Something that occurred to me, today, was to look at the triad in a couple of different ways. I do not profess to be a master of JGB's Systematics, so humbly acknowledge any inaccuracies and shortcomings. Fittingly, if there is something that I've missed, please let me know.
To begin, we'll go over certain terms to set the groundwork. A triad is a three-termed system in and of itself; it works as a model of describing and defining some set of circumstances. Fittingly, there are other systems, each illustrated by its own number of terms*, and each having its particular focus and use. For instance, the monad is a single-termed system, and would be used to illustrate universality or wholeness (more of a point of highest intensity, and gradually fading in intensity**, but that's a conversation for another day!). The tetrad is a four-termed system, styled like a compass, that is used to "give structured activity and combines relativity and order. . . .***"
More directly related to the triad, and germane to this discussion, would be the dyad, or a two-termed system. This is probably most easily visually illustrated as one term on the left, and one term on the right. In a word, complementarity. One can look at this as a simple yin/yang demonstration, or in/out, black/white, salty/sweet, or other dualities. This system can help to clarify a situation, but can also be quite limiting, as it is looking at two extremes only, and not at what lay between, or at an outside influence.
Moving outward from the dyad, we can look at the triad. A simple description of the triad refers to "relatedness without relativity and hence dynamism as distinct from force.***" So, instead of two elements only, one can include a third element, one that moves from a "this or that" to "this and that by way of those". Another way to describe this would be "Subject A and Subject B are related, and share Subject C as common ground." Visually, this would look as such:
Subject CThough this is certainly a little silly, it's a good example: The spoon stirs the cider within the mug; the mug holds the cider that the spoon is stirring; the cider acts as a substance to be stirred by the spoon within the mug; the spoon stirs in the mug that holds the cider; the cider whirls in the mug because of the spoon; and the mug holds the spoon stirring the cider.
Subject A-----Subject B
Subject A-----Subject B
Obviously, we can substitute anything we want into each subject's slot, whether it is useful or not. For fun, we could try something as simple as "Spoon - Mug - Cider".
Why all the attention to order and sentence structure? Each element takes turns becoming the center of focus, which allows one to observe a situation from each possible angle. Though it is true that the spoon is stirring in each version of the story, one's perception of the spoon changes with each permutation. For instance, "The spoon stirs the cider within the mug," and "The spoon stirs in the mug that holds the cider." In the first version, the spoon is actively interacting with the cider, while the mug holds the two--in a sense, it becomes the active element to the passive element of the cider and the reconciling element of the mug. In the second version, the spoon is actively interacting with the mug, while the cider is almost an afterthought--the spoon is now the active element to the passive/receptive element of the mug, with the cider being a sort of reconciling/neutral element. Were one to put this element in a dramatic scene, for instance, the first version would give us the idea that the character stirring the drink is at least interested in the cider--whereas the second version implies that the character wishes to have a hot drink, which happens to be cider.
*The monad, dyad, triad, tetrad, pentad, hextad, heptad, octad, ennead, decad, undecad, and duodecad are all systems that JGB worked with.
***Directly from the Systematics.org website.