There are a lot of paintings and watercolours by JMW Turner in London's public galleries - the Tate alone has nearly 20,000 - which the artist left to the nation on his death in 1851, but the one that I remember most clearly from one visit to the next is in the National Gallery not the Tate. It is his late, great, train picture Rain, Steam and Speed (above).

I call it a train picture, but really the subject is as much the rain as the steam and speed of the title: a luminous blur of weather and light on the Great Western Railway's Maidenhead Viaduct. It's one of two terrific works by Turner in the National Gallery, which, though painted only five years apart, offer very different interpretations of the artist's view of the world. The other is The Fighting Temeraire, a magnificent seascape in which one of the Navy's last, great sailing ships is towed by steam tug to its grave: a heroic relic of Trafalgar, steeped in ghostly grandeur and the poetry of a bygone age, replaced by the ugly efficiency of a new order. There's more at stake here than the fate of a single ship, at least that's the traditional reading of the picture.

Rain Steam and Speed on the other hand shows the artist embracing the future and turning with enthusiasm to the possibilities of an industrial age. I think, in the end, that both interpretations contain an element of Turner's true view of things, but it's the latter notion that is currently in favour and which forms the substance of "Turner and the Scientists" at the Tate Gallery.

There's no doubting that Turner was a forward-thinking artist - to many he's the father of modern art - but the suggestion at the Tate is that his progressiveness went well beyond the studio. They've borrowed Rain, Steam and Speed to help prove the point, and have plumbed the depths of their enormous Turner collection for evidence that his friendship with the likes of Faraday and Humphrey Davy influenced his work. Whichever side you come down on, it's a fresh and unfamiliar context for one of the nation's greatest ever painters.

Turner and the Scientists: an Artist in Two Cultures, Tate Gallery, SWI (0171-887 8000) to 21 Jun