Syllabus [SciRev Fall 2008]

For the Week of 10/8/08

Assignment 6

Galileo Galilei


Galileo’s Bird

“Eppur Si Muove”



It should really be displayed like so…



“Eppur Si Muove”

Read: Koestler (the rest of the material on Galileo) pp. 471-503. 32pp


Read the indicated excerpts and follow the math in this excerpt from Galileo’s Dialogue concerning Two New Sciences. 11pp


This means read with a pencil in your hand. You many need to consult a physics text to refresh your memories on freefall, pendula, and uniform acceleration equations.  Read the beginning (160-173) and read (185.5-end of excerpt).  I marked the numbers in red so that you would not be confused. There are a couple of numbering systems in this reading.


Read this example from Galileo’s Assayer… This is fun reading.  It’s Galileo at his best/worst.

Galileo-ASSAYER-excerpt-Shaded.doc [170 KB] (warning, this is a .doc and will download differently…)

Skip the grayed out text.  Just read the fully black and dark blue text. Pay particular attention to his atomic theories and his style of argumentation. (Feel free to read the gray parts if you want more material for a souped up essay.)  I should point out that Stillman Drake, the scholar who basically owns Galileo and translated this section, has conveniently edited out those arguments of Galileo that are not so convincing or are simply dead wrong by modern standards.  In my opinion Drake has really screwed up Galileo by all of his sly editing.  But Drake is the gateway through which we all must pass in order to read Galileo in English.  28pp



View movie of Medician moons: GalileoMediceanMoonspseudoanimation.pdf [67KB]

To make this work, view it in Acrobat (or similar) in single page view (not scroll view) and hit the next page button over and over again.  It’s not a good animation, but it represents what Galileo had to work with.  I have no evidence that Galileo ever made a flip-card animation similar to this one.  These drawings appear inline in his text (see image below) and cannot work as an animation the way they are arranged on the pages.  In fact, I am unaware of any flip-card animations existing until the 19th century, but this in no way means that similar animation techniques didn’t exist earlier.  I have never looked into it.  Feel free to explore this question.


From Sidereus nuncius (1610)


This is a photograph taken through a Galilean-style

telescope of Jupiter and its largest moons. (I enhanced the contrast.)


Homework Suggestions:

-Analyze his experiments as described in Dialogue concerning Two New Sciences.  You could draw better diagrams and explain the experiments, or you could do the experiments and take pictures and explain the experiments. Be imaginative.  Consider how convincing these are.  Compare with Harvey, or Kepler, or Copernicus… etc.  I find it better and more interesting to write about a detail really well rather than try to cover the whole reading. 


-Write an essay about Assayer: How is Galileo trying to convince us that he is right?  Is Galileo a victim or is he promoting this idea for rhetorical purposes?  Look into various people that he drops into his arguments.  Who are they?  Draw up one or two of his arguments and discuss how convincing it is.  Do you like Galileo? 


Cite all sources.  Make it look good.  Production quality matters. – this is a movie of Mercury passing in front of the sun. 

It gives you an ideas of scale.

Here is an animation of the sunspot drawings of Galileo:


 For souped up essays you could additionally use the parts of the above readings

that we didn’t read and/or select from these below or find your own additional sources.

I’ve put up several of these articles… I’ll try to get the rest up by Friday.



Bean, Jacob. "Two Celestial Virtues by Cigoli." Master Drawings 6, no. 3 (1968): 259-322.


Carman, Charles H. "Cigoli's Annunciation at Montughi: A New Iconography." The Art Bulletin 58, no. 2 (1976): 215-224.


De Santillana, Giorgio. The Crime of Galileo. Chicago: University of Chicago Press, 1955.  Koestler based much of his material on Galileo on this book.


Eastwood, Bruce S. "On the Continuity of Western Science from the Middle Ages: A. C. Crombie's Augustine to Galileo." Isis 83, no. 1 (1992): 84-99.


Edgerton, Samuel Y., Jr. "Galileo, Florentine "Disegno," And The "Strange Spottednesse" Of the Moon." Art Journal 44, no. 3 (1984): 225-232. Edgerton_GalileoSpottedMoonDisegno-1.9MB.pdf


Freedberg, David. The Eye of the Lynx; Galileo, His Friends, and the Beginnings of Modern Natural History. Chicago: University of Chicago Press, 2002.


Galilei, Galileo. "The Assayer." In Discoveries and Opinions of Galileo, pp. 228-280. New York: Anchor Books, 1957 (1623). Galileo-ASSAYER-excerpt-Shaded.doc [170 KB]


Galilei, Galileo. Discoveries and Opinions of Galileo. Translated by and with an Introduction and Notes by Stillman Drake. 1st ed. New York: Anchor Books, 1957.


Galilei, Galileo. Dialogues Concerning Two New Sciences. Translated by Henry Crew and Alfonso de Salvio. New York: Macmillan, 1914. Galileo_Dialogue2NewSciExcerpt.htm


Osler, Margaret J. "Galileo, Motion, and Essences." Isis 64, no. 4 (1973): 504-509.


Ostrow, Steven F. "Cigoli's Immacolata and Galileo's Moon: Astronomy and the Virgin in Early Seicento Rome." The Art Bulletin 78, no. 2 (1996): 218-235.  If you like looking at pictures, you might like this article: Ostrow_CigoliGalileoMoonAstronomy-5.7MB.pdf


Panofsky, Erwin. "Galileo as a Critic of the Arts: Aesthetic Attitude and Scientific Thought." Isis 47, no. 1 (1956): 3-15. Panofsky is one of the best art historical writers out there and this article has some nice pictures: Panofsky_GalileoArtCritic-7.7MB.pdf


Purnell, Frederick. "Jacopo Mazzoni and Galileo." Physis 14 (1972): 273-394.  I like Purnell, but I don’t currently have a copy of this article. The library may be of help.


Rice University’s “Galileo Project.”  There a a lot of material on this site.  I have mixed feelings about it, but it is a good resource for the most part.  You will be sure to find something of interest. 


Rosen, Edward. "Did Galileo Claim He Invented the Telescope?" Proceedings of the American Philosophical Society 98, no. 5 (1954): 304-312. Rosen-Galileo_Claim_Telescope-440KB.pdf


Rosen, Edward. "Galileo's Misstatements About Copernicus." Isis 49, no. 3 (1958): 319-330. Rosen_GalileoMistatementsOnCopernicus-1.8MB.pdf


Shea, William R., and Mariano Artigas. Galileo in Rome : The Rise and Fall of a Troublesome Genius. Oxford ; New York: Oxford University Press, 2003.  Excerpt posted:  Shea_GalileoInRomeExcerpt-3.9MB.pdf. This has some nice detail about what a pain Galileo was.


Smith, A. Mark. "Galileo's Theory of Indivisibles: Revolution or Compromise?" Journal of the History of Ideas 37, no. 4 (1976): 571-588.


Topper, David, and Cynthia Gillis. "Trajectories of Blood: Artemisia Gentileschi and Galileo's Parabolic Path." Woman's Art Journal 17, no. 1 (1996): 10-13.


van Helden, Albert. "Galileo and Scheiner on Sunspots: A Case Study in the Visual Language of Astronomy." Proceedings of the American Philosophical Society 140, no. 3 (1996): 358-396. VanHeldon_GalileoScheinerSunspotsvisuals-3MB.pdf


Walker, D. P. "Some Aspects of the Musical Theory of Vincenzo Galilei and Galileo Galilei." Proceedings of the Royal Musical Association 100 (1973): 33-47.


Walker, D. P. Studies in Musical Science in the Late Renaissance, ed. J. B. Trapp. London: Warburg Institute, 1978. This PDF is a chapter from this book on Galileo: Walker_StudiesInMusicalScience-Galileo-2.7MB.pdf.  I quite like this essay.


Winkler, Mary G., and Albert Van Helden. "Representing the Heavens: Galileo and Visual Astronomy." Isis 83, no. 2 (1992): 195-217. Winkler-Helden_RepresentingHeavensGalileoVisual-1.6MB.pdf


Review Material: posted 10/11/08




Also, be sure you know what the Babylonian and the egg story is. I love asking about this one.





Back to Syllabus [SciRev Fall 2008]


Me –

In the news, coincidentally:

Chang-Sunspots Are Fewest Since 1954, but Significance Is Unclear


Remember Pythagorean tuning? This tuning, based on 1, 2, 3, and 4 had several perfect intervals, like the fifth (3:2) and the fourth (4:3) and the octave (2:1), but other intervals were not so pretty. 

Recall also how intervals were “added” or “subtracted.”  They were actually multiplied or divided. 


E.g. #1: A perfect fifth “plus” a perfect fourth looked like this in monochord (string length) notation:


            3/2 * 4/3 = 12/6= 2/1 = octave.


E.g. #2:  The difference between a fourth (4:3) and a fifth (3:2) is figured out like so…

            3/2  4/3 = 3/2 * 3/4 = 9/8, known as the tonus or tone.


E.g. #3: How many tones (9:8) to get to the fourth (4:3)?

            9/8 * 9/8 = 81/64, which is too low.

            9/8 * 9/8 * 9/8 = 729/512, which is too high.

            Therefore a fourth (4:3) must be made up of two tones (9:8) and another mystery interval…

            9/8 * 9/8 * ? = 4/3

            ? = 265/243, known as the Pythagorean semitone.


In the 17th century, the French mathematician Mersenne wrote Harmonie universelle, and the system for tuning musical instruments we now use, called equal temperament, was formalized and popularized.  [Technically speaking, several mathematicians had come up with the same solution, but they were not well known and had little to no effect on modern harmonic applications.]  In equal temperament, all 12 of the half-steps making up an octave are equal monochord intervals.  The interval between A and A# is mathematically the same as the interval between Bb and B or F and F#. In decimal notation this “half-step” interval is 1.0594630936… In ratio notation similar to the way we notate Pythagorean monochord divisions this could be written as approximately 1.0594630936:1.  If you were to go up 12 “half-steps” from any point you would reach an octave from where you started.  How did I come up with this number?


In standard Pythagorean tuning the equivalent of a half step, the semitone 256:243, does not do this.  If you go up 12 Pythagorean semitones you don’t get to the next octave.  You get to this, 1.86897847902…  [Recall that an octave is 2.]  The Pythagorean semitone is a bit too small to get you to the octave.  It is actually about an equal tempered “half-step” shy. (On a piano if you started at A and went up 12 Pythagorean semitones you would end up pretty close to G#, not A an octave higher.)


Galileo’s father Vincenzo, a famous lutenist (lute player and composer), proposed an altogether different interval upon which to base tuning.  He proposed that the basic interval should be 18:17.  If you go up 12 of these Galilean semitones you get 1.985559952… This is pretty damn close to the goal of 2, the octave.   


For some extra credit do some of all of the following: figure out the semitone interval for equal temperament tuning and explain how it works on a monochord and how it works mathematically.  Compare it to the Pythagorean semitone and the Galilean semitone.  Explain how you came up with your answer and explain how it is applied to a monochord. You will probably need to draw a monochord diagram to explain how it all works.  Just a numerical answer is not enough. Anybody can look this up. The problem is to explain what it means. 


If you really want to get fancy, explain why a lute, a fretted instrument much like a guitar, would have necessitated equal tempered tuning. 


Write this up as an essay like a homework assignment. 


This could be worth some pretty big points if done well, so consider doing it if you need to improve your score.