The Calculus Diaries - Jennifer Ouellette [101]
Numb3rs demonstrates the relevance of mathematics better than any pedagogical method I’ve yet encountered. Week after week, Charlie Epps (Krumholtz) helps his FBI agent brother crack a federal case using the tools of his trade. Math is a tough sell; couching it within the familiar crime-solving framework renders its abstract concepts not only palatable to nonscientists, but downright appealing. The show’s tagline sums it up perfectly: “We all use math every day.” Even Krumholtz confessed to developing a fascination for Pythagoras and the Fibonacci sequence because of their prevalence in nature and art—and were it not for his role as Charlie Epps, he might never have encountered those concepts outside of the classroom. This suggests that his struggles with math weren’t due to a lack of aptitude, but to how the subject matter was presented. Like many of us, he never understood why math was important or how it could possibly be of any use in our daily lives.
There is much weeping and gnashing of teeth in academic circles about the sorry state of U.S. math-and-science education.
I don’t pretend to have an easy answer to a sweeping, complex problem that confounds our best educational experts. Learning is profoundly individual, and what resonates with one student might not resonate with another. How can you systematize all those individual styles? But the power of mimesis to inspire young minds should not be ignored.
Surely it is no accident that a similar interpretation of mimesis can be applied to key breakthroughs in physics: It’s that same creative impulse, finding inspiration in surprising connections. Albert Einstein credited his development of the theory of special relativity to a critical insight gleaned years before, as he sat on a train moving away from the station platform—namely that he would measure time differently from within the moving train than would someone standing on the platform (“this is that”).
Watching an apple fall from a tree gave Isaac Newton his critical insight into gravity and his laws of motion: He realized the apple’s position, when plotted as a function of time, formed a parabolic curve, and connected motion with geometry and algebra (“this is that”). Archimedes found the solution to the problem of Hiero’s golden crown while soaking in the bathtub. My own modest breakthrough came on that fateful day in Santa Barbara, when I saw the connection between an abstract calculus equation and the motion of Saturn’s rings, and realized, à la Archimedes, “Eureka! This is that !”
APPENDIX 1
Doing the Math
The only way to learn mathematics is to do mathematics.
—PAUL HALMOS
Tell me and I’ll forget. Show me and I may not remember. Involve me, and I’ll understand.
—NATIVE AMERICAN PROVERB
So, you’ve made it through The Calculus Diaries and feel as though you’re starting to get a handle on this whole calculus thing. Maybe you’re even toying with the idea of delving a bit further into the topic. This appendix is here to help you take that next step. I deliberately avoided scary equations in the main text, but sooner or later one must bite the bullet and face the actual math head-on. Nothing here is intended to “teach” calculus—this is not a substitute for the experience of an actual class, textbook, and/or a private tutor—but it will give you a taste of how the concepts discussed in the text translate into the language of math. For those who really get bitten by the calculus bug and desire even more details, I recommend The Complete Idiot’s Guide to Calculus by W. Michael Kelley.
Here are the most common terms and symbols you’ll encounter; this will help you “read