A division of (a ‘linear’) infinity into four sections requires three points of partitioning. Three pegs can stake out four regions. The four-division is more stable than the three division. The tetradic frame of mind keeps static and dynamic forces at bay. It is broad, balanced and accommodates the lower kinds of division thinking (with monad, dyad and triad as coagulating agents) within a structured context.
The compartments in a (universal) four-division are called quadrants. They are the most important units within the quadralectic frame of mind, because they are the designated areas of different forms of visibility. Each quadrant has its own type of visibility (which will be discussed later). The definition of the basic element in the four-fold division is as follows:
A quadrant is an autonomous part created in the four-division of a unity.
This qualification does not have a reference to size or shape, because the (ultimate) unity is not defined. A quadrant is a theoretical unit, a reflective compartment, which acts as a storehouse for different forms of visibility and division thinking.
The definition of a quadrant needs some further explanation. It has – in the spatial realm – a reference to the fundamental region, which is a term, derived from symmetry. LAUWERIER (1988) called the area a ‘primitive cell’ in his book on symmetry. Symmetry is, essentially, a division of a given space according to fixed laws. STEVENS (1980) distinguished four types of movements to obtain the multiplication of a pattern:
Stevens gave, in his study on regular patterns, the following definition of a fundamental region:
A fundamental region is the region of a minimum area that can be repeated without gaps of overlaps to make a complete pattern.
This definition of a particular, limited area of space has an affinity with the characteristics of the quadrants (in a quadralectic communication), which make up a unity (or cycle). The quadrants-as-a-whole are valued as a fundamental region, which is defined as an autonomous part and is limited by specific boundaries. The tetradic pattern can extend into infinity, just like a primitive cell in a symmetrical pattern expands in all directions.
Each quadrant is, in a quadralectic setting, related a particular form of (dualistic) visibility (fig. 8). The information starts with a primary pair (visible versus invisible). A further interpretation of the different combinations is derived from a theoretical shift of two four division along each other. The actual procedure and the creation of a universal communication sequence will be dealt with later in this book (p. 90 onwards).
Fig. 8 – The quadrant is a compartment in a universal four-division, which is characterized by a particular form of visibility. The types of visibilities as given here are an approximation from the world of duality. The number of the quadrant does not indicate a hierarchy since the units are placed in a cyclic setting.
It is possible to imagine a ‘growth’ of division thinking (from one to four). An immovable observer (position W) will encounter in the various quadrants a cyclic movement of different types of divisions (fig. 9). The dynamism will increase in the process. The various ‘values’ (of the individual quadrants), which have to be taken into account expand accordingly. The (stable) observer will become, in a later stage, also a fourfold, cyclic entity, which partakes in a dynamic interchange of information.
Fig. 9 – The development of the four-division from a one-division and the valuation of a contact point between the cyclic movement of the division and a fixed (static) observer (position W).
A communication established in the four-division is a most practical way of understanding, because its harmony covers the whole field of human possibilities, ranching from the complete unknown to a subjective interpretation of one’s own, personal choice. All stages of comprehension are ordered in a logical way, allowing for every participant to choose a comfortable niche as a means of operation.
Lower forms of division thinking can be spotted from the higher advantage point of four-fold thinking. The valuation of data exchange, or the quality of a communication, has to be rated accordingly. There is hardly any point to ‘fight’ the oppositional thinker, since that the outcome is not more than a (brief) episode in the conscience of a higher division thinker.
A hind of structuralism seems to be incorporated in the emphasis on division. A multi-divisional communication could be seen as a structure or system, operating independently of its contributors. This impression is, categorically, wrong. A subjective choice at an early stage is necessary, if understanding will ever be possible. That choice is, however, not limited to oppositional pairs – like the binaries in the deconstruction ideas of the French philosopher Jacques Derrida – but encompasses four positions, with the whole scale of possibilities enclosed in each of them. The ‘ultimate’ choice is not restricted to oppositional pairs, but comprises a motivated registration of the position on the communication cycle.
Fourfold thinking is often disguised as a form of wisdom, practiced by elderly people and spiritual leaders. They have reached, by experience or intuition, a state of knowledge, which includes the (four) possible positions in a communication. Any advice offered by the sagacious men and women throughout the ages to the ignorant parties (in a conflict) consisted of a suggestion to broaden their horizons and open their minds to ‘the things that have always been’ (fig. 10).
Fig. 10 – An Ojibway medicine lodge parchment with the ‘things that have always been’. The Mugwa (bear) traveled from east (E) to west (right to left) through the four compartment (lodges) in the earth shelf. Collected by the Canadian Ethnology Service of the National Museum of Man (in: DICKASON, 1984).
Visions of Four Notions 