Math 194 — Newton's Principia and the Scientific Revolution

Please go to moodle.macalester.edu for current information on this course. You will need to be registered for this course, in which case simply select Newton's Principia from among your options.

Fall 2007, 9:40–10:40 am, MWF, 247 Olin-Rice

David M. Bressoud, 224 Olin-Rice, 696-6559, bressoud@macalester.edu

“If it be then your Pleasure, ye Lovers of Study, come always; be not restrained through any Fear, nor retarded by too much Modesty, what you may do by your Right, you shall make me do willingly, nay gladly and joyfully. Ask your Questions, make your Enquiries, bid and command; you shall neither find me averse nor refractory to your Commands, but officious and obedient. If you meet with any Obstacles or Difficulties, or are retarded with any Doubts while you are walking in the cumbersome Road of this Study of Mathematics, I beg you to impart them, and I shall endeavour to remove every Hindrance out of your Way to the best of my Knowledge and Ability.”

Isaac Barrow, March 14, 1664

Description

What is science? What is the role of mathematics in science? Why is mathematics so effective in explaining the intricacies of the physical world?

A lot of people have thought a great deal about these questions, and we will be reading and debating some of the great philosophers of science: Popper, Kuhn, Lakatos, and Feyerabend. But mostly, we will be answering these questions by looking at the role of mathematics in specific scientific accomplishments, in particular Newton's Principia which provided the long-sought explanation for celestial mechanics and in so doing created a new way of thinking about science and the world around us.

This will be a chance to wrestle with original texts, especially the Principia, and come to personal understandings of some of the mysteries of the physical world

There are no prerequisites for this course. A familiarity with the concepts of derivative and integral will be helpful but not necessary. Nothing we see in this course will look anything like what you might have seen in a calculus course.

Background

Newton is one of the greatest scientists of all time. He took a deep and perplexing problem that had puzzled philosophers and scientists for centuries and, using some of the most sophisticated mathematical techniques available at the time, solved that problem so completely that everything that came before was suddenly trivial, and everything that would come after would build upon the foundation of this work.

Newton's problem was celestial mechanics, the motion of the planets. For Maxwell, it was electricity. In both cases, there is a long and fascinating history that is prolog to their masterpieces and helps to put them in context. For Newton, we will look at the development of astronomy, tracing our investigations back to Aristotle, but focusing on the peak of activity that occured in the 17th century: Kepler, Galileo, Descartes as well as many of the lesser known philosophers. We will also spend a good deal of time on Newton's Principia itself, anal;yzing and coming to understand the principal arguments and so coming to an appreciation of its tremendous impact on how we think about our world today.

The seminal events in science have been grist for the mills of philosophers of science. Interspersed among studies of the scientific issues and solutions, we will look at how philosophers have attempted to understand their import. What is science?

Grades

All assignments for this course will be posted on the Moodle site. Grades will be based on

regular writing assignments (30%). These are to be uploaded to the Moodle site by the prescribed dates.
an extended oral and written report on a section of the Principia (30%). You will be assigned a section of the Principia, a partner to work with, and a day in November when you will make your oral presentation.

Presentations are strictly limited to 30 minutes. Thirty minutes goes fast. Your job during the presentation is not to try to cram in all the details of what Newton accomplished in your section, but rather to communicate to your classmates (1) what this section is about, (2) why it is important, and (3) why it is interesting. You will be graded on how well you communicate all three of these. It is up to you and your partner how to divide up the responsibilites of doing the presentation, but you should practice it together.

The final report will start with an introduction that explains what the section is about, why it is important, and why it is interesting. This is where you then go into a full technical explanation of what Newton proves and how he proves it. Include a conclusion that summarizes the important points of your section.

A draft of your final report is due by (date to be determined).

Drafts will not be graded. They will be critiqued and returned for final polishing. Final report is due (date to be determined). When you turn in the final report, each member of the team should also turn in a brief, informal description of how the collaboration went, any problems that were encountered, any feelings that duties were unequally shared. This informal report will be kept confidential.

an annotated bibiliography and project report on a question or problem of your choice (25%). Suggested topics will be made available early in the smester.
a final exam (15%). These will be take-home, essay questions

Late Assignments

Late assignments will be penalized 10% if less than one day late and an additional 5% for each day late after that.

Support Team

Your support team consists of myself and Sarah Sutter, your preceptor.

Required Books

The Principia: a new translation and guide by I. Bernard Cohen and Anne Whitman
The Birth of a New Physics by I. Bernard Cohen
The Structure of Scientific Revolutions by Thomas Kuhn
Science and the Enlightenment by Thomas L. Hankins
Easy Writer by Andrea Lunsford and Robert Connors

There will also be other selected readings that will be posted on the class Moodle site.

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