Pythagorus Read online

  BY THE SAME AUTHOR

  Tycho & Kepler: The Unlikely Partnership That Forever Changed Our Understanding of the Heavens

  Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time

  The Fire in the Equations: Science, Religion, and the Search for God

  Prisons of Light: Black Holes

  Stephen Hawking: Quest for a Theory of Everything

  Previously published in the USA in 2008 by

  Walker Publishing Company, Inc., New York

  Published in the UK in 2010 by

  Icon Books Ltd, Omnibus Business Centre,

  39–41 North Road, London N7 9DP

  email: [email protected]

  www.iconbooks.co.uk

  This electronic edition published in 2010 by Icon Books

  ISBN: 978-1-84831-250-0 (ePub format)

  ISBN: 978-1-84831-251-7 (Adobe ebook format)

  Printed edition (ISBN: 978-1-84831-192-3)

  sold in the UK, Europe, South Africa and Asia

  by Faber & Faber Ltd, Bloomsbury House,

  74–77 Great Russell Street, London WC1B 3DA

  or their agents

  Printed edition distributed in the UK, Europe, South Africa and Asia

  by TBS Ltd, TBS Distribution Centre, Colchester Road,

  Frating Green, Colchester CO7 7DW

  Printed edition published in Australia in 2010

  by Allen & Unwin Pty Ltd,

  PO Box 8500, 83 Alexander Street,

  Crows Nest, NSW 2065

  Text copyright © 2010 Kitty Ferguson

  The author has asserted her moral rights.

  No part of this book may be reproduced in any form, or by any

  means, without prior permission in writing from the publisher.

  To Serafina Clarke

  Contents

  By the Same Author

  Title page

  Copyright

  Dedication

  Contents

  Acknowledgements

  Lifetimes and Other Significant Dates

  Map

  Part I: Sixth Century B.C.

  Chapter 0: ‘At the hinge of legend and history’

  Chapter 1: The Long-haired Samian

  Chapter 2: ‘Entirely different from the institutions of the Greeks’

  Chapter 3: ‘Among them was a man of immense knowledge’

  Chapter 4: ‘My true race is of Heaven’

  Chapter 5: ‘All things known have number’

  Chapter 6: ‘The Famous Figure of Pythagoras’

  Part II: Fifth Century B.C.–Seventh Century A.D.

  Chapter 7: A Book by Philolaus the Pythagorean

  Chapter 8: Plato’s Search for Pythagoras

  Chapter 9: ‘The ancients, our superiors, who dwelt nearer to the gods, have passed this word on to us’

  Chapter 10: From Aristotle to Euclid

  Chapter 11: The Roman Pythagoras

  Chapter 12: Through Neo-Pythagorean and Ptolemaic Eyes

  Chapter 13: The Wrap-up of Antiquity

  Part III: Eighth–Twenty-first Centuries A.D.

  Chapter 14: ‘Dwarfs on the shoulders of giants’: Pythagoras in the Middle Ages

  Chapter 15: ‘Wherein Nature shows herself most excellent and complete’

  Chapter 16: ‘While the morning stars sang together’: Johannes Kepler

  Chapter 17: Enlightened and Illuminated

  Chapter 18: Janus Face

  Chapter 19: The Labyrinths of Simplicity

  Epilogue: Music or Silence

  Appendix

  Notes

  Bibliography

  A Note on the Author

  Acknowledgements

  I wish to thank all those friends who, during the years when I was researching and writing this book, have told me about ways – some of them odd and unexpected – that Pythagoras and the Pythagoreans have made an impact, or at least an appearance, in their own fields of study and interest. I also wish to thank my husband, Yale, for the help he has given me out of his own historical knowledge and library, his wonderful company on research journeys to Samos and Crotone, and his invaluable early critique of this book; Eleanor Robson, for her patient help in the area of Mesopotamian mathematics; John Barrow, for calling my attention to the ‘Sulba-Sûtras’ and reconstructing the tunnel of Eupalinos on Samos for me out of a dinner napkin; the staff of the Museo Archeologico Nazionale di Crotone for their extraordinary helpfulness; and the librarians at the Chester Public Library, for their skill and willingness when I came to them with numerous unusual interlibrary loan requests.

  Lifetimes and Other Significant Dates

  CHAPTER 1

  Pythagoras c. 570–500 B.C.

  Thales fl. c. 585 B.C.

  Anaximander 610–546 B.C.

  Diogenes Laertius fl. c. A.D. 193–217

  Porphyry c. A.D. 233–306

  Iamblichus of Chalcis c. A.D. 260–330

  CHAPTER 2

  Babylonian exile of the Hebrews 598/7 and 587/6 to 538 B.C.

  Rule of the Samian tyrant Polykrates 535–522 B.C.

  CHAPTERS 3–6

  Pythagoras’ arrival in Croton 532/531 B.C.

  Croton defeats and destroys Sybaris 510 B.C.

  Death or disappearance of Pythagoras 500 B.C.

  Second decimation of the Pythagoreans 454 B.C.

  CHAPTER 7

  Philolaus c. 474–399? B.C.

  Parmenides 515 or 540–mid-5th century B.C.

  Melissus early 5th century–late 5th century B.C.

  Zeno of Elea c. 490–mid to late 5th century B.C.

  Socrates c. 470–399 B.C.

  CHAPTER 8

  Plato 427–347 B.C.

  Archytas 428–347 B.C.

  Dionysius the Elder c. 430–367 B.C.

  Dionysius the Younger 397–343 B.C.

  Aristoxenus of Tarentum fl. fourth century B.C.

  CHAPTER 9

  Socrates c. 470–399 B.C.

  Plato 427–347 B.C.

  CHAPTER 10

  Aristotle 384–322 B.C.

  Theophrastus 372–287 B.C.

  Alexander the Great 356–323 B.C.

  Heracleides Ponticus 387–312 B.C.

  Dicaearchus of Messina fl. c. 320 B.C.

  Euclid fl. c. 300 B.C.

  CHAPTER 11

  Cicero 106–43 B.C.

  Numa ruled c. 715–673 B.C.

  Ennius c. 239–c. 160 B.C.

  Marcus Fulvius Nobilior 2nd century B.C.

  Cato the Elder 234–149 B.C.

  Pliny the Elder A.D. 23–79

  Posidonius c. 135–51 B.C.

  Sextus Empiricus fl. 3rd century A.D.

  Eudorus of Alexandria fl. c. 25 BC

  Nigidius Figulus fl. no later than 98–27 B.C.

  Vitruvius fl. 1st century B.C.

  Occelus of Lucania after Aristotle

  CHAPTER 12

  Eudorus of Alexandria fl. c. 25 B.C.

  Sotion 1st century A.D.

  Seneca c. 4 B.C.–A.D. 65

  ‘Sextians’ 1st century A.D.

  Apollonius of Tyana 1st century A.D.

  Alexander of Abonuteichos c. A.D. 110–170

  Julia Domna died A.D. 217

  Philostratus A.D. 170–c. 245

  P
hilo of Alexandria 20 B.C.–A.D. 40

  Ovid 43 B.C.–A.D. 17

  Plutarch A.D. 45–125

  Moderatus of Gades 1st century A.D.

  Theon of Smyrna c. A.D. 70–130/140

  Nicomachus fl. c. A.D. 100

  Numenius of Apamea fl. late 2nd century A.D.

  Ptolemy c. A.D. 100–c. 180

  CHAPTER 13

  Diogenes Laertius fl. A.D. 193–217

  Porphyry c. A.D. 233–306

  Iamblichus of Chalcis c. A.D. 260–330

  Longinus A.D. 213–273

  Plotinus A.D. 204–270

  Macrobius A.D. 395–423

  Boethius c. A.D. 470–524

  CHAPTER 14

  Hunayn 9th century

  Brethren of Purity 10th century

  Al-Hasan 10th century

  Aurelian 9th century

  John Scotus Eriugena c. 815–c. 877

  Regino of Prüm died 915

  Raymund of Toledo 1125–1152

  King Roger of Sicily 1095–1154

  Bernard of Chartres 12th century

  Nicole d’Oresme 14th century

  Nicholas of Cusa 1401–1464

  Franchino Gaffurio 1451–1522

  CHAPTER 15

  Petrarch 1304–1374

  Nicholas of Cusa 1401–1464

  Leon Battista Alberti 1407–1472

  Marsilio Ficino 1433–1499

  Pico della Mirandola 1463–1494

  Giorgio Anselmi 15th century

  Nicolaus Copernicus 1473–1543

  Andrea Palladio 1508–1580

  Tycho Brahe 1546–1601

  CHAPTER 16

  Philipp Melanchthon 1497–1560

  Tycho Brahe 1546–1601

  Michael Mästlin 1550–1631

  Johannes Kepler 1571–1630

  CHAPTER 17

  Vincenzo Galilei late 1520s–1591

  Galileo Galilei 1564–1642

  William Shakespeare c. 1564–1616

  John Milton 1608–1674

  John Dryden 1631–1700

  Joseph Addison 1672–1719

  René Descartes 1596–1650

  Robert Hooke 1635–1703

  Robert Boyle 1627–1691

  Isaac Newton 1642–1727

  Gottfried Leibniz 1646–1716

  Carl Linnaeus 1707–1778

  William Wordsworth 1770–1850

  Pierre-Simon de LaPlace 1749–1827

  Filippo Michele Buonarroti 1761–1837

  Hans Christian Oersted 1777–1851

  Michael Faraday 1791–1867

  James Clerk Maxwell 1831–1879

  CHAPTER 18

  Bertrand Russell 1872–1970

  Arthur Koestler 1905–1983

  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 harbour 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 civilisation’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 artefact for archaeologists to scrutinise, 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 recognise. 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 centre 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 harbour city of Croton, sceptical 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 far-sighted 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.