"I was good at being a delinquent," he says. "I first smoked weed when I was in year 7. I went to the school fete stoned. I saw my parents there. That was freaky - I had to make a quick left turn. Basically, I just wanted to rebel. I shoplifted, did graffiti." Arty graffiti? "No. I just wrote on walls." He says he was driven by "this feeling of not accepting what was handed to you, not doing what you were supposed to do; that I could make my own rules". He got caught shoplifting wallets in a surf store. "My friend forgot to take the tags off one of them," he says. "They were in my backpack, and the thing's gone off - dee-dee-dee-dee! So I got taken home in a police car, and my dad was out the front, watering the garden. I was thinking, 'Oh, f..., this is not happening.' "Everything changed after that, in his perception of me: I wasn't this innocent kid any more. He didn't understand it. That didn't stop me, obviously. A year later, my stepmum found a bag in my room that had a bong, a spray can, some stuff I'd stolen from a hardware store ... and some beer bottles - I didn't have anywhere else to dispose of them. I was about 13, I guess. My dad forbade me from hanging out with these friends of mine who weren't even that bad. It was me - I was the one who wanted to f...ing tear the walls of civilisation down." He laughs. "I was the most rebellious. But he rang up all my friends' parents and told them their son had been giving me weed, which was not true.

"At that point," he says, "I didn't really have any friends, and I never really had a good bunch of friends for the rest of my high-school life. Except for Dom [Simper, Tame Impala bass player]. I met Dom shortly after that." Throughout his career as a menace to society, Parker had led a sinister double life as a serious young musician. He'd started to learn the drums while still living with his mum in Mt Lawley. "My music teacher had to pass me on to another guy," he says, "because I learnt him out of stuff in a few weeks." Drumming gave Parker "this instant sense of identity", he says, "this instant sense of purpose and individuality that I hadn't experienced before: 'It's my thing, I'm a drummer, I'm a musician.' " We wouldn't even know what day it was. If we saw someone walk past with a suit on, we'd know it was a weekday. Jerry had played in cover bands throughout his life, and kept a music room at home with a set of drums, guitars and a keyboard. He showed Parker basic rhythm guitar, and Parker taught himself all the other instruments. Parker began to make multi-track recordings, using two tape recorders, playing along to his own beat.

"The two of us were, by far, the most interested in music in our year at school," Dom Simper tells me later. "It's not as if we were super popular or anything. Kevin was always writing songs. It was like what he did naturally. Every day at school, he'd show me a new song." When Parker was about 15, his parents decided to reunite. "They hadn't even spoken in 10 years," says Parker, "but, for some reason, my mum thought it would be a great idea. And [Jerry] said yes, for some reason, as well. So they left their respective husband and wife, and they got back together, and we all moved into a house in Subiaco. "I didn't believe it," he says. "It didn't seem right. Because it was absolute turmoil to actually leave their spouses. Anyway, that all fell apart after about a month, and about a year of shit ensued, which basically resulted in me and my brother living in the shed at my mum's place. It was kind of turned into a granny flat. My bed was a stretcher." Eventually, the boys went back to live with Jerry. "My dad needed time to reconcile with my stepmum," says Parker. "By the time I was 16, things were back to normal ... It was like nothing had changed, which was really weird because obviously, shit had changed." Parker moved out of home to go to university, where he first studied engineering, then took a year off and returned to start a degree in astronomy, "even though the job prospects weren't that great".

But he had a new bunch of friends, who all lived for music, and who continually reconverged into different bands playing different types of music with slightly differing personnel, without ever leaving the earlier groups. "Pretty soon you're in, like, seven bands," he says. The Perth live scene opened him up to sounds from the 1960s and 1970s, particularly psychedelic rock. "I was living in a share house," he says. "I had a few girlfriends, but we were just these f...ing deadbeat stoners, basically. The idea of having a girlfriend was pretty alien to all of us. I cut myself off from the real world. I went to uni, but that was my only kind of intersection with the real world, until the point came when I wasn't even at uni. We'd sit outside the front porch to the house and we wouldn't even know what day it was. If we saw someone walk past with a suit on, we'd know it was a weekday. We smoked spliffs pretty much constantly." Parker's music became more sophisticated and caught ears at the independent record label Modular, which signed him up as Tame Impala - a home-studio recording project with a touring band. While Parker was recording his first album, his father died, after a year's struggle with cancer. Jerry's death had a "massive" effect, he says. "It was a weird time, extremely confusing, and I didn't really know what to make of it." Tame Impala's debut album, 2010's Innerspeaker, went gold in Australia, and the band took off around the world. "People just dug it," says Parker. "I didn't expect them to. I thought I had failed ... As I do after every album." Innerspeaker's 2012 follow-up, Lonerism, went platinum in Australia, but also broke the top 20 in the UK and the top 40 in the US. A third album, Currents, will be released next month. Lonerism, Parker says, was "an album about being an introvert, separated from the rest of society". Currents "is more about feeling yourself change as a person and wanting to become part of the world". It's the voice of someone who has "got this isolation out of their system" and is "flourishing as a person".

On this balmy afternoon in Fremantle, Parker is optimistic for the future, but there's a piece of his heart in the past. Today is the anniversary of Jerry's death. His father never saw Tame Impala's success, but knew Parker had a record deal, heard the first EP, and perhaps understood that his son devoting his life to music wasn't "a ridiculous decision in the end", says Parker. Tonight at sunset, Parker and his brother Steve will drive to City Beach in Perth where they scattered Jerry's ashes, and think of him. Next week, Tame Impala will tour the world.