研究生下补充课文翻译及习题

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himself. Eager to astound, he was always on the lookout for the really big problems. When he focused on some new puzzle, he saw dimensions that people who really knew the subject (he never did) initially dismissed as na?ve or wrong-headed. Even as a student, his indifference to others’ skepticism, doubt, and ridicule was awesome.

没有人比纳什更对原创力着迷、更蔑视权威、更珍惜自己的独立性。早在青年时代,他的身边就不乏20世纪最伟大的科学权威,比如艾伯特·爱因斯坦、约翰·冯·诺伊曼、诺伯特·维纳,但是他没有加入任何一个学派,不是任何人的门徒,基本上是在既没有引导者,也没有跟随者的状况下前进。在他所做的从博弈论到几何学等多个学科的几乎所有工作之中,他对广为接受的知识、公认的方式以及根深蒂固的规律都持怀疑态度。他差不多一直是独立工作。通常他一边散步,不时用口哨吹出巴赫的作品,一边进行思考。纳什掌握的数学知识,主要并非来源于学习其他数学家已经取得的成果,而是自己重新发现这些成果中蕴藏的真理。他迫切希望取得一鸣惊人的成就,因此随时准备捕捉真正重大的问题。当他全神贯注地思考某个新的难题时,会留意到那些精通这个领域的人(他从来不认为自己已经精通某个领域)最初认为是幼稚或错误从而不予考虑的角度。即便是在学生时代,他对旁人的怀疑、疑虑和嘲笑的漠视就已经到了令人畏惧的地步。

6.Nash’s faith in rationality and the power of pure thought was extreme, even for a very young mathematician and even for the new age of computers, space travel, and nuclear weapons. Einstein once chided him for wishing to amend relativity theory without studying physics. His heroes were solitary thinkers and supermen like Newton and Nietzsche. Computers and science fiction were his passions. He considered “thinking machines”, as he

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called them, superior in some ways to human beings. At one point, he became fascinated by the possibility that drugs could heighten physical and intellectual performance. He was beguiled by the idea of alien races of hyper-rational begins who had taught themselves to disregard all emotion. Compulsively rational, he wished to turn life’s decisions—whether to take the first elevator or wait for the next one, where to bank his money, what job to accept, whether to marry—into calculations of advantage and disadvantage, algorithms or mathematical rules divorced from emotion, convention, and tradition. Even the small act of saying an automatic hello to Nash in a hallway could elicit a furious “Why are you saying hello to me?”

纳什对理性以及纯粹思维的力量抱有旁人难以理解的绝对信念,即使是对一个非常年轻的数学家,即使是在计算机、空间旅行和核武器的新时代,都是如此。爱因斯坦就曾经责备他居然想不学物理学就修正相对论。他的偶像是牛顿和尼采这样的孤独的思想者和超人。计算机和科幻小说使他着迷。他把计算机称做“会思考的机器”,认为它在某些地方比人类优越。他一度被药物可能提高体力和智力水平的主意所蛊惑。他也曾沉迷于由超理性生物组成的外星人能够教会自己将所有感情置之度外的想法。他具有一种强迫性的理性,希望将生活中的决定——是搭乘第一部电梯还是等待下一部,到哪里存钱,接受什么样的工作,是否结婚——都转化为利弊得失的计算,转化为完全脱离感情、习俗和传统的算法法则或数学规则。即便是别人在走廊里随口和他打声招呼这样的小事情,也会引起他愤怒地发问:“你究竟为什么要向我打招呼?”

7.His contemporaries, on the whole, found him immensely strange. They described him as “aloof, “haughty”, “without affect”, “detached”, “spooky”, “isolated”, and “queer”. Nash mingled rather than mixed with his

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peers. Preoccupied with his own private reality, he seemed not to share their mundane concerns. His manner—slightly cold, a bit superior, somewhat secretive—suggested something “mysterious and unnatural”. His remoteness was punctuated by flights of garrulousness about outer space and geopolitical trends, childish pranks, and unpredictable eruptions of anger. But these outbursts were, more often than not, as enigmatic as his silences. “He is not one of us” was a constant refrain. A mathematician at the Institute for Advanced Study remembers meeting Nash for the first time at a crowded student party at Princeton:

I noticed him very definitely among a lot of other people who were there. He was sitting on the floor in the half-circle discussing something. He made me feel uneasy. He gave me a peculiar feeling. I had a feeling of certain strangeness. He was different in some way. I was not aware of the extent of his talent. I had no idea he would contribute as much as he really did.

他的同辈人基本上认为他实在不可理喻。他们说他“孤僻”、“傲慢”、“无情”、“孤立”、“幽灵一般”、“隔绝”和“古怪”。他和同辈人只是混合在一起,却没有真正融合。他沉醉于自己的隐秘世界,根本不能理解别人操心的世俗事务。他的举止稍微有些冷淡,有些高高在上,还有一点秘而不宣的样子,暗示了某种神秘而非自然的东西。他一贯冷漠,但一时兴起也会喋喋不休地谈论外太空和地缘政治趋势,或做出孩子般的恶作剧,或者毫无征兆地勃然大怒。但是这些情感的迸发总是和他的沉默一样神秘莫测。“他和我们不一样”是人们常说的一句话。一位在普林斯顿高等研究院工作的数学家这样描述他在普林斯顿拥挤的学生舞会上第一次遇见纳什的情景:我从那里的一大群人当中一下子就注意到他。当时他坐在地上,身边围了半个圆圈的学生,正在讨论什么问题。他使我感到不安,给我一种奇怪的感觉。我觉察到一种特别陌生的东西,他在某些地

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方与众不同。我并不了解他究竟有多大本事,也根本想不到后来他会作出那么大的贡献。

8.But he did contribute, in a big way. The marvelous paradox was that the ideas themselves were not obscure. In 1958, Fortune singled Nash for his achievements in game theory, algebraic geometry, and nonlinear theory, calling him the most brilliant of the younger generation of new ambidextrous mathematicians who worked in both pure and applied mathematics. Nash’s insight into the dynamics of human rivalry—his theory of rational conflict and cooperation—was to become one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel’s ideas of genetic transmission, Darwin’s model of natural selection, and Newton’s celestial mechanics reshaped biology and physics in their day.

但是他确实作出了贡献,而且非同凡响。而让人感到矛盾的是,他的许多想法本身并不晦涩。1958年,由于纳什在博弈论、代数几何学和非线性理论方面取得的成就,《财富》杂志推举他为同时活跃在纯粹数学和应用数学两个领域的新一代天才数学家中最杰出的人物。纳什对于人类竞争动态变化的洞察——他的理性竞争与合作理论——将会成为20世纪最具影响的思想理论之一。这一理论改变着新兴的经济学,其作用无异于孟德尔的基因遗传、达尔文的自然选择模式和牛顿的天体力学再造了当时的生物学和物理学。

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