“It is a hypothesis of synergetics that forces in both macrocosmic and microcosmic structures interact in the same way, moving toward the most economic equilibrium patternings. By embracing all the energetic phenomena of total physical experience, synergetics provides for a single coherent system of geometric principles and secures a metaphysical and evolutionary advantage for all experiential accounting and prospecting.”
—R. Buckminster Fuller, Synergetics, 209.00

The Geometry of Thinking

In 1975 and 1979, Richard Buckminster Fuller, then in his eighties, published, in two volumes, a highly anticipated treatise on his geometry which promised to be a fulfillment of his life’s work searching for, in his words, “nature’s coordinate system.” Together, Synergetics 1 and Synergetics 2 total more than 1800 pages of difficult, and often exasperating text. By and large, his critics were unimpressed. Even his fans, whose expectations were as expansive as those of the critics were narrow, were disappointed. Part of the problem was categorization. The critics expected a tightly argued mathematical treatise on geometry. His fans expected everything from a revelation to a practical how-to book on geodesic domes.

Fuller’s geometry is no less than a conceptual rethinking of how we know what we know. It is a thesis on human consciousness. It is a collection of concrete tangible models that inform our intuitions and challenge our certainties. It is more art than science. Its models are metaphors that may be used to draw connections between what is apparent and what is obscure, between what is presently known and what is presently unknown, invisible, or disregarded. Fuller often said that to change people’s minds you need to change their environment. For the poet, the environment is language. For Fuller, it was geometry.

This website is a personal journal meant to document and organize my thoughts on a subject that’s fascinated me since I was an architecture student in the 1970’s. I’ve tried to make it accessible by providing lots of cross-referencing to internal links, but if you’re not already familiar with Fuller’s geometry, the informal structure may appear uninviting, or even daunting. The following may help.

A Roadmap For Your Own Explorations

First, and most importantly, build the physical models. Instructions for most of them can be found on the page, Model Making. Take the time. It’s worth the effort. I’ve also begun uploading many of my Sketchup models to 3D Warehouse. To view and/or download them, go to the 3D Warehouse website at https://3dwarehouse.sketchup.com/, and use the search term “geometryofthinking” to view them all.

Then, by way of introduction, I suggest starting with the article, Operational Geometry, and then reading the articles on the Vector Equilibrium and the “VE”, and Isotropic Vector Matrix. These provide a conceptual framework for those who may be unfamiliar with Fuller’s geometry. It is also essential to appreciate the advantages of Fuller’s 60° coordinate system, and why he insisted that triangles and tetrahedra were superior to squares and cubes as units of measurement. See: Areas and Volumes in Triangles and Tetrahedra; Polyhedra With Whole Number Volumes; General Unit Conversions; Calculating Areas of Regular Polygons; and Calculating Volumes of Regular Polyhedra. Fuller’s subdivision of the Universe into rational, whole-number units proceeded from the tetrahedron and octahedron to his A and B quanta modules. These are, I think, are one of Fuller’s most important contributions to geometry. For an introduction, see: A and B Quanta Modules. Other introductory (and hopefully entertaining) material includes: Geodesics; Jitterbug, and; Tensegrity.

If you have questions, criticisms, clarifications, or suggestions for future articles, please post them to my feedback link on the Contact page.

For those interested in digging into the source material, a link to an HTML version of Synergetics 1 and 2 can be found on the Buckminster Fuller Institute’s website, https://www.bfi.org. The direct link is: http://www.rwgrayprojects.com/synergetics/intro/explicit.html. Downloadable PDF versions of Synergetics occasionally surface on the web, but the links seem to be short-lived.

Here’s a taste of what was promised:

“All of the exact sciences of physics and chemistry have provided for the accounting of the physical behaviors of matter and energy only through separate, unique languages that require awkward translation through the function of the abstract interpreters known as the constants. But synergetics now embraces the comprehensive family of behavioral relationships within one language capable of reconciling all the experimentally disclosed values of the xyz [90° Cartesian coordinates] and cgs [centimeter-gram-second] mensuration systems adopted by science. The adoption of the tetrahedron as mensural unity … and the recognition of the isotropic vector matrix as the rational coordinate model, are all that is needed to reveal the implicit omnirationality of all chemical associating and disassociating. Thus we can provide a single language to recognize and accommodate: Avogadro’s law of gases; Bohr’s fundamental complementarity; Bridgman’s operational procedure; Brouwer’s fixed-point theorem; Gibbs’ phase rule; Field equations; Einstein’s energy equation; Euler’s topology of points, areas, and lines; Kepler’s third law; Newton’s theory of gravity; Pauling’s chemical structuring; Pauli’s exclusion principle; Thermodynamic laws; L.L. Whyte’s point system.”
—R. Buckminster Fuller, Synergetics, 201.22