“超以象外 数从安出”——从中国古代彩陶花纹看数的起源

Origin of numbers

早期人类究竟是怎样开始记数的 ,因历史久远而难以考查。古代文献中保存下来的一些零星记载也无法让今人真正了解数的起源。本文作者从《周髀》一书中“数之法出于圆方”的提法获得启示 ,通过对新石器时代大量彩陶等日用器皿上花纹符号的研究 ,发现了其中蕴藏的数理内涵及其规律 ,使中国古代关于数的起源的传说在彩陶花纹的组合形式中得到验证 ,从而得出数的起源正是在对日月往来观测认识的记录中、在“超以象外”

It is tough finding out how on earth human race of early period began to count numbers because of a long history. Some sporadic records preserved from the ancient literatures can hardly help people really understand the origin of numbers. The writer of the paper gets some ideas from the old saying “the principle of the number rests in round and square”in the book Zhou Bi. By conducting researches on the pattern signs of Large quantities of colored crockery and utensils in New Stone Age, the underlying connotation and regularity of number theory was found in it, which has verified the old Chinese lore that numbers were the combination of colored crockery and patterns. Therefore, the impontant conclusion is drawn from the statement that numbers originated from the observed records of the to-and-fro of the sun and the moon.