Long before he became prime minister, David Cameron heeded a piece of advice he'd been given by Barack Obama.

The world's busiest man told the Tory Party leader that he should always make space for "thinking time" in his daily schedule. As a result, Cameron's secretaries are obliged to punch regular holes in his diary, like a mapmaker adding oases to a desert. Usually these are no more than 20 minutes, part of which might be spent making sardines on toast for lunch. But the principle is important. Whether he's staring at the kitchen wall in No. 10, or alone in his office, Cameron makes sure he is given the mental room to breathe. Not for nothing is he described as chillaxed. Having time to think lowers everyone's blood pressure.

Since the invention of the wheel there have been complaints about the growing clamour of life, as distractions and interruptions have mounted. It is not special pleading or hyperbole, however, to say that there have never been more insistent, intrusive and constant demands on people's attention than today. Mobile phones saw the start of this new era, making it impossible to cut the umbilical cord between husband and wife, boss and employee, or mother and child, and rendering the possibility of being briefly uncontactable and free a thing of the past. When emails started arriving by phone then no matter where you went, be it the bath or the bus or boating on a loch, the world and its voice followed, regardless of weekends, holidays or sick leave.

The advent of social media put us all into even higher gear. First Facebook and then Twitter, Instagram, and their like have made it imperative that several times an hour, from breakfast till bed, we check what everyone else is doing, and let them know what we're up to as well. To be part of this crowd you are expected to have a kneejerk opinion on even the most complex issues. Although most tweets and updates are so banal they make Kim Kardashian look like Rowan Williams, they must be read and responded to, lest anyone think you are slacking, or bored or - worst crime of all - not interested in being part of the scene.

For those of us who can happily spend an hour staring out of a window, coffee cup suspended between lap and lip, such perpetual mental motion is a form of torture. Even so, that someone as focussed and worldly as Cameron can see the wisdom of Obama's advice is unsurprising. Few are more aware than politicians how lack of thought can translate in a matter of seconds into career meltdown. A reckless retort, an ill-judged tweet, a half-baked decision - all can result in mistakes and loss of face, or utter disgrace. And yet the world we have created makes it almost impossible to avoid the pitfalls of unthinking action and words.

I know to my own cost the harm of a too hasty answer to an email, or a curt text message, when hours of reconciliation and guilt could have been avoided by taking a moment to consider a wiser, probably nicer, reply. But lack of time on all fronts - home, at work, in the supermarket - is turning us into a population of the ever-harassed, always feeling we are running late, and never quite up to speed with the latest news or knowledge. The queues in the GP's office cannot be entirely unrelated to the pressure to be always scrolling and always communicating. Hence the growing number of holiday homes advertising no broadband connection, where people can leave their gadgets behind, in order properly to recharge.

The response of some to this modern malaise is to go to the other extreme. Sara Maitland's account of her search for solitude in deepest Galloway, A Book of Silence, is just one example. But few of us could last a week, let alone a lifetime somewhere so remote. A friend of mine regularly spends a week in retreat at Pluscarden Abbey, imbibing the tranquillity. The one occasion I visited, for a couple of nights, I found being alone in a tiny white-washed room, and a cavernous abbey, deeply dispiriting. I thought more clearly and fruitfully on the long train journey home, where the rattle of the refreshments trolley helped rather than hindered my reflections.

Long before Twitter, the Irish poet Derek Mahon wrote wistfully that "Even now there are places where a thought might grow..." His preferred location was a rundown old shed, but not even that is necessary. All it takes is a change of heart: refusing to be enslaved by technology, and giving ourselves permission to go awol now and again, in mind if not in body. Doing so might prove easier than we think.