1. Quadriformis ratio

Four and more

Whatever god it was, who out of chaos

Brought order to the universe, and gave it

Division, subdivision, he moulded earth

In the beginning, into a great globe,

Even on every side.

 

Ovid, Metamorphoses, 4

Most people do not have a firm grip of the fourfold way of thinking, although it is a classical concept with a long history. Its roots go back to the early days of mankind.
What is tetradic thinking? A look of incomprehension and raised eyebrows are often followed by a request to explain. Then it is my turn how to tell, in a few sentences, a complete philosophy of life.
Usually I decide, to preserve the light touch of conversation, to give some examples like the four directions of the winds or the four seasons. Sometimes I mention the four temperaments or the evangelists.  Yes, that is common terrain, we know about them. I feel less comfortable as the conversation continues. We are only talking about illustrations and images, which allow a glimpse in the universe of the mind. Even so, the world itself remains hidden.
We all know the spirit of survival, the reflexes which save our life. The prehistoric man knew what to do when he stumbled across a ferocious animal crossing his path. Fight or flight. His reaction was not much different from a modern pedestrian trying to cross a street, while cars are approaching. The distance to the cars and their speed are vital and appropriate action has to be taken in a split second: either cross or stay. You make it or you don’t. A mistake, the wrong choice between yes and no, can make the difference between life and death.
Biological survival is based on dual thinking. The hostile environment constantly requires elementary decisions. We all know that and most of us are pretty good in taking them (otherwise we wouldn’t be here). The dual mind is geared to recognize opposites and stereotypes. The law of the jungle is a simple one. A mouse does not benefit from the idea that not all cats are killers.
One step further brings us out of the jungle with its danger zone and into the realm of rational consideration. Survival is no longer the name of the game – although it still urges constant attention. We can now sit back and think things over. Time is on our side. Decisions can be made in a thoughtful way: the ‘either’ and ‘or’ is joined by a third possibility, the ‘somewhere in between’. Or, like Goethe put it in a more poetic way (in the ‘Westöstlicher Divan’):

Dein Lied ist drehend wie das Sterngewölbe
Anfang und Ende immerfort dasselbe,
Und, was die Mitte bringt, ist offenbar
Das, was zu Ende bleibt und anfangs war.

Triple division offers new possibilities. Life becomes more complex, and sometimes less secure, but it is also more rewarding. The intermediate position adds an element of play to the communication. There is more than survival alone. Ideas, theories and dreamed visions will influence the communication. The threefold frame of mind offers a comprehensible context for the visible and invisible. It is the backbone of intellectual thinking. Its historical crown was shaped in the dialectic philosophy of Hegel (1770 – 1831), with the thesis, antithesis and the synthesis as the representatives of the threefold division.
The matter (of a primary division) is taken here to yet another magnitude: the fourfold division. Now the emphasis of a communication includes the previous steps, but adds another one to it. The survival-techniques and intellectual play gave us our basic existence and a world of technology, but more and more questions remained unanswered. In particular, those connected with human feelings. The deeper questions of life, which are fueled by an unknown source, do not have room for expansion in the confines of lower divisions thinking.
It is acknowledged that the complexity rises again in a tetradic vision. Subjectivity and objectivity are on equal terms and the boundaries between fact and fiction become less clear. The established world of science does not like that situation. Fact should be facts. The interpretation of facts should be unambiguous. Unfortunately, that is not the case (which even the modern scientists have to admit). The observer has transgressed into a dynamic interaction with the observed. The view depends on the width of thinking, with changing limitations.
The tetradic way of thinking caters for the different types of divisions. It is a frame of mind – this must be accepted – which has never been adopted as a philosophical ‘system’. However, its basics are as old as mankind itself. The last book solely dedicated to the fourfold (division) was written nearly thousand years ago by an anonymous Anglo-Saxon monk. It was titled the ‘Tractatus de Quaternario‘ and can be found in the Gonville and Caius College in Cambridge (Ms. 428). Nobody bothered, in the following ages to highlight this manuscript as a monument of a system of thought. The first mentioning by Montague Rhodes James in a descriptive catalog in 1908, and further references by Elizabeth SEARS (1986) and BURROW (1986) did not cause a stir.
These events put the present study into perspective. However, it also deprived our endeavor of its revolutionary character. There is nothing new under the sun, said Salomon, and how right he was. We are obliged to call the present book a ‘rediscovery’ of a world view in which intuition, thoughts, observation and feelings are equally important. Our insight will not be the first and will be not the last: it is a distinct stage in consciousness, which always occurs if the observer is provided with the peace to reach it.
The attentive reader will notice that the above-described development of division thinking – from dual to triple and quadruple – has an evolutionary connotation. The brain provides a conceptual picture, which is capable of producing ever-increasing divisions of a mental universe. The insight of an  observer moving towards higher division thinking is a linear one, but that is only part of the story. Higher division offers the opportunity to leave the straitjacket of the linear and to develop a cyclic outlook. We can learn another language, with words and images derived from four different abstract departments, interacting in a circular way. Together they provide a grammar of a universal language. The Greek physician and skeptic philosopher Sextus Empericus pointed in that direction by saying: ‘Eyes and ears are poor witnesses for men if their souls do not understand the language’.
Communication is not only a matter of close observation, but also of registration in the right frame of mind. Life in general, and perhaps philosophy, in particular, should be an investigation into those structures: where are the boundaries of the concepts used to define and validate our visibility?
The answer lies in the division as the ultimate unity in a communication. And therefore, the number of parts on the outset is of prime interest. Like the Greek philosopher Pythagoras already stated in 550 BC: Number is the base of all. This statement – which is often misunderstood and used in a numerological context – refers to the fact that every type of information-exchange is rooted in a specific number of initial parts, a priori established on the outset of a communication.
A theoretical communication-model, based on a cyclic four-division was formulated in an earlier stage of the study (‘De Vier Landen’ (The Four Areas), 1992; unpublished). Abstract movements were caught in figures and graphs. Neologisms were used to express hitherto unknown concepts, in a spirit of what TATON (1957/1963) called:

‘To name a thing is to create it’.

A graphic representation of a ‘universal communication’ emerged at the end of this cognitive exercise. The graph showed the values of a ‘communication-factor’ (CF) during every conceivable communication. So there was a measure, derived from the initial partition of unity in a cyclic model, to approach the relation between the observer and the observed. This understanding is fascinating material, with some reminiscence to the ‘Philosopher’s Stone’ or the ‘Elixir of Life’ of the alchemists (fig. 1).

alchemy

Fig. 1 – An alchemical laboratory as seen on an engraving of the middle of the eighteenth century (1747). The laboratory can be regarded as the first ‘scientific’ place of collection. The alchemist aimed at a transformation of the material to higher values, like gold and/or the Philosopher’s Stone (THOMPSON, 1932).

There will be no elaboration of the theoretical side of the model at present. It may be of historical interest, that the term ‘quadralectic‘ (or quadralistic) was first used (by the writer) as a neologism in November 1983 (in an unpublished book called ‘Van God Los’). The nomen of ‘quadralectic’ is closely related to the term ‘dialectic’. This expression signified in Greek philosophy a kind of practical logic and was used in a discussion to understand each other. The dialectic way is based on a dichotomous division in an oppositional setting. The quadralectic condition aims to be a logic tool of the same standard, but in a non-oppositional environment.
The tetradic perception conveys a world of difference in the dynamics of data interchange: not only the facts are important, but also the context in which they are presented. Visibility, as a powerful process, looses its ignorance. What we see and at which particular time is – in a cyclic setting – the key to the whole circle in time. The observer is a player in his or her own observation. It is a matter of energetic interplay from both sides. The active double dialectics can create a new world of insight.
These preliminary observations might have a philosophical touch, but readers should not be scared away. This study will be a preparation of the ground for further investigation in the unlimited land of the four-fold. My background as a geologist gave me a good insight in the scale of time and the floating character of divisions. That’s all. This knowledge remained in the back of my mind when I turned my attention to cultural history, in search of a fossilized system of thought. And when traces were found, it invited to a deeper understanding. This representation is a first report of that journey.

—-

BURROW, J.A. (1986). The Ages of Man. A Study in Medieval Writing and Thought. Clarendon Press, Oxford. ISBN 0-19-811188-6

SEARS, Elizabeth (1986). The Ages of Man. Medieval Interpretations of the Life Cycle. Princeton University Press, Princeton, New Jersey. ISBN 0-691-04037-0

TATON, René (1957/1963)(tr. A.J. Pomerans). Ancient and Medieval Science – from Prehistory to AD 1450. Thames & Hudson, London.

THOMPSON, C.J.S. (1932). The Lure and Romance of Alchemy. George G. Harrap & Comp., London.

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2. The Four Quartets

Burnt Norton House

The turn-off to Mickleton is easy to miss while driving down from Aston Subedge over the B4035. All the attention is focused on the beautiful road, which climbs up the Cotswold-plateau to Chipping Campden.

burnt nortonIt was a late afternoon in July 1991 just after the longest day. The sun still gave its warmth at this time of the day. The first road to the left directed to Attlepin Farm. The road festooned through the park-like landscape. A small ‘Private‘-sign was ignored as a consequence of the importance of the mission. For this was not a simple tourist outing. This was a visit to Burnt Norton House, a place of inspiration for the first poem in T.S. Eliot’s ‘Four Quartets’.

Sometimes there was an occasional visitor, the caretaker of the house told me. He even kept a visitor’s book for the select adepts of T.S. Eliot, who found the road to the house and wanted to taste its atmosphere. I signed the book and went along ‘the door that never opened‘ – into the garden – that famous rose garden with the ‘huge tree with figured leaves‘. It was all still there, presumably in the same serene quiescence where Eliot found it in the thirties. Something strange was going on with the time: Time present and time past. Are both perhaps present in time future? And time future contained in time past.

 These opening lines of Eliot’s poem (ELIOT, 1963) became reality. Look: on the heavy stone styles of the entrance to the rose garden were four squares, who (probably) provided the name of the poem. This was living history, at arm length (fig. 2).

bn

Fig. 2 – Marten Kuilman at Burnt Norton House. Visit: 19 July 1991.

Footfalls echo in the memory
Down the passage
which we did not take
Towards the door
we never opened
Into the rose garden

(T.S. Eliot – Four Quartets, 1944)

To be honest: it wasn’t a seasoned T.S.Eliot-connoisseur, who trotted through the fields of the Cotswold. I had recently come across the title of the poem of T.S. Eliot in the library of Birmingham. And I didn’t even see the poem itself, but my attention was drawn to a reference heading an article of Eleanor SIMMONS GREENHILL (1954). She wrote over ‘The Child in the Tree‘ and used a quotation of Eliot’s ‘Four Quartets’ as an introduction. It was only this title, which put me on the trail of the four-parted poem and made me – in due course – an admirer of Eliot’s work.

That very moment on the edge of the Cotswold, in the last glow of the sun descending in the west, I knew – for a short, but momentous long instant – that Paradise still existed. That the ‘Tree of Knowledge of Good and Evil‘ (fig. 3) was just a part of Paradise. Besides this crude division, there was a rose garden and other figured trees, who threw their shadows onto the grass.

adameve

Fig. 3 – The Tree of Knowledge of Good and Evil and the Seven Deadly Sins is seen here in an illustration from Boccaccio’s ‘De Claris Mulieribus’ (Louvain, 1487). The symbolism of the (Judeo-Christian) creation-myth is strongly influenced by the two-fold way of thinking. Good and evil, God and Satan, man and woman are part of a world in which a division of incompatible opposites is highlighted (and in which, without saying the first item is good and the second is bad). The acceptance of this Christian imagery had a strong hold on the subsequent development of the cultural history of Europe.

HENINGER (1974) draws an interesting comparison between the world of Dante in his ‘Divina Commedia’ (1304 – 1321) and Eliot in ‘The Waste Land‘ (1922). The world view of Dante (1265 – 1321) is geocentric, within limits and based on order. This view is emphasized in the tripartite of Inferno, Purgatorio and Paradiso, recalled in hundred ‘cantos‘ and written in the ‘terza rima‘ (HARDT, 1973; LOOS, 1984).

Eliot (1888 – 1965) accumulates fragments, parts of personal memory. The parts do not seem to be ordered or bound by limitations. In the ‘Four Quartets‘ (1935 – 1942) is a certain order, but this is of a different character than in Dante’s poem. WHITMAN (1958/1963, p. 107) speaks of ‘some dross, a residue of unavoidable discursiveness which one may as well treat as frankly unpoetic.’

The four locations in Eliot’s ‘Four Quartets’ are Burnt Norton, East Coker, The Dry Salvages en Little Gidding. They can be viewed as four elementary stages in the communication with the world (GARDNER, 1978).

1. Burnt Norton is the Garden of Eden, the Paradise, the rosegarden.

2. East Coker is a village in Somerset near Yeovil. This stage is concerned with cyclical movement of the seasons and birth and dead (fig. 4).

eastcoker

Fig. 4 – East Coker,  a village in Somerset near Yeovil. Photo: Marten Kuilman. Visit: 10 May 1994.

3. The Dry Salvages are to be found near Cape Ann (U.S.A.), where the incarnation took place (fig. 5).

drysalvages

Fig. 5 – The Dry Salvages are seen in the far distance between the the island and the mainland. Photo: Marten Kuilman. Visit: 8 Sept. 1998.

4. Little Gidding is a village in Cambridgeshire, where Nicolas Ferrar founded a Christian commune in the seventeenth century, close to the world’s end (fig. 6) (DRABBLE, 1979, p. 35):

There are other places

Which also are the world’s end, some at the sea jaws,

Or over a dark lake, in a desert or a city –

But this is the nearest, in place and time

littlegidding28682649887_b343091bf6_b

Fig. 6 – Little Gidding in Cambridgeshire (England). The fourth and last stage in Eliot’s ‘Four Quartets’, described as ‘a place where prayer has been valid.’ Here the quadrilogue finds its end and beginning again. Photo: Marten Kuilman. Visit: 28 Sept. 1996.

For Eliot this is the place where personal history will be left behind and replaced by a cosmic being for which ‘history is a pattern, of timeless moments’. The quadrilogue ends with the disappearance of the elements and a return to the beginning:

We shall not cease from exploration

And the end of all our exploring

Will be to arrive where we started

And know the place for the first time

This is a picture of the human existence in a cyclic world view. Our presence is a continuous voyage to unknown lands. All we have to do is use our eyes and senses and get hold of some sort of map to lead the way. Or, like HARRIES (1983) put it: ‘Reflection on the facts alone does not suffice to let us understand these facts as parts of a meaningful whole. That requires a creative reading born of faith or love.’

ELIOT, T.S. (1963). Collected Poems 1909 – 1962 (Pp. 187 – 223: ‘Four Quartets’). Faber & Faber, London/Boston. ISBN 0 571 10548 3

GARDNER, Helen L. (1978). The Composition of Four Quartets. Faber & Faber, London/Boston. ISBN 10 0571110487

HARDT, Manfred (1973). Die Zahl in der Divina Commedia. Linguistica et Litteraria, 13, Atheneüm Verlag, Frankfurt/M.

HARRIES, Karsten (1983). Thoughts on a Non-Arbitrary Architec­ture. Pp. 9 – 20 in: Perspecta, 20. The Yale Architectural Journal. Inc., and the Massachusetts Institute of Technology.

HENINGER Jr., S.K. (1974). Touches of Sweet Harmony. Pythagorean Cosmology and Renaissance Poetics. The Huntington Library, San Marino, California. LCCC 73-78049

LOOS, Erich (1984). Der logische Aufbau der ‘Commedia’ und die Ordo-Vorstellung Dantes. Akademie der Wissenschaften und der Literatur, Mainz/Franz Steiner Verlag GmbH, Wiesbaden. ISBN 3-515-04191-5

SIMMONS GREENHILL,  Eleanor (1954).  The Child in the Tree. A Study of  the Cosmological Tree in Christian Tradition.  Pp.  323 – 371 in: Tradition: studies in ancient and medieval history, thought and religion. New York, Fordham University Press, Vol. X, 1954.

WHITMAN,  Cedric H.  (1958/1965). Homer and the Heroic Tradition. Harvard University Press, Cambridge, Massachusetts/W. W. Norton and Company, Inc. LCCC 58-7252/ISBN 0393003132

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3. Fourfold visibility

Binaries

A practical example of a fourfold visibility will be given here. It involves the so-called ‘variable double stars‘ who appear to the human observer as one star with a varying light intensity. Various reasons may account for this inconsistent luminosity (PETIT, 1987), but we are especially interested in the ‘eclipsing double stars’. In this relative small class of stars the changes in luminosity are due to geometrical circumstances (ASIMOV, 1966/1971; FLAMMARION, 1968). The light-intensity of some of these ‘doubles’ (binaries) is measured and graphical represented in fig. 7. The most famous binary is the star Algol in the configuration of Perseus (Beta Persei). Four phases can be recognized in the brightness of the double star:

1. A Small Double star is right in front of the Large Double star and ‘covers’ the brightness of it. The result is a decrease in total luminescence for an observer on earth and produces the first deep low on the brightness-graph.

2. The Small Double star moves to the right and slips away from the Large Double star (from the point of view of an earthly observer, in reality, it follows an orbit around the LD). Now they are both shining to their full advantage and the nightly observer notices a relative high: a saddle on the graph.

3. However, the Small Double star, continuing its orbit, will disappear behind the Large Double star and the light will be ‘lost’. Since the Small Double star bears his name with proud, this movement will only result in a relative minor diminution of the total brightness. The earthly observer marks the temporary disappearance as a small depression on the graph paper.

4. The Small Double star reappears behind the Large Double star and the maximum luminosity returns. It is a mirror-situation of the earlier phase when both stars were ‘free’ and effectuates in a second high on the brightness-graph.

When the Small Double star continues its orbit around the Large Double star the cycle will start all over again. It is the cyclic interplay between two partners, which makes the link with the present subject.

doublestar

Fig. 7 – This representation gives the graphs of the luminosity of eclipsing double stars (binaries) according to ASIMOV (1966/1971). They have a general succession in common: a period of brightness (in time) is characterized by three depressions (two deep and one shallow low) and two saddles or highs.

The above-mentioned example represents a cosmic displacement system. However, it also has strong similarities with the interaction in a communication based on a fourfold division.

Initially, there is a twofold division (the Double star) out of a primeval unity (the cosmos). The Greek meaning of ‘kosmeo‘ is ‘to establish order’ or ‘getting an army into line’. Brightness is the result of a simultaneous action. An observer, who joins the communication at this stage, will be able to recognize four phases: two phases when the Double star appears to be a unity (producing less brightness) and two phases when the Double star shows itself as a real double (marked by maximum brightness).

This mechanism of alternating unity and division can be transposed on to any human communication in a cyclic context. We have to assume that the opposite communication-partner is ‘part of ourselves’ and belongs to our (division) ‘system’. There are two options after the initial (two) division: either my ‘other half’ is static, or it is dynamic.  There are four phases to compare in the latter case, just like the Small Double star (SD) orbiting the Large one (LD).  The ‘brightness’ of a four-fold communication can be expressed – like binaries – in a graphic representation. The graph provides a tool to monitor a communication at any given moment.

This natural phenomenon offers a new dimension of thinking. Observer and the observed are involved in an impelling interaction in which the changing intensities can be measured. And this is all the result of a different appreciation of the starting point, putting an initial two-division in a dynamic and cyclic environment. Visibility – as an intermittent interaction – is the result of fundamental decisions taken on the outset of the mutual exchange of information.

Plutarch resumed the words of Heraclitus as he indicated the dynamic visibility in a communication (KAHN, 1979):

One cannot step twice into the same river,

nor can one grasp any mortal substance

in a stable condition, but it scatters and again

gathers; it forms and dissolves, and

approaches and departs

Those who understand the language of quadruple thinking achieve a much wider perspective in life. Not only in the direct interaction with the environment, which becomes richer and more differentiated, but also in view of the cultural history of which we are a part. Events get a new meaning. It is not only the opposites, the hatred and the wars which determine our historical consciousness, but also – and more preferably – the harmony, beauty and insight.

ASIMOV, Isaac (1966/1971). The Universe. From Flat Earth to Quasar. Penguin Books Ltd., Harmondsworth, Middlesex, England.

FLAMMARION, G.C. (1968). The Flammarion Book of Astronomy (Andre Danjon, Ed.). Readers Union/George Allen and Unwin, Ltd., London.

KAHN, C.H., (1979). The Art and Thought of Heraclitus. Cambridge University Press, Cambridge.

PETIT, Michel (1987). Viariable Stars. John Wiley & Sons, Chichester. ISBN 0 471 90920 3

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4. Tetragonus mundus

The fourfold division

 

‘Why do we recognize four seasons? Why not two, or three, or five?’ This basic question was posed by BURROW (1986) in his description of the general classifications in the Middle Ages. He did not find a unanimous answer. In the end, he said, it must be the power of numerology and the legacy of Pythagoras (who is always ready to carry the philosophical load if numbers are concerned).

This view is too limited. The fourfold division is more than just a numerological toy or a mythic belief in figures. It is a language of the mind and a way of communication. It is a system in which the complexities of the universe can be assessed and unified in a logical order.

This line of thinking leads to a search for earlier occurrence of quadruple thinking. The descriptive term ‘Tetragonus Mundus’ has an ambiguous meaning in the European cultural history. It points to a corpus of thoughts in which the fourfold division occurs in all kinds of images. Major fragments of Greek philosophy are present, but also remnants of Alexandrian and Syrian interpretations of Egyptian and ‘Eastern’ wisdom. Furthermore, last but not least, a substantial part of the Babylonian and ‘magical’ knowledge has entered the early Christian belief and was transmitted to Europe. In this muddle of intellectual material, in combination with Europe’s own cultural background, the structural element of a division in four parts was not far beyond the surface.

The constant interest in the ‘Tetragonus Mundus’ over ages of human soul-searching never resulted in a ‘system of thought’. People utilized the four-fold, scholars – like Peter Lombard in his ‘Sentences’ (Sententiae) – employed four methods for ordering their material and endless artists created visual references to the quaternary (fig. 8). There is, in short, a constant tetradic background noise throughout history, but it was never realized that this division holds the key to a deeper understanding.

Jerusalem

 Fig. 8 – The New Jerusalem described in a vision of the Prophet Ezekiel. An illustration from Nikolaus of Lyra ‘Postille’, printed by Ulrich Zell in Cologne in 1485. The square city and its twelve gates (4 x 3) can be viewed at in four different ways: 1. The anagogical or highest unknown meaning (the Celestial City); 2. The allegorical interpretation of looking at the facts, but referring to something else (the Church); 3. The literal, historical approach (the city of Jerusalem), and finally: 4. The tropological meaning, where the image of Jerusalem includes moral values (the faithful soul) (PILTZ, 1981).

Centuries passed with the murmuring of a tetradic state of mind, being so normal that nobody paid special attention to it. The Holy Fathers of the Church in the third and fourth century and the Celtic missionaries of the seventh and eighth century brought the torch to the Carolinian times and the Scholastics of the twelfth and thirteenth century. Then the light diminished, only to return in a most artificial way in the Renaissance. There it became a thing to be toyed with. This game lasted for at least three centuries, when – at the end of the eighteenth and the beginning of the nineteenth century – the quadruple mind returned as a viable option in the communication.

From that time onwards to the present day, the ‘Tetragonus Mundus’ has been with us, side-by-side with strong dualistic forces, fighting for identity. If a tetradic mind becomes involved in this struggle, it looses out. Because, by its very nature, it is a peaceful way of thinking. It understands the basic mechanisms of strife and cannot propagate its ideology in a forceful way.

Even today there are people, who only have an inkling of what the ‘Tetragonus Mundus‘ is all about. They mention the four elements – fire, air, earth and water – as building stones, know the seasons and the cyclic movements of the universe, but can’t put the fragments together into a unity of thought.

The tetradic imagery – and not necessary the tetradic way of thinking – can be followed from the proto-history to the present. From the caves of Lascaux in Southern France – where human beings decorated their paintings of horses and bison’s with tetramorphic signs – to the outlay of motorway crossing in the shape of a cloverleaf: they are all tributes to fourfold symmetry. The distribution of these signs in time and place is world-wide and indicates an elementary and human way of expression.

The signs might be a reference to the sun and the Central Fire, where all division starts, and to cyclic movements in time.  There is also a division in place, a matter of position and orientation. The graphic utterances often don’t give any clue to the state of mind of its creators. Furthermore, to put any serious inquirer on the wrong foot, tetradic imagery might simply be ‘natural’ or ornamental with no visible connection with a particular way of thinking.

The modern investigator arrives here at a dilemma. Which signs are germane and which are not? The answer must be formulated in an Orwellian way: all signs are relevant, but some signs are more relevant than others are. Or better: the question should not be put in an either-or way. All tetradic signs are, in our present view, part of a wider context. The ‘context’ is directly relegated to the way of thinking and the number of initial parts in the division of the unity (of communication). Only a further investigation into the significance of a sign within a framework of thoughts can give a clue towards its real meaning.

A number of figures with a tetradic imagery is given in fig. 9 a/d. The selection has been arbitrary and only serves the purpose of showing the extraordinary versatility of the sign. Some have strong links with a quaternary way of thinking, like the Mexican and Buddhist examples. Our knowledge of the ancient beliefs of Aztecs and Maya-Indians makes it clear, that cyclic-tetradic thoughts were far advanced and resulted in a complete different approach to reality. Fragments of these thoughts were brought back to Europe by Spanish ‘conquistadores‘ and clergymen, who were born and bred in a world of dualistic thinking in opposites. It is not at all surprising that these men were only fixed on the material rewards of the gold and silver and had no imagination of the spiritual world they destroyed in the meantime.

Other examples of fourfold symmetry go back to an animistic world of shamanism and sorcery (like the symbols from Russia, China, Polynesia and Indonesia). In these worlds, the quaternary images are not necessary part of a distinct system. However, the attention paid to the ‘subjective’ aspects of a communication brings these artifacts of mind-practices in the realm of the unknown realms of the mind. They point to a deliberate attempt to explore areas of human sentiment.

Furthermore, there are stylized and ornamental signs on plates and coins. A direct relation to a tetrad philosophy is difficult to establish. It might be a geometric division, offered by the shape of the object, without reference to any wider implications. A square – like a tile – is tetradic in itself and any decoration tends to follow the given restrictions. These artistic appearances are the most difficult to interpret: how occasional are they? Are these signs part of a wider context?

Natural occurrences, like the images of Chladni’s sand figures, do not give such problems of definition. They show that tetradic imagery can be an regular thing, without any (human) philosophy involved.

four1-8

Fig. 9a – Some examples of tetramorphic imagery in time and place are given here to show the versatility of the four-fold. 1. Signs for thunder, China (HENTZE, 1967); 2. Boat and sun-symbolism, Scandinavia (GELLING & DAVIDSON, 1969); 3. Chumash painting, Santa Barbara, California (HADINGHAM, 1984); 4. Aztec-calendar, Mexico (ENDRES & SCHIMMEL, 1984); 5. Korean signs for ‘longevity’ (SCHMELTZ, 1891); 6. Design of the Bouriates, Russia (SANDSCHEJEW, 1928); 7. Geometric drawing of the New Hebrides. (DEACON, 1934); 8.  Minoussinsk, Russia. (HENTZE, 1928).

four9-15

Fig. 9b – Examples of tetramorphic imagery in time and place. 9. Pyramid of the Maya, Yucatan, Mexico. The building period of the temple cities is between AD 317 – 650 (Tzakol-phase in pottery) (HENTZE, 1967); 10. Borobudur, Java, Indonesia. Build as a Bhoeddist-temple, eighth century A.D. (KROM, 1930); 11. Bowl, prov. Honan, China (HENTZE, 1967); 12. Ceramics from Susa I, Persia (HENTZE, 1928) ; 13. TLV-board, Shih divination, Han Dynasty, China (KAPLAN, 1937); 14. Plate from Sighisoara (Germany) Sighisoara-Wietenberg culture (MELLINK & FILIP, 1974); 15. A ‘mandoedoe‘, Sumatra, Indonesia (SCHNITGER,  1939).

four16-21

Fig. 9c – Examples of tetramorphic imagery in time and place. 16/left: Penny of the Quatrefoil-type, c. 1018-24; right: Penny of the Short Cross type, c. 1030-35 (BACKHOUSE et al., 1984); 17. Knot of Salomo on a tile in Bebenhausen, Germany (1228)  (WIENAND, et al, 1977); 18. Graffiti in Martin’s church in Little Waltham (Essex, England) (PRITCHARD, 1967); 19. The Fuller Brooch. Late ninth cent., British Museum, London (BACKHOUSE et al., 1984); 20. The Sutton Brooch. First half eleventh cent. British Museum, London (BACKHOUSE et al., 1984); 21. Exlibris, Altzella. Univ. Library of Leipzig, Ms. Nr. 675  (WIENAND, et al, 1977).

four22-27

Fig. 9d – Examples of tetramorphic imagery in time and place. 22. The name of Allah. Calligraphy in quadratic Kufi, Baghdad, 12/13th cent. (BRENTJES & RÜHRDANZ, 1979); 23. Chinese incense-clock, 1329 (WRIGHT, 1968); 24. Bowl from the Cyclads, Greece (KERENYI, 1950); 25. Chladni’s sandfigures, caused by vibrations on a metal plate (SOMERVILLE, 1834 in: ALIC, 1986); 26. The road to hell, Aztecs. Codex Borgia (ENDRES & SCHIMMEL, 1984); 27. Diagram of the world with the central mountain, the Meru. West-India, seventeenth century, Ajit Mookerjee, New Delhi (RAWSON, 1973).

BURROW, J.A. (1986). The Ages of Man. A Study in Medieval Writing and Thought. Clarendon Press, Oxford. ISBN 0-19-811188-6

PILTZ, Anders (1981). The World of Medieval Learning. Basil Blackwell, Oxford. ISBN 0-631-12712-7

Fig. 9 a – d:

1. HENTZE,  Carl (1967).  Funde in Alt-China. Das Welterleben im altesten China. Sternstunden der Archäologie. Musterschmidt Verlag, Göttingen.

2. GELLING, Peter & DAVIDSON, Hilda Ellis (1969).  The  Chariot  of  the Sun – and other Rites and  Symbols  of  the Northern Bronze  Age.  J.M.  Dent,  London.

3.  HADINGHAM,  Evan (1983).  Early Man and the Cosmos. William Heinemann Ltd., London (redrawn).

4. ENDRES,  Franz Carl & SCHIMMEL, Anne-marie (1984). Das Mysterium der Zahl. Zahlensymbolik im Kulturvergleich. Eugen  Diederichs Verlag,  Köln.

5.  SCHMELTZ, J.D.E. (1891). Die Sammlungen aus Korea im Ethnogr.  Reichsmuseum zu Leiden. Internationales Archiv für Ethnographie, IV (1891), p. 105.

6. SANDSCHEJEW, Garma (1928). Weltanschauung und Schamanismus der Alaren-Burjaten.  Anthropos, Vol.  XXIII. In: HENTZE, Carl (1922). Mythes et Symboles Lunaires. Editions ‘De Sikkel’,  Antwerpen. fig. 58, p. 83.

7.  DEACON,  A.  Bernard (1934).  Geometrical drawings  from Malekula  and other islands of the New Hebrides.  The Journal  of the Royal Anthropological Institute of Great Britain and Ireland.  Vol.  LXIV, pp. 129 – 176.

8. HENTZE, C. (1922). Op. cit. p. 180;

9. HENTZE, C. (1967). Op. cit.

10. KROM, N.J. (1930). Baraboedoer. Het heiligdom van het Boeddhisme op Java. H.J.  Paris,   Amsterdam;

11. HENTZE, C. (1967). Op. cit.

12. HENTZE, C (1922). Op.  cit. fig. 14.

13. KAPLAN, Sidney M. (1937). On the Origin of  the TLV Mirror.  pp.  21 – 24 in:  Revue des Arts Asiatiques, XI.

14.  MELLINK,  M.  & FILIP, J. (1974). Propyläen Kunstgeschichte. Band 13. Propäen Verlag, Berlin.

15.  SCHNITGER,  F.M. (1939).  Forgotten Kingdoms in Sumatra. E.J. Brill, Leiden.

16. BACKHOUSE,  Janet;  TURNER, D.H.; WEBSTER, Leslie (Ed.)(1984). The Golden Age of  Anglo-Saxon Art 966 – 1066.  British Museum Publications Limited, London.  ISBN 0-7141-0532-5 (fig. 212/215).

17. WIENAND, Adam; BICKEL, Wolfgang & COESTER, Ernst (1977). Die Cistercienser. Geschichte. Geist. Kunst. Wienand Verlag, Köln.

18. PRITCHARD, V. (1967). English Medieval Graffiti. Cambridge University Press. LCC 66-11034.

19. BACKHOUSE, Janet et al. (Ed.) (1984). Op. cit. fig. 11.

20. BACKHOUSE, Janet et al. (Ed.)(1984). Op. cit. fig.  105.

21. WIENAND, Adam; BICKEL, Wolfgang & COESTER, Ernst (1977).  Die Cistercienser.  Geschichte.  Geist.  Kunst. Wienand Verlag, Köln. ISBN 3 87909 074 2

22. BRENTJES, Burchard & RÜHRDANZ, Karin (1979). Mittelasien. Kunst des Islam. VEB/E.A. Seemann Verlag, Leipzig.

23. WRIGHT, Lawrence (1968). Clockwork Man. Elek Books  Ltd., London. Source: BEDINI, Silvio A. (1963). The Scent of Time – A Study of the Use of fire and incense for time measurements in Oriental Countries. The Transactions of the American Philosophical Society,  Vol.  53,  Part 5,  Aug. 1963.

24.  KERENYI, Karl  (1950). Labyrinth-Studien. Labyrinthos als Linien-reflex  einer mythologischen Idee.  Albae Vigiliae.  Neue Folge, Heft X. C.G. Jung  zum  fünfund-siebzigsten Geburtstag 26. Juli 1950 gewidmet. Rhein Verlag,  Zürich. Or: PURCE, Jill (1974). The Mystic Spiral. Journey of the Soul. Thames & Hudson, London. ISBN 0 500 81005 2

25.  SOMERVILLE, Mary (1834). Of the Connections of the Physical Sciences.  John Murray,  London. In: ALIC, Margaret (1986). Hypatia’s  Heritage – A History of Women in Science from Antiquity to the late Nineteenth Century. The Women’s Press, London. ISBN 0-7043-3954-4

26. ENDRES, Franz Carl & SCHIMMEL, Annemarie (1984). Das Mysterium der Zahl.  Zahlensymbolik im Kulturvergleich. Eugen Diederichs Verlag, Köln. ISBN 3-424-00829-X

27. RAWSON, Philip  (1973). Tantra – De Indiase cultus der extase. De Haan, Bussum.  ISBN  90 228 3973 9; A larger illustration  in: MICHEL, George  (1977). The  Hindu Temple.  An Introduction to its  Meaning  and  Forms. Paul Elek, London. ISBN 0 236 40088 6

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5. Regularity through the ages

Regular patterns

The reconnaissance journey of the fourfold division leads into the world of regular patterns. STEVENS (1980) wrote a comprehensive book on the phenomenon of symmetry, dealing with the basic ingredients of repetition in two-dimensional patterns. He distinguished four types of movements to obtain multiplication of patterns:

 —————–    1. translation         from     b    to     b

—————–     2. rotation                            b    to     q

—————–     3. reflection                         b    to     d

—————–     4. glide reflection                b    to     p

These movements can be recognized in the basic fourfold division of a communication. The translation is the Prime Originator in the first quadrant. The prime shift generates space and the opportunity for comparison. The rotation in the second quadrant has a cyclic overtone and adds a different dynamic element to the exchange of information. The reflection in the third quadrant is a confrontation with boundaries, a view in the mirror. The glide reflection in the fourth quadrant is an elaborated combination of translation and reflection.

The essential feature in the recognition of patterns – including the mind patterns – is the so-called fundamental region. STEVENS (1980; p. 57) gave the following definition: ‘a fundamental region is the region of minimum area that can be repeated without gaps of overlaps to make a complete pattern.’ LAUWERIER (1988) called this unit a ‘primitive cell’, to indicate the repeating element. It is instructive to look at the anatomy of a fundamental region and the way it is created. Because in the end the human memory is just a set of (mind) patterns, constructed from various fundamental regions.

Four steps are necessary to outline the smallest unit, or to ‘create our own fundamental region’ (STEVENS (1980, p. 177)(fig. 10):

 1. An irregularity on a horizontal line between A and B; any shape is permitted. ESCHER (1958/1986, p. 118) recommends a simple contour line without too many deep incisions.

 2. The shape of the horizontal irregularity is repeated on a parallel line in C and D; it is essential for the creation of a pattern that the shape is the same as between A and B;

 3. An irregularity on the vertical line, starting at A and ending at C; again any shape is permitted.

 4. The shape of the vertical irregularity is repeated on a parallel line between B and D; now a geometric form is created, which is called a fundamental region: the region of minimum area that can be repeated to obtain a whole pattern.

These are the four distinct (mind)actions required to build-up a fundamental region, which forms a pattern by repetition.

escherdevelopment

Fig. 10 – The four phases in the development of a fundamental region, the minimum area that can be repeated to obtain the whole pattern.

STEVENS (1980) and LAUWERIER (1988) referred to the Dutch mathematician and graphic artist Maurits C. Escher (1898 – 1972), who plays a major role in the (re)discovery of visible regularity and symmetry in the early decades of the twenties century. Escher’s book ‘Regelmatige Vlakverdeling‘ is an excellent introduction to his work (ESCHER, 1958/1986).

ESCHER (1959/1970, p. 11) described the regular cover of a plane as ‘the richest source of inspiration I ever discovered. And it is still not exhausted. The symmetry drawings show how a plane can be divided in or filled up with regular shapes, who border each other without overlap. The Mores were masters in this art. They have, particular in the Alhambra in Spain decorated the walls and the floors by  congruent, multicolored pieces of majolica, which fits perfectly. What a great pity that they were not allowed to make portrayals! They only used figures with an abstract-geometric design. Not a single Moorish artist has ever, as far as I know, ventured (or maybe he never imagined) to use natural or recognisable figures like fishes, birds, reptiles or human beings as elements in a division of a plane. This restriction seems to me unbelievable, because it are just the recognisable elements in the patterns which is the reason of my continuous interest in this domain.’

Escher finds a response in the modern computer-generated graphics. The fascination to create regular patterns within certain boundaries is the common interest. William KOLOMYJEC (1976) rendered homage to Escher in an article on the appeal of computer graphics. He uses a computer program to draw ever-smaller fundamental regions in a square or circle (fig. 11). The dynamics are of a rotational nature and focuses on the size-reduction towards the edges. Escher has also ventured this terrain in several pictures, like ‘Vierkantslimiet’ and ‘Cirkellimiet I – IV’.

escherround

Fig. 11 – Escher in the round. Computer-graphic by William Kolomyjec, 1975. The use of computers to generate regular patterns has contributed to the popularity of the Escher’s graphic work, which was born in an artistic craftsmanship.

The modern attention to the generation of patterns can be seen in a long history of division (in any imaginable sense) and the visible aspects of it (again in the whole specter of visibility from mathematics to art). The most notable preoccupation came to the surface in the Renaissance (fig. 12).

flagellation2

Fig. 12 – Piero della Francesca’s painting ‘The Flagellation of Christ’ in the Galleria Nazionale delle Marche in Urbino, Italy.

Marlyn ARONBERG LAVIN (1972) said of the floor of Piero della Francesca’s painting ‘The Flagellation of Christ’: ‘The geometric floor pavements in the front and back bays of the Praetorium, disguised by their perspective foreshortening, are similar in design to certain kinds of Renaissance horoscope drawings. Recent studies have shown these pavement designs, in their reconstructed state, to be special purveyors of mathematical symbolism. The eight-pointed stars that form their central motifs, are the astrological sign for the planets’ (in: WITTKOWER & CARTER, 1953) (fig. 13).

flagellation

Fig. 13 – The reconstruction of the eight-pointed star in the floor of the Praetorium in Piero della Francesca’s painting ‘The Flagellation of Christ’. Ducal Palace, Urbino (Italy).

A Dominican priest, Dominique Douat, again raised the interest for patterns in the early eighteenth century. He published a treatise ‘Methode pour faire une infinite de desseins differents avec des carreaux mi-parts de deux couleurs par une ligne diagonale’ (Paris, 1722). It is an elaboration of an idea put forward in 1704 by another Dominican clergyman, Sebastian Truchet. He published in the ‘Memoires de l’Academie Royale des Sciences’ a number of possibilities to arrange square tiles, which were divided by a diagonal line into two coloured parts (GOMBRICH, 1979; LAUWERIER, 1988).

Truchet took a pair of bi-colored tiles, and studied their position and orientation. He found ’64 combinations de deux Carreaux mipartis de deux couleurs’ (Table I in Truchet’s publication; fig. 14). The four different stages in the position of a two-fold division (ABCD) has similarities with the example of the binary stars in a cyclic (rotational) environment.

truchet

Fig. 14 – Sebastian Truchet gave sixty-four possibilities to arrange a pair of bi-colored tiles in his ‘Memoires sur les Combinations’ (‘Treatise on Combinations’), 1704.

The significance of Truchet’s arrangements (for the present investigation) lies in the graphical treatment of combinatories. The handling of a two-fold division (or bi-colored tiles) in a topological manner is ‘a kind of metaphor for the hierarchy of separations and connection in all things.’ (SMITH & BOUCHER, 1987; p. 378)

Quadralectic thinking is closely related to this figure of speech: it is a topological approach to communication and an effort to valuate the relation between the ‘invisibilia’ and ‘visibilia’ in a mathematical way. In this case ‘hierarchy’ must not be regarded as a scale from high to low, but as a measure of distance between the partners in a communication. In the end this measure is a simple number, which acts as an expression of visibility.

ARONBERG LAVIN, Marilyn (1972). Piero della Francesca: the Flagellation. University of Chicago Press. ISBN 0-226-46958-1.

ESCHER, Maurits C. (1958/1986). Regelmatige Vlakverdeling. De Roos, Utrecht (De Roos Foundation), Museum Meermanno-Westreenianum, ‘s-Gravenhage.

– (1959/1970). Grafiek en tekeningen. Koninklijke Uitgeverij J.J. Tijl N.N., Zwolle.

KOLOMYJEC, William (1976). The Appeal of Computer Graphics. Pp. 45 – 51 in: LEAVITT, Ruth (Ed.) (1976). Artist and Computer. Creative Computing Press, New Jersey/Harmony Books.

LAUWERIER, Hans A. (1988). Symmetrie. Regelmatige structuren in de kunst. Aramith Uitgevers, Amsterdam. ISBN 90 6834 032 8

SMITH, Cyril S. & BOUCHER, Pauline (1987). The Tiling Pattern of Sebastien Truchet and the Topology of Structural Hierachy. Pp. 373 – 385 in: Leonard (Journal of the International Society for the Arts Sciences and Technology), 20th Anniversary Special Issue. Volume 20, Number 4, 1987. Pergamon Press, Oxford/New York.

STEVENS, Peter S. (1980). Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions. The MIT Press, Cambridge, Mass./ London. ISBN 0-262-19188-1

WITTKOWER, Rudolf & CARTER, B.A.R. (1953). The Perspective of Piero della Francesca’s ‘Flagellation’. Pp. 294 – 302 in : Journal of the Warburg and Courtauld Institutes. Vol. 16 (1953).

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6. The four senses

Divina Quaternitas

The best introduction to the four-fold way of thinking can be found in the excellent Ph.D. thesis of ESMEIJER (1973/1978), titled ‘Divina Quaternitas’. She gave a comprehensive and illustrated survey of the occurrences of the ‘ordine quadrato’ in the Western European culture. The book is concerned with the medieval ‘quadriga mundi’ (the four-fold world), which is an important part of the present field of investigation (fig. 15).

monreale

Fig. 15 –  Four-fold symbolism is prominent in the church of Monreale (Sicily); Photo: Marten Kuilman, 2012).

Focal point in the exegesis (of Bible texts) is the handling of the four ‘senses’, the Latin expression for the ways of observation or the basic viewpoints in a communication:

————————-    Historia                        the (historical) fact

————————-    Allegoria                       the deeper meaning

————————-    Tropologia                   the moral meaning

————————-    Anagogia                      the higher meaning

These four different types of ‘seeing the world’ were established by Augustine, bishop of Hippo (354 – 430) in his ‘De Doctrina Christiana’ (PUSCHMANN, 1983), but their home ground can be found in the Nile-delta in Egypt, in the Alexandrian melting-pot of ideas at the beginning of the Christian era. The fourfold interpretation was well-known in the medieval ‘memoria technica’ and summarized in the following expression (MÂLE, 1910/1961, p. 139):

 Littera gesta docet, quid credas allegoria

Moralis quid agas, quo tendas anagogia

ECO (1985/1991, p. 218) – in relation to the use of the four senses in the work of Dante (in the ‘Convivio’ and Epistola XIII in the ‘Letter to Cangrande della Scala’; see also de LUBAC (1959/1964), Partie II, Tome II, p. 321) – attributed this distichon to Nicholas de Lyra or Agostine of Dacia. He called the theory of the four senses a ‘manner of interpretation, which was very common during the whole of the mediaeval culture’.

1. The literal meaning (or historia) is based on an empirical approach to reality. Only the visible aspect counts.

2. The deeper meaning based on the allegory. This word is derived from the Greek ‘allos’ (other) and ‘agora’ (marker/forum, creation) and has the connotation: to say something, but mean something else (HAWORTH, 1980). ALLERS (1944) spoke in this context of an ‘example by translation’.

3. The moral meaning or tropologia is an observation supplemented with certain values. ‘Tropos’ is a way of turning (‘conversio’) an expression into another meaning. In the vocabularies of the exegesis, it was a practical synonym with ‘allegoria’ (de LUBAC, 1959/1964; Partie I, Tome II, p. 551/552).

4. The highest meaning or anagogia reaches into the unknown. Within the communication is a distinct area, where the observer is excluded to verify the facts. Nevertheless this area is considered to be of importance and plays a role in the communication-as-a-whole.

The afore-mentioned four ‘senses‘ are placed in a particular sequence. Or, as Henry de LUBAC (1959/1964; I, II, p. 416) could say: ‘La formule classique, celle du quadruple sens, est au fond de structure plus simple‘ (The classical formula of the four senses has, in fact, a simple structure). First the facts, then other facts, followed by the moral of the story and finally the unknown. This is  an empirical approach to the environment. The human observer is placed in the middle of the known world, like the medieval scientist, who thought that the earth was the centre of the cosmos. In a modern (quadralectic) understanding, there has to be a rearrangement to fall in line with a neutral perception.

I.   First Quadrant        –   anagogia     –  the invisible invisibility

II.  Second Quadrant   –   allegoria      –  the invisible visibility

III. Third Quadrant      –   historia        –  the visible visibility

IV. Fourth Quadrant   –   tropologia    –  the visible invisibility

This positioning is scaling new ground. There is, as far as I known, no publication, which associates the above-given classification of the ‘senses’ with a specific type of visibility in a communication. And the mutual position is the heart of the matter. The four ‘senses‘ can be seen in a numerological way, as individual members of a linear visibility, but also as the outcome of an interaction in a cyclic communication. In the latter case, the sequence of names is not haphazard. They point to a distinct phase in a cross-exchange. The ‘senses‘ bear (in a quadralectic interpretation) a topological message and must be viewed in their right perspective.

CAVINESS (1983) gave a well-documented survey of the fourfold ‘visio‘ at the end of the twelfth century. She, like NOLAN (1977), did not place the senses in a particular sequence, but they have something to say about order. Instrumental in their approach was Richard of St. Victor – the Magnus Contemplator – who died in 1173. He was correctly regarded as a key-figure in the interpretation of the spiritual attitude in the later Middle Ages. His utilization of the four ‘senses‘ marked the historic schism between the old, non-hierarchical (four-fold) way and the new, hierarchical (two-fold) way.

At the end of the twelfth century the four, individual – but interrelated – ways of seeing were gradually moulded into a scheme based on opposites: low, simple, down to earth, visible versus high, difficult, heavenly and invisible:

                                                         Low/easy reach/weak

————————–    1. Corporal view    –   the visible world

————————–    2. Mystical view     –   the spiritual world

————————–    3. Figurative view  –   the moral world

————————–    4. Anagogic view   –   the visionary world

                                                       High/unattainable/strong

Richard of St. Victor’s ‘orbis quadratus’, so vividly described by Barbara BRONDER (1972), moved to a lower division, if the opposites of low-high, human-godlike and body-soul are emphasized. The fourfold ‘visio‘ only returned to a new understanding after six hundred year of  Renaissances, Ages of Reason and Romanticism (STAUDINGER LANE et al, 2009).

SEARS’ book ‘The Ages of Man‘ (1986) will be mentioned next to the work of Esmeijer. The medieval division – not only fourfold – was here the well-researched area of interest. Sears gave many examples of division in ages, cosmological speculations and pointed to the symbolism of figures. She drew the conclusion, that ‘the quadripartite life was defined within a cosmological system developed in antiquity and subsequently transmitted to the Middle Ages’ (fig. 16).

agesofman

Fig. 16 – The four ages of man in Aldobrandino of Siena’s ‘La regime du corps‘ (1287). In:
BURROW (1986).

The relation between the ‘antique tetradic thought’ and the mediaeval equivalent was painted from Pythagoras as a source (JOOST-GAUGIER, 2006), to Empedocles (four elements), Hippocrates (four humors), Ovidius (Metamorphosis) to Theon of Smyrna (the tetractys as ordering-principle), Ptolemy (Tetrabiblos) and Antiochus of Athens (with a tetradic program). Followed by Ambrosius (the ‘syzygy’ of elements, ‘virtues cardinales‘), Isidore of Seville (Liber de Natura Rerum) and the ‘quarternarius’ of the Anglo-Saxon monk Byrhtferth, with a culmination in the anonymous, early twelfth century, publication of the ‘Tractatus de Quaternario’, concerned with the ‘force and power of the number four’ (fig. 11). This sequence is, to a certain extend, rather eclectic and suggestive, but proves, nevertheless, that the tetradic interest has a long and colorful history.

CAPLAN (1929) and SMALLEY (1931) took up the importance of the four senses as a guiding line in the Scholastic period. The latter, in her article on ‘Stephen Langton and the Four Senses of Scripture‘ stated that ‘the multiple interpretation, its technique, and its value to those who used it, are just beginning to be discussed.’ She referred to Cassian, who gave a clear definition in his ‘Collationes’ (XIV, 8). Guibert of Nogent (MIGNE, 1844/64, PL. CLVI, col. 26) gave the example of the four meanings (senses) of the word ‘Jerusalem’ (fig. 4), but there is no proof that Guibert was the originator.

The first influences of lower division thinking became manifest in the second half of the twelfth century. Stephen Langton, whose class notes lectures in Paris are preserved, never expounded in the Fourth Sense (anagoge). He followed Hugh of St. Victor, who also used a threefold division. The anagogic sense gradually merged with the allegorical and the moral. ‘Langton was grinding the corn (farina) of the Scriptures into the bread of tropology’ (SMALLEY, 1931; p. 69), but ‘it does not occur to him to distinguish between the teaching of Scripture and his own ingenuity’.

The most comprehensive research in the medieval ‘senses‘ was performed by Henri de LUBAC (1959/1964) in his four-parted study ‘Exégèse médiévale. Les quatre sens de l’Ecriture’. This erudite book was written with a firm knowledge of even the most obscure medieval writers and provides a wealth of facts in relation to the fourfold way of thinking in the Scholastic period. He demonstrated the important role of Beda (c. 673 – 735) in the establishment of the theory of the four ‘senses‘ (LeGOFF, 1984/1987, p. 163). De LUBAC (1959, Part I, Tome II, p. 422) speaks of Beda as ‘le premier auteur qui nous offre pour ainsi dire un tableau developpe du quadruple sens‘ (the first author who offers us so to speak a developed overview of the four senses).

ALLERS,  Rudolf (1944). Microcosmus – from Anaximandros to Paracelsus. Pp. 319 – 407 in: QUASTEN, Johannes & KUTTNER,  Stephan (Ed.).  Traditio,  Vol.  II. Cosmopolitan Science & Art Service Co., Inc.      New York, 1944.

BRONDER, Barbara (1972). Das Bild der Schöpfung und Neuschöpfung der Welt als ‘orbis quadratus’. Pp. 188 – 210 in: HAUCK, Karl (Ed.) Frühmittelalterliche Studien. Jahrbuch des Instituts für Frühmittel-alterforschung der Universität Münster, Band 6, Walter de Gruyter, Berlin/New York.

BURROW, J.A. (1986). The Ages of Man. A Study in Medieval Writing and Thought. Clarendon Press,Oxford

CAPLAN, Harry (1929). The Four Senses of Scriptural Interpretation and the Mediaeval Theory of Preaching. Pp. 282 – 290 in: Speculum 4.

CAVINESS, Madeline H. (1983). Images of Divine Order and the Third Mode of Seeing. Pp. 99 – 120 in: Gesta, XXII/2. The International Center of Medieval Art.

ECO, Umberto (1985/1991). Wat spiegels betreft (‘essays’) (tr. Aafke van der Made). Uitgeverij Bert Bakker, Amsterdam. ISBN 90 351 0863 9

ESMEIJER, Anna C. (1973/1978). Divina Quaternitas. Een onderzoek naar methode en toepassing der visuele exegese. Proefschrift Rijksuniversiteit Utrecht, 29-06-1973. Also as:

–   (1978). Divina Quaternitas. A Preliminary Study in Method and Application of Visual Exegesis. Van Gorcum, Assen/Amsterdam.

GOFF, Le, Jacques (1984/1987).  De cultuur van middeleeuws Europa (La civilisation de l’Occident medieval). Les Editions Arthaud, Paris/Uitgeverij Wereldbibliotheek, Amsterdam. ISBN 90 284 1521 1

HAWORTH, Kenneth R. (1980). Deified virtues, demonic vices and descriptive allegory in Prudentius’ Psychomachia. Adolf M. Hakkert, Amsterdam. ISBN 90-256-0823-X

JOOST-GAUGIER, Christiane L. (2006). Measuring Heaven. Pythagoras and His Influence on Thought and Art in Antiquity and the Middle Ages. Cornell University Press, Ithaca and London. ISBN 976-0-8014-7409-5

LUBAC, de, Henry (1959/1964). Exégèse médiévale. Les quatre sens de l’Ecriture. Tome I – IV. Editions Montaigne; Aubier, Paris.

MÂLE, Émile (1910/1961). The Gothic Image. Religious Art in France of the Thirteenth Century (tr. Dora Nussey). J.M. Dent & Sons, London, Glasgow/Harper, New York (1958).

MIGNE, J.P. (1844/64). Patrologiae cursus completus sive bibliotheca   universalis… omnium s.s. patrum… Series secunda in qua prodeunt  patres… ecclesiae latinae… (= Patrologia latina; PL.), Paris.

NOLAN, Barbara (1977). The Gothic Visionary Perspective. Princeton University Press, Princeton, New Jersey. ISBN 0-691-06337-0

PUSCHMANN,  Rosemarie  (1983).  Magisches  Quadrat und Melancholie  in  Thomas Manns Doktor Faustus:  Von der musikalischen Struktur  zum  semantischen Beziehungsnetz. AMPAL Verlag, Bielefeld. ISBN 3-922986-07-2

SEARS, Elizabeth (1986). The Ages of Man. Medieval Interpretations of the Life Cycle. Princeton University Press, Princeton, New Jersey. ISBN 0-691-04037-0

SMALLEY, Beryl (1931). Stephen Langton and the Four Senses of Scripture. Pp. 60 – 76 in: Speculum, VI (1931).

– (1968). L’Exegèse biblique. Pp. 273 – 293 in: GANDILLAC, de, Maurice & JEAUNEAU, Eduard (Ed.) (1968). Entretien sur la Renaissance du 12e siècle. Décades du Centre Culturel International de Cerisy-la-Salle, Nouvelle serie 9; Mouton,Paris/La Haye.

STAUDINGER LANE, Evelyn; PASTAN, Elizabeth & SHORTELL, Ellen M. (Ed.) (2009). The Four Modes of Seeing. Approaches to Medieval Imagery in Honor of Madeline Harrison Caviness. Ashgate Publishing Limited, Farnham, Surrey (UK). ISBN 0754660109

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7. Mappa mundi

The fourfold division in place

 

The division in place is elementary. Where are we? Where is our position? This is the type of questions that every human being poses in an early stage of existence. Knowledge of the location is of prime importance. Or, like GROENEWEGEN-FRANKFORT (1951) put it in connection with the visual art: ‘The problem of space is a problem of relation. ‘Only with an active knowledge of the place and its possibilities are we able to survive’ (fig. 17).

fourfold

Fig. 17 – The fourfold-division in place as a natural scheme. The classical ‘Tetragonus mundus‘ is often attributed to the Greek philosopher Aristotle (384 – 322 BC). He, indeed, summarized the scheme and moulded it in a well-developed philosophical system, but the roots are older. Four directions enclose a square world, divided in three parts (Asia, Africa, and Europe). South (Auster) is placed at the top and East (Oriens) to the left, which is in defiance with the present map drawing. The picture originates from a ninth century manuscript of Beda’s ‘De Natura rerum’ (Clm. 210, fol. 132v; Bayerische Staatsbibliothek, München) (ESSLING, 1909; BROWN,  1978).

To find a location is a matter of division of space and subsequent valuation of distances. The first positioning is based on a division-concept. The early history of geographic orientation in the Europe has many examples of a strong awareness of the importance of division, in particular, the three- and fourfold variety.

Konrad MILLER (1926/1986) referred in a contribution to the Arabian cartography (‘Zur Geschichte der arabischen Kartographie’) to the possible origin of the three-fold division of world-space. He placed the source of the first cartographic division (in Asia, Europe and Africa) at the joining point of these cultures in the Aegean Sea, on the isles of Rhodos and Samos and at Milete in Asia Minor.

This observation was supplemented by the remark that the Asian cultural influence pointed to a four-fold rather than to a three-fold division: the names of Europe and Africa do not occur in the Bible, and Asia is only mentioned as a Roman province. Furthermore, the Arabs in the Middle Ages did not use a three-fold division of the world. They imagined a cup-like appearance symbolized by the old-Sumerian sign (4000 BC) of two concentric circles: the inner circle as the earth, surrounded by sea and an outer circle. The ‘Four Corners of the Earth’ were known as ‘kanephot‘. They were the seat of the four winds and divided the world in four parts.

The history of the ‘mappa mundi‘ (world-maps) was divided in four subperiods by WOODWARD (in: HARLEY & WOODWARD, 1987; part 3: Medieval Mappae mundi, p. 286ff):

1. The ‘patristic period’ (of the Church fathers) from the beginning of the fifth to the end of the seventh century;

2. The period from Bede (672/73 – 735) to Lambert of Sint Omer (ca. 1100);

3. The period from Henry of Mainz (1100) to Richard of Haldingham (1300);

4. The last period, starting around 1209, was dominated by Franciscan monks. Roger Bacon (c. 1214 – 1294), John Duns Scotus (c. 1265 – 1306) and William of Occam (c. 1290 – c. 1349) were influential.

Unfortunately, Woodward did not state the criterion on which this division was based. It seems, likely, to be the ideological environment in historical time: a ‘classical’-patristic group, a missionary group, a cosmological group and finally a Franciscan group, all spaced over a period of nearly thousand years from 400 – 1400. Within these groups, the variety of forms is considerable. Some points of interest – with particular attention to the number of divisions in each group – will be highlighted here:

1. The world views of Crates (of Mallos), Macrobius, Orosius and Isidore of Seville are labeled together. They are typified as the ‘patristic group’ because they are also used by the Church fathers. Crates (c. 150 B.C) embodied the ‘older tradition’ of a four-parted world. In this view, the globe had four occupied quarters, bearing the names: Perioikoi, Oikomene, Antoikoi and Antipodes (fig. 18). Oikomene was the term originally used in the Greco-Roman world to refer to the inhabited earth.

crates

Fig. 18 – The world-view of Crates of Mallos, c. 150 BC, a grammar scholar from Pergamum. He envisaged four inhabited quarters on the globe: Perioikoi, Oikomene, Antoikoi and Antipodes.

Macrobius (c. 395 – 436) used an elaborate method, with a Pythagorean undertone, to arrive at a five-fold division of a circle. Some hundred-and-fifty ‘mappae mundi‘ using Macrobius’ scheme are known. They became models for many medieval mappae mundi (ANDREWS, 1925).

The following quadruple procedure was used, which became known – some four hundred years later in the time of Rabanus Maurus (died 826 AD) – as the ‘ratiocinationis quadrivium‘ (fig. 19):

a. Division: Lines of 24, 30 and 36 degrees are drawn in a quarter-pie of a circle; this procedure results in a division of 4/60-, 5/60- and 6/60th parts of a quarter circle,

b. Definition: Lines are drawn (in a half-circle) through the intersection of the angle-lines with the circle (A, B). The result is a horizontal three-partition (of the quarter circle).

c. Demonstration: The mirror image of the half-circle three-division results in a six-division of a full circle.

d. Resolution: The mirror-plane is now left out and the full circle is divided in five parts, build up of the following division of the circle: 36, 30, 48 (24 + 24), 30 and 36 degrees.

rationes

Fig. 19 – The four stages, later known as the ‘ratiocinationis quadrivium’, to arrive at a ‘Macrobian’ world map, based on a five-division of a circle.

The writings of Paulus Orosius (c. 383 – post 417) had a great influence on later map makers, but no specific maps of this Christian historian are known. The knowledge was derived from his book ‘Historiarum Adversum Paganos Libri VII’ (Seven Books of History against the Pagans’), which was dedicated to St. Augustine (354 – 430).

Isidore of Seville (c. 560 – 636) was the most influential member of the ‘classical’ group. He lived around the same period as Gregorius (c. 540 – 604). His books ‘De natura rerum’ (612 – 615) and the ‘Etymologiarum sive originum libri XX’ (622 – 633) became the sources of references of much later mediaeval knowledge. He was influenced by Ambrose, Augustine, Boëthius, Cassiodorus, Lucretius, Lucan, Macrobius, Orosius, Pliny the Elder, Sallust, Servius and Solinus. Some six hundred and sixty ‘Isidorean’ world maps in manuscripts remained (DESTOMBES, 1964).

Often the ‘Isidorean’ maps were – without much criticism – associated with the so-called T-O maps, who got their name from a three-fold division of a circle: Asia in the upper half, Europe (left) and Africa (right) share the lower half (fig. 20). The biblical association with the sons of Noach – Sem, Japheth and Cham – was generally known.

Careful classification is essential here: most of these maps were, according to DESTOMBES (1964) and ARENTZEN (1984), copied between the eleventh and fourteenth century, thus in a different frame of mind with regards to the number of divisions used in a communication.

three-fold

Fig. 20 – Three-fold division in map-making. 1. A T-O-map of Brunetto Latini, early fourteenth century (Bodleian Library, MS Douce 319); 2. From an eleventh century manuscript of a ‘Commentary on the Apocalypse of Sint John’ by Beatus of Liebana (Bibl. Nat. Paris, MS Lat. 8878, fol. 7r); 3. From a twelfth century manuscript of Bede’s ‘De natura rerum‘ (Bibl. Nat., Paris, MS Lat. 11130, fol. 82r); 4. World map of Isidore of Seville, 1492; printed by Gunther Zainer, Augsburg.

Von den BRINCKEN (1970, p. 264) states firmly that ‘eine Vierteilung nach den vier Weltreichen Daniels ist übrigens Kartographisch nicht belegt‘ and also: ‘Die T-Karte ist die weitaus verbreitetste Form der mittelalterlichen Karte.’ In a general sense this statement is true, like earlier figures in DESTOMBES’ catalogue (1964) of the ‘mappae mundi’ (between AD 1200 – 1500) confirm. The T-O-map was sanctioned by the Church and fitted in the three-fold way of thinking, which manifested itself in Europe after the year 1200. Scrutiny  of the total number of maps might actually show that the majority of T-O-maps were drawn in or after the twelfth century.

2. The second period in the drawing of ‘mappae mundi‘ is indicated from Bede (672/73 – 735) to Lambert of Sint Omer (c. 1100). They are loosely grouped as ‘missionary’. The world map of Bede is preserved in fifteen original manuscripts, and hundred-and-seventy-five secondary versions are known. In this same period Pope Zacharias (pope from 741 – 752) had a world map painted on the wall of the Lateran Palace (now lost). Charlemagne (described in the ‘Vita Karoli Magni‘) possessed three silver tables with pictures of Constantinople, Rome and the ‘whole world’. Another source of pictures came from the ‘Commentary on the Apocalypse of Saint John’ by Beatus of Liebana (between 776 – 787), copied in many ‘scriptoria‘ in Spain and Southern France (KLEIN, 1976). Towards the end of this period the encyclopaedic ‘Liber Floridus‘ of Lambert of Saint Omer provided many pictures of mediaeval conceptions (DEROLEZ, 1968) (fig. 21/22).

augustusFig. 21 – A miniature of Emperor Augustus with a mappa mundi in Lambert of St. Omer’s ‘Liber floribus’ . c. 1120. In: ARENTZEN (1984).

The ‘Liber Floridus‘ was composed in the years before 1120 and offers a broad survey of all types of divisions: fol. 19v en 20v mentioned the six periods of the world, fol. 24r the winds, fol. 24v the five zones of the earth and fol. 25v gives the positions of the moon, winds and elements (eight-division). Fol. 88r figures the elements and the year (Annus) on the ‘altare Dei‘, situated at the ‘abissus‘. Fol. 221v depicted the zones of Macrobius and the ‘Sphera Platonis‘. Finally, on fol. 241, a ‘Europa Mundi Pars Quarta‘ is visualized (fig. 22/23). These examples show that no particular division thinking is dominant in the ‘Liber Floridus‘.

Europamundiparsquarta

Fig. 22 – Europa in four parts. Liber floribus. Gent, Universiteitsbibliotheek, Ms 92, f. 241r. The numerological character (of the number 4, pars quarta) is obvious in this incomplete map.

liberfloribus

Fig. 23 – The original ‘Liber floribus‘ (1121) in the Stadsmuseum Gent (STAM) exhibition ‘The world in a book’ from September 30th 2011 – January 8th 2012 (photo: Marten Kuilman, 27 November 2011).

3. The third period was fixed – according to Woodward (in: HARLEY & WOODWARD, 1987) – between Henry of Mainz (1100) and Richard of Haldingham (1300). This ‘cosmological group’ reflected a whole new approach to world and cosmos. Charles Homer HASKINS (1924/1960) called this renewal the ‘Twelfth Century Renaissance’. The tetradic way of thinking reached a new level of consciousness, but with ever-stronger numerological undertones. The Crusades to the Holy Land resulted in a fresh geographic awareness and the translations of the Arabs and Greek documents opened up long-forgotten worlds. This knowledge resulted in ever more elaborate maps.

The famous Ebstorf-map (1235) (fig. 24) and the Hereford-map (around 1290) showed, in the climax of the ‘allegorical’ cartography in the thirteenth century, a wealth on details and did not belong to any distinct type of division.

ebstorf

Fig. 24 – The central part of the Ebstorf mappa mundi shows the square city of Jerusalem. The original map was destroyed in World War II during the bombing of Hanover. A set of black and white photographs of the original map was taken in 1891. Several color copies were made before its destruction in 1943 (Wikipedia).

4. The last period has an overlap with the previous one and runs from 1209 to 1400. It is dominated by the work of Franciscan monks. Influential names were Roger Bacon (c. 1214 – 1294), John Duns Scotus (c. 1265 – 1306) and William of Occam (c. 1290 – c. 1349). The small, but very important book ‘De Sphaera‘ of John Sacrobosco (John of Holywood) is dated between 1220/30 and is therefore earlier than a book with the same title by Robert Grosseteste (1175 – 1253). The idea of a spherical world was well established. It contradicts the opinion of nineteenth century authorities that the earth of the thirteenth century scholars was thought of as flat.

An exceptional relict of the fourfold, ‘conceptual’ approach to map making can be found in a schoolbook for young clergyman, printed in 1475 in Germany (fig. 25).

brandiss

Fig. 25 – A late conceptual, four-fold world view. From a woodcut in the ‘Rudimentum novitiorium‘, published in 1475 by Lucas Brandiss in Lübeck. The top of the map is to the east (Oriens) with the four rivers of Paradise flowing from it. At the center, the Holy Land Palestine (and Judea), but no special reference is made to Jerusalem. The land Ophir is in the south (to the right, Auster) and the Pillars of Hercules are visible to the bottom of the map (west). In: STRAUSS (1981).

rudimentum

The ‘Rudimentum Novitiorum‘ (Lübeck, 1475) in a colored version. The book was re-issued from new blocks from Paris in 1488 and Lyons in 1491. In: SHIRLEY (2001).

All these endeavors in map making reflected the basic need of humanity to locate themselves in a seemingly boundless space and draws attention to the problem of relation. In the end, it is the concept of division, which shapes this relation, and which makes it possible to bring structure in an otherwise incomprehensible environment.

The four directions – North, East, South and West – are now generally accepted as the basic division of place. They are – which is much less understood – the living examples of the possibility to think in a structural-spatial fourfold pattern.

ANDREWS, Michael C. (1925). The study and classification of medieval mappae mundi, Pp. 61-76 in:  Archeologia, Oxford, LXXV (1925-26).

ARENTZEN, Jorg-Geerd (1984). Imago Mundi Cartographica. Studien zur Bildlichkeit Mittelalterlicher Welt- und Oekumene Karten unter besonderer Berucksichtigung des Zusammenwirkens von Text und Bild. Wilhelm Fink Verlag, Munchen. ISBN 3-7705-2258-3

BRINCKEN,  von den, Anna-Dorothee (1970). “…Ut describeretur univer-sus orbis“.  Zur Universal Kartographie des Mittelalters. Pp. 249 – 278 in: ZIMMERMANN, Albert & HOFFMANN, Rudolf (Ed.). Miscellanea Mediaevalia. Band 7: Methoden in Wissenschaft und Kunst des  Mittelalters. Walter de Gruyter & Co, Berlin.

BROWN,  Hanbury  (1978).  Man and the  Stars.  Oxford  University  Press, Oxford. ISBN 0-19-851001-2 (Ann Ronan Library).

DESTOMBES, Marcel (Ed.) (1964). Mappemondes AD 1200 – 1500. Catalogue préparé par la Commission des Cartes Anciennes de l’Union Geographique Internationale. N. Israel, Amsterdam.

ESSLING,  Prince d’ (1909).  Les Livres a figures venitiens de la  fin  du XVe Siecle et du Commencement du XVIe.  Librairie Leo  S.  Olschki, Florence/Librairie Henri Leclerc, Paris.

GROENEWEGEN-FRANKFORT, H.A. (1951). Arrest and Movement. An Essay on Space and Time in the representational Art of the ancient Near East. Faber and Faber Limited, London.

HARLEY, J.B. & WOODWARD, David (1987). The History of Cartography. Vol. I: Cartography in Prehistoric, Ancient and Medieval Europe and the Mediterramean. The University of Chicago Press, Chicago/ London.

HASKINS,  Charles H. (1924/1960). Studies in the History of Mediaeval Science. Frederick Ungar Publishing Co., New York.

– (1927). The Renaissance of the Twelfth Century. Harvard University Press, Cambridge, Mass.

MILLER,  Konrad (1926/1986).  Mappae Arabicae. Beihefte zum Tübinger Atlas des Vorderen Orients, Reihe B, Geisteswissenschaften, Nr. 65; GAUBE, Heinz (Ed.)/Dr. Ludwig Reichert Verlag, Wiesbaden. ISBN 3-88226-293-1

SHIRLEY, Rodney W. (2001). Mapping of the World. Early Printed World Maps 1472 – 1700. Early World Press Ltd., Riverside (USA). ISBN 0 970351801

STRAUSS, L. (Ed.)(1981). The Illustrated Bartsch,  80, Part I: Anonymous Artists, 1457 – 1475. Abaris Books, New York. ISBN 0-91-3870-50-1

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8. Orientation

The directions of the wind

 

The orientation by  the four winds is very old, but its origin cannot be precisely indicated. The Greek seafarers used them and Erathosthenes, in his book ‘Geography’, mentioned the Boreas, Apeliotes, Notos and Zepyros. He subdivided the earth by parallel east-west and north-south lines and could  measure the circumference of the earth by these directions and the height of the sun.

Hipparchus of Nicaea (c. 165 – c. 127 BC) amended Erathothenes’ division of the earth – in sixty parts – by drawing ‘climata‘-lines at regular intervals (360 parts, the modern ‘degrees’). In that way, it was possible to locate every place on earth by co-ordinates. Ptolemy (AD 90 – 168) provided in his ‘Geography‘ the latitude and longitude of eight thousand places.

The importance of the winds was emphasized by Andronicus of Cyrrhus, who built, around 50 BC, the octagonal ‘Tower of the Winds’ in Athens, also called the ‘Horlogeion‘ (fig. 26).

horlogium

Fig. 26 – The ‘Tower of the Winds’ or Horlogium in Athens (Greece). Photo in: BOARDMAN (1993).

Orientation is fairly well documented in the maritime and shipping history. Every ship leaving a harbor and sailing at an empty sea, away from the shoreline, is comparable with a human mind on a ‘tabula rasa‘: the observer has to invent some sort of dynamic structural framework for guidance. Alternatively, like Daniel BOORSTIN (1983, p. 47) rightly put it in his book ‘The Discoverers‘: ‘When people set out to explore the oceans, they found it more than ever necessary to know the heavens.’ But to approach the heaven in an orderly way, one has to take decisions over the type of division in a comprehensive composition.

hainzel

Fig. 27 – This wooden quadrant was built by Paul Hainzel, Burgomaster of Augsburg, and a friend of Tycho Brahe. It is an illustration from Tycho Brahe’s work ‘Astronomia Instaurate Mechanica‘ (1598). Many types of quadrants were built during the development of navigation- and surveying-tools in the sixteenth century. A star was focused through the small rings E and D, and the angle could be read at the quarter-circle with a graduated scale (H). The whole contraption of the nineteen-foot radius quadrant and a brass scale could  turn from a platform. Without a reliable quadrant, it was impossible to fix any of the cardinal points of the sky.

The position and movement of the sun and the stars were the most obvious points of references in maritime orientation.  The sun comes up at a certain point, reaches it height and sinks to another point on the horizon. ‘The operative line was not that from N. to S., but that from E. to W’, said Eva TAYLOR (1937/1957, p. 23). ‘A seaman “oriented” himself by facing the north (the pole of heavens) and spreading out his arms to east and west.’ Instruments were made to measure angles. The simplest  one is the measuring staff, but more elaborated forms are the quadrant (fig. 27), the theodolite and the astrolabe (fig. 28). In the late sixteenth century, these instruments found their apex in the armillary, or a small-scale model of the universe.

astrolabium

Fig. 28 – The four parts of an astrolabe: 1. Mater. Round disc with graduation on the outer edge (limbus), divided in 360 degrees or 24 hours; 2. The planisphere or tympana. Tables for different pole-elevations; 3. Rete. Disk with fixed stars from Zodiac; 4. Alhidade (Al-hidada). Indicator turning around a fixed point (not shown here). The illustration to the lower right shows the backside of the astrolabe with additional tables. From a manual made for the Spanish king Alfonso the Sage (around 1300).

The astrolabe or ‘star-shooter’ is a quadrant to measure the height of stars compared to the earthly horizon (DREIER, 1979; LEHR, 1981). One of the oldest descriptions of the instrument is by Hermann the Lame from Reichenau (who died in 1054). Chaucer (1340? – 1400) wrote, in 1391, a ‘Treatise for the Astrolabium‘ for his ten-year old son Lewis. This is the oldest early scientific work in English. The drawings in fig. 28 were prepared for King Alfonso the Sage at the end of the thirteenth century.

In the thirteenth and fourteenth century, the use of the astrolabe was sporadic, but this changed drastically when the spirit of discovery took hold in the fifteenth century. Orontius Fine (1532) issued many treatises and construction rules in the sixteenth century, like the beautiful book ‘Protomathesis’.

astrolabe

Fig. 29 – This astrolabe is from the seventh tablet of the series ‘Sapihal-al-Afakiyah’ (pictures of the horizon), a description of a Persian astrolabe, constructed for Shah Husain Safawi, around 1700.

The seafarer could, apart from the sun and the stars, also rely on the winds as a sailing aid. ‘The Spanish sailors on Columbus’ crew’, says BOORSTIN (1983, p. 217) ‘thought of direction not as degrees of compass bearings but as ‘los vientos‘, the winds. Portuguese sailors continued to call their compass card a ‘rosa dos ventos’, a wind rose’. Before the general use of the compass a direction was understood to be a certain wind, blowing from a given direction.

Windroses flowered, even before the introduction of the compass, as detailed indicators of direction, based on a division of the circle in four, eight, twelve, sixteen or even thirty-two parts.  The ancient system of ‘winds’ (or ‘plagae‘) was essentially a system of division.

The Greek geographer Timosthenes, a direct predecessor of Erathosthenes, knew the so-called ‘twelve-wind’ system. TAYLOR (1937) noted – in an article over Matthew Paris’ ‘De Ventis‘ (written on the last folio of the ‘Historia S. Albani’, Cotton MSS. Nero D.5, dated after 1250):

The twelve-fold division, associated with the name of Aristotle, and later with that of the sea-admiral Timosthenes, is an astronomer’s system, harmonizing with the twelve hours of the day and of the night, the twelve signs of the Zodiac, and the twelve ‘houses’ used in prognostication, i.e. in general with the duodecimal numeration.’

The division is related to the 360 degrees circle and angles of 60, 30, 15 and 5 degrees, and therefore, finally, based on a combination of three- and fourfold division. The Romans, although lesser seafarers than the Greek, also use the twelve-division.

Erathosthenes abandoned the ‘twelve-wind system’ in favour of the ‘eight-wind system’, because it was too difficult for mariners (BROWN, 1949/1979 and HAPGOOD, 1966/ 1979). This may be true, but another consideration can be put forward: maybe this change came about by a shift in division thinking (from ‘triple-four’ to ‘dual-four’).

The eight-wind system (or, one step further, the sixteen fold division) was generally used on navigation charts known as portolan-maps. This particular type of map making flourished in the fourteenth century and was used by sailors (mostly in the Mediterranean) to chart their way from harbor to harbor. The maps were based on a sixteen-fold division (‘quadruple-four’) of the circle.

hapgood

Fig. 30 – The construction of the eight-wind system of the Portolan Charts as given by Livengood, Estes and Woitkowski in HAPGOOD (1966/1979). A circle is bisected eight times, resulting in sixteen lines from the centre to the periphery at equal angles of 22,5 degrees. Horizontal and vertical lines through the intersections form a grid of sixteen squares. Geographical details, like a coastline, are marked within this grid.

The stages to construct this system by bisecting the circle four times (fig. 30) results in angles of 22,5 degrees (HAPGOOD, 1966/1979; p. 14/15). This procedure displays the ‘ratiocinationis quadrivium‘ (as mentioned earlier):

1. Division:  Four times division of a circle results in angles of 22,5 degrees.

2. Definition:   Horizontal and vertical lines are drawn from the intersections of the angle-lines with the circle. This results in a grid of sixteen squares, a theoretical framework.

3. Demonstration: Geographical landmarks are indicated on this grid.

4. Resolution: The procedure of sixteen directions – or ‘plagae‘ – within a theoretical framework filled with empirical data, enables an observer to known a location in a given context.

The aforementioned scheme has little to do with the elaborate mathematical projections, employed by later map makers like Gerard Mercator (1512 – 1594), Abraham Ortelius (1527 – 1598) and the Blaeu family to catch the spherical earth in a convenient flat plane. It is a strictly theoretical approach to the communication between an observer and the environment, based on an ‘a priori‘ definition of division. It has, simultaneously, a philosophical connotation, inherent to this choice. This aspect is much less obvious in the ‘scientific’ map making of later centuries.

It is important to realize that the orientations of the great Portuguese and Spanish discoverers originated in a theoretical division-framework and not in any form of mathematical projection.

Pedro de Medina published in 1545 in Valladolid (Spain) his book ‘Arte Del Navegar’ and gives a sketchy, but remarkably complete picture of the earth, encompassed by eight winds (fig. 31). Here we see the merger of a well-developed theoretical division-idea with an emerging mathematical approach based on projection. The book was translated in French, German, English and Italian and the map figures in the editions printed in Venice in the years 1554, 1555 and 1609, but not – due to rivalry – in the French edition.

navegar2

Fig. 31 – The world with eight winds. An illustration of Pedro de Medina’s book ‘Arte Del Navegar‘ (Valladolid, 1545). This fairly complete world picture, in some sort of fantasy-projection, is surrounded by eight winds as indicators for the main directions.

The compass, although known from the twelfth century, was in its initial stages a rather crude instrument and did not contribute substantially to the geographical discoveries of the fourteenth and fifteenth century. In fact, it was surrounded by superstition and seen as a magical force. Alexander Neckam (1157 – 1217) could write: ‘When the mariners cannot see the sun clearly in murky weather, or at night, and cannot tell which way their prow is tending, they put a needle above a magnet which revolves until its point looks north and then stands still.’

There might have been other than ‘mechanical’ reasons for the initiation of the great journeys, which resulted in the discovery of new lands. It could well be that this urge was caused by a desire for delimitation, for finding the end of the earth. This spirit could only develop in a mind that valuates an awareness of boundaries in the first place. A world without fixed limits is incomprehensible – and unacceptable – in a mind that operates on the lower division-level. So towards the end of the fifteenth century – in the Renaissance as the identity crisis of the European cultural history – these limits had to be found at all costs. That might be the true reason Columbus set sail.

And maybe it would have been better for the credibility of oppositional thinking as Columbus had dropped of the earth and was forever vanished. Then the world would, at least, have a definitive end. The reality was different when, three decades later, the diminished crew of Fernao de Magelhaen – he died in 1521 on an island of the Philippines – returned home in 1522 with the physical proof of a round world. A world with no beginning and no end. The Captain-General had shown the four lights (meaning: get under way), but the great search for boundaries and limitation came to no avail: cyclic thoughts had to be with us for the years to come, they were part of our living world. The two-fold way of thinking took its first blow, despite the immediate success of material discoveries, rich booty and fulfillment.

The upheaval in mental images can be seen in many pictures of the early sixteenth century, indicating the tension between the lower and higher forms of division thinking and the confusion of old symbolism. Fig. 32 shows an example of a reversed interpretation of (Eriugena’s) ‘Seven Steps to Heaven’: the cosmic/heavenly elements (the winds) are four-fold and the earth (in T-O representation) is three-fold.

reversion

Fig. 32 – The four winds and the world. A symbolic representation of a four-fold cosmic (heavenly) division and a three-fold terrestrial (earthly) division. This is a reversal of the interpretation of Eriugena (in the ninth century). The highest power (in three-partition) is shifted from God to earth (man). From the Florentine Codex, Vol. II, fol. 236r. , completed 1577.

The Greek traveler and geographer Kosmas Indicopleustes already figured out the theoretical implications of a cyclic approach in the sixth century AD (fig. 33). He was fiercely against the idea, because it did not fit in the Biblical interpretation. The geographer tried – in his book ‘Topographia Christiana‘ – to shape the Christian and Biblical representations into a comprehensive world view (WOLSKA, 1962). The earth has, in Kosmas’ opinion, the shape of a disk and is on four sides surrounded by oceans. The sun is each day raised by angels. And a round shape is impossible because on the Youngest Day the antipodes would be unable to see the Lord come down from the clouds (DIJKSTERHUIS, 1950, I: 119 – 120).

antipodes

Fig. 33 – The antipodes are seen here in a manuscript of the ‘Topographia Christiana‘ of Kosmas Indicopleustes, sixth century AD. This picture tried to prove the impossibility of a round earth. In:  Laur.  fol.  98v – Topographie Chretienne van Cosmas Indicopleustes. WOLSKA  (1962).

Later, in the thirteenth century, the picture of two observers leaving each other in opposite directions, was revived by Gauthier de Metz and Vincent of Beauvais just to prove the spherical shape of the earth (fig. 34). The late fourteenth-century French bishop Nicole Oresme went even a step further: ‘Suppose that Plato leaves Athens heading westward on his way to circling the world, and Socrates does the same heading eastward. They return after three years, coming from the opposite directions. Now, did Plato, Socrates and the Athenians, who stayed behind, have the same time or not?’ He also knew the answer, long before the establishment of time zones and the international data-line: Plato would have lived one day longer than the Athenians and Socrates one day less.

gauthierdemetz

Fig. 34 – Two observers would meet each other, if they set out in the opposite direction on a round earth: Gautier de Metz shows, in the thirteenth century, the consequences of a round earth. This picture is of the printed version of Vincent of Beauvais’ influential book ‘Speculum maior‘. (In: HARLEY, J.B. & WOODWARD, D. (1987) and Ch. XVII of: VINCENTIUS  (1481/1979)

The directions of the winds were gradually changed by magnetic bearings in the sixteenth century, but the main division in four directions (north, east, south and west) continued to be the structural setting for any orientation by a traveler or observer. It is now often forgotten that the four-division of the winds represents an ancient orientation system, which had philosophical implications as well.

The last, great book to offer a prominent position to the wind-directions is the publication by Cesare Cesariano (1484 – 1543) of Vitruvius’ ‘De Architectura’ (Como, 1521). All classical ideas about direction, in particular in relation to the building of cities and buildings, are brought together in this book (fig. 35).

ventorumregiones

Fig. 35 – The division of the wind rose in ‘Ventorum regiones‘ as given in Vitruvius’ book ‘De Architectura‘, published by Cesare Cesariano (Como, 1521). In the classical writings of Vitruvius, the direction was found by means of a sundial. Note the central spine for casting a shadow from the sun. Meridies (South) is, for this reason, placed at the top. In: KRINSKY (1969).

The ‘Cosmographia‘ of Peter Apianus (1495 – 1552) was edited and published in Antwerp by Gemmae Frisius in 1553. Apianus treated all sorts of cosmological and geographical divisions: a ‘Schema praemissae divisionis‘ with the ‘Circulis sphaerae‘ in Chapter III (folio 3) elaborates on ‘De Sex Circulis Sphaerae‘, ‘De Quatuor Circulis Minoribus‘ and ‘De Quinque Zonis‘. No particular division is prominent. Chapter (XV, folio 24) deals with the winds (De Ventis) and gives an illustration of a ‘quadratum nauticum‘ (fig. 36).

quadratumnauticum

Fig. 36 –  A ‘Quadratum Nauticum‘. Example of a combination of ‘rosa dei venti‘ and magnetic bearings on a compass described in the ‘Cosmographia‘ (f. 24) of Petrus Apianus and Gemmae Frisius (1553). This edition has revolving diagrams on verso of l. 8 and 11, and on recto of l. 30 and 57. Inscriptions on these diagrams, also on some of the illustrations in the text, are in French. In: GUNTHER (1976).

The classical division in ‘rosa dei venti‘ is moved to the outer edge, while the more modern, ‘scientific’ division fills up the central part, with the four primary direction (Septentrio, Oriens, Meridies, Occidens) in a circle. This ‘quadratum nauticum‘ was used in combination with a magnet, and the orientation is therefore to the North. Map making since the sixteenth century has adopted this orientation (at the expense of the orientation to the East). It is another sign of the increased influence of the material elements (earth) over the immaterial (heaven).

The directions of the wind, and the way they are treated over the ages, provide a narrative of observation, which is closely related to the history of division-thinking. The roots are firmly embedded in the characteristics and relations of the four elements. Air and water are the elements of the multitude, whereas fire and earth are thought of as unities.

Orientation in the multitude is far more difficult than to establish a direction in a unity. The central fire of the sun is an easy fixture, just as the magnetic pole is a sure point of reference, but to find a way in the sky or over the waves of the sea is a different matter. Some frame of reference has to be developed. The stars and the winds have provided the material for the building of a mental structure, which could support the observation and direction-finding in the multitude or the unknown. And in the end it was not only the seafarer that benefited from that knowledge, but everybody who wanted to chart a route through life.

BOARDMAN,  John (Ed.)(1993). The Oxford History of Classical Art.  Oxford University Press, Oxford. ISBN 0-19-81433386-9

BOORSTIN, Daniel J. (1983). The Discoverers. Random House, New York. ISBN 0-394-40229-4

BROWN, Lloyd A. (1949/1979). The Story of Maps. Dover Publications, New York.

DIJKSTERHUIS, Eduard J. (1950). De Mechanisering van het wereldbeeld. Meulenhoff, Amsterdam. ISBN 90 290 1570 5

DREIER, Franz A. (1979). Winkelmessinstrumente. Vom 16. bis zum frühen 19. Jahrhundert. Ausstellung im Kunstgewerbemuseum vom 9. November 1979 bis 23. Februar 1980, Kunstgewerbemuseum Berlin.

GUNTHER,  Robert T.  (1976). Astrolabes of the World. Vol. I. The  eastern astrolabes. The Holland Press, London

HAPGOOD, Charles H. (1966/1979). Maps of the Ancient Sea Kings. Evidence of Advanced Civilization in the Ice Age. Turnstone Books, London. ISBN 855500 018 X

KRINSKY, Carol Herselle (Intr.)(1969).  Vitruvius.  De Architectura.   Cesare Cesariano (Como,  1521). Wilhelm Fink Verlag,  München.

LEHR,   Andre  (1981). De  Geschiedenis  van  het  Astronomisch  Kunstuurwerk. Martinus Nijhoff, Den Haag. ISBN 90-247-9082-4

TAYLOR, Eva G.R. (1937). The ‘De Ventis‘ of Matthew Paris. Pp. 23 – 26 in: Imago Mundi 2. A Periodical Review of Early Cartography. Edited by Leo Bagrow and Edward Lynam. Henry Stevens, Son & Stiles, London.

– (1957). The Haven-Finding Art. History of Navigation from Odysseus to Captain Cook. Hollis & Carter, London/Institute of Navigation.

VINCENTIUS (Vincent of Beauvais). The Mirrour of the World (Westminster, 1481)(1979). Number 960. The English Experience. Its Record in Early Printed Books published in facsimile. Walter J. Johnson, Inc. Theatrum Orbis Terrarum, Ltd., Amsterdam/Norwood, N.J. ISBN 90 221 0960 7

WOLSKA, Wanda (1962). La Topographie Chretienne de Cosmas Indicopleustes. Theologie et Science au VIe Siecle. Bibliothèque Byzantine – Etudes 3. Presses Universitaires de France, Paris.

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9. Continents

The four parts of the world

The notion of four parts of the world dates back to Antiquity and was based on ‘a priori‘ ideas closely related to the four-fold way of thinking. When the first outlines of a European cultural identity took shape, these impressions were still in existence. On the earliest known, oval-shaped oekumene-map of Isidore of Seville – dated in 775 A.D. – a great island is drawn to complement the four-division with the antipode-continent. The written text says: ‘Insula incognita enim sunt IIII partes mundi‘ (VERRYKEN, 1990). Reality is forced here into a conceptual scheme, because nothing was known of the ‘insula incognita‘ (fig. 37).

isidoreworldmap

Fig. 37 – The Vatican world map of Isidore of Seville, dated 775 A.D. The elongated island in the left-hand corner carries the inscription: ‘Insula incognita enim sunt IIII partes mundi‘, referring to a conceptual world view based on four parts. The city of Jerusalem is schematically drawn near the centre. The rivers of Paradise are clearly visible to the right.

After the discovery of America by Christopher Columbus in 1492, the conceptual four-part world turned out to be true. Because of the structural and metaphorical background, the four parts of the world (Europe, Africa, Asia and America) caught on very fast. The expression was popular by the Jesuits in the Contra-Reformation of the sixteenth century to indicate the long-known truth of a christian unity on the earth and a reference to a ‘holy’ fourfold-division thereof.

The symbolic expression of the parts of the world is pioneered by Cesare Ripa, in his ‘Iconologia‘ (1603). This book, with a wide field of influence, gave a review of a great number of abstract notions, that circulated in Europe at the time. The four parts of the world are shown as female figures in a distinct symbolic setting (fig. 38):

ripa

Fig. 38 – This symbolic representation depicts the continent Africa as a woman with a scorpio in her hand and a lion and snakes at her feet. It is part of a series of the four continents in the ‘Iconologia‘, an influential book by Cesare Ripa, printed in 1603.

HYDE (1924/1927) made a specialized study of the pictures of the four continents in theater- and ballet form. One of the publications opens with the appeal: ‘The author would be grateful for any information about symbolical representations of the Four Quarters of the World in the Fine and Applied Arts’.

The heydays for the representations of the continents are in the early seventeenth century. The symbolic forms of Europe, Asia, Africa and America are depicted on wall-paintings, ceilings, tapestry (fig. 39), folding screens, etchings and paintings.

tapestry

Fig. 39 – The four parts of the world are used here as designs of four tapestries by G. Maes, executed by J. van der Beurght in Bruxelles. End of the seventeenth century. Top left: Europe as a queen with the horn of plenty (cornucopia). This horn was the symbol of Fortune, the Roman goddess, shaped after Tyche. The Greek mythical roots lay by Amaltheia, the goat which fed Zeus and became a ‘cornu copiae‘. Top right: Asia with a pagoda; Bottom left: Africa, with a pyramid; Bottom right: America with exotica. Collection J.H. Hyde, Paris.

The symbolism of the continents is often supported by the following characteristics (HALL, 1974)(fig. 40):

1. Europe – Queen of the world, with crown and sceptre; temple (relation to religion); arms-array – horse or bull; horn of plenty (cornucopia), reference to art and science.

2. Asia – Flowers, jewels; odours – perfumes from the East; palm and camel.

3. Africa  – Person with black skin, coral beats; scorpio; lion/ snake; head of an elephant.

4. America – Native inhabitant with feather headdress; bow and arrow; caiman/ crocodile.

animalsymbolism

Fig. 40 – The four parts of the world and its animal symbolism: Europe with a horse, Africa with an elephant, a camel for Asia and a panther-like animal for America. End of the seventeenth century. Panneaux d’Aubusson royal. Collection J.H. Hyde, Paris.

The theme is elaborated in books and plays. CHEW (1962) mentioned, in an interesting commentary of that period, the ‘tedious allegorical drama’ of Barten Holyday, titled ‘Technogamia, or the Marriages of the Arts‘ (1618). The tetradic thoughts are reduced in this period of the European cultural history to mythological paraphernalia. On the ‘fêtes galantes‘ only  the exterior remains of the tetradic world are used. The symbols are known, but the world in which they originate, seems to be forgotten (fig. 41).

guerra d'amore

Fig. 41 – La Guerra d’Amore. A symbolic parade in the seventeenth century representing the continents. Etching of Jacques Callot (Florence, 1616), working at the court of the Medici. The seventeenth century was for many countries in Europe, despite the continuing struggles in the first half of it, a ‘Golden Age’, with hitherto unknown material wealth and a feeling of power and command. A fourfold division was often demonstrated, but in a far more symbolic way than in the twelfth century. It was not felt as a basic starting-point for a communication, for which the two-fold way seemed much more appropriate and practical, but as a relict of bygone times, a living memory, used in plays.

Some ten years after the enacting of the ‘la Guerra d’Amore‘ a ballet was performed in Paris under the title ‘The Dowager of Billebahaut’ (The widow of Bilbao) for the carnaval of 1626. Daniel Rabel made several drawings of the (lost) costumes of the personifications of the continents, who played in the ballet (fig. 42).

dowager

Fig. 42 – Africa (left) and America (right). Costumes used by the ‘Ballet of the Dowager of Billebahaut’, performed at the carnaval of Paris in 1626. Pen drawings by Daniel Rabel, Louvre Museum, Paris.

Michael Maier described in his book ‘Symbola aureae mensae’ (1617) a symbolic ‘peregrinatio‘ to the four corners of the earth: the journey begins in Europe to America and Asia and finally the quest for Mercure and the phoenix ends in Africa (FRICK, 1972; pp. 572ff; JUNG, 1953/1968, p. 369).

Around 1800, as the fourfold way of thinking is revitalized, the symbolism of the four continents is strongly represented. Schlegel complained in his ‘Cours d’histoire universelle‘ (1805 – 1806):

It should be noted that in our time the division in the four parts of the world is overemphasized and used to compare different kind of nations; it has gone so far as to apply the division in South, North, East and West not only to physical but also moralistic entities.’

While the two-fold division is so much easier: ‘It is better to distinguish only two parts of the world, the North and the South’ (ANSTETT, 1939). East and west are, in Schlegel’s approach, only ‘relative’, and north and south are fixed. It seems like a voice from the past, a memory of the years of Absolutism, when people thought that things were fixed and acted accordingly. By the start of the nineteenth century, this time was over and the last great cultural change was about to happen.

Schlegel’s contemporary F.W.J. von Schelling (1775 – 1854) had strong ties with the tetradic thoughts, sometimes with a relapse into numerology. He was, in his later life, influenced by Jacob Boehme (1575 – 1624), the German alchemist (BROWN, 1977).

Von Schelling considered the four parts of the world and the four directions as a basic division-method. He applied this scheme to the four elements nitrogen (N), carbon (C), hydrogen (H) and oxygen (O) by placing them in a quinquennial position with water as an undifferentiated medium in the middle (DÜSING, 1988).

As a possible source is pointed to a publication of Franz von Baader (1765 – 1841): Über das pythagoräische Quadrat in der Natur oder die vier Weltgegenden‘ (Tübingen, 1798). This reference has not yet been found. Access to the work of von Baader is provided by Eugène SUSINI (1967), who edited his correspondence (in six volumes between 1943 and 1983). The activities as a mining engineer in Schwabing (near Münich) and his political manipulations played a more important part in this correspondence than his philosophical thoughts.

Von Baader’s main publications were mentioned in a letter from 1819: ‘Beyträge zur dinamischen Philosophie’, a ‘Begründung der Ethik‘, an essay on the French revolution, contributions to Von Schelling’s ‘Journal‘ and a publication titled Über die Vierzahl des Lebens‘ (Berlin, 1818). His ‘Fermenta cognitionis‘ was published between 1822 en 1825, and referred to Jacob Boehme as a source of inspiration.

ANSTETT,  Jean-Jacques  (1939).  Cours d’histoire universelle (1805  –  1806).  Friedrich Schlegel. These l’université de Paris. Imprimerie de Trevoux.

BROWN, Robert F. (1977). The Later Philosophy of Schelling. The Influence of Boehme on the Works of 1809 – 1805. Brucknell University Press, Lewisburg.

CHEW, Samuel C. (1961). The Allegorical Chariot in English Literature of the Renaissance.  In: MEISS, Millard (Ed.) De Artibus Opuscula   XL. Essays in Honor of Erwin Panofsky. Vol. I. New York University Press, New York.

  –  (1962). The Pilgrimage of Life. Yale University Press, New Haven/London. LCCC 62-8239

DÜSING, Klaus (Ed.) (1988). Schellings und Hegels erste absolute Metaphysik (1801 – 1802). Zusammenfassende Vorlesungsnachschriften von I.P.V. TROXLER. Text von Troxlers Nachschriften der Vorlesung Schellings vom Sommersemester 1801 und der Vorlesung Hegels vom Wintersemester 1801/1802. Jürgen Dinter, Verlag für Philosophie, Köln. ISBN 3-924794-6-5

FRICK, Karl R.H. (1972). Michael Maier’s ‘Symbola Avreae Mensae Dvodecim Nationvm’ (1617) (Facs.). Akademische Druck- u. Verlaganstalt, Graz, Austria.

HALL, James (1974).  Dictionary of Subjects and Symbols in Art. John Murray, London. ISBN 0 7195 3103 9

HYDE, James H. (1924). L’Iconographie des Quatre Parties du Monde dans les tapisseries. Extrait de la Gazette des Beaux-Arts, Paris.

–  (1927). The four parts of the world as represented in old-time pageants and ballets. Apollo. A Journal of the Arts, London

JUNG, Carl G. (1953/1968). The Spirit Mercurius. The Collected Works of C.G. Jung,  Vol. 13. Bollinger Series XX, New York. Routledge & Kegan Paul, London.

SUSINI, Eugène (1967). Lettres inédites de Franz von Baader. Presses Universitaires de France, Paris. Publications de la faculté des lettres et sciences humaines de Paris-Sorbonne. Serie ‘Textes et Docu-ments’. Tome XVI.

VERRYCKEN, Amber (1990). De middeleeuwse wereldverkenning. Dossiers geschiedenis; nr. 15. Acco Leuven/Amersfoort. ISBN 90-334-221-5

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10. Time and division

The fourfold division in time

 

Time and division are both abstract entities. They have a distinct connection in thoughts, and the one can hardly exist without the other. Both cannot be made visible and only come to live in a comparison. ‘Moments cannot exist if there are no objects’ says WHITROW (1972) in his book ‘What is time?’ And because the visibility is always specifically related to the observer every observer has basically his own time(frame).

And time and division find their identity in a division-model. So, for instance, the period between the sunrise and sunset is called a ‘day’, with a certain duration, which can be divided in hours, minutes, etc. In classical times the day was divided in twelve hours (and twelve hours night). If the sun reached the highest point in the daytime it was six o’clock (rather than twelve o’clock nowadays) (HAGEN, 1981).

Time becomes meaningful in a comparison with the sun. The same holds for the division: boundaries can be drawn, but they only become significant, if they have taken part in a comparison with something else. Time and division are the abstract quantities of the First Quadrant, ruled by the invisible invisibility, the ‘holy’ aspect of creation.

The fourfold division of a (twenty-four hours) day results in the time-units of morning, afternoon, evening and night. Michelangelo has sculptured this division at the tomb of Giuliano de Medici in the Medici Chapel in Florence (PANOFSKY, 1939/67). ELSEN (1985) suggested that the representation of the ‘Morning‘ might have been a model for Rodin’s ‘Thinker‘.

The new day, as a fresh beginning, has been a source of inspiration. In poetry the image is used in connection with light and a renewed visibility. The morning holds the promise of a new start. The motif has also been used in a literally sense as a source or spring. The four rivers of the Garden of Eden play a symbolic role here.

newday

Fig. 43 – The new day as a source of inspiration. Left: an illustration of ‘TWonderboek‘ of David Joris (1542), inspired by the opening of Psalm 45: ‘My heart is inditing a good matter’.  In:  BOHEEMEN (1986); Right: Der Morgen (The Morning). Etching of Philipp Otto Runge, 1805. In: HOFSTÄTTER (1965).

TWonderboek‘ of David Joris (dated 1542) depicted a face above a heart, floating on water (fig. 43 left). Five fountain-like streams flow from the mouth of the head. Four return to the earth and one disseminates as rain. The (Dutch) caption says: ‘Een zeer goede Reden berst mij ter herten uit‘ (A good reason flows from my heart). These words are the opening lines of Psalm 45 in the Holy Bible, now reading in the authorized King James version as:

 ‘My heart is inditing a good matter: I speak of the things which I have made touching the king: my tongue is the pen of a ready writer.’

This same symbolism of a spring can also be found in the work of Philipp Otto Runge (1777 – 1810), at the beginning of the nineteenth century. This German salesman developed into a painter of a new religiosity (‘die neue individualistische Religiosität‘; HÜTT, 1986), first in Dresden (1801) and later in Hamburg (1804).

rungeThe theme of the ‘Tageszeiten‘, as an expression of ‘Werden und Vergehen’, was central in his thoughts. In 1803 he made sketches and completed in 1805 a copper-etching of the ‘Morning’ (fig. 43 right). The fountains are shaped into flowers and a new day burgeoning from the earth. In 1808, just before his premature dead on the age of thirty-three due to tuberculosis, he painted an oil-painting of the same motif: ‘Der Morgen‘, kleine Fassung (109 x 85,5 cm) (fig. 44). The full cycle could not be completed due to his death in 1810.

Fig. 44 – Oil painting of Der Kleine Morgen (109 x 85,5 cm) by Otto Runge, 1808. Hamburger Kunsthalle.

The fourfold division of the day is moralized in a seventeenth century etching of Abraham Bach ‘Die Vier Zeiten dess Tages’ (fig. 45). Morning, afternoon, evening and night are depicted in four illustrations of the Holy family, with Josef, Maria and the child Jesus as leading figures in a rural and homely setting.

bach

Fig. 45 – The four times of the day: morning, afternoon, evening and night. A woodcut by Abraham Bach, around 1670. Germanisches Nationalmuseum, Nürnberg. The fourfold division of a twenty-four hours day is relatively little used by artists.

The distinction between the twofold division in day and night and the fourfold classification in morning, afternoon, evening and night is a matter of time-consciousness. This fundamental psychological human quality is important:  behavior, motivation and emotion are strongly intertwined with the time-perspective of individuals (LEWIN, 1942; WINNUBST, 1975).

A short time-perspective is related – according to FRANK (1939) – to an impulsive, naive and consumptive behavior, while a long time-perspective is correlated with preparatory and instrumental behavior, aiming at control over the environment. The time-perspective is – essentially – a matter of choice with regards to the fundamental region in division-thinking. A lower partitional approach (black-and-white thinking) results in a short time-perspective, while a higher partitional way (the fourfold way of thinking) gives a longer time-perspective. Oppositional thinking is characterized by easy-made and quick switches, while a consciousness of multiple parts requires more time to change.

This connection between time-perspective and division thinking has never been made in psychology – as far as I know – and deserves a further elaboration. A whole new, four-fold context of human existence could be described, leaving Freud’s two-fold, gender-based approach to psychological behavior as a historical relict.

The association of day and night with good and evil is very old and can be seen as a monument of two-fold thinking. In the North-European saga-world, as captured in the works of the Icelander Snorri Sturluson (1179 – 1241) the figure of Odin, is the messenger of the light and the good, opposite Ymer, the representative of the night. Odin kills Ymer and from his blood springs a race of giants (of which Loki is the most prolific). Loki personifies the bad habits and the weakness and is assisted by the wolf Fenris, who has to eat the sun.

The light, as the medium of the day, allows the observation of physical reality, the (visible) visibility. This quality is often rated as positive. The human being is in control. The night, on the other hand, makes observance difficult. Darkness is a form of (invisible) invisibility, which can only be appreciated on a spiritual level. It can evoke, from a material point of view, a sense of fear and is for that reason regarded as negative.

The antithesis between day and night – as a two-fold element – is part of the four-fold way of thinking. ROSENBERG (1961) pointed to an illustration of the ‘four birds of the day’, fighting with the bird of the night (the owl). The illustration is used in the ‘Dialogus creaturarum‘ (fig. 46). This popular work was published in Gouda in 1480 and had several reprints. The first English edition of 1511 was reissued in 1816 in London by Joseph Haslewood as ‘The Dialogus of Creatures Moralized’.

fourbirds1

Fig. 46 – The owl is attacked by four birds of the day. A woodcut from the ‘Dialogus creaturarum’; Gouda, 1480. This motif is commonly explained as strife between the good, represented by the four birds of the day and evil, portrayed by the bird of the night, the owl.

The little used symbolism and its explanation can be seen – in a four-fold context – as a derivative of the visualization of Concordance (or Harmony) between the one and the many, as birds coming from four directions. Albrecht Dürer applied the same motif – between 1509 and 1511 – in a woodcut, which was printed in Nürnberg (ROSENBERG, 1961) (fig. 47).

fourbirds2

Fig. 47 – The owl fighting with other birds. Woodcut from Albrecht Dürer (Nürnberg, 1509 – 1511). Four birds attack a central-seated, frightened owl from four directions. The traditional explanation, in a two-fold frame of mind, is a confrontation of the Good (the four birds) and the Evil (the owl). There are reasons to question this explanation, or at least to consider other possibilities. The owl  (associated with wisdom) is a symbol of unity, while the four birds (associated with imagination) represents multiplicity.

The trail to a more appropriate explanation starts in the publication of Alciatus’ ‘Emblemata’, where the birds are an expression of ‘Concordia‘. LEEMAN (1984) points to the evolution of the motif in the various editions between 1534 and 1614. In the edition published in Paris in 1534 are only two birds, but in the edition of the ‘Emblemata’ of Roville and Bonhomme (Lyon, 1614; XXXIX) are clearly four birds (fig. 48), with a strong reminiscence to the picture of Dürer.

fourbirds3

Fig. 48 – The different forms of the ‘Concordia‘-motif in various editions of  Alciates’ ‘Emblemata’ (LEEMAN, 1984). The illustration at the top shows ‘Concordia‘ as four birds of which one is crowned (Augsburg-edition, 1531). Their sharp claws have a distinct violent undertone. Some three years later, in the edition of ‘Emblemata’ published in Paris in 1534, the ‘Concordia‘-motif (bottom-left) is more symmetrical (and peaceful), with two birds on a square frame and a flock of birds in the sky. In the 1614 edition of Roville and Bonhomme in Lyon (bottom-right), the four birds are equally centered on the top of a sarcophagus, with a flock of birds in the far distance. The setting of the attacking birds reminds of the representation of Dürer’s four birds some hundred years earlier.

Four birds, but in a complete different setting, are encountered in a remarkable picture by William Caxton, the first printer in England. He gives an illustration of Evilmerodach, ‘a jolly man without justice who did  hew his father in pieces’. It shows four birds making fun with the extremities of Nebuchadnezar (fig. 49). No sign of Concordantia or Harmony here, rather the opposite.

fourbirds4

Fig. 49 – Evilmerodach cuts his father, Nebuchadnezer, in pieces: ‘Evilmerodach, a jolly man without justice who did hew his father in pieces‘. This woodcut is by William Caxtor, the first printer in England. The four birds are depicted as scavengers, and represent the complete opposite of concord and harmony.

The connection between (tetradic) space, the (four) winds and birds has always been a strong one in symbolic representation. In the Bibliotheque Municipale at Reims (MS 672, fol. 1r) is a manuscript of the so-called ‘False Decretals‘, written around 1180. The frontispiece showed the ‘Harmony of Spheres’ (fig. 50).

air

Fig. 50 – Harmony as the Goddess Air and as a symbol of unity in the four directions of space. Multitude and abundance are eminent in the nine-division of the muses. From a manuscript of the so-called ‘False Decretals’ in the Bibliotheque Municipale at Reims (MS 672, fol. 1r), written around 1180.

The goddess Air (Aer), with reminiscence to Christ, is placed in a syndesmos-posture, holding the winged winds: Aquilo, Oriens, Zephir and Auster. In the inner circle are three representatives of the spiritual world: Arion on a dolphin (symbol of literature), Pythagoras (science) and Orpheus (music). The medallions in the outer circle depict the nine muses according to Martianus Capella, who described them in a mixture of verse and prose in his popular ‘De nuptiis Mercurii et Philologiae’ (‘On the Marriage of Mercury and Philology’).

Harmony, as a concept, is related to the multitude. It is no coincidence that this theme emerged at the end of the twelfth century. The depiction of the nine muses is an indication of over-specialization in the tetradic way of thinking. The first signs of a teratological development are clear. The goddess Air has to hold its winds in a rather forced way, afraid – so it seems – that they may fly away.

The division of a day into morning, afternoon, evening and night is accepted as very common and the associated symbolism follows the four seasons: the morning (spring) is a new beginning and is a positive sign. The afternoon attracts the least symbolical value. It is a time of work and little reflection. In analogy, it is linked with the summer: the sun has passed its highest point, it is harvest time. The evening is the autumn of the day. The natural light is fading. The work is done. And finally the night, as wintertime, is a time of darkness, things coming to a halt. A time of sleep and entrance into a world of the unseen. However, it is also a time of expectation, of a new dawn and the trust in the cyclic recurrence of light.

BOHEEMEN, Petra, van (1986) De vorm van het gedrukte boek in de Noordelijke Neder-landen in de 16e eeuw. In: EKKART,  R.E.O. (1986). Het boek in Nederland in de 16e eeuw. Ter gelegenheid van de tentoonstelling “De eeuw van de Beeldenstorm”.  Rijks-museum Meermanno-Westreenianum, Den Haag. Staatsuitgeverij, ‘s-Gravenhage. ISBN 90 112 05234 3

ELSEN, Albert E. (1985). Rodin’s Thinker and the Dilemma’s of Modern Public Sculpture. Yale University Press, New Haven/London. ISBN 0-300-03334-6

FRANK, L.K. (1939). Time perspectives. Pp. 293 – 312 in: Journal of Social Philosophy, 4 (1939).

HAGEN, M.J. (1981). Zonnewijzers aan Hollandse Kerken. Pp. 3 – 23 in: Bulletin van de Stichting Oude Hollandse Kerken. No. 12.

HOFSTÄTTER, Hans H. (1965). Symbolismus und die Kunst der Jahrhundertwende. Verlag M. DuMont, Schauberg, Köln.

HÜTT, Wolfgang (1986). Deutsche Malerei und Grafik 1750 – 1945. Henschelverlag Kunst und Gesellschaft, Berlin. ISBN 3-362-00023-1

LEEMAN, Frederik W.G. (1984). Alciatus’ Emblemata. Denkbeelden en voorbeelden. Proefschrift ter verkrijging van het doctoraat in de letteren aan de Rijksuniversiteit te Groningen. 14 juni 1984. Bouma’s Boekhuis BV., Groningen.

LEWIN, K. (1942). Time perspective and morale. In: GOODWIN WATSON (Ed.) (1942). Civilian morale. Houghton Mifflin, New York.

PANOFSKY, Erwin (1939/1967). Studies in Iconology. Themes in the Art of the Renaissance. Mary Flexner Lectures, 1937. Oxford.

ROSENBERG, Jacob (1961). On the Meaning of a Bosch Drawing. Pp. 402 – 421 in: MEISS, Millard (Ed.)(1961). De Artibus Opuscula XL. Essays in Honor of Erwin Panofsky. Vol. I. New York University Press, New York.

WHITROW, Gerald J. (1972). What is time? Thames and Hudson, London. ISBN 0-500-01085-4

WINNUBST, J.A.M. (1975). Het Westerse tijdssyndroom. Conceptuele integratie en eerste aanzet tot construct validatie van een reeks molaire tijdsvariabelen in de psychologie. Stichting Studentenpers, Nijmegen/Swets & Zeitlinger B.V., Amsterdam. ISBN 90 265 0218 4

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