12.4.1 Prelogical Reasoning
The man of the middle Ages was Christian. It was from the dogma as starting point that he tried to understand the world. The Roman version of the dogma was a stable entity with fortunately many points to define. The Catholic frame was given but this did not mean that everything was given with it.
220.127.116.11 Richard of Saint Victor
This mystic Scottish monk analyzed the Bible and attributed a hidden sense to the text. Since the Church never rejected the Old Testament, some texts had to be interpreted. For example the Song of Songs had to have, according to Richard, the sense of union of the Church with the Creator, especially at a time when Hildebrand was fighting the mariage of priests. Other texts were interpreted in the same vein: Lia and Rachel, the two wives of a bigamous Jacob (Gen. 29:15-30), meant Fecundity and Beauty. The children of Jacob meant different levels of mystical experience.
The important point is not what Richard found but his coherency of thought, which was logically articulated. Richard had a scientific preoccupation to understand with exactitude what happens in a man’s mind on his way to ecstasy. He rationalized experience that seemed beyond rationalization. The necessity felt by Richard to interpret the Bible indicates that this book began to be read and followed literally by integrists.
18.104.22.168 Saint Anselm
This Italian became the Primate of England in 1099. He achieved in Canterbury his treatise “Cur Deus Homo” (The Incarnation of God: Why God a Man). From the outset, the author states his preoccupation to demonstrate that man was made to enjoy immortality, as if Faith were not existing. This Truth, claims Anselm, can be deduced through objective reasoning, as if we ignored the existence of Christ.
The Primate of England is Christian and the Dogma is not put in question but, whereas his soul needs no philosophy, his intelligence demands one. For Anselm, if there appears a contradiction between reason and faith, then reason is at fault. However, Anselm made his demonstration precisely because “strong minds”, i.e. libertines, had appeared who did not believe that the will of God should have the last word when reason seems to contradict it. The answer of Anselm did not rely on arguments of authority but proceeded with reason alone; he fulfilled the Western need to rationally verify its beliefs.
The Primate of England was in constant opposition to the king of England, who indulged heavily in the selling of ecclesiastical preferments, i.e. simony. As a result, Anselm spent much time at Cluny. Anselm is one of the founders of Scholasticism, further developed by Thomas. One may anachronically sneer at scholasticism, oblivious of the situation that existed at the time. Cluny attempted to humanize the Western civilization and largely succeeded, with unforeseen consequences. Cluny had promoted the education of children: the teaching was dispensed in the abbeys 11, free of charge. Cluny also promoted the social elevation of women, by allowing aristocratic widows to create convents. The women of the aristocracy usually married young, against their will, warriors who quite frequently died in combat, leaving widows in the mature force of their mental and physical capacities. The widows created beguine convents (beguinages). A beguinage consisted in a wall-enclosed neighbourhood of several hectares within a city, occupied by widows and singles who had taken transient vows : they could leave the beguinage during the day, receive visitors within their house but only during the day and could abandon their vows and rejoin the outside world as they wished. Clemens V, the French pope in Avignon, resented this unacceptable freedom and forbade the founding of beguinages. In the northern parts of Christendom, i.e. what is now the Benelux and the West of Germany (Aachen, Cologne), he was ignored and beguinages flourished well within the eighteenth century. Elsewhere, widows eagerly founded or else joined Clunisian convents as soon as they had gained their freedom because these Clunisian convents were harbors of civilized behavior totally protected against any encroachment by either the religious Hierarchy or else the local political powers. Needless to precise that chastity was not their main concern. These refined women brought their possessions with them. Cluny, finally, favored technical and managerial gifts at least as much as contemplative piety. This preoccupation with practical applications fostered a spirit of Logic, dispensed to anyone who cared to follow the teaching. The whole Clunisian movement disrupted the social and mental stratification of that period. Cluny faced two problems: on one side, integrist ascetic Cistercians had appeared within the Clunisian ranks, who favored violence to defend the Faith with all means at their disposition, including murder, and on the other side, strong minds, i.e. libertines, began to question the compatibility of Faith with Reason. The scholasticism developed by Anselm was an attempt to conciliate Reason with Faith in a humane approach.
The conflict between the dogma and the exigencies of reason flared up in the middle of the 12th century. The Cistercian Bernard of Clairvaux defended the Dogma. This vigorous, active monk opposed a scholar, the Norman theologian Abelard, whose main ambition was to find the truth and thereby gain the applause of his students, at the risk of being deprived of the comfortable life rulers grant to their faithful servants.
In the eyes of Bernard, Abelard was much worse than the heretics, schismatics and infidels he relentlessly persecuted all his life. And indeed Bernard was right in his judgment because both antagonists were not belonging to the same world. Abelard was the first of a new race of half-starved but free intellectual adventurers willing to pay for their freedom with shocking poverty and loneliness. He was, in all senses, a modern intellectual, saying in his preface for “Sic et Non” (Yes and No, written in 1122): “this is the first key to wisdom: an assiduous or at least frequent interrogation. Because it is by doubting that we arrive at investigation and it is by investigating that we grasp the truth”. In the midst of Christendom totally relying on Faith, such a position could not be held durably without repression. This type of man, who followed his own logic, who recognized no master but himself, could not live at that time because he had lost the sense of the sacred, had reduced the Dogma to a rational concept and Mystery to a philosophical phenomenon. The inadmissible error of Abelard was to question.
Abelard did indeed debate questions that created confusion and doubt about our Mother the Holy Church. For example “that God knows everything, et contra”, “that one should believe in God only, et contra”, “that nothing happens against the will of God, et contra”.
In a great debate in opposition to Bernard, he left the floor to Orthodoxy, which won the day. Abelard indeed could not push his reasonings to their final consequences. He was a Christian and had no desire to appear a heresiarch, with all its consequences, while crusades were going on. For the Hierarchy, what was most dangerous were not the conclusions reached by Abelard, it was the way he was thinking which was redoubtable. The Dogma, the supreme reference point, was questioned. Abelard retired to Cluny. But the authority of Cluny, under the three-pronged assault of libertine reasoning, internal Christian integrism and simoniacal practices, began to decline.
Following Abelard (died 1142), systematic doubt continued to advance in the conscience of men through the works of Francis Bacon (died 1626), for whom “a fact is more important than a Lord Mayor”, and the advice of Descartes (died 1650) to doubt.
22.214.171.124 The rise of militant orders
The Benedictan rule was formulated for the pioneer cenobites at mount Cassino around AD 529. This was still during roman times and the Benedictine abbey looked less as a house of prayer than it did a richly adorned, colorful roman villa. It was an agricultural colony fully autonomous for the survival of an isolated community that produced everything necessary: fields of graminaceae for bread, gardens for fruit and vegetables, ponds for fish, sheep for wool, leather for sandals and manuscripts, wood for furniture, and what have you. The Benedictine abbey was a closed economy, with nothing produced in surplus. Many monks were not working but administered the goods and directed the work of serfs. The Benedictine abbey Cluny was founded in 910 and depended directly from Rome. It became extremely rich and was richly adorned (see fig. 12.7). The sack of the abbey by the French revolutionaries started with the guillotination of 6 monks and the looting of the silver (116 kilos) in 1791. The destruction of the buildings started in 1793 and was achieved in 1815. Practically nothing subsists of an abbey that was the glory of Christendom and of civilization.
Figure 12.7. The stained glass of Cluny was destroyed in April 1798. The Sainte Chapelle in Paris is not a Benedictine abbey. It was built in 1243 as a giant reliquary for the precious relic of the Crown of Thorns, brought from Palestine to Paris in 1239. The French Revolutionaries spared the Chapel.
Figure 12.8. The baroque style as understood by Cistercians: inside view of a Cistercian church build during the 17th century in Bruges. Sculpture, color, stained glass are kept to a minimum.
Stained glass, abundantly used at Cluny, is a way of painting on a monumental scale with colored light. The earliest stained glass windows go back to the eleventh century. Here, we have Asianism, the curvilinear style, at its best. Integrist movements will attempt to suppress the glorification of God by rich adornments. In Christendom, the “iconoclasts” took an extreme position and destroyed large portions of representational art and color.
The rule of Benedict consisted more in general directives than in severe definitions of monacal conduct. He had adapted his monastery rules on those followed in Roman family life: the abbot was the pater familias of the community and the arbiter who said the law. When the family grew too numerous, a daughter abbey was founded, but the new family so created was independent and autonomous.
Time and human weakness confronting immense richness and an easy life induced accommodations with the rule and called for reforms, which were quite regularly enforced. In 1112, St Bernard made his entry in the Benedictine abbey of Citeaux, with 30 companions. He advocated poverty and asceticism, stamped art and color out of the buildings (fig. 12.8), imposed complete isolation of the monks and imposed work. Their exploitation of natural resources diverged in substantial ways from the Benedictine model.
Outside the hours of communal praying, the Cistercian monk was in the fields, silently working. And arduous work was needed because the Cistercians choose by preference arid lands, which had to have a river, lake or whatever source of water indispensable to develop it. The Cistercians admitted lay brothers to help them in this work, but no serfs: all serfs working on the premises became lay brothers and were therewith automatically freed. The concern of the monks for agriculture was extraordinary and they succeeded in transforming deserts (e.g. the Belgian coast) in highly productive lands. Since all monks had to assemble every day for prayer, settlements that lay further than a day’s walk were not possible: their domain was homogeneous, with lay brothers working the outermost laying fields, whose duty it was to rejoin every Sunday the abbey for attendance to mass.
Cistercian abbeys sprang up like mushrooms and became extremely rich because the links among them were very strong and intense exchange of know-how in agricultural and artisan practices, as metallurgy, hydraulic works, wind mills, ship building, swamp draining, wine and beer making etc. took place. The numerous brands of excellent Belgian beers made by Cistercians (trappists) is traced to this willingness to exchange information. The Jesuits will adopt the same policy of sharing when they developed very successfully the Guarani Republic in Paraguay.
Very rapidly, surplus goods were produced, which went on the market in exchange of goods not produced by the abbey, and immense incomes ensued.
The order of the Dominicans was founded in Toulouse in 1206, to combat the Cathartic heresy. The Dominicans are not attached to an abbey nor do they work. They are a begging order exclusively devoted to study and predication of the Evangel. Other orders whose style diverged in a considerable manner from that of the Benedictines were the knights’ orders, as the Teutonic order, the order of St John and the order of Templars. These orders were a product of the crusades. The monks took the normal vows and, in addition, made the promise to fight the enemies of the Church with military means. They also maintained hostels and hospitals. They became so rich that Philip the fair of France confiscated the goods of the Templars.
The integrist tendency introduced by Bernard was a disaster for ancient art. The destruction of classical art is usually traced to barbaric invasions but it took also place on a large scale at the end of the Middle Ages, when pagan temples began to systematically provide construction material for new Christian buildings. The knights of St John destroyed the mausoleum of Halicarnasse in 1403; Pope Pius II destroyed the Coliseum in 1460. In 1624, Bernini lifted enormous bronze beams from the roof of the Pantheon, a structure that had survived the sack of Rome by barbarians (fig. 12.9), to include them into the bronze pillars that formed the baldacchino in St Peter’s cathedral (fig. 12.10).
Figure 12.9. The Pantheon, Rome, erected by Hadrian c. 118-128 A.D. A vast dome covers a rotunda 43.6 meters in diameter. The Pantheon was built as a single monumental structure. The dome could be built because the Romans had invented concrete, which allowed construction feats forbidden to the Greek architects.
Figure 12.10. The baldacchino was made by Bernini in 1642. It is a masterpiece of bronze smelting and a masterpiece of sculpture, perfectly in harmony with the interior of St Peter’s cathedral. Only the pope, according to Urbain VII who commissioned the work, is allowed to say mass under the baldacchino.
Whereas preservation measures began to be taken in Christendom as early as 1471, when Sixte IV began the collection of the antique sculptures of the Capitol, destruction went on: the Turks transformed the Parthenon in a mosque and fully destroyed the art objects and buildings of Byzantium while the Venetians, who had themselves also looted Constantinople two hundred years earlier, bombed the Acropolis in 1687 because the Turks used it as an arsenal. The iconoclasts in Europe destroyed paintings and sculptures, Orthodox iconoclasts disfigured the personages of wall paintings (fig. 12.11), the French revolutionaries took pride in destroying their Christian heritage, and the Allies destroyed Monte Cassino in 1944.
Figure 12.11. Mural painting in the monastery of the Pantanassa, Mistra (Greece). The monastery was founded in 1426 and is still occupied today by orthodox nuns. The mural painting “Entrance in Jerusalem” (fragment) had the personages disfigured by iconoclasts.
Calculus is the spearhead of Western dominance over the world. Engineers, chemists, physicists and managers able to apply to machine building, products synthesis and management of human work forces the mathematical tools developed by the mathematicians, forged its supremacy.
The Mayas were masters in mathematics, which they applied essentially for the elaboration of calendars. The savagery of their culture prohibited further developments in technology. Hellas took the direction of rational behavior and technological progress. Its ultimate failure may be traced to inherent political weaknesses, to the destructive activity of the Hellenistic successor states and to the final blow inflicted by Rome, but the refusal of the Greeks to develop calculus was also a reason for their downfall. The Greeks had developed a Geometry that was dedicated to the study of static structures, applied to the creation of architectural designs. In addition, barely emerging from a culture of assertive creeds, they aimed at a communion with nature and at natural laws that show harmony. Hence their inclination to study “perfect” shapes and forms, as the cube, the sphere, the square and the circle and attribute erroneously to celestial bodies movements that espouse these forms.
The Greeks never developed the mathematical tools needed to analyze movements. Their failure to develop mathematics, even if the achievement of Archimedes was impressive, resulted in the downfall of their civilization, accomplished by Rome. Archimedes had devised the war machines needed to keep the Roman enemy at bay but it was not enough: he himself was killed when Syracuse fell, and the Romans adopted for additional conquests the war machinery devised by the Greeks. Rome imposed a cultural regression from which we have fully emerged only in the 18th century. Descartes still conceived mathematics as the study of static, geometrical structures. Pascal was a mathematical genius who, in his discussions with Leibnitz, indicated to the latter the path needed to analyze movement in a mathematical spirit, by integrals. This heralded the beginning of the dominance of the West.
126.96.36.199 The first developments in arithmetic
Humans have had an enormous difficulty in mastering addition. Contrary to parrots, which can count up to twenty, primitive human cultures were unable to count beyond one: more than one was “many”. The mental process for the mastering of addition improved in the course of time. Today, the Siriona Indians of Bolivia and the Brazilian Yanoama people count one, two, three, many.
Improvements 12 in the mental operation of adding numbers were introduced by stringing numbers in a row. The Bacairi and Borobro people of Brazil count one, two, two and one, two and two, two and two and one, etc. This is the binary system. Cro-Magnon man and primitive Greeks apparently counted by groups of five, i.e. the number of fingers of a hand. This is the quinary counting system. Babylonians counted by groups of tens and sixty, Celts apparently had a vigesimal number system, still discernible in that the French say “quatre-vingt-dix”, i.e. four times twenty plus ten, for ninety. Today, the decimal system is widely used but different cultures use it in different ways. For example, the Malawians indicate 100 by shaking their two fists twice. They thus use a logarithmic system of calculation, which Europeans never achieved. For Westerners, hundred is indicated not by ten fingers shaken twice, i.e. 102, but is ten times ten : the two open hands are shaken ten times. Ninety means nine times ten. We use the decimal system regularly but count sometimes also in other systems: the days are counted on base seven, the angles are counted on base 60, the hours and the months have a base 12 as does the counting of eggs in local markets. The best systems are the ones based on 12, because this number is divisible by 2, 3, 4 and 6, and the binary system, not based on “one and two” but based on “zero and one”. This binary system is universally used in computers.
A second challenge was the way numbers are written and named. The easiest and also the most primitive way to write them is by drawing lines. One would be 1, two would be 11, three would be 111, and ten is 1111111111. Such a system of recording numbers cannot go on indefinitely; numbers are best associated in groups and different signs are introduced to denote different groups.
The Sumerians and Babylonians used a mixture of decimal and sexagesimal counting system, where the number one is noted as a wedge Y, the number five by an assembly of 5 wedges, ten is represented by a hook (‹) and sixty is noted by a bigger wedge, i.e. Y. The Babylonians used different sticks to imprint these numbers in soft clay. Like us, they wrote numbers from right to left. Seventy-two was written: Y‹YY (sixty, ten and two). They put initially emphasis on size and the only difference between 62 (YYY) and 3 (YYY) is the larger first wedge. This system led to utter confusion until the place where the wedges were written stood for their value (multiples of 60). This was a genial improvement because the size of the signs lost significance: large or small, YYY YY meant 182 (3 times 60 and 2), Y ‹YY meant 72 (60 plus 10 plus 2) and YYY ‹‹YY meant 202 (3 times 60 plus two times 10 and 2). Larger numbers were written with three positions. For example 3,661 is written Y Y Y i.e. (1 x 60 x 60) plus (1 x 60) plus (1). However, YYY remains three. One sees how confusion arises. This system is approaching ours, based on logarithm ten, where 3,661 stands for (3 x 10 x10 x10) plus (6 x 10 x10) plus (6 x 10) plus 1. A final improvement of clarification, introduced by the Babylonians around 700 BC, was to mark the separations, the spacings, with a special sign standing in effect for “nothing in this column”. To this effect, we use the sign zero (0). The Babylonians ignored the existence of zero and used a double slanted edge (GG), which was however never used at the end of a number because it made no sense there. So, in their system, 125 was noted YY YYYYY: (2 x 60) plus (5) whereas 7,205 is noted YYGGYYYYY: (2 x 60 x 60) plus (no 60) plus (5). According to Kaplan, the late Babylonians of around the IIIrd century BC used zero.
188.8.131.52 The achievements of the Greeks
The Achaeans of Homer’s time counted l, ll, lll, llll, for one, two, three and four, and used the first letter of the words designating numbers, as Pi (P, pente in Greek) for five, ? (D, deka in Greek) for ten, and ? (H, hekaton) for 100. In their system, 318 was written: HHH ? ? lll (i.e. 3 times hundred, 1 time ten, one time five and three times one. This rustic system was also the one used by the Romans: in Latin, the number five is noted V (i.e. the half of ten, X), the number ten is noted X, the number hundred is C (which stands for cente), five hundred is D and thousand is M (mille). For example, the number 1234 is expressed in the Roman notation as MCCXXXIV, i.e. one time thousand, two times hundred, three times ten and one time one taken from five. You note that the number 4 is expressed as one minus five (IV). If one had wanted to express the number six, it would have been written VI, i.e. five plus one, and 1236 is then MCCXXXVI. The number 1036 is written MXXXVI. No positional notation, which makes this notation more primitive than that used by the late Babylonians. In our decimal positional notation, the number 1234 is one time 10 x10 x 10, two times 10 x 10, three times 10 and four times one; 1024 is one time 10x10x10, no time 10×10, 2 times 10 and 4 times one.
The Dorian invasion of Greece, initiated around 1200 BC, created in 800 BC an alphabetic script after the Phoenician alphabet, which heralds the beginning of the Hellenic civilization. Commerce and colonization of surrounding lands began in 775 BC. The colonization was essential for the subsequent development of a scientific spirit rooted in the concept of individual liberty: whereas Athens resisted this development, going as far as forbidding the study of astronomy, enlightened and progressive scientists poured in from the colonies: Pythagoras, Anaxagore, Empedocle, Democrite, Hyppocrate originated all from the colonies. Aristotle was Macedonian, condemned to death by Athens.
In 500 BC, numbers are linked to the Greek alphabet: alpha (a) stood for 1, beta (b) was 2, gamma (g) was 3, delta (d) was 4. Iota (i), the tenth letter of the alphabet, was ten and the following letter, kappa (k), stood for 20, lambda (l) for 30, mu (m) for 40. Omicron (?-o), stood for 70. Tau (t), was the twenty-first letter in the alphabet and represented 300. The majuscule of the letter mu, (?), stood for 10,000, i.e. a myriad. To distinguish words from numbers, the numbers were with a bar drawn over them. There was no positional notation and no symbol for zero. The Greeks discovered the usefulness of zero when they occupied Babylon during Alexander’s conquest, in 331 BC. It is indeed during the third century BC that the symbol 0 for zero appears in Greek astronomical papyri. Curiously, it remained restricted to their astronomical writings. The merchants, who used counting boards, did not need it: the absence of counters in a column was sufficient for their calculations, which could be visually followed. Counters representing zero were superfluous and not needed.
The Greeks were perfectly able to master the concept of zero, yet, although they knew it, they declined to apply it. We have here our next challenge, which is theological and philosophical. First of all, nothingness is impossible to imagine. If the reader attempts it, we may be almost certain that he imagines it black. Secondly, in an emerging civilization as the Greek, the tendency was to find harmony in nature as well as a communion with it. Pythagoras had founded a sect in the VIth century BC that claimed to find in numbers such a harmony. Hence the rejection of irrational numbers and of course also of the concept of nothingness. Pythagoreans, around 450 BC, announced the theory of the atomic constitution of matter. Matter was, they said, composed of indivisible atoms, which were eternal. This find was remarkable because, as late as 1870, there was hardly any direct experimental evidence for atoms. This concept, which re-emerged in the West only in the seventeenth century, denied the creation of the Universe from nothingness. The Pythagorean sect was active well within Roman times. Their contribution to the progress of science, as well as that of other Greek scientists living between the VIth and IIIth century BC, is undeniable and considerable. Science, i.e. the understanding of natural phenomena through intelligence and logic, was extraordinarily developed in ancient Greece, and the level reached by them in all fields, astronomy, medicine, anatomy, architecture, geometry was reached again only in the seventeenth century, in Europe. One essential motive of Greek progress in medicine was their agnosticism. The abandon of the intervention of gods and devils as the cause of disease allowed the emergence of a medical science based on observation and inference.
However, the Greeks had a fatal weakness in the handling of mathematical concepts. Archimedes, who was born and lived in Sicily, and was killed there in 212 BC at the age of 75 by a Roman soldier, was a scientific genius. He mastered huge numbers in an extraordinary way yet he never used the number zero despite the fact that he knew of its existence and use by the Babylonians in astronomical measurements, and proved unable to meet the mathematical challenge of limits and infinitesimals. After him, excellent Greek scientists continued to work in Alexandria but the essential progress needed in mathematics, i.e. the concept of zero, of infinitesimals, of irrationals and of limits, eluded them although they were fully aware of the shortcoming of their mathematical tools, pointed out to them by Zeno, born in 490 BC.
The paradox announced by Zeno is well known: if the fastest sprinter of all times, Achilles, puts up a race with a tortoise with a handicap of, say, a meter, Achilles will never catch up with the lumbering tortoise. To demonstrate this, let us assume that the tortoise has a head start of one meter and speeds at half a meter per second. Achilles speeds ahead at a meter per second and, in a second, has caught up to where the tortoise was. But the tortoise has in the mean time moved ahead by half a meter. Achilles makes up this half meter in half a second. But the tortoise has, in the mean time, moved ahead by 25 centimeters, which Achilles covers in a quarter second. The tortoise, during that time, has progressed by 12.5 cm, distance which Achilles covers in a eighth of a second. But the tortoise lumbers ahead during that time by 6.25 cm. No matter how close Achilles gets to the tortoise, by the time he reaches the point where the tortoise was, the tortoise has moved. Logic proves that Achilles never catches up. It took mankind 2,400 years to solve the paradox. Leibnitz, in the years 1676, put elementary logic aside and showed with calculus based on infinitesimals and limits that it took 2 seconds to Achilles to catch up with the tortoise, which is a conclusion also based on common sense.
184.108.40.206 Greek cultural regression
The educated Greeks of the Golden Age had reached a cultural level such that the existence of Gods or God was rejected. Agnosticism was prevalent: no educated Greek of the Golden Age believed in either God or immortality of the soul. And we find here the next challenge, which proved essential in the disappearance of the spirit of liberty and inventiveness of the Greek civilization: morality.
Agnosticism was accompanied by a breakdown of all moral values, as seems to be the case now in the West. Abortive practices, promiscuity (fig. 12.12) and homosexuality (fig. 12.13) steadily diminished the number of the free citizens versus the foreigners living among them (the meteques) and the slaves, who continued the worship of their Gods and continued to procreate.
Figure 12.12. Promiscuity in Greece. Fragment of a vase, Louvre, Paris. Prostitution was admitted for slaves. This led to frequent attempts of marriage with citizens, which Pericles prohibited in 451. The promiscuity problem became acute after the Peloponnesian war (431- 404) and worsened when the Athenian society faced the hegemonic ambitions of the king of Macedonia, around 340 BC.
Figure 12.13. Homosexuality in Greece. Fragment, Louvre, Paris. Scenes depicting promiscuity and homosexual activities are very often represented, as if there was nothing incongruous in doing so.
Homosexuality was not a crime but citizens seeking public office were prosecuted if their role within the sexual games was subservient. The decadence of the Greeks amplified after the Peloponnesian war (431-404). Plato opened his academy around 385 BC. to prepare citizens for moral leadership of the city.
The defeat of Xerxes (480 BC.) was followed by the creation of an Athenian Empire led by Pericles, that recklessly plundered, extorted and pillaged its allies and subjects, for the sole benefit of Athens (e.g. the building of the Parthenon, the purchase of masterpieces of sculpture). The revolt against spoliation was led by Sparta and ended up in the Peloponnesian war that drastically impoverished both states and reduced even further the population of free men. Soon came Alexander, who considerably diminished the political autonomy of the cities that had, by that time, almost completely abandoned their pride.
Alexander’s conquest of Egypt and Mesopotamia was the confiscation of the national treasuries of these countries. The Hellenic successor states, Egypt, Macedonia, the Near East, Persia, which emerged after the premature death of Alexander, continued this policy of spoliation, with the difference that the treasuries were not moved to the Capital city of the aborted Empire but remained in the successor states: a formidable system of taxation directed the wealth of each country into the hands of the dominant Greeks, who used it for their own satisfaction only; the population at large did not benefit from it and did not participate in the economic and scientific development of their own land. This was true also in Alexandria, where the scientific development of the city was restricted to Greeks and assimilates. Slowly and inexorably, the spurious Greek culture receded before the demographic and cultural pressure of the prolific native populations that continued the worship of their gods.
The Romans delivered the last blow to the spirit of freedom, individual liberty and inventiveness. We attribute to Rome qualities this civilization never had. The expansion of Rome was the subjugation of the surrounding populations for the sole benefit of the Roman ruling class: the role of the subjugated populations was to provide wealth, leisure and pleasure for the Roman elite. These pleasures were not any more Olympic games and tragedies but appealed to the most vulgar, debased and brutal sentiments: plebeian comedies, bacchanals, horse races and circus games that had nothing to envy to the games played by the Mayans and Aztecs.
The bacchanals were an orgiastic cult that arrived at Rome via the Etruscans and Greeks. They took place at night several times per month, under the guidance of a priest or priestess. In 186 BC., the Roman Senate took drastic measures against bacchanals, condemning the participants to death and destroying the places of worship. Other orgiastic cults were left unmolested.
Gluttony replaced gastronomy, with vomitoria available for the disposal of the ingested food, to leave place for a second and third round of ingestion of food. The excellence of Rome was manifest essentially in military weaponry and tactics: the superiority of the Roman legion over the Greek phalanx and over the Celtic hordes. Otherwise, Rome was good at building monumental palaces, which they did very well with a masterpiece as the Pantheon, casernes and garrison towns.
The Roman rulers never considered themselves anything other than landlords who exploited their domain with the help of slaves. The Roman law applied initially solely to Roman Senators. It was extended later to Romans and these were extremely few in numbers. It finally applied also to the inhabitants of the peninsula. To the rest of the population of the Empire, the law that was applied was the good will of the Roman. The Empire the Romans carved out was built on mountains of slaughtered people: Caesar conquered Gaul by physically eliminating a quarter of its population. Spain was taken from the Carthaginians and its whole population reduced to slavery. The conquest of Palestine was achieved after ruthless destruction not only of the Temple but also of the population. The sole culture that was spared was the superior Greek culture, which was immediately adopted by the wealthy Romans: Greek teachers were used to educate Roman children and the completion of their studies at the end of adolescence was achieved by spending a year or two in Athens, where they learned rhetoric and philosophy, essentially stoicism. Greek rapidly became the language of the Roman elite, which imported Greek sculpture and Greek copies of sculptures to Rome in huge numbers.
Agnosticism among the Roman elite was the rule, but this agnosticism was restricted to them while the rest of the population took refuge in myths.
The devastation of the lands of the Empire, inflicted during their conquest, was further accentuated by the policy of Rome to favor on all occasions and at all times the status quo: within the empire, the rich remained rich as long as they behaved as expected from them, and the poor remained poor. In this way, the Roman ruler secured the help of the local elites but alienated the vast majority of the population, which manifested its discontent by slave rebellions, quelled in blood. It is in this context of an utterly spurious society that emerged in Palestine a creed claiming Justice and Happiness for the righteous, in another world. After the destruction of the Temple and the massacre of the population, no other means was found to give some courage and help to the population for the overcoming of its ordeal. The immortality of the soul in another world was needed to punish in another life those whose life on this earth had been immoral, and reward those who had lived in righteousness. Several such religions appeared in different parts of the Roman Empire.
220.127.116.11 Subtraction and division
The regression of the science of arithmetic due to the introduction of the Roman system of numeration did not facilitate the last obstacle to the evolvement of arithmetic into algebra and calculus. This last obstacle was the intrinsic difficulty of the operations of subtraction and division. For practical minds, an empty corral may receive, say, two cows. If one introduces thereafter two additional cows in the corral, we end up with 2 + 2= 4 cows. But what if one does the reverse operation, and takes away two cows from a corral that contains two cows? What we obtain is an empty corral, not a corral with zero cows because zero leads to confusion: zero may mean not only no cow but also no dromedary nor elephant, nor whatever. Worse is 2 cows + 3 cows, which equals five cows. But how much is 2 cows – 3 cows? There is no such thing as a negative cow. For primitive minds, and also for our own children, negative numbers are no numbers at all.
If multiplication is easily understood as an extension of addition, division, which consists in a reduction to unity, could not be accepted as an extension of subtraction: the primitive mathematical mind tackling division problems was really in terra incognita. Who would know how much is 0 divided by 1? And what results from 1 when divided by 0? These are incredibly complex problems to solve, which neither the Greeks nor Romans nor Byzantines cared to tackle.
On the basis of the Greek acquisitions, further progress in algebra was made in India and Islam. Both cultures were favored by an adequate system of numeration and by the acceptance of the notion of indeterminate, for the Indians, and nothingness for Islam. The Koran explicitly states that God created the world from nothing. This implies that the world is contingent, i.e. it was not necessarily there, and also that the world is rational and obeys to the rules imposed by the creator. To Islam, the concept of zero is not foreign. This was not true for the Christian faith, which advocated the concept of God ruling initially over chaos. The Arabs were further favored by their mastery of commerce, which demanded operations of addition and subtraction, as well as their propensity to wage war in far-away countries, which demanded a solid organization.
18.104.22.168 Contribution of Arabic science to mathematics and astronomy
The beginnings of Muslim expansion, during the 7th and 8th century, were sustained by a drive for logic and discipline that made it the period in which Arabic science knew its greatest vitality. Logic was a discipline considered useful and even indispensable for the scholars of the Sacred Law and theology. This drive for logic is perhaps the reason why scientific treatises were copied at the Nizamiya colleges. These religious and legal schools were supposed not to have offered their students any courses in “the foreign sciences” and “the sciences of the ancients”, yet numerous scientific treatises were copied, which means also published, in these establishments. This explains, at least in part, the enigma of Islamic science, which flourished so long and to such an extent without any support from the educational establishment and even with its hostility.
The first treatise on algebra in Arabic is the Algebra (al-jabr) written by al-Khwarizmi (born ca 783 – died after 847). To illustrate his case, al-Khwarizmi set out to solve the equation x2 + 10x = 39. This numerical example, which was thereafter consistently used during the following four centuries up to Fibonacci, stands for ax2 + bx = c. Al-Khwarizmi formulated the problem as follows: a square and ten of its roots equal 39 dirhems, which means, which square, when you add to it an equivalent of 10 roots, amounts to 39?
Nowadays, the solution of ax2 + bx – c = 0 is obtained by an algebraic operation, consisting in
In this example, 1x2 + 10x – 39= 0 resolves into
We all learned this at high school. There were times when the solution was not so easily obtained. The solution proposed by al-Khwarizmi was based on geometrical considerations. For al-Khwarizmi, a square X2 was really a surface whose sides were of equal length (x). He proceeded as follows:
halve the coefficient of the roots, i.e. in this case, divide 10 by 2, which is 5,
square this: 52, which is 25,
add to it the number 39: 25 + 39 equals 64,
extract the root of 64: that is 8,
subtract from 8 half of the coefficient : 8- 10/2= 3, which is the value of x.
These operations were deduced from complex geometrical considerations and, even if arduous, yielded the correct answer. Of course, the negative number -13 was not considered.
About fifty years later, Thabit ibn Qurra (ca 830-901) studied the same problem (fig. 12.14). He considerably simplified the approach and reduced the problem to a premised proposition of geometry (in this case: Euclid II.6). He drew a square of sides x, whose surface is x2, to which he adjoined a rectangle of which one side corresponded to the coefficient of the roots, in this particular case 10. The entire plane, i.e. the square (x2) plus the rectangle (10x), stands then for x2 + 10x=39, of which a segment is known to be 10, which allows to deduct the value of x (figure 12.14). In this geometrical development, it is clear that negative values have no place.
The next Arabic development was due to Abu Kamil (ca. 850-930), who commented on al-Khwarismi’s treatise and extended it by adding a solution that leads immediately to finding the square. The geometrical proof is based on the construction of 3 adjacent surfaces and is remarkable because x2 is not anymore a square but is made equal to a line-segment ((red in) figure 12.15).
A square is built, whose side is 10x and surface is 100x2 (green). The line segment 10x plus x2 equates 39. If the other side of the rectangle is set at 100, then the total surface of the two rectangles is 39 x 100 i.e. 3900 from which, with the help of Euclidian geometry, one deducts that x2 is 9. The direct solution of x2 is new.
One of the initial principles inherent in ancient mathematics was a sharp demarcation between the concepts of “number” (a discrete entity) and “magnitude” (a physical geometric object). Aristotle distinguished five classes of continuous quantities, viz. lines, areas, solids, space and time. Euclid treated the theory of numbers independently from the theory of magnitudes. The all-important concept of ratio was defined separately for numbers and magnitudes. The idea of irrationality concerned only magnitudes, expressing the incommensurability of two homogeneous magnitudes, as two segments or two areas that were devoid of a common measure. The best-known example of irrationality is p, i.e. the ratio of a circumference to its diameter.
This contrast between the science concerned with continuous magnitudes, i.e. geometry, and the science of discrete quantities, i.e. arithmetic, caused the main logical difficulties which the Greek mathematicians encountered in their attempt to unify their science through geometry. The perplexities disappear when the contents are transformed into algebraic language. The major contribution of medieval oriental mathematicians in this domain is that they expressed Euclid’s theory of irrational magnitudes in an arithmetical form. Arabic commentaries on Book X of Euclid’s Elements attempt to explain the propositions in an arithmetical form and also to substantiate this arithmetization. They looked in Book X in order to disclose the nature of the root of a number and to find a rigorous base for deducing rules of operations on number irrationalities. They fused together the geometric and the arithmetical notions of irrationality, which enabled the application of geometric considerations in order to prove propositions rigorously: geometric and arithmetical terminologies became persistently blended.
The problem of Arabic mathematicians was that they had no followers. In the 12th and 13th centuries, European scholars became acquainted with the theory, owing to translations of Euclid’s Elements and of the Arabic commentaries on Book X. The first translation of the Arabic treatises was in Hebrew by Abraham bar Hiyya (died 1136) in Barcelona, itself thereafter translated in Latin.
22.214.171.124 The birth of calculus in the West
In Christendom, zero was not totally ignored: pope Sylvester II, braving the accusation of heresy, attempted in the eleventh century to introduce counters representing zero. This attempt bore no fruits because such counters were not needed on counting boards. The absence of counters in a column was sufficient for calculations. The first true successful impulse toward elaborated mathematical developments came from the Lombard merchants, more precisely Fibonacci of Pisa, who published in 1202 “the Book of the Abacus”, wherein he described Arabic numerals as the best of the calculating systems he came upon during his travels in the Near East. Fibonacci (died after 1240), a merchant and also the first great mathematician of the Christian world, took up the classical example x2+ 10x = 39, and solved it as al-Khwarazmi did. This indicates how much Fibonacci was influenced by the heritage of a chain of Arab mathematicians. Fibonacci did not visit India and the teaching of the Indian mathematicians was not assimilated: Fibonacci described only nine Arabic numerals and zero was not put on an equal footing with other numbers.
The concept of negative numbers appeared in the books of North-Italian merchants sometime before 1340, with the invention of double-entry bookkeeping, enabling them to monitor profit and debit and balance them out. This new way of accounting made negative numbers as real as their positive counterparts and redefined zero.
The tables of decimal (instead of sexagesimal) trigonometric sine, cosine, tangent and cosecant functions were introduced in Western mathematics about 1450 by Giovanni Bianchini (died ca 1470) and applied by him for astronomical calculations 13. Zero was treated like an actual quantity for the first time in 1484. From then on, calculus could evolve in Europe as all other experimental sciences, by experimentation and verification of the results of the experiments, accepting the conclusions even if they defied logic or preconceived ideas.
Von Leibnitz (1646-1716) was not only an excellent mathematician but also a mystic who wove aside formal logic to grasp the meaning of infinitesimals. Infinitesimals and limits, which easily solved the paradox posed by Zeno, did not follow the rules of logic accepted at that time; Newton used them only with the greatest reluctance. However, it worked, against logic, and this is what counted: with their help, and also the help of negative numbers and irrational numbers, a junction could be made between algebra, geometry and trigonometry, whereby the fundamental problems posed by movement (falling of balls, movement of sun, moon and stars, ballistics, pistons, etc.) could be successfully handled.
The merging of the concepts of “number” and “magnitude” into a more general idea of numbers, be these rational or irrational, was eventually solved in the 19th century.
In Babylon, in India, in the Islamic realm and also in Western Europe, the ultimate purpose of astronomical observations was to determine the constants of an astronomical system. The aim was to compute tables based on that system, for the use by astrologers 14. The most important celestial bodies, in this respect, were the planets.
The simplest way to account for the observations of the motions of the planets was to assume that they circled around the sun. About 280 BC, Aristarchos of Samos proposed the heliocentric hypothesis. Archimedes reports that Aristarchos brought out a book consisting of certain hypotheses wherein it appears that the universe is many times greater than commonly mentioned. Aristarchos’ hypothesis is that the fixed stars and the sun remain unmoved, and that the earth revolves about the sun in the circumference of a circle. Aristarchos did not dispose of a sufficient number of observations to determine the constants of his theory. In addition, the accurate determination of these constants requires trigonometry, which was not developed at the time of Aristarchos. But it was available to Seleukos (second century BC), which allowed the latter to consolidate the heliocentric hypothesis. Seleukos was an excellent astronomer who knew that the tides are due to the action of the moon and also knew that the height of the tides depends on the position of the moon relative to the sun. He assumed the universe to be infinite.
Traces of the heliocentric theory are discerned in the work of the Indian Aryabhata, in AD 510. This astronomer assumed a rotation of the earth, although his geocentric system did not require it. Traces of heliocentric systems are also discerned in Persian and Babylonian sources 15.
In the history of astronomy, we observe a tendency to get away from the idea of a motion of the earth. It is always possible to transform a heliocentric theory into an equivalent geocentric theory by putting the earth at rest, while retaining the relative motions of the sun and the planets as seen from earth. A return to a geocentric system from a heliocentric hypothesis is not abnormal. Tyco Brahe transformed the system of Copernicus into a geocentric system in just this way.
Aristotle (in De Caelo), and Ptolemy (Almagest I.7) explained why the heliocentric hypothesis of Aristarchos was wrong. The idea of a motion of the earth was impiety, the earth being by nature suited to a position of rest. The basis of the cosmology of Ptolemy was the principles of absence of a void and finitude of the heavens, and the doctrine that the celestial bodies move with a simple uniform rotation. To account for the movements of the planets in Ptolemy’s model, all the planets, except Mercury, move around the earth in a perfect circle, the center of which is removed from the earth by an eccentricity. But the observations do not fit this simple motion along a great eccentric circle, and Ptolemy in addition assumed that the planets themselves move in a small circle (an epicycle) having its center on the circumference of this greater eccentric circle (fig. 12.16).
Figure 12.16. Geocentric theory of celestial bodies’ movements. Ptolemy thought that the sun and planets circle around the earth (terre) in a perfectly circular movement (deferent) that was eccentric. This eccentricity is needed to take into account the anomaly of the apparent motion of the sun. The planets move also on a smaller circular epicycle having its center at the center of the sun. The equant is an imaginary point serving for complex calculations of angular speed of rotation. The computations of the movements of planets according to this scheme demanded difficult and lengthy calculations.
The astronomical observations of Claudius Ptolemy had been translated in full in Arabic by Al-Haggag in 827, published under the name Kitab al-Migistî (The greatest Book). Parts of the work bowdlerized of mathematical demonstrations and other offensive considerations were published in Rome in Latin in 1175 under the same name, Almagest.
Though the uniform circular motion of the heavens might have to do with souls, it was also something that could be taken as an observational fact. Sanad delivered the first assault on the Ptolemaic system. In a neat, simple and logically argued text of two pages, Sanad evaluated the relative size of the Sun and Moon. Assuming that the light of the Moon and of all the planets comes from the Sun, he concluded that the Sun is bigger than the Earth and the sphere of the Moon is much smaller than the sphere of the Earth 16.
With additional accurate observations and logical deductions, it became clear to Arabic astronomers at the end of the 10th century that an unobjectionable system could not be obtained simply by assigning a physical mover to each motion, since Ptolemy himself resorted to motions that violated the principles of uniformity and circularity. By the late medieval period, 16 violations of these principles were recorded and Nasir al-Din al-Tusi (1201-1274) attempted a reform of the Ptolemaic system, which bears a striking resemblance to that of Copernicus, except that Copernicus envisioned a rotation of the earth around the sun, which Tusi did not. Tusi was still bound by the basic approach of Ptolemaic astronomy and by an Aristotelian view of the world. Yet he managed to effect a number of new departures that were both mathematically and physically sound. By showing that one could reform the Ptolemaic system according to accepted physics, he gave legitimacy to a program of reform that had been, until his time, talked about but not acted upon.
Since antiquity, the most puzzling aspect of celestial motions was that, while planets drift eastward against a background of stars, they periodically come to a standstill and then move in the opposite direction for a few weeks. Mars, for example, goes westward about every two years during a few weeks, as it did in April of 1999. What Ptolemy failed to see, or choose not to see, was that the retrogression always occurs when the planet is opposite the sun in the sky. When Mars is retrograde, it raises at about the same time the sun sets, in opposition to the sun. Copernicus extended this observation to other planets and offered a completely natural explanation: the planets revolve around the sun at different speeds. Mars appears retrograde when the faster-moving earth bypasses it, which happens when the earth is closest to Mars and the sun is then necessarily opposite to Mars in the sky.
12.4.4 Ultimate stagnation of science
Why did science and technology ultimately fail to progress in these civilizations and also in China, Japan and Russia? Macfarlane and Martin 17 suggest that glass was the key factor involved in the emergence of the West. According to them, wine and beer, inherited from the Greeks and Romans, favored by the monks during the Middle Ages, could be served in glass vessels, which is not the case for hot tea. Hence, the development of glass in the West, ending up in binocles, telescopes, microscopes, glass fibers etc. Where glass was absent, scientific stagnation results. Maybe so, but Aristarchos and Seleucos had not at their disposal a telescope as did Galileo, and yet they knew that the earth circled the sun. One may assume that the development of glass lenses in the West is a consequence of the scientific spirit, not a cause.
Apparently, the culprits for the stagnation in Japan were the administration and politics of the island by the indigenous leadership. In Russia and China, the culprits are these also, plus the Nomad, the Koran and war waged in the name of God by Timberline and the Islamic Turks. The Mongol who occupied Orthodox Russia during many centuries branded the people in a regressive way. The domination of India, Persia, the Near East, North Africa and parts of Eastern Europe by the Muslim Ottoman Turks was realized with such a sterilizing savagery that these countries never recovered from the blow. However, indigenous shortcomings were also at work. The political support of mathematical sciences and astronomy initially provided by the Arab rulers did not last much longer than about three centuries. Ben Sa’id (died 1070), an astronomer working in Toledo with 12 assistants, most of them Arabs but also some Jews, gives a sober account on the conditions of work of astronomers in Spain in 1068. He describes these conditions as favorable only insofar as the rulers, no longer interested in scholarship of any kind, left individual initiatives in the pursuit of science unmolested by repression and persecution. Astronomy and mathematics, according to Sa’id, were more threatened by religious persecutions than medicine, which was largely exempt from zealot persecution in al-Andalus, as the Arabs knew Spain. Note that contemporary India develops in a remarkable manner whereas Pakistan, the land of the Pure Muslims, lags desperately behind although both were exposed to western influence in the same way.
The basic reason for the progress of the West was the possibility of scientists to apply their discoveries to practical applications. Fibonacci was, before being an excellent mathematician, an audacious merchant who applied mathematics to the purchase and sale of goods. Unfortunately, this concern with practical applications is not general in the countries that make up the western world.
12.4.5 The mathematization of the Western world
Mathematics affected all aspects of life. During the 15th century, the Flemish painters made a revolution in the representation of space but the rules of perspective were not strictly followed (fig. 12.17). Memling painted a masterpiece.
Figure 12.17. H. Memling. Altarpiece of St John the Baptist and St John the evangelist. 1479. Bruges, St John’s hospital.
This painting still pertains to the old school, flowing naturally from what preceded it. The pragmatic revolution in art that took place in Flanders is distinct but just as important as the intellectual revolution that took place at the same time in Italy. It relied on a new technique of painting in oils instead of egg yolks. Although the painting shows brilliant realism in terms of details, it is securely linked to the mystical current in Flanders.
This representation of epiphany by Memling is a world apart from the representation made in 350 AD (fig. 12.24), where St Joseph is absent, the kings are without crowns, are all three white and none of them is kneeling. There is almost no background.
The evolution of representational art from the primitive painting of the 4th century (fig. 12.18) to the achievements observed in the paintings made by Memling (fig. 12.17) and Raphael at the beginning of the 16th century (see fig 12.22) was by no means straightforward. Contingency played a tremendous role in this achievement.
Figure 12.18. Wall painting in the catacomb St Callixte, Rome, about 350 A.D.
The Apocalypse (meaning revelation in Greek) written by John between the years A.D. 70 and 90 betrays the hatred of the early Christians for Rome. One must here evoke the horrendous vulgarity of this civilization. The story goes that the expert lips, tongue and fingers of Cleopatra satisfied in one night 100 Roman officers. The aging Tiberius bathed surrounded by babies whose mission it was to suck out the aging emperor into erection. The sexual depravation of Caligula is well documented and the persecutions prompted by demagogy (Nero) did not improve the desire of the early Christians to adopt the cultural habits of Rome. They rejected the refined Roman and Greek representational art, which was unfortunate because the catholic preachers were therewith deprived of an all-important visual tool needed to convert illiterate people. Without adequate visual tools to illustrate their teaching, the preachers could rely only on narratives and parables. Gregory the great, in the fourth century, complained about this lack of educational supports.
In those early days, Roman Christianity was still orthodox. The successful resistance of Byzantium to the onslaught of Islam, the eviction of the Muslims from the Occidental part of the Mediterranean sea by the Vikings, the reconquest of large parts of the western part of the Empire by Belizarius gave to Byzantium the possibility to impose the cultural values of Christian Byzantium to Italy. These were pregnant with imperial connotations. Religious icons representing the passion of Christ poured into Italy. The apostle St Lucas and Nicodemus themselves were assumed to have painted them. The icons were holy and were reproduced in innumerable exemplars. At that time in Western History, painters had by no means the status of artists, which was acquired only in the 16th century. They were artisans, belonged to the ‘Doctors and Apothecaries’ Guild and were drilled in the faithful reproduction of the models that were given to them by their patrons, essentially theologians. There was in no way among the artisans a drive to creativity.
Rome separated from Byzantium in 1054 and the Church underwent a severe reform with Hildebrand, in the direction of a negation of man’s sexuality. In 1071 occurred the disaster of Manzikiert: the Turks smashed the Byzantine army and the Basileus was taken prisoner. The Frankish popes who acceded to the Holy See after Hildebrand seriously considered the possibility to have Rome take the place of Byzantium as the navel of the civilized world and they initiated the first crusade in 1095. In 1098, the integrist order of Citeaux was created and popes were chosen within their ranks. Followed the creation by the Franks of the Latin Empire in Constantinople in 1204. Byzantine icons supporting the idea of an Imperial Roman Christendom poured into Italy, essentially via the harbours of Pisa and Venice. Saint Dominique, who founded the very conservative Order of the Dominicans (in latin: domini canes, i.e. the dogs of the lord) reinforced the imperial aloofness and distantness of the reformed Church by carrying in 1221 a Maria-icon in procession in the streets of Rome. Mary was the Mother of God, was a queen whose son Christ nailed on the cross was not a human suffering to redeem the sins of the believers but was Christ triumphant over death. The Roman Church was marching in the footsteps of the Orthodox Church.
Saint Francis of Assisi received between the years 1205 and 1208 a mandate from God to rebuild the Church. In 1210, pope Innocent III approved the Franciscan rule that made, from the companions of Francis, beggars and preachers. Some popes issued thereafter from the Franciscan Order. Their vision of what the Church should be was diametrically opposed to the vision shared by the Dominicans and the majority of the Church’s princes. The Franciscans addressed their preaches to illiterate city dwellers and the Order rapidly felt the need to dispose of visual means of communication able to sustain their advocacies to poverty and simplicity of life. Roger Bacon joined the ranks at age 37, in 1257. This researcher in light and colour had probably noticed well before his entrance into the Order the importance of pictures not only for the common folk but also for the most popular predicators, and now that he himself had felt the appeal to convert the common people, he sensed even more acutely the shortcomings of adequate visual means of support to this end.
Between 1266 and 1268 he concluded, in his “Opus majus” dedicated to the pope, that the pictures of his time misled the viewer. He proposed that the pictures representing holy texts be presented to the viewer in the most real and concrete way so that the message be received in the entirety of its allegoric, moral and mystique significance. That this was not the case with the bland and soulless icons in circulation at that time was, according to him, the fault of the theologians who were ignorant of perspective and geometry. They were not guided by the “Elementa” of Euclid nor the discoveries of other scientists-theologians in giving their assignment to the artisans in charge of the paintings. These artisans were utterly unable to proceed to a renovation of the visual arts that would bring forward and state the wisdom of God and the magnificence of his creation by paintings presenting nature in three-dimensional forms.
The postulate elaborated by Bacon is a most important document in the field of history of perception. He pointed out the cliff existing at that time between the exigencies that commanded art and the actual state of that art. The contemporary and stultified art represented events segregated from space, time and surroundings that made them unreal. The viewers saw austere pictures of which they already knew by heart the significance and it was left up to the preachers to fill in and comment them to make them vividly acceptable to their contemporaries.
Bacon sent his Opus to Clemens IV in 1268 but the pope died that same year. Epidemics, famines and war joined forces to dwarf the attempt of Francis and his followers to inject humanity in Roman Christendom. It took several additional years before the postulate of Bacon could take hold in western art because the Dominicans and the Jesuits in later times, fiercely fought it. The Dominicans in fact won the battle of preponderance and the Franciscan Order lost its glory and access to the Holy See during the following centuries, with the dramatic consequence that the humility and humanity of the Roman Church striven at by the Franciscans went into hibernation, to be revived only in the 20th century under the impulse of John XXIII. However, the postulate of Bacon survived. It was so well adapted to the needs of the times that the whole world of Western art followed this naturalist model within a few decennia. The realisation of Bacon’s postulate was one of the most significant events in the history of Western art. It meant the return of an objective rule of measurement for the inner “adequateness” of an art object. This objective rule was God’s creation, the existing natural world as everyone could admire it, as initially advocated by Francis. The Florentine Giotto took the lead. He broke away from the stereotyped forms of Italo-Byzantine art and gave passion and imagination to his scenes (see fig. 12.2).
Figure 12.19 dates from the 12th century, well before Giotto, who had painted beginning 1300. The kings wear crowns, are white and one of them, Melchior, begins to kneel. Joseph is present and is as tall as the door from which he exits. There is no background. In a painting by Bosch (fig. 12.20) that was performed only 4 years before that of Memling (fig. 12.17), one king is black, another is kneeling. The proportions begin to be respected.
Figure 12.20. Anonymous, work-shop J. Bosch. Epiphany, 1474. Metropolitan museum of Art. Fragment.
In Italy, the century is known as the Quattrocento. The painters of Florence, city whose trading and banking systems were most sophisticated, operated an extraordinary mutation in the techniques of space representation of which Giotto was a long neglected precursor (see fig. 11.2). Masaccio (1409-1428) initiated the movement (fig. 12.21).
Figure 12.21. Masaccio, The tribute Money, 1427, Fresco Brancacci Chapel, Santa Maria del Carmine, Florence. Masaccio is one of the founders of modern painting. The painting is reminiscent of Giotto in its command of dramatic action but the figures stand freely in space, which is new. The massive dignity of Christ and his followers displays a new solidity and strength of articulation that remains unsurpassed by any other High Renaissance artist. Much of later 15th century painting (Mannerism) contradicts the principles enunciated in the Brancacci Chapel. Michelangelo was the follower of Masaccio for the decoration of the Sixtine Chapel in the Vatican.
Alberti, a clergyman in charge of the construction of churches and palaces, assembled in 1435 the accumulated practical knowledge of the painters into a treatise that exposed with a mathematical spirit the rules of perspective. Alberti did not arrive at the idea that parallel lines within one plane join at infinity. Da Vinci did not either. Only Kepler recognized this nowadays universally accepted postulate. This progressive mathematization and geometrization of space took place in the Italian and Flemish city-states and extended to the novel arts of cartography, seafaring, artillery, banking and agriculture. In 1420 it was apparent even in politics in that the states of Florence and Milan drew a border that was neither a road, a river, a mountain chain or other outstanding physical feature but an abstract line. For North Americans, borders may be abstract lines. This was by no means the case in earlier times. The French have fought endless wars and brought unending sorrow to generations of Europeans because of their desire to possess “natural” borders: the Schelde, the Rhine, the Alps, the Atlantic and Mediterranean coasts, the Pyrenees.
In the years 1480-90, the wealthy Lorenzo de Medici of Florence opened wide open the windows of the world and invited each scientist, as Pico della Mirandola, and each artist, as Botticelli, Leonardo da Vinci and Michelangelo, to reach out to the limits of their genius. Lorenzo died at age 43, on 8 April 1492, allegedly assisted by the Dominican Savonarole, although accused by the latter to have made a corrupt cesspool of Florence. The premature death of this gifted diplomat was perceived by Charles VIII of France as a signal for the invasion of North Italy in September 1494, at the invitation of Ludovic Sforza of Milan, with the destruction of Europe’s greatest collection of art and manuscripts in Florence, approved by Savonarole, and the ephemeral French conquest of the Spanish kingdom of Naples, lost in 1497, taken again and lost again in 1504, but Lombardy remained for a while French possession.
In 1517, the epiphany painted by Raphael, now at the Vatican, indicates that the Italian revolution in painting is achieved (fig. 12.22).
Figure 12.28. The Epiphany, Raphael.
During the Renaissance, an insatiable curiosity was sustained by the discovery of the New Worlds of Africa, the Far East and America. Astronomic, geographic, botanical, zoological, ethnographic, linguistic and even biblical observations were made. The epistemological frame of Scholasticism became thereby unbearable (fig. 12.23) but no adequate systematization was at hand that would allow a renewal of the basic structures of Reason. A unified view of the physical world was impossible to realize.
Figure 12.23. J. Bosch: the pebble excision. Fragment. 1494, Museo National del Prado, Madrid .Bosch derides the University and those who trust it: Lubbert Das, a fool, begs the surgeon to operate him of a pebble. The pebble that grows in the head like a flower is a symbol of foolishness. The surgeon bears a funnel, symbol of foolishness. A nun with a book flat on her head represents mindless thinking. The jug in the hand of the monk represents debauchery.
Bosch agreed with Sebastian Brant (1457-1521) who had written Narrenschiff, i.e. ship of fools. In the painting, fools operate a fool. Before Erasmus, Bosch describes the foolishness of his days. This Flemish painting landed in Spain because the duke of Alba confiscated the goods (at least 9000 confiscations) of opponents to the Spanish regime in the Low Countries, and transferred them to Spain.
The minds, cluttered with assertive beliefs and facing an inflation of new facts among which the discovery of the Americas was significant, were still reticent to the idea of progress and were still not accustomed to distinguish between what was intrinsically true and intrinsically false. No boundaries were established between verified truth and fairy tales 18. This is apparent in the writings of Montaigne (died 1592). He complains about the appearance of new theories that drive away the old ones that had been accepted as true during centuries by the most learned men of their time, the new theory being, in his eyes, bound to give way again to the old one in due time. He rejects progress because the concept of progress based on the discovery of new true facts is not part of his intellectual equipment.
This is apparent in the essay of the Tuscan Vasari, published in 1550, on the lives of the greatest painters, sculptors and architects. To him, progress in painting is based on the Greek-Roman criterion of representation of nature. The best painting is the one that most closely depicts reality. Byzantine, Egyptian, African, Far Eastern and Middle Ages paintings are primitive efforts that tend to the ideal achieved by da Vinci, Rafael and Michelangelo. According to Vasari, progress in art is not anymore possible after the achievements of these masters and painting will, from then on, start anew again, from scratch.
This is apparent also in the anatomical investigations of the Tuscan da Vinci: when he draws a heart, he drills in it, against the evidence of his own eyes, a nonexistent passage between the left and right parts (fig. 12.24) because the accepted theory of blood circulation of his days demanded the existence of such a passage. He knew about the constrictions of the heart, knew about blood vessels and blood circulation, but did not connect the two; in his days, blood was thought to descend to the lower limbs by gravity and rise again by heat.
Figure 12.24. Da Vinci. Organs of the thoracic cavity-Quad. Nat. I, fol. 12r, fragment.
Most Renaissance scholars read Arabic. Drawing on the mathematical knowledge accumulated by the Muslims, influenced by the merchants and technicians who used and applied mathematics in everyday life, admiring finally the good sense demonstrated by architects and administrators, de la Ramée published his thesis “All that Aristotle said is false” in 1526. The Parisian Theological Faculty of the Sorbonne was scandalized and de la Ramée was put to death. From that time on, more and more seditious works appeared, and Pope Paul IV instituted the Index in 1557.
A century later, Francis Bacon, Chancellor of England, proceeded to a work of mental hygiene in 1620 by the publication of “Novum Organum”. He suggested the creation of scientific institutes, defined for each of the sciences the most urgent problems to solve and attempted without success the formulation of a new scientific method. Seventeen years later, Descartes (Discours de la Méthode) urged the philosopher to doubt everything and exposed the scientific method of analysis and synthesis. Most important was the writing of Father Gassendi that appeared in 1624: “Scholastic is dead, Aristotle is a liar, the corpuscular theory of Lucrecius explains everything”. Lucrecius (98-55 BC) had elaborated on the idea that Matter resolved ultimately into atoms. He also thought that the enjoyment of life is preferable to the fear of death and of the Gods, with the consequence that the corpuscular theory of this heathen had virtually been abandoned 19.
The burgeoning realism favored by Aquinas had put the biological approach of Aristotle in favor and Father Gassendi questioned this philosophy. Gassendi criticized Descartes, who had detached matter from soul, and tried to reconcile Christianism with the Epicurean moral 20. Gassendi rationalized the real in its plenitude and accustomed the Occidental Mind to pass from the simple to the complex and from the complex to the simple in the fundamental processes of analysis and synthesis. The scientific explanation consists then in finding a corpuscular model to account for the sensible appearances and this is a tool of scientific analysis that Bacon did not have. Angels, demons and sorcerers are from then on not needed anymore to make things move, be it the sun, rivers, springs, rain, wind, blood or respiration. It is all a mechanism (as advocated by Descartes) that may be submitted to mathematical analysis. This approach allowed a remarkable simplification of science and a great economy of thought, in that varied disparate phenomena were reduced to a small number of uniform causes.
12.4.6 The social complexity
During the Renaissance, the social life of Christendom was as extremely difficult as the scientific life was complicated. Power was exercised by barons, boiards, princes, Church princes and dukes who all had their own concept of authority, so that rules changed not only by the whim of the ruler but also from one village to the next. The relationships of power, as established by feudality, had become inextricable. Erasmus, an intelligent man impatient and irritated with the display of stupidity of the world he lived in, facing conformism and haughtiness, wrote the “Praise of Folly” while he was in London with Holbein and T. More, around 1500. Popes, kings, monks, scholars, war, theology, he spared nobody and nothing.
Grünewald painted in 1514 a crucifixation that expresses the tragic situation of the day with such an intensity one dares not any more pronounce the word “civilization” (fig. 12.25).
Figure 12.25 M. Grünewald. The Issenheim Altarpiece (closed). c 1514. Oil on panel. Musée Unterlinden, Colmar, France. Christ is gigantic, with emphasis on painful details. The arms are pulled out of their sockets and the torso is covered with lacerations and bristles with splinters of wood. The group on the left is the most famous expression of grief in art. It shows how the intensely devoted worshippers of that period tried to identify themselves as closely as possible with Christ’s sufferings, perhaps as an escape from the secularism and religious controversies of the time, which were tearing a once familiar world apart.
A lucid Machiavelli wrote “The Prince” in 1512, for the counsel of the Medicis’. Counselling a petty Florentine tyrant, Machiavelli took the opposite stand of the counsellors of the former Persian, Greek, Roman, Byzantine and Arabic rulers, and medieval Emperors: these emphasized the need for a humane approach of government while Machiavelli taught deceit, treason and banking on human weaknesses.
According to Machiavelli, to be good and do good make no sense in a world of scoundrels. He depicted the savagery of Man and demonstrated that politics is not an applied moral nor a religion but is essentially physics, a mechanic where the law of the strongest prevails. The conduct of Men is not determined, as professed during a millenary, by the desire to save one’s soul but by greed, fear and ambition. Although Machiavelli made the difference between Good and Bad, in his eyes the greatest good was the greatness of the State, not to have hands without stains of blood. The welfare of the State is the criterion against which the exercise of power must be evaluated. Statesmen are innocent of the death of men provided this death enhances the State. The medieval myth of Christendom assuming a community of interests embracing the whole of Humanity was therewith abandoned. Machiavelli heralded the return of Europe to a primitive tribal mentality: the end justifies the means and the citizens are at the service of the State.
Machiavelli acknowledged the evidence that Europe had desagregated into tribal subunits and had become decivilized. This demythification of the moral rules accomplished by the Florentine diplomat was as scandalous in his days as were thereafter the demythifications accomplished by Galileo, Lavoisier, Freud and Darwin. The facts soon followed: Henry VIII refused to defend Belgrade against the Turks, alleging that his true enemy was Francis I while France supported the protestants in the Empire and allied consistently with Orthodox Serbs and Russians, and with Muslim Turks, against the Germanic Empire.
12.4.7 The religious complications
During the Renaissance, the religious life in Christendom was as complicated as was the social life. In the course of the centuries, the Church had allowed the accumulation of fairy tales, miracles, relics and pardons, which changed from village to village and appeared utterly ridiculous.
The Church was under attack. Let alone the dismal episode of the French popes of Avignon, but the loss of the crusades, the fall of Constantinople, the wealth of the Muslims, the penetration of the Turk in Latin lands, the occupation of Russia by the Mongol indicated that the true Faith was the Muslim creed. Also, the discovery of new lands by Columbus, Cabral and Goma made it impossible to continue to believe that the Word had been brought on Earth by Christ to all men of Good Will since the newly discovered inhabitants of these lands could not, with the best of good will, have been converted for nearly 1450 years.
Finally, the Church had relapsed in depravation. Erasmus, an Augustinian monk, admitted that many abbeys and convents were little more than brothels. The Canterbury tales and the stories of Boccace and Petrarque reflect the reality of those days: for a female sinner, absolution at confession was obtained by a coition. Erasmus further reports that the title of cleric, priest, monk, was a cruel insult. In Vienna, no priest was ordained during the twenty years that preceded the Great Apostasy.
Boccace, Petrarque and Rabelais 21 took distance from the prevalent religious axiomatic and advocated enjoyment of life. Man, not Redemption, became the center of interest and value. The rulers of the Church had wholeheartedly endorsed this view and had evolved a segregated society that progressed towards Reason and Epicurianism. The common man of the Renaissance, facing the many absurdities and difficulties of life, witnessing the lavish extravagancy of the Vatican that so much chocked Luther (fig. 12.26), did not participate in this progress, could not manage it and ultimately rejected it.
Figure 12.26. The stairways of Constantine are taken by the pope and his court to go to the basilica and to the St Peter’s place. The Swiss Guard on the left gives an idea of the extravagant size of the building.
The Reform advocated a return to a simpler life, to assertive creeds, to primitive tribal hegemonies. The Great Apostasy was the refusal of an agrarian society to face the modernity slowly developed during a millenary by some monastic orders of the Roman branch of the Catholic Church, favored by the Hierarchy but not tolerated by the low clergy and the mass of the believers.
The present day fundamentalist stance observed in some religious circles of France, in Algeria, in Iran, in Afghanistan etc. is a similar refusal of the new Weltanschauung proposed by the West, and more particularly the US. The avocation to simpler values is because these populations are unable to face the changes imposed. The rise of Hitler in the immensely stressed Germany of the Weimar Republic was a movement of the same nature.
11. There is still an inscription, at the abbey of Fontenay, asking the children not to be obnoxious! At the priory of Charlieu, depending on Cluny, one may still read : “Troquo lude alias fuge!”, meaning “trundle your hoop somewhere else”.
16. Copied in the Nizamiya College of Baghdad in the first ten days of 1161, now kept in Lahore, Pakistan, translated by A. Heinen and published in «From deferent to equant», D. King and G. Saliba: ANYAS 500 (1987), 167-174