从出土简牍文献看中国早期的正负数概念

THE CONCEPTS OF POSITIVE AND NEGATIVE NUMBERS IN EARLY CHINA REFLECTED IN THE UNEARTHED BAMBOO AND WOODEN SLIPS

Through the analysis of the contents related to the official evaluations in the unearthed documents with the references of the historical literature,some misunderstandings to the concepts of positive and negative numbers in ancient China could be corrected and the early history of the concepts of the positive and negative numbers could be constructed.This paper pointed out that the standard to judge if the ancient people used the concepts of positive and negative numbers is that the opposite natures were grafted into amounts and became parts of the amounts;argued that the character Suan算 in the Yi医(the Doctor)entry of Suanshu Shu算数书(Writings on Reckoning)could not be a tax unit or a currency unit in general meaning and this entry was neither for the income and tax of a doctor practicing medicine nor for the earning and cost.This paper proved that the Yi entry was the rules defining the lowest ratio of successes to failures of a qualified doctor’s treating cases,and the Suan was the scoring unit for assessing the effects of the treatments of the doctor.By grammatical analyses,this paper proved that the concepts of positive and negative numbers do have been applied in the Yi entry of Suanshu Shu and the Chapter "Kao Gong Ming考功名(Appraise Achievement and official position)" in Chunqiu Fan Lu(Luxuriant Dew of the Spring-and-Autumn Annals)by Dong Zhongshu;however,those suspected cases seen in the wooden slip documents unearthed from the sites of the Han Dynasty in Juyan and Dunhuang are still waiting for confirmation because of insufficient information.This paper argues that the opposite meanings such as gains and losses,successes and failures,etc.were indeed the foundations for the concepts of positive and negative numbers,but the special structure of the Fangcheng(juxtaposed examinations of standards)algorithm in pre-Qin Period was the decisive factor to prompt the emergence of these concepts.The new concepts of positive and negative numbers influenced the evaluation and examination methods to the officials,the traces of which could be seen in the Yi entry of Suanshu Shu and the Chapter "Kao Gong Ming考功名"in Chunqiu Fan Lu(possibly including some contents of the wooden slip documents of Juyan and Dunhuang).This paper also analyzed the features of using concepts of positive and negative numbers in these assessing methods.At the end,this paper gave a preliminary discussion to the research methods and emphasized the importance of grammatical analyses and the idea of knowledge structure.

Through the analysis of the contents related to the official evaluations in the unearthed documents with the references of the historical literature, some misunderstandings to the concepts of positive and negative numbers in ancient China could be corrected and the early history of the concepts of the positive and negative numbers could be constructed. This paper pointed out that the standard to judge if the ancient people used the concepts of positive and negative numbers is that the opposite natures were grafted into amounts and became parts of the amounts; argued that the character Suan 算 in the Yi 医 （the Doctor） entry of Suanshu Shu 算数书 （Writings on Reckoning） could not be a tax unit or a currency unit in general meaning and this entry was neither for the income and tax of a doctor practicing medicine nor for the earning and cost. This paper proved that the Yi entry was the rules defining the lowest ratio of successes to failures of a qualified doctor＇s treating cases, and the Suan was the scoring unit for assessing the effects of the treatments of the doctor. By grammatical analyses, this paper proved that the concepts of positive and negative numbers do have been applied in the Yi entry of Suanshu Shu and the Chapter ＂Kao Gong Ming 考功名 （Appraise Achievement and official position）＂ in Chunqiu Fan Lu （Luxuriant Dew of the Spring-and- Autumn Annals） by Dong Zhongshu; however, those suspected cases seen in the wooden slip documents unearthed from the sites of the Han Dynasty in Juyan and Dunhuang are still waiting for confirmation because of insufficient information. This paper argues that the opposite meanings such as gains and losses, successes and failures, etc. were indeed the foundations for the concepts of positive and negative numbers, but the special structure of the Fangcheng （juxtaposed examinations of standards） algorithm in pre-Qin Period was the decisive factor to prompt the emergence of these concepts. The new concepts of positive and negative numbers influenced the evaluation and examination methods to the officials, the traces of which could be seen in the Yi entry of Suanshu Shu and the Chapter ＂Kao Gong Ming 4~ 5）J J/~＂in Chunqiu Fan Lu （possibly including some contents of the wooden slip documents of Juyan and Dunhuang）. This paper also analyzed the features of using concepts of positive and negative numbers in these assessing methods. At the end, this paper gave a preliminary discussion to the research methods and emphasized the importance of grammatical analyses and the idea of knowledge structure.