If the pensioner walking his dog stops to chat but can't recall your name - or that of his pet - it is hardly earth-shattering.

We all assume this is what happens when age creeps up on us, no matter that once we could rattle off the periodic table or the premier league results. Both parties usually shrug off the incident with a laugh, a rueful smile, the knowledge that whatever point of mental erosion the older of us has reached, we are eventually headed there also.

Not that it's always a sign of advancing years. I know a youthful professor who turned to introduce his fiancee to a friend, and couldn't remember her name. When I was a child, my mother used to call me in from the garden by my brother's name then my sister's - sometimes even the cat's - before reaching mine. It was as if she was taking the class attendance register.

Such lapses are the currency of ordinary life, whatever our age, though as anyone who's seen 50 wooshing past can confirm, the coins start to slip faster through the fingers after this. Some days you feel you're catching the payout from a fruit machine. And yet, when it was reported that Jack Nicholson might be retiring because he can no longer remember his lines, it was a brutal awakening to the fact that he is every bit as human and fallible as the rest of us.

Although there has been no official confirmation, Nicholson has apparently turned down the lead role in a major film because of "memory issues". But is this really so surprising? Only last month, Michael Gambon confessed he was twice rushed to hospital after a memory blank while rehearsing at the National Theatre. Not being able to recall his lines, he said, was the culprit: "I think I got so frightened that I collapsed."

Countless others in the arts have withdrawn from theatre or film or live performances for similar age-related reasons. Country singer Glen Campbell told fans a couple of years ago he had Alzheimer's. A recovered alcoholic, he was packing it in because he did not want to appear confused on stage and have his audience think he was drinking again. Maggie Smith said she could not face theatre work after debilitating cancer treatment, and pianist Alfred Brendel retired because of arthritis, the scourge of the aged, yet a curse one always assumed could not afflict such maestros. Meanwhile, Sean Connery's denial last week of having Alzheimer's does not change the fact that he is a much diminished figure, a far cry from the debonair hero of his pomp.

Such cases are distressing, but at the same time so commonplace for everyone else, we ought surely to be able to take them in our stride. Why then, do we think some people are invincible, that in their mid-seventies those like Nicholson ought still to be in peak condition, when we'd never expect that of a painter and decorator, or advocate, and most certainly not ourselves?

The answer, I suspect, has less to do with compassion for the frailties of those who, like Icarus, have fallen from a great height, and more to do with our darkest private fears. Nicholson and his ilk are talismans for those, like me, who have grown up in their shadow.

They represent youth and vigour, glamour and charm, and not just theirs, but ours too when we were in our prime. When they quit the stage, literally or metaphorically, it becomes clear we're uncomfortably close behind, every day bringing us nearer to the lip of the infinity pool of life, whose edge we'll all slither over one day.

Our greatest anxiety, it seems to me, is not death itself, but the loss of dignity as we approach it. In an era that puts so much emphasis on the individual, failing memory is a deleting of the self that is not only inconceivable but an affront. When performers whose livelihood depended on their memory are forced to step down, it is a stark reminder that even those with the sharpest powers of recall are not immune from the ravages of time. And since deep down each of us feels as if we'll live for ever, whenever the gods of screen and stage stumble, that childlike belief takes a bad knock.