Mathematical Modeling for Medial Motion (al-ḥarakat ʾal-tawassuṭiyyah) and Traversal Motion (al-ḥarakat ʾal-qaṭʿiyyah)

One of the debates concerning concepts of “medial motion” and “traversal motion” is the question of which of these two concepts of motion corresponds to motion in the corporeal world. In the present article we intend to employ the language of mathematics to present a model for each of these two concepts to study the above mentioned problem. As a result, medial motion represents a covering function and traversal motion represents a continuous function of motion across distance which, taking into account two different interpretation of the definitions, are either one-to-one or are constant in no sub-interval of the range. It is seen that, medial motion does not preclude sudden changes, and, because of the fact that continuity is absent in medial motion, traversal motion alone guarantees that changes in the moving body will be gradual. Consequently, the concept of motion which corresponds to motion in the external world is traversal motion.