4.4. The Fourth Quadrant (IV)

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The last multiplicity  

The Fourth Quadrant harbors the last multiplicity and the principle of existence. That is to say: the partial unity of the Third Quadrant is activated in a dynamic appreciation. Its major carrier is the analogy. Delineations (‘things’) are compared on a physical base, bit by bit. A new reality is born in this comparison. The possibilities increase to a maximum, because the given facts and the interpretation of facts join into a pact.

Ethical and spiritual values contribute to complete the visibility given by the facts. A different form of oneness emerges, finding its roots in the increased knowledge of the past, the present and the future, and – of equal importance – a recognition of a ‘fourth dimension’: the understanding of the cognitive framework in terms of division thinking. All facts are coming together, including those facts, which have contributed to their own initial demarcation.

The last stage (of visibility) is – in many aspects – a very interesting one, but it should not be rated higher than the previous positions. The main feature of the fourth stage is the cognate increase of consciousness and the notion of relativity (of scale and value). It is understood that visibility is established in a process of transposition and can be seen as a direct result of the initial choice of division. The circle of interaction closes, so to speak. The beginning, born in innocence, is also the end, steeped in understanding and fading away in a reaffirmed clarity.

This theme of cyclicity (without actually knowing the radius of the circle) is a predominant element in the Fourth Quadrant. Man has seen it all during the circumnavigation of its own mind: first, an unawareness of the self, then some vague notions of relations, subsequently the linear tendencies of the hereabouts and finally, an alienation due to a wider, cyclic perspective. In the end, it is found that the beginning is relative, just a matter of definition and choice of division.

All creation myths bear the stamp of that primary and ultimate choice. Marcelo GLEISER (1997), in his quest for understanding the origins and place of mankind in the universe, looked at the nature of creation myths. He saw them as the bridge connecting the all-encompassing Absolute to our structured reality. ‘The Absolute is the central element in all credos, giving creation myths a deeply religious character’, according to Gleiser (p. 9), and he continues: ‘This Absolute could be God, or the realm of many gods, or the primordial Chaos, or even the Void, the non-being’.

The origin of the Universe and different mythological responses to the question of the origin of the Universe. This representation assigned the myth to an oppositional environment. GLEISER, Marcelo (1997). The Dancing Universe. From Creation Myths to the Big Bang. Dutton/Penguin Books Ltd., Harmondsworth, Middlesex, England. ISBN 0-525-94112-6

His classification of the creation myths comprised two main groups, according to how they address the question of ‘the beginning’ (see above). Either there is a specific moment of creation, or they assume that the Universe existed forever. The former type was subdivided into three groups, depending on the agent of creation being. 1. A positive being (a God, Creator or gods), 2. A negative of non-being (an absolute emptiness) or 3. A primordial Chaos (where being and non-being coexist). The latter type (no-creation myths) were subdivided into two groups. 1. The Universe had an eternal existence, never created and never destroyed, or 2. The Universe is continually being created and destroyed, in a cycle that repeats itself forever.

The Last Multiplicity of the Fourth Quadrant leads to the very end of human imagination and points, by recollection or speculation, also to the beginning. The boundary between the Fourth Quadrant and the (following) First Quadrant holds the great enigma of life. By crossing this line – if only on a mental scale – we enter a complete different world.

The definition of the final boundary of a communication cycle is probably just as important as the notion of a first beginning, since the two events are, in essence, the same. The Ginnungagap in the Norse and Germanic myth of creation comes to mind. This time-space was the great void or abyss, where neither sand, sea, heaven nor earth was created. Its emptiness held the primordial energy source, which later gave birth to the world’s creation. In the south was Muspell, a place of light and fire, the first world. To the north is the dark and cold realm of Niflheim. The Muspell recurs at the end, when the world is consumed by fire.

The Muspilli is a German medieval poem, which describes the judgement day, the final end of the world (by fire) and the establishment of the great beyond (FINGER, 1977). These eschatological lines, by an anonymous author, were discovered in 1817 in a manuscript from the St. Emmeran monastery. The poem is probably written in the late nine century and has a strong dualistic style. Angels fight with the devil over the souls of the dead. Heaven and hell are painted. Elias (as a representative of God) struggles against the Antichrist (or Satan). The destruction of the earth starts when Elias’ blood reached the earth. The living and the dead appear for the final judgment, under the cross of Jesus. The souls are bound to heaven or hell.

Apocalyptic visions often bear the stamp of oppositional thinking. Their message is, in most cases, a sign of narrow mindedness rather than a reflection of the great things to come. The recent predictions of the Second Coming of Christ have in extreme cases led to (mass) suicides, because a strong dualistic belief offers no way out.

Another good example of a dichotomy at the end of the visibility area is found in the conception of heaven in the Christian belief. The kingdom of heaven was envisaged as an infinite space where the (righteous) souls would live forever after death. This view of the traditional theology was based on a linear and dualistic point of departure. A body was opposed to a soul, a visible life to an invisible afterlife, and a finite existence here on earth contrasted with an infinite life in heaven. The Kingdom offered, despite these contrarieties, the quiver of the eternal life in which the oppositional forces were silenced.

A Capuchin friar, Martin of Cochem (1634 – 1712), in the apogee of oppositional thinking in Europe, departed from this view. He was of the opinion that ‘heaven is not something spiritual as some suppose, but something corporeal, made of some kind of matter and having form and substance’ (in: McDANNELL & LANG, 1988). He projected the past visibility area right into the future, because ‘what joys could the saints’ five senses have, if in heaven, nothing could be seen except for a huge, immense space?’ Such an extrapolation of the visible world into the field of the invisible is an effort to ‘conquer’ the next visibility cycle.

The Fourth Quadrant-as-a-whole offers the width of thinking and freedom of imagination to development a creative model of commensurability. The latter faculty is defined here as a common measure between like quantities. The application of a wide field of observation (and implementation) makes it possible to discover a greater intrinsic coherence between the focus points.

The scholastic philosopher Nicole Oresme (1323 – 1382), a dean of Rouen and adviser of King Charles V on financial matters, carried out pioneering work on the subject of commensurability as early as the fourteenth century (fig. 53). He translated Aristotle’s ‘Nicomachean Ethics’, ‘Politics’ and ‘On the Heavens’ from Latin into French and invented co-ordinate geometry long before Descartes (1596 – 1650). The use of a graph for plotting a variable magnitude was another ingenious achievement (CLAGETT, 1968). Geometry became a tool to represent intensity, as a representation of the intensio and remissio within a given communication.

Fig. 53 – Nichole Oresme (1323 – 1382), seen here writing behind his desk, was an important scholastic philosopher, who ventured in many different terrains, ranging from translations (of Aristotle), mathematical and geometrical problems, to economic ideas of the use of currency.

Oresme was concerned with the mathematical aspects of the circulatio: the return of one mobile along a circular path from any point to the same point. (GRANT, 1971). This knowledge was directly applicable to the conjunctions of planets and had its bearing on astrology. This ancient art used the kinematics of the stars to predict terrestrial events. Oresme rejected – in his book ‘Livre de divinacions’ (c. 1366) – its validity, because he believed that the foundations of astrology were wrong: celestial incommensurability would lead to an inherent unpredictability. He further stressed his point in the book ‘Contra divinatores horoscopios (c. 1370).

Just one step further on the path of commensurability is the assumption that the observer is not a static unit, but is a dynamic and divided self. In quadralectic terms that would mean a shift from the Third Quadrant (III) to the Fourth Quadrant (IV). The latter position provides the perceptive space for the observer to become object and subject at the same time. There is no distinct ‘before’ or ‘after’ in a cyclic setting.

The consequences of these dynamics in the Fourth Quadrant are drastic. The implications change the complete scope of a communication, its outlook and expectations. Borders become relative, motion becomes relative and the whole event of visibility in a communication is a matter of fluctuation. What we are and what we do, is a reconstruction of facts collected during an interchange with the universe. The New Man – or any other description of a rejuvenated insight – is not new at all, but existed all the time. If only we are able to read its profile.

The Fourth Quadrant provides the space to put the split vision into perspective. It is only in a wider environment that the nature of relations becomes clear. Nothing could be counted on as firm foundations, but that does not mean that the relations and the structure of the system-as-a-whole are not significant. On the contrary, a conscious and contemplative mind, actively engaged to know its own position at any given time and place, is of the utmost importance to be able to judge the pressures of life. The graphical representation of the universal communication offers such a footing. Observations reach a sophisticated level of depth when they are placed in a context of multiplicity and can be given some sort of value.

The ‘subjectivity’ of the Fourth Quadrant and the accepted and approved influence of feelings are not a vague and weakened addition to the communication, like many scientists suggest or imply. The inclusion of what was formerly called ‘subjectivity’ leads to a very distinct pattern of inter-relationship. Feelings are the conscious registrations of a premeditated circumscription in a communication.

The choice of a four division is the most important act to create a world view, which goes beyond the rigidity of duality and the lopsided way of three- (or five-) divisional thinking. The principle of life is an augmented world view, and a cosmic understanding based on the interaction between division and movement. The observer cannot exist without a division perception and cannot comply with reality without being engaged in movement. Both actions are designed to create space in order to throw light on the universe.

The principle of life finds an ultimate challenge in the Fourth Quadrant, by a fulfillment of the promise, which hides itself in the infinity of time: by imagining the invisible invisibility within ourselves and seeing a spectacular universe emerging from its depth. That is a magnificent thought.

4.5. A Recapitulation

A recapitulation of the previous theoretical description of the quadralectic communication will be given here. It is essential at this point to understand the nature of the four-fold division and the character of the various quadrants before the implications of this knowledge can be used in practical situations.

The CF-graph, consisting of sixteen line fragments, is the universal expression of a communication between two parts in a tetradic division environment. The abbreviation CF (for values on the Y-axis) stands for the so-called Communication Factor. This figure is a measure for the distance between the communication partners at a certain point in time and place. The universal expression of the quadralectic communication was completed by the author in 1985.

The First Quadrant (I)

The First Quadrant is the first compartment on the universal communication division. The area is understood to be void of any recognizable particulars, of which the absence of division is the most prominent feature. Therefore, any distinction of an outline is impossible. The ‘visibility’ in the First Quadrant is a projection from temporal and locally determined distinctions made after a division took place.

The environment of the First Quadrant can be compared with the space in a tunnel. What is a tunnel? A hole or an empty space with walls? The emptiness in the tunnel only gets its meaning by the walls that limit its existence. Not every empty space is the same, and the denotation is established in a description of its boundaries.

The First Quadrant is the ’empty space’ in a communication cycle. Paracelsus called the primary emptiness the ‘IIiaster‘ (Primum Ilech; Illeias) (WAITE, 1894). The First Quadrant provides the opening in which a communication can develop in due course. The sense and concealed contents of the First Quadrant can only be measured from another quadrant. It would – in a dualistic perspective – be called the invisible invisibility. This type of visibility is just as important as the visible visibility of the material: presence is, in the end, not only a matter of observation, but also of faith.

The acceptance of a transcendental area of complete inaccessibility has consequences for man in a cosmic environment. This is the terrain of unsolved questions and unimaginable distances and, above all, the knowledge that we are literally, the Small Part (SP) or Minor in a communication. Our own shortcomings determine the outcome of our interaction with the universe, our world, our fellow men and, finally, ourselves.

The invisible and incomprehensible part in the field of observations is a basic human understanding. Religions have been built on it. God and gods are worshiped as the representatives of some imperceptible empire, with other rules and outside a direct observation. The different types of religious beliefs have one characteristic in common: they all try to express the abstract world of the First Quadrant in terms of the known. Man is not satisfied with an ’empty space’ within his mind. Something has to be there. The First Quadrant became a great place of extrapolations from the visible world, a gathering place of (creation) myths, orientations and projected experiences.

The First Quadrant is the birthplace both of division-thinking and religious opinions. It will come to no surprise, that within this context, the name(s) of the god reflects the relation with the elementary division thinking and consists of three or four letters. The choice of the word for the godhead provides a point of reference to the division in which the god springs to life. ‘Belief’ – in its most general form – is encouraged within the quadralectic way of thinking. Not as a means to conquer the truth or pretend to find the ultimate reconciliation, but as a means to get access to the creativity of the invisible. Belief is a means to join and enjoy the huge space of the invisible invisibility and use its unimaginable possibilities. No communication can do without it.

The Second Quadrant (II)

In the Second Quadrant starts the Odyssey, a quest for an overture. There is a tendency to an approach. This advance is a process, which results at a given moment in a first sense of ‘visibility’ – like an idea, an interpretation. These initial notions can only occur when a division (of the Oneness of the First Quadrant) has taken place – on the border of the First and Second Quadrant. A structure of thoughts develops into a first visibility (FV). This moment of equilibrium in the second quarter of the Second Quadrant (II, 2), is a period of preparation for the things to come, for a further advance towards to ultimate possibilities of a communication.

The exact position of the visibility moment cannot be established in the Second Quadrant, because the official unit of measurement has not yet been introduced. In dualistic terms one could speak of an invisible visibility. That means: the visibility has a cognitive framework (build from the components of the third quarter of the Second Quadrant (II, 3), but lacks the visible measurements of the Third Quadrant.

The difference of approach to visibility has a direct bearing on the duration of a communication. Visibility consists – in a dualistic model – of two parts, and the moment of first visibility is in the middle of the communication cycle. The first visibility occurs in a quadralectic model at 5/16th of the cycle, and 11/16th part of the cycle is still to come. This difference leads to the important conclusion that the moment of visibility is tied up with the primary division. The expectations of a two-tier thinking are fundamentally different from those of a four-tier.

The Third Quadrant (III)

The visibility of the Third Quadrant has a dual character, also known as the ‘classical’ visibility. The observation is secured to an empirical reality, which is incorporated as a material unit of measurements (the part).

The quadrant starts (and finishes) with a CF-value of 11, the value which was chosen as the (arbitrary) boundary of visible visibility. The definition of this ‘double’ perception can be interpreted in the oppositional spirit of the Third Quadrant: the ‘ultimate’ physical visibility is either absolute or relative.

The first type of observation takes place in a closed system with (temporary) fixed boundaries. The object of observation (like an apple falling off a tree or an atomic system) should be an independently existing physical reality. The observer is just watching the process and gains empirical knowledge. The metaphor of a clockwork has been used to indicate this outlook in Newtonian physics.

The second type of attention is active in an open system with dynamic boundaries. Nothing is ‘fixed’ in the classical sense, but randomness becomes a central theme. Modern physics, involved in the observation of physical phenomena, devotes a lot of attention to the statistical tendencies of the material and its behavior according to the laws of probability.

The Fourth Quadrant (IV)

The Fourth Quadrant gives a mirror image of the Second Quadrant. Visibility increases rapidly in the first phase, to reach the point of greatest approach (CF = 6) for the second time. Then a strong climb to end of the communication cycle (CF = 15), passing the Receding Point (RP) and Last Visibility (LV). There is, however, a great difference with the Second Quadrant, because the observer in the Fourth Quadrant has all the tools at hand to express the four types of visibility. This abundance possesses its own problems and creates a growing invisibility, caused by the shear impossibility to take all possibilities into account.

The Fourth Quadrant offers the chance to utilize the four quadrants simultaneously. The (old) opposition between the linear, straightforward approach and the cyclic setting breaks down. Both motions merge, because in the full understanding of things, there is no difference. Any linear progress, if carried out long enough, becomes cyclic. And any large cyclic move can be regarded as linear if the scale is small enough. The very end of the Fourth Quadrant opens a perspective with innumerable positions and situations. This richness can only be perceived in the right consciousness of scale.

The theoretical and descriptive side of the quadralectic way of thinking will at this point left behind, and the attention will shift to the practical applications of the communication model. Several comparisons with existing ‘shift’ operations will be given first, later some direct usage of the new apprehension is added. The quadralectic way of thinking must prove its viability in the real world, just like any other theory. The final aim (of the quadralectic postulate) is to be of use as a universal hypothesis, applicable in all imaginable situations.

 

 

 

 

5. Comparisons

The quadralectic philosophy is based on a dynamic interpretation of reality, and the width of its outlook makes it possible to delineate a whole quadrant (IV) to the process of analogy. This most basic of the Aristotelian entities was often not seen as a separate device in the great mechanisms of comparison: induction and deduction.

It is, even now, closely linked to the lower type of division thinking. A comparison is often, without speaking, a matter between two things. Analogy – and the process of its application – is regularly seen as a static commodity dealing with the opposition between two entities. A comparison (analogy) in the quadralectic approach is, on the other hand, a dynamic interaction between the four quadrants simultaneously – which includes an evaluation of its own position (in the Fourth Quadrant).

The (multiple) comparison is the hallmark of the Fourth Quadrant. It is, in a linear view, the apex of the communication in its stride through the quadrants. Now, towards the end of the circle, a full view is possible. Everything is at our disposal. This statement might be true, but is not appropriate in the full understanding of the (cyclic) quadralectic philosophy.

The translation of our experiences as a culmination in a last segment of a communication finds its roots in oppositional division thinking.

The tetradic nature, including the position of analogy as a comparison mechanism in its fourth member, was realized much earlier. A picture of cyclic equality emerged as soon as the decision to communicate in a four-fold setting was taken. There is no apex or climax, except perhaps in the limited view of the Third Quadrant. Only intensio and remissio are the leading agents throughout the cyclic movement.

However, the CF-graph can be used as a means of comparison itself. This operation was already theoretically captured in the Second Quadrant, but can now be made fully operational between the third and fourth quarter of the Fourth Quadrant. It is only at this late moment that the observer has the full advantage of the empirical achievements in the Third Quadrant and transposes them in the context of a Fourth Quadrant. The CF-graph becomes the yardstick for creation.

Mankind has always been fascinated by the forces, which exercise within a communication. These mutual influences can only be measured in a comparison. Crucial in such an effort is the importance of time and place. They provide the extension in which a comparison can take place. A brief excursion into the complicated philosophical world of time-place will be made in order to place a comparison (as an analogy) in its proper context.

The philosophy of Time has a long history and the question ‘What is time?’ has been posed repeatedly. The Greek god Kronos stood at the beginning of time and was revived by the Romans as Saturn. His reign was associated with prosperity (Golden Age). He was also the god, who castrated his father Uranus (Ouranos, sky), because his offspring became threatening and to many for his wife Gaia (earth) (fig. 54).

Fig. 54 – The unmanning of (Uranus by) Saturn. The symbolism is slightly mixed-up in this woodcut of 1484, which depicts the moment of emasculation. Kronos (Saturn), as the ruler of time carrying a scythe and an ouroboros, is here the one who is unmanned, rather than his father Uranus.

The analysis of time is often, in one way or another, a concealed effort to search for the principles of division and movement. The great enigma of the spatial existence in time can only be solved – or better: described in a dynamic setting – if the lasting influence of the primordial division (in the Second Quadrant) is realized.

The famous paradoxes of Zeno (from Elea, fifth-century BC) challenged the notion of time and space as infinitely divisible. Four paradoxes reached eternal notoriety: the dichotomy (or motionless runner), the Achilles, the arrow and the stadium. His apparent contradictions are practical examples of the untenable position of extreme oppositional thinking. The results of this confrontation and the changing nature of division and movement – the two fundamental building stones of a communication (see fig. 4, p. 13) – are confusing for someone, who is reluctant to leave the save environment of observational security (in the Third Quadrant).

Zeno’s paradoxes are, in principle, inquiries into the ‘in between’: the areas of immeasurability (see also p. 96). We know that a certain interaction in a communication takes place, just like the observer sees Zeno’s arrow in motion, but its actual position can only be measured in a reconstruction, when (two) fixed points are known. A straightforward, dual mind can now draw the conclusion that no motion occurs when such points of reference are absent.

Any definition (of time) will lead to conceptual questions ‘having to do with the nature of the concepts of truth, events, things, knowledge, causality, identification, action and change’ (GALE, 1968). This being granted, it has also to be taken down that none of these entities make any sense if they are not placed in a division environment. Any discussion of time and place – and the comparisons, which are used to measure them – is of little use if the type of division thinking is not stated.

Donald C. WILLIAMS (1966) took such a clear position in his book ‘Principles of Empirical Realism’. The title pointed firmly to a Third Quadrant stance, but the actual ‘realism’ was found in the theory of the manifold. ‘I believe that the universe consists, without residue, of the spread of events in space-time, and that we thus accept realistically the four-dimensional fabric of juxtaposed actualities. We can dispense with all those dim nonfactual categories, which have so bedeviled our race: the potential, the subsistential, and the influential, the noumenal, the nominous, and the nonnatural.’

These drastic measures were taken by someone who looked steadfast ahead from the Third to the Fourth Quadrant and did not look back. Otherwise he would have seen that those ‘dispensable categories’ were nothing less than (Second Quadrant) ideas, which fill the very real position of the ‘in between’. To speak of a conflict between determinism and the indeterminate – like Williams does (in: GALE, 1968; p. 345) – is another indication of oppositional thinking. Furthermore, the ‘static versus the dynamic temporal’ (or the B- and A-Theory of Time), as pioneered by ‘one of the last British Hegelians’, J.M.E. McTaggert (1866 – 1925), followed that same route and ends up with a ‘paradox’ or a denial (McTAGGART, 1908; 1927).

The incompatibility of the static and dynamic (temporal) is only the result of a particular way of looking at Time. If Time is placed in an oppositional environment (like the Third Quadrant), there is no way out. It is either…or. Impossible paradoxes lurk at the horizon, and long and fruitless attempts are made to bring things together.

Aristotle had connected time with movement by stating that time is the ‘number of movement in respect of ‘before’ and ‘after’. The reference to ‘number’ seems to suggest a certain division, or at least a succession or repetition. Plotinus, living in the third century AD, pointed rightly to the circularity in Aristotle’s definition. Time cannot be a number, but what is numbered. Before and after can only exist in time, and should not have a place in the definition of time. The presence of a Number does not give Time. Plotinus therefore placed (in the Third Ennead) Time as something apart, a thing ‘within itself’. A proper comparison (or measurement) of Time-in-itself is bound to fail.

Locke (1632 – 1704), who was earlier encountered in relation to language (p. 41), saw time as the space between (two) ideas: ‘The distance between the appearance of any two ideas in the mind is what we call duration.’ (Essay II, XIV). The ideas have since moved to a humbler levee and are replaced in recent epistemology by ‘sense-data’. This means effectively a move from the dynamic Second to the dynamic Fourth Quadrant, but it still does not throw more light in the nature of time. Nevertheless, the great American psychologist and philosopher William James (1842 -1910), in his book ‘Principles of Psychology’ (1890, Vol. I, p. 642), tried to be more precise. He stated: ‘We are constantly aware of a certain duration – the specious present – varying from a few seconds to probably not more than a minute, and this duration (with its content perceived as having one part earlier and another part later) is the original intuition of time’.

This definition has several attractive sides to it when placed in the light of a quadralectic interpretation. The description consists of four sections: there is a distinct unit (the specious present), which has a subjective time limitation (up to one minute) and can be placed in a sequence (one after another) to provide an intuitive unity (time). The specious present is an idea (Second Quadrant), that takes measurable shape (Third Quadrant) in a sequence (Fourth Quadrant) which leads to an intuition (First Quadrant). James gave in his notion (or definition) of time a complete overview of a quadralectic cycle. Time starts – in human time – in the invisible visibility (II), becomes measurable in the visible visibility (III), is placed in the multitude of the visible invisibility (IV) and finds its ultimate being in the invisible invisibility (I). Time is in every division and type of visibility.

The flow of time and the moment of time are appearances of the same phenomenon, just like there is a river and a drop of water. The conception behind these two ‘types’ is the same: the actual and the becoming are members of the same communication. The German philosopher Martin HEIDEGGER (1889 – 1976) expressed, in his book ‘Sein und Zeit’ (Being and Time; 1927/2010), this opinion. Time is, in his view, not a sequence of temporary moments (now’s), but a temporal spread or field. The future-present-and past (of human existence) are experienced as Ek-sistenz, literally the standing beyond oneself.

The present quadralectic line of thinking follows space (in time and place) from its ‘absolute’ beginning (in the First Quadrant) to its ‘final’ resolution in the multiplicity (of the Fourth Quadrant) and generates in the meantime the playground for comparisons. The specific type of division thinking determines the rules of the game (on that playground). Time and place, either as Kantian transcendental objects or seen as elements of a Heideggerian ontological framework, have to obey to the same rules (of division thinking). Even the empirical and ontic things (the Third Quadrant visibilities) cannot escape that same understanding, although they seem to thrive in an oppositional environment.

Martin Heidegger might have noticed the ‘Fourth Quadrant’ character of time (as a ‘field’) and being, but his stand in the matter of human identity was not neutral. The division between an authentic and inauthentic human existence fits in an oppositional vision (and might indirectly explain his temporary sympathies for the emerging Nazi regime).

The authentic man is aware of the basic possibilities of life (including death) and creates a temporal order by which to regulate present and future. A quadralectic interpretation of this ‘authenticity’ suggests a First Quadrant environment, but the creation of a temporal order can only take place after a division-decision. The uncountable possibilities of infinity (presumably of the First Quadrant) are counteracted by a move to relative safety in the establishment of limitations and partiality of conditions). The responsive projection in time (Entwurf) is essential in Heidegger’s philosophy, because this projection also includes our life as a whole. The authentic and conscious being is one and the same thing, born in unity (of the First and/or Third Quadrant) and geared towards the understanding of multiplicity.

The inauthentic man experiences time as a passive flow, and a formless passing-by. It can either have a frightening speed, sweeping the individual away, or it can be noticed as minutes slowly ticking away. In both cases, the person does not have a firm grip on the passage of time. The environment of multiplicity (flow) points, in a quadralectic interpretation, to the Second or Fourth Quadrant as a place of action. Heidegger judged the absence of conscious limitations as vulgar. Furthermore, the counting (or ‘killing’) of the time is, in Heidegger’s view, objectionable.

These subjective judgements aim to demonstrate the ontological difference between the various natures of Time. It might well be, that Heidegger had a four-fold division setting in mind when he posed the opposition of the authentic (conscious) and the inauthentic (vulgar) man. However, it is unfortunate that he was unable to elucidate his vision in a more accessible way.

William BARRETT (in: GALE, 1968) rightly indicated that the flow of time might also act as the ultimate concept of a primordial temporality. He also noticed that the emphasis shifted, in Heidegger’s later writings, from Time to Being. This gradual move resulted in notions like ‘das Anwesen des Anwesendes’, rendered as ‘the presence of that-which-is-emerging-as-present’. This typical Heidegger-expression tries to cover the essence of concepts (at simultaneous levels in time) in one word. The presence and the process (of presencing) are one and the same if the appropriate position in a communication is chosen.

Barrett also points to the section in HEIDEGGER’s ‘Introduction to Metaphysics’ (1935) where he praises the early Greek philosophers for the absence of a dualism between Being and Becoming. He (Barrett) reinforced his idea that – if there is no dualism – Becoming (and the flow of time) might be equally primordial and basic as Being. This conclusion resembles an effort to place Being and Becoming in one primordial space (identified here as the First Quadrant) in order to dissolve the complicating influences of division.

There is no need for that, although there is also no objection to do it. The absence of dualism (of the early Greek thinkers) does not necessarily involve a move to the Absolute, but can also be explained from a cognitive position in the (second division of the) Second Quadrant (II, 2), i.e. before the oppositional forces of the Third Quadrant become active. Being and Becoming are, in that situation, just ideas at an early stage of the fragmentation process, seen as ‘pure’ items in a realm of higher division thinking, without the direct interference of oppositional tendencies.

The two most prominent human inventions to conquer place and time – in order to make a fundamental comparison possible – are the map and the clock. Both items have a long history running from the 12th century BC Egyptian map of the gold mines to aerial photography and from the ancient sundial to the atomic clock. The mappae mundi and most of the mediaeval maps have their symbolic and exegetic character in common. Most of them were made to glorify the Lord rather than being of any help by finding a route on earth. This mental setting was well understood by Hugh of Saint Victor (ca. 1097 – 1141) when he defined the symbol as ‘ a collecting of visible forms for the demonstration of invisible things’ (LADNER, 1979).

The discovery of the world – from a European point of view – and the subsequent growing importance of map making gained momentum from the beginning of the fourteenth century onwards (HARLEY & WOODWARD, 1987). The so-called portolan maps (‘from port to port’) were produced by sailors of the Mediterranean and Black Sea and reached a great accuracy. ‘The portolan maps of the beginning of the 14th century are as good as those from the 16th’ (HAPGOOD, 1966/1979; this author believes that the origin of the portolanos must be found in a culture with a higher level of technology than was obtained in medieval or ancient times. His speculative thoughts, including a ‘lost continent’ (Antarctica) and a vanished worldwide civilization, have never fully convinced the scientific community).

Fig. 55 – This symbolic world map was given in the ‘Rudimentum novitiorium’ and printed by Lucas Brandiss in Lübeck in 1475.

The art of map making kept pace with the geographic discoveries, which followed each other in rapid succession from the end of the fifteenth century onwards. The symbolic four-fold world map in the ‘Rudimentum novitiorium’ (fig. 55) was one of the last examples of a conceptual map. It was printed as a guide for young clerics and not intended for practical use. The Paradise and the four rivers are drawn at the top (east) to indicate a close relation with the heaven. Rivers run all over the world and leave most countries as islands or mountains. The ‘Pillars of Hercules’ are drawn in the very west (occidens), at the bottom of the picture.

Hans Holbein the Younger produced, little more than half a century later (in 1532), a fairly comprehensive world map (the ‘Typus Cosmographia Universalis’), which showed a round earth. The Flemish-born Gerardus Mercator (1512 – 1594) was the first to use the term ‘atlas’ for a collection of maps. The map projection, which bears his name, was first deployed in 1569. His friend Abraham Ortelius (1527 – 1598), also working in Antwerp, published a year later his ‘Theatrum Orbis Terrarum’ (Theatre of the World) which is considered the first true atlas consisting of a collection of uniform map sheets. Earlier map books (after ca. 1400) were based on the work of Claudius Ptolemy, whose ‘Geographia’ was a compilation of (Greek) geographical knowledge around the second century AD.

German world map of Ptolemaeus. Geographia, c. 1490, Nuremberg. Unknown source.

The history of clocks shows a remarkable parallel to the one of map making. Different types of clocks were known from ancient times, like the water clock and sundial, but the appearance of mechanical clocks on a large scale (in Europe) started at the beginning of the fourteenth century.

Daniel J. BOORSTIN (1983) pointed to the impact that was caused by the change in the idea of duration from a gradual flow of a shadow across a dial, or water running from a bowl, to a mechanical clock with a hammer and a bell. ‘The needs of mechanical timekeeping, the logic of the machine itself, imposed a new feeling. Instead of being synonymous with the repeated cycles of the sun, which varied as the cycles of the seasons commanded, or with the shorter cycles of other flowing media, time now was to be measured by the staccato of a machine.’ (p. 38).

The invention of the pendulum clock by the Dutch scientist Christiaan Huygens (1629 – 1695) around the year 1650 was the pinnacle of a Zeitgeist, which was obsessed by finding the limits of partitioning.

The distinction of logarithms (by John Napier) and the creation of a logarithmic scale (by Edmund Gunter in 1620) were the visible results of that same quest, born in a spirit of oppositional thinking pushed to its limits. Now, more than three-and-a-half centuries later, the clock has reached an incredible precision by the fitting of a quartz or cesium atom to give the intermittent signal. Boorstin’s staccato has silenced.

The CF-graph combines, in many respects, the intentions of cartography and the clock in one drawing: it gives a standard for a specific division of infinity. The maps and the clockworks are the products of a division of real place and time, while the CF-graph sets a standard for the virtual division of time and place. Any form of subsequent visibility, after the acceptance of the communication factor (CF) as a yardstick, is subject to the regulations of its representation. For instance, the distance on a map (as a comparison between two places) is determined by their coordinates, and the notion of time (as before and after) is measured by minutes or hours. The introduction of the ‘virtual’ CF-graph offers a medium to scale the visible and invisible entities of life and opens up a way of comparison in the boundless of place and time. The keyword is communication, which is more than just reading a map or measuring time. Communication is, in its bare essentials, the understanding of a method of valuation.

A quadrigital computer would be of great help to reach that goal. This type of computer is not driven by electricity, because its expression in a language of one’s and zero’s puts it in an oppositional environment. The new machine has to be powered by a four-fold type of interaction. Present and future inventors will have to think about a tool other than the traditional dual-natured electricity as a medium to reach decisions. It has to include the outcomes of a subjective intervention and has to be found in the realm of a human-psychological transfer. In the end, we might have to look at the invention of a living (bio)computer (in a quadrigital setting) rather than a dead, mechanical one (wired on a digital circuit).

Research in that vital direction started in the 1990’s and was based on the molecular nature of DNA (or deoxyribose nucleic acid), a component of the nuclear material of the cell. The knowledge of the structural setting of the DNA molecule increased rapidly. It opened up insights and possibilities for computational molecular biology. In particular, the chemical bonding and its subsequent genetic coding can be regarded as the most elementary form of (human) communication and is of the utmost importance for the present investigation.

Johann Friedrich Miescher first isolated DNA from cells in open wounds and fish sperm as early as 1869. He called his molecule nuclein, now regarded to be DNA and RNA. The importance of the discovery was not recognized at that time. DNA consists of four types of bases:

——————— Adenine   (A)                             Thymine   (T)

——————— Guanine   (G)                             Cytosine   (C)

The bases guanine (G) and adenine (A) are relative large molecules in which atoms are arranged in a hexagon and a pentagon joined together. The bases thymine (T) and cytosine (C) are small molecules, consisting of atoms of carbon, nitrogen, oxygen and hydrogen, and arranged in a hexagon. The bases of nucleid acids are paired together via hydrogen bonds. Adenine and thymine (A-T) are connected with two hydrogen bonds and guanine-cytosine (G-C) by three hydrogen bonds (fig. 56).

Fig. 56 – The schematic representation of the molecular structure of DNA consists of a central component with four nitrogenous bases, arranged along a sugar-phosphate backbone in a particular order (the DNA-sequence).

Griffith first discovered the process of exchange of genetic material or transformation in 1928. Crick and Wilkens, together with Watson, proposed the double-helix structure of DNA in 1953. The replication mechanism of DNA became evident in 1958: the two parental strands of DNA unwind during replication, as predicted by the model of Watson and Crick.

Coding theorists tried to learn the language of the genes in order to be able to translate the message enclosed in them. The ultimate aim is to crack the genetic code, which carries the units of inheritance from parent to child.

Arrays are used to analyze a sample for the presence of gene variations or mutations or for patterns of gene expression. Thousands of immobilized DNA sequences can now be presented on a miniaturized surface. Laser lithographic processes help to read the bio- (or gene) chips.

A future quadrigital computer might use these sequences to find answers to quadralectic problems. It will be a giant step further – from a philosophical point of view – than the present digital computers, which are based and programmed to the positive and negative qualities of the electric current.

It is important to notice the formal method, which is used in this investigation. The cogent results of gene research are obtained in a process of comparison, which is not unlike the way the CF-graph was generated. Strings of DNA are compared to each other over a given length, and the degree of analogy is measured. The difference with the ‘classical’ type of measurement must be noticed here. This latter type uses a given length (say a ruler or measuring tape) and compares a standard length with other extensions. The result is a certain figure of multiplication (of the original standard). The measurement of DNA strands deals with the degree of analogy between shared restricted fragments. The ‘standard’ is not a given entity, but is created in the process of comparison, in the same way as (two) four-fold divisions shift along each other and generate a new measuring system.

The commercializing in biotechnology started in the 1980’s and the ‘Human Genome Project’ followed in 1990 in order to find all the genes on every chromosome in the body and to determine their biochemical nature. The results generate an enormous increase in knowledge at this point, but also pose new questions. If a precise location (of a certain human feature) can be found, then the subsequent doctoring of this position is the next step in line. This action might be accepted to eradicate deadly diseases, but does the bug stops there? The future of knowledge is an uncertain one.

 

5.1. A cosmic comparison

The history of astronomic discoveries provides, seen as a whole, an insight in human observation. The early attention of mankind to the heavens was guided by a fear for the gods, who were supposed to live in the firmament. In general, it could be said that the initial stage of looking to the sun, the moon and the stars had a static character: the heavenly bodies and space represented a timeless existence, which was associated with the invisibility of the gods.

Certain dynamic ideas about the earth and the sun and their relation as physical bodies in the sky developed in an early age. The Babylonians in Mesopotamia (around 2000 BC) were imaginative in their interpretation of the stars and their role in an astronomical system. Their creation epic, the Enuma Elish (When Skies Above), was written on a clay tablet in cuneiform (i.e. wedge-shaped) symbols, started off with a description of the beginning:

 ——————–  When skies above were not yet named

———————  Nor earth below pronounced by name,

——————— Apsu, the First One, Their begetter

——————— And Mummu Tiamat, who bore them all,

——————— Had mixed their waters together,

——————— But had not formed pastures, nor discovered reed-bed,

——————— When yet no Gods were manifest,

——————— Nor Names pronounced, nor destinies decreed,

——————— Then Gods were born within Them.

The Babylonians were skilled astronomers. They developed the number system of the Sumerians (a culture which flourished before 3500 BC) to provide the mathematical background for the calculations of the heavenly bodies. Their sexagesimal system, with a base of 60, resulting in hours of 60 minutes and minutes of 60 seconds, is still in use today.

The Ancient Greeks were the first to ponder about a cosmological model of the heavenly bodies. Practical knowledge of the stars had been available for a long time. The poet Hesiod, living around 700 BC, described the farmers life in a poem called ‘Works and Days’. Demetrius Chalcondyles printed the first edition around 1493. The complete works were published by Aldus Manutius in Venice in 1495. Hesiod was aware of the rising and setting of constellations in order to start certain agricultural actions:

But when Orion and Sirius are come into mid-heaven,and the rosy-fingered Dawn sees Arcturus, then cut off all the grapes-clusters, Perses, and bring them home. Show them to the sun ten days and ten nights: then cover them over for five, and on the sixth day draw off into vessels the gifts of joyful Dionysus.

The physical properties of the stars (and their positions) were, in the Greek way of thinking, subordinate to an idea and their ultimate significance was found in an abstract configuration. The position of the stars was imagined as lying on a celestial sphere, which rotated about the spherical Earth every twenty-four hours. This idea provided a psychological framework, which consciously accepted the partly subjective nature of its observations (in order to reach a state of beauty).

The mathematician Eudoxus of Cnidus (Asia Minor), who lived from 408 to 355 BC, build an observatory in his birthplace and another one near Heliopolis (in Egypt), just to develop an ideal planetary theory. Two works on the results of the observations on the rising and setting of stars, the ‘Mirror’ and the ‘Phaenomena’, have now been lost. His most famous book ‘On velocities’, in which he developed a system of homocentric spheres to describe the movement of planets, is also not preserved. Aristotle handed down the particulars (of the complete system with twenty-seven spheres) in his book ‘Metaphysics’. A subsystem of three spheres was set into a fourth sphere to enable the description of the daily rotation of stars.

Eudoxus’ theory was influenced by the philosophy of the Pythagoreans through his teacher Archytas, who was a follower of Pythagoras. It is likely that Eudoxus regarded his ideas of the spheres in terms of an abstract geometrical model rather than a description of the physical world (like Aristotle did).

Eratosthenes of Cyrene (276 – 194 BC) was a librarian at the famous library of Alexandria. He came up with more solid results. He measured the distance to the sun as 804.000.000 stadia and the distance to the Moon as 780.000 stadia. The length of the circumference of the Earth was established as 250.000 stadia, using an inventive system of comparison between the shadow of a pole (obelisk) of a given length at Syene (now Aswan) and Alexandria. The accuracy of these values depends on the length of the stadium, but are still fairly near the mark if a value of 157.2 meter is used (as deduced from values given by Pliny).

At about the same time Archimedes (died 212 BC) discussed in his ‘Sand-Reckoner’ the way to represent very large numbers. He posed the problem of the counting of all the sand grains in the universe. To complicate the matter, he did not choose a geocentric setting, which was accepted at the time, but a heliocentric cosmos as proposed by Aristarchus of Samos (ca. 310 – 230 BC). The idea of an earth out of the center was therefore known long before Nicolas Copernicus’ (1473 – 1543) publication of ‘De Revolutionibus Orbium Coelestium’ in 1543 put the sun in the center again. It still took nearly a century (and a proper telescope) before Galileo’s ‘Dialogue Concerning the Two Chief World System’ (1632) had the scientific minds turned away from Aristotle’s fixed earth.

The Greek astronomer (Claudius) Ptolemy, living in Alexandria from around 85 – 165 AD, was perhaps the most influential in the history of astronomy. His book, called the ‘Almagest’ (corrupted from the Arabic, meaning ‘the greatest’), was written around 140 AD and is a treatise in thirteen books. Book I gives a broad outline of the geocentric plan of the solar system. Book II deals with the trigonometry of the stars. A star catalog (based on that of Hipparchus, 129 BC) is given in book VII and VIII.

The scientific text of the ‘Almagest’ was, together with Euclid’s ‘Elements’, historically the longest in use. Ptolemy’s representation of the world and the sky was a model using circles (and circles upon circles, so-called epicircles) around a fixed Earth. These universal attributes (a point and a circle) made his model acceptable to all types of division thinkers, and might explain the long period of its acceptance.

The general acceptance of Ptolemy’s geocentric model came to an end when the dual way of thinking reached an all-time high during the sixteenth and seventeenth century in Europe. The concentration on antagonism (of earth and cosmos) either led to nowhere (in the speculative thoughts about the infinity of worlds by Giordano Bruno) or to the acceptance of a new cosmic reality (by Copernicus and Galileo). The rigorous limitations in the number of initial divisions in a communication created a focus on identity (in the social realm) and facts (in the scientific domain). The socio-political implications were sorted out in a considerable number of revolutions and wars (ASTON, 1965).

The idealistic cosmology (of Ptolemy), partly grown on the fertile subjective soil of higher division thinking, was superceded by a heliocentric cosmos, based on objective facts. Copernicus still retained the circular motion. Johannes Kepler (1571 – 1630) assumed, in his book ‘Astronomia Nova … de Motibus Stellae Martis’ (Prague, 1609), an elliptical motion of the planets. The slight aberration in the orbit of Mars, as already meticulous recorded by Tycho Brahe (1546 – 1601), provided the vital evidence for the rejection of the cyclic motion of the planets.

Further conformation of an unstable universe came to light in November 1572, when the Italian mathematician Francesco Maurolyco (1495 – 1575) discovered a ‘new’ star in the configuration of Cassiopeia. This supernova was also seen by Tycho Brahe and later described in 1574 (fig. 57). It had the brilliance of Jupiter and could be seen in daylight for about two weeks. The ‘Stella Nova’ subsequently became to bear his name.

Fig. 57 – The position of the ‘Stella Nova’ (I) as seen in 1572 by the Danish astronomer Tycho Brahe. The appearance coincided with a new awareness of motion in the communication with the universe.

A cosmic phenomenon of special interest to the present study is the shift in brightness of a certain class of variable stars. The discovery of the variable stars started with David Fabricius (1564 – 1617) in the year 1596, when he detected a star of non-equal brightness. He observed the star Omicron Ceti, located in the constellation of Cetus (the Whale). The brightness varied from a magnitude of two to be virtually too dim to see. The period of variation was about eleven-month. Mira (‘wonderful’), as the star was subsequently called, is a red super giant, pulsing by inner actions.

This observation of new stars, like the ‘Stella Nova’ (supernova) of 1572 and 1604 (the latter named after Kepler), comets and stars with variable brightness did not fit into the scientific belief of the time. The universe was regarded to consist of fixed stars, which remained steady and unaltered. Due to this fact, it lasted more than seventy years before the Italian polymath Geminiano Montanari (1633 – 1687) discovered another variable star. He noted in 1670 that the second brightest star in the constellation of Perseus (beta Perseï) was changing in light intensity (fig. 58).

 

Fig. 58 – The graph of the light intensity of the eclipsing binary of Algol in the configuration of Perseus (beta Persei) is derived from the four stages in the position of a small star circling the large star.

The star Algol became the best-known example of the eclipsing binaries, in particular, after the astronomer John Goodricke, again some hundred years later, calculated the period of Algol to 68 hours and 50 minutes.

The eclipsing binaries are part of a class of variable stars (or ‘variables’) which have their variation in brightness in common. However, the causes of the variability might differ considerably (and the eclipsing type is only a small minority). About thirty thousand are now known, and many more are to be discovered. In fact, most stars, including our own Sun, vary in brightness if measured in great detail. Some display regular variations of light intensity, while others lack any particular pattern.

The most famous example is the star Altais or Delta Cephei, a pulsating variable in the constellation of Cepheus, discovered by John Goodricke. He calculated its period to 128 hours and 45 minutes. The super giant has nearly completed its life cycle (by using the majority of the hydrogen thermonuclear energy). The change in brightness is due to an interaction between gravity and radiation. Delta Cephei became the prototype of the so-called Cepheid variables. This kind of stars became later the major players in the quest for the boundaries and age of the universe.

The English astronomer John Goodricke (1764 – 1786) was born in Groningen (northern Netherlands) as a son of a British diplomat and a Dutch merchant daughter. He was born deaf-mute, but learned to read lips, to speak and use an early method of sign language. His parents send him to Edinburgh for further education. As a seventeen-year-old boy, while living in Yorkshire (England), he began watching the stars and in particular, the star Algol. He noticed during his observations of this star a regular loss of a full magnitude of brightness.

The young astronomer reported his findings in 1783 at the Royal Society of London. Two theories were brought forward as an explanation: either a dark body periodically occults a distant sun or the star itself had a darker region that faced the earth periodically. The first theory, which was the right one (but could only be proven in 1889), made him the first discoverer of occultating variable stars. Goodricke was admitted to the Royal Society in April 1786, but he could not recognize this honor anymore, because he died that same month in York by pneumonia.

Algol (or beta Perseï) is a multi-star system in the configuration of Perseus, some ninety-six light-years away with a massive, bright central star and an orbiting secondary star with a yellow-red color. The later one circles around the central star in an orbit, which was nearly edge-on to the Earth. Light from the main source is taken away when the orbiting star passes in front of the main source. The decrease in brightness is less if the orbiting star is at the backside of the central star. A third star (and possibly more) orbits the double star system of Algol, but its influence on the brightness is only slight, with a change in the spectrum over a period of 1862 years.

An eclipsing binary is – in general – a double star oriented so that the two stars alternately pass in front of each other. The variation in brightness is called a light curve and exhibits two depressions and a shallow one in the middle (fig. 59). The recline is caused by an eclipse of the bright star, while the shallow one is the result of an eclipse of the dim star. A full period is the distance between two deep depressions. The depth in the curve also depends on the angle of the orbital inclination (zero degrees is edge-on).

Fig. 59 – The graphs of the light intensity of various variable stars. The vertical axis gives the sum of the brightness, the horizontal axis the change in time. One period covers the full cycle of a Small Star circling around a Large Star, starting in a position when the Small Star is right in front of the Large Star.

The movement of the orbiting star (a period) can be broken down in four particular stages, which represent the ultimate positions in brightness:

1. The Small Doublestar is positioned right in front of the Large Doublestar. The Small Doublestar ‘blackened’ the Large Doublestar as a matter of speaking, resulting in a diminishing of the total light intensity for the earthly observer;

2. The Small Doublestar moves to the right and ‘dissolves’ from the Larger Doublestar. The collective light intensity of the two stars reaches a maximum for an observer on earth;

3. The Small Doublestar disappears – for the observer – behind the Great Doublestar. Again, some light gets ‘lost’, but since the Small Doublestar contributes a fraction to the total of light intensity, and the diminishing luminosity is only marginal;

4. The Small Doublestar reappears behind the large Doublestar and again, the maximum collective light intensity is reached. The situation is a mirror image of stage two.

The graph may differ in detail, depending on the form and behavior of the Small Star, looping around the Large Star, but the structural setting remains the same: a large depression, a saddle, a small depression, a saddle, and a large depression. A period is measured between the two largest depressions, i.e. as the Small Star is right in front of the Large Star and causes the maximum loss of light. These features bear a remarkable resemblance to the visibility period X in the CF-graph (as pictured in fig. 45 and in more detail in fig. 51).

The similarity between the graph of the light-intensity of the ecliptic double stars (like the star Algol) and a part (X) of the CF-graph is not a coincidence. In both cases, it concerns the movement of two units passing each other in a cyclic setting. This movement can be divided in four phases. The double star derives the quadruple division from the geometric positions, while the abstract four-division consists, by definition, of four quadrants. The graphic results of the change in light intensity (of certain binary stars) and the depiction of the shift between two four-divisions are similar because their major premises are the same: a Small and a Large Part occultating in a circular setting.

The understanding of the quadralectic intensity (as expressed in the degree of commensurability in the CF-graph) may be enhanced by looking at the discoveries made in astronomy, with regard to a visibility-in-general and the conceptual position of ‘Observation-point Earth’ in the huge universe. The keyword in the search is an understanding of distance, not measured in a static comparison, but in a dynamic shift.

A special tribute must be given here to Henrietta Swan Leavitt (1868 -1921). She graduated from the Society for Collegiate Instruction of Women (later Radcliffe College) and joined the Harvard College Observatory as a volunteer in 1895. She was appointed to the permanent staff in 1902 and later became head of the photometry department (fig. 60).

Fig. 60 – The American astronomer Henrietta Leavitt (1868 – 1921). She discovered the Cepheid variable period-luminosity relationship. Photo: AAVSO/ American Association of Variable Star Observers.

The variable stars (of the delta Cephei type) of the Small Magellanic Cloud had her special interest. The discovery (in 1908) of the relation between the length of a cycle (period) and its average brightness (its luminosity as observed from earth) can be regarded as a major breakthrough. She found that the longer the period, the brighter the star. Large, bright Cepheids pulsate over a longer period, just as large bells resonate at a lower frequency (or graphically seen as a longer period). A circular (no. 173; March 3, 1912) of the Harvard College Observatory (under the direction of Edward C. Pickering) pointed towards the difficulties of obtaining the data:

‘A Catalogue of 1777 variable stars in the two Magellanic Clouds is given in H.A. 60, no. 4. The measurements and discussion of these objects present problems of unusual difficulty, on account of the large area covered by the two regions, the extremely crowded distribution of the stars contained in them, the faintness of the variable, and the shortness of their periods. As many of them never become brighter than the fifteenth magnitude, while very few exceed the thirteenth magnitude at maximum, long exposures are necessary, and the number of available photographs is small. The determination of absolute magnitudes for widely separated sequences of comparison stars of this degree of faintness may not be satisfactorily complete for some time to come. With the adoption of an absolute scale of magnitudes for stars in the North Polar Sequence, however, the way is open for such a determination.’

The distance of a Cepheid can be calculated from its period (the length of its cycle) and its average apparent brightness. Miss Leavitt published her findings in the above-mentioned circular with a chart of twenty-five Cepheid periods and their apparent brightness. Later, she calibrated the photographic magnitudes of forty-seven stars to which all other stars could be compared.

The observation of a Cepheid’s variation in luminosity over time will give an average apparent luminosity. The apparent luminosity decreases as the light travels longer. In theory, it falls off in proportion to the square of the distance to the object. The apparent luminosity can be compared with an absolute luminosity (that is, the apparent brightness the star would have if it were a standard distance of 10 parsecs away). The ratio of its absolute brightness to its apparent brightness will give an indication of its distance.

This method of cosmic distance-calculation has a strong resemblance, at least as a theoretical method, with the generation of CF-values in the quadralectic domain.

Once the relation between the period and luminosity was established these stars became distant markers for galaxies and offered the first hint for the distances within the universe. It became the ‘yardstick to the universe’, used by Edwin P. Hubble (1889 – 1953) and others to shape their view of the universe. However, there are some problems in the method. The dust between stars, for instance, can diminish the apparent luminosity and the chemical composition of the Cepheids might also influence the brightness. Therefore, some secondary distance indicators were developed, which use the Cepheid distance scale to calibrate. The study of a special category of supernovae, which show catastrophic explosions signaling the death of certain low mass stars, might give further answers. Furthermore, the measurement of the brightness and rotations of velocities of entire spiral galaxies (the Tully-Fisher relation) can hold a clue. The high luminosity galaxies (or the Large Part) have more mass than low-luminosity galaxies (the Small Part), and so the bright galaxies rotate slower than the dim galaxies. The relation of the velocities of the communication partners might give a theoretical shift-pattern, which can be used to measure distances.

The eclipsing binaries, or rather their physical setting, gained interest in the beginning of the twentieth century when their potential was recognized. The principle of a (slight) decrease in light intensity due to the passing of an object in front of a star, became the very condition for finding new planets orbiting other stars. The idea that the earth would be the only planet around a star (the sun) in a Milky Way galaxy consisting of hundred billion stars seems very unlikely.

Harlow SHAPLEY (1958) summed up the arguments in his popular work ‘Of Stars and Men’. The discovery that the nebulae are actually galaxies of stars meant that there are ‘more than one hundred million million million sources of light and warmth for whatever planets accompany these radiant stars.’ Also the average density in the expanded universe must initially have been much greater and therefore, collisions of stars and gravitational disruptions happened more often: ‘at that time countless millions of other planetary systems must have developed, for our sun is of a very common stellar type’ (DICK, 1998).

John Gribbin’s conclusion that ‘it may, indeed be not only possible but likely that life exists on other planets circling other suns’ – as quoted here in the beginning of this book – offers a daring prospect. The key to their discovery lies in the geometrical characteristics similar to an eclipsing binary, which cause small fluctuations (perturbations) in the light intensity curve. Many stars may, in fact, have planets circling around them.

The search for new planets has been fairly successful recently, and the latest count of Sun-like stars with perturbations, pointing to a body orbiting them, is out of date the moment it is published. These structures reveal a staggering variety in size, distance, revolution time and shape of the orbits. Several extrasolar planets are at least three times as massive as Jupiter, which is the largest planet in our solar system. Known physical laws seems to break down when such large planets (‘hot Jupiters’) are formed in the proximity of their intense hot mother star. The migration theory suggests that they arrived from elsewhere and might be on a collision course.

In particular, any relative smaller planet, like the earth, is – as yet – difficult to detect around a far-away star. Michael Mayor and Didier Queloz of the Geneva Observatory in Switzerland found the first earth-like planet in 1995. They used the Doppler planet-detection technique to discover a ‘telltale wobble’ in the spectrum of 51 Pegasi in the constellation of Pegasus. The orbital period of the planet – our ‘year’ – was established at 4.2 days. Other research revealed six more planets of which Tau Bootis, 55 Cancri and Upsilon Andromedae are in the same class as 51 Peg. Their orbital periods are 3.3, 14.7 and 4.6 days respectively. It can be expected that more planets will be found soon.

The relation between ‘seeing’ a planet as a wobble in a light intensity curve and the ‘seeing’ of an object (or being) in a cosmic communication poses a great challenge. The ‘absolute brightness’ can be translated in an ‘absolute being’ and this quality is estimated from a period of light change (or intensity change in more general terms). The conclusion can be drawn that the ultimate existence (or being), which has been the philosopher’s grail for such a long time, is found in the reading of an intensity change.

The trail leads to the visibility boundaries of the CF-graph and the interpretation of the inflection points. This action is probably the most important event in the quadralectic philosophy (from an empiric point of view): the use of the CF-graph as a tool in the understanding of life. The transfer of the communication-model from the theoretical Second Quadrant into the practical Third Quadrant is a moment of truth: the ‘wobble’ takes on the life of a real planet.

The actual fact-creating act in this process comprises the definition of two points on the CF-graph. Such a demarcation or imprint is called the point of recognition (POR).

A point of recognition (POR) is a marker point in an exchange of information and is established by an observer in a process of comparison between the visibility in a particular situation and a similar representation on the universal communication graph.

It is a mathematical necessity within the application of quadralectic thinking to know at least two points of the communication graph to be able to project its full course. If two points of recognition (POR’s) are known, then the whole CF-graph is known and the nature of a communication can be known.

These primary choices carry a ‘subjective’ load, but that is typically for the higher stages of multiplicity thinking. The communication partner has to recognize a ‘something’ (a certain type of visibility – not necessarily a visible visibility) and compare the given impression – in a quadralectic analogy-process – with the characteristics of the known universal (CF) graph. These markers, in turn, are not fixed in an absolute sense, but are established in a process of maximum comparison (affinity) with other facts and situations within the known context.

The decision-making process towards the Points of Recognition constitutes the most essential act in a communication. It introduces an empiric structure in the continuous shifting pattern of visibility and provides the outlines for further progress in due course. The practical implications of this approach will be dealt with in the remainder of this book. From this day forwards, there are only calculated and subjective decisions, which will lead us to the boundaries of imagination.

It is worthwhile to learn, before we are carried away in this fascinating world, that certain phenomena in the human history might have had the same function as the CF-graph, i.e. as a tool in the search for a valuation of a particular displacement. The old remains of standing stones and stone circles, which are found over greater parts of Europe, could have been our earliest indicators of a ‘shift’. They will be our next point of interest.

 

5.2. A terrestrial comparison

The previous example of a shift in a communication was taken from light-years away. However, it is not necessary to travel such a long distance to come across circular movements and their interpretation in terms of a displacement. We only have to think of the archaeological stone circles to see the dynamic possibilities of change at work. The best-known example is, of course, the site of Stonehenge near Salisbury in Southern England, build from around 2000 BC in different phases (fig. 61). Many more stone features are known from Great Britain, Ireland and the Continent.

Fig. 61 – Part of the large stone circle of Stonehenge on the Salisbury Plain in England. The stone circle was already mentioned by Diodorus Siculus in his ‘Bibliotheca Historica (II, Ch. 47-48) as ‘a notable temple which is adorned with many votive offerings and is spherical in shape’ devoted to the god Apollo. Many theories of their origin have been posed over the years. Sometimes they are perceived as indicators to cosmic directions and regarded as time indicators. Their function as ritual center is stressed in the present approach.

The traditional explanation of the position of the stones pointed to a relation with cosmic directions. Astronomical alignments were drawn, using the position of the sun and the moon on certain days of the year as time markers. The emphasis is on the position of the stones as ‘calendar stone’, or cosmic clocks, which provided a time for recurrent religious and agrarian activities. Furthermore, their role to predict the seasonal eclipses of the sun and the moon was indicated (HAWKINS, 1973).

The engineer Alexander Thom (1894 – 1985) was a determined and lifelong investigator of stone circles. He believed that the siting of the stones (in Cumbria) was ‘controlled by the desire to indicate the rising or setting positions of the sun at important times’ (THOM & THOM, 1978).

The cardinal points were another point of observation, besides the correlation with calendrical delineation. It was noticed (at the Long Meg stone circle), some two hundred and fifty years ago, that ‘the four stones facing the cardinal points are by far the largest and most bulky of the whole ring.’ Fred R. Coles surveyed between 1895 and 1911 more than thirty Scottish Four-Posters and was the first to realize that these previously unrecognized rectangular megalithic settings were a special form of stone circle (fig. 62).

Fig. 62 – The stone ring of Brodgar (Orkney Islands) is given here on a map by Charles Calder (1929). The feature is one of the many stone circles discovered in Great Britain and Ireland.

This is not the place to criticize these explanations and interpretations, since there can be no conclusive proof of any astro-archaeological construction. Critical observation, preferably without any preconceived ideas, will be of the utmost importance. Aubrey Burl (in: RUGGLES, 1988; p. 197) noted, rightly, that ‘with 365 days in a year and with several opposed pairs of stones in a circle, an enthusiast could construct a megalithic calendar out of almost any ring.’

Burl insisted that only the repetition of comparable alignments and the study of many sites could unveil some of the significance of these features. His conclusion, as an authority on prehistoric stone circles, is clear enough. ‘The lines discovered are never so fine that they could have been used for celestial prediction, but they are consistent enough to show that in Neolithic and Bronze Ages of the British Isles people had an obvious interest in the sun and the moon.’

Stone circle of Avebury (England) (Photo: Marten Kuilman, May 2010).

My opinion is that more attention should be given to the aspect of place rather than of time. That is to say: direction, which was used not (only) to measure time, but had its own importance as the indicator of a position in a general (personal) communication. The stone circle can be seen as a ‘communication-model’, in the widest sense. The geometrical setting was used to solve critical questions, which arise in any communication.

The stone circle gives not only an insight in the relation between cosmos and man, but also between man and his environment, his interaction with other human beings and finally provides the knowledge of the division as an objectification of man himself. The circles – and maybe the long rows of stones like those at Carnac in Brittany as well – might have had the same function as the CF-graph in the quadralectic environment, i.e. a universal slide-ruler for every imaginable and unimaginable situation within a communication to determine a position.

The importance of Time and the whole idea of a ‘calendar’ should, in my opinion, not be over-emphasized. The persistence to draw this aspect in front of our attention tells us more about the priority of the Western scientific researchers in their quest to solve the meaning of the Stone Age buildings and their obsession with time in general. It is questionable if the actual state of mind of the megalithic people, living some four millennia before us – having no other time-conscious than that of the diurnal rhythm and the seasons – was really geared towards the passing of time. It seems more likely, that their main concern in life was focused on their position on this world and universe. Where do I stand? What do I see? Why am I here? That sort of questions must have been inexplicably more important for them (and for us) than the date of the next sun- or moon eclipse.

It is imaginable that the stone circles were used in the same way as churches have been over the ages: as places of (personal) worship and orientation. BURL (1988, p. 2) put it as follows: ‘Each community built its own ring, sometimes with the assistance of neighbours. It was accepted that four stones were needed, but, after that, not only did each region differ in its architectural foibles but each group within the region also differed in the features it chose to incorporate or to exclude in its own monument’. The physical position (in the field), in combination with the conscious experience of a cyclic motion (walking around the stones) might have given some spiritual and/or ritual experience. If the stones were valued, in one way or another (in reference to their shape), it is imaginable that a calculation could be made in relation to one’s position inside or outside the circle (or row) (fig. 63).

Fig. 63 – A hypothetical stone circle and its function as a place of terrestrial worship. The positions outside the circle (P1 and P2) can be valued (encircled) according to a line of sight. It is obvious that the positions, and the ‘valuation’ can vary endlessly.

The stone circles as a universal means of worship and orientation in the widest sense, should be further investigated. The stone circle (and possibly also the enigmatic elongated rows of stones in Brittany) could be an ancient measure of communication. Not an astronomical clock (highlighting some cosmic event), not a compass (to give a linear direction in space), but a real item for measuring the human mind in its interaction with the surrounding earth. The stone circle might have been a genuine ‘communication machine’ at the center of an ancient worship.

A particular physical position (or viewpoint) outside the circle would result in a specific lining-up of rocks. This line can produce a ‘value’, and gives a clue for that position. With some imagination even a variation of the children’s game of Blind Mans Bluff can be proposed. The generation of a ‘shift-figure’, very much like the CF-values in the quadralectic approach, might be a convenient explanation for the occurrence of so many megalithic stone circles. This rather down-to-earth solution of the archaeological puzzle is probably just as plausible as the, often wildly speculative, cosmic explanations for the many outstanding relics of early communication.

 

 

 

 

6. To the boundaries of imagination

The foregoing comparisons show, if nothing else, that the notion of time and place is connected to the ability of an observer to create a frame of reference. The Neolithic man around the stone circle and the modern astronomer looking at the period-luminosity relation of a Delta Cephei star have their belief in certain basic assumptions in common. Both individuals know that communication is a scheme based on division and movement, and that visibility is the result of a valuation that combines both fields.

The understanding of a communication as a complete tetradic cycle points the way to a fresh vision. History is not only a matter of past, present and future, but also of the awareness of the valuation mechanisms derived from its division. That knowledge makes all the difference in the world. Tetradic history – which means the description of general history in a quadralectic perspective – is fundamentally different from an outlook based on lower division thinking. The main distinction lies in the addition of a personal involvement in the observation right from the start.

Writing a quadralectic history, from the origin of the universe to our own existence on earth, is the ultimate challenge for a human being. It is a great thought to be part of a history, knowing that our personal contribution does matter. Because, at the edge of imagination, we know that history is written in the language of our own understanding.

The problem of a sudden widening of view, with all its implications in the natural field, is not new. The Greek philosopher Epicures, living in the fourth century BC, believed in an infinity of worlds, meaning other ordered systems beyond the visible universe as it was then conceived. His outlook clashed with the general accepted ideas of Aristotle, who regarded the earth as the center of the universe. The Italian intellectual Giordano Bruno (1548 – 1600) held a similar view on the plurality of worlds:

‘This space in which is our world would without it be indeed a void, since where the world is not, there we must infer a void. Beyond our world then, one space is as another; therefore the quality of one is also that of the other; wherefore too this quality cometh to action, for no quality is eternal without action, and indeed it is eternally linked to action or rather is itself action, for in eternity there is no distinction between being and potential being (nor therefore between action and potential action).’ (Seventh argument of the First Dialogue in his ‘De l’infinito universo e mondi’ (On the Infinite Universe and Worlds, published in 1584; PETERSON, 2000).

Bruno proclaimed the inconsistency of sense perception. ‘Sense is no source of certainty, but can attain thereto only through comparison and reference from one sensible percept to another, from one sense to another, so that truth may be inferred from diverse sources.’ The Italian scholar was also against Aristotle, because he had made other choices in the world of two-division, which led to the central place of the earth in the universe. He pitied him for his inability to grasp ‘profound magic’.

Bruno’s ideas were such a threatening prospect at the time, that he ended up at the stake in 1600 AD.

The European intellectual history faced half a century later a new challenge on the chronology of the earth. The Biblical story, with its sacred history based on the Mosaic chronology, came to a total of 5617 years for the age of the earth. Problems arose when the duration of the Egyptian and Chinese histories became known. The continuous study of the profane history unearthed wisdom, which was more ancient than the Mosaic one. The conclusion seemed inescapable, namely that the oldest history was not in the Bible. The authority of the Book was put in jeopardy – in particular for those fixed in an oppositional frame of mind. The Dutch philosopher Isaac Vossius (1577 – 1649) added some 1440 years to the (Christian) calendar in order to turn the tide. However, his efforts did not suffice.

Another professor in Leiden named Georg Horn caught – in his ‘Dissertatio de vera aetate mundi’ (1659) – the spirit of oppositional thinking. He stated the question in a black and white way: ‘either you admit that the various chronologies are all the work of the Devil and you refuse to take them into consideration, or you try to discern what, and how much, is fabulous in them’ (ROSSI, 1984; p. 158). This same professor Horn, by the way, was mentioned by Oswald Spengler in the epoch-making book ‘Der Untergang des Abendlandes’ (The Decline of the West) as the first one to introduce the term ‘mediaeval’ in the year 1667 (SPENGLER, 1917/1927).

Further thoughts on the embarrassing fact that there must have been people living before Adam were elaborated by the French Protestant Isaac Lapeyrere (1596? – 1676) in his book ‘Prae-adamitae’ (1655). The popular preacher Edward Stillingfleet (1635 – 1699), who became the bishop of Worcester in 1689, researched the origins of the universe in his book ‘Origines sacrae’ (1662) and made the following hypotheses:

1. The world existed from all eternity (Aristotle),

2.  The world was created by God, but matter existed from eternity (Stoics),

3. There is no eternity of the world, but there is a chance combination of atoms (Epicureans),

4.  The mechanical laws rule the motions of matter (Descartes).

 The real authority on the subject of sacred chronology (and geography) was the French bishop Pierre-Daniel Huet (1630 – 1721; almost ninety-one years old). He was, according to ROSSI (1984), ‘a master in the undertaking to draw all of profane history together into the single course of sacred history’.

The trend towards a wider time conscience was firmly set. The publication of a book called ‘Telluris Theoria Sacra’ (The Sacred Theory of the Earth) in 1681 (in Latin) and 1684 (in English) by Thomas Burnet (c. 1635 – 1715) gave the subject of cosmogony a ‘scientific’ foundation. His speculative ‘sacred’ theory dealt with four phases in the (re) shaping of the surface of the earth:

——————— Creation

——————— Deluge

——————— Conflagration

——————— Consummation

The present position of the earth was – as one might expect of a dualistic thinker – right in the middle of the process. After the Deluge followed the Conflagration, with the sun as an active agent in the drying out the planet. This process was still going on now. Thomas Burnet can be seen, with some imagination, as the first visionary, who drew attention to global warming!

Burnet was convinced that the terrestrial globe had changed considerably since God created it. The primeval earth had a flat and smooth surface, like an eggshell. Underneath the surface were subterranean waters. A world-wide deluge was explained by the pouring out of these waters over the earth and seen as the breaking up of ‘the fountains of the great deep’. When the floodwaters had retreated into internal caverns, the earth had become ‘a gigantic and hideous ruin… a broke and confused heap of bodies.’ Burnet had an interest in the overpowering aspects of nature and looked at the material world in terms of a historical development.

Bernard de FONTENELLE (1657 – 1757; his age indicate that the study of history is not an unhealthy pastime after all) played a formative role in the conception of human history. This French scholar became known from his one liners (Quotations) like ‘Toute la philosophie n’est fondée sur deux choses: sur ce qu’on a l’esprit curieux et les yeux mauvais’ (Science originates from curiosity and bad eyesight).

His book ‘Entretiens sur la pluralité des mondes’ (A Plurality of Worlds, 1686) pointed directly to the insignificance of man in relation to the physical existence of the earth. He followed the earlier suggestions by the Greek philosopher Empedocles, the French bishop Nicole Oresme and Giordano Bruno that our world might be one of many possible inhabited worlds.

The discovery of time in nature is an important phenomenon in the history of division thinking. It is a widening of view (and sparking of imagination) due to a reduction. The idea of aging and a slow corruption of the world originated in oppositional thinking: the good and the bad were applied to everything, including the earth itself. It meant that God – as the deputy of the Good – was shifted back in time, because it took a long time for the world to deteriorate.

Some ‘geological’ works were known from classical times, like Aristotle’s book on the ‘Meteorologica’ and Theophrastus’ treatise ‘On Stones.’ Pliny’s ‘Natural History’ offered a range of practical knowledge of the earth (ADAMS, 1938). It was used by many medieval scholars. The ‘Etymologies’ of Isidore of Seville (570 – 636) and the encyclopedias of Neckam, Bartholomew the Englishman and Vincent of Beauvais were employed as sources of general knowledge, including the spiritual power of rocks. Books on natural history, like Conrad von Megenberg’s ‘Book of Nature’, several ‘Herbals’ and the ‘Hortus Sanitatis’ provided the knowledge of nature.

Lastly, the ‘Lapidaries‘ have their own place as early works on the earth science. Major writers were Marbodus (Bishop of Rennes, died in 1123), Petrus Hispanus, a Portugese physician, who was probably also Pope John XXI (FORBES, 1963), John de Mandeville (Le Grand Lapidaire), Camillus Leonardus (Speculum Lapidum, The Mirror of Stones) and Anselmus de Boodt (1550 – 1632; Gemmarum et Lapidum Historia). Their books described precious stones and gave an overview of the medical and/or talismanic properties of the rocks. Wonderful stories and local lore were components of these works. They had these fabulous characteristics in common with the so-called ‘Bestiaries’, compendiums of (mythical) animals.

Fig 64 – An illustration of the search for traces of the Deluge in the Swiss mountains. The Swiss naturalist Johann Jakob Scheuchzer (1672 – 1733) is portrayed here by a pile of fossils, which – in his view – were formed during the Biblical Deluge. An etching from his book ‘Museum diluvianum’, published in 1716.

It was at the end of the seventeenth and the beginning of the eighteenth century (of the European cultural history) that the larger fossils were first ‘seen’ as the markers of some sort of event – in general concerning the Biblical deluge (fig. 64). Before that era, rocks were mostly cherished for their practical purposes (in mining) and used for their magical or healing properties.

The Swiss medical doctor and naturalist Johann Jacob Scheuchzer (1672 – 1733) was in this respect a key-figure on the edge of the latest under-standing of nature. He was born in Zürich, stemming from one of the leading families in that town (his father was a successful physician). After schooling in Altdorf (near Nuremberg) and in Utrecht, he received his M.D. in 1694. His interest in the mountains never wavered during his study in the Lowlands and after his graduation, he spent several months exploring the Alps.

After his journey and a failed attempt to study astronomy and mathematics in Nuremberg, he became assistant municipal physician and supervisor of the orphanage in Zürich. This Swiss town was ideally situated for further exploration in the surrounding mountains. The municipality supported him in 1702 with money for his excursions, which took place summer after summer. His ‘Itinera per Helvetiae alpinas regiones’ (1723) gave the details of his travel, anecdotes, oddities, and antiquities.

The Terrible Head in the Valley near Milcorath. St. Gallen, Stiftsarchiv, Handschriften der Abtei Pfäfers, Cod. Fab. XVI, 92rb. Das furchtbare Haupt in dem Tal bei Milcorath.

For instance, chapter five of the book, with details of the 1706 voyage, dealt with alpine dragons. He produced eye-witness accounts in the various cantons, with dates and times of encounter as well as the names and professions of the witnesses. The book fitted in a large number of travel guides published in that (Baroque) period, but the novelty was in the systematic approach. It became a reference book for later travel writers, like another ‘classic’ from the Swiss mountains written by Johann-Georg Altmann, called ‘L’Etat et délices de la Suisse’ (published in four volumes in Amsterdam in 1730).

Scheuchzer became a member of the Royal Society in London in 1708 and continued his extensive scientific correspondence. The Society – including Isaac Newton, who contributed twenty pounds – supported him in the publication of his book ‘Ouresiphoites sive Hinera Tria’. His illustrated masterpiece was the ‘Physica sacra’ (1731/1735), which explained the natural history in the first five books of the Bible. Further historical fame was gathered with the discovery of a presumed petrified human being, the ‘Homo diluvii testis’, or ‘a human being who witnessed the Flood’. This specimen was bought (by Van Marum) from his grandchildren in 1802 and is now in the Teylers Museum in Haarlem (Nederland). It turned out to be the fossil of an amphibian…

Two lines of thinking were developed in the late eighteenth century in relation to the possible formation of the earth. The first interpretation was called the Neptunist school or Neptunism. A second approach to the earth became known as the Plutonist school (or Plutonism). Their oppositional character (of water and fire) can be seen as the heritage of the dualism associated with Rationalism.

The leading school was called the Neptunians and was initiated by Abraham Gottlob Werner (1750 – 1817), a professor in Freiberg. He was an eminent mineralogist and postulated the importance of water (the sea), in which all rocks and minerals were deposited. The Mosaic Deluge once covered the whole earth and the rock formations were subsequently laid as the Flood subsided. The rock layers had a universal and specific sequence. Werner rejected the belief that the geological evolution was a uniform and continuous process. Certain events from the past can be unknown to us, in his view.

The great challenge of the Neptunian theory came from the vulcanists (or Plutonists). They suggested, that the major changes in the earth crust were caused by central heat and internal pressures. John Hutton (1726 – 1797) put the arguments forwards in his book ‘Theory of the Earth’ (1795/1798). The whole process had, in Hutton’s view, a lawful regularity and the ‘operations of nature are equable and steady’. He concluded that ‘time is to nature endless and as nothing’. Stephen Jay GOULD (1987) described Hutton as ‘the all-time worst writer among great thinkers’. However, the popularization by John Playfair (‘Illustrations of the Huttonian Theory of the Earth’; 1802) helped a great deal to spread Hutton’s ideas.

The Scottish scientist Charles Lyell (1797 – 1875) elaborated further upon those matters in his epoch-making ‘Principles of Geology; or the Modern Changes of the Earth and its Inhabitants considered as illustrative of Geology’ (1830 – 1833; three volumes). He had a recurrent view of time: ‘The huge iguanodon might reappear in the woods, and the ichthyosaur in the sea, while the pterodactyle might flit again through umbrageous groves of tree-ferns’. He is remembered for his opinion – which still prevails today – that the visible causes of geological change are of the same kind and intensity as those that have always acted. The principle – known as uniformitarianism – stated that the present is the key to the past.

The notion that magma was a molten rock from the inner parts of the earth, and not a sedimentary deposit sealed the faith in Neptunism. The priority of volcanoes and massive cataclysmic events gave rise to a further insight in the history of the earth, called catastrophism.

Catastrophism was highlighted around 1800 by the French naturalist George Cuvier (1769 – 1832). He noticed that fossilized specimen suddenly disappeared from the geological record. His study of the rocks around Paris revealed sudden breaks in the sequence, which could point to catastrophic events. He believed that the earth was several millions years old.

These ideas were not endorsed in England. Scholars in that country busied themselves with a search to bring the geological sequence in concordance with the Biblical story and uniformitarianism (and gradualism) in general. The influence of major interruptions (other than the Flood) were played down in the later part of the nineteenth century and the first half of the twentieth century.

However, catastrophism was back on the geological agenda in the 1950’s when Immanel Velikovsky (1895 – 1972) painted a science-fiction type of scenario of the destruction of the earth by extraterrestrial forces (Worlds in Collision). A scientific paper by Alvarez et al (in 1980) suggested that a comet struck the earth at the end of the Cretaceous period. The massive impact (west of Mexico) might have been instrumental in the extinction of many animals, including the Dinosaurs.

The writer at the Bottaccione Gorge near the town of Gubbio (Italy), a geological hotspot (May 2014).

Gubbio is also known among geologists and palaeontologists as the discovery place of what was at first called the “Gubbio layer”, a sedimentary layer enriched in iridium that was exposed by a roadcut outside of town. This thin, dark band of sediment marks the Cretaceous–Paleogene boundary, also known as the K–T boundary or K–Pg boundary, between the Cretaceous and Paleogene geological periods about 66 million years ago, and was formed by infalling debris from the gigantic meteor impact responsible for the mass extinction of the dinosaurs (Wikipedia) (Photo: Marten Kuilman, May 2014).

In hindsight, it is clear, that the creative-intellectual events around the year 1800 in Europe marked a formidable leap of imagination in human history. BOWLER (1984, p. 14) noted that ‘increasingly, the suspicion has grown that scientific knowledge is not just a matter of gathering new facts but is also influenced by the cultural and social environment within which scientists work’. Man became to understand its own presence, as being part of the subjectivity of nature. I believe that the four-fold way of thinking was responsible for this change.

 

6.1. Imagination on a human scale

A proposal for a new European history

The European history can – at least in theory – be seen as a confined narrative, comprising all the significant historical events, which have taken place, or are generated in, a limited geographical area called ‘Europe’. Clearly, this statement invokes a number of questions of which the most important one is the definition of its unity in time and space.

Of those two, the definition of space is probably the easiest one to establish. The central part of the geographical area, consisting of the large countries like Great Britain, France, Germany, and Italy has been generally recognized as the historical core of Europe. A number of countries along their fringes were included. The Scandinavian countries towards the north, Poland and Russia (up to the Ural Mountains) to the east, Spain and Portugal towards the south and Ireland towards the west were naturally included in a greater Europe. The central countries of Austria and Hungary have put their mark on an important earlier part of the European history. The boundary towards the south east has always been problematic and remains so to the present day (Croatia versus Serbia), because it was historically felt that the real threat to the European identity came from that direction.

The definition of time (of the visible visibility of Europe) is more difficult to determine. The actual term ‘Europe’ was used by the Roman historian Dio Cassius (c. 150 – 235), who distinguished in his ‘Historia Augusta’ (Roman History) a difference between Europeans and Syrians in the army of Septimus Severus, using the terms ‘res europeenses’ and ‘europeenses exercitus’ (HEER, 1966).

A general feeling of a ‘beginning’ can be found in the Christian calendar, which started with the birth of Christ. This marker point was first used by Dionysius Exiguus in 525 AD, who improved on a timetable of St. Cyril of Alexandria (which went back to Emperor Diocletian (284 AD).

Easter cycle of Dionysius Exiguus. Marble. Ravenna, 6th cent. Museum Ravenna. In: BORST, Arno (1990). Computus. Zeit und Zahl in der Geschichte Europas. Bnd. 28 in: Kleine Kulturwissenschaftliche Bibliothek. Verlag Klaus Wagenbach, Berlin. ISBN 3 8031 51287

The Western time scale was firmly established at the Synod of Whitby (664), where Dionysius’ chronology was accepted (among other preferences of Roman Catholicism over Celtic Catholicism). The Venerable Beda (673 – 735) wrote a ‘computus’, or a manual for the calculation of specific events. The ‘Reckoning of Time’ (‘De Temporum Ratione’ (725 AD) was a significant intellectual monument in the European history (WALLIS, 1999/2004). The book was used by missionaries to support the Christian setting of time. However, it took at least another two centuries before the beginning of the Christian era was generally agreed upon.

It seems reasonable, with this history in mind and the general acceptance of the Christian era as a yardstick, to put the beginning of the CF-graph (of the European cultural period) at the beginning of the Christian era, i.e. in the year 1. The actual context and name of Europe were not known at that time. This fact fits into the quadralectic approach, whereby an area of invisible invisibility (with no definition or name) precedes the visible visibility (or empirical presence) sensu stricto.

The name ‘Europe’ only gained a (geographical) significance in the eighth century during the reign of Charlemagne, the Aachen-based emperor who did a first successful attempt to join great parts (of the present Europe) together. OAKLY (1979, p. 29) noted that ‘already in Charlemagne’s day ecclesiastical writers had begun to equate the term Europe with the territories over which he ruled.’ A document on the victory of Charles Martel in Tours, also mentioned the term ‘Europeenses’ (ROBERTS, 1985).

Certainly, there is a history of ‘Europe’ before this date. The Celtic cultural expanse between the seventh and ninth century spearheaded into France and Germany and brought about a feeling of recognition. Monks from Clonnard (in Ireland), Iona and Lindisfarne (in England) traveled to the continent and founded monasteries, which were centers of belief and knowledge (McNEILL, 1974; MACKEY, 1989).

The ‘struggle’ between the Celtic and Roman Catholicism in that period is a truly pre-European event. The confrontation did initially not result in a sense of togetherness, but acted as a catalyst to increase awareness (of certain common Celtic roots). The period of the early Middle Ages (350 – 750) can be seen as a preparation of a unity-in-the-making.

The boundary of the first (visible) visibility of ‘Europe’ – in a very general intellectual notion – is put in the year 750 AD, at the end of the rule of the Merovingians (751). The previous experienced ‘local’ history changed dramatically when the Carolingian leader Pepin the Short took over the royal throne, followed – in 768 – by his son Charles, better known as Charlemagne (742 – 814).

The latter forced upon the various countries a feeling of belonging (to a great Christian Roman empire) during his fifty-three campaigns. The integration of the local tribes did not have a peaceful character. The Saxons on the eastern frontier, for instance, were pagans and were given the choice by Charlemagne between baptism or death. Some four-thousand-five-hundred Saxon rebels made the wrong decision and were beheaded in one day (the Massacre of Verden, 782).

The forcefully established unity (of Europe) broke down soon after Charlemagne’s death (in 814). The tripartion of Europe in 806 – when the power was divided among his three sons – failed because Pepin and Charles died in 810 and 811 respectively and only Louis remained. He was more interested in spiritual matters and was unable to continue the political achievements of his father. However, the fact that Europe had been united for some time and had become aware of a common heritage, never waned. The cultural and political developments in the Middle Ages must therefore be placed in a ‘European’ context, up to the present day.

Two points of recognition (POR) are now established on the CF-graph of the European cultural period (fig. 65). Firstly, there is the very beginning of the CF-muun in the year 1 – i.e. the universal accepted beginning of the Christian calendar. And secondly, the establishment of the ‘real’, empirical visibility of Europe in the year 750 AD, at a time when the first integration of Europe took place and the name of the continent became imprinted in the mind of its inhabitants.

Fig. 65 – The CF-graph of the European (cultural) history, constructed from two points of recognition (POR). The beginning of the communication cycle is situated at the start of the Christian era in the year 1. The first, empirical visibility is chosen in the year 750 AD. The full cycle (V) has a length of 2400 years. The visible visibility area (X) lies between the years 750 and 2250 AD.

These two data provide the key to the length of the full communication cycle (between the geographical and temporal entity of a part in the world called ‘Europe’ and an observer at the beginning of the twenty-first century, who established the boundaries of that visibility). These two known points on a CF-graph enable the construction of the whole communication cycle.

It is known – from the theoretical calculation (see p. 115, fig. 48) – that the first visibility (FV) is situated at 5/16V of the CF-graph, therefore the full muun-cycle (V) has a length of:

5/16V = 750   therefore V = 16/5 . 750 = 2400 years

The inflection points (of the CF-graph) and the years are given below:

—————— Beginning of the First Quadrant (I)                                         1 AD

—————— Beginning of the Second Quadrant (II)                                    600

—————————— FV – First Visibility                                                        750

—————————— AP – Approach Point                                                     900

—————————— FMA – First Major Approach                                     1050

—————— Beginning of the Third Quadrant (III)                                    1200

—————————— FVC – First Visibility Crisis                                        1350

—————————— PP – Pivotal Point                                                        1500

—————————— SVC – Second Visibility Crisis                                   1650

—————— Beginning of the Fourth Quadrant (IV)                                  1800

—————————— SMA – Second Major Approach                                 1950

—————————— RP – Receding Point                                                     2100

—————————— LV – Last Visibility                                                        2250

——————- End of the Fourth Quadrant                                                    2400 AD

The psychological and spiritual foundation of Europe was laid down long before the actual geographical entity was established. In particular, the Church fathers (patres) – of which Augustine, bishop of Hippo (354 – 430 AD) was possible the most important – created a large corpus of work, which influenced the intellectual development for times to come.

Early manifestations of division thinking often had a numerological nature (concerning references to the Bible) or were disguised as interpretations of symbols (like the shape of the cross). Justin the Martyr and Irenaeus explained the cross as a symbol of four dimensions: latitudo, longitudo, sublimitas and profundum.

The beams of the cross were of unequal length in the ‘western’ or Latin interpretation of the cross. Good works were, in Augustine’s view, metaphorical associated with the horizontal cross beam (latitudo). The vertical top beam renders the hope of reward in heaven (sublimitas). The longer vertical lower beam translates the continuous perseverance (longitudo) and the part of the beam in the ground (profundum) is the ‘abyssus et profundum crucis’, the depth of grace. This inequality (in length and meaning) points to lower division thinking and a search for distinction.

The ‘eastern’ or Greek cross had equal beams, reflecting a general equality in all four directions. This approach conforms with the aims of higher (four-fold) division thinking. LADNER (1955) noted, that the apparent opposition (west versus east) in the preference of the shape of the cross should not be over-accentuated, since the (pagan/Pythagorean) tradition of a cross with equal beams was also well-known in the (Celtic/Christian) history of western Europe.

Augustine advocated both a three-division (of Father, Son and Holy Ghost) and a four division (in the four senses). He described – in his book ‘De Doctrina Christiana’ – the ‘senses’ as ways of seeing and followed ideas, which originated in the intellectual melting pot, which existed in Alexandria at the beginning of the Christian era. Texts could be approached in four different ways: in a literal meaning (or historia), in a deeper meaning (or allegoria), in a moral meaning (or tropologia) and in the highest meaning (or anagogia). The Roman consul and writer Cassiodorus (484/90 – died in 583/590?) took up this basic method of exegesis in his important and influential book ‘Institutiones divinarum et saecularium lectionum (litterarum)’ or, in short, the ‘Institutiones’ (562). De LUBAC (1959/1964) wrote a massive standard work on the early Christian and medieval way of interpretation. A comparison of the four senses with the present practice of quadralectic thinking would be as follows:

——————— 1. First Quadrant         –     anagogia        –       invisible invisibility

——————— 2. Second Quadrant    –     allegoria         –      invisible visibility

——————— 3. Third Quadrant       –     historia           –       visible visibility

——————— 4. Fourth Quadrant    –      tropologia      –       visible invisibility

De Lubac (Part I, Tome II, p. 422) pointed to the important role of Beda as ‘le premier auteur qui nous offre pour ainsi dire un tableau developpe du quadruple sens’ (the first author that offers us, so to speak, a developed overview of the four senses).

Ambrosius (c. 339 – 397) was perhaps the most enthusiastic patron of the four-division. He summarized a tetradic list in his book ‘De Abraham’ (four Gospels, apocalyptic animals, parts of the world, and ages), and gave the example of the syzygy of the elements and the virtues (virtues cardinales). His resistance against Arianism (the separation of Christ from God) can also be placed within the context of a conflict between the three- and four divisions. The former (including Arianism) aims at a separation and distinctions of powers (in order to control them), while the latter is not interested in power play and gives all (four) subdivisions an equal value.

The patristic movement-in-general had not decided on any particular form of division thinking as a way to salvation. It was a time of searching for the right context and making statements focused on a strong belief (in one God). Therefore, the four basic divisions could live together in harmony.

A compilation/suggestion of the interpretation of the visibility area (X) of the new European history is given hereafter.

The year 750 or First Visibility (FV) was arbitrary chosen as the start of the empirical (European) history because Charlemagne (742 – 814) was the first to unite the greater part of Europe under his reign. The political integration was accompanied by an effort to raise the intellectual standard.

Johannes Scotus Eriugena (810 – 877) was a scholar, who supplied the foundations of a quadriformis ratio (STOCK, 1980), consisting of a balanced search for the truth. The ratiocinationis quadrivium – as initiated in the ninth century – consisted of four stages:

——————–  1. division

——————– 2. definition

——————– 3. demonstration

——————– 4. resolution

Johannes Scotus major work was aptly called ‘De Divisione Naturae’ (The Division of Nature) pointing to the action in the First (or Holy) Quadrant. The English translation by SHELDON WILLIAMS (1987, revised by John J. O’Meara) is a gold mine of insight, culminating in the ‘Seven Steps to Heaven’. This expression pointed to two types of unification: the ‘holy’ three-division (three steps) and the ‘human’ four-division (four steps) leading to the consummation of all things (GARDNER, 1900).

‘For it is agreed that this visible world is composed of the four elements as of four general parts, and is, as it were, a body built up of its parts, from which, namely from these universal parts, coming together in a wonderful and ineffable mingling, the proper and individual bodies of all animals, trees, and plants are composed, and at the time of their dissolution return to them once more’. (De Div. Nat. I, 474D).

The Holy Trinity became the symbol of power in the realm of the invisibility, while the quaternity was reserved for the empirical, human world (as constructed from the four elements: fire, air, earth and water). However, this distinction was frequently mixed up throughout history. The political record shows a preference for the lower three-division, because it makes the distribution and control of power easier to handle.

The year 900 AD, or the Approach Point (AP), was the onset of just such a development. The infant Europe learned from Charlemagne that the exercise of physical power could lead to clarity. The Vikings ravaged the coasts of Europe and enforced their culture on the occupied coastal areas. The Hungars, with their base in Pannonia, made many raids deep in the heart of Europe. It was only in 955 AD, that the influence of the Magyars waned after being beaten by Otto I on the Lech near Augsburg. These violent political movements – which attracts often the most attention in the history books – were accompanied by more peaceful developments in the areas of farming, husbandry, social interaction and art.

Europe had reached the limits of its conscious potential in the year 1050 AD, when the First Major Approach (FMA) took place. The young unity touched the essential aspects of its being in the deep belief of Christian faith and eagerness of progression. The occurrences of the Crusades (which started at 1095 and lasted until 1270) and the building of many cathedrals all over Europe were visible proof of such an advance. The transition from the Roman to the Gothic architecture took place around this date, pointing to a growing awareness of openness and inner force. It is here that the so-called High Middle Ages (1050 – 1300) started, because the cultural, economic and political achievements became a continuous narrative.

The ‘Tractatus de Quaternario’, written by an anonymous Anglo-Saxon monk around 1100 (Gonville and Caius College Cambridge, Ms. 428) was a celebration of the number four. It can be seen as a manual for the tetradic cosmology (SEARS, 1986). This work, now virtually unknown, is a forgotten monument to tetradic thinking, overgrown by ages of polarity.

A better-known work, with a lasting influence, was written around 1150 by Petrus Lombardus and called the ‘Sententiae’ – or with its full name: ‘Libri Quattor Sententiarum’. This important work was composed of many bits and pieces from the Bible, the Church fathers, decisions of the Councils and quotations from the works of Abelard and Gratian’s Decretum. The scholarly script, followed – despite its diversity – in its main headings the four-fold division:

———————  1. God

——————— 2. Creation

——————— 3. Incarnation

——————— 4. Sacraments

These four expressions of belief fit seamless into the modern interpretation of the (quadralectic) quadrants.

The gradual change from a four- to a three-division can be observed in the work of Joachim of Fiore (c. 1132 – 1202). He was the last of the great thinkers of the Second Quadrant and – in terms of division thinking – a protagonist of the changes to come. His work showed all the wild and precursory experiments of lower division thinking. The lure of the dual comparison (or concordance) opened up a whole new field of speculation. ‘Joachim broke with the traditional theory of the four senses of Scripture to create an ideosyncratic scheme of twelve in which seven ‘typical’ senses manifest the action of the Trinity throughout the history’ (McGINN, 1979; p. 127). BLOOMFIELD (1957) cast him lenient as ‘a lyrical, not a systematical thinker’.

The year 1200 marks the start of the Third Quadrant and the rationalistic age of visible visibility. Power struggle became the name of the game and started noticeable in the Roman Catholic Church as the strongest political body. Individualism showed its impetuous face. The controversy between Petrus Lombardus and Joachim of Fiore offered a rare glimpse in the basic operation (reduction) of division thinking (see also p. 26).

Joachim accused Petrus Lombardus of being a ‘quaternator’, who made God into a quaternity. Lombardus placed God in a separate conceptual entity and added an (extra) part to the trinity of Father-Son-Holy Spirit. The same complaint was expressed by Gautier (Gualtieri) of St. Victor in his writings ‘Contra quatuor labyrinthos’ (1177/78). DOOB (1990, p. 164/200) pointed out that the word ‘labyrinthos’ was a metaphorical expression to indicate persons who had lost the right way in a labyrinth of error.

Walter of Saint Victor (died c. 1190) also labeled, in a futile protest against Aristotelianism, the four dissidents Peter Abelard, Peter Lombard, Peter Pictaviensis and Gilbert of Poitiers as the ‘four labyrinths of France’. He despised their dialectical method, and condemned the use of logic to explain the enigmas of belief. The intellectual quarrel marked the boundary of a new era. It showed the importance of a particular form of division thinking for those who aim at a visible (or physical) visibility and, ultimately, power.

The English philosopher William of Ockham (c. 1285 – 1347/49) gave, towards the end of this period, the trend towards simplicity a formal respectability. His conception of universals as merely names became known as ‘nominalism’. The expression ‘Entia praeter necessitatum non sunt multiplicanda’ (don’t multiply entities except by necessity), also known as Ockham’s razor, means – in a quadralectic scenario – that one should not think in a higher type of division thinking than is necessary for the given situation.

The year 1350 or the First Visibility Crisis (FVC) was a crisis in a real, physical sense, because the plague rampaged over Europe and the Black Death wiped out approximately one-fourth of the population at some places. The indirect consequences were devastating of the social and political structures of Europe. A further reduction of division thinking was the immediate result in the period between 1350 and 1500. This course was intellectually taken by Nicolas de Cusa (Cusanus; 1401 – 1464) in his book ‘de Docta Ignorantia’ (On Learned Ignorance). The book is essentially a forceful advocate of the triple division. The existence of a four division was simply denied (Book I, Ch. XX). Cusanus aimed at the ‘coincidentia oppositorum’: a total reduction (of division thinking) towards a unity, which he equated with God.

The attention towards the minuscule was another feature of this period and came to expression in numerous ‘Book of Hours’ of which ‘Les Tres Riches Heures du Duc de Berry’ is perhaps the most famous one. The illuminated manuscripts treated the ‘Divine Office’ (the rituals for the eight periods of the day), often with additions of liturgical calendars, prayers, psalms and litanies of the saints. The magnificent calendar section of the ‘Tres Riches Heures’ was painted between 1412 and 1416. The epoch can be described as a time of Christian consolidation. Jesper HEDE (1998) quoted Robert BARLETT (1994) by saying that ‘in the medieval period the terms ‘Europe’ and ‘European’ were known, but they were used rather infrequently and hardly ever with much political and cultural significance‘.

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Book of Hours – Catherine of Cleves. Pierpont Morgan Collection p. 28. PLUMMER, John (1964). Het getijdenboek van Catharina van Kleef. Meulenhoff, Amsterdam. LCCCN 66-23096

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The year 1500 or the Pivotal Point (PP) was in many respects a pivotal year, a highlight of an extending visibility with new discoveries in geography (America) and industrial activity (printing, dynamite). The Renaissance blossomed as an artistic proof of a rediscovered human creativity derived from ancient times. The spirit was deeply dualistic, but the (ancient) pool of references (mainly derived from the Fourth Quadrant of the Roman Empire) was saturated with forms of higher division thinking. The four division was often used in a metaphorical and numerological sense.

The worldwide conquest of the seafaring nations was accompanied by a component of violence and cultural arrogance. The lower forms of division thinking turned out to be most effective – from the materialistic point of view – to subdue cultures macerated in tetradic thinking. The plundering of foreign lands brought a kind of affluence to Europe, but also initiated a struggle in the distribution of that wealth. The Peasant War (1524/25) in Germany and the Sack of Rome, in 1527, indicated only the beginning of an ‘Age of Intolerance’. The Inquisition was tightened up in 1542 and the persecution of Huguenots in France started in 1562. On the peaceful side, it can be noted, that many practical inventions came entrenched in daily life. A modern historian – in particular, one emerged in oppositional thinking – will have no difficulty to proclaim that the European history really took off from the year 1500.

The year 1650 or the Second Visibility Crisis (SVC) brought a crisis of a different kind. The social unrest of that period was caused by a (relative) material wealth consumed in an environment of absolutist thinking. The great number of insurgencies and revolts all over Europe during the seventeenth century found their common denominator in a combination of a limited view – expressed as intolerance – and the genuine effort to establish a frame of reference for a personal and/or collective identity.

The ‘crisis’ in Europe took about a century to develop, from approximately 1560 until 1660. It was felt at a time ‘that cyclical theories of history became fashionable and the decline and fall of nations was predicted, not only from the Scriptures and the stars, but also from the passage of time and the organic processes of decay’ (TREVOR-ROPER, in: ASTON, 1965). It will come to no surprise, that the term ‘Middle Ages’ was coined around this time (in the year 1667 by professor Horn), indicating roughly the thousand years between the fall of the Roman Empire and the birth of the ‘new’ European history in 1500. The crisis was, in many respects, a stagnation after the expansive years of the early sixteenth century. Oppositional thinking had reached the limits of its creative power. Paul HAZARD (1936) described the general mood in the period between 1680 and 1720 as ‘La crise de la conscience européenne’.

The year 1800 marked the end of the Third Quadrant and the beginning of the Fourth Quadrant. The start of the nineteenth century saw a widening in division thinking to a four-division. Freedom of the mind was a prerequisite to enter this novel sphere. The French Revolution (1789) started with just that aim in mind, but felt back into violence and the power politics of Napoleon. His expansion policy failed miserably. The unification of Europe relapsed into nationalistic sentiments, chauvinism and lack of economic insight. It became clear, for the second time (after Charlemagne), that force was not the way to unite Europe.

Neo-Classicism and Romanticism were the terms used – by later cultural historians – to describe the mood of venturing into the territory of the fourfold, giving way to a customary form of subjectivity. The broadening of outlook became most apparent in the world of technology and general knowledge. Many branches of modern science, like sociology, economy, biology and geology, had their veritable birth-ground at the beginning of the nineteenth century. The steam engine (developed by James Watt; 1736 – 1819) introduced a ‘mechanical’ approach to nature, making human (muscle) power partly expendable and – more important – shifted the personal attention away from the process of making. The process of industrialization started in England, but soon spread all over Europe. Roads and railways were part of an ever-growing infrastructure, which brought people and ideas together.

The year 1950 or the Second Major Approach (SMA) was the second time that Europe hit the roots of its existence. In the period just after World War II a fresh elan came to surface in a generation, which was prepared to build the ruins up again. For the third time, a unification of Europe (now under the guidance of Nazi Germany) did fail as a direct result of its violent nature. However, times did change. The dualistic inspired Cold War (between Western and Eastern political powers) lost its appeal, just like the use of violence became increasingly palled upon. Power- and identity-seeking individuals turned to hijacking and guerrilla tactics, always on a small-scale and aiming at maximum media attention. The news bulletins doggedly followed the outbreaks of violence in their misguided intention to create some kind of reality. These acts of violence dwindled of importance in the light of the enormous achievements in many other fields. The landing on the Moon (in 1969) was a psychological zenith. It also put forward the limitations of life in space. The development of the gene technique raised fresh hope in biology and the world of medicines. The gigantic scale of plate tectonics reformed geology. These examples were only a small part of the enormous increase in scientific knowledge. All fields of research also greatly benefited from the introduction of computers.

The present (2011) has a CF-value of 8.03, which is fairly low (on a visible visibility scale from 6.00 to 11.00). The European cultural history is ‘on the way up’ in the second part of the Fourth Quadrant (IV, 2). This position might give a splendid inspiration for historical descriptions. Europe, as a cultural unit, has seen a lot. Certain comparisons (with other cultures) can give a clue as to where we are going next. At present, I will leave this terrain open for future (quadralectic) historians to work on.

The year 2100 or the Receding Point (RP) will be the beginning of a time of consolidation. No real development can be expected, but there is a firm interest in the past. The time can be compared to the 25^th/26th Dynasty (740 – 525 BC) in the Egyptian cultural period, known for its ‘Late Renaissance’. Old ideas revived, up to a point of decadence. Whoever visited the graves of the Apis-bulls (Serapeum) in Sakkara, knows what that means.

The year 2250 is the year of the Last Visibility (LV). The socio-political entity of Europe will not disappear after that date. Its geographical unity will continue in the same way as  countries like Egypt and Greece or the Roman Empire. It is all there, but it has no medium to create a new visibility. Europe will remain a continent, witness its own history, but other (large) countries or continents will, by that time, have taken over its cultural importance. However, a cyclic view implies that a future is somewhere, and visibility will open once again. The gateway to another universe is open.

 

6.2. Imagination on a geological scale

The presence of life in time

This chapter will enlarge the circle of our imagination by looking at the history of the earth. The chronicle of the planet and its ever-changing features is written in the rocks and can be inferred from the large-scale movements of the continents as they drift over the surface of the earth. However, the present approach to the geological history will differ from the ‘classical’ story as told in the textbooks. It will be an effort to perform historical research in a quadralectic way by using the CF-graph (and its characteristics) as a yardstick. Most important of this exercise will be an understanding of the method, which is employed. The following points of interest will be treated in more detail:

1. The definition of the boundaries of two extinct marine animals (Trilobites and the Ammonites) in the geological history and the significance of these boundaries for their ecological existence (6.2.1);

2. The presence of Large Animals (Visible Life) on the planet Earth as established in the geological history and the prediction of the total presence of large animals in the future (6.2.2);

3. The presence of Man, ‘Homo sapiens’ on the earth and the prediction of the complete visibility area of the human species (6.2.3);

4. The description of the geological history of the Earth (as a planet in the Solar System) and its existence within the Solar System and the Universe will be treated in the next chapter (6.3).

These investigations are carried out in a genuine quadralectic way and are never performed before. The theoretical framework and its premises are put to the test. The procedure gives way to a distinct enlargement of historical understanding. The only thing to do – in order to enter this vast outwardness – is to make a (personal) choice in a comparison between a given ‘fact’ (as a delimited visibility) and a recognized feature on a universal communication graph (as an indication of participation).

The major criticism will be – in particular from the established science – that (geological) data cannot be used in this way. Any personal (or collective) choice or intervention should be banned from a scientific inquiry. At least, that is the theory. Science should be neutral, just like nature. The gap between the facts and the interpretation of facts (see Ellenberger, p. 9) is experienced as a real dividing line between two different constellations. Firstly, there is the collection of facts, supposedly chosen from an infinite number in a strict objective way and, secondly, there is the – admittedly subjective – interpretation of (limited) facts.

Unfortunately, science itself is now so far transgressed, and the human involvement with its own inventions so thorough, that this procedure can no longer maintain credibility. Most scientists today know – if they are able to uphold their independent spirit – that any knowledge is deeply connected with the (subjective) choices, which are made earlier in the collection of facts. There simply is no objective way of data gathering. Sampling is always a process of selection influenced by a (personal or collective) method, which is stipulated in time and place. It is, for that very reason, that science can be as flexible as it is. The paradigm – as a collective scientific agreement – can be discarded at any time when the need is felt, and a better alternative crops up.

However, many scientists still hold on to a past, and a frame of reference, which is no longer generally applicable. They hang on to an old, abandoned rationality, which is built on oppositional thinking. The ghost of Descartes’ dualism lingers on, but it has lost its flavor and creativity. Oppositional thinking only works within the rigid boundaries of the observer’s point of view. Dualism is effective when participants in a communication are able to forget the self-imposed boundaries, for the time being. The reward for this temporary absent-mindedness is paid out as a ‘result’. One might ask what those results are really worth.

Any modern scientist would not like to perform an investigation in a state of trance or reverie, pretending that the self-imposed limitations do not exist. Nature, and the study of nature, is not something outside ourselves, but we are part of it. Nature’s choices are our choices and vice versa, and a modern scientist should face these realities with an open mind. There is no point to gain some success by fiddling the rules.

On the other hand, for those who renounce self-deception, there is no way back. One cannot pretend not to see in a wider psychological setting. The freshly gained subjectivity must have an expression in a scientific way. For a moment, it might seem as if this amplification will lead to chaos, but fortunately, there is a mathematical model, which comes to the rescue. One has to go simple back to the basics of communication – which is division and movement – and state a clear point of departure – which is the four- fold CF-graph, applicable to any given communication.

Visibility becomes meaningful in a process of shifting values within a comparison. Earlier in this book (p. 51) it has been stated that analogy (AN) must be regarded as a separate way of understanding. The mode of inquiry is distinct from the trial-and-error (TE), induction (IN) and deduction (DE) processes in other parts of the communication cycle (although it is used in all these ways of reasoning).

The point of recognition (POR) is important in the analogy method, because it is in this choice that the subjectivity of the observer becomes measurable. These points hold the key to a creative historical experience of everything imaginable. The registration of life in time – which is studied next – is probably the highest form of wisdom, which can be acquired as a human being, because it provides the boundaries of our existence.

 

6.2.1. Two groups of extinct animals

Before we enter the geological records of two specific groups of extinct animals, it is worthwhile to consider the full history of the earth as it is known at the moment and given in the textbooks (fig. 66).

Fig. 66 – The geological time scale, as divided in eons, eras and periods, is a compilation. The sequence and the (sub)divisions are the result of a comparison of information derived from rock sequences all over the world. The formation of the timescale is an example of the analogy method, which yields results of its own.

The history of the earth is usually presented in a linear fashion, as a development from a barren and inhabitable planet some 4.5 billion years ago towards the lush and populated place it is today. The quadralectic aim will be to place this story in a cyclic context. The present is, in that view, not the end of a steady development, but just a stage in a visibility curve.

The determination of the area of visible visibility (X) of two extinct groups (Trilobites and Ammonites) in the geological history is a matter of practical observation in the field: fossils are preserved in the rocks and act like the business cards of a salesman. They tell – to some extend – the story of a presence in place and time. Animals are called ‘extinct’ if no living forms of the genera are known within the time-presence of the observer. However, the animal appears as a given object within view and is not completely invisible. In the peculiar shape of a given rock (fossil) lies the remembrance of an animal, which was once alive. The form gets involved in a history-making process by a comparison between its initial environment and the present circumstances.

The way of a ‘thing’ to find its place in history is highly dependent on the (division) context in which it is placed. The dual framework uses the formal parameters ‘present’ or ‘not present’. The nature of an observation is decided by the observed (the fossil), and not by the observer. Any legitimate scientific statement insists on objectivity and can only be arrived at from an observable presence. Any personal interpretation of the observer should be left out of the picture. This idealistic goal can – unfortunately – only be achieved in the lower forms of division thinking.

The quadralectic approach takes a wider look. It aims at a (re) construction of the boundaries of empirical visibility within the course of a communication. The presence or non-presence – at a certain time and place – of an observable entity is placed in the context of a universal communication (as given in the CF-graph). The moment and setting (of the interaction between the observer and the observed) is a historical event, which cannot be ignored. Every given fact, which is used in a quadralectic context, should be stated with a clear reference to the credentials of the observer in terms of his or her type of division-thinking.

This means, in practice, that any investigation (on a quadralectic level) should be accompanied by an explicit mentioning of the selective notions, which have been employed in the process of description and interpretation. No scientific work (in the realm of higher division thinking) can be complete without the indication of these chosen boundaries.

The establishment of limitations in the case of fossils like Trilobites and Ammonites is fairly straightforward, at least on the level of a class (Trilobita) or subclass (Ammonoidea). Both consist of genera and species, which are known as index fossils, i.e. widely distributed fossils with a limited time span, which helps the dating of other fossils found in the same rock layer and pinpoint the position of a certain sedimentary deposit in time.

Eocene rocks in John Day National Park, Oregon (USA) (Photo: Marten Kuilman, 2010).

Fossilized leaves in John Day National Monument, Clarno Unit (Oregon, USA). Forty-four million years ago a series of volcanic mudflows, swept up a (tropical) forest and preserved a diverse assortment of plants and animals. (Photo: Marten Kuilman, 2011).

The stratigraphic correlation with index fossils is a good example of modern analogy-thinking. The fossils are initially qualified as time-markers between rocks. Next they are used in the age determination of other rocks. This seemingly ‘circular argument’ represents a quadralectic shift over the communication trajectory. The comparison of analog information effects in dynamic values, which indicate the distance of the communication partners.

6.2.1.1. Trilobites

The extinct animal class of the Trilobita is chosen here to give an example of a new way of looking at the geological history. The Trilobites are a group of Paleozoic marine arthropods, which lived from the beginning of the Cambrian (545 my) up to the end of the Permian (245 my). The name tri-lobite (L. tri – three, + lobus, lobe) refers to the transverse as well as the longitudinal trilobation of the exoskeleton (fig. 67).

Fig. 67 – Some examples of Trilobites from various ages. The Ordovician Cryptolithus has cephalic fringes with pits (1). The genus Acaste (2) is part of the Phacopina suborder and of Silurian age. The genus Scutellum (3) was found in rocks of the Lower Devonian. Paradoxides (4) from the Middle Cambrian is much older. The genus Orometopus (5) has long genal spines and dated from the Lower Ordovician. The genus Homagnostus (6) is a genus of the order Agnostida. They were diverse in the Early Cambrian, but died out at the end of the Ordovician.

Trilobites have a hard outer skeleton, which contains carbonate and chitin. They periodically molted (ecdysis), like all other arthropods. Many trilobites were capable of curling their body for protection. A still growing and amended classification of the Trilobites contains more than fifteen thousand species (MOORE, 1959/1997).

The average trilobite was small and looked like a bug, but larger examples are known, up to 70 cm. All trilobites lived in the sea, navigating in shallow water, walking on the bottom and probably feeding on detritus. Some, like the Agnostids, were swimming in deeper waters. The highly-developed forms in the early Cambrian were the dominant invertebrates of that time until the cephalopods displaced them in the Late Ordovician. There seems to be a trend towards a life in deeper water after the Ordovician, when many trilobite groups declined or went extinct. The Great Permian Extinction in the Upper Permian (245 mya) mend the end of all Trilobites.

The fossil record of the class of Trilobita is, in a quadralectic approach, equated with the visible visibility period (X) on the CF-graph. The period of Trilobites occurrence, from the Lower Cambrian (545 mya) to the Upper Permian (245 mya), covered some 300 million years. This duration is accepted as a given empirical fact (which is, in a true scientific spirit, always open to correction if new data prove otherwise).

The total length of the CF-graph, the so-called muun-length (V), can be calculated when the duration of the visible visibility period (X) is known:

              10                                                              8

X =     ——— . V = 300 my   therefore     V = ——— . 300 = 480 my

              16                                                              5

The length of the basic unit (BU), i.e. the length between two inflection points, can now be calculated. This length is 1/16th V, and works out for the Trilobites as 30 million years.

                      1

     BU =   ——— . V = 30 my

                     16

The point of first visibility (FV) is established at 545 my. This means that the ‘absolute’ point of beginning can be calculated by looking at the area of invisibility (O), preceding the FV in the Second Quadrant. This area consists of five basic units (BU), which is a total of 5 x 30 = 150 my. Therefore, the actual quadralectic cycle begins:

545 + 150 = 695 my ago

There was a sudden advanced stage of development in the Lower Cambrian rocks, but it seems certain that the Trilobites had a long pre-Cambrian history, possibly as soft-bodied creatures without much of an integument. At several localities, sedimentary rocks with trace fossils of trilobite activity underlie the oldest rocks with trilobite body fossils. The actual ‘beginning’ of the Trilobites becomes for that reason an awkward topic. The beginning of the Trilobite V-cycle – some 695 mya – coincides with the beginning of the Vendian period – and is a purely theoretical affair.

The same holds for the actual ‘end’. The empiric end of the visible visibility (area X) is fixed some 245 mya in the cataclysmic events at the end of the Permian, but there were still some 30 millions years of (theoretical) ‘existence’ to go. The formal end of the CF-graph is positioned in 215 mya., i.e. somewhere in the middle of the Trias.

It has to be understood that the relative differences between the practical (empirical) and theoretical boundaries (of the visibility of the Trilobites) are pack-and-parcel of a quadralectic approach, where nothing is absolute. The differences are a reflection of two positions in a communication: either in the third (static) or fourth (dynamic) quarter of the Fourth Quadrant.

The knowledge of the basic unit (BU = 30 my) together with the information at the beginning of the visibility (First Visibility (FV) = 545 mya) allows a calculation of the more important (inflection) points on the CF-graph of the Trilobites:

X = – 545            Y = 11.00 (FV)                                   X = – 365            Y = 13.00 (SVC)

X = – 515            Y = 11.00 (AP)                                   X = – 305            Y =   6.00 (SMA)

X = – 485            Y =   6.00 (FMA)                                X = – 275            Y = 11.00 (RP)

X = – 425            Y = 13.00 (FVC)                                 X = – 245            Y = 11.00 (LV)

X = – 395            Y = 10.00 (PP)

The abbreviations of the inflection points on the CF-graph are as follows (in the general appraisal of the graph, see p. 122, fig. 51): FV = First Visibility; AP = Approach Point; FMA = First Major Approach; FVC = First Visibility Crisis; PP = Pivotal Point; SVC = Second Visibility Crisis; SMA = Second Major Approach; RP = Receding Point and LV = Last Visibility.

It is interesting to compare these inflection points – and their meaning in a quadralectic communication – with the description of the evolutionary development of Trilobites as given in the textbooks. The history of the Trilobites becomes in this way a sequence of approach (intensio) and recession (remissio) between a class (of animals) and an observer. The Trilobites go through a cyclic interaction and their ‘ups and downs’ – as described in the classical geological textbooks – can be marked on the CF-graph (fig. 68). The specifics of the CF-graph itself – as briefly given on p. 122ff, fig. 51) – can be reciprocal be projected on the familiar history of the Trilobites in time.

The interaction between these two approaches, one from the ‘given history’ and one from the ‘characteristics of the CF-graph’ have to merge in order to come to a full quadralectic understanding. The modern way to describe the (geological) history has to come to a contemplated compromise between these two approaches. None of these accesses has a priority: the ‘textbook history’, derived from a maximum number of authorities, is equal to the ‘framework of the CF-graph’, decided upon after a choice from as many sources as possible.

Fig. 68 – The (visible) visibility area X of the CF-graph for the extinct Class of Trilobita. These Arthropods lived from the early Cambrian to the end of the Permian, i.e. from around 545 to 245 million years ago, a time span of 300 my.

The greatest number and diversity of forms of the Trilobites occurred during the Cambrian and Ordovician periods. This expansion is positioned in the Second and the first quarter of the Third Quadrant of the communication. The Trilobites were truly part of the ‘Cambrian Explosion’. This popular term is used for the ‘sudden’ appearance of Larger Animals at the beginning of the Cambrian.

The sheer quantity of specimens made it possible to divide the Cambrian system in stratigraphical units solely on the base of Trilobites (CLARKSON, 1979). The number of families reached a maximum of around seventy in the Upper Cambrian (fig. 69). A first ‘crisis’ occurred soon thereafter when a number of non-specialized genera perished. A possible cause was a regression of the sea level and/or the appearance of more efficient animals.

Fig. 69 – The number of Trilobites families during their existence on earth from the Lower Cambrian to the Upper Perm. A part of the CF-graph (visibility area X) is drawn as a comparison. The end of every period also implied a diminishing number of Trilobites families, with major reduction at the end of the Ordovician and the Devonian. This phenomenon was not a coincidence, since it must be remembered, that these boundaries find their very origin in the changes of a fossil record like the Trilobites.

The first major decline of species started at the end of the Ordovician (440 mya) in favor of the Cephalopods. The Agnostida, Olenina, and certain Asaphida completely disappeared from the scene. The extinction of a number of Trilobites groups was part of a major event, which also reduced the biodiversity of organisms like the Bryozao, Brachiopods, Corals and the Graptolites. The transition from the Ordovician to the Silurian was marked by higher sea levels, probably due to the partial melting of Ordovician glaciers. Subsequently, the sea levels began to drop again in the Late Silurian in much of the world. Plate tectonics caused mountains to form. This unimaginable and gigantic event is known as the Caledonian orogeny.

The actual First Visibility Crisis (FVC) in the fossil record of the Trilobites lies around 425 mya, which is in the Lower to Middle Silurian. This particular inflection point, known as a ‘psychological’ crisis in a universal communication, happened some fifteen million years after the termination of the Ordovician. The Trilobites had to face new enemies in their reduced territories such as sea scorpions of up to 1.5 meters (Eurypterus remipes) and the first jawed fishes (Acanthodians). No wonder that the supremacy of the Trilobites got dented in the company of such fierce creatures! They did no longer ‘rule the waves’ and their importance was taken over by the fishes. The history of the earth between 400 – 350 mya is, for that very reason, called the ‘Age of Fishes’.

A majority of the Trilobite families continued to the end of the Devonian (345 mya), when rough times appeared for the second time. This boundary is situated some twenty million years after the Second Visibility Crisis (SVC), which occurred 365 mya. This inflection point is characterized – in a general quadralectic model – by the occurrence of visible (material) damage within the communication. The advent of sharks and other early fishes might have contributed to the demise of the Trilobites (SHROCK & TWENHOFEL, 1953; p. 601). The number of families and species was greatly reduced in the Carboniferous and Permian periods.

The three primary divisions of the body and the three-lobed longitudinal division of the Trilobites remained constant over the whole duration of their geological presence. Occasionally, there were changes in size (from humble beginnings as Agnostida to the larger specimen, which were too big for predators to handle) and a wide variation in eyes, thorax, spines and other morphological features, but the basic triple building plan remained the same. The triple division of head, body and tail resulted in a versatile, marine animal, which was capable of surviving radically changes in the history of the earth and showed an amazing adaptability on a local facies scale.

The appearance of the first Tetrapods in the Devonian was more than just another group of animals appearing on the scene. The introduction of a four-fold plan (Tetrapods) in stead of a tri-fold (Trilobites) proved a challenging innovation of nature and a more serious threat to the Trilobites in the long run. This event happened at the pivotal point (PP = 395 mya) of the Trilobites visibility area X. The four-fold configuration offered an option to further development of form and function. The quadralectic adagio ‘not too few and not too many’ is not only the hallmark of tetradic apprehension, but also fits the principal characteristics of nature-in-general. A further refinement in two pairs of ‘opposites’ (arms and legs) – working together as a unit – proved enormously effective.

This change from a trifold- to a fourfold plan was part of the main morphological development in the Large Visible Animals (LVA) in the geological history. The extinct group of the Trilobites played a modest, but important part in the biological expansion of life from its early beginning to the world as it is known today. The three-division proved extraordinary successful in an environment, which was open for discovery and boundless activity. Somewhere along the (time) line, some three-hundred-and-ninety-five millions year ago, a better concept cropped up, based on the four-division. The reason for this ‘jump’ will always be a mystery.