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An image of tractography, a technique that tracks the movement of water molecules in the brain to create a 3-D map of its highly complex network of axons. 

Not everything in life can be achieved with hard work. Creative insights have the perverse tendency to come when we’re not working at all. The more we hunker down and focus, the more creative thought flutters out of reach.

This seems to be the case for the various components into which scientists have broken creativity down. One of the most widely studied is a process called divergent thinking — a kind of mental exploration measured by such tasks as inventing new uses for a brick or a paper clip. In a Scientific American article that ran last week, psychologist Holly White argues that people with ADHD are more likely than the rest of us to summon divergent thinking as well as other facets of creative thought.

White identified two other creative processes where people with ADHD may have an edge. There’s conceptual expansion, which is tested by, say, asking people to invent a fruit that would exist on another planet. And there’s the ability to overcome prior knowledge — to see ways to do something differently from the way it’s been done before.

And what about those of us who like to be creative but haven’t been diagnosed with an attention problem? MIT professor Alan Lightman tackles this in his new book, “In Praise of Wasting Time.” Lightman is trained as a physicist but became a professor of the humanities.

Divergent thinking happens, he suggests, when our brains are running through many combinations of ideas until a good one emerges. This isn’t something most of us can make our brains do by straining. The only hope, for many of us mere mortals, is to give ourselves time.

Lightman argued that in the U.S. and other fast-paced modern societies, we’re suffering from a time-use crisis. He quoted students who reported that they had no downtime: Every waking hour was crowded with school work, jobs and extracurricular activities that didn’t feel optional. When he was in school, he wrote, he used to have time to watch tadpoles and ponder whether they knew they were going to become frogs. He had time for home chemistry experiments, done just for fun, not an attempt to win any national science fairs.

And in adulthood, people often undergo the stressful experience of being expected to work 40 hours a week, but also expected to spend some of that time producing ideas that can only be conjured up from not working. I experienced this when I worked for the Philadelphia Inquirer. I had proposed writing a weekly science column; instead I was asked to write a sex column.

To do this, I needed a lot divergent thinking and overcoming of prior knowledge. I did manage to come up with something every week for three years, and it worked well enough that readers, including my parents, liked it. It even got picked up in other newspapers. I worked hard at parts of the process, but at other times the only way to move forward was to goof off until my brain produced an idea divergent enough to keep things interesting.

I began to sympathize with the “Mad Men” of the television series popular at the time. Apart from the sexual harassment, heavy drinking and deadly amount of smoking, they had the right idea.

And even as recently as the 1990s, I knew lots of journalism colleagues who got their writing wit and sparkle from a muse who visited them only while they were smoking. Cigarettes, so people said, could summon the muse. Maybe recognizing the need for downtime would take off some of the pressure that drove so many to smoke. Maybe the crucial part of the cigarette break turns out to be the break, not the cigarette.

Lightman concludes that in Western culture, wasting time is considered a sin. But it’s also sometimes considered a sin to waste talent. That means it’s sinful to squelch the talents of people with ADHD because they can’t always conform to demands of school. And it’s sinful to starve other potentially creative people of necessary playtime and downtime. It’s when we look idle that our brains are most likely to perform miracles.

Faye Flam is a columnist with Bloomberg Opinion.