The Music of Pythagoras (20 page)

Plato himself provided a window through which we view Archytas. No matter how accurately Archytas reflected Pythagoras and Pythagorean thinking, we see him through
Plato’s
eyes and with Plato’s mind, the eyes and mind of one of the most creative thinkers in all history. It is in the nature of such a man, if he is impressed with an idea, to take the ball and run with it—to say, “This is, of course, what you mean,” and restate someone else’s good idea with a spin that makes it absolutely brilliant—and his own, not the original. Assuming Archytas was an exemplary Pythagorean, when Plato got the ball to the other end of the field, was it anything like the same ball he had caught in the pass from Archytas? That is one of the most debated questions in all the long history of those who have yearned to know what Pythagoras himself, and Pythagoreans before Plato, really discovered and thought.

On one significant issue, Plato disagreed with Archytas, and that disagreement is a welcome clue, a clear indication of something in pre-Platonic Pythagorean thinking, undiluted by Plato, that differed from Plato. Archytas, Plato complained, was too concerned with what one could see and hear and touch, and with searching for mathematics and numbers to explain it. For Plato, the goal of studying mathematics was to turn away from experience that humans have through their five senses to a search for abstract “form,” out of reach of sensory perception.
Numbers and mathematical understanding were a venture into abstract form, but not the same, he thought, as his own concept of the ultimate understanding of “the beautiful and the good.” This difference, in Plato’s view, made Archytas an inadequate philosopher and himself a better one.

P
LATO’S KNOWLEDGE ABOUT
Pythagoras and Pythagoreans was not confined to what he learned through Archytas. There is evidence in his dialogues that he heard about them from Socrates; also, Plato and Archytas both knew of Philolaus. If the characters in Plato’s dialogue
Phaedo
are not entirely fictional, he was acquainted with contemporaries who were “disciples of Philolaus and Eurytus” in Phlius, a community west of Corinth, as well as with Echecrates, who speaks for them in the dialogue, and Simmias and Cebes. Plato also knew about Lysis of Tarentum who, like Philolaus, had emigrated to Thebes. The Pythagorean community there was apparently still in existence in Plato’s time.

Plato could not have avoided also knowing about
acusmatici
Pythagoreans who did not agree that scholars like Archytas were Pythagoreans.
⁸
The Greek public in the fourth century
B.C
. generally failed to recognize a distinction between
mathematici
and
acusmatici
and lumped all “Pythagorists” together as an eccentric lot. Athenian comic dramatists lampooned them as unwashed, secretive, arrogant characters who abstained from meat and wine and went about ragged and barefoot. Plato’s pupils, educated at his Academy in the “Pythagorean sister sciences”—the quadrivium of arithmetic, geometry, astronomy, and music—spoke of their philosophy and that of Pythagoras as one and the same and featured him in their books. They were certainly more in the
mathematici
tradition than in the
acusmatici
, but they nevertheless were the targets of the same jibes.

The unshakable conviction of the men who inspired the caricature—that they were following in the authentic footsteps of Pythagoras and preserving a precious tradition—caused some of their contemporaries to feel, a bit uncomfortably, that even the most eccentric were favored by the gods and privy to mystical secrets. Antiphanes, in his play
Tarentini
(the title connects it with Tarentum) spoke of Pythagoras himself as “thrice blessed,” and Aristophon had one of his characters report:

He said that he had gone down to visit those below in their daily life, and he had seen all of them and that the Pythagoreans had far the best lot among the dead. For Pluto dined with them alone, because of their piety.

Lest anyone conclude that Aristophon approved of Pythagoreans, another character commented that Pluto had to be a very easygoing god, to dine with such filthy riffraff.
⁹

Diodorus of Aspendus, who was not fictional, was described as a vegetarian with long hair, a beard, and a “crazy garment of skins” who with “arrogant presumption” drew followers about him, although “Pythagoreans before him wore shining bright clothes, bathed and anointed themselves, and had their hair cut according to the fashion.”
¹⁰

Aristoxenus—who interviewed the tyrant Dionysius in his Corinthian “retirement”—would have none of this. He was effectively a propagandist for the
mathematici
, taking pleasure in contradicting the
acusmatici
by insisting that Pythagoras ate meat and that the aphorisms were ridiculous, and he tried to disassociate “true Pythagoreans” from what he saw as this unsavory, superstitious group who were giving the movement a bad name. He listed the pupils of Philolaus and Eurytus and called them “the last of the Pythagoreans” who “held to their original way of life, and their science, until, not ignobly, they died out.” Because these men died a few decades before the comic allusions in the plays, dubbing them “the last of the Pythagoreans” was making the point that the butts of the jokes were only pretending to be Pythagoreans.

Aristoxenus’ public relations efforts did not succeed well. Through the fourth century
B.C
., the popular image of Pythagoreans continued to resemble the
acusmatici
more than the
mathematici
. But after the fourth century, the
acusmatici
, with a few exceptions, dwindled and vanished from notice. Had there been no other Pythagorean tradition than theirs, and if they did indeed represent the truer image of Pythagoras and his earliest followers, it would be almost impossible to explain how such an odd cult figure, not far different from others in antiquity, became so dramatically and rapidly transformed in the minds of intelligent men and women as to inspire deep and effective scientific thinking and seize the imagination of centuries of people to come.

Was it all due to Plato? Did he get so excited about something that was mainly legend that he elaborated on it himself until he had made it
hugely significant? At a minimum there had to have been the discovery in music of pattern and rationality underlying nature, and the accessibility of that rationality through numbers—and that was of no small significance. It seems much more reasonable to conclude that Pythagoras, responding to different types of interest and intelligence among his followers, encouraged both kinds of thinking—
acusmatici
for those who needed something naive and more regimented and conservative, and
mathematici
for those with minds eager to grasp difficult, nuanced concepts and explore their implications. He was personally, perhaps, not entirely unlike either group.

However that may be, from the time of Plato, what survived as “Pythagorean” and “Pythagoras” was largely
mathematici
, and that included the conviction that right from the time of Pythagoras himself, and attributable to him, there had been a truly remarkable new approach to numbers, mathematics, philosophy, and nature.

Fourth Century
B.C
.

S
OCRATES WAS NOT
P
LATO’S
fictional creation. Born about thirty years after the death of Pythagoras, near the time Philolaus was born, he fought in the Peloponnesian Wars and then lived a life of intentional poverty as a teacher in Athens. He wrote nothing, and information about what he taught comes only through Plato’s dialogues and similar conversations recorded by Xenophon, another of Socrates’ pupils. Socrates’ teaching method consisted of asking questions. Plato’s dialogues are not word-for-word accounts of real question-and-answer lessons, but are almost certainly faithful to the philosophy as it emerged in conversations like these. When Socrates was seventy, he was accused of impiety and corrupting the youth of Athens. A jury of his fellow citizens sentenced him to death, probably through a dose of hemlock. He died surrounded by his friends and pupils.

In the dialogues Plato wrote, the character Socrates usually directed the discussions, but in Plato’s
Timaeus
he relinquished center stage for many pages to a fictional character named Timaeus of Locri. Timaeus was supposed to be a statesman and scientist from southern Italy, and the ideas Plato put in his mouth were heavily indebted to Archytas, with whom he had apparently spent long hours in Tarentum deep in conversation and bent over mathematical diagrams. Perhaps what Timaeus tells
Socrates and his friends in the dialogue is close to what Archytas laid out for Plato. Or maybe Archytas’ ideas were only a springboard for Plato. Though many opinions have been expressed about those possibilities, no one knows for certain, and the truth likely lies somewhere in between.

Plato carried forward two great Pythagorean themes: (1) the underlying mathematical structure of the world and the power of mathematics for unlocking its secrets; and (2) the soul’s immortality.
¹
The stage is set for discussion of the first when Socrates asks Timaeus, an expert on such matters, to “tell the story of the universe till the creation of man.”
²
Timaeus’ response to this daunting request is a number-haunted, Pythagorean creation story: The mathematical order of the universe was the work of a creative god, whom Plato called the demiurge—not the chief god or the only god, but a figure loosely comparable to Ptah, the Egyptian god at Memphis, or to Jesus acting in the role of the
logos
in the opening of the Gospel of John—“through him all things were created.” This craftsman god, says Timaeus, decided that the universe should be a “living being,” spherical and moving in “a uniform circular motion on the same spot; unique and alone.” Timeaus sets forth a numerical construction of the “world soul”:

• First the creator god took his material and “marked off a section of the whole.”

• Then he marked off another section “twice the size of the first.”

• Next he marked off a third section, “half again the size of the second section and three times the size of the first.”

• Next he marked off a fourth section, “twice the size of the second.”