On Models for Transdisciplinarity

The transdisciplinarity ([1,2]) is a new approach about disciplines and what is between disciplines, above them and beyond them. Its purpose is the understanding of the current world. For example, this paper, written at a transdisciplinary level, abides somewhere between epistemology and abstract algebra, with implications in physics, topology, etc. In abstract algebra, two diferent algebraic structures, which are dual concept, were unified at another level by [3]. This was posible by embedding them in the category of the Yang-Baxter structures. (Recasting some objects in another setting, in order solve certain problems is a nonstandard tehnique in mathematics.) The celebrated Yang-Baxter equation traverses statistical mechanics, theoretical physics ([4]), knot theory ([5]), quantum qroups ([6]), etc. Similarly, one can view the transdisciplinarity as a unification for interdisciplinarity and pluridisciplinarity. Our analogy is based on the observation that interdisciplinarity appears at the border of two different disciplines, while in pluridisciplinarity we deal with several disciplines serving a certain discipline. Consequently, the current paper attemps to clarify the transdisciplinary terminology for the interested mathematicians, gives an informal introduction to the coalgebra theory and proposes the use of mathematical models in the development of the transdisciplinary thinking. The organization of the paper is the following. In section 2 we detail our algebraic model for transdisciplinarity. The third section contains algebraic details about duality extensions and explanations.