Assignment 3: Due 9/20/07


Exam Review Materials:

All sorts of cosmological animations are found here for downloading: Animastronomia

I suggest looking at the Ptolemaic, the Tychonic, and the Keplerian models at this site. 

Here are some links to the ones I like best, but they may not work properly

… they should be flash animations, but the .sitx looks wrong to me and my not like Windows Op. Sys

… all are available at the above link in multiple formats.


Here are some lecture review materials.

EarlyKeplerReviewsm.pdf [6.2 MB]


HolbeinAndWitchesReview.pdf [5.7 MB]

I spent part of the last class on harmonic theory and Pythagorean tuning. 

Also very important to Kepler were the so-called 5 Platonic Solids. 

This will become clearer in the Koestler reading. 

Here are some statistics on the solids for your quick reference.



Read: I’ve added a short description of Ptolemaic celestial mechanics.  I went over some of this in class, but very quickly.  This is only a few pages long and the drawings pretty much say it all.  Lindberg_PtolemyCirclesexcerpt.pdf [1 MB] (ca. 6pp)


Read all the parts on Francis Bacon in Boas.  (Look him up in the index.)  It is less than 21 pages of reading.


Read this excerpt usually called “Salomon’s House” from The New Atlantis (1627) by Francis Bacon.  This is a utopian novella about a land called Bensalem supposedly located somewhere near America’s west coast. This is the world of scientific investigation as Bacon dreamed about it.  I have indicated which pages to read closely on the first page of this .doc. 

Bacon_New_Atlantis.doc [113 KB- note that this is a .doc]


Read this section from Arthur Koestler’s book The Sleepwalkers.  This is most of his section on Kepler.  This is one of the more entertaining books in the History of Science. [I included the endnotes at the end of the PDF and I also added (PDF p. 20) an image from Mysterium Cosmographicum because the reproduction in Koestler is not so good.  I translated some of the Latin in the lower right of this image.]  This reads like a novel and goes quickly. For class, do some wiki or similar research on Koestler.  Figure out what and who he was.  Follow one or two details about him so that you could possibly tell the class about them.

KoestlerWatershedpp225-87sm.pdf [6.4 MB]



Write an essay on a reading[s].  Find a section that interests you and run with it. [1.5 or more single-spaced pages for the basic assignment.]  Below are some additional readings that may be of interest for a souped-up essay. As always, pictures and diagrams are welcome as are stylistic alterations to this assignment.  So long as you do 1.5 pages worth of work and refer to the materials to which I asked you to refer, I should be happy.  Write me if you are unsure.  Cite all sources.


Possible things to think about: harmony, geometry, the cosmic-cup in mechanical terms (how might it work and/or look like), astrology in science, mothers and witches, architecture, micro-macro-cosm, scientific methods, research institutions, Christianity, Judaism, Religion, name symbology, chickens, research institutions, music,  ESP, open society, Protestant vs. Catholic, Calvin vs. Luther, patronage, Rudolf II, magic, Pythagoreanism, … etc.  Compare Bacon’s view of science with Kepler’s practice of science.  Cosmic correspondences in terrestrial things.  …etc….etc…etc….


Listen to the following pieces of music.

- In Hydraulis by Busnois (mp3) [9.9 MB] [A hydraulus is a water organ.  I am not exactly sure why this is significant.  Feel free to figure this out.] This motet is by Antoine Busnios (possibly a student of Ockeghem) from ca. 1465.  It is written to exemplify Pythagorean tuning and harmonic theory.  The lyrics talk about Pythagoras and the entire structure (harmonically and rhythmically) reflect the ratios 6:4:3:2, which, with some manipulation, yield the octave, fifth, fourth, and tone.  In much the same way that Kepler was trying to use Pythagorean (Platonic) quadrivial theory to explain the structure of the cosmos, Busnois was making music that reflected pretty much exactly the same philosophy.  The macrocosm reflected in the microcosm is a general feature of much of the theory of this period.  I don’t expect you to count the harmonic structures or identify the fifths and fourths… etc.  Just listen and enjoy and get a feel for the sorts of music that might have been heard by people in this period.


-Dufay_NuperRosarumFlores.mp3 [8 MB]  Guillaume Dufay’s Nuper rosarum flores (Our? Rose Blossoms) from 1436.  This piece was written for the dedication ceremony of the new cathedral in Florence, the “Duomo,” Santa Maria del Fiore (St. Mary of the Flower[s]).  It is called the “Duomo” because it was the largest free standing dome of the period and was designed by the now-famous Filippo Brunelleschi.  Several scholars think that it was written to echo the proportions of the Duomo itself which it is though echo the harmonic relationships of the heavens and/or the harmonic relationships of Solomon’s Temple as described in the Bible.  Anyone interested should email me for further sources and a possible project topic on harmonics in architecture, medicine, art, and other stuff.


-TallisSchol_LullyLulla-TheCoventryCarol.mp3 [4.6 MB] This is the traditional and familiar Christmas carol, the Coventry Carol.  Note the really strange dissonant moment in the chorus.  It happens a few times.  This is probably not how it was originally sung, but sheet music from the time did not notate accidentals.  It was assumed that singers would avoid this tritone (and other dissonances) by altering their pitches on the fly.  This was standard counterpoint practice.  This particular dissonant honker is actually interesting to our modern sensibilities but probably not accurate historically. 


Here are citations to the readings for this week along with some additional sources that could be used for a souped-up homework.  Please feel free to use sources not listed in this bibliography.  This is by no means complete. 


Bacon, Francis. The New Atlantis New York: Collier & Son, The Colonial Press, 1901, accessed 2006; Available from University of Adelaide Library Electronic Texts Collection.


Beer, Arthur, Peter Beer, and Martha List. Kepler, Four Hundred Years : Proceedings of Conferences Held in Honour of Johannes Kepler. 1st ed. Vistas in Astronomy ; V. 18. Oxford ; New York: Pergamon Press, 1975.


Boas [Hall], Mary L. The Scientific Renaissance, 1450-1630. New York: Harper and Row, 1962. [One of our text books.]


Boner, Patrick J. "Kepler’s Living Cosmology: Bridging the Celestial and Terrestrial Realms." Centaurus 48 (2006): pp. 32-39. [58 KB]


Busnois, Antoine. "In Hydraulis (Motet in 4 Voices).", ca. 1465.


Connor, James A. Kepler's Witch: An Astronomer's Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother. 1st ed. San Francisco: Harper San Francisco, 2004.


Field, Judith V. "Astrology in Kepler's Cosmology." In Astrology, Science and Society: Historical Essays, ed. Patrick Curry, 143-170. Suffolk: Boydell Press, 1987.


Field, Judith V. "Kepler's Rejection of Numerology." In Occult and Scientific Mentalities in the Renaissance, ed. Brian Vickers, pp. 273-296. New York: Cambridge University Press, 1986.


Field, J. V. Kepler's Geometrical Cosmology. Chicago: University of Chicago Press, 1988.


Grafton, Anthony. "Kepler as Reader." Journal of the History of Ideas 53, no. 4 (1992): 561-572. [1.4 MB]


Kepler, Johannes, and Edward Rosen. Kepler's Somnium; the Dream, or Posthumous Work on Lunar Astronomy. Madison,: University of Wisconsin Press, 1967.


Kepler, Johannes, and E. J. Aiton. The Secret of the Universe (Mysterium Cosmographicum). Translated by A.M. Duncan and with introduction and commentary by E.J. Aiton and a preface by I. Bernard Cohen. New York: Abaris Books, 1981.


Kepler, Johannes. The Harmony of the World (Harmonice Mundi). Translated by and commentary by E. J. Aiton, A. M. Duncan and J. V. Field. Philadelphia: The American Philosophical Society, 1997, first Latin ed. 1618.


Kepler, Johannes. The Six-Cornered Snowflake. Oxford,: Clarendon P., 1966.


Kepler, Johannes, and William H. Donahue. Optics: Paralipomena to Witelo & Optical Part of Astronomy. Santa Fe, N.M.: Green Lion Press, 2000.


Koestler, Arthur. The Sleepwalkers : A History of Man's Changing Vision of the Universe. New York: Macmillan, 1959.


Lindberg, David C. "The Beginnings of Western Science : The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. To A.D. 1450." 220. Chicago: University of Chicago Press, 1992.


Lindberg, David C. "The Genesis of Kepler's Theory of Light: Light Metaphysics from Plotinus to Kepler." Osiris, 2nd Series 2 (1986): 4-42. [1.4 MB]


Nicolson, Marjorie. "Kepler, the Somnium, and John Donne." Journal of the History of Ideas 1, no. 3 (1940): 259-280. [656 KB]


Ptolemy. "Harmonics." In Greek Musical Writings II, ed. and trans. Andrew Barker, pp. 270-391. New York: Cambridge University Press, 1984, original in Greek, 2nd century A.D.


Rabin, Sheila J. "Kepler's Attitude toward Pico and the Anti-Astrology Polemic." Renaissance Quarterly 50, no. 3 (1997): 750-770. [572 KB]


Rosen, Edward. "Kepler's Harmonics and His Concept of Inertia." American Journal of Physics 34, no. 7 (1966): 610-613.


Rosen, Edward. "Kepler's Early Writings." Journal of the History of Ideas 46, no. 3 (1985): 449-454. [212 KB]


Rosen, Edward. "Kepler's Attitude toward Astrology and Mysticism." In Occult and Scientific Mentalities in the Renaissance, ed. Brian Vickers, pp. 253-272. New York: Cambridge University Press, 1986.


Schneer, Cecil. "Kepler's New Year's Gift of a Snowflake." Isis 51, no. 4 (1960): 531-545. [2 MB]


Stephenson, Bruce. Kepler's Physical Astronomy. Princeton, N.J.: Springer, 1994.


Stephenson, Bruce. The Music of the Heavens : Kepler's Harmonic Astronomy. Princeton, N.J.: Princeton University Press, 1994.


Trachtenberg, Marvin. "Architecture and Music Reunited: A New Reading of Dufay's Nuper Rosarum Flores and the Cathedral of Florence." Renaissance Quarterly LIV, no. 3 (2001): 741-773. [1.2 MB]


Wright, Craig. "Dufay's "Nuper Rosarum Flores", King Solomon's Temple, and the Veneration of the Virgin." Journal of the American Musicological Society 47, no. 3 (1994): pp. 395-427, 429-441. [1.2 MB]


Wright, Craig. "Reply to Charles Turner." Journal of the American Musicological Society 48, no. 1 (1995): 158.

Warren, Charles W. "Brunelleschi's Dome and Dufay's Motet." The Musical Quarterly 59, no. 1 (1973): pp. 92-105. [404 KB]



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