Nam June Paik, Tate & Fact, Liverpool

In the 1960s and onwards, Nam June Paik (1932-2006) spread his restless talents fairly thinly across a range of emerging disciplines. He was an avant garde composer, a performance artist, a pioneer of video and laser art and a creator of elaborate installations using multiple television monitors.

This full-scale retrospective at two locations in Liverpool ranges far and wide. You could say that it ranges too far and too wide. It not only gives us a comprehensive overview of Paik's many projects around the world – born in Korea, he lived in Japan, Germany and the US – but it also documents many of those projects with far too many letters, exhibition invitations, flyers, posters and incomprehensible scribblings. What we want to see are the realised works. But despite the fact that Paik worked for more than 40 years, there are fewer of these than we might imagine. Many of his projects were unrealised dreams, sketched out in puzzling sentences on the back of an envelope.

What Paik did was to recognise the creative potential of television and the moving image. He thought that the cathode ray tube would be as important to art as tubes of paint. In 1965, he bought the first hand-held video camera, a Sony Portapak, and began to make recordings of himself, scrutinising his own shy and inscrutable gaze. With Shuya Abe, he created the first video synthesizer. He saw that television would open up the possibility of instantaneous global exchange.

Being something of a naïve idealist-cum-visionary nut, Paik thought that global satellite broadcasting could bring global peace. Ho hum. He was a crazy man, a post-Dadaist who played the piano tunelessly and encouraged a cellist called Charlotte Moorman to collaborate in mad performances. In one performance documented here Moorman plays the cello naked, her breasts covered by small TVs – "boob tubes". This was tolerated in Europe. In New York, it led to criminal proceedings. In another film, Moorman wears a television set on her head as she plays. Paik, who believed that classical music and sex were too far apart, wanted to yoke them together with violence.

Sometimes his works look like coiled nests of humdrum wires and beaten up brown boxes, messy as a crime scene. We tiptoe around them, looking for ways in.

Paik was a technophile – he coined the term '"electronic superhighway" – and his most impressive and ambitious works involved the bringing together of television monitors in unusual ways. In TV Garden (1972-74), an extended family of televisions are playing hide and seek across a floral landscape. Video clips and TV programmes (we spot images of Richard Nixon, John Cage and that wild Beat Allen Ginsberg) seem to emerge organically. This is the point Paik wanted to make: that technology and human concerns were not poles apart. In Video Fish, (1979), a monitor showing colourful, morphing abstract forms serves as the back wall of an aquarium. Fish swim in front of the images, living shapes in a perpetually changing dance with the unliving.

Nothing ever stops with Paik. He is always on the move. He never quite reaches where he wants to go.

To 13 March (www.tate.org.uk/liverpool; www.fact.co.uk)