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BenoitMandelbrot_2010-_分形和粗糙的艺术_
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| Thank you very much. |
非常感谢。 |
| Please excuse me for sitting; I'm very old. |
请原谅我坐着讲; 我很老了。 |
| (Laughter) |
(笑声) |
| Well, the topic I'm going to discuss is one which is in a certain sense very peculiar because it's very old. |
我要讨论的主题 在某种意义上很古怪, 因为它很古老。 |
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peculiar:adj.特殊的;独特的;奇怪的;罕见的;n.特权;特有财产;
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| Roughness is part of human life forever and forever. |
粗糙永永远远是 人类生活的一部分。 |
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Roughness:n.粗糙(度);粗暴;猛烈;篷乱毛发;未加工;
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| And ancient authors have written about it. |
古代的作者描写过它。 |
| It was very much uncontrollable . |
它很不受控制。 |
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uncontrollable:adj.无法控制的;无法管束的;难以驾驭的;
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| And in a certain sense, it seemed to be the extreme of complexity , 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。 |
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extreme:adj.极端的;极度的;偏激的;尽头的;n.极端;末端;最大程度;极端的事物; complexity:n.复杂性;难以理解的局势 mess:n.混乱;餐厅;杂乱;肮脏;v.使不整洁;弄脏;弄乱;随地便溺;
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| There are many different kinds of mess. |
有许多不同类型的混乱。 |
| Now, in fact, by a complete fluke , |
那么,实际上 完全是出于偶然, |
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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;
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| I got involved many years ago in a study of this form of complexity. |
我在许多年前 涉足于这种复杂性的研究。 |
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involved:adj.有关的; v.涉及; (involve的过去式和过去分词)
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| And to my utter amazement , |
让我非常惊讶的是, |
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utter:v.说;出声;讲;adj.完全的;十足的;彻底的; amazement:n.惊异;惊愕;
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| I found traces -- very strong traces, I must say -- of order in that roughness. |
我发现了—— 很清晰的踪迹,我必须说—— 粗糙中秩序的踪迹 |
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traces:v.跟踪;探索;n.痕迹;踪迹;(trace的复数和第三人单数)
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| And so today, I would like to present to you a few examples of what this represents . |
今天,我想向你们展示 几个 有代表性的例子 |
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represents:v.代表;维护…的利益;相当于;(represent的第三人称单数)
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| I prefer the word roughness to the word irregularity because irregularity -- to someone who had Latin in my long-past youth -- 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 |
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prefer:v.更喜欢;宁愿;提出;提升; irregularity:n.不规则;无规律;不整齐; Latin:adj.拉丁语的;用拉丁语写成的;n.拉丁语; contrary:adj.相反的;对立的;adv.相反地;n.相反;反面;
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| But it is not so. |
其实并非如此。 |
| Regularity is the contrary of roughness because the basic aspect of the world is very rough. |
“规则”是“粗糙”的反义词 因为世界的基本面 是很粗糙的。 |
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aspect:n.方面;层面;外观;方位;
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| So let me show you a few objects. |
那么让我给你们展示几个东西。 |
| Some of them are artificial . |
有些是人造的 |
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artificial:adj.人造的;仿造的;虚伪的;非原产地的;武断的;
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| Others 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。 |
| Now this is the real. It's a cauliflower . |
这个是真实的,这是一个菜花。 |
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cauliflower:n.花椰菜,菜花;
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| Now why do I show a cauliflower, a very ordinary and ancient vegetable? |
我为什么展示一个菜花, 一种非常普通和古老的蔬菜？ |
| Because old and ancient as it may be, it's very complicated and it's 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。 |
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complicated:adj.复杂的;难懂的;v.使复杂化;(complicate的过去分词和过去式) at the same time:同时;另一方面;与此同时;
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| If you try to weigh it, of course it's very easy to weigh it. |
如果您想称它的重量,当然称它是非常容易的。 |
| And when you eat it, the weight matters. |
当你吃它时,你关心的是重量。 |
| But suppose you try to measure its surface. |
但是假设您想 测量它的表面积。 |
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suppose:v.推断:假定:假设:设想:
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| Well, it's very interesting. |
那么,非常有意思。 |
| If you cut, with a sharp knife, one of the florets of a cauliflower and look at it separately , you think of a whole cauliflower, 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。 |
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sharp:锋利的,尖的 florets:n.小花;绢丝(等于florette);菜茎; separately:adv.分别地;分离地;个别地;
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| And then you cut again, again, again, again, again, again, again, again, again. |
您然后再切, 再切,再切,再切,…. |
| And you still get small cauliflowers . |
您得到仍然是小菜花。 |
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cauliflowers:n.花椰菜;白菜花(cauliflower的复数形式);
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| So the experience of humanity has always been that there are some shapes which have this peculiar property, that each part 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 |
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humanity:n.人类;人道;仁慈;人文学科;
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| Now, what did humanity do with that? |
现在人类是否对此做了些什么呢？ |
| Very, very little. |
非常非常少。 |
| (Laughter) |
(笑声) |
| So what I did actually is to study this problem, and I found something quite surprising. |
我实际上做的就是 研究这个问题, 我发现了相当惊奇的事情。 |
| That 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 |
| One day, a friend of mine, to bug me, brought a picture, and said, "What is the roughness of this curve ?" |
一天,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？” |
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bug:n.臭虫,小虫;故障;窃听器;v.烦扰,打扰;装窃听器; curve:n.曲线;弯曲;曲面;弧线;v.(使)沿曲线移动;呈曲线形;
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| I said, "Well, just short of 1.5." |
我说,“好的,小与1.5。” |
| It was 1.48. |
是1.48。 |
| Now, it didn't take any time. |
这一点也不费事。 |
| I've been looking at these things for so long. |
我观察这些事物很长时间了。 |
| So these numbers are the numbers which denote the roughness of these surfaces. |
这些数字表示 这些表面的粗糙度。 |
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denote:vt.表示,指示;
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| I hasten to say that these surfaces are completely artificial. |
我急切地说这些表面 完全是人造的, |
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hasten:vt.加速;使赶紧;催促;vi.赶快;急忙;
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| They were done on a computer. |
是用计算机产生的。 |
| And the only input is a number. |
唯一的输入是一个数字. |
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input:n.投入; v.把(数据等)输入计算机;
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| And that number is roughness. |
那个数字就是粗糙度. |
| And so on the left, |
在左边 |
| I took the roughness copied from many landscapes . |
我取的是从许多风景中复制的粗糙度 |
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landscapes:n.风景; v.从事庭园设计;
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| To the right, I took a higher roughness. |
在右边,我采取了更高的粗糙度 |
| So 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. |
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distinguish:vt.区分;辨别;使杰出,使表现突出;vi.区别,区分;辨别;
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| Humanity had to learn about measuring roughness. |
人类必须了解粗糙度的测量. |
| This is very rough, and this is sort of smooth, and this perfectly smooth. |
这个非常粗糙,这个有点光滑,这个非常光滑。 |
| Very few things are very smooth. |
很少东西是很光滑的。 |
| So then if you try to ask questions: what's the surface of a cauliflower? |
所以你如果要问: 一个菜花的表面积是多少？ |
| Well, you measure and measure and measure. |
那么,你反复地测量。 |
| Each time you're closer it gets bigger, down to very, very small distances. |
测量得越精确,得到的数值就会越大, 直到非常、 非常小的差距。 |
| What's the length of the coastline of these lakes? |
这些湖泊的湖岸线 长度是多少？ |
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coastline:n.海岸线;
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| The closer you measure, the longer it is. |
你测量得越精确,结果越长。 |
| The concept of length of coastline, which seems to be so natural because it's given in many cases, is, in fact, completely fallacy; there's 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。 |
| You must do it differently. |
你必须换种方式对待它。 |
| What good is that, to know these things? |
知道这些事情有什么好处呢？ |
| Well, surprisingly enough, it's good in many ways. |
足以让人吃惊的是, 它的好处是多方面的。 |
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surprisingly:adv.令人惊讶地;出乎意料地
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| To begin with, artificial landscapes, which I invented sort 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。 |
| We see mountains in the distance . |
我们看远处的群山。 |
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in the distance:在远处;
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| They may be mountains, but they may be just formulae , just cranked on. |
他们可能是山,也可能只是个公式,是手摇出来的。 |
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formulae:n.公式(formula的复数);规则;客套话; cranked:adj.有曲柄的,弯曲的;v.转动曲柄;使成曲柄状;曲折行进(crank的过去分词);
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| Now it's very easy to do. |
现在很容易做。 |
| It used to be very time consuming , but now it's nothing. |
它曾经是非常耗时的,但现在没有什么。 |
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consuming:adj.消费的;强烈的;v.消耗(consume的ing形式);
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| Now look at that. That's a real lung. |
现在看看这个,这是一个真正的肺。 |
| Now a lung is something very strange. |
肺是很奇怪的东西。 |
| If you take this thing, you know very well it weighs very little. |
如果你把它拿在手里, 你就会知道它的重量很小。 |
| The volume of a lung is very small. |
肺的体积也很小。 |
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volume:n.体积;容积;音量;响度;一册;合订本
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| But what about the area of the lung? |
但肺的面积呢？ |
| Anatomists were arguing very much about that. |
解剖学家们对此争论很大。 |
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Anatomists:n.解剖学家;剖析者;
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| Some say that a normal male's lung has an area of the inside of 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。 |
| And the others say, no, five basketball [courts]. |
有人说,不对,是五个篮球。 |
| Enormous disagreements. |
分歧很大。 |
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Enormous:adj.庞大的,巨大的;凶暴的,极恶的;
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| Why so? Because, in fact, the area of the lung is something very ill-defined . |
为何如此？因为实际上肺的面积的定义 非常含糊不清。 |
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ill-defined:adj.不清楚的;不明确的;
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| The bronchi branch, branch, branch. |
支气管分枝,分枝,分枝。 |
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bronchi:n.细支气管(bronchus的复数);
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| And they stop branching, not because of any matter of principle , but because of physical considerations , the mucus , 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。 |
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principle:n.原理,原则;主义,道义;本质,本义;根源,源泉; physical:adj.[物]物理的;身体的;物质的;符合自然法则的;n.体格检查; considerations:n.考虑;注意事项(consideration的复数形式);体贴; mucus:n.粘液;黏液;
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| So what happens is that it's the way you have a much bigger lung, but if it branches and branches, down to distances about 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。 |
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rodent:adj.啮齿类的;咬的,嚼的;侵蚀性的;n.[脊椎]啮齿动物;
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| Now, what good is it to have that? |
那么,这有什么好处呢？ |
| Well, surprisingly enough, amazingly enough, the anatomists had a very poor idea of the structure of the lung until very recently . |
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 |
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structure:n.结构;构造;建筑物;vt.组织;构成;建造; recently:adv.最近;新近;
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| And I think that my mathematics , surprisingly enough, has been of great help to the surgeons studying lung illnesses and also kidney illnesses, all these branching systems, for which 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。 |
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mathematics:n.数学;数学运算; surgeons:n.外科医生;(surgeon的复数) kidney:n.[解剖]肾脏;腰子;个性; geometry:n.几何学;几何结构;
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| So I found myself, in other words, constructing a geometry, a geometry 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。 |
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constructing:n.构造;v.构造(construct的现在分词);
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| And a surprising aspect of it is that very often, the rules of this 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。 |
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extremely:adv.非常,极其;极端地;
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| You have formulas that long. |
你的公式只有这么长。 |
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formulas:n.[数]公式;配方;规则(formula的复数);
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| And you crank it several times. |
你把它迭代多次。 |
| Sometimes repeatedly , again, again, again. |
有时需要一次一次地重复, |
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repeatedly:adv.反复地;再三地;屡次地;
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| The same repetition . |
重复同样的运算。 |
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repetition:n.重复;重做;重说;重做的事;重说的话;
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| And at the end you get things like that. |
最后,你将得到这样的东西。 |
| This cloud is completely, 100 percent artificial. |
这朵云彩是完全地, 100%地人造的。 |
| Well, 99.9. |
好吧,99.9%。 |
| And the only part which is natural is a number, the roughness of 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。 |
| Something so complicated like a cloud, so unstable , so varying , 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。 |
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unstable:adj.不稳定的;变化莫测的;(行为、情绪)反复无常的 varying:adj.不同的;变化的;v.变化,改变(vary的现在分词);
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| Now this simple rule is not an explanation of clouds. |
这个简单规则 不是对云的一个解释。 |
| The seer of clouds had to take account of it. |
云的观察者必须 把它考虑在内。 |
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seer:n.预言家;幻想家;先知者; take account of:考虑到;顾及;体谅;
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| I don't know how much advanced these pictures are, they're old. |
我不知道这些图片有多先进, 他们是旧的。 |
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advanced:adj.先进的; v.前进; (advance的过去式和过去分词形式)
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| I was very much involved in it, but then turned my attention to other phenomena . |
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。 |
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phenomena:n.现象(phenomenon的复数);
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| Now, here is another thing which is rather interesting. |
这是另一件 相当有趣的事情 |
| One of the shattering events in the history of mathematics, which is not appreciated by many people, occurred about 130 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。 |
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shattering:adj.给人以极大打击的; v.(使)破碎,碎裂; (shatter的现在分词) appreciated:v.欣赏;感激;理解;(appreciate的过去分词和过去式) occurred:v.发生;出现;存在于;出现在;(occur的过去分词和过去式)
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| Mathematicians began to create shapes that didn't exist. |
数学家开始创造 不存在的形状 |
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Mathematicians:n.[数]数学家(mathematician的复数形式);
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| Mathematicians got into self-praise to an extent which was absolutely amazing that man can invent things that nature did 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。 |
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extent:n.程度;范围;长度; absolutely:adv.绝对地;完全地;
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| In particular , it could invent things like a curve which fills the plane. |
具体来说,人类可以发明 填装飞机的曲线。 |
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In particular:尤其,特别;
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| A curve's a curve, a plane's a plane, and the two won't mix. |
曲线是曲线,飞机是飞机, 二者不会混淆 |
| Well they do mix. |
哦,他们还真混淆了。 |
| A man named Peano did define such curves , and it became an 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。 |
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curves:n.曲线; v.(使)沿曲线运动; (curve的第三人称单数和复数) extraordinary:adj.非凡的;特别的;离奇的;临时的;特派的;
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| It was very important, but mostly interesting because a kind of break, a separation between the mathematics coming from reality on the one hand and new mathematics coming from pure man's 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。 |
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separation:n.分离;分开;分割;隔离; on the one hand:一方面;
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| Well, I was very sorry to point out that the pure man's mind has, in fact, seen at long last what had been seen for a long time. |
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 |
| And so here I introduce something, the set of rivers of a plane-filling curve. |
那么在这里我要介绍一下 一套飞机填装曲线。 |
| And well, it's a story unto itself. |
那么, 它本身就是一个故事。 |
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unto:prep.到,直到;向(等于to);
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| So it was in 1875 to 1925, an extraordinary period in which mathematics 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。 |
| And the objects which were used as examples, when I was a child and a student, of the break between mathematics and visible reality -- 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, |
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visible:adj.明显的;看得见的;现有的;可得到的;n.可见物;进出口贸易中的有形项目;
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| I turned them completely around. |
我完全地拿它们另作他用。 |
| I used them for describing some of the aspects of the complexity of nature. |
我用它们来描述 自然复杂性的某些方面。 |
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describing:v.描述;形容;把…称为;做…运动;(describe的现在分词) aspects:n.方面;相位;面貌(aspect的复数);
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| Well, a man named Hausdorff in 1919 introduced a number which was just a mathematical joke. |
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。 |
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mathematical:adj.数学的,数学上的;精确的;
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| And I found that this number was a good measurement of roughness. |
我发现这个数字 是一个很好的测量粗糙度的值。 |
|
measurement:n.测量;度量;长度;
|
| When I first told it to my friends in mathematics they said, "Don't be silly. It's 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。” |
| Well actually, I was not silly. |
事实上我不傻。 |
| The great painter Hokusai knew it very well. |
大画家葛饰北斋很了解它。 |
| The things on the ground are algae . |
地面上长的是海藻。 |
|
algae:n.[植]藻类;[植]海藻;
|
| He did not know the mathematics; it didn't yet exist. |
他不懂数学;那时还没有数学。 |
| And he was Japanese who had no contact with the West. |
他是日本人,没有接触过西方文化。 |
|
contact:n.接触,联系;v.使接触,联系;
|
| But 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。 |
|
fractal:n.不规则碎片形;
|
| I could speak of that for a long time. |
我讲这个可以将很长时间。 |
| The Eiffel Tower has a fractal aspect. |
埃佛尔铁塔也有分数维的方面。 |
| And I read the 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。 |
| And indeed it was astonishing how much he understood. |
他了解的程度的确使我吃惊。 |
|
astonishing:adj.令人十分惊讶的;v.使十分惊讶;使吃惊;(astonish的现在分词)
|
| This is a mess, mess, mess, Brownian loop . |
这是一个乱糟糟的布朗环。 |
|
loop:n.循环;回路;环路;圈;v.使成环;使绕成圈;成环形移动;
|
| One day I decided that halfway through my career , |
一天,我决定 在我职业生涯的半途中, |
|
career:n.职业;事业;生涯;经历;
|
| I was held by so many things in my work, |
我被工作中太多的事情所缠绕, |
| I decided to test myself. |
我决定考验一下自己。 |
| Could I just look at something which everybody had been looking at for a long time and find something dramatically new? |
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？ |
|
dramatically:adv.戏剧地;引人注目地;adv.显著地,剧烈地;
|
| Well, 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——只是来回转圈. |
|
motion:n.动作;移动;手势;请求;意向;议案;v.运动;打手势;
|
| I 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。 |
|
for a while:adv.片刻;暂时;一会儿;一时; origin:n.起源;起因;源头;出身;
|
| Then I was telling my assistant, "I don't see anything. Can you paint 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？” |
| So he painted it, which means he put inside everything. He said: "Well, this thing came out ..." 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！ |
| I see, it's an island." |
我看到了,这是一个岛。” |
| And amazing. |
太神奇了。 |
| So Brownian motion, which happens to have a roughness number of two, goes around. |
所以布朗运动, 碰巧粗糙度为2,就是转圈圈。 |
| I measured it, 1.33. |
我测量了它,1.33 |
|
measured:adj.缓慢谨慎的; v.测量; (measure的过去分词和过去式)
|
| Again, again, again. |
一次又一次 |
| Long measurements , big Brownian motions, 1.33. |
长的测量,大型的布朗运动 1.33。 |
|
measurements:n.测量值,尺寸(measurement的复数);
|
| Mathematical problem: how to prove it? |
数学问题:怎样证明它？ |
| It took my friends 20 years. |
这花了我朋友20年的时间。 |
| Three of them were having incomplete proofs . |
其中三个人得到了一个不完整的证明。 |
|
incomplete:n.未完成;adj.不完整的;不完全的;不完善的; proofs:n.证明;证据(proof的复数);校稿;
|
| They got together, and together they had the proof. |
他们不断地聚在一起研究,得到了这个证明。 |
| So they got the big [Fields] medal in mathematics, one of the three medals that people have received for proving things which I've seen without being able to prove them. |
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 别人看到了但无法证明的事情的人们。 |
| Now everybody asks me at one point or another, "How did it all start? |
大家经常问我, “这一切是怎么开始的？ |
| What got you in that strange business?" |
是什么让你做起了这个奇怪的行当？” |
| What got me to be, at the same time, 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？ |
|
mechanical:adj.机械的;力学的;呆板的;无意识的;手工操作的; geographer:n.地理学者; physicist:n.物理学家;物理学研究者;
|
| Well, actually I started, oddly enough, studying stock market prices. |
那么,很奇怪的是,我实际上是从 研究股市价格开始的 |
|
oddly:adv.古怪地;奇妙地;单数地; stock market:股票市场;证券市场;股票交易;
|
| And so here |
于是 |
| I had this theory, and I wrote books about it, |
我提出了这个理论 并且写了关于它的书, |
| Financial prices increments . |
金融价格增量。 |
|
Financial:adj.金融的;财政的,财务的; increments:n.[数]增量(incremment的复数);增加数;
|
| To the left you see data over a long period. |
在左边您看到的是长期数据。 |
| To the right, on top, you see a theory which is very, very fashionable . |
在右上角, 您看到是一个非常非常时髦的理论。 |
|
fashionable:adj.流行的;时髦的;上流社会的;
|
| It was very easy, and you can write many books very fast about it. |
它非常容易,您可以很快地写出许多关于它的书。 |
| (Laughter) |
(笑声) |
| There are thousands of books on that. |
有数以千计的写它的书。 |
| Now compare that with real price increments. |
现在把它与真实的价格增量比较一下。 |
|
compare:v.比较;对比;n.比较;
|
| and where are real price increments? |
真实的价格增量在哪里呢？ |
| Well, these other lines include some real price increments and some forgery which I did. |
这些曲线包括了 真实的价格增量 和我的伪造。 |
|
forgery:n.伪造;伪造罪;伪造物;
|
| So the idea there was that one must able to -- how do you say? -- model price variation . |
这里的想法是 人必须能 --怎么说呢? – 模拟价格变化。 |
|
variation:n.变异;变体;变奏;变种;
|
| And it went really well 50 years ago. |
50年前这方法运行的很好。 |
| For 50 years people were sort of pooh-poohing me because they could do it much, much easier. |
50年来,人们有点儿看不起我, 因为他们可以很容易地做到它。 |
|
pooh-poohing:v.说…不真实;对…不屑一顾(或嗤之以鼻)(pooh-pooh的现在分词)
|
| But I tell you, at this point, people listened to me. |
但是我告诉您,此时此刻,人们听我的。 |
| (Laughter) |
(笑声) |
| These two curves are averages. |
这两条曲线是均线。 |
| Standard & Poor, the blue one. |
标准普尔,蓝色的那个 |
|
Standard:n.标准;水准;旗;度量衡标准;adj.标准的;合规格的;公认为优秀的;
|
| And the red one is Standard & Poor's, from which the five biggest discontinuities are taken out. |
而红色的一个是 去掉不连续性最大的五个股票后的 标准普尔。 |
|
discontinuities:n.不连续(discontinuity的复数);间断点;
|
| Now discontinuities are a nuisance . |
不连续性是有害的。 |
|
nuisance:n.麻烦事;讨厌的人(或东西);妨害行为;
|
| So in many studies of prices, one puts them aside. |
因此所有价格研究, 人们总是把它们放到一边。 |
| '"Well, acts of God. |
“哦,不可抗力 |
| And you have the little nonsense which is left. |
您就没有什么好胡搅蛮缠的了。 |
|
nonsense:n.胡说;废话;adj.荒谬的;int.胡说;
|
| Acts of God." In this picture five acts of God are as important as everything else. |
不可抗力。”在这张图片中, 五个不可抗力同其它因素是同样重要的。 |
| In other words, it is not acts of God that we should put aside. |
换句话说, 不可抗力是不应该被放到一边的。 |
| That is the meat, the problem. |
那才是肉,是问题的所在。 |
| If you master these, you master price. |
如果您掌握了这些,您就掌握了价格。 |
| And if you don't master these, you can master the little noise as well as you can, but it's not important. |
如果您掌握不了这些, 您可以尽量掌握小噪音。 但是这不重要。 |
|
as well as:也;和…一样;不但…而且;
|
| Well, here are the curves for it. |
那么,这是它的曲线。 |
| Now, I get to the final thing, which is the set of which my name is attached . |
现在,我讲最后一个事情, 用我名字命名的一个集合。 |
|
attached:adj.依恋;v.重视;把…固定;(attach的过去分词和过去式)
|
| In a way it's the story of my life. |
在某种意义上它是我生命的故事。 |
| My adolescence was spent during the German occupation of France. |
我的青春期是在 德军占领下的法国度过的。 |
|
adolescence:n.青春期; occupation:n.职业;占领;占用;工作;
|
| And since I thought that I might vanish within a day or a week, |
因为我认为我也许会 在一天或一个星期之内消失 |
|
vanish:v.消失;突然不见;成为零;n.弱化音;
|
| I had very big dreams. |
我过有大的梦想。 |
| And after the war, |
战争过后, |
| I saw an uncle again. |
我又见到我的叔叔。 |
| My uncle was a very prominent mathematician and he told me, "Look, there's a problem which I could not solve 25 years ago, and which nobody can solve. |
我的叔叔是一位非常著名数学家,他告诉我, “你看,有一道难题, 我花了25年也没有解决, 别人也没有解决。 |
|
prominent:adj.突出的,显著的;杰出的;卓越的;
|
| This is a construction of a man named [Gaston] Julia and [Pierre] Fatou. |
这是一个名叫（加斯顿）朱丽叶和 一个名叫（皮埃尔）费托的人提出来的。 |
|
construction:n.建设;建筑物;解释;造句;
|
| If you could find something new, anything, you will get your career made." |
如果你能够 有任何新发现 你将成就你的事业。” |
| Very simple. |
非常简单。 |
| So I looked, and like the thousands of people that had tried before, |
于是我就看这道题, 象之前做过尝试的成千上万的人一样, |
| I found nothing. |
我什么也没有发现。 |
| But then the computer came. |
然后出现了计算机。 |
| And I decided to apply the computer, not to new problems in mathematics -- like this wiggle wiggle, that's a new problem -- but to old problems. |
我决定研究计算机, 而不是新的数学问题- 例如这个“摆动”的问题,这是新问题- 而是建立在旧问题上。 |
|
apply:v.申请;涂,敷;应用;适用;请求; wiggle:v.扭动;摆动,起伏;n.摆动,摇动,起伏;
|
| And I went from what's called real numbers, which are points on a line, to imaginary , complex numbers, which are points on a plane, which is what one should do there. |
我由所谓“实数”开始, 也就是数轴上的点, 到虚的“复数”, 也就是平面上的点, 人们应该在平面上研究。 |
|
imaginary:adj.虚构的,假想的;想像的;虚数的;
|
| And this shape came out. |
这个形状出来了。 |
| This shape is of an extraordinary complication . |
这个形状异常复杂。 |
|
complication:n.并发症;复杂;复杂化;混乱;
|
| The equation is hidden there, z goes into z squared, plus c. |
公式就隐藏在那里, z等于 z的 平方加c。 |
|
equation:n.方程式,等式;相等;[化学]反应式;
|
| It's so simple, so dry. |
它是那么简单,相当简单。 |
| It's so uninteresting . |
一点意思也没有 |
|
uninteresting:adj.无趣味的,乏味的;令人厌倦的;
|
| Now you turn the crank once, twice, twice, marvels come out. |
现在你把它重复一次、 两次, 两次 奇迹出现了 |
|
marvels:奇迹(marvel的名词复数);
|
| I mean this comes out. |
我是说这个出现了 |
| I don't want to explain these things. |
我不想解释这些东西。 |
| This comes out. This comes out. |
这个出来了。这个出来了。 |
| Shapes which are of such complication, such harmony and such beauty. |
多么复杂、多么和谐、 多么美丽的形状啊。 |
|
harmony:n.协调;和睦;融洽;调和;
|
| This comes out repeatedly, again, again, again. |
这个出来了, 不断地,一而再,再而三地出来, |
| And that was one of my major discoveries was to find that these islands were the same as the whole big thing, more or less . |
这就是我的一个主要发现 我发现这些小岛的形状 与整体的大形状相同,或多或少 |
|
more or less:或多或少;
|
| And then you get these extraordinary baroque decorations all over the place. |
于是你得到这些 随处可见的非凡的巴洛克式装饰。 |
|
baroque:adj.巴洛克式的;结构复杂的,形式怪样的;n.巴洛克风格;巴洛克艺术; decorations:n.装饰品;装饰图案;装饰风格;(decoration的复数)
|
| All that from this little formula, which has whatever, five symbols in it. |
所有这些来自这个 只有五个符号的小小的公式 |
|
symbols:n.符号;象征;标志;符号表(symbol的复数);
|
| And then this one. |
然后这一个 |
| The color was added for two reasons. |
加颜色是由于两个原因 |
| First of all , because these shapes are so complicated, that one couldn't make any sense of the numbers. |
首先,因为这些形状 是如此的复杂, 以至于人根本意识不到这些数字。 |
|
First of all:adv.首先;
|
| And if you plot them, you must choose some system. |
如果你想突出它们,您必须选择一些系统 |
|
plot:n.情节;阴谋;布局;小块土地;v.密谋;暗中策划;(在地图上)标出;绘制(图表);
|
| And so my principle has been to always present the shapes with different colorings , because some colorings emphasize that, and others it is that or that. |
所以我的原则是 总是在展示不同的形状时 涂上不同的颜色 因为有些颜色突出这个, 有些颜色突出那个。 |
|
colorings:v.着色(color的ing形式);出现颜色;n.着色;着色剂;配色;天然色;外貌; emphasize:v.强调;重视;着重;使突出;
|
| It's so complicated. |
非常复杂。 |
| (Laughter) |
（笑声） |
| In 1990, I was in Cambridge , U.K. |
1990 年,我在英国的剑桥大学 |
|
Cambridge:n.剑桥(英国城市);坎布里奇(美国马萨诸塞州城市);
|
| to receive a prize from the university. |
接受了一个奖项。 |
| And three days later, a pilot was flying over the landscape and found this thing. |
三天后, 一个飞行员在飞行时发现了这个。 |
| So where did this come from? |
这是从哪里来的？ |
| Obviously, from extraterrestrials . |
显然,从外星人那里来的。 |
|
extraterrestrials:外星人(extraterrestrial的复数);
|
| (Laughter) |
(笑声) |
| Well, so the newspaper in Cambridge published an article about that "discovery" |
于是剑桥的校报上 发表一篇有关这一“发现”的文章。 |
| and received the next day 5,000 letters from people saying, "But that's simply a Mandelbrot set very big." |
第二天, 收到了5000封来信,人们说: “那只是一个放得很大的曼德尔布罗特图形。” |
| Well, let me finish. |
好吧,让我结束演讲。 |
| This shape here just came out of an exercise in pure mathematics. |
这个形状仅仅出自 纯数学的一个练习 |
| Bottomless wonders spring from simple rules, which are repeated without end. |
无边的奇迹源自简单规则的 无限重复。 |
|
Bottomless:adj.无底的;深不可测的;难解的;取之不尽的;
|
| Thank you very much. |
非常感谢。 |
| (Applause) |
（掌声） |