That is a sound which, sundered by unequal intervals, that nevertheless are exactly marked off in due proportion, is produced by the movement and impulse of the orbs themselves, and, commingling high and low tones, causes varying harmonies in uniform degree; for such swift motions cannot be produced in silence, and nature ordains that the extremities sound low at one end, high at the other. Hence the course of the starry heaven at its highest, where the motion is exceedingly rapid, moves with a sharp, quick sound; while the moon in its course (which is the lowest of all) moves with a heavy sound; for earth, the ninth of these bodies, biding immovable in one place, ever holds fast in the center 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 tones, with measured intervals between.” By imitating this harmony with strings and voices, “skilled men have opened for themselves a way back to this place, as have others who with outstanding genius have all their lives devoted themselves to 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, just as “where the Nile at the Falls of Catadupa pours down from lofty mountains, the people who live hard by lack the sense of hearing because of the cataract’s roar.”17 He gave no indication that he knew Pythagoreans had thought the Earth was not the center 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) realization 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 realization of Vitruvius’ works
Vitruvius’ book referred to an unusual application of musical fourths, fifths, and octaves used in an amplification system in Greek theaters. A Roman theater, he pointed out, being made of wood, had good acoustics, but in a Greek theater, 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 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 center 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.* 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 changeable, 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.” † 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 “philosophizing 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
By the first century B.C., it had become widely accepted that Pythagoras himself had left no writing, though Diogenes Laertius would later claim otherwise. Works like the Notebooks and a three-part book supposedly by Pythagoras (actually from the late third century B.C.) on education, politics, and physics were no longer generally credited, but that did not end the forgeries. It became fashionable to “discover” writings by Pythagoreans like Lysis, the fictional Timaeus, Archytas, and the women Theano and “Phyntis, Daughter of Callicrates.” Some offered advice and maxims for daily living. Others claimed to be authentic Pythagorean scientific and philosophical treatises. Many give themselves away today by showing heavy influence from Plato and his pupils, from Aristotle, and from the Stoics, or because their authors made inept attempts to imitate the Doric dialect spoken by the Greeks in Magna Graecia in Pythagoras’ time.27 Even when it was not in “Doric,” the writing often had a flowery, pseudo-poetic flavor. (Think of modern attempts to sound like “merrye olde England” and the only slightly more sophisticated efforts of Victorian authors to reproduce medieval speech.) Other Pythagorean forgeries betray themselves simply by their banality; had these been the works of Pythagoras and his followers, the Pythagoreans would hardly have been worth remembering.*
According to one count, at the height of the era of Pythagorean forgeries, there were eighty works “by Pythagoras” in circulation and two hundred purporting to be by his early followers.28 How could so many readers have been fooled? Not all were. Callimachus, in the mid-third century B.C., declared that a poem Pythagoras was supposed to have written was not authentic. He worked at the Library of Alexandria, and if anyone could spot a forgery, he could. Most readers cannot, however, be seriously blamed for failing to recognize that the pseudo-Pythagorean books were not genuine. The words from the fragment of Posidonius, to the effect that a certain view “was originally that of Pythagoras but Plato developed it and made it more perfect,” reflected the assumption that Pythagorean and Platonic doctrines were virtually one and the same—that Plato’s philosophy derived from Pythagoras. For readers who believed that, and especially for those who were not aware of how different the philosophies of Plato and Aristotle were from each other, it was an easy step to believe that Aristotle also got his ideas from Pythagoras. So when Platonic and Aristotelian ideas showed up in works claiming to come from before the lifetimes of these two philosophers, why wonder? Was it not from these very documents that Plato and Aristotle had learned?
Pseudo-Pythagorean literature continued to appear for several centuries and was immensely popular. You could pick up a knowledge of “Pythagorean doctrine,” unaware or ignoring that it combined some genuinely old material with simplified or summarized Plato and Aristotle, mixed with a good dose of Stoicism, and (in the later books) given a neo-Platonic overcast. You could memorize the maxims of the Golden Verses of Pythagoras, or require your children to do so. As was true of The Prophet by Khalil Gibran in the twentieth century, you might not notice, or might not care, that what came in the format of authentic ancient wisdom was mostly a contemporary poetic invention and interpretation. The maxims were wise and some of them beautiful. You could find out what “Pythagoras” had recommended regarding the medicinal and magical powers of plants. If it caused you to feel better, this, rather than any scholarly debate, proved the efficacy and authenticity of the book. You could learn what “Archytas” had contributed to knowledge about architecture, agriculture, flutes, ethics, mechanics, wisdom, prosperity, adversity, and “intermediary comfort”—never mind that he had actually had little or nothing to say about some of these subjects. Roman and Hellenistic readers could devour these works, share them, discuss them, make gifts of them, have them read beautifully at weddings and funerals, find themselves uplifted and improved by their high-minded ideas and sometimes enlightened by information that was helpful or challenging no matter where it came from. Romans could feel that they knew something about—and had derived benefit from—their own, magnificent, nearly home-grown sage.
The pseudo-Pythagorean texts outlasted the Roman Empire. On the World and the Soul, supposedly by “Timaeus of Locri,” was still being recopied in the Middle Ages by scholars who believed this was the early Pythagorean work from which Plato got his cosmology. Copernicus translated Lysis’ Letter to Hipparchus. One begins to realize the enormous research difficulties, distinguishing Pythagorean fact from fiction, that would confront Diogenes Laertius, Porphyry, and Iamblichus.
CHAPTER 12
Through Neo-Pythagorean and Ptolemaic Eyes
First and Second Centuries A.D.
FASCINATION WITH PYTHAGORAS among Roman and Alexandrian philosophers and scholars of the first century B.C. led to a movement in the first and second centuries A.D. called middle-Platonic or neo-Pythagorean. Books and fragments from men powerfully drawn to what they believed were Pythagorean philosophical and mathematical ideas survive from this period. Some of these writers called themselves Pythagoreans. All regarded Pythagoras as a well-spring, in some cases as the unique wellspring, of a precious intellectual and philosophical heritage that had reached them through Plato.1 The association of Pythagoras with magic and the occult also continued. Nigidius Figulus’ first-century-B.C. version of Pythagoreanism contributed to a growing popular image of Pythagoras—and, oddly, Archytas—as magicians. Nigidius’ desire to bring back Pythagoreanism as a way of life and an ongoing approach to the world would attract others in the centuries to follow.
The most important neo-Pythagorean philosophers were, to a man, not from Rome but from other parts of the Empire—Alexandria, predictably, but also from what is now Turkey, from Syria, and even from the Atlantic coast of Spain. The cultlike groups flourished in Rome itself. Information about one of these came through Lucius Annaeus Seneca, an eminent Roman statesman and orator of the first century A.D. Seneca was a pupil of Sotion, who belonged to a philosophical movement known as the Sextians. The founders, Quintus Sextius and his son, wer
e men of strong moral fiber whose ideal was moral perfection. Theirs was a staunch, Roman approach in which the important thing about a philosophy was how it affected a man’s everyday behavior and practical life. Sextians were hard to distinguish from Stoics, but two of their practices were definitely considered to be “Pythagorean”: they did not eat the flesh of animals and they performed a self-evaluation at the end of each day, to take stock of personal moral improvement or decline. While no trace of that practice can be found in early Pythagorean communities, it had begun to be associated with “Pythagoreans” in the first century B.C., and Cicero called it a “Pythagorean custom.” Seneca described it, as he had learned it from Sotion: A Sextian asked himself, “What bad habit have I cured today?” “What temptation have I resisted?” “In what ways am I a better man?” Similar questions had appeared in the pseudo-Pythagorean booklet called the Pythagorean Golden Verses:
Never let slumber approach thy wearied eyelids
Ere thrice you review what this day you did:
Wherein have I sinned? What did I? What duty is neglected?
All, from the first to the last, review; and if you have erred, grieve in your spirit, rejoicing for all that was good.2
Sotion had also urged Seneca to adhere to a vegetarian diet, for “souls and animals return in regular cycles. Great men have believed this is so. If these things are true, you avoid guilt by abstaining from meat; if false, you gain in self-control.”3 Seneca’s father, who abhorred philosophy, frowned on all this, but Seneca ignored him and avoided meat for more than a year, until under the reign of Tiberius it became dangerous to practice what might be interpreted as a foreign cult.
The Music of Pythagoras Page 19