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Acknowledgments
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.
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
A Note on the Author
Kitty Ferguson is the author of the highly acclaimed 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; and Stephen Hawking: Quest for a Theory of Everything. She is also a Juilliard-trained professional musician.
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
Philo 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
Copyright © 2008 by Kitty Ferguson
All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission from the publisher except in the case of brief quotations embodied in critical articles or reviews. For information address Walker & Company, 175 Fifth Avenue, New York, NY 10010.
Published by Walker Publishing Company, Inc., New York
Maps by Jeffrey Ward
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* The stories of the three biographers themselves are in Chapter 13.
* There was an Olympic victor in the 588 B.C. games whose name was Pythagoras of Samos, as recorded in the highly reliable lists of Eratosthenes, the famous librarian at Alexandria who first measured the circumference of the earth. Eratosthenes conjectured that this man and Pythagoras the philosopher were one and the same. In order for that to be true, Pythagoras the philosopher would have had to have been born a few decades earlier than is usually supposed, in the late seventh century. For the Olympian Pythagoras to have been Eurymenes (who might have adopted the name of his teacher as the son of Eratocles did), Pythagoras the philosopher would have had to have been earlier still. What the appearance of the name in the Olympic victory lists probably does mean is that the name Pythagoras was current on Samos before Mnesarchus decided to name his son in honor of the Pythian oracle at Delphi.
* Both tunnel and harbor still exist, though the harbor is now hidden below sea level, under later construction. You can visit the tunnel and walk a good distance into it. In an ingenious design, the walkway is separate and above the watercourse.
* Iamblichus linked the date with the Olympic victory of Eryxidas of Chalcis, his own home city. Diogenes Laertius agreed that it had to have been between 532 and 528 B.C.
* Milo is also known as Milon. His name has come to symbolize extraordinary strength. He was the most famous wrestler in the ancient world.
* In the twenty-first century, 2,600 years later, the people of former Magna Graecia still do not totally identify with the modern, centralized Italy. Old attitudes and identities die hard.
* Porphyry said he got this information from Dicaearchus.
* In some of the remoter villages of those mountains, the people in the twenty-first century still speak a form of Greek that linguists identify as neither modern Greek nor the Byzantine Greek that arrived with Byzantine Christian Greeks in late antiquity and the early Middle Ages, but as an ancient form of the language that is spoken almost nowhere else in the world.
* Diogenes Laertius took the story from the writing of Diodorus, a scholar of the first century B.C. who in turn got the story from the writing of Plato’s pupil Heracleides of Ponticus.
* Scholars regard this quotation as likely to be genuinely early, because it made light of Pythagorean belief, rather than extol it as would have happened later, in an overly adulatory period.
* Think of having the lowest string tuned to C on the piano, the fourth string tuned to F above the C, the next to G a whole step above that, and then the top string tuned at C an octave above the lower C.
* Musical instruments and human voices, because of intricate differences in the way their structures resonate and amplify sound, emphasize or “bring out” certain overtones more than others, and that is what causes the great variety of sounds they make. That is how a trumpet ends up sounding like a trumpet while a clarinet sounds like a clarinet.
† On the piano, equivalent notes might be, for example, middle C (ground note); c (octave above that ground note); g (fifth above that octave); c (fourth above that g). For a demonstration using the piano: Press down gently on the c above middle C without allowing it to sound (removing the damper from the strings). Strike middle C (the ground note) and you will clearly hear the octave. Press carefully on the g above that octave. Strike middle C and you will hear that fifth
above the octave. A piano is not tuned to the Pythagorean system, but it is close enough for you to hear these overtones.
* A gnomon is an instrument for measuring right angles, like the device used by carpenters called a “carpenter’s square.”
* Not all pyramids have only four sides. The Great Pyramid that Pythagoras may have seen in Egypt is not a pyramid of this sort. It has five sides: a square base and four triangular sides.
* In some later ancient mathematics, whose roots can be traced to the “Pythagorean” tradition and which by some scholars’ interpretation existed separately and in parallel with the Euclidean tradition, the number 2 also had no status as a “number.” It was not considered even or odd or prime. Like “1,” it was not a number at all, but the “first principle of number.”
* Heracleides Ponticus is not to be confused with the earlier Heraclitus who so severely criticized Pythagoras. Heracleides Ponticus lived in the fourth century B.C. and was a pupil of Plato.
* Part of their “present condition” was an economy that was more primitive than Croton’s. They used no coinage, and would not until more than a century later. See W. K. C. Guthrie (2003), p. 178 n.
* “Theorem” has implications, in modern terminology, that do not apply to the earliest knowledge of this rule. With that in mind, this book will nevertheless continue to use “theorem” to avoid seeming to mean something different from what everyone calls the Pythagorean theorem.
† There were more than one Apollodorus, but this one was probably Apollodorus of Cyzicus, who lived in the fourth century B.C.
* The claim has never been that Pythagoras discovered the right angle or right triangle, but that he discovered the relationship between the three sides of a right triangle—what we call the Pythagorean theorem.
* You can think of 3–4–5 as 3 inches, 4 inches, and 5 inches, though it could just as well be centimeters, miles, parsecs or any other unit of measurement.
† Unfortunately, most of Babylon of the early second millennium B.C. cannot now be excavated because it is well below the water table.
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