研究生下补充课文翻译及习题

1 A Beautiful Mind 1 John Forbes Nash Jr mathematical genius inventor of a theory of rationed behavior visionary of the thinking machine had been sitting with his visitor also a mathematician for nearly half an hour It was late on a weekday afternoon in the spring of 1959 and though it was only May uncomfortably warm Nash was slumped in an armchair in one corner of the hospital lounge carelessly dressed in a nylon shirt that hung limply over his unbelted trousers His powerful frame was slack as a rag doll s his finely molded features expressionless He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey hardly moving except to brush his long dark hair away from his forehead in a fitful repetitive motion His visitor sat upright oppressed by the silence acutely conscious that the doors to the room were locked Mackey finally could contain himself no longer His voice was slightly querulous but he strained to be gentle How could you began Mackey how could you a mathematician a man devoted to reason and logical proof how could you believe that extraterrestrials are sending you message How could you believe that you are being recruited by aliens from outer space to save the world How could you 小约翰 福布斯 纳什 数学天才 理性行为理论创立者 预见会思考 的机器出现的预言者 已经和他的同样是数学家的来访者一起坐了差不多半 个小时 那是 1959 年春季一个工作日的傍晚时分 虽然才是 5 月 天气却很 热 令人不太舒服 纳什颓然坐在医院会客室一角的扶手椅上 身上随意穿 着的那件尼龙衬衫 松松垮垮地盖在他没有系皮带的长裤上 他的魁梧身躯 现在就像一个布娃娃一样缺乏活力 他的线条优美细致的五官没有任何表情 2 他一直目光呆滞地盯着哈佛教授乔治 麦基左脚前方不远的地方 除了一次 次重复着将垂在前额的略长的黑发拨开的动作 他几乎一动不动 麦基正襟 危坐 被沉默压得透不过气来 并且非常清楚地意识到会客室的所有门都锁 上了 麦基再也控制不住自己 他尽量使语气温和 但听上去仍有些愠怒 你 一个数学家 他开始说道 一个致力于研究理性和逻辑证明的人 怎么 能相信外星人正在给你发送消息呢 怎么能相信你被来自太空的外星人选中 要来拯救世界呢 怎么能 2 Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake Because Nash said slowly in his soft reasonable southern drawl as if talking to himself the ideas I had about supernatural beings came to me the same way that my mathematical ideas did So I took them seriously 纳什终于抬起头 用类似某种鸟类或者蛇一样冰冷而不动声色的目光 紧紧盯着麦基 因为 他慢慢地回答 带着温和适度的南方人特有的慢条斯 理的语气 好像自言自语一般 我的有关超自然生物的想法出现在我的脑海 里的方式 是和我的数学思想一样的 所以我会认真对待 3 The young genius from Bluefield West Virginia handsome arrogant and highly eccentric burst onto the mathematical scene in 1948 Over the next decade a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind s survival Nash proved himself in the words of the eminent geometer Mikhail Gromov the most remarkable mathematician of the second half of the century Games of strategy economic rivalry computer architecture the shape of the universe the geometry of imaginary spaces the mystery of prime numbers all 3 engaged his wide ranging imagination His ideas were of the deep and wholly unanticipated kind that pushes scientific thinking in new directions 这个来自西弗吉尼亚州布卢菲尔德的年轻天才 英俊 傲慢 而且非 常古怪 在 1948 年闯入数学界 在接下来的十年 在那既以对人类理性 抱有无上信念而著称 又以对人类生存怀有无尽忧虑而闻名的十年 纳什 用知名几何学家米克哈尔 格罗莫夫的话说 证明了自己是 20 世纪后半叶 最杰出的数学家 策略博弈 经济竞争 计算机建筑学 宇宙的形状 虚构 空间的几何学 素数的神秘 都是他广阔的想象力涉猎的领域 他的想法属 于那种非常深奥而又完全出人意料的类型 无疑会推动科学思考进入新的方 向 4 Geniuses the mathematician Paul Halmos wrote are of two kinds the ones who are just like all of us but very much more so and the ones who apparently have an extra human spark We can all run and some of us can run the mile in less than 4 minutes but there is nothing that most of us can do that compares with the creation of the Great G minor Fugue Nash s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences It wasn t merely that his mind worked faster that his memory was more retentive or that his power of concentration was greater The flashes of intuition were nonrational Like other great mathematical intuitionist Georg Friedrich Bernhard Riemann Jules Henri Poincare Srinivasa Rammanujan Nash saw the vision first constructing the laborious proofs long afterward But even after he d try to explain some astonishing result the actual route he had taken remained a mystery to others who tried to follow his reasoning Donald Newman a mathematician who knew Nash at MIT in the 1950s used to say about him 4 that everyone else would climb a peak by looking for a path somewhere on the mountain Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak 数学家保罗 哈莫斯写道 天才 分为两种 一种就像我们大家一样 只 是更为出色 另一种则是那些明显具备超凡人类灵感的人 我们都能跑步 有些人还能在四分钟内跑完一英里 但是我们大多数人所做的一切无论如何 也无法与谱写出 小调赋格曲相提并论 纳什的天分就属于那种常与音乐和 艺术而非与最古老的科学紧密相连的神奇异禀 这不仅仅是指他的头脑运转 更加灵敏 记忆力更加出众 或是他更能集中精力 事实上 直觉的火花稍 纵即逝 不能用常理解释 就像其他伟大的数学直觉大师格奥尔格 费里德 里希 伯恩哈德 黎曼 朱尔斯 亨利 庞加莱 斯里尼瓦萨 拉马努金一样 纳什先看到一个结论 然后才开始构筑耗费心力的证明过程 不过 即便在 他尝试解释某个令人震惊的结论之后 对于那些企图跟随他的逻辑的人而言 他所选择的真正途径却始终是一个谜 20 世纪 50 年代就在麻省理工学院认 识纳什的唐纳德 纽曼曾经这样描述他 其他人通常会在山上寻找攀登顶峰的 道路 纳什却干脆爬上另外一座山 再反过来从那个遥远的山峰用探照灯照 射这座山 5 No one was more obsessed with originality more disdainful of authority or more jealous of his independence As a young man he was surrounded by the high priests of twentieth century science Albert Einstein John von Neumann and Norbert Wiener but he joined no school became no one s disciple got along largely without guides or followers In almost everything he did from game theory to geometry he thumbed his 5 nose at the received wisdom current fashions established methods He almost always worked alone in his head usually walking often whistling Bach Nash acquired his knowledge of mathematics not mainly from studying what other mathematicians had discovered but by rediscovering their truths for 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 6 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 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 7 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 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 8 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 9 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 0 I Vocabulary 1 Another common use of the tag question is in small talk when the speaker is trying to conversation Sure is hot here isn t it A illicit B elicit C solicit D explicit 2 Napster says it is delaying the launch of its subscription service yet again after running into serious problems in its talks with other firms So here is Napster s Still not ready A refrain B renown C restraint D retention 3 The path from initial lab work on a drug to final approval of the drug by the Food and wisdom in the sense of comprehensive vision is not necessarily present in specialists in the pursuit of knowledge 构成智慧有几个要素 其中须要置于首位的是轻重缓急之分 将一个问题的所有重要因素考 虑进去并且掂量每一个因素应有的分量的能力 鉴于各类技术员所需的专门知识的范围和复杂程 度 这种能力变得比过去更难具备 比如 假设你从事医学研究 这份工作本身很难做 可能会 耗费你的全部智慧 你没有时间去考虑你的发明或发现可能带来医学领域以外的影响 你成功了 我们假设 正如现代医学所做到的 婴儿死亡率不仅在欧洲和美洲 而且在亚洲和非洲也大大 的降低了 但是完全非你所愿的结果产生了 在世界上人口最为稠密的地区 食物供应匮乏 生 活水平下降 再举一个甚至更为引人注目的例子 当前人们都在关注此事 你渴望探求知识 不 带功利的去研究原子的结构 却意外地将摧毁人类的手段置于狂人的手中 因此 如果知识不能 与智慧同在 对知识的追求就可能变得有危害性 就全方位来看 追求知识的专家并一定具备智 慧 3 3 Comprehensiveness alone however is not enough to constitute wisdom There must be also a certain awareness of the ends of human life This may be illustrated by the study of history Many eminent historians have done more harm than good because they viewed facts through the distorting medium of their own passions Hegel had a philosophy of history which did not suffer from any lack of comprehensiveness since it started from the earliest times and continued into an indefinite future But the chief lesson of history which he sought to inculcate was that from the year A D 400 down to his own time Germany had been the most important nation and the standard bearer of progress in the world Perhaps one could stretch the comprehensiveness that constitutes wisdom to include not only intellect but also feeling It is by no means uncommon to find men whose knowledge 2 is wide but whose feelings are narrow Such men lack what I am calling wisdom 然而 仅有综合能力还不足以构成智慧 还必须思考人类生活的目标 这一点在历史研究中 得到说明 许多杰出的历史学家干的坏事多于好事 因为他们是通过自己的热情这种扭曲的媒介 观察事实的 黑格尔的历史哲学始于亘古 止于无限的未来 也不是不缺乏综合能力 但是他努 力想要说明的历史教义主要是从公元 400 年到自己的年代 德国一直都是最为重要的民族以及世 界进步的标准榜样 或许构成智慧的综合概念可以延伸 它不仅涵盖智力而且还包括感情 知识 面宽但感觉迟钝的人不是不常见 这样的人缺乏我认为的智慧 4 4 It is not only in public ways but in private life equally that wisdom is needed It is needed in the choice of ends to be pursued and in emancipation from personal prejudice Even an end which it would be noble to pursue if it were attainable may be pursued unwisely if it is inherently impossible of achievement Many men in past ages devoted their lives to search for the Philosopher s Stone and the Elixir of Life No doubt if they could have found them they would have conferred great benefits upon mankind but as it was their lives were wasted To descend to less heroic matters consider the case of two men Mr A and Mr B who hate each other and through mutual hatred bring each other to destruction Suppose you go to Mr A and say Why do you hate Mr B he will no doubt give you an appalling list of Mr B s vices partly true partly false And now suppose you go to Mr B he will give you an exactly similar list of Mr A s vices with an equal admixture of truth and falsehood Suppose you now come back to Mr A and say You will be surprised to learn that Mr B says the same things about you as you say about him and you go to Mr B and make a similar speech The first effect no doubt will be to increase their mutual hatred since each will be so horrified by the other s injustice But perhaps if you have sufficient patience and sufficient persuasiveness you may succeed in 3 convincing each that the other has only the normal share of human wickedness and their enmity is harmful to both If you do this you will have instilled some fragment of wisdom 智慧不仅为公共生活所需 而且同样为个人生活所需 选择追求目标 以及从个人偏见中解 放出来 都需要智慧 如果一个目标本身不可能被达到 即便如果它可以被达到 追求它的行为 一定是高贵的 对这个目标的追求也可能不是明智的 在过去 许多人毕其一生搜寻哲学家的点 金石和长生不老药 毫无疑问 如果她们找到了这些东西 他们就为人类谋取了巨大福祉 但事 实上 他们浪费了生命 退而说不那么伟大的事情 想想两个人 A 先生和 B 先生 他们相互憎恨 并通过相互憎恨而相互摧毁 假设你到 A 先生那里说 你为什么不喜欢 B 先生 他一定会向你 数落一大堆 B 先生的邪恶 部分真实 部分虚假 现在 假设你到 B 先生那里 他会向你数落一 大堆 A 先生的邪恶 内容完全一样 真实和虚假的混合程度也完全一样 假设你现在回到 A 先生 那里说 你会很吃惊 要知道 B 先生说你的话跟你说 B 先生的活是一样的 然后你到 B 先生 那里发表同样言论 毫无疑问 直接的结果就是他们的相互仇恨程度增加 因为他们每人都为对 方的偏颇感到震惊 但或许 如果你有足够的耐心和足够的说服力 你可能成功说服他们 对方 只不过是有人类邪恶的通病 他们的敌意对对方都有伤害 如果你能这样做 你就向他们灌输了 点滴的智慧 5 5 I think the essence of wisdom is emancipation as far as possible from the tyranny of the here and the now We cannot help the egoism of our senses Sight and sound and touch are bound up with our own bodies and cannot be made impersonal Our emotions start similarly from ourselves An infant feels hunger and discomfort and is unaffected except by his own physical condition Gradually with the years his horizon widens and in proportion as his thoughts and feelings become less personal and less concerned with his own physical states he achieves growing wisdom This is of course a matter of degree No one can view the world with complete impartiality and if anyone could he would hardly be able to remain 4 alive But it is possible to make a continual approach towards impartiality on the one hand by knowing things somewhat remote in time or space and on the other hand by giving to such things their due weight in our feelings It is this approach towards impartiality that constitutes growth in wisdom 我认为智慧的本质就是逃离此时此地的藩篱 越远越好 我们无法遏制感觉的自我性 视力 声音和触觉都捆绑在我们自己的身体上 不可能不被私有化 我们的感情始于我们自己 婴儿感 觉饥饿和不舒服 他只受自己身体条件的影响 渐渐地 随着年龄的增长 他的视野增加 他的 思想和感情变得不那么私人性 更少与自己身体状况相关 他不断获取智慧 这个当然有个程度 问题 没有人对世界的看法能够完全客观 即便有这样的人 他也很难存活 但是不断接近客观 是可能的 办法是 一方面 了解在时空上多少有些遥远的事情 另一方面 让这些事物在我们 的感情中占据应有的分量 就是这种对客观的接近 构成智慧的增加 6 6 Can wisdom in this sense be taught And if it can should the teaching of it be one of the aims of education I should answer both these questions in the affirmative We are told on Sundays that we should love our neighbor as ourselves On the other six days of the week we are exhorted to hate him You may say that this is nonsense since it is not our neighbor whom we are exhorted to hate But you will remember that the precept was exemplified by saying that the Samaritan was our neighbor We no longer have any wish to hate Samaritans and so we are apt to miss the point of the parable If you want to get its point you should substitute communist or anticommunist as the case may be for Samaritan It might be objected that it is right to hate those who do harm I do not think so If you hate them it is only too likely that you will become equally harmful and it is very unlikely you will induce them to abandon their evil ways Hatred of evil is itself a kind of bondage to evil The way out is through understanding not through hate I am not advocating 5 non resistance But I am saying that resistance if it is to be effective in preventing the spread of evil should be combined with the greatest degree of understanding and the smallest degree of force that is compatible with the survival of the good things that we wish to preserve 这种意义上的智慧可以被传授吗 并且 如果能 传授智慧应当成为教育的目的吗 我对这 两个问题的答案是肯定的 我们在做礼拜的时候被告知要爱邻如爱己 而在一周的其他六天里 我们被劝导去憎恨 但你要记得 这个箴言的例子是说撒玛利亚人是我们的邻居 我们不再有任 何憎恨撒玛利亚人的企图 所以有可能领会不到这个寓言的要旨 如果你想要理解它 你就应该 用你现在的敌人来替代撒玛利亚人 这要视具体情况而定 可能有人会反对说 人们有权利去憎 恨那些有危害性的人物 我不这样认为 如果你憎恨他们 你极有可能变得和他们一样有危害性 并且你根本不可能诱导他们放弃自己那种邪恶的方式 憎恨邪恶本身就是一种对邪恶的依附 解 决的办法是理解而不是憎恨 我不是倡导不抵抗 我是说 抵抗 如果能有效制止邪恶的蔓延 就当与最大程度的理解和最小程度的武力 不破坏我们希望保留的美好事物的生存 相结合 7 7 It is commonly urged that a point of view such as I have been advocating is incompatible with vigor in action I do not think history bears out this view Queen Elizabeth I in England and Henry IV in France lived in a world where almost everybody was fanatical either on the Protestant or on the Catholic side Both remained free from the errors of their time and both by remaining