6.2.1.2. Ammonites

The second group of extinct animals to warrant a special investigation in the light of the quadralectic approach to history are the Ammonites. The Ammonoidea is the largest and most important subdivision of the Class Cephalopoda, which includes the modern squids, cuttlefishes and octopu-ses. The Ammonites derived their name from the Egyptian god Ammon, with ears in the shape of ram’s horns. The predecendants of these versatile sea animals were one of the first types of fossils, which attracted the interest of early naturists (fig. 70).

Fig. 70 – This illustration of some Ammonites or ‘snake stones’ (Cornus ammonis) was given in Robert Hooke’s book ‘Discourse on Earthquakes’ (1703).

Jurassic ammonites from Les Nattes near Niort (France). (Photo: Marten Kuilman, May 2006).

The earliest known ‘ammonoid’ (Eobactrites) occurred in rock layers from the Ordovician age (505 – 440 million years ago). This genus was the proto-type of a major development of the subclass, which started in the Upper Silurian and the beginning of the Devonian, some 395 mya. Ninety genera appeared in fairly short time.

The difference (in time) – 45 mya – between the first and the massive visibility poses a classical problem in the quadralectic approach to history. The question is: do we focus on the first occurrence of Eobactrites in the Ordovician as the beginning of the (empiric) visibility of the ammonites or do we concentrate on the (sudden) presence of many ammonoid genera after the Silurian-Devonian boundary?

The same question might be posed in a general way: is the visible visibility governed by the boundary of the first sighting (of a single item) or does the empirical existence start at a point when a widespread occurrence is evident? Anybody who has experience in the arduous task of observing nature – be it of fossils, plants, birds, butterflies or any other object of interest – will be familiar with the problem of scarcity. Things can be rare, on a given place and at a particular time. However, once a singular item of interest has been located – by chance or in a combined effort of specific observation and knowledge – then it is often not uncommon at all.

This observational problem is created in the tension between the single and the multitude. It is, for this reason, related to quadralectic division problems and the position of the observer therein. The answer to the dilemma of the separation between the one and the many must be clear. It all depends on the location of the observer who defines the boundaries in the first place. The observant individual is either situated in the Third Quadrant (III) in absolute surroundings or in the third quarter of the Fourth Quadrant (IV, 3) with knowledge of a subjective intervention.

Both positions of observation have their own merit. None is better than the other. The first view is precise, but limited, while the other perception is sometimes vague, but applicable in a wide field. We are inclined, as explorers of a quadralectic vision, to choose for the latter option and its associated dynamism. Even so, we must be conscious all the time, that the preference for the multitude (in a delineation process) is a choice.

The ammonoids found their demise at the end of the Cretaceous, together with the Dinosaurs. The reasons of their disappearance might have been the same: the mass extinction due to a meteorite or comet, which struck the earth and disturbed the ecological circumstances for a long time. Other possibilities, less fearsome in their immediate effects, like the changes in temperature or large-scale volcanism (as seen in the Decan Traps in India) which influenced the composition of sea and air – have to be taken into account. The explanation of the extinction (of the Dinosaurs) as a ‘catastrophic’ Third Quadrant event (extraterrestrial intervention) or as a gradual Fourth Quadrant episode is also a philosophical one, based on a personal point of view.

The actual mechanism of the Ammonites extinction is, at present, not of our concern, because we are only interested in the total time-era of (visible) visibility of the subclass of Ammonoidea. Scientific facts and the definition of our position as observer (the choice for multitude) fix the boundaries of the visibility area between 395 and 65 million years ago. The total visible visibility period (X) is therefore 330 million years.

The theoretical base of the CF-graph (V = 8/5.X) can be calculated in the same way as the Trilobites. The Ammonites have a total muun-length (V) of 528 million years, which is slightly less than the Trilobites. The length of a basic unit (BU) between two points of inflection (1/16th V) is computed for the Ammonites as 33 million years.

10 8

X = ——— . V = 330 my V = ——— . 330 = 528 my

16 5

BU = ——— . V = 33 my

The inflection points in the CF-graph for the Ammonites can be calculated when the basic unit (BU) and the First Visibility (FV) are known:

X = – 395 Y = 11.00 (FV) X = – 197 Y = 13.00 (SVC)

X = – 362 Y = 11.00 (AP) X = – 131 Y = 6.00 (SMA)

X = – 329 Y = 6.00 (FMA) X = – 98 Y = 11.00 (RP)

X = – 263 Y = 13.00 (FVC) X = – 65 Y = 11.00 (LV)

X = – 230 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.

The history of the subclass Ammonoidea (of the Class Cephalopods) is now examined in quadralectic terms and compared with the more traditional (scientific) descriptions. The subclass is regarded as a unity (in time), which follows the rules of the universal communication (graph) expressed in an approach (intensio) and/or alienation (remissio) (fig. 71).

Fig. 71 – The visible visibility period (X) of the CF-graph for the extinct subclass of Ammonoidea, which lived from the early Devonian to the end of the Cretaceous, i.e. from around 395 to 65 mya., a time span of 330 million years.

The Approach Point (AP) marks the end of the primary visibility equilibrium of CF = 11 and is situated in time around 362 mya. This period is known on the geological time scale as the Upper Devonian (Givetian – Frasnian and Famennian). It was a time with a greenhouse climate, a high sea level and the development of vast carbonate platforms with extensive reef constructions. Locally, there were (evaporite) basins amidst deep rifts associated with volcanism. The large oil and gas reserves of the North Caspian Basin are situated in these rocks (CLARKE, 2000).

One of the major ‘catastrophes’ of the earth history happened in the Upper Devonian when most of the reefs were wiped out in the latest Frasnian. Organic carbon-rich sediments with debris from the continental forests did affect the shallow-water ecosystems. The deeper water Nautiloides, Orthoceroids and Ammonoides escaped the impact of these events.

The First Major Approach (FMA) took place at the end of the first quarter of the Carboniferous (395 – 2 x 33 = 329 mya). Here the maximum approach (and possibilities) in the communication was reached. The maximum intentio is situated on the geological time scale at the boundary between the Lower (Mississippian) and Upper (Pennsylvanian) Carboniferous. In particular the Goniatites – cephalopods with a simple infolded chamber wall (sutures) – developed into a large variety of forms. A new group with so-called ceratite sutures arrived in the Mississippian (Lower Carboniferous). The ceratite suture was characterized by a smooth rounded saddle and crinkled lobes. Their existence reached a maximum in the Triassic (the genus Ceratites is a typical example). The latter geological period (Triassic) has been called the ‘Age of the Ceratites’.

The Ammonites sensu stricto – distinguished by complex infolded chamber walls – first appeared in the Pennsylvanian Period (Upper Carboniferous). This geological era is known for its large quantities of coal. The surplus of carbon was derived from tropical forests, which kept on growing due to favorable biological, climatological and tectonic circumstances.

The First Visibility Crisis (FVC) was around 263 mya, at the beginning of the Perm. This picture of ‘crisis’ fits pretty well, because the Permian was – in general – rather hostile to the marine life. Sea level dropped, and continental movements became important. Some of the ammonites had a hard time in the changing environment, with locally developed into shallow seas with high concentrations of copper and salt (Zechstein). The ancient crustal cores of the Southern Hemisphere (Brazil, Africa, India, Australia and eastern Antarctic) had emerged from the Silurian-Devonian seas as a new continent called Gondwanaland. A large glaciation took place here during the Upper Carboniferous and Permian.

The folding of the inner septa (chamber walls) – visible as the curled sutures – continued to prosper in the surviving ammonites, but there was little sign of decorations of the outer shell. It was only after the turn of the Paleozoic into the Mesozoic (245 mya) that new shapes and design could develop.

The Pivotal Point (PP) in the visibility area of the Ammonoidea was situated in the middle of the Triassic Period (230 million years ago). The earlier mentioned Ceratites, with highly decorated shells, had their hey-days. The old Nautiloids, which first appeared in the Cambrian Period with smooth, gently infolded chamber walls, relived palmy days for the second time. The expansion was, in hindsight, a rearrangement of the deck chairs on the Titanic: both the Nautiloids and the Ammonoids nearly died out at the end of the Triassic (210 mya). The former only continued with a single species (the present day Nautilus). The latter started their development all over again from simple basic forms (taken from the surviving Phylloceras and Lytoceras) into forms with very complicated sutures (lobes in the chamber walls).

The Second Visibility Crisis (SVC) at 200 mya – a mere 10 million years after the events at the Triassic-Jura boundary – contained all the drama of these times of change for the Ammonites. Melting glaciers and large-scale magmatism caused a continuous changing landscape. The pattern of transgression and regressions – as it reflected in the deposits of the Triassic (a name pointing to the triple division: Buntsandstein – Muschelkalk – Keuper) – continued into the Jurassic. After a severe regression (in the Upper Triassic or Rhaetium stage), the Jurassic was again a period of transgression. Newly flooded parts of land offered rich, relative shallow seas. The adventurous Ammonites had to adapt to these sea level changes, and they did so brilliantly, becoming the leading time-indicating fossils of the Jurassic Period (210 – 145 mya).

The ‘Golden Age’ of the Ammonites was the beginning of the Jura period, which was also in other respects a time with a rich fossil record (fig. 72). The small Foraminifera (plankton) staked their claim as widespread index fossils from the Jurassic onwards. Reef building was as important in this epoch (particular in the Malm) as it was in the Silurian, Middle Devonian, Lower Carboniferous and Middle Triassic.

Fig. 72 – Ammonites of the Lias (Lower Jurassic) showed a rich variety of ornaments and complicated sutures. Still, their survival had only some millions years earlier hung in the balance, when nearly the whole population of Ammonoidea died out. The Second Visibility Crisis (200 mya) coincided, within a margin of 10 million years, with the boundary between Triassic and Jurassic, when these radical changes occurred.

The Second Major Approach (SMA) took place some 135 million years ago, at the beginning of the Cretaceous (145 – 65 mya). The Ammonites touched their basic existence (as a subclass) in an environment, which mirrored the desirable settings of the Jurassic Period. Further expansion of the (Upper) Cretaceous seas offered more space for development. The great transgression of seas in Europe had submerged lands that had not been covered by water since the Palaeozoic.

A large transgression, known as the Comanchean Sea, spread in the Lower Cretaceous over the southern states of northern America. Later, in the Upper Cretaceous, the Colorado Sea extended even further from Mexico up into the Arctic. These circumstances were favorable for the Ammonites and they proliferated in a wide variety of forms.

The Ammonites were finally caught up in the mass extinction at the end of the Cretaceous. This event at the K/T (Cretaceous-Tertiary) boundary killed about seventy-five percent of all species, including marine, freshwater and terrestrial organisms. The mass extinction included all the Ammonoids and Belemnoids, large groups of organisms such as Foraminifera, Echinodermata and Molluscs, flying reptiles (Pterosaurs) and the complete wipe-out of the Dinosaurs.

Fig. 73 – The number of Ammonoid families and superfamilies during their existence on earth from the Lower Devonian to the Upper Cretaceous, i.e. from around 395 to 65 mya.

The evolution of the Ammonoids was not a gradual affair, as will be clear from the graph in fig. 73 (the number of families and superfamilies are adapted from MOORE (1959/1997) and CLARKSON (1979). It is a history of successes and disasters in what may be called a ‘paleontological relay’. The ancestral stock gave from time to time rise to short-lived groups, which replaced each other in due course. This picture, as observed here within one subclass, might be the blueprint for the evolution of the Large Visible Animals (LVA) as a whole.

The Ammonoids (as the Trilobites before them) have been so important because they provided a marker point in the geological history and a subsequent scale of measurements. The end of these flexible groups, which nearly died out at earlier occasions, brings about the real character of visibility. A suture or break in the unity of life (because a species or group vanished from the earth) calls for a choice. The disappearance of the Ammonoids (and all other extinct species) from view – for whatever reason – will lead, if nothing else, to the notion of a boundary. The nature of this distinction, as interpreted by the observer in a particular division setting, will eventually contribute to the insight of visibility-in-general.

Life on earth is a matter of coming and going, trying new chances, adapt to changes or simply disappear altogether. Existence is a moment in space and part of a specific communication. The fact that certain life forms have disappeared only proves that they have left the visible visibility area of a communication cycle between Man, as the observer, and the earth, as it is known here and now. It could mean that their existence continues – this very moment – in other communication cycles between other participants. This prospect means that nothing is lost forever.

6.2.2. Large animals as time indicators

The previous visibility-periods (from Trilobites and Ammonites) were ‘closed’. They did not pose problems of a beginning and end (if particular difficulties with regards to the establishment of boundaries, and the definitions of the participants are left untouched). There is no element of prediction, because their life span is known. It is only a matter of comparing their occurrences in time with the general characteristics of the CF-graph in terms of intensio and remisso to describe their characteristics.

The Trilobites and Ammonites are only two of the many extinct animals in the geological record to which the quadralectic method can be applied. Their disposition as index fossils is a major advantage, but other groups of extinct animals can be treated in the same way. The next step will lead to the study of all Large Animals on the planet Earth, dead or alive. Large Visible Animals (LVA) are defined as all the living bodies in nature, which are part of the animal kingdom and can be observed by a human being without the help of artificial equipment to enhance visibility.

This definition reflects a straightforward approach to nature from the human point of view. It means that certain primitive cells, which have been found in very old rocks (fig. 74) do not qualify, although they play an important role in the definition of life on earth-in-general.

Fig. 74 – These curled fossils are the first signs of life as found in the geological record. They were dated as 2.15 billion years old. These eukaryotic (multicellular) organisms are known as Grypania spiralis. The photosynthetic algae were discovered in the 1980’s and caused a stir because they were over one billion years older than the next closest in age eukaryote.

GOULD (1989) stated that ‘the first uncontested appearance in the fossil record took place some 570 million years ago – and with a bang, not a protracted crescendo.’ ‘The Cambrian explosion’, as he called the sudden change in the geological record, ‘marks the advent (at least into direct evidence) of virtually all major groups of modern animals – and all within the minuscule span, geologically speaking, of a few million years.’

The beginning of the ‘large’ animals is clear as long as the finer details are left alone. The Large Visible Animals (LVA) occur in rocks, which are not older than around 600 million years old. The figure of 590 mya has been used in publications, based on Rubidium-Strontium ages. Recent research, coordinated by the International Subcommision on Cambrian Stratigraphy (I.U.G.S.), put the boundary at a considerably younger age, i.e. 545 mya.

The coarse boundary between the so-called Cambrian rocks – named after an area in Great Britain (Wales) where these rocks surface on a large scale – and the underlying Proterozoic rocks was primary chosen on the grounds of the occurrence of ‘larger animals’. Nevertheless, a precise boundary, which is useful on a worldwide scale, is much more difficult to give. The study of early shelly macrofossils (SSF; small shelly fossils) did not provide enough correlation potential.

The so-called trace-fossils (imprints of animals, but not the animal itself, like burrows) offered a better opportunity and the ichnofossil Tricophycus pedum was subsequently chosen by the specialists to indicate the lower Cambrian boundary. The rock section (Chapel Island Formation) at Fortune Head, southeastern Newfoundland, became the type section of the Protozoic-Cambrian boundary. Researchers (GEHLING, et al, 2001) found that the range of Treptichnus pedum – an index trace fossil for theTreptichnus pedum Zone – extends some 4 meters below the Global Standard Stratotype-section and point for the base of the Cambrian Periodat this location. The results prove the ambivalence of the ‘accuracy’ of a particular geological boundary. This scientific bickering does not mean that such a boundary cannot be of practical use in the field.

The ‘Cambrian explosion’ (or better: Cambrian bio-radiation event) consists of four significant periods:

1. The Vendian period (565 – 543 mya) former to the ‘Cambrian explosion’ with the sudden emergence of the metazoa with soft body, including the so-called Ediacara fauna.

2. The S.S.F. appearance (Small Shelly Fossils) characterized by many small organisms with shells, spicules and a low diversity (543 – 530 mya).

3. The Tommotian-Atdabanian radiations (530 – 525 mya) with the emergence of most modern lines and many extinct specimen (with hard skeleton and soft body). The first macroscopic faunas occur at the end of the Siberian Tommotian Stage, when major reefal complexes were formed by Archaeocyaths (simple sponges).

4. The Burgess Shale fauna (towards 520 mya). This Middle Cambrian shale from the Burgess Pass, Yoho National Park, British Columbia, was discovered by Charles Walcott in 1909 and yielded strange and previously unknown animals with no modern analogues.

Fossil from the Burgess Shale, British Columbia – Side view of Marrella. Drawing by Marianne Collins. In: GOULD, Stephen J. (1989). Wonderful Life. The Burgess Shale and the Nature of History. Penguin Books, Harmondsworth, England. ISBN 0-14-013380-1

The extremely rapid diversification of multicellular animals is unique in the geological history. The sudden event provides a good point of recognition (POR) on the CF-graph of the communication between the Large Visible Animals (LVA) and the world. The start of the visible visibility of the LVA’s is put at the beginning of the Tommotian, i.e. 530 mya.

If the creation of the Earth is put at some 4600 mya and the beginning of the Large Visible Animals (LVA) at the end of the Early Cambrian (530 mya) then two points of recognition (POR) are known. The basic unit (BU) (1/16^th of the communication cycle V) can be calculated as follows:

Beginning of V (communication cycle) = 4600 mya

Beginning of FV (first visibility of LVA) = 530 mya

5/16 V (invisibility area 0¹) = 4070

V = ——— . 4070 = 13024 my (communication cycle V)

10 5

X = ——— . V = ——— . 13024 = 8140 my (visibility area X)

16 8

BU = ——— . V = 814 my (basic unit)

The Large Visible Animals (LVA) figure in the history of the world from their starting point in the Early Cambrian (- 530 mya) to the final (or last) visibility far away in the future, some 7610 million years from now (fig. 75).

X = – 530 Y = 11.00 (FV) X = 4354 Y = 13.00 (SVC)

X = 284 Y = 11.00 (AP) X = 5982 Y = 6.00 (SMA)

X = 1098 Y = 6.00 (FMA) X = 6796 Y = 11.00 (RP)

X = 2726 Y = 13.00 (FVC) X = 7610 Y = 11.00 (LV)

X = 3540 Y = 10.00 (PP)

The abbreviations of the inflection points on the (visible) visibility area X of the CF-graph are given on p. 122, fig. 51.

Fig. 75 – The communication between the Large Visible Animals (LVA) and the planet Earth as expressed in a CF-graph.

The present, or ‘here and now’ as experienced by the observer, is situated in the second part of the Second Quadrant (II, 2). This position falls relative early in the development of the visibility, i.e. between the First Visibility (FV) and the Approach Point (AP), when the CF-values remain a steady 11. All the geological epochs so far, with their huge changes in climate, the ongoing process of continental drift, the appearance of new species and the extinction of others, are – in the perspective of the LVA’s – a minor opening act to the great developments, which are about to come.

The stage of equality (CF = 11) will last another 284 million years. Most likely, the geological epochs will continue to happen in their own way. New species will turn up. There is plenty of time and opportunity for the development of a new stock of huge reptiles (like the Dinosaurs). The present-day Nautiloides might give rise to a renovated breed of curled and chambered see animals (like the Ammonoids). Other groups (including mankind) will most likely disappear. However, it is more than likely that other clever vertebrates (or some unknown animal with other building materials) will take their place. The fate of Homo sapiens will be looked at in the next chapter.

The First Major Approach (FMA), with the CF-value 6, will take place some 1100 million years in the future (which is more than the geological history of the LVA’s to date). The full potential of the Large Visible Animals within the realm of the planet Earth is reached at that particular time. It will be hard to imagine how such an animal kingdom will look like at that given time. Also the further development – including the major ‘crisis’ in 2726 (FVC) and 4354 (SVC) million years time – go beyond the frame of reference of the present day observer. The only certain thing to say – with the universal communication (CF) graph at hand – is that the large visible animals will disappear from the earth after 7610 million years.

Another basic unit (BU) further on the CF-graph – i.e. 814 million years – spells the end of (large) life altogether. The earth is in 8424 million years time as barren, as it was when the formation of the solid earth by accretion took place some 4600 million years ago. In the meantime, the great changes in the position of the continents in the past six hundred million years will most likely continue.

The breaking up of a single supercontinent called Rodinia (in the early Cambrian), its merging again (in Pangaea) in the Permian and the subsequent breaking up in Gondwana and Laurasia in the Jurassic and Cretaceous times are only minor disturbances in the light of history. It is fair to assume that these movements will continue in the future. At some stage, the continents will come together again to form a new supercontinent. Life, as it is then, will have to adapt to the boundaries of land and sea.

Charles HAPGOOD’s book ‘The Path of the Pole’ (1970) was a controversial, mind-provoking piece of work on this subject. The polar wandering was brought forward as the mechanism that causes the displacement of continents. He pointed to the accumulated centrifugal force, generated by the unsymmetrical ice packs of the poles, which caused enough momentum to displace the crust.

Nowadays, this theory is of lesser importance, since the mechanism of ocean floor spreading (for instance from the Mid-Atlantic Ridge) is held responsible for the movement of continents. The cyclic character of the latter fits better in a realistic picture of nature. Hapgood’s suggestion that these continents have a connection with the lost continent of Atlantis does not enhance his popularity with the established sciences.

The recent interest in the loss of ozone in the lower stratosphere over Antarctica, as first noticed by a research group from the British Antarctic Survey in the 1970s, has culminated in wild speculations of global warming and the effect of man’s activities on the environment. Even the Nobel Prize was awarded to scientists, who sincerely believed that man made chemicals containing chlorine (CFC’s), could have caused the changes they observed for such a relative short period.

The degree of instability of the atmosphere has many causes, both terrestrial as extraterrestrial, and a research period of several decades is not enough to pinpoint a particular source. The measurements of the so-called ‘Ozone Hole’ over a relative short period does not provide the scientific foundation for a postulate of large changes in climate (let alone it possible causes).

The concern with the planet Earth is, nevertheless, a good thing and a worthy cause. However, the arguments to ‘better’ the environment should be kept free of unscientific, fashionable or political interference. The end of the ‘Age of Steam’ and the replacement of coal-fired energy sources by oil and gas has done more for the well-being of the people on the earth than the Montreal Protocol in 1987 aiming to reduce the use of CFC’s. On the other hand, the use of fossil fuels (by airplanes and cars) has taken now such an enormous flight that a moment of reflection is appropriate.

The consciousness of scale – which was mentioned in the beginning of this book as the best quality to approach life – should never be an excuse to dodge responsibility. The important ‘law’ in quadralectic thinking that the boundaries of a communication are determined by the smallest part (p. 93) implies that the relation between mankind and the earth is ‘ruled’ by our vision as Homo sapiens. Mankind, even in their great number, is the Small Part in the communication with the Earth (as the Large Part). Therefore, our boundaries stipulate the width of the interaction, and our view is the yardstick of measurements. The earth, as a planet, which has been around for some 4600 million years, will help itself. There is no doubt about that. It will survive any onslaught – be it by man or otherwise – and continue its course through the universe.

Imagination on a geological scale – with its millions of years – does not shirk us of our obligations. Life in time is a precious thing. It has to be respected, if only for our own good. The curious fossils of the Burgess Shales and the bones of Dinosaurs point to an earth in a different setting, but it will still be our world. And the developments in the future can be no different, whatever happens, even if mankind is gone.

The ill-famous ‘Club of Rome’, which shock-waved the world in 1972 with its report ‘Limits to Growth’, has again allayed the message with a new publication called ‘Factor Four: Doubling Wealth, Halving Resource Use’ (VON WEISZÄCKER et al, 2000). This title points, once again, to dualistic tendencies to the problem of resources, which is bound to fail. The real ‘Factor Four’ should be the quadralectic outlook in the conversation with the earth, with understanding as a key word.

6.2.3. The relation between Man and planet Earth

The brief discussion of the Large Visible Animals (LVA) and their function as time indicators would not be complete if Man-itself was not included as a LVA. The very existence of man on earth at the moment means that its presence belongs in an ‘open’ period. In our company are all the animals, which still living today: their existence might have a long history (like the crocodiles and the tortoises), but the end of their (biological) life cycle is not reached yet. The existence of Homo sapiens on planet Earth can only be appreciated if another point of recognition is found.

The position of man on the planet Earth will first be considered in order to put the present choice into perspective. A very important innovation in thought – as far as our own position in the universe is concerned – took place around the year 1800. The ‘Age of Reason’ opened up because the bonds of oppositional thinking were thrown off. A description will be given of some participants in this transition, which is closely related to the (conceptual) position of Man on the planet Earth. Two contributants, Charles Bonnet (1720 – 1793) and George de Buffon (1707 – 1788) lived before 1800, one (Georges Cuvier (1769 – 1832) lived on both sides of this year, and two others (Robert Chambers (1802 – 1871) and Charles Darwin (1809 – 1882) lived after 1800.

A. The Swiss lawyer Charles Bonnet (1720 – 1793) had a creative mind, which was geared towards the natural history. He described, in his ‘Memoires autobiographiques’, a special interest in and dedication towards such subjects as the Aphids (tree-lice), freshwater worms, the respiration of butterflies, caterpillars and tapeworms. The Aristotelian concept of a ‘Great Chain of Being’, running from man, at the top, to the ethereal matter at the bottom became a credo in Bonnet’s book ‘Contemplation de la nature’ (1764). The writing must have been a very difficult undertaking, because an eye disease in the year 1744 caused a virtual blindness in 1746.

Charles Bonnet (1720 – 1793) (Photo: Wikipedia).

Later, in 1770, he turned to visionary speculations in his book ‘Philosophical Palingesis, or Ideas on the Past and Future States of Living beings’. The idea was proposed that all females carry within them the future generations in a miniature form (the homunculus). These miniature living beings, which pre-existed reproduction, could survive the great cataclysms in the history of the earth (like the biblical Flood) and were able to bring about evolutionary change. The preformation- or ‘encapsulation’ theory, based on the emboitement, attributes to the first female of each animal the destiny of the entire species. He believed that the part should be reflective of the whole, and the whole is a grand order from lower up to higher (closer to human).

Bonnet pioneered, with his ideas on the homunculi, in the field of quadralectic thinking. Here also, is the past, present and future embedded in each (sub) quadrant. Everything what is, is (was) already there. This view is the logical outcome of a cyclic setting. The oppositional view of an epigenetic system, with its idea of development, fits in a general outlook. Bonnets position, shifting from the ‘Great Chain of Being’ to the Homunculi, anticipated the great change from lower to the higher forms of division thinking at the beginning of the nineteenth century. He called for a ‘History of the Attention’. This phenomenon would cover a history of all true discoveries. And probably he was right: ‘Attention, not creativity, is the mother of genius’ (ANDERSON, 1982).

Bonnet’s quadripartite division of all beings reflects his insecure position in terms of division thinking:

1. Brute ——————————— Unorganized

2. Organised————————— Inanimate

3. Organised ————————– Animate

4. Organised ————————- Animate ——————— Reasoning

This representation is not a balanced four division like the quadralectic segmentation. Three kinds of antithesis are mixed up. The brute (a physical force) versus the reasoning (an intellectual force) play a part in another antithesis (organized versus unorganized) situated in a world, which is either inanimate or animate. The triple division (organized – animate – reasoning) is finally the ‘highest’ form in a hierarchical context.

B. The French naturalist and mathematician George Louis Leclerc Count de Buffon (1707 – 1788) lived in the same ‘Age of Enlightenment’ as Charles Bonnet. He might be the first to put the ideas of development and organic evolution (transmutation) on the intellectual track. At twenty, he discovered the binomial theorem and introduced differential and integral calculus into the probability theory (Sur le jeu de franc-carreau). These endeavors can now be seen as a (mathematical) approach to the ultimate boundaries of the Third Quadrant. His ‘Historie Naturelle’ – an encyclopedia of forty-four volumes – described everything known about the natural world and is a monument and tribute to the visible visibility of the Third Quadrant.

George Louis Leclerc Count de Buffon (1707 – 1788) (Photo: Wikipedia).

Buffon is now remembered for a probability experiment known as ‘Buffon’s Needle’. The problem was first stated in 1777. The story goes that Buffon calculated pi by throwing some French stick loaves over his shoulder onto a tiled floor and counted the number of times the loaves covered the lines between the tiles.

The dropping of a random number of needles on a lined sheet of paper will have the same effect of determining the probability of a needle to cross one of the lines. The lengths of the needles and the distance between the lines play a role in the theoretical discussion of this matter (SCHROEDER, 1974), but the outcome will be always approximate pi. Pi can be calculated from the needle drops by multiplying the number of drops by two and divide the outcome by the number of hits: 2 (total drops) / (number of hits) = pi (approximately) (fig. 76).

Fig. 76 – Buffon’s needle. Two parallel lines indicate a divided world, which is invaded by a multitude (the French loaves or pins). The probability of crossing a line is a value derived from a cyclic environment (pi). It is relevant in the history of division thinking, because it bridged a gap between the linear (Third) and the circular (Fourth Quadrant) perception.

C. Georges Cuvier (1769 – 1832) was a prolific vertebrate anatomist and paleontologist, who used the comparative (analogy) method in the study of nature. He was opposed to Lamarck’s transmutation theory. The latter pointed to the heriditical nature of acquired properties. Cuvier did not believe in the development of life forms over time. Organisms were functional wholes and any change (of a part) would destroy their delicate balance. He was more impressed by the results of his field trips, which pointed to the fact of extinction of past-life forms.

Georges Cuvier (1769 – 1832) (Photo: Wikipedia).

Cuvier was a distinct (four) division-thinker. He classified animals into four ‘branches’ or embranchements:

1. The Vertebrata

2. The Articulata (arthropods and segmented worms)

3. The Mollusca (all other soft, bilaterally symmetrical invertebrates)

4. The Radiata (cnidarians and echinoderms)

Cuvier proved (in 1816) that these four main groups had distinctive differences in their building plans. Man (order ‘Bimana’) was taxonomically separate from the apes (order ‘Quadrumana’). He noticed revolutionary periods in the earth history and constructed the first biostratigraphy in the Paris Basin (‘Description geologiques des environs des Paris’ (1811; in co-operation with Alexandre Brongniart).

The comparative embryological investigations of the Estonian scholar Karl Ernst von Baer (1792 – 1876) showed independently that the building plans of the four main groups were already present in the development of the egg (BOEGNER, 1983). The idea of a hierarchical progress from the ‘lower’ to the ‘highest’ animals (Bonnet’s chain of being) was therefore, seriously questioned by the four basic types of Cuvier and Von Baer. The unity in the animal kingdom was broken up, in favor of four groups (divisions).

D. Robert Chambers (1802 – 1871) gave, in his book ‘Vestiges of the Natural History of Creation’ (CHAMBERS, 1844), an impressive summary of the scientific issues some fifteen years before the intellectual landslide caused by Darwin’s ‘Origin of Species’ (1859). It is known that Alfred Russell Wallace (1823 – 1913) started his search for a lawful explanation of the species after reading ‘Vestiges’ in 1845. The book showed clearly that many of Darwin’s ideas and causal explanations fitted into the narratives of progress and developmental models, which were current in the middle of the nineteenth century.

Robert Chambers (1802 – 1871) (Photo: Wikipedia).

Chambers was enthusiastic about the circular or ‘quinarian’ classification system as proposed by the naturalist and entomologist William Sharp Macleay (1792 – 1865). He developed a biological classification, which held that all organisms could be arranged in hierarchically, circular sets of five taxa. The taxonomic circles were held together by affinities and not by the misleading functional analogies. All natural groups were circular.

‘Starting from one portion of the group, when it is properly arranged, we can proceed from one to another by minute gradations, till at length, having run through the whole, we return to the point whence we set out.’ (‘Vestiges’, p. 238). The component circles were invariably five in number: five sub-kingdoms, five classes, and five orders, etc.

Chambers distinguished, in a good Macleayan spirit, five leading races in the history of mankind (p. 277ff):

Caucasian or Indo-European
The Mongolian
The Malayan
The Negro
The aboriginal American

He noted colour as the most conspicuous element in the (racial) transition from a white to yellow, black and red skin. These colour differences were, in his view, explicable on the ground of development. ‘Our brain goes through the various stages of a fish’s, a reptile’s, and a mammifer’s brain, and finally becomes human. There is more than this, for, after completing the animal transformations, it passes through the characters in which it appears, in the Negro, Malay, American, and Mongolian nations, and finally is Caucasian’ (‘Vestiges’, p. 306).

The conclusion is that ‘the leading characters, in short, of the various races of mankind, are simply representations of particular stages in the development of the highest or Caucasian type.’ And he continued: ‘The Negro exhibits permanently the imperfect brain, projecting lower jaw, and slender bent limbs, of a Caucasian child, some considerable time before the period of its birth. The aboriginal American represents the same child nearer birth. The Mongolian is an arrested infant newly born. And so forth.’

Chambers’ conclusions were as straightforward as degrading (p. 309): ‘According to this view, the greater part of the human race must be considered as having lapsed or declined from the original type. In the Caucasian or Indo-European family alone has the primitive organization been improved upon. The Mongolian, Malay, American, and Negro, comprehending perhaps five-sixth of mankind, are degenerate.’

It is amazing, that Chambers’ circular (and five-fold) way of thinking can lead to such a bizarre hierarchical outlook, which seem to be fueled by oppositional thinking. The conclusion should be that the unbalanced five-division can be misinterpreted in the same way as the three-division, by emphasizing the inequality (unevenness). It has to be remembered, in this context, that the idea of progress is, in essence, a linear thought, based on a two-division in quality of the things in the past and the present.

E. Charles Darwin (1809 – 1882) is probably the most notorious as far as the relation of man and earth is concerned. He is the founder of the evolution theory as expressed in his book ‘The Origin of Species’ (1859). The story of its intellectual and practical realization is well known. It is only in the closing part (conclusion) of the work that a visionary remark pointed to the possibility that ‘much light will be thrown on the origin of man and his history’. Later in his life he took up that challenge and traced the (evolutionary) history of man.

Charles Darwin (1809 – 1882) (Photo: Wikipedia).

The result of his (scientific) speculation of the human origin was presented in ‘The Descent of Man (and Selection in Relation to Sex)’. The first edition of the book was published in two volumes in February 1871. The descent or origin of man was, in his view, derived from some lower form, mainly because of homologous structures, embryological development and rudimentary organs. Darwin was, as usual, careful in his conclusions. He pressed the importance of natural selection (‘my conviction of the power of sexual selection remains unshaken’), but also stressed that ‘great weight must be attributed to the inherited effects of use and disuse, with respect both to the body and mind.’

The disciplines of sociology and psychology widely absorbed aspects of Darwin’s way of thinking in the late nineteenth and twentieth century. The intentions of his original ideas were not always properly understood in these young sciences. For instance, the survival of the fittest, a phrase first used by the British philosopher and sociologist Herbert Spencer (1820 – 1903), was often placed in a dualistic setting where oppositional forces are at work. The principle of natural selection reached its greatest manifestation in the empirical realm (strength, physical energy, colour, etc.).

Unfortunately, Darwin himself contributed to this limiting interpretation. He proved a prolific oppositional thinker in the discussion of the sexual differences in animals in Chapter IX – XVII (more than 230 pages) of his ‘The Descent of Man’. His knowledge was impressive, but his ranch of division thinking was more limited than in his earlier work. The inevitable conclusion of an emphasis on power leads to a ‘Law of Battle’, first noticed with birds (p. 551) ‘Almost all male birds are extremely pugnacious, using their beaks, wings, and legs for fighting together’ (fig. 77), later also observed with Mammals. The impression is given that the fittest is the (physically) strongest as well.

Fig. 77 – The Ruff or Machetes pugnax (from Brehm’s ‘Thierleben’) is notorious for his extreme pugnacity. The fighting birds get a lot of attention in Darwin’s book ‘The Descent of Man’, because they support his ‘Law of Battle’. The stronger males gain advantage over their rivals in battles, and their victory leads, combined with the ‘choice’ of the female bird, eventually to a better offspring.

Chapter XVII (‘The Descent of Man’, p. 763) opened with the statement: ‘With mammals the male appears to win the female much more through the law of battle than through the display of his charms’. Then a long list of fighting mammals is produced from the guanacos in Patagonia, the reindeer in Norway, to the wild bulls in Chillingham Park, the descendants of the gigantic Bos primigenius. Tusks and horns were objects of great interest for Darwin (and many modern wildlife programs on television follow this approach). Finally, Darwin admitted that ‘we might feel sure, that the law of battle had prevailed with man during the early stages of development.’

Interhuman relationships are – even today – often placed in an ‘animal’ framework, with the emphasis on domination, power and violence. The choice takes place in the visible realm and is based on physical aspects. However, the definition of the ‘fittest’ as the outcome of a battle is just one viewpoint of evolutionary development. Surely, the ‘Third Quadrant’ view ought to be present, but it is just one of the available possibilities (of which the number depends on the initial choice in division thinking). Darwin himself was possibly aware of such a wider frame of mind. He did not discount the (Lamarckian) ‘inherited effects’ – which are hard to materialize – and left ample room for the possibility that other factors might contribute to the evolution of species.

It was only at the beginning of the twentieth century, that discoveries of human (-like) skulls in Africa, Asia (Java and China) and Australia brought the idea of human evolution to live. The subsequent incidental founds on isolated places of the world carried a theoretical framework build with a great deal of imagination. The problem of boundaries was and still is pressing in the case of the fossil record of the Human Being.

A further complication arises because its historic presence (or non-presence) is a political-theological issue. A firm (Christian) belief, in an oppositional setting, which says that God created the first man, does not leave room for a progressive development from the apes. The same inflexible kernel can be found in the interpretation of the geological record as being the result of gradual processes (uniformitarianism) or the Biblical Flood (catastrophism). The latter debate is – just as the ongoing creation versus evolution controversy – a (deliberate or naive) misunderstanding of the distinctive thinking methods of an observer in a lower or a higher division environment.

The skulls of man-ape and apes are different from the modern human skull, but it is often difficult – due to the scarcity of fossil material – to put a clear demarcation line. The position of the First Visibility (FV) of Man on the CF-graph is therefore a subjective matter. The relative short period of time of the geological track record of the human being on earth gives specific problems in the field of formal limitation. The crucial point, as far as the visibility of the first human presence is concerned, has to be a knowledge of the moment when the human lineage split from the apes.

There was, for some time, a reasonable consensus among scientist with regards to the evolution of man (JORDAN, 1984). A jaw fragments and several teeth were found in the 1930’s (by Louis Leakey and his collaborators) and some more finds (also jaws and teeth) dated from 1977. The Ramapithecus was then identified as the first representative of the hominid evolution line, who started to appear some fifteen million years ago.

However, more recent research has put the idea of the Ramapithecus as the first human in doubt. ‘The dethroning of Ramapithecus’, wrote Roger LEWIN in his book ‘Bones of Contention’ (1987; p. 86), ‘from putative first human in 1961 to extinct relative of the orang-utan in 1982 – is one of the most fascinating, and bitter, sagas in the search for human origin.’ If this is so, new contenders for the role of first man must be found.

The Australopithecus, living some four million years ago, seemed to fit the qualifications. This choice also met with resistance. The earliest known species of the genus Homo was the Homo habilis, discovered by Louis Leakey in the early 1960’s in East Africa. Our ancestors seemed to emerge from an evolutionary line approximately 2.2 to 1.6 million years ago. The fossils found by Leakey and his colleagues were about 1.75 million years old.

The first species to migrate from Africa during the Pleistocene glacial period was called the Homo erectus. The species was widely found in the time frame 1.8 – 1 million years ago in Europe, India, China and Indonesia and includes the Java- (Pithecanthropus) and Peking Man. It is currently believed (in the scientific world) that mankind developed either from a single African stock, or from the before mentioned multiple (geographical) centres.

It is possible (as can be seen in the chaos theory) that mutations do occur in clusters and that when a particular mutation has occurred once, it’s repetition is more likely (GLEICK, 1988). In that situation, the genetic action (mutations) in the different centres would follow a similar pattern.

The early Homo sapiens, like the Neanderthal Man, appeared about 250.000 years ago (with a range between 200.000 and 300.000 years). The Homo sapiens structure is similar to that of the Homo erectus, but the latter has a slightly rounder and larger skull. The boundary between the two species is not clear. A recent predecessor of the present Homo sapiens sapiens is the Cro-Magnon Man, which goes back to about 30.000 years.

This variety of names and dates of the ‘first appearance’ of Man poses a serious obstacle to any clear definition of First Visibility (FV). The best way to attack this problem – from a quadralectic point of view – is a preliminary proposal for a first visibility, bypassing the scientific problems of names and limitations. This action seems a bold step, but it is the only way forward. Three examples (or choices) will be given here, leading to very different results. Neither of them claims, in a genuine quadralectic spirit, to present the ultimate truth. The names and boundaries are just suggestions, aiming at a faithful representation, and not more than that. This method gives, in the meantime, a perfect example of a quadralectic approach to the uncertainties of science.

I. The first example places the Ramapithecus (15 mya) at the beginning of the communication cycle V (the CF-graph) – even if its direct hominid origin is not established or in doubt – and the Australopithecus (4 mya) is seen as the first visibility point (FV).

The following figures can now be calculated as follows:

Beginning of V (communication cycle) = – 15 mya

Beginning of FV (first visibility of Man) = – 4 mya

5/16 V (invisibility area 0¹) = 11

V = ——— . 11 = 35.2 my (full communication cycle V)

X = ——— . 35.2 = 22 my (visibility area X)

BU = ———- . V = 2.2 my (basic unit)

The basic calculations follow the theoretical rules, in which the invisibility area (O¹) in the First and Second Quadrant consists of five units (BU). One basic unit (BU) is 11: 5 = 2.2 million years. The visible visibility area (X), consisting of ten BU’s, has a duration of 22 million years. The total communication cycle (V) lasted 16 x 2.2 = 35.2 million years.

The inflection points (Y) for the visible visibility period (X) of Man (Homo spec.) on earth are given below. The Points of Recognition (POR) are the appearance of Ramapithecus, some 15 mya and the first visibility (FV) of mankind in the form of Australopithecus at 4 mya. X is expressed in million years.

X = -4 Y = 11.00 (FV) X = 9.2 Y = 13.00 (SVC)

X = -1.8 Y = 11.00 (AP) X = 13.6 Y = 6.00 (SMA)

X = 0.4 Y = 6.00 (FMA) X = 15.8 Y = 11.00 (RP)

X = 4.8 Y = 13.00 (FVC) X = 18 Y = 11.00 (LV)

X = 7.0 Y = 10.00 (PP)

The abbreviations of the inflection points on the (visible) visibility area X of the CF-graph are given on p. 122, fig. 51.

These values characterize the CF-graph, which represents the occurrence of Man as interpreted by a human being in the beginning of the twenty-first century. Fig. 78 gives the full communication cycle V (for this particular interaction) and also indicates the position of the observer.

Fig. 78 – The CF-graph for the occurrence of Man on the planet Earth. The POR’s (Point of Recognition) are placed respectively at 15 mya (Ramapithicus) and 4 mya (Australopithecus).

The CF-communication graph shows the beginning (-4 mya) and the end (18 my in the future) of the visible human presence on the planet earth (as derived from the given premises). Our present point of observation (OP) is situated in the third part of the Second Quadrant, which is fairly at the beginning of the visible time span, heading towards the First Major Approach in 400.000 years time. Problematic times will occur in about 4.8 (FVC) and 9.2 million years (SVC). Mankind will be around on the earth for another 18 million years.

II. The second example of the expected occurrence of man on earth takes two different Points of Recognition as references. The beginning of the communication cycle V is determined at the Australopithecus (at 4 mya) and the First Visibility (FV) of Man is put at the Homo erectus appearing some 1.8 million years ago on the earth.

The main features of the CF-graph are calculated as follows:

Beginning of V (communication cycle) = – 4 mya

Beginning of FV (first visibility of Man) = – 1.8 mya

5/16 V (invisibility area 0¹) = 2.2

V = ——— . 2.2 = 7.04 my (full communication cycle V)

X = ——— . 7.04 = 4.4 my (visibility area X)

BU = ——— . V = 0.44 my (basic unit)

The basic calculations follow the same route as before assuming that the invisibility area (O¹) in the First and Second Quadrant consists of five units (BU). One basic unit (BU) is now 0.44 million years. The visible visibility area (X), consisting of ten BU’s, has a time span of 4.4 million years. The total communication cycle (V) is 16 x 0.44 = 7.04 million years.

The specific inflection points (Y) of the visible visibility period (X) of Man (Homo spec.) on earth are as follows (X is expressed in million years.

X = – 1.80 Y = 11.00 (FV) X = 0.84 Y = 13.00 (SVC)

X = – 1.36 Y = 11.00 (AP) X = 1.72 Y = 6.00 (SMA)

X = – 0.92 Y = 6.00 (FMA) X = 2.16 Y = 11.00 (RP)

X = – 0.04 Y = 13.00 (FVC) X = 2.60 Y = 11.00 (LV)

X = 0.40 Y = 10.00 (PP)

The abbreviations of the inflection points on the (visible) visibility area X of the CF-graph are given on p. 122, fig. 51.

Fig. 79 – The CF-graph for the occurrence of Man on the planet Earth. The POR’s (Point of Recognition) are placed respectively at the Australopithecus, appearing some 4 mya and the First Visibility (FV) at the arrival of Homo erectus, some 1.8 mya.

The communication graph (fig. 79) shows the beginning (- 1.8 mya) and the end (over 2.6 my) of the visible human presence on the planet earth. The present (OP) is situated in the second part of the Third Quadrant, just after the First Visibility Crisis (which took place some 40.000 years ago).

The Pivotal Point (PP) will be reached in 400.000 years and the Second Visibility Crisis (SVC) takes place in 840.000 years (SVC). Mankind-as-a-whole will be around on the earth for another 2.6 million years.

III. The third example comprises the most recent approach to the Points of Recognition. Homo erectus is placed at the beginning of the communication cycle (V) as the first sign of any real human presence on earth (about 1.8 million years ago). Homo sapiens is chosen as the beginning of the first visibility of man, appearing some 250.000 years ago. The following calculations can be made:

Beginning of V (communication cycle) = – 1.8 mya

Beginning of FV (first visibility of Man) = – 0.25 mya

5/16 V (invisibility area 0¹) = 1.55

V = ——— . 1.55 = 4.96 my (full communication cycle V)

X = ——— . 4.96 = 3.1 my (visibility area X)

BU = ——— . V = 0.31 my (basic unit)

The features of the communication graph (in particular the inflection points) are known with this basic data at hand (fig. 80). One basic unit (BU) has, in this example, a length of 0.31 million years. The visible visibility area (X), consisting of ten BU’s, comprises a time span of 3.1 million years.

The important inflection points (Y) for the visible visibility period (X) of Man (Homo spec.) on earth are given below. The Points of Recognition (POR) are the appearance of the Homo erectus at 1.8 mya and the first visibility (FV) of mankind with the Homo sapiens at 0.25 mya. X is expressed in million years.

X = – 0.25 Y = 11.00 (FV) X = 1.61 Y = 13.00 (SVC)

X = 0.06 Y = 11.00 (AP) X = 2.23 Y = 6.00 (SMA)

X = 0.37 Y = 6.00 (FMA) X = 2.54 Y = 11.00 (RP)

X = 0.99 Y = 13.00 (FVC) X = 2.85 Y = 11.00 (LV)

X = 1.30 Y = 10.00 (PP)

The abbreviations of the inflection points on the (visible) visibility area X of the CF-graph are given on p. 122, fig. 51.

Fig. 80 – The CF-graph for the occurrence of Man on the planet Earth. The POR’s (Point of Recognition) are placed at 1.8 mya (Homo erectus) as the very beginning of the communication cycle (V) and the occurrence of Homo sapiens at 250.000 years ago as the first visible visibility (FV).

The human presence on the planet earth begins 250.000 years ago and will end in 2.85 million years (as derived from the chosen assumptions). The observational present (OP) is situated at the end of the second part of the Second Quadrant. The First Major Approach is 370.000 years away. Problematic times will occur in about 0.99 (FVC) and 1.61 million years (SVC). Mankind will be around on the earth for another 2.85 million years.

These three examples can be placed in a wider field in order to find more general rules in the relation between the different choices of visibility. A summary of the three positions of mankind follows here first:

The most notable feature is the observational present (OP), which is different in the three examples. The position (of the present) is situated in the Second Quadrant in the first and third example and in the Third Quadrant in the second example. The time towards the First Major Approach (FMA) will take another 400.000 years in the first example and some 37.000 years in the third example. This particular moment (FMA) has already been past in the second example. An important question looms: What is the real present?

An observer in the present (OP) has to determine two parameters on the communication cycle to find out. The beginning of the communication cycle (V) and the moment of the First Visibility (FV) are two possibilities (fig. 81). If the beginning is put further backward in time (to the left; and the FV remains fixed) then the place of observation (OP) will shift towards the first visibility FV (i.e. to the left). Say, for example, that Ramapithecus is not 15 but 24 million years old, then the OP shifts 1.8 million years back in time (BU = 4 instead of 2.2). The OP is then situated at the inflection point of the second and third part of the Second Quadrant. If, on the other hand, the beginning (of V) is closer towards the FV (moving to the right; and FV remains fixed) than the OP moves further along the CF-graph (to the right). The present gets older…

This play of movement (making choices in visibility) can also be inverted. The two parameters are no longer used to find OP, but the OP and FV are used to find the beginning of the communication cycle V. This approach implies the crucial question: where is the present (on the CF-graph)? The question becomes even more interesting if FV is not fixed, but also flexible.

Fig. 81 – The four parameters (a – d) involved in the choice of a visibility, which determines the observational present. The interpretation and definition of the beginning of the communication cycle V and the First Visibility (FV) are essential elements (situated in the past) to anchor an observer in a communication – including the position of man on earth. Other subjective characteristics of the (universal) communication graph (either in the past and/or in the future) can also be used to determine that position.

The presence of a Fourth Quadrant, allowing the inversion of (the Third Quadrant) and the choices/subjectivity (of the Fourth Quadrant) at the same time, offers a new scope on the history and future of mankind. Ultimately, we are in the mind of the beholder. Roger Lewin’s conclusion, as written down at the end of his detailed and somewhat depressing book on scientific bickering (‘Bones of Contention’ (1987; p. 318), is worth mentioning:

‘The truth about man’s place in nature is therefore to be sought in four quite separate dimensions. In the first three levels – of time, form, and behavior – there is scientific evidence, from fossils, stone tools, comparative anatomy and behavior, and molecular biology. Using this evidence, it may one day be possible accurately to draw lines back through time, connecting ourselves with our forebears, their forebears with theirs, and so on until a detailed evolutionary tree traces the link between humanity and brute nature. Exactly where brute nature ends, however, and humanity begins is not a question for molecular or comparative biology. Here there are no lines accurately to be drawn, no hypotheses to be tested, for humanity’s view of itself is constantly shifting, depending on the experience of the moment.’

It might, indeed, be the fourth dimension of subjectivity – as experienced in the Fourth Quadrant – which holds the key to the real position of man at the moment. The graciousness of our being is – in the most veracious investigation – found in the definition of visibility.

6.3. Imagination on a cosmic scale: existence in space

A further insight into the quadralectic approach of nature is given in the position of the planet Earth itself, as a distinct entity in the universe. Earth and universe are part of a communication in which Man is only a minor spectator as far as duration is concerned. The cosmic partners, on the other hand, know each other for a long time. Their communication is going on for millions of years. It is interesting to study the interaction of our home ground (the earth) with the world outside from the quadralectic point of view.

Looking into Deep Space. Photo: Ruimtevaart museum (Space Expo) ESA/ESTEC, Noordwijk (The Netherlands).

The first act of reconnaissance (by a human observer) is the interpretation of the sizes. Every quadralectic communication is ‘ruled’ by the partner with the smallest size. It is generally accepted that the planet Earth is the Small Part (Minor) in this relation and the boundless Universe the Large Part (or Major). The creation of the Earth stipulates that the Universe was already there and provided the actual space for the event to happen.

This statement seems logical enough, but it has to be remembered that such a proposition can always be attacked on philosophical grounds (or maybe even on physical grounds). This line of inquiry, however, will not be followed here. It is fully accepted that the duration, or life span, of the Earth is the controlling factor in the communication between Earth (SP) and Universe (LP).

Man or the human being can communicate with themselves, other people, mankind, the earth and the universe. In addition, all these elements can communicate with each other, because in the initial realm of division thinking is no place for hierarchy. However, the interactions between the before-mentioned entities do not take place in a vacuum. They are based – as we now know – on choices. If, for instance, the fundamental interaction between earth and universe will be meaningful for a human observer, then the latter must make (division) choices to make it comprehensive.

A communication between ‘the earth’ and ‘the universe’ means, in a quadralectic context, that the two communication partners are placed in a division environment. Preferably, in a high division setting, because that is where understanding comes to the maximum gratification. The imagination of a cosmic scale is a process of careful consideration of options in the full knowledge that every step is a conscious execution of a choice. The exploration of our existence in space has to proceed along well-defined lines.

First, the cosmic history of the earth will be looked at from the perspective of the Large Visible Animals (LVA) – of which the species Homo sapiens is a minor, but important element – and the very beginning of the earth (as scientifically established in isotopic dating). The choice of these two points of recognition (POR) provides a position of the observer (O) and the observational present (OP) on the communication graph V. The latter is the universal CF-graph applied to these two entities. This explicit anthropo-centric position can be used – in the full knowledge of its subjectivity – as a departure point for a new location in space. The quadralectic view point opens up a different conformation of our being in the world, held in the palm of our hand.

6.3.1. The cosmic history of the earth

The first approach in the communication will be from the side of the Earth, i.e. the large solid and fluid sphere which acts as a substratum for human observations. The earth is part of a Solar System, which formation took place some 5000 million years ago as a planetesimal accretion of long-dead stars. It was fairly early in the history of the system that the proto-Earth developed and cooled down to the Earth (4.6 billion years ago).

A process of radioactive and gravitational heating led to a differentiated interior structure. Molecules of water, methane, ammonia, hydrogen, nitrogen and carbon dioxide were gassed out during the transformation. At the same time, atmospheric water was photo-dissociated by ultraviolet light in oxygen and hydrogen atoms. The former shaped an ozone layer, while the latter escaped into space. Around 3800 million years ago the crust of the earth was solidified, and the condensation of atmospheric water resulted in the oceans.

The very beginning of the earth cannot be determined from (the sequence) of rocks, because the oldest rocks have been recycled and destroyed by the process of plate tectonics. Moreover, there are no determinable fossils in rocks older than 3500 My. Prokaryotic cells only started to develop after that tentative date. Biological (fossil) evidence is of little help to establish the first visibility of the earth, and the geological sciences had to resort to physics to come up with an acceptable answer.

The age of the earth (and the Moon) is nowadays measured by the decay of long-lived isotopes of elements that occur naturally in rocks and minerals. This process is called radiometric dating. Its theory is grounded in physics and based on the half-life of isotopes: the time lapse during which a radioactive mass loses one-half of its radioactivity. In particular, the isotopic composition of lead, expressed in the ratio of lead-207 to lead-206, has proven to be a good indicator of the age of the earth. The ratio changes over time due to the decay of radioactive uranium-235 and uranium-238.

Ancient rocks older than 3.5 billion years old are found in such divers places as Canada, western Greenland, Swaziland, and western Australia. Zircon crystals from the latter locality – found in younger sedimentary rocks – gave radiometric ages of 4.3. billion years. It must therefore be assumed that the earth has at least that age. The oldest dated moon rocks have ages between 4.4 and 4.5 billion years, which provide a minimum age, but fits in well with the history of the earth. Some meteorites have given ages from 4.53 and 4.58 billion years. It is fairly certain (if radiometric dating is accepted) that the earth gained its first visible visibility some 4600 mya.

The Earth is part of a solar system, with our ‘Sun’ as the main point of attraction. The Sun is, in turn, a star amidst millions of stars in the universe. It is situated in a galaxy. A galaxy is a gravitationally bound system of stars and stellar remnants, with gas, interstellar clouds, dust and dark matter as contributors. ‘Our’ galaxy is visible at night in the form of the Milky Way and has to be visualized as a giant disk floating in an immense space. Other galaxies, similar like ours, can be viewed at great distances in the universe (fig. 82).

Fig. 82 – The nearest neighbor of our own galaxy is the spiral galaxy M31 (NGC 224) in the direction of Andromeda at around 1.5 million light-years away from our galaxy. The object was known as the ‘little cloud’ to the Persian astronomer Al-Sufi, who described it in his ‘Book of Fixed Stars’. Two bright dwarf elliptical galaxies (NGC 205 and 221) are visible. The picture was taken with the Schmidt telescope at Mount Palomar (Photo: Hale Observatories).

The dimensions and size of the universe can only be understood if our own position is known within its setting. This cosmic consciousness has to be built up in steps, starting from the observer and the present (OP) to a more general verity valuable in a longer period. These phases will now be followed in more detail and will end in a statement over the duration of the universe as the largest imaginable entity of Man.

The first action is a specification of the Observer in place and time. The exact position of an Observer on a communication graph is all-important to know in order to draw any sort of conclusion with regards to visibility. The first question will be: where do we, as conscious members of the species Homo sapiens, stand in place and time on this Earth?

Two Points of Recognition (POR) are chosen to pinpoint that position. The beginning of the communication cycle (between Man and Earth) is placed at the beginning of the Earth some 4600 million years ago. That seems a fair choice, supported by the scientific evidence of isotopic dating. The second POR is the beginning of the first appearance of the Large Visible Animals (LVA) on earth, of which the species Homo sapiens is a member. A date of 600 mya, situated in the so-called Vendian period, is chosen as the first visibility of the LVA’s. The first macroscopic fossils of soft-bodied organisms were found in the latest Proterozoic (2500 – 545 mya) and fit in the definition of LVA. They had a simply plan and resembled modern-day soft-bodied organisms such as sea pens, jellyfish and worms. It was only in the Cambrian Period and the beginning of the Phanerozoic (545 mya – present) that the first shelly fauna appeared.

The dating of the first visibility of the LVA (at 600 mya) is – in all scientific honesty – an effort to make the ‘best choice’. However, this subjectivity is lately joint by a scientific correction of the ‘objective’ dating by radiometric methods. The beginning of the Cambrian Period (and therefore the Phanerozoic Eon) has shifted some 55 million years from 590 to 545 mya, which is about 10% of the total presence of the LVA’s. The following comparison (fig. 83) reflects the two different dates (of first visibility) and their consequences for the position of the Observational Present (OP) on the CF-graph. The start of the communication graph remains fixed at 4600 mya. It is also imaginable that new ‘corrections’ will change this date in the future, but this scenario will not be followed now.

Fig. 83 – The comparison between the position op the Observational Present (OP) in relation to the choice of the First Visibility of the Large Visible Animals (FV/LVA). The First Visibility is chosen as 600 and 545 mya. The Observational Present (OP) moves relatively to the left (to FV) if the BU increases.

The situation bears resemblance to the problems in the determination of the Observational Present by means of the visibility of the genus Homo (as earlier described on page 223). In the given example (of a changing starting date for the Ramapithecus) the First Visibility was fixed (at 4 mya) and the beginning of the communication cycle V was moved (from 15 to 24 mya). The OP moved in that example to the left, towards the FV.

Now, in the example of the LVA’s on earth, the last sentence of page 223 (‘Where is the present?’) is put to the test. The First Visibility (FV) becomes flexible (changing the beginning of the first visibility of the LVA’s from 600 to 545 mya). The beginning of the communication cycle V (of LVA and the earth) remains fixed at 4600 mya. The result is an increase in length of the invisibility period O¹ (consisting of 5 BU’s) and a relative movement of the Observational Present (OP) to the left (towards FV).

The conclusion of the two examples together (Ramapithecus and the Large Visible Animals on earth) is inevitable. It must be concluded that any enlargement of the invisibility period O¹ (consisting of five BU’s) results in a relative dislocation of the Observational Present towards the First Visibility (i.e. to the left). The enlargement can be achieved by either moving the beginning of the communication cycle V to the left or by shifting the First Visibility (FV) to the right. The following ‘law’ can therefore be formulated:

The Observational Present (OP) moves relatively towards the First Visibility (FV) if the communication cycle V is enlarged.

The opposite of this ‘law’ is also true. It means that a narrowing down of the invisibility period O¹ (diminishing V) results in a dislocation of the Observational Present (OP) to the right, away from the First Visibility.

The philosophical implications of this principle are – to say the very least – interesting. It seems as if we are dealing here with a ‘communicational spectrum shift’. The relation between the direction of relative movement (of an observer or observational present) along the communication graph and the changing length of the communication cycle (V) is established. The nature and setting of this relation, within the distinct ‘wave’ environment of the CF-graph, immediately brings to mind the so-called Doppler effect, as it is known in physics.

The Austrian mathematician Christian Doppler (1803 – 1853) proposed this principle in 1842 in a publication called ‘Concerning the coloured light of double stars’. He noticed that the pitch of a sound would change if the source of the sound is in motion. An approach towards the observer leads to compression of the (sound) waves. Moving away results in a stretching of the waves relative to the observer.

By analogy, the electromagnetic radiation emitted by a moving object also exhibits the same effect. A transposition towards the observer means compression (squeeze), which is visible in the spectrum as a shift to the right (blue). If the object moves away, there is a shift in the spectrum to the left (red). Radiation is red-shifted when the wavelength gets longer and is blue- shifted when the wavelength is shortened.

The American astronomer Edwin Hubble (1889 – 1953) studied distant galaxies around 1920 and used the theoretical results of the Doppler effect. He noted a shift in the spectrum of Cepheids in nearby galaxies towards the red end and concluded that they were moving away from the observer (the earth). ‘Hubble’s law’ states that the distances between galaxies or clusters of galaxies continuously increase and that the universe is expanding. Edwin Hubble and the consequences of his law will be met later (in Chapter 6.4) in the discussion of the quadralectic universe.

The ‘communicational spectrum shift’, as now observed in the CF-graph of the LVA’s, has a great similarity with the cosmic situation, although there are no actual spectral lines. However, the same principles with regards to relative movement seem to be applicable. The spectral ‘red shift’’ and ‘blue shift’ (as observed in moving galaxies) is replaced by a shift of the Observational Present (OP) on the CF-graph. The former (red shift) is seen when an expansion takes place and can be compared with the enlargement of the Basic Units (BU) and a longer communication cycle (V). The latter (blue shift) is the result of compression and comparable with smaller BU’s (and a smaller communication cycle V).

The spectrum of the visible light is normally drawn on a linear scale from long wave/least energy/low frequency/red colour on the left-hand side to short wave/high energy/high frequency/blue colour on the right-hand side (fig. 83). A red shift (in physics) therefore means a movement to the left (on the spectral scale) and a blue shift a movement to the right.

The directions of the Observational Present (OP) along the communication (CF) graph follow the same pattern as given in the physical example of light waves. An enlargement of the communication cycle V (‘red shift’) results in a movement of the Observational Present (OP) to the left (towards the FV). A diminishing of the communication cycle V (‘blue shift’) leads to a movement of the OP to the right (away from the FV).

Fig. 84 – A comparison between the physical characteristics in the spectrum of visible light (above) and certain features of the communication cycle V (below) in a quadralectic setting.

The theoretical implications of the comparison might be further explored, to find the rate of a shift. The number of ‘beginnings’ (or First Visibilities) of the Large Visible Animals (LVA’s) is in this investigation extended to four. The beginning of the communication cycle remains fixed at 4600 mya, generally accepted as the age of the earth. The following lengths of a basic unit (BU) can be calculated for the various FV-values.

The length of BU can now be plotted against the First Visibility (FV). The result is a linear correlation (fig. 85).

Fig. 85 – The representation of a graph, showing the linear correlation between (four) different First Visibilities (FV) of the Large Visible Animals (LVA) – given on the horizontal axis – and the corresponding Basic Units (BU or 1/16.V) – as marked on the vertical axis.

The present interest is primary focused on the behavior of the Observational Present (OP), our present, in the visibility game. Therefore, the variable distances between the Observational Present (OP) and the Approach Point (AP) are plotted against the First Visibility (FV). The result is also a linear correlation. Some random (FV) values will mark a trend:

— FV —————————– BU ——————————— OP – AP

– 600 4600 – 600 = 4000 : 5 = 800 200

– 530 4600 – 530 = 4070 : 5 = 814 284

– 500 4600 – 500 = 4100 : 5 = 820 320

– 200 4600 – 200 = 4400 : 5 = 880 680

0 4600 – 0 = 4600 : 5 = 920 920

The last example shows the highly hypothetical case of the ‘sudden appearance’ of the Large Visible Animals (LVA) in the observational present of today. The Observation Present coincides in the latter case with the First Visibility of something we already know to exist! The First Visibility is no First Visibility after all, it is now. The circle is closed.

These observations must have a psychological meaning for an observer in the present. Some might even find the outcome disturbing. A subjective choice – based on objective facts – led to an outcome in which the observer has to doubt the very foundation of visibility (which was initially based on a First Visibility). The outcome points to a weird form of ‘transcendental geology’, an untraditional direction, which has not been described before. These genuine investigations – based on established scientific facts – could never be verified, neither now nor in the future. (Earth) history might get a new appearance, but its features will not be recognized in the present world of academic thinking.

Why do observations with a micro- or telescope contribute to a progress in science and why do the results of a probing in space and time by the CF-graph not qualify to be scientific (at present)? The answer is a matter of emplacement: the former efforts are rooted in the Third Quadrant, while the latter endeavors are situated in the Fourth Quadrant. The microscope and the CF-graph are examples of dissimilar types of observation aids located at different points in the communication.

A light beam going through the lenses and/or bouncing on mirrors gives a visible pattern, which is recognized as an objective physical entity. Certain subjective meanings only enter the observational reality in the interpretation stage (like the use of spectrum analysis). Visibility derived by the CF-graph also results in patterns and a perceptional reality, with the subjectivity as a given fact within itself. The choices (of the Points of Recognition) are indicated, and a new reality develops after that choice.

There should be no hierarchical classification of these two types of intellec-tual navigation. Both approaches are just as valuable in the understanding of the world. The most important thing to know, in any communication, is probably our own position as an observer and make that clear.

6.4. The ultimate consciousness: the universe

The universe seems to be the last station in a ‘universal’ communication. Its existence and nature have been an object for long debates throughout the ages. Often, it was associated with spiritual elements and/or projections of fear. Anything from outside the direct realm of the earth was unknown and could be dangerous. The cosmic history of the earth is a human story of wavering views and confusion.

The universe as the ultimate consciousness comprises the last boundaries of our imagination. Copernicus’ revolutionary proposal (in his book ‘De revolutionibus orbium coelestium‘ (On the Revolutions of the Celestial Spheres), published just before his death in 1543 and stating that the earth was not the centre of the universe) was not the outcome of wider division thinking, but just the opposite. It was the rigid application of a process of natural observation in a dualistic framework, which led to the possibility of inversion: not the earth in the centre but the sun.

The world view changed in the sixteenth and seventeenth century after Copernicus placed the sun in the center, overruling Ptolemaeus who had seen the earth as a center point. The observations with a telescope provided new information, like the four moons of Jupiter. KENTON, Warren (1974). Astrology. The Celestial Mirror. (Art and Cosmos. Jill PURCE (Ed.). Avon Books, New York/Thames and Hudson Ltd., London. LCCC 73-89279.

The Italian monk Giordano Bruno (1548 – 1600), who was encountered earlier (p. 72) as the man who looked at the First Quadrant from a Third Quadrant-viewpoint, envisaged the sun as just another star in an infinite space. His speculations were, basically, also the result of consequent op-positional thinking. Either the sun is a unique point of light, and the stars were some other minor light spots (the accepted opinion) or the sun was just a spot among others, only much clearer (Bruno’s proposition).

The suggestion that his astronomical ideas led to the condemnation by the Church and a subsequent burning at the stake might be false. His melodramatic last words (‘Today you burn me, but in the future all men will believe as I believe’) only added to the rhetoric. There are serious reasons, as noted by POGGE (1999) and BLACKWELL (2006), to believe that the Church’s complaints were more theological than astronomical. They had to do with the retaining of power, both spiritual as worldly. The official condemnation of Copernicanism by the Church – in the ‘Sacred Congregation of the Index’ – took place some sixteen years after Bruno’s death (1616).

Unfortunately, all the relevant records of Bruno’s conviction and trial in 1600 were lost, so any judgement must be a conjecture. It seems more likely that his rigid way of thinking, based on polarity and inversion, was the real reason for concern by the Church. Any belief, which is put under pressure of oppositional thinking, will be faced with extremism (or in a more modern variety called fundamentalism). No man in power – be it religious or profane – is happy with developments, which will, sooner or later, question the centre of power itself (as happened in the Catholic Church in the early sixteenth century and in many later revolutionary political movements). Deep down, the Church might have felt this threat.

Isaac Newton, born in 1642, developed a comprehensive theory of gravity, which can be regarded as a universal communication model based on two-fold thinking. It will come to no surprise, that one of his first theoretical successes (in 1665) was the (re) discovery of the binomial theorem. A binomial is an algebraic expression with two terms. Newton’s intellectual journey started with the mathematical adventures of the multiplication of two terms.

The general terms (a + b) can be raised to a power (1, 2, 3 or more). This action is called a binomial expansion. The equation (a+b)² = a² + 2ab + b² is just an example in which n = 2 and the number of terms (on the right hand side of the equation) is 3.

The expanded form consists of the terms a and b to the power n and some intermediate terms. The total number of terms in the expanded form of (a+b) to the power n is always n + 1. For instance, (a + b) to the power 5 gives n = 5, and the number of terms is 6. If the various values of n (1,2,3, etc.) are written down, then the coefficients will follow an array called ‘Pascal’s triangle’ (see below).

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

Note that every number in the interior of the triangle is the sum of the two numbers directly above it (except at the top). This type of computing (or the construction of the Pascal triangle) was already known to the Baghdad-based mathematician al-Karaji (953 – about 1029). He wrote a treatise on algebra called ‘Al-Fakhri’. The formation of the triangle was also recorded in a description of al-Karaji’s work by the Muslim mathematician al-Samawal (or Samau’al Al-Maghribi, 1130 – c. 1180).

The famous astronomer-poet of Persia, Omar Khayyam (1048 – 1131), author of a ‘Treatise on Demonstration of Problems of Algebra’, referred to the Pascal triangle. Khayyam (the ‘tent-maker’) is better known as a poet of nearly six hundred four-line poems called the ‘Rubaiyat’ (translated by Edward Fitzgerald in 1859). For instance, Rubaiyat, no. XVI (First Edition) expressed the futility of human expectations in the light of eternity:

—————— The Worldly Hope men set their Hearts upon

—————— Turns Ashes – or it prospers; and anon,

—————— Like Snow upon the Desert’s dusty Face,

—————— Lightning a little hour or two – is gone

Pascal’s triangle was likewise known in China some three hundred years before Blaise Pascal (1623 – 1662). The great Chinese mathematician Zhu Shijiei (1270 – 1330), living in the Yuan Dynasty, gave an example of the triangle to a depth of 8 (fig. 86).

Fig. 86 – The ‘Zhu Shijiei triangle’ to a depth 8. The ‘triangle of Pascal’, as it later became known, is not only an algebraic curiosity, but it also points to an intellectual desire to reach into the depth of dual thinking.

Persian-Iraqi mathematicians like al-Karaji (Karaj being a city in Iran; the other rendering of his name as al-Karkhi points to a suburb of Baghdad) and Omar Khayyam felt attracted to the unequivocal possibilities of oppositional thinking. The germinal inspiration of a long established Zoroastrian dualism cannot be excluded by these twelve-century scientists.

Let us now return to Isaac Newton and his gravitational communication model. His study at Trinity College in Cambridge was temporary suspended due to a severe outbreak of the plague, and he returned to his birthplace Woolsthorpe Manor in Lincolnshire (England). This year at home (1666) became his Annus Mirabilis, a marvelous year. The simultaneous achievements in the fields of gravity, optics and mechanics were the results of a fruitful application of mathematics to the various fields of nature. A strict adherence to dualistic principles is the premise of his thoughts.

Newton’s proposition that every particle of matter attracts every other particle in a certain way was captured in the inverse square law. It stated that the force of gravitational attraction between two bodies decreases with increasing distance between them as the inverse of the square of that distance, so if the distance is doubled, the force is down by a factor of four.

The vision of a universal communication between particles (of matter) had by the middle of the seventeenth century become a measurable correlation. It opened the way for a gratifying field of investigation. All imaginable material substances in the universe were now intrinsic connected with each other, and their distances were captured in a deterministic law.

This state of affairs remained more or less unshaken until Albert Einstein (1879 – 1955) questioned the peculiar setting of participants in the (universal) communication in the first quarter of the twentieth century. He challenged the flat, Euclidean space and the uniform, absolute time of everyday experience. The idea was presented that attraction and repulsion (intensio and remissio) in a communication were no longer measured only from a deterministic point, but also from an agent moving at different speeds (up to the speed of light). The intellectual exercise posed a mind-provoking challenge, shaking the foundation of physics.

The concept of relativity in the gravitational field sparked a new conscious about movement, distance, time and the importance of a position. Different gravitational laws had to be applied in the order to capture this setting. The observer was no longer the noble and stable watcher of nature, but became an uncertain, subjective spectator endowed – at best – with common sense. Science got a shudder since the laws of physics were supposed to be independent of any particular reference frame. The established Newtonian laws needed a revision in order to make them ‘universal’. Any theory of the origin of the universe had to take this relativistic advance into account.

At present, there are four major theories with regards to the origin of the universe (DODSON, 1984). The relative direction of the cosmic matter is the main criterion for the present (four) divisions. The speculations are given here in a ‘quadralectic’ sequence:

The condensation theory

The primordial universe is situated in the invisible invisibility (of the First Quadrant). A reaction (attraction) takes place in an invisible gas-like state, resulting in a visible form of material presence (condensation). The philosopher Immanuel Kant (1724 – 1804) introduced already the idea that the Sun and planets could have formed by condensing out of a great rotating disk of gas and dust. Nowadays, it is known that (Kant’s) gaseous disks are frequently found around most young stars forming in the Milky Way.

The explosion theory

The most popular theory at the moment looks at the birth of the universe as a single event: the Big Bang. The model is highly theoretical and finds its real origin in mathematical calculations focused on a singularity. The initial, first division is thought to have taken place as a creatio ex nihilo, in the invisible visibility (of the Second Quadrant). This theory perceived one large explosion in which – in a very short period of time (the fireball phase) – matter is formed. This scattered material is later – under the influence of forces of attraction and repulsion – ordered in cosmic configurations like galaxy and planets.

De Sitter (1917) produced the first non-static model as an alternative of the static model of Einstein. The latter introduced a cosmical constant in order to keep the relativistic forces of the universe at bay. In the meantime, the brilliant Russian mathematician Alexander Friedmann (1888 – 1925) spent his time as a volunteer on airships, bombing the Austrian troops and became involved in the Revolution of October 1917, but also found the time to discover the expanding matter-filled world model in 1922. He stated, in his article ‘On the curvature of Space’ in the ‘Zeitschrift für Physik’, that the radius of curvature of the universe can be either an increasing or a periodic function in time.

Georges Lemaitre (1894 – 1966) was one of the pioneers of a dynamic universe (BERGER, 1984). He stated (in 1927) that the universe was unstable and that the perturbation tended to grow. ‘The evolution of the universe can be compared to a display of fireworks that has just ended: some few wisps, ashes and smoke. Standing on a well-chilled cinder, we see the slow fading of the suns, and we try to recall the vanished brilliance of the origin of the worlds’ (Georges Lemaître (1931). Rev. des Quest. Sci., Nov. p. 391).

The steady state-theory

This theory on the origin of the universe was put forward around 1920 by the English mathematician and physicist James Jeans (1887 – 1946) and revised in 1948 by Hermann Bondi and Thomas Gold. In the sixties, Fred Hoyle became a keen advocate of this theory in its competition with the alternative Big Bang theory.

The Steady State theory suggests a situation of equilibrium, in which the universe has no beginning or end and maintains a constant average density. Material is continuously created to form new stars and galaxies and also discarded at other places (or becoming unobservable as a consequence of their increasing distance and velocity of recession).

This cosmological theory is firmly rooted in the visible visibilities (or Third Quadrant qualities) of the universe. However, for its explanation of the visibility (of matter), it has to resort to higher division thinking. Newly formed material is either the result of one of four possibilities:

1. The creation of matter

2. An infinite cyclical passage through singular conditions

3. A single passage after an infinite initial delay

4. A deep-going modification of the idea of time

The discovery of cosmic background radiation by Arno Penzias and Robert Wilson (in 1963), awarded with the Nobel Prize in 1978, put a strong case for the ‘Big Bang model’ and virtually put the ‘Steady State theory’ to rest. Some technical alterations (by HOYLE et al, 1993 and NARLIKAR, 1999) resulted in a revised quasi-steady state cosmology (QSSC).

An inventive steady-state theory was put forward by the writer Brian LUMLEY (1999), who concocted a convincing case in his approach to the history of the universe. The theoretical boundary of the universe, he said, is the speed of light. He believed that the so-called ‘black holes’ (where gravity is so great that even light cannot escape) are the traces left behind after a body has reached the speed of light, past it and ‘left’ our universe. At that very moment, time is frozen and the vortex left by the departure lasts indefinitely. Any object passing beyond the boundary (of the speed of light) will end up in the Big Bang itself. In fact, is the Big Bang.

The apparent lack of weight of the universe can be explained by the existence of a surplus in gravity in the fast-fleeing galactic bodies on the rim of the universe approaching the speed of light. The result of all those bodies breaking through the space-time boundary of our universe and finding themselves back in the Big Bang would be, indeed, a ‘steady state’. Lumley’s conclusion – ‘The universe is self-perpetuating, and the Big Bang is happening now and always will be but on the other side of the space continuum’ – is certainly a valuable contribution to the history of the universe.

The cyclic theory

Finally, there is the theoretical possibility of a cyclic expansion and contraction by the forming of matter. The Austrian mathematician Ludwig Boltzmann (1844 – 1906), known as the inventor of statistical mechanics, suggested that the order in the universe might be just a very rare occasion with a temporal character. It is possible that after an enormous duration, another ordered universe would appear. And the line of ordered universes might get so long, that – after a very, very long time – the same universe (like ours) turns up again. This theoretical (statistical) approach fits into a quadralectic outlook, in which order (measurability) and chaos (immeasurability) are seen as stages in a shift between four- divisions (and depend on a coincidence of boundaries; see p. 96).

The cyclic view does not give a practical solution for the moment of creation, but it points to a certain period of visibility. A theoretical beginning of a cycle (on the circle) can subsequently be calculated from the given, empirical entity.

The Big Bang-theory, which is most fashionable at the moment and will be followed here, provides a reference to the quadralectic discussion. The creative act of a ‘Great Explosion’ offers a solution to the problem of the ‘first division’ in the realm of division thinking. The origin of matter is placed in its first theoretical visibility and represented as a mathematical singularity. There is no objection to this procedure, as long as the nature of the division environment is clearly stated. The beginning (and continuation) of a communication in a dualistic universe is quite different from the same event in a quadralectic setting.

The First Beginning (or Big Bang) – as an act of creation – is thought to have taken place some 15 billion (15.000.000.000) years ago. This ‘date’ was calculated from a distance, i.e. the furthest cosmic communication partners known at the time. Edwin P. Hubble discovered in 1929 that the velocity of a galaxy’s recession is proportional to its distance. He calculated an expansion rate (the Hubble constant) of 500 km/s/Mpc. This initial estimate turned out far too high.

A number of scientists met at the Aspen Center for Physics in 1985 to find the ‘HST Key Project on the Extragalactic Distance Scale’. They could bring the error in the expansion rate of the Universe and the Cosmic Distance Scale back to 10%. At present, a rate between 50 – 100 kilometers per second per megaparsecs (one megaparsec = light travels in 3.26 million years) is generally used. The lower values pointed to a universe, which was far older and larger than suggested by the earliest measurements by Georges Lemaitre and Jan Oort.

The determination of the Hubble constant (Hº) required the measurements of velocity and distance. The measuring of a galaxy’s velocity was straight-forward, because of its light dispersing in a spectrum. The spectral lines shift to a longer wavelength by amounts proportional to the velocity (the earlier mentioned red-shift). However, problems do occur. Firstly, because the galaxies interact gravitationally with their neighbors and secondly because an accurate distance scale is difficult to establish.

The distance to galaxies is measured by a Cepheid variable. These stars change in brightness in a periodic and distinctive way. The distance to a Cepheid can be calculated from its period (the length of its cycle) and its average apparent brightness (its luminosity as observed from earth).

A Cepheid’s brightness is proportional to its surface area. Large bright Cepheids pulsate over a long period just as large bells resonate at a low frequency (or longer period). The period and the average luminosity give an absolute luminosity (that is the apparent brightness if it were a standard of 10 parsecs away). It was mainly due to the painstaking work of Henrietta Leavitt (1868 – 1921) – as referred to earlier in this book (p. 162, fig. 60) – that this relation became a ‘yardstick to the universe’.

The problem of the Cepheid method was the occurrence of dust between the stars (diminishing the apparent luminosity) and the presence of chemical elements, which differ in brightness. Hubble’s constant is now given at 70 km/s/Mpc or somewhat less in the middle 60 range. This value gives an age estimate for the universe of 9 – 12 billion years. A higher (Hubble) constant of, for instance, 100 km/s/Mpc would result in a universe of about 6.5 – 8.5 billion years old. A lower (Hubble) constant of say 50 km/s/Mpc gives a universe with an estimated age of 13 – 16.5 billion years.

Wendy L. FREEDMAN (1992) and her team proposed, in an article on ‘The Expansion Rate and Size of the Universe’ (Scientific American – Nov. 1992), a high expansion rate and therefore a relative young universe of perhaps 10 billion years.

A similarity with the origin of Man comes to mind: when does the actual communication cycle start? The answer lies, in the case of Man (Homo sapiens), in the discovery of a skull or skeleton as a physical proof. The very origin of the universe will never be found in that way, but will remain a theoretical matter, without a final scientific proof.

It is possible, despite the innate uncertainties of the Hubble constant, to construct the communication cycle of the Universe in a comparison with the Solar System (as our largest frame of reference from an earthly point of view). One only has to make a choice of two age-determinations. Different options (of starting dates) remain open, and they can be compared (after-wards) in their own right and judged accordingly.

The same procedure was followed by the appearance of Homo Sapiens on earth (see fig. 78/79/80) and the presence of the earth as determined by the LVA’s (Large Visible Animals), and will be followed here again. The assumptions are that the initial creative event of the ‘Big Bang’ took place 15 billion years ago and the first visibility (FV) of ‘our’ solar system is dated at 5 billion years ago. Fig. 87 gives the CF-graph for the universe as related to the solar system (of which the earth is a part).

Fig. 87 – This communication graph (CF) gives the relation between the Universe and the presence of the earthly solar system.

The ‘Big Bang’-event, at the beginning of the communication cycle, is placed some 15 billion years ago (based on calculations of the furthest removed objects in the universe). The first visibility (FV) of the (earthly) solar system is put at 5 billion years ago.

The components of the communication between our (earthly) solar system and the universe are calculated as follows:

Beginning of V (communication cycle) = – 15 billion ya

Beginning of FV (first visibility of solar system) = – 5 billion ya

———————————————————————————————————

5/16 V (invisibility area 0¹) = 10

V = ——— . 10 = 32 billion years (full communication cycle V)

X = ——— . 32 = 20 billion years (visibility area X)

BU = ——— . V = 2 billion years (basic unit)

The universe has a total life cycle (V) of 32 billion (32000 million) years. The visibility of the solar system is established from -5 billion (in the past) to 15 billion years (in the future). The (observational) present (OP; 15 billion years from the theoretical beginning of the universe) is situated in the fourth quarter of the Second Quadrant (II, 4; with a CF-value of 8.5).

This result is not final, as was pointed out before. Different ages of the origin of the universe (as a result of a different value given to the Hubble constant) can be considered, assuming that the starting date of the solar system remains the same at 5 billion years. Figure 88 (on the next page) is a representation of the different positions of the Observational Present (OP) on the CF-graph of the communication cycle of the universe. The origin of the universe (‘Big Bang’) is respectively chosen at 16, 12 and 8 billion years ago. The graphs are indicated with the letters A, B and C. The relevant figures to construct the diagram are given below. The abbreviation ‘bya’ stands for billion years ago, the length of BU, V and X have to be multiplied by a billion (thousand million or 1000000000):

Start V 5BU BU Length of V Length of X End of V

————————————————————————————————————————–

A – 16 bya 11 2.2 35.2 22 19.2

B – 12 bya 7 1.4 22.4 14 10.4

C – 8 bya 3 0.6 9.6 6 1.6

Fig. 88 – A graphic rendering of three different CF-graphs (A, B and C), which represent the relation between the universe and the earth solar system, based on the start of the communication cycle V (the Big Bang) respectively 16, 12 and 8 billion years ago.

The positions of the observer (OP) move to the left (‘red-shift’) if the cycle V becomes longer (as the result of the ‘Big Bang’-event being further away into the past). The opposite (a ‘blue-shift’) occurs when V becomes smaller and the OP advances to the right on the CF-graph (eventually moving into a new, successive communication cycle). This phenomenon was earlier encountered (p. 229) and described as a communicational spectrum shift.

The graph of the shifting present in relation to the variable duration of the ‘Big Bang’ and a fixed beginning of the solar system (at 5/16V) is given in fig. 89. The X-axis gives the position on the communication graph (expressed as a value of V). The Y-axis marks the increasing length of the invisibility area (O¹ = 5 BU). The combined result is an asymptotic function.

Fig. 89 – The graph of an asymptotic line, representing the shifting present (OP) in relation to the age of the origin of the universe (Big Bang) and the position (of the Observational Present) on the communication graph V.

The graph of a shifting present indicates clearly that our observational present depends greatly on the parameters, which are chosen to define that position. A place on earth, measured in the history of the universe is highly dependent on the choice of the beginning of the communication cycle.

Our history depends on the choices made by the observer to define it.

That choice is, on the one hand, a single and static affair with a distinct delimitation (recognized in the quadralectic approach as positions in the First of Third Quadrant). However, the choice is also, on the other hand, a dynamic event in a multitude setting, part of a communicational spectrum shift (which occurs in the Second and Fourth Quadrant). The study of the character of the spectrum shift might be as far as an observer can go in any communication.

The boundless universe as the space of the ultimate consciousness will be left at this point. The return to the limited world of our personal observation holds a new knowledge in stock. Every communication has its own Big Bang, regardless of its size. The uncertainty of the very beginning and the subjectivity of the first visibility (or any other choice on the CF-graph) will always be with us. The character of the present will never be the same.

This state of affairs can better be accepted then denied. The view on the asymptotic values, running away in infinity, is the best representation of our definition in place and time. We are an asymptotic man in an asymptotic time.

Will this incertitude have a crippling effect on science? Can there ever be an ultimate truth? It looks as if the search for certainty took a terrible blow after the foundations of its system were questioned. The universal laws of nature have lost their unshakeable character. Is there no certainty left? Maybe this is so, but only in the (limited) conceptual environment in which the ‘laws’ were found in the first place.

There is no reason to be concerned in the wider visibility of quadralectic thinking: science will get its respectable place in the communication, just like the laws of nature. Any investigation of nature can go ahead as planned. There is a truth, but its validity (and visibility) depends on the position in a division system. The observer has to face the fact that a system, a theory or philosophy that explains everything, independent of the position of the observer, does not exist. And if it would exist on a pure theoretical level – after a (four) division is decided upon – it occurs in the invisible invisibility areas of the First Quadrant and early Second Quadrant. Cognitive truth, on the other hand, is born in a multiplicity, after boundaries have been stated.

The observer has the freedom to compare different frames of reference in order to enrich the observational present (OP). It is possible, for instance, to compare a CF-graph of the Universe with a communication graph of the planet Earth, as long as the (subjective) notions of beginning and first visibility are clearly affirmed. One can imagine to ‘calibrate’ various CF-graphs with the OP as a line of reference (fig. 90). This analogical procedure opens an infinite field of inquiry in all kinds of comparisons and makes the observer aware of the scale of things.

Fig. 90 – The comparison between the CF-graphs of the Universe (above) and the Earth (below), with the Observational Present (OP) on earth as a line of reference. The illustration gives an impression of the scale of the history of the earth in relation to the existence of the universe.

The partnership of earth and universe has some interesting details in stock if the CF-graphs are compared over a limited distance. In particular, the events around the First Visibility Crisis (FVC) are worth looking at (fig. 91).

Fig. 91 – The relation between the CF-graph of the universe and the earth around the First Visibility Crisis (FVC) in the Third Quadrant.

The FVC is known – in the general characteristics of the CF-graph – as ‘difficult times’ (identified on a human level as an identity crisis). The earth will reach that stage in the communication over some 2.6 billion years. The Universe will arrive at this point some 400 million years later (3.0 billion years). It might be possible that the problems of the Earth are the introduction to the dramatic circumstances of the Universe-itself.

Another possibility is the ‘wrong’ choice for one of the parameters, which determined the first beginning of the communication cycle and/or the first visible visibility in one of the two graphs. Some ‘calibration’ in (one of) the four parameters can make the First Visibility Crisis coincide, assuming that the Observational Present (OP) remains stable. A shift of 400 million years ‘to the right’ for the FVC (of the earth) will mean a beginning of the (earth/ LVA) communication cycle some 5307 million years ago (if OP remains static). A shift of 400 million years ‘to the left’ for the FVC of the universe would result in a Big Bang some 13 (12.9975) billion years ago (in stead of 15 billion).

These exercises show unquestionably the flexibility with regards to the choices made by an observer in the present (OP) and the impact of these options in the experience of the future. A ‘double’ past (the beginning of the communication cycle and the definition of visible visibility) and a shifting present are facts, which must be considered by any observer. A new kind of science has to take the width of thinking into account.

7. Perspectives

The notions in a quadralectic communication reveal the far corners of the earth and beyond. The thoughts of man are a multiplicity, which provides us with infinite views. Some might even be afraid that a deepening of reflection leaves the human self-image out of control. The great unknown has, at any given time, major surprises in stock. However, there is also the reassuring fact that the quadruple experience offers resources as well.

The wandering mind (crossing division boundaries at will) sees things, which were unknown before and can be most helpful to establish an emotional self. The very moment of realization that our experiences are the result of deliberate division choices in the field of reality means the end of naivety and a time for commitment. Facts are, at scrutiny, just events determined by the person, which takes the responsibility to define them.

The history of philosophy shows various stages of cognitive building activity. The Greek philosophers have put down the fundamentals in a way, which can hardly be improved upon. The Neo-Platonic thoughts at the turn of the Christian era provided the translucent sketches for the continuation of the building, which were readily picked up by the Renaissance and Baroque thinkers. The walls formed the different rooms (in a rationalistic setting) and the metaphysical structure of the European culture became recognizable. The flag went in the top during the participation of contractor Immanuel Kant, because the highest point of the roof was reached.

The assiduity continued after that victorious moment (at the beginning of the nineteenth century) with further beautification. The progress in other fields of nature was incorporated in the basic understanding of the human mind, leading to the cognition that knowledge itself was relative. The flag on the roof was put down, and construction became known as deconstruction. The question of today is no longer a matter of wisdom, but rather of human opportunity: is anyone prepared to live in the finished product of our philosophical investigations?

The metaphor of construction has earlier been used in the development of thought. The German philosopher Johann Fichte (1762 – 1814) remarked:

‘Knowledge is a building; the main purpose of this building is solidity. The foundation is solid, and as it has been laid, the purpose is already attained. But since one cannot live in a mere foundation, since it does not provide sufficient protection against intentional attacks of the enemy or against the unintentional attacks of the weather, lateral walls are built, and over them a roof. All parts of the building fit in with the foundation and with one another, and thus the building as a whole becomes solid; but one does not build a solid building for the sake of joining it together, one joins it together to make the building solid; and it is solid if all parts of it rest on a solid foundation.’ (J.G. Fichte (1794). Ueber den Begriff der Wissenschatfslehre. In: Sämtliche Werke, ed. I.H. Fichte (Berlin, 1854), vol. 1, p. 42).

Johann Gottlieb Fichte (1762–1814)

A communication – seen as a building act – can be divided into four phases, with the visible visibility (of construction) as a plane of reference:

1. preconstruction

2. reconstruction

3. construction

4. deconstruction

These arbitrary (and hierarchical) stations will, once more, been used to review the quadralectic way of thinking. The course through the quadrants is at the same time compared with the handling of a relict in the Middle Ages, to give an example of the way a precious thing was picked up in the past. STRUBBE & VOET (1960/1991) described the four stages in the conservation process from the original uncovering to the subsequent veneration of the holy object.

INVENTIO the discovery (of the body or bones)

ELEVATIO the raising or exhumation and storage in a relict shrine

TRANSLATIO the transportation (of the relict) to another place

EXCEPTIO the reception (of a relict) at its new place

Both examples (of building and relict handling) have a linear character in common. Actions are spaced in time from a beginning (out of an undiscovered past) to a completion (in an arbitrary present or future). The examples, therefore, have, unmistakably, a dualistic background – from becoming to being – which is not in line with the general intentions of quadralectic thinking. The latter type of division thinking assumes that every point of view is simultaneously present during the whole interaction of a communication. Philosophers – from Schleiermacher and Dilthey to Heidegger and Gadamer – have used the term hermeneutic circle to indicate the circularity of all understanding. Comprehension can only come about through a tacit foreknowledge and interpretative assumptions.

The quadralectic vision recognizes four notions. They are equal in value and significance during the whole course of the communication. The absence or presence of a ‘construction’ (or relict) in an interchange only points to a certain type of visibility in the relation between an observer and the observed. The physical presence (as visible visibility) does not rate ‘higher’ than other types of visibility (like the total absence of presence in the invisible invisibility).

This impartial four-fold setting has to be kept in mind in the following recapitulation in terms of construction and relict finding. It might look like a (linear) ‘development’, in the way of sequential presentation, but it should not be understood that way. The (fictional) observer can take a position at any of the given stages and regard this location as a point of view.

7.1. The Roots of Understanding

Preconstruction is a term derived from the building and construction world, indicating the administrative and logistical requirements before the actual building takes place. It includes the estimation of construction costs, plan revisions and modifications or the building of models (one company used the slogan: find problems before they find you!).

The word preconstruction is used here (for the first time?) in a more philosophical setting, pointing to the conceptual requirements before an immanent construction is carried out. It is – in the ‘dualistic’ triplet of past – present and future – the First Past, an age of preparation.

Preconstruction, in a quadralectic sense, is an intelligible stage in the formation of a communication. The preparation can be seen, from a linear point of view, as the beginning of a process, but in a cyclic vision, there is no beginning. The preparatory phase is with us all the time, not only at the first dawn of awareness, but far before that stage. And it will continue to influence the communication long after the moment of first visibility.

The theme of the circle was already persistent in the thoughts of Hegel as he wrote (in: SCHMIDT, 1988; p. 115):

‘every part of philosophy is a philosophic whole, a circle which closes in upon itself … the solitary circle breaks through … and founds a further sphere; the whole presents itself therefore as a circle of circles of which each is a necessary moment, so that the system of its proper elements constitutes the whole Idea which equally appears in every particular’ (Enzyklopädie der Philosophischen Wissenschaften (1969; par. 15).

The preconstruction phase requires a deep understand of the fundamental differences between a beginning in a linear and a circular environment. Our past is not as unambiguous as it seems.

The difference is between a static starting point with a succession of facts and a dynamic beginning which ‘spins new possibilities into the present, shifting the locus of the present.’ Martin Heidegger (who was earlier in this book encountered as touching the four-fold way of thinking; p. 151/152) has understood the latter situation, when he said that ‘the beginning con-cealedly contains the end’. Heidegger regarded the circle not as a symbol of the unity of thought (and its inherent infinity), but rather as a metaphor of limitation and originality of the ontological difference.

The poet T.S. Eliot (1888 – 1965) has expressed the same idea in his quadrilogue ‘The Four Quartets’. ‘Time present and time past are both perhaps present in time future and time future contained in time past’ is the opening phrase of ‘Burnt Norton’, the ‘First Quadrant’. And the poem ‘East Cooker’, as a representation of the Second Quadrant, starts with the sentence ’in my beginning is my end’. SCHMIDT (1988) reckoned that Heidegger would have liked to change these words into a more congenial: ‘in my end is my beginning’ (p. 232).

The preconstruction phase can be compared with the inventio, or the first handling of a relict as described earlier. The term inventio is derived from the rhetorical literature, where it points to a search for arguments in order to convince the communication partner(s). A speaker’s first concern is an analysis of the audience and an evaluation of their reactions. The inventio is a preview of the communication process to come.

The closely related term dispositio or arrangement (placement) aims at the same target, but in a slightly wider (theoretical) setting. Three basic actions characterise the preparation of an oration, as already indicated by Cicero:

Selecting. The selection is an important preparatory act of inventio and implies the choice of the arguments to convince the audience;

Arranging. This mental process is also partially completed during the inventio. The strategic planning of an argument implies a good position in the communication in order to convince the audience. Mark KNAPP and James McCROSKEY (1966), in their article on the subject of the ‘Siamese twins’ of inventio and dispositio,placed the communication process in construction terms: ‘This rhetorical process is similar to that of an engineer building a bridge over a river. The engineer must know the nature of both banks and then plan a bridge, which will lead from one to the other. Similarly, the speaker must know what his audience’s present position is on the issue to be considered and what he wants it to be. Then he builds a speech that will lead to that end.’

Apportioning. The act of judging the audience implies the taking of a decision with respect to the number of arguments to be used. The question how far to go into the inquiry has to be answered somewhere in the process. Apportioning is about drawing lines and facing the consequences of division.

The ‘difference’ between inventio and dispositio can be found in the mental positions in a division environment. The former operates in the realm where discussions on boundaries (apportioning) are not yet taken or realized (First Quadrant and first part of Second Quadrant), while the latter operates both in the area of uncertainty, and in an environment where decisions are consciously taken (the rest of the Second Quadrant).

A rhetoric communication is, according to Cicero, a matter of organizing (dispositio) at an early stage. However, he stated clearly that the process of inventio had to be completed first:

‘When the point for decision and the arguments which must be devised for the purpose of reaching a decision have been diligently discovered by the rules of art, and studied with careful thought, then, and not until then, the other parts of the oration are to be arranged in proper order.’

The unanswered question in this citation (Book I, De Inventione) is Cicero’s meaning of ‘discovered by the rules of art’. He might refer here, in a somewhat cryptic way, to the classical topoi or ‘positions’ in a communication (and consequently, to the number of divisions). Aristotle, as the creator of the rhetorical topoi, used the term (in his book ‘Topics’, written 350 BC) to describe the place or region of an argument.

The particular setting (of an argument) is important for the effectiveness of responses in a communication. Opposites, altered choices, attributed motives, conflicting facts, decisions, consequences, ambiguous terms and division are some items on a long list of common arguments, utilized to make a point more believable and let the audience participate in the debate. The same prominence of position is found in the quadralectic communication: an argument in a Fourth Quadrant setting, arranged by conscious subjectivity, might fail to convince a purely rational listener in the Third Quadrant.

The development of a discourse (communication) takes place essentially through tropes, which are basic strategies for organizing all kinds of texts. A trope is, in a rhetorical context, a figure of speech. In quadralectic terms, it is the creative mechanism, which enables an observer to cross the boundaries of a quadrant. The American thinker Kenneth BURKE (1945/1969) gave, in his book ‘A Grammar of Motives’, the four ‘master’ tropes:

1. metaphor – expressing the familiar in terms of the unfamiliar;

2. metonymy – substituting a word for another word closely associated with it;

3. synecdoche – mentioning of a part when the whole is to be understood or vice versa;

4. irony – use of words to express something different from and often opposite to their literal meaning

This sequence reflects, by and large, the positions in a quadralectic field. The metaphor has been placed in a ‘First Quadrant’ or ‘protocommunication’ setting (in the Second Quadrant (II, 1); see p. 87). The other tropes (2 – 4) seem to be a further subdivision of this particular position.

Frank d’ANGELO (1990) proposed to use the four ‘master’ tropes as a conceptual framework to build a theoretical model (of organizing texts). He pointed to Giambattista Vico (see p. 53; fig. 19), who used the four tropes to represent the stages through which all societies must pass from primitivism to high civilization. Vico (1668 – 1744) – living just after the pinnacle of Cartesian (or critical) thinking in Europe (1650) – aimed to overcome the dualism of pathos (form) and logos (content) (GRASSI, 1980/2001; 1990). Vico sought a solution in the ‘humanistic’ tradition, with its strong rhetorical component. By doing so, he opened up a classical road to higher (tetradic) division thinking.

Hayden WHITE (1978) suggested that the four (master) tropes underlie and inform every historical text. History does not consist of given facts, but has to be ‘constituted’ by the historian. ‘In the writing of history, there is interpretation from the very beginning’.

The (master) tropes, acting as a dynamic mechanism of creativity (in the multiple sense), bear the stamp of their origin. There is a connection between the type of ‘story’ and the trope, which is responsible for its constitution. The Canadian literary critic Northrop FRYE (1957/2006) recognized the following pregeneric plot structures, which were connected (by D’Angelo, 1990) with the tropes:

Romance – Metaphorical identification

Tragedy – Metonymic displacement

Comedy – Synecdochic integration

Satire – Ironic detachment

The rhetorical topoi and tropes can be identified as the representatives of the elementary communication qualities of Division (A) and Movement (B) (see also p. 15). Both entities are strategies of interpretation in a given invisible invisibility. The former provides the boundaries and the latter the mechanism to structure a communication.

The roots of understanding are found in these basic qualities of communication. The first question in any observation has to be: in which division frame do I perceive this impression? And the second question will be: what sort of movement takes place to valuate this impression. These two queries – posed at the same time – are the cornerstone of any logical conclusion.

Often, the language offers the key to the answer of these basic questions. The invisible language of intuition, the partly visible language of ideas (logos), the clearly visible language of the material (science) and the partly visible language of feelings (pathos) have their own matter of speech. The quadrants (in a quadralectic frame of mind) provide the operational base for the various means of expression.

The primary, preconstruction phase may look, for that very reason, like a chaos or Babel-like confusion of tongues. The discovery (or inventio) causes initially an awe-inspiring feeling of wonder and confusion: this is communication, but what is it all about? What is going on?

Information comes from all directions and there is, for the time being, no other response possible then to look and to think (because that is what intuition is all about). There is no visible expression of the interaction at this stage in a communication, but the signs of preparations are everywhere.

7.2. Inventarisation

The ‘Second Past’ is the (theoretical) reconstruction, which aims at an objective interpretation of communication elements and put them together to something real. The major mental act is the introduction of the division as a tool to limit the horizon. Any type of division can fulfill these requirements. The two-division (or binary) is probably the most familiar form, but not necessary the most suitable one. The linear or hierarchical development in the application of division thinking is just an arbitrary start.

Other (higher) divisions can be imagined (in time and space), and the interpretation of a contact can be placed in a cyclic environment to transcend all hierarchies. Cyclicity also introduces a sense of infinity. Communication is an eternal move along a line without beginning and end. This is the type of movement, which opens the gates to an intuitive understanding, and offers a view to the universe.

The act of reconstruction – as a Second Quadrant activity – ought to be an inventarisation and organization (dispositio) of the available elements in a communication. The full width of the communication (cycle) must be understood at this point, derived from the given (chosen) division environment. The principle of the interaction – and the way a value is established – has to be in tune in order to grasp the nature of visibility. The elevatio (the act of recovery and storage in a shrine) means that one has to pass through every stage of the communication process at least once. The ‘language’ of a communication (in the quadralectic sense of a creative interaction between various quadrants) must be understood before any sensible word can be spoken.

The principle of reconstruction gained fresh acclaim in the systematic study of language in the beginning of the twentieth century, as initiated by Ferdinand de Saussure (Course in General Linguistics, 1916). Language (in a literary sense) was seen as an empirical entity and its constituents (the words) were interpreted as linguistic signs. These (visible) signs had an arbitrary meaning and could only gain significance in a (binary) system. Text became an object (of study). Structuralism, the name given to this ‘Third Quadrant’ approach (in the Second Quadrant!) gave literary criticism the status of a science of language.

The interpretation of texts may generally be called hermeneutics. The term also designates a critical approach of the reading process rather than the text as object. The reader (observer) and the text (the observed) are both involved in the recovery of a meaning. The position (of action) has now shifted to a ‘Fourth Quadrant’ approach, but still in the (theoretical) environment of the Second Quadrant. All the rigors of ‘meta-thinking’ can now be unleashed on an intellectual level, leading to the phenomenological endeavors of Edmund HUSSERL (1999), the post-structuralism (or deconstruction) of Jacques DERRIDA (1978/1989) and the self-regulating (autopoietic) notions of Humberto MATURANA (1988). All these visions are already present in the reconstruction phase, but will reach their glory in the final stage of exceptio.

The elevatio is as the unveiling of a divine secret. The actual relict is taken out of its original place in order to be transported to a place of worship. The veneration of relics is a primitive instinct, which is associated with many other religious systems besides that of Christianity. The classical Greek worshiped the supposed remains of Oedipus and Theseus and the present relic worship among Buddhists is well known. The Catholic Church regulated the veneration of relics and the sacred use of images in a decree of the Council of Trent, trying to avoid the misuse and abuse of the relicts. The Church did not encourage the belief in a magical virtue or physical curative efficacy in the relic itself.

The relic is – in the view of the Catholic Church – a material support for the belief in God. Alternatively, translated in quadralectic terms, a Third Quadrant entity pointing to the First Quadrant. The ‘primitive’ qualities (of a relict) have to be understood as a regressive creativity, leading to the ultimate Unity. However, it would be naive to think that such a (dualistic) direction could be prescribed by force, in particular in an environment of wider division thinking.

It is, in historical hindsight, no surprise that the finding of more and more ‘Nails of the Cross’, and bodies of martyrs took predominantly place in the first ages of the Christian era, now identified as the First Quadrant of the European cultural history (see p. 178/179, fig. 65). The trade of objects of devotion and its economic spin off marked a progressive creativity in which relics were used as means to reach deeper into the unity of the Third Quadrant (by creating material wealth). This road was open because the width of thinking made it possible to go back and forwards at the same time. The basic principles of materialism and capitalism were well-known in the invisible ‘Dark Ages’ of the European history.

The elevatio corporis was the introduction to the translation (translatio) of the relict, or the actual start of the removal (from its original place). The boundary between the two events is not always sharp, because the elevatio (raising and storage) has an element of movement. These actions, however, are confined to the place of discovery.

This difference (in position) is of major importance in the philosophical interpretation of the handling of the relic (or of any other powerful discovery, for that matter). The first (visible) visibility discloses the width of a communication, but only to the one who makes the finding. Someone has to take a decision in a comparison between communication partners (in a particular division environment). The elevatio (or reconstruction) is, in essence, the act of taking that particular decision.

The act of finding something (as a discovery, I), putting it in a division environment (II), give it a valuation (as a visible entity, III) and act accordingly (IV) are the very stages in a quadralectic reconstruction. The finding and limitation of the Smallest Part (or Minor) and the subsequent determination of the width of the communication trajectory (CT) are the major activities in the Second Quadrant.

These (four) processes, however, are repeated in the subdivisions of the other quadrants. Reconstruction (or elevatio) is not only confined to the Second Quadrant. It consists of a continuous action (of comparison). Its ‘return’ in the second part of the Fourth Quadrant (IV, 2) – in the form of ‘memories’ – adds a great deal to a communication.

7.3. Substantiality

The ‘present’ is the most physical experience of a human being in time and place. Reality is a practical construction, using the given consequences (of a particular division setting) as an application. The reconstruction becomes a construction. This act is bound to meet with resistance and opposition, regardless of the choice of division. The present narrows things down to the essentials of visibility, with no further proof. The Chilean biologist Humberto MATURANA (1995), in his article on ‘The Nature of Time’, described the living (in the present) as follows:

‘Living takes place in the now, in the moment in which it is taking place. Living is a dynamics that disappears as it takes place. Living takes place in no time, without past or future. Past, present and future are notions that we human beings, we observers, invent as we explain our occurrence in the now. We invent past as a source of the now or present, and we invent future as a dimension that arises as an extrapolation of the features of our living now, in the present. As past, present and future, are invented to explain our living now, time is invented as a background in which past, present and future can take place. But life, living, takes place as now, as a flow of changing processes. To say this, of course, is a manner of explaining the experience being now in which we find ourselves as we ask for the explanation of our living, of time…’

The present-as-construction is a temporary halt, a sudden consciousness of limitation, in a dynamic process of living. Its (theoretical) place can be pinpointed in a quadralectic communication at the departure of the Pivotal Point (PP) – or the beginning of the third part of the Third Quadrant (III, 3). There, at that very point, the dynamics of interaction seem to be frozen in order to experience the maximum of self-existence. The ‘Golden Age of Being’ is found in the formal notion of limitation, boundary and finity.

Jos de MUL (1993), in his perspicacious book on the German philosopher Wilhelm Dilthey (1833 – 1911), dealt with this very subject of limitation. Any formative way of interpretation (or hermeneutics) has to face its boundaries at some stage. Dilthey’s book ‘Kritik der historischen Vernunft’ was written in answer to Kant’s ‘Kritik des reinen Vernunft’ (Critique of PureReason, 1781) and tried to extend his lines of thought. Kant’s book was, as a whole, a reflection on the subjectivity of external observation and an effort to delimit that subjectivity.

The titles of Kant’s major works, like ‘Kritik der reinen Vernunft’ (1781), ‘Kritik der praktischen Vernunft’ (1787) and ‘Kritik der Urteilskraft’ (1790), present the various positions on the road to limitation. They can, in a quadralectic evaluation, be identified as respectively a Second, Third and Fourth Quadrant stance. The ‘missing’ First Quadrant might be found in Kant’s thoughts about an a priori-synthesis. De Mul hinted that the distinct subjectivity of the ‘anthropologia transcentalis’, as broached in Kant’s ‘Logik’ (1800), could be the fourth and final member in the line of ‘Kritiks’.

The philosopher Edmund HUSSERL (1859 – 1938) defined an ‘original present’ in his lectures on the internal time-consciousness, given in the 1920’s. The present is never merely present, but always include past and still to come. The ‘now’ appears an unstable and ever-changing entity ‘running off’ into the past. Most important of all, in Husserl’s view, is the dominance of intuition as a driving force in the creation of concepts. He rated it higher than experience and expressed this opinion, in his not-to-easy to follow style, as follows:

‘The true method is therefore this: that not in experience, but in the pure essential interconnection, that not in empirical psychology, but in rational phenomenology, the entire work of differentiating essences and of conceptual apprehension of essences is performed, and that then in experiential science the mere application of the pheno-menological results takes place.’ (HUSSERL, 1971/1980).

These thoughts were further elaborated in his posthumously published book ‘Erfahrung und Urteil’ (Experience and Judgement, 1964/1973). If we want to return to the origin of truth, it is necessary to contact the world that lies behind our judgements and the categories they embody. Husserl reformed the transcendence into intentionality (a word cast by Brentano).

Husserl believed that the origin of truth was to be found in the intuition of something absolute. He saw, as a result, a structure as ‘a new reality which emerges from the special form in which a number of necessarily interdependent parts or elements combine’ (Husserl, Third Investigation, ‘The Logic of Parts and Wholes’; EDIE, 1981).

The phenomenology, which was described by Husserl as a ‘science of consciousness’ (Inaugural Lecture at Freiburg im Breisgau, 1917). It is – in a quadralectic outlook – a ‘Third Quadrant’ construction, which offers a view onto the succeeding deconstruction (in the ‘Fourth Quadrant’). The outlook shifts from the ‘objective’ (III) to the ‘subjective’ (IV) setting. It casts from here an even wider vista towards the intuition of the First Quadrant (I).

The introduction of dynamism in an ‘objective’ thought is a typical feature for higher (four)-division thinking and marks the departure of oppositional thinking. The act of construction (of a thought) could be interpreted, in the ‘objective’ side of the ‘Third Quadrant’, as a static affair, limited to distinct and premeditated boundaries (of a plan). However, construction carries also, on the ‘subjective’ side of the ‘Third Quadrant’, the dynamism of multiplicity in its meaning when it is placed in the third part of the Second (II, 3) or Fourth Quadrant (IV, 3).

The same can be said for the translatio (or transportation) of the relict (or any other matter of ‘holy’ importance) (fig. 92). The action of movement from A to B comes alive when the relict – as a visible ‘Third Quadrant’ entity – is compared with similar positions in other quadrants (II, 3 and/or IV, 3). The latter stages – named respectively the muun and the whole (see the ‘Tao of quadralectic thinking’, p. 82, fig. 24 and p. 113, fig. 47) – bring the empirical visibility to a higher level. The insight that a (holy) feature, which is static and dynamic at the same time, can be placed in a larger frame of reference, is an enormous breakthrough. It might be its very ‘holiness’ which opens the view to wider horizons.

Fig. 92 – The Sant’Andrea Church in the Via Flaminia in Rome was commissioned by Pope Julius III and designed by Giacomo Vignola (1550/1554). The small church was built as a celebration of the triumphant transportation (translatio) of the head of the apostle Andreas to Rome (BUSSAGLI, 1999). The history of Saint Andrew’s relics is interesting. He was crucified on a crux decussata (X-shaped cross) in Patras (Greece) in 60/70 AD. His remains were moved around 357 to Constantinople by the Roman Emperor Constantius II. The Byzantine ruler Thomas Palaeologus donated the head of Saint Andrew to Pope Pius II in 1461. The remains were stored in one of the four central piers of the Saint Peter in Rome. Pope Paul VI sent the relics back to Patras in 1964. Other parts had been kept (since 1208) in Amalfi (Italy). Saint Andrew is the patron saint of Scotland. The Boundary Cross (barrier) on the flag of Scotland has a symbolic meaning. The oval dome and the square lay-out of the Sant’Andrea in Via Flamina mark a step in the development of central building (HUERTA, 2007).

Visions of Four Notions

Introduction to a Quadralectic Epistomology

6.2.1.2. Ammonites

6.2.2. Large animals as time indicators

6.2.3. The relation between Man and planet Earth

6.3. Imagination on a cosmic scale: existence in space

6.3.1. The cosmic history of the earth

6.4. The ultimate consciousness: the universe

7. Perspectives

7.1. The Roots of Understanding

7.2. Inventarisation

7.3. Substantiality