Why do idea cities grow faster? What is the connection between being a knowledge-based city and economic prosperity?
Well, one way this works is that the dense, knowledge-based city is one that will become a center of communications. London becomes the British communications center, Paris the French, New York the U.S. People naturally gravitate toward communications centers. The print publications are more interesting because they represent a greater variety of views.
But another way is the generation of commercializable ideas from scholarly excellence, a concept actively promoted during the Depression by Karl Compton and Frederick Terman:
Karl Compton was President of MIT and worked with Boston's business and political leaders to figure out how to replace the dying New England textile mills with other activities. He and Ralph Flanders, President of the Federal Reserve Bank of Boston (later President of the Jones & Laughlin Machine Tool Company in Vermont) promoted the idea of the knowledge economy as the future of the Boston area. They decided to to provide risk capital to technologically innovative companies of the type that might be founded by MIT professors, students and graduates. Compton worked with Donald David, Dean of the Harvard Business School, to create American Research and Development as a joint effort to incubate and finance startups. This was a predecessor of the Small Business Investment Company, which was authorized in 1958.
Frederick Terman received his Ph.D. in electrical engineering from MIT and picked up Compton's vision and message. He joined Stanford's electrical engineering department in 1925 and soon headed it. Using the MIT financing philosophy, Stanford encouraged the creation of electronics firms. Two of them - Heintz and Kaufmann (HK), and Federal - started the West Coast electronics industry in the 1930s. Two students named Hewlett and Packard in the late 1930s started their firm based on a resistance-tuned oscillator. 
The key idea behind the knowledge-based community is communication among business, government and the academic sectors. The enemy of communication is rivalry - within or among each of these sectors - which can produce secretiveness out of fear or a preference for the status quo.
 Office of the Comptroller, City of New York, "The NYC Software/IT Industry: How NYC Can Compete More Effectively in Information Technology," April 1999, 60-61 (Compton), 68-69 (Terman).