Abstract:

Only since about three hundred years, with the start of modern science, has the Western unified worldview which governed knowledge transmission and acquisition, polarized into synoptic and reductionist approaches and everything in between. The seven faculties or classical areas of knowledge believed to accommodate all knowledge at that time have been replaced by a multitude of disciplines expanding with knowledge acquired under the science and other modern paradigms.
At present, knowledge is increasingly becoming more complex. In particular, much new knowledge is produced by combining basic known knowledge elements. Examples of complex combined knowledge products are manifold, whether in software, arts, genomics or medical devices. Interdisciplinary (multi- and trans-disciplinary) science is almost by definition dealing with complex knowledge products from different domains whereas the prime knowledge elements are a domain of monodisciplinary science. However, increasingly more so, complex knowledge products are indispensable also for the development of new monodisciplinary knowledge elements.
We provide a mathematical description of the field of knowledge. The results provide the intriguing insight that the ratio of the volume of monodisciplinary (basic) knowledge over the volume of interdisciplinary (multi- and trans-disciplinary) knowledge decreases so much that the relative importance of monodisciplinary knowledge dwindles rapidly. Modified by constraints of complexity and hierarchy the model still stresses a move of major knowledge domains away from classical or basic disciplines.
The number of possible combinations of knowledge elements increases according to:

where β and γ are positive constants and N0 is the initial number of knowledge elements. The constant γ is the number of primary knowledge elements. Hence, the growth of combined knowledge elements is exponentially faster than the number of prime knowledge elements and the ratio of prime to combined knowledge elements has the limit of 0. In other words, combined knowledge elements should totally dominate science in some time.
Most Higher Education Institutions (HEIs) are organized around classical disciplinary departments and faculties of disciplines with similar research paradigms, and their organizational structures strongly favor and promote monodisciplinary knowledge. Although examples of the development of environments for interdisciplinary, multi- and trans-disciplinary research and teaching in HEIs can be found, these movements are not likely to become significant in many higher education environments for some time to come. Our models provide a scientific basis for understanding why HEIs should increasingly consider emphasizing interdisciplinary, multi-and trans-disciplinary research and teaching unless they run the risk of becoming peripheral in the area of knowledge creation and transfer. Indeed, science and knowledge development outside of higher education is flourishing in areas not represented in HEIs, eventually challenging the education and degree granting monopoly HEIs enjoy at present.

Keywords:

knowledge, disciplines, complexity, higher education.