小分享：0的起源

分享一个今天在新闻上看到小趣事——（我自己翻译了一下 -v- 末尾有附上原文和原文链接）

“不存在”的价值

古希腊人计算出了三角形的斜边，领会了无理数，但他们并没有创造出代表“虚无”的符号——零。而最古老的“占位符”概念，是由巴比伦人发展出来的，它的含义是，当把数字1000和1相加，得到的结果是1001，这个数跳过了中间的“百”和“十”，仅由数位“千”和“一”组成，所以“百”和“千”在这个数里是不存在的，而巴比伦人设计出的双头镐形状的“占位符”，就用来表示这种不存在。但现代数学中的“0”却并不是由双头镐符号演化而来，而是起源于一份古老的印第安人数学手稿 (Bakhshali manuscript) 上的一个点。这份写在桦树皮上的破碎手稿在1881年被发现于如今的巴基斯坦地区。而在本周发表的，对这份手稿的碳同位素测定结果显示，它来自公元3或4世纪，比考古学家们的预期结果早了5个世纪，而手稿上表示0的“点”也随着时间逐渐演变成了我们今天书写的圆圈“0”。然而直到公元7世纪以前，这个最初的“0”点都没有被它的创造者和使用者看作一个单独的，表示“不存在”的数学概念。看到“不存在”的价值，却需要真正的眼力。
——《经济学人: Espresso》2017年9月16日

原文：

Nothing matters: mathematics

Ancient Greeks calculated the length of a triangle's hypotenuse and had a grasp of irrational numbers. But they had no symbol for absence—zero. The Babylonians developed a "placeholder" much earlier, representing zeroes in a number like 1,001: a sum of one thousand and one one, but no hundreds or tens. Their double-wedge indicator, though, went no further in the annals of mathematics. The symbol that became the modern zero started as a dot in the Bakhshali manuscript, a fragmented birch-bark document found in 1881 in modern Pakistan. Radiocarbon dating, reported this week, pushes its age back to the third or fourth century AD, five centuries earlier than thought. Over time, the dot's depiction progressed into a circle like today's zero. However, its creators didn't think of their dots as separate, mathematical nothingnesses; that idea arose in the seventh century. It takes real vision to see what isn't there.

---Sep 16th 2017, Economist: Espresso
原文链接