"Madness is about friction in a relationship, resolving conflict with a loved one and the madness of being caught up in fighting with someone you love," he says of a situation where he had to go, tail between his legs, to the house of Hudson's mum, Goldie Hawn, after the couple had argued.
But put Bellamy on a stage and, well, you've seen his grand theatrics and rock star posing.
It was most recently in full effect when Muse played their Olympic song, Survival. which is included on the new album, at the London Games' closing ceremony. He's a man possessed and, by his own admittance, a little unhinged.
So why, Mr Bellamy, are you such a show pony? Where does that bravado come from?
"Somewhere ... who knows? That's a good question," he laughs loudly down the phone from London. "On stage you could say I'm unhinged a bit. I think everybody has that in them, but not everybody has the opportunity to let it out. It's a place where I can go and be completely out there. That's what it is for me. That's where I get to go crazy."
And while we're at it then, what were Muse - Bellamy with old mates Chris Wolstenholme (bass) and Dominic Howard (drums) - thinking when they came up with the idea for an album about the depletion of energy sources around the world, both in terms of natural resources and in human beings themselves? What gives?
"That's a good question," he laughs again. "I suppose I've always been vaguely interested in that subject."
He remembers back to when he was in his teens, reading about the concept of Peak Oil at school and thinking "the oil is going to run out".
"That was probably the first time I realised that maybe things aren't forever. And I think that thought got me interested in various things over the years, my interest in sci-fi and space, our relationship with space and the Earth, and evolution, and about how energy works.
"And the energy that I suppose we all need to live; the physical energy and the emotional and spiritual energy; I've always been intrigued by it."
The band - who are big in New Zealand, having headlined the local Big Day Out in 2010 - have always focused on grand concepts and ideas over the years. Absolution from 2003, with songs like Hysteria and Stockholm Syndrome on it, was apocalyptic in scope, and 2009 album Resistance included the 15-minute long Exogenesis: Symphony Pt 1-3.
Bellamy got the initial inspiration for The 2nd Law after watching a panel discussion about the financial crisis hosted by outspoken BBC Newsnight presenter Jeremy Paxman.
"Somebody said, 'you have to admit, an economy based on endless growth is just unsustainable'. That really jumped out at me. I went, 'f***, there you go. Someone has finally said it'."
Cutting a long story short, because Bellamy loves talking about this stuff, Muse wrote a song about it, threw in some brain-rattling dubstep influences and doomsday vocals and called it The 2nd Law: Unsustainable, which is the first part of the two-part title track.
Initially the song freaked out a few Muse fans who thought their beloved pomp 'n' roll prog heroes had gone dubstep. They haven't, and though the band were impressed after seeing a live Skrillex show, there are only brief flashes of bass music influence.
"[Unsustainable] was a song where we put something together that was electronic-sounding but then we recreated that electronic sound using amps, guitars and old-school rock equipment."
But as well as the big world issues stuff, The 2nd Law also offers a personal insight into the band members' lives, especially Bellamy, and Wolstenholme, who wrote two songs about his battle with alcoholism.
"We're singing about things like relationships for the first time. Actually, I did that for a bit on the first album [1999's Showbiz] but then I started doing interviews and thought, 'oh my God, I can't answer these questions they're getting too personal'. So that's when we started getting all conceptual and pretending the album was about the end of the world, or whatever," he laughs.
Animals, one of the highlights of the new album, stands out because it shows restraint and escalates, rather than exploding in that traditional Muse dynamic.
"Every album we do we try to find new ground and new sounds to play with and new instruments, new styles of songwriting and new styles of production. Because change is what creates momentum in a band and I think we're lucky, all three of us are very open to exploring new avenues.
"So with this album we just set out on this same old objective that we normally have and just discovered some new things along the way."
Who: Muse
New album: The 2nd Law, out September 28
Essential listening: Origin of Symmetry (2001); Black Holes and Revelations (2006); The Resistance (2009)
- TimeOut
