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TPO51托福听力Lecture 2原文文本

标题：The Transmission of A Number System

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

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 evolved over long periods of time is cultural diffusion. Now, cultural diffusion is generally defined as the transmission of culture from one society to another. And by culture, we mean anything from artistic styles to……um……you know, technology, science. So we use culture very broadly. A common means of this process taking place is trade, travelling merchants or trading hubs, places where people from various areas all come together and ideas get exchanged.

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.

Ok, so before this cultural diffusion happened, the dominant number system in Western Europe was the Roman Numeral System. The Roman Numeral System developed primarily as a means of record-keeping, as a way to keep track of commercial transactions, um, taxes, censors’ records, things of that sort. As a consequence, this system started with the number One.

Student:

With One? Not with Zero?

Professor:

Right. See in Roman Numerals, Zero isn’t really a value in and out itself. It wasn’t used independently as a number on its own. If your primary concerns just basic types of record-keeping……

Student:

Oh, yeah. I guess you wouldn’t need a Zero to count livestock.

Professor:

Or to keep track of green production or do a census. 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.

But other number systems developed in Asia, systems that do incorporate Zero. The mathematics these societies developed included things like negative numbers. So you start to get more sophisticated levels of mathematics.

So one of the earliest written text sub mathematics, that has Zero, negative numbers, even some sort of basic algebra, is written in South Asia in the early 7th century. This text makes its way into the Middle East, to Baghdad. And it’s eventually translated into Arabic by a Persian astronomer and mathematician. Once he began his translation, he quickly realizes the advantage of this system, the types of math that can be done. Soon, the text begins to be more widely circulated through the Middle East. And other mathematicians start to advocate using this number system.

So by the 10th 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. Meanwhile, in Western Europe, the Roman Numeral System, a system without Zero, was still in place.

In the late 12th century, an Italian Mathematician named Fibonacci was travelling in North Africa along with his father, a merchant. And while he’s there, Fibonacci discovers this Arabic text. He translates the text into Latin, and returns to Europe. And he promotes the adoption of this number system because of the advantages in recording commercial transactions, calculating interests, things about nature. Within the next century in the half, that becomes the accepted dominant number system in Western Europe.

Any questions? Robert?

Robert:

Um, this Fibonacci, is he the same guy who invented that……um…….that series of numbers?

Professor:

Ah……yes. The famous Fibonacci sequence. Although he didn’t actually invent it, it was just an example that had been used in your original text. I mean, can you imagine? Introducing the concept of Zero to Western Europe? And this is what you go down the history for?

Carol?

Carol:

So, do we feel like an actual change in everyday life in Europe after the Zero comes in? Or they really just……

Professor:

Well, well, the change takes place is in the development of sciences.

Carol:

Oh.

Professor:

Even in basic engineering. It isn’t a radical change. Um, but as you start to get into, again, the theoretical sciences, ah, higher forms of mathematics, calculus, Zero had a much bigger influence in their development.

Ok, now note that as cultural diffusion goes, this was a relatively slow instance. Some things tend to spread much quicker, um, for example, artistic, or architectural styles, such as domes used in architecture. We see evidence of that being diffused relatively quickly from Rome to the Middle East to South Asia……

TPO51托福听力Lecture 2题目

TPO51 12

What does the professor mainly discuss?

The advantages and disadvantages of the Roman numeral system

The importance of the number zero in tracking commercial transactions

How a new number system affected trade

How a number system spread from one society to another

TPO51 13

What does the professor imply about the record-keeping methods used by early Western Europeans?

They led directly to advances in basic engineering.

They required an understanding of elementary algebra.

They did not require a counting system that included the number zero.

They were more sophisticated than those used in the Middle East.

TPO51 14

What role did the Italian mathematician Fibonacci play in the example of cultural diffusion that the professor describes?

He introduced a text in Europe that he had translated from Arabic.

He was the first to use the number zero in higher-level mathematics.

He encouraged the use of a new number system in tracking grain production.

He translated an Italian text into Arabic during his travels through the Middle East.

TPO51 15

What is the professor's opinion about the effects of the new number system on European society? Its most important effects were on merchants and tradespeople.

It had little impact on daily life.

It affected engineers more than other scientists.

It quickly caused most people’s lives to change radically.

TPO51 16

重听题What can be inferred about the professor when she says this:

She wants the students to appreciate the mathematical significance of the Fibonacci sequence.

She believes that Fibonacci’s contributions to mathematics were unoriginal.

She is impressed by the breadth of Fibonacci's genius.

She is surprised at the reason that Fibonacci is primarily remembered today.

TPO51 17

Why does the professor mention domes in architecture?

To point out a style of architecture that was not spread by traveling merchants

To emphasize that the speed at which cultural diffusion occurs can vary widely

To give an example of a type of engineering that is only possible with the use of zero

To explain that domes were invented in Asia but were more popular in Rome

TPO51托福听力Lecture 2答案解析

12.答案：D

解析：

此题出处是：

Professor:

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.

讲座开头教授就说明，这节课要用数字系统传播的例子来说明文化扩散这个现象。选项D符合。选项A是说罗马计数系统的优劣，选项B是说0在记录商业交易方面的重要性，选项C是说新的计数系统是如何影响贸易的，都不合适。选择D。

13.答案：C

解析：

此题出处是：

Professor:

Right. See in Roman Numerals, Zero isn’t really a value in and out itself. It wasn’t used independently as a number on its’ own. If your primary concerns just basic types of record-keeping……

Student:

Oh, yeah. I guess you wouldn’t need a Zero to count livestock.

这里教授和学生一问一答，表明如果仅仅是为了一些简单的计数的话，其实西欧本身的罗马计数法也是可以胜任的，所以这个计数法里面不包括0，选项C符合。选项A是说它们能直接导致了基础工程学的进步，选项B说它们需要对于基础代数的理解，选项D说它们比中东的计数法更复杂，都不合适。选择C。

14.答案：A

解析：

此题出处是：

Professor:

Fibonacci discovers this Arabic text. He translates the text into Latin, and returns to Europe. And he promotes the adoption of this number system because of the advantages in recording commercial transactions, calculating interests, things about nature.

斐波那契的贡献就是把一篇计数法的文章翻译成了拉丁语，并回到欧洲进行推广，选项A合适。选项B说他是第一个在高等数学里使用0的，选项C说他鼓励用新计数系统记录谷物产量，选项D说他把意大利语的文章翻译成了阿拉伯语，都不正确。选择A。

15.答案：B

解析：

此题出处是：

Carol:

So, do we feel like an actual change in everyday life in Europe after the Zero comes in? Or they really just……

Professor:

Well, well, the change takes place is in the development of sciences.

Carol:

Oh.

Professor:

Even in the basic engineering. It isn’t a radical change.

这里通过师生问答我们可以知道，其实0引入欧洲以后，并没有对人们的日常生活产生大的影响，而是对于例如高等数学这种领域的进展产生了重要影响。选项B合适。选项A是说它最多地影响到了商人，选项C是说它影响工程师比影响科学家要多，选项D说它导致大多数人的生活剧烈改变了，都不合适。选择B。

16.答案：D

解析：

此题出处是：

Professor:

Ah……yes. The famous Fibonacci sequence. Although he didn’t actually invent it, it was just an example that have been used in your original text. I mean, can you imagine? Introducing the concept of Zero to Western Europe? And this is what you go down the history for?

这里教授用一个反问句来说明，其实她认为斐波那契靠把0引入欧洲而留名青史是很惊奇的。选项D正确。选项A是说她要学生感激斐波那契数列的发现，选项B说她相信斐波那契的贡献不是原创的，选项C是说她对于斐波那契广泛的才能印象深刻，都不合适，选择D。

17.答案：B

解析：

此题出处是：

Professor:

Ok, now note that as cultural diffusion goes, this was a relatively slow instance. Something’s tend to spread much quicker, um, for example, artistic, or architectural styles, such as domes used in architecture.

这里教授提到圆顶，是为了举例说明文化扩散的过程不仅有慢的，也有快的，不同事物的文化扩散速度是不同的。选项B合适。选项A是说要指出一种通过商人旅行传播的建筑风格，选项C是说为了举出一个必须有0才能进行的一种工程，选项D是为了解释为什么圆顶在亚洲发明却流行于欧洲，都不合适。选择B。

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