The mystery of who wrote a 50-year-old Beatles song is solved, thanks to math

Which member of The Beatles wrote "In My Life," from the 1965 album Rubber Soul? It turns out that math has the answer.

Debates have long raged across pop culture about who wrote which Beatles song, both before and after the internet was born. The melody from "In My Life" in particular has been one of the bigger sources of consternation among fans.

John Lennon said in a 1980 interview with Playboy that it was his, even singling it out as "the first song I wrote that was consciously about my life." He did say McCartney helped with part of the song, the "middle-eight," he said.

Several years later, in a 1984 interview (also with Playboy), bandmate Paul McCartney offered a different account of the song's origin.

"I think I wrote the tune to that; that’s the one we slightly dispute. John either forgot or didn’t think I wrote the tune. I remember he had the words, like a poem–sort of about faces he remember. . . . I recall going off for half an hour and sitting with a Mellotron he had, writing the tune. Which was Miracles inspired, as I remember. In fact, a lot of stuff was then."

Now jump ahead to the 21st century. Around 10 years ago, mathematics professor and Beatles fan Jason Brown stepped forward with an answer to one of the band's other mysteries, how the dramatic chord that kicks off the classic song "Hard Day's Night" was played.

He figured it out, but that's a whole other journey.

Since then, according to a new NPR report, Brown has been working to solve the "In My Life" puzzle. And now, thanks to a little help from a pair of mathematicians from Harvard -- Mark Glickman and Ryan Song -- there's an answer.

Glickman presented their findings earlier this month at the Joint Statistical Meetings conference in Canada. The talk had an extremely unsexy title -- "Assessing Authorship of Beatles Songs from Musical Content: Bayesian Classification Modeling from Bags-Of-Words Representations" -- but it asserted that Lennon wrote "In My Life."

Speaking to NPR, Stanford mathematician Keith Devlin tried to break down exactly how Brown and his colleagues sleuthed out an answer, starting with this idea of "bags-of-words."

"It actually goes back to the 1950s. [The term is] used by the computer scientists who created spam filters," Devlin said. A bag-of-words representation, he explained, takes a piece of text and strips away all the grammar and word order.

"You just regard it as a collection of words," Devlin added. "And once you've done that, you can counter the frequencies of the different words in the bag of words."

If you've ever come across a word cloud infographic on the internet, it's the same idea. In a word cloud, the size of the text for each word is determined by how frequently it appears in whatever container is being measured, such as, say, a person's Twitter feed.

In applying this idea to music, Brown, Glickman, and Song analyzed an assortment of snippets pulled from around 70 Beatles tunes. They ended up with bags of "notes and chords," rather than words, but were able to apply their results in the same manner.

"They found there were 149 very distinct transitions between notes and chords that are present in all Beatles songs," Devlin said. "And those transitions will be unique to one person or the other person."

Once they had these band member-specific transitions mapped out, finding the true author of "In My Life" became a simple matter of counting.

"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," Devlin said. He added that the finding is "pretty well definitive" and that he'd trust the math over personal recollections, "especially given they collaborated writing it in the '60s with an incredibly altered mental state due to all the stuff they were ingesting."

You might grimace at all of this, since math can't go back in time and show us what actually transpired. But, to Devlin's point, what we do know of the "In My Life" writing process comes from interviews conducted 15-20 years after the album on which it appeared was released.

Brown already has an established background in dissecting the music of The Beatles. If his math shows that Lennon wrote "In My Life," so be it. That said, Mashable reached out to McCartney's publicist to see if the ex-Beatle has any thoughts to share on this new finding.