Neither The Poet nor The Lover, whose portraits open the this heart-stopping Van Gogh exhibition, were quite what they seem. The Lover’s eyes gazes dreamily from a face of blue-green tints, wearing a red cap flaming against an emerald sky, in which a gold moon and star twinkle. In reality, he was an army officer called Paul-Eugène Milliet, whose affairs were less ethereal than the painting suggests. “He has all the Arles women he wants,” wrote Van Gogh enviously. The Poet’s face, meanwhile, is anxious and gaunt, its ugliness badly hidden by a thin beard, as the night around him bursts into starshine. He was a Belgian painter called Eugène Boch whose work Van Gogh thought so-so. But beggars can’t be choosers. They were among the few friends Van Gogh had in Arles, after he arrived in February 1888 to renew himself. Why does this exhibition start with these two paintings, instead of the blossoming trees or golden fields he painted that spring? The answer lies in the portraits’ very lack of prosaic fact. Van Gogh is an artist we’re still catching up with. We all know his turbulent story – that less than a year after arriving in Arles, he would cut off his ear, and be narrowly saved from bleeding to death – but we’re not so clear what made his art so extraordinary. Wasn’t he just an especially intense observer of sunflowers? The Van Gogh this great show explores, with moving and addictive aplomb, is barely an observer at all. He transfigures what he sees. It starts with those portraits of ordinary blokes in whom he sees eternal romance and poetry, proof of how utterly he remade the world around him. This is a journey not to the actual town of Arles, where if you go looking for The Yellow House you’ll find just a plaque, but the Provence in Van Gogh’s mind – or, I want to say, his soul. It’s a journey through the shady walks and undergrowth of a gnarly, greened imagination. Between the two portraits hangs The Poet’s Garden, a view of a small park across the road from The Yellow House. It was an ordinary spot where people sought shade, but in his repeated paintings its trees take on mysterious expansive shapes, and strolling people become charged with feeling as he pours out his love of everywoman and everyman. You snuffle on through the undergrowth, hunting Van Gogh’s truffles of genius. And you are suddenly no longer in Arles but the enclosed garden of the nearby asylum in Saint-Rémy where he became a patient in May 1889. In his great painting Hospital at Saint-Rémy, inmates walk sadly past the low yellow building while above it, spiralling trees creep into the heavens, their spiky green waves of foliage mixing into a sky that becomes an ever-deepening blue as it ascends. This is where the daring of the exhibition hits you. In a conventional telling, Van Gogh’s life in Provence was brutally split, as his first ecstatic months ended in self-harm and hospitalisation. Here, the translation to Saint-Rémy is not a tragedy at all. You see how his style got ever more free there. A later room is filled with landscapes he painted around Saint-Rémy that teeter on total abstraction: in The Olive Trees, the earth erupts in waves like the sea, trees dance, and a cartoon cloud is so free from rules it could be by Picasso. Van Gogh, here, is the first completely rule-breaking modernist and he just gets ever more radical. He’d toiled for years doing brown studies of northern life before he met the avant garde in Paris: within weeks of his arrival in Arles, he took the impressionist ideas he’d encountered to the next level. Describing his painting of a man sowing, he wrote in June 1888: “There are many touches of yellow in the soil … but I couldn’t care less what the colours are in reality.” The Sower is here, silhouetted against a godlike sun in a field streaked with purple. Next to it hangs Starry Night over the Rhône, a painting that lifts you into the air and leaves you floating: the sheer brightness of the stars, which seem so close, make the earth below dreamy and vague. Reality is not real. The visionary is. These paintings take you outside yourself. They hang in the most extraordinary room of the show. Don’t look too long at Van Gogh’s 1889 Self-Portrait, in which he looks back at you with those sapphire eyes, in his blue smock in a wavy blue sky. This room does something an immersive Van Gogh “experience” would love to emulate: it puts you inside The Yellow House. You see this little square house from outside in Van Gogh’s painting of it. Then you enter through its green front door. Vincent’s Chair is an aching, symbolic self-portrait : a wooden straw-seated chair, with his pipe and tobacco resting on it. Then you get to The Bedroom, Van Gogh’s tender depiction of his own room with its immeasurably solid and welcoming wooden bed. We all know how badly it ended. The ideals Van Gogh invested in his little home couldn’t withstand the shock of sharing it with Gauguin, and after his ear-cutting and further crises he decided he was better off in an asylum. But here, that never happens. We experience not the sordid facts, but Van Gogh’s dream of The Yellow House. It still exists, always, out there among the painted stars. We should really call him Vincent. That’s how he signed himself and it’s how close you feel to him in this show. In the end, it isn’t enough to analyse Vincent. You have to love him. He craved it and he earned it – and this show loves him as he deserves. Van Gogh: Poets and Lovers, at the National Gallery, London, opens 14 September