托福tpo51聽力lecture2 The Transmission of A Number System

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The Transmission of A Number System托福聽力原文翻譯及問題答案

一、The Transmission of A Number System托福聽力原文：

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托福聽力中文翻譯：

旁白：在世界歷史課上聽講座的一部分。女教授：所以，世界歷史上出現(xiàn)的一個比較常見的話題是文化傳播，因為它對不同的社會在很長一段時間內(nèi)的演變產(chǎn)生了相當(dāng)大的影響?，F(xiàn)在……文化傳播通常被定義為文化從一個社會傳播到另一個社會，文化指的是從藝術(shù)風(fēng)格到，呃……你知道……技術(shù)、科學(xué)……所以，我們非常廣泛地使用“文化”。這一過程的一種常見方式是貿(mào)易……旅行商人，或貿(mào)易中心，來自不同地區(qū)的人們聚在一起交流思想的地方。

讓我們從數(shù)字系統(tǒng)的傳輸示例開始，該系統(tǒng)使用從南亞到西歐的數(shù)字零。好吧，在這種文化傳播發(fā)生之前，西歐占主導(dǎo)地位的數(shù)字系統(tǒng)是羅馬數(shù)字系統(tǒng)。羅馬數(shù)字系統(tǒng)最初是作為一種記錄手段發(fā)展起來的，作為一種跟蹤商業(yè)交易、稅收、人口普查記錄等的方式。因此，這個系統(tǒng)從數(shù)字一開始。女學(xué)生：一個？沒有零錢？女教授：對。在羅馬數(shù)字中，零本身并不是一個真正的值。它并沒有單獨用作數(shù)字。如果你主要關(guān)心的只是記錄的基本類型…女學(xué)生：哦，是的，我想你不需要零來計算牲畜數(shù)量。女教授：或者跟蹤谷物產(chǎn)量，或者進行人口普查。就基礎(chǔ)工程而言，這也不妨礙他們建造建筑物、道路之類的東西。

但亞洲開發(fā)的其他數(shù)字系統(tǒng)，確實包含零。這些社會發(fā)展的數(shù)學(xué)包括負(fù)數(shù)之類的東西，所以你開始獲得更復(fù)雜的數(shù)學(xué)水平。所以……最早的數(shù)學(xué)書面文本之一，有零，負(fù)數(shù)，甚至一些基本代數(shù)，是在七世紀(jì)初寫于南亞的。這篇文章傳到了中東、巴格達，最終被一位波斯天文學(xué)家和數(shù)學(xué)家翻譯成了阿拉伯語。一旦他開始翻譯，他很快就意識到這個系統(tǒng)的優(yōu)點，即可以完成的數(shù)學(xué)類型。很快，這本書開始在中東更廣泛地傳播，其他數(shù)學(xué)家開始提倡使用這種數(shù)字系統(tǒng)。

因此，到了10世紀(jì)，它成為中東的主導(dǎo)系統(tǒng)，因此，代數(shù)和其他更復(fù)雜的數(shù)學(xué)形式開始蓬勃發(fā)展。與此同時，在西歐，羅馬數(shù)字系統(tǒng)，一個沒有零的系統(tǒng)，仍然存在。

十二世紀(jì)末，一位名叫斐波那契的意大利數(shù)學(xué)家與他的父親，一位商人一起在北非旅行。當(dāng)他在那里的時候，斐波那契發(fā)現(xiàn)了這段阿拉伯文字。他把…呃，這段文字翻譯成拉丁語，然后返回歐洲。他提倡采用這種數(shù)字系統(tǒng)，因為它在記錄商業(yè)交易、計算利息等方面具有優(yōu)勢。在接下來的一個半世紀(jì)內(nèi)，這將成為西歐公認(rèn)的、占主導(dǎo)地位的數(shù)字系統(tǒng)；

有什么問題嗎？羅伯特？

男學(xué)生：嗯，這個斐波那契數(shù)列是他發(fā)明的……嗯，那個數(shù)列的同一個人嗎？女教授：啊，是的，著名的斐波那契數(shù)列。雖然他實際上并沒有發(fā)明它，但它只是原文中使用的一個例子……我的意思是，你能想象把零的概念引入西歐嗎&nbsp；

頌歌

女學(xué)生：那么……我們看到了，比如說，在零點到來之后，歐洲日常生活發(fā)生了實際的變化，還是真的只是……女教授：嗯，變化發(fā)生在科學(xué)的發(fā)展中。女學(xué)生：哦。

女教授：即使在基礎(chǔ)工程領(lǐng)域，這也不是一個根本性的改變。嗯，但當(dāng)你再次開始進入理論科學(xué)，嗯，更高形式的數(shù)學(xué)…微積分…零對它們的發(fā)展有著更大的影響。好，現(xiàn)在注意，隨著文化傳播的發(fā)展，這是一個相對緩慢的例子。有些東西往往傳播得更快，例如，藝術(shù)或建筑風(fēng)格，例如建筑中使用的圓頂。我們看到的證據(jù)表明，從羅馬到中東再到南亞，傳播速度相對較快…

三、The Transmission of A Number System托福聽力問題：

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托福聽力答案：

A1:正確答案：D

A2:正確答案：C

A3:正確答案：A

A4:正確答案：B

A5:正確答案：D

A6:正確答案：B

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