MA177---Re-reading Daston's "Fitting Numbers to the World"

Wednesday next week we want to discuss the ideas in Lorraine Daston's article on ``Fitting Numbers to the World,'' This handout contains an outline and discussion questions that you may find helpful as you re-read the paper in preparation for the discussion.

1. Daston opens her essay by raising the question about why mathematics is useful in trying to understand the real world. She claims that this is a harder question today than in the eighteenth century, because our views of how mathematics fits in with other parts of human knowledge has changed.

2. Daston claims that the question of the applicability of mathematics is a difficult one in the twentieth century, but was easy in the eighteenth. On the other hand, the question about why we feel mathematical knowledge is certain is not too hard to answer today, but was a real problem in the eighteenth century. What changes in worldview and philosophy are behind this change?

3. Daston makes a very strong distinction between ``applied mathematics'' and ``mixed mathematics.'' What is the difference? Is she correct in claiming that the distinction is not merely semantic?

4. How does the St. Petersburg paradox fit into the article's theme? What does it illustrate? (Daston's other article in the coursepack has more information on reactions to the paradox.)

5. What were the assumptions behind the mathematical analysis of the ``probability of judgments''? Is Daston right in saying that they now seem ludicrous? Daston describes this example by saying that here mathematics lost a real of application. Why did the loss happen? What does this teach us about the issue of relating mathematics to the real world?

6. Daston hints at a connection between the loss of confidence in the ``probability of judgments'' and the French Revolution. What do you think?

7. Does Devlin's article about probability issues in trials mean we're moving back to the stuff Daston says we have left behind?

8. How does the story of the application of probability to Insurance fit into the theme of the article? Why was there resistance to probability-based insurance? How was it that the probabilistic approach came to be successful?

9. Daston claims that in each of these cases there has been a fundamental change in attitude between our time and the eighteenth century. What are these changes? How significant are they? (Here's a chance to show off what you've learned in the other classes of the E&R cluster.)

10. What makes a certain area of life or of nature amenable to mathematical study?

11. Is it true that mathematics is being applied to an ever-broader range of subjects? Is it healthy?