In St Peter's Square in Rome yesterday, Pope Benedict XVI canonized seven new saints.

To the rousing strains of an organ playing at full throttle, thousands of pilgrims watched as four women and three men were added to the Catholic Church's register of people in whose name miracles have been performed. They included two martyrs, a lay woman and the first Native American saint, Kateri Tekakwitha, a young Mohawk convert from the 17th century who healed the sick in her lifetime and, it is said, many since. The recent miracle that led to her sainthood is the story of a five-year-old American boy who in 2006 lay close to death from a flesh-eating disease. The last rites had been performed when his parents were given a fragment of Tekakwitha's bone to place upon him. Shortly thereafter, the hospital laboratory reported the deadly bacteria had stopped spreading.

Sceptics hearing this account, or watching Sunday's ceremony – the portraits of the saints fluttering on the Vatican's white walls, the solemn procession, the mitres and crosses and the Rubenesque robes – could be forgiven for thinking they had slipped through a wormhole into the middle ages. It would take a flinty heart not to be struck by the conviction of those who believe in the power of divine intervention, batty though it seems.

I was once in St Peter's Square, waiting amid the masses for the pope to appear, like Juliet, from one of his many windows. When empty, St Peter's Square is an eery, barren space where litter drifts and clergy bustle, their cassocks catching their heels. Filled with a crowd, however, it is transformed. Despite my doubts about religion and the dangers of indoctrination, it was hard to resist the buoyant mood of those who had gathered from all corners of Italy to catch a glimpse of the pontiff. Indeed, in the midst of the singing, laughing throng it was almost possible to understand how collective belief can be infectious. Just to be safe I moved quickly on.

One can see how in previous centuries phenomena which today would be easily explained might have been regarded as miraculous. That in an age of the Hadron Collider and the mission to Mars such belief persists, is trickier to fathom. Atheists of the Dawkins variety dismiss such attitudes as proof that religion rots the brain. It takes a wilful suspension of reason, they argue, to think the laws of nature can be over-ridden or suspended for an individual's personal benefit.

No-one can deny that belief in miracles looks like an extreme form of superstition which, if it were found only in those from less developed countries would be viewed as primitive. That Jimmy Savile's mother prayed to a Scottish nun for his recovery when he was a toddler, and her prayer was seemingly answered, will only deepen the mistrust felt by those who scoff at such credulity. There's no denying it's odd, yet how does one explain the intelligent, sophisticated modern millions across many religions whose faith in miracles is adamant? Are the six million who flock to Lourdes each year simpletons? Do those who chuck away their crutches at Santiago de Compostela only to find they have not been cured lose their faith in God, or turn to acupuncture instead?

No doubt some do, but the multitudes who persist in going to such shrines, or in praying for a saint's intercession, suggests that unanswered prayer does not lead to mass renunciation of belief. That itself is a miracle. Meanwhile, the instances of inexplicable cures, or narrow escapes, or confounding of scientific odds continue. Even in these super-rational times, some events can only be labelled miraculous. Whether one thinks they have come about through divine help or through some random quirk of chance or luck is almost irrelevant. Whatever their cause, the possibility of outside intervention clearly remains as necessary today as it ever was, reassuring evidence that there might be something at work in the universe that's beyond our understanding. You can call it whatever you like – God, fate, defying the odds, or a freak of nature. All I know is that at some point everyone needs a miracle, and a world without the hope of unexplained good fortune would be too grim for comfort.