The musican and the artist met at the Venice Biennale but didn't quite hit it off at first...

James Lavelle, 40

As co-founder of the electronic-music label Mo'Wax, Lavelle (right in picture) helped shape 1990s dance music, while with his trip-hop outfit Unkle, he has worked with guest vocalists including Richard Ashcroft and Thom Yorke. He has also provided soundtracks for films including 'Sexy Beast'. He lives in London

I met Joseph at the Metropole Hotel at 2am during the last Venice Biennale. It had been a long, strange first day there for me, with no time to chill out. I was sat in the foyer waiting for someone, and feeling pissed off, when I saw a guy sitting in front with a hat on, similar to my own Borsalino, which I was wearing. He was looking at me while talking to a lady with a lot of New York bravado, when he turned to me and said, "Who are you?" I wasn't in the mood, so I was like, "I got to go." Later, my friend, a curator, said, do you know who that was? That's Joseph Kosuth!"

I met him properly the next day, on a water taxi, going to a party I was DJing at. After the party, I remember a mad ride home with a bunch of artists, including Joseph. When you meet someone in that environment and spend an intense period of time with them, you can get close. And through a five-day period, along with [the artist] Gavin Turk and [the sculptor] Fiona Banner, we rocked Venice.

He set up a studio in London, and we started talking about working together. He's a text-based artist, and we'd talk about how to translate those words into music. He jokes about how he gave his words to [Velvet Underground's] John Cale.

He's nearly my father's age but I'm fascinated by this childlike person with a constant lust for life. He tells great stories filled with energy; he has mad tales about hanging out with famous artists and musicians such as Bob Marley and Mick Jagger.

On one level I think he's very tough and self-assured. He'll say to me, "I've got this work going up, the biggest in Paris – it's the only neon you will see from the Eiffel Tower." And you think, wow, he's so confident. But I felt an insecurity in him when he entered my world, working on this lyric project together.

He's also incredibly sensitive. He got pissed off with me recently over Meltdown. We were chatting, and the next minute, he was like, "You didn't invite me to your show. You didn't call!" I was like, sorry, let's get dinner and work it out. We're both emotional people.

We've spent most of our time around each other socially, experiencing this weird, nocturnal world filled with a fascinating mix of people from all walks of life.I frequently go to his openings and he comes to see some of the mad things I've done, such as when I was DJing to 4,500 people, playing acid house – he was right at the front, fascinated.

Joseph Kosuth, 69

A pioneer of conceptual art, the American's 1965 work 'One and Three Chairs' explored the nature of his industry. But Kosuth is perhaps best known for his neon word sculptures, which can be seen in collections around the world, including in New York's Moma and the Louvre in Paris. He lives in New York and London

I don't particularly like men – I prefer the company of women. Other men remind me of aspects of my character that I'm not that happy about. And when I first met James, during the Venice Biennale last year, we didn't like each other at all.

I was in a bad mood; I was in five shows and having problems with the group-show venues. But mutual friends kept throwing us together. I have fragmented memories through the alcohol haze of us getting over our initial, unenthusiastic, take on each other.

The Biennale is like a professional convention, curators, collectors and artists all networking, and I was exhausted from the conversations about work, so it was a pleasure to talk to someone with whom nothing was at stake.

I see him as the riverboat gambler out of an old western type: his style is kind of slow, he speaks with this poker-face style, while I'm much more the exuberant Yank.

Back in London, where I'm now based, we have lunch a lot; we keep thinking about doing a project together that plays to both our interests. We've not quite found it yet, but it's been fun to expand my brain a bit by thinking in terms other than my normal work.

James's [trip-hop group] Unkle is very respected – which I really got to understand when I introduced my daughter Noema to him over dinner. She's 21 and goes to a lot of concerts, and was really excited to meet him.

I'm probably too serious in my work – but not on occasions when I'm drinking, so it's a different side of my personality that James engages with. I've been to his DJ events at the Groucho Club – I have a lifetime membership there, as that neon in the bar is mine – and we go on evenings out, too.

I was with him earlier this year when he was invited to curate [the Southbank music arts festival] Meltdown. He immediately invited me to apply my own capacities to that context, but he never followed up, which was a little disappointing. I saw him DJ at Meltdown, and I was impressed at how an audience responds to him; seeing him work with the crowd, and his engagement with it, has been an eye-opener.

As an artist, my activity is really about the process, which can be forgotten when the market reduces it to an expensive commodity. The interesting thing about working with music is that the audience can experience the artist as they deal with their ideas; contrasting his practice with mine has been inspiring.

Joseph Kosuth's first UK retrospective, 'Amnesia: Various, Luminous, Fixed', is at Sprüth Magers, London W1, until 14 February. An exhibition of Mo'Wax's 'urban archaeology' archive, Build and Destroy, is at the Saatchi Gallery, London SW3, until 5 Januar