The ‘Tetractus’ age (1000 – 1350 AD)
The population of Europe increased after the year 1000. A kind of prosperity gave rise to the building of churches, monasteries and castles. A widening of the cultural outlook took place in this period, which was later described as the Romanesque style. PEVSNER (1943/1961, p. 54) put it as follows: ‘The most significant innovations of the late 10th century are those of the ground plan (…) caused by a new will to articulate and clarify space. This is most characteristic. Western civilization was only just beginning to take shape, but already at that early stage its architectural expression was spatial, as against the sculptural spirit of Greek and Roman art – and spatial in an organizing, grouping, planning way, as against the magic floating of space in Early Christian and Byzantine art’.
The (Romanesque) style form was modest and introvert, with all the characteristics of a growth process. The round and half-circle shape discontinued the fairly massive structures, which allowed little light into the interior. Light became an increasingly more important element when the size of the buildings increased.
The year 1000, as the start of the ‘Tetractus’-period, is more or less arbitrary. The year does not have a specific significance in history and one wonders if the inhabitants of Europe, at that time, even realized its numerological curiosity. The painting of the closure of the first millennium as a period of disaster and misfortune was certainly improper (ORTEGA Y GASSET, 1904; SWOBODA, 1979).
The Spanish philosopher ORTEGA Y GASSET (1883 – 1955) dedicated his dissertation – which could not be found, so we follow the authority of SWOBODA (1979) – to ‘the myth of the year 1000’. Ortega proved that the story of immanent disaster and fear originated in the seventeenth century and subsequently developed in the early nineteenth century into a historical ‘fact’. The Spanish philosopher later became known from his epoch-making book ‘The Revolt of the Masses’ (1930/1994). This book gave, maybe for the first time in (European) history, a description of a ‘Fourth Quadrant’ man, characterized by its visible invisibility.
The standard work over the historical situation around the year 1000 by Henri FOCILLON (1952) mentioned the apocalyptic images and a general feeling of ‘mundus senescit‘ and ‘un declin progressif de la civilation‘, but this apprehension of decline had already started with the disintegration of the empire of Charlemagne. The only ‘proof’ of a Doomsday-prediction was, according to Focillon, given by the Frankish monk Marculfe of Saint Denis. He wrote in his ‘Marculfi monachi formulae’ (or ‘Formularies of Mardulf’, c. 650): ‘Mundi terminum ruinis crescentibus appropinguantem indicia certa manifestant…’
FOCILLON (1952) observed that: ‘l’humanite de son temps avait été en proie, precisement à la veille de l’an 1000, a des terreurs collectives en motivées‘ (Mankind had been subject, towards the eve of the year 1000, to collective fears). There is no written record of a general ‘panic’ around the end of the first millennium: ‘n’en trouvions pas trace dans les actes officiel ou chez les chroniqueurs contemporains‘ (There is no trace in the official papers or in the writings of contemporaneous chroniclers).
In addition, the example of Beatus, abbot of Liebana (c. 730 – 798), in his ‘Commentary on the Apocalypse of St. John’ (written between 776 and 784 AD), was mentioned. This ‘Commentary’ was distributed from the different ‘scriptoria‘ (write- and copying establishments attached to monasteries) in north-western Spain: San Millan de la Cogolla, San Martin de Albelda, San Juan de la Pena and Santo Domingo de Silos (KLEIN, 1976) (fig. 139).
Fig. 139 – Santo Domingo de Silos (Photo: Marten Kuilman (1997).
Abbon of Fleury, born around 940 AD, was aware of apocalyptic predictions and warned for troubled times in his ‘Liber apologeticus’ (998). The monk and historian Raoul Glaber (c. 980 – c. 1046) put the history of France on paper during that time in his ‘Chronicle’. He was worried about the coming of the antichrist and put his faith in the ‘divina quaternitas’. The year 1000 had in his chronology a pivotal character, as a marker where the evil becomes visible. The attention of this critical point is, from a (quadralectic) division point of view, indicative of the two-fold way of thinking. The apocalyptic character (of the year 1000) was created in a sphere of opposition.
McGINN (1979) proclaimed that ‘the eleventh century did not produce anything new in the history of apocalypticism’. He blamed the French historians as the culprits: ‘French historians created a picture of wide-spread terror in Christendom at the approach of the year 1000.’ POGNON (1981) is more specific and pointed to the French historian Michelet with his suggestive observation, that ‘C’etait und croyance universelle au Moyen Age, que le monde devait finir avec l’an 1000 de l’Incarnation.’
The fanciful interpretations of history of the nineteenth century must be put in perspective. BRUGMANS (1952, p. 248) remarked that: ‘The romantic intuition was a new and outstanding scientific tool, and there is much truth in the words of Novalis (in particular in respect to Michelet): ‘When I think things over, it seems to me, that a historian should also be a poet, because only the poets are able to connect the facts in a proper way’. The present scientific method has abandoned such a poetical approach.
The objections against the alleged ‘Terreurs de l’an mille‘ started at the end of the nineteenth century. The Benedictin Francois Plaine wrote an article in 1883 in the ‘Revue des Questions historiques’ and Jules Roy drew, in his book ‘L’An mille‘ (1885), the conclusion that the Doomsday-character of the year 1000 was a hoax.
KNOWLES (1962) summarized the story: ‘the myth of a Christendom awaiting imminent dissolution in the year 999 and surging forward in relief in 1001 has been effectively banished from serious historical writing‘. Chiliasm, as the belief in a historical period of thousand years before the resurrection (Revelation 20: 2 – 7) and its supposed practical application in the year 1000 (or 2000?), indicated a belief in fixed divisions and boundaries.
This approach is typical for the thinking in opposites and extremes. A belief in the end of the world was not in line with the predominant mood in the early part of the Tetractus Age. The historic frame of mind was inclined to ‘understand’ the feelings of powerlessness in the face of hardships and miseries with where, indubitable, part of this historical period.
Works like the earlier-mentioned, anonymous ‘Tractatus de Quaternario‘ offered, in the eleventh century, the fourfold way of thinking as a cosmological model of consolation. Its conceptual image catered for individual and collective happiness and misery and was, conscious or unconscious, used by innumerable unnamed people to come to terms with their own existence in place and time.
The winds of change eroded the confidence in a balanced system a century later. This transformation is best illustrated in the life of Gerhoh of Reichersberg (1093 – 1169), abbot of the monastery of the same name in Germany (fig. 140). He experienced the immanent changes (in division-thinking) in his own lifetime and tried, in a last effort, to hang on to the established/conservative values, embedded in the Christian catholic faith before the struggle for worldly power.
Fig. 140 – Gerhoh of Reichersberg (to the right) kneels for bishop Konrad I of Salzburg. www.heiligen-3s.nl/heiligen/06/27/06-27-1169-Gerhoh-Reich…
Gerhoh was in his earlier works, like the ‘Liber de Aedificio Dei’ (1128), concerned with the problem of the multitude and the ‘libertas ecclesiae‘. His aim is the ‘Erfassung der vielgestalteten, insbesondere historisch-politischen Wirklichkeit, unter einheitlichem Gesichtspunt‘. (The generation of the multiform, historico-political reality from a unifying point of view) (MEUTHEN, 1959; p. 155). He followed closely the writings of Rupert of Deutz (who died in 1130). Gerhoh is more spiritually involved in his subject and is, together with Walther of St. Victor (died c. 1180) and Petrus Abaelard (1079 – 1142), one of the few exceptions in the use of passionate fierceness. This vehemence reflected the fear of a pessimistic mind, which feels unable to change the circumstances.
Gerhoh was interested – just like Rupert of Deutz – in the symbolism of the four horses (from the Revelation of St. John): (1) The red horse was the period of the Roman tyrants up until Diocletian. (2) The black horse was the period of disbelievers until St. Gregory the Great. (3) The grey horse indicated the hypocrites of his own time (twelfth century). (4) The pale horse – symbolizing the end of times -was due to come, possibly soon.
Gerhoh of Reichersberg’s historical writings showed a concern about degeneration and decline. The support of the fourfold way of thinking slips away in his expectation of the worst. At the end of his life – with nothing left to loose – he wrote his ‘ultimate’ book under the title ‘De quarta Vigilia noctis’ (1167)(The four watches of the night). The theme is the Biblical story of Jesus’ walking on the water (St. Matthew 14 : 22 – 33; St. Mark 6 : 45 – 52; St. John 6 : 16 21) in the fourth watch of the night.
Gerhoh conveyed the synoptic account of the miracle into a four-age pattern of the Church and distinguished four periods (quadrants) in history. The story of the enjoyment of power and materialism of pope Gregory VII, and his conflict with Henry IV (1056 – 1106) – which was relevant just before his lifetime – became known as the Investiture Controversy (HEER, 1961; McGINN, 1979). The nature of the schisms – due to ‘Habsucht und Hochmut‘ (avarice and arrogance) – grew into serious disruptions. The twenty-seventh schism of 1130, under Pope Innocent II (fig. 141 left), was a relative minor one, but the twenty-eighth schism of 1159, under Pope Alexander III (fig. 141 right), lasted for five anti-popes.
Fig. 141 – Pope Innocent II (left) and Alexander III (right) were in the holy office during turbulent times in the Roman Catholic Church, when the church got involved in a power struggle. Illustrations from Francois DUCHESNE (1653). Histoire des Papes et sovverains chefs de l’eglise. (Deux Tomes). Jean Roger, Paris.
Further political involvement became clear, when the papacy moved to Avignon in 1309 and remained there for some seventy years. The city of Rome was governed in the meantime by lawless nobles. This period ended when pope Urban V returned to Rome in 1367 (because the Anglo-French war made France unsafe). Local Roman politics was still too strong, and he returned to Avignon shortly before his death. Now the forces of a weakened France and a stronger Italy came to clash. The Great Schism started in 1378, with both parties choosing their own pope: Urban VI in Rome and Clement VII in Avignon. The schism was only healed at the Council of Constance in 1414.
Gerhoh of Reichersberg interpreted the parable of the ‘Watches of the Night’ as a four-fold historical model (MEUTHEN, 1959; p. 129):
THE FOUR WATCHES OF THE NIGHT
1. first watch – martyrs triumph over persecution;
2. second watch – holy confessors’ triumph over heretics;
3. third watch – struggle of the holy preachers of morality
(like Gregory the Great, pope between 590 – 604 AD)
4. fourth watch – new avarice in the city of Rome.
God assists believers in the first three watches, but in the fourth watch (avarice) there is no aid. This representation was linked with a world view as expressed in the Revelation of St. John (Ch. 8), where one quarter of a circle is black (fig. 142).
Fig. 142 – A square in a circle as a concept of a tetradic world view. One quarter of the circle is black, referring to a text in the Revelation of St. John dealing with the seven seals. This is the upper part of an illustration in the Saint-Pierre de Roda Bible, Bibliotheque Nationale, Paris. In: DURLIAT (1963).
The ‘Tetractus‘-age (1000 – 1350) was a time of transition, reflected in the definition of two cultural style groups: the Roman and the Gothic. This is not the place to elaborate on their specific features, but some references will be made to their position within the history of division thinking.
The denominator of ‘Roman art’ was first made by Auguste le Prevost in 1819 (SALET, 1968; p. 210) in a wide ‘romantic’ setting: ‘il englobait toutes les architectures et toutes les manifestations plastiques depuis la fin de l’empire romain jusqu’a la naissance de cet art gothique que l’on appelait alors ogival‘ (it encompasses all architecture and all sculptural display from the end of the Roman empire until the birth of the Gothic art which was then called ogival (typified by the ogive or lancet arch). This definition circumscribed in its widest sense, all the cultural means of expression between 500 and 1200 AD (fig. 143).
Fig. 143 – Some of the many Roman(esque) tetradic motifs, which were used as ornamentation on various items in Germany and France. 1. Enamelled copper reliquary chest of Emperor Heinrich, twelfth century. The four medallions depict the saints St. Mauritius, St. Sebastian, St. Eustachius and St. Gereon. The ‘Hundorp Chest’ from the Gudbrandsdal Valley in Norway has eleven similar enamel plaques that show Christ, saints and the symbols of the Evangelists. They were made in Limoges in the mid thirteenth century. 2. A tombstone from Cluny, twelfth century; 3. Roman frieze and copestone; 4. Different Roman ornaments. In: GODEFROY (1912).
The timing of the first denomination of the ‘Roman art’, as a cultural entity is important for the present (quadralectic) approach. The classification was given at a time when the European history entered a new phase around the year 1800. Apparently there was some sort of instinctive connection between the expression of the ‘l’art romain’ and the sentiments at the beginning of the nineteenth century.
The boundary between the Roman (or more precise: the Romanesque Style from c. 1000 – c. 1200; PEVSNER, 1943) and Gothic period is difficult to draw, just like the historic change from the four- to the three-fold division as a cognitive guideline. SALET (1968) puts the beginning of the Roman(esque) period, after careful considerations, in the year 1000 (‘enfin admettons que la periode romane commence vers l’an Mil‘ – let us at last acknowledge that the Roman period starts towards the year 1000). The end of the style period is even more difficult to establish (‘il est tout a fait impossible d’affirmer a quel moment finit l’art roman‘, p. 211 – it is quite impossible to indicate when the period of the roman art ends).
The complex character became clear in the definition of the ‘beginning’ of the Gothic style. Architectural features between 1130 and 1140 indicated, in the surroundings of Paris, the first overtures to a new style. These specific features developed in the countryside only in the second half of the twelfth, the thirteenth and even the fourteenth century.
The year 1200 is therefore a rather arbitrary historical marker. However, it is within a wider context of the architectonic field still the best option. The precision, like any definition of historical boundaries, diminishes when more knowledge of the events and features around the actual marker point comes to be available.
SALET (1968) referred to the ‘round’ and ‘lancet’ shape of arches as the typical representatives of the ‘Roman’ and ‘Gotic’ style, and the difficulties which occur by the implementation of these architectonic elements. At close scrutiny, there are several ‘arts romans’: ‘On a peut-etre eu tort de mettre une seule etiquette sur des manifestations extremement diverses‘ (Maybe one has wrongfully labeled all these different representations under the same name).
It is the prerogative of the specialist to expose ‘romantic’ ideas about historic divisions – that is to say: born in a spirit of higher division-thinking – and bring them back to a factual world. Even so, it must also be known, that the scientific appraisal is just one way to approach historical reality. There are other ways, and other positions as an observer, which are not necessarily less valuable.
‘The most significant innovations of the late 10th century are those in the ground plan’, said PEVSNER (1943, p. 55), ‘…and all caused by a new will to articulate and clarify space.’ ECKSTEIN (1975; p. 87) expressed the complications in the transition of Roman and Gothic art as lines and (cross)forms change gradually in place and time (fig. 109): ‘It is noteworthy that in the Romanesque epoch central spaces were build, either in the form of rotunda or as an application of the Greek cross – one has to remember the Saint-Front in Perigueux – but that these experiments were rather uncertain. The constructive powers were far more concentrated on the development in a longitudinal direction, which created, in particular in combination with quadripartition, transept and galleries, the fabulous complex spatial buildings which remained the main theme in the gothic epoch in North-western France and Britain.’
Life became harsh in the fifty years towards the end of the ‘Tetractus‘-age (1350). Failure of the harvest led to famine and when Europe lost about one quarter of its population in the plague, it was a time of crisis. In certain areas was a genuine feeling of desperation, which was stronger and more outspoken, then the alleged crisis around the year 1000. The obvious weakness of the Church to avoid or alleviate this disaster had far-reaching consequences, which laid the roots for the diminishing power of the church.
Dante Alighieri (1265 – 1321) touched the spirit of the time in his ‘Divina Commedia‘ (Divine Comedy), a three-parted vision of heaven, purgatory and hell. He encountered in his wanderings through heaven – assisted by Vergil – the twelve chosen one’s in the Fourth Heaven – the place of the wise man: St Thomas of Aquinas, Albert the Great, Gratianus, Petrus Lombardus, Salomon, Dionysius the Areopagite, Orosius, Boethius, Isidore of Seville, Bede, Richard of St. Victor and Siger of Brabant. They were, more or less, the heroes of tetradic imagination. Dante paid homage to them, because these persons contributed to the propagation of a balanced and differentiated view, which could be called wisdom.
The thirteenth and fourteenth century saw a gradual parting of the unknown as a thriving force of understanding in favor of a more stringent and economic use of the known. Arithmeticians set out to map the invisible parts of the mind in geometric terms. Leonard of Pisa started the new trend with his ‘Liber Abaci’, written in 1202 and revised in 1228 (ROSE, 1975). He applied the works of Arab scholars like Al-Khwarizmi and Abu-Kamil. Alexander of Villa Dei (who died in 1240) put his thoughts on paper in a ‘Carmen de algorismo‘. About that same time Jordanus Nemorarius wrote his ‘De proportionibus’ and ‘Algorismus demonstratus’. More lasting influence came from John of Holywood (Johannes de Sacrobosco)’s book ‘Algorismus vulgaris‘, written in Paris around 1250 (EVANS, 1977).
The arithmetical notion found an ever-increasing number of supporters in the fourteenth century: measurability gave a new form of security (which the belief in God no longer could offer). The Englishman Thomas Bradwardine, and his ‘Tractatus de propotione velocitatum’ (1328), was an example of the new type of scholar. The ‘Ars mensurandi‘ were a much-discussed topic in the intellectual circles in the period between 1350 and 1360. LEFF (1976, p. 10) made the following statement: ‘It is striking that greater advances were made in the fourteenth century in mathematics, physical theory, and logic than at any time in the Middle Ages before or after, that is to say, in the interval between the abandonment of the embracing systems to which all knowledge had tended to be subordinated and the congealing in the fifteenth century of the new conceptions which had succeeded the older ones in the fourteenth century.’
Central figure in this development was the Frenchman Nicole Oresme, born between 1320 and 1325 and died in 1382 at Caen. He is buried in the cathedral of Liseux, where he was a bishop during his lifetime. Besides his clerical duties, he studied the planetary theories as part of a greater understanding of communication.
Oresme wrote an ‘Algorismus proportionum‘ and his main interest was in the mathematical treatment of the movement along a circle. The ‘circulatio‘ is concerned with the concentric movement of objects and their relative distances. Oresme used the geometry of the circle-movement in several treatises as a measure for the intensity of mutual approach (CLAGETT, 1968).
Fig. 144 – This illustration by Oresme is one of the oldest known diagrams of the changes in latitude (vertical division) of planets in relation to the longitude (horizontal division). From MS 14435, Münich.
Oresme developed a rational communication model. He produced one of the first diagrams in European scientific literature (fig. 144). His ‘Tractatus de commensura-bilitate vel incommensurabilitate motuum celi’ (GRANT, 1971) dealt with the convergence of celestial bodies in a cyclic model. He drew the conclusion, that the cosmic movements were unpredictable. Or, as given in his ‘Ad pauca respicientes‘ (Prop. XIX): ‘One does not know (on forehand) if the movements coincide or not; and if one does not know the previous history it is impossible to know the continuation’.
Oresme gave prominence to the invisible invisibility (in the quadralectic way of thinking). He rejected in the same spirit the scientific merits of astrology. He tried – in his ‘Livre de Divinacions’ (Book on Divinations) – to convince the stargazers that the smallest degree of uncertainty in the course of heavenly bodies was enough to weaken any prediction based on the stars and their mutual positions (COOPLAND, 1952).
Johannes de Muris (c. 1300 – c. 1350) wrote in the same period, around the middle of the fourteenth century, a ‘Quadripartitum numerorum’ (1343). The first book (‘De Unitate‘) gave a summary of the work of Boethius. It followed the general trend in which Boethius is seen as the authority in this field: ‘L’arithmetique speculative au Moyen Age est fondée sur l’Arith-métique de Boèce‘ (The speculative arithmetic of the Middle Ages is based on the arithmetic of Boethius) (L’HUILLER, 1990).
The bulky second book of the ‘Quadripartitum numerorum‘ deals with the number theory (like subtractione fractionum, multiplicatione fractionum novem modis, and divisione fractionum novem modis).
The third book discussed the relations (ratio) and algebra according to Al-Kwarizmi. This book was followed by a list of forty-five questions and a ‘semiliber‘. The fourth book is a compilation of different kinds of subjects, mostly derived from the ‘Liber Abaci’ (1202) of Leonard of Pisa.
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