Rojo-Garibaldi Berenice, Rangoni Costanza, González Diego L, Cartwright Julyan H E
Posgrado en Ciencias del Mar y Limnología, Universidad Nacional Autónoma de México, Av. Universidad 3000, Col. Copilco, Del. Coyoacán, Cd.Mx. 04510, Mexico.
Istituto per la Microelettronica e i Microsistemi, Area della Ricerca CNR di Bologna, 40129 Bologna, Italy.
Heliyon. 2021 Mar 23;7(3):e06580. doi: 10.1016/j.heliyon.2021.e06580. eCollection 2021 Mar.
Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 × 20, …, 18 × 20 . We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written in different ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems.
前哥伦布时期的中美洲是数字系统发展的肥沃新月地带。从最早的奥尔梅克文明开始，一种二十进制系统的形式似乎就已存在，后续民族也为其做出了贡献。我们讨论了玛雅人在其长纪年历中对表示冗余的运用，长纪年历是一种非幂次位置数字表示系统，乘数为1、20、18×20、……、18×20 。我们证明，中美洲人不需要同时发明位置记数法和发现零，因为他们不惧怕使用同一个数字可以用不同方式书写的数字系统。后来可以看到，一个数字从0到20的长纪年数字系统转变为一个数字从0到19的系统，这使我们提出，甚至更早之前可能存在一个最初没有零的双射记数系统，其数字从1到20。由于熟悉多种和冗余的数字表示系统，中美洲能够在概念上向基数零的概念迈进以进行算术运算。
