Opening in Conclusion: An Anthropological Approach to Transformation—Shaping Shapes

Abstract

Since D’Arcy Thompson’s pioneering work On Growth and Form published in 1942, continuous efforts have been made in Western academic fields to understand and capture forms and evaluate their similarities and differences, their continuities (invariants) and their discontinuities through time. Mathematics has been used intensively to capture forms such as those of cells, gases and animal or plant shapes. It has also been used by anthropologists to capture what has been interpreted as the forms or structure of languages, myths and symbols. That is, mathematics has supported the attempt to give a form to non-tangible, immaterial human expressions and thoughts. Organizations and companies also feel the need to define their structure or the shape taken by their relationships and interconnections. Here again, mathematics is at work in this attempt to give a form to how they function. This paper focuses mainly on the Western quest for form and structure and gives some examples of the methods used to address this quest. In so doing, it formulates the following interdisciplinary research question: can we think about the transformation of functions which do not have any intrinsic shape? How does the idea of “environmental shape” captures the function of sharing in order to renew our perception of sustainable development?