Coyne and Cyrus met through Twitter. "We knew for a while that she was a fan," Coyne recalls. "We knew her from , but we could sort of tell, even back then, from artists that she would cover, that she had cool taste in music. When she became the new, completely freaked-out version of that she is now, I think it was known in the world that we loved her. She was aware that we liked her, and she liked us."

To Coyne's surprise, Cyrus wished him a happy 53rd birthday on Twitter, to "one of my favourite artists of all time". Coyne was tickled. "So I guess I direct messaged her back," he says. "And just a couple minutes later she messaged me, I gave her my number, and by the end of that day we were already texting back and forth saying, 'I think we should do something'."

That something became , one of the best tracks on the album. Like much of the album, the rendition is sexy, unorthodox and understated. And it beautifully underscores the dusky, innocent loveliness of Cyrus' voice.

The track was born last New Year's Eve, when The Flaming Lips spontaneously tossed a Beatles set into a big show. " was the best of the batch," says Coyne. Later, Cyrus came over and they recorded the track. "When we recorded with Miley, there wasn't anyone there but us. She just shows up with her friend, and everybody gets a little bit stoned, and makes some music, and gets a little drunk, and gets some tattoos."

Yes, tattoos. Cyrus posted the evidence on Instagram: an illustration drawn by Coyne of her dog Floyd, who had recently been killed by coyotes, plus the words, "With a Little Help From My Fwends". Coyne recalls, "All of us were like, that's just a magic drawing." Now, Coyne's drawing graces the ribs of Cyrus, Coyne, and his girlfriend, Katy Weaver. Some of the album's proceeds will go to an animal welfare organisation in Oklahoma.

Coyne says about Cyrus: "The more we got to know each other, the more we seemed, as it went, to be so much in the same mindset about how to do music. We just love her to death. She's just absolutely creative, she's on fire. If you're around her, I think in the same way that if you were around me, you will make music. That's just what she's doing all the time."

"The Flaming Lips have made lots and lots of records," Coyne says. "And there's nothing like an infusion of a new, enthusiastic, unique freak. Miley has done that for us. She's so open and so full of love, and I think that will reflect in our own work. She'll definitely end up influencing us more that we influence her."

The Flaming Lips feel like two bands: on one hand, your neighbourhood stoners trying to have a good time. That's the band behind . On the other hand, the band are serious musicians preoccupied with profound questions. If the former band is marketing the music, the latter is driving it.

"I don't think in the beginning we had any idea how we could do that, or if we did it," Coyne says, "we'd get it by accident. When we made our first record, we thought that would be the only record we would make. Then we made another one, and we thought that would be the last one. Little by little, we were creating a style that we could be."

Years later, Coyne is a famous rock star. Time has justified his accidental artistry. But he's humble in his own appraisal: "I've been lucky that people started to like the things that I would sing about, and my way of singing about them. I'm lucky people like it, because I'm not very good at it."

Some fans are dismayed at Coyne's collaboration with Cyrus, implying that he was slumming it, musically. But the charm of The Flaming Lips always lays in their unpredictable inclusivity. Coyne's entire musical philosophy is nothing if not one big cosmic hug. Friendly and engaging, he exudes the affectionate, bemused presence of a good-natured bear. He always sounds on the verge of a shrug: so what? Why can't we all just get along? And with a little help from their friends, The Flaming Lips are getting along just fine.