McGill University, Montreal, Canada.
Stud Hist Philos Sci. 2021 Aug;88:92-101. doi: 10.1016/j.shpsa.2021.03.001. Epub 2021 Jun 2.
The design of good notation is a cause that was dear to Charles Babbage's heart throughout his career. He was convinced of the "immense power of signs" (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage's writings, for the first time in a systematic way. Babbage's desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed.
好的记法设计是查尔斯·巴贝奇（Charles Babbage）整个职业生涯中所珍视的事业。他深信“符号的巨大力量”（1864，364），既可以严谨地表达复杂的思想，也有助于发现新的思想。年轻时，他在英国推广了莱布尼茨微积分记法，后来又为设计他的计算引擎开发了机械记法。此外，他还思考了良好的数学记法设计所依据的原则。本文首次以系统的方式讨论了这些在巴贝奇的著作中有些零散的思考。巴贝奇对数学记法的要求被提出作为与记法设计及其在单个符号和复杂表达式中的应用相关的十条准则。为了说明这些准则在非数学领域的适用性，还讨论了他的机械记法的一些方面。
