美国国家公共电台 NPR A Songwriting Mystery Solved: Math Proves John Lennon Wrote 'In My Life'

 

SCOTT SIMON, HOST:

You'll see a lot of Lennon-McCartney in the composer credits for Beatles songs. Obviously, they were famous collaborators. But who really took the lead in writing some of that music?

(SOUNDBITE OF SONG, "IN MY LIFE")

THE BEATLES: (Laughter) There are places I'll remember all my life, though some have changed.

SIMON: So we know John Lennon wrote the lyrics¹ to this song. But Lennon and Paul McCartney told different stories about who wrote the music. To help solve the dispute, math now comes to the floor. Our number cruncher, Keith Devlin, tells us the subject came up at a statistics conference last week. A paper was presented with the title "Assessing Authorship Of Beatles Songs From Musical Content: Bayesian Classification Modeling from Bags-Of-Words Representations." Obviously, they didn't have a lot of important things to talk about.

Keith Devlin joins us from Stanford. Keith, thanks so much for being with us.

KEITH DEVLIN: Hi, Scott. Good to be with you again.

SIMON: I don't understand bags-of-words representations, although, I've sometimes been called a bag of words myself.

DEVLIN: (Laughter) We'll get to that, yeah. First of all, just to say that this is really serious stuff in terms of what was done. The three co-authors of this paper - there was someone called Mark Glickman, who was a statistician at Harvard. He's also a classical pianist. Another person, another Harvard professor of engineering called Ryan Song. And the third person was a Dalhousie University mathematician² called Jason Brown. And you may - if you may recall back to 2008, you and I talked about him...

SIMON: I do, yes.

DEVLIN: ...When he figured - that's right - when he out how the The Beatles created that striking opening chord in "Hard Day's Night."

SIMON: Yeah.

DEVLIN: And when we did that piece, I actually said he was working on who wrote the music for "In My Life." And 10 years later, here we are talking about the discovery. It took him a long time, but he's now got it.

SIMON: Now, bags of words - I mean, what are they?

DEVLIN: Yeah, that's a term - it actually goes back to the 1950s. It's used by the computer scientists who create spam filters. What you do is you take a piece of text. And you ignore the grammar. You ignore the word order. And you just regard it as a collection of words. And once you've done that, you can count the frequencies of the different words in the bag of words. To do it for music, you had to get little snippets, and the way they did that was they - the team analyzed³, I think, about 70 songs from Lennon and McCartney. And they found that there were 149 very distinct transitions between notes and chords that are present in almost all Beatles songs. And those transitions will be unique to one person or the other person.

SIMON: So they'd be bags of notes and chords?

DEVLIN: Bags of notes and chords, pairs of notes and chords. Those are the little items, and you just count them.

SIMON: Part of the confusion is that Paul McCartney said he wrote the music. John Lennon said that Paul McCartney wrote only this section of music.

(SOUNDBITE OF SONG, "IN MY LIFE")

THE BEATLES: (Singing) All these places have their moments. With lovers and friends, I still can recall some are dead and some are living. In my life, I've loved them all.

SIMON: So what did this trio of mathematicians⁴ detect there?

DEVLIN: Well, cutting to the chase, it turns out that Lennon wrote the whole thing. When you do the math by counting the little bits that are unique to the people, the probability that McCartney wrote it was .018 - that's essentially⁵ zero. In other words, this is pretty well definitive⁶. Lennon wrote the music. And in situations like this, you'd better believe the math because it's much more reliable than people's recollections, especially given that they collaborated⁸ writing it in the '60s with an incredibly altered mental state due to all the stuff they were ingesting.

SIMON: I know what you are saying, yeah.

DEVLIN: (Laughter) I would go with mathematics.

SIMON: But Keith, all right. I ask you - what about the artistic⁹ process of collaboration¹⁰? Isn't it possible that they were such close and accomplished¹¹ collaborators that they inhaled¹² a little bit of each other's technique? And Lennon could write like McCartney and McCartney like John Lennon?

DEVLIN: For sure. And that's why it's hard for the human ear to tell the thing apart. It's also hard for them to realize who did it. And this is why, actually, the only reliable answer is the mathematics - because no matter how much people collaborate⁷, they're still the same people, and they have their preferences without realizing it. Lennon would use certain kinds of things over and over again. So would McCartney. It was a collaboration that made those two things come together that worked, but they were still separate little bits. The mathematics isolates¹³ those little bits that are unique to the two people.

SIMON: Mathematician at Stanford University and executive director of Stanford's H-STAR Institute. You bag of words, notes and chords. Thanks so much, Keith.

DEVLIN: (Laughter) My pleasure, Scott. My pleasure.

(SOUNDBITE OF SONG, "IN MY LIFE")

THE BEATLES: (Singing) I know I'll often stop and think about them. In my life, I love you more. In my life, I love you more.

1 lyrics   

n.歌词

参考例句：

• music and lyrics by Rodgers and Hart 由罗杰斯和哈特作词作曲
• The book contains lyrics and guitar tablatures for over 100 songs. 这本书有100多首歌的歌词和吉他奏法谱。

2 mathematician   

n.数学家

参考例句：

• The man with his back to the camera is a mathematician.背对着照相机的人是位数学家。
• The mathematician analyzed his figures again.这位数学家再次分析研究了他的这些数字。

3 analyzed   

v.分析( analyze的过去式和过去分词 )；分解；解释；对…进行心理分析

参考例句：

• The doctors analyzed the blood sample for anemia. 医生们分析了贫血的血样。 来自《简明英汉词典》
• The young man did not analyze the process of his captivation and enrapturement, for love to him was a mystery and could not be analyzed. 这年轻人没有分析自己蛊惑著迷的过程，因为对他来说，爱是个不可分析的迷。 来自《简明英汉词典》

4 mathematicians   

数学家( mathematician的名词复数 )

参考例句：

• Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗？ 来自英汉文学
• Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分

5 essentially   

adv.本质上，实质上，基本上

参考例句：

• Really great men are essentially modest.真正的伟人大都很谦虚。
• She is an essentially selfish person.她本质上是个自私自利的人。

6 definitive   

adj.确切的，权威性的；最后的，决定性的

参考例句：

• This book is the definitive guide to world cuisine.这本书是世界美食的权威指南。
• No one has come up with a definitive answer as to why this should be so.至于为什么该这样，还没有人给出明确的答复。

7 collaborate   

vi.协作，合作；协调

参考例句：

• The work gets done more quickly when we collaborate.我们一旦合作，工作做起来就更快了。
• I would ask you to collaborate with us in this work.我们愿意请你们在这项工作中和我们合作。

8 collaborated   

合作( collaborate的过去式和过去分词 )； 勾结叛国

参考例句：

• We have collaborated on many projects over the years. 这些年来我们合作搞了许多项目。
• We have collaborated closely with the university on this project. 我们与大学在这个专案上紧密合作。

9 artistic   

adj.艺术(家)的，美术(家)的；善于艺术创作的

参考例句：

• The picture on this screen is a good artistic work.这屏风上的画是件很好的艺术品。
• These artistic handicrafts are very popular with foreign friends.外国朋友很喜欢这些美术工艺品。

10 collaboration   

n.合作，协作；勾结

参考例句：

• The two companies are working in close collaboration each other.这两家公司密切合作。
• He was shot for collaboration with the enemy.他因通敌而被枪毙了。

11 accomplished   

adj.有才艺的；有造诣的；达到了的

参考例句：

• Thanks to your help,we accomplished the task ahead of schedule.亏得你们帮忙,我们才提前完成了任务。
• Removal of excess heat is accomplished by means of a radiator.通过散热器完成多余热量的排出。

12 inhaled   

v.吸入( inhale的过去式和过去分词 )

参考例句：

• She closed her eyes and inhaled deeply. 她合上双眼，深深吸了一口气。
• Janet inhaled sharply when she saw him. 珍妮特看到他时猛地吸了口气。 来自《简明英汉词典》

13 isolates   

v.使隔离( isolate的第三人称单数 )；将…剔出（以便看清和单独处理）；使（某物质、细胞等）分离；使离析

参考例句：

• The transformer isolates the transistors with regard to d-c bias voltage. 变压器可在两个晶体管之间隔离直流偏压。 来自辞典例句
• In regions with certain isolates of TRV, spraining is more prominent. 在具有TRV某些分离物的地区，坏死是比较显著的。 来自辞典例句