It has been one month since I learnt a wonderful new word that came my way thanks to swimmers Joseph Schooling and Michael Phelps and the history they made in the Olympic pool in Rio.

That word is generativity, a golden word that ties different generations together, deepens understanding of how people grow to selflessness and inspires hope that society improves with age.

On Aug 13, the day Schooling beat Phelps in the 100m butterfly to win Singapore's first Olympic gold, I shared on Facebook an article from The Guardian in which journalist Andy Bull observed that Phelps, the most bemedalled athlete in Olympic history with 23 golds, three silvers and two bronzes, had "found a satisfaction in defeat that seemed almost to matter more to him than another gold medal".

Let me quote a few more lines: "I'm not happy, obviously, nobody likes to lose," Phelps said. "But I'm proud of Joe." He was in a reflective mood. "I wanted to change the sport of swimming," he said. "With the people we have in the sport now I think you are seeing it."

He explained he wanted to teach kids "to believe in themselves, to not be afraid, to know that the sky is the limit". And that's exactly what he has done.

"Just being beside him," Schooling said, "walking alongside him and celebrating, I will cherish that for the rest of my life."

An American friend re-shared the article, prefacing it with this post: "One of the joys of maturity is the joy of generativity, the joy of seeing others come to greatness around you. Phelps understands that."

This is the joy of parents, grandparents and teachers as they see those they have nurtured grow up and take flight, the joy of an older generation of Olympians on seeing worthy successors break their records and take their spot at the top of the podium. But what is generativity exactly? And how does it inspire even in one so keenly competitive as Phelps a generosity in defeat marvellous to behold?

In the work of psychologist Erik Erikson, generativity is a stage that persons go through in mature adulthood, from age 35 onwards. Erikson, perhaps better known for his work on "identity crisis", constructed a theory of psychosocial development with eight distinct stages. Generativity emerges in the seventh stage.

Generative adults "seek to pass on the most valued traditions of a culture, to teach the most valued skills and outlooks, to impart wisdom, to foster the realisation of human potential in future generations", Ed de St Aubin, Dan P. McAdams and Tae-Chang Kim wrote in the introduction to a book they co-edited, entitled The Generative Society: Caring For Future Generations.

In the case of Phelps and Schooling, generativity - the intergenerational transmission of that which is valued - went like a dream. Phelps wanted to imbue in younger swimmers self-confidence and the courage to dream big. Schooling wanted to be like Phelps. After the swim that made him a global sensation for pipping his hero to the wall, Schooling said: "A lot of this is because of Michael. He is the reason I wanted to be a better swimmer."

But younger generations are not always as receptive to their elders, as parents, grandparents and teachers well know. And that can be a tragedy. For in Erikson's theory, adults' failure to pass on what they value to the young can lead to stagnation and feelings of being useless.

In the book, The Generative Society, Erikson's son Kai reflects on the sadness of many of his father's generation who migrated from Europe to America, to unfamiliar surroundings and a life they found bewildering. "The deepest of their sorrows, often, was the realisation that they had so little to pass on to their children," Kai Erikson observed. "The skills they had learnt in the rural countryside and the moralities that had been part of their cultural background offered little guidance to their children as they tried to adjust to a new set of realities."

"No one," the younger Erikson added, "knew less about the intricacies of this new land than parents, and no one was a less adept role model for children seeking new opportunities, moving into new occupations, and learning new ways of behaving."

I wonder if my grandmother had felt this same sadness - not because she was a migrant for she was born in Singapore, but because the country changed so much so fast it might have morphed from familiar to foreign in her lifetime. I wonder too if parents today share this sadness because they find the pace of technological change bewildering, and wonder what help, if any, they can be to their children in a world they struggle to understand and keep up with.

What happens in an ageing society when in place of intergenerational bonds, there are instead yawning generation gaps that leave both young and old feeling alienated and bereft? What, if anything, can help to bridge these gaps?

Beyond family values that emphasise mutual respect and support, one idea worth exploring is intergenerational learning. For all the talk of lifelong learning, classrooms here and around the world remain largely age segregated. But in parts of America and Europe, educators have experimented with intergenerational learning and found the process transformative.

At the North Carolina Centre for Creative Retirement, Dr Ronald J. Manheimer ran intergenerational courses where half the students were undergraduates aged 18 to 21 and half were seniors aged 60 to 75.

One such course, 1946 - The Meaning Of A Year, explored the transition from the Great Depression period through World War II and into the start of the post-war years.

For many of the younger students, the classes were when they held their first sustained serious conversations with an older person, Dr Manheimer wrote. Both groups said the close contact transformed their negative stereotypes of each other, with the young impressed by the seniors' life experiences and passion for learning and the seniors impressed by the undergraduates' intellectual abilities, energy and enthusiasm.

Besides such exposure, a way across the generation gap can also come with time and maturity. "Parents often make sacrifices that their children do not understand until they are older and, perhaps, in similar circumstances," observed Dr Manheimer, adding: "The wisdom of the elderly is sometimes conveyed in enigmatic ways, for example a poem or recipe... that make little sense until we discover an attitude, an outlook on life, that may unlock the mystery as we might discover the cipher that unlocks a coded message."

That was true too of Michael Phelps who had to face down his own demons before he came to care as much for the success of younger swimmers as he did about his own. The joy of generativity is hard won.

We are all on a journey to learn how to care across generations. It's a journey that calls for patience and perseverance. When I feel like giving up, I will call to mind the image of the greatest Olympian of all time embracing a 21-year-old Singaporean at the end of their race in Rio and the peace he exuded in defeat.