Pope Benedict is calling it a day at 85, but he is only one of millions who work beyond the retirement age. Now we're living longer, shouldn't we think differently about work?

At 85, the pope has reached the conclusion that he no longer has the strength of body or mind to continue. His predicament is not unusual: we live in a time when we are less likely than ever before to be felled by a random infection, when even serious illness can be treated. Elderly minds falter, strength fades. But the body refuses to give out.

It is a grim prospect – hanging on, contemplating loss of power and self – so it is not altogether surprising that old age has come to be feared or is viewed with a mixture of patronising "compassion" and loathing. The ageing population is talked about in doomy tones with the emphasis on expense, infirmity, "burden".

What is actually going on is rather more interesting. Half the people who have ever lived to the age of 65 in the world are alive today. That is a phenomenal shift in human society. And, by and large, they are fitter and healthier than old people have ever been before.

Alex Ferguson is dominating the Premier League at the age of 71. Warren Buffett is outsmarting the stock markets, wisecracking as he goes, at 82. Mary Berry is enthusing the nation's bakers and despatching our soggy bottoms at 77; and 81-year-old Rupert Murdoch's tweets are obsessively parsed for clues to his corporate strategy. The Queen topped the Woman's Hour Power List at 86.

Many of us are going to have to emulate them. Pensions were dreamed up for a time when people lived a handful of years after retirement. The idea that we should now be able to look forward to 30 or 40 "golden years" is absurd. There is only a limited amount of golf anyone can play and walking on a beach with a silver-haired partner looking like something out of an insurance advert isn't really a life plan.

Extended retirement isn't affordable and it isn't terribly good for us. All the research on healthy longer lives shows that the more engaged and involved we feel, the better we age, physically and mentally. Assuming that people will bow out of being useful because they have hit a numerical age – 65 isn't very old these days – is a waste of their capabilities.

Which is not to say that we will necessarily stay in the same jobs. On Sunday night, Ben Affleck accepted his Bafta for what he described as his second act, dedicating it to all the other people who were starting theirs. The second act is a more developed idea in the United States, where a cohort of later-life entrepreneurs, teachers, activists and volunteers seems determined to confound F Scott Fitzgerald's assertion that there aren't any second acts in American lives by proving that there are, in fact, millions.

There is certainly a case for a second act on the grounds of allowing the next wave of managers to take over running the first. Queen Beatrix of the Netherlands retired in January to make way for her son. David Attenborough has said that if he had a torch, he would pass it on to Professor Brian Cox (admittedly, he slightly undermined this by also saying retirement would be "boring"). Still, in a lot of jobs, you tend to get very disgruntled team members if you don't make room.

Some work is also undeniably better suited to young people; we are not about to see a new wave of 50-year-old fighter pilots. Research by Barbara Strauch, detailed in her book The Secret Life of The Grown-Up Brain, shows that young people invariably score better in cognitive tasks requiring speedy reactions. But in tests to do with making connections, assessing the quality of competing arguments and emotional intelligence – the ingredients of what we commonly call wisdom – people go on improving for a long time.

Not everyone wants to stay in the job they have been doing for the past 20 or 30 years anyway (though evidence would seem to suggest that where that job offers lots of autonomy, influence and satisfaction – such as, say, managing Manchester United or being the world's most successful investor or leading television naturalist – people are quite happy to carry on).

The good news for second actors is that entrepreneurs over the age of 50 have a significantly higher success rate than their younger counterparts. Marc Freedman, who founded the Purpose prize for social entrepreneurs over the age of 65 in the US (which gets thousands of entries every year), identifies a growing body of research that points to a different attitude to work among older people.

After around the age of 50, he argues in his latest book, The Big Shift, people start to appreciate that their lives are not infinite. There is a sense of time running out, but also of enough years left still to be useful. It is not uncommon for older people to wish to leave a legacy that is not merely financial, but social, and which focuses particularly on the next generation. This impulse would seem to be borne out by rates of volunteering and the help grandparents give with childcare.

The negative view of longevity, then, as a period of inevitable decline and burden on the family and state, is pretty misleading. Of course it is important to focus on dementia, to look for cures and to be concerned about care. But the loss of self does not come to everyone and, with luck, it comes to most of us late. It is not the only story about getting old.

Increased longevity, if we can avoid plagues of modernity such as obesity and death by horsemeat, offers us a huge opportunity to think differently about the life course. It is crazy, for example, that people have to build their careers at the same time that their children are young; that lifetime prosperity and status hinge so crucially on the effort of a few years. In doing his rather big job through his 70s and 80s, the pope is (though one suspects this is something he generally resists) a trendsetter. Bring on those second acts.

Geraldine Bedell is editor of Gransnet