The Music of Pythagoras (52 page)

3
. 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.

4
. Plutarch,
On the Face in the Moon
929AB, quoted in Barnes, p. 89.

5
. From Plutarch,
Pericles
; passage quoted in full in Barnes, p. 92.

6
. Quoted from Aristotle’s
Metaphysics
, in W. K. C. Guthrie (2003), pp. 287–88.

7
. See W. K. C. Guthrie (2003) p. 248, for the seed of this idea.

8
. W. K. C. Guthrie (2003) wrote that Philolaus was Aristotle’s “favorite author” (p. 260). The quotation is in W. K. C. Guthrie (2003), pp. 307–308.

9
. Quoted in ibid., p. 309.

10
. See ibid., p. 233, for the arguments each way concerning Alcmaeon’s dates. The quotation appears in W. K. C. Guthrie (2003), p. 313.

11
. Plato,
Phaedo
, quoted in ibid., p. 310.

12
. Quoted in ibid., p. 311.

13
. Quoted in ibid., p. 312.

1
. 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).

2
. The discussion of Archytas’ work is based on Kahn, p. 40 ff. Most of the quotations from Archytas are drawn from Kahn’s book.

3
. Burkert, p. 68.

4
. 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).

5
. From Eudemus (also mentioned by Aristotle), quoted in Kahn, p. 43.

6
. Archytas’ description of a bull-roarer, or
rhomboi
, is in W. K. C. Guthrie (2003), p. 227.

7
. Aristotle, quoted in ibid., p. 335.

8
. 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
.”

9
. 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.

10
. Quotations are from the musician Stratonicus and from Sosicrates, in Burkert, p. 202.

1
. Kahn, p. 50 ff, is especially helpful in interpreting Plato’s thought as it related to the Pythagoreans, and he pinpoints these two themes.

2
. The quotations from Plato’s
Timaeus
, unless otherwise noted, are taken from the translation by Desmond Lee (London: Penguin, 1977).

3
. From Plato’s
Philebus
, in Kahn, p. 14.

4
. Ibid., p. 58.

5
. From Plato’s
Gorgias
, Quoted in W. K. C. Guthrie (2003), p. 305.

6
. Book 7 of Plato’s
Republic
, quoted in ibid., p. 162.

7
. Plato,
Timaeus
, in the Stephanus edition (1578), p. 52.

1
. 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.

2
. Burkert lists the writers in whose work fragments from Aristotle appear (pp. 28, 29).

3
. “What the sky encloses” is a quotation from Burkert (p. 31), but he was paraphrasing Aristotle.

4
. 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.

5
. Burkert, pp. 45–46.

6
. W. K. C. Guthrie (2003), p. 259.

7
. The quotation is from Burkert (p. 431), in his discussion of these different possibilities, but he did not favor this choice.

8
. This discussion draws on W. K. C. Guthrie (2003), p. 266 ff, and Burkert, p. 68 ff.

9
. Ibid., p. 226n.

10
. Burkert’s paraphrase of Aëtius, in which he seems to have given only the final four words in direct quotation (Burkert, p. 70).

11
. Quoted in W. K. C. Guthrie (2003), pp. 263–64.

12
. 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).

13
. Specifically in the
Elements
, Book VII.

14
. 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).

15
. For information and discussion, see Burkert, p. 432.

16
. 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.

1
. Marcus Tullius Cicero,
On The Republic
, Book 2, 28, 29. Reprinted in translation by Niall Rudd, in
Cicero: The Republic and The Laws
(Oxford, U.K.: Oxford University Press, 1998), pp. 43–44.

2
. Quoted in Kahn, pp. 89–90.

3
. From Pliny,
Natural History
34.26. As retold in Kahn, p. 86.

4
. From the
Pythagorean Notebooks
, excerpt quoted in Diogenes Laertius’
The Life of Pythagoras
, reprinted in K. S. Guthrie, pp. 148–49.

5
. Quoted in Simon Hornblower and Antony Spawforth, eds.,
The Oxford Companion to Classical Civilization
(Oxford, U.K.: Oxford University Press, 1998), p. 245.

6
. 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.

7
. Sextus Empiricus, quoted in Kahn, p. 84.

8
. Elizabeth Rawson,
Intellectual Life in the Late Roman Republic
(Baltimore: Gerald Duckworth & Co., 1985), p. 310.

9
. Cicero,
Timaeus
, “Introduction.” Quoted in Kahn, p. 73.

10
. Kahn, p. 88.

11
. Cicero,
Vatinium
6. Quoted in Kahn, p. 91.

12
. Cicero,
On the Commonwealth
, quoted from the edition translated by George Holland Sabine and Stanley Barney Smith (New York: The Liberal Arts Press, 1929), pp. 114–15.

13
. Ibid., p. 206.

14
. Cicero,
On Divination
, quoted in Barnes, p. 165–66.

15
. Cicero, “Scipio’s Dream,” from
On the Republic
, translated by Cyrus R. Edmonds and Moses Hadas, in
The Basic Works of Cicero
(New York: Random House, 1951), p. 165.

16
. Ibid., p. 166.

17
. Ibid., p. 166.

18
. 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).

19
. Cesariano’s drawing for Vitruvius: ccat.sas.upenn.edu/george/vitruvius.html. The quotation is from Book IX of Vitruvius.

20
. Vitruvius, Book I.

21
. Ibid.

22
. 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.

23
.
Lysis’s Letter to Hipparchus
, quoted in Diogenes Laertius,
The Life of Pythagoras
, in K. S. Guthrie, pp. 141–55.

24
. 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).

25
. Introduction to the Occelus piece in K. S. Guthrie, p. 203.

26
. 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.

27
. 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.”

28
. Kahn, p. 76.

1
. For the discussion of the neo-Pythagorean philosophers and cults, I have relied on Kahn and Centrone.

2
. From the
Pythagorean Golden Verses
, reprinted in K. S. Guthrie, p. 164.

3
. Seneca, in a “Letter to Lucilius” (108.17–21). Quoted in Kahn, p. 151.

4
. 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.

5
. Philostratus, in Fox, p. 248.

6
. Eudorus, quoted or paraphrased in Arius Didymus. Quoted in Kahn, p. 96.

7
. 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.

8
. Quoted in Kahn, p. 101.

9
. Centrone, p. 561n.

10
. Philo of Alexandria,
De opific
, quoted in Kahn, p. 100n.

11
. The two descriptions come from Harry Austryn Wolfson and Valentin Nikiprowetsky, as reported by Centrone, p. 561.

12
. Centrone, p. 561.

13
. Number 41 in
The Catalogue of Lamprias
, a list of Plutarch’s works that probably was compiled in the fourth century
A.D
.

14
. This was how Porphyry reported Moderatus’ views: see Kahn, p. 105.

15
. As quoted and/or paraphrased by Porphyry: see Kahn, p. 106.

16
. Theon of Smyrna,
Mathematics Useful for Understanding Plato
, excerpted as Appendix 1 in K. S. Guthrie.

17
. W. K. C. Guthrie (2003), p. 406.

18
. Dodds (1963), p. 259; quoted in Kahn, p. 118.

19
. Numenius fragment #2; quoted in Kahn, p. 122.

20
. Numenius fragment, no number; quoted in Kahn, p. 122.

21
. Numenius fragment #52; quoted in Kahn, p. 132.

22
. Johannes Kepler,
Johannes Kepler Gesammelte Werke
, Max Caspar et al., eds. (Munich: Deutsche Forschungsgemeinschaft, and the Bavarian Academy of Sciences, 1937–), vol. 6, p. 289.

23
. Pliny,
Natural History
, 2:20, translated by Bruce Stephenson, p. 24, in Stephenson
The Music of the Heavens: Kepler’s Harmonic Astronomy
(Princeton, N.J.: Princeton University Press, 1994).

24
. Stephenson, p. 29. Stephenson cites Von Jan, “Die Harmonie der Sphären,”
Philologus
52 (1893).

25
. Simplified by the author from Stephenson, p. 31.

26
. Stephenson, p. 37.

1
. E. R. Dodds,
The Greeks and the Irrational
(Berkeley, Calif.: University of California Press, 1951), p. 296.

2
. Ibid., p. 285.

3
. Description of Rome in this era is based on Michael Grant,
History of Rome
(London: Faber & Faber, 1978), p. 284 ff.

4
. Edward Gibbon,
Decline and Fall of the Roman Empire
, Chapter X. Quoted in Russell (1945), p. 287.

5
. Description taken from Grant, p. 294.

6
. Ibid.

7
. Plotinus quoted in Dodds, pp. 285–86.

8
. Ibid., pp. 286–87.

9
. Kahn, p. 134.