Synergetics

As a practicing builder and architect since at least 1995, I have long been preoccupied with the work of R. Buckminster Fuller. Not just because I think domes are cool. I first encountered domes in 1988 as a high-school student, wandering among the ruins of an abandoned hippy encampment in the Vermont woods. I spent many hours in these handmade domes, replete with stained glass windows, tattered Persian rugs, macrame glass planters, and a deeply sorrowful impression of a happy life that could have been. This led me to the Dome and Shelter books (Lloyd Kahn), and eventually Bucky and Synergetics which I read cover to cover. I was struck then by a kind of displaced nostalgia for what the 1960’s might have been, had we not taken a darker turn, and I’ve been quasi-obsessed with Fuller’s Design Science and the Revolution he claimed was necessary for humanity to track from Oblivion to Utopia.

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Fuller’s claim was that ephemeralization, or dematerialization through better engineering, mathematics and geometry, could result in improvements in resource efficiency to such an extent, that we could collectively provide a more universal standard of living to the global populace. I have tested this in every project over my 30-year career (notably through the concept of Factor10 design principles), and it has born only partly true in my small sphere of influence.

One example of ephemeralization in tech, that Bucky referred to as the shift to ‘wireless’. While this tech convergence has made more powerful tools, it has also resulted in Jevon’s Paradox, where we demand an ever increasing number and diversity of such gadgets and tools, primarily through the disease of planned obsolescence over durable design.

This push for ephemeralization is regularly met with a friction or resistance that I can only call the habits of convention: Traditional notions of what a house or any building should look like. The rigid tools available to designers, rooted in Cartesian geometry do not help at all. These tools are at their very foundation a XYZ or cube-based labelling of space through (0,0,0) coordinate geometry addresses, which is inherently irrational for nearly every polyhedron except the cube.

There is another way: a Tetrahedron shown in ABCD.EARTH’s ABCD coordinate framework (which can also toggle into XYZ for convenience- not necessity), where tetrahedral edge lengths are defined in terms of Quadrance and Spread, rather than Distance and Angle, resolving in rational values rather than the cube’s diagonal expressions of √3 and √2.

This rootedness of XYZ is so deeply prevalent in most of math, physics and basically all of science, that an alternative is scarcely conceivable to any serious practitioner. This is akin to asking the fish “what do you think of all of this water?” The response is nearly similar, “What do you mean, water?” If you have never known anything else, no less practiced any other method, it is difficult to escape, intellectually and physically. We even use the term ‘three dimensions’ as if physical space is defined by three orthogonal axes. Why not four Isogonal axes? (tetrahedral coordinates). By the time you add the signed directions of XYZ±: you actually have six vectors to define all 8-Octants of the space, which maps better to an Octahedron that the cube. The Tetrahedron actually spans all space with just 4-vectors addressed as [0,0,0,0]. This ‘Cartesian Disease’ has created a false (Newtonian) intuition about space itself, one where its infinite extension of a cubic lattice is understood as some kind of absolute truth. Formerly the ancients considered the infinite the antithesis of time, not its extension. Conflating time and space as Minkowski timespace has compounded the problem. Einstein was the first to dismantle this notion, by proving that space is not uniform, that it is shaped by gravity or even vice-versa, and he developed the metric tensor to define vectors in this curved space, (which we use in the ABCD.EARTH software). The shift to ABCD thinking pushes us from considering Universe as an infinite abstraction, back towards an unfathomably massive, but finite, self-regenerative, energetic/informational system.

For a speculative reach into the physics of Synergetics: https://www.researchgate.net/publication/400054293_Extending_the_Janus_Point_from_Temporal_to_Spatial_Geometry_via_Tetrahedral_Quadray_Coordinates

Fuller demanded a wholesale change in thinking, which he rigorously applied to himself and his use of langauge. The problem is, the rest of us have been thinking for thousands of years in the same geometric terms since Euclid (300 BCE) and even before. While there is evidence of a more rational foundation of trigonometry dating back to Babylonian times (the Plimpton 322 tablet is evidence of this, from 1762 BCE), these methods have been lost to the sands of time, until resurrected by Canadian/Australian mathematician NJ Wildberger, professor at the UNSW, Australia. Fuller’s magnum Opus, Synergetics 1 & 2, has never reached mainstream academia, with notable exceptions (ie. https://wyss.harvard.edu/team/executive-team/), not for lack of novelty or rigour, but arguably because of the impenetrable prose Fuller used to formalize his research. In private correspondence with theoretical physicist Julian Barbour, he emphasized that:

“I do find things like the Platonic solids very interesting. This is because I’m getting more and more convinced that science should be about shapes rather than dynamics. In fact one can see from early Greek thinking, starting with the myths associated with the constellations, and then the ideas of Plato and the atomists, who according to Lucretious were trying to explain the shapes of microscopic object and creatures of different genera, that very naturally they were trying to understand the origin of shapes. I think it is just possible that the development of dynamics, which happened at about the same time as Lucretious wrote his book when Hipparchus developed the first dynamical theory, his theory of the motion of the Sun around the ecliptic with the rotation of the Earth defining time, may have marked a wrong turn. I’m currently writing a book which will include discussion of that.”
Julian Barbour: 2026.02.22 in email correspondence

What I have done is apply a consistent mathematical frame to Fuller’s concentric hierarchy of polyhedra, with the whole of Wildberger’s approach to Trigonometry, on a tetrahedral coordinate framework, extending Fuller’s work, (originally developed by Kirby Urner and Tom Ace), and then apply this functionally to a completely new, Rust-based application for Apple Silicon machines, that contains a geometry and math engine based on the entire corpus of Bucky’s En Syn Geom or Synergetic/Energetic Geometry. The results you can see here at https://ABCD.EARTH.

ABCD.EARTH contains a novel rational math and geometry CAD kernel that generates forms and renders right to clip space all in pure ABCD coordinates, and feeds user interaction with the geometry through an inverse of the same projection pipeline, bypassing XYZ coordinates entirely, from CPU to Clip-space (the user’s 2D screen), and proving that Descartes 350-yr old XYZ coordinate address mapping is not a pre-requisite for computational geometry.

My hope is that by developing this software, which I am now actively using for building design, I can finally arrive at the buildings I have always dreamed of, lightweight, natural, resource efficient and inexpensive, with a self-balancing and load distributing structural frame inherent in every instance. I have experimented through decades of prefab design and construction, large span vaulted structures and panelized structures. Now finally I can assemble all of this through software. Panelized, prefabricated, Synergetics-faithful homes with fully-automated fabrication documentation, all on a rational trigonometry foundation. But not only can ABCD.EARTH be used for building design, with rational precision to (in many cases) near infinite arithmetic precision, the tools can be used to design everything from molecules to spacecraft. The promise of Bucky’s work was to make the world work for 100% of Humanity. I wish only to be of service to this aim.