Book Review: The Calculus Diaries

Math frequently features in my dreams, and never in a good way. In the latest nightmare I was punted back to high school to retake precalculus. I sat there, embarrassed, hoping to will myself into invisibility. My attempts were unsuccessful. While telling us about the required book for the class the teacher looked over her glasses at me to say “And, Brian, I know you know what to expect, so maybe you’ll actually pass this time.” I was mortified, and I was almost glad to be snapped out of my dream by the 5:30AM alarm telling me it was time to go to work.

My relationship with math has never been good. Even the mention of the word “math” brings up shameful memories of failing grades and terrifying moments spent in front of the class at the blackboard. From elementary school through college, I have done everything in my power to avoid, evade, and escape math. If I never take a math course again, it will be too soon.

As she recounts in her new book The Calculus Diaries, science writer Jennifer Ouellette had her own difficulties with math. While not intellectually crippled by the very sight of a math problem like me, she still fell into the familiar pattern of avoiding the difficult mathematic formulas and equations behind the scientific ideas she loved. (There is nothing so ugly as an equation in a scientific paper. As a friend once told me, an equation in a paper looks like a dog turd on the lawn – the only reason you want to look at it is to know how to go around it.) Just the physics, please – the math behind all those enthralling concepts was abstract, complicated, and best left alone. When she saw the relatively simple arithmetic behind  the famous question of why two objects – regardless of mass – fall at the same rate, however, Jennifer realized that the math behind physics was not as inaccessible or forbidding as she had thought. Textbooks in hand, she set about teaching herself calculus, and The Calculus Diaries recounts a mathematical roadtrip in which Jennifer uses concepts from calculus to look into everything from the odds of winning big in Vegas to the likelihood of surviving a zombie apocalypse.

“Calculus” is a term often associated with engineering labs, physics, advanced computers, and other hi-tech, scientific pursuits. In other words, calculus is an esoteric language spoken by egg-heads in white lab coats (complete with the obligatory pocket protectors). Yet, from Disneyland’s Splash Mountain to the search for an affordable home, Ouellette shows that understanding even a minor amount of calculus presents a new perspective on the world around us. Just as my understanding of paleontology and evolution has altered the way I look at nature, Jennifer’s newfound understanding of calculus allowed her to see its applications in the construction of St. Louis’ Gateway Arch, the curling waves of the Hawaiian coast, and the way in which fungal parasites overtake ant populations. Once you know what you are looking for – or have developed your mathematical “search image” – the relevance of calculus jumps out at you.

Oddly enough, however, I found the historical portions of the book to be the most accessible. The entire book is written in an accessible, engaging manner, but some of my favorite stories and subplots involve quirky, charismatic, and crazy scholars of centuries past. Throughout the book Jennifer provides the historical context of the scholars who identified and solved a variety of mathematical enigmas. I was often able to follow the logic better in these sections than those about the application of calculus to modern life. The stories of Buffon’s needle and the attempts of Archimedes to determine the area beneath a curve resonated more strongly with me than the math involved in rollercoasters. This may be a subjective experience on my part, but at the very least the inclusion of the historical background enriched the modern-day storytelling of the book.

I can’t say that I learned very much calculus from the book. I can’t explain the mathematical meanings of the words “integral” or “derivative”, and the very sight of a calculus equation still causes my brain to freeze up. I am still very much math-phobic, but The Calculus Diaries allowed me to gain a slightly deeper appreciation for math. Just like detailed knowledge of a particular scientific discipline, an understanding of calculus highlights connections which are otherwise hidden in plain sight.

Calculus does require a certain amount of effort and discipline to comprehend, but it is not so arcane, inaccessible, or irrelevant to modern life as I have made myself believe. I have not yet had my mimetic moment – the flash of insight Jennifer describes in which the abstract becomes connected to something concrete and tangible – but The Calculus Diaries gave me a little nudge to be more receptive to the tangle of symbols and ideas which has caused me no small amount of frustration over the years. Like many monsters, math is often feared because it is not understood. With enough effort, that fear can be turned into fascination.

Full disclosure: I am the math-phobic Brian mentioned in the book’s epilogue. Jennifer has also been one of my biggest supporters as I have tried to become a science writer, and she recently gave my book Written in Stone an excellent review at io9.