Pythagorus (33 page)

In the twelfth century, in many universities, the geometry section of the quadrivium was taught from a much better book, Euclid's
Elements
. Though translated into Latin earlier, it had never caught on or become widely available. Now there were fresh translations from the Arabic by Gerard of Cremona and Abelard of Bath, another of Archbishop Raymund's translators. Early in the century, Abelard had journeyed the whole length of the Mediterranean collecting ancient texts.

In the third section of the quadrivium, music, Boethius'
De institutione musica
was the text. Through Boethius' music books, again probably taken originally from Nicomachus, the ‘Scale of Timaeus' had already become a significant part of medieval music theory. There is good evidence that this scale did not, in fact, originate with Plato but was used by Philolaus and perhaps earlier, so medieval scholars were dealing with something of impressively ancient origin.
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They accepted Boethius' divisions of music into
musica mundana
(harmony of the spheres),
humana
(relationship of music to the human soul), and
instrumentalis
(what we normally think of as music), and most agreed that all three were essential parts of their subject.

In spite of a few doubters such as the Florentine Coluccio Salutati, who insisted that the motions of the heavenly bodies could not possibly produce sound, the idea of
musica mundana
was still favoured in the fifteenth and sixteenth centuries in Italy, when Franchino Gaffurio, the most important music theorist of his time, made every attempt to be a true Pythagorean. He refused to consider any but the intervals approved by Boethius as consonant intervals, which made him something of a throwback. Boethius had not regarded major thirds and sixths as consonant, and musicians among Gaffurio's contemporaries certainly did. Tradition had it that only Pythagoras himself could hear the music of the spheres, but Gaffurio amended that slightly to insist that only men of significantly great virtue could hear it.

As for the fourth part of the quadrivium, astronomy, the stationary-Earth-centred systems of Aristotle and Ptolemy prevailed unchallenged and unquestioned until one tentatively raised hand in the fourteenth century. It belonged to a Parisian, Nicole d'Oresme, who went only so far as to argue that Aristotle had fallen short of proving Earth does
not
move. Otherwise, no one anywhere in the Middle Ages and until the fifteenth century took seriously the Pythagorean suggestion mentioned by Philolaus that the Earth does not stand still, or even that it rotates. When a more aggressive challenge eventually came, in the fifteenth century, it would be from a man with a decidedly Pythagorean cast of mind: Nicholas of Cusa.

The influence of
Pythagoras and the Pythagoreans was not confined to the universities during the Middle Ages.
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Freemasons included Pythagoras among their
ars geometriae
. Gerbert of Aurillac, who became Pope Sylvester II, in the tenth century referred to Pythagoras in his geometry. Gobar numerals – direct ancestors of modern Arabic numerals – were widely believed to have been the invention of Pythagoras.
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A work supposedly (though not really) by Boethius included a method called
mensa Pythagorea
for calculating with these numbers on an abacus.
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In truth they were originally Hindu and were transmitted to the West through Islamic countries and Spain, with Arabic numerals first appearing in a Latin manuscript in 976.
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For Nicomachus, the neo-Pythagorean numerology in his book had been even more significant than the arithmetic, and this numerology too continued to be important in the Middle Ages, for had not even St. Augustine himself taken enthusiastically to the Pythagorean-like idea of the allegorical interpretation of numbers in the Bible? Like Philo of Alexandria, Augustine had written about the six days of creation in the Genesis account and pointed out that six was a perfect number.

Whoever chose what to celebrate in the sculptures adorning the doors of the cathedral at Chartres, one of the architectural wonders of the Middle Ages, decided to include a series of statues representing the Seven Liberal Arts and selected Pythagoras to symbolise music. The sculptor made him long-haired and bearded, hands and face middle-aged at least, seated and clothed in a beautifully adorned robe as he bent intensely over his work. At the cathedral school in Chartres, in the twelfth century, the scholastic movement's long endeavour to bring together Platonic and scriptural narratives and concepts, including giving the Genesis account of creation a more Greek (in modern terms ‘scientific') interpretation, reached its zenith. John of Salisbury called Bernard of Chartres, head of the Chartres school in the first part of the century, ‘the finest Platonist of his time'. The Platonism of Bernard and his fellows was based mainly on Augustine and other early Christian scholars, the writings of Boethius, Macrobius' commentary on Cicero's ‘Dream of Scipio', and Plato's
Timaeus
in a translation by Chalcidius. The Chartres scholars saw
Timaeus
as an explication of Genesis. Bernard had Pythagoras and Plato in mind when he praised the ancients in words usually attributed to Isaac Newton five centuries later:

We are dwarfs perched on the shoulders of giants. Although we may see more and further than they, it is not because our sight is keener or our stature greater, but because they bear us up and add their gigantic stature to our height.
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Pythagoras depicted in a frieze of the Seven Liberal Arts on the western front of the Cathédrale Notre-Dame de Chartres

The scholars of the Chartres school were addressing an old question: What is the best guide on the journey towards God, or (if one wished to use more Pythagorean/Platonic language) towards reunion with the divine? Was it ‘reason' or ‘faith'? Is it not best that the two work together? Boethius had written, ‘As far as you are able, join faith to reason', and that was the goal of the scholastics. The hope at Chartres was to stake out intellectual and spiritual ground where one could accept what God had revealed but still strive for more comprehensive knowledge of truth. Faithful to their Platonism, and also to their Christianity (St. Paul had said that humans could only see ‘through a glass, darkly'), these scholars accepted that full knowledge could not be had in this life. Nevertheless, they thought it essential, insofar as humanly possible, not only to believe but also to understand what one was believing. Plato's
Timaeus
seemed a splendid example of this effort and this understanding, albeit from a pagan philosopher. Not surprisingly, these ideas offended some who accused the Chartres scholars of undervaluing religious revelation and mocking simple faith.
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The masters at Chartres influenced thinkers in Paris in the following century, when scholarship took a far more Aristotelian turn, prioritising sense perceptions, experience, and experiment in the pursuit of knowledge. The church continued to sound much more like Plato – for whom the ‘Forms' were real and the sense-perceived world a shifting illusion – by encouraging rejection of the perceptible, sin-ridden world.

Though in the late Middle Ages and early Renaissance, scholastic and humanist scholars continued to have success meeting the challenges of new translations, broadening knowledge and reconciling Greco-Roman and Christian thought, even as late as the seventeenth and eighteenth centuries sporadic resistance to their efforts would continue. Some still pointed to doctrines they felt had entered early church thinking as a ‘pagan corruption' from the philosophy of Plato. This resistance did not come from ignorant people. Isaac Newton dismissed the doctrine of the Trinity on those grounds.
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So did the late eighteenth century English Unitarian religious dissenter Joseph Priestley, who thought the dualism between matter and spirit was not inherent in the Gospels but had entered the early church through Greek philosophy.
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CHAPTER 15

‘Wherein Nature shows herself most excellent and complete'

Fourteenth–Sixteenth Centuries

In the fourteenth century,
most educated people in Europe regarded foreign languages as completely impenetrable and unlearnable, so the author Francesco Petrarca (Petrarch) was being venturesome when he decided to learn Greek. He engaged a teacher, a monk named Barlaam of Seminara, but the project was not a success and Petrarch was fated to go on lamenting that he would never arrive at the best understanding of philosophy because his Greek was not good enough.

He was disarmingly modest. Perhaps he did, as he claimed, merely chuckle when he was an old man and heard the news – it was being repeated all over Venice and beyond – that four young aristocrats, who had dined and drunk exceedingly well, had off-handedly dismissed him as ‘certainly a good man but a scholar of poor merit'. In a letter written just a few years before that Venetian slight, Petrarch described himself:

You must realise, my friend, how far I fall short, in my own opinion and in reality, from this judgement of yours: I am not any of the things you attribute to me. What am I? A scholar? Hardly that. A backwoodsman, a solitary man in the habit of muttering foolishness in the shade of lofty beech trees, and – the height of arrogance and rashness! – wielding a shaky pen under a laurel sapling. Fervent in labour, but not happy with the results; lover of letters, but not fully versed in them; adherent of no sect, but greedy for truth. That is hard to find, and I, feeble in my search, often lose confidence and, fearing error, accept doubt in place of truth. Thus I have gradually become a squatter in the academy, and, like many, I have rallied to that humble band that claims nothing, holds nothing certain, doubts everything except what it is sacrilege to doubt.
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Some of the ‘lofty beech trees' among whom Petrarch muttered his foolishness were Augustine and Cicero, Aristotle and Plato (he read them in Latin translations), and Pythagoras, whom he knew through those other authors.

Collecting works from the classical period, tracking down manuscripts and early copies, had become the fashion among those sufficiently educated and wealthy, and the acquisition of something interesting was a matter of great excitement to share with like-minded friends. Petrarch's own large library reflected that fashion and his love of learning, but, for all his modesty, the library he stored in his head was vaster than most men's collections. He read more than anyone else, remembered most of it verbatim, and had a habit of imagining himself personally involved in history and literature. As one commentator wrote,

Since he was such a keen observer of actual life and so lovingly devoted to the investigation of the human heart, all the records of the past became a living reality to him, and he felt himself sharing in the drama as if he had an active part in the cast. It was not just a whim that he, the untiring letter writer, started to ‘correspond' with characters of ancient times, as if they could answer him. When he read their works, he almost forgot that they were long since dead.
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No wonder Shakespeare so often found inspiration and material for his plays in Petrarch. Through Shakespeare and others who read Petrarch, he played an influential role in shaping future culture.

Petrarch was no fan of the Pythagorean doctrine of reincarnation, which he thought was an example of the way a wise and brilliant man can be perfectly capable of coming up with nonsense. ‘Who does not know', he wrote, ‘that Pythagoras was a man of exalted genius? However, we also know his Metempsychosis. I am amazed beyond belief that this idea could spring up in the brain, not of a philosopher, but even of any human being.' Pythagoras' claim to have been Euphorbus in an earlier life was ‘an empty lie' and ‘deceitful pretense'. But then Petrarch also scorned Democritus' suggestion that ‘heaven and earth, and all things in general, consist of atoms'.
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Petrarch, as imagined by engraver Rob Hart, 1835

A few pages after his disparaging words, Petrarch turned around and referred to Pythagoras in reverential tones as ‘the most ancient of all natural philosophers'. No one knows where he got the quotation that he attributed to Pythagoras and used to defend not only the Christian faith but also Plato and Moses from those who ‘blind and deaf as they are, do not even listen to Pythagoras, who asserts that “it is the virtue and power of God alone to achieve easily what Nature cannot, since He is more potent and efficient than any virtue or power, and since it is from Him that Nature borrows her powers.”'
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Petrarch did not believe that Pythagoras had actually written this, or, indeed, anything, but he thought that others had written down ‘what he expounded in his conversations'.

Petrarch is often called the first humanist. He trusted God so devoutly and completely that he felt free to leave the deepest religious issues alone and concentrate instead on philosophy, which he preferred to define as the study of the art of happiness and living well.
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Pythagoras, Plato, and Christianity seemed a natural, logical continuum to him.

In the middle
of the next century, the fifteenth, no less a personage than Lorenzo de Medici lent his patronage to an attempt to re-create Plato's Academy at the villa of his acquaintance Marsilio Ficino, near Florence. The Accademia Platonica was Ficino's brainchild and dream. He translated all of Plato's works into Latin directly from the Greek, wrote commentaries on them, and gathered a group of writers, thinkers, and artists to study them in a congenial setting. When Ficino had also finished translating Porphyry, Iamblichus, Proclus, and Plotinus, those who knew no Greek could read nearly the entire surviving output of the Platonic and neo-Platonic writers in Latin. It is a pity that Petrarch had lived a century too early to enjoy all these works in translation!

One of Ficino's Academy members was the artist Botticelli, whose painting
Primavera
was supposed to be a visual metaphor for the music of the spheres, relating mythological creatures to planetary orbits and the notes of an octave in music. Ficino himself developed an elaborate system of heavenly music. He was also interested in the early church fathers and, like Petrarch, thought that Platonic doctrine and reasoning (which he thought were divinely inspired) were in harmony with Christianity, having particular value in that they could provide independent confirmation of Christian beliefs in a manner that would satisfy those among Ficino's contemporaries who were of a sceptical and even atheistic frame of mind. He gave a Pythagorean/Platonic spin to his treatment of the fall and salvation of man, referring to the belief that the earthly existence of the soul is an exile from its divine home. The Pythagoreans and Platonists agreed, he wrote, that ‘because of a certain old disease of the human mind, everything that is very unhealthy and difficult befalls us; but, if anyone should restore the soul to its previous condition, then immediately all will be set in order.' To Ficino, that sounded like humanity in its fallen state looking towards the salvation of Jesus, in Christian doctrine. A yearning to turn back to God was built into human nature:

Just as when an element is situated outside its proper location, its power and natural inclination toward that natural place are preserved together with its nature, in so far as it is able at some time to return to its own region; so, they [the Pythagoreans and Platonists] think, even after man has wandered from the right way, the natural power remains to him of returning first to the path, then to the end.
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Ficino agreed with those neo-Pythagoreans who had concluded that the same primordial wisdom had emerged in different ages and cultures. The truth of philosophy, religion, and natural science, in all times and places, was, at some deep, so far unplumbed level, one consistent truth. This, Ficino thought, was a manifestation of the ‘unity' that the Pythagoreans had held so in awe.

In the city of Parma during this same period, the musician and physician Giorgio Anselmi (some thought he was also a magician) developed the first system since Eriugena's to take into account the fact that the planets change their distances from Earth. In Anselmi's cosmic musical plan, a planet produced not one tone but many different notes as its distance changed, so that each planet sang its own song. All the planet songs together produced magnificent counterpoint and harmony. Though no music of his time went beyond a three-octave range, Anselmi's planetary scale, calculated from the planets' periods, was eight octaves long from the stars to the Moon.

Ficino's younger Florentine friend Giovanni Pico, Count of Mirandola (known as Pico della Mirandola), was fond of using the phrase, the ‘ancient theology of Pythagoras'. He regarded Pythagoras as no less than a Christian sage and connected the peace promised by Jesus – ‘Come unto me, ye that labour, and I will give you peace, which the world and nature cannot give' – with a Pythagorean ‘longed-for' peace in which

all minds do not merely accord in one intellect that is above every intellect but in some inexpressible fashion become absolutely one. This is that friendship which the Pythagoreans say is the end of all philosophy. This is the peace of God, which the [Christmas] angels descending to earth announced to men of good will, that by this peace men themselves, ascending into heaven, might become angels.
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Until that time, ‘Let us desire this peace for our friends, for our age, for every house into which we enter, for our souls.'

Pico did not always write so clearly and simply. One of his more impenetrable documents was ‘Fourteen Conclusions after Pythagorean Mathematics',
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which arose out of his fascination with ‘the method of philosophising through numbers' as it was taught by ‘Pythagoras, Philolaus, Plato, and the first Platonists'. Aristotle would have summoned his Delian diver!

1. Unity, duality, and what is, are the causes of numbers. Unity is the cause of unitary numbers, duality, of generative numbers, what is, of substantial numbers.
   
2. In participating numbers some are species of numbers, others unions of species.
   
3. Where the unity of the point moves to the duality of the binary, there the first triangle is.
   
4. He who knows the series I, II, III, IV, V, XII, will possess exactly providence's distribution.
   
5. By one, three, and seven we understand, in Pallade, the unification of the separate, the causative and beatifying power of intellect.
   
6. The triple proportion, Arithmetic, Geometric, and Harmonic, indicates to us three daughters of Themidos, symbolising judgement, justice, peace.
   
7. The secret of straight, reflected, and refracted lines in the science of perspective reminds us of triple nature: intellectual, animal, and corporeal.
   
8. Reason is in the proportion of an octave to the concupiscent nature.
   
9. Irascibleness is in the proportion of a fifth to the concupiscent nature.
   
10. Reason is in the proportion of a fourth to anger.
    
11. The judgement of the senses in music is not to be heeded, only of the intellect.
    
12. In the numbering of forms we should not go beyond forty.
    
13. Any equilateral plane number can symbolise the soul.
    
14. Any linear number can symbolise God.
    

Not surprisingly, when the twenty-three-year-old Pico went to Rome and offered to debate another of his lists,
Nine Hundred Conclusions
, there were no takers. Like the ‘Fourteen Conclusions', the
Nine Hundred
were short sentences, covering the subjects of scholastic and earlier theology, Arabic and Platonic philosophy, the Chaldean Oracles, the Zoroastrian Magi, and Orphic doctrines.
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All, Pico insisted, were reconcilable with one another, and he was prepared to debate anyone who disagreed. Truth was universal. What might seem to be opposing schools of thought and doctrine really were all the same primordial wisdom of humankind, sharing a common truth.

Pico's interest was piqued by the Jewish Cabalistic literature, in which words and numbers serve as a form of mystical code. Cabala is a form of Jewish mysticism that, though it had roots as early as the first century A.D., fully emerged in the twelfth century. Though a text of Merkava mysticism (a precursor of Cabala) had included a creation story with ten divine numbers, and one of the most important Cabalistic texts, the twelfth-century
Sefer ha-bahir
(‘Book of Brightness'), introduced into Judaism the idea of the transmigration of souls, in neither case was there a known link with Pythagoras. But another man who immersed himself in the Cabala at about the same time as Pico, insisted there was a connection. Johann Reuchlin, a German humanist, set out to combine the study of Hebrew, Greek, theology, philosophy, and the Cabala, and to link it all with the name of Pythagoras. He wrote to Pope Leo X that, just as Ficino had so admirably done for Plato in Italy, he would ‘complete the work with the rebirth of Pythagoras in Germany'. He rationalised the connection with the Cabala by drawing attention to the (questionable) fact that ‘the philosophy of Pythagoras was drawn from the teachings of Chaldean science'.
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