When historians of the future write about rock's great rivalries, the Pink Floyd Axis of Upheaval will require a longer chapter than most.
Ever since Waters left the band in 1985, describing them as a "spent force", he and guitarist David Gilmour have tended to communicate via their lawyers or by trading veiled insults in interviews. It's a somewhat frosty relationship, to say the least.
In 2005 the relationship thawed for long enough for the pair to work together again, at the Live 8 show in London's Hyde Park, when Waters agreed to "roll over for one night only", and joined his old band onstage for a short set. And five years later, Gilmour and Waters appeared together at a charity concert in Oxfordshire, performing semi-acoustic versions of Phil Spector's To Know Him Is To Love Him, plus Floyd classics Wish You Were Here, Comfortably Numb and Another Brick In The Wall, Part 2.
A couple of months later, Waters took Floyd's The Wall album on the road. It's very much a Roger Waters album, but its most popular song, Comfortably Numb, is perhaps the standout moment in David Gilmour's career. The song's drama escalates with each passing verse, and Gilmour delivers a pair of similarly dramatic solos, instrumental stretches that are now are now a staple of any breakdown of the greatest guitar solos in rock.
After winding its way around North America in the months up to Christmas, The Wall tour picked up again in Europe in March 2011, arriving in London for a six-show run in May. And, if you had a ticket for the second of those six shows, you got the unexpected bonus to end all unexpected bonuses.
Half a dozen songs into the second set, Waters sings the opening verse of Comfortably Numb, and then he throws upstairs. It's Gilmour, bathed in white light, standing alone, on top of the wall that spans the width of the stage.
It's a moment of the purest magic, and the crowd's reaction reflects that. It's almost as if the roars that greet Gilmour's surprise arrival come in waves, as different parts of the huge arena realise exactly what's happening.
The first solo is a little ragged by Gilmour's high standards, as if he's still getting used to the vertigo-inducing surroundings, but the second is near-perfect, and at the end, as the final notes ring out and Waters raises a fist in an apparent show of solidarity with his old friend, you could be forgiven for thinking that a full Pink Floyd reunion was but a negotiation away.
It never happened, of course. The two went back to talking about each other rather than to each other – publicly, at least – and by 2015 Gilmour couldn't have been happier about not being in a band with Waters.
"I have turned down an incredible offer to go on tour with the original Pink Floyd line-up," he told Classic Rock. "That is a real victory for me. At the moment I would be absolutely incapable of making another record with Roger and the others."
So that night in 2011 remains the last time the pair performed together onstage (Gilmour also played mandolin on the set-closing Outside The Wall, with Nick Mason a delighted extra on tambourine). But for those who were in the audience, it's Comfortably Numb they'll treasure most. That song. That surprise. That solo.