Invention and innovation are huge enough subjects that you rarely get any sense of their grand organization--instead, you have to settle for telling bits and pieces, like a blind man palpating the proverbial elephant. But occasionally a bird's-eye view arrives thanks to an unexpected source--in this case, Quirky, a site that gives inventors with little more than a sketch on a cocktail napkin a shot at realizing their ideas.
If you don't know Quirky, a bit of explanation first. The company, which is currently the subject of a TV show  on the Sundance Channel, takes submissions from anyone with an invention. These are then voted on by Quirky's thousands of users, and eventually the best ideas go into production. All of which is to say, among the thousands of entries that Quirky receives, you get a little bit of a sense of what people are trying to invent--and by extension, the areas of daily life where people find problems every day:
The top-most chart is sort of a blur of information, so I'm going to focus on the bottom two, which actually tell you some pretty fascinating things. Let's start with the last one. Innovations seem to be centered around electronics, kitchen, and organization. Not terribly surprising in a way, but it tells you that those are the places where people find the most room for improvement in their lives. Put another way, these are the avenues that are already filled with the most tools that we interact with on a daily basis--and we invent by improving what we encounter every day.
With that in mind, let's move onto the map. Obviously, most of the ideas seem to be flowing from the big cities around the country: New York, L.A., San Francisco, Washington, etc. But adding up those figures, over half of Quirky's submissions come from states with mega-cities.* Doing a quick back-of-the-envelope calculation, about half of America's 300 million people live in those same states. In other words, the innovations seem to be flowing at a steady per capita rate; cities are not over-represented.
This is precisely the opposite of what most studies of innovation would tell you: That cities account for the lion's share of inventions  flowing from countries around the world. This is usually attributed to the fact that cities and their greater densities afford amplified possibilities for interaction and idea exchange--which leads to more innovation. (For two brilliant explorations of this idea, listen to this episode  of Radiolab and this article  from the New York Times Magazine.) But what makes a site like Quirky interesting is that everyone gets a shot. Just look at the craziest outlier on the map: Montana, one of the most sparsely populated states in the country, accounts for nearly 7% of all the submissions to Quirky.
Of course, the social scientists who praise cities as innovation engines are almost certainly right, in general: For one, the raw numbers of ideas being submitted is only a vague proxy for innovation activity. (The ideas coming from the hinterlands might simply be worse than the ideas coming from the cities, for example.) And the numbers I've crunched are undoubtedly crude, since they're based on statewide figures.
But there is, nonetheless, anecdotal evidence that the nature of innovation is changing thanks to the Internet. Internet hype-men used to bleat about this idea in 2000, but it's taken 10 years for it to happen, thanks to a uniquely 2011 business model such as Quirky's.
*NY, CA, IL, TX, PA, AZ, TX, GA, VA, MA