'It would be a combination of The Matrix and a Clint Eastwood film, some kind of western on Mars with lasers and intergalactic war', laughs Matt Bellamy, describing latest album Black Holes and Revelations' stand out track 'Knights of Cydonia'. And he's right: it's an addictive, utterly unhinged prog-stampede transposing the spirit of Ennio Morricone to Mars' northern hemisphere, complete with laser beams and wild horses.

Like everything to do with Muse, the song is epic, both in scope and ambition. Not tethered by the norms of commercial music, they have constantly strived for the next level, a cosmic leap into the universe beyond the confines of 'rock'. Crossing the fury of Rage Against the Machine with the operatic bombast of Queen, they have evolved beyond the Radiohead comparisons of debut album, Showbiz, into a fusion of dexterous guitar stylings and forward thinking space rock.

Formed in the decidedly un-rock Devonshire town of Teignmouth, the band have surpassed all expectations. Early singles, the juddering 'Muscle Museum' and screaming 'Sunburn', hinted at great talent. Second album Origin of Symmetry took them one step further, being an all out rock assault that shared as much with Rachmaninov as it did their indie or metal brethren. 'New Born', 'Bliss', 'Plug in Baby' and their unique take on Nina Simone's 'Feeling Good' finally showed the level of intelligence, not to mention the invention, the fury, the expert musicianship. The follow up, Absolution, was similarly grandiose, further exemplifying their skills and laying out a distopian world view of conspiracies and men in black. And it was the most uplifting album about the end of the humanity the world has ever seen, a feat which propelled the band on to headlining Glastonbury in 2004.

But Muse's real skill lies in taking complex concepts and making them instantly appealing. Black Holes and Revelations takes one more bold step for mankind: it's a soaring, addictive slice of cyber electro pomp, packed with flamenco flourishes, astounding guitar theatrics, brutal metal assaults and sci-fi operatics. 'There is an optimism in the album that came out of this feeling of being at the bottom of the pyramid and wanting to topple the people at the top and take the power back. I hope that is something that will happen in the next few years,' explains Bellamy, daintier in person than you'd imagine, his voice and personality looming so large on records.

Not only is Bellamy the vocalist, guitarist and, at times, pianist, he writes pretty much all the material. That's not to dismiss the work of bassist Chris Wolstenholm or drummer Dominic Howard. Their tight rhythm section underpins everything, ensuring that the excess doesn't spiral off into psychosis. 'There are certain songs where Matt comes in and they're finished in his head before we've even heard them, and then there are other songs that have a very simple chord structure or melody and we'll just play it, sometimes for hours, waiting for something to happen,' explains Wolstenholm, the most personable member of the band. 'But a lot of the drum parts, basslines and grooves come from me and Dom.'

'We've always wanted to make the bass and drums sound very strong,' adds Howard. 'Being just three instruments helps rein in that insanity.' Except of course on 'Assassin', the one metal song on the album. 'On that song we were just trying to use insanity as a means to be heavy, rather than a typical rock idea of being heavy using a fat riff.' And it's precisely this insanity that Muse have become famous for. Bellamy is often portrayed as a paranoid conspiracy theorist, living in fear of alien abduction. 'It happens all the time; you say things like "aliens are coming down to take us all away" as a joke, obviously, then you get portrayed as some kind of mental bloke,' he laughs. ' It's quite funny to read some of it back, this alien thing keeps coming up, I only briefly mentioned that I read this David Icke book and that all the conspiracy theories seemed quite logical until it descended into lizards and nonsense.'

Bellamy comes across as far more sane in the flesh, more than willing to proffer a healthy dose of scepticism. 'We've seen some of the biggest protests of all time in the world over the last few years. It seems people are waking up to the fact that those in power aren't going in the right direction. I like the idea that people will rise up and create a revolution, otherwise we will all end up in a George Orwell Big Brother future, with people being treated like cattle,' he says. 'Before you know it we'll have ID cards, and job interviews will just be a swipe of a card. It'll keep going in that direction until you can't do anything out of the ordinary without being stamped on.'

Meeting Bellamy, you can see there is great intelligence at play. Obviously well read, he moves from being guarded to excitable during the course of the interview. If the music is anything to go by his mind must be constantly striving to discover something new to fend off the oppressive boredom of modern life. 'Sometimes people think we take ourselves very seriously, people miss the fact that we do have a fun side to the band.'

In Bellamy we have one of rock's virtuoso musicians, a startling talent whose breadth of vision has given Muse one of the most unique sounds in modern music, even if he does confess to a fondness for ABBA songs at karaoke. There is a definite black humour running thorugh their work, a knowing wink as they spout lyrics about 'the end of days'. It's their unfaltering skill in translating these ambitious soundscapes in the live arena that sets them apart from the crowd. Live, Muse are breathtaking; an intense bombardment of music and ideas. And as they take to the stage as part of T on the Fringe - before heading down south to headline Reading and Leeds - it will be fascinating to see how they bring Black Holes and Revelations to life. 'I think it's probably the first time we've ever gone into a studio and thrown the idea of playing it live out the window,' explains Wolstenholm. 'If you think too much about playing live, you're placing limitations on the music. We went in there with freedom to do what we wanted; now we're trying to work out how to play it live.'

'You have to give it everything; if you don't it just falls apart,' says Bellamy. 'Live, there's this tradition of chaos that creeps in and I think it's that unpredictable element that keeps the shows exciting.'

And Muse revel in chaos. Prepare to be astounded.