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Hesiod's Anvil: Falling and Spinning through Heaven and Earth

Mathematical Assciation of America
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I remember my eleventh grade physics teacher reading to my class an excerpt from a pulp fiction novel. In this electrifying passage, a character was pushed through a window of a skyscraper. The unlucky victim fell earthward, crashing to the sidewalk below. Seconds later he was pelted by shards of broken window glass. As an afterthought, the author reminds the readers that heavy objects fall faster than light ones. This last line got a good laugh from the class, all of whom knew better.

It is not uncommon for authors to inject physics into their writing. Some authors have a good sense for the physical world and do it well, and some, like this forgotten paperback novelist, do not. In Hesiod’s Anvil , Andrew J. Simoson analyzes some such passages. He looks at classic works by Jules Verne, H. G. Wells, Arthur C. Clarke, Edgar Allen Poe, Dante, the ancient Greek poet Hesiod, and others.

Hesiod wrote that it would take nine days for an anvil to drop from heaven to earth, Arthur C. Clarke wrote about artificial gravity on the space station in 2001, H. G. Wells wrote about a spaceship’s journey to the moon and back accomplished by turning on and off a gravity-blocker, and so forth. Simoson does not confine himself to the physics of writers. He also looks at theories of famous scholars, such as Edmond Halley’s hollow earth hypothesis, Euler’s analysis of gravitation inside the earth, and Galileo’s investigation of the motion of a ball dropped through a hole bored through the center of the earth.

Simoson takes these interesting ideas and picks them apart. Are they true? Could they be true? If so, what would they imply? Then he looks at them with a more sophisticated eye. What if we take the rotation of the earth into account? What if we do not assume that the density of the earth is constant? What if we assume that the acceleration of gravity is not constant? What if we take into account the motion of the planets? What if we assume that the speed of light is finite?

In 2007 Simoson won the MAA Chauvenet Prize for his article “The Gravity of Hades.” The material from this and other articles published in MAA journals or PRIMUS, constitute nine of the fifteen chapters of Hesiod’s Anvil. Before each chapter is a brief preamble — a short anecdote from Simoson’s own life that is tangentially related to the content of the chapter. Each chapter focuses on one aspect of (as the book’s subtitle so aptly states) falling and spinning through heaven and earth — usually with one or more connections to literature or old scientific theories. The questions are interesting and the conclusions surprising. The chapters conclude with exercises for the reader.

The questions I asked myself as I read the book were: who is the audience for this book, and how is it to be read? In the introduction the author asserts, “anyone who has successfully taken a year-long calculus course should be able to understand most of this book.” I would argue that he overestimates the sophistication of a sophomore mathematics student. Yes, much of the mathematics is differential and integral calculus (although the book contains a nontrivial amount of multivariable calculus, linear algebra, differential equations, and physics), but it is the use of the mathematics and the density of the mathematics that would likely overwhelm such an audience. There is a lot of technical mathematics that takes the form of sequences long intimidating equations. A student (or professor) who wants to absorb the contents of this book would have to slowly work through the mathematics line by line, a technique that most students are not accustomed to. This is not a pop-math book to sit down and read leisurely.

That said, anyone who is interested in physics and is not squeamish about mathematical manipulations should get something out of this book. A strong student could get a nice project from the exercises at the end of the chapters. Perhaps most importantly, this book gives the reader ideas for how to ask questions. For example, suppose the character in my high school teacher’s novel was pushed out the window of a building that was 100 miles tall and located at the equator, he had the mass of a white dwarf star, the earth was rotating beneath him, and the gravitational pull of the moon was taken into account…

Dave Richeson is an Associate Professor of Mathematics at Dickinson College in Carlisle, PA. His interests include dynamical systems, topology, and the history of mathematics.

Date Received: 
Friday, May 18, 2007
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Andrew J. Simoson
Dolciani Mathematical Expositions 30
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David Richeson
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Wednesday, March 26, 2008