Writing one book is a major undertaking. Don Lemons has written seven. Lemons, an emeritus professor of physics at Bethel College in Kansas, began his career as an author in 1997 with Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics. Since then, Lemons has drawn on his extensive undergraduate teaching experience to write books on entropy, the history of physics, and stochastic processes.
His latest book, A Student’s Guide to Dimensional Analysis, aims to teach undergraduates the powerful mathematical technique that uses a system’s dimensions—mass, distance, and time, for example—to yield insight into the relationships among variables in that system. In the July issue of Physics Today, Hong Lin praises the textbook for its approachable style; the book reads, she says, “as if [Lemons] were talking to his students and giving them step-by-step guidance.”
PT: You’ve written several books aimed at undergraduates. How has your experience in the classroom shaped the way you write for students?
LEMONS: Not only my experience as a physics teacher but also my experience as a student has shaped these books. I recall my students at Bethel College and elsewhere, their strengths and weaknesses, their particular virtues and vices, and then I write for their benefit. I also recall my younger self and ask, “What kind of book would I have liked?” and “What kind of book would have been good for me?” Of course, those memories are idealizations, but they are potent idealizations.
My writing is also guided by the fundamentals of the fields in which I have developed an interest, rather than by their wonderful and exotic applications or their most elegant formulations. Learning the foundations seems to me the natural way to begin the study of any subject.
PT: What led you to choose dimensional analysis as the subject of your most recent book?
LEMONS: As an undergraduate I was charmed as I watched one of my teachers, the late Harold Daw of New Mexico State University, work a dimensional problem with great relish. But when I applied its rather simple analytical method to my own problems, the result was either disappointingly obvious or incorrect.
Much later, when researching and writing A Student’s Guide to Dimensional Analysis, I realized that there is much more to dimensional analysis than ensuring the dimensions of every term in every equation and inequality are the same. One must choose the dimensional quantities and then one must choose the dimensions of those quantities—and there are a number of ways to make those choices incorrectly. Percy Bridgman did not quite hit the nail on the head when he famously said, “Dimensional analysis is the analysis of an analysis.” Rather, I believe that dimensional analysis is the analysis of a dimensional model. And, as we know, model building is an art as well as a science.
PT: The book applies dimensional analysis to situations from everyday life, for example, by calculating the hydraulic jump of a kitchen faucet. Do you have a favorite example?
LEMONS: The applications of dimensional analysis are fun. One in the book that I enjoy recalling is the growth of Arctic ice, a problem inspired by Fridtjof Nansen’s memoir Farthest North. Nansen, an intrepid explorer and admirable diplomat, was also something of a hidden physicist. He remarked, concerning his voyage to the North Pole, “From measurements that were constantly being made, it appeared that the ice which was formed in the autumn in October or November continued to increase in size during the whole of the winter and out into the spring, but more slowly the thicker it became.” That last phrase, “increase in size . . . more slowly the thicker it became” yields to dimensional analysis.
PT: You’re also the author of Drawing Physics: 2,600 Years of Discovery from Thales to Higgs, a collection of 51 essays about the history of science, each illustrated with black-and-white diagrams of the experiment or concept in the essay. How did you approach the collaboration with artist Jesse Graber?
LEMONS: My initial impulse was to publish my own drawings. After all, the preface of the book advises that we should all do our own drawing when thinking through the physics of a problem. But my drawings were not so attractive, and I was aware that Jesse, a former student in my college, was a professional cartoonist. The purpose of the drawings was to replace at least part of the work usually performed by mathematics. I would send Jesse my own best rendition of the drawing along with the accompanying essay. Jesse would read the essay and then make my drawing more attractive and sometimes improve on its concept. Sometimes we would pass a drawing back and forth several times before I was completely satisfied.
PT: What is your next project?
LEMONS: MIT Press will publish Thermodynamic Weirdness in March 2019. Classical thermodynamics has the unusual reputation of being either too trivial, too hard, or somehow both. The book responds by making clear, in largely nonmathematical language, what was unusual about classical thermodynamics and what motivated the founders as they developed the subject. Each foundational piece of classical thermodynamics was a response to an empirical requirement. Even so, classical thermodynamics did not fit within the then current Newtonian synthesis and, for this reason, was perceived as weird. Current students, steeped as they are in the Newtonian synthesis, also sense the subject’s strangeness. After all, F = ma does not apply to classical thermodynamics.
My belief is that studying the origins of classical thermodynamics helps one understand its formulation. Thus, the book’s chapters are interspersed with generous selections from important original sources by Gabriel Fahrenheit, Antoine Lavoisier, Benjamin Thompson, Sadi Carnot, Lord Kelvin, and Rudolf Clausius. I am afraid that not only the history but also the very meaning of classical thermodynamics are being squeezed out of thermal physics texts and courses. The field’s founders had their own answers to questions like “What is the second law of thermodynamics?” and “What is entropy?”—answers that cannot be captured in a formula.
PT: What are you reading?
LEMONS: At present, I am rereading and discussing Fyodor Dostoevsky’s Brothers Karamazov with a group at St. John’s College in Santa Fe, New Mexico, and reading Joseph Conrad’s Nostromo aloud with my wife. I am also catching up on current planetary science from a variety of online sources while looking for a good book that summarizes the subject.
