UnMind 91. Geodesics & Zen — Atlanta Soto Zen Center

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Falling through a curve —
Sum total of all forces…
Zen’s “total function”!

In this segment we will return our attention back to the more personal sphere of meditation practice. Beyond any consideration of what unlikely intersections we may find between Design thinking and the complex ethical and political issues of our times — other than personal solutions that may help mitigate the worst consequences of the seemingly incompetent or malicious intentions on the part of the powers that be — the deeper implications of some of the most advanced Design thinking and their association with Zen may not be readily apparent. One such example would be the Geodesic geometry of R. Buckminster Fuller, one of my many mentors. In case you are unfamiliar with it, a bit of background.

Bucky and his students started out exploring what would become a new branch of geometry by modeling what he called the “closest-packing” of spheres, in the form of ping pong balls or cast acrylic spheres, stacking and gluing them in various configurations. Spheres are the closest approximation to a point in space, having the same radius in all directions, and stand as reasonable analogies to atoms in a molecular structure, or molecules in the structure of the periodic table of elements, as the familiar stick-and-ball models representing the geometry or shape of microscopic components, such as DNA.

To illustrate the two simplest versions, imagine holding three balls in the palm of one hand, where they will nest and form a triangle. Then place a fourth ball on top, and you have a tetrahedron. This is the first and simplest geometrical solid that divides space into inside and outside, the technical engineering definition of a “system” according to Fuller. Theoretically, any system of whatever complexity can be reduced to four major components, or subsystems. If you can define the four major divisions, and describe their six connections — the edges of the tetrahedron — it can be said that you “understand” or comprehend that particular system, or so Bucky asserts.

So the tetrahedron is the shape that represents the first level of closest packing of molecules, or any other singular entities, with a void at the center. The second example starts with a single sphere at the center, packing one layer around it. Surprisingly, the classic solid that results is the rhombi-cube-icosahedron, the unique solid that Bucky referred to as the “vector equilibrium.” Its surface planes consist of alternating triangles and squares, six of the latter and eight of the former. He called it a vector equilibrium because the tensional vectors, representing the outer edges of the surface, are exactly balanced by the compressive vectors, meaning the connections between the outer vertices and the central sphere. Interpreted as vectors, as in a soap bubble, they are in equilibrium, represented by the distance between all points being the same.

I think the connection to Zen practice is pretty obvious, as our seated meditation posture, zazen, is basically a tetrahedron, especially when we brace ourselves by placing our hands on our knees. The arms complete the six edges of the tetrahedron. Similarly, the 12-pointed model of the rhombi-cube-icosahedron is the model for Buddhism’s Twelvefold Chain of Interdependent Origination, with the 13th point being the center. I have used this geometry as semantic models of the main teachings of Buddhism (See Fig. 1). But how does Fuller’s geodesic geometry reflect Design thinking?

Figure 1. The Internet of Buddhadharma — Five Mahayana Teachings

Fuller’s first application of geodesic design thinking was in the form of a map of the earth. The geodesic domes came much later. In this design, the continents are laid out on a triangular grid, called a tessellation, that allows the two-dimensional flat projection to be folded into a three-dimensional solid that represents the globe. (See Fig. 2) The outlines of continents and oceans are projected from the center of the Earth rather than from outside, like the familiar Mercator projection. Compared to that standard, this approach distributes the distortion in the projection evenly to every triangle, rather than exaggerating it depending on how far away the area is from the center. A second advantage is that the flattened map can represent a one-continent map as illustrated, or unfolded a different way, a one-ocean map, with the continents at the edges.

Figure 2. R. Buckminster Fuller’s Dymaxion World Map

The question may arise, what is the design intent underlying this exercise? What would be the point in designing another kind of world map? Bucky was interested in precision in communication. It bothered him that scientists, who know better, would still refer to the sun as “rising” and “setting.” Far from picking nits, for Fuller these lazy tropes continue to reinforce ignorant conceptions of reality. It bothered him that the maps we were using distorted our perception of the interconnectedness of the world. You may argue that looking at a globe provides the same data — that is, accurate distances between points of interest — but this ignores the fact that you can see only one side of the map in 3D representation. It is more difficult to think and conceive in three dimensions, as the increased level of difficulty of three-dimensional chess illustrates. We tend to miss obscure connections, such as that the Japanese might fly over the North Pole to attack Pearl Harbor, the shortest distance from a world-around perspective.

Zen and Design thinking share this premise: that we are limited mainly by self-imposed strictures and ways of thinking, adopted from the cultural memes and worldviews of our community, parents and peers. Breaking out of these constraints is common to the mission of Design as well as that of Zen. The seminal teachings of Buddha himself were basically correctives to the received wisdom of the time. He would welcome these challenges to conventional thinking.

In fact one could argue that the foundational premise of Zen is that there is something missing in our apprehension of reality. Matsuoka Roshi would often say that people go through life with this sense of “something missing.” They don’t know what it is, to belabor the obvious, but they definitely know that it is missing. They come to Zen to find it. This “IT” is the big carrot that Zen and other insight-based endeavors dangle to attract sincere students of the Way. It is the “that” of suchness, in Japanese inmo, the ineffable realization of Buddha’s wisdom, to quote Master Dogen’s definition of the meaning of zazen. The implication is that our present “normal” awareness is limited by dualistic thinking, or in the worst case scenario, limited to dualistic thinking. Only you know for sure.

What is your worldview, exactly and in detail? How can you mount challenges to it? Bucky modified his worldview via the empirical scientific method — studying particular case experiences and deriving general principles therefrom — his definition of the standard operating procedure of human intelligence, itself. We can hopefully achieve higher approximations to reality by relinquishing the choke-hold that dualistic thinking has on our perception. In Zen, the way to that eventuality is zazen. Ride the cushion into that geodesic reality.