“It’s an amazing context to be showing in Florence, the home of so many of the artists that I love the work of and am in dialogue with,” he says, part corporate detachment (he was a Wall Street commodity broker in the 1980s), part Zen master. In among recent-day cartoon characters, animals and ballerinas, there are Venus, Apollo and Diana, eternal subjects of the great masters.

“I enjoy making references because, if you look at other artists, as soon as you find something greater than the self, you’re able to have transcendence,” he says. “Leonardo’s referencing Verrocchio and Masaccio. As soon as you’re able to find something outside the self, all the energies of the world emerge.”

Here in Florence, it feels like Koons is soaking up the powers of his predecessors, which seem to course through civic energy lines. “Life flows through these streets, the way of looking at life and pleasures, and the respect for human history,” he says. “I want to have an intense life experience and the Renaissance was a time that was very much about the pursuit of pleasure. It was about becoming. It was about transcending.”

When he first worked with mirrors in New York during the late 1970s, Koons had his own major sense of artistic transcendence. He says in the show’s catalogue that, after playing with found objects and mirrors, “The reflection seemed to move a little slower than the object and somehow heightened one’s awareness to time itself, so it became sort of a hyper situation. After creating one of the first pieces like this – my ‘Inflatable Flower’ and ‘Bunny’ – I had to go out and drink a couple of beers to come down from the heightened experience. It felt so supercharged and I felt my work had moved onto another level. The intensity of the colours and experience were so fresh.”

To many, it might sound a little farfetched that reflections could cause such an epiphany, but walk round his large sculptures, such as “Metallic Venus” (2010–2012) and “Seated Ballerina” (2010–2015), and we defy you not to find them mind-warpingly mesmerising, not to feel yourself melting into their sublime, seemingly liquid form. It’s art and beauty as pure pleasure and visceral thrill and it takes you to a place that few works ever do. Why is that?

“The art happens inside the viewer,” he says. “It’s all about our own chemical reactions. It’s all about our own excitement. It’s about the essence of our potential. Shine has always been a symbol of transcendence.”

Koons refers to Apollo in one of his Gazing Ball sculptures as a, er, shining example of what he’s describing. “Apollo was the god of light, and not only the god of light, but the god of everything,” he says. “Light has always been the symbol of life’s energy. For me, the surfaces of my work reflect the abundance of everything and shine reflects the affirmation of us and the affirmation of everything. It shows abstraction and the possibility of transcendence because of light and the intoxicating quality of the reflection.”

It’s that feeling you get through the gilded objects of the Catholic church, Paris’ gleaming gold monuments, or even the intense lights of a sports stadium (or fashion show).

Most artworks would still have this brilliant quality today if they hadn’t degraded and become dirty over the years. Koons tells a story of a visit to the Rijksmuseum in Amsterdam, where its director, the fabulously named Mr Taco Dibbits, told him that the medieval art there would once have been highly polished and reflective. “If those artists had access to the tools you are working with today, everything in this room would look like your work,” he said.

Likewise, Mr Vinzenz Brinkmann, curator of the Liebieghaus museum in Frankfurt and an expert on polychrome (when something’s painted, printed, or decorated in several colours), once said to him, “Jeff, if the ancients had the technology we have today, they would be making work just like you.” So, such shiny art is by no means a sign of flashy modernity – it’s something that artists have strived for for centuries.

The show’s curator, Mr Joachim Pissarro, says Shine “is also about philosophically viewing the world as Apollo or maybe even Silenus or Dionysius would.” How does Koons think the Greek gods would see things if they were knocking around today?

“It would be looking at the world for the pleasure of the moment and to embrace light,” he says. “The removal of fear. People live in constant fear. It’s so slow for biology to change and I think our world has changed much more quickly than our bodies have been able to adapt to fear and anxiety. If we can remove that fear and anxiety, we can be much more open to our potential life experience. We like to believe that we’re open. The average art viewer believes that they’re open, but generally we’re quite closed and we’re not really open to experience. Apollo would be blazing in the pleasures. So would Dionysus. And Aphrodite.”