Scaling of Knowledge in Random Conceptual Networks

We use a weighted count of the number of nodes and relations in a conceptual network as a measure for knowledge. We study how a limited knowledge of the prerequisite concepts affects the knowledge of a discipline. We find that the practical knowledge and expert knowledge scale with the knowledge of prerequisite concepts, and increase hyper-exponentially with the knowledge of the discipline specific concepts. We investigate the maximum achievable level of abstraction as a function of the material covered in a text. We discuss possible applications for student assessment.

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