I’d be the first to concede that the image of Archimedes yelling “Eureka” as he ran naked through the streets of Syracuse makes one fine visual for the concept of discovery.

Which is a shame, not only because it most likely didn’t happen–the story first appeared in a book two centuries after the Greek scholar had died–but also because it has long fed the fantasy of discovery as a solitary and sudden experience. Both history and research tell us that it rarely is–most of the time innovation is an iterative process that fits and starts over months, years, decades. And way more often than not, invention is the result of human friction, of people with different backgrounds and skills and ideas bumping into one another, sparking fresh thoughts and collaborative visions.

One of the better examples of this messy, but fruitful dynamic played out after World War II in a nondescript structure at M.I.T known simply as Building 20. In his book, “Where Good Ideas Come From,” published in 2010, Steven Johnson wrote about how, because the building was used to handle overflow from fast-growing science departments, it scrambled together an eclectic mix of nuclear scientists, electrical engineers, computer scientists, acoustical engineers and even linguists.

And that resulted in hallway conversations and random exchanges that made Building 20 one of the more creative places on Earth, a place that incubated an amazing sweep of scientific breakthroughs, from the first computer video game (SpaceWar!) to major advances in both microwaves and high-speed photography to the earliest attempts at computer hacking.

The beauty of congestion

Social scientists will tell you it’s that same swirl of commingled ideas and constant interactions–albeit on a much larger scale–that makes cities founts of creativity. In fact, research published earlier this month by scientists from M.I.T. concluded that productivity and innovation in urban areas grow at roughly the same rate as population, largely because the greater density of people living in a city increases the opportunities for personal interactions and exposure to different ideas.

The research team, led by Wei Pan, analyzed all kinds of factors to tabulate the “social-tie density” of different cities–that’s the average number of people each resident will interact with personally. They looked at everything from the number of call partners with whom a cellphone user will end up sharing a cell tower to the number of people connecting through location-based social networks like Foursquare to the contagion rates of diseases spread only through personal contact. And they found that the higher a city’s social-tie density, the higher its levels of productivity and patents awarded.

Says Pan:

“What really happens when you move to a big city is you get to know a lot of different people, although they are not necessarily your friends. These are the people who bring different ideas, bring different opportunities and meetings with other great people that may help you.”

His model doesn’t hold up, however, for some huge African and Asian cities that have even denser populations than cities in the West. But Pan has an explanation for that. Generally, those cities have terrible transportation systems. If people can’t get around, can’t have those serendipitous interactions, a city’s density has less impact.

It’s all about the friction.

Creative thinking

Here’s other recent research on what makes us more–and less–creative:

They are, however, extremely cranky: Lose the image of the creative genius so inflamed with inspiration that he or she can go days without sleep. Not likely. According to a study at the University of North Carolina at Greensboro, people who don’t get enough sleep tend not to be all that creative.

Lose the image of the creative genius so inflamed with inspiration that he or she can go days without sleep. Not likely. According to a study at the University of North Carolina at Greensboro, people who don’t get enough sleep tend not to be all that creative. Does “Words With Friends” count?: On the other hand, if you are staying up late, it may do you good to read a little fiction. Research done at the University of Toronto determined that people who read fiction were more comfortable with disorder and uncertainty than people who read an essay and that fostered more sophisticated thinking and greater creativity.

On the other hand, if you are staying up late, it may do you good to read a little fiction. Research done at the University of Toronto determined that people who read fiction were more comfortable with disorder and uncertainty than people who read an essay and that fostered more sophisticated thinking and greater creativity. Do not disturb. Daydreamer at work: And it turns out that being bored at work may not be such a bad thing. A team of British scientists found that people who do tasks they find boring tend to daydream more and that can lead to more creative thinking. The question that needs to be answered now, says lead researcher Sandi Mann, is: “Do people who are bored at work become more creative in other areas of their work — or do they go home and write novels?”

And it turns out that being bored at work may not be such a bad thing. A team of British scientists found that people who do tasks they find boring tend to daydream more and that can lead to more creative thinking. The question that needs to be answered now, says lead researcher Sandi Mann, is: “Do people who are bored at work become more creative in other areas of their work — or do they go home and write novels?” Take a hike: It may not come as such a big surprise, but now there’s more evidence that spending time out in nature and getting away from all your digital devices sharpens your creativity. Researchers from the University of Kansas and the University of Utah worked with a group of people going on Outward Bound excursions and found that those who took tests the fourth day into their trips showed considerably more creativity than those who did so before their journeys started.

It may not come as such a big surprise, but now there’s more evidence that spending time out in nature and getting away from all your digital devices sharpens your creativity. Researchers from the University of Kansas and the University of Utah worked with a group of people going on Outward Bound excursions and found that those who took tests the fourth day into their trips showed considerably more creativity than those who did so before their journeys started. They also looked better: Meanwhile, in Germany, researchers concluded that people who were tested in a dimly-lit room exhibited more “freedom from constraints” and performed with more creativity than those who took the same test under bright lights.

Meanwhile, in Germany, researchers concluded that people who were tested in a dimly-lit room exhibited more “freedom from constraints” and performed with more creativity than those who took the same test under bright lights. Pretend to smell the coffee: It was just a matter of time. Near the end of last year a team of researchers from the University of Illinois at Urbana-Champaign published a study reporting that people showed more creativity in an environment of ambient sound–such as a coffee shop–than in a silent room. And now, if you’re too lazy to go out for coffee, you can head right down to a website called Coffitivity and it will play a coffee shop soundtrack for you–minus the mindless cell phone chatter.

Video bonus: When it comes to how good ideas come to pass, writer Steven Johnson is a big believer in what he calls the “slow hunch” theory.

Video bonus bonus: But wait, there’s more. Creativity author and expert Ken Robinson shares on his take on the components of truly creative environments.

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