Last Wednesday, I mentioned that the Orkney Islands were a hot spot of innovation many moons ago. This weekend, the Financial Times picks up on the same story: "But why such a remote spot became Britain's hotbed of cultural innovation 5,000 years ago remains a mystery." On Thursday, Richard Florida pre-emptively solved the mystery:

Large companies, universities, and other anchor institutions help spread the fixed costs of research (think buildings, suppliers, etc.). And by massing large numbers of research and development workers together in large organizations, they give the capacity to capitalize on new inventions. The authors argue that the presence of just one large-scale firm can be a huge advantage in providing the institutional heft behind a fledgling innovative economy.

But these big companies tend to focus on things that relate to their existing products and may overlook inventions in other areas. Regions with large numbers of smaller, more entrepreneurial companies can gain an edge in capitalizing on these innovations that larger companies might pass over. The story of Steve Jobs' trip to Xerox's Palo Alto Research Center — walking away with a whole host of ideas Xerox hadn't brought to market — is perhaps the most legendary example of this.

Take a look at Portland, Oregon, and Rochester, New York, on the [graph above]. Both are at the same place on the horizontal axis, with about 1,000 inventors apiece. But Portland had twice the number of quality-adjusted patents per inventor. One explanation, it turns out, could be the number of smaller tech firms. Though both metros had similar numbers of large labs, Portland registered a whopping five times as many smaller labs as Rochester. The study concludes that having a diverse firm base — with at least one large lab and many smaller labs — can increase innovation by 17 percent.

Florida ends with a shrug. No one is sure why Portland is more innovative than Rochester given the same number of smartypants. Nonetheless, the two metros provide a nifty natural experiment. The large organization is Big City, ripe with talent density. Collisions abound. The small firm is Peter's Cafe in Horta (Azores) or the Orkney Islands. Migration matters.

If someone asked me to explain the disparity between innovation in Portland and Rochester, I'd begin and end with migration. Portland is a destination for ambition. Rochester is the place the prodigal daughter leaves. The more parochial a place, the more ineffective the talent.

Richard Florida described this geography way back in June. Where are America's brainiest cities? The surprising results:

While we usually think of the knowledge economy as having a strong bi-coastal orientation, most of Lumosity's top 25 brainiest places are in the Midwest.

The table below shows the 20 highest ranked large metros (those with over one million people) on Lumosity's overall cognitive performance index. The table also includes their overall rank among all CBSAs on this measure. Milwaukee is the highest-ranked large metro. Minneapolis-St. Paul is second, Boston third, Pittsburgh fourth, and Indianapolis fifth. Kansas City, Rochester, Seattle, Cincinnati, and Austin round out the top 10 among large metros. San Francisco is 11th, San Jose (the Silicon Valley) 13th, and D.C. 14th among large metros.

Emphasis added. Milwaukee is the brainiest. Milwaukee isn't the most innovative. Interestingly, according to a report Richard Florida references, Milwaukee is among the most dense:

The population-weighted density approach reveals that the areas with people living at the highest density levels—metro areas with 5,000 or more people per square mile—were clustered mainly in California and along the corridor stretching from Boston to Washington. Other very dense metro areas included Chicago, Honolulu, Laredo, Las Vegas, Miami, Milwaukee, and San Juan. Low-density metro areas, on the other hand—those with fewer than 1,000 people per square mile— were generally clustered in the South.

Slice it any way you like. Density does a poor job of explaining innovation. Don't take my word for it. Listen to Mr. Creative Class.

Photo Credit: Urban Density and Innovation/shutterstock