【英语语言学习】数字0的曲折历史

ERIC WESTERVELT, HOST:

Think of all the numbers you've encountered today - the clock in your smartphone, maybe the date on your calendar, the numbers on that highway sign. And those are just the ones you can see. It's easy to take numbers for granted. They're the scaffolding that our economy, our technology, huge parts of our daily life, are built on. But there was a time when a zigzagging¹ line didn't mean two and a vertical² line didn't mean one and a circle didn't mean zero. Just how that system developed is a question that's fascinated Amir Aczel since his childhood. He's a math and science writer, and his new book is "Finding Zero: A Mathematician's Odyssey³ To Uncover The Origins Of Numbers."

AMIR ACZEL: To me, the invention or discovery of numbers is the greatest intellectual invention of the human mind. I have say invention or discovery because that's a huge problem in the philosophy of mathematics. Did we invent numbers, or do they exist regardless of us? But writing numbers is certainly an invention, and that invention is what has obsessed⁴ me all of my life.

WESTERVELT: You also explore some of the faults, starts and dead-ends along the way to our current system of numbers, which are known as Hindu- Arabic numerals. Could you talk about some of the number systems that, I guess you could say, have gone extinct?

ACZEL: Right. The Maya had a very interesting number which they used in calendars. And there was a zero there, actually. That number system didn't go anywhere. And then of course, there's the Babylonian number, (unintelligible) numbers, and they did not really have a zero. Sometimes they'd leave a space. And the best example - and my favorite - is the Roman numerals. And if you want to try something interesting with the Roman numerals, try to create the multiplication⁵ table and you can see it's very complicated. So and, the reason is that the numbers don't cycle. They have to use, say, L for 50 and C for 100. So it's unique, while we can use the same sign, like two, in different places. Two with a zero after it is 20. Two alone is just two. You can create numbers using the cyclicity of the numerals. And that's something that no other number system that I know of has.

WESTERVELT: Why is zero, specifically, so important?

ACZEL: Without a zero, you couldn't allow the numerals to cycle. You couldn't do this example that I gave, the two followed by zero stands for 20, creating that great economy where just nine signs plus a zero allow us to write any number that we want.

WESTERVELT: What sparked your interest in finding the origin of zero? You take us on this quest around the world.

ACZEL: I first became interested in numbers - my father was a ship's captain for cruise ship in the Mediterranean⁶, and one of the favorite ports was Monte Carlo. And what I saw there were these numerals, and they're very beautiful, on a roulette table in the fanciest casino in the world. These numerals just captured me, my attention and my fascination⁷. And it sort of - that really led me to pursue a career in mathematics and statistics. And then I became very interested in where these numerals came from. Everybody says, oh, numbers come from India. And I wanted to know how they came from India, and then I became aware of the big controversy⁸ with British scholar G. R. Kaye.

WESTERVELT: Who was convinced that the zero came from the West.

ACZEL: Exactly, and he was actually an expert on India, but he was biased⁹. He writes in one of his papers, like, Indians think that their history started several million years ago and of course this is nonsense and the numerals don't come from India.

And the person I follow in the book, Georges Coedes, a French scholar, tried to prove the opposite. And this particular style that I'm after throughout this book that I'm trying to find is that zero that he used to defeat Kaye and his followers¹⁰.

WESTERVELT: Your book is called "Finding Zero," so this isn't really a spoiler. I mean, you traced the earliest-known written representation of zero to this crumbling¹¹ 7th century tablet that you find in Cambodia, and its stacked amid ruins of other ancient artifacts. What was going through your mind?

ACZEL: It's the greatest euphoria in my life. And I have a feeling I'll never have a moment like that ever again. And I just looked at it. I couldn't dare touch it, as if it were fragile - which it wasn't, it's a piece of stone weighing several tons. Greatest moment in my life.

WESTERVELT: Tell us its significance, what it said. Where was the zero, and what did the zero mean there in that writing?

ACZEL: Well, it says Chaka 605 began in the fifth day of the waning¹² moon. So it's really an astronomical¹³ description of the beginning of a year and a calendar called Chaka. So luckily, they had the date there. So because the date has a zero, we have the first zero. And they had to write a zero. And what the rest of the tablet talks about is about slaves to be given to a king and sacks of white rice and several other things. So it's a list of gifts to a local king.

WESTERVELT: Amir, we knew this tablet existed. I mean, why was it so important to find the physical object?

ACZEL: Well, often times you read when you do research about something that disappeared. And when something is gone, it's really far from being the same anymore. To me, it was important to recover this artifact with the earliest zero because I feel it's important to see it and continue to study it. And there's a monument to this great invention of the human mind, the ability to write something down that represents complete nothingness.

WESTERVELT: Amir Aczel speaking with us from WGBH in Boston. His new book is called "Finding Zero." Thanks so much for speaking with us.

ACZEL: Thank you very much. It was my pleasure.

1 zigzagging   

v.弯弯曲曲地走路，曲折地前进( zigzag的现在分词 )；盘陀

参考例句：

• She walked along, zigzagging with her head back. 她回头看着，弯弯扭扭地向前走去。 来自《简明英汉词典》
• We followed the path zigzagging up the steep slope. 我们沿着小径曲曲折折地爬上陡坡。 来自互联网

2 vertical   

adj.垂直的，顶点的，纵向的；n.垂直物，垂直的位置

参考例句：

• The northern side of the mountain is almost vertical.这座山的北坡几乎是垂直的。
• Vertical air motions are not measured by this system.垂直气流的运动不用这种系统来测量。

3 odyssey   

n.长途冒险旅行；一连串的冒险

参考例句：

• The march to Travnik was the final stretch of a 16-hour odyssey.去特拉夫尼克的这段路是长达16小时艰险旅行的最后一程。
• His odyssey of passion, friendship,love,and revenge was now finished.他的热情、友谊、爱情和复仇的漫长历程，到此结束了。

4 obsessed   

adj.心神不宁的,鬼迷心窍的,沉迷的

参考例句：

• He's obsessed by computers. 他迷上了电脑。
• The fear of death obsessed him throughout his old life. 他晚年一直受着死亡恐惧的困扰。

5 multiplication   

n.增加，增多，倍增；增殖，繁殖；乘法

参考例句：

• Our teacher used to drum our multiplication tables into us.我们老师过去老是让我们反覆背诵乘法表。
• The multiplication of numbers has made our club building too small.会员的增加使得我们的俱乐部拥挤不堪。

6 Mediterranean   

adj.地中海的；地中海沿岸的

参考例句：

• The houses are Mediterranean in character.这些房子都属地中海风格。
• Gibraltar is the key to the Mediterranean.直布罗陀是地中海的要冲。

7 fascination   

n.令人着迷的事物，魅力，迷恋

参考例句：

• He had a deep fascination with all forms of transport.他对所有的运输工具都很着迷。
• His letters have been a source of fascination to a wide audience.广大观众一直迷恋于他的来信。

8 controversy   

n.争论，辩论，争吵

参考例句：

• That is a fact beyond controversy.那是一个无可争论的事实。
• We ran the risk of becoming the butt of every controversy.我们要冒使自己在所有的纷争中都成为众矢之的的风险。

9 biased   

a.有偏见的

参考例句：

• a school biased towards music and art 一所偏重音乐和艺术的学校
• The Methods: They employed were heavily biased in the gentry's favour. 他们采用的方法严重偏袒中上阶级。

10 followers   

追随者( follower的名词复数 )； 用户； 契据的附面； 从动件

参考例句：

• the followers of Mahatma Gandhi 圣雄甘地的拥护者
• The reformer soon gathered a band of followers round him. 改革者很快就获得一群追随者支持他。

11 crumbling   

adj.摇摇欲坠的

参考例句：

• an old house with crumbling plaster and a leaking roof 一所灰泥剥落、屋顶漏水的老房子
• The boat was tied up alongside a crumbling limestone jetty. 这条船停泊在一个摇摇欲坠的石灰岩码头边。

12 waning   

adj.（月亮）渐亏的，逐渐减弱或变小的n.月亏v.衰落( wane的现在分词 )；（月）亏；变小；变暗淡

参考例句：

• Her enthusiasm for the whole idea was waning rapidly. 她对整个想法的热情迅速冷淡了下来。
• The day is waning and the road is ending. 日暮途穷。 来自《现代汉英综合大词典》

13 astronomical   

adj.天文学的，（数字）极大的

参考例句：

• He was an expert on ancient Chinese astronomical literature.他是研究中国古代天文学文献的专家。
• Houses in the village are selling for astronomical prices.乡村的房价正在飙升。