Narrator: Listen to part of a lecture in a world history class.

旁白：请听一段世界史讲座的节选片段。

Female professor: So, one of the more common topics that comes up in world history, because it's had a pretty dramatic effect on how different societies evolve over long periods of time, is cultural diffusion.

女教授：因此，在世界历史上出现的一个比较普遍的话题是文化传播，因为它对不同社会在很长一段时间内的发展产生了相当大的影响。

Now…cultural diffusion is generally defined as the transmission of culture from one society to another.

现在……文化传播通常会被定义为文化从一个社会传播到另一个社会。

And by culture, we mean anything from artistic styles to, um… you know, technology, science. So, we use "culture" very broadly.

这里的文化，我们是指很多事物，从艺术风格到……嗯……到技术、科学……所以我们这里所指的"文化"其实是个很广泛的概念。

A common means of this process taking place is trade, traveling merchants, or trading hubs, places where people from various areas all come together and ideas get exchanged.

这一过程的一个常见方式是贸易，商人奔走交易或者通过贸易中心，在这些地方，来自不同地区的人们聚集在一起，交换想法。

Let's start with the example of the transmission of a number system, a system that used the number zero, from South Asia into Western Europe.

我们从计数系统传播的例子讲起，这个系统是使用数字0的，它从南亚传到了西欧。

OK, so before this cultural diffusion happened, the dominant number system in Western Europe was the Roman numeral system.

好的，在这种文化传播之前，西欧占主导地位的数字系统是罗马数字系统。

The Roman numeral system developed primarily as a means of record keeping, as a way to keep track of commercial transactions, um, taxes, census records, things of that sort.

罗马数字系统的发展主要是作为一种记录手段，作为一种记录商业交易的方式，嗯……税收，人口普查记录，诸如此类。

As a consequence, this system started with the number one.

因此，这个系统从1开始。

Female student: With one? Not with zero?

女学生：从1开始？不是从0开始吗？

Female professor: Right. See, in Roman numerals, zero isn't really a value in and of itself.

女教授：是的。你看在罗马数字系统里，数字0本身并不是一个数值。

It wasn't used independently as a number on its own. If your primary concern's just basic types of record keeping…

它不是一个单独的数字。如果你主要关心的只是基本的记录方式……

Female student: Oh, yeah, I guess you wouldn't need a zero to count livestock.

女学生：哦，是的，我猜并不需要数字0去计数家畜。

Female professor: Or to keep track of grain production, or do a census.

女教授：也不需要用它来记录谷物产量或者统计人口。

And it wasn't an impediment as far as sort of basic engineering was concerned, either, um, to their ability to construct buildings, roads, stuff like that.

直到人们开始考虑一些关于基础工程学的事情，嗯，也就是去建造建筑、修路这种事情之前，没有0并不会造成任何阻碍。

But other number systems developed in Asia, systems that do incorporate zero.

但是亚洲开发的其它数字系统，确实包含零。

The mathematics these societies developed included things like negative numbers, so you start to get more sophisticated levels of mathematics.

这些社会研究出来的数学成果还包含了负数之类的东西，所以这就开始达到更加复杂的数学水平。

So… one of the earliest written texts sub-mathematics that has zero, negative numbers, even some sort of basic algebra, is written in South Asia in the early seventh century.

所以……最早的书面文本之一是子数学，它有零，负数，甚至一些基本的代数，是于7世纪早期在南亚写成的。

This text makes its way into the Middle East, to Baghdad, and is eventually translated into Arabic by a Persian astronomer and mathematician.

这个文字记录被传到了中东，到达巴格达，它最后由一位波斯天文学家兼数学家翻译成阿拉伯语。

Once he begins his translation, he quickly realizes the advantages of this system, the types of math that can be done.

在他开始翻译的时候，他很快就意识到这个计数系统的优越性，及其可以完成的数学运算。

Soon, the text begins to be more widely circulated through the Middle East, and other mathematicians start to advocate using this number system.

很快，这个文字记录经中东广为流传，另一些数学家开始提倡使用这一个计数系统。

So, by the tenth century, it's the dominant system in the Middle East and as a consequence, algebra and other more sophisticated forms of mathematics start to flourish.

因此，到了10世纪，它成为中东地区的主导系统，因此，代数和其它更复杂的数学形式开始蓬勃发展。

Meanwhile, in Western Europe, the Roman numeral system, a system without zero, was still in place.

同时，在西欧，不包含0的罗马计数系统依旧被使用着。

In the late twelfth century, an Italian mathematician named Fibonacci was traveling in North Africa along with his father, a merchant.

在公元12世纪末期，一位名为斐波那契的意大利数学家同他的商人父亲在北非旅行。

And while he's there, Fibonacci discovers this Arabic text. He translates the… uh, the text into Latin and returns to Europe.

他在那里发现了这篇阿拉伯语的文字。他把这篇文字翻译成了……拉丁语，然后回到了欧洲。

And he promotes the adoption of this number system because of the advantages in recording commercial transactions, calculating interest, things of that nature.

他提倡采用这个数字系统，因为它在记录商业交易，计算利息等方面具有优势。

Within the next century and a half, that becomes the accepted, dominant number system in Western Europe.

在接下来的一个半世纪里，这成为了西欧公认的、占主导地位的数字系统。

Any questions? Robert?

有问题吗？罗伯特？

Male student: Um, this Fibonacci, is he the same guy who invented that… uh, that series of numbers?

男学生：嗯，这个斐波那契，他是发明那个……嗯那个数列的人吗？

Female professor: Ah...yes, the famous Fibonacci sequence. Although he didn't actually invent it, it was just an example that had been used in the original text…

女教授：啊，是的，著名的斐波那契数列。尽管实际上不是他发明的，它只是一个被用在你们课本上的例子而已……

I mean, can you imagine? Introducing the concept of zero to Western Europe? And this is what you go down in history for? Carol?

我是说，你能想象吗？将零的概念引入西欧？这就是你被载入史册的原因？卡罗尔？

Female student: So… do we see, like, an actual change in everyday life in Europe after the zero comes in, or is it really just…

女学生：所以……在0被引进欧洲以后，我们感受到了切实的日常生活的改变吗，或者它们仅仅是……

Female professor: Well, where the change takes place is in the development of sciences.

女教授：改变是发生在科学发展的进程中的。

Female student: Oh.

女学生：哦。

Female professor: Even in basic engineering, it isn't a radical change.

女教授：即使在基础工程领域，这也不是一个根本性的改变。

Um, but as you start to get into, again, the theoretical sciences, uh, higher forms of mathematics… calculus… zero had a much bigger influence in their development.

但是当你开始进入理论科学，更高形式的数学……微积分……0对它们的发展有更大的影响。

OK, now note that, as cultural diffusion goes, this was a relatively slow instance.

注意，随着文化传播，这是一个相对缓慢的例子。

Some things tend to spread much quicker, um, for example, artistic or architectural styles, such as domes used in architecture.

有些东西传播得更快，比如艺术或建筑风格，比如建筑中使用的穹顶。

We see evidence of that being diffused relatively quickly, from Rome to the Middle East to South Asia…

我们可以看到，从罗马到中东再到南亚，穹顶相对迅速地传播的证据……