Systematics was developed by the mystic, research scientist and philosopher, John Bennett (1897-1974). Its origins are in the occult teachings of Gurdjieff and Ouspensky, higher-dimensional geometries, the philosophies of Peirce and Whitehead and, possibly, Jan Smuts' holism. It was described by Bennett as a 'method of understanding' and, as such, is suited to ongoing creative interpretation. Bennett understood understanding as 'the subjective aspect of will' and, hence, to be associated with what we can do, rather than with what we can know.
The main properties of what is called a 'system' in systematics are said to arise entirely from the NUMBER of elements of which it is composed. This marks systematics off from general systems theory as defined by Bertalanffy and others. Wholeness is regarded as multi-valued, arising in different and discrete degrees. The elements of a system (originally called 'terms') represent the various degrees of wholeness. The number of basic systems there are is, in principle, unlimited.
Systematics is the study of ORGANISED COMPLEXITY, a theme of growing interest now. Every elementary part of a system is complex. These elements are not things, or atoms, or any simple substance. A Monad has one element, a Dyad has two elements, a Triad has three elements, a Tetrad has four elements, and so on. Every element of every system is at least as complex as the monad.
The first system, the Monad, which has only one element or 'part', is a complex whole. The Monad is before definition, and concerns our recognition of something by means of an aesthetic sense of belonging. We know the Monad through 'indeterminate exemplification'. If people are to have a fruitful exchange on some topic, then it is good if they can address the 'same thing', or share in the same Monad! It is only when people go to the trouble of exemplifying to each other what they mean by something that a sufficient information field for mutual understanding can be established. There are an indefinite number of monads in reality. A Monad is not the absolute of monism, nor can it be identified with the Monadology of Leibniz. It is nearest to the idea of 'organic unity' to be found in Goethe's work.
A Dyad has two elements. These two stand side by side. They are not 'connected' but simply require each other to be what they are. In this sense, we have the example of male and female. Dyads appear to us in the emotional experience of 'force' and 'tension', and in the cognitive modes of paradox and contradiction.
A Triad has three elements. These three revolve around and between each other. This sense of movement leads to the defining characteristic of 'dynamism in a circle': there is change but within a pattern. As in all the systems, there are specific defining characteristics for each of the constitutive elements, so each of the three 'parts' of the triad represents a different role in the dynamism. These roles can be understood according to the kind of situations experienced and studied. One common expression is to define them as: affirmative, receptive and reconciling.
As we go from one system to the next, there are steps of CREATIVE NOVELTY. This means that some new aspect of experience is revealed in every system. It may or may not be possible for us to realize what these steps are, and we can always provide some approximation to a creative step by a combination of previous steps.
What we look for in any given system is the 'sameness' that appears through diverse experience when only the number of elements is the common factor. This means that other aspects of experience are omitted and it is highly likely that general systems theory and other approaches concern themselves with these features. It also means that systematics cannot claim to be a universal explanation. Indeed, it is primarily phenomenological and does not concern anything like a 'scientific model'.
Systematics ties in with powerful forces embedded in cultures and belief systems. Though numbers have been associated with numerology and superstition, they also play a formidable part in the formulation of religions, Christianity being a strong example. There are historical fashions in cultures such as the current one of believing that dualistic thought is 'bad'. Patterns of number are built into our languages and exert a largely unseen influence on thought. It is always an interesting question to ask: How many ideas do I have? Or, for a culture: how many gods are there?
Other streams of thought have concerned themselves with much the same issues as systematics: Jung, and his successor Marie von Franz in particular, in psychology, religion and divination (synchronicity); René Guenon in occult studies; Eliot Jacques in management and organizations; Arthur Young and David Foster in cosmology; Joseph Rael in the Amerindian tradition. And so on.
Besides systematics as a contemplative discipline, what takes it out of being a version of Hesse's Glass-Bead Game is the heuristic value it has in creative action. We can build systems, bring systems together, realize systems through what we do. One of Gurdjieff's stimulating neologisms was 'triamazikamno' for the 'law of three' or the triad, which roughly translates as: 'I put three together and do'. So, besides the investigative studies which build an insight into the character of the various systems there are pragmatic approaches to making systems happen.
Coda: what is systematics about, essentially?
The underlying thinking in systematics is similar to, but far from identical with, mathematics. There are 'pure forms' to be explored, far from any particular experience. To suppose that simply the NUMBER of elements in a situation determine - in some unknown way - the character of that situation is a remarkable assertion. It accords more with synchronistic than with causal thinking. The idea that number has concrete significance amounts to magic.
It is more than likely that number is only one out of some range of features - as yet unspecified - that can be used to see into the nature of things. The central power of number comes from the fact that we have to do things in sequence and this involves us in counting. Evolution is seen as series of steps along a line of increasing CONCRETENESS. Such an idea is echoed in the spiritual belief held by some that, in evolution, spirit and matter increasingly coalesce. The sequence of the systems is a kind of time that relates ordinary time with the will. It becomes what we call 'the process of understanding'.