The principle of causality in Zen is not simply that what goes around comes around. That is, the relationship of cause and effect may not be obvious, especially when we embrace the theory of karmic causality, which is said to transcend life and supercede death. The Buddhist view of rebirth is not the same as reincarnation, which further complicates matters, as it goes to the uncertainty principle as regards the self. Since the imputed or imagined self is called into question in Zen, it follows that “simple” reincarnation, the rebirth of the same person in a different body, is also called into question. The “person” that is born is not the same as the one that dies, but cannot be entirely separated, either. According to the traditional theory, there is a “karmic remainder” that carries over from the consciousness of the prior life to that of the present birth. Added to the causes and conditions operative in our present life, such as our parentage, DNA, country of origin and cultural influences, the big picture is comprised of a complex stew of intricately interconnected causes and effects, in which every cause is also an effect, and all effects are also causes.

So the linear model that we would like to apply to our concept of how this all goes together must be set aside from the beginning, and more complex models imagined, in order to get to a higher approximation of the reality. This suggests that we will never be able to actually “understand” causality, as, like the rainbow, the closer we get to it, the more it moves away from us. However, this should not dissuade us from trying. As a great mentor of mine would often say, “What else are you going to do until the doctor comes?” I never asked him what he meant by that, precisely, but as I have grown older, and hopefully somewhat wiser, I think it is becoming clearer every day.

Another mentor, R. Buckminster Fuller, was a genius at modeling structure, starting from a simple premise that Mother Nature must employ a different geometry than calculating pi times the radiussquared in order to make a single bubble (this epiphany occurred to him while staring at the wake of the ship he captained in the Merchant Marines during the real World War). Building models of closest-packing of molecules, utilizing plastic spheres, he and his students (I was never one, but met the great man on a few occasions, and taught with a close colleague of his) developed a new 3-dimensional geometry, called “geodesic geometry,” which led to the most famous of his vast array of inventions, the geodesic dome. The relevance of all this to the 12-Fold Chain of Causation, otherwise known as Dependent or, more correctly, Interdependent Origination, is that he also investigated the modeling of information, using 3-dimensional constructs to model semantic relationships between words.

As a person who taught himself to draw as a child, and as a professional designer trained in 2-dimensional visual graphics as well as 3-dimensional industrial design, it is natural for me to think in images. I have taken a visual approach in trying to illustrate the relationship between the various parts of the buddhadharma as enumerated in Buddhist literature, for the sake of clarity, and to provide a cogent image as a mnenomic, to help us remember the teachings, as we suspect the enumeration functioned in early India. The simplest model of any system, according to Bucky, is the tetrahedron, which can be represented by three spheres (think marbles or ping pong balls) nesting together (e.g. in your palm), with a fourth one resting on top. This is a stable structure, especially if glued together, or in thrall of the fundamental forces that hold natural elements together:

Expanding the model with connecting rods, as in a stick-and-ball molecular model, reveals that there are six struts connecting the four spheres, each to the other. Bucky made the point that this model of a “system” — defined technically as anything that divides the universe into inside and outside — can be a model of understanding information as well. He pointed out that if we can identify the four fundamental constituent parts of something — say, a business, an atom, or the four fundamental forces themselves — and then describe the six relationships between them, it may be said that we “understand” that system. Thus, this simple, four-pointed model makes a useful analytical tool to simplify and analyze any system.

For now, let’s turn to the more complex 12-fold chain, and see if we can begin to grasp its implications. In the chart below, the Buddhist theory of origins is modeled as a kind of Mobius strip, folding back on itself to have only one surface. Note that its four-part form consists of previous existence; present existence; fruits thereof; and future existence:

This is a good example of the formlessness of form, or the form of formlessness, in that it calls into question the shape of space, so to speak. How can a 3-dimensional form have only one surface? Various expressions in Zen have this same kind of koan-like quality, such as the “mirror of Zen” or “precious mirror Samadhi,” (J. Hokyo Zammai) in which “form and reflection behold each other.” This “through the looking-glass” approach to questioning — not reality, but our concept of it — is intrinsic to Zen, as well as to scientific investigation, and creative thinking. All models are, in this sense, mere approximations — hopefully closer than their predecessors — of the form (or formlessness) of reality, as it really is.

In thinking about this fundamental teaching attributed to Buddha, it occurred to me that he described it as a vision, and that visualizing it might make its dynamic more clear, rather than simply considering it in words. From the perspective of working in media, and designing for communication, words may be considered one-dimensional; images 2-dimensional, and models 3-dimensional. A graphic in which 2D images illustrate 3D connections begins to transcend the limitations of strictly 2-dimensional representation, necessarily engaging our imagination. So we can clearly see, for example, that if we can move one way on the strip, we could possibly move the other way, instead. Which illustrates the Buddhist principle that, in one direction, the 12-Fold Chain can represent the typical sequence of growth from an infant to an adult, and on through the natural cycle of aging, sickness and death, as constituents of “suffering” or change; but going backward, can represent the maturation of practice, the withdrawal from our intoxication with existence that is a central characteristic of Zen meditation.

Another result of visualizing information is that it reveals inconsistencies in the model. For example, I noticed that one of the traditional Five Skandhas — the third, or middle one, of Perception — is not included as such in the traditional 12-Fold Chain, yet the other four are. This did not make sense (a rather amusing expression in this context) to me, but Okumura Roshi kindly explained that Perception is subsumed under one of the other links in the chain, perhaps Contact or Sensation, which one I do not recall. As a creative person, I have the right to be wrong, so I took the liberty of inserting Perception into the chain in its own right, which resulted in the following model, a “13-Fold Chain”:

The coincidence that there are 12 links in the chain, and 12 colors in the classic spectrum, inspired my decision to color-code them in the prior model, but having a thirteenth link threw a wrench into the works. So I simply placed a black link in the middle, with the other 12 radiating out from it, which dictated that the black one had to be Ignorance. So this model suggests that underlying any and all of the links in the chain, considered separately, is a primordial ignorance. At each point, we can return to ignorance, so to say.

Considering where to place the new kid on the block, Perception, in the logical sequencing of the others, I chose to insert it between Sensation and Craving, reasoning that a raw sensation would not likely become a craving, unless some sort of perception were to arise. However, you might argue that a fetus craves nutrition, without having a clear perception of what is causing it; or that the baby of an addicted mother will feel terrible craving with no recognition of where it is coming from. So perhaps Perception (along with its twin, conception) should find its home between Craving and Clinging, as we cannot cling to something we cannot perceive, as such, other than to life itself.

In the following illustration, I connect the 12-Fold Chain to the Four Noble Truths:

I rationalize the connection to the second Noble Truth, usually translated as Craving, in that the Chain represents an expansion of the origin of suffering writ large, or how things got to be the way they are. The Existence of suffering (S. dukkha), on the other hand, states how things are, presented as an uncomfortable truth, take it or leave it. Thus the first Noble Truth is most closely connected to the Five Skandhas, which articulate the main aggregates of experience of sentient life – form; sensation; perception; mental formation or impulse; and consciousness; how things are:

The third Noble Truth of the possibility of Cessation of suffering, via relinquishing craving, is most akin to the other seminal teaching of the Six Paramitas — Generosity, Precepts, Endurance, Patience, Contemplation — which must be perfected in order to see our way through to Wisdom, or the end of suffering:

The fourth Noble Truth, the Path, is expanded into the Eightfold Path, which repeats some of the Paramitas, e.g. Right Concentration, Contemplation, or meditation (S. dhyana), but in a different context, that of perfecting the dynamic of daily life. The color-coding indicates how the individual practices and attitudes, from both the Paramitas and the Path, fit into the simplified tripartite model of Right Conduct (external), Discipline (internal) and Wisdom (transcendental). The overall trajectory of Zen practice witnesses these seemingly disparate activities coming together over time, our view or understanding and thought evolving to approximate that of Buddha, or awakening to reality.

Finally, to examine the 12-Fold Chain for its internal consistency, we separate it from the Four Noble Truths:

In this last iteration of the 13-Fold Chain, once again I place Ignorance at the center, as it is listed as number one in the original teaching; and array the other 12 around it, color-coded to reinforce the traditional number sequence. But this time, they form a layer of 12 spheres around the center sphere. If, in your imagination, you remove all the connecting struts, or build such a model by packing one layer of spheres around a center sphere, you will find that it makes this shape. This results in a Euclidian solid — called a rhombicube icosahedron for the math geeks in the audience. Bucky referred to this as the “vector equilibrium,” if memory serves. This idea is based on regarding the circumferential connecting struts as tensional, the radial struts as compressional, interpreting the system as energy structure. The distance from the center of each sphere on the surface is the same as the distance to the center sphere, thus the tension and compression forces are exactly in equilibrium. It also constitutes an alternative to the Cartesian XYZ system of spatial coordinates, wherein we arrive at irrational distances from point zero to any unit point outward on any axis. In Bucky’s system, the distances are all integral: one unit out from zero is one unit from the neighboring axes. Take my word for it.

For our purposes, this lovely model suggests that the content of the 12-Fold Chain — indicating various dimensions of existence, and our place in it — are all interconnected, and in equilibrium. This is an apt metaphor for Samadhi, I think, usually interpreted as a centered and balanced state, or of form floating, so to say, in emptiness.

This model also visualizes the intricately interrelated nature of all of the links in the chain. Just as the Four Noble Truths as vertices have six connections, three from each to the others, visualized as the edges of the tetrahedron; just so the Eightfold Path exhibits twenty-eight such, each having seven connections to the others, taken not only as the twelve edges of the cube, but also the diagonals on each square facet (12 more), as well as the internal diagonals (4 of which).

In our usage, these are not structural connections, however, but informational: they illuminate meaningful relationships, such as that between Right Speech and Right Action: you talk the talk, but you do not walk the walk. Thus, this modeling approach can clarify the complexity and comprehensiveness of these seminal, multidimensional teachings of the Buddha. I leave it to you to calculate the number of connections between the thirteen links. Hint: the formula is the same as for the cube.

The most important aspect of these original teachings is not, of course, to understand them in any conventional sense of the term, mathematically or otherwise. They are instead, I think, all-embracing ways of comprehending, in the sense of a holistic embrace, the actual conditions of our lives. The breadth and depth of the causes and conditions may be impossible to comprehend in any complete sense, but making the effort sets the context, the big picture, against which our more trivial travails are set in perspective. Einstein, with all his intuition and comprehension, said something to the effect that the most incomprehensible thing about the universe is that it is, to some degree, comprehensible. This is the kind of awe-inspired appreciation that Zen engenders.

Zen holds out the hope and promise that we can, indeed, come to a kind of understanding, if needs be one that surpasseth understanding. Regarding the grand, diamond-like crystalline structure of the buddhadharma, frozen in these verbal and visual snapshots of a dynamic, ever-changing reality, we hope that they can inform that process, and inspire our practice. If such an effort leads to a kind of cosmic, cognitive dissonance, so much the better. It may presage the opening of the actual dharma gate.