What was going on in the minds of all those monks on Iona when, more than 1,000 years ago, they created the Book of Kells? Whatever they were fuelled by, they made an artistic masterpiece of medieval Christianity, up there with Durham Cathedral, the Palace of the Popes in Avignon, and the frescoes of Giotto. But it is older than any of these, and far stranger, one of the most ecstatic and psychedelic artworks ever created, an enchanted book that leads you on curling, coiling journeys of endless reverie in which a single letter in a word can become an object of obsession.

Now that waywardness has gone immersive. This already mighty exhibit, in the Old Library of Trinity College Dublin, has been transformed into The Book of Kells Experience, taking you inside its illuminated pages to uncover the manuscript’s history.

The Book of Kells – an illuminated manuscript of the Four Gospels of Matthew, Mark, Luke and John – is unusual not just for its beauty, but for its near-intact survival, despite being created in the ninth century. Generally agreed by scholars to have been painted anonymously by three monks – known as Hands A, B and C – in the Irish monastic community of Iona in today’s Inner Hebridean Isles, it was removed from there to Kells on the Irish mainland to guard it from the Vikings. Much later, in the 17th century, it was moved to Dublin to protect it from Oliver Cromwell’s army, and in 1661 given to Trinity College Library.

There it rests on permanent public view in an atmosphere-controlled display. But there was always a difficulty. Being a book, the manuscript could only be opened one spread at a time. So the expanded visibility provided by The Book of Kells Experience is a welcome way to virtually open those pages that are physically closed.

The Book of Kells belongs in a library in the heart of Dublin for it is surely the foundation of Irish literature. James Joyce thought so anyway. “It is the most purely Irish thing we have,” he said, claiming that the huge illustrated letters helped inspire his own verbal effects in Ulysses and Finnegans Wake. “Indeed, you can compare much of my work to the intricate illuminations.”

That’s because in The Book of Kells, as in Joyce’s writing, the logical meaning of words is replaced by something much harder to rationalise. Joyce’s fantastically complex language intentionally hinders meaning. Similarly, the three monks who created the Book of Kells lost themselves joyously in a work of art that defies function. For it completely fails in any practical purpose of “illustrating” a text. Its visual splendour overwhelms the words.

And these words are holy writ, no less. Yet there are a surprising number of copying errors in the text and it is arranged in a way that’s hard to follow. The creators, it appears, cared much more about visual beauty than the words of the evangelists. They drown the Christian message in heightened, rapturous abstract patterns and wild-eyed portraits.

Perhaps the textual slackness suggests the scribes themselves only partly understood what they were copying. In Umberto Eco’s The Name of the Rose, a fundamentalist attempts to censor and control the artistic excesses and free imaginations of scribes and illuminators in a 14th-century monastery. Six hundred years earlier, there seems to have been a similar battle in the colony of Iona – except imagination won hands down.

There are other outstanding manuscripts from the same era. The Irish style of book illumination influenced Saxon Northumbria, where the Lindisfarne Gospels were created. On the main continent of Europe, the Holy Roman Emperor Charlemagne commissioned an entire library’s worth of illuminated manuscripts including pagan Latin authors. Yet none have quite got the delirious quality of the Book of Kells.

All the monks who worked on it shared a sense of revelation liberated from verbal meaning. Circles and spirals, squares within squares are repeated across pages in intense blues, greens and pinks, spiced, always, with gold. The opening page of the Gospel of St John has them all. There are stars, planets and crosses – if you want to be figurative – revolving inside larger circles, which are inside dark voids full of swirling matter. There are rectangular designs that resemble the floorplan of a palace. There are twisting lattices and tangled braids.

This passion for extrapolating abstract patterns is shared by the Great Mosque of Córdoba in Andalucía, built at almost exactly the same time. Wandering through the Book of Kells is like walking in that Islamic masterpiece’s famous forest of mathematically placed columns.

So the question comes again: what were these monks drunk on? On the title page of the St John Gospel is a portrait of a man holding a huge red glass to his mouth. This is John himself, who is said to have been offered a poisoned goblet of wine but blessed it, extracting the poison, which slithered away as a snake. As he drinks, he stares into the serpent’s eye as if having a vision. This is entirely in keeping with the elaborate patterns of the page, which glory in the intoxicating repetition of swirling images. This is a party in a monk’s head to which we are invited.

The Book of Kells is profoundly religious, yet in a way that’s wildly remote from how we might imagine Christian art. It is a quest for transcendental vision. As the monks worked, they were seeking some hidden elusive beauty in the very fabric of the cosmos. They were on a voyage of discovery. These early Irish monks had a powerful spirit of adventure. Some sailed in currachs, small leather-covered boats, as far as the Faroe Islands and Iceland in search of the perfect place to live as a hermit.

The island of Iona, where the Book of Kells was created, is a much softer, even pastoral place that must have been a comparatively comfortable home by the standards of Irish monks – at least until the Vikings killed 68 monks in a single raid in 806 AD. Yet here the greatest adventure of all took place. It was a journey inward, past giant letters and staring holy faces, to see something beyond the gospels’ words. Beyond any words.

• The Book of Kells Experience is at Trinity College Dublin.