A Simple Model of Knowledge Scaffolding Applied to Wikipedia Growth

We illustrate a simple model of knowledge scaffolding, based on the process of building a corpus of knowledge, each item of which is linked to "previous" ones. The basic idea is that the relationships among the items of corpus can be essentially drawn as an acyclic network, in which topmost contributions are "derived" from items at lower levels. When a new item is added to the corpus, we impose a limit to the maximum unit increase (i.e., "jumps") of knowledge. We analyzed the time growth of the corpus (number of items) and the maximum knowledge, both showing a power law. Another result was that the number of "holes" in the knowledge corpus always remains limited. Our model can be used as a rough approximation to the asymptotic growth of Wikipedia, and indeed, actual data show a certain resemblance with our model. Assuming that the user base is growing, at beginning, in an exponential way, one can also recover the early phases of Wikipedia growth.