Testing a Power Law Model of Knowledge Propagation: Case Study of the Out of Eden Walk Project

摘要

To improve teaching and learning, it is important to understand how knowledge propagates. In general, when a new piece of knowledge is introduced, people start learning about it. Since the potential audience is limited, after some time, the number of new learners starts to decrease. Traditional models of knowledge propagation are based on differential equations; in these models, the number of new learners decreases exponentially with time. Recently, a new power law model for knowledge propagation was proposed. In this model, the number of learners decreases much slower, as a negative power of time. In this paper, we compare the two models on the example of readers' comments on the Out of Eden Walk, a journalistic and educational project in which informative messages ("dispatches") from different parts of the world are regularly posted on the web. Readers who learned the new interesting information from these dispatches are encouraged to post comments. Usually, a certain proportion of readers post comments, so the number of comments posted at different times can be viewed as a measure characterizing the number of new learners. So, we check whether the number of comments is consistent with the power law or with the exponential law. To make a statistically reliable conclusion on which model is more adequate, we need to have a sufficient number of comments. It turns out that for the vast majority of dispatches with sufficiently many comments, the observed decrease is consistent with the power law (and none of them is consistent with the exponential law).