印度文字记数法及其文化背景探析  

An Analysis of Indian Letter Numeral Systems and Its Cultural Background

作　　者：吕鹏 纪志刚 LYU Peng;JI Zhigang

机构地区：[1]上海交通大学马克思主义学院科学史与科学文化研究院,上海200240

出　　处：《上海交通大学学报（哲学社会科学版）》2024年第6期110-119,共10页Journal of Shanghai Jiao tong University(Philosophy and Social Sciences)

基　　金：教育部人文社会科学研究青年项目“基于梵语原典的印度中世历算书《婆罗摩修正体系》研究”(18YJCZH121);陕西高校青年创新团队“丝绸之路科技文明交流研究创新团队”项目。

摘　　要：基于原典史料整理了古代印度数学文献中对于数的四种文字表记方法,根据先后年代,分别是:《吠陀》中的十进制数词;《阿耶波多历算书》中的字母表记法,采用百进制,以梵语元音-辅音来对应数,用于表示巨大的天文常数;具象数词,以朴素集合观念为基础,用表示自然人文事物的词来表记数量;Ka-T a-Pa-Ya式表记法,辅音表示1~9和0,再适当选择元音就可用富有意义的词来表记数量。了解以上数表记法的用法和特点后,可以发现古代印度数学文献虽以数学内容为主,但在撰写过程中还兼及修辞,具有简洁优美及易于传诵的特点。这一现象的根源在于印度数学的发展与印度独特的文化背景,如帕尼尼语法学、宗教神话和哲学等,都有着密切的联系。Chronologically,the four ancient Indian letter numeral systems are the decimal numeral first appeared in the earliest Indian canon Vedas;the alphabetical numeral of ryabha t a used in his ryabha tīya,which is based on the grammatical classification of vowels and consonants and centesimal system,and can express large astronomical constants;the being-numeral which is based on the concept like the set theory,and uses the natural or ideal beings for expressing numbers;and the alphabetical numeral of Ka-T a-Pa-Ya,which,regarding consonants as quantities 1 to 9 and 0,and depending on choice of proper vowels,can express numbers by meaningful words.From the using and the characteristic of the four kinds of numerals,it is known that the ancient Indian mathematical texts are not only the description of the mathematical knowledge but also the literary composition full of flowery rhetoric made for the purpose of recitation,the root of which lies in the close relationship between the development of mathematics and the Indian distinctive culture such as Panini's grammar,mythology and philosophy.

关 键 词：印度数词 《阿耶波多历算书》 具象数词 印度神话 梵语修辞 

分 类 号：O11[理学—数学] K351.2[理学—基础数学] G135.1[历史地理—历史学] H711[历史地理—世界史]