John G. Bennett described Systematics as “the study of systems and their application to the problem of understanding ourselves and the world.”

The Twelve Systems

In his four-volume masterwork The Dramatic Universe, written between 1956 and 1961 (Bennett, 1956-61; Bennett 1993), Bennett worked to find a way to identify and understand the underlying pattern and structure of a particular thing—be it an object, action, relationship, situation, process, or whatever—by turning to the experienced quality of number. Thus Bennett contended that the qualitative significance of oneness could be drawn upon to indicate the particular whole in which one is concerned, while the qualitative meaning of twoness could be used to indicate the various differences, polarities, and complementarities present in the whole. Yet again, he contended that threeness could help to define relationship and process, while four-ness could help define activity; fiveness, significance; sixness, event; seveness, transformation; and so forth. The central assumption of Systematics is that there is something inherent in number itself that is fundamental to the way the world is and the way we can understand it. As Bennett’s colleague Anthony Blake explains, “If we are able to penetrate more deeply into the nature of number, then we must become able to see reality more clearly” (Blake 1991, 2).

Bennett used the word system to designate the underlying pattern that a specific number represents. Further, by using the Greek word for the particular number followed by the suffix –ad, he gave each system a name. Thus the monad represents one-ness; the dyad, twoness; the triad, threeness; the tetrad,fourness, and so forth. Bennett argued that each of these systems would offer varying but equally accurate perspectives on the particular thing in which the researcher is interested. In this way, he or she might gain a more comprehensive and integrated understanding of the thing and be better able to appreciate and to work with it.¹

Function, resting on the world as interaction, has no inherent principle of its own and can therefore be understood in many different ways according to the categories. Will, however is through and through relatedness and must contain the principle of three foldness. This is not at first obvious, until one reflects that will as an urge by itself can never “do” anything, and that there must be a resistance for something to happen. This resistance itself must have a will character. One can then grasp that no condition of affirmation - urge and denial - resistance can in and by itself lead to anything without mediation. This is the third force of reconciliation which allows for independence from purpose and mechanism, urge and resistance. In the domain of Being, the essential characteristic is subsistence: Being is. This is more than relatedness or dynamism and corresponds to four-foldness. Again, this is not immediately obvious, until one grasps how it is that a four-fold structure allows for the establishment of a definite order that can be maintained while allowing for internal differentiation. An anthropomorphic way of putting this is that it allows consciousness, which gives being access to itself without dissolving its own structure (consciousness is far more puzzling than it at first seems).²

“Numbers then become typical psychological patterns of motion about which we can make the following statements: One comprises wholeness, two divides, repeats and engenders symmetries, three centers the symmetries and initiates linear succession, four acts as a stabilizer by turning back to the one as well as bringing forth observables by creating boundaries, and so on.” (Marie Louise von Franz)

One striking thing is that Bennett often spoke of the pentad as enabling us to identify the monad: whereas the monad itself is like a collection, the pentad shows a self-sufficient whole. With the pentad, the monad discovers its ‘name’.³

Using Pascal's Triangle, Anthony Blake's Lattice Systematics⁴ provide “infinite depth and infinite exemplification. In Lattice Systems the systems are no longer isolated constructs but form one intricate and possibly dynamic whole.”

¹Threeness, the Triad and Christopher Alexander (D. Seamon)
²Blake's introduction to Bennett's Dramatic Universe, vol. 4
³The Systematics Code, pt 1
⁴Lattice Systematics (A. Blake)