Pythagorus (32 page)

John Scotus Eriugena also lived in the ninth century, at about the same time as Hunayn and Aurelian.
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Nothing is known about his early life, though his name must indicate he was from Ireland (‘Eriugena' can be translated as ‘Erin born'), which escaped the barbarian invasions overrunning most of Europe until the Vikings arrived later in the century. Eriugena may have started out as a scholar connected with one of the great Irish monasteries, but in the 840s, Charles the Bald, grandson of Charlemagne, invited him to France to be head of his court school. It is thought he may have travelled to Greece and Italy, and studied Greek, Arabic, and Chaldean. Legend has him moving later to Oxford at the invitation of Alfred the Great of England, and finally teaching at the Abbey of Malmesbury. Eriugena was the scholar who translated the works of ‘pseudo-Dionysius' into Latin.

The idiosyncratic cosmological scheme that Eriugena developed made him one of the most remarkable scholars of his era – in fact, of all who predated Latin Europe's tenth–twelfth century rediscovery of the classical literature. In his cosmos, the stars, Moon, Sun, and Saturn orbited the Earth, but Mercury, Venus, Mars, and Jupiter orbited the Sun. This arrangement was not at all harebrained; in fact, it was an insightful step in the direction of Copernican astronomy. However, it presented a challenge to the harmony of the spheres. In Eriugena's cosmos, the four planets with Sun-centred orbits were of course continually changing their distances from Earth. A change of distance meant a change in the musical pitch of a planet, and so a theory of cosmic harmony had to allow for varying pitch. That was an idea that no one but Eriugena would explore until Giorgio Anselmi in the early fifteenth century and Johannes Kepler in the late sixteenth and early seventeenth – Kepler, at last, with a correct understanding of the solar system and much more fruitful results.

Eriugena worked out the problem of the varying pitches of the heavenly bodies in his own way in an elaborate system involving numbers, ratios, and musical intervals, drawing examples from organ pipes and stringed instruments: ‘Here one must admire the wonderful virtue of Nature; for what anyone can accomplish on a four-stringed lyre is achieved in the eight celestial sounds. But the method by which it is done must be sought out with diligent investigation.'
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He explained some of the results of this investigation in language that he tried to make reader-friendly:

As you see, the sounds do not always relate by the same intervals, but according to the altitude of their orbits. No wonder, then, that the Sun sounds an octave with Saturn when it is running at the greatest distance from it, but when it begins to approach it, it will sound a fifth and when it gets closest, a fourth. Considered in this manner, I think it will not disturb you when we say that Mars is distant from the Sun sometimes by a tone, sometimes by a semitone.
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Eriugena also urged his readers to keep in mind that when comparing the distances of planets, one was talking about the ratios and relationships of the distances between the planets, not the absolute distances in
stadia
(or, in modern terms, in miles or parsecs).

He had his own take on the agreement between neo-Pythagoreanism/Platonism and Christianity: Everything in creation derived from the One, and the One was the same thing as God. From this One, who was universal, all-containing, infinite, and incomprehensible, emanated the realm of Plato's Forms. Under the influence of the Holy Spirit, the Forms manifested themselves in created things. All creatures would eventually be drawn back to reunion with the divine level of being from which they had fallen. God was both ‘the source of all things and the final end of all things'.

For Eriugena,
all
was ‘fairest harmony', including not only the heavenly spheres but ‘even the sounds that will arise from the punishment of evil, for punishments are good when they are just, and so are rewards when they are more in the nature of gifts than payments for what is earned'. The result of punishment and reward would be a final purification and redemption, even of animals and devils, and reunification into the divine One, with full knowledge of God, seen ‘face to face', as St. Paul had written. For Eriugena, the great harmony of creation was a ‘combination of low, high, and intermediate sounds making a certain symphony between them through their proportions and proportionalities'.
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A younger contemporary of Aurelian and John Scotus Eriugena, Regino of Prüm, referred to the Pythagoreans in the introduction to a book he wrote about the plainsong melodies used in Trier, his native town. Claiming that he got his information from Boethius'
De musica
, he offered what he believed was the Pythagorean argument for the existence of heavenly music.
[6]

The Pythagoreans argue the presence of music in the heavenly motions thus: how, they say, could the heavenly apparatus, so rapid in its course, move in silence? Even though it does not reach our ears, it is still quite impossible that such headlong speed should lack sound, especially since the course of the stars are arranged in so convenient and well-adapted a way that nothing so enmeshed and conjoined can be imagined. Some are higher, others lower, yet all are turned with an equal impulse so that their unequal and disparate orbits fall into a determined order. From this it is argued that there is a harmonious arrangement in the heavenly motion.
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The more important issue for Regino was not whether the heavenly motions produced a sound but whether they took place in a ‘harmonious arrangement'. For him, ‘harmony' was a beautiful scheme of numbers and number relationships pervading the universe, underlying both music and the arrangement and movements of the planets and stars.

Regino was a musician, not an astronomer, but before moving on from the introduction of his book to its main subject matter – plainsong – he wrote a paragraph that sounded like Archytas' idea about the connection between pitch and fast and slow motion and the beating of the air, described the connections between the planets and strings or cords on a lyre, and paid tribute to Cicero's ‘Dream of Scipio'. To cover all bases, Regino closed his introduction with the words ‘We would just add that not only the heathen philosophers but also vigorous commenders of the Christian faith give their assent to this heavenly harmony.'
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In the eleventh
century, a Europe that had been relentlessly tormented for two hundred years by waves of marauding invaders experienced an era of relative peace and optimism. The pace of life quickened, and populations and trade increased, including trade with regions under Islamic rule.

Teaching and study in Europe during the centuries of upheaval had never come to a halt, and monks had gone on preserving ancient writings and copying and illuminating manuscripts. However, in the eleventh century new centres of learning started to appear not in the monasteries but in the cathedral precincts and in the larger medieval cities.
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At first, these amounted to no more than one or a few learned men with a huddle of students gathered around them, and most of the teaching was oral. In the twelfth and thirteenth centuries, these groups became formalised, with better defined roles and obligations for students and teachers, better established relations with local populations and governments (often a touchy matter), and student lodgings resembling the colleges of Cambridge and Oxford. Universities on this model were an authentically European development.

Among the earlier gatherings of teachers and scholars, and later in the universities, a critical and discursive (‘combative', Thomas Kuhn called it) tradition emerged that became known as scholasticism. Many giants of medieval thought who engaged in these combats are still familiar names today – Thomas Aquinas, Peter Abelard, Anselm of Canterbury, to name only a few. A primary goal of scholasticism was to integrate classical Greek ideas and learning with Christian belief. With the reintroduction to Latin Europe of the works of Aristotle, translated into Latin in the twelfth century but not immediately available to all scholars, this became a much greater and more complicated undertaking. Scripture was given a more metaphorical, less literal reading, and Aristotle came to be considered, after Scripture, the supreme authority. Scholars revered him not just as a philosopher, but as ‘the Philosopher', no other identification required.

The groundwork for the rediscovery of classical literature had been laid in the tenth century, when Christian knights gradually began to take over what is now Spain and Portugal from the Muslims who had ruled there for more than three hundred years. The culture of the Iberian peninsula was one of the highest on Earth, the best of both Jewish and Muslim. Because the population of Christian Europe – from which the conquering knights came – was, on the whole, much rougher and less civilised and literate, the situation somewhat resembled the Roman conquest of the Greeks many centuries before. This newer ‘conquest' was glacially slow, allowing time for a remarkable intermingling of the three different faiths and cultures. Eventually, in 1492, the Christians would drive the Muslims out of Spain, but for centuries before that the Christians who came there found themselves in the presence of, and mingling with, a long-established, intellectually confident, highly cultivated Muslim and Jewish society.

Clergy who accompanied or followed the knights were awed by the beauty of the cities, the architecture and gardens, the peace in which minority communities coexisted, and the level of learned discussion and scholarship – but most of all by the libraries of Cordoba, Toledo, Segovia, and Lisbon. As long as any cleric in Latin Europe could remember, there had been rumours that priceless manuscripts and books, containing the lost knowledge of the ancients, still existed somewhere in the Muslim countries. The old rumours turned out to be true to a degree beyond their dreams. Here in Spain was the fabled material – much of it translated into Arabic – that had been in the repositories of Christian scholars before the Muslims had taken over most of the former Roman Empire in the seventh century. Since then, Muslim and Jewish translators and scholars had treasured and preserved these works.

By 1100, Christians controlled Toledo and Lisbon. Archbishop Raymund of Toledo invited the cream of the scholarly world to join in an effort to translate a vast collection of ancient writings into Latin. The first translators were representatives of the three faiths, Christian, Jewish, and Muslim, who were already living in Spain, but soon scholars joined them from all over – Christian clergy from Latin Europe and England, Jews and Muslims, Latin, Greek, and Slavic scholars – to work with no censorship, no banning of any book, no rewording to give a Christian spin to pagan words. Some of the translators were not just bilingual but multilingual. Michael Scot, from England, knew some Arabic and was fluent in Latin, Greek, Hebrew, Syriac, Chaldean, and several other languages. When not enough men could be found who had mastered both Arabic and Latin, two translators with a common language worked together. The effort continued for years. One particularly prolific translator, Gerard of Cremona, translated seventy or eighty books in all, including Ptolemy's
Almagest
and Euclid's
Elements
.
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Similar work was going on in Palermo, Sicily, under the patronage of the Norman King Roger. Known for an opulent court befitting an Eastern potentate, Roger considered it essential to surround himself with intellectuals, and he was patron to a number of them – Roman Catholic, Byzantine Christian, Jewish and Muslim alike. The translation in Palermo was more often directly from ancient Greek manuscripts into Latin, rather than via Arabic translations, for Sicily in the time of Pythagoras had been a Greek colony and had retained the Greek language through the Roman and Byzantine eras. Roger's retinue included a number of Greek-speaking scholars. Plato's
Meno
and
Phaedo
were, fittingly, first translated into Latin there on the island where one of the earliest Pythagorean communities had existed and where Plato himself had dabbled in court politics and almost lost his life.

With no printing presses yet in existence, copyists devoted long hours to reproducing the translations. The dissemination of the new books was slow, but for the first time in many centuries, scholars in Latin Europe were reading the ancient Greeks, and in the universities Aristotle joined Plato.

The basic medieval curriculum had begun as none other than the Pythagorean quadrivium of Archytas, and students also had to master dialectic, as Plato had required. But when Aristotle's works began to influence university education, they became the foundation of philosophical and theological studies in a ‘trivium' that followed after the quadrivium. The seven subjects of the combined
quadrivium
and
trivium
– arithmetic, geometry, music, astronomy, grammar, rhetoric, and dialectic – became known as the Seven Liberal Arts.
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The standard arithmetic text was the old, familiar
Introduction to Arithmetic
by Nicomachus, the second-century neo-Pythagorean who had clung doggedly to ‘Pythagorean mathematics' and identified himself as a Pythagorean. Boethius' slightly reworked Latin version of his book had been in the libraries of Latin Europe for centuries. Now, thanks to the translation projects in Spain and Palermo, scholars and students were able to circumvent Boethius' rewrite and read Nicomachus in direct translation from the original. Whichever version they read – Boethius'
De institutione arithmetic
from the early sixth century, or Nicomachus' original
Introduction to Arithmetic
from the second – they encountered Pythagoras before they encountered any arithmetic, for the opening passages lauded him. Medieval students thus learned their arithmetic in the neo-Pythagorean form, which they took to be
the
form; and almost entirely through this one book, the Pythagorean faith in the power of numbers to unlock the secrets of nature and the universe was conveyed to the Middle Ages and beyond. It was a tremendously significant channelling of thought. The image of Pythagoras as the creator of Greek mathematics became entrenched.