The change in setting – from tranquility, contemplation to representation – reflects, by and large, the distinctive features of the First, Second and the Third Quadrant of the quadralectic world view. These stages lead to the Fourth Quadrant, which is characterized here as the essentials. This qualification has a touch of superiority, but does not pretend to be better or ‘higher’ than the previous ones. It just wants to get things clear and straight, go into depth by touching the indispensable requirements in the relation between a way of thinking and a way of building. Those elements can be divided in the two main characteristics: space and time.
The former entity (space) is an abstract unity where a division takes place, the latter (time) is an invisible image, pointing to the existence of movement (fig. 781). Every communication is ‘ruled’ by these supra-human, natural variables. Their distribution in a four-fold (quadralectic) setting is proposed as follows:
Fig. 781 – A quadralectic interpretation of the main constituents of any conceivable communication. The characterization of the visibilities is derived from the duality visible – invisible. The assignment of the foursome Space/Time – Division – Time/ Space – Movement to the quadrants is a very general indication of the nature of these positions.
The essentials in architecture can only be expressed if the value system of the internal relations is understood. We have to know what visibility means (and how it comes about) before any sensible word about architecture can be said. A deliberate choice in the division-environment is the primary action before any judgment of a building or urban design can be given. What is beauty? Alternatively, why are certain designs better than others? The answer to this type of fundamental questions should be found in the knowledge of a measuring system, which provides the parameters to come to a result (an opinion, a judgment).
This chapter will try to convey some aspects of the abstract entities, which regulate a communication and in particular with regards to the world of architecture. The inquiry starts with the nature of Space, the great Enigma in architecture (and science in general). The journey continues to the more visible items of volume, surface and outlay (plan). The understanding of the multiplicity of architecture-as-a-whole is the final step. All approaches will be described briefly, but the main aim of this overview is the notion that any valuation of architecture is a matter of going through these motions in a conscious way.
Quadralectic architecture aims at the understanding of a value system, which underlies any creative activity. The old-fashioned division in an objective or subjective approach – which is still at the roots of classical science – has to be abolished. The human mind has since Descartes’’ hypotheses in the early seventeenth century made an enormous progress. Einstein’s theory of relativity opened the doors to a wider view, adding the speed of light as a philosophical contingency. Observation found a new boundary (limit) in the invisible invisibility, which can now be measured in a proper division environment.
A new cadre had to be found to accommodate the revealing insight that broke the opposition between objectivity and subjectivity. It is believed that the quadralectic philosophy can provide this width of thinking – or is, at least, a pointer in the right direction. The oppositional survival strategy is replaced by an equilibrium of four stages, providing a deeper and richer insight in the nature of our communication with the world. The journey (of life) is no longer a matter of ‘to be or not to be’, but can be calculated in terms of a concordance between ourselves and the universe in a four-fold setting.
The essential understanding of architecture – and life in general – depends on the position in a divided reality. This ‘choice’ is given to every individual in a point of recognition (POR), where and when our being in the world gets its identity and historical meaning. The correspondence of these points of recognition with those of other people gives in a common understanding and realization of a mutual history.
A remarkable correspondence was found between the interpretation of the (quadralectic) quadrants and the way in which Roget’s Thesaurus of English Words and Phrases (1962/1966) was organized (fig. 782). This similarity might be a case of pure coincidence, but it seems more likely that the ordering followed lines of thinking, which are similar to the four-fold way of thinking. The classification was (first?) applied in the above mentioned Penguin Edition of the early sixties and not yet in the American Signet Books edition of 1958.
Peter Mark Roget (1779 – 1869), who was a medical doctor, started to collect lists of words as a hobby and grouped them when they were related. Synonyms like illegal and unlawful and antonyms, like peaceful and warlike, were joined together. The first publication of Roget’s list of words took place in 1852 and was called a thesaurus, or treasury of words.
The various classes in Roget’s Thesaurus in the Penguin Edition of 1962/66 might be applied in quadralectic architecture to find its essentials.
Fig. 782 – The organization of Roget’s Thesaurus of English Words and Phrases (1962/1966) contains distinct ‘quadralectic’ elements. The organization of the great quantity of words probably followed similar lines of thinking as those, which led to the interpretation of the (quadralectic) quadrants.
The six classes can be brought back to a four division by joining the classes 4, 5 and 6 in the Fourth Quadrant (because they are all dealing with ‘feelings’ as subjective mind actions, in one way or another):
———— First Quadrant ————— Class 1 ———— Abstract relationship
———— Second Quadrant ———– Class 2 ———— Space
———— Third Quadrant ————- Class 3 ———— Matter
———— Fourth Quadrant ———– Class 4, 5, 6 —– Intellect, will and affects
This overview is most remarkable, because it offers in this form a perfect guideline to place the essentials of architecture in perspective. Any building of a certain stature can be ‘measured’ along the lines of these four classes and its significance rated accordingly.
Another example of the quadripartite approach was found in the work of the anthropologist Mark MOSKO (1985). He studied the inter-human relations in the Bush Mekeo, a Papuan tribe living in southeastern part of New Guinea. Some anthropological questions with regards to the position of the observer (with his or her own cultural background) and the application of certain concepts in the description of another culture (structuralism) are treated in the introduction.
Anthropological studies often focused on binary or dualistic forms, putting opposing entities in a frame of reference (nature/culture, sacred/ profane, male/female, etc.). Mosko acknowledged this fact, but he extended his frame of reference: ‘Categories distinguished and mutually defined as belonging to the same set systematically come in fours. Each fourfold category group is initially composed of a single binary opposition, which is itself bisected by its own inverse or reverse’ (p. 3).
Mosko illustrated the structure of bisected dualities, which systematically underlie the category distinctions of Bush Mekeo culture, in their notion of the relation between village and bush, inside and outside, resource and waste, etc. There is a transfer of things between village and bush, where the latter is seen – curiously enough – as the ‘inside’ (resources) and the former as ‘outside’ (waste producing). However, a notion of a reversal or inversion of each accompanies this opposition in the mind of the Mekeo people.
The outside village has its own inside place (i.e. an inverted outside), and the inside bush has its own outside (i.e. a reverted inside). A Bush Mekeo village normally has a central, elongated open space (abdomen), and the dwellings are arranged in parallel rows (fig. 783). This rectangle empty space is the ‘inside’ of the outside (the inverted outside). The spatial categories in this seemingly ‘primitive’ human society provide a model for an approach to ‘space’ in modern architecture. City development has to deal – at least in a quadralectic approach – with four types of space consciousness. The invisible invisibility of space is present as a notable aspect in the other quadrants.
Fig. 783 – The sphere of ordinary transfers in and around a Bush Mekeo village, Papua New Guinea as described by Mark MOSKO (1985). The bush is in the view of the villagers seen as the ‘inside’, while the village is the ‘outside’. Goods (food) are brought in from the inside of the (remote) bush to the outside (peripheral) of the village (a). After consumption the waste is collected on the inside of the village abdomen (b) and returned to the (adjacent) bush (c).
A city can be regarded – just like the Bush Mekeo did – as an ‘outside’ place, ‘feeding’ on the countryside (bush) and bringing its waste back to nature. A city square becomes in that vision a new ‘inside’, a place of ‘production’ (of community feeling?). These options of reversal should be kept open, even if the contemporary city sees itself often as the ‘inside’ place. The city is, in a modern view, the place of ‘production’, and the countryside is just the ‘outside’ to dump the waste. The city square (or park) is in this urban centrism a reminiscence to nature, the outside place. In particular the dog owners understand and utilize this modern function of an open space within the city limits, as can be observed in any city park today.
The essentials of architecture are illustrated here in a very compact form. The message is the understanding of four types of relations to a building (or a group of buildings, like a village or a city). Every architectonic entity has its boundaries – and subsequent value – in a ‘double’ interaction, taking place between the participants of the communication.
A particular awareness of space was found in the conception of a village plan by the Batak people, living in the Toba region of Sumatra (Indonesia). A drawing in a bius pustaha (accordeon book of bark with a wooden cover) shows the concentric conception of space with the bindu matoga motif, consisting of two squares turned over forty-five degrees (fig. 784). The same motif, now called a mandoedoe, is used as a warding off of a bad omen and obtain happiness and bliss. The magic figure is drawn on the ground in yellow, white and black flour close to the entrance of the house, where the mandoedoe is to be held by the wizard (SCHNITGER, 1939).
Fig. 784 – This drawing from a bius pustaha (a bark book of agricultural rituals) gives two snakes encircling a central bindu matoga (the turned squares) (after NIESSEN, 1985).
The (basic) four posts to support a house are orientated with respect to the cardinal directions or facing a mountain. The substructure of the house consists of wooden pillars resting on flat stones as protection against damp. The number of pillars varies from six to eight lengthways. The front of the house is made of two transverse rows of pillars to support the entrance through a trap-door. The peak of the house is made half circle. The interior of a Toba Batak house is divided into four main parts called ‘jabu’, which have the same principles of ordering as the erection of the house-posts and holds a similar ideology (NIESSEN, 1985; p. 256-258).
The four-fold way of thinking (in anthropology) was also noted by van FRAASSEN (1987) in his study of the social organization on the island of Ternate in the Indonesian archipelago. This island played a key-role in the priority question of the evolution theory by Charles Darwin and Alfred Wallace. The latter wrote down his ideas about the ‘survival of the fittest’ in Ternate when he was ill of malaria. His letter to Darwin was sent on March 9, 1858, when Darwin prepared his ‘Origin of Species’ (published one-and-a-half year later in November 1859). In how far Darwin used Wallace ‘law’ of natural selection and altered his manuscripts is still a matter of debate (BROOKS, 1984).
Van Fraassen noted a possible geographical origin of the four-fold division on the island Ternate (fig. 785). The so-called soa’s (social units, the equivalent of the Maleian kampung) consisted of the villages Soa Sio, Sangaji, Héku and Cim. The etymological and semantic aspects are less clear. The term bobula raha (the four parts) or ampat pihak (four sides, four categories, and four groups) was used, but not very often. Van Fraassen (I, p. 381) noticed the absence of a general term to indicate the four parts of the society, and concluded that the (four) division was at present less important.
Fig. 785 – This map indicates the territorial four-division of the island of Ternate at the beginning of the seventeenth century (given by van FRAASSEN, 1987).
The four division is more prominent in texts where the four parts are related to the geographical areas and used in the same sequence. Sao Sio and Sangaji are mentioned together, just as Héku and Cim. The latter words mean ‘upper’ and ‘lower’ and are related to the directions of the winds. Inversions are possible (in relation to the island of Halmahera or in the history of Ternate itself) and the direction can have a metaphorical sense.
The two-division (as a conceptual setting) also becomes visible (within the four-division) as a dominance of one of the members of the pairs. Sao Sio is slightly dominant over Sangaji and Héku over Cim. The following scheme expressed the distribution of political power:
Sao Sio + Héku
Sangaji + Cim
This complementary opposition can be followed in the history of the island group of the Molucs (Maluku, Indonesian archipelago). There were four political powers concentrated on the following islands: 1. Ternate; 2. Tidore; 3. Jailolo and 4. Bacan. They teamed up in much the same way as the smaller power units on the island of Ternate did (only in a different sequence). Ternate and Tidore were rivals (and as such ‘locked together’) just as the political partners Jailolo and Bacan. The scheme would be as follows:
Ternate + Bacan
Tidore + Jailolo
The sense of opposition is even more visible in the architecture of the forts (Benteng) Toloko and Kaya Merah, who depict in their plan in a straight-forwards way the male and female genitals (left and fig. 786).
Fort Toloko (Photo: Garuda Magazine).
The former fort (male orientated, left) was built by the Portuguese naval general Aphonso de Albequerque in 1512 and the latter (female orientated, right) by the English in 1518. Fort Oranje, built by the Dutch in 1607, is the largest fort on the island Ternate, following a rectangular design.
Fig. 786 – The forts (Benteng) Toloko and Kayu Merah (Red Wood) are situated respectively north and south of the city of Ternate on the island of the same name. A sexual symbolism is obvious.
Fig. 787 – The design for a House of Pleasure in Montmartre (Paris) by the French architect Ledoux, created in 1787.
This type of symbolic architecture was repeated by the French architect Ledoux, who gave his House of Pleasure in Paris (fig. 787) and later his Oikèma in Chaux (fig. 788) a phallic layout (VIDLER, 1990; LISS, 2006). These explicit efforts, with admittedly little followers, are the extreme specimens of dualistic architecture. The first (colonial) examples, by the Portuguese and British, were built in the middle of the Third Quadrant – at the Pivotal Point (1500) – of the European cultural history. The later (French) examples did not materialize, but remained in the planning stage at the end of the Third Quadrant (1800).
Fig. 788 – The phallic plan of the Oikèma or a temple dedicated to libertine pleasures was designed by Ledoux for the city of Chaux. To the left: the basement plan, to the right: the ground floor.
The connection of architecture and sexuality is also evident in the buildings of the Dogon, an African ethnic group living in Mali, south of the River Niger. The sculptural art of the Dogon was often hidden in houses, sanctuaries or kept by the Hogon (spiritual leader) in order to protect their symbolic meaning. The animist religion of the Dogon people is focused on ancestral spirits (like Nommo, a twin pair from the God Amma born in the second creation) and the star Sirius seems to play an important role (although recent investigations put question marks by the possibility of a Dogon astrology based on scientific facts, which cannot be seen with the naked eye).
The differentiation in gender is a far better documented element in the Dogon society. This division (in male and female) is a typical sign of lower division thinking – as it is known from the people on the eastern side of the Mediterranean. A typical house is modeled on the human female form, with a round kitchen (respiratory organ) as head of the house. The living room (body) has two storage rooms on either side. The house has no windows and is therefore dark (and cool) inside.
The obsession with sexuality (as manifested in fig. 789) is the result of psychological forces, which belong – in a quadralectic interpretation – in the Third Quadrant of a communication. It is remarkable, that the Dogon fled for the Muslims to the remote places along the escarpment of the Dogon plateau, for the very reason of their oppositional thinking. The beauty of the Dogon architecture seems to have a link to this form of division thinking. A preliminary conclusion can be that architecture needs this component of antagonism. It could also explain why many of the great modern architects have their roots in geographical areas were oppositional thinking is dominant.
Fig. 789 – The Mosque of Sangha in the Dogon valley displays male sexual symbols, reflecting the emphasis on a division in gender in the patriarchal Dogon culture.
Architecture in mud, like it was described by DETHIER (1981), has resulted in explicit architecture in other arid areas as well (fig. 790).
Fig. 790 – A traditional house for the celibataires (celibates) of the Bozo tribe, in the Mopti region of Mali, has several tetradic features.
A four-fold notion of the personality was described by Jean-Paul LEBEUF (1978) in the Likouba tribe in the northeast of the Republic of Congo Brazzaville. These people see the personality (nzoto) as consisting of four elements, the masotu, the molimo, the elimo and the elilingi, coming together in life (bomoy).
The masotu is the perishable body, connected with the earth. The molimo is the invisible temperament, providing the (creative) thoughts, which influence the movements in life. When the molimo leaves the body, man dies. It is connected with water. The elimo is the invisible and immaterial soul, which stimulate action in much the same way as the molimo. It is connected with air. Molimo and elimo are closely connected as spiritual entities, giving a consciousness and an intellectual power. Finally, elilingi is the shadow of the body, which appears at birth and finishes after death, and is a reflection of the molimo and elimo of the individual. A connection with fire – creating the shadow – is made.
A quadralectic interpretation of the tetradic personality of the Likouba would be: I. First Quadrant – elilingi (fire); II. Second Quadrant – elimo (air); III. Third Quadrant – masotu (earth) and IV. Fourth Quadrant – molimo (water). Their division also includes the human body, which has four principal parts: the head (motu), the upper extremities (maboko), the trunk (moy) and the lower extremities (makolo). Leboeuf does not mention any relation with architecture, but he noticed a close correspondence of the material and spiritual aspects of the human personality.
The four elements and their representations on a human level provide for the Likouba the immortal framework of their existence and shape their character, their aptitudes, attitudes and sentiments. It is a clarifying matter that these so-called ‘primitive’ people, living as fishermen and hunters in the tropical forests of the Congo, stage a self-knowledge, which is highly advanced in terms of division thinking. It proves that a cultural content can be present in a group of people, even if the material proof of their enlightenment is lacking. This conclusion was one of the major findings of the (field)work done by Claude Levi-Strauss (1908 – 2009). His notion, that the Western civilization was neither superior nor unique, is still valuable. Levi-Strauss emphasized the mutual influences in a communication between representatives of different cultures: the observer and the observed are part of a reciprocal interaction, which partakes in a continuous process.
Maybe the continent of Africa, with its relative lack of ancient architecture, should be seen in a different light. ‘Invisible’ values (like story-telling and myths) are rated higher than or are equal with the material world. This approach to the people of Africa – drifting away from the basic principle of many western scientific researchers, with their interest in the empirical traces of a culture – could change our view to the continent. The essential element in quadralectic architecture, all over the world, is the abstract experience of a four-fold division, surpassing the opposition of the two-fold and the indeterminable character of the three-fold. The ‘neutrality’ of the quadralectic approach also rules out any feelings of superiority. The only measure in a communication is the degree of understanding between the contributing partners.
The word ‘architecture’ is allowed, at this stage, to go beyond its most common meaning as ‘the process of building with an aesthetic appeal’. The essential understanding of architecture includes all the forms of organization in a particular division environment. The emphasis of building (with physical materials) can shift to the organization of the building process (with conceptual elements) and even further to a type of ‘philosophical architecture’ (in which the cognitive elements question their own identity). One has to realize that ‘architecture’, in a quadralectic setting, moves through all the different quadrants and its meaning is related to the prominent type of visibility in a particular subdivision.
Architecture in the First Quadrant (I) is in the realm of the invisible invisibility with its unknown properties. One could minimize the relevance of this type of architecture, because there is no substantial proof of its existence, but that would be wrong. In fact, it is very important to account for this ‘empty space’ in a communication, since it gives the other types of visibility room to maneuver.
Architecture of the Second Quadrant (II) emerges in a field of general ideas about habitation. Every man aims at a place of its own and the characterizing of such a place can have many faces. The specter runs from a realization of an identity in a psychological setting to the physical presence in a personal living place. This type of architecture runs from the partly visible to the greatest highlight of creative possibilities (when the CF-graph reaches its lowest value of CF = 6).
Architecture of the Third Quadrant (III) is the common-classical architecture as it is known in daily life, referring to the realization of a building from its earliest conception to its material finalization The descriptions in hand-books mainly deal with this type of historical architecture. Style periods are distinguished – often in an oppositional environment – by pointing to certain obvious architectonic features.
Architecture of the Fourth Quadrant (IV) is the quadralectic architecture proper. The quadralectic model – with the CF-graph as its visible representation – is accepted as a guide into the interpretation of structures in the widest sense. Most important is a relative feeling of the essential.