Yorke's children are 10 and 6. He has lived with Rachel, their mother, in Oxford since they met studying fine art at Exeter University in southwest England. Those facts are clearly very important to him. "Making a record, going on tour is a huge commitment, particularly the way we do it, a lot of work. And when we first had young kids we were all like, 'Christ! Do we really want to be doing this the rest of our lives?'. Much as people still seemed to want us to, there were big knock-on consequences for the ones we love."
One tentative escape for Yorke from those questions was his 2006 album The Eraser, a twitchy, experimental, electronic collection of doomy dance tracks that grew out of his laptop, and which he put together with producer Nigel Godrich. He promoted it at the time with a typically defensive blog to Radiohead fans: "I want no crap about me being a traitor or whatever splitting up blah blah this was all done with their blessing," he wrote. "And I don't wanna hear that word solo." The album contained Harrowdown Hill, his examination of the death of chemical weapons inspector Dr David Kelly, who apparently committed suicide after being linked to an intelligence leak about weapons of mass destruction.
But the album's primary impulse, he said at the time, was anxiety about climate change. In among it was a song called Atoms for Peace, once the motto of the International Atomic Energy Agency. The opening lines sounded a bit like a personal manifesto for a new kind of lightness (they were, he later claimed, something of an admonition from Rachel): "No more going to the dark side with your flying saucer eyes. No more falling down a wormhole that I have to pull you out ... " Having made the album out of loops that began in his head and ended up on his computer, Yorke became intrigued to see if it could be played live. In 2009 he gathered a band of friends - don't say the word "supergroup" - he thought might be up for the challenge: Flea, the bassist of the Red Hot Chili Peppers; Joey Waronker, drummer with Beck and REM; Mauro Refosco, a Brazilian percussionist who plays with David Byrne; and Godrich, to help pull it together. Working out how to do some of the digital sounds, they spent a lot of time in the hardware store, "buying rivets and stuff".
"The first time we got together was in this place in Laurel Canyon in LA," he recalls. "We did a song called The Clock and it sounded like a bomb going off, it was just amazing. The Eraser is a headphone record really, so to hear it go bang in a room was quite something."
The band, initially billed warily as "??????", subsequently known as Atoms for Peace, did a short American tour playing The Eraser. At the end of it, and having had "a total blast", they locked themselves in a studio for three days and started improvising some more.
"I had these very small ideas," Yorke recalls, "just beats mostly. And we just played off them for about three days solid."
The 10 hours or so of usable music they created Yorke edited into a new album, adding lyrics and again working closely with Godrich. It's called Amok and is by turns dense, trippy, danceable and occasionally, whisper it, upbeat. Does he see it, I wonder, as coming from a different, less angry kind of emotional place to archetypal Radiohead?
"Well," he says, "when I originally wrote that 'No more going to the dark side' line, it was kind of taking the piss. And the irony is that Radiohead have just done this big world tour last year and for the most part we had the best time we have ever had. And a lot of dance music is very angry in a good way. But yes, the idea was for once in my life just to enjoy the energy of it and not want to pull it apart. Nigel was constantly on at me: 'Don't make it dark!"'
Does he think that's a permanent shift? "No, it depends where I am, I think. Maybe literally. I've been working at home over the winter and everything I've been doing is dark as f***. But we did a lot of this away in Los Angeles and it was sunnier. It was something to do in the afternoon and evening before you went out. There is no way I'm really going to lose the old heavy work ethic. But we got close a few times."
Ever since Radiohead's first worldwide hit single, Creep, a song that Yorke sometimes refuses to play these days but that did define a certain alienated, contrarian idea about the band and himself - "I wish I was special" and "I don't belong here" and "I'm a creep, I'm a weirdo" - he has seemed weary of the cliche it implied.
In profiles, much was made of Yorke's childhood difficulties, the fact that he was born with one eye fixed shut and only subsequently half-opened by a series of failed operations. The fact that because of his father's job as a chemical salesman he moved schools frequently, was picked on because of his eye, and withdrew. The fact that, at fee-paying Abingdon School, he found his refuge in the music room.
One way of looking at his career has been as a sort of journey away from the limitations of that analysis. The apparent absence of introspection on Amok must come as something of a relief, I say.
He smiles from under his stubble. "To begin with, writing songs was my way of dealing with shit. Early on it was all, 'Come inside my head and look at me'," he says. "But that sort of thing doesn't seem appropriate now. Tortured often seems the only way to do things early on, but that in itself becomes tired. By the time we were doing Kid A [their fourth album, released in 2000] I didn't feel I was writing about myself at all. I was chopping up lines and pulling them out of a hat. They were emotional but they weren't anything to do with me." In that sense, he suggests, he hopes the music became much closer to what he feels we all experience day to day: a stream of words and images from different sources that you try to make some emotional sense of.
The important thing, he thought, was to be open properly to that kind of white noise. He learned the habit directly from REM's Michael Stipe, who started as a hero and has long been a friend. "Michael is still my favourite lyricist," he says. "I loved the way he would take an emotion and then take a step back from it and in doing so make it much more powerful."
Radiohead have often riffed on the edge of that thoroughly modern disjunction between digitised and live sound. From their landmark album OK Computer onwards, the band seemed like evangelists for the revolutionary possibilities of a digital world, self-releasing 2007's In Rainbows on a pay-what-you-want download.
His recent work has seemed less confrontational in tone, not just with Atoms for Peace but also in the Buddhist inflections of the last Radiohead album, King of Limbs, which memorably featured Yorke doing a kind of manic tai chi dance in the video of his song Lotus Flower. Where has that antic spirit emerged from? Partly, he says, it's a deliberate response to depressive tendencies. He armed himself against any midlife despair, he says, with "running, yoga, meditation". He wouldn't describe himself as centred yet, he says, but he tries.
While working on King of Limbs he took himself into the park early every morning and sat on a bench for an hour. "It was important at the time," he says. "I wanted to be properly open-minded about what would happen in the studio." He suggests that approach might be a different kind of politics for him. "Just being looser in your thinking allows you to avoid fixed ideas." It allows him to take more pleasure in singing, he says, "how it makes you feel physically". He has come to discover that the best things that happen musically "are often when you're super-unsure and kind of flailing around. You just work at it and wait."
While in California, Yorke became an unlikely surfing convert. Though he is still "pretty crap at it", he found the experience a useful exercise in patience. "I used always to try to force things, in the studio. But it's like, you can sit out there on a board for ages waiting for the right wave to come along. You can't get angry about it. You know it will happen eventually and you start to understand the waiting itself might be part of it. Part of the fun. "
Who: Thom Yorke
What: Album Amok with Atoms for Peace
When: Out now
- TimeOut / Observer