2.5. There is more to five

Thinking in a five division is, in a practical sense, the ultimate extension of the human mind. Any higher division – although possible on an intellectual level – is too far away from the material world to be of any use. The distinction between pure division thinking and the numerological approach should be clear at this point. The former relates to a corpus of interactions in which every compartment contributes to the operation of the whole. The latter is only a distinction in the number of contributors, without any internal structural relation to the whole, except in certain features.

The Pythagoreans (described by Plato in the Timaeus) were attracted by the five regular geometrical solids, as found in certain crystals, and regarded them as fundamental building stones (of a tangible world).


The ‘Platonic’ solids or regular polyhedra are polygons whose vertices and faces are all of the same type. In three dimensions there are only five regular polyhedra: the tetrahedron (number of faces 4), the cube (6), the octahedron (8), the dodecahedron (12) and the icosahedron (20).
Plato (in the Timaeus) associated the cube with the four-squareness of the earth, the tetrahedron with fire, the icosahedron with water and the octahedron with air. The dodecahedron (12) was, according to Plato, for ‘embroidering the constellations’, pointing to the zodiac and the cosmos.

The Chinese culture also ventured in the terrain of the five-division. The way of classifying things by fives was already given in the famous Tao Te Ching and the Shu Ching (the Book of History), both of uncertain date and authorship. The actual theory of the five elements was provided by Tsou Yen (c. 350 – 270 BC), of the Ying-Yang or ‘Cosmologist’ School. He was seen as the founder of Chinese scientific thinking, the latter so thoroughly described by Joseph NEEDHAM (1954/1988; RONAN, 1978/1986).

The four cosmological elements (wood, fire, metal and water) are jointed in the center by a pivotal unit, the earth (fig. 11). This setting leaves a flexible, but uneven configuration of (sub) units. The pentagonal division has this unbalanced character in common with the three-division, but the wider symmetry pattern around the centre compensates for the small scale of triple thinking. The deep and rich world of the five division will, at this point, not further elaborated.


Fig. 11 – The five elements in the Chinese culture, as established by Tsou Yen in the third century B.C. offer the theoretical foundation to introduce the five-fold way of thinking. The elements are related to colours, symbols seasons and directions.


3. Preliminary movements

Division and movement were marked as the most important constituencies of a communication. The division has been briefly indicated as a rational act of slicing up a unity into parts. More parts (in a primary division) mean more opportunities to distinguish detail, but their presence also complicates the understanding.

Personal communication has, for that very reason, always been an act of compromise. Certain situations, mostly in the field of biological survival, ask for decisive and immediate action. Two-fold thinking is most effective in this way. This decisiveness by lower division thinking, however, also operates in complicated situations or crisis in which no rational solution is at hand. When nobody knows what to do, people tend to drift to elementary answers. Dictators are masters in using these tendencies in the human mind. They use the arsenal of oppositional devises, aiming at some sort of existential fear to continue their power.

Fortunately, there are in history also times in which the primary survival techniques are not of direct interest. Then the range of division can be widened, leaving room for nuances and attention to detail. It is granted that the decision speed has to suffer in this process, but the depth of investigation is enhanced. At first, a third term is added, as a go-between, to the ‘either – or’ of dualistic thinking. The triple division system offers more dynamic possibilities, but is, in essence, unbalanced. This fundamental inequality gives the chance to create new value systems, but has also been used to the advantage of those who were interested in power play and hierarchical predominance.

Later, generally as a mature step in the practical application of division thinking, a fourth term can be introduced. The communication system is back as equilibrium. The hierarchy is not the main characteristic of the quadripartite order, and the gradations will be confined to specific places within the subsections. Lower division arrangements also get their own place within the boundaries of the four-fold system.

All these theoretical accomplishments within the evolutionary range of division thinking are only possible when a second conceptual act is performed: the movement of the (hypothetical) parts along each other. An observer can only compare, validate and make visible if a shift in the division is performed.

A division without movement is a static affair, situated and received on an abstract level. Mathematicians can play with it, just like Mandelbrot did with his fractals, born in the highly theoretical environment of broken dimensions (MANDELBROT, 1982). A division becomes ‘visible’ when the parts are involved in a dynamic process of comparison with the observer. When I see an object (a part), it is only because I notice boundaries between the object and its environment. Observation is a continuous process of to-and from or in short: movement. A comparison (leading to a form of ‘visibility’) can only take place as a movement takes place.

The four major means of transportation (or movement) of the initial material in a communication can be listed as follows:


These four types are related to each other in a circular way. The signal gives rise to a symbol, which is understood as a sign and used in a language. The opposite movement is also possible in which a language produces signs, which are interpreted as symbols, functioning as signals. A graphic representation of the arrangement is given in fig. 12:


 Fig. 12 – This scheme indicates the means of transportation in a quadripartite communication. The sequence must be seen in a cyclic setting whereby each element is related to, and included in, the other elements. The sequence of quadrants does not indicate a hierarchy of importance.

The four major components of every communication will be discussed briefly, because they reach into the heart of the quadralectic issue. The four constituents are the ‘faces’ of the quadrants. Their character can be read in their expression.


3.1. The signal

The signal is the primary feature of a communication. It stands at the very base of understanding. Without a signal there would be no vestige of a communication at all. The signal as a singularity is a rare phenomenon, if not impossible to imagine. Its definition encounters the same problems as the one, which was experienced in the concept of unity. The very moment a definition (limitation) is given, the spell of its existence is broken. The undivided world cannot be caught in definitions without breaking its authenticity. The same characteristic is applicable to the signal, as a voice from the deep unknown. Its initial unity is broken the very moment it is noticed by an onlooker.

The observer deals more often with an array: a multitude of signals of the same nature. Radar and sonar are examples of array signals, which are used to build up a new kind of visibility. Acoustic and vibration signals are illustrations of the practical application of signals, for instance, in seismic prospecting. The present age of computerization is highly indebted to communication signals, which are sent by modem, cable or wireless. The human body itself creates physiological signals, including clinical and speech signals, which can be registered and analyzed. The world is full of noises of a natural or synthetic character. And last, but not least, there are signals from outer space, which possess the challenging prospect of a contact with other creations in the universe.

The Croatian genius Nikola Tesla (1856 – 1943) was one of the first experts to see the potential of the signal as a source of communication. His experiments with electricity and the wireless transmission of energy (including the possible cause of the Tunguska catastrophe in 1908) are a specimen of the incredible forces, which could be unleashed when the potentiality of the unseen is tapped. Tesla followed in the footsteps of Michael Faraday (1791 – 1867), the blacksmith’ son, who pointed the way – some sixty years earlier in 1831 – to the production of electricity by magnetism (if it was accompanied by motion).

Tesla’s inventions included the AC-power (both 2-phase and 3-phase), broadcast power (radio wave propagation), microwaves and radar. The Tesla Coil is a transformer, which generate very high voltages at high frequencies. A most common form of the transformer is used in neon signs. It is interesting to note here that a signal (high voltage) is used to power a sign.

Tesla’s vision included the transmission of electrical energy through the earth to be picked up wherever it was needed. The globe, even with its great size, responded to electrical currents just like a metal ball. He expressed his original idea in 1911 as follows: ‘The entire apparatus for lightning the average country dwelling will contain no moving parts whatever, and could be readily carried about in a small valise.’

The research in signal processing has taken a huge flight since then and continues to do so. The signal is the messenger of the invisible invisibility of the First Quadrant, who brings never-ending opportunities to mankind. The present interest focuses on the domains of influence, which form a direct link to a division-based communication. In particular, the geometric representation of tessellations could be a practical tool in the interpretation of signals used in human relationships. The verb ‘to tessellate’ points to the arrangement of squares in a mosaic pattern. The Greek word ‘tessares’ means ‘four’, because initially square tiles were used.

The so-called Voronoi tessellation (or its name equivalents like the Dirichlet domain, Wigner-Seitz cell, Thiessen polygon or Brillouin zone) is applied for analyzing cell-like structures and the division of space into regions (fig. 13). The Voronoi diagram can be used in a wide field ‘from archeology to zoology’ (DRYSDALE, 1993). The representation of lattices is useful in the identification of clusters (in astronomy), the location of areas of growth (in biology), the modeling of sphere packing in chemistry, the pattern of settlement (in geography), the estimation of mineral reserves (in geology), data analyzing in marketing and much more. A further investigation into its use in quadralectic thinking might be a worthwhile undertaking.


Fig. 13 – The Wigner-Seitz (WS) cell is a volume made up of space which is closer to a given lattice point than to any other point. The construction starts from a lattice point and the drawing of lines to its neighbours. Next is the drawing of perpendicular bisecting planes to these lines, half way along. The smallest volume enclosed within these planes is the WS cell. The example gives a rhombic dodecahedron for a face-centered cubic lattice.

3.2. The symbol

The symbol is a sign that informs by convention. Alternatively, like WHITTICK (1960) put it: ‘A symbol includes all that is meant by a sign, mark or token.’ Such an appealing definition pinpoints, in its shortness, to the different directions of its meaning. The main constituencies are the sign and the convention. The first (sign) is a static description of reality, finding its place (in a quadralectic environment) in the empirical visibility (of the Third Quadrant). The second (convention) is a dynamic, swerving and swaying entity in the multitudes of a domain, which is later identified as that of a language (in the Fourth Quadrant). The original Greek meaning of the word ‘symbol’ as a ‘bringing together’ is applicable here.

The given definition lacks, unfortunately, an important element of the character of the symbol. The convention – or communis opinio – must have a specific intention, which is different from the apparent meaning. The sign is not what it really is (a cross, a car or whatever), but it stands for something else (a Christian faith, wealth or some other substitution value). This transitory quality is the hallmark of the symbol-sign.

The conclusion of the above given definition would be – in a linear and hierarchical line of thinking – that the symbol only finds its reason of being in the things to come. Its ‘Second Quadrant’ identity is based on a ‘Third Quadrant’ entity, which gets another (double or multiple) meaning by the interpretation in the ‘Fourth Quadrant’. Another possibility would be, that the association of the sequence (signal, symbol, sign, language) with the quadrants is invalid and should be arranged in another way.

The solution to this sequential problem is a transposition from a linear (and hierarchic) to a cyclical (and non-hierarchical) way of thinking. Everything is in everything, not only at the very beginning – like the linear view often prescribes – but also during the whole process of data exchange. There is no ‘before’ or ‘after’ in a general overview, only on a local and limited scale. The essence of the whole quadralectic communication lies embedded in every single moment and every single place.

The position of the symbol in the dynamic Second Quadrant is well earned, because the transitory nature is typical for this phase, just after the first division took place. It is the world of ideas, non-coherent connections and preliminary interpretations, which might substantiate itself after some form of a convention (in the fourth (sub)division of the Second Quadrant) has taken place.

This symbol-forming course is, in many ways, a proficient reflection of the communication-as-a-whole because the observer has to go through all the various stages to get the picture (of a symbol) right. The initial signal manifests itself in an invisible visibility (after its diffusion in an array). This array is picked up by an observer, interpreted (symbolized), established and communicated (compared) with the findings of other observers. The first full round along the observational stands yields a personal symbolism, based on an individual impression (which was, in essence, already explored in the second phase of interpretation).

The last stage in the path of signal processing, i.e. the actual participation in a communal comparison, gives the communication a sudden ‘human touch’ (and associated subjectivism). The newly experienced reality (for the observer) is no longer noncommittal, but assimilates in a group and mingles as a component in a language (defined here as the collective construction of the visible invisibility).

The language-entity has the capacity to become a new signal. The array of this (language) signal makes a second round (along the observational stages of the language group), which results in a group symbolism. Interaction between different (cultural) groups can result in a third round, a fourth, and so on.

Symbols, as a particular expression of understanding, are very versatile. They can be manifest as a separate presence, like a down-to-earth sign in the Third Quadrant or cluster together as an icon in the Fourth Quadrant (fig. 14). The various meanings (and operational places within a communication) have to be fully understood to grasp the intention of a symbol within a language.


Fig. 14 – The symbol is a sign, which informs by convention and points to something else. The Hitler Jugend of Zernikow (100 kms north of Berlin) planted these larch trees just before the Second World War. The yellow foliage formed in autumns a swastika pattern amidst the other trees. The swastika itself is an ancient sun-sign, which became a symbol in Nazi Germany. The pattern was discovered from the air in 1992. The trees were cut down in December 2000 in fear of becoming a place of pilgrimage for extreme-right wing groups.

3.3. The sign

The sign is a familiar point of visibility. The main characteristics of the sign are its limitation (as an object) and its capability of establishing a connection. The sign brings the signal to its destination: the understanding by an observer. The study of the sign is a ‘Third Quadrant’ venture, initially ruled by the two- and three divisions.

The American mathematician Charles Sanders PIERCE (1839 – 1914) caught the spirit of this new field of psychological investigation, which he labelled semeiotic (in the current use and spelling the word semiotics includes all the various studies of signs). He emphasized the subjective character of the sign (in: PIERCE, 1963; par. 2.308) by saying that ‘nothing is a sign, unless it is interpreted as a sign’.

The three-division became a central point of departure in his mathematical or symbolic logic. The process of signification, for instance, consisted of three stages. Firstly, the sign in itself (representamen, Third Quadrant), secondly the object (the sign as used by its observer, Second Quadrant) and thirdly, the sign as an image as created by itself (interpretant, Fourth Quadrant). These three connections were again placed in trichotomies. The object was divided by Pierce in:

The icon is a representation of an object shaped after nature,

The index  is a reference to an object (a gesture): anything that focuses attention is an index;

The symbol rules about the use of an object as a representamen, and can be expressed in words and sentences.

The threefold division of signs as a sign vehicle, designatum and interpreter (at present rendered as respectively second, third and fourth quadrant expressions of the sign) was further advanced by Charles Morris (1901 – 1979) in his book ‘Foundations of the Theory of Signs’ (1938).

Van SCHALKWIJK (1989), in his eminent study of the sign of the cross, gave a more elaborate division of communication-elements, which is closer to the modern, quadralectic way of thinking:

Signals    ———————–  extrinsic

Signs —————————– intrinsic

Symbols ———————— analogy, metaphor

   subdivided in:

  —————     Icons             –       clusters of ‘symbols’

   ————–      Gestures      –       sign language

   ————–      Proxemics   –       silent language of non-verbal communication

The quadralectic sequence (of quadrants) can be reduced from these given distinctions, but some ‘juggling’ is necessary. Signs (III) and symbols (II) have to change places. The icons remain with the symbols, but the gestures belong more to the world of signs and can even bridge the gap to a language (the sign language as a way of expression).

Finally, the proxemics – cultural interaction, the feel of distance, smell, or the angle of vision – is a genuine expression of a Fourth Quadrant ‘language’, based on subjective intervention and a collective construction of the visible invisibility (IV).

The sign is – in a quadralectic communication – not only a simple visible visibility (positioned in the Third Quadrant), but also an interactive element in the (third part) of the Second Quadrant and in the (third part) of the Fourth Quadrant. It acts as an object with a certain content and is a constituent in several regimes. The various positions, seen as a centre of significance, have a specific formalization of expression. The sign is the ‘decoder’ in the communication process. The interaction can be divided in:

1. a source, sending a signal (or array of signals),

2. which can be regarded as encoded messages (symbols)

3. to a receiver, who tries to understand them (as a decoder) and

4. leading them to the destination (of understanding).

This sequence is derived from the coding theory (a branch of mathematics concerned with transmitting data across noisy channels and recovering the message). The various positions are given in fig. 15.


Fig. 15 – The sign is a receiver in a communication, which translates a message (or an array of signals) from a sender (using these encoded messages as symbols) to a destination. The destination can be described as a language, capturing the understanding of the original signals to the participants in the communication. Its use and meaning can become a new message source for another (communication) cycle.


Radio telescope Kootwijk (1948 – 1955). The Netherlands – An example of a receiver (of cosmic signals).

3.4. The language

The language is the most complicated form of a communication, because it employs all the previous communication elements at the same time. The word ‘language’ is used here in a general sense, as the denominator of any form of communication in which signals, symbols and signs are combined in a meaningful set of rules to articulate thoughts.

Language deals, firstly, with signals, which are emitted from any given source. Secondly, there are a meaning and setting of such signals transferred by man to symbols. These symbols can have several meanings and are joint together in a concept. Thirdly, there are the actual signs (words), which are used to visualize (and/or make audible) the message. Finally, there is the knowledge of the whole process, expressed in such terms as ‘speaking the language’.

The understanding of (any) language means, when conceived in its most complete manifestation, a knowledge and mastering of all the meaningful elements of a particular communication under the given circumstances. Experience gives an insight in the bond between primary knowledge, language and a fruitful understanding within a communication specter.


Fig. 16 – The English philosopher John Locke (1632 – 1704) studied the nature and development of knowledge in the heydays of oppositional thinking. He reached conclusions, which had – at some points – a resemblance with the quadralectic philosophy.

The English philosopher John Locke (1632 – 1704) traced the intellectual development of knowledge in his book ‘An Essay Concerning Human Understanding’ (first published in 1689; he worked on the book for almost twenty years). He was a rationalist and dualist at heart, just like his major sources of influences, René Descartes (1591 – 1650) and Robert Boyle (1627 – 1691). It is remarkable, that his strict and often sceptical approach to knowledge opened up an occasional glimpse in the world of higher division thinking. One may wonder if such insights were just a coincidence, born in a creative mind, or that they are part and parcel of any inquisitive reasoning power at the boundaries of two-fold thinking.

The division of his ‘Essay’ in four books reflected perspicuously the present quadralectic approach of understanding. The contents of the book will be briefly discussed here:

Book 1. Introduction

The object of Locke’s book was an enquiry into understanding, with the idea (defined as the object of the understanding when a man thinks) at the centre of attention. The bounds between opinion and knowledge were of special interest. Locke employed a threefold method to reach his goal:

 A search for the original of those ideas (or notions), which a man has in mind;

  1. The extent and limits of knowledge gained by such ideas; and
  2. The foundations of faith or opinion.

He regarded the origin of ideas as two-fold: there were speculative and practical principles. The former propositions were self-evident and logic. The latter gave guidance for conduct and moral duties in everyday life. There were, according to Locke, in contrast to the Cartesians, no innate (or preconceived) ideas: his ‘First Quadrant’ was seen as a complete empty place. Any idea of cyclicity (and division thinking), that gives a different view on the character of the First Quadrant, was unknown to Locke.

Book 2. Ideas

Locke moved in the second book to the ‘great and principal actions of the mind, which are most frequently considered, and which are so frequent that everyone that pleases may take notice of them in himself: perception or thinking, and volition or willing’. The power of thinking was called the Understanding, and the power of volition called the Will’ (Book II, Ch. 6).

Locke considered sense experience (sensation) and reflection as the primary sources of ideas. Again, an immediate, two-fold division followed: simple ideas (derived from one sense only, which also included the results of sensation and reflection – like pleasure and pain, power, existence and unity) and complex ideas (of substances).

The interpretation of the ‘Second Quadrant’ of Ideas is, from a modern, quadralectic point of view, rather hodgepodge. Sensation is a ‘Fourth Quadrant’ feature. Reflection takes place mainly in the ‘Second Quadrant’ (and also in the ‘Fourth Quadrant’). Unity and existence are ‘First Quadrant’ items. And the source of power and various oppositions (such as pleasure/pain, heat/cold, light/darkness, white/black and motion/rest) have their home ground in the ‘Third Quadrant’.

The dualism of Locke did not arrange the products of his simple ideas any further in a comprehensive way, but it must be granted that the mere mentioning of these diverse items under one heading (identified as the Second Quadrant) touches the tetradic perception of a communication.

Book 3. Substance

There is no clear idea of substance in general, concluded Locke (still in Book II, Ch. 23). He referred to the Platonic line of thinking that our observation of physical things (like a horse or a stone) is interwoven with the idea we have of such substances. There can hardly be, in other words, a clear-cut ‘horse’ or ‘stone’. The differentiation between the ‘real thing’ (realist) and ‘the idea of a thing’ (nominalism) has kept philosophers busy for a long time after Plato. The efforts always boiled down to the eternal question: What is real?

The controversy found a new lease of life in the Middle Ages, with William of Ockham (c. 1285 – 1347/49) as a major pioneer on the ‘via moderna’ (rejecting the universals). He maintained that science had to do with propositions, not with things as such. Things are always singular, while science was concerned with general concepts. The last word on the subject (of ideas) was still not said in the middle of the seventeenth century and in the lifetime of Locke.

John Locke compared the physical things with the substance of spirit: ‘It is plain, then, that the idea of corporeal substance in matter is as remote from our conceptions and apprehensions as that of spiritual substance or spirit’. He used a three-division to connect the complex ideas of corporeal substances with the senses:

1. The ideas of primary qualities are discovered by our senses (like bulk, figure, number, situation etc.)

2. The sensible secondary qualities are nothing but the powers those substances have to produce several ideas in us by our senses.

3. The alterations of primary qualities can be noticed (active) or unnoticed (passive powers), but are – in the end – always traceable to sensible simple ideas.

This celebration of the senses – in the end of Book II and prior to the subject of their substratum (substance or visible visibility) – is an indication of the unconscious use of a higher division model. A modern interpretation would place his thoughts in the fourth (sub)quadrant of the Second Quadrant (II, 4) or in the Fourth Quadrant (IV, which Locke could not grasp in his life and times).

Book III of the ‘Essay’ dealt directly with words or language in general. The capacity to make general signs (expressed in words) was retraced to common sensible ideas. ‘Words stands for nothing but the ideas in the mind of him that uses them’ (Book III, Ch. 2). There is, again, a pointing finger to the Second Quadrant.

Locke gave, in the same chapter, an example of words, which stand on their own (i.e. as ‘Third Quadrant’ entities). Words can be learned before the ideas are known for which they stand. He referred to the parrot, as the symbol of ignorant repetition, but he did not realize the weakening of his prior argument (saying that words were solely derived from ideas). Words may, in their primordial existence, also have been the building stones of a language in their own right.

The next remark on the real existence of things (in Book III, Ch. 3) was the rejection of the general and universal. These features do not belong to things themselves, he stated, but are invented by man and are creatures of his understanding. He proved himself here a follower of the nominalism of William of Ockham. Universality belongs not to things themselves. Things are always particular in their existence.

This clearness of thinking denies a unity to be capable of harboring a multiplicity (in itself). This fundamental difference of insight can be traced back to the expressions of lower and higher division thinking. A dualistic thinker is not willing to see more in a unity than there is: the opposition of a multiplicity. Unity – in the quadralectic mind – is, on the other hand, seen as a transitory position within a given interaction. It includes all the aspects of the whole communication, being either visible (matter or substance) or invisible (spirit and idea), being it either single or multiple.

Locke’s view of substance, as a Third Quadrant issue, was a mirror image of his notion of the First Quadrant, which could not hold innate ideas. Unity is unity. It is only in higher forms of division thinking that such basic statements are put in perspective.

Book 4. Knowledge in general

The author of the ‘Essay’ reached his zenith in Book 4, which investigated knowledge, as the ultimate proof of understanding. He regarded this commodity as ‘nothing but the perception of the connexion and agreement, or disagreement and repugnancy of any of our ideas.’ (Book IV, Ch. I). Such an opposition can be reduced, in Locke’s view, to four sorts:

1. The identity  or diversity – the first act of the mind to know what an idea is;

2. The relation – the perception of the relation between two ideas;

3. The coexistence or necessary connexion – the notion of substance. There is a complete ignorance of the substance either of spirit or of body;

4. The real existence – the conformity between our ideas and the reality of things.

Again, he followed a ‘quadralectic’ scheme, with a typical sequence of static-dynamic-static-dynamic phases, which is a reminder to the unity and separation (love and strife) cycle of Empedocles. However, Locke gave his credentials away in the choice of identity as the first act of the mind. The understanding is not the primary (quadralectic) division-principle, but a choice between two members of a duality: identity and diversity. Locke found, as a good dualist, his security in the safe haven of visible visibility (predominant in the Third Quadrant).

This choice was not surprising, since John Locke (1632 – 1704) witnessed during his lifetime the apex of European oppositional thinking. Bertrand Russell called Locke ‘the most fortunate of philosophers’, because his ideas were understood and welcomed by many of his contemporaries (COLLINSON, 1998). The present indication of the venturing of his critical and methodical mind in the realms of some sort of tetradic setting is a curious phenomenon.

Locke introduced, in addition to the reduction of knowledge into four varieties, also a hierarchy of knowledge. He proved himself here, again, a faithful thinker-in-opposites applying a trifold scheme. The hierarchy was based on ‘a different clearness of our knowledge’ with regards to ‘the different way of perception of the mind in the agreement of disagreement of any of its ideas’ and consisted of three ‘degrees’.

The dualistic theme (of dis/agreement) was used here to define a certain ‘clearness’. This transparency can be transferred to the quadralectic way of thinking and restated as ‘visibility’ and the awareness of distance. Locke’s linear differentiation of knowledge is then substituted, in modern thinking, by the ‘intensio’ and ‘remissio’ in a cyclic setting.

The division (of knowledge), as given in the ‘Essay’ (Book IV, Ch. 2) corresponds with the characteristics of the First, Third and Fourth Quadrant in the quadralectic way of thinking. They are:

  1. Intuitive knowledge (I)

The mind (in the ‘First Quadrant’) has ‘no other immediate object but its own ideas, which it alone does or can contemplate, it is evident that our knowledge is only conversant about them.’ Sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other. This is the most basic and clearest kind of understanding: the intuitive knowledge.

The ‘First Quadrant’ of Locke is, at scrutiny, not as empty as he described it earlier (in the introduction) as a place without any innate ideas. Apparently, agreement and disagreement (of ideas) – or in other words: division – are present in the whole specter of communication. Which is fair enough, and in agreement with the quadralectic approach, but it did not enhance his statement on the absence of innate ideas. If ideas have the power to ignite themselves as intuition, seemingly without our intervention, why should there be no innate (or preconceived) ideas?

The type of division thinking and environment might hold, again, the key here. In a rational world of opposites is no place for innate ideas, because they point to an area before the actual existence. Preconceived ideas are no real problem in a cyclic framework. They might be the remnants of an earlier communication cycle, passed through before the present one. Intuition is, in a cyclic outlook, just the assemblage of the invisible in-visibility (I), bearing the full history and future of a communication in it.

 2. Demonstrative knowledge (II/III)

This second type of knowledge is much more imperfect than the intuitive knowledge. There is no immediate recognition, instead the mind had to proceed by reasoning (understood as an interchange of ideas). Some work has to be done, before results can be obtained.

Locke pointed out that the intermediate ideas had to be found and brought to agreement or disagreement, i.e. proof. Once this dynamic process was completed, it was called a demonstration. The method of intervening proofs did not deliver its certainty so easily as intuitive knowledge.

The dynamic development and use of ideas find – in a modern, quadralectic understanding – its basis in the Second Quadrant. The main cognitive setting of this quadrant is the invisible visibility. The primary division sparks off an intellectual action, characterized by the introduction of a value system. Locke’s demonstration is the outcome of such an active operation. It carries the initial (intuitive) ideas through the Second Quadrant into the Third Quadrant, where the visible visibility (or proof) is fabricated. The demonstrative knowledge (of Locke) covers therefore two quadrants.

  1. Sensitive knowledge (of particular existence) (IV)

This knowledge is again narrower, reaching no further than the existence of things actually present to our senses. Locke is not very clear on this type of knowledge, even to the extend of being evasive (pointing to sidelines of faith and opinion). The existence of ‘particular finite beings without us’ goes, in his view, beyond bare probability. However, he has no idea, as an oppositional thinker, how to imagine such a world-outside-ideas. There simply is no place for the effects of senses in relation to a real existence other than ‘ideas’.

The nature of sensitive knowledge is much more understandable in a quadralectic approach. Here a situation is visualized in which the senses have their own ‘ideas’ transferred to ‘knowledge’ in the second quarter of the Fourth Quadrant (IV, 2).

His conclusion that knowledge (IV) comes short of the reality of things (III) but even of the extent of our own ideas (II), is in line with his hierarchical view. The notion that knowledge is narrower than our ideas is, in essence, an assumption, based on the subjective preconception that ideas are the ‘highest’ contributors to a communication.

It is remarkable that Locke, despite his lack of a wider frame of mind, came close to many viewpoints of the quadralectic way of thinking. One may wonder about the connection between an in-depth two-fold study (like Locke did) and a proper four-fold approach (in a modern quadralectic analysis). They seem to come very close at a certain point, despite an a priori difference in initial division. Somewhere in the mind seems to be a cognitive bridge connecting a (double) duality with a (quadralectic) quaternity. Further psychological research will be necessary at this point.

His four degrees in reason (Book IV, Ch. 17), for instance, summarized near the end of the ‘Essay’, are just another indication of this curious tendency.

 1. First and highest is the discovering and finding of proofs;

  1. The regular and methodical disposition of them;
  1. Laying them in a clear and fit order to make their connection and force be plainly and easily perceived;
  1. The making of the right conclusion.

Proof – use – order – conclusion is a familiar sequence. Locke ended his book, rather conventionally, in a triple-division mood and conform to the basic oppositional ideas at the end of the seventeenth century (of the European cultural history). The three stages or ‘the first division of the objects of knowledge’ (Book IV, Ch. 21), in his view, are:

  1. The nature of things (as they are in themselves knowable);
  1. The actions to reach a goal (especially happiness) and
  1. The use of signs (in which knowledge can be attained).

These entities are the major constituencies of John Locke’s philosophy, or ‘the three great provinces of the intellectual world’. Locke’s frantic emphasis on ideas and the senses seemed to be a reflection of his need to bring the human understanding in areas of multiplicity (in a tetradic view identified as positions in the Second and Fourth Quadrant).

Locke’s contribution to the knowledge of an intellectual ‘language’ – used here as an expression for ways in which a communication is performed – was considerable. The links between an unwavering dualistic framework and a (partly unconscious?) understanding of the tetradic way of thinking are instructive in their own way.

The English philosopher will be left behind here, but the investigation into the development of an intellectual interaction (defined as a language) will be continued in his spirit. The actual mechanisms of a communication will be described in a rationalistic and comprehensive way. It implies that facts are primary rooted in an oppositional substratum and are transported from there into areas of greater expansion.

The dual way of thinking distinguishes two basic kinds of argument in a communication: the inductive and the deductive way. The former manner of reasoning (induction) is usually pictured as moving from the specific to the general (from one to many). A specific delineation – the one – is compared with other delineations – the many – in order to reach a conclusion based on similarities. The latter kind of reasoning (deduction) begins with the general and ends with the specific (from many to one). The observer compares the quantity – the many – with itself in order to deduct a generality – the one.

Inductive arguments are usually based on experience or observation and are comparisons between two or more sets of events, ideas or things. The importance of the comparison gave rise to the use of the name analogical argument as an equivalent expression of inductive reasoning. The strength of inductive arguments depends upon the genuine nature of the comparison between the particular and the items chosen from a generalization.

The major premise of deductive arguments is based on a rule, law, principle or generalization. A deductive argument can be expressed as a syllogism or as a conditional. Both forms deal with the same logic reasoning, but use another way to reach its conclusion. The technicalities of logic are here of no concern to us, but it is important to note that the deduction uses various methods to reach the same goal.

The difference between inductive and deductive of reasoning is mostly in the way the arguments are expressed. Any inductive argument can also be formulated in a deductive way, and vice versa. This reversal is a logic consequence of the oppositional environment (one versus many) in which the arguments were positioned in the first place.

The quadralectic mind – as may be expected – differentiates between four forms of argumentation. The wider view includes the above-mentioned pair of inductive-deductive reasoning, but is joined by two other operational means. The first addition, better known as trial-and-error reasoning, is a very basic form of argumentation. Certain elements are joined together without any preconceived ideas or intentions. The results can be weird and devoid of all common sense. The method is unsuitable, due to its volatile and transient nature, to be productive in a dualistic (or scientific) environment. It is, for this very reason, in the past largely neglected as a viable option for a logical sequence.

The second addendum, the analogical argument, is mentioned before as part of the inductive method. This amalgamation is a simplification born in lower division thinking. The use of analogies is instrumental in all types of argumentation, but also has a coordinating function on its own.

The four basic argumentations in a quadralectic communication are given here:

  1. The Trial-and-error method (TE):

Catching haphazard elements and join them together to some new form. No plan or fixed idea is used to select the individual elements, even the outline of these units is not considered. This form was never favored in scientific circles, because of its transcendental nature.

  1. The Inductive method (IN):

Using specifics to reach generalities. By choosing a distinct element and compare it with a multitude in order to find a general expression. This is a long established and respected scientific method, starting with the Pre-Socratici like Thales, Anaximander, Parmenides and Pythagoras. There is a distinct a priori element (the choice of a part) in this way of reasoning.

3. The Deductive method (DE):

Using generalities to reach specifics. Selection in a dynamic multitude will give a static limitation. The terms of certain laws or rules are compared with the multitude. It is considered the more advanced scientific method, already used by Aristotle and his followers. The nature of an a priori choice is hidden away behind the acceptance and use of the law or rule as a (temporary) truth.

4. The Analogy method (AN):

A combination of the previous methods with a special emphasis in the mechanism of the argumentation in the context of a language (the term language is used here as a summary of all the elements used in the data exchange between communication partners). Analogy is a tentative method. NORTH (1989, p. 285) said, in his essay on ‘Science and Analogy’: ‘Analogy is the basis for much scientific conjecture, but even conjecture is an art, which can be done rationally, that is, even though it might prove in the end to have yielded a false conclusion’.

These four ways of understanding fit in the context of multiple division thinking. Every mode of inquiry is connected with a particular quadrant. This implies – in a reciprocal way – also an indication of the position of the communicator when a specific method is used. The way of reasoning is a structural part of the communication as a whole (fig. 17).


Fig. 17 – This summary gives the four ways of argumentation and their relation to the various positions in a quadralectic communication. The type of action is an approximation of the movement in a particular quadrant.

The conclusion of the preliminary movements in the quadralectic field is faithful to its own starting-point: each division-component (quadrant) has its process (method), but also its own world of expression and typification. This conceptual step implies a move from the Second Quadrant (the process) to a Third Quadrant environment. A distinct form (of division thinking) can be narrowed down in this latter field to an opposition of unity versus plurality.

  1. Unity- and part-thinking, centered around the One (Unity), and

2.   Muun– and multiplicity thinking, centered around the Many (Plurality)

The term muun is introduced here as a neologism. The word is an amalgamation of the word multiplicity (mu) and unity (un). It wants to express the connection between these two items in a single, cognitive component.

The muun is a symbolic unity in multiplicity.

Its closest conceptual neighbor is perhaps the ‘Idea’, used in a Platonic sense. Plato was, despite his pioneering contemplative activities, never an accomplished four-fold thinker. This specific disposition came to the foreground in the interpretation of his beloved idea. Although a division-thinker by heart, he did not recognize the vital importance of the first division.

Examples of mind-constructions like value, category, abstraction, concept, attitude, stability, variable, mechanism, opinion, behavior, trust, power, freedom (and many more) are covered by the definition of a muun. These terms present themselves as a unity – and are used as such in a language – but they are composed of many different subunits. Their unity is symbolic.

A classification of the quadralectic system can be based on the previous qualifications. The various characteristics are placed in the quadrants in which they have their major field of influence (fig. 18).


Fig. 18 – A quadralectic scheme to indicate the environment of the various quadrant and the associated mind constructions and their representation.

This scheme should not be treated as a fixed entity but rater as a guideline to the dynamics of quadralectic thinking. This means that none of the entities mentioned in fig. 18 are limited to the positions as given above.

Creativeness plays an important part in the quadralectic epistemology as a criterion of visibility. The act of creation is, in a modern view, a movement from one (sub) quadrant into another. This conceptual transpose means, implicit, a change in the type of visibility. Creation as ‘making something’ (creativity) is closely related and interchangeable with ‘seeing something’ (visibility).

The Italian philosopher Giambattista Vico (1668 – 1744; fig. 19) communicated, early in the eighteenth century, the same relation between the origin and the actual appearance in his dictum verum et factumconvertuntur.


Fig. 19 – Giambatista Vico (1668 – 1744) – ‘a prophet without honor in his own country in his own day’ (BURKE, 1985) – proposed at the first quarter of the eighteenth century a ‘New Science’, based on a triple-division. The beginning of the twentieth century saw a revaluation of his ideas, starting with a footnote in Karl Marx ‘Das Kapital’ to a full reinstatement by the Italian philosopher Bernedetto Croce (1866 – 1952).

The verum-factum theory, as it became later known (MORRISON, 1978), stated that the Truth (of knowing) could only be reached in an act of making. ‘Vico’s doctrine required that one make, collect, order, or generally do something with (the elements of) a thing in order to know it’ (HENDERSON, 1985). Or, as Vico put it himself: ‘But in the night of thick darkness enveloping the earliest antiquity, so remote from ourselves, there shines the eternal and never failing light of a truth beyond all question: that the world of civil society has certainly been made by men, and that its principles are therefore to be found within the modifications of our own mind’ (Scienza Nuova, Book I, Section III).

Vico idea’s were fully developed in his book Scienza Nuova (1725/1744) or ‘Principles of a New Science concerning the Common Nature of the Nations…’ (BERGIN & FISCH, 1948/1968). He presented – at the age of fifty-seven – a universal historical model, his ‘New Science’, of which the three fundamental components were given in the title of the book: principles – nature – nations. These catchwords will be briefly mentioned here, in order to place the phenomenon of ‘creativity’ (as related to division) in a historic perspective.


Book 1 of the ‘New Science’ started with the establishment of principles. ‘We might expect that the term ‘principles’ should mean not merely the principles as such’, said Vico in his introduction, ‘but the science and the world of nations as constructed from those principles’. He mentioned Euclid’s Elements as an example, in which ‘we understand not merely the elements in the strict sense – that is the definitions, axioms and postulates – but the system of geometry constructed from those elements.’

Vico was full of great intentions. He was determined to place the traditional sciences, like history, law and philology, on the same footage as the new, analytical sciences, promoted by the philosopher René Descartes (1596 – 1650) in his ‘Discours de la méthode’ (1637).

There are three different types of ‘principles’ in Vico’s view. They are the building stones of his intellectual construction.

A. The principle of science. Any inquiry should start with a chronological table in which the materials are set in order (Book I, Section I). An example is provided in a folded chart based on the principle of the three ages (gods, heroes, men), which gives, in seven parallel columns, the chief events of Hebrew, Chaldean, Scythian (with only one entry), Phoenician, Egyptian, Greek, and Roman history, from the Universal Flood to the Second Punic War. The same seven-division is encountered (in Book II, Section I, Chapter II) in the corollaries (consequences) concerning the principal aspects of his ‘New Science’. It started with the divine providence and ended with the principles of universal history.

B. The principle of the elements (with axioms, definitions and postulates) was dealt with in Section II of Book I. In this passage he formally introduced his famous triple division of history. ‘Two great remnants of Egyptian antiquity have come down to us. One of them is that the Egyptians reduced all preceding world time to three ages; namely, the age of gods, the age of heroes, and the age of men. The other is that during these three ages three languages had been spoken, corresponding in order to the three aforesaid ages; namely, the hieroglyphic or sacred language, the symbolic or figurative (which is the heroic) language, and the epistolary or vulgar language of men employing conventional signs for communicating the common needs of their life.’ And finally,

C. The principle of the three primary institutions of religion, marriage and burial (Section III of Book I). These social foundations provide divine providence, moderation of the passions and the immortality of human souls. These institutions, upon all men agree and always have agreed, give us the universal and eternal principles. Vico saw the ‘terror of Jove’ (the wielder of the thunderbolt) as the instigator of frightful ideas of God. ‘The idea’, he said (Book II, Section III), ‘was of course not shaped by reasoning, for they were not yet capable of that, but by the senses, which, however false in the matter, were true enough in their form’. The god-fearing giants created a moral virtue from impulse by checking their bestial habits. They became the founders of the nations and the lords of the first commonwealths.

The introduction of marriage was ‘a chaste carnal union consummated under the fear of some divinity’. Vico rated the unbroken companionship of life very high as a stabilizing factor in human society. The solemn matrimony was a heritage of the innocence of the golden age observed in the first gentile nations.

‘Afterwards, the god-fearing giants, those settled in the mountains, must have become sensible of the stench from the corpses of their dead rotting on the ground near by, and must have begun to bury them.’ The universal belief in the immortality of human souls is the third basic principle in society.

 2.  Nature

Nature is, in Vico’s vision, the process of being born. The nature (natura) of nations is nothing but their birth (nascimento). ‘Whenever the time and guise are thus and so, such and not otherwise are the institutions that come into being’ (Book I, Section II). Vico offers here a very clean-cut definition of ‘visibility’ (in the modern sense): something is visible if it becomes visible.

The very beginning (of a nation) is characterized by the birth of a religion. Some wandering people, reduced to bestiality, were frightened by thunder and lightning and called for help to the gods. In the meantime, ‘the act of copulation and frightened copulating pairs in nearby caves’ resulted in the beginning of matrimony and of settled life. The institutions of religion and matrimony have a common birth.

The nature of peoples goes, according to Vico, through various (5) stages: first crude, then severe, then benign, then delicate, and finally dissolute. The human race first appears huge and grotesque (like the Cyclopes). Next are the proud and magnanimous men (like Achilles), then we have the valorous and just (like Aristides and Scipio Africanus or Alexander and Caesar). They were followed by tendencies of melancholy and reflectiveness (like Tiberius) and finally, the dissolute and shameless madmen take power (like Caligula, Nero and Domitian).

The stages are linked to different (6) forms of power distribution: the transfer from a family- to a city-state, an aristocratic commonwealth (based on families), popular liberty, the start of monarchies, the establishment of monarchies and finally, their overthrow.

This sequence seems a rather haphazard use of human virtues and vices, mainly following the Greek and Roman history as a guideline. However, Vico regarded these regional successions as ‘the principle of the ideal eternal history traversed in time by every nation in its rise, development, maturity, decline and fall’ (a five-division again).

Later on, Vico returned to the ‘three languages of the Egyptians’ and the triple division of a divine, heroic and human nature (Book II, Section II, Chapter III). His emphasis on a ‘language’ as the symbol of communication was widely appreciated in the early decennia of the twentieth centuries by linguists such as Noam Chomsky.

The first language was the language of the gods. It consisted of the first true hieroglyphs, or sacred or divine characters. Vico saw the Divine Providence as the founder of the commonwealth and so the true God instituted the natural law of the gentes.

Secondly, the heroes founded the heroic or poetic language. They used symbols and symbolic emblems as a kind of speech. ‘They must have been metaphors, images, similitudes or comparisons, which, having passed into articulate speech, supplied all the resources of poetic expression.’ The nature of the politics in the heroic age was basic indeed.

The effective power had nothing to do with the refined ideas of the philosophers about ‘people’, ‘king’ and ‘liberty’, as they were associated with (later) plebeian, monarchistic and popular institutions. On the contrary: Achilles, ‘the greatest of the Greek heroes’, did not have any respect of the dead. He (Achilles) was quite clear to his opponent Hector: ‘If I kill you, I shall drag you naked, bound by my chariot, three days around the walls of Troy and finally I shall give your body to my hunting dogs to eat’.

Thirdly, there was – in the age of men – the epistolary speech of the Egyptians, which was suitable for expressing the needs of everyday life. ‘This language must be understood as having sprung up by their free consent, by this eternal property, that vulgar speech and writing are a right of the people’. And Vico continued: ‘The vulgar languages were introduced by the vulgar, who were the plebs of the heroic people.’ They were not fixed by convention, but must have had natural significations. ‘In general metaphor makes up the great body of the language among all nations.’

3. Nations

Vico stated that doctrines or theories must begin where the matters they treat begin. A nation is etymologically a birth or a being born, being characterized by a common language. Vico did not have a modern national state in mind and made no reference to a particular political institution. However, three conditions must – ideally – be met in order to qualify as a nation:

  1. it is a system of institution

 2. a nation is isolated from other nations

 3. the institutions are continually changing due to internal stresses

These major entities can be reduced to the ultimate constituents of Vico’s thoughts: a unity – a boundary (limitation) – and a change (movement). Vico aimed, in a modern view, to identify a communication unit within a large civil world. ‘The world of nations’ (il mondo delle nazioni) must be understood as a collection of visibilities within a Greek kosmos or a Latin mundus.

The last part of his book (of the New Science) was devoted to ‘the course the nations run’. Vico started in the introduction with a recapitulation of the main (four)-division of its contents: Book I is concerned with the principles. Book II investigated the origin of all the divine and human institutions. Book III discovered the poems of Homer as the treasure stores of the natural law of the gentes of Greece’. Finally, Book IV follows the course of the nations, ’again in constant uniformity upon the division of the three ages which the Egyptians said had elapsed before them in their world, namely, the successive ages of gods, heroes, and men.’

Giambattista Vico concluded his book with eleven triadic entities. There are, in his view, three kinds of natures (divine, heroic, human), customs (religion/ piety, choleric/punctilious, dutiful/civil duty) and natural law. Furthermore, he recognized three governments, three languages and three characters (divine hieroglyphics, imaginative universals, vulgar words). They were followed by a three division of jurisprudence, authority, reason, judgements, and three sects of times (religious, punctilious, civil).

It is clear, from this list of examples, that Vico approach to creativity was based on a (numerical) three-fold division. This type of division is characterized by a dynamic component. There is an element of play between two opposites and their middle part. Thoughts can go back-and-fro and a ‘heroic’ compromise can be found. ‘Knowing for Vico is never passive but always requires some creative activity of the knower’ (HENDERSON, 1985). Only what is made can be seen: it is a world view that still holds it values, because – in a way – it is true (from the human perspective). But the picture changes in a move away from the anthropocentric perception. It is only in the four-fold way of thinking that (human) creativity gets a new meaning, as part of a new visibility.

A creation can be defined, in a modern approach, as a border-crossing event within a communication cycle. Creativity, as a move from one (sub)division of a quadrant into another, is not only a form of ‘making’ (like it was in Vico’s drift towards the Third Quadrant). In the quadralectic view, it might include a ‘not-making’, and a move into an environment of lesser visibility (like the First Quadrant). Four-fold thinking provides, in the end – which is also a beginning (T.S. Eliot) – a greater freedom of conceptual interpretation.  

4. Modern knowledge and new names

The tetradic way of thinking is probably just as old as mankind itself. Signs on the wall of the cave of Lascaux in Southern France, drawn by Stone Age people some fifteen thousand years ago, show the combination of circles and crosses. This universal graphic symbolism points to a four-fold division of space, which can only be visualized if there is also a mental division at the same time.

This historic setting seems logic: the individual development of man – starting with birth and growth and ending with old age and death – is a re-enactment of the development of mankind as a whole. BRONOWSKI (1973/1977) sketched in his book ‘The Ascent of Man’ a picture of man as a unique animal climbing to the top of its intellectual capacities. The title was a direct reference to Darwin’s book, which was written a century earlier and was called ‘The Descent of Man’ (1871).

Both titles (and evolutionary intentions) carry the linear thought within them. Darwin’s ideas could be interpreted as an effort to pull man down from its statue at the pinnacle of creation. He proposed a decendency of mankind from the apes. Bronowski put the human race back again on the ladder of creation, culminating in a gigantic knowledge about the universe, the world and ultimately, itself.

The long journey from the forming of amino acids towards the proteins, the configuration of the four fundamental constituents into the genetic alphabet (of DNA) led eventually to the origin of life. The self-copying molecules differentiated in ever more complex forms. Hundred of millions of years ago life forms left the seas and settled on land, either in a rather stationary way as plants or in a more dynamic way as burrowing, crawling, walking or flying creatures known as animals.

It was the enormous variety of nature and the richness (of species) which puts Charles Darwin (1809 – 1882) and Alfred Wallace (1823 – 1913) on the trail of discovering the theory of evolution by natural selection. They found the key to their discovery in many field observations and the notion that the environment (geography) played a major part in the distribution of the species. Both naturalists were equipped with a new sense of multitude thinking, which could envisage the local setting of nature in a much wider context.

Darwin observed on the Galapagos Island and Wallace in the Amazon Basin and the Malay Archipelago (Borneo) that isolation, due to geographical circumstances and geological changes in time, led to a differentiation of species. Wallace drew (in 1855) the conclusion that new species arose from related, pre-existing species. Darwin wrote a ‘Sketch’ (in 1842, two years later retitled ‘Essay’) on natural selection.


Coast of Bako National Park, Serawak (N. Borneo). The ‘Sleeping Lady’ in the back ground was the peninsula where Wallace did part of his studies (on evolution) (Photo: Marten Kuilman, November 2013)


Leaping Blenny – Bako National Park – Serawak (N. Borneo). The Leaping Blenny or Alticus saliens is a saltwater fish. It gets its name from the ability to jump from place to place, outside of water. Animals like these might have inspired Wallace in his ideas about evolution (Photo: Marten Kuilman, November 2013).

The most important result of their investigations – and the subsequent popularity of their conclusions – was the return of dynamism in thinking. The visibilities of the Third Quadrant (observations) became flexible and people came to realize that a particular fragment of nature (in time and place) was not immovable, but was part of a development.

The understanding was gained that any presence in the world (including our own) is a matter of time and place and is part of a sequence of events, which are determined by the principles of visibility. The cries and joys of the early existence are followed by the first conscious experience of an outside world. Than the process of division can start to distinguish and order the outlines and features of the environment. This process starts, again, in an unconscious environment, but will develop into real visibility and an understanding of its creation. Finally, the new understanding of visibility will be celebrated and extended into all realms of life.

The present study tries to follow the implementation of the four-fold way of thinking in our personal life, the world-as-a-whole and the existence of the universe. This seems ambitious and maybe far-fetched, but it is just the consequence of a line of thinking. A complete novel world will open on the very moment we are able to comprehend the importance of higher division thinking as a means to enrich a communication. So why not follow this line of thinking into an unknown and uncharted territory?

The guided tour follows a trail, which has a close resemblance to the way of thinking itself. It aims at a familiarization with the landscape and gives an introduction to innovative terms. The exploration into the unknown will give us a variety of views, both in the country behind us (called: history) and towards a distant horizon (better known as: future). However, those are only two directions in a linear fashion. The new vision aims at all directions and includes the ground we are standing on and the sky above us. None of these four outlooks will be rated higher than another. There is in the four-fold way of thinking no hierarchical position. The past is of no more importance than the future or visa versa, and the universe might be overwhelming, but is still of the same class as the earth beneath us.

Sometimes knowledge has to find new terms to express itself. The discovery of an original set of references poses basic problems in terms of communication. Words have to be developed to catch the intentions of hitherto unknown meanings. Often the new discoveries might sound like a modern gnostic belief. The use of the term ‘invisible invisibility’, for instance, will sound as a tautology to a person, who is still trapped in oppositional thinking. And the term ‘communication factor’, abbreviated to a cryptic CF, does not mean much for someone, who is not introduced in the theory of quadralectic unification.

Hopefully, these, and other, terms will come to live during the acquaintance with the rich and colorful world of tetradic (quadralectic) thinking. The course will be run in an educational spirit. That means a repetition of the major themes at certain intervals, with a recapitulation at the end (Chapter 4.5). A shortcut to the practical side of quadralectic thinking – for those readers who are not interested in a theoretical background (which is quite excusable) – can be made to Chapter 5. A glance at the Universal Communication Sequence (UCS) in fig. 44 and the names of the inflection points of the CF-graph (in fig. 50) is then recommended to follow the line of reasoning.

A glossary with definitions and descriptions of various quadralectic terms is added at the end of this book to facilitate the understanding of the (new) names.