Change is the Only Constant

Does calculus make you giggle? Have you ever cracked a smile when thinking of a derivative? Math teachers, instructors, and professors know the very comprehensive and robust textbooks they use are not the most entertaining reads. Textbooks do not make the reading of calculus enjoyable to the point of a giggle, but Ben Orlin’s second book Change Is the Only Constant: The Wisdom of Calculus in a Madcap World does. This book is a uniquely entertaining piece focused on conceptualizing the rationale and development of one of the most feared courses. It certainly provides many connections that are not traditionally included in a standard calculus curriculum.

 

The book presents calculus almost purely conceptually. Orlin does his best to leave the algebra procedures aside. He instead attempts to explain each topic with cleverly placed analogies and anecdotal stick figures. He describes the book as written for those who want the mystery of calculus but haven’t had the inclination or the desire to pursue it mathematically. When Orlin begins a topic, he first sets the stage with an enlightening historical situation or a clever adaptation of the concept. He then moves to describe the plot of the topic through various examples and well-thought-out stories. Placed amongst his writing, which makes this work unique, are quick witty graphics (stick figures) that add faces or even personalities to the topics.

 

Change Is the Only Constant follows much of the same sequence that one would expect from a calculus book. The format, like a textbook, uses chapters to break up the topics, but the chapters are not labeled as one would expect. Orlin attempts to use a chapter’s title to act as a hook, which means each chapter must be read to determine the calculus topic. The book is broken into two distinct labeled analogical themes: Moments and Eternities. The Moments section of the book is where the reader is introduced to limits, derivatives, optimization, and related rates. The Eternities section covers antiderivatives, integrals, areas, and volumes. Intertwined are significant results such as the Fundamental Theorem of Calculus, Mean Value Theorem, and Intermediate Value Theorem. 

 

Ben Orlin has been a math teacher, a speaker, and an author. This book is accessible to a wide, but definitely limited, range of readers. This includes his target audience who are those interested enough in the theories on which calculus is based. They would not need extreme math knowledge, nor the algebra often required for a traditional calculus course. Without conscious and continuous analytical thought however, this book would not be as enjoyable. While Orlin may have not intended it, a math instructor would find value as well. Ben Orlin’s light look at the structures that build calculus would relate well in the classroom. I noticed that some ideas I already use but found many more, new ways to engage future students. To that point, any instructor of mathematics will find this book beyond enjoyable. It will fill many history lessons avoided during one’s early math career. In the absence of strong algebraic manipulations, clever turns of a phrase and math innuendos are placed. It would be a challenge for any teacher to hold back a smile.

 

The book is not entirely smooth. In Chapter XXI, it feels as though Orlin struggles to connect a rushed story of Einstein with the related plus c of an indefinite integral.  The order is also odd in the second half of the book with the trapezoidal method being mentioned so late after Riemann sums. These instances are pointed out as only mild deviations, possibly based on my lack of understanding. The remainder of the book entertains and flows fantastically. Orlin, for instance, masterfully explains the limitations of extrapolating from instantaneous change in a dialog with Mark Twain. He also notably brings in and credits others with explanations. As an example, he tells the story of William Stanley Jevons who plotted the intensity of emotions against time to illustrate the area under the curve. All the while Orlin is constantly adding his own comic drawings.

 

Change is the Only Constant explores the concepts and rational of a beginning calculus course.  While not a textbook, Orlin claims, it is written for those curious and outside the math world. Contradictorily, it is also a book most entertaining to those in the profession who teach the course. There are many secrets hidden amongst the drawings that may not even be noticed until a second reading. It is thoroughly enjoyable read, even to the point of giggles.  Ben Orlin provides the combination of a history lesson, a comedy tour, and serious conceptual math content.

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Luke Audette is a mathematics instructor at Western Wyoming Community College in Rock Springs, WY. He had previously taught 8 years high school mathematics in Minnesota.  He is currently pursuing his doctorate in Mathematics Education through the University of Wyoming. He can be contacted at laudette@westernwyoming.edu