Though we have to wonder whether it's density or the presence of world-class research universities that have the bigger impact (or is that a chicken-egg question?), Richard Florida presents some interesting ideas about urban density and the creation of patents.
"It's not surprising that San Jose (Silicon Valley) tops the list with .831 patents per square kilometer or that nearby San Francisco is second with .446 patents per square kilometer. Los Angeles is third with .41 patents per square kilometer, followed by Trenton, Bridgeport-Stamford, Connecticut, Greater Boston, Boulder, Greater New York, Ann Arbor, and New Haven.
The density of patents is closely associated with key regional economic outcomes such as regional wages (.668), regional incomes (.588), and regional economic output (.459). (As usual, I point out that these correlations only suggestion associations between variables. They do not specify any causation or make any claims about the direction of causality. Other intervening variables may come into play)."
Read the rest here