On the relevance of percolation theory to the acquisition of human skills

Knowledge can be seen as a complex system that does not reveal clearly how it works. However, some mathematical models have proved day after day their relevance to the description of complex phenomena in fields that are apparently unrelated. This is especially the case for Percolation Theory. After a survey of the percolation mechanism, it will be seen that Percolation Theory has proved to be relevant in a number of cases. From problems in physics or chemistry to questions in social sciences, Percolation Theory offers an unified method to approach the problems in a systematic way. Thus, the paper examines the assumption that knowledge defines a network inside the brain, where sites are knowledge bricks that are connected (or not-connected) by p-efficient binds. This allows us to use the Percolation Theory as a model for the way our brain adopts to solve a problem (using implicitly this knowledge). It also gives a good idea of what happens when the human « insight » occurs, from the Archimede’s cry « Eureka » to the “I have understood it” of our students. As a conclusion, we illustrate the contribution of this theory, especially concerning the design of pedagogic scenarios.