In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions

College freshmen are notorious for doing stupid things on occasion, and unfortunately I was no exception. Even though I knew from the beginning of my college career that I was going to be a mathematics major, I studiously avoided taking any physics courses at all, largely because my high school physics course had not been a good experience. The upshot was that I graduated from college knowing quite a lot of mathematics but having little or no intuitive sense of how physics works. Memorizing formulas is one thing, but learning how to think in the subject is quite another.

Over the years, I have developed some strategies for improving this situation, including bothering knowledgeable friends with questions (thank you, Michael) and also going through phases of attempting to read up on some aspects of physics, typically selecting as reading material books that are designed for lay people with at least some mathematics background, and which attempt to relate the physics to everyday life or at least some aspect of current culture. (See, for example, Adler’s Wizards, Aliens and Starships: Physics and Math in Fantasy and Science Fiction.)

Anyone perusing such books will quite likely quickly run across the name Paul Nahin. He is very prolific, and has written over a dozen books on various aspects of mathematics and physics, usually generating enthusiastic reviews. I first encountered him when I checked his book Time Machines out of the public library; I liked it so much that I filed his name away for future reference, and later reviewed, for the Mathematical Gazette, his book Mrs. Perkins’s Electric Quilt, a collection of essays about what the author referred to as the “mutual embrace” of mathematics and physics. It was from this latter book that I first learned about a “dimensional analysis” proof of the Pythagorean Theorem, which is so short, clever and elegant that I have made it part of a course on advanced Euclidean geometry that I have been teaching for the last couple of years. It was, therefore, not surprising that I would seize the opportunity to obtain his most recent book, the one now under review.

In Praise of Simple Physics is, like Electric Quilt, a series of independent chapter-essays, the unifying theme this time being how basic physics can be used to answer a number of questions relating to ordinary events. There are about two dozen such issues discussed in the book, so any kind of detailed summary here is obviously impracticable, but here is a representative sample:

• Chapter 2 addresses the “traffic light dilemma”: as you approach an intersection at which the light has just turned yellow, should you “‘go for it’ and pray the rear ends of both you and your car get through the intersection before the light turns red, or should you hit the brake pedal and pray your car’s front end isn’t stopped sticking out into the intersection?”
• Chapter 7 uses vector calculations to analyze this question: if a person is initially walking in the same direction as the wind, in one direction should that person turn so that the wind is now perpendicular to him or her?
• Chapter 12 discusses the physics of communications satellites.
• Chapter 14 asks why the night sky is dark, a question the author considers to be “among the most profound… that physicists have ever asked.”
• Chapter 21 uses physics to analyze the path of a kicked football, and addresses the question of the angle at which the ball should be kicked to obtain the longest path of the ball in the air.

There’s a lot more, of course, including an introductory chapter (of a somewhat different nature than the ones following), in which nine short vignettes, each involving the application of mathematics (sometimes just logical reasoning) to real-life problems are given, and also a Postscript, in which Nahin returns to the theme of dimensional analysis. The proof of the Pythagorean Theorem that I referred to above is reproduced here, and other examples of dimensional analysis to physics are given.

Nahin’s writing style, as in previous books, is clear, conversational, humorous and chatty. However, it should be emphasized that this is not a book for the hypothetical “person on the street”. A mathematical background through multivariable calculus is assumed of the reader; derivatives and integrals (including, on occasion, double and triple integrals) appear without apology, and the discussions in the book are careful and appropriately rigorous. Some background in physics is also assumed, though the author does a good job of reminding readers of the appropriate physical principles as they turn up. The assumption of such a background is, I think, a good thing; it would be impossible to discuss the topics in this book with any real degree of honesty without using mathematics at this level.

Given the prerequisites stated above, this book should appeal to a broad audience. Physics and mathematics students who want to see interesting applications of the ideas they have studied should certainly find it attractive, as should faculty members in either of these departments who are looking for interesting ideas for lectures or enrichment material. And of course this book should also appeal to faculty members who are, thanks to ill-advised youthful choices, now in need of “remedial intuition”.

Mark Hunacek (mhunacek@iastate.edu) teaches mathematics at Iowa State University.