All theoretical and empirical diffusion studies agree that an innovation diffuses along a S-shaped trajectory. Indeed, the S-shaped pattern of diffusion appears to be a basic anthropologic phenomenon.

This observation dates as far back as 1895 when the French sociologist Gabriel Tarde first described the process of social change by an imitative “group-think” mechanism and a S-shaped pattern.1 In 1983 Everett Rogers, developed a more complete four stage model of the innovation decision process consisting of: (1) knowledge, (2) persuasion, (3) decision and implementation, and (4) confirmation.

Consequently, Rogers divided the population of potential adopters according to their adoption date and categorized them in terms of their standard deviation from the mean adoption date. He presented extensive empirical evidence to suggest a symmetric bell shaped curve for the distribution of adopters over time. This curve matches in shape the first derivative of the logistic growth and substitution curve as shown below.

In the graph above I applied the Rogers adopter characterization to the data we have on the adoption of smartphones in the US. The latest data covering September is included.

Continue reading “The diffusion of iPhones as a learning process”

- Tarde was probably influenced by mathematician Pierre François Verhulst who first published the logistic function in 1845 [↩]