WH Davies and Leonardo da Vinci would have understood one another. The Welsh poet’s most famous work, Leisure, is an encomium to the art of looking intently: “What is this life if, full of care, / We have no time to stand and stare…. / No time to see, in broad daylight, / Streams full of stars, like skies at night. / No time to turn at Beauty’s glance, / And watch her feet, how they can dance. / No time to wait till her mouth can / Enrich that smile her eyes began.”

Leonardo is one of history’s great starers. He looked and he looked and he looked some more. And he saw. “There are some birds that move their wings more swiftly when they lower them than when they raise them, and this is the case with doves and such birds,” he wrote. “There are others which lower their wings more slowly than they raise them, and this is seen with crows and similar birds … Birds with short tails have very wide wings, which by their width take the place of the tail; and they make considerable use of the helms set on the shoulders when they wish to turn… When birds are descending near the ground and the head is below the tail, they lower the tail, which is spread wide open, and take short strokes with the wings; consequently, the head is raised above the tail, and the speed is checked so that the bird can alight on the ground without a shock.” As Walter Isaacson asks the reader in his masterful new biography of the great Renaissance polymath, “Ever notice all that?”

Leonardo put his staring to good use. It inspired his scientific adventures – his various flying machines were based on his ornithological peering. It also revolutionised the composition of art: his relentless gawking brought us the practice of sfumato (from the Italian for “smoke”), which deploys subtle shading to blur contours and avoids stark lines. His insight was that in real life people do not see hard stops: “When you paint shadows and their edges, which cannot be perceived except indistinctly, do not make them sharp or clearly defined, otherwise your work will have a wooden appearance.”

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It could be argued that, at times, healthy curiosity spilled over into obsession. Leonardo’s attempts to measure and catalogue the proportions of the human body – “when the arm is bent, the fleshy part shrinks to two-thirds of its length;when a heel is raised, the tendon and ankle get closer to each other by a finger’s breadth” – led him to the unlikely conclusion that “when a man sits down, the distance from his seat to the top part of his head will be half of his height plus the thickness and length of the testicles”. Nevertheless, by the time the great master passed in 1519 he had surely noticed and described more of the world around him than any human before or since.

It seems always to become harder to break from the crowd and simply stand and stare. We are even pre-programmed for the rat race: entrainment is a process by which living creatures’ natural rhythms unconsciously adjust to each other, which is why when you walk down the street you find yourself marching in lockstep with everyone else. It’s toughest of all for urbanites – a child brought up in a city will zoom around a supermarket twice as fast as one from a small town, who is more likely to dally and inspect the produce or talk to staff. Experiments have found that today we cover the same stretch of ground 10 per cent more quickly than 25 years ago, and the larger the town or city the faster we move. The number of Europeans finding their work schedule too strenuous rose from 49 per cent in 1990 to 60 per cent by 2000.

The writer Robert Colvile has named this phenomenon “the great acceleration”. We are tied to work through computers and smartphones, trends come and go at exhausting speed, addictions are on the up. “A study of Christmas round-robin letters sent since the Sixties shows not only a remarkable rise in the use of words like ‘hectic’, ‘whirlwind’… or ‘crazy’ to describe people’s lives, but their being deployed in an almost boastful fashion, as a proclamation of worth,’ writes Colvile.

We are sometimes too ready to overlook the tremendous gains this quickening has brought – radical convenience, instant access to information, culture and networks, heightened prosperity, cheaper goods and food. But it is also true that life for many has lost a sense of balance. The deeper part of ourselves, the bit that requires calm, quiet immersion, can be ill-served by the demands of the modern economy. We can forget to look after ourselves until it’s too late and we are suddenly in the grip of depression, stress, relationship breakdown, physical illness and the other spectres that are always keeping pace in the shadows.

I’ve been pondering these matters recently because, for the first time since my teenage years, and after two decades of punishing hours in frenetic workplaces, I have some spare bandwidth in my life. I recently gave up my full-time job and now work from home; I take the kids to school and to evening clubs; I take long weekday walks with the dog in the countryside around Stirling, where I live. I look at the mountains and the heather and the pine trees and the stretches of water. I breathe and think and notice and write. I have rediscovered my sense of wonder (a bit). And if I’ll never quite reach Leonardo’s state of grace – “draw Milan”; “Ask Benedetto Protinari by what means they walk on ice in Flanders”; “get the measurement of the sun promised me by Maestro Giovanni Francese, the Frenchman”; “observe the goose’s foot”; “describe the tongue of a woodpecker – I have at least recovered my ability to stand and stare, and for that I am glad.