A visitor to the Uffizi Gallery in Florence has had a heart attack while contemplating Botticelli’s The Birth of Venus. The man is recovering in hospital, but it is the latest apparent case of Stendhal syndrome, a medical condition specific to the Tuscan city in which people become ill after too much beauty. I suspect the occult. Could there be some old black magic lingering in this Renaissance wonderland that gives its art a unique potency? For Botticelli may have intended The Birth of Venus as a magical spell, and Michelangelo’s David, another Florentine must-see, was accused in the early 1500s of casting an evil eye over the city.

There is substantial evidence that Stendhal syndrome is real and unique to Florence. It is named after one of the earliest recorded cases, when the French novelist and critic Stendhal made himself sick on art here in 1817. Why don’t people succumb to the same symptoms, from dizziness to heart trouble, in galleries elsewhere? In London, Tate Modern has occasionally given me a headache, but that’s more to do with its labelling. And people look at Botticellis in the National Gallery with no noticeable ill effects.

It is surely the sheer concentration of great art in Florence that causes such issues. Its historical centre is compact, a small area uniquely stuffed with statues, altarpieces, fountains, frescoes, domes and sculpted doors. Even Santa Maria Nuova hospital, which treats tourists for the syndrome, dates from the 15th century – Leonardo da Vinci dissected corpses there. For art lovers, the thrill of arriving somewhere that gathers so much famous art is like meeting all your heroes at once. More cynically, some might say the long queues do add a layer of stress on the heart.

This strange aesthetic sickness is surely evidence of the special power of Renaissance art. This lovely stuff, and the way it has been displayed in Florence since Giorgio Vasari began building the Uffizi in the 1560s, created the very idea of “art” as we know it, as something with a hypnotic allure. The Medici family and other Florentine merchants and bankers believed art could make them happy, wise and civilised like the ancient Romans, whom they revered. They also thought that a painting or statue could be a talisman or charm to promote sexual fertility or ward off disaster.

To this day, a “miraculous” Annunciation said to have been painted with angelic help is unveiled to its devotees in the church of Santissima Annunziata. And the magic still works. Botticelli died in 1510 but his art can literally floor someone more than 500 years later. There was a unique constellation of genius in this place at that time – Botticelli, Leonardo and Michelangelo all at once – that has left an afterglow you can still feel despite the tour guides and overpriced cafes. If you haven’t felt woozy in Florence, you haven’t really been there.