Some authors were meanwhile more focused on attempting to convey authentic Pythagorean doctrine. When Cicero was in Rhodes for part of his education, he sat at the feet of the Stoic philosopher Posidonius, who lived from about 135 to 51 B.C. Many young enthusiasts were seeking out Posidonius as a teacher and role model. Born in Syria, he had travelled widely, and daringly, to Spain, Africa, Italy, Sicily, and what is today France, into regions that were still frontiers, and his accomplishments and physique had earned him the nickname Posidonius the Athlete. Students and contemporaries respected him as one of the most stimulating and learned men of their time.
Only fragments survive of more than twenty books by Posidonius. He apparently discussed what he believed were Pythagorean ideals of good government in a history of the Roman Republic, arguing that Rome’s decline in public and political morality was linked to her final defeat of the Carthaginians in 146 B.C. With no enemy on the horizon, Rome had degenerated into a morally weak city, rank with unrestrained behaviour and torn by internal political violence and competition for power and wealth.6 Posidonius treasured Plato’s Timaeus and attributed part of his own philosophy to the Pythagoreans. According to one of the Posidonius fragments: ‘Not only Aristotle and Plato held this view about emotion and reason but others even earlier, including Pythagoras, as Posidonius says, who claims that the view was originally that of Pythagoras but Plato developed it and made it more perfect.’
Much that is known about Posidonius comes through the Sceptic philosopher and historian Sextus Empiricus, who lived at the turn of the second to third centuries A.D. He apparently took his information from Posidonius when he explained why the Pythagoreans thought that if you claim something is true, mathematical logic is the only standard by which your claim can be judged. ‘Number’ was the principle underlying the structure of the universe: ‘And this is what the Pythagoreans mean when, in the first place, they are in the habit of saying “all things resemble numbers”, and, in the second place, they swear this most naturalistic oath.’ The oath was the tetractus oath.7 Sextus went on in familiar fashion to point out how the tetractus embodied the numbers 1, 2, 3, and 4 that were also in the musical ratios. He listed the four steps, point–line–surface (tetractus)–solid (pyramid) – ‘the first form of a solid body’. So ‘both body and what is incorporeal are conceptualised according to the ratios of these four numbers’. To reinforce this idea, Sextus Empiricus gave numerous examples of the ways the numbers and ratios play out in bodily substances, in incorporeal things like time, in everyday life, and in the arts and architecture.
Sextus Empiricus, living at the turn of the second to third centuries A.D., got all this information from an earlier source, but why have scholars concluded it was Posidonius? The clue lies in a sad story set in Posidonius’ adopted home, the island of Rhodes. The sculptor Chares of Lindos was engaged to construct an enormous bronze statue, the Colossus at Rhodes. He submitted his estimate of the cost. Then the citizens decided they wanted a statue twice as large. How much would that add to the cost? Chares merely doubled his original estimate – a fatal error. ‘Twice as large’, he remembered too late, did not only mean twice as tall. He had to increase all the dimensions. Chares realised his mistake when all the money was used up on the first phase of the work, and he committed suicide. Sextus included this story in a discussion of numbers and ratios, and scholars see it as Posidonius’ fingerprint on Sextus’ explanation of Pythagorean theory. The information Sextus preserved was probably what Cicero learned about Pythagoras when he studied with Posidonius.
By the mid-first century B.C., a cultlike group flourished in Rome under the leadership of Nigidius Figulus, a ‘Pythagorean and magus’ in whose Pythagoreanism the line between science and magic grew fuzzy to the point of extinction. Pythagoreanism ‘for Nigidius and his friends meant primarily a belief in magic’, wrote the historian Elizabeth Rawson.8 Nigidius’ reputation for having second sight and occult powers qualified him to work up a birth horoscope of the later-to-be-emperor Augustus, which correctly foretold a brilliant future. Romans of that era did not consider such a scholar out of the mainstream or on the lunatic fringe. Cicero wrote in the introduction to his own translation of Plato’s Timaeus that Nigidius ‘arose to revive the teachings of the Pythagoreans which, after having flourished for several centuries in Italy and Sicily, had in some way been extinguished’, and that he was ‘a particularly acute investigator of those matters which nature has made obscure’.9 Nigidius was an educated, prolific author of books on the planets, the zodiac, grammar, natural philosophy, dreams, and theology, with an extensive knowledge of religions and cults from much of the known world.
Romans often invoked Pythagoras’ name to represent wisdom and integrity. The scholar and satirist Marcus Terentius Varro, considered by many the most learned Roman of the first century B.C., began his book Hebdomades with Pythagorean-sounding praise of the number 7 and a quotation about astronomy from Nigidius. When Varro died he was buried, according to Pliny, in the ‘Pythagorean mode’, in a clay coffin with myrtle, olive, and black poplar leaves.10 Cicero, for his part, attempted to undermine the credibility of one ‘Vatinius’, a supporter of Julius Caesar, by righteously accusing him of impiety: for he ‘calls himself a Pythagorean and, with the name of that most thoroughly learned man, tries to shield his monstrous, barbarous behaviour.’11 Cicero seems never to have joined a Pythagorean cult, but he made a pilgrimage to Metapontum to visit the house where tradition said Pythagoras died.
Pythagoras made appearances in many of Cicero’s works. In a scene from The Republic, set at Scipio Africanus’ country estate, Africanus and his nephew Quintus Tubero, the first of several expected visitors to arrive, recline on couches in the Roman fashion, awaiting another guest, Panaetius, who investigates problems of astronomy ‘with the greatest enthusiasm’. In anticipation of his arrival, Scipio mentions a matter that has come up in the Senate about a ‘second sun’,[5] then remarks,
SCIPIO AFRICANUS: I prefer to be guided by Socrates, who wisely declined all such speculation, saying that the investigation of nature was far above human reason, or would contribute little to the enjoyment of human life.
TUBERO: I know not, Africanus, why it should be reported that Socrates declined all such investigations and confined himself to those which touched on life and manners. For what author is fuller of his praise than Plato, in whose books, in numerous places, Socrates is represented as discoursing not only on morals, on virtue, and on politics, but, as Pythagoras did, on numbers, geometry, and harmony.
SCIPIO: It is as you say; but, I believe, Tubero, you have heard that Plato, after the death of Socrates, in order to acquire information, visited first Egypt, and then Italy and Sicily, that he might make himself acquainted with the theories of Pythagoras; and he appears to have associated very much with Archytas of Tarentum and with Timaeus the Locrian,[[6]] and to have studied the commentaries of Philolaus. Observing at that time that the name of Pythagoras flourished in those parts, he devoted himself to Pythagorean studies and associates. As he had become especially charmed with Socrates, to whom he attributed everything, he managed to mingle a certain subtlety peculiar to Socrates with the mystery of Pythagoras and his profound knowledge of many of the arts.12
Tubero thinks of Pythagoras in connection with arithmetic, geometry, and harmony. Scipio associates him with mysticism and profound, ‘varied lore’. Later in the same conversation, they invoke his authority on the natural foundation of laws protecting life:
No ordinary men, but the ablest and best educated, such as Pythagoras and Empedocles, have declared that there should be only one rule of law for all living animals, and they would condemn to eternal punishment those by whom any animal was injured.13
Cicero even weighed in on the bean issue: Pythagoreans avoided them because they cause ‘considerable flatulence and thus are inimical to those who seek peace of mind’.14
It was in Cicero’s ‘Dr
eam of Scipio’ that he sounded most Pythagorean – and also much like Plato. The ‘Dream’ concluded Cicero’s De republica, and in a graceful parallel, he modelled it on the ‘Myth of Er’ that ended Plato’s Republic. Cicero’s ‘Dream’ takes him to a region accessible only to those who through music, learning, genius, and devotion to divine studies have achieved permanent reunion with the highest level of existence. His ears are filled with a sound ‘strong and sweet’, and he asks Scipio what it is. Scipio replies,
That is caused by the impulse and motion of the orbs themselves, which are separated by precise but unequal intervals, set in exact proportion, high sounds mingling with low, producing a variety of harmonies in equal degree; nor can such rapid movement be excited without noise, for nature has ordained that sound shall be ordered from the extremities of low at one end to high at the other. Hence that star of the heaven whose course is the highest, and whose revolution is very rapid, moves with a sharp and quick sound, whilst the moon, being the lowest, moves with a very low, heavy sound; and the earth, the ninth, remains immovable; always occupying the same seat, fixed in the middle of the universe.15
Because Venus and Mercury ‘are in unison’, there are only seven sounds – matching the number of strings on the seven-stringed lyre – ‘seven distinct sounds with equal intervals’. By imitating this harmony with strings and voices, ‘learned men have endeavoured to win their way back to this place, whilst others, endowed with pre-eminent ability, have, during their whole lives, cultivated these divine studies.’16 Cicero’s metaphor to explain why most humans never hear the celestial music was that their ears are deafened to the sound, ‘like those people on the Nile at the place called Catadupa, who, living where the waters fall from very high mountains, have by its roar lost the sense of hearing.’17 He gave no indication that he knew Pythagoreans had thought the Earth was not the centre of the cosmos. In fact, nowhere in the surviving ancient literature is there a hint of anyone bringing the concept of an audible ‘music of the spheres’ together with the cosmology that included the central fire and the counter-earth, even though the musical ratios had probably played a role in the development of the Pythagorean ten-body model of the cosmos.
In a different realm of scholarship, one extremely successful younger Roman contemporary of Cicero, the architect Marcus Vitruvius Pollio, authored an overview of architecture of his era, De architectura or Ten Books on Architecture. He recommended Pythagorean ratios and extrapolations on them for the dimensions of rooms, not using any shapes for temples other than one whose length was twice its width (ratio 2:1), or circular. Greek forums were square, but Vitruvius’ had a width 2/3 its length, because an audience for gladiatorial combat was better accommodated in that space. For houses, ‘the length and breadth of courts [atria] are regulated in three ways’, two of which employed Pythagorean ratios: ‘The second, when it is divided into three parts, two are given to the width’. The third: ‘A square being described whose side is equal to the width, a diagonal line is drawn therein, the length of which is to be equal to the length of the atrium’.18
This design was based on Socrates’ lesson in Plato’s Meno. ‘By numbers this cannot be done’, wrote Vitruvius. Socrates had used no numbers. The length of that diagonal was incommensurable; so was the length of one side of Vitruvius’ room. He frequently mentioned Pythagoras and the Pythagoreans. The Pythagorean theorem was a shortcut in designing staircases, and he unhesitatingly attributed it to Pythagoras.
Vitruvius’ books had illustrations, but copies that reached the Renaissance did not. The drawing below, by Cesare Cesariano, is a Renaissance (1521) realisation of Vitruvius, who was not easy to interpret. According to the architect Leon Battista Alberti, ‘Greeks thought he was writing in Latin; Latins thought he was writing in Greek.’ Nevertheless, this drawing probably faithfully represents his instructions:
This proposition is serviceable on many occasions, particularly in measuring [and] setting out the staircases of buildings so that each step has its proper height. If the height from the pavement to the floor be divided into three parts, five of them will be the exact length of the inclined line which regulates the blocks of which the steps are formed. Four parts, each equal to one of the three into which the height from the pavement to the floor was divided, are set off from the perpendicular for the position of the first or lower step. Thus the arrangement and ease of the flight of stairs will be obtained, as the figure shows.19
Drawing by Cesare Cesariano that represents a Renaissance realisation of Vitruvius’ works
Vitruvius’ book referred to an unusual application of musical fourths, fifths, and octaves used in an amplification system in Greek theatres. A Roman theatre, he pointed out, being made of wood, had good acoustics, but in a Greek theatre, made of stone, the voices of the actors needed amplification:
So [the Greeks placed vessels] in certain recesses under the seats of theatres, fixed and arranged with a due regard to the laws of harmony and physics, their tones being fourths, fifths, and octaves; so that when the voice of the actor is in unison with the pitch of these instruments, its power is increased and mellowed by impinging thereon.20
This was by way of demonstrating that an architect must be the master of many subjects – not so difficult as it might seem, thought Vitruvius, for a very Pythagorean reason:
For the whole circle of learning consists in one harmonious system. . . . The astronomer and musician delight in similar proportions, for the positions of the stars answer to a fourth and fifth in harmony. The same analogy holds in other branches of Greek geometry which the Greeks call λóγος πτικòς: indeed, throughout the whole range of art, there are many incidents common to all.
Music, wrote Vitruvius, assists an architect ‘in the use of harmonic and mathematical proportion. He would, moreover, be at a loss in constructing hydraulic and other engines, if ignorant of music.’21
Meanwhile, the insidious trickle of pseudo-Pythagorean works that had begun in the third century B.C. had become a veritable industry by the first, with publishers and authors trying to meet a continuing demand for books supposedly written by Pythagoras or his earliest followers, or by Philolaus or Archytas. Rome and Alexandria were the places to buy, sell, and collect these scrolls, but those who snapped them up were not only Roman and Alexandrian readers. King Juba II of Numidia, who came to Rome for his schooling, was one of the most avid collectors.22 The pseudo-Pythagorean books are no help in discovering the real Pythagoras, and would represent unfortunate pitfalls for Pythagoras’ biographers, but they are time capsules of what scholars and the public in the third through first centuries, and well beyond, thought Pythagoras had taught and who he had been.
The Pythagorean Notebooks were relatively early, from the period when Alexandria was the centre of Hellenistic culture and Greco-Roman culture was still largely a thing of the future, and they did not survive long even in complete copies. Their originals are almost as lost in the past as their supposed author. No one knows who wrote them, but it was not Pythagoras, for the author clearly had read the Timaeus and was familiar with Plato’s unwritten doctrines. In an excerpt preserved by Diogenes Laertius, one of the first sentences mentioned the Indefinite Dyad.[7] Traces of pre-Platonic material received an unintentional Platonic update, while passages that depended on later knowledge appear to have been intentionally reworked with an early-Pythagorean twist. Regarding the gestation period of a human embryo: ‘According to the principles of harmony, it is not perfect till seven, or perhaps nine, or at most ten months’. The ‘harmony’ sounded Pythagorean, and ‘ten months’ like a Pythagorean stretch of nature, but other passages having to do with medical matters seem to have mimicked Hippocrates, for whom there was also a large body of ‘pseudo’ literature. A discussion of the significance of opposites in the cosmos rapidly segued into Aristotle, made to sound more ‘primitive’. Aristotle had written that the region below the orbit of the Moon is impure and chang
eable, but beyond it, all is pure and unchanging, while the Notebooks told of the ‘mortal’ area near the earth being stale and ‘pregnant with disease’, and the ‘upper air’ ‘immortal and on that account divine’.[8] Modern scholarship dates the Notebooks to the second or third centuries B.C., not earlier, and certainly not to the sixth century.
Another best-selling pseudo-Pythagorean work was Lysis’ Letter to Hipparchus, supposedly authored by the Lysis who moved to Thebes after the dispersal of the Pythagoreans in Magna Graecia. Lysis was a real person, teacher of the general Epaminondas, but he did not write this letter. In it, ‘Lysis’ accuses Hipparchus, another Pythagorean, of ‘philosophising in public, which Pythagoras deemed unworthy’. To prove that Pythagoras frowned on such lack of discretion, the letter writer tells of Damo, ‘daughter of Pythagoras’. Diogenes Laertius quoted:
When he had entrusted his commentaries to his daughter Damo, he charged her not to divulge them to anyone outside of the house. Though she might have sold his discourses for much money, she did not abandon them; for she thought that obedience to her father’s injunctions, even though this entailed poverty, was better than gold, and for all that she was a woman.23
Linguistic analysts place the Letter in the first century B.C., but some scholars prefer to think it was written at the time of the appearance of the Pythagorean Notebooks in order to support their authenticity.24 The claim would have been that the Notebooks were the very discourses that Damo had refused to sell, just recently rediscovered. If the Letter was a concoction to support the Notebooks, then it was written earlier than 100 B.C. and probably earlier than 200 B.C. But no scholar today believes that Lysis’ Letter to Hipparchus was written in the fifth century B.C. by the historical Lysis.
The fate of another book, On the Nature of the Universe by Occelus of Lucania, is an example of the confusion that occurred even when scholars were well-intentioned. Although Occelus probably lived in the second century B.C., in the early half of the first century A.D. his book was mistakenly regarded as an authentic early Pythagorean text. Occelus and his family considered themselves to be Pythagoreans, but the innocent Occelus had apparently been writing for himself, not trying to pass his book off as something written earlier.25 However, no less a scholar than Philo of Alexandria, the first-century Grecian-Jewish philosopher, was fooled. Occelus had insisted that the cosmic order was eternal; there was no need for a doctrine of creation. Philo, unaware that Occelus lived after Aristotle, treated his book as evidence that early Pythagoreans, not Aristotle, were the first to introduce the idea that the world is eternal.26
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