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This is Coldplay's brilliance, creating the illusion of intimacy in a stadium setting. It wins them few critical plaudits, but it's harder than it looks, especially when the size of your fan base limits you to playing arenas. "A song arrives and you just follow it," Martin says. "And of course we sometimes sit down and have discussions, can we do this song, can we do that song, and occasionally it doesn't fit with the remit."
What's the remit? "Well sometimes you might get sent a reggae song that's amazing, but if we did it as Coldplay, it would not serve the song and it would not serve us either, it would just look stupid." (For proof, see YouTube footage of Martin dancing alongside Beyonce and Bruno Mars at this year's Super Bowl.) It's not, he says, a matter of trying to give fans what they want, "but what we think might make people feel something. We never want to be wilfully obtuse."
I think we're all made alive by that feeling of singing with thousands of people at the same time, it's what makes people feel connected to everyone.
Chris Martin
The word "sent" is important here. "When the song Yellow came through, something in my body was like – oh, there's something different about this," he says. "Occasionally you get a song where you think, oh, this is here for a reason, it's not just crafted, it's arrived. But that initial thing comes from a place you don't really understand.
"It's like if you're running a hot springs and taking credit for the hot springs. You can't. My point is music kind of gets sent through, from wherever it comes from, and sometimes you know when something is really going to connect." So do the songs belong to you, or the fans? "That's my point. They never belong to any of us. Only the shitty ones belong to us!"
Cynics will offer their own rejoinders to Martin's cheerful self-deprecation. A quick straw-poll of friends – what would you like to ask Chris Martin? – presents the following: "Is it still all yellow? And have you seen a doctor about that?"; another suggests the terse, more existential "Why are you?" Among them, a meek voice: "I don't mind Coldplay. I know that's not cool, but they have some lovely songs."
"Often the things people criticise us for are the same things other people like," Martin says. "Everything in life is how you look at it, isn't it? It's about trying to see the value and beauty of everybody, and the joy of togetherness, but at the same time the accepting of differences of opinion. So I take it, if people are still able to say Coldplay are shit, well, there can't be too big a problem going on in their lives."
Buckland, who offers thoughtful rejoinders in between cracking up at his band mate's woolly philosophising, doesn't sweat the small stuff, either. "I think we just feel incredibly lucky for everything we've had. I mean, honestly, we'd be arseholes for wanting this to be even better."
"You can't go around the world playing stadiums and complain that something's awful. It just doesn't work," Martin says. "You can't say, it's great we sold this many [records], and all these people seemed to have a nice time, but we didn't make the end-of-year poll on that thing.
"It's OK, we're OK. And we stand for what we stand for and we're true to ourselves and so we're not pretending anything, that's the key thing. It's not like someone's going to discover something about us that we're trying to hide."
Since their early days, Coldplay have been frequently compared to U2, and more and more – in their longevity; their staggering success (80 million records and counting: surely, as someone once said of Elvis, all those fans can't be wrong); their unflagging belief in the ability of music to solve the world's ills and their frequent forays into activism, it appears true.
I ask Martin and Buckland about the mood in post-Brexit Britain. (The band had vocally endorsed a vote to remain within the European Union.) "It's very hard to not sound like a knob when you say that really, borders and all that stuff shouldn't need to exist, should they, in an ideal world," Martin says. "If you're an alien and you landed on earth and you come from somewhere else in the galaxy and you saw the fractiousness of everything, I think you'd be surprised."
Come again?
"We imagine when we land on another planet that all the aliens there get along just great, do you see what I mean?" he expands, Buckland hooting with mirth beside him. "No one ever thinks about, like, the election on planet Cybertron, you know what I mean – 'Oh, these guys hate those people and these people want to leave that bit…' So I personally am all for…"
He doesn't finish that bit, but rolls on. "And we in our job get to go around the world, seeing how people respond the same way to certain music. I don't know. My personal feeling is that this is the storm before the calm."
You really are an incurable optimist, aren't you?
"Yeah, I really am. Otherwise I'd just go and jump off a bridge. But even then I'd have a parachute and make it great fun!"
And with the interview done – thinking, perhaps, I'm in need of some love - he plucks the badge off his shirt, and presses it into my palm.