"I would go into a room to get something, and by the time I got there I'd forget what I was looking for," said Alex Pang, a Stanford University technologist who'd barely turned 40 when he began to feel that life online was melting his brain. "For someone who had got through life on raw brainpower, this was unsustainable, and a little terrifying."

Carr, like any number of technology sceptics, would probably have advised Pang to take a break: disconnect from the internet and head for the mountains; declare a gadget-free "digital sabbath" one day a week; get rid of his smartphone or never check e-mail at night. But Pang is a techno-enthusiast, to put it mildly, so his instinctive first thought was the opposite. What if there were a way to use the internet - and all our web-connected phones and tablets and laptops and games consoles - to foster rather than erode our attention spans, and to replace that sense of edgy distractedness with calm.

This is the question motivating the embryonic movement known variously as "calming technology", "the slow web", "conscious computing" or - Pang's preferred term - "contemplative computing".

Its members hope that we might be able to perform a sneaky bit of jiu-jitsu on the devices that dominate our lives: to turn the agents of distraction into agents of serenity. Their inventions so far include wearable sensors that deliver rewards ("calm points") for breathing well while you work, developed by Stanford University's calming technology laboratory; iPad apps to help you meditate yourself into a state of super-focused concentration; software that lets friends decide collectively to disable their smartphones for the duration of a restaurant meal; and scores of pieces of "zenware" designed to block distractions, with names such as Isolator and StayFocused and Shroud and Turn Off The Lights.

I wrote most of this article using OmmWriter, which filled my screen with a wintry backdrop of bare trees and my headphones with the hypnotic clanking of old railway engines. I also used f.lux, which changed the glare of my screen to yellowy evening light, precisely timed to synchronise with the sunset going on outside.

Such are the annoying ironies of work and play in the 21st century. More and more of us are "knowledge workers", doing jobs that require deep concentration, yet we do so on machines that seem deliberately designed to interrupt us all the time and to keep us on edge. Then, in the evenings, we try to relax using similar machines, which all too often whip us up into a state that isn't relaxing at all.

The dirty secret of the internet is that all this distraction and interruption is immensely profitable. Web companies like to boast about "creating compelling content", or offering services that let you "stay up to date with what your friends are doing", "share the things you love with the world" and so on. But the real way to build a successful online business is to be better than your rivals at undermining people's control of their own attention. Partly, this is a result of how online advertising has traditionally worked: advertisers pay for clicks, and a click is a click, however it's obtained.

But let's be honest: this war for your attention isn't confined only to Facebook or Twitter or Pinterest, or to the purveyors of celebrity gossip or porn.

"We're living in a moment when even institutions that used to be in the business of promoting reflection and deep thinking are busy tearing up the foundations that made these things possible, in favour of getting more traffic," says Pang, whose book on "contemplative computing", , will be published in August. "Even universities and churches end up doing this when they go online, never mind newspapers and magazines."

To explain what makes the web so addictive, the advocates of conscious computing usually end up returning to the psychologist B. F. Skinner, who conducted famous experiments on pigeons and rats at Harvard University in the 1930s.

Trapped inside "Skinner boxes", equipped with a lever and a tray, the animals soon learned that pushing or pecking at the lever caused a pellet of food to appear on the tray. After that, they'd start compulsively pecking or pushing for more. But Skinner discovered that the most powerful way to reinforce the push-or-peck habit was to use "variable schedules of reward" - in other words, to deliver a pellet not every time the lever was pushed, but only sometimes, and unpredictably.

There's a slightly depressing view of the web in which we're essentially just "Skinner pigeons", compulsively clicking in hopes of a squirt of dopamine, the so-called "feel good" hormone in the brain. Once you've learned about Skinner, it's impossible not to see variable schedules of reward everywhere you look online.

It's this vicious Skinnerian cycle that conscious computing seeks to break. That's why one of the simplest pieces of advice - to check your e-mail at fixed points during the day - works so well. If you're checking only occasionally, you're virtually guaranteed the "reward" of new messages, so the lure of the variable reward dies away, and with it the constant urge to check.

We can all agree that Facebook and smartphones aren't the first ever examples of "cognitive entanglement", Pang's term for the way we use technology as extensions of our own minds. Writing things in a notebook is entanglement; so is using a library or a landline or sending a postcard or a smoke signal. "Entanglement is nothing new or revolutionary," Pang writes. "It's what makes us human."