It took centuries of endeavour before the first man ran a four-minute mile. Yet as soon as he did, it happened again just two months later. Since Roger Bannister broke that barrier in 1959, many athletes have done the same. That, says playwright David Greig, is how things are in his profession as well. ‘Until it’s done, you don’t know it can be done,’ he says. ‘And when it’s done, you’ll do it again. It’s a bit like that with plays. Until David Harrower’s Blackbird is written, you don’t know it’s possible to write a play like Blackbird. And once it is written, you think, “well, I want to do something like that.”’

We’re talking about Harrower because, for the first time, he and Greig are presenting their plays in a double bill. The centrepiece of the Traverse Theatre’s festival programme kicks off with Harrower’s Good with People, which was nominated for a CATS award for Blythe Duff’s performance on its debut in Glasgow’s A Play, a Pie and a Pint. Then we move to Greig’s The Letter of Last Resort, starring Belinda Lang, which was the highlight of a ten-play season at London’s Tricycle Theatre that went under the blanket title of The Bomb.

The former is a two-hander about a prim Helensburgh landlady, living near the Faslane nuclear base, trying to be pleasant to a guest who, many years before, bullied her son at school. The latter is a discussion between a prime minister and a civil servant about the crazy logic of nuclear weapons. Despite the sober themes, both are very funny.

In over 20 years of friendship and mutual professional admiration, it’s the closest Greig and Harrower have come to a collaboration. Neither their working methods nor their writing styles would normally allow such a thing, but they both happened to have short plays worthy of a second airing and there was a small but interesting overlap with a nuclear theme that is understated in Harrower’s play, foregrounded in Greig’s. Both writers are looking forward to seeing whether the plays will generate new meanings when they rub up alongside each other.

‘His play is set in Helensburgh and has a very Harrowerian backdrop,’ says Greig. ‘It’s like how he uses terrorism in A Slow Air: somehow there’s an incredible darkness that you’re almost not sure is there, but it’s really powerful. He does that with nuclear weapons in Good with People. My play is explicitly about nuclear weapons, and it has a little glimpse of Harrower in a moment that is about Faslane and the community around the military base. But they’re not trying to do the same thing; mine is obviously a political comedy and his is a tangential personal story. I hope audiences enjoy the plays’ reflection off each other, but there is no correct answer and no puzzle to be solved.’

For audiences, it’s a rare chance to see two of Scotland’s most formidable playwrights in a single sitting. There’s Harrower, a master of the spare, elliptical and poetical, internationally celebrated for Knives in Hens and Blackbird. Then there’s Greig, a more prolific and gregarious theatremaker, whose biggest hits are Dunsinane, Midsummer and The Strange Undoing of Prudencia Hart. Since their first meeting at a workshop run by the late Tom McGrath in the early 1990s, they have done more than most at shaping modern Scottish theatre.

‘I had moved back to my mum’s house in Edinburgh to try to become a writer,’ recalls Harrower. ‘I phoned him up from the aridity of my mother’s hallway and heard all this commotion at the other end of the line. He was holding auditions for something and it just felt like there was a queue of people wandering through his flat in Glasgow. So my initial thing was, “Christ, this guy has really got it sorted and I’m still standing in my mother’s hallway.”’ Greig, however, was equally impressed by Harrower: ‘He was the first person I met in Scottish theatre that I thought, “you take this as seriously as I do.”’

‘I think that’s why I phoned,’ agrees Harrower. ‘There was almost a writer crush. There was a solitary couple of years for me before the Traverse took Knives in Hens, so I was thinking, “oh, there’s someone who is almost the same age as me who wants to do the same thing. Possibly he is a kindred spirit.”’

‘Ever since then, the relationship has been very creative,’ says Greig. ‘We mostly gossip or talk about cycling, but there’s a moment in the conversation when you say, “you know when there’s a scene, how would you push at this?” and you know the language and you respect the craft. I’ve had that for 20-odd years with David and that is invaluable.’ The relationship is not one of competitiveness but of mutual artistic inspiration, each delighted and enthused when the other breaks another four-minute mile. ‘You push each other,’ says Greig. ‘When somebody does really good work, it raises the bar. I think every playwright needs to find their David Harrower.’

‘For me, there’s never been any rivalry,’ says Harrower. ‘He’s somebody I can bounce ideas off. I can open my mouth wider with him than I can with anyone else. I know he knows what I’m talking about and vice versa. He just spurs me on. He’s also totally different from me. He’s so prolific, so eloquent and he’s got such a surgical brain. I’m not. I’m the hospital porter next to his surgeon – but I’m the hospital porter that people rely on. I save people’s lives as well; I just do it in a different way.’

The double bill will not be the end of Greig’s writerly collaborations this August. Together with Orla O’Loughlin – in her first Fringe as the Traverse’s artistic director – he is challenging 12 playwrights, including Sue Glover, David Ireland and Douglas Maxwell, to submit Dream Plays (Scenes from a Play I’ll Never Write) that will be given one-off early-morning readings.

‘We’re not asking people to write a play,’ he says. ‘We’re asking them to give us material and, during a day in the rehearsal room, we’ll find the drama in it. The collaboration with the writer is us saying, “you know that thing in your bottom drawer that you never quite know what it is? Give us that.” My experience is it’s those things that turn out to be brilliant.’