Charles Darwent on Edinburgh Art Festival - Three's company, one's a crowd

A trio of big hitters defy a co-operative festival theme with exhibitions that are individual and rewarding

Collaboration is the theme of this year's Edinburgh Art Festival, so my first review focuses on three non-collaborative shows, two contemporary and one historical, with the rest of the Fest next week.

Peter Doig (No Foreign Lands, Scottish National Gallery, to 3 November) is definitely not a collaborator. He is, in fact, a bit of an oddball, as an artist at least. For one thing, he paints, and paints properly, not as a Postmodern critique of Neo-Colonial appropriation or any art-theory bollocks of that kind. His studio isn't in Clapton or Peckham, but in Trinidad, a faraway country of which

we know nothing. (Unless, like me and Doig, we are from there.) He is, unfashionably, a figure painter. And then there are the prices. In February, his Architect's Home in the Ravine went at auction for a shade under £9m, which makes Peter Doig a very successful oddball indeed.

And so, a Festival question: why? Like any phenomenon painter, Doig's art speaks to its time. His life seems to have been spent in perpetual motion – birth in Edinburgh, childhood in Trinidad, youth in Canada, art school in London, a career now divided between Port-of-Spain, Dusseldorf and New York. This is a contemporary way of being, and it shows in his art.

What is the word? Yearning? Displacement? Like the artist himself, Doig's work seems forever in transit. Formally, it hovers between Modernism and old-fashioned figure painting – Ping-Pong elides both by dropping what looks like a large Mondrian behind a man playing table tennis. (Doig says the grid is a stack of blue Carib beer crates. I have my doubts.) Historically, pictures such as Gasthof might have been painted a century ago, when art was still digesting Van Gogh.

The main thing, though, is the work's alienation. Peter Doig, the modern nomad, makes us all displaced – left out of the picture by screens of dragged paint, unsure of narrative or locale, ignored by the man who walks past the titular Lapeyrouse Wall.

Like Doig's Trinidadian reprise, Gabriel Orozco's thinking in circles (Fruitmarket Gallery, to 18 October) is a homecoming, although a formal rather than geographic one. From the start, the Mexican was entranced by circles. This has historical form. According to the fanciful biographer Vasari, Giotto, asked by Benedict XI to prove his genius, drew a perfect freehand circle and handed it to the Pope's messenger. But the circle is also the simplest gestural form, art reduced to a sweep of the hand; what Orozco calls "an instrument".

His festival show is thus circular both in returning to this first fascination and in being about circles. The image you see as you enter is the 2005 painting The Eye of Go – a conflation of the artist's initials, the Chinese game whose black counters its own dots resemble, and the phrase, "Eye of God". If you're looking for a way in, you might reach for the word "conceptual" – The Eye of Go was certainly made with thinking aforethought – although the work is also a straightforward piece of abstraction, a direct descendant of Malevich.

Maybe this is what makes Orozco good: a sense, manifest in this show, that his art is both clever and visceral. From The Eye of Go, you can navigate by any circular route – by date (the wonderful acetates upstairs have been stored, unseen, since 1995); by colour (Orozco moves back and forth between black-and-white and naval semaphore primaries); by form. The newest work, downstairs, is three-dimensional – spherical sculptures carved from river stones, with one that looks like a football. Spheres, you will recall, are circular.

Last, but most wonderful of all, is Nam June Paik's Transmitted Live (Talbot Rice Gallery, 9 August to 19 October). The Korean Fluxus artist, certifiably nuts, was the first to put televisions into art. Upstairs at the Talbot Rice is work from his 1963 show in Wuppertal, including black-and-white televisions whose thick copper aerials frame the face of Richard Nixon. There, too, is Paik's endlessly self-regarding TV Buddha, gazing for all time at its own cathode navel.

Downstairs is where you really want to be, though, between the robots called Beethoven and Schubert. Paik built these himself out of old television sets, and lovable creatures they are – threatening, stupid, but somehow amusing, and very, very humane. I imagine Nam June Paik was, too. But since he died in 2006, I'll never know.

Critic's Choice

Eileen Agar, John Piper and Ben Nicholson are among artists experimenting in Modern British Collage and its Legacy at Pallant House Gallery, Chichester (to 29 Sept). At Dulwich Picture Gallery, A Crisis of Brilliance recalls a golden era of 20th-century British painting with Gertler, Nash, Nevinson and Spencer (to 22 Sept).