09:53And I read the
43、book that Mr.Eiffel wrote about his tower.我读了埃菲尔先生写的关于他这座塔的书。09:56And indeed it was astonishing how much he understood.他了解的程度的确使我吃惊。09:59This is a mess,mess,mess,Brownian loop.这是一个乱糟糟的布朗环。10:02One day I decided that halfway through my career,I was heldby so many things in my work,I decided to test m
44、yself.一天,我决定 在我职业生涯的半途中,我被工作中太多的事情所缠绕,我决定考验一下自己。10:05Could I just look at something which everybody had beenlooking at for a long time and find something dramaticallynew?我能否在 每个人都很熟悉的事物中 找到一些戏剧性的新发现呢？10:15Well,so I looked at these things called Brownian motion-just goes around.于是我观察这些 被称作布朗运动的现象只是来回
45、转圈.10:23I played with it for a while,and I made it return to the origin.我玩了一会儿之后,又把它放回到原处。10:29Then I was telling my assistant,I dont see anything.Can youpaint it?然后我对我的助手说:“我没有看到任何东西。你能画出它来吗？”10:34fractal:n.不规则碎片形So he painted it,which means he put inside everything.Hesaid:Well,this thing came out.
46、And I said,Stop!Stop!Stop!于是他画将它画了出来,这意味着 他把一切都装进心里了。他说:“那么,事情是.”我说:“停！停！停！10:38I see,its an island.我看到了,这是一个岛。”10:45And amazing.太神奇了。10:48So Brownian motion,which happens to have a roughnessnumber of two,goes around.所以布朗运动,碰巧粗糙度为2,就是转圈圈。10:50I measured it,1.33.我测量了它,1.3310:55Again,again,again.一次又一次
47、10:57Long measurements,big Brownian motions,1.33.长的测量,大型的布朗运动 1.33。10:59Mathematical problem:how to prove it?数学问题:怎样证明它？11:03It took my friends 20 years.这花了我朋友20年的时间。11:06Three of them were having incomplete proofs.其中三个人得到了一个不完整的证明。11:09They got together,and together they had the proof.他们不断地聚在一起研究,得
48、到了这个证明。11:12So they got the big Fields medal in mathematics,one of the所以他们获得到了一个数学大奖（菲尔茨奖）,是三大数学奖项之一,用来奖励那些证明了 别人看到So they got the big Fields medal in mathematics,one of thethree medals that people have received for proving thingswhich Ive seen without being able to prove them.三大数学奖项之一,用来奖励那些证明了 别人看
49、到了但无法证明的事情的人们。11:16Now everybody asks me at one point or another,How did itall start?大家经常问我,“这一切是怎么开始的？11:27What got you in that strange business?是什么让你做起了这个奇怪的行当？”11:32measurements:n.测量值,尺寸(measurement的复数)medals:n.劳经奖章;勋章(medal的复数)/v.授予奖章(medal的第三人称单数)www.XiYuS锡育软件What got me to be,at the same time,
50、a mechanical engineer,a geographer and a mathematician and so on,a physicist?是什么使我 同时成为一名机械工程师、一名地理学家 和一名数学家,等等,还有物理学家？11:35Well,actually I started,oddly enough,studying stock marketprices.那么,很奇怪的是,我实际上是从 研究股市价格开始的11:43And so here I had this theory,and I wrote books about it,Financial prices increme