| 单词 | 数学概念 |
| 释义 | 〔fraction〕One might think that a word likefraction as well as its ancestors might have always referred to the mathematical fraction. Certainly the mathematical notion of a fraction was known to the Babylonians, perhaps as early as 2000b.c. But our wordfraction goes back only to the Latin word frangere, "to break.” From the stem of the past participlefrāctus is derived Late Latin frāctiō, "a breaking" or "a breaking in pieces,”as in the breaking of the Eucharistic Host.In Medieval Latin the wordfrāctiō developed its mathematical sense, which was taken into Middle English along with the word.The earliest recorded sense of our word is "an aliquot part of a unit, a fraction or subdivision,”found in a work by Chaucer written about 1400.One of the next recorded instances of the word recalls its origins, referring to the "brekying or fraccioun" of a bone.人们也许认为一个词如fraction 以及它的词源总是指数学上的分数。 当然，分数的数学概念也许早在公元前 2000年就已被巴比伦人所熟知。 但fraction 一词仅能追溯到拉丁词 frangere ，“打碎”。 源自过去分词fractus 的词干是派生的后期拉丁语 fractio ， 意为“破裂”或“碎成一片片的”，如感恩节的饼的碎块。在中世纪拉丁语中，fractio 一词出现了数学意义， 这个词连同此意义都被记入中世纪英语中。这个词最早记载的意义是“一个数学单元，繁分数或再分数的约数”，出现在约1400年乔臾写的一部作品里。后来此词有记录的例子之一，指骨头上的“裂痕或碎片”，使人回忆起它的起源〔innumerate〕Unfamiliar with mathematical concepts and methods.对数学概念和方法不熟悉的〔innumerate〕A person who is unfamiliar with mathematical concepts and methods.对数学概念和方法不熟悉的人〔parallel〕In its mathematical usageparallel is an absolute term— two lines either do or do not intersect—and as such does not admit of qualification as to degree.Some grammarians have arguedthat this restriction should apply as well to nontechnical uses of the word.According to this logic,one may not sayThe two roads have been made more parallel, except perhaps as a loose way of saying what is rendered more precisely by expressions such asmore nearly parallel. Like the analogous objection that has been made to the comparison ofequal, the point betrays a misconception about the relation between mathematical concepts and their ordinary-language equivalents.Applied to objects in the world,parallel can only denote a rough approximation to a geometric ideal. A pair of rails or parked cars cannot be truly parallel in the mathematician's sense of the termbut only more or less so,just as a road or shelf cannot be truly straight in the geometric sensebut nonetheless may be described as very straight or relatively straight.The grammarians' compunctions make even less sense when applied to metaphorical uses ofparallel, as inThe difficulties faced by the Republicans are quite parallel to those that confronted the Democrats four years ago, in which the intended meaning has nothing to do with the possibility of intersectionbut instead suggests the structural correspondence of two distinct situations.In this sense, parallelism is clearly a matter of degreeand the wordparallel can be modified accordingly. See Usage Note at equal ,perfect ,unique 在数学用法中，parallel 是一个绝对的表达法—— 两条线要么相交，要么就不相交——它既没有限定性也没有程度差别。一些语法学家曾提出，这种限制也应该适用于该词在非科技方面的用法，按照这种逻辑，人们不能说这两条路已被修得更加平行了， 除非作为用例如更接近于平行 这样的表达方法更精确地表示的东西的不够精确的说出方法。 象对equal 的比较所做的类似反对一样， 这个观点使数学概念与普通用语中等价词之间的关系引起误解。当运用到世间的实物时，parellel 仅能指与几何理想状态大致接近的状况。 一对铁轨或停放的车辆不可能按数学家对于这个术语的理解来真正地相互并行，而不过是大致平行而已，正如公路和架子不可能是真正几何意义上的笔直，但仍可被描绘成很直的或相对而言的笔直。在用到parallel 的比喻用法时，语法学家的不安就更显得意义不大了， 例如：共和党人所面临的重重困难与四年前民主党人遇到的困难十分相似， 在这句话中，该词的引申意义与相交的可能性毫无关系，然而它暗指了两种不同情况结构上的一致。在此意义上，相似性明显是程度的问题，相应地，parallel 一词也能被其它词限定修饰了。 参见 equal,perfect,unique〔equal〕It has been argued thatequal is an absolute term— two quantities either are or are not equal—and hence cannot be qualified as to degree.Therefore one cannot logically speak ofa more equal allocation of resources among the departments. However, this usage was accepted by 71 percent of the Usage Panel in an earlier survey.What is more, objection to the usage betrays a widespread but questionable assumptionthat it is in mathematics and logic that we find the model of accuracy most appropriate to the everyday use of language,a supposition that also underlies traditional grammatical discussions of words such asunique, parallel, and center. According to this account,the "precise" or "literal" meaning ofequal is realized in the use of the equal sign in an arithmetic expression such as 5 + 2 = 7; and the ordinary-language uses of the term,though they may be permissible,represent "loose" or "imprecise" extensions of that sense.But in fact the mathematical concept of equality is a poor model for using the wordequal to describe relations between things in the world. As applied to such things,statements of equality are always relative to an implicit standard of tolerance.When someone saysThe two boards are of equal length, we assume that the equality is reckoned to some order of approximation determined by the context;if we did not,we would be required always to usenearly equal when speaking of the dimensions of physical objects. What is more,we often want to predicate equality of things that do not admit of quantitative measurement,as when we sayThe college draft was introduced in an effort to make the teams in the National Football League as equal as possible, orThe candidates for the job should all be given equal consideration. In all such cases,equality is naturally a gradient notionand so is amenable to modification in degree.This much is evident from the existence of the wordunequal. The prefixun- attaches only to gradient adjectives: we sayunmanly but not unmale; and the worduneven can be applied to a surface (whose evenness may be a matter of degree) but not to a number (whose evenness is an either-or affair). ·The adverbequally is generally regarded as redundant when used in combination with as, and the following examples employingequally as were termed unacceptable by 63 percent of the Usage Panel in an earlier survey: 单词equal 一向被认为是一个很绝对的词语—— 两个数量要么相同要么不同——这样就不能有程度上的差别。所以，如果有人说在各部门间对资源更公平的分配 ，那么就不合逻辑了。 但是这种用法在早先的用法调查中被百分之七十一用法使用小组的人接受。而且，对这种用法的反对体现出了一种很流行但却值得怀疑的假设，那就是我们从数学和逻辑中得出适用于日常语言准确性的实例，而这种假设也可从我们对一些词，如unique，parallel 和 center 传统的语法讨论中体现出来。 根据这个解释，equal “准确”或“书面”的意思则是由在算术表达式，如5+2=7中所运用的相同的符号而表达清楚的； 而该词在日常语言中的用法，虽然被允许，但却代表了其含意“松散”或“不严谨”的引申。但是实际上用数学概念上的相等来运用equal 这个词描述世上各种事物之间的关系是一个很差劲的例子。 当该词应用于生活中的事物时，相等的观念往往与暗含的容忍相关联。当有人说两块木板同样长 时， 我们会认为由于上下文的关系，相等可以被看作大约近似；如果我们不这样想，那么当我们谈到物体的尺寸时，就要经常使用nearly equal 。 另外，我们常常会预测和数量无关的事物的相同性，比如我们会说，引入大学的要求是为了使全国足球联合会中的各队尽可能平等 ， 或者应给予该项工作的应征者同等的考虑 。 在所有这些例子中，相等是个可变化的概念，所以可在程度有所不同。Unequal 这个词的存在就是很好的证明。 un- 这个前缀只附加于有程序变化的形容词， 我们说unmanly 但不说 unmale ； 而uneven 这个词只能用于某物的表面（其平坦可有程度上的差别）， 而不能用于数目（数目只能说相等或不相等）。Equally 这一副词在与 as 连用时通常被认为是多余的， 在早先的用法调查中，以下这些使用equally as 的句子遭到百分之六十三使用小组的人反对： |
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