Abstract

（第二版：非正式双语版本，含中文原文，含部分英文翻译） (Version 2: Partial Bilingual Edition, Chinese manuscript with a selected English Translations) 摘要（简体中文版/Simplified Chinese Version）： 本文探讨了道家「无」与「有」以及相关概念在数学与信息技术框架下的对应表达，并从语言学、认知论、知识论等角度分析「无」与数学中的0。本文拟将「无」对应0而「有」对应1：主要包括以下三种对应方式——二进制对应「有无相生」，「无」对应0，「有」对应与1；实数集与复数集中「无」对应0这一加法单位元，「有」对应1这一乘法单位元；线性空间中「无」对应0向量，而「有」对应模长为1的单位向量所组成的基向量，基向量张成整个空间对应「天下万物生于有」，所有向量数乘0后变成0向量对应「有无相生」和「有生于无」；0以及零向量等作为加法单位元在代数结构中的不可或缺对应「太初有无」和「有生于无」。本文试从语言学与知识论（epistemology）与认知论（cognitivism）的角度，探讨「无」的通俗表达「没有」一词的命名中的标出性（markedness）与部分语言文字或数字系统中数字0的缺位，探讨文化中「无」与0的概念所受的忽略与轻视或，并用结构化的角度分析文化中这种忽略可能的成因、分析人类个体与文明对于相对更抽象化的概念的认知过程。 关键词：道家；道德经；老庄；跨学科；加法单位元；语言学；线性代数；二进制；系统性偏差 Abstract (English Version): This essay investigates the interdisciplinary connection between the philosophy of Daoism(/Taoism/道家思想) and mathematics and investigates the linguistics in the naming of concepts and number systems, to discuss how this reflects how people build perception of abstract or conceptual content. This essay discusses how the Daoist philosophical concepts of Wu (/absence/not being/nothingness) and You (presence/being/having) can correspond to concepts in mathematics and how philosophical concepts like the conversion between Wu and You can be expressed in mathematics. This essay maps the philosophical concept of Wu and You to 0 and 1 in mathematics in the three following approaches: under binary system, map Wu to 0 and You to 1; in real and complex number sets, map Wu to additive identity like 0 and You to multiplicative identity; in linear space, map Wu to zero vectors and You to basis vectors especially unit basis vectors (basis vectors of norm=1). Keywords: Daoism, Taoism, interdisciplinary studies, zero vectors, linguistics, markedness