托福tpo51听力lecture2 The Transmission of A Number System

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The Transmission of A Number System托福听力原文翻译及问题答案

一、The Transmission of A Number System托福听力原文：

NARRATOR:Listen to part of a lecture in a world history class.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.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,uh…you know…technology,science…so,we use“culture”very broadly.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.

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,uh,taxes,census records,things of that sort.As a consequence,this system started with the number one.FEMALE STUDENT:With one?Not with zero?FEMALE PROFESSOR:Right.See,in Roman numerals,zero isn't really a value in and of itself.It wasn’t used independently as a number on its own.If your primary concern's just basic types of record keeping…FEMALE STUDENT:Oh,yeah,I guess you wouldn't need a zero to count livestock.FEMALE PROFESSOR:Or to keep track of grain 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 texts of mathematics that has zero,negative numbers,even some sort of basic algebra,is written in South Asia in the early seventh century.This text makes its way into the Middle East,to Baghdad,and is eventually translated into Arabic by a Persian astronomer and mathematician.Once he begins his translation,he quickly realizes the advantages 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 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.Meanwhile,in Western Europe,the Roman numeral system,a system without zero,was still in place.

In the late twelfth century,an Italian mathematician named Fibonacci was traveling in North Africa along with his father,a merchant.And while he's there,Fibonacci discovers this Arabic text.He translates the…uh,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 interest,things of that nature.Within the next century and a half,that becomes the accepted,dominant number system in Western Europe. 

Any questions?Robert?

MALE STUDENT:Um,this Fibonacci—is he the same guy who invented that…uh,that series of numbers?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…I mean,can you imagine—introducing the concept of zero to Western Europe,this is what you go down in history for? 

Carol?

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…FEMALE PROFESSOR:Well,where the change takes place is in the development of sciences.FEMALE STUDENT:Oh.

FEMALE PROFESSOR:Even in basic engineering,it isn't a radical change.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.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…

二、The Transmission of A Number System托福听力中文翻译：

旁白：在世界历史课上听讲座的一部分。女教授：所以，世界历史上出现的一个比较常见的话题是文化传播，因为它对不同的社会在很长一段时间内的演变产生了相当大的影响。现在……文化传播通常被定义为文化从一个社会传播到另一个社会，文化指的是从艺术风格到，呃……你知道……技术、科学……所以，我们非常广泛地使用“文化”。这一过程的一种常见方式是贸易……旅行商人，或贸易中心，来自不同地区的人们聚在一起交流思想的地方。

让我们从数字系统的传输示例开始，该系统使用从南亚到西欧的数字零。好吧，在这种文化传播发生之前，西欧占主导地位的数字系统是罗马数字系统。罗马数字系统最初是作为一种记录手段发展起来的，作为一种跟踪商业交易、税收、人口普查记录等的方式。因此，这个系统从数字一开始。女学生：一个？没有零钱？女教授：对。在罗马数字中，零本身并不是一个真正的值。它并没有单独用作数字。如果你主要关心的只是记录的基本类型…女学生：哦，是的，我想你不需要零来计算牲畜数量。女教授：或者跟踪谷物产量，或者进行人口普查。就基础工程而言，这也不妨碍他们建造建筑物、道路之类的东西。

但亚洲开发的其他数字系统，确实包含零。这些社会发展的数学包括负数之类的东西，所以你开始获得更复杂的数学水平。所以……最早的数学书面文本之一，有零，负数，甚至一些基本代数，是在七世纪初写于南亚的。这篇文章传到了中东、巴格达，最终被一位波斯天文学家和数学家翻译成了阿拉伯语。一旦他开始翻译，他很快就意识到这个系统的优点，即可以完成的数学类型。很快，这本书开始在中东更广泛地传播，其他数学家开始提倡使用这种数字系统。

因此，到了10世纪，它成为中东的主导系统，因此，代数和其他更复杂的数学形式开始蓬勃发展。与此同时，在西欧，罗马数字系统，一个没有零的系统，仍然存在。

十二世纪末，一位名叫斐波那契的意大利数学家与他的父亲，一位商人一起在北非旅行。当他在那里的时候，斐波那契发现了这段阿拉伯文字。他把…呃，这段文字翻译成拉丁语，然后返回欧洲。他提倡采用这种数字系统，因为它在记录商业交易、计算利息等方面具有优势。在接下来的一个半世纪内，这将成为西欧公认的、占主导地位的数字系统；

有什么问题吗？罗伯特？

男学生：嗯，这个斐波那契数列是他发明的……嗯，那个数列的同一个人吗？女教授：啊，是的，著名的斐波那契数列。虽然他实际上并没有发明它，但它只是原文中使用的一个例子……我的意思是，你能想象把零的概念引入西欧吗&nbsp；

颂歌

女学生：那么……我们看到了，比如说，在零点到来之后，欧洲日常生活发生了实际的变化，还是真的只是……女教授：嗯，变化发生在科学的发展中。女学生：哦。

女教授：即使在基础工程领域，这也不是一个根本性的改变。嗯，但当你再次开始进入理论科学，嗯，更高形式的数学…微积分…零对它们的发展有着更大的影响。好，现在注意，随着文化传播的发展，这是一个相对缓慢的例子。有些东西往往传播得更快，例如，艺术或建筑风格，例如建筑中使用的圆顶。我们看到的证据表明，从罗马到中东再到南亚，传播速度相对较快…

三、The Transmission of A Number System托福听力问题：

Q1:1.What does the professor mainly discuss?

A.The advantages and disadvantages of the Roman numeral system

B.The importance of the number zero in tracking commercial transactions

C.How a new number system affected trade

D.How a number system spread from one society to another

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

A.They led directly to advances in basic engineering.

B.They required an understanding of elementary algebra.

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

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

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

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

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

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

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

4.What is the professor's opinion about the effects of the new number system on European society?

A.Its most important effects were on merchants and tradespeople.

B.It had little impact on daily life.

C.It affected engineers more than other scientists.

D.It quickly caused most people's lives to change radically.

5.What can be inferred about the professor when she says this:

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

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

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

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

6.Why does the professor mention domes in architecture?

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

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

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

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

四、The Transmission of A Number System托福听力答案：

A1:正确答案：D

A2:正确答案：C

A3:正确答案：A

A4:正确答案：B

A5:正确答案：D

A6:正确答案：B