I SHOOK the hand of my old teacher on Saturday and I queued to do it because his name is Seamus Heaney.

Usually, I make an awkward fan. My habit is to side-step my heroes but my memories of him were so fond, I couldn't resist.

He was still on stage at the conclusion of an event at the Edinburgh Book Festival as a large part of his admiring audience rushed to the signing tent to secure a place in the queue.

Other well-wishers were grabbing the moment to talk to him. So I too held my hand out and when he shook it I said: "You were my tutor." He cupped his other hand over mine. "Tell me," he said with all the warmth and twinkling amusement I remembered.

"Tell me." How often must he say it?

It's a gentle way to say, "I don't know you. I don't remember you." There's no pretence in it, but with the cupping of the hand and that smile there's human warmth and an invitation to talk. "Tell me."

So I did. I was one of six lumpen students who used to go to his office in the English Department of Queen's University, Belfast, for weekly tutorials.

I recalled our first encounter, how he'd regarded us with a blank expression as we filed into his presence, how he'd walked over to a window, pushed it open half-way, leaned out and shouted to another tutor: "Hey, Basil, what's on the syllabus?"

As I told him of the incident his hands left mine and went to cover his face in mock despair at his past catching up with him. I moved on to let others take my place, but it occurred to me what an unusual and remarkable type of celebrity his is.

In the decades since I was his unremembered student, he has become a figure of international renown. He is Ireland's first Nobel laureate since WB Yeats, and one of the English-speaking world's best-loved poets. Yet fame doesn't appear to have changed or spoiled him. His audience in Edinburgh last weekend met the same down-to-earth, charming, self-effacing and humble man who taught me all those years ago.

In his case, it occurred to me as I walked home, celebrity is admirable, a reward for dedication and a determination to excel. Like all those Olympians who won gold in London, it is the result of struggling for hours, days, months and years without applause or fame. And it made me hope that along with Mo, Jess, Chris and all the others who have now become household names, celebrity culture in Britain might be changing.

Are we finally learning to revere excellence rather than tinny fame for fame's sake?

It seems to me that acknowledging who and what you are is an essential component of this type of celebrity. During the evening, Seamus Heaney recited his poem, Digging. In part it's a tribute to his grandfather's skill as a turf cutter. "My grandfather could dig more turf in a day/ Than any other man on Toner's bog-

"Nicking and slicing neatly, heaving sods/Over his shoulder, digging down and down/For the good turf. Digging."

Then, in an aside he told the audience how a neighbour who read the poem said: "Oul' Heaney never worked that hard."

He also told of being called out of class when doing teacher training because there was a phone call for him "from London"'. It was the editor of the New Statesman accepting two poems, a breakthrough for him.

That's where it all began. And what was so reassuring was that he still owned that moment; is still in part that young aspirational man, not some grand personage convinced of his own exceptionality.

After a stroke in 2006 he realised he hadn't stopped working for decades. He told the journalist Robert McCrum: "I looked at the calendar and thought: 'My God you've never stopped, Seamus.'"

When you listen to such a gifted man and when you think of the Olympians we have just enjoyed, you might wonder why school teachers are anxious about the detrimental effect of celebrity culture on school children.

They fear that worthwhile aspiration is shrivelling in the face of it. But although it travels by the same name, the celebrity associated with today's popular culture is the antithesis of true achievement.

The children of Raploch in Stirling may aspire to be the next Nicola Benedetti because they have been fortunate enough to have her as a mentor. For so many others being famous is an end in itself.

When questioned a few years ago more than a third said they wanted to be like Paris Hilton – a young woman who is famous for being famous. Other young women want to marry a footballer and spend the rest of their lives shopping.

People say this epidemic of empty-headedness springs from reality shows like the X Factor which has recently returned to our screens for a new season. Instant celebrity will remain a draw and a dream for the lazy and the untalented just as the lottery exerts an illogical pull for those of us who want to get rich quick. Fame, fortune, celebrity – we meld them in our heads as an amorphous Utopian state into which we aspire to parachute. Reality is simpler. The route to the fame and fortune that is admirable is a dogged uphill climb. It involves honing our natural talent all day, every day.

It is said to take 10,000 hours to forge a genius. Nicola Benedetti has been playing the violin between four and six hours a day since she was six years old. Laid-back Usain Bolt trains longer and harder than his contemporaries. Mo Farah, when interviewed after winning gold in the 5000 metres said: "It's about hard work. Work hard and you will succeed."

Work hard and you will also stay real, stay in touch with the truths that are essential to greatness – as Seamus Heaney demonstrates in spades.