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

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 lyrics 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 mathematician 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 analyzed, 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 mathematicians 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 essentially zero. In other words, this is pretty well definitive. 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 collaborated 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 artistic process of collaboration? Isn't it possible that they were such close and accomplished collaborators that they inhaled 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 collaborate, 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 isolates 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.