The Music of Pythagoras (53 page)

10
. Dodds, p. 287.

11
. Ibid.

12
. Fox, p. 190.

13
. John 1:1–5, 9–12, 14. Paraphrased from the Oxford New International Version translation.

14
. Augustine,
City of God
, translated by Gerald Walsh et al. (Garden City, N.Y.: Doubleday, 1958), pp. 241–42.

15
. H. J. Blumenthal and R. A. Markus, eds.,
Neo-Platonism and Early Christian Thought: Essays in Honour of A. H. Armstrong
(London: Variorum Publications, 1981), p. 90. This concept is the “
soma-sema
formula.”

16
. Information about this period comes from H. G. Koenigsberger,
Medieval Europe: 400–1500
(London: Longman, 1987).

17
. Most of the information about Macrobius is from Stephenson, pp. 38–41.

18
. Quoted in Richard E. Rubenstein,
Aristotle’s Children: How Christians,
Muslims, and Jews Rediscovered Ancient Wisdom and Illuminated the Dark Ages
(New York: Harcourt, 2003), p. 62, from Josef Pieper,
Scholasticism: Personalities and Problems of Medieval Philosophy
, translated by Richard and Clara Winston (New York: McGraw-Hill, 1964), p. 30.

1
. Joscelyn Godwin,
The Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music
(Rochester, Vt.: Inner Traditions International, 1993).

2
. Quotations from Hunayn’s
Nawadir al-Falasifa
are from excerpts translated by Isaiah Sonne and reprinted in Godwin, pp. 92–98.

3
. Hunayn, quoted in Godwin, p. 92.

4
. Quoted in David C. Lindberg,
The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600
B.C
. to
A.D
. 1450
(Chicago: University of Chicago Press, 1992), p. 176.

5
. From
The Epistle on Music of the Ikhwan al-Safa
’, translated by Amnon Shiloah; quoted from an excerpt reprinted in Godwin, p. 113.

6
. Ibid., p. 113.

7
. Ibid., p. 115.

8
. Ibid.

9
. From Al-Hasan Al-Katib,
Kitah Kamal Adal Al-Gina
’, translated by Amnon Shiloah; quoted from an excerpt reprinted in Godwin, p. 122.

10
. The information about Aurelian comes from Godwin, p. 99.

11
. Aurelian of Réôme,
Musica Disciplina
, translated by Joseph Ponte; quoted from an excerpt reprinted in Godwin, pp. 101–102.

12
. Information about Eriugena comes from ibid., pp. 104–105.

13
. John Scotus Eriugena,
Commentary on Martianus Capella
, translated by Joscelyn Godwin; quoted from an excerpt reprinted in ibid., p. 105.

14
. Ibid., p. 106.

15
. John Scotus Eriugena,
Periphyseon
or
De Divisione naturae
, quoted in ibid., p. 104.

16
. Regino of Prüm, “Epistola de harmonica institutione,” the introduction to his book about plainsong melodies,
Tonarius
. This excerpt translated by Sister Mary Protase LeRoux and reprinted in Godwin, p. 110.

17
. Ibid., p. 111.

18
. For the emergence of the universities, see Thomas Kuhn,
The Structure of Scientific Revolutions
(Chicago: University of Chicago Press, 1962), p. 102.

19
. The archbishop’s translation project is described at length in Rubenstein.

20
. Information about the Seven Liberal Arts is from Koenigsberger, p. 199 ff.

21
. As discussed by Burkert, beginning on p. 386.

22
. Information from Burkert, p. 406, including footnote 31.

23
. For the
Ars Geometrae
supposedly composed by Boethius, see Burkert, p. 406.

24
. Koenigsberger, p. 202.

25
. Quoted in Koenigsberger, p. 201.

26
. This information comes in part from a website of the University of Notre Dame Jacques Maritain Center: (
http://maritain-nd.edu
) Ralph McInerny,
A History of Western Philosophy
, vol. 2, part III, chapter IV.

27
. John Hedley Brooke,
Science and Religion: Some Historical Perspectives
(Cambridge, U.K.: Cambridge University Press, 1991), p. 45.

28
. Ibid., p. 25.

1
. Letter from Petrarch to Francesco Bruni, October 25, 1362, reprinted in Ernst Cassirer, Paul Oskar Kristeller, and John Herman Randall, Jr., eds.,
The Renaissance Philosophy of Man: Selections in Translation
(Chicago and London, University of Chicago Press, 1948, 1969), p. 34.

2
. From the introduction to the excerpts from Petrarch in ibid., p. 25.

3
. Petrarch,
On His Own Ignorance
, reprinted in ibid., p. 92.

4
. Ibid., p. 94.

5
. Ibid., p. 24.

6
. Marsilio Ficino,
Five Questions Concerning the Mind
, reprinted in ibid., pp. 209–210.

7
. Pico della Mirandola,
On the Dignity of Man
, reprinted in ibid., pp. 232–33.

8
. G. Pico della Mirandola,
Conclusiones sive Theses
, edited and translated by Bohdan Kieszowski, reprinted in Godwin, p. 176. For an attempt to make some sense out of this list, and connections with Plato, Nicomachus, Ptolemy, and, indeed, Oscar Wilde, see Godwin, p. 447.

9
. See Cassirer et al., p. 245.

10
. “Letter to Leo X,” quoted in Kahn, p. 158, from A. E. Chaignet,
Pythagore et la philosophie pythagoricienne
, vol. II (Paris, 1873), p. 330.

11
. Leon Battista Alberti,
The Ten Books of Architecture
(Mineola, N.Y.: Dover replica Edition, 1987), Chapter 5 of Book 9.

12
. Nicholas of Cusa,
Of Learned Ignorance
(1440). Quoted in Koenigsberger, p. 367.

13
. Prefatory letter to
De revolutionibus, Gesamtausgabe. Vol. II: De revolutionibus.
Kritischer Text
, eds. H. M. Nobis and B. Sticker (Hildesheim, Germany: 1984), p. 4, as quoted in T. S. Kuhn,
The Copernican Revolution: Planetary Astronomy in the Development of Western Thought
(Cambridge, Mass.: Harvard University Press, 1957), p. 137.

14
. Prefatory letter to
De revolutionibus, Gesamtausgabe
. Vol. II,
De revolutionibus
, p. 4, as quoted in Kuhn,
Copernican Revolution
, p. 142.

15
. Mentioned in Brian L. Silver,
The Ascent of Science
(Oxford, U.K.: Oxford University Press, 1998), p. 177.

16
. Book 1, Chapter 10 of
De revolutionibus, Gesamtausgabe. Vol. II, De revolutionibus
, p. 4, as quoted in Kuhn (1957), pp. 179–80.

17
. Andrea Palladio,
I quattro libri dell’ architettura
. In a reproduction of the Isaac Ware 1738 English edition:
The Four Books on Architecture
(New York: Dover, 1978).

18
. See, for example, Rudolph Wittkower,
Architectural Principles in the Age of Humanism
(New York: Norton, 1971).

19
. It was Victor Thoren who called attention to these specifics about the way Tycho carried out Pythagorean/Palladian ideals in the design of Uraniborg; see his
The Lord of Uraniborg: A Biography of Tycho Brahe
(Cambridge, Mass.: Cambridge University Press, 1990).

1
. Johannes Kepler, letter to Michael Mästlin, June 11, 1598,
Johannes Kepler Gesammelte Werke
, Max Caspar, Salther von Dyck, Franz Hammer and Volker Bialas, eds. (Munich: Deutsche Forschungsgemeinschaft and the Bavarian Academy of Sciences, 1937–), vol. XIII, p. 219.

2
. Godwin, pp. 104–105.

3
. Kepler,
Harmonice mundi
, Book V, in
Gesammelte Werke
, vol. 6, p. 289.

4
. Stephenson is an extraordinarily thorough and invaluable guide through the labyrinth of Kepler’s
Harmonice mundi
.

5
. Plato,
Timaeus
(London: Penguin, 1965), p. 15, p. 50n.

6
. Kepler,
Harmonice mundi
, in
Gesammelte Werke
, vol. 6, p. 289.

7
. For Kepler’s complete table, see p. 150 in Stephenson.

8
. For a much more detailed explanation, see Stephenson, p. 171.

9
. Kepler,
Harmonice mundi
, in
Gesammelte Werke
, vol. 6, p. 323.

10
. Kepler,
Harmonice mundi
, in
Gesammelte Werke
, vol. 6, p. 356.

11
. Stephenson points out that Kepler had read Proclus’s Platonic/neo-Pythagorean hymns.

12
. Kepler, in a letter to Vincenzo Bianchi, February 17. Letter number 827 in
Gesammelte Werke
17.326.213–19. Quoted in Stephenson, p. 241.

1
. Galileo Galilei,
Il Saggiatore
, 1623. Quoted and translated in Daniel T. Max,
The Family That Couldn’t Sleep
(New York: Random House, 2006), p. 5.

2
. The episode having to do with Galileo’s father is retold in Silver, p. 176.

3
. Barrow, p. 127.

4
. Silver, p. 158.

5
. Ibid., p. 177; Bronowski (p. 234) also mentions Newton’s attribution to Pythagoras.

6
. Quoted in Barrow, p. 127.

7
. Quoted in ibid., p. 128, from G. Leibniz,
The Philosophical Works of Leibniz
, translated by G. Duncan (New Haven, Conn.: Tuttle, Morehouse and Taylor, 1916).

8
. Joseph Addison, paraphrase of Psalm 19:1–6. Hymn 409 in
The Hymnal 1982, according to the use of the Episcopal Church
.

9
. The paragraphs about how the image of Pythagoras was used by revolutionaries are based on James H. Billington,
Fire in the Minds of Men: Origins of the Revolutionary Faith
(New York: Basic Books, 1980). All quotations, unless otherwise noted, also come from quotations in his book.

10
. Information about Buonarroti comes from Elizabeth L. Eisenstein,
The First Professional Revolutionist: Filippo Michele Buonarroti (1761–1837)
,
A Biographical Essay
(Cambridge, Mass.: Harvard University Press, 1959).

11
. From Jevons,
Principles of Science
, quoted in Lindberg, pp. 371–72, n. 15.

1
. The two books discussed in this chapter are Bertrand Russell,
The History of Western Philosophy
(London: George Allen & Unwin, 1945); and Arthur Koestler,
The Sleepwalkers: A History of Man’s Changing Vision of the Universe
(London: Hutchinson, 1959). All quotations are from these works except where otherwise footnoted.

2
. Whitehead, Alfred North, and Bertrand Russell,
Principia Mathematica
, 3 vols. (Cambridge, U.K.: Cambridge University Press, 1910, 1912, 1913).

3
. Aristotle, quoted in Russell (1945), p. 136.

4
. Frege’s labors were not wasted; his book is considered a classic. It is
The Foundations of Arithmetic: A Logico-mathematical Enquiry into the Concept of Number
, available in an edition translated by J. R. Austin (Oxford, U.K.: Blackwell, 1980).

5
. Bertrand Russell, “How to Read and Understand History,” in
Understanding History and Other Essays
(New York: Philosophic Library, 1957).

6
. Barrow, p. 293.

7
. Bertrand Russell, “The Value of Free Thought,” in
Understanding History
.

1
. Quoted in Kitty Ferguson,
Prisons of Light: Black Holes
(Cambridge, U.K.: Cambridge University Press, 1996), p. 114.

2
. Bryan Appleyard, “Master of the Universe: Will Stephen Hawking Live to Find the Secret?”
Sunday Times
(London)

3
. Richard Feynman,
QED: The Strange Theory of Light and Matter
(Princeton, N.J.: Princeton University Press, 1985), p. 4.

4
. John Archibald Wheeler,
Journey into Gravity and Spacetime
(New York: Scientific American Library, 1990), p. xi.

5
. Barrow, p. 129.

6
. These paragraphs about the new music of the spheres rely on information from Kristine Larsen, “From Pythagoras to WMAP: The ‘Music of the Spheres’ Revisited,” paper presented to the Society of Literature, Science, and the Arts (November 13, 2005), and published on the Internet (
www.physics.ccsu.edu/larsen/wmap.html
). The articles and papers cited below are all cited in Larsen’s paper.

7
. Richard A. Kerr, “Listening to the Music of the Spheres,”
Science 1991
, 253: 1207–1208.

8
. P. Demarque and D. B. Guenther (1999) “Helioseismology: Probing the Interior of a Star,”
Proceedings of the National Academy of Sciences 96
: 5356–69.

9
. ESO (May 15, 2002), “Ultrabass Sounds of the Giant Star Xi Hya.”
http://www.eso.org/outreach/press-rel/pr-2002/pr-10-02.html
. The ESO is the European Organization for Astronomical Research in the Southern Hemisphere, or European Southern Observatory.

10
. Marcia Bartusiak,
Einstein’s Unfinished Symphony: Listening to the Sounds of Space-time
(Washington, D.C.: National Academies Press, 2000).

11
. Steve Roy and Megan Watzke, “Giant Galaxy’s Violent Past Comes into Focus,” Harvard University press release, May 10, 2004.
http://chandra.harvard.edu/press/04_releases/press_051004.html