The Music of Pythagoras

by Kitty Ferguson

  The Music of Pythagoras

  How an Ancient Brotherhood Cracked

  the Code of the Universe and Lit the Path

  from Antiquity to Outer Space.

  KITTY FERGUSON

  Contents

  Cover

  Title Page

  Map

  Lifetimes and Other Significant Dates

  PART I: SIXTH CENTURY B.C.

  0. “At the hinge of legend and history”

  1. The Long-haired Samian

  2. “Entirely different from the institutions of the Greeks”

  3. “Among them was a man of immense knowledge”

  4. “My true race is of Heaven”

  5. “All things known have number”

  6. “The Famous Figure of Pythagoras”

  PART II: FIFTH CENTURY B.C.–SEVENTH CENTURY A.D.

  7. A Book by Philolaus the Pythagorean

  8. Plato’s Search for Pythagoras

  9. “The ancients, our superiors, who dwelt nearer to the gods, have passed this word on to us”

  10. From Aristotle to Euclid

  11. The Roman Pythagoras

  12. Through Neo-Pythagorean and Ptolemaic Eyes

  13. The Wrap-up of Antiquity

  PART III: EIGHTH–TWENTY-FIRST CENTURIES A.D.

  14. “Dwarfs on the shoulders of giants”: Pythagoras in the Middle Ages

  15. “Wherein Nature shows herself most excellent and complete”

  16. “While the morning stars sang together”: Johannes Kepler

  17. Enlightened and Illuminated

  18. Janus Face

  19. The Labyrinths of Simplicity

  Epilogue: Music or Silence

  Appendix

  Notes

  Bibliography

  Acknowledgments

  A Note on the Author

  By the Same Author

  Imprint

  To Serafina Clarke

  PART I

  Sixth Century B.C.

  CHAPTER 0

  “At the hinge of

  legend and history”

  ON THE AEGEAN ISLAND OF Samos, on the narrow arm of the harbor that juts farthest out to sea, there is a stark, skeletal structure. Immense shards of iron look as though they have fallen from the sky in the shape of a huge right triangle. One end of the diagonal has buried itself in the ground. Instead of a vertical line rising from the right angle, there is the statue of a man—lean, elongated, taller than life. He is reaching up with his right arm as though to conjure down the broken piece of iron that, if it were complete, would form the vertical of the triangle. Between his fingers and its lowest tip is a gap, such a gap as separates the finger of God from the finger of Adam in the ceiling of the Sistine Chapel. The triangle is not this man’s creation. It is as old as the universe, as old as truth.

  There is no argument but that this monument captures Western civilization’s image of Pythagoras, a native son of this magical island. The triangle is his classic symbol . . . but, more authentically, he has become the icon of an unexplained but undeniable gift: the ability of human minds to connect with the bedrock rationality of the universe.

  Behind all the veneration of Pythagoras and the undeniably great heritage attributed to him and his followers, behind the assumptions about his accomplishments, the uncritical early biographies, the legends, the debunkings, the forgeries, there was a real person. Who he was, actually—except for illusive wisps of information—is lost in the past.

  Pythagoras and the devotees who surrounded him during his lifetime were obsessively secretive. As far as is known, they left no writings at all. There is no scroll, no text, no fragment, no firsthand account by any witness, no artifact for archaeologists to scrutinize, no tablet to decipher. If such ever existed, they no longer did by late antiquity. The earliest written evidence about Pythagoras himself that modern scholarship accepts as genuine consists of six short fragments of text from the century after his death, found not in their originals but in works of ancient authors who either saw the originals or were quoting from earlier secondary copies. The Pythagorean doctrine of reincarnation is the subject of three of these fragments, two of which also mention Pythagoras’ courage, knowledge, and wisdom. Two others are scornful and derogatory. The sixth is a backhanded compliment in the middle of an unrelated story by the historian Herodotus, who termed Pythagoras “by no means the feeblest of the Greek sages.” None name any discoveries, pinpoint any quotable wisdom or scientific contribution, or give biographical details. Though some treatises about Pythagoras tell you that his contemporaries seem not to have been aware of his existence, that was not the case, for all these fragments assume that Pythagoras was a famous man whose name readers would recognize. That, of course, has continued to be true for two thousand, five hundred years, in spite of the fact that as early as the time of Plato, in the fourth century B.C., Pythagoras and the Pythagoreans were already a mystery, and today they are often described as “an ancient cult about whom almost nothing is known.”

  Those six early fragments are not, however, the full extent of the available evidence about the Pythagoreans—those men and women who followed Pythagoras during his lifetime and who in later generations went on trying to live out his teachings. Philolaus, a not-so-secretive Pythagorean, wrote a book fifty to seventy-five years after Pythagoras’ death, revealing that early Pythagoreans proposed that the Earth moves and is not the center of the cosmos. Plato knew Pythagoreans in the fourth century B.C., was strongly influenced by the idea of the role of numbers in nature and creation, and tried to incorporate what he thought of as a Pythagorean curriculum—the “quadrivium”—at his Academy in Athens. Aristotle and his pupils wrote extensively about the Pythagoreans a few years later, relying on earlier material that still existed then but has since vanished, and on carefully chosen living spokesmen for the oral tradition, before a time when that became contaminated by forgeries. This present book will return frequently to the issues of evidence and how it was and is evaluated. It seems no other group has ever made such an effort to remain secret, or succeeded so well, as the Pythagoreans did—and yet become so celebrated and influential over such an astonishingly long period of time.

  In an attempt to cut through the multilayered veil of twenty-five centuries that hangs between us and whatever happened on the ancient isle of Samos and in the harbor city of Croton, skeptical twentieth-century historians insisted on discarding all but the most concrete, “hard” historical evidence. Though certainly they were right to believe a corrective was needed, they arguably pruned too much, applying standards of their own time to an era for which it was inappropriate and even misleading to do so. The tiny “core of truth” left after discounting all folk wisdom, semi-historic tradition, legend or what might be only legend, and blatant forgeries and inventions can be stated in one paragraph:

  Pythagoras of Samos left his native Aegean island in about 530 B.C. and settled in the Greek colonial city of Croton, on the southern coast of Italy. Though the date of his birth is not certain, he was probably by that time about forty years old and a widely experienced, charismatic individual. In Croton, he had a significant impact as a teacher and religious leader; he taught a doctrine of reincarnation, became an important figure in political life, made dangerous enemies, and eventually, in about 500 B.C., had to flee to another coastal city, Metapontum, where he died. During his thirty years in Croton, some of the men and women who gathered to sit at his feet began, with him, to ponder and investigate the world. While experimenting with lyres and considering why some combinations of string lengths produced beautiful sounds and others did not, Pythagoras, or others who were encouraged and inspired by him, discovered that the connections between lyre string lengths and
human ears are not arbitrary or accidental. The ratios that underlie musical harmony make sense in a remarkably simple way. In a flash of extraordinary clarity, the Pythagoreans found that there is pattern and order hidden behind the apparent variety and confusion of nature, and that it is possible to understand it through numbers. Tradition has it that, literally and figuratively, they fell to their knees upon discovering that the universe is rational. “Figuratively,” at least, is surely accurate, for the Pythagoreans embraced this discovery to the extent of allowing numbers to lead them, perhaps during Pythagoras’ lifetime and certainly shortly after his death, to some extremely farsighted and also some off-the-wall, premature notions about the world and the cosmos.

  One might assume that the above paragraph is a summary merely touching the highlights of what is known about events in sixth-century B.C. Croton, but it is, in fact, all that is known. Though you and I might wish to ask many more questions, the answers are irretrievably lost. No one can claim to tell how Pythagoras and his followers arrived at the religious and philosophical doctrines they espoused, or even precisely what these were . . . or in what specific ways Pythagoras and his followers influenced and changed the culture and civic structure of Croton and the surrounding area . . . or whether whatever caused Pythagoras and his followers to make such volatile enemies was something we would condemn or applaud today . . . or whether the great discovery in music of the power of numbers to reveal truth about the universe was made by Pythagoras himself. It may come as a particular surprise that there has been no mention of a Pythagorean triangle or a Pythagorean theorem in this “core of knowledge” about Pythagoras.

  While historians in the twentieth century were clearing the deck, archaeologists were also playing a role in bringing down the legendary Pythagoras. They uncovered evidence that the “Pythagorean theorem” (or the “Pythagorean rule,” for “theorem” implies a concept that was unrecognized this early) was known long before Pythagoras. Those revelations were not the end of the discussion, for with regard to such knowledge, there is more to be answered than the question of who had it “first.” The way it passed—or may have passed—or failed to pass—from society to society and era to era is a complex, fascinating subject. Was it known and then lost? Or only partly lost? Were there separate discoveries? Equally significant is the way different societies and eras regarded such knowledge, what meaning they attached to it. Was it useful for surveying and building? Was it valued for the way it helped produce beautiful design? Was it considered holy? Was it something to be shared, or to be held in strictest secrecy, or taught only to a few? Was it intriguing in and of itself? Or did it imply something about—or raise questions about—the nature of all being? Did it buttress, or tear down, a trust in the power of numbers to uncover secret truth about the universe? Was there a “proof”? What constituted “proof” before the modern concept of “proof”? With questions like those, the origin of the “Pythagorean theorem” becomes an extremely interesting and complicated issue.

  Numbers and mathematics had been in use for eons before Pythagoras was born, sometimes with more sophisticated understanding than his and his followers’. Their insight in the realm of music was extraordinary in a different way—different from the practical use of numbers or from an artist’s appreciation for a beautiful geometric figure. Different even from the more abstract thinking of an early Babylonian teacher or student who found it an interesting exercise to do the math for a grain pile far larger than could ever be constructed. Imagine a carpenter looking at the hammer and chisel that he holds in his hands, that he has been taking for granted as a useful part of his daily work, and in an instant of dumbfounded recognition seeing that he holds the keys to unlock the doorway to vast hidden knowledge. That was what numbers became for the Pythagoreans and, through them, for the future. With this fresh appreciation—indeed, veneration—of the power of numbers, Pythagoras and his followers made one of the most profound and significant discoveries in the history of human thought. They stood at the sort of threshold that humanity has crossed only a few times. This particular door would not close again.

  The brutally pared-down picture of Pythagoras and the events of his life offered by the twentieth century was no more satisfactory a representation than the one that overcredulous earlier centuries had accepted. All that could be said for it was that it was probably not wrong. But, for me, it has caused a dramatic refocusing of my attention onto the enormous, rich, multilayered, continuously reimagined story of “Pythagoras”—as seen separately from the life and person of the historical Pythagoras. That is the reason this book ends in the twenty-first century rather than in antiquity.

  Amazingly it is the uncertainty about what really occurred and who Pythagoras really was and what he accomplished that has allowed something astounding to happen through the centuries. One truly powerful idea did come authentically from Pythagoras and his earliest followers—the recognition that numbers are a pathway from human ignorance to an understanding of the deepest mysteries of a universe that on some profound level makes perfect sense and is all of a piece. That vision has been a premier guide in the development of science and remains so today. However, the scarcity of sure knowledge about nearly everything else connected with Pythagoras and the Pythagoreans has encouraged generation after generation, beginning as early as Plato and still continuing in the twenty-first century, to reimagine him, to recreate him, to fashion their own variations on the theme of Pythagoras. As composers do in music, such figures as Plato, Aristotle, Ptolemy, Copernicus, Kepler, heroes of the French Revolution, Bertrand Russell, Einstein, and those who are now seeking extraterrestrial intelligence have taken a very slim theme indeed and composed intricate, sometimes whimsical, sometimes weird, often magnificent variations—a metaphor not inappropriate for a story that began with the strings of a lyre.

  Two and a half millennia of writing and thinking and myth-making and composing variations about Pythagoras in one context after another, with one agenda after another, have of course multiplied the difficulties for a “biographer.” Even more difficult to sort out than the outspoken detractors and obvious distortions and forgeries are those who, encountering Pythagorean or pseudo-Pythagorean thought, have joyfully recognized its links with their own thoughts and taken off from there, calling it all Pythagorean, even attributing their best ideas to Pythagoras himself—as Isaac Newton, of all people, did. Or calling none of it Pythagorean, but leaving the way open for others to say it was. Perhaps an author should abandon all hope of nonfiction and write a novel. To a certain extent, that is what two and a half millennia have written.

  All of which might cause one to conclude that this book must be a postmodern parable. It would be difficult to find a better example of ideas, a life story, or a person being re-imagined time after time, century after century. Instead, I have come to see “Pythagoras” as a cubist painting, a Picasso or a Braque—either of whom would have insisted that there is more truth in their cubist paintings than in a photolike portrait. Life and history are impossible to fit together in a completely satisfying, coherent picture—and are continually reinvented in the eye of the beholder.

  This book begins with something resembling a conventional “biography,” indulging in calculated speculation, recounting legends and rumors, reporting intriguing and sometimes conflicting information, trying to discern what most likely happened—or might have happened—given the time and place and context. Much of the information comes through the research of three authors who wrote biographies of Pythagoras seven to eight hundred years after his death, in the third and early fourth centuries A.D., who in their time pieced together second-, third-, and fourth-hand accounts, legends and hearsay, oral tradition, what people believed or guessed, and other writers’ references to lost works—ancient material that ranges from the reliable to the well-meaning and intelligent to the ridiculous. Pythagoras was already a cubist painting, but these three accounts more than any other sources have influenced what the world has thought i
t knew and still thinks it knows about him.

  From the time of those biographies, the Pythagorean story wound its way into the Middle Ages and eventually into the modern world. It followed what is by no means a satisfying linear path. There are threads and trends, but more remarkable is the unavoidable impression that the idea of Pythagoras existed and still exists on an almost subliminal level. It shows up not only where you might expect it, underpinning the work of Copernicus, Kepler, Newton, and Stephen Hawking, but also in odd, unlikely places such as the architecture of Palladio and the philosophical interpretation of the French Revolution, and a grandfatherly figure in a novel by Louisa May Alcott. In spite of all the twentieth-century skepticism, impressive thinkers like Bertrand Russell, Arthur Koestler, and Jacob Bronowski regarded Pythagoras as a towering, foundational figure. Pythagorean principles have become imbedded in our worldview, and the original Pythagorean cracking of the code underpins the continuing development of science.

  Lament the lost story of the life and person of Pythagoras, if you will, but join me in attempting to understand why and how it has birthed and nurtured such a rich tradition and wealth of interpretation, and in celebrating what is not a myth or a lie or even a legend . . . but one beautiful instance of realization about the truth of the universe.

  CHAPTER 1

  The Long-haired Samian

  Sixth Century B.C.

  IN IMPERIAL ROME, THERE WAS a popular myth that the ancient sage Pythagoras had been the son of Apollo. The story was spread in the first century A.D. by Apollonius of Tyana, an itinerant wonder-worker who claimed he was the reincarnated Pythagoras and could speak with authority. The empress Julia Domna, wife of the emperor Septimus Severus, saw to it that Apollonius’ tales were well publicized, in the hope of rivaling Jesus of Nazareth, whose followers believed that he was the son of the god of the Hebrews.