Nova：The Great Math Mystery《新星：数学大谜思（2015）》完整中英文对照剧本

1、Roger, copy mission.收到 确认任务We live in an age of astonishing advances.我们生活在一个快速发展的时代Descending at about 75 metersper second.减速到每秒75米Engineers can land a car-size rover on Mars.工程师们可以让一个汽车大小的飞行器在火星上着陆Touchdown confirmed.着陆成功Physicists probe the essence of all matter,物理学家探索所有事物的本质while we communicate w

2、irelessly on a vast worldwide network.我们在一个巨大的网络里通过无线电交流But underlying all of these modern wonders但在这些现代奇迹背后is something deep and mysteriously powerful.是一深刻而且神秘强大的事物It's been called the language of the universe,它被称为宇宙的语言and perhaps it's civilization's greatest achievement.它可能是人类文明最伟大的成就I

3、ts name?它的名字叫做Mathematics.数学But where does math come from?但是数学从何而来And why in science does it work so well?为什么数学在科学领域很适用Albert Einstein wondered,阿尔伯特 爱因斯坦好奇"How is it possible that mathematics为什么数学does so well in explaining the universe as we see it?"在解释我们所见地宇宙时如此适用呢Is mathematics even huma

4、n?数学是人类的吗There doesn't really seem to be an upper limit动物的数字能力似乎to the numerical abilities of animals.并没有一个上限And is it the key to the cosmos?数学是宇宙的关键吗Our physical world我们的物理世界doesn't just have some mathematical properties,不是有一些数学特质but it has only mathematical properties.而是由数学构建而成的"The G

5、reat Math Mystery," next on NOVA!数学大迷思尽在NOVA节目Major funding for NOVA is provided by the following:感谢以下机构对NOVA的赞助the David H. Koch Fund for Science supporting NOVA and promoting public understanding of science感谢David H.Koch科学基金会赞助NOVA 且普及公众科学知识And the Corporation for Public Broadcasting,感谢公共广播协会

6、and by PBS viewers like you, thank you感谢各位观众 谢谢你们Major funding for "The Great Math Mystery" is provided by:数学大迷思的主要赞助者the Simons Foudation, working to advance research in the basic sciences and mathematics.Simons基金会 推动基础科学与数学的研究Additional funding is provided by: John Templeton Foundation另外

7、还要感谢John Templeton基金会and the George D. Smith Fund.以及George D. Smith基金会Human beings have always looked at nature人类一直在观察自然and searched for patterns.寻找万物运行的模式Eons ago, we gazed at the stars亿万年前 人类观测星星and discovered patterns we call constellations,发现了星辰排列的规律 称其为星座even coming to believe they might contro

8、l our destiny.甚至开始相信星座可能控制着我们的命运We've watched the days turn to night and back to day,我们看到斗转星移 日夜交替and seasons as they come and go,四季变换and called that pattern "time."我们把这个模式称之为 时间We see symmetrical patterns in the human body and the tiger's stripes我们发现了人体内和虎纹的对称图案and build those pat

9、terns into what we create from art to our cities.我们把这类图案运用到了人类的创作之中 从艺术作品到城市建筑But what do patterns tell us?但是这些图案告诉了什么Why should the spiral shape of the nautilus shell为什么鹦鹉螺壳的螺旋be so similar to the spiral of a galaxy?和银河系的旋涡如此之像Or the spiral found in a sliced open head of cabbage?和切开的卷心菜的旋涡如此相像When

10、scientists seek to understand当科学家们想了解the patterns of our world,世界上的各种图案的时候they often turn to a powerful tool: mathematics.他们都是寻求数学这个强大的工具的帮助They quantify their observations他们量化观察到的结果and use mathematical techniques to examine them,运用数学公式去检验这些结果hoping to discover the underlying causes of nature's

11、rhythms and regularities.希望能够发现这些自然规律的深层原因And it's worked, revealing the secrets数学果真为我们揭示了谜底behind the elliptical orbits of the planets从揭露星球的椭圆形轨道的秘密to the electromagnetic waves that connect our cell phones.到联络着手♥机♥的电磁波Mathematics has even guided the way,数学甚至有着指导作用leading u

12、s right down引领我们深入了解to the sub-atomic building blocks of matter.物质的亚原子构造Which raises the question: why does it work at all?这就引出了一个问题 为什么数学适用于所有的事物Is there an inherent mathematical nature to reality?真实存在的事物是否本身就有数学特质Or is mathematics all in our heads?还是数学都存在于人类的大脑中Mario Livio is an astrophysicistMari

13、o Livio是一位天体物理学家who wrestles with these questions.他一直在探索这些问题He's fascinated by the deep and often mysterious connection between mathematics and the world.他一直痴迷于数学和自然之间深刻而又常常神秘难懂的联♥系♥If you look at nature, there are numbers all around us.如果你观察自然 你会发现我们周围有着很多的数字You know, look

14、 at flowers, for example.比如你看这些花So there are many flowers花的种类非常之多lthat have three petals ike this, or five like this.有三片花瓣的也有五片花瓣的Some of them may have 34 or 55.有的是34片或者55片These numbers occur very often.这些花瓣的片数很常见These may sound like random numbers,这些数字看起来很随机but they're all part of what is known

15、 as the Fibonacci sequence,但是他们全是斐波那奇数列的中的数字a series of numbers developed by a 13th century mathematician.这是十三世纪的一个数学家发明的一连串数字You start with the numbers one and one,开始是数字1和1and from that point on,从此开始you keep adding up the last two numbers.一直把最后两位数字相加So one plus one is two,1加1等于2now one plus two is

16、three,1加2等于3two plus three is five,2加3等于5three plus five is eight, and you keep going like this.3加5等于8 一直这样加下去Today, hundreds of years later,近百年后的今天this seemingly arbitrary progression of numbers这些看似随机的数列fascinates many, who see in it clues吸引着许多人 他们发现斐波那奇数列出现在to everything from human beauty to the s

17、tock market.所有事物中 从人体美学到股票市场While most of those claims remain unproven,但是这些说法大多数没有得到证实it is curious how evolution seems to favor these numbers.为什么生物进化好像很钟情于这些数字And as it turns out,事实证明this sequence appears quite frequently in nature.斐波那奇数列经常出现在自然里Fibonacci numbers show up in petal counts,斐波那奇数列出现在花瓣

18、数里especially of daisies, but that's just a start.尤其是在雏菊花瓣里 但这仅仅是个开始Statistically, the Fibonacci numbers从统计学来看 斐波那契数列do appear a lot in botany.经常出现在植物中For instance, if you look at the bottom of a pine cone,比如 如果你有看松果的底部you will see often spirals in their scales.你会发现许多排列规律的螺纹You end up counting th

19、ose spirals,如果你最后数这些螺纹的话you'll usually find a Fibonacci number,你会发现一个斐波那契数字and then you will count the spirals going the other direction如果你从另一个方向再数螺纹and you will find an adjacent Fibonacci number.你会发现另一个临近的斐波那契数字The same is true of the seeds on a sunflower head向日葵的种子也是这样two sets of spirals.两个方向的

20、螺纹And if you count the spirals in each direction,如果你从两个方向数这些螺线both are Fibonacci numbers.两个都是斐波那契数字While there are some theories尽管有些理论explaining the Fibonacci-botany connection,能够解释斐波那契数列和植物学的关系it still raises some intriguing questions.但这依然提出了有趣的问题So do plants know math?植物会数学吗The short answer to tha

21、t is "No."答案显然是 不会They don't need to know math.它们不需要会数学In a very simple, geometric way, they set up a little machine用很简单的几何方法 它们建造了一个小的机器that creates the Fibonacci sequence in many cases.能够在很多情况下创造出斐波那契数列The mysterious connections between the physical world and mathematics run deep.物理世

22、界和数学之间的神秘关系非常之深刻We all know the number pi from geometry我们都知道几何学中的the ratio between the circumference of a circle是一个圆形的周长and its diameter and that its decimal digits和直径的比率 的小数点后面的数字go on forever without a repeating pattern.永远是无规律不循环的As of 2013,到2013年it had been calculated out to 12.1 trillion digits.

23、人们计算出它后面有12.1万亿位数But somehow, pi is a whole lot more.但是远不止这些Pi appears in a whole host of other phenomena出现在很多现象中which have, at least on the face of it,这些现象表面上nothing to do with circles or anything.和圆之类的没有任何关系In particular, it appears in probability theory quite a bit.尤其 还经常出现在概率论里Suppose I take thi

24、s needle假设我拿了这个针So the length of the needle这个针的长度is equal to the distance between two lines on this piece of paper.和这张纸上的两条线之间的距离相等And suppose I drop this needle now on the paper.如果我把这个针扔到纸上Sometimes when you drop the needle, it will cut a line,有的时候你扔这个针 它会切断线and sometimes it drops between the lines

25、.有的时候它会掉到两条线中间turns out the probability结果显示that the needle lands so it cuts a line针切断线的概率is exactly two over pi正好是分之2or about 6♥4♥%.也就是约百分之6♥4♥Now, what that means is that, in principle,这也就意味着 理论上I could drop this needle millions of times.如果我扔这个针几百万次I coul

26、d count the times when it crosses a line我可以计数它切断线的次数and when it doesn't cross a line,和它没有切断线的次数and I could actually even calculate pi我甚至可以计算出even though there are no circles here,尽管这里没有圆no diameters of a circle,nothing like that.或者圆周长之类的 任何东西It's really amazing.这真的很神奇Since pi relates a round

27、 object, a circle,因为将圆形物体 圆with a straight one, its diameter,和它的直径联♥系♥在一起it can show up in the strangest of places.它可以出现在最奇怪的地方Some see it in the meandering path of rivers.有人发现它出现在弯曲的河道A river's actual length一条河的实际长度as it winds its way from its source to its mouth一路曲折从源头到入海

28、口compared to the direct distance on average seems to be about pi.和其直线距离的比率接近Models for just about anything involving waves任何有波纹的模型里will have pi in them, like those for light and sound.都会有的出现 比如光波和音波Pi tells us which colors should appear in a rainbow,告诉我们哪些颜色会出现在彩虹里and how middle C should sound on a

29、piano.告诉我们中C音在钢琴里发出什么音Pi shows up in apples,出现在苹果里in the way cells grow into spherical shapes,出现在细胞生长成球形的过程中or in the brightness of a supernova.出现在一个超级新星的光亮里One writer has suggested一个作家曾说过it's like seeing pi on a series of mountain peaks,这就像是在一群山峰上面看到了poking out of a fog-shrouded valley.捅破浓雾笼罩着的

30、峡谷We know there's a way they're all connected,我们都知道他们互相关联着but it's not always obvious how.但是却不清楚它们是如何关联的Pi is but one example of a vast interconnected web of mathematics只是数学中巨大的关系网的一个例子that seems to reveal似乎要向我们的世界揭露an often hidden and deep order to our world.一个总是深不可测的规律Physicist Max Teg

31、mark from MIT thinks he knows why.来自MIT的物理学家Max Tegmark认为他知道原因He sees similarities between our world and that of a computer game他能看到我们的世界和电脑游戏之间的相似点If I were a character in a computer game如果我是一款游戏里的人物that were so advanced that I were actually conscious这款游戏高级到我这个人物是有自我意识的and I started exploring my vi

32、deo game world,我开始探索游戏世界it would actually feel to me like it was made这个游戏世界对我来说就像是of real solid objects made of physical stuff.由实物组成的Yet, if I started studying, as the curious physicist that I am,然而当我以一个物理学家的身份开始研究这个游戏时the properties of this stuff,研究物体的特性the equations by which things move研究物体运动的方程式a

33、nd the equations that give stuff its properties,研究给予物体属性的方程式I would discover eventually我最终会发现that all these properties were mathematical所有这些特性都是和数学有关的the mathematical properties这些数学特性that the programmer had actually put into the software实际上是由程序员植入到游戏软件中去的that describes everything.描绘了一切The laws of ph

34、ysics in a game游戏中的物理规律like how an object floats, bounces, or crashes比如一个物体如何漂浮 弹跳或者坠落are only mathematical rules created by a programmer.都是程序员发明的数学规则Ultimately, the entire "universe" of a computer game最终整个电脑游戏中那个所谓的宇宙is just numbers and equations.就只是数字和方程式That's exactly what I perceiv

35、e in this reality, too,这和我在现实中发现的一样as a physicist作为一个物理学家that the closer I look at things that seem non-mathematical,我越是近距离地观察非数学的东西like my arm here and my hand,比如我的胳膊和我的手the more mathematical it turns out to be.其结果越是数学化Could it be that our world also then是否有可能我们的世界is really just as mathematical as

36、the computer game reality?事实上和电脑游戏世界一样数学化To Max, the software world of a game isn't that different from the physical world we live in.对Max来说 游戏世界和我们生活其中的物理世界没有什么不同He thinks that mathematics works so well to describe reality他认为数学能很好地描述现实because ultimately, mathematics is all that it is.因为最终所有一切都可

37、以归为数学There's nothing else.别的什么也没有Many of my physics colleagues我的许多物理学家同事will say that mathematics describes our physical reality会说数学能描绘我们的物理世界at least in some approximate sense.至少程度近似I go further and argue that it actually is our physical reality我觉得数学不止这样 它事实上就是我们的物理世界because I'm arguing tha

38、t our physical world因为我认为我们的物理世界doesn't just have some mathematical properties,不是有一些数学特性but it has only mathematical properties.它是由数学构建而成的Our physical reality is a bit like a digital photograph,我们的物理世界有点像一张数码相片according to Max.据Max所说The photo looks like the pond,比如这张湖的照片but as we move in closer

39、and closer,但是当我们不断放大we can see it is really a field of pixels,我们会看到它事实上是许多个像素点each represented by three numbers每个像素点由三个数字代表that specify the amount of red, green and blue.这三个数字分别规定了红 绿 蓝的数量While the universe is vast in its size and complexity,虽然宇宙是巨大而复杂的requiring an unbelievably large collection of n

40、umbers需要无可计量的数字to describe it来描绘它Max sees its underlying mathematical structureMax认为其潜在的数学结构as surprisingly simple.出乎意料地简单的It's just 32 numbers constants只有32个数字不变like the masses of elementary particles像是许多基本粒子的集♥合♥along with a handful of mathematical equations和几个数学方程式the fu

41、ndamental laws of physics.基本物理规则And it all fits on a wall,它们全嵌在一面墙上though there are still some questions.但是还有有一些疑惑But even though we don't know但是尽管我们不知道what exactly is going to go here,这里究竟发生着什么I am really confident that what will go here但是我确信这里发生的事情will be mathematical equations.可以用数学方程解决That e

42、verything is ultimately mathematical.所有一切最终都是和数学有关的Max Tegmark's Matrix-like viewMax Tegmark的矩阵式观点that mathematics doesn't just describe reality认为数学不仅仅能够描绘现实世界but is its essence may sound radical,还能描绘数学本身的本质 这种说法听起来有些激进but it has deep roots in history.但是它由来已久going back to ancient Greece,追溯到古

43、希腊时期to the time of the philosopher and mystic Pythagoras.追溯到那时候的哲学家 谜一般的毕达哥拉斯Stories say he explored the affinity据说他探索了between mathematics and music,数学和音乐之间的密切关系a relationship that resonates to this day这个关系至今仍和in the work of Esperanza SpaldingEsperanza Spaldin的研究有着共鸣an acclaimed jazz musician who

44、9;s studied music theoryEsperanza Spalding是一名很受欢迎的爵士音乐家 她研究音乐理论and sees its parallel in mathematics.探索音乐与数学之间的相似处I love the experience of math.我喜欢体验数学The part that I enjoy about math我喜欢数学的地方I get to experience through music, too.我在音乐里也感受到了At the beginning,一开始you're studying all the little equati

45、ons,当你在研究所有的小的方程式的时候but you get to have this very visceral relationship with the product of those equations你本能地与这些方程式的产物有了联♥系♥which is sound and music and harmony and dissonance声音和音乐 和谐音和不和谐音and all that good stuff.以及所有美好的事物So I'm much better at music than at math,所以我更擅长音乐b

46、ut I love math with a passion.但是我还是很热爱数学的They're both just as much work.他们都很重要They're both, you have to study your. off.你都必须努力学习它们Your head off, study your head off.努力学习 努力The Ancient Greeks found three relationships between notes especially pleasing.古希腊人发现了音调之间的三种关系 尤其是悦耳的音调Now we call them

47、 an octave, a fifth, and a fourth.如今我们称之为八度音阶 五度音阶 和四度音阶An octave is easy to remember八度音阶很容易记住because it's the first two notes of "Somewhere Over the Rainbow."因为它是 彩虹之上 的前两个调La, la.啦 啦That's an octave- "somewhere."somewhere 是八度音阶A fifth sounds like this:五度音阶听起来是这样的La, la.

48、啦 啦Or the first two notes of "Twinkle, Twinkle, Little Star."比如一闪一闪亮晶晶 前两个调And a fourth sounds like:四度音阶听起来是这样的La, la啦 啦You can think of it as the first two notes你可以想象一下of "Here Comes the Bride."新娘来了 的前两个调In the sixth century BCE,公元前六世纪the Greek philosopher Pythagoras is said to

49、have discovered据说希腊哲学家毕达哥拉斯that those beautiful musical relationships发现了这些美妙的音乐关系were also beautiful mathematical relationships还是迷人的数学关系by measuring the lengths of the vibrating strings.他通过测量震动琴弦的长度In an octave, the string lengths create a ratio of two to one.在八度音阶里震动的弦长是2比1In a fifth,the ratio is t

50、hree to two.五度音阶里 是3比2And in a fourth, it is four to three.四度音阶里是4比3Seeing a common pattern throughout sound,通过发现音乐里的这个普遍规律that could be a big eye opener of saying,就可以大胆说Well, if this exists in sound,如果这个规律存在于音乐里and if it's true universally through all sounds,如果它存在于所有声音里面this ratio could exist u

51、niversally everywhere, right?这个比率可以存在于宇宙上任何地方 是吧And doesn't it?不是这样吗Pythagoreans worshipped the idea of numbers.毕达哥拉斯崇拜这个数字想法The fact that simple ratios produced harmonious sounds事实上那些能够发出和谐音的简单的比率was proof of a hidden order in the natural world.是这个自然世界里存在着隐藏规律的证据And that order was made of numbe

52、rs,这个规律是由数字组成a profound insight that mathematicians and scientists这是一个深刻的见解 数学家们和科学家们continue to explore to this day.至今还在研究In fact, there are plenty of other physical phenomena事实上 还有许多其他物理现象that follow simple ratios, from the two-to-one ratio of hydrogen atoms to oxygen atoms in water遵从着简单的比率关系 从水分子

53、中的氢氧2比1to the number of times the Moon orbits the Earth compared to its own rotation: one to one.到月球公转和自传次数比 1比1Or that Mercury rotates exactly three times到水星自转3周when it orbits the Sun twice, a three-to-two ratio.的同时绕太阳两周 这个比率3比2In Ancient Greece, Pythagoras and his followers在古希腊 毕达哥拉斯和他的追随者们had a p

54、rofound effect on another Greek philosopher, Plato,对另一位古希腊哲学家 柏拉图 有着深远的影响whose ideas also resonate to this day,他的思想在今天仍有回响especially among mathematicians.特别是在数学领域Plato believed that geometry and mathematics柏拉图认为几何学和数学exist in their own ideal world.存在于理想世界中So when we draw a circle on a piece of paper

55、,比如我们在纸上画一个圆圈this is not the real circle.但这不是真的圆The real circle is in that world,真的圆存在于那个理想世界中and this is just an approximation这个圆只是近似于of that real circle,真正的圆圈and the same with all other shapes.其他图形也是一样道理And Plato liked very much these five solids,柏拉图非常喜欢这五个多面体the platonic solids we call them today

56、,我们现在称之为柏拉图多面体and he assigned each one of them to one of the elements而且五个多面体对应了五种元素that formed the world as he saw it.共同组成了我们所看到的这个现实世界The stable cube was earth.立方体象征土The tetrahedron with its pointy corners was fire.有尖角的正四面体象征着火The mobile-looking octahedron Plato thought of as air.这个看起来易变的正八面体 柏拉图认为是空气And the 20-sided icosahedron was water.有二十条边的正二十面体象征水And finally the dodecahedron,最后 正十二面体this was the thing that signified the cosmos as a whole.则象征着整个宇宙So Plato's mathematical forms因此 柏拉图的数学形式were the ideal version of the world around us,就是我们这个世界的理