I recently attended a talk by the prolific composer Philip Glass, as part of Amsterdam Dance Event. The event was designed as a Q&A session in which audience members - most of them musicians - could ask him about his creative process.
Like the rest of the audience, I had plenty of questions, but my interest turned elsewhere as soon as the man himself appeared on the stage.
It transpires that Glass, who turned 80 earlier this year, is one of those rare octogenarians whose fire and passion continue to burn bright. Sure, his face is etched with the wear and tear of life, but his mind is as sharp as a pin, and his muse is still right by his side.
It didn't take long for me to realise that the composer shares many of the traits of ageless people: he has no intention of retiring (which is probably why he avoided questions that asked him to look at his work retrospectively); he makes it his business to stay connected with younger people; and while many of his contemporaries have decided that there is nothing new under the sun, he continues to be relentlessly, boundlessly curious.
Think of any older person you know who continues to sparkle with a youthful spirit and you'll notice that their curiosity has not been diminished by cynicism or world-weariness.
You'll also notice that they are considerably more flexible in their thinking. Truly curious people aren't afraid to ask questions or change their opinion, hence they are less likely to become stubborn, intolerant or bigoted as they get older.
The famous biochemist Mahlon Hoagland, who died in 2009 at the age of 87, often talked about the link between curiosity and innovation.
"As children we all possess a natural uninhibited curiosity," he said, "a hunger for explanations, which seems to die slowly as we age - suppressed, I suppose, by the need not to appear ignorant."
Thankfully, some people never let go of their child-like curiosity. They continue to search and seek and ask, and it's no coincidence that they tend to age remarkably well.
The rest of us stop growing when we stop asking.
"We are all trapped in our own way of thinking, trapped in our own way of relating to people," writes Brian Grazer, the author of A Curious Mind: The Secret to a Bigger Life. "We get so used to seeing the world our way that we come to think that the world is the way we see it."
Curious people, however, are less inclined to get caught in this trap, largely because their minds are more nimble and their opinions and beliefs less entrenched.
Curiosity, remember, is more than mere inquisitiveness. In its purest form, it is dynamic open-mindedness. That's why curious people don't become set in their ways - they know there is always another way to take.
Studies show that a curious state of mind can help us retain information, develop empathy and establish deeper connections with others: the knock-on effects on longevity and vitality are obvious.
Curiosity can also help to allay the trepidation that tends to creep in with age.
Grazer puts it best: "Curiosity will conquer fear even more than bravery will," he writes. "Indeed, it has led many people into dangers which mere physical courage would shudder away from, for hunger and love and curiosity are the great impelling forces of life."
Of course, cultivating a spirit of curiosity isn't as simple as learning facts and figures. Truly curious people live by the belief that they can learn something from everyone they encounter. Hence they tend to ask more questions than they answer, and make more acquaintances than most.
This interest in others has another considerable benefit: it makes curious people more world-aware than they are self-aware, and more people-centred than self-centred. The knock-on effect here is that they are less inclined to dwell on their problems or become stressed by their circumstances.
Curiosity, in other words, is a gift that keeps on giving, as Ian Leslie explains in Curious: The Desire to Know and Why Your Future Depends On It.
"Whoever you are and whatever start you get in life, knowing stuff makes the world more abundant with possibilities and gleams of light more likely to illuminate the darkness," he writes. "It opens the universe a little."
We all know the first signs of physical ageing: grey hair, wrinkles and whatever you're having yourself. But perhaps it's time we started to think about the first signs of psychological ageing, and the role that dwindling curiosity plays.
Likewise, we can curtail the physical ageing process by making the right choices in regards to diet and fitness, but it's worth thinking about how we can keep our minds nourished and flexible too.
A curious mind continues to grow, even as the body ages, so older people ought to consider their overall outlook as much as they take into account their daily intake of vitamins and minerals.
Curiosity may have killed the cat, but as Arnold Edinborough said, "the cat died nobly" (and it probably lived longer too).