Intro – Cities, Elephants and Mice, Power Laws and Power Couples

Here’s the first idea in the book: dense areas of populations – like large cities – generate ideas much more effectively than do smaller cities.. Double the size of a city and you get more than double the number of ideas. The size of the city and rate of innovation is not a linear relationship – it’s a power law relationship.

Apparently, a similar thing happens with animals. Some scientist back in the day measured a bunch of factors having to do with metabolic rates – heart beat rate and how quickly energy was consumed, for example – and found that animal size perfectly predicted these rates. The bigger the animal, the slower the heart rate, for example. This relationship apparently holds true for an astonishing number of animals.

But the scientists found that the relationship was not linear – it was a negative power law. All “power law” really means is that when you change the input, the output is changed much more substantially. With a 2x power law, doubling the input quadruples the output. With a 3x power law, the output is raised to the power of 3.

What the hell does any of this have to do with ideas? Using metrics like “patents per capita,” it turns out that large cities are highly effective at creating a lot of patents, and as you increase population, the number ideas goes up exponentially. Johnson says reason for this is that networks are key to innovation, and the larger the network, the better.

Why? See the next post…