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Course Description

Summary

I would (and will) argue that Newton's Principia is the most important book yet written. It is certainly the most important book that a vanishingly small number of people have actually read.

Written about 150 CE, Ptolemy's Almagest collected and systematized the knowledge of astronomers of the time to give a system which roughly predicted the complex paths of the five known wandering stars ("planets"), against the backdrop of the myriad fixed stars: a system of the heavens. As well, it predicted the paths of the Sun and Moon, allowing predictions of eclipses. The most remote parts of Nature were shown to be predictable, and the predictions shown to be within the reach of humanity.

But the Almagest was a ferociously complex system of circles upon circles, with no hint of the reasons why it worked. In 1543 CE, Copernicus published his system which put the Sun at the center of the solar system and the Earth in motion, rediscovering an idea of Aristarchus. His system reduced the complexity of Ptolemy's system, and increased its accuracy. But there were still many mysterious circles upon circles. In 1609, Kepler published his revolutionary and vastly simplified system, in which the dozens of circles of Ptolemy and Copernicus were replaced with a single elliptical orbit for each planet, with the Sun at the focus. Kepler's system greatly increased accuracy, and made exciting new explanations. But why would Nature choose slightly lopsided circles? Where was the perfection and reason of the heavens?

In 1687, Newton published the Principia. In this phenomenal work, Newton created calculus, and created physics as we now understand it, in order to derive all of Kepler's system from a few simple principles. Newton showed that, not only was Nature predictable, but it was comprehensible. We could understand reasons. And further, he showed that those reasons were accessible to us, but that they could be operating in a manner initially hidden from us. This began the modern era of science, and more broadly, our relationship to reality.

In this class, our goal will be to work through and understand the main argument of the Principia, from the original text and in its original form. We will find that Newton's way of thinking is different in intriguing ways from modern reformulations. We will see why Newton's laws about force, and particularly the gravitational force, imply Kepler's laws about the motion of planets.

This class has no formal prerequisites. Comfort with Euclidean geometry would be helpful, and the class would be a very good follow-up for those who took Euclid's Elements, but we will review what we need. Prior experience with calculus and/or physics would be helpful, but is not necessary. Although no special background is necessary, this will be a rather intense class. The Principia is famously difficult for a reason. We will work together through the text and make sense of Newton's thinking and his revolutionary system.

NOTE: Students must purchase the course text: Newton's Principia, The Central Argument: Translation, Notes, Expanded Proofs, by Dana Densmore, since we will be using the text intensively.