Voltaire's Riddle - no. 39

Did you know that Voltaire was the first to publish the legend of Isaac Newton discovering gravity upon seeing an apple fall?

That he tried for about eight years to be a mathematician?

That in 1752 he wrote Micromegas, a story about a French expedition to the arctic (1736-7) whose purpose was to test Newton's controversial theories about gravity?

This book is about that story and its underlying mathematics.

In summary, an alien giant visits earth and encounters the expedition returning from north of the Baltic Sea.

Their ensuing dialogue ranges from measurements of the very small to the very large, from gnats and microorganisms to planets and stars, from man's tendency to make war to dreams of understanding his own spirit.

At the end of their conversation, the giant gives man a book with the answers to all things.

But when they open it, it is blank. That is the riddle of this book. What does such an ending mean? As a series of vignettes and chapters, the author gives some riddle resolutions.

The vignettes (requiring no special mathematics knowledge) describe the people, traditions, and events of the expedition and story.

The chapters (accessible to anyone with a background in undergraduate linear algebra, vector calculus, and differential equations) show why a rotating earth must be flattened at the poles, why the tip of the earth's polar axis traces out a curve with period of nearly twenty-six thousand years, why the path of a small black hole dropped at the earth's equator must be a hypocycloid, why an old problem studied by Maupertuis (the leader of the French expedition) is a pursuit curve, and why in measuring phenomena we sometimes get it wrong.

All in all, this book is a case study in how mathematical and scientific knowledge becomes common knowledge.