下面是经济学人的文章内容，标题加黑的三篇文章大家能够在第二部分找到对应内容。
一、目录
[2013.06.01] Urbanisation: Some are more equal than others
[2013.06.01] Drawing the battle lines 保守派vs.改革派：划分战线
[2013.06.01] The strange rebirth of liberal England自由主义怪异重生
[2013.06.01] Martian space flight: Red dreams 火星之旅
[2013.06.01] Killer drones: Out of the shadows 无人机杀手
[2013.06.06] Why so little Chinese in English? 英语的汉语借词太少
[2013.06.08] Lexington: The China syndrome 中国综合症
[2013.06.08] Too much of a good thing 领导人优势过多
[2013.06.08] America’s non-banks: The anointed美国金融机构封神榜
[2013.06.08] Palaeontology: A heroic find 古生物学史诗般的发现
[2013.06.08]Democrat or sultan? 土耳其的抉择：民主还是王权?
[2013.06.08] Luxury in the Arab world 阿拉伯奢侈品市场
[2013.06.08]Turkey's troubles:Democrat or sultan?土耳其受难记
[2013.06.08] Turkey erupts: The new young Turks 土耳其新一代的年轻人
[2013.06.15]Secrets, lies and America's spies 监控网络错在哪
[2013.06.15] Surveillance: Look who’s listening 揭开监控黑幕
[2013.06.15] AIDS in India: The cost of living 生命的价值
[2013.06.15] Europe’s reluctant hegemon 心不甘情不愿的欧洲盟主
[2013.06.15] Energy: Tilting atwindmills 德国能源：无的放矢
[2013.06.15] Online privacy: How to disappear 如何抹去线上痕迹
[2013.06.20] The Big Mac Index goes to North Korea 巨无霸指数走进朝鲜
[2013.06.22] Persian power: Can Iran be stopped? 难道伊朗已经无人能挡
[2013.06.22] China's Bank: the Shibor Shock 中国央行坐视钱荒加剧
[2013.06.22] The start of history 中日战争，历史的开篇
[2013.06.22] Cement industry: Ready-mixed fortunes 水泥业复苏在望
[2013.06.22] Henry Cecil 悼～传奇驯马师亨利·塞西尔
[2013.06.22] Money and happiness: Buy buy love 买来的“爱”
[2013.06.29] Mediobanca: A little less tangled 意大利中期银行
[2013.06.29] Defining financial bigotry: Disparate times 金融偏执的认定
纤云无语探苍穹——用方程式描述的数学故事
二、文章内容
[2013.06.29] Mediobanca: A little less tangled 意大利中期银行
Mediobanca
意大利中期银行
A little less tangled
剪不清，那就理清楚
Italian finance is at last being reshaped
终于开始重塑意大利金融业了
Jun 29th 2013 | Rome |From the print edition
I call it web 2.0
笔者称之为网络2.0版
1 GOOD food, fine wines and outstanding culture: Italy offers much to the world, but few would look to Rome or Milan for models of business or financial conduct. Yet there are encouraging signs that some bad old ways are being abandoned. Even Mediobanca, Italy’s most important investment bank, is moving with the times.
美酒佳肴、灿烂文化，这就是世人眼中的意大利，但罗马与米兰的商业和金融的管理模式却是名不见经传。不过，这只是过去的印象。时代在不断地进步，不合时宜的方略愈渐退出历史的舞台。即使是意大利核心的投资银行中期银行(Mediobanca)也开始随其流而扬其波。
2 Mediobanca has long been at the centre of an incestuous web of relationships that connect many of Italy’s leading firms. It owns chunks of Pirelli, a tyremaker, and Telco, which has effective control of Telecom Italia. It is the largest shareholder of RCS MediaGroup, the owner of Corriere della Sera, Italy’s daily newspaper of record. Mediobanca is also the biggest shareholder in Assicurazioni Generali, Italy’s leading insurer, which itself owns 2% of Mediobanca and also has stakes in Pirelli, RCS and Telco.
中期银行长期以来始终处于意大利商业金融网络的中心地位，并与诸多意大利领军企业有着千丝万缕的联系。无论是意大利轮胎制造商倍耐力(Pirelli)，还是意大利电信(Telecom Italia)的实际控制人电话公司(Telco)，中期银行都大量持有这些企业的股份。该行还是RCS传媒集团(RCS MediaGroup)的第一大股东。作为意大利的老牌日报企业，《晚邮报》(Corriere della Sera)的母公司正是RCS集团。中期银行和意大利保险业龙头企业忠立保险(Assicurazioni Generali)则是互持股份。中期银行是忠立保险的第一大股东，而忠立保险又持有中期银行2%的股权。忠立保险还与中期银行一样，参股了倍耐力、RCS和电话公司。
3 Mediobanca’s grip on Italian corporate life has been helped by chains of “nested” stakes that allow control despite ownership of relatively small shareholdings; by cross-shareholdings and back-scratching directorships; and by shareholders’ pacts that lock up control. On June 21st Alberto Nagel, Mediobanca’s boss, told investors that all the bank’s equity stakes will be reclassified as “available for sale”. The bank will exit its shareholder agreements (although the pact among Mediobanca’s own shareholders, who include Silvio Berlusconi’s Fininvest group and Mediolanum, a financial group where Mr Berlusconi is the biggest shareholder, is intact).
中期银行对于意大利商业活动的成功掌控源于许多因素。通过层层“暗持”其他公司的股份，中期银行以相对较少的股权取得了这些公司控制权。该行还善于运用交叉持股、互派高管、股东协议等方式，成功锁定它对其他公司的控制权。6月21日，中期银行的老总阿尔贝托•耐高尔(Alberto Nagel)告知该行的投资者，公司将重新梳理目前持有的所有“可供出售性”股权，并将撕毁银行此前的股东协议书。但中期银行内部的股东协议仍将保留，这些内部股东包括西尔维奥•贝卢斯科尼(Silvio Berlusconi)名下的菲宁维斯特集团(Fininvest)，以及贝卢斯科尼作为第一大股东持有的美迪奥兰金融集团(Mediolanum)。
4 The bank will not move too fast. It plans to cut its stake in Generali from 13.2% to 10% by 2016; the insurer will account for more than 40% of Mediobanca’s net earnings between now and then. But Mr Nagel says his intention is to reduce the stake to zero over time: “Our strategic focus will be 100% on banking.”
中期银行并不会选择快刀斩乱麻的方式急于求成。银行计划在2016年前减持忠立保险的股份，持股比例从13.2%降至10%。而从现在起至2016年，中期银行至少40%的净收益仍将来源于该保险公司。但耐高尔表示，他的目标是最终将持股数降为零，“我们的战略方向是100%地从事银行业务”。
5 This shift in strategy has many catalysts. One is the rotten state of the Italian economy: Mediobanca is keen to diversify its exposure. The Basel 3 rules, which will turn the bank’s equity stakes in other companies into a drag on capital, are another. A third is a broader movement against shareholder pacts. The number of companies listed on the Milan stockmarket and controlled by shareholder pacts has fallen from 57 in 2009 to 43 last year. Mario Greco, Generali’s newish boss, has also ditched the idea of holding “strategic stakes”.
有许多因素会加快这种战略上的转变。首先是意大利萧条的经济背景，中期银行也正有意分散风险敞口。另外则是《巴塞尔协议三》，该协议认为银行对其他企业的股权投资会消耗银行的资本金。第三是逐渐蔓延的反对股东协议行为。米兰证券市场中受制于股东协议书的公司数量，已经从2009年的57家下降到了去年的43家。忠立保险最近上任的老总马里奥•格里克(Mario Greco)也认为，“战略持股”的策略已经过时了。
6 All of this underlines a change in stature as well as direction. Rather than pulling strings as it did under Enrico Cuccia, who was chairman from 1946 until 1982 and connected to the bank until his death in 2000, Mediobanca now wants to be more normal. Good. The bank has long been the epitome of salotto buono, or “drawing-room”, culture, in which the chiefs of Italian industry and finance meet to stitch up deals. Any progress towards leaving that era behind is welcome.
这些都暗示了企业在规模和战略上的一种变化。恩里科•古希亚(Enrico Cuccia)曾于1946年至1982年间担任中期银行的董事长，其影响力并一直持续到2000年过世。在恩里科时代，中期银行逐渐织就起了一张巨大的商业网络，而如今该行的思路有所调整，不再热衷于曾经的背后操纵。长期以来，中期银行都象征了一种“休息室文化”(salotto buono culture)，意大利各工商金融业高管都齐聚“休息室”，共同商讨交易事项。尽快给这种“休息室文化”画上一个句号吧!
[2013.06.29] Defining financial bigotry: Disparate times 金融偏执的认定
Defining financial bigotry
金融偏执的认定
Disparate times
差异的时刻
A vital test case for the theory of disparate impact
差别影响理论的一项关键判例
Jun 29th 2013 | New York |From the print edition
1 THE court judgments come so thick and fast in finance nowadays that this one was easy to miss. Earlier this month the Supreme Court decided to hear an appeal by Mount Holly, a town in New Jersey, against a ruling that it had illegally discriminated against minority residents. The Obama administration has been trying to prevent the case from being heard. The civil-rights division of the Department of Justice (DoJ) weighed in with a brief urging the court to deny a hearing. It was signed by its director, Thomas Perez, whose role in blocking a similar case from reaching the Supreme Court last year has mired his nomination as labour secretary in controversy. If Mount Holly is indeed heard, it will be one of the most important in years for lenders.
当今，法院的金融裁决又快又多，这次裁决很容易错过。本月早些时候，美国最高法院决定审理新泽西(New Jersey)小镇芒特霍利(Mount Holly)提起的上诉，反对非法歧视当地少数族裔的裁定。奥巴马政府一直阻碍受理此案。美国司法部((DoJ)民权局局长佩雷斯(Thomas Perez)签发指示，敦促法院不要受理此案件。去年，佩雷斯也阻止了最高法院审理一份相似的案件。此举让他陷入困境，使他提名为劳工部长受到争议。假如芒特霍利案得到审理，这将是当地贷款方多年来最重要的一年。
2 The Mount Holly case began more than a decade ago, when the town decided to tear down 329 homes on 30 acres of land. Years of litigation in state courts upheld the town’s contention that the area was in need of redevelopment. Between 2002 and 2008 Mount Holly purchased 200 homes and demolished 70. Remaining residents challenged the actions in various courts, arguing the redevelopment would result in higher-priced homes that would have a lower percentage of minorities and thus violate the Fair Housing Act, a linchpin of 1960s civil-rights legislation that bans discrimination based on race, colour, religion or gender.
此事还得从十多年前说起。当时，小镇决定将建筑在30英亩的土地上的329家住房拆除。小镇认为此地需要重新开发，经过多年诉讼得到了州法院的支持。2002 至 2008年间，芒特霍利购买了200家住房，并拆除了70家。剩余居民到不同的法院上诉，反对拆迁。他们认为，重新开发将会导致房价上升，降低少数族裔居民比例，最终破坏《公平住房法案》。1960年代进行了民权立法，禁止进行种族、肤色、宗教以及性别歧视，而《公平住房法案》就是关键。
3 The town’s arguments were upheld in the district court, which concluded that there was a legitimate government interest in redevelopment; that no distinction had been made been “minorities and non-minorities”; and that there had been no intentional discrimination. That, argues the DoJ, misses the point, which is “whether the proposed redevelopment would have a disproportionate effect on a protected group”. What matters is not intent, in other words, but impact. An appeals court endorsed this view, prompting the town’s appeal to the Supreme Court.
小镇的诉求得到了地区法院的支持。法院得出结论认为，镇政府重新开发利益是合理的;没有区别对待“少数族裔和非少数族裔”;没有歧视的故意。美国司法部认为，地区法院的说法没有击中要害。此案的要点在于“重新开发是否会对受保护的群体产生过分影响”。意图不重要，关键是有没有影响。有一家上诉法院支持芒特霍利将案件上诉到最高法院。
4 The theory of “disparate impact” emerged first in the field of employment during the 1970s. It has since gained popularity among financial regulators, where the idea creates vast potential for falling foul of the rules. “Unless income, assets and credit performance are equally distributed among all racial and ethnic groups, any approach based on something even as basic as a credit score will produce a disparate impact,” says Thomas Noto of Morrison & Foerster, a law firm. Rather than risk litigation based on this theory, Wells Fargo, SunTrust Bank and Bank of America have within the past 12 months paid large settlements in cases tied to housing-lending fees and policies (and emphatically denied discrimination at the same time).
1970年代，就业领域首次出现了“差别影响”理论，此后得到金融监管机构的拥护。但是此理论又产生了与规则相冲突的巨大可能性。“假如收入、资产以及信贷机会不能在所有种族和民族平均分配，任何方法，就算以个人信用评分为基础，也会产生差别影响”，美富律师事务所(Morrison & Foerster)的托马斯•斯诺(Thomas Noto)说。美国富国银行(Wells Fargo)、太阳信托银行(SunTrust Bank)以及美国银行(Bank of America)摆脱了基于此理论的官司，他们在近12个月里，支付巨款了结了涉及住房贷款费用以及政策案件(期间着重拒绝歧视)。
5 Hence the importance of the Mount Holly case. Because of the role the Fair Housing Act has played in framing anti-discrimination policies more broadly and the similarities between anti-discrimination laws, whatever the Supreme Court rules in Mount Holly may well be echoed in standards applied to car loans, credit cards and even business credit. The newly established Consumer Financial Protection Bureau has said it will use disparate-impact analysis in its evaluation of lenders: that could change if the Supreme Court strikes down the standard.
这就是芒特霍利案的关键。因为《公平住宅法案》在反歧视政策框架制定中发挥了较为明显的作用，以及各种反歧视法之间的重合性，无论最高法院如何裁决芒特霍利案，适用于汽车贷款、信用卡以及商业信贷的各种标准都得到震荡。美国新设立的消费者金融保护局(Consumer Financial Protection Bureau)说，评估银行时会使用差别性影响分析：假如最高法院废弃此标准，那么银行评估方法有可能改变。
6 That outcome is widely expected if the case is heard in the autumn: the idea of disparate impact goes beyond the language in the Fair Housing Act itself, as passed by Congress. But the court may yet be bypassed: there are reports that a financial settlement is being negotiated with the residents. Those seeking an end to the use of disparate impact, or even a clearer sense of how it is defined, may have to wait for a new administration.
假如秋天审理此案，人们已经预料到了结果：差别影响的概念早已超出当年国会批准的《公平住房法》的条款范畴。但这宗官司也可能会撤销：据报道，政府正在与住户们商讨财务结算。那些希望结束使用差别性影响的人，或者是希望差别影响论的适用范围能够更清楚地定义的人，他们只有寄希望于新一届政府了。
纤云无语探苍穹——用方程式描述的数学故事
The Universe in Zero Words:
The Story of Mathematics as Told Through Equations
By Dana Mackenzie
没有文字的世界
——用方程式描述的数学故事
达纳•麦肯齐著
(标题的另一种译法：)
纤云无语探苍穹
——以数学方程为引：开启吧，时空的大门!
@yannanchen @nayilus @echo.chan @Dezazer @contrary @migmig
One afternoon in Rio de Janeiro, the Nobel Prize-winning physist Richard Feynman was eating dinner in his favorite restaurant. It wasn’t actually dinnertime yet, so the dining room was quiet … until the abacus salesman walked in. The waiters, who were presumably not interested in buying an abacus, challenged the salesman to prove that he could do arithmetic faster than their customer. Feynman agreed to the challenge.
里约热内卢的一个下午，诺贝尔奖金得主、物理学家理查德•费曼1 正在他喜欢的一家餐馆里用餐。其实这还不到吃晚饭的时间，所以餐厅里静悄悄的……但当一位算盘推销员走进来之后，一切就都不同了。侍应生们应该对买算盘没啥兴趣，但他们向推销员起哄，要他证明，他做算术题能比他们的一位顾客更快。费曼同意进行这一挑战。
At first, the contest wasn’t even close. On the addition problems, Feynman wrote, the abacus salesman “beat me hollow.” He would have the answer before Feynman even finished writing down the numbers. But then the salesman started getting cocky. He challenged Feynman to multiplication problems. Feynman still lost to the abacus, but not by as much. The salesman, not satisfied with his narrow margin of victory, challenged Feynman to harder and harder problems, and got more and more flustered. Finally he played his trump card. “Raios cubicos!” the salesman said. “Cube roots!”
开始时比赛完全一边倒。做加法时，费曼用笔算，算盘推销员把他打得“落花流水”。还不等费曼把数字写完，推销员就已经报出了答案。但接着推销员就趾高气扬起来了。他提出要跟费曼比赛乘法。这一盘费曼依旧败北，但输得没有第一次惨。推销员对自己没有大获全胜不满意，又不断地在越来越难的问题上向费曼挑战，但他的优势却越来越小，人也变得越来越慌张了。最后他祭出了杀手锏：“立方根!”推销员说。
Obviously, by this point the competition was more about pride than about selling an abacus. It’s difficult to imagine why a restaurant manager would ever need to compute a cube root. But Feynman agreed, provided that the waiters, who were watching the competition and enjoying it immensely, would choose the number. The number they picked was 1729.03.
显然，到了这一步，竞赛跟出卖算盘已经没多大关系了，更重要的是荣誉之争。很难想象一家餐馆的经理为什么会有一天需要计算立方根。但费曼同意了，条件是让兴致盎然地在周围观战的侍应生出题。他们选定了1729.03这个数字。
The abacist set to work with a passion, hunching over the abacus, his fingers flying too fast for the eye to follow. Meanwhile, Feynman writes, he was just sitting there. The waiters asked him what he was doing, and he tapped his head: “Thinking!” Within a few seconds, Feynman had written down five digits of the answer (12.002). After a while, the abacus salesman triumphantly announced “12!” and then a few minutes later, “12.0!” By this time Feynman had added several more digits to his answer. The waiters laughed at the salesman, who left in humiliation, beaten by the power of pure thought.
算盘高手热情洋溢地投入了工作。他伏在算盘上运指如飞，让观战者目不暇给。费曼写道: 与此同时，他却坐在那里一动也不动。侍应生们问他在干什么，他点了点自己的脑袋说：“思考!”几秒钟之内费曼就写下了五位数的答案(12.002)。过了一会儿，算盘推销员得意洋洋地喊出了“12”!几分钟后他又报出了“12.0”!但到这时，费曼的答案上已经又多出了几位数字。侍应生们嘲笑那位推销员。他在纯粹的思考面前惨遭败绩，铩羽而去。
Like all good tales, Feynman’s duel with the abacist has many layers of meaning. On the most superficial level, it is a story about genius; the Nobel Prize winner beating the machine. However, Feynman’s intention when he told this story about himself was quite different. He was not a boastful man. In the context of his book, the point of the story was that ordinary people—not Nobel Prize winners, not geniuses—could do just the same thing as he did, with a little bit of number sense and mathematical knowledge. There were two secrets behind his seemingly magical feat. First, he needed to know that 1728 was a perfect cube: 123 = 1728 (not common knowledge, perhaps, but it’s something most physicists would be aware of, because a cubic foot is 123 or 1728 cubic inches.) And he needed to know a famous equation from calculus, called Taylor’s formula—a very general approximation method that allows you to go from the exact equation:
17281/3 = 12
to the approximate equation: 1729.031/3 ≈ 12.002
这是一个很好的故事。一切好的故事都含有多层意义，费曼与算盘高手对决的这一故事也不例外。从最表面的意义上说，这是一个关于天才的故事;诺贝尔奖金得主击败了机器。然而，费曼在讲述这个有关自己的故事时有着与此大不相同的目的。他不是一个喜欢自夸的人。从他书中讲述的前因后果中可以看出，这个故事要说明的是：对数字有一定感觉、有一定数学知识的普通人也能跟他做得一样好。这些人用不着染指诺贝尔奖金，用不着是天才。他的技巧看上去如同魔法，但后面隐藏着两个秘密。首先，他需要知道1728是一个完全立方数：123 = 1728(或许这并不是人人都知道的常识，但大部分学物理的人都会知道，因为1立方英尺是123 或者说1728立方英寸2。)。而且他需要知道微积分中一个叫做泰勒公式的著名等式;这是一个非常普适的近似方法，可以让人通过已有的准确等式得到近似式，即从
17281/3 = 12
得到 1729.031/3 ≈ 12.002
Equations are the lifeblood of mathematics and science. They are the brush strokes that mathematicians use to create their art, or the secret code that they use to express their ideas about the universe. That is not to say that equations are the only tool that mathematicians use; words and diagrams are important, too. Nevertheless, when push comes to shove—for instance, when they have to compute the cube root of 1729.03—equations convey information with an economy and precision that words or abaci can never match.
公式是数学与科学的命脉。它们是数学家用来建造自己的艺术殿堂的一砖一石，或者说是他们用来表达他们有关宇宙的想法的密码。这并不是说，公式是数学家使用的唯一工具;语言与图表也很重要。但无论如何，在他们必须应付紧急情况时，例如在必须计算1729.03的立方根时，公式就能向他们传达简捷而又准确的信息，这是语言或者算盘永远无法比拟的。
The rest of the world, outside of science, does not speak the language of equations, and thus a vast cultural gap has emerged between those who understand them and those who do not. This book is an attempt to build a bridge across that chasm. It is intended for the reader who would like to understand mathematics on its own terms, and who would like to appreciate mathematics as an art. Surely we would not attempt to discuss the works of Rembrandt or Van Gogh without actually looking at their paintings. Why, then, should we talk about Isaac Newton or Albert Einstein without exhibiting their “paintings”? The following chapters will try to explain in words—even if words are feeble and inaccurate—what these equations mean and why they are justly treasured by those who know them.
在科学以外的世界中，人们不使用公式这种语言，因此在理解公式的人和不理解公式的人之间横亘着一条宏大的文化鸿沟。本书是在这一鸿沟上架设桥梁的一次尝试。本书的对象是那些愿意理解数学本身的意义、也愿意把数学作为一种艺术来欣赏的读者。毫无疑问，如果我们试图讨论伦勃朗3 或者凡高4 的作品，我们就必须观看他们的油画。既然如此，在说到艾萨克•牛顿或者阿尔伯特•爱因斯坦时，我们难道能够不去展示他们的“画作”吗?尽管语言贫乏而又不那么准确，但在以下各章中，我还是试图用语言来解释这些公式的意义，以及那些理解它们的人恰如其分地视它们如珍宝的原因。
Let's go back now to Richard Feynman and that abacus salesman, because there is more to say about them. In all likelihood, neither of them knew that they were playing out a scene that had already been enacted centuries before, when Arabic numerals first arrived in Europe.
让我们重新谈起理查德•费曼和算盘推销员吧，因为关于他们还有别的事情要说。非常可能的是，他们都不知道，他们这场竞赛的擂台其实在许多个世纪之前就已经搭起，那正是阿拉伯数字刚刚来到欧洲的时刻。
When the new number system appeared around the beginning of the thirteenth century, many people were deeply suspicious of it. They had to learn nine new and unfamiliar symbols: 1, 2, 3, 4, 5, 6, 7, 8, and 9—or, to be more precise, they had to learn the somewhat distorted thirteenth-century versions thereof. The new symbols looked to some people like occult runes, instead of the nice solid Roman letters (I, V, X, etc.) they were accustomed to. To make things worse, they were Arabic—not even Christian—which made them appear even more suspicious to a deeply religious society. And finally, they included an innovation that was especially hard to grasp: the number zero, a something that meant nothing.
当这一新的数字系统在大约十三世纪初出现的时候，许多人对它颇有疑虑。他们必须学习九个自己不熟悉的新符号：1，2，3，4，5，6，7，8，9;嗯，其实更准确地说，是与我们熟知的那些符号略有不同的十三世纪版本。对于某些人来说，这些新符号看上去不像他们习惯的罗马字母(I、V、X等等)那么好看，那么硬朗，而像是神秘的如尼5 符号。而让事情雪上加霜的是，它们甚至不是基督教世界的产物，而是阿拉伯的泊来品，这就更让一个笃信宗教的社会感到怀疑了。而且，最后，这些符号中还包括了一个更令人难以把握的新玩意，数字零，一个意味着什么都没有的东西。
Nevertheless, Arabic numbers had an undeniable power. Unlike Roman numerals, which were useful for writing numbers but impractical for calculating with them, the decimal place-value system made it possible to do both. In a sense, Arabic numbers democratized mathematics. In many ancient societies, only a specially trained class of scribes could do arithmetic. With decimal notation, you did not need special training or special tools, only your brain and a pen.
尽管如此，阿拉伯数字的力量是无可抗拒的。罗马数字在书写数字时很有用，但用它们计算则实在不敢恭维;而十进位制数字无论写或算都没有问题。从某种意义上说，阿拉伯数字让数学民主化了。在许多古代社会中，只有经过特殊训练的书吏阶层才能演算算术。但有了十进位制之后，人们再也不需要特殊训练或者特殊工具了，只要动脑子，再加上一支笔就成。
The struggle between the old and new number systems went on for a very long time—well over two centuries. And, in fact, open competitions were held between abacists (people who used mechanical tools to do arithmetic) and algorists (people who used the new algorithmic methods). So Feynman and the abacus salesman were re-fighting a very old duel!
新老数字系统之间的对决经历了漫长的岁月——远远超过两个世纪。而且事实上，在算盘高手(使用机械工具做算术的人)和算学大师(使用新算法的人)之间也曾有过多次公开较量。所以，费曼和算盘推销员之间的对撼是一场非常古老的决斗的重演!
WE KNOW HOW the battle ended. Nowadays, everyone in Western society uses decimal numbers. Grade school students learn the algorithms for adding, subtracting, multiplying, and dividing. So clearly, the algorists won. But Feynman’s story shows that the reasons may not be as simple as you think. On some problems, the abacists were undoubtedly faster. Remember that the abacus salesman “beat him hollow” at addition. But the decimal system provides a deeper insight into numbers than a mechanical device does. So the harder the problem, the better the algorist will perform. As science progressed during the Renaissance, mathematicians would need to perform even more sophisticated calculations than cube roots. Thus, the algorists won for two reasons: at the high end, the decimal system was more compatible with advanced mathematics; while at the low end, the decimal system empowered everyone to do arithmetic.
我们知道这场斗争的结局。如今，西方社会中的每一人都在使用十进位制数字。小学生用这种方法学习算术的加减乘除。所以，很明显的是，十进位算法取得了胜利。但费曼的故事告诉我们，背后的原因可能并不像人们想象的那么简单。对于某些问题，使用机械无疑要快些。记得吧，算盘推销员在加法问题上把费曼打得“落花流水”。但与机械装置相比，十进位制启迪人们，让他们对于数字有了更为深邃的洞察力。所以，问题越难，算学大师的表现就越好。当科学在文艺复兴时期发展、进步的时候，数学家就需要进行比求取立方根更为深奥的计算。因此，算学大师获胜的原因有二：其一，从高端来说，十进位制数字与高等数学更为匹配;其二，从低端来说，十进位制数字让人人都能做算术。
But before we start feeling too smug about our “superior” number system, the tale offers several cautionary lessons. First is a message that is far from obvious to most people: There are many different ways to do mathematics. The way you learned in school is only one of numerous possibilities. Especially when we study the history of mathematics, we find that other civilizations used different notations and had different styles of reasoning, and those styles often made very good sense for that society. We should not assume they are “inferior.” An abacus salesman can still beat a Nobel Prize winner at addition and multiplication.
且慢。在开始对自己“优越”的数字系统过分自鸣得意之前，我们还应该注意到，这个故事还给我们上了几堂有关谨慎的课程。首先，有一条对大多数人来说远非明显的信息，就是人们可以用许多不同的方法做数学。特别是在研究数学史时，我们会发现，其他文明的人类使用不同的计数法且有不同的推理方式，而那些方式经常合乎他们的社会的情理。我们不应该认为这些方式“低人一等”。一位算盘推销员照样可以在加法和乘法上击败一位诺贝尔奖金得主。
Feynman’s tale exemplifies also how mathematical cultures have collided many times in the past. Often this collision of cultures has benefited both sides. For instance, the Arabs didn’t invent Arabic numbers or the idea of zero—they borrowed them from India.
费曼的故事也是一个例子，它说明了不同的数学文化在历史上是如何多次发生冲突的。这种文化冲突时常让双方获利。例如，阿拉伯人并没有发明阿拉伯数字或者零这个理念，他们是从印度人那里学来的。
Finally, we should recognize that the victory of the algorists may be only temporary. In the present era, we have a new calculating device; it’s called the computer. Any mathematics educator can see signs that our students’ number sense, the inheritance bequeathed to us by the algorists, is eroding. Students today do not understand numbers as well as they once did. They rely on the computer’s perfection, and they are unable to check its answers in case they type the numbers in wrong. We again find ourselves in a contest between two paradigms, and it is by no means certain how the battle will end. Perhaps our society will decide, as in ancient times, that the average person does not need to understand numbers and that we can entrust this knowledge to an elite caste. If so, the bridge to science and higher mathematics will become closed to many more people than it is today.
最后，我们应该认识到，算学大师的胜利可能只是暂时的。当今之世，我们有了一种叫做计算机的新型计算机器。任何数学教育工作者都能够看到以下迹象：当代的学生正在逐步丢失算学大师为我们留下的遗产——对于数字的感觉。今天的学生们对数字的了解不如过去了。他们依赖于计算机的尽善尽美;万一他们打错了键盘，他们没有能力检查计算机的结果是否正确。现在，我们又一次发现，我们正处于两种观念对抗的年代，而人们还完全不清楚这一战役会以何种结局收场。或许，我们的社会会像古时候一样认为，一般人没有必要了解数字，这种知识可以交由特别的精英人士处理。如果情况果真如此，将有比今天多得多的人发现：对于他们来说，通往科学与高等数学的桥梁将无异于一架不可企及的天梯。
1. 理查德•费曼(Richard Phillips Feynman，1918 -1988)，美国物理学家。1965年诺贝尔物理奖得主。他提出的费曼图、费曼规则和重整化的计算方法是研究量子电动力学和粒子物理学的重要工具。
2. 英制1英尺 = 12 英寸。1英寸 ≈ 2.54厘米。
3. 伦勃朗(Rembrandt，1606 – 1669)，荷兰画家。
4. 凡高(Van Gogh，1853 – 1890)，荷兰画家。
5. 如尼符号(runes)，古代北欧人使用的字母和文字，西欧人过去有时认为它们带有神秘色彩。
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