‘Finding Zero’: A Persistent Journey Far Into the Past, for Naught
追根究柢 尋找零的起源
By Amir Alexander

Most tourists who venture to the tiny town of Khajuraho, India, are drawn by the thousand-year-old Jain and Hindu temples, especially the explicit sex depicted in the statues adorning the walls.
前來印度卡傑拉霍鎮旅遊的人，多半是被有千年歷史的耆那和印度教寺廟所吸引，尤其是牆面裝飾雕像描繪的露骨性愛。

But when the mathematician Amir Aczel visited in January 2011, he was looking for a four by four “magic square” carved into the wall. Among the 16 numbers was a familiar-looking “10,” written in Hindu numerals. It is one of the earliest known representations of the numeral zero.
不過，數學家艾克塞爾2011年1月來參觀時，找的卻是刻在牆上、橫豎各四格的「魔術方陣」。在16個數字中有一個看起來像「10」，用印度文數字寫成。這是人類所知最早用來表達「數字0」的符號之一。

“Finding Zero” is Dr. Aczel’s story of his quest for the origins of the most elusive of numbers: zero. It is zero that makes our place-value number system possible. Without it, there is no way to distinguish among 48, 480 and 4,080. Zero is indispensable for our arithmetical operations, and it is half of the binary language of modern computers.
「尋找0」是艾克塞爾尋找「0」這個最難捉摸數字的起源的故事。是「0」讓我們的位置--數值數字系統得以運作。沒有它，就無法分辨48、480和4080。我們的算術少不了0，在現代電腦二進制語言中它也占了一半。

And yet, Europeans had no concept of zero until the 13th century, when they referred to it as an Indian or Arabic numeral.
不過，歐洲人直到13世紀才有0的概念，認為它是個來自印度或阿拉伯的數字。

So Dr. Aczel turns to the East.
艾克塞爾因此轉而到東方世界尋覓。

Dating from 954, the magic square at Khajuraho predates European zeros by a full three centuries, and yet it is not the oldest zero in India. This is in Gwalior, where a temple inscription from 876 records a grant of land 270 “hastas” long. But Dr. Aczel is looking for something even older: The date of the Gwalior zero, he worries, is contemporaneous with the Baghdad Caliphate, which might lend credence to the theory that the zero was transmitted to India from the West by Arab traders.
卡傑拉霍方陣的年代是西元954年，比歐洲的0早了整整三世紀，但這還不是印度最古老的0。最古老的在圭勒爾市，一則西元876年的寺廟碑文記載，一片轉讓的土地有270「hastas」長。不過艾克塞爾還在尋找年代更久遠的，他思忖的是，圭勒爾的0跟巴格達哈里發國同時期，這使得「0的概念從西方透過阿拉伯商人傳到印度」的推測更為可信。

But the zero, he is sure, is the creation of “the Eastern mind.”
不過他很確定，0是「東方心智」的產物。

In Eastern thought the rigid oppositions between existence and nonexistence are blurred. This fluidity, Dr. Aczel believes, allows for the juxtaposition of mathematics and sex at Khajuraho. It accounts for “shunyata,” goal of Buddhist meditation. And zero, in Hindi, is “shunya.”
在東方人的觀念裡，存在和不存在的壁壘分明變模糊了。艾克塞爾認為，就是這種流動性讓卡傑拉霍同時呈現數學與性愛。這種流動性能夠解釋「空性」（shunyata），也就是正面的空無，是佛教禪修的目標，而印地語的0就是shunya。

But the recording of dates and measurements in Gwalior and elsewhere suggests that ancient Indians could be as practical in their use of numbers as Europeans. And exchanges between the Indian subcontinent and the Mediterranean world date to at least to the Persian Achaemenid Empire, about a thousand years before the Baghdad Caliphate.
不過，圭勒爾和其他地方的日期和丈量紀錄顯示，古代印度人使用數字就跟歐洲人一樣實際。印度次大陸和地中海世界的貿易至少要追溯到波斯阿契美尼德王朝，大概比巴格達哈里發國早一千年。

Back in 1929, Dr. Aczel learns, the French archaeologist George Coedès translated an inscription found in the ruins of a Cambodian temple, which includes the date 605, equivalent to A.D. 683. The discovery was celebrated at the time, but the inscription had since been lost.
艾克塞爾得知，1929年時，法國考古學家戈岱司把在柬埔寨一座寺廟廢墟發現的一則碑文翻譯為法文，碑文中寫有日期「605」，年代約當西元683年。當時學界對這個發現相當高興，之後碑文卻失蹤了。

Dr. Aczel hunts for clues in Thailand, Cambodia, Laos and Vietnam, slowly piecing together the whereabouts of the stele.
艾克塞爾在泰國、柬埔寨、寮國、越南尋找線索，慢慢拼湊出石碑的下落。

Dr. Aczel finds himself in an antiquities storage shed near the famous Cambodian temples of Angkor Wat. He comes across a stone with an inscription. And there, clearly discernable, was the oldest known zero, lost for nearly a century. Did Dr. Aczel rediscover the true origins of zero? That is questionable. But his tale is filled with the passion and wonder of numbers.
艾克塞爾發現自己身在柬埔寨著名寺廟群吳哥窟附近的古物庫房。他偶然發現一塊石頭上有碑文，碑文明顯可辨，正是已知最古老、失蹤近一世紀的0。艾克塞爾是否重新發現了0的真正起源？不無疑問，不過他的故事充滿了對數字的熱情和驚嘆。

原文參照：
http://www.nytimes.com/2015/04/21/science/finding-zero-a-long-journey-for-naught.html

2015-05-12聯合報/G5版/UNITED DAILY NEWS 李京倫譯 原文參見紐時週報十版下