(CNN) -- There's a story about a man who spent his hours daydreaming. He may have been at Ford; he may have been at IBM. He was simply a man who spent his time in his office, feet up on the desk, looking at everything and nothing.
One day, an efficiency expert came by. The efficiency expert had been hired to cut costs and improve operations. He saw the man daydreaming, and he thought certainly this was some dead wood to cast on the pile.
The efficiency expert went to the boss -- Henry Ford or Thomas Watson or some other towering magnate of early 20th-century corporate America -- and offered his recommendations. Among them: Fire the daydreaming man.
The boss refused.
"But, sir," the efficiency expert replied, "every time I walk by his office he's staring into space. As far as I can tell, he does no work."
"That man," the boss replied, "once had an idea that saved this company millions of dollars, and he was sitting in just that position when he had that idea."
The story, of course, is probably apocryphal, but the idea behind it is as current as the latest iPhone app.
Which is: If you want to get any creative thinking done, shut off the damned smartphone and detach, reflect and recharge.
"You can't make headway without thinking about a problem for a long time, in collaboration with smart researchers from different fields, as well as reading a lot," says epidemiologist Caroline Buckee, one of CNN's 10 Thinkers for 2013. "But sometimes that hard work reaches fruition or comes together at a random time once you have let thoughts settle down."
We know this -- as surely as that 20th-century magnate knew it -- and yet we regularly ignore the advice. We surf the Web; we scan news on our phones; we keep our minds digitally occupied in a million ways. When we have a few minutes of down time now, we pull out our mobile devices instead of daydreaming.
It's no wonder Nicholas Carr raised so much interest with his 2010 book "The Shallows," which was an expansion of his Atlantic Monthly cover story, "Is Google Making Us Stupid?" Carr's point is that we aren't thinking, we're browsing.
It is hard, some observers admit, to make time for thinking. John Seely Brown, the former head of Xerox's Palo Alto Research Center lab, worries about the generations who have known little but the cyberworld.
"I think kids today are afraid of being bored," he told CNN for a series on creativity. "And that (when you're bored) is when you imagine something."
When it comes to intuition -- which undergirds thinking -- mood makes a difference, too.
In his book, "Thinking, Fast and Slow," Nobel Prize-winning economist Daniel Kahneman mentions an experiment in which subjects were shown three words and were given two seconds to guess if they were linked.
"Putting the participants in a good mood ... more than doubled accuracy," Kahneman writes. Unhappy subjects, on the other hand, made guesses that were no better than random.
This is not to dismiss everything else we use to fill our brains. The Internet is a tool for thinking.
So are meetings, mystery novels, video games and quiz shows, for that matter. And sometimes thinking has to be done on the fly. Impending deadlines, to paraphrase Samuel Johnson's line about the prospects of being hanged, can focus the mind wonderfully.
But perhaps the best tool is time alone, feet up on the desk, staring at the ceiling.
Motorola executive and CNN Thinker Regina Dugan may have put it best.
"I find that the quietest times of my life," she says, "speak the loudest."