Back in the day, it wasn't all that rare for a top-selling band to make music that was both clever and accessible. But even by those long-ago and occasionally commonplace standards, the Police still managed to stand out as a pop group that was always one step ahead of its peers.

Name-dropping Lolita author Vladimir Nabokov in a Top 10 hit and playing songs that switched from polyrhythmic world music to virtuosic jazz fills to jagged New Wave and then back again will do that. It also got them labeled as both visionaries and pretentious art rockers by fans and critics alike.

With 1981's Ghost in the Machine, their fourth album, they pushed it all to new levels.

The previous year's Zenyatta Mondatta made them stars, with the album reaching No. 5 (their first Top 10) and two of its singles – "De Do Do Do, De Da Da Da" and "Don't Stand So Close to Me" – also cracking the Top 10 for the first time. When they started work on Ghost in the Machine in January 1981, the Police were ready to take their music to yet another place. They even started over, in a sense, by recording in new studios with a new producer.

With the leap in sales and chart position came more control, and the band took the opportunity to delve deeper into subjects and themes not typically found in pop music. The album's title – the band's first in English – was based on Arthur Koestler's The Ghost in the Machine, a 1967 philosophy book about the mind-body relationship ... not exactly squeeze-my-lemon stuff.

Singer, bassist and main songwriter Sting incorporated many of the book's philosophical and psychological theories (as well as some vaguely religious ones) into his new songs, including the opening "Spirits in the Material World," a three-minute musical summation of Koestler's work. But he also included several standbys, like love songs ("Every Little Thing She Does Is Magic") and political numbers ("Invisible Sun").

But mostly they're about information overload and the crowding of modern lives (and this was before anyone even realized they'd be spending most of their time online and staring at screens someday), and the personal perspectives they were now allowed to pursue thanks to more creative freedom.

Watch the Police's 'Every Little Thing She Does Is Magic' Video

Musically, the Police grew too, incorporating synthesizers, horns and piano into the songs – Sting even plays saxophone – giving them more definition and a larger sense of scale compared to the earlier records, especially the first two, where the trio sounds bounded by whatever instruments they happen to be holding.

On Ghost in the Machine, the songs got bigger and more dynamic, a crucial element in the band's development. By the time they made their next album, 1983's Synchronicity, they sounded like the arena band they had become: tighter, more expansive, constricted by expectations and occasionally soulless.

Weeks after its release on Oct. 2, 1981, Ghost in the Machine shot up the chart and stopped at No. 2. The singles were hits too, starting with "Every Little Thing She Does Is Magic" (which made it to No. 3), followed by "Spirits in the Material World" (No. 11) and "Secret Journey" (which just missed the Top 40). The Police got even bigger with Synchronicity – their only No. 1 album, which yielded their only No. 1 single, "Every Breath You Take."

But the infighting and struggle for control that eventually tore the band apart after that record had already seeped in. Ghost in the Machine, darker than any of the group's previous records, was the beginning and the end. It was the last time everyone in the band sorta got along with one another; it was also their smartest and trickiest work. It was better than everything that came before it, but it was leaner than what came after.

All these years later, it's easy to see that it's more than just the Police's transitional album. It's their masterpiece.

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