The Music of Pythagoras (30 page)

There had been hints before of a way of looking at the world in which physical matter was evil or at least negative, and in Moderatus this view came much more to the fore. Physical matter was a “shadow,” and that, to him, meant something more negative than it had to Plato. It was “not-being.” But Moderatus thought that everything including matter came from the One, and the One was “the Good.” He failed to address the question of how anything wholly good can produce evil, but the problem of the origin of evil was looming on the philosophical horizon.

At the opposite extreme of the Empire, in about
A.D
. 125, Theon of Smyrna wrote
Mathematics Useful for Understanding Plato
. It included arithmetic, harmonics, astronomy, geometry, the symbolism of the numbers 1 through 10, different forms of the
tetractus
, and the
tetractus
’ link with music and the cosmos.
¹⁶
“The one who bestowed it was Pythagoras,” wrote Theon, “and it has been said that the
tetractus
appears indeed to have been discovered by him.” One passage sounded like a collage of almost everything that had been Pythagorean, or been
thought to be, up to Theon’s time. But if Theon’s mathematics were “useful,” the mathematics of Nicomachus of Gerasa, a generation later, in the mid-second century, would prove, for better or worse, much more so over a very long period of time. Nicomachus was one of those mathematicians who rejected Euclid’s abstract theorems of numbers and their proofs, preferring to stick to what he thought were “Pythagorean mathematics” and to offer only numerical examples. His
Introduction to Arithmetic
was intended to be not an original contribution, but, essentially, a textbook, and that was what it turned out to be for most of Europe for more than a thousand years, until the Renaissance. The opening passages were a paean to Pythagoras, and largely because of that, for centuries—long past the Renaissance, in fact—the Pythagoreans were regarded as the source of Greek mathematics. W. K. C. Guthrie was not overstating the case when he wrote,

Everyone comes upon the name of Pythagoras for the first time in school mathematics; and this has been true from the earliest stages of the Western cultural tradition. None of the ancient textbooks which formed the basis of the medieval curriculum forgets Pythagoras. . . . the origin of this tradition: Nicomachus.
¹⁷

Nicomachus also wrote a
Handbook of Harmony
that linked the ratios of music with the movements of the heavenly bodies. That book has survived complete, while his two-volume, avowedly Pythagorean
Theology of Numbers
survives in fragments. Nicomachus set up a correlation between the numbers 1 through 10 and the gods of Olympus that Iamblichus and Proclus would later use in a last-ditch defensive effort against Christianity, on behalf of Greek philosophy and pagan religion.
¹⁸
Nicomachus’
Life of Pythagoras
, now lost, was a source for the Pythagorean miracle stories.
*

The neo-Pythagorean philosophical tradition ended on a strong note with an extraordinary writer and thinker named Numenius of Apamea. Born in Syria, he produced his most important work, only fragments of which survive, around
A.D
. 160. His books were available, however, long enough for Porphyry and others to read and discuss them in the next century when they studied with the philosopher Plotinus.
*

Numenius believed that the teaching of Plato’s Academy in its purest form came from Pythagoras, but he wanted to know where Pythagoras had, in turn, got his ideas and knowledge. He took at face value all the stories of Pythagoras’ travels, and he unearthed what seemed to him “Platonic” philosophy (that Plato got via Pythagoras) among the Egyptians, the ancient peoples of India, and the Magi of Mesopotamia, as well as in the Hebrew Scriptures. His goal was to trace knowledge to the earliest, highest, primal sources, because, in his opinion, it had all been downhill from there. “Who is Plato but Moses speaking Greek?” he asked, and retold the story of Moses and the plagues in Egypt from a more Egyptian point of view, in which Pharaoh’s magicians had more success combating the plagues than they did in the Hebrew Scriptures.

According to Numenius’ most ambitious work, his six-volume
On the Good
, “the Good” or “the First God” (what other neo-Pythagoreans called the One) was not completely inaccessible. Sense perceptions were not helpful, but a human could work on finding access. In an exquisite passage, Numenius described the degree of solitude necessary for an approach to the Good or the First God:

Like someone seated in a lookout post, who, straining his eyes, manages to catch a glimpse of one of those little fishing vessels, a one-man skiff all alone, isolated, engulfed in the waves, even so must one remove oneself far from the things of sense, and consort alone with the Good alone, where there is neither human being nor any other living thing, nor any body great or small, but some unspeakable and truly indescribable wondrous solitude—there, are the accustomed places, the haunts and celebrations of the Good, and it itself in peace, in
benevolence, the tranquil one, the sovereign, mounted graciously upon Being.
¹⁹

Numenius also urged a more active approach: disregarding “sensibles” and devoting oneself enthusiastically to learning the sciences and studying numbers, so as to attain the knowledge of what is Being.
²⁰
He did not regard Plato as a high point in the history of knowledge—rather as part of a downward slide—but he was not unappreciative and gave him a backhanded compliment: “He was not superior to the great Pythagoras, but perhaps not inferior either.” He called Socrates a Pythagorean, and Plato a brilliant mediator between Pythagoras and Socrates.

Numenius introduced a doctrine of “three gods” that he called “typically Pythagorean.” Though it might have been possible to find hints of the idea in the work of other neo-Pythagoreans (Moderatus, for example, thought the Pythagoreans believed in three “unities”), in Plato, and in the pseudo-Pythagorean literature, “typically Pythagorean” was an overstatement. Numenius’ “three-god” passages suggest he was clinging to the theology of Pythagoras/Plato and the polytheism of the pagan world, while at the same time reaching for the concept of the Christian trinity—a prodigious intellectual and theological balancing act. He saw a philosophical need for a trio of roles in the creation and sustenance of the universe and came close to what others would call the Father, Son, and Holy Spirit.

Numenius’ First God was intrinsically good, the source of all goodness, and, more than anything else, rational, an intellect—what the earliest Pythagoreans had touched in the discovery of the ratios of musical harmony. This god was “the Good” of Plato, “the One” of the Pythagoreans and neo-Pythagoreans. The “thinking” of this god was the source of life. In the work of Numenius—in a mind deeply informed by Plato but moving beyond him—what had come to the first Pythagoreans as a revelation was, at last, receiving a brilliant philosophical and theological workout.

Numenius’s Second God was responsible for the reincarnation of souls and also a mediator between the First God and the material, human, physical world, and had therefore to have two natures in order to understand and focus on both. Numenius gave a great deal of thought to the roles of the Second God and the paradoxes involved. Difficulties
that would be the subject of debate in the early Christian church regarding the nature of Christ were already being given deep consideration by the pagan Numenius.

The Third God was either the created cosmos or the world soul. Numenius did not make clear his ideas about which it was and seemed not to think the question was important. But he struck a note firmly in the Judeo-Christian tradition (Numenius loved the Hebrew Scriptures) of creation in the image of God when he wrote that “the nature and Being that possess knowledge is the same in the god who gives and in you and me who receive.” He laid all this at the feet of Pythagoras with the words “and that is what Plato meant when he said that wisdom was brought by Prometheus to mankind together with the brightest of fires.” Ever since Plato wrote that passage, the intellectual world had thought he was speaking of Pythagoras. Numenius did not disagree.

With him, the problem of the origin of evil at last reared its head in Western philosophy. Numenius wrote that all living things, including the world itself, have two souls. The good soul was the soul he was referring to when he wrote “the nature and Being that possess knowledge is the same in the god who gives and in you and me who receive.” The bad soul was made up of primeval matter originating before any god “adorned it with form and order.” What was the source of the bad soul? Was there only one source of everything, a good god, who then “withdrew from its own nature,” as Numenius put it, to make room for the existence of evil? (Asking the question in Pythagorean words: Did the One have to give up something of itself so that “plurality” and the rest of a table of opposites could exist—including the opposite of good, evil?) Numenius’ answer was no. Evil did not emerge from Good or from God. Good or God did not relinquish anything or move aside. Evil was as old as God. There was no One overarching the opposites. Both good and evil were part of primordial reality. Anything else was an incorrect interpretation that had emerged when “some Pythagoreans did not understand this doctrine.”
²¹

After Numenius, it became impossible to differentiate neo-Pythagoreanism from neo-Platonism.

N
EAR THE END
of the second century
A.D
., Ptolemy (or Claudius Ptolemaeus), who did not call himself a Pythagorean and was sometimes
critical of the Pythagoreans, picked up strongly on the idea of the harmony of the spheres and gave it a long future. He lived and worked at Alexandria and was interested in a great variety of subjects, including acoustics, music theory, optics, geography, and mapmaking. His most brilliant accomplishment was to draw together, from previous ideas and knowledge and out of his own mathematical genius, the Earth-centered astronomy that would dominate Western thinking about the cosmos for more than a thousand years. Ptolemy’s book
Harmonics
also had an impact on the history of science, because Johannes Kepler read it in the seventeenth century. One of Ptolemy’s sources was probably Archytas.

Ptolemy knew that harmony in music was based on mathematical proportions showing up in sound, and he agreed with the earliest Pythagoreans that mathematical principles underpin the entire universe, including the movements of the heavens and the makeup of human souls. He devoted nine chapters in
Harmonics
to the harmony of the spheres, applying harmonic theory to planetary motions.

One principle Ptolemy followed was to “save the appearances”—that is, not to make up theories that contradicted what one actually saw happening. He would not have proposed ten heavenly bodies because of the importance of the number 10, if he could not see ten in the sky. His astronomy looks superficially, to modern eyes, as though its inventor made up rules and patterns but never looked up. Indeed, Kepler wrote that “like the Scipio of Cicero he seems to have recited a kind of Pythagorean dream rather than advancing philosophy.”
²²
But the evidence that seems overpowering now could not be detected in Ptolemy’s day. When Aristarchus of Samos proposed a Sun-centered astronomy in the third century
B.C
., his theory was dismissed on the sound basis that the evidence for it was, simply, not there. For Ptolemy, with musical harmony, “what one actually saw happening” translated to what one actually
heard
happening. The judgment of the human ear about what was pleasing was of first importance when considering theoretical possibilities.

The system of heavenly harmony that Ptolemy worked out was more complicated than previous ones. The early Pythagoreans may have connected the intervals of the octave, fourth, and fifth (rather than a complete scale) to a cosmic arrangement. Or perhaps the ten-body cosmos, with an octave separating the central fire and the outer
fire, did constitute a complete scale once all the intervals between were filled in. Plato’s “Myth of Er” and Cicero’s “Dream of Scipio” proposed cosmic scales of eight or seven notes respectively. Pliny, much more specifically, would have had the cosmos sounding the following scale:

Ptolemy, from a medieval book illustration