I popped into a pub in Avebury last week while filming a documentary about the famous Avebury rings, the extraordinary complex of standing stones that looms up all around you in this strange Wiltshire village. Because of the unimaginable effort that must have gone into erecting this mysterious prehistoric temple, Avebury is a good place to re-examine your cultural values, to see things from a global perspective. In particular, it’s an excellent place to think about Islamic art.

The pub was one of those traditional-looking ones, packed with horse brasses and serving pub grub. In the middle of every table was a yellow flower in a vase. Only when I sat down and rubbed a leaf did I confirm that the flowers were fake. Every table in the pub had exactly the same synthetic tulip on it. Here we were, in a picturesque village packed with English flowers, roses and dahlias in every direction, yet this seemingly traditional village pub couldn’t even be bothered to get us some real ones.

My thoughts turned immediately to the magnificent collection of Islamic art I had just seen back in London, at the Ismaili Centre, opposite the V&A. There are manuscripts in this show that took 20 years to paint. There are pieces of jewellery of such impossible intricacy that you cannot believe a human hand could ever have made itself small enough to fashion them. In some of the Korans, a single letter took a team of scribes a month to lay down. It was all done for the love of God. And how thoroughly it shamed the plastic flower on my pub table in Avebury. What kind of a culture have we become that we cannot even be bothered to pop into the garden once a week to find a real flower?

I’m an atheist, so there is much about Islam that I don’t approve of. I question the mind-set of all religions. But one thing that always delights me about this noticeably fierce faith, and leads me always to thank God for it, even though I know there is no God, is the effort that went into the creation of Islamic art. If it took a lifetime, it took a lifetime. If you grew old making it, you grew old making it. It’s the acceptable product of blind faith: without our imaginary gods, we humans could never have become the artists we were.

Yet the colossal effort that went into producing the finest Islamic wares seems never to result in art that feels laborious or heavy or sweaty. On the contrary. The huge team of painters, calligraphers and illuminators who beavered away for 20 years on the greatest Persian manuscript in existence, the extra-special Shahnama, made in the 1530s for Shah Tahmasp, emerged with something as delightful and buoyant as a butterfly flitting through an Avebury garden. The single page from this masterwork on display here, showing musicians performing at a gift-giving ceremony, is such a happy creation. The patterns shimmer busily. The colours swirl like music itself. And the crowded scene conveys such a vivid impression of lots of pleasures being shared by lots of people. If you want to know why life is worth living, stare at the great Shahnama.

Called Spirit & Life, the show features work from the private collection of the Aga Khan. Those who know the Aga Khan only from his colourful appearances in the gossip columns of Private Eye, or the frequent namechecks his horses get in the Saturday-afternoon racing, may be surprised by the thoughtfulness of his Islamic holdings. Islam can, of course, do gaudy as spectacularly as any Russian jeweller at the tsarist court. If you’ve been in the Topkapi Palace, in Istanbul, you will know how big the rubies and emeralds can grow when Islamic art decides to be showy. But the Aga Khan’s collection isn’t like that.

His fine selection of objects from all corners and all epochs of the Islamic world – precious books, painted miniatures, glass, metalwork, jewels, plates, vases; by Fatimids, Safavids, Mughals, Ottomans and Qajars – manages somehow to convey an impression of modesty and restraint. For instance, there’s a page in the show from one of the most celebrated of all early Korans, the Blue Koran, made in North Africa in the 10th century, and written in gold on blue parchment. First the koranic verses were traced on the blue background with animal glue. Then the powdered gold was painstakingly added.

Enjoying Islamic calligraphy is generally a difficult task for us western art critics. With the best will in the world, staring at page after page of swirling arabesques whose language you do not understand and whose sentiments are beyond your religious scope is a demanding cultural experience. But not with the Blue Koran. This is a piece of calligraphy with the mood of a celestial map. Besides, the discovery that blue and gold go together magically well is not unique to Islam. Van Gogh’s Starry Night comes in these colours precisely because they are immediately reminiscent of the sky and the stars. The ceiling of the Sistine Chapel, before Michelangelo repainted it, was blue speckled with gold. Henry VIII had his walls at the Palace of Whitehall decorated in the same combination. The difference between all these and the Blue Koran is that they are easy to date, while this startling piece of 10th-century Islamic minimalism might have been finished yesterday.

Everywhere in this show, there is unimpeachable historical proof of the fact that Islam’s original ambitions were completely different from the dark and dour thinking that motivates the modern Islamist. The beliefs that drive today’s petrol bombers and honour killers are a grotesque mutation of what is an uplifting and happy faith. The evidence is all around you here.

From 10th-century Egypt, there’s a rock-crystal dish cut from a single block of quartz with unimaginable precision and nerve. From India, in 1700, there’s a perfectly delightful scene of redheaded cranes dipping in a river. In Kashan, in modern Iran, 1,000 years ago, someone painted a seated ruler beaming at you with tangible niceness from the centre of an amber-coloured lustre dish. And, though I have seen some beautiful Iznik bowls in my time – let’s face it, they’re all gorgeous – I may not have seen one that combines tulips and hyacinths and carnations quite as intoxicatingly as the one placed here in the Ottoman section.

The show has a decent go at organising its material into dynasties and themes. Images of Paradise take up one display case, Love and Literature another. The Fatimids have a section. The Safavids have a section. But I’m afraid I kept being successfully tempted by something in the corner of my eye, and scuttling off the prescribed track. No matter. Another of the defining characteristics of Islamic art is the way it resists easy groupings and seems to come at you from all angles at once.

I’ve walked past the Ismaili Centre countless times on my way to and from the V&A, and never before ventured inside – partly because it is such an ugly building, but chiefly because I didn’t have much of a clue about who or what the Ismailis actually were. I now know that they are a branch of Shi’ite Muslims, and that their leader, the Aga Khan, is the 49th imam, descended directly from the prophet’s daughter, Fatima. I don’t know for sure that the 49th imam set out deliberately to challenge the prevailing attitudes to Islam with his exhibition. But I suspect he did. He certainly knows that art doesn’t lie.

Spirit & Life: Masterpieces of Islamic Art from the Aga Khan Museum Collection, at the Ismaili Centre, SW7, until August 31

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