CF = 11 – The beginning of the Fourth Quadrant
The boundary between the Third and Fourth Quadrant (III – IV) has a dual character, just like the boundary between the Second and Third Quadrant (II – III). Those points have their ambivalence in common. The quadralectic visibility must be fully understood to appreciate the position at these points of the CF-graph. They are either part of the absolute approach (unity-seeking) to visibility, in which CF = 11 is the ultimate boundary between visibility and invisibility (the ‘Third Quadrant’ approach) or belong to the relative (multiplicity-seeking) approach, which is typical for the Fourth Quadrant. The beginning of the Fourth Quadrant implies a major change of visibility within the quadralectic communication.
CF = 6 – The Second Major Approach (SMA)
The Second Major Approach (SMA) in the Fourth Quadrant (IV) is in many aspects the apotheosis of the insight in a communication. The low CF-values (CF = 6) are reached for a second time and indicate a maximum of intensio (approach). This point at the end of the second quarter of the Fourth Quadrant (IV, 2) marks the final act of coming-together and understanding. Its character is totally different from the First Major Approach (FMA) in the Second Quadrant. The FMA was a creative move to the boundaries of possibilities, carried out in an atmosphere of innocence. The ideas of our experience had to be formed in due course, and a frantic search for references was on. The youthful confrontation with life had its own moments of glory, but they were all the result of that slightly naive enthusiasm, which accompanied those who see things for the first time.
The situation in the Second Major Approach is just the opposite. Now, the whole specter of visibility can be understood. Experience has grown to a formidable force in its own right. All the highs and lows of life have been accomplished at this point of a communication. There are no excuses any more. We should have seen it all at this point.
CF = 11 – The Receding Point (RP)
This point in the middle of the Fourth Quadrant is often regarded, in the somewhat dramatic setting of the empirical mind, as ‘the beginning of the end’. The CF-value reached the borderline again (CF = 11), that elongated margin between seeing and not seeing. The communication finds itself in a position of critical stability between intensio and remissio, and is for a brief period ‘at rest’. The third quarter of the Fourth Quadrant (IV, 3) is a mirror image of the second quarter of the Second Quadrant (II, 2), but its nature is, again, completely different. Whereas sweet innocence was the major hallmark of that first period in the Second Quadrant, it is now – in the Fourth Quadrant – the full awareness of the communication. The drifting into visibility with ideas, but hardly any frame of reference – which is typical for the youthful approach – is replaced by a thorough knowledge of the interaction between ideas and visibility.
So many points of references, stored in memories, contribute to the insight and perception in the period following the Receding Point. Maybe the originality has weakened, and the influence of reminiscences has increased, but the wealth of experience can compensate for that. A ‘Late Renaissance’ – with an inverted, conscious creativity (in contrast to the sweet innocent originality of the Second Quadrant) – is possible in the closing stages of the visible visibility of a communication.
CF = 11 – The Last Visibility (LV)
The visible visibility phase (X) discontinues at this point of the communication cycle. It is a marker point, which indicates the end of the visibility area X and the (second) beginning of the invisibility area O. This state of affairs does not mean that the interchange stops here. It is just the end of a particular phase in the character (and definition) of visibility, which changes. There is, in a quadralectic approach, no special importance associated with this point: the end of an empirical presence is a convenient way to determine a boundary, but not more than that. The cyclic communication continues.
The moment of departure is much heavier felt in the dualistic frame of mind. It is associated with death and eternal darkness. The tears at a funeral are shed as worldly sacrifices for the two-fold way of thinking. They signify the will to return to a ‘Third Quadrant’ world of security, but also with its limited understanding of visibility.
The last visibility is not the end of the communication. The interchange continues for 1/16th of the total communication cycle V in the ‘second part’ of the invisibility area O. The mutual relation is a mirror image from the situation at the end of ‘first’ invisibility area O, when the CF values dropped from 15 to 11.
CF = 15 – The end of the communication cycle
The end of the communication cycle holds the great mystery of the quadralectic way of thinking. Because it is here that the ‘proof’ of a cyclic character should be given. The end is also a beginning. Here, in this very realm of invisibility and outside the understanding of the communication partners, is the apotheosis of an inter-action, which was notable in place and time. The end is, just like the beginning, an enigma in itself. Its position can only be reconstructed from points, which has a certain distance from the end (or beginning) and are governed by the initial choice of division.
The first visibility area (X¹) might, in a cyclic context, repeat itself in a second visibility area (X²), but the question can be posed if this second appearance is a genuine part of the first presence. If so, then the character of the first visibility-object has to be reconsidered and changed.
The crucial matter of the causality between two appearances in place and time comes down to a (subjective) judgment of the observer, who decides if these phenomena belong to one and the same event or not. It means, if the answer is positive, that the first visibility area (X¹) must be extended to include the second visibility area X². In that situation, every repetition of a visible visibility (in future) is immediately ‘swallowed up’ by the original visibility event as soon as an observer incorporates the new unit in the initial part. The fixation on the ‘part’-aspect of the communication is typical for a ‘Third Quadrant’ approach.
The problem of a relation between two ‘visibility events’ came to ahead in the early twentieth century in the theory of quantum physics. The position of the observer and the position of the observables (like atoms and ions) are – in a multi-division environment – not necessarily fixed to one and the same spot in the visibility area. ‘The impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear’ let to the definition (by the Danish physicist Niels Bohr and others) of the principle of complementarity. It implied that ‘evidence obtained under different experimental conditions cannot be comprehended with a single picture, but must be regarded as com-plementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.’ The principle acknowledged, in short, the occurrence of different ‘Third Quadrants’ in the subdivision of a primary four division.
The ‘Fourth Quadrant’ way of thinking does not concern itself with the question of belonging (to one part or a single picture), because the spatial relations are not directly translated in terms of immutable boundaries. The principle of complementarity is not an escape from some sort of physical controversy (like the wave-particle duality), but belongs to the nature of the communication itself. Bohr regarded complementarity as ‘a “rational generalization” of the classical framework’ because ‘the discontinuities expressed by the quantum postulate were so relatively small that they could be ignored and the interactions between systems described continuously’ (FOLSE, 1985; p. 66).
The discontinuities of Bohr’s stationary states and the continuities of the classical framework find their collective cause in the difference in division thinking. Historically, the physical nature was extended from a three (Newton) to a fourfold (Bohr) setting. Newton’s atoms were situated (from a quadralectic point of view) in the third quarter of the Third Quadrant (III, 3), while Bohr’s atoms were measuring units in the third quarter of the Fourth Quadrant (IV, 3).
It is no longer necessary, if this positional aspect is realized, to verge on a (sub) atomic level to see that the observer and the observed are not in the same room together. The ‘room’ – regarded as an observational space under any given circumstance – is just a convenient cadre in which the division pattern in a communication can develop.
The causality in a communication can only be established by a realization of one’s own position expressed in terms of division thinking.
And when the question of unity (between two events) is posed, the (quadralectic) philosophers’ answer will depend on the actual viewpoint and division frame of the original observation. If the interaction is situated in the final quarter of the Fourth Quadrant (with CF-values climbing from 11 to 15), then all past and future appearances are included, and no possession or claim can be laid on them. The last, visible invisibility offers the crude environment to place the cosmic causality in a clear and subjective way, adding the ultimate touch to the understanding of the observer.
The end of the communication cycle is also, as seen from the third quarter of the Fourth Quadrant (IV, 3), determined by the smallest part, which contributes to the interaction. And since a part is an entity, which needs a space and a limitation to exist, these characteristics are reflected in the termination of a communication cycle.
Duality remains with us to the very end, and gives rise to such expressions as ‘the abyss’ or ‘the deep’, to capture the seemingly inconceivable boundary between one communication cycle and the next. But obviously, such a bottomless pit does not exist. One has to look at the CF-graph to learn that the journey continues into an ever-increasing greater remissio with higher CF-values, just as it did at the ‘beginning’.
Visions of Four Notions 