The Tate's Mark Rothko exhibit: a room with a view of the subconscious

The set of Mark Rothko paintings originally commissioned for the Four Seasons restaurant in New York are the treasure of Tate Modern. They occupy a room of their own, low-lit and filled with brooding intensity. The hazy outlines of what might be doors, windows, or the gates of heaven and hell hover on the wine red and imperial purple surfaces of Rothko's mural-scale abstractions. In all of them darkness beckons, mordantly inviting the beholder to imagine vast apocalyptic landscapes, undefinable events on a cosmic scale.

Almost everyone who enters the room feels an urge to sit down on the benches in the middle of the space. It's as if the emotional weight of these sombre works instinctively makes you sit, instantly drained by them. Before you even have time to try to compose a rational understanding of them, they have a psychological impact.

Rothko was a fan of the book The Birth of Tragedy by German philosopher Frederick Nietzsche. In this provocative 19th-century work, Nietzsche argues that ancient Greek tragedy grew out of the rites of the god of wine and ecstasy, Dionysus. When he was planning his paintings for the Four Seasons restaurant in the Seagram Building in Manhattan, Rothko toured Italy. He went to Pompeii and studied the ancient Roman murals there. Deep reds, abstract and empty, and illusory depictions of doors leading to spaces beyond, are characteristic of ancient Roman fresco painting. But perhaps the most tantalising potential source of Rothko's cycle of paintings is the Villa of the Mysteries in Pompeii, where people are depicted celebrating a Dionysian mystery cult against rich red backgrounds. It seems to me that Rothko, a reader of Nietzsche, must have seen connections here between deep red and black walls and the idea of art as a tragic Dionysian experience that opens up the imagination like a raw wound.

Another inspiration he spoke of on his trip to Italy was the vestibule of the Laurentian Library, an architectural masterpiece by Michelangelo built off the cloister of San Lorenzo in Florence. Rothko was impressed by the blind windows that grimly decorate this room – classical window frames that, instead of letting in light, are blocked off by Michelangelo to close down the spectator's curiosity. As well as these blind window frames, it has gargantuan stone scrolls, a staircase that sprawls like an octopus on a fish stall, and overwhelming colours of grey and bone white.

The Rothko room at Tate Modern strives to recapture the claustrophobic, disorientating feel of Michelangelo's room. The Laurentian Library vestibule also has a deliberately oppressive effect on you – and here, too, it starts as soon as you step into the room, as if you had crossed a threshold from normal life into some waiting room in hell.

Rothko was fascinated by the idea of shaping a room with art, using abstract painting as a type of architecture. After the restaurant commission – and his decision not to let his great paintings go in a restaurant after all, but to give them to the Tate – he "made a place", as he put it, in the Rothko Chapel in Houston, where echoes of Michelangelo abound once again. The chapel's interior actually has false doors that lead nowhere, or rather into dead spaces behind the paintings. But the paintings here are more deathly and absolute than the rich visionary works at the Tate – the Houston chapel is funereal, the consummation of a tragic view of life.

In London, the Rothko room is disturbing, but liberating too. It frees the imagination. It creates the effects of great architecture and fresco painting using abstract daubings hung in a gloomy chamber. It always makes me think of Caravaggio's Bacchus, proffering a glass of stilled red wine. Home in on the wine, enlarge it, until the screen of your mind's eye is red, red, red. That is Rothko's vision you are drinking in.