Twombly and Poussin: Every picture tells a story

Abstract versus figurative art, can the one ever equal the other? The argument has been going on for very nearly a century now. But, in its latest show, comparing the contemporary American artist Cy Twombly with the 17th century French painter Nicolas Poussin, the Dulwich Picture Gallery gives an enlightening, and at times surprising, answer.

Poussin was from early on a hero and influence on the American artist, which is one good reason for holding this exhibition and why Twombly, now 83 and one of the pre-eminent figures of modern American art, seems to have been keen to cooperate with it. While their art is quite different on the surface – Poussin cool, classical and figurative, Twombly free-style, multi-material and largely abstract – they had a lot in common. Both artists went to Rome at the age of 30 and stayed there for long after. Both artists saw in Italy the gateway into the past as well as a window on an entrancing landscape. And both, extremely well-read, made classical myth and allusion the subject of much of their work.

Not that the show, thank heavens, aims to do a compare-and-contrast exercise on the two artists. We've had a run of galleries hanging modern artists against the classical forebears of late and, while it often refreshes the masters, it is becoming somewhat tired as a concept. Rather, the Dulwich exhibition – a labour of love by Tate Modern's curator of international modern art, Nicholas Cullinan – aims to show how the two artists developed their separate answers to a similar ambition. Poussin sought to refresh the great tradition of Renaissance and post-Renaissance artists grown florid and (in his eyes) frivolous by a return to a cool, considered art of harmony and moral purpose. Twombly, in the same way, has reacted against the dominant style of American abstract art of Jackson Pollock and others by introducing words and themes and drawing to his work.

One of the real masterpieces on display, Twombly's Hero and Leandro from 1985, a great swirling, passionate canvas of finger-smeared red, white and grey, is made infinitely more moving by the knowledge not so much of the Christopher Marlowe poem which inspired it, but the story itself. Hero and Leander were lovers on opposite sides of the Hellespont. Every evening, Leander would swim the straits to his lover until, in a storm, he drowned. She, in grief at his non-appearance, then threw herself into the turbulent waters as well. Knowing this doesn't necessarily make the work – with its rich red and extremes of passion facing the churning waters – more powerful or even more effective, but it does make it richer.

Hung opposite is Poussin's Rinaldo and Armida. The story is of a Crusader knight entrapped by a Saracen sorceress who, as she approaches to finish him off, is struck by love and restrained by cupid. Know the story and you can free your mind to appreciate not just the circle of woman's arms and man's body that make up the centre of the picture, but also the touching way in which her drooping arm comes to rest on his sleeping hand upon his head in a moment that is both tactile and sensual. Poussin may have gone down in British reputation as a cold, calculating artist of little warmth, but this is a vision of peculiar delicacy and feeling.

Can the abstract communicate ideas and stories as well as figurative? Yes and no. The show starts by placing a dark landscape of A Roman Road by Poussin, in which the trees overhang the road in an arch of dark green, in between two of a series of untitled "Green Paintings" on shaped wooden panels by Twombly from the 1980s, which closely match the French artist in their concentration on colour and Italian light. Thereafter, the exhibition shows the two diverging sharply in their responses to similar subjects.

Poussin believed that a painting could tell a story with as much force as words, especially poetry, and he organised his canvases with a precise composition and particular details which told exactly the stories without words. Twombly introduced words from early on as direct descriptions, as backgrounds and as elusive messages. It didn't meet the approval of critics at the time but, in retrospect, gives him a sense of improvisation that Poussin would never have countenanced. A brilliant drawing by the French artist of Joshua's Victory over the Amorites, all swirling muscle and bloody action in the manner of Michelangelo, is framed by two paper sheets by Twombly covered with pencil squiggles which he drew freehand at night when it was too dark to see what he was doing. They are not the same thing and yet they are related.

In terms of figurative art, Twombly comes closest in his sculptures, the lesser-known aspect of his art. Dulwich has gained a first public viewing of his dryly humorous wooden box on which a stone with a plastic rose is placed, the box inscribed with the statement, "That Which I Should Have Done I Did Not Do", a direct riposte to Poussin's self-epithet, "I have neglected nothing". In terms of abstract, Poussin – who was the great master of colour composition – comes closest in The Triumph of Pan from the National Gallery, a riot of blue dress and exposed flesh against the vertical lines of narrow trees. Half close your eyes and it could be abstract.

Read the detailed introductions to each themed gallery, by all means. They are full of fascinating facts and explanations. But they are not necessary. This is a show to relish in the regard of the works themselves and one's individual responses to them.

It ends with a display not of the two painters side by side, but of Twombly's wonderful Quattro Stagioni from the Tate. Poussin did a series on the same theme (Les Quatre Saisons) and there's a group of photographs of the Louvre set to remind you of his Arcadian vision. But the room belongs to Twombly, and his quartet stand on their own, powerful evocations of the light and mood of the seasons. It helps knowing what they are about. Total abstraction, as Twombly has always argued, has its limitations. But then so has figuration.

And if this would seem to give Twombly the edge in the show (and his name does come first after all) you can always – and should – pop across to the other side of the gallery to the room where the Picture Gallery's extensive holdings of Poussin are normally hung. The gallery has moved adeptly to replace them with the series of five Sacraments held by the Duke of Rutland. The first series on the subject, they were painted as concentrated subjects of meditation, full of calm, permanence and humanity. The last and one of the best, Ordination (pictured outdoors), has been sold to an anonymous buyer abroad. We have only to mid-August to save it (at the cost £15m).

Whether it can be saved is uncertain. Poussin is not that well-known a figure among the public. The country has a sizable number of his works. But to break up a series in this way and to sell it on the basis of anonymity (why does the buyer wish to keep his name secret, one might ask) seems an act of unnecessary self-harm to a country whose care of culture has grown quite casual.

Poussin was one of the greats. By showing the work of a contemporary, and considerable, artist against his, visitors will come away refreshed by both. They might also go away sensing just how much this country has lost by throwing away its common educational inheritance of classical allegory and myth. But then that is another issue.

Twombly and Poussin: Arcadian Painters, Dulwich Picture Gallery, London SE21 (020 8693 5254) to 25 September