Bennett’s systematics method was based on properties of systems distinguished by number. Bennett and his colleagues looked at contemporary thinking as well as tradiitonal systems to draw up a set of characteristics for each of the first twelve systems. These are briefly described in the section http://www.systematics.org/pmwiki/pmwiki.php?n=Main.Structures.¤¤
In nearly all traditions and nearly all disciplines a key role is played by number systems. For example, Jungian psychology is dominated by the tetrad or quaternary, while Christianity is of course triadic or threefold. A pioneering thinker in terms of systems was the American philosopher C S Peirce, who wrote:
“Perhaps I might begin by noticing how different numbers have found their champions. Two was extolled by Peter Ramus, Four by Pythagoras, Five by Sir Thomas Browne, and so on. For my part, I am a determined foe of no innocent number; I respect and esteem them all in their several ways; but I am forced to confess to a leaning to the number Three in philosophy. In fact, I make so much use of threefold divisions in my speculations, that it seems best to commence by making a slight preliminary study of the conceptions upon which all such divisions must rest. I mean no more than the ideas of first, second, third — ideas so broad that they may be looked upon rather as moods or tones of thought, than as definite notions, but which have great significance for all that. Viewed as numerals, to be applied to what objects we like, they are indeed thin skeletons of thought, if not mere words. If we only wanted to make enumerations, it would be out of place to ask for the significations of the numbers we should have to use; but then the distinctions of philosophy are supposed to attempt something far more than that; they are intended to go down to the very essence of things, and if we are to make one single threefold philosophical distinction, it behooves us to ask beforehand what are the kinds of objects that are first, second, and third, not as being so counted, but in their own true characters. That there are such ideas of the really first, second, and third, we shall presently find reason to admit.”[click Peirce in the list for more material]
The main influences on Bennett were GURDJIEFF and OUSPENSKY but he was familiar with Peirce, Whitehead, Smuts and scientists such as Bernal who had attempted to form a total picture of the domain of natural science.
- Systems are distinguished not only by number but by their FORM, which has to do with how they are represented for us. This gives rise to a MANIFOLD of interpretations.
- Each system represents a FORM OF UNDERSTANDING such that different people thinking in terms of different systems will not understand each other.
- Systematics is relevant to DIALOGUE. ¤¤Bennett averred that the number term systems were the barest abstractions from the real world of ORGANIZED COMPLEXITY.
In this sense, systematics has to be linked into recent studies such as complexity theory, small world theory, cellular automata and so on. MUSIC is a relevant area for considering structure and number and there are many links to composition and tuning systems. Systematics also has a resonance with principles of organization that are explored in creative art of all forms.
The method of systematics contains an idea of PROGRESSION, starting in the MONAD and going up in steps through the various numbers, in a series that in principle has no end. Bennett described the progression as going towards more and more CONCRETENESS and in his description, the ‘infinite term system’ is GOD. We begin from a vague apprehension of ‘something’ and then go on to articulate this sensed whole as a whole universe of experience, involving our own consciousness, will and existence. ¤¤The progression of systems – as Monad-Dyad-Triad-Tetrad etc. – can draw our attention to the gaps between them and this is an advanced form of the method. The straight linear series of systems is only a first order approximation. The series itself is an exemple of ‘progressive approximation’.
Systematics then involves
- meaning of number
- progressive approximation
- progressive articulation
- organised complexity
- sense of wholeness
- forms of understanding
- geometrical symbolism
- and much more.
Below are some references (restricted to the World Wide Web for easy access) to the background and context of Bennett’s development of systematics. They do not claim to be actual sources for Bennett’s thinking. They extend over the use of number as a method of understanding but also ‘number’ in its widest sense as series, progression, pattern and so on, extending into the ‘transfinite’ and the qualitative sense of connectedness and, above all, the meaning of concrete experience.
The references are as best as can be mustered in a short time span and will give at least starting points for further enquiry. The choice of people is subjective and relates to my own background sense of what systematics is ‘about’. This includes not only number symbolism but also geometry, generative progressions, language, transformation, etc.
Clicking on a name or term will take you to an extract from a web page (see below for an illustration) the address of which is then given. You can then go to the original page or follow links in the text as you will.
Precursors of Bennett’s Systematics