Quoted in Richard Buxton, ed., From Myth to Reason: Studies in the Development of Greek Thought (Oxford, U.K.: Oxford University Press, 1999), p. 74.
Kurt A. Raaflaub, ‘Poets, Lawgivers, and the Beginnings of Political Reflection in Archaic Greece’, in Christopher Rowe and Malcolm Schofield, eds., The Cambridge History of Greek and Roman Political Thought (Cambridge, U.K.: Cambridge University Press, 2000), p. 51.
Plato, Thaetetus, 174 A., quoted by Thomas L. Heath, Greek Astronomy (London: J. M. Dent and Sons, 1932), p. 1, and Arthur Koestler, The Sleepwalkers: A History of Man’s Changing Vision of the Universe (London: Hutchinson, 1959), p. 22.
The story of Thales and the river Halys was one of those collected by Herodotus and included in his Histories I 75.3–5. Reprinted in Barnes, p. 10.
Ian Shaw, Ancient Egypt: A Very Short Introduction (Oxford, U.K.: Oxford University Press, 2004). p. 12.
Porphyry’s biography is reprinted in K. S. Guthrie, p. 124.
Chapter 2: ‘Entirely different from the institutions of the Greeks’
For the information about what Pythagoras might have learned in Egypt, I have relied on David P. Silverman, ed., Ancient Egypt (New York: Oxford University Press, 1997).
For information about Babylon in this era, I have relied on H. W. F. Saggs, Everyday Life in Babylonia and Assyria (Assyrian International News Agency, 1965); and Joan Oates, Babylon (London: Thames & Hudson, 1979). Speculation about the historical timing of Pythagoras’ abduction from Egypt is based on Saggs, p. 25. Modern scholarly knowledge about the city of Babylon during this period comes from a variety of sources: the biblical and Greek tradition, Nebuchadnezzar’s building inscriptions, business, legal and administrative records, and the excavation of the city, which together give a fairly clear picture of life in the Babylonian capital under Nebuchadnezzar II, though there are many details which we do not yet know and may never know.
Chapter 3: ‘Among them was a man of immense knowledge’
Exhibits in the Museo Archeologico Nazionale di Croton suggest the appearance of the ancient city.
Information about Achaea comes from N. G. L. Hammond, A History of Greece to 322 B.C. (Oxford, U.K.: Oxford University Press, 1986), pp. 13 and 118.
Porphyry’s The Life of Pythagoras, reprinted in K. S. Guthrie, 1987, p. 135.
Acts 17:21.
Kurt A. Raaflaub, ‘Poets, Lawgivers, and the Beginnings of Political Reflection in Archaic Greece’, in Christopher Rowe and Malcolm Schofield, eds., The Cambridge History of Greek and Roman Political Thought (Cambridge, U.K.: Cambridge University Press. 2000), p. 57.
Guthrie, William Keith Chambers, The Earlier Presocratics and the Pythagoreans, Vol.1 of A History of Greek Philosophy. (Cambridge, U.K.: Cambridge University Press, 2003), pp. 176–177. Guthrie refers to the historian C. T. Seltman.
Ibid., pp. 176–77.
Chapter 4: ‘My true race is of Heaven’
This overview of Greek beliefs about immortality and the manner in which Pythagorean doctrine fits into this context is based on the discussion in Guthrie (2003), beginning on p. 196, and on W. K. C. Guthrie, The Greeks and Their Gods (Cambridge, U.K.: Cambridge University Press, 1951).
See Betrand Russell, The History of Western Philosophy (London: George Allen & Unwin, 1945).
This is the way the verse in Homer was translated by Alexander Pope.
The story was told by Diogenes Laertius and also by Diodorus in his Universal History X, quoted in Barnes, p. 34.
See W. K. C. Guthrie (2003), pp. 201–202.
Quoted in ibid, p. 199.
Ibid, p. 199.
Ibid.
Eudemus, Physics, fragment quoted by Simplicius in Commentary on the ‘Physics’ 732.23–33. Quoted in Barnes, p. 35.
See Barnes, pp. 167–68.
Material is from Aulus Gellius, Attic Nights, Book IV, xi 1–13. Attic Nights was twenty volumes long, a compendium of miscellaneous knowledge. It and parts of it are available in a number of editions.
For the discussion around the suggestion that the miraculous stories were meant to discredit Pythagoras, see Walter Burkert, Lore and Science in Ancient Pythagoreanism (Cambridge, Mass.: Harvard University Press, 1972), p. 146
Chapter 5: ‘All things known have number’
Ibid, p. 377.
W. K. C. Guthrie (2003), p. 178.
Chapter 6: ‘The famous figure of Pythagoras’
Bronowski, p. 156.
From ‘Surveying’ article in the Encyclopaedia Britannica, 2007, Online, 3 Mar. 2007 http://www.britannica.com/eb/article-51763, p. 2.
This information comes from a conversation with John Barrow and from his book Pi in the Sky: Counting, Thinking, and Being (Oxford, U.K.: Clarendon Press, 1992), pp. 73–75. The information about Indian women and their doorstep paintings comes from personal experience in Kothapallimitta, South India, in 2000, and trying to do it myself.
W. K. C. Guthrie (2003), p. 187.
Except where otherwise footnoted, and except for some information about Tell Harmal, the information in these paragraphs about Babylonian mathematics comes primarily from Eleanor Robson, ‘Three Old Babylonian Methods for Dealing with Pythagorean Triangles’, Journal of Cuneiform Studies (1997) 49, pp. 51–72.
Robson, ‘Mesopotamian Mathematics: Some Historical Background’, in Victor Katz, ed., Using History to Teach Mathematics: An International Perspective (Cambridge, U.K.: Cambridge University Press, 2000), p. 154
Plimpton 322 is now in the collection of Columbia University, in New York City.
See Taha Baqir, ‘An Important Mathematical Problem Text from Tell Harmal’, Sumer 6 (1950), pp. 39–55. Taha Baqir was curator of the Iraq Museum.
Diagram and text reconstruction are from Robson, ‘Three Old Babylonian Methods’, p. 57.
See, for example, Ross King, Brunelleschi’s Dome: How a Renaissance Genius Reinvented Architecture (London: Penguin, 2000).
John Noble Wilford, ‘Early Astronomical Computer Found to Be Technically Complex’, New York Times, November 30, 2006.
For discussion, see Robson, ‘Mesopotamian Mathematics: Some Historical Background’, pp. 154–55. The quotation is from Robson, ‘Influence, Ignorance, or Indifference? Rethinking the Relationship Between Babylonian and Greek Mathematics’, The British Society for the History of Mathematics, Bulletin 4 (Spring 2005), pp. 2, 3.
Ibid., p. 14.
Ibid., p. 10.
See discussion in ibid, pp. 2, 3.
Charles H. Kahn, Pythagoras and the Pythagoreans: A Brief History (Indianapolis: Hackett, 2001), p. 134.
Marcus Vitruvius Pollio, De Architectura, Book IX. Vitruvius’ work is reprinted as Vitruvius: Ten Books of Architecture (Cambridge, U.K.: Cambridge University Press, 2001).
Bronowski, p. 160.
Chapter 7: A Book by Philolaus the Pythagorean
For the discussion of the acusmatici and the mathematici and the question about which were truer to the original teachings of Pythagoras, I have relied on Burkert, particularly the section entitled ‘Acusmatici and Mathematici’.
The names of some mathematici have survived. One was Archytas of Tarentum, and he mentioned Eurytus of Tarentum as one of his predecessors. This was the same Eurytus linked with Philolaus in Plato’s Phaedo. Eurytus and Philolaus had students whose names Aristoxenus listed. They were from Chalcidice in Thrace and from Phlius.
I have mostly followed Burkert regarding the authenticity of fragments of Philolaus; I have also relied on W. K. C. Guthrie (2003) in the discussion of Philolaus’ book and on Guthrie and Jonathan Barnes, Early Greek Philosophy (London: Penguin Books, 1987), for translations of quotations.
Plutarch, On the Face in the Moon 929AB, quoted in Barnes, p. 89.
F
rom Plutarch, Pericles; passage quoted in full in Barnes, p. 92.
Quoted from Aristotle’s Metaphysics, in W. K. C. Guthrie (2003), pp. 287–88.
See W. K. C. Guthrie (2003) p. 248, for the seed of this idea.
W. K. C. Guthrie (2003) wrote that Philolaus was Aristotle’s ‘favourite author’ (p. 260). The quotation is in W. K. C. Guthrie (2003), pp. 307–308.
Quoted in ibid., p. 309.
See ibid., p. 233, for the arguments each way concerning Alcmaeon’s dates. The quotation appears in W. K. C. Guthrie (2003), p. 313.
Plato, Phaedo, quoted in ibid., p. 310.
Quoted in ibid., p. 311.
Quoted in ibid., p. 312.
Chapter 8: Plato’s Search for Pythagoras
Information about Plato’s visits to Megale Hellas (as he would have called it) and Syracuse can be found in many sources. I have used W. K. C. Guthrie (2003), and Malcolm Schofield, ‘Plato and Practical Politics’, in Christopher Rowe and Malcolm Schofield, eds., The Cambridge History of Greek and Roman Political Thought (Cambridge, U.K.: Cambridge University Press, 2000). See also Plato’s own letter (the authenticity of which is debated) addressed to ‘Friends and Followers of Dion’, Letter #7 in his Letters.
For information about Archytas and his work I have relied on Kahn, p. 40ff, and Carl Huffman, Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King (Cambridge: Cambridge University Press, 2005). Unless otherwise noted, the quotations from Archytas are drawn from Kahn.
Burkert, p. 68.
Modern scholars such as Kahn have made a distinction that sets Archytas a little more apart from the earlier Pythagoreans but still keeps him in the tradition. Kahn described Archytas’ harmonic theory as ‘work of original genius . . . working in the Pythagorean musical tradition that is represented for us by the earlier theory of Philolaus’ (pp. 32–43).
From Eudemus (also mentioned by Aristotle), quoted in Kahn, p. 43.
Huffman, pp. 105–6.
Archytas’ description of a bull-roarer, or rhomboi, is in W. K. C. Guthrie (2003), p. 227.
Aristotle, quoted in ibid., p. 335.
For this discussion and the question about which were truer to the original teachings of Pythagoras, I have relied on Burkert, particularly the section entitled ‘Acusmatici and Mathematici’.
The original is Aristophon, fragment 12; see Burkert, p. 199, for the quotation. Burkert was not sure the Greek word used actually referred to the Pythagoreans.
Quotations are from the musician Stratonicus and from Sosicrates, in Burkert, p. 202.
Chapter 9: ‘The ancients, our superiors . . .’
Kahn, p. 50 ff, is especially helpful in interpreting Plato’s thought as it related to the Pythagoreans, and he pinpoints these two themes.
The quotations from Plato’s Timaeus, unless otherwise noted, are taken from the translation by Desmond Lee (London: Penguin, 1977).
From Plato’s Philebus, in Kahn, p. 14.
Ibid., p. 58.
From Plato’s Gorgias, Quoted in W. K. C. Guthrie (2003), p. 305.
Book 7 of Plato’s Republic, quoted in ibid., p. 162.
Plato, Timaeus, in the Stephanus edition (1578), p. 52.
Chapter 10: From Aristotle to Euclid
W. K. C. Guthrie (2003), p. 331. I have closely followed Guthrie in his discussion of Aristotle’s reactions to the Pythagoreans. Where not otherwise noted, the quotations from Aristotle are drawn from Guthrie’s book.
Burkert lists the writers in whose work fragments from Aristotle appear (pp. 28, 29).
‘What the sky encloses’ is a quotation from Burkert (p. 31), but he was paraphrasing Aristotle.
It is no longer generally accepted that, as Burkert states, ‘like all pre-Socratics they take everything that exists in the same way, as something material’ (Burkert, p. 32). That does not apply correctly either to the Pythagoreans or to the other pre-Socratics.
Burkert, pp. 45–46.
W. K. C. Guthrie (2003), p. 259.
The quotation is from Burkert (p. 431), in his discussion of these different possibilities, but he did not favour this choice.
This discussion draws on W. K. C. Guthrie (2003), p. 266 ff, and Burkert, p. 68 ff.
Ibid., p. 226n.
Burkert’s paraphrase of Aëtius, in which he seems to have given only the final four words in direct quotation (Burkert, p. 70).
Quoted in W. K. C. Guthrie (2003), pp. 263–64.
Historical information about this era comes in part from Greg Woolf, ed., Cambridge Illustrated History of the Roman World (Cambridge, U.K.: Cambridge University Press, 2003); and from Paul Cartledge, ed., Cambridge Illustrated History of Ancient Greece (Cambridge, U.K.: Cambridge University Press, 1998).
Specifically in the Elements, Book VII.
One scholar, the German B. L. van der Waerden, insisted that there were writings before Archytas and long before Euclid that dealt with this same material. Kahn calls some of his claims ‘excessive’ (Kahn, p. 41n.). Propositions in Book II of the Elements have very early Babylonian precursors, as the Pythagorean theorem did, that Euclid probably was not aware of (Robson [2005], p. 4).
For information and discussion, see Burkert, p. 432.
This quotation is from Iamblichus, On Common Mathematical Knowledge 91.3–11, translation in I. Mueller, ‘Mathematics and Philosophy in Proclus’s Commentary on Book I of Euclid’s Elements’, in J. Pépin and H. D. Saffrey, eds., Proclus, Lecteur et Interprète des Anciens (Paris: CNRS, 1987). Quoted in S. Cuomo, Ancient Mathematics (London: Routledge, 2001), pp. 236–37.
Chapter 11: The Roman Pythagoras
Marcus Tullius Cicero, The Republic, Book II: xv, translated by G.G. Hardingham (London: Barnard Quaritch, 1884), pp. 137–9.
Quoted in Kahn, pp. 89–90.
From Pliny, Natural History 34.26.
From the Pythagorean Notebooks, excerpt quoted in Diogenes Laertius’ The Life of Pythagoras, reprinted in K. S. Guthrie, pp. 148–49.
Quoted in Simon Hornblower and Antony Spawforth, eds., The Oxford Companion to Classical Civilization (Oxford, U.K.: Oxford University Press, 1998), p. 245.
Thomas Wiedemann, ‘Reflections of Roman Political Thought in Latin Historical Writing’, in Christopher Rowe and Malcolm Schofield, eds., The Cambridge History of Greek and Roman Political Thought (Cambridge, U.K.: Cambridge University Press, 2000), p. 526–27.
Sextus Empiricus, quoted in Kahn, p. 84.
Elizabeth Rawson, Intellectual Life in the Late Roman Republic (Baltimore: Gerald Duckworth & Co., 1985), p. 310.
Cicero, Timaeus, ‘Introduction’. Quoted in Kahn, p. 73.
Kahn, p. 88.
Cicero, Vatinium 6. Quoted in Kahn, p. 91.
Cicero, The Republic, Book I:x, p. 19.
Ibid., Book III:xi, p. 245.
Cicero, On Divination, quoted in Barnes, p. 165–66.
Cicero, The Republic, Book VI:xviii, p. 363 (passages known as ‘Scipio’s Dream’).
Ibid.
Ibid., p. 365.
Vitruvius (Marcus Vitruvius Pollio). De architectura, Book VI. Vitruvius’ work has been reprinted as Vitruvius: Ten Books of Architecture (Cambridge, U.K.: Cambridge University Press, 2001).
Cesariano’s drawing for Vitruvius: ccat.sas.upenn.edu/george/vitruvius.html. The quotation is from Book IX of Vitruvius.
Vitruvius, Book I.
Ibid.
The information about King Juba is from a footnote in Kahn (p. 90) to E. Zeller, Die Philosophie der Griechen in ihrer geschichtlichen Entwicklung I–III (Leipzig: Reisland 1880–92), p. 97.
Lysis’s Letter to Hipparchus, quoted in Diogenes Laertius, The Life of Pythagoras, in K. S. Guthrie, pp. 14
1–55.
Burkert dates the letter to the third century B.C. A. Staedele dates it to the first. Kahn, p. 75, mentions contemporaneity as Burkert’s suggestion, citing Walter Burkert, ‘Hellenistische Pseudopythagorica’, Philologus 105 (1961).
Introduction to the Occelus piece in K. S. Guthrie, p. 203.
Mentioned in Kahn (p. 79), where the footnote refers to a quotation in J. Dillon, The Middle Platonists (Ithaca, NY: Cornell University Press, 1977), p. 156n.
See Bruno Centrone, ‘Platonism and Pythagoreanism in the Early Empire’, in Cambridge History of Greek and Roman Political Thought (Cambridge, U.K.: Cambridge University Press, 2000). In Centrone’s words (p. 568): ‘Here it is an artificial language, which only reproduces the commonest features of Doric.’
Kahn, p. 76.
Chapter 12: Through Neo-Pythagorean and Ptolemaic Eyes
For the discussion of the neo-Pythagorean philosophers and cults, I have relied on Kahn and Centrone.
From the Pythagorean Golden Verses, reprinted in K. S. Guthrie, p. 164.
Seneca, in a ‘Letter to Lucilius’ (108.17–21). Quoted in Kahn, p. 151.
Philostratus, Life of Apollonius of Tyana, quoted in Robin Lane Fox, Pagans and Christians in the Mediterranean World from the Second Century A.D. to the Conversion of Constantine (London: Penguin Books, 1986), p. 245.
Philostratus, in Fox, p. 248.
Eudorus, quoted or paraphrased in Arius Didymus. Quoted in Kahn, p. 96.
Information about the Alexandrian Jewish community is from Greg Woolf, ed., Cambridge Illustrated History of the Roman World (Cambridge, U.K.: Cambridge University Press, 2003), p. 277.
Quoted in Kahn, p. 101.
Centrone, p. 561n.
Philo of Alexandria, De opific, quoted in Kahn, p. 100n.
The two descriptions come from Harry Austryn Wolfson and Valentin Nikiprowetsky, as reported by Centrone, p. 561.
Centrone, p. 561.
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