(... continued): Like the light bulb, most world-changing innovations required a low marginal cost to implement, allowing every person in a society to quickly and cheaply reap the benefit of one man's genius. The rate at which an innovation can be spread throughout a civilization is directly dependent on that civilization's interconnectedness, and its functional density. Consider the written word, the cotton gin, mass production, agriculture, the wheel, sidereal navigation… each of these innovations had a low marginal cost of implementation and provided a huge benefit to any people-group that could take advantage of it.
The benefits of a high functional density are twofold: first, the benefits of innovation spread more quickly through a civilization; and second, there is less duplication of effort among geniuses because they are more aware of each other and are better able to collaborate together. The net result of all this is that functional density fuels innovation, and innovation reinvests to yield ever-increasing functional density (through the spoken word, writing, the printing press, the internet, &c).