I've asked him what he makes of Robert Burns, considering the duo are heading to Glasgow to headline a Jamaican Burns Night at Celtic Connections. The idea behind the evening is to explore, through music and West Indian grub, what might have been had Burns gone to Jamaica, as he had planned to, in 1786 to work as a bookkeeper on a sugar plantation. The success of the Kilmarnock Edition of his poems kept him from setting sail from Greenock, but it's a difficult, morally complex part of the bard's history that has only been discussed in recent years.
Dunbar, however, is more interested in the music. From his home in Kingston, Jamaica, he tah-dah-da-da's the first few bars of 'Auld Lang Syne' and then says: "He was the one who wrote that, no? Someone told me he was a great writer."
As for what a Jamaican Burns Night means to him, it's all about "playing some really hardcore reggae". When I ask Dunbar about his Scottish surname, I get a story about being mistaken for a relation of the drummer Aynsley Dunbar. He does say, though, that he and Robbie Shakespeare, who have been playing drums and bass together since the Seventies, will also be playing for Burns. "I know my name is Scottish, so maybe my roots go back there," he says. "Maybe I'm from Scotland."
It's a sunny response to a thorny question about Jamaican ancestry being tied up with a history of Scots heading to the Caribbean since the 1600s, many of them becoming slave owners. For Dunbar, the simple act of playing alongside Scottish musicians and singers including Karine Polwart, Edwyn Collins and Sushil K Dade is the point. This, he believes, is the way to heal and strengthen the bond between Scots and Jamaicans in the 21st century.
It's a principle that this duo, who have worked with everyone from Peter Tosh, Black Uhuru, Grace Jones and Bob Dylan to, more recently, Britney Spears and Madonna, have been putting into practice for more than 30 years, mixing Jamaican rhythms with rock, funk and disco, and in the process reinventing reggae – and pop music for that matter – over and over again. They are both very touching on their fruitful partnership, which some say has made them the most prolific artists ever, with upwards of 200,000 recordings. Neither of them is counting because, says Shakespeare, "it's about quality, not quantity. We're just playing music as easy as we come, and we try to get the best every time."
They may no longer play upwards of 50 tracks a day – yes, 50 – but they're not far off. On the day I chat to these men, both in their late fifties, their plan is to head to the studio at lunchtime and stay there until 2am.
They met in Kingston in 1973, when they were playing in clubs next door to each other. Both checked the other out, and they decided to play together. Since then, the longest they've spent apart is three weeks. "The first time we played together I think it was magic," says Dunbar. "We locked into that groove immediately. I listen to him and he listens to me. We try to keep it simple."
Shakespeare, the more gruff and withdrawn of the two, comes to life when he's talking about Dunbar. "When I'm away I miss him a lot," he says. "Even now, when he plays I say: 'Damn, boy.' You can never tell what he's going to come up with. We smile and joke and have fun. We keep happy."
What is the secret of their long-lasting relationship? "We have respect for each other, no ego, and we never forget where we come from," says Dunbar.
It's this openness that keeps them listening to new music from all over the world and that, in the Eighties, led to their pioneering the electronic revolution in music. "I listen to anything that's fresh," says Dunbar. "R&B, hip-hop, African, pop. I'm always searching… always looking for the sound that I think people want to hear, and then what I do is merge everything with reggae and get some new flavour in there. I may take 5% of American music, 10% of English and 20% of Africa, and the rest is Jamaican. It's like cooking up a meal, you know? I cook up a little bit of this, a bit of that and then I stir it all together and one sound comes out."
Shakespeare, meanwhile, simply describes music as "one big root with a lot of branches".
The world started to take notice when, with Peter Tosh, they opened for the Rolling Stones' 1976 tour. But it was in New York in the Eighties, when they heard about a certain Jamaican model living in Paris, that their talent was truly seen. "Chris Blackwell (of Island Records] said he had this girl who wanted to do some recording with us and gave us some of her records, which we still haven't listened to," says Dunbar of Grace Jones. "We got a band together and flew to Nassau to Compass Point studio. Robbie said: 'We're not going to rehearse, let's just go into the studio and cut the tracks.' The first song we cut was 'Warm Leatherette', the second was 'Private Life', which I would still say is one of the top five reggae tracks ever written."
They both have long lists of artists with whom they would love to work. Shakespeare mentions Quincy Jones, Michael Jackson and Gladys Knight, while Dunbar says, rather surprisingly, that he loves Take That.
There is no sign that Sly and Robbie are going to slow down. "If you sit down and wait for things to come to you they might not come," says Dunbar. "You have to go and make it."
Shakespeare agrees: "If you're chosen by music, I don't think you get to say it's time to retire. It's a very gentle gift, and we've been trusted with it."
• Jamaican Burns Night with Sly and Robbie and guests is on January 25, 8.30pm, Old Fruitmarket, Glasgow, www.celticconnections.com
Robbie Shakespeare was taught to play bass by Aston 'Familyman' Barrett, bassist for the Wailers.
Sly was credited with transforming reggae in the Seventies by adding to the classic one-drop rhythm a double drumming style known as rockers, which gave it an American disco sound.
While opening for the Rolling Stones in the Seventies, Sly is inspired by rock drumming and starts incorporating it into reggae.
The Eighties saw Sly and Robbie collaborating with everyone from Bob Dylan to Yoko Ono. They fall out with James Brown during a session with Robbie later saying: "I told James to f*** off because he was handling people like a dog."
Last year, Sly and Robbie remixed Madonna's track 'Give It To Me', as well as Grace Jones' latest album, Hurricane.