论数以及数字符号的产生

Expounding the Evolution of Numbers and Numerical Symbols

本文讨论数字符号的产生及其逻辑发展过程。数学符号是对于数的抽象 ,因此文章从数的本质谈起 ,认为数是一种感官 ,是对于生存环境的一种悟性 ,其本质是“多少”。关于数的第一步抽象是计数 ,第二步抽象才是数学符号。从第一步抽象过渡到第二步抽象 ,人类用了漫长的时间 ,越过了三个重要的障碍。基于上述的论证 ,文章在最后提出了一个问题 :数学到底是发明还是发现 ?

The article aims at expounding the emergence and the logical evolution procedures of numerical symbols. Numerical symbols are the abstract of numbers, so the article starts its expounding from finding the hypostasis of numbers. The author holds that numbers are a kind of sense, it is a kind of savvy of certain surroundings. The hypostasis of number is how to express 'more or less'. The first step of abstracting a number is how to count while the second step is the appearance of numerical symbols. It takes a fairly long time for human kind to finish the transition from the first step to the second one. Amongst, people have overcome three significant impediments. Grounding on the above theories, the article raises a question: is mathematics an invention or a finding?