Very often there will be (1) a matter-of-fact question, and (2) a question that gets behind the scenes, so to speak, a sort of meta-question. It should make our discussions more fun and more interesting if we remember that we can operate at these different levels.
Thursday, Jan. 31:
What is meant by Pythagorean ideas in music?
How is a primary source different to read than a secondary source?
Tuesday, Feb. 5:
Galilei's table shows two ratios representing the "tone" (or whole step), namely 10:9 and 9:8. He calls these the minor tone and the major tone, meaning simply "smaller" and "bigger", but why are there two different tones? Similarly for semitones -- why is this necessary? Didn't we already figure out that the tone is 9:8?
Galileo, writing in the Two New Sciences -- some 50 years after his father's book -- also talks about music and ratios. What differences do you notice between his treatment and his father's?
Thursday, Feb. 7:
Euclid's Elements of Geometry is one of the most influential books ever written. It sets a standard of exposition which is remarkably high. Have a look at its overall organization. Then start in on Book I and see how it builds carefully and logically. The aim isn't to learn the mathematics, as it might have been when you saw geometry in school, but to get the overview -- what is going on? How does it work?
Tuesday, Feb. 12:
Galileo's little book on the Geometric and Military Compass claims to be a textbook on geometry. How is it different from Euclid's text? What clues do you find that something more complicated than geometry is going on?
Thursday, Feb. 14:
There are two versions of the story of Archimedes and the crown in today's readings. How do they differ?
Why does Archimedes' Proposition I in the Equilibrium of Planes need proving? Isn't it included in the postulates?
Tuesday, Feb. 19:
These are difficult texts! What are they about? What is the relationship between them? (By the way, what I have called Galileo's Early Notes is the very first thing in the first volume of his collected works, as edited in the late 19th century.)"Aristotle's philosophy is just codified common sense." -- agree?
Thursday, Feb. 21:
The Inferno Lectures have been almost completely ignored by Galileo scholarship. They are catalogued in the collected works in Volume 9, the "Literary Writings." Do they seem like literary commentary or criticism to you? If they aren't literary, what are they? What seems to be their purpose?Galileo was 24 years old in 1588, he had dropped out of the university, and he had no position. He was, however, from a family that was well regarded, if impoverished. Needless to say, he was not a scholar of Dante. Why would he be asked to give two very public lectures?
Tuesday, Feb. 26:
The reading today is two texts which are, I think, typical of Galileo's time at Padua, where he was professor of mathematics for 18 years. Aristotle's Questions on Mechanics is a peculiar and interesting little book -- certainly not by Aristotle, rather a sort of pre-Archimedes book of conjectures about mathematics and physics. Galileo seems to have been very fond of it. It very imaginatively applies the Law of the Lever to all kinds of situations. See in particular Problems 3-6, 14-16, 20-22. In Problem 23 a very interesting observation about "compound motion" is made, quite unlike anything Aristotle would say, and important to Galileo later. Problem 33 puzzles about the motion of a thrown object. Problem 35 raises a puzzle which Einstein wrote a little essay about. And some problems, like Problem 25, on how to make a bed, it is safe to say that no one understands!The dialogue by Ceccho Ronchitti is really Galileo's, under a pseudonym. You can figure out the situation by reading between the lines: a new star (nova) appeared in 1606, and observations seemed to indicate it was NOT sublunar. This opinion was opposed by certain professors of philosophy (meaning Aristotelian philosophy, of course).
For discussion: (1) pick a problem from the Questions on Mechanics, and explain what it seems to be saying. (2) What is parallax, and how do the two peasants explain it? (3) Why do you think Galileo uses this peculiar literary form (rustic dialect, pseudonymous authorship, etc.) on a question of genuine importance?
Thursday: Feb. 28
(1) What new discoveries does Galileo announce in the Starry Messenger?
(2) Do any of these things threaten the Aristotelian world view?
(3) What is the function of the Dedication to the Grand Duke Cosimo?
Tuesday: March 5
(1) What are the circumstances of Galileo's writing the Discourse on Floating Bodies? Why was he working on this and not astronomy? Use internal evidence as well as external sources, like Dava Sobel.
(2) How does Galileo use the Law of the Lever and ideas from Aristotle's Questions on Mechanics to understand Archimedes' Principle of floating?
(3) Archimedes' Principle is sometimes stated as "A floating body is buoyed up by a force equal to the weight of the water displaced." How is it possible, then, as Galileo says, for a 1000 lb beam to float in 50 lb of water? Is this right??
Thursday: March 7
(1) Be ready to describe Aristotle's theory of floating as precisely as possible, based on On the Heavens, Book IV.
(2) How does Galileo use Archimedes' Principle to explain the floating of things which are denser than water (like the ebony chip)?
Tuesday: March 26
(1) What is the Ptolemaic system? What questions does Ptolemy address, and what are his arguments?
(2) What is the Copernican system? How did Copernicus discover that the Earth moves? How is it possible that this elementary fact was not noticed before?
Thursday: March 28
(1) What traditions of the Church, according to Galileo, were relevant to an examination of the Copernican question?
(2) How does Galileo's scientific knowledge shape his argument? What specific discoveries does he seem to allude to?
Tuesday, April 2:
(1) How did the Inquisition work? How did cases come before it, and how did it proceed with them?
(2) How did the Index work?
(3) Why did the experts' panel rule on the 2 propositions' status in philosophy?
Thursday, April 4:
(1) What was Galileo's personal experience in the banning of Copernicanism? To what extent was this a decision about Copernicanism, and to what extent a decision about Galileo?
(2) What were the scientific positions in the controversy on the comets of 1618? What do you find surprising or noteworthy?
Thursday, April 11:
(1) In Galileo's Dialogue, what should the discerning reader discern in "To the Discerning Reader"?(2) How does Galileo attack Aristotle's On the Heavens on the First Day?
Tuesday, April 16:
(1) What is the Second Day about, and how is it organized?
(2) The basic argument against the motion of the earth is that if it were moving, we would notice it. How does Salviati argue against this?
Thursday, April 18:
(1) Following the general plan laid out earlier in the book, we expect the Third Day to be about the question whether the earth orbits the sun. What arguments are presented?
(2) Another very interesting theme of the Third Day is the use of experiment, including the difficulty of interpreting experiments. What are the ideas here?
Tuesday, April 23:
(1) Many of the objections to the Dialogue found in the various reports refer specifically to the 4th Day. What is the problem with the 4th Day?
(2) How does Galileo's theory of the tides not contradict the Principle of Galilean Relativity (that you can't tell by any internal experiment whether you are moving uniformly or not)?