MA177--Change, Probability, and Numbers

Midterm Exam

This is a take-home midterm exam. It consists of six questions, of which you are asked to answer four. Each answer should be a short essay, no more than two pages long. You should turn in the exam before 5:00 PM on Tuesday, October 21. While you work on the exam, you are free to consult your notes, any books, the material in your coursepacks, and you may talk to me. Feel free to include ideas and themes from other courses in the integrated cluster if they are relevant. You may use no other sources of information.

As usual, be careful when you write. You should write up your answers in good English prose. Don't turn in first draft material. When you're writing mathematics, don't just put down symbols on the page; instead, tell me a mathematical story that has a beginning, middle, and end and that hangs together and makes sense. When you're writing history, don't just recite facts or put down references to the book(s); instead, weave together facts, interpretations and impressions into a cohesive and logical account.

As we discussed in class, the main goal of this exam is to invite you to do some overall reflection on the themes of the course so far. I hope you will find that even writing an exam can be a pleasant learning experience. What I'll be looking for as I read your answers is evidence of serious reflection about the issues, stories, people, and ideas we discussed in class and that you encountered in your reading. This is your opportunity to display your mastery of the material.

1. Discuss the following quote in the light of what we have learned about science and mathematics in the Enlightenment.

If you grant a small favour to a lover, you will soon afterward have to grant him more, and eventually that can go far. In the same way, grant a mathematician the slightest principle and he will draw a consequence from it that you'll have to grant him too, and from that consequence yet another; and in spite of yourself, he will lead you farther than you would ever have thought possible. (From Entretiens sur la Pluralité des Mondes, by Bernard le Bovier de Fontenelle, who was secretary of the French Academy from 1697 to 1757.)

2. When one studies science and mathematics in the eighteenth century, one meets two Isaac Newtons. The first is the historical Newton, and the second is Newton as he was viewed by the thinkers of the Enlightenment. In what ways are the two alike, and in what ways are they different?

3. What were the goals of the expedition to Lapland led by Maupertuis? Were they achieved? Why was the expedition important?

4. The quote below is part of a letter from Turgot to Louis XVI. Discuss what it tells us about the place of mathematics in Enlightenment thought and society.

The famous Leonard Euler, one of the greatest mathematicians of Europe, has written two works which could be very useful to the schools of the Navy and the Artillery. One is a Treatise on the Construction and Maneuvering of Vessels; the other is a commentary on the principles of artillery of Robins... I propose that Your Majesty order these to be printed;...

It is to be noted that an edition made thus without the consent of the author injures somewhat the kind of ownership he has of his work. But it is easy to recompense him in a manner very flattering for him and glorious to Your Majesty. The means would be that Your Majesty would vouchsafe to authorize me to write on Your Majesty's part to the lord Euler and to cause him to receive a gratification equivalent to what he could gain from the edition of his book, which would be about 5,000 francs. This sum will be paid from the secret accounts of the Navy.

The quote is taken from C. Truesdell, "Leonard Euler, Supreme Geometer (1707-1783)," in H. E. Pagliaro (ed.), Irrationalism in the Eighteenth Century, Case Western Reserve University Press, 1972, p. 51.

5. In Geoffrey Sutton's Science for a Polite Society (Westview, 1995), we read:

The French Enlightenment was a sufficiently diffuse movement that it is often characterized through the examination of a single individual rather than through the statement of generalities. In literary circles the place of the paradigmatic philosophe is almost always assigned to Voltaire. Ernst Cassirer, seeking a symbol for the "mind of the Enlightenment," chose Jean Le Rond d'Alembert as his representative, largely owing to d'Alembert's multiple roles as a mathematical prodigy delving into questions of the celestial mechanics, as a literary lion at the Académie Française and in the salons, and as an editor and champion of the great Encyclopédie. ... Our window into the mind of the Enlightenment will be Gabrielle Émilie Le Tonnier de Breteuil, Marquise du Châtelet. (p. 242)
Discuss how well each of the persons mentioned fits the role. If you had to choose a "representative mind of the Enlightenment," who would you choose and why?

6. One of your friends, who is a government major, has heard that our class spent a week discussing the complexity and difficulty of making social choices by means of elections, and she is quite intrigued. Write her a letter explaining what we discussed and why it is (or is not) important.

Fernando Q. Gouvea
Sat Nov 15 10:16:37 EST 1997