Hogben, Lancelot: Mathematics, the Mirror of Civilization

数学,人类文明的镜子

I

人类文明早期,数学与神学关系密切。最早的掌握数学的是神职人员,如埃及的神职人员可测量尼罗河的涨落,他们在普通人面前使用不同的“语言”以隐藏真相。

早期的普通人不能读写。普通的语言可看作是“种类语言”(sort language)。宗教改革后建立语法学校,人们可以阅读《圣经》。

现代社会的人必需学会“测量语言”(language of measurement) 才能理解现代科学中的“圣经”。 今天的人们的快乐生活依赖于正确解释公开的统计数据。

To-day the lives and happiness of people depend more than most of us realize upon the correct interpretation of public statistics which are kept by government offices.

时代在变,数字更多地进入人们的日常生活,size language 演化。人们受圉于社会遗产。

The most brilliant intellect is a prisoner within its own social inheritance.

举例 Achiles and tortoise,  从历史的角度引入极限的分数小数,进一步说明数学家也不能脱离现实社会。

Beyond a certain point clever people can never transcend the limitations of the social culture they inherit.

II

数学如语言一样是工具。

Tyranny has no enemy so formidable as the pen.

To-day economic tyranny has no more powerful friend than the calculating prodigy.

然而,数学在历史上解放人类的作用常常被忽视。

教育系统的建立,削弱了教皇的地位。

数学语言在商业的应用。

几何学起初为有闲阶层的游戏。

柏拉图教育观物质观使数学更神秘。

III

本书从社会进化的角度来谈数学,而非其他书着重于习题

两种看待数学的观点:

柏拉图:数学代表永恒的真理 (Mathematical statements represent eternal truths)。

另一观点:   数学是有关大小的语言(Mathematics is the language of size, and that is an essential part of the equipment of an intelligent citizen to understand this language. )

数学语言的特点: The language of size have no place for private sentiment, either of the individual or of the nation.

IV

数学的发展很慢。数学的历史就是文明史的镜子。

The history of mathematics is the mirror of civilization.

 (GGB, Vol. 9, pp. 3-23; originally Chapter 1 of Mathematics for the Million)

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