Some Perspectives of Fuller’s Mathematics

An Undergraduate’s Assessment by William R. Morrell, Yale College, Class of 1986

Editors note: In proposing synergetics, Fuller s aim was to derive its generalizations from all of physical and metaphysical experience; thus his concepts invade a variety of academic disciplines as broad as philosophy and physics and psychology and mathematics. Within mathematics, synergetics employs methods analogous to topology, crystallography, and combinatorial geometry. But since the Synergetics books were published as trade books, they were largely ignored by the scholarly journals, and academics in general have felt no obligation to assess Fullers philosophical and geometrical strategies in the context of their own disciplines. William Morrells recent paper is a happy departure from this posture of neglect; it is a sympathetic attempt to relate synergetics to the world of conventional mathematics. That this first venture should come from an undergraduate would have been a particular gratification to Fuller.

Mathematics is a troublesome discipline. It is difficult to define clearly where it fits into society and to understand what role it plays. Buckminster Fuller was displeased with the path humanity had chosen for math and science in general. Since the problems he found in math were not in its conclusionswhich were deductively reasonablebut rather in its philosophical foundations, he tried to reformulate mathematics in a way that was consistent with his physical and metaphysical experience. Synergetics and Synergetics 2 are his attempts to accomplish this task. He found it necessary to define a system of thought and method that would allow the math and geometry to be applicable not only to themselves but also to any field of thought. Math for Fuller is not a self-contained system based on axioms and divorced from reality, but rather the science of generalizations; math is generalized learning; it is the study of patterns in nature and universe, regardless of where they appear.

Accordingly he presented in Synergetics a system of analyzing system interactions; he avoided the "thingness of things" and "things as they are in themselves" and he examined only interactions, for interactions are all we can ever experience. We may never know how and what things really are, but we can speak of how they behave, both in and of themselves, and with respect to the rest of universe.