A Simple Model of Knowledge Scaffolding

We introduce a simple model of knowledge scaffolding, simulating the process of building a corpus of knowledge based on logic derivations starting from a set of "axioms". The starting idea around which we developed the model is that each new contribution, still not present in the corpus of knowledge, can be accepted only if it is based on a given number of items already belonging to the corpus. When a new item is acquired by the corpus we impose a limit to the maximum growth of knowledge for every step that we call the "jump" in knowledge. We analyze the growth with time of the corpus and the maximum knowledge and analyzing the results of our simulations we managed to show that they both follow a power law. Another result is that the number of "holes" in the knowledge corpus always remains limited. Using an approach based on a death-birth Markov process we were able to derive some analytical approximation of it.