剑桥雅思6Test2 PASSAGE 3 参考译文：计数发展史

新航道雅思为各位考生推荐复习材料-剑桥雅思6Test2 PASSAGE 3 参考译文：计数发展史；本单元其他相关译文，有需求的同学请：剑桥雅思6TEST 2 PASSAGE 2 参考译文：老龄人口健康依旧。

　　TEST 2 PASSAGE 3 参考译文：

　　Numeration

　　计数发展史

　　One of the first great intellectual feats of a young child is learning how to talk, closely followed by learning how to count. From earliest childhood we are so bound up with our system of numeration that it is a feat of imagination to consider the problems faced by early humans who had not yet developed this facility. Careful consideration of our system of numeration leads to the conviction that, rather than being a facility that comes naturally to a person, it is one of the great and remarkable achievements of the human race.

　　学说话是儿童最初掌握的主要智力技能之一，而紧随其后他们就要学会数数。从小我们就对数数这件事十分熟悉，所以真得费番心思才能想象出不会数数的先祖们的境遇。深思熟虑之后，我们确信计数不是人们生来就拥有的技能，而是人类伟大而非凡的成就之一。

　　It is impossible to learn the sequence of events that led to our developing the concept of number. Even the earliest of tribes had a system of numeration that, if not advanced, was sufficient for the tasks that they had to perform. Our ancestors had little use for actual numbers; instead their considerations would have been more of the kind Is this enough? rather than How many? when they were engaged in food gathering, for example. However, when early humans first began to reflect on the nature of things around them, they discovered that they needed an idea of number simply to keep their thoughts in order. As they began to settle, grow plants and herd animals, the need for a sophisticated number system became paramount. It will never be known how and when this numeration ability developed, but it is certain that numeration was well developed by the time humans had formed even semi-permanent settlements.

　　现在，我们无法了解人类创造数字这一概念的发展历程。即使没有先进的技术，连最原始的部落也拥有足够他们日常生活所需的计数方法。我们的祖先并不需要使用具体的数字;比如当他们采集食物时，他们会更多地考虑“够了吗?”而不是“有多少?”来代替具体数字的使用。然而，当早期人类开始思考周围事物的本质时，他们发觉自己需要数字的概念以保持思路的淸晰。随着他们开始定居生活、种植作物和放牧牲畜，需要一套复杂数字系统的要求变得极为重要。我们永远无法了解这种计数能力是如何以及何时发展起来的，但可以确定的是，当人类刚刚开始建立暂时的定居点时，计数方法已经发展得比较完备了。

　　Evidence of early stages of arithmetic and numeration can be readily found. The indigenous peoples of Tasmania were only able to count one, two, many; those of South Africa counted one, two, two and one, two twos, two twos and one, and so on. But in real situations the number and words are often accompanied by gestures to help resolve any confusion. For example, when using the one, two, many type of system, the word many would mean, Look at my hands and see how many fingers I am showing you. This basic approach is limited in the range of numbers that it can express, but this range will generally suffice when dealing with the simpler aspects of human existence.

　　关于早期算术和计数方法的证据并不难寻找。澳大利亚塔斯马尼亚州的土著民族民仅能计数“一”、“二”和“许多”;南非当地的土著民族能够计数“一”、“二”、“二加一”、“二加二”、“二加二加一”等等。然而，在实际情况中，数字和词语经常伴随着手势使用以帮助解决混乱的状态。例如，在使用“一、二和许多”计数系统时，“许多”一词可能表示“看我的手并数出我向你伸出了几根手指”。这种基本的方法限制了可表示的数字范围，但此范围对于处理人类生存方面的简单问题来说通常是足够的。

　　The lack of ability of some cultures to deal with large numbers is not really surprising. European languages, when traced back to their earlier version, are very poor in number words and expressions. The ancient Gothic word for ten, tachund, is used to express the number 100 as tachund tachund. By the seventh century, the word teon had become interchangeable with the tachund or hund of the Anglo-Saxon language, and so 100 was denoted as hund teontig, or ten times ten. The average person in the seventh century in Europe was not as familiar with numbers as we are today. In fact, to qualify as a witness in a court of law a man had to be able to count to nine!

　　一些文化缺少处理较大数字的能力，这并不令人惊讶。当追溯到早期彤式时，欧洲的各语种在数字及其表达方式上均十分贫乏。古哥特语中代表十的词语“tachund”在表示数字100时写作“tachund tachund”。到 公元7世纪，“teon”一词变得可以与盎格鲁一撒克逊语中的词语“tachund”或“hund”相互交换，因此100被表示为“hund teoning”或者“十乘十”。在7世纪的欧洲，普通人对数字的熟知程度远不及今天的人们。事实上， 当时人们必须具备数到9的能力才有资格作为证人出庭作证。

　　Perhaps the most fundamental step in developing a sense of number is not the ability to count, but rather to see that a number is really an abstract idea instead of a simple attachment to a group of particular objects. It must have been within the grasp of the earliest humans to conceive that four birds are distinct from two birds; however, it is not an elementary step to associate the number 4, as connected with four birds, to the number 4, as connected with four rocks. Associating a number as one of the qualities of a specific object is a great hindrance to the development of a true number sense. When the number 4 can be registered in the mind as a specific word, independent of the object being referenced, the individual is ready to take the first step toward the development of a notational system for numbers and, from there, to arithmetic.

　　或许，要发展对数字的领悟能力，最重要的一步不是拥有计数的能力，而是能够理解数字是相当抽象的概念，而并不只是与个别物品相联系的附属品。早期人类一定能够明白两只鸟与四只鸟的不同;然而. 他们却不具备将与四只鸟相关的数字4和与四块石头相关如数字4联系起来的基本能力。将数字与特定事物的性质之一相联系，对于发展真正的数宇感而言是巨大的障碍。当数字4在头脑中变成一个特定的词语并与其所指的事物相分离时，人类便向数字符号系统的发展迈出步，并继而发展算术学。

　　Traces of the very first stages in the development of numeration can be seen in several living languages today. The numeration system of the Tsimshian language in British Columbia contains seven distinct sets of words for numbers according to the class of the item being counted: for counting flat objects and animals, for round objects and time, for people, for long objects and trees, for canoes, for measures, and for counting when no particular object is being numerated. It seems that the last is a later development while the first six groups show the relics of an older system. This diversity of number names can also be found in some widely used languages such as Japanese.

　　至今，在有些现存的语言中依然可以寻找到早期计数方法的发展痕迹。在加拿大英属哥伦比亚省，根据计数的物品种类，钦西安语的计数系统包含截然不同的七组表达数字的词语：计数扁平物体和动物的词语，计数圆形物体和时间的词语，计算人数的词语，计数长条物体和树木的词语，计算独木舟数目的词语，计量尺寸的词语，以及在不计数具体事物时所用的词语。看起来最后一组词语是后来发展起来的，而前六 组则带有古代计数方法的痕迹。在一些诸如日语等广泛使甩的语言中，同样可以发现数字名称的多样性。

　　Intermixed with the development of a number sense is the development of an ability to count. Counting is not directly related to the formation of a number concept because it is possible to count by matching the items being counted against a group of pebbles, grains of corn, or the counter’s fingers. These aids would have been indispensable to very early people who would have found the process impossible without some form of mechanical aid. Such aids, while different, are still used even by the most educated in today’s society due to their convenience. All counting ultimately involves reference to something other than the things being counted. At first it may have been grains or pebbles but now it is a memorised sequence of words that happen to be the names of the numbers.

　　数字感与计数能力的发展相互融合。计算与数字概念的形成并非直接相关，因为我们完全有可能将被计数的物品用一堆石子、一把谷粒或者计数者的手指代替来进行计算。这些辅助工具对于早期人类而言是必不可少的，一旦离开某些形式的工具辅助，计数过程便无法完成。由于使用方便，类似的辅助工具在当今社会中仍然以不同的方式被人们——甚至是最有学识的学者们——使用。所有的计算最终都将由某事物、而不是被计数的物品指代。最初，这种指代或许是谷粒或石子，但现在已经变成一串被记忆的单词，而这些单词只是恰巧成为数字的名称而已。

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