Galileo's infinities and infinitesimals
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The purpose of this assignment is to re-live the quandary of infinities and
infinitesimals that plagued the Greeks and later Europeans until the
nineteenth century. In this assignment you'll examine the difficulties through
Galileo's eyes and mind by studying parts of the first dialogue in his
book Dialogues Concerning Two New Sciences.
General directions
Do the following exercises and prepare to present your work to the class.
Exercise 1 - Read and Summarize
Individually read pages 30-36 in the handout fragment from Galileo's
first dialogue. As you read, keep a list of major difficulties and
arguments concerning infinities and indivisibles in the dialectic
between the Salviati, Sagredo, and Simplicio.
Exercise 2 - Analysis
Identify and clearly state the most important points Galileo is
trying to make about the continuum. Analyze each claim and supporting
argument to make sure you understand the reasoning and
can recite the argument yourself.
Exercise 3 - Recapitulation
Based on your analysis in the previous exercise, prepare an outline that will
recapitulate Galileo's position and arguments on nature of the continuum.
Your outline should focus on the way Galileo proposes to work around the
apparent contradictions that he acknowledges in the constitution of the
continuum.
Exercise 4 - Summary Paragraph
Convert your outline from the previous exercise into one or two paragraphs
(at most) that you can present to the class. Your paragraph should
include a brief introduction, a thesis, and an argument defending your
thesis with supporting citations from the text. Remember,
focus on what you think is Galileo's most important insight rather
than trying to cover everything that Galileo says.
Exercise 5 - Class Presentation
Read your paragraph to the class and be prepared to defend your thesis.